diff --git a/.gitattributes b/.gitattributes index 9cdc0412f3c84a84fd752e57a1656d92b5106577..1a269f9a5d50a06bbd2142a86702974fd7f12299 100644 --- a/.gitattributes +++ b/.gitattributes @@ -34,3 +34,10 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text *.zst filter=lfs diff=lfs merge=lfs -text *tfevents* filter=lfs diff=lfs merge=lfs -text lietorch-0.2-py3.10-linux-x86_64.egg filter=lfs diff=lfs merge=lfs -text +slahmr/teaser.png filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/droid_backends.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch_backends.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid_kernels.o filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_gpu.o filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/DROID-SLAM/thirdparty/lietorch/examples/registration/assets/registration.gif filter=lfs diff=lfs merge=lfs -text +slahmr/third-party/ViTPose/demo/resources/demo_coco.gif filter=lfs diff=lfs merge=lfs -text diff --git a/slahmr/.gitignore b/slahmr/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..9c4fdf806824894f1573961bf6dba14212a26980 --- /dev/null +++ b/slahmr/.gitignore @@ -0,0 +1,140 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# data +*outputs* +*renders* +*cache* +*checkpoints* +*_DATA + +*.swp +*.out +*.err + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +pip-wheel-metadata/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ diff --git a/slahmr/.gitmodules b/slahmr/.gitmodules new file mode 100644 index 0000000000000000000000000000000000000000..42eacc310d010935465eeab73aa5edd133e29694 --- /dev/null +++ b/slahmr/.gitmodules @@ -0,0 +1,6 @@ +[submodule "third-party/DROID-SLAM"] + path = third-party/DROID-SLAM + url = https://github.com/princeton-vl/DROID-SLAM.git +[submodule "third-party/ViTPose"] + path = third-party/ViTPose + url = https://github.com/ViTAE-Transformer/ViTPose.git diff --git a/slahmr/LICENSE b/slahmr/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..1f6316d246804b789e263f3c1e9f38c84e3f16fd --- /dev/null +++ b/slahmr/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2023 vye16 + +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/slahmr/README.md b/slahmr/README.md new file mode 100644 index 0000000000000000000000000000000000000000..3df615e5950ad1dfd75424df5d9acc44881ae2cd --- /dev/null +++ b/slahmr/README.md @@ -0,0 +1,167 @@ +# Decoupling Human and Camera Motion from Videos in the Wild + +Official PyTorch implementation of the paper Decoupling Human and Camera Motion from Videos in the Wild + +[Project page](https://vye16.github.io/slahmr/) | [ArXiv](https://arxiv.org/abs/2302.12827) + + + +## [ You can run SLAHMR in Google Colab](https://colab.research.google.com/drive/1knzxW3XuxiaBH6hcwx01cs6DfA4azv5E?usp=sharing) + +## News + +- [2023/07] We updated the code to support tracking from [4D Humans](https://shubham-goel.github.io/4dhumans/)! The original code remains in the `release` branch. +- [2023/02] Original release! + +## Getting started +This code was tested on Ubuntu 22.04 LTS and requires a CUDA-capable GPU. + +1. Clone repository and submodules + ``` + git clone --recursive https://github.com/vye16/slahmr.git + ``` + or initialize submodules if already cloned + ``` + git submodule update --init --recursive + ``` + +2. Set up conda environment. Run + ``` + source install.sh + ``` + +
+ We also include the following steps for trouble-shooting. + + * Create environment + ``` + conda env create -f env.yaml + conda activate slahmr + ``` + We use PyTorch 1.13.0 with CUDA 11.7. Please modify according to your setup; we've tested successfully for PyTorch 1.11 as well. + We've also included `env_build.yaml` to speed up installation using already-solved dependencies, though it might not be compatible with your CUDA driver. + + * Install PHALP + ``` + pip install phalp[all]@git+https://github.com/brjathu/PHALP.git + ``` + + * Install current source repo + ``` + pip install -e . + ``` + + * Install ViTPose + ``` + pip install -v -e third-party/ViTPose + ``` + + * Install DROID-SLAM (will take a while) + ``` + cd third-party/DROID-SLAM + python setup.py install + ``` +
+ +3. Download models from [here](https://drive.google.com/file/d/1GXAd-45GzGYNENKgQxFQ4PHrBp8wDRlW/view?usp=sharing). Run + ``` + ./download_models.sh + ``` + or + ``` + gdown https://drive.google.com/uc?id=1GXAd-45GzGYNENKgQxFQ4PHrBp8wDRlW + unzip -q slahmr_dependencies.zip + rm slahmr_dependencies.zip + ``` + + All models and checkpoints should have been unpacked in `_DATA`. + + +## Fitting to an RGB video: +For a custom video, you can edit the config file: `slahmr/confs/data/video.yaml`. +Then, from the `slahmr` directory, you can run: +``` +python run_opt.py data=video run_opt=True run_vis=True +``` + +We use hydra to launch experiments, and all parameters can be found in `slahmr/confs/config.yaml`. +If you would like to update any aspect of logging or optimization tuning, update the relevant config files. + +By default, we will log each run to `outputs/video-val//`. +Each stage of optimization will produce a separate subdirectory, each of which will contain outputs saved throughout the optimization +and rendered videos of the final result for that stage of optimization. +The `motion_chunks` directory contains the outputs of the final stage of optimization, +`root_fit` and `smooth_fit` contain outputs of short, intermediate stages of optimization, +and `init` contains the initialized outputs before optimization. + +We've provided a `run_vis.py` script for running visualization from logs after optimization. +From the `slahmr` directory, run +``` +python run_vis.py --log_root +``` +and it will visualize all log subdirectories in ``. +Each output npz file will contain the SMPL parameters for all optimized people, the camera intrinsics and extrinsics. +The `motion_chunks` output will contain additional predictions from the motion prior. +Please see `run_vis.py` for how to extract the people meshes from the output parameters. + + +## Fitting to specific datasets: +We provide configurations for dataset formats in `slahmr/confs/data`: +1. Posetrack in `slahmr/confs/data/posetrack.yaml` +2. Egobody in `slahmr/confs/data/egobody.yaml` +3. 3DPW in `slahmr/confs/data/3dpw.yaml` +4. Custom video in `slahmr/confs/data/video.yaml` + +**Please make sure to update all paths to data in the config files.** + +We include tools to both process existing datasets we evaluated on in the paper, and to process custom data and videos. +We include experiments from the paper on the Egobody, Posetrack, and 3DPW datasets. + +If you want to run on a large number of videos, or if you want to select specific people tracks for optimization, +we recommend preprocesing in advance. +For a single downloaded video, there is no need to run preprocessing in advance. + +From the `slahmr/preproc` directory, run PHALP on all your sequences +``` +python launch_phalp.py --type --root --split --gpus +``` +and run DROID-SLAM on all your sequences +``` +python launch_slam.py --type --root --split --gpus +``` +You can also update the paths to datasets in `slahmr/preproc/datasets.py` for repeated use. + +Then, from the `slahmr` directory, +``` +python run_opt.py data= run_opt=True run_vis=True +``` + +We've provided a helper script `launch.py` for launching many optimization jobs in parallel. +You can specify job-specific arguments with a job spec file, such as the example files in `job_specs`, +and batch-specific arguments shared across all jobs as +``` +python launch.py --gpus 1 2 -f job_specs/pt_val_shots.txt -s data=posetrack exp_name=posetrack_val +``` + +## Evaluation on 3D datasets +After launching and completing optimization on either the Egobody or 3DPW datasets, +you can evaluate the outputs with scripts in the `eval` directory. +Before running, please update `EGOBODY_ROOT` and `TDPW_ROOT` in `eval/tools.py`. +Then, run +``` +python run_eval.py -d -i -f +``` +where `` is the same job file used to launch all optimization runs. + + +## BibTeX + +If you use our code in your research, please cite the following paper: +``` +@inproceedings{ye2023slahmr, + title={Decoupling Human and Camera Motion from Videos in the Wild}, + author={Ye, Vickie and Pavlakos, Georgios and Malik, Jitendra and Kanazawa, Angjoo}, + booktitle={IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, + month={June}, + year={2023} +} diff --git a/slahmr/download_models.sh b/slahmr/download_models.sh new file mode 100644 index 0000000000000000000000000000000000000000..d8fb9a1ad3fc9496229457844cc86ef301237286 --- /dev/null +++ b/slahmr/download_models.sh @@ -0,0 +1,5 @@ +#!/usr/bin/bash +# download models +gdown https://drive.google.com/uc?id=1GXAd-45GzGYNENKgQxFQ4PHrBp8wDRlW +unzip -q slahmr_dependencies.zip +rm slahmr_dependencies.zip diff --git a/slahmr/env.yaml b/slahmr/env.yaml new file mode 100644 index 0000000000000000000000000000000000000000..55a1ca1b2a806dd46ed32d386dfe91af9f279fd2 --- /dev/null +++ b/slahmr/env.yaml @@ -0,0 +1,45 @@ +name: slahmr +channels: + - conda-forge + - pytorch + - nvidia + - rusty1s +dependencies: + - python=3.9 + - pytorch + - pytorch-cuda=11.7 + - torchvision + - pytorch-scatter + - suitesparse + - pip + - pip: + - git+https://github.com/facebookresearch/detectron2.git + - git+https://github.com/brjathu/pytube.git + - git+https://github.com/nghorbani/configer + - setuptools==59.5.0 + - torchgeometry==0.1.2 + - tensorboard + - smplx + - pyrender + - open3d + - imageio-ffmpeg + - matplotlib + - opencv-python + - scipy + - scikit-image + - scikit-learn==0.22 + - joblib + - cython + - tqdm + - hydra-core + - pyyaml + - chumpy + - gdown + - dill + - motmetrics + - scenedetect[opencv] + - einops + - mmcv==1.3.9 + - timm==0.4.9 + - xtcocotools==1.10 + - pandas==1.4.0 diff --git a/slahmr/env_build.yaml b/slahmr/env_build.yaml new file mode 100644 index 0000000000000000000000000000000000000000..b647839b4678f58fbc06ef209662bbc60e477479 --- /dev/null +++ b/slahmr/env_build.yaml @@ -0,0 +1,127 @@ +name: slahmr2 +channels: + - defaults +dependencies: + - _libgcc_mutex=0.1=main + - _openmp_mutex=5.1=1_gnu + - bzip2=1.0.8=h7b6447c_0 + - ca-certificates=2023.05.30=h06a4308_0 + - ld_impl_linux-64=2.38=h1181459_1 + - libffi=3.4.4=h6a678d5_0 + - libgcc-ng=11.2.0=h1234567_1 + - libgomp=11.2.0=h1234567_1 + - libstdcxx-ng=11.2.0=h1234567_1 + - libuuid=1.41.5=h5eee18b_0 + - ncurses=6.4=h6a678d5_0 + - openssl=3.0.9=h7f8727e_0 + - python=3.10.12=h955ad1f_0 + - readline=8.2=h5eee18b_0 + - sqlite=3.41.2=h5eee18b_0 + - tk=8.6.12=h1ccaba5_0 + - tzdata=2023c=h04d1e81_0 + - xz=5.4.2=h5eee18b_0 + - zlib=1.2.13=h5eee18b_0 + - pip: + - addict==2.4.0 + - ansi2html==1.8.0 + - appdirs==1.4.4 + - asttokens==2.2.1 + - attrs==23.1.0 + - av==10.0.0 + - backcall==0.2.0 + - beautifulsoup4==4.12.2 + - certifi==2022.12.7 + - charset-normalizer==2.1.1 + - click==8.1.4 + - comm==0.1.3 + - configargparse==1.5.5 + - configer==1.4.1 + - configparser==5.3.0 + - contourpy==1.1.0 + - cycler==0.11.0 + - cython==0.29.36 + - dash==2.11.1 + - dash-core-components==2.0.0 + - dash-html-components==2.0.0 + - dash-table==5.0.0 + - debugpy==1.6.7 + - decorator==5.1.1 + - droid-backends==0.0.0 + - executing==1.2.0 + - fastjsonschema==2.17.1 + - flask==2.2.5 + - fonttools==4.40.0 + - gdown==4.7.1 + - hmr2==0.0.0 + - idna==3.4 + - imageio-ffmpeg==0.4.8 + - importlib-metadata==6.7.0 + - ipdb==0.13.13 + - ipykernel==6.24.0 + - ipython==8.14.0 + - ipywidgets==8.0.7 + - itsdangerous==2.1.2 + - jedi==0.18.2 + - jinja2==3.1.2 + - json-tricks==3.17.1 + - jsonschema==4.18.0 + - jsonschema-specifications==2023.6.1 + - jupyter-client==8.3.0 + - jupyter-core==5.3.1 + - jupyterlab-widgets==3.0.8 + - kiwisolver==1.4.4 + - lietorch==0.2 + - matplotlib==3.7.2 + - matplotlib-inline==0.1.6 + - mmcv==1.3.9 + - munkres==1.1.4 + - nbformat==5.7.0 + - nest-asyncio==1.5.6 + - oauthlib==3.2.2 + - open3d==0.17.0 + - pandas==1.4.0 + - parso==0.8.3 + - pexpect==4.8.0 + - phalp==0.1.3 + - pickleshare==0.7.5 + - pillow==9.3.0 + - pip==23.1.2 + - plotly==5.15.0 + - prompt-toolkit==3.0.39 + - psutil==5.9.5 + - ptyprocess==0.7.0 + - pure-eval==0.2.2 + - pyasn1==0.5.0 + - pyasn1-modules==0.3.0 + - pyparsing==3.0.9 + - pyquaternion==0.9.9 + - pysocks==1.7.1 + - pytz==2023.3 + - pyyaml==6.0 + - pyzmq==25.1.0 + - referencing==0.29.1 + - requests==2.28.1 + - retrying==1.3.4 + - rpds-py==0.8.8 + - scikit-learn==1.3.0 + - scipy==1.11.1 + - setuptools==59.5.0 + - six==1.16.0 + - soupsieve==2.4.1 + - stack-data==0.6.2 + - tenacity==8.2.2 + - timm==0.4.9 + - torch==1.13.0+cu117 + - torch-scatter==2.1.1+pt113cu117 + - torchgeometry==0.1.2 + - torchvision==0.14.0+cu117 + - tornado==6.3.2 + - traitlets==5.9.0 + - urllib3==1.26.13 + - wcwidth==0.2.6 + - werkzeug==2.2.3 + - wheel==0.38.4 + - widgetsnbextension==4.0.8 + - xtcocotools==1.13 + - yapf==0.40.1 + - zipp==3.15.0 diff --git a/slahmr/install.sh b/slahmr/install.sh new file mode 100644 index 0000000000000000000000000000000000000000..7431839a21b677b414f16808251bb96a992226b3 --- /dev/null +++ b/slahmr/install.sh @@ -0,0 +1,35 @@ +#!/usr/bin/env bash +set -e + +export CONDA_ENV_NAME=slahmr + +conda create -n $CONDA_ENV_NAME python=3.10 -y + +conda activate $CONDA_ENV_NAME + +# install pytorch using pip, update with appropriate cuda drivers if necessary +pip install torch==1.13.0 torchvision==0.14.0 --index-url https://download.pytorch.org/whl/cu117 +# uncomment if pip installation isn't working +# conda install pytorch=1.13.0 torchvision=0.14.0 pytorch-cuda=11.7 -c pytorch -c nvidia -y + +# install pytorch scatter using pip, update with appropriate cuda drivers if necessary +pip install torch-scatter -f https://data.pyg.org/whl/torch-1.13.0+cu117.html +# uncomment if pip installation isn't working +# conda install pytorch-scatter -c pyg -y + +# install PHALP +pip install phalp[all]@git+https://github.com/brjathu/PHALP.git + +# install remaining requirements +pip install -r requirements.txt + +# install source +pip install -e . + +# install ViTPose +pip install -v -e third-party/ViTPose + +# install DROID-SLAM +cd third-party/DROID-SLAM +python setup.py install +cd ../.. diff --git a/slahmr/requirements.txt b/slahmr/requirements.txt new file mode 100644 index 0000000000000000000000000000000000000000..6f230db019d9d6144b3a6d624db5f94635b14a67 --- /dev/null +++ b/slahmr/requirements.txt @@ -0,0 +1,27 @@ +git+https://github.com/nghorbani/configer +setuptools==59.5.0 +torchgeometry==0.1.2 +tensorboard +numpy==1.23 +smplx +pyrender +open3d +imageio-ffmpeg +matplotlib +opencv-python +scipy +scikit-image +joblib +cython +tqdm +hydra-core +pyyaml +chumpy +gdown +dill +motmetrics +einops +mmcv==1.3.9 +timm==0.4.9 +xtcocotools +pandas==1.4.0 diff --git a/slahmr/setup.py b/slahmr/setup.py new file mode 100644 index 0000000000000000000000000000000000000000..cf532bf575b100ec37884e7abbed9daada589ffb --- /dev/null +++ b/slahmr/setup.py @@ -0,0 +1,9 @@ +from setuptools import find_packages, setup + +setup( + name="slahmr", + packages=find_packages( + where="slahmr", + ), + package_dir={"": "slahmr"}, +) diff --git a/slahmr/slahmr.zip b/slahmr/slahmr.zip new file mode 100644 index 0000000000000000000000000000000000000000..7b68e1086854be6a49669b29b5ce0ad416024835 --- /dev/null +++ b/slahmr/slahmr.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4e59655cc88dc71f3a9ac20425310bf996da3b6f15619497d17c67e7b60a671a +size 5662244525 diff --git a/slahmr/slahmr/__init__.py b/slahmr/slahmr/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/slahmr/body_model/__init__.py b/slahmr/slahmr/body_model/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..b66fb81b2d0a57150b3fb7c76189b6a5217b0627 --- /dev/null +++ b/slahmr/slahmr/body_model/__init__.py @@ -0,0 +1,3 @@ +from .body_model import * +from .specs import * +from .utils import * diff --git a/slahmr/slahmr/body_model/body_model.py b/slahmr/slahmr/body_model/body_model.py new file mode 100644 index 0000000000000000000000000000000000000000..ea145e1f8c2e300e996389742d41004ab5665db7 --- /dev/null +++ b/slahmr/slahmr/body_model/body_model.py @@ -0,0 +1,142 @@ +import numpy as np + +import torch +import torch.nn as nn + +from smplx import SMPL, SMPLH, SMPLX +from smplx.vertex_ids import vertex_ids +from smplx.utils import Struct + + +class BodyModel(nn.Module): + """ + Wrapper around SMPLX body model class. + """ + + def __init__( + self, + bm_path, + num_betas=10, + batch_size=1, + num_expressions=10, + use_vtx_selector=False, + model_type="smplh", + kid_template_path=None, + ): + super(BodyModel, self).__init__() + """ + Creates the body model object at the given path. + + :param bm_path: path to the body model pkl file + :param num_expressions: only for smplx + :param model_type: one of [smpl, smplh, smplx] + :param use_vtx_selector: if true, returns additional vertices as joints that correspond to OpenPose joints + """ + self.use_vtx_selector = use_vtx_selector + cur_vertex_ids = None + if self.use_vtx_selector: + cur_vertex_ids = vertex_ids[model_type] + data_struct = None + if ".npz" in bm_path: + # smplx does not support .npz by default, so have to load in manually + smpl_dict = np.load(bm_path, encoding="latin1") + data_struct = Struct(**smpl_dict) + # print(smpl_dict.files) + if model_type == "smplh": + data_struct.hands_componentsl = np.zeros((0)) + data_struct.hands_componentsr = np.zeros((0)) + data_struct.hands_meanl = np.zeros((15 * 3)) + data_struct.hands_meanr = np.zeros((15 * 3)) + V, D, B = data_struct.shapedirs.shape + data_struct.shapedirs = np.concatenate( + [data_struct.shapedirs, np.zeros((V, D, SMPL.SHAPE_SPACE_DIM - B))], + axis=-1, + ) # super hacky way to let smplh use 16-size beta + kwargs = { + "model_type": model_type, + "data_struct": data_struct, + "num_betas": num_betas, + "batch_size": batch_size, + "num_expression_coeffs": num_expressions, + "vertex_ids": cur_vertex_ids, + "use_pca": False, + "flat_hand_mean": False, + } + if kid_template_path is not None: + kwargs["kid_template_path"] = kid_template_path + kwargs["age"] = "kid" + + assert model_type in ["smpl", "smplh", "smplx"] + if model_type == "smpl": + self.bm = SMPL(bm_path, **kwargs) + self.num_joints = SMPL.NUM_JOINTS + elif model_type == "smplh": + self.bm = SMPLH(bm_path, **kwargs) + self.num_joints = SMPLH.NUM_JOINTS + elif model_type == "smplx": + self.bm = SMPLX(bm_path, **kwargs) + self.num_joints = SMPLX.NUM_JOINTS + + self.model_type = model_type + + def forward( + self, + root_orient=None, + pose_body=None, + pose_hand=None, + pose_jaw=None, + pose_eye=None, + betas=None, + trans=None, + dmpls=None, + expression=None, + return_dict=False, + **kwargs + ): + """ + Note dmpls are not supported. + """ + assert dmpls is None + out_obj = self.bm( + betas=betas, + global_orient=root_orient, + body_pose=pose_body, + left_hand_pose=None + if pose_hand is None + else pose_hand[:, : (SMPLH.NUM_HAND_JOINTS * 3)], + right_hand_pose=None + if pose_hand is None + else pose_hand[:, (SMPLH.NUM_HAND_JOINTS * 3) :], + transl=trans, + expression=expression, + jaw_pose=pose_jaw, + leye_pose=None if pose_eye is None else pose_eye[:, :3], + reye_pose=None if pose_eye is None else pose_eye[:, 3:], + return_full_pose=True, + **kwargs + ) + + out = { + "v": out_obj.vertices, + "f": self.bm.faces_tensor, + "betas": out_obj.betas, + "Jtr": out_obj.joints, + "pose_body": out_obj.body_pose, + "full_pose": out_obj.full_pose, + } + if self.model_type in ["smplh", "smplx"]: + out["pose_hand"] = torch.cat( + [out_obj.left_hand_pose, out_obj.right_hand_pose], dim=-1 + ) + if self.model_type == "smplx": + out["pose_jaw"] = out_obj.jaw_pose + out["pose_eye"] = pose_eye + + if not self.use_vtx_selector: + # don't need extra joints + out["Jtr"] = out["Jtr"][:, : self.num_joints + 1] # add one for the root + + if not return_dict: + out = Struct(**out) + + return out diff --git a/slahmr/slahmr/body_model/specs.py b/slahmr/slahmr/body_model/specs.py new file mode 100644 index 0000000000000000000000000000000000000000..5a6b4c8d340c4097aa0cbdd4d7fc2ee3ae43e894 --- /dev/null +++ b/slahmr/slahmr/body_model/specs.py @@ -0,0 +1,554 @@ +import numpy as np + +SMPL_JOINTS = { + "hips": 0, + "leftUpLeg": 1, + "rightUpLeg": 2, + "spine": 3, + "leftLeg": 4, + "rightLeg": 5, + "spine1": 6, + "leftFoot": 7, + "rightFoot": 8, + "spine2": 9, + "leftToeBase": 10, + "rightToeBase": 11, + "neck": 12, + "leftShoulder": 13, + "rightShoulder": 14, + "head": 15, + "leftArm": 16, + "rightArm": 17, + "leftForeArm": 18, + "rightForeArm": 19, + "leftHand": 20, + "rightHand": 21, +} +SMPL_PARENTS = [ + -1, + 0, + 0, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 12, + 12, + 12, + 13, + 14, + 16, + 17, + 18, + 19, +] + +SMPLH_PATH = "./body_models/smplh" +SMPLX_PATH = "./body_models/smplx" +SMPL_PATH = "./body_models/smpl" +VPOSER_PATH = "./body_models/vposer_v1_0" + +# chosen virtual mocap markers that are "keypoints" to work with +KEYPT_VERTS = [ + 4404, + 920, + 3076, + 3169, + 823, + 4310, + 1010, + 1085, + 4495, + 4569, + 6615, + 3217, + 3313, + 6713, + 6785, + 3383, + 6607, + 3207, + 1241, + 1508, + 4797, + 4122, + 1618, + 1569, + 5135, + 5040, + 5691, + 5636, + 5404, + 2230, + 2173, + 2108, + 134, + 3645, + 6543, + 3123, + 3024, + 4194, + 1306, + 182, + 3694, + 4294, + 744, +] + + +""" +Openpose +""" +OP_NUM_JOINTS = 25 +# OP_IGNORE_JOINTS = [1, 9, 12] # neck and left/right hip +OP_IGNORE_JOINTS = [1] # neck +OP_EDGE_LIST = [ + [1, 8], + [1, 2], + [1, 5], + [2, 3], + [3, 4], + [5, 6], + [6, 7], + [8, 9], + [9, 10], + [10, 11], + [8, 12], + [12, 13], + [13, 14], + [1, 0], + [0, 15], + [15, 17], + [0, 16], + [16, 18], + [14, 19], + [19, 20], + [14, 21], + [11, 22], + [22, 23], + [11, 24], +] +# indices to map an openpose detection to its flipped version +OP_FLIP_MAP = [ + 0, + 1, + 5, + 6, + 7, + 2, + 3, + 4, + 8, + 12, + 13, + 14, + 9, + 10, + 11, + 16, + 15, + 18, + 17, + 22, + 23, + 24, + 19, + 20, + 21, +] + + +# +# From https://github.com/vchoutas/smplify-x/blob/master/smplifyx/utils.py +# Please see license for usage restrictions. +# +def smpl_to_openpose( + model_type="smplx", + use_hands=True, + use_face=True, + use_face_contour=False, + openpose_format="coco25", +): + """Returns the indices of the permutation that maps SMPL to OpenPose + + Parameters + ---------- + model_type: str, optional + The type of SMPL-like model that is used. The default mapping + returned is for the SMPLX model + use_hands: bool, optional + Flag for adding to the returned permutation the mapping for the + hand keypoints. Defaults to True + use_face: bool, optional + Flag for adding to the returned permutation the mapping for the + face keypoints. Defaults to True + use_face_contour: bool, optional + Flag for appending the facial contour keypoints. Defaults to False + openpose_format: bool, optional + The output format of OpenPose. For now only COCO-25 and COCO-19 is + supported. Defaults to 'coco25' + + """ + if openpose_format.lower() == "coco25": + if model_type == "smpl": + return np.array( + [ + 24, + 12, + 17, + 19, + 21, + 16, + 18, + 20, + 0, + 2, + 5, + 8, + 1, + 4, + 7, + 25, + 26, + 27, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + ], + dtype=np.int32, + ) + elif model_type == "smplh": + body_mapping = np.array( + [ + 52, + 12, + 17, + 19, + 21, + 16, + 18, + 20, + 0, + 2, + 5, + 8, + 1, + 4, + 7, + 53, + 54, + 55, + 56, + 57, + 58, + 59, + 60, + 61, + 62, + ], + dtype=np.int32, + ) + mapping = [body_mapping] + if use_hands: + lhand_mapping = np.array( + [ + 20, + 34, + 35, + 36, + 63, + 22, + 23, + 24, + 64, + 25, + 26, + 27, + 65, + 31, + 32, + 33, + 66, + 28, + 29, + 30, + 67, + ], + dtype=np.int32, + ) + rhand_mapping = np.array( + [ + 21, + 49, + 50, + 51, + 68, + 37, + 38, + 39, + 69, + 40, + 41, + 42, + 70, + 46, + 47, + 48, + 71, + 43, + 44, + 45, + 72, + ], + dtype=np.int32, + ) + mapping += [lhand_mapping, rhand_mapping] + return np.concatenate(mapping) + # SMPLX + elif model_type == "smplx": + body_mapping = np.array( + [ + 55, + 12, + 17, + 19, + 21, + 16, + 18, + 20, + 0, + 2, + 5, + 8, + 1, + 4, + 7, + 56, + 57, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + ], + dtype=np.int32, + ) + mapping = [body_mapping] + if use_hands: + lhand_mapping = np.array( + [ + 20, + 37, + 38, + 39, + 66, + 25, + 26, + 27, + 67, + 28, + 29, + 30, + 68, + 34, + 35, + 36, + 69, + 31, + 32, + 33, + 70, + ], + dtype=np.int32, + ) + rhand_mapping = np.array( + [ + 21, + 52, + 53, + 54, + 71, + 40, + 41, + 42, + 72, + 43, + 44, + 45, + 73, + 49, + 50, + 51, + 74, + 46, + 47, + 48, + 75, + ], + dtype=np.int32, + ) + + mapping += [lhand_mapping, rhand_mapping] + if use_face: + # end_idx = 127 + 17 * use_face_contour + face_mapping = np.arange( + 76, 127 + 17 * use_face_contour, dtype=np.int32 + ) + mapping += [face_mapping] + + return np.concatenate(mapping) + else: + raise ValueError("Unknown model type: {}".format(model_type)) + elif openpose_format == "coco19": + if model_type == "smpl": + return np.array( + [24, 12, 17, 19, 21, 16, 18, 20, 0, 2, 5, 8, 1, 4, 7, 25, 26, 27, 28], + dtype=np.int32, + ) + elif model_type == "smplh": + body_mapping = np.array( + [52, 12, 17, 19, 21, 16, 18, 20, 0, 2, 5, 8, 1, 4, 7, 53, 54, 55, 56], + dtype=np.int32, + ) + mapping = [body_mapping] + if use_hands: + lhand_mapping = np.array( + [ + 20, + 34, + 35, + 36, + 57, + 22, + 23, + 24, + 58, + 25, + 26, + 27, + 59, + 31, + 32, + 33, + 60, + 28, + 29, + 30, + 61, + ], + dtype=np.int32, + ) + rhand_mapping = np.array( + [ + 21, + 49, + 50, + 51, + 62, + 37, + 38, + 39, + 63, + 40, + 41, + 42, + 64, + 46, + 47, + 48, + 65, + 43, + 44, + 45, + 66, + ], + dtype=np.int32, + ) + mapping += [lhand_mapping, rhand_mapping] + return np.concatenate(mapping) + # SMPLX + elif model_type == "smplx": + body_mapping = np.array( + [55, 12, 17, 19, 21, 16, 18, 20, 0, 2, 5, 8, 1, 4, 7, 56, 57, 58, 59], + dtype=np.int32, + ) + mapping = [body_mapping] + if use_hands: + lhand_mapping = np.array( + [ + 20, + 37, + 38, + 39, + 60, + 25, + 26, + 27, + 61, + 28, + 29, + 30, + 62, + 34, + 35, + 36, + 63, + 31, + 32, + 33, + 64, + ], + dtype=np.int32, + ) + rhand_mapping = np.array( + [ + 21, + 52, + 53, + 54, + 65, + 40, + 41, + 42, + 66, + 43, + 44, + 45, + 67, + 49, + 50, + 51, + 68, + 46, + 47, + 48, + 69, + ], + dtype=np.int32, + ) + + mapping += [lhand_mapping, rhand_mapping] + if use_face: + face_mapping = np.arange( + 70, 70 + 51 + 17 * use_face_contour, dtype=np.int32 + ) + mapping += [face_mapping] + + return np.concatenate(mapping) + else: + raise ValueError("Unknown model type: {}".format(model_type)) + else: + raise ValueError("Unknown joint format: {}".format(openpose_format)) diff --git a/slahmr/slahmr/body_model/utils.py b/slahmr/slahmr/body_model/utils.py new file mode 100644 index 0000000000000000000000000000000000000000..722f8c50de45fac71e323f299c12bb9bf9092ac0 --- /dev/null +++ b/slahmr/slahmr/body_model/utils.py @@ -0,0 +1,56 @@ +import torch +from .specs import SMPL_JOINTS + + +def run_smpl(body_model, trans, root_orient, body_pose, betas=None): + """ + Forward pass of the SMPL model and populates pred_data accordingly with + joints3d, verts3d, points3d. + + trans : B x T x 3 + root_orient : B x T x 3 + body_pose : B x T x J*3 + betas : (optional) B x D + """ + B, T, _ = trans.shape + bm_batch_size = body_model.bm.batch_size + assert bm_batch_size % B == 0 + seq_len = bm_batch_size // B + bm_num_betas = body_model.bm.num_betas + J_BODY = len(SMPL_JOINTS) - 1 # all joints except root + if T == 1: + # must expand to use with body model + trans = trans.expand(B, seq_len, 3) + root_orient = root_orient.expand(B, seq_len, 3) + body_pose = body_pose.expand(B, seq_len, J_BODY * 3) + elif T != seq_len: + trans, root_orient, body_pose = zero_pad_tensors( + [trans, root_orient, body_pose], seq_len - T + ) + if betas is None: + betas = torch.zeros(B, bm_num_betas, device=trans.device) + betas = betas.reshape((B, 1, bm_num_betas)).expand((B, seq_len, bm_num_betas)) + smpl_body = body_model( + pose_body=body_pose.reshape((B * seq_len, -1)), + pose_hand=None, + betas=betas.reshape((B * seq_len, -1)), + root_orient=root_orient.reshape((B * seq_len, -1)), + trans=trans.reshape((B * seq_len, -1)), + ) + return { + "joints": smpl_body.Jtr.reshape(B, seq_len, -1, 3)[:, :T], + "vertices": smpl_body.v.reshape(B, seq_len, -1, 3)[:, :T], + "faces": smpl_body.f, + } + + +def zero_pad_tensors(pad_list, pad_size): + """ + Assumes tensors in pad_list are B x T x D and pad temporal dimension + """ + B = pad_list[0].size(0) + new_pad_list = [] + for pad_idx, pad_tensor in enumerate(pad_list): + padding = torch.zeros((B, pad_size, pad_tensor.size(2))).to(pad_tensor) + new_pad_list.append(torch.cat([pad_tensor, padding], dim=1)) + return new_pad_list diff --git a/slahmr/slahmr/confs/config.yaml b/slahmr/slahmr/confs/config.yaml new file mode 100644 index 0000000000000000000000000000000000000000..0e15b08459fccf9358d2fb07b9dd0e1f295836f3 --- /dev/null +++ b/slahmr/slahmr/confs/config.yaml @@ -0,0 +1,51 @@ +defaults: + - data: posetrack + - optim + - _self_ + +model: + floor_type: "shared" + est_floor: False + use_init: True + opt_cams: False + opt_scale: True + async_tracks: True + +overwrite: False +run_opt: False +run_vis: False +vis: + phases: + - motion_chunks + - input + render_views: + - src_cam + - above + - side + make_grid: True + overwrite: False + +paths: + smpl: _DATA/body_models/smplh/neutral/model.npz + smpl_kid: _DATA/body_models/smpl_kid_template.npy + vposer: _DATA/body_models/vposer_v1_0 + init_motion_prior: _DATA/humor_ckpts/init_state_prior_gmm + humor: _DATA/humor_ckpts/humor/best_model.pth + +humor: + in_rot_rep: "mat" + out_rot_rep: "aa" + latent_size: 48 + model_data_config: "smpl+joints+contacts" + steps_in: 1 + +fps: 30 +log_root: ../outputs/logs +log_dir: ${log_root}/${data.type}-${data.split} +exp_name: ${now:%Y-%m-%d} + +hydra: + job: + chdir: True + run: + dir: ${log_dir}/${exp_name}/${data.name} diff --git a/slahmr/slahmr/confs/data/3dpw.yaml b/slahmr/slahmr/confs/data/3dpw.yaml new file mode 100644 index 0000000000000000000000000000000000000000..e39abb1b6dd66d3d2b74341e9e9bca7e8892ee7e --- /dev/null +++ b/slahmr/slahmr/confs/data/3dpw.yaml @@ -0,0 +1,18 @@ +type: 3dpw +split: test +seq: downtown_arguing_00 +root: /path/to/3DPW +use_cams: True +split_cameras: False +camera_name: cameras_intrins_split +shot_idx: 0 +start_idx: 0 +end_idx: 100 +track_ids: "longest-2" +sources: + images: ${data.root}/imageFiles/${data.seq} + cameras: ${data.root}/slahmr/${data.camera_name}/${data.seq}/${data.start_idx}-${data.end_idx} + intrins: ${data.root}/slahmr/cameras_gt/${data.seq}/intrinsics.txt + tracks: ${data.root}/slahmr/track_preds/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json +name: ${data.seq}-${data.track_ids}-${data.start_idx}-${data.end_idx} diff --git a/slahmr/slahmr/confs/data/3dpw_gt.yaml b/slahmr/slahmr/confs/data/3dpw_gt.yaml new file mode 100644 index 0000000000000000000000000000000000000000..da35923d0f1523fe7c8ed68d36339d3dc6c1b9ab --- /dev/null +++ b/slahmr/slahmr/confs/data/3dpw_gt.yaml @@ -0,0 +1,18 @@ +type: 3dpw_gt +split: test +seq: downtown_runForBus_00 +root: /path/to/3DPW +use_cams: True +split_cameras: False +camera_name: cameras_intrins_split +shot_idx: 0 +start_idx: 0 +end_idx: 100 +track_ids: "longest-2" +sources: + images: ${data.root}/imageFiles/${data.seq} + cameras: ${data.root}/slahmr/${data.camera_name}/${data.seq}/${data.start_idx}-${data.end_idx} + intrins: ${data.root}/slahmr/cameras_gt/${data.seq}/intrinsics.txt + tracks: ${data.root}/slahmr/track_gt/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json +name: ${data.seq}-${data.track_ids}-${data.start_idx}-${data.end_idx} diff --git a/slahmr/slahmr/confs/data/custom.yaml b/slahmr/slahmr/confs/data/custom.yaml new file mode 100644 index 0000000000000000000000000000000000000000..5ae45966b2d10a8ea844ec56e54eaf676fda318d --- /dev/null +++ b/slahmr/slahmr/confs/data/custom.yaml @@ -0,0 +1,17 @@ +type: custom +split: val +video: "" +seq: "" +root: /path/to/custom +use_cams: True +track_ids: "all" +shot_idx: 0 +start_idx: 0 +end_idx: 200 +split_cameras: True +name: ${data.seq}-${data.track_ids}-shot-${data.shot_idx} +sources: + images: ${data.root}/images/${data.seq} + cameras: ${data.root}/slahmr/cameras/${data.seq}/shot-${data.shot_idx} + track: ${data.root}/slahmr/track_preds/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json diff --git a/slahmr/slahmr/confs/data/davis.yaml b/slahmr/slahmr/confs/data/davis.yaml new file mode 100644 index 0000000000000000000000000000000000000000..bcd21940c72eae327e9da6a91aac46a3cb9a9296 --- /dev/null +++ b/slahmr/slahmr/confs/data/davis.yaml @@ -0,0 +1,16 @@ +type: davis +split: all +seq: parkour +root: /path/to/DAVIS +use_cams: True +track_ids: "all" +shot_idx: 0 +start_idx: 0 +end_idx: -1 +split_cameras: True +name: ${data.seq}-${data.track_ids}-shot-${data.shot_idx} +sources: + images: ${data.root}/JPEGImages/Full-Resolution/${data.seq} + cameras: ${data.root}/slahmr/cameras/${data.seq}/shot-${data.shot_idx} + tracks: ${data.root}/slahmr/track_preds/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json diff --git a/slahmr/slahmr/confs/data/egobody.yaml b/slahmr/slahmr/confs/data/egobody.yaml new file mode 100644 index 0000000000000000000000000000000000000000..66485645639bc21d9824980c6ab5af0c7aa8a5e6 --- /dev/null +++ b/slahmr/slahmr/confs/data/egobody.yaml @@ -0,0 +1,18 @@ +type: egobody +split: val +seq: recording_20210921_S11_S10_01 +root: /path/to/egobody +use_cams: True +camera_name: cameras_intrins_split +shot_idx: 0 +start_idx: 0 +end_idx: 100 +split_cameras: False +track_ids: "all" +sources: + images: ${data.root}/egocentric_color/${data.seq}/**/PV + cameras: ${data.root}/slahmr/${data.camera_name}/${data.seq}/${data.start_idx}-${data.end_idx} + intrins: ${data.root}/slahmr/cameras_gt/${data.seq}/intrinsics.txt + tracks: ${data.root}/slahmr/track_preds/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json +name: ${data.seq}-${data.track_ids}-${data.start_idx}-${data.end_idx} diff --git a/slahmr/slahmr/confs/data/posetrack.yaml b/slahmr/slahmr/confs/data/posetrack.yaml new file mode 100644 index 0000000000000000000000000000000000000000..f682e8be94bf39d35c2fb8f952cc4b97d79f37c8 --- /dev/null +++ b/slahmr/slahmr/confs/data/posetrack.yaml @@ -0,0 +1,17 @@ +type: posetrack +split: val +seq: 014286_mpii_train +root: /path/to/posetrack +use_cams: True +track_ids: "all" +shot_idx: 0 +start_idx: 0 +end_idx: -1 +split_cameras: True +name: ${data.seq}-${data.track_ids}-shot-${data.shot_idx} +track_name: track_preds +sources: + images: ${data.root}/images/${data.split}/${data.seq} + cameras: ${data.root}/slahmr/${data.split}/cameras/${data.seq}/shot-${data.shot_idx} + tracks: ${data.root}/slahmr/${data.split}/${data.track_name}/${data.seq} + shots: ${data.root}/slahmr/${data.split}/shot_idcs/${data.seq}.json diff --git a/slahmr/slahmr/confs/data/video.yaml b/slahmr/slahmr/confs/data/video.yaml new file mode 100644 index 0000000000000000000000000000000000000000..52a9a8429245dc3f268bc493208afbe43710bf7d --- /dev/null +++ b/slahmr/slahmr/confs/data/video.yaml @@ -0,0 +1,24 @@ +type: video +split: val +root: /path/to/data # put your videos in root/videos/vid.mp4 +video_dir: videos +seq: basketball +ext: mp4 +src_path: ${data.root}/${data.video_dir}/${data.seq}.${data.ext} +frame_opts: + ext: jpg + fps: 25 + start_sec: 0 + end_sec: -1 +use_cams: True +track_ids: "all" +shot_idx: 0 +start_idx: 0 +end_idx: 180 +split_cameras: True +name: ${data.seq}-${data.track_ids}-shot-${data.shot_idx}-${data.start_idx}-${data.end_idx} +sources: + images: ${data.root}/images/${data.seq} + cameras: ${data.root}/slahmr/cameras/${data.seq}/shot-${data.shot_idx} + tracks: ${data.root}/slahmr/track_preds/${data.seq} + shots: ${data.root}/slahmr/shot_idcs/${data.seq}.json diff --git a/slahmr/slahmr/confs/init.yaml b/slahmr/slahmr/confs/init.yaml new file mode 100644 index 0000000000000000000000000000000000000000..07b844191ab983de17825f068206f7222a7726e7 --- /dev/null +++ b/slahmr/slahmr/confs/init.yaml @@ -0,0 +1,13 @@ +defaults: + - data: posetrack + - _self_ + +gap: 1 +log_root: outputs +save_per_frame: False +print_err: False +stride: 48 + +hydra: + run: + dir: ${log_root}/init/${data.type}-${data.seq}-${data.depth_dir}-${data.fov}fov-gap${gap} diff --git a/slahmr/slahmr/confs/optim.yaml b/slahmr/slahmr/confs/optim.yaml new file mode 100644 index 0000000000000000000000000000000000000000..d17f54dda1bd0fd687cb506821bac4f6f3a02db3 --- /dev/null +++ b/slahmr/slahmr/confs/optim.yaml @@ -0,0 +1,51 @@ +optim: + options: + robust_loss_type: "bisquare" + robust_tuning_const: 4.6851 + joints2d_sigma: 100.0 + lr: 1.0 + lbfgs_max_iter: 20 + save_every: 20 + vis_every: -1 + max_chunk_steps: 20 + save_meshes: False + + root: + num_iters: 30 + + smpl: + num_iters: 0 + + smooth: + opt_scale: False + num_iters: 60 + + motion_chunks: + chunk_size: 10 + init_steps: 20 + chunk_steps: 20 + opt_cams: True + + loss_weights: + joints2d: [0.001, 0.001, 0.001] + bg2d: [0.0, 0.000, 0.000] + cam_R_smooth : [0.0, 0.0, 0.0] + cam_t_smooth : [0.0, 0.0, 0.0] + # bg2d: [0.0, 0.0001, 0.0001] + # cam_R_smooth : [0.0, 1000.0, 1000.0] + # cam_t_smooth : [0.0, 1000.0, 1000.0] + joints3d: [0.0, 0.0, 0.0] + joints3d_smooth: [1.0, 10.0, 0.0] + joints3d_rollout: [0.0, 0.0, 0.0] + verts3d: [0.0, 0.0, 0.0] + points3d: [0.0, 0.0, 0.0] + pose_prior: [0.04, 0.04, 0.04] + shape_prior: [0.05, 0.05, 0.05] + motion_prior: [0.0, 0.0, 0.075] + init_motion_prior: [0.0, 0.0, 0.075] + joint_consistency: [0.0, 0.0, 100.0] + bone_length: [0.0, 0.0, 2000.0] + contact_vel: [0.0, 0.0, 100.0] + contact_height: [0.0, 0.0, 10.0] + floor_reg: [0.0, 0.0, 0.0] +# floor_reg: [0.0, 0.0, 0.167] diff --git a/slahmr/slahmr/data/__init__.py b/slahmr/slahmr/data/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..93013a0a01c298628584bec63b669ae4e2019410 --- /dev/null +++ b/slahmr/slahmr/data/__init__.py @@ -0,0 +1,2 @@ +from .dataset import * +from . import tools diff --git a/slahmr/slahmr/data/dataset.py b/slahmr/slahmr/data/dataset.py new file mode 100644 index 0000000000000000000000000000000000000000..b4ccf80d7697bdf7e39a9ad926caf0a4fcfc8af8 --- /dev/null +++ b/slahmr/slahmr/data/dataset.py @@ -0,0 +1,438 @@ +import os +import glob +import typing + +import imageio +import numpy as np +import json + +import torch +import torch.nn.functional as F +from torch.utils.data import Dataset + +from body_model import OP_NUM_JOINTS, SMPL_JOINTS +from util.logger import Logger +from geometry.camera import invert_camera + +from .tools import read_keypoints, read_mask_path, load_smpl_preds +from .vidproc import preprocess_cameras, preprocess_frames, preprocess_tracks + + +""" +Define data-related constants +""" +DEFAULT_GROUND = np.array([0.0, -1.0, 0.0, -0.5]) + +# XXX: TEMPORARY CONSTANTS +SHOT_PAD = 0 +MIN_SEQ_LEN = 20 +MAX_NUM_TRACKS = 12 +MIN_TRACK_LEN = 20 +MIN_KEYP_CONF = 0.4 + + +def get_dataset_from_cfg(cfg): + args = cfg.data + if not args.use_cams: + args.sources.cameras = "" + + args.sources = expand_source_paths(args.sources) + print("DATA SOURCES", args.sources) + check_data_sources(args) + return MultiPeopleDataset( + args.sources, + args.seq, + tid_spec=args.track_ids, + shot_idx=args.shot_idx, + start_idx=int(args.start_idx), + end_idx=int(args.end_idx), + split_cameras=args.get("split_cameras", True), + ) + + +def expand_source_paths(data_sources): + return {k: get_data_source(v) for k, v in data_sources.items()} + + +def get_data_source(source): + matches = glob.glob(source) + if len(matches) < 1: + print(f"{source} does not exist") + return source # return anyway for default values + if len(matches) > 1: + raise ValueError(f"{source} is not unique") + return matches[0] + + +def check_data_sources(args): + if args.type == "video": + preprocess_frames(args.sources.images, args.src_path, **args.frame_opts) + preprocess_tracks(args.sources.images, args.sources.tracks, args.sources.shots) + preprocess_cameras(args, overwrite=args.get("overwrite_cams", False)) + + +class MultiPeopleDataset(Dataset): + def __init__( + self, + data_sources: typing.Dict, + seq_name, + tid_spec="all", + shot_idx=0, + start_idx=0, + end_idx=-1, + pad_shot=False, + split_cameras=True, + ): + self.seq_name = seq_name + self.data_sources = data_sources + self.split_cameras = split_cameras + + # select only images in the desired shot + img_files, _ = get_shot_img_files( + self.data_sources["shots"], shot_idx, pad_shot + ) + end_idx = end_idx if end_idx > 0 else len(img_files) + self.data_start, self.data_end = start_idx, end_idx + img_files = img_files[start_idx:end_idx] + self.img_names = [get_name(f) for f in img_files] + self.num_imgs = len(self.img_names) + + img_dir = self.data_sources["images"] + assert os.path.isdir(img_dir) + self.img_paths = [os.path.join(img_dir, f) for f in img_files] + img_h, img_w = imageio.imread(self.img_paths[0]).shape[:2] + self.img_size = img_w, img_h + print(f"USING TOTAL {self.num_imgs} {img_w}x{img_h} IMGS") + + # find the tracks in the video + track_root = self.data_sources["tracks"] + if tid_spec == "all" or tid_spec.startswith("longest"): + n_tracks = MAX_NUM_TRACKS + if tid_spec.startswith("longest"): + n_tracks = int(tid_spec.split("-")[1]) + # get the longest tracks in the selected shot + track_ids = sorted(os.listdir(track_root)) + track_paths = [ + [f"{track_root}/{tid}/{name}_keypoints.json" for name in self.img_names] + for tid in track_ids + ] + track_lens = [ + len(list(filter(os.path.isfile, paths))) for paths in track_paths + ] + track_ids = [ + track_ids[i] + for i in np.argsort(track_lens)[::-1] + if track_lens[i] > MIN_TRACK_LEN + ] + print("TRACK LENGTHS", track_ids, track_lens) + track_ids = track_ids[:n_tracks] + else: + track_ids = [f"{int(tid):03d}" for tid in tid_spec.split("-")] + + print("TRACK IDS", track_ids) + + self.track_ids = track_ids + self.n_tracks = len(track_ids) + self.track_dirs = [os.path.join(track_root, tid) for tid in track_ids] + + # keep a list of frame index masks of whether a track is available in a frame + sidx = np.inf + eidx = -1 + self.track_vis_masks = [] + for pred_dir in self.track_dirs: + kp_paths = [f"{pred_dir}/{x}_keypoints.json" for x in self.img_names] + has_kp = [os.path.isfile(x) for x in kp_paths] + + # keep track of which frames this track is visible in + vis_mask = np.array(has_kp) + idcs = np.where(vis_mask)[0] + if len(idcs) > 0: + si, ei = min(idcs), max(idcs) + sidx = min(sidx, si) + eidx = max(eidx, ei) + self.track_vis_masks.append(vis_mask) + + eidx = max(eidx + 1, 0) + sidx = min(sidx, eidx) + print("START", sidx, "END", eidx) + self.start_idx = sidx + self.end_idx = eidx + self.seq_len = eidx - sidx + self.seq_intervals = [(sidx, eidx) for _ in track_ids] + + self.sel_img_paths = self.img_paths[sidx:eidx] + self.sel_img_names = self.img_names[sidx:eidx] + + # used to cache data + self.data_dict = {} + self.cam_data = None + + def __len__(self): + return self.n_tracks + + def load_data(self, interp_input=True): + if len(self.data_dict) > 0: + return + + # load camera data + self.load_camera_data() + # get data for each track + data_out = { + "mask_paths": [], + "floor_plane": [], + "joints2d": [], + "vis_mask": [], + "track_interval": [], + "init_body_pose": [], + "init_root_orient": [], + "init_trans": [], + } + + # create batches of sequences + # each batch is a track for a person + T = self.seq_len + sidx, eidx = self.start_idx, self.end_idx + for i, tid in enumerate(self.track_ids): + # load mask of visible frames for this track + vis_mask = self.track_vis_masks[i][sidx:eidx] # (T) + vis_idcs = np.where(vis_mask)[0] + track_s, track_e = min(vis_idcs), max(vis_idcs) + 1 + data_out["track_interval"].append([track_s, track_e]) + + vis_mask = get_ternary_mask(vis_mask) + data_out["vis_mask"].append(vis_mask) + + # load 2d keypoints for visible frames + kp_paths = [ + f"{self.track_dirs[i]}/{x}_keypoints.json" for x in self.sel_img_names + ] + # (T, J, 3) (x, y, conf) + joints2d_data = np.stack( + [read_keypoints(p) for p in kp_paths], axis=0 + ).astype(np.float32) + # Discard bad ViTPose detections + joints2d_data[ + np.repeat(joints2d_data[:, :, [2]] < MIN_KEYP_CONF, 3, axis=2) + ] = 0 + data_out["joints2d"].append(joints2d_data) + + # load single image smpl predictions + pred_paths = [ + f"{self.track_dirs[i]}/{x}_smpl.json" for x in self.sel_img_names + ] + pose_init, orient_init, trans_init, _ = load_smpl_preds( + pred_paths, interp=interp_input + ) + + n_joints = len(SMPL_JOINTS) - 1 + data_out["init_body_pose"].append(pose_init[:, :n_joints, :]) + data_out["init_root_orient"].append(orient_init) + data_out["init_trans"].append(trans_init) + + data_out["floor_plane"].append(DEFAULT_GROUND[:3] * DEFAULT_GROUND[3:]) + + self.data_dict = data_out + + def __getitem__(self, idx): + if len(self.data_dict) < 1: + self.load_data() + + obs_data = dict() + + # 2D keypoints + joint2d_data = self.data_dict["joints2d"][idx] + obs_data["joints2d"] = torch.Tensor(joint2d_data) + + # single frame predictions + obs_data["init_body_pose"] = torch.Tensor(self.data_dict["init_body_pose"][idx]) + obs_data["init_root_orient"] = torch.Tensor( + self.data_dict["init_root_orient"][idx] + ) + obs_data["init_trans"] = torch.Tensor(self.data_dict["init_trans"][idx]) + + # floor plane + obs_data["floor_plane"] = torch.Tensor(self.data_dict["floor_plane"][idx]) + + # the frames the track is visible in + obs_data["vis_mask"] = torch.Tensor(self.data_dict["vis_mask"][idx]) + + # the frames used in this subsequence + obs_data["seq_interval"] = torch.Tensor(list(self.seq_intervals[idx])).to( + torch.int + ) + # the start and end interval of available keypoints + obs_data["track_interval"] = torch.Tensor( + self.data_dict["track_interval"][idx] + ).int() + + obs_data["track_id"] = int(self.track_ids[idx]) + obs_data["seq_name"] = self.seq_name + return obs_data + + def load_camera_data(self): + cam_dir = self.data_sources["cameras"] + data_interval = 0, -1 + if self.split_cameras: + data_interval = self.data_start, self.data_end + track_interval = self.start_idx, self.end_idx + self.cam_data = CameraData( + cam_dir, self.seq_len, self.img_size, data_interval, track_interval + ) + + def get_camera_data(self): + if self.cam_data is None: + raise ValueError + return self.cam_data.as_dict() + + +class CameraData(object): + def __init__( + self, cam_dir, seq_len, img_size, data_interval=[0, -1], track_interval=[0, -1] + ): + self.img_size = img_size + self.cam_dir = cam_dir + + # inclusive exclusive + data_start, data_end = data_interval + if data_end < 0: + data_end += seq_len + 1 + data_len = data_end - data_start + + # start and end indices are with respect to the data interval + sidx, eidx = track_interval + if eidx < 0: + eidx += data_len + 1 + self.sidx, self.eidx = sidx + data_start, eidx + data_start + self.seq_len = self.eidx - self.sidx + + self.load_data() + + def load_data(self): + # camera info + sidx, eidx = self.sidx, self.eidx + img_w, img_h = self.img_size + fpath = os.path.join(self.cam_dir, "cameras.npz") + if os.path.isfile(fpath): + Logger.log(f"Loading cameras from {fpath}...") + cam_R, cam_t, intrins, width, height = load_cameras_npz(fpath) + scale = img_w / width + self.intrins = scale * intrins[sidx:eidx] + # move first camera to origin + # R0, t0 = invert_camera(cam_R[sidx], cam_t[sidx]) + # self.cam_R = torch.einsum("ij,...jk->...ik", R0, cam_R[sidx:eidx]) + # self.cam_t = t0 + torch.einsum("ij,...j->...i", R0, cam_t[sidx:eidx]) +# t0 = -cam_t[sidx:eidx].mean(dim=0) + torch.randn(3) * 0.1 + t0 = -cam_t[sidx:sidx+1] + torch.randn(3) * 0.1 + self.cam_R = cam_R[sidx:eidx] + self.cam_t = cam_t[sidx:eidx] - t0 + self.is_static = False + else: + Logger.log(f"WARNING: {fpath} does not exist, using static cameras...") + default_focal = 0.5 * (img_h + img_w) + self.intrins = torch.tensor( + [default_focal, default_focal, img_w / 2, img_h / 2] + )[None].repeat(self.seq_len, 1) + + self.cam_R = torch.eye(3)[None].repeat(self.seq_len, 1, 1) + self.cam_t = torch.zeros(self.seq_len, 3) + self.is_static = True + + Logger.log(f"Images have {img_w}x{img_h}, intrins {self.intrins[0]}") + print("CAMERA DATA", self.cam_R.shape, self.cam_t.shape, self.intrins[0]) + + def world2cam(self): + return self.cam_R, self.cam_t + + def cam2world(self): + R = self.cam_R.transpose(-1, -2) + t = -torch.einsum("bij,bj->bi", R, self.cam_t) + return R, t + + def as_dict(self): + return { + "cam_R": self.cam_R, # (T, 3, 3) + "cam_t": self.cam_t, # (T, 3) + "intrins": self.intrins, # (T, 4) + "static": self.is_static, # bool + } + + +def get_ternary_mask(vis_mask): + # get the track start and end idcs relative to the filtered interval + vis_mask = torch.as_tensor(vis_mask) + vis_idcs = torch.where(vis_mask)[0] + track_s, track_e = min(vis_idcs), max(vis_idcs) + 1 + # -1 = track out of scene, 0 = occlusion, 1 = visible + vis_mask = vis_mask.float() + vis_mask[:track_s] = -1 + vis_mask[track_e:] = -1 + return vis_mask + + +def get_shot_img_files(shots_path, shot_idx, shot_pad=SHOT_PAD): + assert os.path.isfile(shots_path) + with open(shots_path, "r") as f: + shots_dict = json.load(f) + img_names = sorted(shots_dict.keys()) + N = len(img_names) + shot_mask = np.array([shots_dict[x] == shot_idx for x in img_names]) + + idcs = np.where(shot_mask)[0] + if shot_pad > 0: # drop the frames before/after shot change + if min(idcs) > 0: + idcs = idcs[shot_pad:] + if len(idcs) > 0 and max(idcs) < N - 1: + idcs = idcs[:-shot_pad] + if len(idcs) < MIN_SEQ_LEN: + raise ValueError("shot is too short for optimization") + + shot_mask = np.zeros(N, dtype=bool) + shot_mask[idcs] = 1 + sel_paths = [img_names[i] for i in idcs] + print(f"FOUND {len(idcs)}/{len(shots_dict)} FRAMES FOR SHOT {shot_idx}") + return sel_paths, idcs + + +def load_cameras_npz(camera_path): + assert os.path.splitext(camera_path)[-1] == ".npz" + + cam_data = np.load(camera_path) + height, width, focal = ( + int(cam_data["height"]), + int(cam_data["width"]), + float(cam_data["focal"]), + ) + + w2c = torch.from_numpy(cam_data["w2c"]) # (N, 4, 4) + cam_R = w2c[:, :3, :3] # (N, 3, 3) + cam_t = w2c[:, :3, 3] # (N, 3) + N = len(w2c) + + if "intrins" in cam_data: + intrins = torch.from_numpy(cam_data["intrins"].astype(np.float32)) + else: + intrins = torch.tensor([focal, focal, width / 2, height / 2])[None].repeat(N, 1) + + print(f"Loaded {N} cameras") + return cam_R, cam_t, intrins, width, height + + +def is_image(x): + return (x.endswith(".png") or x.endswith(".jpg")) and not x.startswith(".") + + +def get_name(x): + return os.path.splitext(os.path.basename(x))[0] + + +def split_name(x, suffix): + return os.path.basename(x).split(suffix)[0] + + +def get_names_in_dir(d, suffix): + files = [split_name(x, suffix) for x in glob.glob(f"{d}/*{suffix}")] + return sorted(files) + + +def batch_join(parent, names, suffix=""): + return [os.path.join(parent, f"{n}{suffix}") for n in names] diff --git a/slahmr/slahmr/data/tools.py b/slahmr/slahmr/data/tools.py new file mode 100644 index 0000000000000000000000000000000000000000..0c457895a7d0ebb469ad91896821f80127ff60a6 --- /dev/null +++ b/slahmr/slahmr/data/tools.py @@ -0,0 +1,108 @@ +import os +import json +import functools + +import numpy as np + +from body_model import OP_NUM_JOINTS +from scipy.interpolate import interp1d +from scipy.spatial.transform import Rotation, Slerp + + +def read_keypoints(keypoint_fn): + """ + Only reads body keypoint data of first person. + """ + empty_kps = np.zeros((OP_NUM_JOINTS, 3), dtype=np.float) + if not os.path.isfile(keypoint_fn): + return empty_kps + + with open(keypoint_fn) as keypoint_file: + data = json.load(keypoint_file) + + if len(data["people"]) == 0: + print("WARNING: Found no keypoints in %s! Returning zeros!" % (keypoint_fn)) + return empty_kps + + person_data = data["people"][0] + body_keypoints = np.array(person_data["pose_keypoints_2d"], dtype=np.float) + body_keypoints = body_keypoints.reshape([-1, 3]) + return body_keypoints + + +def read_mask_path(path): + mask_path = None + if not os.path.isfile(path): + return mask_path + + with open(path, "r") as f: + data = json.load(path) + + person_data = data["people"][0] + if "mask_path" in person_data: + mask_path = person_data["mask_path"] + + return mask_path + + +def read_smpl_preds(pred_path, num_betas=10): + """ + reads the betas, body_pose, global orientation and translation of a smpl prediction + exported from phalp outputs + returns betas (10,), body_pose (23, 3), global_orientation (3,), translation (3,) + """ + pose = np.zeros((23, 3)) + rot = np.zeros(3) + trans = np.zeros(3) + betas = np.zeros(num_betas) + if not os.path.isfile(pred_path): + return pose, rot, trans, betas + + with open(pred_path, "r") as f: + data = json.load(f) + + if "body_pose" in data: + pose = np.array(data["body_pose"], dtype=np.float32) + + if "global_orient" in data: + rot = np.array(data["global_orient"], dtype=np.float32) + + if "cam_trans" in data: + trans = np.array(data["cam_trans"], dtype=np.float32) + + if "betas" in data: + betas = np.array(data["betas"], dtype=np.float32) + + return pose, rot, trans, betas + + +def load_smpl_preds(pred_paths, interp=True, num_betas=10): + vis_mask = np.array([os.path.isfile(x) for x in pred_paths]) + vis_idcs = np.where(vis_mask)[0] + + # load single image smpl predictions + stack_fnc = functools.partial(np.stack, axis=0) + # (N, 23, 3), (N, 3), (N, 3), (N, 10) + pose, orient, trans, betas = map( + stack_fnc, zip(*[read_smpl_preds(p, num_betas=num_betas) for p in pred_paths]) + ) + if not interp: + return pose, orient, trans, betas + + # interpolate the occluded tracks + orient_slerp = Slerp(vis_idcs, Rotation.from_rotvec(orient[vis_idcs])) + trans_interp = interp1d(vis_idcs, trans[vis_idcs], axis=0) + betas_interp = interp1d(vis_idcs, betas[vis_idcs], axis=0) + + tmin, tmax = min(vis_idcs), max(vis_idcs) + 1 + times = np.arange(tmin, tmax) + orient[times] = orient_slerp(times).as_rotvec() + trans[times] = trans_interp(times) + betas[times] = betas_interp(times) + + # interpolate for each joint angle + for i in range(pose.shape[1]): + pose_slerp = Slerp(vis_idcs, Rotation.from_rotvec(pose[vis_idcs, i])) + pose[times, i] = pose_slerp(times).as_rotvec() + + return pose, orient, trans, betas diff --git a/slahmr/slahmr/data/vidproc.py b/slahmr/slahmr/data/vidproc.py new file mode 100644 index 0000000000000000000000000000000000000000..ff53e00990341341d17cd83e7a598a540e76ce3c --- /dev/null +++ b/slahmr/slahmr/data/vidproc.py @@ -0,0 +1,82 @@ +import os +import numpy as np +import subprocess + +import preproc.launch_phalp as phalp +from preproc.launch_slam import split_frames_shots, get_command, check_intrins +from preproc.extract_frames import video_to_frames + + +def is_nonempty(d): + return os.path.isdir(d) and len(os.listdir(d)) > 0 + + +def preprocess_frames(img_dir, src_path, overwrite=False, **kwargs): + if not overwrite and is_nonempty(img_dir): + print(f"FOUND {len(os.listdir(img_dir))} FRAMES in {img_dir}") + return + print(f"EXTRACTING FRAMES FROM {src_path} TO {img_dir}") + print(kwargs) + out = video_to_frames(src_path, img_dir, overwrite=overwrite, **kwargs) + assert out == 0, "FAILED FRAME EXTRACTION" + + +def preprocess_tracks(img_dir, track_dir, shot_dir, overwrite=False): + """ + :param img_dir + :param track_dir, expected format: res_root/track_name/sequence + :param shot_dir, expected format: res_root/shot_name/sequence + """ + if not overwrite and is_nonempty(track_dir): + print(f"FOUND TRACKS IN {track_dir}") + return + + print(f"RUNNING PHALP ON {img_dir}") + track_root, seq = os.path.split(track_dir.rstrip("/")) + res_root, track_name = os.path.split(track_root) + shot_name = shot_dir.rstrip("/").split("/")[-2] + gpu = os.environ.get("CUDA_VISIBLE_DEVICES", 0) + + phalp.process_seq( + [gpu], + seq, + img_dir, + f"{res_root}/phalp_out", + track_name=track_name, + shot_name=shot_name, + overwrite=overwrite, + ) + + +def preprocess_cameras(cfg, overwrite=False): + if not overwrite and is_nonempty(cfg.sources.cameras): + print(f"FOUND CAMERAS IN {cfg.sources.cameras}") + return + + print(f"RUNNING SLAM ON {cfg.seq}") + img_dir = cfg.sources.images + map_dir = cfg.sources.cameras + subseqs, shot_idcs = split_frames_shots(cfg.sources.images, cfg.sources.shots) + shot_idx = np.where(shot_idcs == cfg.shot_idx)[0][0] + # run on selected shot + start, end = subseqs[shot_idx] + if not cfg.split_cameras: + # only run on specified segment within shot + end = start + cfg.end_idx + start = start + cfg.start_idx + intrins_path = cfg.sources.get("intrins", None) + if intrins_path is not None: + intrins_path = check_intrins(cfg.type, cfg.root, intrins_path, cfg.seq, cfg.split) + + cmd = get_command( + img_dir, + map_dir, + start=start, + end=end, + intrins_path=intrins_path, + overwrite=overwrite, + ) + print(cmd) + gpu = os.environ.get("CUDA_VISIBLE_DEVICES", 0) + out = subprocess.call(f"CUDA_VISIBLE_DEVICES={gpu} {cmd}", shell=True) + assert out == 0, "SLAM FAILED" diff --git a/slahmr/slahmr/eval/__init__.py b/slahmr/slahmr/eval/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/slahmr/eval/associate.py b/slahmr/slahmr/eval/associate.py new file mode 100644 index 0000000000000000000000000000000000000000..1480d57c5afb1ae4431a60a23632eb552e935989 --- /dev/null +++ b/slahmr/slahmr/eval/associate.py @@ -0,0 +1,161 @@ +import os +import glob +import json +import joblib +import numpy as np +import torch + +from data.tools import read_keypoints + + +def associate_phalp_track_dirs( + phalp_dir, img_dir, track_ids, gt_kps, start=0, end=-1, debug=False +): + """ + Associate the M track_ids with G GT tracks + returns (M, T) array of best matching GT person index + :param phalp_dir (str) directory with phalp track folders + :param img_dir (str) directory with source images + :param track ids (list) M tracks to match + :param gt_kps (G, T, J, 3) gt keypoints for G people, T times, J joints + :param start (optional int default 0) + :param end (optional int default -1) + """ + img_names = sorted([os.path.splitext(x)[0] for x in os.listdir(img_dir)]) + N = len(img_names) + end = N + 1 + end if end < 0 else end + sel_imgs = img_names[start:end] + G, T = gt_kps.shape[:2] # G num people, T num frames + assert len(sel_imgs) == T, f"found {len(sel_imgs)} frames, expected {T}" + + track_ids = [f"{int(tid):03d}" for tid in track_ids] + M = len(track_ids) + # find the best matching GT track for each PHALP track + match_idcs = torch.full((M, T), -1) + for t, frame_name in enumerate(sel_imgs): + track_kps = [] # get track keypoints + for tid in track_ids: + kp_path = f"{phalp_dir}/{tid}/{frame_name}_keypoints.json" + track_kps.append(read_keypoints(kp_path)) + track_kps = np.stack(track_kps, axis=0) # (M, 25, 3) + for g in range(G): + kp_gt = gt_kps[g, t].T.numpy() # (18, 3) + m = associate_keypoints(kp_gt, track_kps, debug=debug) + if m == -1: + continue + match_idcs[m, t] = g + return match_idcs + + +def associate_phalp_track_data( + phalp_file, track_ids, gt_kps, start=0, end=-1, debug=False +): + """ + Get the best GT person for each phalp track + :param phalp_file (path) to phalp result pickle file + :param gt_kps (G, T, 3, 18) gt keypoints + :param track_ids (list) of phalp track ids + :param start (optional int) + :param end (optional int) + return (M, T) array the matching GT person index for each phalp track + """ + data = joblib.load(phalp_file) + img_names = sorted(data.keys()) + N = len(img_names) # number of frames + end = N + 1 + end if end < 0 else end + sel_imgs = img_names[start:end] + + G, T = gt_kps.shape[:2] # G num people, T num frames + assert len(sel_imgs) == T, f"found {len(sel_imgs)} frames, expected {T}" + + M = len(track_ids) + track_idcs = {tid: m for m, tid in enumerate(track_ids)} + # get the best matching GT track for each PHALP track + match_idcs = torch.full((M, T), -1) + for t, frame_name in enumerate(sel_imgs): + frame_data = data[frame_name] + for g in range(G): + kp_gt = gt_kps[g, t].T.numpy() # (18, 3) + # get the best track ID for the GT person + tid = associate_frame_dict(frame_data, kp_gt, track_ids, debug=debug) + if tid == -1: + continue + m = track_idcs[tid] + match_idcs[m, t] = g + return match_idcs + + +def associate_keypoints(gt_kps, track_kps, debug=False): + """ + :param gt_bbox (25, 3) + :param track_bboxes (M, 25, 3) + return the index of the best overlapping track bbox + """ + gt_kps = gt_kps[gt_kps[:, 2] > 0, :2] + if len(gt_kps) < 1: + return -1 + bb_min, bb_max = gt_kps.min(axis=0), gt_kps.max(axis=0) + gt_bbox = np.concatenate([bb_min, bb_max], axis=-1) # (4,) + + track_kps = track_kps[..., :2] # (M, 25, 2) + track_min, track_max = track_kps.min(axis=1), track_kps.max(axis=1) + track_bboxes = np.concatenate([track_min, track_max], axis=-1) # (M, 4) + + ious = np.stack([compute_iou(bb, gt_bbox)[0] for bb in track_bboxes], axis=0) + return np.argmax(ious) + + +def associate_frame_dict(frame_data, gt_kps, track_ids, debug=False): + """ + For the GT keypoints, find the PHALP track in track_ids with best overlap + :param frame_data (dict) PHALP output data + :param gt_kps (25, 3) + :param track_ids (list of N) PHALP track ids to search over + return the id in track_ids with the biggest overlap with gt_kps + """ + gt_kps = gt_kps[gt_kps[:, 2] > 0, :2] + if len(gt_kps) < 1: + return -1 + bb_min, bb_max = gt_kps.min(axis=0), gt_kps.max(axis=0) + gt_bbox = np.concatenate([bb_min, bb_max], axis=-1) # (4,) + + # use strs for track ids + tid_strs = [str(tid) for tid in track_ids] + # get the list indices of the PHALP tracks + track_idcs = { + str(int(tid)): i + for i, tid in enumerate(frame_data["tid"]) + if tid in frame_data["tracked_ids"] + } + # select the track with the biggest overlap with the gt kps + ious = [] + for tid in track_ids: + if tid not in track_idcs: + ious.append(0) + continue + bb = frame_data["bbox"][track_idcs[tid]] # (min_x, min_y, w, h) + bbox = np.concatenate([bb[:2], bb[:2] + bb[2:]], axis=-1) + iou = compute_iou(bbox, gt_bbox)[0] + ious.append(iou) + ious = np.stack(ious, axis=0) + idx = np.argmax(ious) + if debug: + print(track_ids[idx], track_ids, ious) + return track_ids[idx] + + +def compute_iou(bb1, bb2): + """ + :param bb1 (..., 4) top left x, y bottom right x y + :param bb2 (..., 4) top left x, y bottom right x y + return (...) IOU + """ + x11, y11, x12, y12 = np.split(bb1, 4, axis=-1) + x21, y21, x22, y22 = np.split(bb2, 4, axis=-1) + x1 = np.maximum(x11, x21) + y1 = np.maximum(y11, y21) + x2 = np.minimum(x12, x22) + y2 = np.minimum(y12, y22) + intersect = np.maximum((x2 - x1) * (y2 - y1), 0) + union = (x12 - x11) * (y12 - y11) + (x22 - x21) * (y22 - y21) - intersect + return intersect / (union + 1e-6) diff --git a/slahmr/slahmr/eval/egobody_utils.py b/slahmr/slahmr/eval/egobody_utils.py new file mode 100644 index 0000000000000000000000000000000000000000..3f8b2adf07a9d3ff25926b8a9e09f3941c66d2b7 --- /dev/null +++ b/slahmr/slahmr/eval/egobody_utils.py @@ -0,0 +1,171 @@ +import os +import itertools +import glob +import pickle +import json +import pandas as pd + +import numpy as np +import torch + +from tools import load_body_model, move_to, detach_all, EGOBODY_ROOT + + +def get_sequence_body_info(seq_name): + info_file = f"{EGOBODY_ROOT}/data_info_release.csv" + info_df = pd.read_csv(info_file) + seq_info = info_df[info_df["recording_name"] == seq_name] + return seq_info["body_idx_fpv"].values[0] + + +def get_egobody_split(split): + split_file = f"{EGOBODY_ROOT}/data_splits.csv" + split_df = pd.read_csv(split_file) + if split not in split_df.columns: + print(f"{split} not in {split_file}") + return [] + return split_df[split].dropna().tolist() + + +def get_egobody_seq_paths(seq_name, start=0, end=-1): + img_dir = get_egobody_img_dir(seq_name) + # img files are named [timestamp]_frame_[index].jpg + img_files = sorted(os.listdir(img_dir)) + end = len(img_files) if end < 0 else end + print(f"FOUND {len(img_files)} FILES FOR SEQ {seq_name}") + return img_files[start:end] + + +def get_egobody_seq_names(seq_name, start=0, end=-1): + img_files = get_egobody_seq_paths(seq_name, start=start, end=end) + frame_names = ["_".join(x.split(".")[0].split("_")[1:]) for x in img_files] + return frame_names + + +def get_egobody_img_dir(seq_name): + img_dir = f"{EGOBODY_ROOT}/egocentric_color/{seq_name}/**/PV" + matches = glob.glob(img_dir) + if len(matches) != 1: + raise ValueError(f"{img_dir} has {len(matches)} matches!") + return matches[0] + + +def get_egobody_keypoints(seq_name, start=0, end=-1): + img_dir = os.path.dirname(get_egobody_img_dir(seq_name)) + kp_file = f"{img_dir}/keypoints.npz" + valid_file = f"{img_dir}/valid_frame.npz" + + # missing keypoints aren't included, must fill in + kp_dict = {} + valid_dict = {} + kp_data = np.load(kp_file) + valid_data = np.load(valid_file) + + zeros = np.zeros_like(kp_data["keypoints"][0]) + for img_path, kps in zip(kp_data["imgname"], kp_data["keypoints"]): + img_name = os.path.basename(img_path) + kp_dict[img_name] = kps + + for img_path, valid in zip(valid_data["imgname"], valid_data["valid"]): + img_name = os.path.basename(img_path) + valid_dict[img_name] = valid + + img_paths = sorted(glob.glob(f"{img_dir}/PV/*.jpg")) + end = len(img_paths) + 1 + end if end < 0 else end + img_names = [os.path.basename(x) for x in img_paths[start:end]] + kps = np.stack([kp_dict.get(name, zeros) for name in img_names], axis=0) + valid = np.stack([valid_dict.get(name, False) for name in img_names], axis=0) + return kps, valid + + +def load_egobody_smpl_params(seq_name, start=0, end=-1): + frame_names = get_egobody_seq_names(seq_name, start=start, end=end) + body_name = get_sequence_body_info(seq_name) + body_idx, gender = body_name.split(" ") + smpl_dir = ( + f"{EGOBODY_ROOT}/smpl_interactee_val/{seq_name}/body_idx_{body_idx}/results" + ) + if not os.path.isdir(smpl_dir): + raise ValueError(f"EXPECTED BODY DIR {smpl_dir} DOES NOT EXIST") + + print(f"LOADING {len(frame_names)} SMPL PARAMS FROM {smpl_dir}") + smpl_dict = {"trans": [], "root_orient": [], "pose_body": [], "betas": []} + for frame in frame_names: + with open(f"{smpl_dir}/{frame}/000.pkl", "rb") as f: + # data has global_orient, body_pose, betas, transl + data = pickle.load(f) + smpl_dict["trans"].append(torch.from_numpy(data["transl"])) + smpl_dict["pose_body"].append(torch.from_numpy(data["body_pose"])) + smpl_dict["root_orient"].append(torch.from_numpy(data["global_orient"])) + smpl_dict["betas"].append(torch.from_numpy(data["betas"])) + smpl_dict = {k: torch.cat(v, dim=0)[None] for k, v in smpl_dict.items()} + smpl_dict["genders"] = [gender] + return smpl_dict + + +def load_egobody_intrinsics(seq_name, start=0, end=-1, ret_size_tuple=True): + path = f"{EGOBODY_ROOT}/slahmr/cameras_gt/{seq_name}/intrinsics.txt" + assert os.path.isfile(path) + intrins = np.loadtxt(path) # (T, 6) + end = len(intrins) if end < 0 else end + intrins = intrins[start:end] + if ret_size_tuple: + img_size = intrins[0, 4:].astype(int).tolist() # (2) + intrins = torch.from_numpy(intrins[:, :4].astype(np.float32)) + return intrins, img_size + img_size = torch.from_numpy(intrins[:, 4:].astype(int)) + intrins = torch.from_numpy(intrins[:, :4].astype(np.float32)) + return intrins, img_size + + +def load_egobody_gt_extrinsics(seq_name, start=0, end=-1, ret_4d=True): + path = f"{EGOBODY_ROOT}/slahmr/cameras_gt/{seq_name}/cam2world.txt" + assert os.path.isfile(path) + cam2world = np.loadtxt(path).astype(np.float32) # (T, 16) + end = len(cam2world) if end < 0 else end + cam2world = torch.from_numpy(cam2world[start:end].reshape(-1, 4, 4)) + if ret_4d: + return cam2world + return cam2world[:, :3, :3], cam2world[:, :3, 3] + + +def load_egobody_extrinsics(seq_name, use_intrins=True, start=0, end=-1): + camera_name = "cameras_intrins" if use_intrins else "cameras_default" + path = f"{EGOBODY_ROOT}/slahmr/{camera_name}/{seq_name}/cameras.npz" + assert os.path.isfile(path) + data = np.load(path) + w2c = torch.from_numpy(data["w2c"].astype(np.float32)) # (N, 4, 4) + end = len(w2c) if end < 0 else end + w2c = w2c[start:end] + c2w = torch.linalg.inv(w2c) + return c2w[:, :3, :3], c2w[:, :3, 3] + + +def load_egobody_meshes(seq_name, device, start=0, end=-1): + params = load_egobody_smpl_params(seq_name, start=start, end=end) + _, T = params["trans"].shape[:2] + + with torch.no_grad(): + gender = params["genders"][0] + body_model = load_body_model(T, "smpl", gender, device) + smpl_res = body_model( + trans=params["trans"][0].to(device), + root_orient=params["root_orient"][0].to(device), + betas=params["betas"][0].to(device), + pose_body=params["pose_body"][0].to(device), + ) + + res = {"joints": smpl_res.Jtr, "vertices": smpl_res.v, "faces": smpl_res.f} + return move_to(detach_all(res), "cpu") + + +def load_egobody_kinect2holo(seq_name, ret_4d=True): + # load the transform from kinect12 to holo + # bodies are recorded in the kinect12 frame + path = f"{EGOBODY_ROOT}/calibrations/{seq_name}/cal_trans/holo_to_kinect12.json" + with open(path, "r") as f: + kinect2holo = np.linalg.inv(np.array(json.load(f)["trans"])) + kinect2holo = torch.from_numpy(kinect2holo.astype(np.float32)) + if ret_4d: + return kinect2holo + return kinect2holo[:3, :3], kinect2holo[:3, 3] diff --git a/slahmr/slahmr/eval/run_eval.py b/slahmr/slahmr/eval/run_eval.py new file mode 100644 index 0000000000000000000000000000000000000000..0e45547bebd46b4d77891f6dc4c44423b1d93d67 --- /dev/null +++ b/slahmr/slahmr/eval/run_eval.py @@ -0,0 +1,289 @@ +import os +import glob +import joblib +import json +import pickle + +import pandas as pd +import numpy as np +import torch + +import egobody_utils as eb_util +from tools import ( + load_body_model, + load_results_all, + local_align_joints, + global_align_joints, + first_align_joints, + compute_accel_norm, + run_smpl, + JointRegressor, + EGOBODY_ROOT, + TDPW_ROOT, +) +from associate import associate_phalp_track_dirs + + +def stack_torch(x_list, dim=0): + return torch.stack( + [torch.from_numpy(x.astype(np.float32)) for x in x_list], dim=dim + ) + + +def load_3dpw_params(seq_name, start=0, end=-1): + seq_file = f"{TDPW_ROOT}/sequenceFiles/test/{seq_name}.pkl" + with open(seq_file, "rb") as f: + data = pickle.load(f, encoding="latin1") + + M = len(data["poses"]) + T = len(data["poses"][0]) + end = T + 1 + end if end < 0 else end + T = end - start + trans = stack_torch([x[start:end] for x in data["trans"]]) # (M, T, 3) + poses = stack_torch([x[start:end] for x in data["poses"]]) # (M, T, 72) + betas = stack_torch([x[None, :10] for x in data["betas"]]).expand( + M, T, 10 + ) # (M, T, 10) + keypts2d = stack_torch([x[start:end] for x in data["poses2d"]]) # (M, T, 3, 18) + valid_cam = stack_torch( + [x[start:end] for x in data["campose_valid"]] + ).bool() # (M, T) + valid_kp = (keypts2d.reshape(M, T, -1) > 0).any(dim=-1).bool() # (M, T) + valid = valid_cam & valid_kp + genders = ["male" if x == "m" else "female" for x in data["genders"]] # (M) + return { + "root_orient": poses[..., :3], + "pose_body": poses[..., 3:], + "trans": trans, + "betas": betas, + "keypts2d": keypts2d, + "valid": valid, + "genders": genders, + } + + +def load_egobody_params(seq_name, start=0, end=-1): + """ + returns dict of + - trans (1, T, 3) + - root_orient (1, T, 3) + - pose_body (1, T, 63) + - betas (1, T, 10) + - gender (str) + - keypts2d (1, T, J, 3) + - valid (1, T) + """ + smpl_dict = eb_util.load_egobody_smpl_params(seq_name, start=start, end=end) + kps, valid = eb_util.get_egobody_keypoints(seq_name, start=start, end=end) + smpl_dict["keypts2d"] = torch.from_numpy(kps.astype(np.float32))[None] + smpl_dict["valid"] = torch.from_numpy(valid.astype(bool))[None] + return smpl_dict + + +def eval_result_dir( + dset_type, res_dir, out_path, joint_reg, dev_id=0, overwrite=False, debug=False +): + if os.path.isfile(out_path) and not overwrite: + print(f"{out_path} already exists, skipping.") + return + + # get the output metadata + track_file = f"{res_dir}/track_info.json" + if not os.path.isfile(track_file): + print(f"{track_file} does not exist, skipping") + return + + with open(track_file, "r") as f: + track_dict = json.load(f) + start, end = track_dict["meta"]["data_interval"] + seq_name = os.path.basename(res_dir).split("-")[0] + print("EVALUATING", res_dir, seq_name, start, end) + + # get the associations from PHALP tracks to GT tracks + track_info = track_dict["tracks"] + track_ids = sorted(track_info, key=lambda k: track_info[k]["index"]) + print("TRACK IDS", track_ids) + + if dset_type == "egobody": + # load the GT params + gt_params = load_egobody_params(seq_name, start, end) + phalp_dir = f"{EGOBODY_ROOT}/slahmr/track_preds/{seq_name}" + img_dir = eb_util.get_egobody_img_dir(seq_name) + elif dset_type == "3dpw": + gt_params = load_3dpw_params(seq_name, start, end) + phalp_dir = f"{TDPW_ROOT}/slahmr/track_gt/{seq_name}" + img_dir = f"{TDPW_ROOT}/imageFiles/{seq_name}" + else: + raise NotImplementedError + + # (M, T) GT track index for each frame and each PHALP track + match_idcs = associate_phalp_track_dirs( + phalp_dir, + img_dir, + track_ids, + gt_params["keypts2d"], + start=start, + end=end, + debug=debug, + ) + # M number of PHALP tracks + M = len(track_ids) + + # get the GT joints + G, T = gt_params["pose_body"].shape[:2] + device = torch.device(f"cuda:{dev_id}") + gt_joints = [] + for g in range(G): + body_model = load_body_model(T, "smpl", gt_params["genders"][g], device) + gt_smpl = run_smpl( + body_model, + betas=gt_params["betas"][g].to(device), + trans=gt_params["trans"][g].to(device), + root_orient=gt_params["root_orient"][g].to(device), + pose_body=gt_params["pose_body"][g].to(device), + ) + gt_joints.append(joint_reg(gt_smpl["vertices"])) # (T, 15, 3) + gt_joints = torch.stack(gt_joints, dim=0) + J, D = gt_joints.shape[-2:] + + # select the correct GT person for each track + gt_valid = gt_params["valid"] # (G, T) + idcs = match_idcs.clone().reshape(M, T, 1, 1).expand(-1, -1, J, D) + idcs[idcs == -1] = 0 # gather dummy for invalid matches + gt_match_joints = torch.gather(gt_joints, 0, idcs) + gt_match_valid = torch.gather(gt_valid, 0, idcs[:, :, 0, 0]) + valid = gt_match_valid & (match_idcs != -1) + + # use the vis_mask to get the correct data subsequence + vis_mask = torch.tensor( + [track_info[tid]["vis_mask"] for tid in track_ids] + ) # (M, T) + vis_tracks = torch.where(vis_mask.any(dim=1))[0] # (B,) + vis_idcs = torch.where(vis_mask.any(dim=0))[0] + sidx, eidx = vis_idcs.min(), vis_idcs.max() + 1 + L = eidx - sidx + + valid_seq = valid[vis_tracks, sidx:eidx] # (B, L) + gt_seq_joints = gt_match_joints[vis_tracks, sidx:eidx] # (B, L, *) + gt_seq_joints = gt_seq_joints[valid_seq] + + if debug: + print(f"vis start {sidx}, end {eidx}, L {L}") + print("valid track matches", (match_idcs != -1).sum()) + print("filtered gt joints", gt_seq_joints.shape) + + # get the outputs of each phase + PHASES = ["root_fit", "smooth_fit", "motion_chunks"] + metric_names = ["ga_jmse", "fa_jmse", "pampjpe", "acc_norm"] + phase_metrics = {name: [-1 for _ in PHASE] for name in metric_names} + cur_metrics = {name: np.nan for name in metric_names} + for i, phase in enumerate(PHASES): + res_dict = load_results_all(os.path.join(res_dir, phase), device) + if res_dict is None: + print(f"PHASE {phase} did not optimize") + # update all metrics for this phase + for name in metric_names: + phase_metrics[name][i] = float(cur_metrics[name]) + print(phase, phase_metrics) + continue + + # (M, L, -1, 3) verts, (M, L) mask + res_verts = res_dict["vertices"][valid_seq] + res_joints = joint_reg(res_verts) # (*, 15, 3_ + + for name in metric_names: + if name == "acc_norm": + target = compute_accel_norm(gt_seq_joints) # (T-2, J) + pred = compute_accel_norm(res_joints) + else: + target = gt_seq_joints + if name == "pampjpe": + pred = local_align_joints(gt_seq_joints, res_joints) + if name == "ga_jmse": + pred = global_align_joints(gt_seq_joints, res_joints) + if name == "fa_jmse": + pred = first_align_joints(gt_seq_joints, res_joints) + else: + raise NotImplementedError + cur_metrics[name] = torch.linalg.norm(target - pred, dim=-1).mean() + phase_metrics[name][i] = float(cur_metrics[name]) + print(phase, name, cur_metrics[name]) + + df_dict = {"phases": PHASES} + df_dict.update(phase_metrics) + df = pd.DataFrame.from_dict(df_dict) + df.to_csv(out_path, index=False) + print(f"saved metrics to {out_path}") + + +def parse_job_file(args): + subseq_names = [] + with open(args.job_file, "r") as f: + for line in f.readlines(): + cmd_args = line.strip().split() + seq_name, start_str, end_str = cmd_args[:3] + start = start_str.split("=")[-1] + end = end_str.split("=")[-1] + track_name = "longest-2" if args.dset_type == "3dpw" else "all" + if len(cmd_args) > 3: + track_name = cmd_args[3].split("=")[-1] + subseq_names.append(f"{seq_name}-{track_name}-{start}-{end}") + return subseq_names + + +def main(args): + joint_reg = JointRegressor() + out_root = args.out_root if args.out_root is not None else args.res_root + os.makedirs(out_root, exist_ok=True) + + subseq_names = parse_job_file(args) + for subseq in subseq_names: + res_dir = os.path.join(args.res_root, subseq) + out_path = os.path.join(out_root, f"{subseq}.txt") + eval_result_dir( + args.dset_type, + res_dir, + out_path, + joint_reg, + overwrite=args.overwrite, + debug=args.debug, + ) + + metric_paths = glob.glob(f"{out_root}/[!_]*.txt") + dfs = [pd.read_csv(path) for path in metric_paths] + + merged = pd.concat(dfs).groupby("phase").mean() + merged.to_csv(f"{out_root}/_final_metrics.txt") + print(merged) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument( + "-d", + "--dset_type", + required=True, + choices=["egobody", "3dpw"], + help="dataset to evaluate on, choices: (3dpw, egobody)", + ) + parser.add_argument( + "-i", "--res_root", required=True, help="root directory of outputs to evaluate" + ) + parser.add_argument( + "-f", + "--job_file", + required=True, + help="job file specifying the examples to run and evaluate", + ) + parser.add_argument( + "-o", + "--out_root", + default=None, + help="directory to save computed metrics, default is res_root", + ) + parser.add_argument("-y", "--overwrite", action="store_true") + parser.add_argument("-d", "--debug", action="store_true") + args = parser.parse_args() + main(args) diff --git a/slahmr/slahmr/eval/split_3dpw.py b/slahmr/slahmr/eval/split_3dpw.py new file mode 100644 index 0000000000000000000000000000000000000000..6e58e93205cb4ab8c68d7afc3d6459ab66c69053 --- /dev/null +++ b/slahmr/slahmr/eval/split_3dpw.py @@ -0,0 +1,99 @@ +import os +import glob +import itertools +import joblib + +from eval_3dpw import load_3dpw_params +from associate import associate_frame +from tools import TDPW_ROOT + + +""" +Script to find the associations of ground truth 3DPW tracks with the detected PHALP tracks +Will write a job specification file to ../job_specs with which track IDs to run optimization on +""" + +IMG_ROOT = f"{TDPW_ROOT}/imageFiles" +SRC_DIR = f"{TDPW_ROOT}/sequenceFiles" +PHALP_DIR = f"{TDPW_ROOT}/slahmr/phalp_out/results" + + +def load_split_sequences(split): + assert split in ["train", "val", "test"] + split_dir = f"{SRC_DIR}/{split}" + seq_files = sorted(os.listdir(split_dir)) + return [os.path.splitext(f)[0] for f in seq_files] + + +def select_phalp_tracks(seq_name, split, start, end, debug=False): + """ + Select the best phalp track for each GT person for each frame. + Returns all phalp tracks that match GT over sequence + """ + phalp_file = f"{PHALP_DIR}/{seq_name}.pkl" + track_data = joblib.load(phalp_file) + img_names = sorted(track_data.keys()) + sel_imgs = img_names[start:end] + + gt_params = load_3dpw_params(f"{SRC_DIR}/{split}/{seq_name}.pkl", start, end) + gt_kps = gt_params["keypts2d"] + G, T = gt_kps.shape[:2] # G num people, T num frames + assert len(sel_imgs) == T, f"found {len(sel_imgs)} frames, expected {T}" + + track_ids = set() + for frame in sel_imgs: + frame_data = track_data[frame] + for tid in frame_data["tracked_ids"]: + track_ids.add(str(tid)) + track_ids = list(track_ids) + M = len(track_ids) + track_idcs = {tid: m for m, tid in enumerate(track_ids)} + + # get the best matching PHALP track for each GT person + sel_tracks = set() + for t, frame_name in enumerate(sel_imgs): + frame_data = track_data[frame_name] + for g in range(G): + kp_gt = gt_kps[g, t].T.numpy() # (18, 3) + # get the best track ID for the GT person + tid = associate_frame(frame_data, kp_gt, track_ids, debug=debug) + if tid == -1: + continue + sel_tracks.add(int(tid)) + return list(sel_tracks) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--seq_len", type=int, default=100) + parser.add_argument( + "--split", default="test", choices=["train", "val", "test", "all"] + ) + parser.add_argument("--prefix", default="3dpw") + args = parser.parse_args() + + seqs = load_split_sequences(args.split) + + job_arg_strs = [] + for seq in seqs: + num_imgs = len(glob.glob(f"{IMG_ROOT}/{seq}/*.jpg")) + splits = list(range(0, num_imgs, args.seq_len)) + splits[-1] = num_imgs # just add the remainder to the last job + for start, end in zip(splits[:-1], splits[1:]): + sel_tracks = select_phalp_tracks(seq, args.split, start, end) + if len(sel_tracks) < 1: + continue + track_str = "-".join([f"{tid:03d}" for tid in sel_tracks]) + arg_str = ( + f"{seq} data.start_idx={start} data.end_idx={end} " + f"data.track_ids={track_str}" + ) + print(arg_str) + job_arg_strs.append(arg_str) + + with open( + f"../job_specs/{args.prefix}_{args.split}_len_{args.seq_len}.txt", "w" + ) as f: + f.write("\n".join(job_arg_strs)) diff --git a/slahmr/slahmr/eval/split_egobody.py b/slahmr/slahmr/eval/split_egobody.py new file mode 100644 index 0000000000000000000000000000000000000000..7fc6adc56decc6090731470eeaeefe174c8a02d0 --- /dev/null +++ b/slahmr/slahmr/eval/split_egobody.py @@ -0,0 +1,123 @@ +import os +import glob +import joblib +import itertools + +import numpy as np +import pandas as pd + +from associate import associate_frame +from tools import EGOBODY_ROOT + + +""" +Script to find the associations of ground truth Egobody tracks with the detected PHALP tracks +Will write a job specification file to ../job_specs with which track IDs to run optimization on +""" + +IMG_ROOT = f"{EGOBODY_ROOT}/egocentric_color" +PHALP_DIR = f"{EGOBODY_ROOT}/slahmr/phalp_out/results" + + +def load_split_sequences(split): + split_file = "{EGOBODY_ROOT}/data_splits.csv" + df = pd.read_csv(split_file) + if split not in df.columns: + print(f"{split} not in {split_file}") + return [] + return df[split].dropna().tolist() + + +def get_egobody_keypoints(img_dir, start, end): + kp_file = f"{img_dir}/keypoints.npz" + valid_file = f"{img_dir}/valid_frame.npz" + img_paths = sorted(glob.glob(f"{img_dir}/PV/*.jpg"))[start:end] + img_names = [os.path.basename(x) for x in img_paths] + + kp_dict = {} + valid_dict = {} + kp_data = np.load(kp_file) + valid_data = np.load(valid_file) + + zeros = np.zeros_like(kp_data["keypoints"][0]) + for img_path, kps in zip(kp_data["imgname"], kp_data["keypoints"]): + img_name = os.path.basename(img_path) + kp_dict[img_name] = kps + + for img_path, valid in zip(valid_data["imgname"], valid_data["valid"]): + img_name = os.path.basename(img_path) + valid_dict[img_name] = valid + + kps = np.stack([kp_dict.get(name, zeros) for name in img_names], axis=0) + valid = np.stack([valid_dict.get(name, False) for name in img_names], axis=0) + return kps, valid + + +def select_phalp_tracks(seq_name, img_dir, start, end, debug=False): + """ + Get the best phalp track for each GT person for each frame + Returns all phalp tracks that match GT over sequence + """ + phalp_file = f"{PHALP_DIR}/{seq_name}.pkl" + track_data = joblib.load(phalp_file) + img_names = sorted(track_data.keys()) + sel_imgs = img_names[start:end] + + kps_all, valid = get_egobody_keypoints(img_dir, start, end) + T = len(kps_all) + assert len(sel_imgs) == T, f"found {len(sel_imgs)} frames, expected {T}" + + track_ids = set() + for frame in sel_imgs: + frame_data = track_data[frame] + for tid in frame_data["tracked_ids"]: + track_ids.add(str(tid)) + track_ids = list(track_ids) + M = len(track_ids) + track_idcs = {tid: m for m, tid in enumerate(track_ids)} + + # get the best matching PHALP track for each GT person + sel_tracks = set() + for t, frame_name in enumerate(sel_imgs): + frame_data = track_data[frame_name] + # get the best track ID for the GT person + tid = associate_frame(frame_data, kps_all[t], track_ids, debug=debug) + if tid == -1: + continue + sel_tracks.add(int(tid)) + return list(sel_tracks) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--seq_len", type=int, default=100) + parser.add_argument("--split", default="val", choices=["train", "val", "test"]) + parser.add_argument("--prefix", default="ego") + args = parser.parse_args() + + seqs = load_split_sequences(args.split) + + job_arg_strs = [] + for seq in seqs: + img_dir = glob.glob(f"{IMG_ROOT}/{seq}/**/")[0] + num_imgs = len(glob.glob(f"{img_dir}/PV/*.jpg")) + splits = list(range(0, num_imgs, args.seq_len)) + splits[-1] = num_imgs # just add the remainder to the last job + for start, end in zip(splits[:-1], splits[1:]): + sel_tracks = select_phalp_tracks(seq, img_dir, start, end) + if len(sel_tracks) < 1: + continue + track_str = "-".join([f"{tid:03d}" for tid in sel_tracks]) + arg_str = ( + f"{seq} data.start_idx={start} data.end_idx={end} " + f"data.track_ids={track_str}" + ) + print(arg_str) + job_arg_strs.append(arg_str) + + with open( + f"../job_specs/{args.prefix}_{args.split}_len_{args.seq_len}_tracks.txt", "w" + ) as f: + f.write("\n".join(job_arg_strs)) diff --git a/slahmr/slahmr/eval/tools.py b/slahmr/slahmr/eval/tools.py new file mode 100644 index 0000000000000000000000000000000000000000..d721263d9338c53e14a641bff311bdb73cef743c --- /dev/null +++ b/slahmr/slahmr/eval/tools.py @@ -0,0 +1,181 @@ +import os +import sys +import glob +import json +import joblib +import numpy as np +import smplx +import torch + +from util.loaders import load_smpl_body_model +from util.tensor import move_to, detach_all, to_torch +from optim.output import load_result, get_results_paths +from geometry.pcl import align_pcl +from geometry.rotation import batch_rodrigues + +BASE_DIR = os.path.abspath(f"{__file__}/../../../") +JOINT_REG_PATH = f"{BASE_DIR}/_DATA/body_models/J_regressor_h36m.npy" + + +# XXX: Sorry, need to change this yourself +EGOBODY_ROOT = "/path/to/egobody" +TDPW_ROOT = "/path/to/3DPW" + + +class JointRegressor(object): + def __init__(self): + # (17, 6890) + R17 = torch.from_numpy(np.load(JOINT_REG_PATH).astype(np.float32)) + # (14,) adding the root, but will omit + joint_map_h36m = torch.tensor([6, 5, 4, 1, 2, 3, 16, 15, 14, 11, 12, 13, 8, 10]) + self.regressor = R17[joint_map_h36m] # (14, 6890) + + def to(self, device): + self.regressor = self.regressor.to(device) + + def __call__(self, verts): + """ + NOTE: RETURNS ROOT AS WELL + :param verts (*, V, 3) + returns (*, J, 3) 14 standard evaluation joints + """ + return torch.einsum("nv,...vd->...nd", self.regressor, verts) # (..., 14, 3) + + +def compute_accel_norm(joints): + """ + :param joints (T, J, 3) + """ + vel = joints[1:] - joints[:-1] # (T-1, J, 3) + acc = vel[1:] - vel[:-1] # (T-2, J, 3) + return torch.linalg.norm(acc, dim=-1) + + +def global_align_joints(gt_joints, pred_joints): + """ + :param gt_joints (T, J, 3) + :param pred_joints (T, J, 3) + """ + s_glob, R_glob, t_glob = align_pcl( + gt_joints.reshape(-1, 3), pred_joints.reshape(-1, 3) + ) + pred_glob = ( + s_glob * torch.einsum("ij,tnj->tni", R_glob, pred_joints) + t_glob[None, None] + ) + return pred_glob + + +def first_align_joints(gt_joints, pred_joints): + """ + align the first two frames + :param gt_joints (T, J, 3) + :param pred_joints (T, J, 3) + """ + # (1, 1), (1, 3, 3), (1, 3) + s_first, R_first, t_first = align_pcl( + gt_joints[:2].reshape(1, -1, 3), pred_joints[:2].reshape(1, -1, 3) + ) + pred_first = ( + s_first * torch.einsum("tij,tnj->tni", R_first, pred_joints) + t_first[:, None] + ) + return pred_first + + +def local_align_joints(gt_joints, pred_joints): + """ + :param gt_joints (T, J, 3) + :param pred_joints (T, J, 3) + """ + s_loc, R_loc, t_loc = align_pcl(gt_joints, pred_joints) + pred_loc = ( + s_loc[:, None] * torch.einsum("tij,tnj->tni", R_loc, pred_joints) + + t_loc[:, None] + ) + return pred_loc + + +def load_body_model(batch_size, model_type, gender, device): + assert model_type in ["smpl", "smplh"] + if model_type == "smpl": + num_betas = 10 + ext = "pkl" + use_vtx_selector = False + else: + num_betas = 16 + ext = "npz" + use_vtx_selector = True + + smpl_path = f"{BASE_DIR}/body_models/{model_type}/{gender}/model.{ext}" + body_model, fit_gender = load_smpl_body_model( + smpl_path, + batch_size, + num_betas, + model_type=model_type, + use_vtx_selector=use_vtx_selector, + device=device, + ) + return body_model + + +def run_smpl(body_model, *args, **kwargs): + with torch.no_grad(): + results = body_model(*args, **kwargs) + return { + "joints": results.Jtr.detach().cpu(), + "vertices": results.v.detach().cpu(), + "faces": results.f.detach().cpu(), + } + + +def run_smpl_batch(body_model, device, **kwargs): + model_kwargs = {} + B = body_model.bm.batch_size + kwarg_shape = (B,) + for k, v in kwargs.items(): + kwarg_shape = v.shape[:-1] + model_kwargs[k] = v.reshape(B, v.shape[-1]).to(device) + res_flat = run_smpl(body_model, **model_kwargs) + res = {} + for k, v in res_flat.items(): + sh = v.shape + if sh[0] == B: + v = v.reshape(*kwarg_shape, *sh[1:]) + res[k] = v + return res + + +def cat_dicts(dict_list, dim=0): + """ + concatenate lists of dict of tensors + """ + keys = set(dict_list[0].keys()) + assert all(keys == set(d.keys()) for d in dict_list) + return {k: torch.stack([d[k] for d in dict_list], dim=dim) for k in keys} + + +def load_results_all(phase_dir, device): + """ + Load all the reconstructed tracks during optimization + """ + res_path_dict = get_results_paths(phase_dir) + max_iter = max(res_path_dict.keys()) + if int(max_iter) < 20: + print("max_iter", max_iter) + return None + + res = load_result(res_path_dict[max_iter])["world"] + # results is dict with (B, T, *) tensors + trans = res["trans"] + B, T, _ = trans.shape + root_orient = res["root_orient"] + pose_body = res["pose_body"] + betas = res["betas"].reshape(B, 1, -1).expand(B, T, -1) + body_model = load_body_model(B * T, "smplh", "neutral", device) + return run_smpl_batch( + body_model, + device, + trans=trans, + root_orient=root_orient, + betas=betas, + pose_body=pose_body, + ) diff --git a/slahmr/slahmr/geometry/__init__.py b/slahmr/slahmr/geometry/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..d04e763a7ef8c3a0429c318d6cdc5d6e475c8670 --- /dev/null +++ b/slahmr/slahmr/geometry/__init__.py @@ -0,0 +1,5 @@ +from . import camera +from . import mesh +from . import pcl +from . import plane +from . import rotation diff --git a/slahmr/slahmr/geometry/camera.py b/slahmr/slahmr/geometry/camera.py new file mode 100644 index 0000000000000000000000000000000000000000..559aa824925c4906b0a2c6038fa7f0cb553add63 --- /dev/null +++ b/slahmr/slahmr/geometry/camera.py @@ -0,0 +1,348 @@ +import torch +import numpy as np + + +def perspective_projection( + points, focal_length, camera_center, rotation=None, translation=None +): + """ + Adapted from https://github.com/mkocabas/VIBE/blob/master/lib/models/spin.py + This function computes the perspective projection of a set of points. + Input: + points (bs, N, 3): 3D points + focal_length (bs, 2): Focal length + camera_center (bs, 2): Camera center + rotation (bs, 3, 3): OPTIONAL Camera rotation + translation (bs, 3): OPTIONAL Camera translation + """ + batch_size = points.shape[0] + K = torch.zeros([batch_size, 3, 3], device=points.device) + K[:, 0, 0] = focal_length[:, 0] + K[:, 1, 1] = focal_length[:, 1] + K[:, 2, 2] = 1.0 + K[:, :-1, -1] = camera_center + + if rotation is not None and translation is not None: + # Transform points + points = torch.einsum("bij,bkj->bki", rotation, points) + points = points + translation.unsqueeze(1) + + # Apply perspective distortion + projected_points = points / points[..., 2:3] + + # Apply camera intrinsics + projected_points = torch.einsum("bij,bkj->bki", K, projected_points) + + return projected_points[:, :, :-1] + + +def reproject(points3d, cam_R, cam_t, cam_f, cam_center): + """ + reproject points3d into the scene cameras + :param points3d (B, T, N, 3) + :param cam_R (B, T, 3, 3) + :param cam_t (B, T, 3) + :param cam_f (T, 2) + :param cam_center (T, 2) + """ + B, T, N, _ = points3d.shape + points3d = torch.einsum("btij,btnj->btni", cam_R, points3d) + points3d = points3d + cam_t[..., None, :] # (B, T, N, 3) + points2d = points3d[..., :2] / points3d[..., 2:3] + points2d = cam_f[None, :, None] * points2d + cam_center[None, :, None] + return points2d + + +def focal2fov(focal, R): + """ + :param focal, focal length + :param R, either W / 2 or H / 2 + """ + return 2 * np.arctan(R / focal) + + +def fov2focal(fov, R): + """ + :param fov, field of view in radians + :param R, either W / 2 or H / 2 + """ + return R / np.tan(fov / 2) + + +def compute_lookat_box(bb_min, bb_max, intrins): + """ + The center and distance to a scene with bb_min, bb_max + to place a camera with given intrinsics + :param bb_min (3,) + :param bb_max (3,) + :param intrinsics, (fx, fy, cx, cy) of camera + :param view_angle (optional) viewing angle in radians (elevation) + """ + fx, fy, cx, cy = intrins + bb_min, bb_max = torch.tensor(bb_min), torch.tensor(bb_max) + center = 0.5 * (bb_min + bb_max) + size = torch.linalg.norm(bb_max - bb_min) + cam_dist = np.sqrt(fx**2 + fy**2) / np.sqrt(cx**2 + cy**2) + cam_dist = 0.75 * size * cam_dist + return center, cam_dist + + +def lookat_origin(cam_dist, view_angle=-np.pi / 6): + """ + :param cam_dist (float) + :param view_angle (float) + """ + cam_dist = np.abs(cam_dist) + view_angle = np.abs(view_angle) + pos = cam_dist * torch.tensor([0, np.sin(view_angle), np.cos(view_angle)]) + rot = rotx(view_angle) + return rot, pos + + +def lookat_matrix(source_pos, target_pos, up): + """ + IMPORTANT: USES RIGHT UP BACK XYZ CONVENTION + :param source_pos (*, 3) + :param target_pos (*, 3) + :param up (3,) + """ + *dims, _ = source_pos.shape + up = up.reshape(*(1,) * len(dims), 3) + up = up / torch.linalg.norm(up, dim=-1, keepdim=True) + back = normalize(target_pos - source_pos) + right = normalize(torch.linalg.cross(up, back)) + up = normalize(torch.linalg.cross(back, right)) + R = torch.stack([right, up, back], dim=-1) + return make_4x4_pose(R, source_pos) + + +def normalize(x): + return x / torch.linalg.norm(x, dim=-1, keepdim=True) + + +def invert_camera(R, t): + """ + :param R (*, 3, 3) + :param t (*, 3) + returns Ri (*, 3, 3), ti (*, 3) + """ + R, t = torch.tensor(R), torch.tensor(t) + Ri = R.transpose(-1, -2) + ti = -torch.einsum("...ij,...j->...i", Ri, t) + return Ri, ti + + +def compose_cameras(R1, t1, R2, t2): + """ + composes [R1, t1] and [R2, t2] + :param R1 (*, 3, 3) + :param t1 (*, 3) + :param R2 (*, 3, 3) + :param t2 (*, 3) + """ + R = torch.einsum("...ij,...jk->...ik", R1, R2) + t = t1 + torch.einsum("...ij,...j->...i", R1, t2) + return R, t + + +def matmul_nd(A, x): + """ + multiply batch matrix A to batch nd tensors + :param A (B, m, n) + :param x (B, *dims, m) + """ + B, m, n = A.shape + assert len(A) == len(x) + assert x.shape[-1] == m + B, *dims, _ = x.shape + return torch.matmul(A.reshape(B, *(1,) * len(dims), m, n), x[..., None])[..., 0] + + +def view_matrix(z, up, pos): + """ + :param z (*, 3) up (*, 3) pos (*, 3) + returns (*, 4, 4) + """ + *dims, _ = z.shape + x = normalize(torch.linalg.cross(up, z)) + y = normalize(torch.linalg.cross(z, x)) + bottom = ( + torch.tensor([0, 0, 0, 1], dtype=torch.float32) + .reshape(*(1,) * len(dims), 1, 4) + .expand(*dims, 1, 4) + ) + + return torch.cat([torch.stack([x, y, z, pos], dim=-1), bottom], dim=-2) + + +def average_pose(poses): + """ + :param poses (N, 4, 4) + returns average pose (4, 4) + """ + center = poses[:, :3, 3].mean(0) + up = normalize(poses[:, :3, 1].sum(0)) + z = normalize(poses[:, :3, 2].sum(0)) + return view_matrix(z, up, center) + + +def project_so3(M, eps=1e-4): + """ + :param M (N, *, 3, 3) + """ + N, *dims, _, _ = M.shape + M = M * (1 + torch.rand(N, *dims, 1, 3, device=M.device)) + U, D, Vt = torch.linalg.svd(M) # (N, *, 3, 3), (N, *, 3), (N, *, 3, 3) + detuvt = torch.linalg.det(torch.matmul(U, Vt)) # (N, *) + S = torch.cat( + [torch.ones(N, *dims, 2, device=M.device), detuvt[..., None]], dim=-1 + ) # (N, *, 3) + return torch.matmul(U, torch.matmul(torch.diag_embed(S), Vt)) + + +def make_translation(t): + return make_4x4_pose(torch.eye(3), t) + + +def make_rotation(rx=0, ry=0, rz=0, order="xyz"): + Rx = rotx(rx) + Ry = roty(ry) + Rz = rotz(rz) + if order == "xyz": + R = Rz @ Ry @ Rx + elif order == "xzy": + R = Ry @ Rz @ Rx + elif order == "yxz": + R = Rz @ Rx @ Ry + elif order == "yzx": + R = Rx @ Rz @ Ry + elif order == "zyx": + R = Rx @ Ry @ Rz + elif order == "zxy": + R = Ry @ Rx @ Rz + return make_4x4_pose(R, torch.zeros(3)) + + +def make_4x4_pose(R, t): + """ + :param R (*, 3, 3) + :param t (*, 3) + return (*, 4, 4) + """ + dims = R.shape[:-2] + pose_3x4 = torch.cat([R, t.view(*dims, 3, 1)], dim=-1) + bottom = ( + torch.tensor([0, 0, 0, 1], device=R.device) + .reshape(*(1,) * len(dims), 1, 4) + .expand(*dims, 1, 4) + ) + return torch.cat([pose_3x4, bottom], dim=-2) + + +def normalize(x): + return x / torch.sqrt(torch.sum(x**2, dim=-1, keepdim=True)) + + +def rotx(theta): + return torch.tensor( + [ + [1, 0, 0], + [0, np.cos(theta), -np.sin(theta)], + [0, np.sin(theta), np.cos(theta)], + ], + dtype=torch.float32, + ) + + +def roty(theta): + return torch.tensor( + [ + [np.cos(theta), 0, np.sin(theta)], + [0, 1, 0], + [-np.sin(theta), 0, np.cos(theta)], + ], + dtype=torch.float32, + ) + + +def rotz(theta): + return torch.tensor( + [ + [np.cos(theta), -np.sin(theta), 0], + [np.sin(theta), np.cos(theta), 0], + [0, 0, 1], + ], + dtype=torch.float32, + ) + + +def relative_pose_c2w(Rwc1, Rwc2, twc1, twc2): + """ + compute relative pose from cam 1 to cam 2 given c2w pose matrices + :param Rwc1, Rwc2 (N, 3, 3) cam1, cam2 to world rotations + :param twc1, twc2 (N, 3) cam1, cam2 to world translations + returns R21 (N, 3, 3) t21 (N, 3) + """ + twc1 = twc1.view(-1, 3, 1) + twc2 = twc2.view(-1, 3, 1) + Rc2w = Rwc2.transpose(-1, -2) # world to c2 + tc2w = -torch.matmul(Rc2w, twc2) + Rc2c1 = torch.matmul(Rc2w, Rwc1) + tc2c1 = tc2w + torch.matmul(Rc2w, twc1) + return Rc2c1, tc2c1[..., 0] + + +def relative_pose_w2c(Rc1w, Rc2w, tc1w, tc2w): + """ + compute relative pose from cam 1 to cam 2 given w2c camera matrices + :param Rc1w, Rc2w (N, 3, 3) world to cam1, cam2 rotations + :param tc1w, tc2w (N, 3) world to cam1, cam2 translations + """ + tc1w = tc1w.view(-1, 3, 1) + tc2w = tc2w.view(-1, 3, 1) + # we keep the world to cam transforms + Rwc1 = Rc1w.transpose(-1, -2) # c1 to world + twc1 = -torch.matmul(Rwc1, tc1w) + Rc2c1 = torch.matmul(Rc2w, Rwc1) # c1 to c2 + tc2c1 = tc2w + torch.matmul(Rc2w, twc1) + return Rc2c1, tc2c1[..., 0] + + +def project(xyz_c, center, focal, eps=1e-5): + """ + :param xyz_c (*, 3) 3d point in camera coordinates + :param focal (1) + :param center (*, 2) + return (*, 2) + """ + return focal * xyz_c[..., :2] / (xyz_c[..., 2:3] + eps) + center # (N, *, 2) + + +def convert_yup(xyz): + """ + converts points in x right y down z forward to x right y up z back + :param xyz (*, 3) + """ + x, y, z = torch.split(xyz[..., :3], 1, dim=-1) + return torch.cat([x, -y, -z], dim=-1) + + +def inv_project(uv, z, center, focal, yup=True): + """ + :param uv (*, 2) + :param z (*, 1) + :param center (*, 2) + :param focal (1) + :returns (*, 3) + """ + uv = uv - center + if yup: + return z * torch.cat( + [uv[..., :1] / focal, -uv[..., 1:2] / focal, -torch.ones_like(uv[..., :1])], + dim=-1, + ) # (N, *, 3) + + return z * torch.cat( + [uv / focal, torch.ones_like(uv[..., :1])], + dim=-1, + ) # (N, *, 3) diff --git a/slahmr/slahmr/geometry/mesh.py b/slahmr/slahmr/geometry/mesh.py new file mode 100644 index 0000000000000000000000000000000000000000..eb539d0537975e17bec9251de2272a2ff5818bb8 --- /dev/null +++ b/slahmr/slahmr/geometry/mesh.py @@ -0,0 +1,110 @@ +import os +import numpy as np +import trimesh + + +def get_mesh_bb(mesh): + """ + :param mesh - trimesh mesh object + returns bb_min (3), bb_max (3) + """ + bb_min = mesh.vertices.max(axis=0) + bb_max = mesh.vertices.min(axis=0) + return bb_min, bb_max + + +def get_scene_bb(meshes): + """ + :param mesh_seqs - (potentially nested) list of trimesh objects + returns bb_min (3), bb_max (3) + """ + if isinstance(meshes, trimesh.Trimesh): + return get_mesh_bb(meshes) + + bb_mins, bb_maxs = zip(*[get_scene_bb(mesh) for mesh in meshes]) + bb_mins = np.stack(bb_mins, axis=0) + bb_maxs = np.stack(bb_maxs, axis=0) + return bb_mins.min(axis=0), bb_maxs.max(axis=0) + + +def make_batch_mesh(verts, faces, colors): + """ + convenience function to make batch of meshes + meshs have same faces in batch, verts have same color in mesh + :param verts (B, V, 3) + :param faces (F, 3) + :param colors (B, 3) + """ + B, V, _ = verts.shape + return [make_mesh(verts[b], faces, colors[b, None].expand(V, -1)) for b in range(B)] + + +def make_mesh(verts, faces, colors=None, yup=True): + """ + create a trimesh object for the faces and vertices + :param verts (V, 3) tensor + :param faces (F, 3) tensor + :param colors (optional) (V, 3) tensor + :param yup (optional bool) whether or not to save with Y up + """ + verts = verts.detach().cpu().numpy() + faces = faces.detach().cpu().numpy() + if yup: + verts = np.array([1, -1, -1])[None, :] * verts + if colors is None: + colors = np.ones_like(verts) * 0.5 + else: + colors = colors.detach().cpu().numpy() + return trimesh.Trimesh( + vertices=verts, faces=faces, vertex_colors=colors, process=False + ) + + +def save_mesh_scenes(out_dir, scenes): + """ + :param scenes, list of scenes (list of meshes) + """ + assert isinstance(scenes, list) + assert isinstance(scenes[0], list) + B = len(scenes[0]) + if B == 1: + save_meshes_to_obj(out_dir, [x[0] for x in scenes]) + else: + save_scenes_to_glb(out_dir, scenes) + + +def save_scenes_to_glb(out_dir, scenes): + """ + Saves a list of scenes (list of meshes) each to glb files + """ + os.makedirs(out_dir, exist_ok=True) + for t, meshes in enumerate(scenes): + save_meshes_to_glb(f"{out_dir}/scene_{t:03d}.glb", meshes) + + +def save_meshes_to_glb(path, meshes, names=None): + """ + put trimesh meshes in a scene and export to glb + """ + if names is not None: + assert len(meshes) == len(names) + + scene = trimesh.Scene() + for i, mesh in enumerate(meshes): + name = f"mesh_{i:03d}" if names is None else names[i] + scene.add_geometry(mesh, node_name=name) + + with open(path, "wb") as f: + f.write(trimesh.exchange.gltf.export_glb(scene, include_normals=True)) + + +def save_meshes_to_obj(out_dir, meshes, names=None): + if names is not None: + assert len(meshes) == len(names) + + os.makedirs(out_dir, exist_ok=True) + for i, mesh in enumerate(meshes): + name = f"mesh_{i:03d}" if names is None else names[i] + path = os.path.join(out_dir, f"{name}.obj") + with open(path, "w") as f: + mesh.export(f, file_type="obj", include_color=False, include_normals=True) diff --git a/slahmr/slahmr/geometry/pcl.py b/slahmr/slahmr/geometry/pcl.py new file mode 100644 index 0000000000000000000000000000000000000000..5ff0feaca05881f2ae8b3f1861253c5d562fa333 --- /dev/null +++ b/slahmr/slahmr/geometry/pcl.py @@ -0,0 +1,60 @@ +import numpy as np +import torch + + +def read_pcl_tensor(path): + pcl_np = read_pcl(path) + return torch.from_numpy(pcl_np) + + +def align_pcl(Y, X, weight=None, fixed_scale=False): + """align similarity transform to align X with Y using umeyama method + X' = s * R * X + t is aligned with Y + :param Y (*, N, 3) first trajectory + :param X (*, N, 3) second trajectory + :param weight (*, N, 1) optional weight of valid correspondences + :returns s (*, 1), R (*, 3, 3), t (*, 3) + """ + *dims, N, _ = Y.shape + N = torch.ones(*dims, 1, 1) * N + + if weight is not None: + Y = Y * weight + X = X * weight + N = weight.sum(dim=-2, keepdim=True) # (*, 1, 1) + + # subtract mean + my = Y.sum(dim=-2) / N[..., 0] # (*, 3) + mx = X.sum(dim=-2) / N[..., 0] + y0 = Y - my[..., None, :] # (*, N, 3) + x0 = X - mx[..., None, :] + + if weight is not None: + y0 = y0 * weight + x0 = x0 * weight + + # correlation + C = torch.matmul(y0.transpose(-1, -2), x0) / N # (*, 3, 3) + U, D, Vh = torch.linalg.svd(C) # (*, 3, 3), (*, 3), (*, 3, 3) + + S = torch.eye(3).reshape(*(1,) * (len(dims)), 3, 3).repeat(*dims, 1, 1) + neg = torch.det(U) * torch.det(Vh.transpose(-1, -2)) < 0 + S[neg, 2, 2] = -1 + + R = torch.matmul(U, torch.matmul(S, Vh)) # (*, 3, 3) + + D = torch.diag_embed(D) # (*, 3, 3) + if fixed_scale: + s = torch.ones(*dims, 1, device=Y.device, dtype=torch.float32) + else: + var = torch.sum(torch.square(x0), dim=(-1, -2), keepdim=True) / N # (*, 1, 1) + s = ( + torch.diagonal(torch.matmul(D, S), dim1=-2, dim2=-1).sum( + dim=-1, keepdim=True + ) + / var[..., 0] + ) # (*, 1) + + t = my - s * torch.matmul(R, mx[..., None])[..., 0] # (*, 3) + + return s, R, t diff --git a/slahmr/slahmr/geometry/plane.py b/slahmr/slahmr/geometry/plane.py new file mode 100644 index 0000000000000000000000000000000000000000..69dad0b41f695e90bcf5da8b880007c831b5cfeb --- /dev/null +++ b/slahmr/slahmr/geometry/plane.py @@ -0,0 +1,101 @@ +import torch + + +def fit_plane(points): + """ + :param points (*, N, 3) + returns (*, 3) plane parameters (returns in normal * offset format) + """ + *dims, N, D = points.shape + mean = points.mean(dim=-2, keepdim=True) + # (*, N, D), (*, D), (*, D, D) + U, S, Vh = torch.linalg.svd(points - mean) + normal = Vh[..., -1, :] # (*, D) + offset = torch.einsum("...ij,...j->...i", points, normal) # (*, N) + offset = offset.mean(dim=-1, keepdim=True) + return torch.cat([normal, offset], dim=-1) + + +def get_plane_transform(up, ground_plane=None, xyz_orig=None): + """ + get R, t rigid transform from plane and desired origin + :param up (3,) up vector of coordinate frame + :param ground_plane (4) (a, b, c, d) where a,b,c is the normal + :param xyz_orig (3) desired origin + """ + R = torch.eye(3) + t = torch.zeros(3) + if ground_plane is None: + return R, t + + # compute transform between world up vector and passed in floor + ground_plane = torch.as_tensor(ground_plane) + ground_plane = torch.sign(ground_plane[3]) * ground_plane + + normal = ground_plane[:3] + normal = normal / torch.linalg.norm(normal) + v = torch.linalg.cross(up, normal) + ang_sin = torch.linalg.norm(v) + ang_cos = up.dot(normal) + skew_v = torch.as_tensor([[0.0, -v[2], v[1]], [v[2], 0.0, -v[0]], [-v[1], v[0], 0.0]]) + R = torch.eye(3) + skew_v + (skew_v @ skew_v) * ((1.0 - ang_cos) / (ang_sin**2)) + + # project origin onto plane + if xyz_orig is None: + xyz_orig = torch.zeros(3) + t, _ = compute_plane_intersection(xyz_orig, -normal, ground_plane) + + return R, t + + +def parse_floor_plane(floor_plane): + """ + Takes floor plane in the optimization form (Bx3 with a,b,c * d) and parses into + (a,b,c,d) from with (a,b,c) normal facing "up in the camera frame and d the offset. + """ + floor_offset = torch.norm(floor_plane, dim=-1, keepdim=True) + floor_normal = floor_plane / floor_offset + + # in camera system -y is up, so floor plane normal y component should never be positive + # (assuming the camera is not sideways or upside down) + neg_mask = floor_normal[..., 1:2] > 0.0 + floor_normal = torch.where( + neg_mask.expand_as(floor_normal), -floor_normal, floor_normal + ) + floor_offset = torch.where(neg_mask, -floor_offset, floor_offset) + floor_plane_4d = torch.cat([floor_normal, floor_offset], dim=-1) + + return floor_plane_4d + + +def compute_plane_intersection(point, direction, plane): + """ + Given a ray defined by a point in space and a direction, + compute the intersection point with the given plane. + Detect intersection in either direction or -direction. + Note, ray may not actually intersect with the plane. + + Returns the intersection point and s where + point + s * direction = intersection_point. if s < 0 it means + -direction intersects. + + - point : B x 3 + - direction : B x 3 + - plane : B x 4 (a, b, c, d) where (a, b, c) is the normal and (d) the offset. + """ + dims = point.shape[:-1] + plane_normal = plane[..., :3] + plane_off = plane[..., 3] + s = (plane_off - bdot(plane_normal, point)) / (bdot(plane_normal, direction) + 1e-4) + itsct_pt = point + s.reshape((-1, 1)) * direction + return itsct_pt, s + + +def bdot(A1, A2, keepdim=False): + """ + Batched dot product. + - A1 : B x D + - A2 : B x D. + Returns B. + """ + return (A1 * A2).sum(dim=-1, keepdim=keepdim) diff --git a/slahmr/slahmr/geometry/rotation.py b/slahmr/slahmr/geometry/rotation.py new file mode 100644 index 0000000000000000000000000000000000000000..a0dead90b9b872e0ae957bc96880619c0cf4c056 --- /dev/null +++ b/slahmr/slahmr/geometry/rotation.py @@ -0,0 +1,284 @@ +import torch +import numpy as np +from torch.nn import functional as F + + +def batch_rodrigues(rot_vecs, epsilon=1e-8, dtype=torch.float32): + """ + Taken from https://github.com/mkocabas/VIBE/blob/master/lib/utils/geometry.py + Calculates the rotation matrices for a batch of rotation vectors + - param rot_vecs: torch.tensor (N, 3) array of N axis-angle vectors + - returns R: torch.tensor (N, 3, 3) rotation matrices + """ + batch_size = rot_vecs.shape[0] + device = rot_vecs.device + + angle = torch.norm(rot_vecs + 1e-8, dim=1, keepdim=True) + rot_dir = rot_vecs / angle + + cos = torch.unsqueeze(torch.cos(angle), dim=1) + sin = torch.unsqueeze(torch.sin(angle), dim=1) + + # Bx1 arrays + rx, ry, rz = torch.split(rot_dir, 1, dim=1) + K = torch.zeros((batch_size, 3, 3), dtype=dtype, device=device) + + zeros = torch.zeros((batch_size, 1), dtype=dtype, device=device) + K = torch.cat([zeros, -rz, ry, rz, zeros, -rx, -ry, rx, zeros], dim=1).view( + (batch_size, 3, 3) + ) + + ident = torch.eye(3, dtype=dtype, device=device).unsqueeze(dim=0) + rot_mat = ident + sin * K + (1 - cos) * torch.bmm(K, K) + return rot_mat + + +def quaternion_mul(q0, q1): + """ + EXPECTS WXYZ + :param q0 (*, 4) + :param q1 (*, 4) + """ + r0, r1 = q0[..., :1], q1[..., :1] + v0, v1 = q0[..., 1:], q1[..., 1:] + r = r0 * r1 - (v0 * v1).sum(dim=-1, keepdim=True) + v = r0 * v1 + r1 * v0 + torch.linalg.cross(v0, v1) + return torch.cat([r, v], dim=-1) + + +def quaternion_inverse(q, eps=1e-8): + """ + EXPECTS WXYZ + :param q (*, 4) + """ + conj = torch.cat([q[..., :1], -q[..., 1:]], dim=-1) + mag = torch.square(q).sum(dim=-1, keepdim=True) + eps + return conj / mag + + +def quaternion_slerp(t, q0, q1, eps=1e-8): + """ + :param t (*, 1) must be between 0 and 1 + :param q0 (*, 4) + :param q1 (*, 4) + """ + dims = q0.shape[:-1] + t = t.view(*dims, 1) + + q0 = F.normalize(q0, p=2, dim=-1) + q1 = F.normalize(q1, p=2, dim=-1) + dot = (q0 * q1).sum(dim=-1, keepdim=True) + + # make sure we give the shortest rotation path (< 180d) + neg = dot < 0 + q1 = torch.where(neg, -q1, q1) + dot = torch.where(neg, -dot, dot) + angle = torch.acos(dot) + + # if angle is too small, just do linear interpolation + collin = torch.abs(dot) > 1 - eps + fac = 1 / torch.sin(angle) + w0 = torch.where(collin, 1 - t, torch.sin((1 - t) * angle) * fac) + w1 = torch.where(collin, t, torch.sin(t * angle) * fac) + slerp = q0 * w0 + q1 * w1 + return slerp + + +def rotation_matrix_to_angle_axis(rotation_matrix): + """ + This function is borrowed from https://github.com/kornia/kornia + + Convert rotation matrix to Rodrigues vector + """ + quaternion = rotation_matrix_to_quaternion(rotation_matrix) + aa = quaternion_to_angle_axis(quaternion) + aa[torch.isnan(aa)] = 0.0 + return aa + + +def quaternion_to_angle_axis(quaternion): + """ + This function is borrowed from https://github.com/kornia/kornia + + Convert quaternion vector to angle axis of rotation. + Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h + + :param quaternion (*, 4) expects WXYZ + :returns angle_axis (*, 3) + """ + # unpack input and compute conversion + q1 = quaternion[..., 1] + q2 = quaternion[..., 2] + q3 = quaternion[..., 3] + sin_squared_theta = q1 * q1 + q2 * q2 + q3 * q3 + + sin_theta = torch.sqrt(sin_squared_theta) + cos_theta = quaternion[..., 0] + two_theta = 2.0 * torch.where( + cos_theta < 0.0, + torch.atan2(-sin_theta, -cos_theta), + torch.atan2(sin_theta, cos_theta), + ) + + k_pos = two_theta / sin_theta + k_neg = 2.0 * torch.ones_like(sin_theta) + k = torch.where(sin_squared_theta > 0.0, k_pos, k_neg) + + angle_axis = torch.zeros_like(quaternion)[..., :3] + angle_axis[..., 0] += q1 * k + angle_axis[..., 1] += q2 * k + angle_axis[..., 2] += q3 * k + return angle_axis + + +def quaternion_to_rotation_matrix(quaternion): + """ + Convert a quaternion to a rotation matrix. + Taken from https://github.com/kornia/kornia, based on + https://github.com/matthew-brett/transforms3d/blob/8965c48401d9e8e66b6a8c37c65f2fc200a076fa/transforms3d/quaternions.py#L101 + https://github.com/tensorflow/graphics/blob/master/tensorflow_graphics/geometry/transformation/rotation_matrix_3d.py#L247 + :param quaternion (N, 4) expects WXYZ order + returns rotation matrix (N, 3, 3) + """ + # normalize the input quaternion + quaternion_norm = F.normalize(quaternion, p=2, dim=-1, eps=1e-12) + *dims, _ = quaternion_norm.shape + + # unpack the normalized quaternion components + w, x, y, z = torch.chunk(quaternion_norm, chunks=4, dim=-1) + + # compute the actual conversion + tx = 2.0 * x + ty = 2.0 * y + tz = 2.0 * z + twx = tx * w + twy = ty * w + twz = tz * w + txx = tx * x + txy = ty * x + txz = tz * x + tyy = ty * y + tyz = tz * y + tzz = tz * z + one = torch.tensor(1.0) + + matrix = torch.stack( + ( + one - (tyy + tzz), + txy - twz, + txz + twy, + txy + twz, + one - (txx + tzz), + tyz - twx, + txz - twy, + tyz + twx, + one - (txx + tyy), + ), + dim=-1, + ).view(*dims, 3, 3) + return matrix + + +def angle_axis_to_quaternion(angle_axis): + """ + This function is borrowed from https://github.com/kornia/kornia + Convert angle axis to quaternion in WXYZ order + :param angle_axis (*, 3) + :returns quaternion (*, 4) WXYZ order + """ + theta_sq = torch.sum(angle_axis**2, dim=-1, keepdim=True) # (*, 1) + # need to handle the zero rotation case + valid = theta_sq > 0 + theta = torch.sqrt(theta_sq) + half_theta = 0.5 * theta + ones = torch.ones_like(half_theta) + # fill zero with the limit of sin ax / x -> a + k = torch.where(valid, torch.sin(half_theta) / theta, 0.5 * ones) + w = torch.where(valid, torch.cos(half_theta), ones) + quat = torch.cat([w, k * angle_axis], dim=-1) + return quat + + +def rotation_matrix_to_quaternion(rotation_matrix, eps=1e-6): + """ + This function is borrowed from https://github.com/kornia/kornia + Convert rotation matrix to 4d quaternion vector + This algorithm is based on algorithm described in + https://github.com/KieranWynn/pyquaternion/blob/master/pyquaternion/quaternion.py#L201 + + :param rotation_matrix (N, 3, 3) + """ + *dims, m, n = rotation_matrix.shape + rmat_t = torch.transpose(rotation_matrix.reshape(-1, m, n), -1, -2) + + mask_d2 = rmat_t[:, 2, 2] < eps + + mask_d0_d1 = rmat_t[:, 0, 0] > rmat_t[:, 1, 1] + mask_d0_nd1 = rmat_t[:, 0, 0] < -rmat_t[:, 1, 1] + + t0 = 1 + rmat_t[:, 0, 0] - rmat_t[:, 1, 1] - rmat_t[:, 2, 2] + q0 = torch.stack( + [ + rmat_t[:, 1, 2] - rmat_t[:, 2, 1], + t0, + rmat_t[:, 0, 1] + rmat_t[:, 1, 0], + rmat_t[:, 2, 0] + rmat_t[:, 0, 2], + ], + -1, + ) + t0_rep = t0.repeat(4, 1).t() + + t1 = 1 - rmat_t[:, 0, 0] + rmat_t[:, 1, 1] - rmat_t[:, 2, 2] + q1 = torch.stack( + [ + rmat_t[:, 2, 0] - rmat_t[:, 0, 2], + rmat_t[:, 0, 1] + rmat_t[:, 1, 0], + t1, + rmat_t[:, 1, 2] + rmat_t[:, 2, 1], + ], + -1, + ) + t1_rep = t1.repeat(4, 1).t() + + t2 = 1 - rmat_t[:, 0, 0] - rmat_t[:, 1, 1] + rmat_t[:, 2, 2] + q2 = torch.stack( + [ + rmat_t[:, 0, 1] - rmat_t[:, 1, 0], + rmat_t[:, 2, 0] + rmat_t[:, 0, 2], + rmat_t[:, 1, 2] + rmat_t[:, 2, 1], + t2, + ], + -1, + ) + t2_rep = t2.repeat(4, 1).t() + + t3 = 1 + rmat_t[:, 0, 0] + rmat_t[:, 1, 1] + rmat_t[:, 2, 2] + q3 = torch.stack( + [ + t3, + rmat_t[:, 1, 2] - rmat_t[:, 2, 1], + rmat_t[:, 2, 0] - rmat_t[:, 0, 2], + rmat_t[:, 0, 1] - rmat_t[:, 1, 0], + ], + -1, + ) + t3_rep = t3.repeat(4, 1).t() + + mask_c0 = mask_d2 * mask_d0_d1 + mask_c1 = mask_d2 * ~mask_d0_d1 + mask_c2 = ~mask_d2 * mask_d0_nd1 + mask_c3 = ~mask_d2 * ~mask_d0_nd1 + mask_c0 = mask_c0.view(-1, 1).type_as(q0) + mask_c1 = mask_c1.view(-1, 1).type_as(q1) + mask_c2 = mask_c2.view(-1, 1).type_as(q2) + mask_c3 = mask_c3.view(-1, 1).type_as(q3) + + q = q0 * mask_c0 + q1 * mask_c1 + q2 * mask_c2 + q3 * mask_c3 + q /= torch.sqrt( + t0_rep * mask_c0 + + t1_rep * mask_c1 + + t2_rep * mask_c2 # noqa + + t3_rep * mask_c3 + ) # noqa + q *= 0.5 + return q.reshape(*dims, 4) diff --git a/slahmr/slahmr/humor/__init__.py b/slahmr/slahmr/humor/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/slahmr/humor/amass_utils.py b/slahmr/slahmr/humor/amass_utils.py new file mode 100644 index 0000000000000000000000000000000000000000..29b75eea1cb4d7cfb59e7867d4eb1e9c1a96e545 --- /dev/null +++ b/slahmr/slahmr/humor/amass_utils.py @@ -0,0 +1,148 @@ +""" +Taken from https://github.com/davrempe/humor +""" + +from body_model.utils import SMPL_JOINTS + + +TRAIN_DATASETS = [ + "CMU", + "MPI_Limits", + "TotalCapture", + "Eyes_Japan_Dataset", + "KIT", + "BioMotionLab_NTroje", + "BMLmovi", + "EKUT", + "ACCAD", +] +TEST_DATASETS = ["Transitions_mocap", "HumanEva"] +VAL_DATASETS = ["MPI_HDM05", "SFU", "MPI_mosh"] + + +SPLITS = ["train", "val", "test", "custom"] +SPLIT_BY = [ + "single", # the data path is a single .npz file. Don't split: train and test are same + "sequence", # the data paths are directories of subjects. Collate and split by sequence. + "subject", # the data paths are directories of datasets. Collate and split by subject. + "dataset", # a single data path to the amass data root is given. The predefined datasets will be used for each split. +] + +ROT_REPS = ["mat", "aa", "6d"] + +# these correspond to [root, left knee, right knee, left heel, right heel, left toe, right toe, left hand, right hand] +CONTACT_ORDERING = [ + "hips", + "leftLeg", + "rightLeg", + "leftFoot", + "rightFoot", + "leftToeBase", + "rightToeBase", + "leftHand", + "rightHand", +] +CONTACT_INDS = [SMPL_JOINTS[jname] for jname in CONTACT_ORDERING] + +NUM_BODY_JOINTS = len(SMPL_JOINTS) - 1 +NUM_KEYPT_VERTS = 43 + +DATA_NAMES = [ + "trans", + "trans_vel", + "root_orient", + "root_orient_vel", + "pose_body", + "pose_body_vel", + "joints", + "joints_vel", + "joints_orient_vel", + "verts", + "verts_vel", + "contacts", +] + +SMPL_JOINTS_RETURN_CONFIG = { + "trans": True, + "trans_vel": True, + "root_orient": True, + "root_orient_vel": True, + "pose_body": True, + "pose_body_vel": False, + "joints": True, + "joints_vel": True, + "joints_orient_vel": False, + "verts": False, + "verts_vel": False, + "contacts": False, +} + +SMPL_JOINTS_CONTACTS_RETURN_CONFIG = { + "trans": True, + "trans_vel": True, + "root_orient": True, + "root_orient_vel": True, + "pose_body": True, + "pose_body_vel": False, + "joints": True, + "joints_vel": True, + "joints_orient_vel": False, + "verts": False, + "verts_vel": False, + "contacts": True, +} + +ALL_RETURN_CONFIG = { + "trans": True, + "trans_vel": True, + "root_orient": True, + "root_orient_vel": True, + "pose_body": True, + "pose_body_vel": False, + "joints": True, + "joints_vel": True, + "joints_orient_vel": False, + "verts": True, + "verts_vel": False, + "contacts": True, +} + +RETURN_CONFIGS = { + "smpl+joints+contacts": SMPL_JOINTS_CONTACTS_RETURN_CONFIG, + "smpl+joints": SMPL_JOINTS_RETURN_CONFIG, + "all": ALL_RETURN_CONFIG, +} + + +def data_name_list(return_config): + """ + returns the list of data values in the given configuration + """ + cur_ret_cfg = RETURN_CONFIGS[return_config] + data_names = [k for k in DATA_NAMES if cur_ret_cfg[k]] + return data_names + + +def data_dim(dname, rot_rep_size=9): + """ + returns the dimension of the data with the given name. If the data is a rotation, returns the size with the given representation. + """ + if dname in ["trans", "trans_vel", "root_orient_vel"]: + return 3 + elif dname in ["root_orient"]: + return rot_rep_size + elif dname in ["pose_body"]: + return NUM_BODY_JOINTS * rot_rep_size + elif dname in ["pose_body_vel"]: + return NUM_BODY_JOINTS * 3 + elif dname in ["joints", "joints_vel"]: + return len(SMPL_JOINTS) * 3 + elif dname in ["joints_orient_vel"]: + return 1 + elif dname in ["verts", "verts_vel"]: + return NUM_KEYPT_VERTS * 3 + elif dname in ["contacts"]: + return len(CONTACT_ORDERING) + else: + print("The given data name %s is not valid!" % (dname)) + exit() diff --git a/slahmr/slahmr/humor/humor_model.py b/slahmr/slahmr/humor/humor_model.py new file mode 100644 index 0000000000000000000000000000000000000000..72aa3d2514e42ec77bf4fd74224a3d1be19ec2f7 --- /dev/null +++ b/slahmr/slahmr/humor/humor_model.py @@ -0,0 +1,1655 @@ +""" +Taken from https://github.com/davrempe/humor +""" + +import time, os +import numpy as np +import torch +import torch.nn as nn +import torch.nn.functional as F +from torch.distributions.normal import Normal + +from .amass_utils import data_name_list, data_dim +from .transforms import ( + convert_to_rotmat, + compute_world2aligned_mat, + rotation_matrix_to_angle_axis, +) + +from body_model.specs import SMPL_JOINTS, SMPLH_PATH +from body_model.body_model import BodyModel + + +IN_ROT_REPS = ["aa", "6d", "mat"] +OUT_ROT_REPS = ["aa", "6d", "9d"] +ROT_REP_SIZE = {"aa": 3, "6d": 6, "mat": 9, "9d": 9} +NUM_SMPL_JOINTS = len(SMPL_JOINTS) +NUM_BODY_JOINTS = NUM_SMPL_JOINTS - 1 # no root +BETA_SIZE = 16 + +POSTERIOR_OPTIONS = ["mlp"] +PRIOR_OPTIONS = ["mlp"] +DECODER_OPTIONS = ["mlp"] + +WORLD2ALIGN_NAME_CACHE = { + "root_orient": None, + "trans": None, + "joints": None, + "verts": None, + "joints_vel": None, + "verts_vel": None, + "trans_vel": None, + "root_orient_vel": None, +} + + +def step( + model, loss_func, data, dataset, device, cur_epoch, mode="train", use_gt_p=1.0 +): + """ + Given data for the current training step (batch), + pulls out the necessary needed data, + runs the model, + calculates and returns the loss. + + - use_gt_p : the probability of using ground truth as input to each step rather than the model's own prediction + (1.0 is fully supervised, 0.0 is fully autoregressive) + """ + use_sched_samp = use_gt_p < 1.0 + batch_in, batch_out, meta = data + + prep_data = model.prepare_input( + batch_in, + device, + data_out=batch_out, + return_input_dict=True, + return_global_dict=use_sched_samp, + ) + if use_sched_samp: + x_past, x_t, gt_dict, input_dict, global_gt_dict = prep_data + else: + x_past, x_t, gt_dict, input_dict = prep_data + + B, T, S_in, _ = x_past.size() + S_out = x_t.size(2) + + if not use_sched_samp: + # fully supervised phase + # start by using gt at every step, so just form all steps from all sequences into one large batch + # and get per-step predictions + x_past_batched = x_past.reshape((B * T, S_in, -1)) + x_t_batched = x_t.reshape((B * T, S_out, -1)) + out_dict = model(x_past_batched, x_t_batched) + else: + # in scheduled sampling or fully autoregressive phase + init_input_dict = dict() + for k in input_dict.keys(): + init_input_dict[k] = input_dict[k][ + :, 0, :, : + ] # only need first step for init + # this out_dict is the global state + sched_samp_out = model.scheduled_sampling( + x_past, + x_t, + init_input_dict, + p=use_gt_p, + gender=meta["gender"], + betas=meta["betas"].to(device), + need_global_out=(not model.detach_sched_samp), + ) + if model.detach_sched_samp: + out_dict = sched_samp_out + else: + out_dict, _ = sched_samp_out + # gt must be global state for supervision in this case + if not model.detach_sched_samp: + print("USING global supervision") + gt_dict = global_gt_dict + + # loss can be computed per output step in parallel + # batch dicts accordingly + for k in out_dict.keys(): + if k == "posterior_distrib" or k == "prior_distrib": + m, v = out_dict[k] + m = m.reshape((B * T, -1)) + v = v.reshape((B * T, -1)) + out_dict[k] = (m, v) + else: + out_dict[k] = out_dict[k].reshape((B * T * S_out, -1)) + for k in gt_dict.keys(): + gt_dict[k] = gt_dict[k].reshape((B * T * S_out, -1)) + + gender_in = np.broadcast_to( + np.array(meta["gender"]).reshape((B, 1, 1, 1)), (B, T, S_out, 1) + ) + gender_in = gender_in.reshape((B * T * S_out, 1)) + betas_in = meta["betas"].reshape((B, T, 1, -1)).expand((B, T, S_out, 16)).to(device) + betas_in = betas_in.reshape((B * T * S_out, 16)) + loss, stats_dict = loss_func( + out_dict, gt_dict, cur_epoch, gender=gender_in, betas=betas_in + ) + + return loss, stats_dict + + +class HumorModel(nn.Module): + def __init__( + self, + in_rot_rep="aa", + out_rot_rep="aa", + latent_size=48, + steps_in=1, + conditional_prior=True, # use a learned prior rather than standard normal + output_delta=True, # output change in state from decoder rather than next step directly + posterior_arch="mlp", + decoder_arch="mlp", + prior_arch="mlp", + model_data_config="smpl+joints+contacts", + detach_sched_samp=True, # if true, detaches outputs of previous step so gradients don't flow through many steps + model_use_smpl_joint_inputs=False, # if true, uses smpl joints rather than regressed joints to input at next step (during rollout and sched samp) + model_smpl_batch_size=1, # if using smpl joint inputs this should be batch_size of the smpl model (aka data input to rollout) + ): + super(HumorModel, self).__init__() + self.ignore_keys = [] + + self.steps_in = steps_in + self.steps_out = 1 + self.out_step_size = 1 + self.detach_sched_samp = detach_sched_samp + self.output_delta = output_delta + + if self.steps_out > 1: + raise NotImplementedError("Only supported single step output currently.") + + if out_rot_rep not in OUT_ROT_REPS: + raise Exception( + "Not a valid output rotation representation: %s" % (out_rot_rep) + ) + if in_rot_rep not in IN_ROT_REPS: + raise Exception( + "Not a valid input rotation representation: %s" % (in_rot_rep) + ) + self.out_rot_rep = out_rot_rep + self.in_rot_rep = in_rot_rep + + if posterior_arch not in POSTERIOR_OPTIONS: + raise Exception("Not a valid encoder architecture: %s" % (posterior_arch)) + if decoder_arch not in DECODER_OPTIONS: + raise Exception("Not a valid decoder architecture: %s" % (decoder_arch)) + if conditional_prior and prior_arch not in PRIOR_OPTIONS: + raise Exception("Not a valid prior architecture: %s" % (prior_arch)) + self.posterior_arch = posterior_arch + self.decoder_arch = decoder_arch + self.prior_arch = prior_arch + + # get the list of data names for this config + self.data_names = data_name_list(model_data_config) + self.aux_in_data_names = ( + self.aux_out_data_names + ) = None # auxiliary data will be returned as part of the input/output dictionary, but not the actual network input/output tensor + self.pred_contacts = False + if ( + model_data_config.find("contacts") >= 0 + ): # network is outputting contact classification as well and need to supervise, but not given as input to net. + self.data_names.remove("contacts") + self.aux_out_data_names = ["contacts"] + self.pred_contacts = True + + self.need_trans2joint = ( + "joints" in self.data_names or "verts" in self.data_names + ) + self.model_data_config = model_data_config + + self.input_rot_dim = ROT_REP_SIZE[self.in_rot_rep] + self.input_dim_list = [ + data_dim(dname, rot_rep_size=self.input_rot_dim) + for dname in self.data_names + ] + self.input_data_dim = sum(self.input_dim_list) + + self.output_rot_dim = ROT_REP_SIZE[self.out_rot_rep] + self.output_dim_list = [ + data_dim(dname, rot_rep_size=self.output_rot_dim) + for dname in self.data_names + ] + self.delta_output_dim_list = [ + data_dim(dname, rot_rep_size=ROT_REP_SIZE["mat"]) + for dname in self.data_names + ] + + if self.pred_contacts: + # account for contact classification output + self.output_dim_list.append(data_dim("contacts")) + self.delta_output_dim_list.append(data_dim("contacts")) + + self.output_data_dim = sum(self.output_dim_list) + + self.latent_size = latent_size + past_data_dim = self.steps_in * self.input_data_dim + t_data_dim = self.steps_out * self.input_data_dim + + # posterior encoder (given past and future, predict latent transition distribution) + print("Using posterior architecture: %s" % (self.posterior_arch)) + if self.posterior_arch == "mlp": + layer_list = [ + past_data_dim + t_data_dim, + 1024, + 1024, + 1024, + 1024, + self.latent_size * 2, + ] + self.encoder = MLP( + layers=layer_list, # mu and sigma output + nonlinearity=nn.ReLU, + use_gn=True, + ) + + # decoder (given past and latent transition, predict future) for the immediate next step + print("Using decoder architecture: %s" % (self.decoder_arch)) + decoder_input_dim = past_data_dim + self.latent_size + if self.decoder_arch == "mlp": + layer_list = [decoder_input_dim, 1024, 1024, 512, self.output_data_dim] + self.decoder = MLP( + layers=layer_list, + nonlinearity=nn.ReLU, + use_gn=True, + skip_input_idx=past_data_dim, # skip connect the latent to every layer + ) + + # prior (if conditional, given past predict latent transition distribution) + self.use_conditional_prior = conditional_prior + if self.use_conditional_prior: + print("Using prior architecture: %s" % (self.prior_arch)) + layer_list = [past_data_dim, 1024, 1024, 1024, 1024, self.latent_size * 2] + self.prior_net = MLP( + layers=layer_list, # mu and sigma output + nonlinearity=nn.ReLU, + use_gn=True, + ) + else: + print("Using standard normal prior.") + + self.use_smpl_joint_inputs = model_use_smpl_joint_inputs + self.smpl_batch_size = model_smpl_batch_size + if self.use_smpl_joint_inputs: + # need a body model to compute the joints after each step. + print( + "Using SMPL joints rather than regressed joints as input at each step for roll out and scheduled sampling..." + ) + male_bm_path = os.path.join(SMPLH_PATH, "male/model.npz") + self.male_bm = BodyModel( + bm_path=male_bm_path, num_betas=16, batch_size=self.smpl_batch_size + ) + female_bm_path = os.path.join(SMPLH_PATH, "female/model.npz") + self.female_bm = BodyModel( + bm_path=female_bm_path, num_betas=16, batch_size=self.smpl_batch_size + ) + neutral_bm_path = os.path.join(SMPLH_PATH, "neutral/model.npz") + self.neutral_bm = BodyModel( + bm_path=neutral_bm_path, num_betas=16, batch_size=self.smpl_batch_size + ) + self.bm_dict = { + "male": self.male_bm, + "female": self.female_bm, + "neutral": self.neutral_bm, + } + for p in self.male_bm.parameters(): + p.requires_grad = False + for p in self.female_bm.parameters(): + p.requires_grad = False + for p in self.neutral_bm.parameters(): + p.requires_grad = False + self.ignore_keys = ["male_bm", "female_bm", "neutral_bm"] + + def prepare_input( + self, + data_in, + device, + data_out=None, + return_input_dict=False, + return_global_dict=False, + ): + """ + Concatenates input and output data as expected by the model. + + Also creates a dictionary of GT outputs for use in computing the loss. And optionally + a dictionary of inputs. + """ + + # + # input data + # + in_unnorm_data_list = [] + for k in self.data_names: + cur_dat = data_in[k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + cur_unnorm_dat = cur_dat.reshape((B, T, self.steps_in, -1)) + in_unnorm_data_list.append(cur_unnorm_dat) + x_past = torch.cat(in_unnorm_data_list, axis=3) + + input_dict = None + if return_input_dict: + input_dict = {k: v for k, v in zip(self.data_names, in_unnorm_data_list)} + + if self.aux_in_data_names is not None: + for k in self.aux_in_data_names: + cur_dat = data_in[k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + cur_unnorm_dat = cur_dat.reshape((B, T, self.steps_in, -1)) + input_dict[k] = cur_unnorm_dat + + # + # output + # + if data_out is not None: + out_unnorm_data_list = [] + for k in self.data_names: + cur_dat = data_out[k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + cur_unnorm_dat = cur_dat.reshape((B, T, self.steps_out, -1)) + out_unnorm_data_list.append(cur_unnorm_dat) + x_t = torch.cat(out_unnorm_data_list, axis=3) + gt_dict = {k: v for k, v in zip(self.data_names, out_unnorm_data_list)} + + if self.aux_out_data_names is not None: + for k in self.aux_out_data_names: + cur_dat = data_out[k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + cur_unnorm_dat = cur_dat.reshape((B, T, self.steps_out, -1)) + gt_dict[k] = cur_unnorm_dat + + return_list = [x_past, x_t, gt_dict] + if return_input_dict: + return_list.append(input_dict) + + # + # global + # + if return_global_dict: + global_gt_dict = dict() + for k in self.data_names: + global_k = "global_" + k + cur_dat = data_out[global_k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + # expand each to have steps_out since originally they are just B x T x ... x D + cur_dat = cur_dat.reshape((B, T, 1, -1)).expand_as(gt_dict[k]) + global_gt_dict[k] = cur_dat + + if self.aux_out_data_names is not None: + for k in self.aux_out_data_names: + global_k = "global_" + k + cur_dat = data_out[global_k].to(device) + B, T = cur_dat.size(0), cur_dat.size(1) + # expand each to have steps_out since originally they are just B x T x ... x D + cur_dat = cur_dat.reshape((B, T, 1, -1)).expand_as(gt_dict[k]) + global_gt_dict[k] = cur_dat + + return_list.append(global_gt_dict) + + return tuple(return_list) + + else: + if return_input_dict: + return x_past, input_dict + else: + return x_past + + def split_output(self, decoder_out, convert_rots=True): + """ + Given the output of the decoder, splits into each state component. + Also transform rotation representation to matrices. + + Input: + - decoder_out (B x steps_out x D) + + Returns: + - output dict + """ + B = decoder_out.size(0) + decoder_out = decoder_out.reshape((B, self.steps_out, -1)) + + # collect outputs + name_list = self.data_names + if self.aux_out_data_names is not None: + name_list = name_list + self.aux_out_data_names + idx_list = ( + self.delta_output_dim_list if self.output_delta else self.output_dim_list + ) + out_dict = dict() + sidx = 0 + for cur_name, cur_idx in zip(name_list, idx_list): + eidx = sidx + cur_idx + out_dict[cur_name] = decoder_out[:, :, sidx:eidx] + sidx = eidx + + # transform rotations + if convert_rots and not self.output_delta: # output delta already gives rotmats + if "root_orient" in self.data_names: + out_dict["root_orient"] = convert_to_rotmat( + out_dict["root_orient"], rep=self.out_rot_rep + ) + if "pose_body" in self.data_names: + out_dict["pose_body"] = convert_to_rotmat( + out_dict["pose_body"], rep=self.out_rot_rep + ) + + return out_dict + + def forward(self, x_past, x_t): + """ + single step full forward pass. This uses the posterior for sampling, not the prior. + + Input: + - x_past (B x steps_in x D) + - x_t (B x steps_out x D) + + Returns dict of: + - x_pred (B x steps_out x D) + - posterior_distrib (Normal(mu, sigma)) + - prior_distrib (Normal(mu, sigma)) + """ + + B, _, D = x_past.size() + past_in = x_past.reshape((B, -1)) + t_in = x_t.reshape((B, -1)) + + x_pred_dict = self.single_step(past_in, t_in) + + return x_pred_dict + + def single_step(self, past_in, t_in): + """ + single step that computes both prior and posterior for training. Samples from posterior + """ + B = past_in.size(0) + # use past and future to encode latent transition + qm, qv = self.posterior(past_in, t_in) + + # prior + pm, pv = None, None + if self.use_conditional_prior: + # predict prior based on past + pm, pv = self.prior(past_in) + else: + # use standard normal + pm, pv = torch.zeros_like(qm), torch.ones_like(qv) + + # sample from posterior using reparam trick + z = self.rsample(qm, qv) + + # decode to get next step + decoder_out = self.decode(z, past_in) + decoder_out = decoder_out.reshape( + (B, self.steps_out, -1) + ) # B x steps_out x D_out + + # split output predictions and transform out rotations to matrices + x_pred_dict = self.split_output(decoder_out) + + x_pred_dict["posterior_distrib"] = (qm, qv) + x_pred_dict["prior_distrib"] = (pm, pv) + + return x_pred_dict + + def prior(self, past_in): + """ + Encodes the posterior distribution using the past and future states. + + Input: + - past_in (B x steps_in*D) + """ + prior_out = self.prior_net(past_in) + mean = prior_out[:, : self.latent_size] + logvar = prior_out[:, self.latent_size :] + var = torch.exp(logvar) + return mean, var + + def posterior(self, past_in, t_in): + """ + Encodes the posterior distribution using the past and future states. + + Input: + - past_in (B x steps_in*D) + - t_in (B x steps_out*D) + """ + encoder_in = torch.cat([past_in, t_in], axis=1) + + encoder_out = self.encoder(encoder_in) + mean = encoder_out[:, : self.latent_size] + logvar = encoder_out[:, self.latent_size :] + var = torch.exp(logvar) + + return mean, var + + def rsample(self, mu, var): + """ + Return gaussian sample of (mu, var) using reparameterization trick. + """ + eps = torch.randn_like(mu) + z = mu + eps * torch.sqrt(var) + return z + + def decode(self, z, past_in): + """ + Decodes prediction from the latent transition and past states + + Input: + - z (B x latent_size) + - past_in (B x steps_in*D) + + Returns: + - decoder_out (B x steps_out*D) + """ + B = z.size(0) + decoder_in = torch.cat([past_in, z], axis=1) + decoder_out = self.decoder(decoder_in).reshape((B, 1, -1)) + + if self.output_delta: + # network output is the residual, add to the input to get final output + step_in = past_in.reshape((B, self.steps_in, -1))[ + :, -1:, : + ] # most recent input step + + final_out_list = [] + in_sidx = out_sidx = 0 + decode_out_dim_list = self.output_dim_list + if self.pred_contacts: + decode_out_dim_list = decode_out_dim_list[:-1] # do contacts separately + for in_dim_idx, out_dim_idx, data_name in zip( + self.input_dim_list, decode_out_dim_list, self.data_names + ): + in_eidx = in_sidx + in_dim_idx + out_eidx = out_sidx + out_dim_idx + + # add residual to input (and transform as necessary for rotations) + in_val = step_in[:, :, in_sidx:in_eidx] + out_val = decoder_out[:, :, out_sidx:out_eidx] + if data_name in ["root_orient", "pose_body"]: + if self.in_rot_rep != "mat": + in_val = convert_to_rotmat(in_val, rep=self.in_rot_rep) + out_val = convert_to_rotmat(out_val, rep=self.out_rot_rep) + + in_val = in_val.reshape((B, 1, -1, 3, 3)) + out_val = out_val.reshape((B, self.steps_out, -1, 3, 3)) + + rot_in = torch.matmul(out_val, in_val).reshape( + (B, self.steps_out, -1) + ) # rotate by predicted residual + final_out_list.append(rot_in) + else: + final_out_list.append(out_val + in_val) + + in_sidx = in_eidx + out_sidx = out_eidx + if self.pred_contacts: + final_out_list.append(decoder_out[:, :, out_sidx:]) + + decoder_out = torch.cat(final_out_list, dim=2) + + decoder_out = decoder_out.reshape((B, -1)) + + return decoder_out + + def scheduled_sampling( + self, + x_past, + x_t, + init_input_dict, + p=0.5, + gender=None, + betas=None, + need_global_out=True, + ): + """ + Given all inputs and ground truth outputs for all steps, roll out model predictions + where at each step use the GT input with prob p, otherwise use own previous output. + + Input: + - x_past (B x T x steps_in x D) + - x_t (B x T x steps_out x D) + - init_input_dict : dictionary of each initial state (B x steps_in x D), rotations should be matrices + - p : probability of using the GT input at each step of the sequence + - gender/betas only required if self.use_smpl_joint_inputs is true (used to decide the SMPL body model) + """ + B, T, S, D = x_past.size() + S_out = x_t.size(2) + J = len(SMPL_JOINTS) + cur_input_dict = init_input_dict # this is the predicted input dict + + # initial input must be from GT since we don't have any predictions yet + past_in = x_past[:, 0, :, :].reshape((B, -1)) + t_in = x_t[:, 0, :, :].reshape((B, -1)) + + global_world2local_rot = ( + torch.eye(3).reshape((1, 1, 3, 3)).expand((B, 1, 3, 3)).to(x_past) + ) + global_world2local_trans = torch.zeros((B, 1, 3)).to(x_past) + trans2joint = torch.zeros((B, 1, 1, 3)).to(x_past) + if self.need_trans2joint: + trans2joint = -torch.cat( + [cur_input_dict["joints"][:, -1, :2], torch.zeros((B, 1)).to(x_past)], + axis=1, + ).reshape( + (B, 1, 1, 3) + ) # same for whole sequence + pred_local_seq = [] + pred_global_seq = [] + for t in range(T): + # sample next step from model + x_pred_dict = self.single_step(past_in, t_in) + + # save output + pred_local_seq.append(x_pred_dict) + + # output is the actual regressed joints, but input to next step can use smpl joints + x_pred_smpl_joints = None + if self.use_smpl_joint_inputs and gender is not None and betas is not None: + # this assumes the model is actually outputting everything we need to run SMPL + # also assumes single output step + smpl_trans = x_pred_dict["trans"][:, 0:1].reshape( + (B, 3) + ) # only want immediate next frame + smpl_root_orient = rotation_matrix_to_angle_axis( + x_pred_dict["root_orient"][:, 0:1].reshape((B, 3, 3)) + ).reshape((B, 3)) + smpl_betas = betas[:, 0, :] + smpl_pose_body = rotation_matrix_to_angle_axis( + x_pred_dict["pose_body"][:, 0:1].reshape((B * (J - 1), 3, 3)) + ).reshape((B, (J - 1) * 3)) + + smpl_vals = [smpl_trans, smpl_root_orient, smpl_betas, smpl_pose_body] + # batch may be a mix of genders, so need to carefully use the corresponding SMPL body model + gender_names = ["male", "female", "neutral"] + pred_joints = [] + prev_nbidx = 0 + cat_idx_map = np.ones((B), dtype=np.int) * -1 + for gender_name in gender_names: + gender_idx = np.array(gender) == gender_name + nbidx = np.sum(gender_idx) + + cat_idx_map[gender_idx] = np.arange( + prev_nbidx, prev_nbidx + nbidx, dtype=np.int + ) + prev_nbidx += nbidx + + gender_smpl_vals = [val[gender_idx] for val in smpl_vals] + + # need to pad extra frames with zeros in case not as long as expected + pad_size = self.smpl_batch_size - nbidx + if pad_size == B: + # skip if no frames for this gender + continue + pad_list = gender_smpl_vals + if pad_size < 0: + raise Exception( + "SMPL model batch size not large enough to accomodate!" + ) + elif pad_size > 0: + pad_list = self.zero_pad_tensors(pad_list, pad_size) + + # reconstruct SMPL + cur_pred_trans, cur_pred_orient, cur_betas, cur_pred_pose = pad_list + bm = self.bm_dict[gender_name] + pred_body = bm( + pose_body=cur_pred_pose, + betas=cur_betas, + root_orient=cur_pred_orient, + trans=cur_pred_trans, + ) + if pad_size > 0: + pred_joints.append(pred_body.Jtr[:-pad_size]) + else: + pred_joints.append(pred_body.Jtr) + + # cat all genders and reorder to original batch ordering + x_pred_smpl_joints = torch.cat(pred_joints, axis=0)[ + :, : len(SMPL_JOINTS), : + ].reshape((B, 1, -1)) + x_pred_smpl_joints = x_pred_smpl_joints[cat_idx_map] + + # prepare predicted input to next step in case needed + # update input dict with new frame + del_keys = [] + for k in cur_input_dict.keys(): + if k in x_pred_dict: + # drop oldest frame and add new prediction + keep_frames = cur_input_dict[k][:, 1:, :] + # print(keep_frames.size()) + if ( + k == "joints" + and self.use_smpl_joint_inputs + and x_pred_smpl_joints is not None + ): + # print('Using SMPL joints rather than regressed joints...') + if self.detach_sched_samp: + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_smpl_joints.detach()], axis=1 + ) + else: + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_smpl_joints], axis=1 + ) + else: + if self.detach_sched_samp: + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_dict[k][:, 0:1, :].detach()], + axis=1, + ) + else: + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_dict[k][:, 0:1, :]], axis=1 + ) + # print(cur_input_dict[k].size()) + else: + del_keys.append(k) + for k in del_keys: + del cur_input_dict[k] # don't need it anymore + + # get world2aligned rot and translation + if self.detach_sched_samp: + root_orient_mat = ( + x_pred_dict["root_orient"][:, 0, :].reshape((B, 3, 3)).detach() + ) + world2aligned_rot = compute_world2aligned_mat(root_orient_mat) + world2aligned_trans = torch.cat( + [ + -x_pred_dict["trans"][:, 0, :2].detach(), + torch.zeros((B, 1)).to(x_past), + ], + axis=1, + ) + else: + root_orient_mat = x_pred_dict["root_orient"][:, 0, :].reshape((B, 3, 3)) + world2aligned_rot = compute_world2aligned_mat(root_orient_mat) + world2aligned_trans = torch.cat( + [-x_pred_dict["trans"][:, 0, :2], torch.zeros((B, 1)).to(x_past)], + axis=1, + ) + + # + # transform inputs to this local frame for next step + # + cur_input_dict = self.apply_world2local_trans( + world2aligned_trans, + world2aligned_rot, + trans2joint, + cur_input_dict, + cur_input_dict, + invert=False, + ) + + # convert rots to correct input format + if self.in_rot_rep == "aa": + if "root_orient" in self.data_names: + cur_input_dict["root_orient"] = rotation_matrix_to_angle_axis( + cur_input_dict["root_orient"].reshape((B * S, 3, 3)) + ).reshape((B, S, 3)) + if "pose_body" in self.data_names: + cur_input_dict["pose_body"] = rotation_matrix_to_angle_axis( + cur_input_dict["pose_body"].reshape((B * S * (J - 1), 3, 3)) + ).reshape((B, S, (J - 1) * 3)) + elif self.in_rot_rep == "6d": + if "root_orient" in self.data_names: + cur_input_dict["root_orient"] = cur_input_dict["root_orient"][ + :, :, :6 + ] + if "pose_body" in self.data_names: + cur_input_dict["pose_body"] = ( + cur_input_dict["pose_body"] + .reshape((B, S, J - 1, 9))[:, :, :, :6] + .reshape((B, S, (J - 1) * 6)) + ) + + if need_global_out: + # + # compute current world output and update world2local transform + # + cur_world_dict = dict() + cur_world_dict = self.apply_world2local_trans( + global_world2local_trans, + global_world2local_rot, + trans2joint, + x_pred_dict, + cur_world_dict, + invert=True, + ) + + if self.detach_sched_samp: + global_world2local_trans = torch.cat( + [ + -cur_world_dict["trans"][:, 0:1, :2].detach(), + torch.zeros((B, 1, 1)).to(x_past), + ], + axis=2, + ) + else: + global_world2local_trans = torch.cat( + [ + -cur_world_dict["trans"][:, 0:1, :2], + torch.zeros((B, 1, 1)).to(x_past), + ], + axis=2, + ) + + global_world2local_rot = torch.matmul( + global_world2local_rot, world2aligned_rot.reshape((B, 1, 3, 3)) + ) + + pred_global_seq.append(cur_world_dict) + + if t + 1 < T: + # choose whether next step will use GT or predicted inputs and prepare them + if np.random.random_sample() < p: + # use GT + past_in = x_past[:, t + 1, :, :].reshape((B, -1)) + else: + # cat all inputs together to form past_in + in_data_list = [] + for k in self.data_names: + in_data_list.append(cur_input_dict[k]) + past_in = torch.cat(in_data_list, axis=2) + past_in = past_in.reshape((B, -1)) + + # GT output is the same no matter what + t_in = x_t[:, t + 1, :, :].reshape((B, -1)) + + if need_global_out: + # aggregate pred_seq + pred_global_seq_out = dict() + for k in pred_global_seq[0].keys(): + if k == "posterior_distrib" or k == "prior_distrib": + m = torch.stack( + [pred_global_seq[i][k][0] for i in range(len(pred_global_seq))], + axis=1, + ) + v = torch.stack( + [pred_global_seq[i][k][1] for i in range(len(pred_global_seq))], + axis=1, + ) + pred_global_seq_out[k] = (m, v) + else: + pred_global_seq_out[k] = torch.stack( + [pred_global_seq[i][k] for i in range(len(pred_global_seq))], + axis=1, + ) + + # aggregate pred_seq + pred_local_seq_out = dict() + for k in pred_local_seq[0].keys(): + # print(k) + if k == "posterior_distrib" or k == "prior_distrib": + m = torch.stack( + [pred_local_seq[i][k][0] for i in range(len(pred_local_seq))], + axis=1, + ) + v = torch.stack( + [pred_local_seq[i][k][1] for i in range(len(pred_local_seq))], + axis=1, + ) + pred_local_seq_out[k] = (m, v) + else: + pred_local_seq_out[k] = torch.stack( + [pred_local_seq[i][k] for i in range(len(pred_local_seq))], axis=1 + ) + + if need_global_out: + return pred_global_seq_out, pred_local_seq_out + else: + return pred_local_seq_out + + def apply_world2local_trans( + self, + world2local_trans, + world2local_rot, + trans2joint, + input_dict, + output_dict, + invert=False, + ): + """ + Applies the given world2local transformation to the data in input_dict and stores the result in output_dict. + + If invert is true, applies local2world. + + - world2local_trans : B x 3 or B x 1 x 3 + - world2local_rot : B x 3 x 3 or B x 1 x 3 x 3 + - trans2joint : B x 1 x 1 x 3 + """ + B = world2local_trans.size(0) + world2local_rot = world2local_rot.reshape((B, 1, 3, 3)) + world2local_trans = world2local_trans.reshape((B, 1, 3)) + trans2joint = trans2joint.reshape((B, 1, 1, 3)) + if invert: + local2world_rot = world2local_rot.transpose(3, 2) + for k, v in input_dict.items(): + # apply differently depending on which data value it is + if k not in WORLD2ALIGN_NAME_CACHE: + # frame of reference is irrelevant, just copy to output + output_dict[k] = input_dict[k] + continue + + S = input_dict[k].size(1) + if k in ["root_orient"]: + # rot: B x S x 3 x 3 sized rotation matrix input + input_mat = input_dict[k].reshape( + (B, S, 3, 3) + ) # make sure not B x S x 9 + if invert: + output_dict[k] = torch.matmul(local2world_rot, input_mat).reshape( + (B, S, 9) + ) + else: + output_dict[k] = torch.matmul(world2local_rot, input_mat).reshape( + (B, S, 9) + ) + elif k in ["trans"]: + # trans + rot : B x S x 3 + input_trans = input_dict[k] + if invert: + output_trans = torch.matmul( + local2world_rot, input_trans.reshape((B, S, 3, 1)) + )[:, :, :, 0] + output_trans = output_trans - world2local_trans + output_dict[k] = output_trans + else: + input_trans = input_trans + world2local_trans + output_dict[k] = torch.matmul( + world2local_rot, input_trans.reshape((B, S, 3, 1)) + )[:, :, :, 0] + elif k in ["joints", "verts"]: + # trans + joint + rot : B x S x J x 3 + J = input_dict[k].size(2) // 3 + input_pts = input_dict[k].reshape((B, S, J, 3)) + if invert: + input_pts = input_pts + trans2joint + output_pts = torch.matmul( + local2world_rot.reshape((B, 1, 1, 3, 3)), + input_pts.reshape((B, S, J, 3, 1)), + )[:, :, :, :, 0] + output_pts = ( + output_pts + - trans2joint + - world2local_trans.reshape((B, 1, 1, 3)) + ) + output_dict[k] = output_pts.reshape((B, S, J * 3)) + else: + input_pts = ( + input_pts + + world2local_trans.reshape((B, 1, 1, 3)) + + trans2joint + ) + output_pts = torch.matmul( + world2local_rot.reshape((B, 1, 1, 3, 3)), + input_pts.reshape((B, S, J, 3, 1)), + )[:, :, :, :, 0] + output_pts = output_pts - trans2joint + output_dict[k] = output_pts.reshape((B, S, J * 3)) + elif k in ["joints_vel", "verts_vel"]: + # rot : B x S x J x 3 + J = input_dict[k].size(2) // 3 + input_pts = input_dict[k].reshape((B, S, J, 3, 1)) + if invert: + outuput_pts = torch.matmul( + local2world_rot.reshape((B, 1, 1, 3, 3)), input_pts + )[:, :, :, :, 0] + output_dict[k] = outuput_pts.reshape((B, S, J * 3)) + else: + output_pts = torch.matmul( + world2local_rot.reshape((B, 1, 1, 3, 3)), input_pts + )[:, :, :, :, 0] + output_dict[k] = output_pts.reshape((B, S, J * 3)) + elif k in ["trans_vel", "root_orient_vel"]: + # rot : B x S x 3 + input_pts = input_dict[k].reshape((B, S, 3, 1)) + if invert: + output_dict[k] = torch.matmul(local2world_rot, input_pts)[ + :, :, :, 0 + ] + else: + output_dict[k] = torch.matmul(world2local_rot, input_pts)[ + :, :, :, 0 + ] + else: + print( + "Received an unexpected key when transforming world2local: %s!" + % (k) + ) + exit() + + return output_dict + + def zero_pad_tensors(self, pad_list, pad_size): + """ + Assumes tensors in pad_list are B x D + """ + new_pad_list = [] + for pad_idx, pad_tensor in enumerate(pad_list): + padding = torch.zeros((pad_size, pad_tensor.size(1))).to(pad_tensor) + new_pad_list.append(torch.cat([pad_tensor, padding], dim=0)) + return new_pad_list + + def roll_out( + self, + x_past, + init_input_dict, + num_steps, + use_mean=False, + z_seq=None, + return_prior=False, + gender=None, + betas=None, + return_z=False, + canonicalize_input=False, + uncanonicalize_output=False, + ): + """ + Given input for first step, roll out using own output the entire time by sampling from the prior. + Returns the global trajectory. + + Input: + - x_past (B x steps_in x D_in) + - initial_input_dict : dictionary of each initial state (B x steps_in x D), rotations should be matrices + (assumes initial state is already in its local coordinate system (translation at [0,0,z] and aligned)) + - num_steps : the number of timesteps to roll out + - use_mean : if True, uses the mean of latent distribution instead of sampling + - z_seq : (B x steps_out x D) if given, uses as the latent input to decoder at each step rather than sampling + - return_prior : if True, also returns the output of the conditional prior at each step + -gender : list of e.g. ['male', 'female', etc..] of length B + -betas : B x steps_in x D + -return_z : returns the sampled z sequence in addition to the output + - canonicalize_input : if true, the input initial state is assumed to not be in the local aligned coordinate system. It will be transformed before using. + - uncanonicalize_output : if true and canonicalize_input=True, will transform output back into the input frame rather than return in canonical frame. + Returns: + - x_pred - dict of (B x num_steps x D_out) for each value. Rotations are all matrices. + """ + J = len(SMPL_JOINTS) + cur_input_dict = init_input_dict + + # need to transform init input to local frame + world2aligned_rot = world2aligned_trans = None + if canonicalize_input: + B, _, _ = cur_input_dict[list(cur_input_dict.keys())[0]].size() + # must transform initial input into the local frame + # get world2aligned rot and translation + root_orient_mat = cur_input_dict["root_orient"] + pose_body_mat = cur_input_dict["pose_body"] + if "root_orient" in self.data_names and self.in_rot_rep != "mat": + root_orient_mat = convert_to_rotmat( + root_orient_mat, rep=self.in_rot_rep + ) + if "pose_body" in self.data_names and self.in_rot_rep != "mat": + pose_body_mat = convert_to_rotmat(pose_body_mat, rep=self.in_rot_rep) + + root_orient_mat = root_orient_mat[:, -1].reshape((B, 3, 3)) + world2aligned_rot = compute_world2aligned_mat(root_orient_mat) + world2aligned_trans = torch.cat( + [ + -cur_input_dict["trans"][:, -1, :2], + torch.zeros((B, 1)).to(root_orient_mat), + ], + axis=1, + ) + + # compute trans2joint + if self.need_trans2joint: + trans2joint = -( + cur_input_dict["joints"][:, -1, :2] + world2aligned_trans[:, :2] + ) + trans2joint = torch.cat( + [trans2joint, torch.zeros((B, 1)).to(trans2joint)], axis=1 + ).reshape((B, 1, 1, 3)) + + # transform to local frame + cur_input_dict = self.apply_world2local_trans( + world2aligned_trans, + world2aligned_rot, + trans2joint, + cur_input_dict, + cur_input_dict, + invert=False, + ) + + # check to make sure we have enough input steps, if not, pad + pad_x_past = x_past is not None and x_past.size(1) < self.steps_in + pad_in_dict = ( + cur_input_dict[list(cur_input_dict.keys())[0]].size(1) < self.steps_in + ) + if pad_x_past: + num_pad_steps = self.steps_in - x_past.size(1) + cur_padding = torch.zeros( + (x_past.size(0), num_pad_steps, x_past.size(2)) + ).to( + x_past + ) # assuming all data is B x T x D + x_past = torch.cat([cur_padding, x_past], axis=1) + if pad_in_dict: + for k in cur_input_dict.keys(): + cur_in_dat = cur_input_dict[k] + num_pad_steps = self.steps_in - cur_in_dat.size(1) + cur_padding = torch.zeros( + (cur_in_dat.size(0), num_pad_steps, cur_in_dat.size(2)) + ).to( + cur_in_dat + ) # assuming all data is B x T x D + padded_in_dat = torch.cat([cur_padding, cur_in_dat], axis=1) + cur_input_dict[k] = padded_in_dat + + if x_past is None or canonicalize_input: + x_past = [cur_input_dict[k] for k in self.data_names] + x_past = torch.cat(x_past, axis=2) + B, S, D = x_past.size() + past_in = x_past.reshape((B, -1)) + + global_world2local_rot = ( + torch.eye(3).reshape((1, 1, 3, 3)).expand((B, 1, 3, 3)).to(x_past) + ) + global_world2local_trans = torch.zeros((B, 1, 3)).to(x_past) + if canonicalize_input and uncanonicalize_output: + global_world2local_rot = world2aligned_rot.unsqueeze(1) + global_world2local_trans = world2aligned_trans.unsqueeze(1) + trans2joint = torch.zeros((B, 1, 1, 3)).to(x_past) + if self.need_trans2joint: + trans2joint = -torch.cat( + [cur_input_dict["joints"][:, -1, :2], torch.zeros((B, 1)).to(x_past)], + axis=1, + ).reshape( + (B, 1, 1, 3) + ) # same for whole sequence + pred_local_seq = [] + pred_global_seq = [] + prior_seq = [] + z_out_seq = [] + for t in range(num_steps): + x_pred_dict = None + # sample next step + z_in = None + if z_seq is not None: + z_in = z_seq[:, t] + sample_out = self.sample_step( + past_in, + use_mean=use_mean, + z=z_in, + return_prior=return_prior, + return_z=return_z, + ) + if return_prior: + prior_out = sample_out["prior"] + prior_seq.append(prior_out) + if return_z: + z_out = sample_out["z"] + z_out_seq.append(z_out) + decoder_out = sample_out["decoder_out"] + + # split output predictions and transform out rotations to matrices + x_pred_dict = self.split_output(decoder_out, convert_rots=True) + if self.steps_out > 1: + for k in x_pred_dict.keys(): + # only want immediate next frame prediction + x_pred_dict[k] = x_pred_dict[k][:, 0:1, :] + + pred_local_seq.append(x_pred_dict) + + # output is the actual regressed joints, but input to next step can use smpl joints + x_pred_smpl_joints = None + if self.use_smpl_joint_inputs and gender is not None and betas is not None: + # this assumes the model is actually outputting everything we need to run SMPL + # also assumes single output step + smpl_trans = x_pred_dict["trans"].reshape((B, 3)) + smpl_root_orient = rotation_matrix_to_angle_axis( + x_pred_dict["root_orient"].reshape((B, 3, 3)) + ).reshape((B, 3)) + smpl_betas = betas[:, 0, :] + smpl_pose_body = rotation_matrix_to_angle_axis( + x_pred_dict["pose_body"].reshape((B * (J - 1), 3, 3)) + ).reshape((B, (J - 1) * 3)) + + smpl_vals = [smpl_trans, smpl_root_orient, smpl_betas, smpl_pose_body] + # each batch index may be a different gender + gender_names = ["male", "female", "neutral"] + pred_joints = [] + prev_nbidx = 0 + cat_idx_map = np.ones((B), dtype=np.int) * -1 + for gender_name in gender_names: + gender_idx = np.array(gender) == gender_name + nbidx = np.sum(gender_idx) + cat_idx_map[gender_idx] = np.arange( + prev_nbidx, prev_nbidx + nbidx, dtype=np.int + ) + prev_nbidx += nbidx + + gender_smpl_vals = [val[gender_idx] for val in smpl_vals] + + # need to pad extra frames with zeros in case not as long as expected + pad_size = self.smpl_batch_size - nbidx + if pad_size == B: + # skip if no frames for this gender + continue + pad_list = gender_smpl_vals + if pad_size < 0: + raise Exception( + "SMPL model batch size not large enough to accomodate!" + ) + elif pad_size > 0: + pad_list = self.zero_pad_tensors(pad_list, pad_size) + + # reconstruct SMPL + cur_pred_trans, cur_pred_orient, cur_betas, cur_pred_pose = pad_list + bm = self.bm_dict[gender_name] + pred_body = bm( + pose_body=cur_pred_pose, + betas=cur_betas, + root_orient=cur_pred_orient, + trans=cur_pred_trans, + ) + if pad_size > 0: + pred_joints.append(pred_body.Jtr[:-pad_size]) + else: + pred_joints.append(pred_body.Jtr) + + # cat all genders and reorder to original batch ordering + x_pred_smpl_joints = torch.cat(pred_joints, axis=0)[ + :, : len(SMPL_JOINTS), : + ].reshape((B, 1, -1)) + x_pred_smpl_joints = x_pred_smpl_joints[cat_idx_map] + + # prepare input to next step + # update input dict with new frame + del_keys = [] + for k in cur_input_dict.keys(): + if k in x_pred_dict: + # drop oldest frame and add new prediction + keep_frames = cur_input_dict[k][:, 1:, :] + # print(keep_frames.size()) + + if ( + k == "joints" + and self.use_smpl_joint_inputs + and x_pred_smpl_joints is not None + ): + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_smpl_joints], axis=1 + ) + else: + cur_input_dict[k] = torch.cat( + [keep_frames, x_pred_dict[k]], axis=1 + ) + else: + del_keys.append(k) + for k in del_keys: + del cur_input_dict[k] + + # get world2aligned rot and translation + root_orient_mat = x_pred_dict["root_orient"][:, 0, :].reshape((B, 3, 3)) + world2aligned_rot = compute_world2aligned_mat(root_orient_mat) + world2aligned_trans = torch.cat( + [-x_pred_dict["trans"][:, 0, :2], torch.zeros((B, 1)).to(x_past)], + axis=1, + ) + + # + # transform inputs to this local frame (body pose is not affected) for next step + # + cur_input_dict = self.apply_world2local_trans( + world2aligned_trans, + world2aligned_rot, + trans2joint, + cur_input_dict, + cur_input_dict, + invert=False, + ) + + # convert rots to correct input format + if self.in_rot_rep == "aa": + if "root_orient" in self.data_names: + cur_input_dict["root_orient"] = rotation_matrix_to_angle_axis( + cur_input_dict["root_orient"].reshape((B * S, 3, 3)) + ).reshape((B, S, 3)) + if "pose_body" in self.data_names: + cur_input_dict["pose_body"] = rotation_matrix_to_angle_axis( + cur_input_dict["pose_body"].reshape((B * S * (J - 1), 3, 3)) + ).reshape((B, S, (J - 1) * 3)) + elif self.in_rot_rep == "6d": + if "root_orient" in self.data_names: + cur_input_dict["root_orient"] = cur_input_dict["root_orient"][ + :, :, :6 + ] + if "pose_body" in self.data_names: + cur_input_dict["pose_body"] = ( + cur_input_dict["pose_body"] + .reshape((B, S, J - 1, 9))[:, :, :, :6] + .reshape((B, S, (J - 1) * 6)) + ) + + # + # compute current world output and update world2local transform + # + cur_world_dict = dict() + cur_world_dict = self.apply_world2local_trans( + global_world2local_trans, + global_world2local_rot, + trans2joint, + x_pred_dict, + cur_world_dict, + invert=True, + ) + # + # update world2local transform + # + global_world2local_trans = torch.cat( + [ + -cur_world_dict["trans"][:, 0:1, :2], + torch.zeros((B, 1, 1)).to(x_past), + ], + axis=2, + ) + # print(world2aligned_rot) + global_world2local_rot = torch.matmul( + global_world2local_rot, world2aligned_rot.reshape((B, 1, 3, 3)) + ) + + pred_global_seq.append(cur_world_dict) + + # cat all inputs together to form past_in + in_data_list = [] + for k in self.data_names: + in_data_list.append(cur_input_dict[k]) + past_in = torch.cat(in_data_list, axis=2) + past_in = past_in.reshape((B, -1)) + + # aggregate global pred_seq + pred_seq_out = dict() + for k in pred_global_seq[0].keys(): + pred_seq_out[k] = torch.cat( + [pred_global_seq[i][k] for i in range(len(pred_global_seq))], axis=1 + ) + + if return_z: + z_out_seq = torch.stack(z_out_seq, dim=1) + pred_seq_out["z"] = z_out_seq + + if return_prior: + pm = torch.stack([prior_seq[i][0] for i in range(len(prior_seq))], axis=1) + pv = torch.stack([prior_seq[i][1] for i in range(len(prior_seq))], axis=1) + return pred_seq_out, (pm, pv) + else: + return pred_seq_out + + def sample_step( + self, + past_in, + t_in=None, + use_mean=False, + z=None, + return_prior=False, + return_z=False, + ): + """ + Given past, samples next future state by sampling from prior or posterior and decoding. + If z (B x D) is not None, uses the given z instead of sampling from posterior or prior + + Returns: + - decoder_out : (B x steps_out x D) output of the decoder for the immediate next step + """ + B = past_in.size(0) + + pm, pv = None, None + if t_in is not None: + # use past and future to encode latent transition + pm, pv = self.posterior(past_in, t_in) + else: + # prior + if self.use_conditional_prior: + # predict prior based on past + pm, pv = self.prior(past_in) + else: + # use standard normal + pm, pv = torch.zeros((B, self.latent_size)).to(past_in), torch.ones( + (B, self.latent_size) + ).to(past_in) + + # sample from distrib or use mean + if z is None: + if not use_mean: + z = self.rsample(pm, pv) + else: + z = pm # NOTE: use mean + + # decode to get next step + decoder_out = self.decode(z, past_in) + decoder_out = decoder_out.reshape( + (B, self.steps_out, -1) + ) # B x steps_out x D_out + + out_dict = {"decoder_out": decoder_out} + if return_prior: + out_dict["prior"] = (pm, pv) + if return_z: + out_dict["z"] = z + + return out_dict + + def infer_global_seq(self, global_seq, full_forward_pass=False): + """ + Given a sequence of global states, formats it (transform each step into local frame and makde B x steps_in x D) + and runs inference (compute prior/posterior of z for the sequence). + + If full_forward_pass is true, does an entire forward pass at each step rather than just inference. + + Rotations should be in in_rot_rep format. + """ + # used to compute output zero padding + needed_future_steps = (self.steps_out - 1) * self.out_step_size + + prior_m_seq = [] + prior_v_seq = [] + post_m_seq = [] + post_v_seq = [] + pred_dict_seq = [] + B, T, _ = global_seq[list(global_seq.keys())[0]].size() + J = len(SMPL_JOINTS) + trans2joint = None + for t in range(T - 1): + # get world2aligned rot and translation + world2aligned_rot = world2aligned_trans = None + + root_orient_mat = global_seq["root_orient"][:, t, :].reshape((B, 3, 3)) + world2aligned_rot = compute_world2aligned_mat(root_orient_mat) + world2aligned_trans = torch.cat( + [ + -global_seq["trans"][:, t, :2], + torch.zeros((B, 1)).to(root_orient_mat), + ], + axis=1, + ) + + # compute trans2joint at first step + if t == 0 and self.need_trans2joint: + trans2joint = -( + global_seq["joints"][:, t, :2] + world2aligned_trans[:, :2] + ) # we cannot make the assumption that the first frame is already canonical + trans2joint = torch.cat( + [trans2joint, torch.zeros((B, 1)).to(trans2joint)], axis=1 + ).reshape((B, 1, 1, 3)) + + # get current window + cur_data_dict = dict() + for k in global_seq.keys(): + # get in steps + in_sidx = max(0, t - self.steps_in + 1) + cur_in_seq = global_seq[k][:, in_sidx : (t + 1), :] + if cur_in_seq.size(1) < self.steps_in: + # must zero pad front + num_pad_steps = self.steps_in - cur_in_seq.size(1) + cur_padding = torch.zeros( + (cur_in_seq.size(0), num_pad_steps, cur_in_seq.size(2)) + ).to( + cur_in_seq + ) # assuming all data is B x T x D + cur_in_seq = torch.cat([cur_padding, cur_in_seq], axis=1) + + # get out steps + cur_out_seq = global_seq[k][ + :, (t + 1) : (t + 2 + needed_future_steps) : self.out_step_size + ] + if cur_out_seq.size(1) < self.steps_out: + # zero pad + num_pad_steps = self.steps_out - cur_out_seq.size(1) + cur_padding = torch.zeros_like(cur_out_seq[:, 0]) + cur_padding = torch.stack([cur_padding] * num_pad_steps, axis=1) + cur_out_seq = torch.cat([cur_out_seq, cur_padding], axis=1) + cur_data_dict[k] = torch.cat([cur_in_seq, cur_out_seq], axis=1) + + # transform to local frame + cur_data_dict = self.apply_world2local_trans( + world2aligned_trans, + world2aligned_rot, + trans2joint, + cur_data_dict, + cur_data_dict, + invert=False, + ) + + # create x_past and x_t + # cat all inputs together to form past_in + in_data_list = [] + for k in self.data_names: + in_data_list.append(cur_data_dict[k][:, : self.steps_in, :]) + x_past = torch.cat(in_data_list, axis=2) + # cat all outputs together to form x_t + out_data_list = [] + for k in self.data_names: + out_data_list.append(cur_data_dict[k][:, self.steps_in :, :]) + x_t = torch.cat(out_data_list, axis=2) + + if full_forward_pass: + x_pred_dict = self(x_past, x_t) + pred_dict_seq.append(x_pred_dict) + else: + # perform inference + prior_z, posterior_z = self.infer(x_past, x_t) + # save z + prior_m_seq.append(prior_z[0]) + prior_v_seq.append(prior_z[1]) + post_m_seq.append(posterior_z[0]) + post_v_seq.append(posterior_z[1]) + + if full_forward_pass: + # pred_dict_seq + pred_seq_out = dict() + for k in pred_dict_seq[0].keys(): + # print(k) + if k == "posterior_distrib" or k == "prior_distrib": + m = torch.stack( + [pred_dict_seq[i][k][0] for i in range(len(pred_dict_seq))], + axis=1, + ) + v = torch.stack( + [pred_dict_seq[i][k][1] for i in range(len(pred_dict_seq))], + axis=1, + ) + pred_seq_out[k] = (m, v) + else: + pred_seq_out[k] = torch.stack( + [pred_dict_seq[i][k] for i in range(len(pred_dict_seq))], axis=1 + ) + + return pred_seq_out + else: + prior_m_seq = torch.stack(prior_m_seq, axis=1) + prior_v_seq = torch.stack(prior_v_seq, axis=1) + post_m_seq = torch.stack(post_m_seq, axis=1) + post_v_seq = torch.stack(post_v_seq, axis=1) + + return (prior_m_seq, prior_v_seq), (post_m_seq, post_v_seq) + + def infer(self, x_past, x_t): + """ + Inference (compute prior and posterior distribution of z) for a batch of single steps. + NOTE: must do processing before passing in to ensure correct format that this function expects. + + Input: + - x_past (B x steps_in x D) + - x_t (B x steps_out x D) + + Returns: + - prior_distrib (mu, var) + - posterior_distrib (mu, var) + """ + + B, _, D = x_past.size() + past_in = x_past.reshape((B, -1)) + t_in = x_t.reshape((B, -1)) + + prior_z, posterior_z = self.infer_step(past_in, t_in) + + return prior_z, posterior_z + + def infer_step(self, past_in, t_in): + """ + single step that computes both prior and posterior for training. Samples from posterior + """ + B = past_in.size(0) + # use past and future to encode latent transition + qm, qv = self.posterior(past_in, t_in) + + # prior + pm, pv = None, None + if self.use_conditional_prior: + # predict prior based on past + pm, pv = self.prior(past_in) + else: + # use standard normal + pm, pv = torch.zeros_like(qm), torch.ones_like(qv) + + return (pm, pv), (qm, qv) + + +class MLP(nn.Module): + def __init__( + self, + layers=[3, 128, 128, 3], + nonlinearity=nn.ReLU, + use_gn=True, + skip_input_idx=None, + ): + """ + If skip_input_idx is not None, the input feature after idx skip_input_idx will be skip connected to every later of the MLP. + """ + super(MLP, self).__init__() + + in_size = layers[0] + out_channels = layers[1:] + + # input layer + layers = [] + layers.append(nn.Linear(in_size, out_channels[0])) + skip_size = 0 if skip_input_idx is None else (in_size - skip_input_idx) + # now the rest + for layer_idx in range(1, len(out_channels)): + fc_layer = nn.Linear( + out_channels[layer_idx - 1] + skip_size, out_channels[layer_idx] + ) + if use_gn: + bn_layer = nn.GroupNorm(16, out_channels[layer_idx - 1]) + layers.append(bn_layer) + layers.extend([nonlinearity(), fc_layer]) + self.net = nn.ModuleList(layers) + self.skip_input_idx = skip_input_idx + + def forward(self, x): + """ + B x D x * : batch norm done over dim D + """ + skip_in = None + if self.skip_input_idx is not None: + skip_in = x[:, self.skip_input_idx :] + for i, layer in enumerate(self.net): + if ( + self.skip_input_idx is not None + and i > 0 + and isinstance(layer, nn.Linear) + ): + x = torch.cat([x, skip_in], dim=1) + x = layer(x) + return x diff --git a/slahmr/slahmr/humor/transforms.py b/slahmr/slahmr/humor/transforms.py new file mode 100644 index 0000000000000000000000000000000000000000..5eedbae14b8875d4a0a2d6c5b541862805da3a0b --- /dev/null +++ b/slahmr/slahmr/humor/transforms.py @@ -0,0 +1,472 @@ +""" +Taken from https://github.com/davrempe/humor +""" + +import copy + +import torch +import numpy as np +from torch.nn import functional as F + +from body_model.utils import SMPL_JOINTS + +# +# For computing local body frame +# + +GLOB_DEVICE = ( + torch.device("cuda:0") if torch.cuda.is_available() else torch.device("cpu") +) +XY_AXIS_GLOB = torch.Tensor([[1.0, 1.0, 0.0]]).to(device=GLOB_DEVICE) +X_AXIS_GLOB = torch.Tensor([[1.0, 0.0, 0.0]]).to(device=GLOB_DEVICE) + + +def compute_aligned_from_right(body_right): + xy_axis = XY_AXIS_GLOB + x_axis = X_AXIS_GLOB + + body_right_x_proj = body_right[:, 0:1] / ( + torch.norm(body_right[:, :2], dim=1, keepdim=True) + 1e-6 + ) + body_right_x_proj = torch.clamp( + body_right_x_proj, min=-1.0, max=1.0 + ) # avoid acos error + + world2aligned_angle = torch.acos( + body_right_x_proj + ) # project to world x axis, and compute angle + body_right = body_right * xy_axis + world2aligned_axis = torch.linalg.cross(body_right, x_axis.expand_as(body_right)) + + world2aligned_aa = ( + world2aligned_axis + / (torch.norm(world2aligned_axis, dim=1, keepdim=True) + 1e-6) + ) * world2aligned_angle + world2aligned_mat = batch_rodrigues(world2aligned_aa) + + return world2aligned_mat, world2aligned_aa + + +def compute_world2aligned_mat(rot_pos): + """ + batch of world rotation matrices: B x 3 x 3 + returns rot mats that align the inputs to the forward direction: B x 3 x 3 + Torch version + """ + body_right = -rot_pos[:, :, 0] # .clone() # in body coordinates body x-axis is left + + world2aligned_mat, world2aligned_aa = compute_aligned_from_right(body_right) + return world2aligned_mat + + +def compute_world2aligned_joints_mat(joints): + """ + Compute world to canonical frame (rotation around up axis) + from the given batch of joints (B x J x 3) + """ + left_idx = SMPL_JOINTS["leftUpLeg"] + right_idx = SMPL_JOINTS["rightUpLeg"] + + body_right = joints[:, right_idx] - joints[:, left_idx] + body_right = body_right / torch.norm(body_right, dim=1, keepdim=True) + + world2aligned_mat, world2aligned_aa = compute_aligned_from_right(body_right) + + return world2aligned_mat + + +def convert_to_rotmat(pred_rot, rep="aa"): + """ + Converts rotation rep to rotation matrix based on the given type. + pred_rot : B x T x N + """ + B, T, _ = pred_rot.size() + pred_rot_mat = None + if rep == "aa": + pred_rot_mat = batch_rodrigues(pred_rot.reshape(-1, 3)) + elif rep == "6d": + pred_rot_mat = rot6d_to_rotmat(pred_rot.reshape(-1, 6)) + elif rep == "9d": + pred_rot_mat = rot9d_to_rotmat(pred_rot.reshape(-1, 9)) + return pred_rot_mat.reshape((B, T, -1)) + + +# +# Many of these functions taken from https://github.com/mkocabas/VIBE/blob/a859e45a907379aa2fba65a7b620b4a2d65dcf1b/lib/utils/geometry.py +# Please see their license for usage restrictions. +# + + +def matrot2axisangle(matrots): + """ + :param matrots: N*num_joints*9 + :return: N*num_joints*3 + """ + import cv2 + + batch_size = matrots.shape[0] + matrots = matrots.reshape([batch_size, -1, 9]) + out_axisangle = [] + for mIdx in range(matrots.shape[0]): + cur_axisangle = [] + for jIdx in range(matrots.shape[1]): + a = cv2.Rodrigues(matrots[mIdx, jIdx : jIdx + 1, :].reshape(3, 3))[ + 0 + ].reshape((1, 3)) + cur_axisangle.append(a) + + out_axisangle.append(np.array(cur_axisangle).reshape([1, -1, 3])) + return np.vstack(out_axisangle) + + +def axisangle2matrots(axisangle): + """ + :param axisangle: N*num_joints*3 + :return: N*num_joints*9 + """ + import cv2 + + batch_size = axisangle.shape[0] + axisangle = axisangle.reshape([batch_size, -1, 3]) + out_matrot = [] + for mIdx in range(axisangle.shape[0]): + cur_axisangle = [] + for jIdx in range(axisangle.shape[1]): + a = cv2.Rodrigues(axisangle[mIdx, jIdx : jIdx + 1, :].reshape(1, 3))[0] + cur_axisangle.append(a) + + out_matrot.append(np.array(cur_axisangle).reshape([1, -1, 9])) + return np.vstack(out_matrot) + + +def make_rot_homog(rotation_matrix): + if rotation_matrix.shape[1:] == (3, 3): + rot_mat = rotation_matrix.reshape(-1, 3, 3) + hom = ( + torch.tensor([0, 0, 1], dtype=torch.float32, device=rotation_matrix.device) + .reshape(1, 3, 1) + .expand(rot_mat.shape[0], -1, -1) + ) + rotation_matrix = torch.cat([rot_mat, hom], dim=-1) + return rotation_matrix + + +def skew(v): + """ + Returns skew symmetric (B x 3 x 3) mat from vector v: B x 3 + """ + B, D = v.size() + assert D == 3 + skew_mat = torch.zeros((B, 3, 3)).to(v) + skew_mat[:, 0, 1] = v[:, 2] + skew_mat[:, 1, 0] = -v[:, 2] + skew_mat[:, 0, 2] = v[:, 1] + skew_mat[:, 2, 0] = -v[:, 1] + skew_mat[:, 1, 2] = v[:, 0] + skew_mat[:, 2, 1] = -v[:, 0] + return skew_mat + + +def batch_rodrigues(rot_vecs, epsilon=1e-8, dtype=torch.float32): + """Calculates the rotation matrices for a batch of rotation vectors + Parameters + ---------- + rot_vecs: torch.tensor Nx3 + array of N axis-angle vectors + Returns + ------- + R: torch.tensor Nx3x3 + The rotation matrices for the given axis-angle parameters + """ + + batch_size = rot_vecs.shape[0] + device = rot_vecs.device + + angle = torch.norm(rot_vecs + 1e-8, dim=1, keepdim=True) + rot_dir = rot_vecs / angle + + cos = torch.unsqueeze(torch.cos(angle), dim=1) + sin = torch.unsqueeze(torch.sin(angle), dim=1) + + # Bx1 arrays + rx, ry, rz = torch.split(rot_dir, 1, dim=1) + K = torch.zeros((batch_size, 3, 3), dtype=dtype, device=device) + + zeros = torch.zeros((batch_size, 1), dtype=dtype, device=device) + K = torch.cat([zeros, -rz, ry, rz, zeros, -rx, -ry, rx, zeros], dim=1).view( + (batch_size, 3, 3) + ) + + ident = torch.eye(3, dtype=dtype, device=device).unsqueeze(dim=0) + rot_mat = ident + sin * K + (1 - cos) * torch.bmm(K, K) + return rot_mat + + +def quat2mat(quat): + """ + This function is borrowed from https://github.com/MandyMo/pytorch_HMR/blob/master/src/util.py#L50 + Convert quaternion coefficients to rotation matrix. + Args: + quat: size = [batch_size, 4] 4 <===>(w, x, y, z) + Returns: + Rotation matrix corresponding to the quaternion -- size = [batch_size, 3, 3] + """ + norm_quat = quat + norm_quat = norm_quat / norm_quat.norm(p=2, dim=1, keepdim=True) + w, x, y, z = norm_quat[:, 0], norm_quat[:, 1], norm_quat[:, 2], norm_quat[:, 3] + + batch_size = quat.size(0) + + w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2) + wx, wy, wz = w * x, w * y, w * z + xy, xz, yz = x * y, x * z, y * z + + rotMat = torch.stack( + [ + w2 + x2 - y2 - z2, + 2 * xy - 2 * wz, + 2 * wy + 2 * xz, + 2 * wz + 2 * xy, + w2 - x2 + y2 - z2, + 2 * yz - 2 * wx, + 2 * xz - 2 * wy, + 2 * wx + 2 * yz, + w2 - x2 - y2 + z2, + ], + dim=1, + ).view(batch_size, 3, 3) + return rotMat + + +def rot6d_to_rotmat(x): + """Convert 6D rotation representation to 3x3 rotation matrix. + Based on Zhou et al., "On the Continuity of Rotation Representations in Neural Networks", CVPR 2019 + Input: + (B,6) Batch of 6-D rotation representations + Output: + (B,3,3) Batch of corresponding rotation matrices + """ + x = x.view(-1, 3, 2) + a1 = x[:, :, 0] + a2 = x[:, :, 1] + b1 = F.normalize(a1) + b2 = F.normalize(a2 - torch.einsum("bi,bi->b", b1, a2).unsqueeze(-1) * b1) + + # inp = a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1 + # denom = inp.pow(2).sum(dim=1).sqrt().unsqueeze(-1) + 1e-8 + # b2 = inp / denom + + b3 = torch.linalg.cross(b1, b2) + return torch.stack((b1, b2, b3), dim=-1) + + +def rot9d_to_rotmat(x): + """ + Converts 9D rotation output to valid 3x3 rotation amtrix. + Based on Levinson et al., An Analysis of SVD for Deep Rotation Estimation. + + Input: + (B, 9) + Output: + (B, 9) + """ + B = x.size()[0] + x = x.reshape((B, 3, 3)) + u, s, v = torch.svd(x) + + v_T = v.transpose(-2, -1) + s_p = torch.eye(3).to(x).reshape((1, 3, 3)).expand_as(x).clone() + s_p[:, 2, 2] = torch.det(torch.matmul(u, v_T)) + x_out = torch.matmul(torch.matmul(u, s_p), v_T) + + return x_out.reshape((B, 9)) + + +def rotation_matrix_to_angle_axis(rotation_matrix): + """ + This function is borrowed from https://github.com/kornia/kornia + Convert 3x4 rotation matrix to Rodrigues vector + Args: + rotation_matrix (Tensor): rotation matrix. + Returns: + Tensor: Rodrigues vector transformation. + Shape: + - Input: :math:`(N, 3, 4)` + - Output: :math:`(N, 3)` + Example: + >>> input = torch.rand(2, 3, 4) # Nx4x4 + >>> output = tgm.rotation_matrix_to_angle_axis(input) # Nx3 + """ + if rotation_matrix.shape[1:] == (3, 3): + rot_mat = rotation_matrix.reshape(-1, 3, 3) + hom = ( + torch.tensor([0, 0, 1], dtype=torch.float32, device=rotation_matrix.device) + .reshape(1, 3, 1) + .expand(rot_mat.shape[0], -1, -1) + ) + rotation_matrix = torch.cat([rot_mat, hom], dim=-1) + + quaternion = rotation_matrix_to_quaternion(rotation_matrix) + aa = quaternion_to_angle_axis(quaternion) + aa[torch.isnan(aa)] = 0.0 + return aa + + +def rotation_matrix_to_quaternion(rotation_matrix, eps=1e-6): + """ + This function is borrowed from https://github.com/kornia/kornia + Convert 3x4 rotation matrix to 4d quaternion vector + This algorithm is based on algorithm described in + https://github.com/KieranWynn/pyquaternion/blob/master/pyquaternion/quaternion.py#L201 + Args: + rotation_matrix (Tensor): the rotation matrix to convert. + Return: + Tensor: the rotation in quaternion + Shape: + - Input: :math:`(N, 3, 4)` + - Output: :math:`(N, 4)` + Example: + >>> input = torch.rand(4, 3, 4) # Nx3x4 + >>> output = tgm.rotation_matrix_to_quaternion(input) # Nx4 + """ + if not torch.is_tensor(rotation_matrix): + raise TypeError( + "Input type is not a torch.Tensor. Got {}".format(type(rotation_matrix)) + ) + + if len(rotation_matrix.shape) > 3: + raise ValueError( + "Input size must be a three dimensional tensor. Got {}".format( + rotation_matrix.shape + ) + ) + if not rotation_matrix.shape[-2:] == (3, 4): + raise ValueError( + "Input size must be a N x 3 x 4 tensor. Got {}".format( + rotation_matrix.shape + ) + ) + + rmat_t = torch.transpose(rotation_matrix, 1, 2) + + mask_d2 = rmat_t[:, 2, 2] < eps + + mask_d0_d1 = rmat_t[:, 0, 0] > rmat_t[:, 1, 1] + mask_d0_nd1 = rmat_t[:, 0, 0] < -rmat_t[:, 1, 1] + + t0 = 1 + rmat_t[:, 0, 0] - rmat_t[:, 1, 1] - rmat_t[:, 2, 2] + q0 = torch.stack( + [ + rmat_t[:, 1, 2] - rmat_t[:, 2, 1], + t0, + rmat_t[:, 0, 1] + rmat_t[:, 1, 0], + rmat_t[:, 2, 0] + rmat_t[:, 0, 2], + ], + -1, + ) + t0_rep = t0.repeat(4, 1).t() + + t1 = 1 - rmat_t[:, 0, 0] + rmat_t[:, 1, 1] - rmat_t[:, 2, 2] + q1 = torch.stack( + [ + rmat_t[:, 2, 0] - rmat_t[:, 0, 2], + rmat_t[:, 0, 1] + rmat_t[:, 1, 0], + t1, + rmat_t[:, 1, 2] + rmat_t[:, 2, 1], + ], + -1, + ) + t1_rep = t1.repeat(4, 1).t() + + t2 = 1 - rmat_t[:, 0, 0] - rmat_t[:, 1, 1] + rmat_t[:, 2, 2] + q2 = torch.stack( + [ + rmat_t[:, 0, 1] - rmat_t[:, 1, 0], + rmat_t[:, 2, 0] + rmat_t[:, 0, 2], + rmat_t[:, 1, 2] + rmat_t[:, 2, 1], + t2, + ], + -1, + ) + t2_rep = t2.repeat(4, 1).t() + + t3 = 1 + rmat_t[:, 0, 0] + rmat_t[:, 1, 1] + rmat_t[:, 2, 2] + q3 = torch.stack( + [ + t3, + rmat_t[:, 1, 2] - rmat_t[:, 2, 1], + rmat_t[:, 2, 0] - rmat_t[:, 0, 2], + rmat_t[:, 0, 1] - rmat_t[:, 1, 0], + ], + -1, + ) + t3_rep = t3.repeat(4, 1).t() + + mask_c0 = mask_d2 * mask_d0_d1 + mask_c1 = mask_d2 * ~mask_d0_d1 + mask_c2 = ~mask_d2 * mask_d0_nd1 + mask_c3 = ~mask_d2 * ~mask_d0_nd1 + mask_c0 = mask_c0.view(-1, 1).type_as(q0) + mask_c1 = mask_c1.view(-1, 1).type_as(q1) + mask_c2 = mask_c2.view(-1, 1).type_as(q2) + mask_c3 = mask_c3.view(-1, 1).type_as(q3) + + q = q0 * mask_c0 + q1 * mask_c1 + q2 * mask_c2 + q3 * mask_c3 + q /= torch.sqrt( + t0_rep * mask_c0 + + t1_rep * mask_c1 + + t2_rep * mask_c2 # noqa + + t3_rep * mask_c3 + ) # noqa + q *= 0.5 + return q + + +def quaternion_to_angle_axis(quaternion: torch.Tensor) -> torch.Tensor: + """ + This function is borrowed from https://github.com/kornia/kornia + Convert quaternion vector to angle axis of rotation. + Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h + Args: + quaternion (torch.Tensor): tensor with quaternions. + Return: + torch.Tensor: tensor with angle axis of rotation. + Shape: + - Input: :math:`(*, 4)` where `*` means, any number of dimensions + - Output: :math:`(*, 3)` + Example: + >>> quaternion = torch.rand(2, 4) # Nx4 + >>> angle_axis = tgm.quaternion_to_angle_axis(quaternion) # Nx3 + """ + if not torch.is_tensor(quaternion): + raise TypeError( + "Input type is not a torch.Tensor. Got {}".format(type(quaternion)) + ) + + if not quaternion.shape[-1] == 4: + raise ValueError( + "Input must be a tensor of shape Nx4 or 4. Got {}".format(quaternion.shape) + ) + # unpack input and compute conversion + q1: torch.Tensor = quaternion[..., 1] + q2: torch.Tensor = quaternion[..., 2] + q3: torch.Tensor = quaternion[..., 3] + sin_squared_theta: torch.Tensor = q1 * q1 + q2 * q2 + q3 * q3 + + sin_theta: torch.Tensor = torch.sqrt(sin_squared_theta) + cos_theta: torch.Tensor = quaternion[..., 0] + two_theta: torch.Tensor = 2.0 * torch.where( + cos_theta < 0.0, + torch.atan2(-sin_theta, -cos_theta), + torch.atan2(sin_theta, cos_theta), + ) + + k_pos: torch.Tensor = two_theta / sin_theta + k_neg: torch.Tensor = 2.0 * torch.ones_like(sin_theta) + k: torch.Tensor = torch.where(sin_squared_theta > 0.0, k_pos, k_neg) + + angle_axis: torch.Tensor = torch.zeros_like(quaternion)[..., :3] + angle_axis[..., 0] += q1 * k + angle_axis[..., 1] += q2 * k + angle_axis[..., 2] += q3 * k + return angle_axis diff --git a/slahmr/slahmr/job_specs/3dpw_test_split.txt b/slahmr/slahmr/job_specs/3dpw_test_split.txt new file mode 100644 index 0000000000000000000000000000000000000000..d220750362983b634cb90642a39d76eb1a1a97df --- /dev/null +++ b/slahmr/slahmr/job_specs/3dpw_test_split.txt @@ -0,0 +1,248 @@ +downtown_arguing_00 data.start_idx=0 data.end_idx=100 +downtown_arguing_00 data.start_idx=100 data.end_idx=200 +downtown_arguing_00 data.start_idx=200 data.end_idx=300 +downtown_arguing_00 data.start_idx=300 data.end_idx=400 +downtown_arguing_00 data.start_idx=400 data.end_idx=500 +downtown_arguing_00 data.start_idx=500 data.end_idx=600 +downtown_arguing_00 data.start_idx=600 data.end_idx=700 +downtown_arguing_00 data.start_idx=700 data.end_idx=898 +downtown_bar_00 data.start_idx=0 data.end_idx=100 +downtown_bar_00 data.start_idx=100 data.end_idx=200 +downtown_bar_00 data.start_idx=200 data.end_idx=300 +downtown_bar_00 data.start_idx=300 data.end_idx=400 +downtown_bar_00 data.start_idx=400 data.end_idx=500 +downtown_bar_00 data.start_idx=500 data.end_idx=600 +downtown_bar_00 data.start_idx=600 data.end_idx=700 +downtown_bar_00 data.start_idx=700 data.end_idx=800 +downtown_bar_00 data.start_idx=800 data.end_idx=900 +downtown_bar_00 data.start_idx=900 data.end_idx=1000 +downtown_bar_00 data.start_idx=1000 data.end_idx=1100 +downtown_bar_00 data.start_idx=1100 data.end_idx=1200 +downtown_bar_00 data.start_idx=1200 data.end_idx=1300 +downtown_bar_00 data.start_idx=1300 data.end_idx=1403 +downtown_bus_00 data.start_idx=0 data.end_idx=100 +downtown_bus_00 data.start_idx=100 data.end_idx=200 +downtown_bus_00 data.start_idx=200 data.end_idx=300 +downtown_bus_00 data.start_idx=300 data.end_idx=400 +downtown_bus_00 data.start_idx=400 data.end_idx=500 +downtown_bus_00 data.start_idx=500 data.end_idx=600 +downtown_bus_00 data.start_idx=600 data.end_idx=700 +downtown_bus_00 data.start_idx=700 data.end_idx=800 +downtown_bus_00 data.start_idx=800 data.end_idx=900 +downtown_bus_00 data.start_idx=900 data.end_idx=1000 +downtown_bus_00 data.start_idx=1000 data.end_idx=1100 +downtown_bus_00 data.start_idx=1100 data.end_idx=1200 +downtown_bus_00 data.start_idx=1200 data.end_idx=1300 +downtown_bus_00 data.start_idx=1300 data.end_idx=1400 +downtown_bus_00 data.start_idx=1400 data.end_idx=1500 +downtown_bus_00 data.start_idx=1500 data.end_idx=1600 +downtown_bus_00 data.start_idx=1600 data.end_idx=1700 +downtown_bus_00 data.start_idx=1700 data.end_idx=1800 +downtown_bus_00 data.start_idx=1800 data.end_idx=1900 +downtown_bus_00 data.start_idx=1900 data.end_idx=2000 +downtown_bus_00 data.start_idx=2000 data.end_idx=2178 +downtown_cafe_00 data.start_idx=0 data.end_idx=100 +downtown_cafe_00 data.start_idx=100 data.end_idx=200 +downtown_cafe_00 data.start_idx=200 data.end_idx=300 +downtown_cafe_00 data.start_idx=300 data.end_idx=400 +downtown_cafe_00 data.start_idx=400 data.end_idx=500 +downtown_cafe_00 data.start_idx=500 data.end_idx=600 +downtown_cafe_00 data.start_idx=600 data.end_idx=700 +downtown_cafe_00 data.start_idx=700 data.end_idx=800 +downtown_cafe_00 data.start_idx=800 data.end_idx=900 +downtown_cafe_00 data.start_idx=900 data.end_idx=1000 +downtown_cafe_00 data.start_idx=1000 data.end_idx=1100 +downtown_cafe_00 data.start_idx=1100 data.end_idx=1201 +downtown_car_00 data.start_idx=0 data.end_idx=100 +downtown_car_00 data.start_idx=100 data.end_idx=200 +downtown_car_00 data.start_idx=200 data.end_idx=300 +downtown_car_00 data.start_idx=300 data.end_idx=400 +downtown_car_00 data.start_idx=400 data.end_idx=500 +downtown_car_00 data.start_idx=500 data.end_idx=600 +downtown_car_00 data.start_idx=600 data.end_idx=700 +downtown_car_00 data.start_idx=700 data.end_idx=800 +downtown_car_00 data.start_idx=800 data.end_idx=900 +downtown_car_00 data.start_idx=900 data.end_idx=1020 +downtown_crossStreets_00 data.start_idx=0 data.end_idx=100 +downtown_crossStreets_00 data.start_idx=100 data.end_idx=200 +downtown_crossStreets_00 data.start_idx=200 data.end_idx=300 +downtown_crossStreets_00 data.start_idx=300 data.end_idx=400 +downtown_crossStreets_00 data.start_idx=400 data.end_idx=588 +downtown_downstairs_00 data.start_idx=0 data.end_idx=100 +downtown_downstairs_00 data.start_idx=100 data.end_idx=200 +downtown_downstairs_00 data.start_idx=200 data.end_idx=300 +downtown_downstairs_00 data.start_idx=300 data.end_idx=400 +downtown_downstairs_00 data.start_idx=400 data.end_idx=500 +downtown_downstairs_00 data.start_idx=500 data.end_idx=600 +downtown_downstairs_00 data.start_idx=600 data.end_idx=700 +downtown_downstairs_00 data.start_idx=700 data.end_idx=857 +downtown_enterShop_00 data.start_idx=0 data.end_idx=100 +downtown_enterShop_00 data.start_idx=100 data.end_idx=200 +downtown_enterShop_00 data.start_idx=200 data.end_idx=300 +downtown_enterShop_00 data.start_idx=300 data.end_idx=400 +downtown_enterShop_00 data.start_idx=400 data.end_idx=500 +downtown_enterShop_00 data.start_idx=500 data.end_idx=600 +downtown_enterShop_00 data.start_idx=600 data.end_idx=700 +downtown_enterShop_00 data.start_idx=700 data.end_idx=800 +downtown_enterShop_00 data.start_idx=800 data.end_idx=900 +downtown_enterShop_00 data.start_idx=900 data.end_idx=1000 +downtown_enterShop_00 data.start_idx=1000 data.end_idx=1100 +downtown_enterShop_00 data.start_idx=1100 data.end_idx=1200 +downtown_enterShop_00 data.start_idx=1200 data.end_idx=1300 +downtown_enterShop_00 data.start_idx=1300 data.end_idx=1449 +downtown_rampAndStairs_00 data.start_idx=0 data.end_idx=100 +downtown_rampAndStairs_00 data.start_idx=100 data.end_idx=200 +downtown_rampAndStairs_00 data.start_idx=200 data.end_idx=300 +downtown_rampAndStairs_00 data.start_idx=300 data.end_idx=400 +downtown_rampAndStairs_00 data.start_idx=400 data.end_idx=500 +downtown_rampAndStairs_00 data.start_idx=500 data.end_idx=600 +downtown_rampAndStairs_00 data.start_idx=600 data.end_idx=700 +downtown_rampAndStairs_00 data.start_idx=700 data.end_idx=800 +downtown_rampAndStairs_00 data.start_idx=800 data.end_idx=984 +downtown_runForBus_00 data.start_idx=0 data.end_idx=100 +downtown_runForBus_00 data.start_idx=100 data.end_idx=200 +downtown_runForBus_00 data.start_idx=200 data.end_idx=300 +downtown_runForBus_00 data.start_idx=300 data.end_idx=400 +downtown_runForBus_00 data.start_idx=400 data.end_idx=500 +downtown_runForBus_00 data.start_idx=500 data.end_idx=600 +downtown_runForBus_00 data.start_idx=600 data.end_idx=731 +downtown_runForBus_01 data.start_idx=0 data.end_idx=100 +downtown_runForBus_01 data.start_idx=100 data.end_idx=200 +downtown_runForBus_01 data.start_idx=200 data.end_idx=300 +downtown_runForBus_01 data.start_idx=300 data.end_idx=400 +downtown_runForBus_01 data.start_idx=400 data.end_idx=500 +downtown_runForBus_01 data.start_idx=500 data.end_idx=600 +downtown_runForBus_01 data.start_idx=600 data.end_idx=783 +downtown_sitOnStairs_00 data.start_idx=0 data.end_idx=100 +downtown_sitOnStairs_00 data.start_idx=100 data.end_idx=200 +downtown_sitOnStairs_00 data.start_idx=200 data.end_idx=300 +downtown_sitOnStairs_00 data.start_idx=300 data.end_idx=400 +downtown_sitOnStairs_00 data.start_idx=400 data.end_idx=500 +downtown_sitOnStairs_00 data.start_idx=500 data.end_idx=600 +downtown_sitOnStairs_00 data.start_idx=600 data.end_idx=700 +downtown_sitOnStairs_00 data.start_idx=700 data.end_idx=800 +downtown_sitOnStairs_00 data.start_idx=800 data.end_idx=900 +downtown_sitOnStairs_00 data.start_idx=900 data.end_idx=1000 +downtown_sitOnStairs_00 data.start_idx=1000 data.end_idx=1100 +downtown_sitOnStairs_00 data.start_idx=1100 data.end_idx=1200 +downtown_sitOnStairs_00 data.start_idx=1200 data.end_idx=1337 +downtown_stairs_00 data.start_idx=0 data.end_idx=100 +downtown_stairs_00 data.start_idx=100 data.end_idx=200 +downtown_stairs_00 data.start_idx=200 data.end_idx=300 +downtown_stairs_00 data.start_idx=300 data.end_idx=400 +downtown_stairs_00 data.start_idx=400 data.end_idx=500 +downtown_stairs_00 data.start_idx=500 data.end_idx=600 +downtown_stairs_00 data.start_idx=600 data.end_idx=700 +downtown_stairs_00 data.start_idx=700 data.end_idx=800 +downtown_stairs_00 data.start_idx=800 data.end_idx=900 +downtown_stairs_00 data.start_idx=900 data.end_idx=1000 +downtown_stairs_00 data.start_idx=1000 data.end_idx=1100 +downtown_stairs_00 data.start_idx=1100 data.end_idx=1240 +downtown_upstairs_00 data.start_idx=0 data.end_idx=100 +downtown_upstairs_00 data.start_idx=100 data.end_idx=200 +downtown_upstairs_00 data.start_idx=200 data.end_idx=300 +downtown_upstairs_00 data.start_idx=300 data.end_idx=400 +downtown_upstairs_00 data.start_idx=400 data.end_idx=500 +downtown_upstairs_00 data.start_idx=500 data.end_idx=600 +downtown_upstairs_00 data.start_idx=600 data.end_idx=700 +downtown_upstairs_00 data.start_idx=700 data.end_idx=845 +downtown_walkBridge_01 data.start_idx=0 data.end_idx=100 +downtown_walkBridge_01 data.start_idx=100 data.end_idx=200 +downtown_walkBridge_01 data.start_idx=200 data.end_idx=300 +downtown_walkBridge_01 data.start_idx=300 data.end_idx=400 +downtown_walkBridge_01 data.start_idx=400 data.end_idx=500 +downtown_walkBridge_01 data.start_idx=500 data.end_idx=600 +downtown_walkBridge_01 data.start_idx=600 data.end_idx=700 +downtown_walkBridge_01 data.start_idx=700 data.end_idx=800 +downtown_walkBridge_01 data.start_idx=800 data.end_idx=900 +downtown_walkBridge_01 data.start_idx=900 data.end_idx=1000 +downtown_walkBridge_01 data.start_idx=1000 data.end_idx=1100 +downtown_walkBridge_01 data.start_idx=1100 data.end_idx=1200 +downtown_walkBridge_01 data.start_idx=1200 data.end_idx=1372 +downtown_walkUphill_00 data.start_idx=0 data.end_idx=100 +downtown_walkUphill_00 data.start_idx=100 data.end_idx=200 +downtown_walkUphill_00 data.start_idx=200 data.end_idx=388 +downtown_walking_00 data.start_idx=0 data.end_idx=100 +downtown_walking_00 data.start_idx=100 data.end_idx=200 +downtown_walking_00 data.start_idx=200 data.end_idx=300 +downtown_walking_00 data.start_idx=300 data.end_idx=400 +downtown_walking_00 data.start_idx=400 data.end_idx=500 +downtown_walking_00 data.start_idx=500 data.end_idx=600 +downtown_walking_00 data.start_idx=600 data.end_idx=700 +downtown_walking_00 data.start_idx=700 data.end_idx=800 +downtown_walking_00 data.start_idx=800 data.end_idx=900 +downtown_walking_00 data.start_idx=900 data.end_idx=1000 +downtown_walking_00 data.start_idx=1000 data.end_idx=1100 +downtown_walking_00 data.start_idx=1100 data.end_idx=1200 +downtown_walking_00 data.start_idx=1200 data.end_idx=1387 +downtown_warmWelcome_00 data.start_idx=0 data.end_idx=100 +downtown_warmWelcome_00 data.start_idx=100 data.end_idx=200 +downtown_warmWelcome_00 data.start_idx=200 data.end_idx=300 +downtown_warmWelcome_00 data.start_idx=300 data.end_idx=400 +downtown_warmWelcome_00 data.start_idx=400 data.end_idx=589 +downtown_weeklyMarket_00 data.start_idx=0 data.end_idx=100 +downtown_weeklyMarket_00 data.start_idx=100 data.end_idx=200 +downtown_weeklyMarket_00 data.start_idx=200 data.end_idx=300 +downtown_weeklyMarket_00 data.start_idx=300 data.end_idx=400 +downtown_weeklyMarket_00 data.start_idx=400 data.end_idx=500 +downtown_weeklyMarket_00 data.start_idx=500 data.end_idx=600 +downtown_weeklyMarket_00 data.start_idx=600 data.end_idx=700 +downtown_weeklyMarket_00 data.start_idx=700 data.end_idx=800 +downtown_weeklyMarket_00 data.start_idx=800 data.end_idx=900 +downtown_weeklyMarket_00 data.start_idx=900 data.end_idx=1000 +downtown_weeklyMarket_00 data.start_idx=1000 data.end_idx=1193 +downtown_windowShopping_00 data.start_idx=0 data.end_idx=100 +downtown_windowShopping_00 data.start_idx=100 data.end_idx=200 +downtown_windowShopping_00 data.start_idx=200 data.end_idx=300 +downtown_windowShopping_00 data.start_idx=300 data.end_idx=400 +downtown_windowShopping_00 data.start_idx=400 data.end_idx=500 +downtown_windowShopping_00 data.start_idx=500 data.end_idx=600 +downtown_windowShopping_00 data.start_idx=600 data.end_idx=700 +downtown_windowShopping_00 data.start_idx=700 data.end_idx=800 +downtown_windowShopping_00 data.start_idx=800 data.end_idx=900 +downtown_windowShopping_00 data.start_idx=900 data.end_idx=1000 +downtown_windowShopping_00 data.start_idx=1000 data.end_idx=1100 +downtown_windowShopping_00 data.start_idx=1100 data.end_idx=1200 +downtown_windowShopping_00 data.start_idx=1200 data.end_idx=1300 +downtown_windowShopping_00 data.start_idx=1300 data.end_idx=1400 +downtown_windowShopping_00 data.start_idx=1400 data.end_idx=1500 +downtown_windowShopping_00 data.start_idx=1500 data.end_idx=1600 +downtown_windowShopping_00 data.start_idx=1600 data.end_idx=1700 +downtown_windowShopping_00 data.start_idx=1700 data.end_idx=1800 +downtown_windowShopping_00 data.start_idx=1800 data.end_idx=1948 +flat_guitar_01 data.start_idx=0 data.end_idx=100 +flat_guitar_01 data.start_idx=100 data.end_idx=200 +flat_guitar_01 data.start_idx=200 data.end_idx=300 +flat_guitar_01 data.start_idx=300 data.end_idx=400 +flat_guitar_01 data.start_idx=400 data.end_idx=500 +flat_guitar_01 data.start_idx=500 data.end_idx=600 +flat_guitar_01 data.start_idx=600 data.end_idx=748 +flat_packBags_00 data.start_idx=0 data.end_idx=100 +flat_packBags_00 data.start_idx=100 data.end_idx=200 +flat_packBags_00 data.start_idx=200 data.end_idx=300 +flat_packBags_00 data.start_idx=300 data.end_idx=400 +flat_packBags_00 data.start_idx=400 data.end_idx=500 +flat_packBags_00 data.start_idx=500 data.end_idx=600 +flat_packBags_00 data.start_idx=600 data.end_idx=700 +flat_packBags_00 data.start_idx=700 data.end_idx=800 +flat_packBags_00 data.start_idx=800 data.end_idx=900 +flat_packBags_00 data.start_idx=900 data.end_idx=1000 +flat_packBags_00 data.start_idx=1000 data.end_idx=1100 +flat_packBags_00 data.start_idx=1100 data.end_idx=1279 +office_phoneCall_00 data.start_idx=0 data.end_idx=100 +office_phoneCall_00 data.start_idx=100 data.end_idx=200 +office_phoneCall_00 data.start_idx=200 data.end_idx=300 +office_phoneCall_00 data.start_idx=300 data.end_idx=400 +office_phoneCall_00 data.start_idx=400 data.end_idx=500 +office_phoneCall_00 data.start_idx=500 data.end_idx=600 +office_phoneCall_00 data.start_idx=600 data.end_idx=700 +office_phoneCall_00 data.start_idx=700 data.end_idx=880 +outdoors_fencing_01 data.start_idx=0 data.end_idx=100 +outdoors_fencing_01 data.start_idx=100 data.end_idx=200 +outdoors_fencing_01 data.start_idx=200 data.end_idx=300 +outdoors_fencing_01 data.start_idx=300 data.end_idx=400 +outdoors_fencing_01 data.start_idx=400 data.end_idx=500 +outdoors_fencing_01 data.start_idx=500 data.end_idx=600 +outdoors_fencing_01 data.start_idx=600 data.end_idx=700 +outdoors_fencing_01 data.start_idx=700 data.end_idx=800 +outdoors_fencing_01 data.start_idx=800 data.end_idx=942 \ No newline at end of file diff --git a/slahmr/slahmr/job_specs/davis.txt b/slahmr/slahmr/job_specs/davis.txt new file mode 100644 index 0000000000000000000000000000000000000000..51261e79c33963da3d6e6451bbe0ac37df86ef0f --- /dev/null +++ b/slahmr/slahmr/job_specs/davis.txt @@ -0,0 +1,24 @@ +parkour data=davis fps=24 +lady-running data=davis fps=24 +dance-twirl data=davis fps=24 +lindy-hop data=davis fps=24 +hike data=davis fps=24 +judo data=davis fps=24 +lucia data=davis fps=24 +tennis data=davis fps=24 +skate-park data=davis fps=24 +boxing-fisheye data=davis fps=24 +crossing data=davis fps=24 +loading data=davis fps=24 +bike-packing data=davis fps=24 +dance-jump data=davis fps=24 +hockey data=davis fps=24 +india data=davis fps=24 +kid-football data=davis fps=24 +longboard data=davis fps=24 +schoolgirls data=davis fps=24 +snowboard data=davis fps=24 +stunt data=davis fps=24 +swing data=davis fps=24 +dancing data=davis fps=24 +kite-walk data=davis fps=24 diff --git a/slahmr/slahmr/job_specs/ego_val_split.txt b/slahmr/slahmr/job_specs/ego_val_split.txt new file mode 100644 index 0000000000000000000000000000000000000000..8ac763f18c932ccbfff9ebdae214e2efc3555e9b --- /dev/null +++ b/slahmr/slahmr/job_specs/ego_val_split.txt @@ -0,0 +1,245 @@ +recording_20210921_S11_S10_01 data.start_idx=0 data.end_idx=100 +recording_20210921_S11_S10_01 data.start_idx=100 data.end_idx=200 +recording_20210921_S11_S10_01 data.start_idx=200 data.end_idx=300 +recording_20210921_S11_S10_01 data.start_idx=300 data.end_idx=400 +recording_20210921_S11_S10_01 data.start_idx=400 data.end_idx=500 +recording_20210921_S11_S10_01 data.start_idx=500 data.end_idx=600 +recording_20210921_S11_S10_01 data.start_idx=600 data.end_idx=791 +recording_20210921_S11_S10_02 data.start_idx=0 data.end_idx=100 +recording_20210921_S11_S10_02 data.start_idx=100 data.end_idx=200 +recording_20210921_S11_S10_02 data.start_idx=200 data.end_idx=300 +recording_20210921_S11_S10_02 data.start_idx=300 data.end_idx=400 +recording_20210921_S11_S10_02 data.start_idx=400 data.end_idx=500 +recording_20210921_S11_S10_02 data.start_idx=500 data.end_idx=600 +recording_20210921_S11_S10_02 data.start_idx=600 data.end_idx=700 +recording_20210921_S11_S10_02 data.start_idx=700 data.end_idx=800 +recording_20210921_S11_S10_02 data.start_idx=800 data.end_idx=900 +recording_20210921_S11_S10_02 data.start_idx=900 data.end_idx=1000 +recording_20210921_S11_S10_02 data.start_idx=1000 data.end_idx=1100 +recording_20210921_S11_S10_02 data.start_idx=1100 data.end_idx=1200 +recording_20210921_S11_S10_02 data.start_idx=1200 data.end_idx=1300 +recording_20210921_S11_S10_02 data.start_idx=1300 data.end_idx=1400 +recording_20210921_S11_S10_02 data.start_idx=1400 data.end_idx=1500 +recording_20210921_S11_S10_02 data.start_idx=1500 data.end_idx=1665 +recording_20210923_S03_S14_01 data.start_idx=0 data.end_idx=100 +recording_20210923_S03_S14_01 data.start_idx=100 data.end_idx=200 +recording_20210923_S03_S14_01 data.start_idx=200 data.end_idx=300 +recording_20210923_S03_S14_01 data.start_idx=300 data.end_idx=400 +recording_20210923_S03_S14_01 data.start_idx=400 data.end_idx=500 +recording_20210923_S03_S14_01 data.start_idx=500 data.end_idx=600 +recording_20210923_S03_S14_01 data.start_idx=600 data.end_idx=700 +recording_20210923_S03_S14_01 data.start_idx=700 data.end_idx=800 +recording_20210923_S03_S14_01 data.start_idx=800 data.end_idx=900 +recording_20210923_S03_S14_01 data.start_idx=900 data.end_idx=1000 +recording_20210923_S03_S14_01 data.start_idx=1000 data.end_idx=1100 +recording_20210923_S03_S14_01 data.start_idx=1100 data.end_idx=1200 +recording_20210923_S03_S14_01 data.start_idx=1200 data.end_idx=1300 +recording_20210923_S03_S14_01 data.start_idx=1300 data.end_idx=1400 +recording_20210923_S03_S14_01 data.start_idx=1400 data.end_idx=1500 +recording_20210923_S03_S14_01 data.start_idx=1500 data.end_idx=1600 +recording_20210923_S03_S14_01 data.start_idx=1600 data.end_idx=1700 +recording_20210923_S03_S14_01 data.start_idx=1700 data.end_idx=1900 +recording_20211002_S03_S18_01 data.start_idx=0 data.end_idx=100 +recording_20211002_S03_S18_01 data.start_idx=100 data.end_idx=200 +recording_20211002_S03_S18_01 data.start_idx=200 data.end_idx=300 +recording_20211002_S03_S18_01 data.start_idx=300 data.end_idx=400 +recording_20211002_S03_S18_01 data.start_idx=400 data.end_idx=500 +recording_20211002_S03_S18_01 data.start_idx=500 data.end_idx=600 +recording_20211002_S03_S18_01 data.start_idx=600 data.end_idx=700 +recording_20211002_S03_S18_01 data.start_idx=700 data.end_idx=862 +recording_20211002_S03_S18_02 data.start_idx=0 data.end_idx=100 +recording_20211002_S03_S18_02 data.start_idx=100 data.end_idx=200 +recording_20211002_S03_S18_02 data.start_idx=200 data.end_idx=300 +recording_20211002_S03_S18_02 data.start_idx=300 data.end_idx=400 +recording_20211002_S03_S18_02 data.start_idx=400 data.end_idx=500 +recording_20211002_S03_S18_02 data.start_idx=500 data.end_idx=600 +recording_20211002_S03_S18_02 data.start_idx=600 data.end_idx=700 +recording_20211002_S03_S18_02 data.start_idx=700 data.end_idx=800 +recording_20211002_S03_S18_02 data.start_idx=800 data.end_idx=902 +recording_20211002_S03_S18_03 data.start_idx=0 data.end_idx=100 +recording_20211002_S03_S18_03 data.start_idx=100 data.end_idx=200 +recording_20211002_S03_S18_03 data.start_idx=200 data.end_idx=300 +recording_20211002_S03_S18_03 data.start_idx=300 data.end_idx=400 +recording_20211002_S03_S18_03 data.start_idx=400 data.end_idx=500 +recording_20211002_S03_S18_03 data.start_idx=500 data.end_idx=600 +recording_20211002_S03_S18_03 data.start_idx=600 data.end_idx=700 +recording_20211002_S03_S18_03 data.start_idx=700 data.end_idx=800 +recording_20211002_S03_S18_03 data.start_idx=800 data.end_idx=900 +recording_20211002_S03_S18_03 data.start_idx=900 data.end_idx=1000 +recording_20211002_S03_S18_03 data.start_idx=1000 data.end_idx=1100 +recording_20211002_S03_S18_03 data.start_idx=1100 data.end_idx=1200 +recording_20211002_S03_S18_03 data.start_idx=1200 data.end_idx=1300 +recording_20211002_S03_S18_03 data.start_idx=1300 data.end_idx=1400 +recording_20211002_S03_S18_03 data.start_idx=1400 data.end_idx=1569 +recording_20211002_S03_S18_04 data.start_idx=0 data.end_idx=100 +recording_20211002_S03_S18_04 data.start_idx=100 data.end_idx=200 +recording_20211002_S03_S18_04 data.start_idx=200 data.end_idx=300 +recording_20211002_S03_S18_04 data.start_idx=300 data.end_idx=400 +recording_20211002_S03_S18_04 data.start_idx=400 data.end_idx=500 +recording_20211002_S03_S18_04 data.start_idx=500 data.end_idx=600 +recording_20211002_S03_S18_04 data.start_idx=600 data.end_idx=700 +recording_20211002_S03_S18_04 data.start_idx=700 data.end_idx=800 +recording_20211002_S03_S18_04 data.start_idx=800 data.end_idx=900 +recording_20211002_S03_S18_04 data.start_idx=900 data.end_idx=1000 +recording_20211002_S03_S18_04 data.start_idx=1000 data.end_idx=1100 +recording_20211002_S03_S18_04 data.start_idx=1100 data.end_idx=1200 +recording_20211002_S03_S18_04 data.start_idx=1200 data.end_idx=1300 +recording_20211002_S03_S18_04 data.start_idx=1300 data.end_idx=1400 +recording_20211002_S03_S18_04 data.start_idx=1400 data.end_idx=1500 +recording_20211002_S03_S18_04 data.start_idx=1500 data.end_idx=1600 +recording_20211002_S03_S18_04 data.start_idx=1600 data.end_idx=1712 +recording_20220215_S21_S22_01 data.start_idx=0 data.end_idx=100 +recording_20220215_S21_S22_01 data.start_idx=100 data.end_idx=200 +recording_20220215_S21_S22_01 data.start_idx=200 data.end_idx=300 +recording_20220215_S21_S22_01 data.start_idx=300 data.end_idx=400 +recording_20220215_S21_S22_01 data.start_idx=400 data.end_idx=500 +recording_20220215_S21_S22_01 data.start_idx=500 data.end_idx=600 +recording_20220215_S21_S22_01 data.start_idx=600 data.end_idx=700 +recording_20220215_S21_S22_01 data.start_idx=700 data.end_idx=800 +recording_20220215_S21_S22_01 data.start_idx=800 data.end_idx=900 +recording_20220215_S21_S22_01 data.start_idx=900 data.end_idx=1000 +recording_20220215_S21_S22_01 data.start_idx=1000 data.end_idx=1100 +recording_20220215_S21_S22_01 data.start_idx=1100 data.end_idx=1200 +recording_20220215_S21_S22_01 data.start_idx=1200 data.end_idx=1300 +recording_20220215_S21_S22_01 data.start_idx=1300 data.end_idx=1400 +recording_20220215_S21_S22_01 data.start_idx=1400 data.end_idx=1500 +recording_20220215_S21_S22_01 data.start_idx=1500 data.end_idx=1600 +recording_20220215_S21_S22_01 data.start_idx=1600 data.end_idx=1700 +recording_20220215_S21_S22_01 data.start_idx=1700 data.end_idx=1800 +recording_20220215_S21_S22_01 data.start_idx=1800 data.end_idx=1900 +recording_20220215_S21_S22_01 data.start_idx=1900 data.end_idx=2000 +recording_20220215_S21_S22_01 data.start_idx=2000 data.end_idx=2100 +recording_20220215_S21_S22_01 data.start_idx=2100 data.end_idx=2200 +recording_20220215_S21_S22_01 data.start_idx=2200 data.end_idx=2300 +recording_20220215_S21_S22_01 data.start_idx=2300 data.end_idx=2400 +recording_20220215_S21_S22_01 data.start_idx=2400 data.end_idx=2500 +recording_20220215_S21_S22_01 data.start_idx=2500 data.end_idx=2600 +recording_20220215_S21_S22_01 data.start_idx=2600 data.end_idx=2790 +recording_20220215_S21_S22_02 data.start_idx=0 data.end_idx=100 +recording_20220215_S21_S22_02 data.start_idx=100 data.end_idx=200 +recording_20220215_S21_S22_02 data.start_idx=200 data.end_idx=300 +recording_20220215_S21_S22_02 data.start_idx=300 data.end_idx=400 +recording_20220215_S21_S22_02 data.start_idx=400 data.end_idx=500 +recording_20220215_S21_S22_02 data.start_idx=500 data.end_idx=600 +recording_20220215_S21_S22_02 data.start_idx=600 data.end_idx=700 +recording_20220215_S21_S22_02 data.start_idx=700 data.end_idx=800 +recording_20220215_S21_S22_02 data.start_idx=800 data.end_idx=900 +recording_20220215_S21_S22_02 data.start_idx=900 data.end_idx=1000 +recording_20220215_S21_S22_02 data.start_idx=1000 data.end_idx=1100 +recording_20220215_S21_S22_02 data.start_idx=1100 data.end_idx=1200 +recording_20220215_S21_S22_02 data.start_idx=1200 data.end_idx=1300 +recording_20220215_S21_S22_02 data.start_idx=1300 data.end_idx=1400 +recording_20220215_S21_S22_02 data.start_idx=1400 data.end_idx=1500 +recording_20220215_S21_S22_02 data.start_idx=1500 data.end_idx=1600 +recording_20220215_S21_S22_02 data.start_idx=1600 data.end_idx=1700 +recording_20220215_S21_S22_02 data.start_idx=1700 data.end_idx=1800 +recording_20220215_S21_S22_02 data.start_idx=1800 data.end_idx=1900 +recording_20220215_S21_S22_02 data.start_idx=1900 data.end_idx=2000 +recording_20220215_S21_S22_02 data.start_idx=2000 data.end_idx=2100 +recording_20220215_S21_S22_02 data.start_idx=2100 data.end_idx=2200 +recording_20220215_S21_S22_02 data.start_idx=2200 data.end_idx=2300 +recording_20220215_S21_S22_02 data.start_idx=2300 data.end_idx=2400 +recording_20220215_S21_S22_02 data.start_idx=2400 data.end_idx=2500 +recording_20220215_S21_S22_02 data.start_idx=2500 data.end_idx=2600 +recording_20220215_S21_S22_02 data.start_idx=2600 data.end_idx=2700 +recording_20220215_S21_S22_02 data.start_idx=2700 data.end_idx=2800 +recording_20220215_S21_S22_02 data.start_idx=2800 data.end_idx=2900 +recording_20220215_S21_S22_02 data.start_idx=2900 data.end_idx=3005 +recording_20220218_S23_S02_01 data.start_idx=0 data.end_idx=100 +recording_20220218_S23_S02_01 data.start_idx=100 data.end_idx=200 +recording_20220218_S23_S02_01 data.start_idx=200 data.end_idx=300 +recording_20220218_S23_S02_01 data.start_idx=300 data.end_idx=400 +recording_20220218_S23_S02_01 data.start_idx=400 data.end_idx=500 +recording_20220218_S23_S02_01 data.start_idx=500 data.end_idx=600 +recording_20220218_S23_S02_01 data.start_idx=600 data.end_idx=700 +recording_20220218_S23_S02_01 data.start_idx=700 data.end_idx=800 +recording_20220218_S23_S02_01 data.start_idx=800 data.end_idx=900 +recording_20220218_S23_S02_01 data.start_idx=900 data.end_idx=1000 +recording_20220218_S23_S02_01 data.start_idx=1000 data.end_idx=1100 +recording_20220218_S23_S02_01 data.start_idx=1100 data.end_idx=1200 +recording_20220218_S23_S02_01 data.start_idx=1200 data.end_idx=1300 +recording_20220218_S23_S02_01 data.start_idx=1300 data.end_idx=1400 +recording_20220218_S23_S02_01 data.start_idx=1400 data.end_idx=1500 +recording_20220218_S23_S02_01 data.start_idx=1500 data.end_idx=1600 +recording_20220218_S23_S02_01 data.start_idx=1600 data.end_idx=1700 +recording_20220218_S23_S02_01 data.start_idx=1700 data.end_idx=1826 +recording_20220218_S23_S02_02 data.start_idx=0 data.end_idx=100 +recording_20220218_S23_S02_02 data.start_idx=100 data.end_idx=200 +recording_20220218_S23_S02_02 data.start_idx=200 data.end_idx=300 +recording_20220218_S23_S02_02 data.start_idx=300 data.end_idx=400 +recording_20220218_S23_S02_02 data.start_idx=400 data.end_idx=500 +recording_20220218_S23_S02_02 data.start_idx=500 data.end_idx=600 +recording_20220218_S23_S02_02 data.start_idx=600 data.end_idx=700 +recording_20220218_S23_S02_02 data.start_idx=700 data.end_idx=800 +recording_20220218_S23_S02_02 data.start_idx=800 data.end_idx=900 +recording_20220218_S23_S02_02 data.start_idx=900 data.end_idx=1000 +recording_20220218_S23_S02_02 data.start_idx=1000 data.end_idx=1100 +recording_20220218_S23_S02_02 data.start_idx=1100 data.end_idx=1200 +recording_20220218_S23_S02_02 data.start_idx=1200 data.end_idx=1300 +recording_20220218_S23_S02_02 data.start_idx=1300 data.end_idx=1400 +recording_20220218_S23_S02_02 data.start_idx=1400 data.end_idx=1500 +recording_20220218_S23_S02_02 data.start_idx=1500 data.end_idx=1600 +recording_20220218_S23_S02_02 data.start_idx=1600 data.end_idx=1700 +recording_20220218_S23_S02_02 data.start_idx=1700 data.end_idx=1800 +recording_20220218_S23_S02_02 data.start_idx=1800 data.end_idx=1900 +recording_20220218_S23_S02_02 data.start_idx=1900 data.end_idx=2000 +recording_20220218_S23_S02_02 data.start_idx=2000 data.end_idx=2159 +recording_20220315_S21_S30_01 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_01 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_01 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_01 data.start_idx=300 data.end_idx=400 +recording_20220315_S21_S30_01 data.start_idx=400 data.end_idx=500 +recording_20220315_S21_S30_01 data.start_idx=500 data.end_idx=600 +recording_20220315_S21_S30_01 data.start_idx=600 data.end_idx=700 +recording_20220315_S21_S30_01 data.start_idx=700 data.end_idx=800 +recording_20220315_S21_S30_01 data.start_idx=800 data.end_idx=900 +recording_20220315_S21_S30_01 data.start_idx=900 data.end_idx=1000 +recording_20220315_S21_S30_01 data.start_idx=1000 data.end_idx=1100 +recording_20220315_S21_S30_01 data.start_idx=1100 data.end_idx=1200 +recording_20220315_S21_S30_01 data.start_idx=1200 data.end_idx=1300 +recording_20220315_S21_S30_01 data.start_idx=1300 data.end_idx=1400 +recording_20220315_S21_S30_01 data.start_idx=1400 data.end_idx=1500 +recording_20220315_S21_S30_01 data.start_idx=1500 data.end_idx=1600 +recording_20220315_S21_S30_01 data.start_idx=1600 data.end_idx=1700 +recording_20220315_S21_S30_01 data.start_idx=1700 data.end_idx=1844 +recording_20220315_S21_S30_02 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_02 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_02 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_02 data.start_idx=300 data.end_idx=400 +recording_20220315_S21_S30_02 data.start_idx=400 data.end_idx=500 +recording_20220315_S21_S30_02 data.start_idx=500 data.end_idx=600 +recording_20220315_S21_S30_02 data.start_idx=600 data.end_idx=700 +recording_20220315_S21_S30_02 data.start_idx=700 data.end_idx=800 +recording_20220315_S21_S30_02 data.start_idx=800 data.end_idx=900 +recording_20220315_S21_S30_02 data.start_idx=900 data.end_idx=1000 +recording_20220315_S21_S30_02 data.start_idx=1000 data.end_idx=1100 +recording_20220315_S21_S30_02 data.start_idx=1100 data.end_idx=1200 +recording_20220315_S21_S30_02 data.start_idx=1200 data.end_idx=1312 +recording_20220315_S21_S30_03 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_03 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_03 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_03 data.start_idx=300 data.end_idx=400 +recording_20220315_S21_S30_03 data.start_idx=400 data.end_idx=500 +recording_20220315_S21_S30_03 data.start_idx=500 data.end_idx=600 +recording_20220315_S21_S30_03 data.start_idx=600 data.end_idx=700 +recording_20220315_S21_S30_03 data.start_idx=700 data.end_idx=876 +recording_20220315_S21_S30_04 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_04 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_04 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_04 data.start_idx=300 data.end_idx=499 +recording_20220315_S21_S30_05 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_05 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_05 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_05 data.start_idx=300 data.end_idx=400 +recording_20220315_S21_S30_05 data.start_idx=400 data.end_idx=500 +recording_20220315_S21_S30_05 data.start_idx=500 data.end_idx=600 +recording_20220315_S21_S30_05 data.start_idx=600 data.end_idx=700 +recording_20220315_S21_S30_05 data.start_idx=700 data.end_idx=800 +recording_20220315_S21_S30_05 data.start_idx=800 data.end_idx=900 +recording_20220315_S21_S30_05 data.start_idx=900 data.end_idx=1000 +recording_20220315_S21_S30_05 data.start_idx=1000 data.end_idx=1100 +recording_20220315_S21_S30_05 data.start_idx=1100 data.end_idx=1300 +recording_20220315_S21_S30_06 data.start_idx=0 data.end_idx=100 +recording_20220315_S21_S30_06 data.start_idx=100 data.end_idx=200 +recording_20220315_S21_S30_06 data.start_idx=200 data.end_idx=300 +recording_20220315_S21_S30_06 data.start_idx=300 data.end_idx=404 \ No newline at end of file diff --git a/slahmr/slahmr/job_specs/pt_val_shots.txt b/slahmr/slahmr/job_specs/pt_val_shots.txt new file mode 100644 index 0000000000000000000000000000000000000000..660deee95a87bf0a70beda929e65c6a8add56a08 --- /dev/null +++ b/slahmr/slahmr/job_specs/pt_val_shots.txt @@ -0,0 +1,249 @@ +000342_mpii_test data.shot_idx=0 +000522_mpii_test data.shot_idx=0 +000583_mpii_test data.shot_idx=0 +000707_mpii_test data.shot_idx=0 +000735_mpii_test data.shot_idx=0 +000737_mpii_test data.shot_idx=0 +000809_mpii_test data.shot_idx=0 +000812_mpii_test data.shot_idx=0 +000814_mpii_test data.shot_idx=0 +000901_mpii_test data.shot_idx=0 +000901_mpii_test data.shot_idx=1 +001001_mpii_test data.shot_idx=0 +001007_mpii_test data.shot_idx=0 +001022_mpii_test data.shot_idx=0 +001486_mpii_test data.shot_idx=0 +001486_mpii_test data.shot_idx=1 +001588_mpii_test data.shot_idx=0 +001735_mpii_test data.shot_idx=0 +001744_mpii_test data.shot_idx=0 +001962_mpii_test data.shot_idx=0 +001969_mpii_test data.shot_idx=0 +002214_mpii_test data.shot_idx=0 +002214_mpii_test data.shot_idx=1 +002276_mpii_test data.shot_idx=0 +002277_mpii_test data.shot_idx=0 +002277_mpii_test data.shot_idx=1 +002364_mpii_test data.shot_idx=0 +002371_mpii_test data.shot_idx=0 +002373_mpii_test data.shot_idx=0 +002374_mpii_test data.shot_idx=0 +002375_mpii_test data.shot_idx=0 +002376_mpii_test data.shot_idx=0 +002835_mpii_test data.shot_idx=0 +002835_mpii_test data.shot_idx=1 +002835_mpii_test data.shot_idx=2 +003124_mpii_test data.shot_idx=0 +003124_mpii_test data.shot_idx=1 +003124_mpii_test data.shot_idx=2 +003203_mpii_test data.shot_idx=0 +003417_mpii_test data.shot_idx=0 +003418_mpii_test data.shot_idx=0 +003418_mpii_test data.shot_idx=1 +003419_mpii_test data.shot_idx=0 +003419_mpii_test data.shot_idx=1 +003420_mpii_test data.shot_idx=0 +003503_mpii_test data.shot_idx=0 +003508_mpii_test data.shot_idx=0 +003511_mpii_test data.shot_idx=0 +003742_mpii_test data.shot_idx=0 +003742_mpii_test data.shot_idx=1 +003747_mpii_test data.shot_idx=0 +003943_mpii_test data.shot_idx=0 +004524_mpii_test data.shot_idx=0 +004524_mpii_test data.shot_idx=1 +004621_mpii_test data.shot_idx=0 +004622_mpii_test data.shot_idx=0 +004687_mpii_test data.shot_idx=0 +004707_mpii_test data.shot_idx=0 +004712_mpii_test data.shot_idx=0 +005066_mpii_test data.shot_idx=0 +005066_mpii_test data.shot_idx=1 +005067_mpii_test data.shot_idx=0 +005067_mpii_test data.shot_idx=1 +005068_mpii_test data.shot_idx=0 +005068_mpii_test data.shot_idx=1 +005290_mpii_test data.shot_idx=0 +005292_mpii_test data.shot_idx=0 +005296_mpii_test data.shot_idx=0 +005337_mpii_test data.shot_idx=0 +005592_mpii_test data.shot_idx=0 +005833_mpii_test data.shot_idx=0 +006537_mpii_test data.shot_idx=0 +006538_mpii_test data.shot_idx=0 +006540_mpii_test data.shot_idx=0 +007128_mpii_test data.shot_idx=0 +007496_mpii_test data.shot_idx=0 +007496_mpii_test data.shot_idx=1 +007496_mpii_test data.shot_idx=2 +007684_mpii_test data.shot_idx=0 +007684_mpii_test data.shot_idx=1 +007793_mpii_test data.shot_idx=0 +007934_mpii_test data.shot_idx=0 +007938_mpii_test data.shot_idx=0 +007950_mpii_test data.shot_idx=0 +008760_mpii_test data.shot_idx=0 +008760_mpii_test data.shot_idx=1 +008827_mpii_test data.shot_idx=0 +008827_mpii_test data.shot_idx=1 +009039_mpii_test data.shot_idx=0 +009039_mpii_test data.shot_idx=1 +009266_mpii_test data.shot_idx=0 +009266_mpii_test data.shot_idx=1 +009266_mpii_test data.shot_idx=2 +009470_mpii_test data.shot_idx=0 +009471_mpii_test data.shot_idx=0 +009473_mpii_test data.shot_idx=0 +009475_mpii_test data.shot_idx=0 +009478_mpii_test data.shot_idx=0 +009479_mpii_test data.shot_idx=0 +009531_mpii_test data.shot_idx=0 +009532_mpii_test data.shot_idx=0 +009607_mpii_test data.shot_idx=0 +009883_mpii_test data.shot_idx=0 +009883_mpii_test data.shot_idx=1 +009883_mpii_test data.shot_idx=2 +010016_mpii_test data.shot_idx=0 +010017_mpii_test data.shot_idx=0 +010017_mpii_test data.shot_idx=1 +010017_mpii_test data.shot_idx=2 +010516_mpii_test data.shot_idx=0 +010516_mpii_test data.shot_idx=1 +010516_mpii_test data.shot_idx=2 +010516_mpii_test data.shot_idx=3 +010516_mpii_test data.shot_idx=4 +010516_mpii_test data.shot_idx=5 +010524_mpii_test data.shot_idx=0 +010529_mpii_test data.shot_idx=0 +010992_mpii_test data.shot_idx=0 +011648_mpii_test data.shot_idx=0 +012834_mpii_test data.shot_idx=0 +012834_mpii_test data.shot_idx=1 +012968_mpii_test data.shot_idx=0 +013293_mpii_test data.shot_idx=0 +013534_mpii_test data.shot_idx=0 +013534_mpii_test data.shot_idx=1 +014102_mpii_test data.shot_idx=0 +014102_mpii_test data.shot_idx=1 +014102_mpii_test data.shot_idx=2 +014140_mpii_test data.shot_idx=0 +014140_mpii_test data.shot_idx=1 +014140_mpii_test data.shot_idx=2 +014140_mpii_test data.shot_idx=3 +014293_mpii_test data.shot_idx=0 +014293_mpii_test data.shot_idx=1 +014384_mpii_test data.shot_idx=0 +014384_mpii_test data.shot_idx=1 +014520_mpii_test data.shot_idx=0 +014520_mpii_test data.shot_idx=1 +014523_mpii_test data.shot_idx=0 +014531_mpii_test data.shot_idx=0 +014611_mpii_test data.shot_idx=0 +014960_mpii_test data.shot_idx=0 +014960_mpii_test data.shot_idx=1 +015239_mpii_test data.shot_idx=0 +015239_mpii_test data.shot_idx=1 +015241_mpii_test data.shot_idx=0 +015241_mpii_test data.shot_idx=1 +015241_mpii_test data.shot_idx=2 +015301_mpii_test data.shot_idx=0 +015302_mpii_test data.shot_idx=0 +015372_mpii_test data.shot_idx=0 +015372_mpii_test data.shot_idx=1 +015374_mpii_test data.shot_idx=0 +015374_mpii_test data.shot_idx=1 +015374_mpii_test data.shot_idx=2 +015498_mpii_test data.shot_idx=0 +015498_mpii_test data.shot_idx=1 +015753_mpii_test data.shot_idx=0 +015860_mpii_test data.shot_idx=0 +015860_mpii_test data.shot_idx=1 +015907_mpii_test data.shot_idx=0 +015907_mpii_test data.shot_idx=1 +015933_mpii_test data.shot_idx=0 +015933_mpii_test data.shot_idx=1 +015933_mpii_test data.shot_idx=2 +015944_mpii_test data.shot_idx=0 +015944_mpii_test data.shot_idx=1 +015946_mpii_test data.shot_idx=0 +016180_mpii_test data.shot_idx=0 +016180_mpii_test data.shot_idx=1 +016195_mpii_test data.shot_idx=0 +016204_mpii_test data.shot_idx=0 +016236_mpii_test data.shot_idx=0 +016239_mpii_test data.shot_idx=0 +016423_mpii_test data.shot_idx=0 +016423_mpii_test data.shot_idx=1 +016662_mpii_test data.shot_idx=0 +017437_mpii_test data.shot_idx=0 +017446_mpii_test data.shot_idx=0 +017448_mpii_test data.shot_idx=0 +017450_mpii_test data.shot_idx=0 +017839_mpii_test data.shot_idx=0 +017839_mpii_test data.shot_idx=1 +018061_mpii_test data.shot_idx=0 +018090_mpii_test data.shot_idx=0 +018090_mpii_test data.shot_idx=1 +018090_mpii_test data.shot_idx=2 +018092_mpii_test data.shot_idx=0 +018092_mpii_test data.shot_idx=1 +018092_mpii_test data.shot_idx=2 +018712_mpii_test data.shot_idx=0 +018713_mpii_test data.shot_idx=0 +018725_mpii_test data.shot_idx=0 +018896_mpii_test data.shot_idx=0 +018898_mpii_test data.shot_idx=0 +018903_mpii_test data.shot_idx=0 +019583_mpii_test data.shot_idx=0 +020031_mpii_test data.shot_idx=0 +020880_mpii_test data.shot_idx=0 +020910_mpii_test data.shot_idx=0 +020910_mpii_test data.shot_idx=1 +021083_mpii_test data.shot_idx=0 +021083_mpii_test data.shot_idx=1 +022430_mpii_test data.shot_idx=0 +022688_mpii_test data.shot_idx=0 +022691_mpii_test data.shot_idx=0 +022691_mpii_test data.shot_idx=1 +022842_mpii_test data.shot_idx=0 +022842_mpii_test data.shot_idx=1 +022842_mpii_test data.shot_idx=2 +023390_mpii_test data.shot_idx=0 +023653_mpii_test data.shot_idx=0 +023717_mpii_test data.shot_idx=0 +023717_mpii_test data.shot_idx=1 +023717_mpii_test data.shot_idx=2 +023744_mpii_test data.shot_idx=0 +023744_mpii_test data.shot_idx=1 +023748_mpii_test data.shot_idx=0 +023748_mpii_test data.shot_idx=1 +023748_mpii_test data.shot_idx=2 +023748_mpii_test data.shot_idx=3 +023749_mpii_test data.shot_idx=0 +023749_mpii_test data.shot_idx=1 +023752_mpii_test data.shot_idx=0 +023752_mpii_test data.shot_idx=1 +023754_mpii_test data.shot_idx=0 +023754_mpii_test data.shot_idx=1 +023754_mpii_test data.shot_idx=2 +023931_mpii_test data.shot_idx=0 +023932_mpii_test data.shot_idx=0 +023933_mpii_test data.shot_idx=0 +023933_mpii_test data.shot_idx=1 +023934_mpii_test data.shot_idx=0 +023962_mpii_test data.shot_idx=0 +023963_mpii_test data.shot_idx=0 +024007_mpii_test data.shot_idx=0 +024154_mpii_test data.shot_idx=0 +024157_mpii_test data.shot_idx=0 +024158_mpii_test data.shot_idx=0 +024159_mpii_test data.shot_idx=0 +024165_mpii_test data.shot_idx=0 +024165_mpii_test data.shot_idx=1 +024199_mpii_test data.shot_idx=0 +024200_mpii_test data.shot_idx=0 +024575_mpii_test data.shot_idx=0 +024577_mpii_test data.shot_idx=0 +024593_mpii_test data.shot_idx=0 +024621_mpii_test data.shot_idx=0 +024907_mpii_test data.shot_idx=0 \ No newline at end of file diff --git a/slahmr/slahmr/launch.py b/slahmr/slahmr/launch.py new file mode 100644 index 0000000000000000000000000000000000000000..668f585a7392a91a530783bbf599d575adb71438 --- /dev/null +++ b/slahmr/slahmr/launch.py @@ -0,0 +1,87 @@ +import os +from datetime import datetime +import subprocess +import multiprocessing as mp +from concurrent import futures + +import argparse + +""" +Helper script for launching batch jobs if without job manager/slurm + +Specify which GPUs are available to use with (--gpus) flag +Specify sequences to run either via a job file (-f `job_file`) + + python launch.py --gpus 0 1 -f job_specs/davis.txt --opt --vis + +or manually with sequence names (--seqs) + + python launch.py --gpus 0 1 -f parkour boxing-fisheye --opt --vis + +and add additional arguments shared by all jobs with (-s) flag + + python launch.py --gpus 0 1 -f parkour boxing-fisheye --opt --vis -s exp_name=experiment_1 + +""" + + +def run(gpus, log_file, seq, run_opt, run_vis, overwrite=False, argstr=""): + cur_proc = mp.current_process() + print("PROCESS", cur_proc.name, cur_proc._identity) + worker_id = cur_proc._identity[0] - 1 # 1-indexed processes + gpu = gpus[worker_id % len(gpus)] + cmd = ( + f"CUDA_VISIBLE_DEVICES={gpu} EGL_DEVICE_ID={gpu} PYOPENGL_PLATFORM=egl " + f"python run_opt.py run_opt={run_opt} run_vis={run_vis} {argstr} " + ) + if seq is not None: + cmd = f"{cmd} data.seq={seq}" + if overwrite: + cmd = f"{cmd} overwrite=True" + + print(f"LOGGING TO {log_file}") + cmd = f"{cmd} > {log_file} 2>&1" + print(cmd) + subprocess.call(cmd, shell=True) + + +def main(args): + seqs = args.seqs + if seqs is None: + seqs = [None] + if args.job_file is not None: + with open(args.job_file, "r") as f: + seqs = [args.strip() for args in f.readlines()] + print(seqs) + + log_dir = "_launch_logs" + os.makedirs(log_dir, exist_ok=True) + job_name = datetime.now().strftime("%Y%m%d_%H%M%S") + + with futures.ProcessPoolExecutor(max_workers=len(args.gpus)) as exe: + for i, seq in enumerate(seqs): + log_file = f"{log_dir}/{job_name}_{i:03d}.log" + exe.submit( + run, + args.gpus, + log_file, + seq, + args.opt, + args.vis, + args.overwrite, + args.argstr, + ) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser() + parser.add_argument("--gpus", nargs="*", default=[8]) + parser.add_argument("-f", "--job_file", default=None) + parser.add_argument("--seqs", nargs="*", default=None) + parser.add_argument("--opt", action="store_true") + parser.add_argument("--vis", action="store_true") + parser.add_argument("-s", "--argstr", type=str, default="") + parser.add_argument("-y", "--overwrite", action="store_true") + args = parser.parse_args() + + main(args) diff --git a/slahmr/slahmr/optim/__init__.py b/slahmr/slahmr/optim/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/slahmr/optim/base_scene.py b/slahmr/slahmr/optim/base_scene.py new file mode 100644 index 0000000000000000000000000000000000000000..a24949641fbef2e960e8ed978110b8a9712132b4 --- /dev/null +++ b/slahmr/slahmr/optim/base_scene.py @@ -0,0 +1,211 @@ +import os +import numpy as np + +import torch +import torch.nn as nn +import torch.nn.functional as F + +from body_model import SMPL_JOINTS, KEYPT_VERTS, smpl_to_openpose, run_smpl +from geometry.rotation import rotation_matrix_to_angle_axis +from util.logger import Logger +from util.tensor import move_to, detach_all + +from .helpers import estimate_initial_trans +from .params import CameraParams + + +J_BODY = len(SMPL_JOINTS) - 1 # no root + + +class BaseSceneModel(nn.Module): + """ + Scene model of sequences of human poses. + All poses are in their own INDEPENDENT camera reference frames. + A basic class mostly for testing purposes. + + Parameters: + batch_size: number of sequences to optimize + seq_len: length of the sequences + body_model: SMPL body model + pose_prior: VPoser model + fit_gender: gender of model (optional) + """ + + def __init__( + self, + batch_size, + seq_len, + body_model, + pose_prior, + fit_gender="neutral", + use_init=False, + opt_cams=False, + opt_scale=True, + **kwargs, + ): + super().__init__() + B, T = batch_size, seq_len + self.batch_size = batch_size + self.seq_len = seq_len + + self.body_model = body_model + self.fit_gender = fit_gender + + self.pose_prior = pose_prior + self.latent_pose_dim = self.pose_prior.latentD + + self.num_betas = body_model.bm.num_betas + + self.smpl2op_map = smpl_to_openpose( + self.body_model.model_type, + use_hands=False, + use_face=False, + use_face_contour=False, + openpose_format="coco25", + ) + + self.use_init = use_init + print("USE INIT", use_init) + self.opt_scale = opt_scale + self.opt_cams = opt_cams + print("OPT SCALE", self.opt_scale) + print("OPT CAMERAS", self.opt_cams) + self.params = CameraParams(batch_size) + + def initialize(self, obs_data, cam_data): + Logger.log("Initializing scene model with observed data") + + # initialize cameras + self.params.set_cameras( + cam_data, + opt_scale=self.opt_scale, + opt_cams=self.opt_cams, + opt_focal=self.opt_cams, + ) + + # initialize body params + B, T = self.batch_size, self.seq_len + init_pose = torch.zeros(B, T, self.latent_pose_dim) + init_betas = torch.zeros(B, self.num_betas) + init_trans = torch.zeros(B, T, 3) + init_rot = ( + torch.tensor([np.pi, 0, 0], dtype=torch.float32) + .reshape(1, 1, 3) + .repeat(B, T, 1) + ) + + if self.use_init and "init_body_pose" in obs_data: + init_pose = obs_data["init_body_pose"][:, :, :J_BODY, :] + init_pose = self.pose2latent(init_pose) + + if self.use_init and "init_root_orient" in obs_data: + init_rot = obs_data["init_root_orient"] + + if self.use_init and "init_trans" in obs_data: + init_trans = obs_data["init_trans"] # (B, T, 3) + # transform into world frame (T, 3, 3), (T, 3) + R_w2c, t_w2c = cam_data["cam_R"], cam_data["cam_t"] + R_c2w = R_w2c.transpose(-1, -2) + t_c2w = -torch.einsum("tij,tj->ti", R_c2w, t_w2c) + init_trans = torch.einsum("tij,btj->bti", R_c2w, init_trans) + t_c2w[None] + else: + # initialize trans with reprojected joints + body_pose = self.latent2pose(init_pose) + pred_data = self.pred_smpl(init_trans, init_rot, body_pose, init_betas) + init_trans = estimate_initial_trans( + body_pose, + pred_data["joints3d_op"], + obs_data["joints2d"], + obs_data["intrins"][:, 0], + ) + + self.params.set_param("latent_pose", init_pose) + self.params.set_param("betas", init_betas) + self.params.set_param("trans", init_trans) + self.params.set_param("root_orient", init_rot) + + def get_optim_result(self, **kwargs): + """ + Collect predicted outputs (latent_pose, trans, root_orient, betas, body pose) into dict + """ + res = self.params.get_dict() + if "latent_pose" in res: + res["pose_body"] = self.latent2pose(self.params.latent_pose).detach() + + # add the cameras + res["cam_R"], res["cam_t"], _, _ = self.params.get_cameras() + res["intrins"] = self.params.intrins + return {"world": res} + + def latent2pose(self, latent_pose): + """ + Converts VPoser latent embedding to aa body pose. + latent_pose : B x T x D + body_pose : B x T x J*3 + """ + B, T, _ = latent_pose.size() + d_latent = self.pose_prior.latentD + latent_pose = latent_pose.reshape((-1, d_latent)) + body_pose = self.pose_prior.decode(latent_pose, output_type="matrot") + body_pose = rotation_matrix_to_angle_axis( + body_pose.reshape((B * T * J_BODY, 3, 3)) + ).reshape((B, T, J_BODY * 3)) + return body_pose + + def pose2latent(self, body_pose): + """ + Encodes aa body pose to VPoser latent space. + body_pose : B x T x J*3 + latent_pose : B x T x D + """ + B, T = body_pose.shape[:2] + body_pose = body_pose.reshape((-1, J_BODY * 3)) + latent_pose_distrib = self.pose_prior.encode(body_pose) + d_latent = self.pose_prior.latentD + latent_pose = latent_pose_distrib.mean.reshape((B, T, d_latent)) + return latent_pose + + def pred_smpl(self, trans, root_orient, body_pose, betas): + """ + Forward pass of the SMPL model and populates pred_data accordingly with + joints3d, verts3d, points3d. + + trans : B x T x 3 + root_orient : B x T x 3 + body_pose : B x T x J*3 + betas : B x D + """ + smpl_out = run_smpl(self.body_model, trans, root_orient, body_pose, betas) + joints3d, points3d = smpl_out["joints"], smpl_out["vertices"] + + # select desired joints and vertices + joints3d_body = joints3d[:, :, : len(SMPL_JOINTS), :] + joints3d_op = joints3d[:, :, self.smpl2op_map, :] + # hacky way to get hip joints that align with ViTPose keypoints + # this could be moved elsewhere in the future (and done properly) + joints3d_op[:, :, [9, 12]] = ( + joints3d_op[:, :, [9, 12]] + + 0.25 * (joints3d_op[:, :, [9, 12]] - joints3d_op[:, :, [12, 9]]) + + 0.5 + * ( + joints3d_op[:, :, [8]] + - 0.5 * (joints3d_op[:, :, [9, 12]] + joints3d_op[:, :, [12, 9]]) + ) + ) + verts3d = points3d[:, :, KEYPT_VERTS, :] + + return { + "points3d": points3d, # all vertices + "verts3d": verts3d, # keypoint vertices + "joints3d": joints3d_body, # smpl joints + "joints3d_op": joints3d_op, # OP joints + "faces": smpl_out["faces"], # index array of faces + } + + def pred_params_smpl(self, reproj=True): + body_pose = self.latent2pose(self.params.latent_pose) + pred_data = self.pred_smpl( + self.params.trans, self.params.root_orient, body_pose, self.params.betas + ) + + return pred_data diff --git a/slahmr/slahmr/optim/helpers.py b/slahmr/slahmr/optim/helpers.py new file mode 100644 index 0000000000000000000000000000000000000000..fd01bedaa1c33c6c33d703bfb91ed45c252cbef6 --- /dev/null +++ b/slahmr/slahmr/optim/helpers.py @@ -0,0 +1,180 @@ +import numpy as np +import torch + +from body_model import OP_EDGE_LIST +from geometry.rotation import batch_rodrigues +from geometry.plane import ( + parse_floor_plane, + compute_plane_intersection, + fit_plane, +) + + +def compute_world2prior(floor_plane, trans, root_orient, origin): + """ + Computes rotation and translation from the camera frame to the canonical coordinate system + used by the motion and initial state priors. + - floor_plane : B x 3 + - trans : B x 3 + - root_orient : B x 3 + - origin: B x 3 desired origin (first joint of human model) + - returns R (B, 3, 3), t (B, 3), root_height (B) + """ + B = trans.size(0) + if floor_plane.size(1) == 3: + floor_plane_4d = parse_floor_plane(floor_plane) + else: + floor_plane_4d = floor_plane + floor_normal = floor_plane_4d[:, :3] + floor_trans, _ = compute_plane_intersection(trans, -floor_normal, floor_plane_4d) + + # compute prior frame axes within the camera frame + # up is the floor_plane normal + up_axis = floor_normal + # right is body -x direction projected to floor plane + root_orient_mat = batch_rodrigues(root_orient) + body_right = -root_orient_mat[:, :, 0] + floor_body_right, s = compute_plane_intersection(trans, body_right, floor_plane_4d) + right_axis = floor_body_right - floor_trans + # body right may not actually intersect - in this case must negate axis because we have the -x + right_axis = torch.where(s.reshape((B, 1)) < 0, -right_axis, right_axis) + right_axis = right_axis / torch.norm(right_axis, dim=1, keepdim=True) + # forward is their cross product + fwd_axis = torch.linalg.cross(up_axis, right_axis) + fwd_axis = fwd_axis / torch.norm(fwd_axis, dim=1, keepdim=True) + + # prior frame is right, fwd, up + prior_R = torch.stack([right_axis, fwd_axis, up_axis], dim=2) + world2prior_R = prior_R.transpose(-1, -2) + + # translation takes translation to origin plus offset to the floor + world2prior_t = -trans + + # compute the distance from root to ground plane + _, s_root = compute_plane_intersection(origin, -floor_normal, floor_plane_4d) + root_height = s_root.reshape(B, 1) + + if False: + # apply transform to origin + origin_prior = torch.matmul(world2prior_R, (origin - trans)[..., None])[..., 0] + root_height = s_root.reshape(B, 1) - origin_prior[:, 2:3] + + return world2prior_R, world2prior_t, root_height + + +def find_cliques(edges): + cliques = [] + N = edges.shape[0] + empty = np.ones(N, dtype=bool) + while empty.sum() > 0: + idcs = np.where(empty)[0] + i = idcs[0] + cur_clique = [i] + for j in idcs[1:]: + if all(edges[c, j] for c in cur_clique): + cur_clique.append(j) + empty[cur_clique] = False + cliques.append(cur_clique) + return cliques + + +def estimate_floor_planes( + smpl_joints, valid_mask, thresh=0.5, group=False, flatten=False +): + """ + :param smpl_joints (B, T, J, 3) + :param valid_mask (B, T) + :param thresh (optional, default 0.5) threshold for separating + :param group (optional, default False) whether to group the planes + :param flatten (optional, default False) whether to estimate one plane for everyone + returns floor_plane (C, 3), floor_idcs (B,) + """ + B, T = valid_mask.shape + device = valid_mask.device + feet_joints = smpl_joints[..., 10:12, :] # (B, T, 2, 3) + points = [feet_joints[b, valid_mask[b]].reshape(-1, 3) for b in range(B)] + + if flatten: + planes = fit_plane(torch.cat(points, dim=0))[None] + labels = torch.zeros(B, device=device, dtype=torch.long) + return planes[..., :3] * planes[..., 3:], labels + + # estimate floors independently + planes = torch.stack([fit_plane(pts) for pts in points], dim=0) # (B, 4) + normals, offsets = planes[..., :3], planes[..., 3:] # (B, 3), (B, 1) + sgn = torch.sign(offsets) + normals, offsets = sgn * normals, sgn * offsets + planes = normals * offsets # (B, 3) + labels = torch.arange(B, device=device) + + if not group: + return planes, labels # (B, 3), (B,) + + # asymetric, project each plane vector onto the other normals + diffs = offsets - (planes[None] * normals[:, None]).sum(dim=-1) + print(diffs) + edges = diffs < thresh + edges = edges.T & edges + clusters = find_cliques(edges) # list of indices of clusters + planes = [] + labels = torch.zeros(B, dtype=torch.long, device=device) + for c, idcs in enumerate(clusters): + plane = fit_plane(torch.cat([points[i] for i in idcs], dim=0)) + planes.append(plane) + labels[idcs] = c + planes = torch.stack(planes, dim=0) # (C, 4) + return planes[..., :3] * planes[..., 3:], labels + + +def estimate_initial_trans(body_pose, joints3d_op, joints2d_op, focal): + """ + use focal length and bone lengths to approximate distance from camera + (based on PROX https://github.com/mohamedhassanmus/prox/blob/master/prox/fitting.py) + :param body_pose + :param joints3d_op OP keypoints in 3d + :param joints2d_op OP keypoints in 2d + """ + B, T, N, _ = joints2d_op.shape + joints2d_obs = joints2d_op[:, :, :, :2] # (B, T, N, 3) + joints2d_conf = joints2d_op[:, :, :, 2] + + # find least-occluded 2d frame + num_2d_vis = torch.sum(joints2d_conf > 0.0, dim=2) + best_2d_idx = torch.max(num_2d_vis, dim=1)[1] + + # calculate bone lengths and confidence in each bone length + bone3d = [] + bone2d = [] + conf2d = [] + for pair in OP_EDGE_LIST: + diff3d = torch.norm( + joints3d_op[:, 0, pair[0], :] - joints3d_op[:, 0, pair[1], :], + dim=1, + ) # does not change over time + diff2d = torch.norm( + joints2d_obs[:, :, pair[0], :] - joints2d_obs[:, :, pair[1], :], + dim=2, + ) + minconf2d = torch.min( + joints2d_conf[:, :, pair[0]], joints2d_conf[:, :, pair[1]] + ) + bone3d.append(diff3d) + bone2d.append(diff2d) + conf2d.append(minconf2d) + + bone3d = torch.stack(bone3d, dim=1) + bone2d = torch.stack(bone2d, dim=2) + bone2d = bone2d[np.arange(B), best_2d_idx, :] + conf2d = torch.stack(conf2d, dim=2) + conf2d = conf2d[np.arange(B), best_2d_idx, :] + + # mean over all bones + mean_bone3d = torch.mean(bone3d, dim=1) + mean_bone2d = torch.mean(bone2d * (conf2d > 0.0), dim=1) + + # approx z based on ratio + init_z = focal * (mean_bone3d / mean_bone2d) + init_trans = torch.zeros(B, T, 3) + init_trans[:, :, 2] = init_z.unsqueeze(1).expand(B, T).detach() + + return init_trans diff --git a/slahmr/slahmr/optim/losses.py b/slahmr/slahmr/optim/losses.py new file mode 100644 index 0000000000000000000000000000000000000000..2d4b4eeb2b31ce3642a48f0fbc87f984926b5a02 --- /dev/null +++ b/slahmr/slahmr/optim/losses.py @@ -0,0 +1,747 @@ +import os +import math +import numpy as np + +import torch +import torch.nn as nn +import torch.nn.functional as F +from torch.distributions import ( + MixtureSameFamily, + Categorical, + Normal, + MultivariateNormal, +) + +from body_model import SMPL_JOINTS, SMPL_PARENTS, OP_NUM_JOINTS +from geometry.rotation import rotation_matrix_to_angle_axis +from geometry import camera as cam_util +from util.logger import Logger + + +CONTACT_HEIGHT_THRESH = 0.08 + + +class StageLoss(nn.Module): + def __init__(self, loss_weights, **kwargs): + super().__init__() + self.cur_optim_step = 0 + self.set_loss_weights(loss_weights) + self.setup_losses(loss_weights, **kwargs) + + def setup_losses(self, *args, **kwargs): + raise NotImplementedError + + def set_loss_weights(self, loss_weights): + self.loss_weights = loss_weights + Logger.log("Stage loss weights set to:") + Logger.log(self.loss_weights) + + +class RootLoss(StageLoss): + def setup_losses( + self, + loss_weights, + ignore_op_joints=None, + joints2d_sigma=100, + use_chamfer=False, + robust_loss="none", + robust_tuning_const=4.6851, + ): + self.joints2d_loss = Joints2DLoss(ignore_op_joints, joints2d_sigma) + self.points3d_loss = Points3DLoss(use_chamfer, robust_loss, robust_tuning_const) + + def forward(self, observed_data, pred_data, valid_mask=None): + """ + For fitting just global root trans/orientation. + Only computes joint/point/vert losses, i.e. no priors. + """ + stats_dict = dict() + loss = 0.0 + + # Joints in 3D space + if ( + "joints3d" in observed_data + and "joints3d" in pred_data + and self.loss_weights["joints3d"] > 0.0 + ): + cur_loss = joints3d_loss( + observed_data["joints3d"], pred_data["joints3d"], valid_mask + ) + loss += self.loss_weights["joints3d"] * cur_loss + stats_dict["joints3d"] = cur_loss + + # Select vertices in 3D space + if ( + "verts3d" in observed_data + and "verts3d" in pred_data + and self.loss_weights["verts3d"] > 0.0 + ): + cur_loss = verts3d_loss( + observed_data["verts3d"], pred_data["verts3d"], valid_mask + ) + loss += self.loss_weights["verts3d"] * cur_loss + stats_dict["verts3d"] = cur_loss + + # All vertices to non-corresponding observed points in 3D space + if ( + "points3d" in observed_data + and "points3d" in pred_data + and self.loss_weights["points3d"] > 0.0 + ): + cur_loss = self.points3d_loss( + observed_data["points3d"], pred_data["points3d"] + ) + loss += self.loss_weights["points3d"] * cur_loss + stats_dict["points3d"] = cur_loss + + # 2D re-projection loss + if ( + "joints2d" in observed_data + and "joints3d_op" in pred_data + and "cameras" in pred_data + and self.loss_weights["joints2d"] > 0.0 + ): + joints2d = cam_util.reproject( + pred_data["joints3d_op"], *pred_data["cameras"] + ) + cur_loss = self.joints2d_loss( + observed_data["joints2d"], joints2d, valid_mask + ) + loss += self.loss_weights["joints2d"] * cur_loss + stats_dict["joints2d"] = cur_loss + + # smooth 3d joint motion + if self.loss_weights["joints3d_smooth"] > 0.0: + cur_loss = joints3d_smooth_loss(pred_data["joints3d"], valid_mask) + loss += self.loss_weights["joints3d_smooth"] * cur_loss + stats_dict["joints3d_smooth"] = cur_loss + + # If we're optimizing cameras, camera reprojection loss + if "bg2d_err" in pred_data and self.loss_weights["bg2d"] > 0.0: + cur_loss = pred_data["bg2d_err"] + loss += self.loss_weights["bg2d"] * cur_loss + stats_dict["bg2d_err"] = cur_loss + + # camera smoothness + if "cam_R" in pred_data and self.loss_weights["cam_R_smooth"] > 0.0: + cam_R = pred_data["cam_R"] # (T, 3, 3) + cur_loss = rotation_smoothness_loss(cam_R[1:], cam_R[:-1]) + loss += self.loss_weights["cam_R_smooth"] * cur_loss + stats_dict["cam_R_smooth"] = cur_loss + + if "cam_t" in pred_data and self.loss_weights["cam_t_smooth"] > 0.0: + cam_t = pred_data["cam_t"] # (T, 3, 3) + cur_loss = translation_smoothness_loss(cam_t[1:], cam_t[:-1]) + loss += self.loss_weights["cam_t_smooth"] * cur_loss + stats_dict["cam_t_smooth"] = cur_loss + + return loss, stats_dict + + +def rotation_smoothness_loss(R1, R2): + R12 = torch.einsum("...ij,...jk->...ik", R2, R1.transpose(-1, -2)) + aa12 = rotation_matrix_to_angle_axis(R12) + return torch.sum(aa12**2) + + +def translation_smoothness_loss(t1, t2): + return torch.sum((t2 - t1) ** 2) + + +def camera_smoothness_loss(R1, t1, R2, t2): + """ + :param R1, t1 (N, 3, 3), (N, 3) + :param R2, t2 (N, 3, 3), (N, 3) + """ + R12, t12 = cam_util.compose_cameras(R2, t2, *cam_util.invert_camera(R1, t1)) + aa12 = rotation_matrix_to_angle_axis(R12) + return torch.sum(aa12**2) + torch.sum(t12**2) + + +""" +Losses are cumulative +SMPLLoss setup is same as RootLoss +""" + + +class SMPLLoss(RootLoss): + def forward(self, observed_data, pred_data, nsteps, valid_mask=None): + """ + For fitting full shape and pose of SMPL. + nsteps used to scale single-step losses + """ + loss, stats_dict = super().forward( + observed_data, pred_data, valid_mask=valid_mask + ) + + # prior to keep latent pose likely + if "latent_pose" in pred_data and self.loss_weights["pose_prior"] > 0.0: + cur_loss = pose_prior_loss(pred_data["latent_pose"], valid_mask) + loss += self.loss_weights["pose_prior"] * cur_loss + stats_dict["pose_prior"] = cur_loss + + # prior to keep PCA shape likely + if "betas" in pred_data and self.loss_weights["shape_prior"] > 0.0: + cur_loss = shape_prior_loss(pred_data["betas"]) + loss += self.loss_weights["shape_prior"] * nsteps * cur_loss + stats_dict["shape_prior"] = cur_loss + + return loss, stats_dict + + +""" +MotionLoss also includes SMPLLoss +""" + + +class MotionLoss(SMPLLoss): + def setup_losses( + self, + loss_weights, + init_motion_prior=None, + **kwargs, + ): + super().setup_losses(loss_weights, **kwargs) + if loss_weights["init_motion_prior"] > 0.0: + self.init_motion_prior_loss = GMMPriorLoss(init_motion_prior) + + def forward( + self, + observed_data, + pred_data, + cam_pred_data, + nsteps, + valid_mask=None, + init_motion_scale=1.0, + ): + """ + For fitting full shape and pose of SMPL with motion prior. + + pred_data is data pertinent to the canonical prior coordinate frame + cam_pred_data is for the camera coordinate frame + + loss rather than standard normal if given. + """ + cam_pred_data["latent_pose"] = pred_data["latent_pose"] + loss, stats_dict = super().forward( + observed_data, cam_pred_data, nsteps, valid_mask=valid_mask + ) + + # prior to keep latent motion likely + if "latent_motion" in pred_data and self.loss_weights["motion_prior"] > 0.0: + # NOTE: latent is NOT synchronized in time, + # the mask is NOT relevant + # Generate the async mask to properly mask motion prior loss + # Helps to calibrate the range of 'good' loss values + B, T, _ = pred_data["latent_motion"].shape + device = pred_data["latent_motion"].device + async_mask = ( + torch.arange(T, device=device)[None].expand(B, -1) + < valid_mask.sum(dim=1)[:, None] + ) + cur_loss = motion_prior_loss( + pred_data["latent_motion"], + cond_prior=pred_data.get("cond_prior", None), + mask=async_mask, + ) + loss += self.loss_weights["motion_prior"] * cur_loss + stats_dict["motion_prior"] = cur_loss + + # prior to keep initial state likely + have_init_prior_info = ( + "joints3d_init" in pred_data + and "joints_vel" in pred_data + and "trans_vel" in pred_data + and "root_orient_vel" in pred_data + ) + if have_init_prior_info and self.loss_weights["init_motion_prior"] > 0.0: + cur_loss = self.init_motion_prior_loss( + pred_data["joints3d_init"], + pred_data["joints_vel"], + pred_data["trans_vel"], + pred_data["root_orient_vel"], + ) + loss += ( + self.loss_weights["init_motion_prior"] * init_motion_scale * cur_loss + ) # must scale since doesn't scale with more steps + stats_dict["init_motion_prior"] = cur_loss + + # make sure joints consistent between SMPL and direct motion prior output + if ( + "joints3d_rollout" in pred_data + and "joints3d" in pred_data + and self.loss_weights["joint_consistency"] > 0.0 + ): + cur_loss = joint_consistency_loss( + pred_data["joints3d"], + pred_data["joints3d_rollout"], + valid_mask, + ) + loss += self.loss_weights["joint_consistency"] * cur_loss + stats_dict["joint_consistency"] = cur_loss + + # make sure bone lengths between frames of direct motion prior output are consistent + if "joints3d_rollout" in pred_data and self.loss_weights["bone_length"] > 0.0: + cur_loss = bone_length_loss(pred_data["joints3d_rollout"], valid_mask) + loss += self.loss_weights["bone_length"] * cur_loss + stats_dict["bone_length"] = cur_loss + + # make sure rolled out joints match observations too + if ( + "joints3d" in observed_data + and "joints3d_rollout" in pred_data + and self.loss_weights["joints3d_rollout"] > 0.0 + ): + cur_loss = joints3d_loss( + observed_data["joints3d"], pred_data["joints3d_rollout"], valid_mask + ) + loss += self.loss_weights["joints3d_rollout"] * cur_loss + stats_dict["joints3d_rollout"] = cur_loss + + # velocity 0 during contacts + if ( + self.loss_weights["contact_vel"] > 0.0 + and "contacts_conf" in pred_data + and "joints3d" in pred_data + ): + cur_loss = contact_vel_loss( + pred_data["contacts_conf"], pred_data["joints3d"], valid_mask + ) + loss += self.loss_weights["contact_vel"] * cur_loss + stats_dict["contact_vel"] = cur_loss + + # contacting joints are near the floor + if ( + self.loss_weights["contact_height"] > 0.0 + and "contacts_conf" in pred_data + and "joints3d" in pred_data + ): + cur_loss = contact_height_loss( + pred_data["contacts_conf"], pred_data["joints3d"], valid_mask + ) + loss += self.loss_weights["contact_height"] * cur_loss + stats_dict["contact_height"] = cur_loss + + # floor is close to the initialization + if ( + self.loss_weights["floor_reg"] > 0.0 + and "floor_plane" in pred_data + and "floor_plane" in observed_data + ): + cur_loss = floor_reg_loss( + pred_data["floor_plane"], observed_data["floor_plane"] + ) + loss += self.loss_weights["floor_reg"] * nsteps * cur_loss + stats_dict["floor_reg"] = cur_loss + + return loss, stats_dict + + +def joints3d_loss(joints3d_obs, joints3d_pred, mask=None): + """ + :param joints3d_obs (B, T, J, 3) + :param joints3d_pred (B, T, J, 3) + :param mask (optional) (B, T) + """ + B, T, *dims = joints3d_obs.shape + vis_mask = get_visible_mask(joints3d_obs) + if mask is not None: + vis_mask = vis_mask & mask.reshape(B, T, *(1,) * len(dims)).bool() + loss = (joints3d_obs[vis_mask] - joints3d_pred[vis_mask]) ** 2 + loss = 0.5 * torch.sum(loss) + return loss + + +def verts3d_loss(verts3d_obs, verts3d_pred, mask=None): + """ + :param verts3d_obs (B, T, V, 3) + :param verts3d_pred (B, T, V, 3) + :param mask (optional) (B, T) + """ + B, T, *dims = verts3d_obs.shape + vis_mask = get_visible_mask(verts3d_obs) + if mask is not None: + assert mask.shape == (B, T) + vis_mask = vis_mask & mask.reshape(B, T, *(1,) * len(dims)).bool() + loss = (verts3d_obs[vis_mask] - verts3d_pred[vis_mask]) ** 2 + loss = 0.5 * torch.sum(loss) + return loss + + +def get_visible_mask(obs_data): + """ + Given observed data gets the mask of visible data (that actually contributes to the loss). + """ + return torch.logical_not(torch.isinf(obs_data)) + + +class Joints2DLoss(nn.Module): + def __init__(self, ignore_op_joints=None, joints2d_sigma=100): + super().__init__() + self.ignore_op_joints = ignore_op_joints + self.joints2d_sigma = joints2d_sigma + + def forward(self, joints2d_obs, joints2d_pred, mask=None): + """ + :param joints2d_obs (B, T, 25, 3) + :param joints2d_pred (B, T, 22, 2) + :param mask (optional) (B, T) + """ + if mask is not None: + mask = mask.bool() + joints2d_obs = joints2d_obs[mask] # (N, 25, 3) + joints2d_pred = joints2d_pred[mask] # (N, 22, 2) + + joints2d_obs_conf = joints2d_obs[..., 2:3] + if self.ignore_op_joints is not None: + # set confidence to 0 so not weighted + joints2d_obs_conf[..., self.ignore_op_joints, :] = 0.0 + + # weight errors by detection confidence + robust_sqr_dist = gmof( + joints2d_pred - joints2d_obs[..., :2], self.joints2d_sigma + ) + reproj_err = (joints2d_obs_conf**2) * robust_sqr_dist + loss = torch.sum(reproj_err) + return loss + + +class Points3DLoss(nn.Module): + def __init__( + self, + use_chamfer=False, + robust_loss="bisquare", + robust_tuning_const=4.6851, + ): + super().__init__() + + if not use_chamfer: + self.active = False + return + + self.active = True + + robust_choices = ["none", "bisquare", "gm"] + if robust_loss not in robust_choices: + Logger.log( + "Not a valid robust loss: %s. Please use %s" + % (robust_loss, str(robust_choices)) + ) + exit() + + from utils.chamfer_distance import ChamferDistance + + self.chamfer_dist = ChamferDistance() + + self.robust_loss = robust_loss + self.robust_tuning_const = robust_tuning_const + + def forward(self, points3d_obs, points3d_pred): + if not self.active: + return torch.tensor(0.0, dtype=torch.float32, device=points3d_obs.device) + + # one-way chamfer + B, T, N_obs, _ = points3d_obs.size() + N_pred = points3d_pred.size(2) + points3d_obs = points3d_obs.reshape((B * T, -1, 3)) + points3d_pred = points3d_pred.reshape((B * T, -1, 3)) + + obs2pred_sqr_dist, pred2obs_sqr_dist = self.chamfer_dist( + points3d_obs, points3d_pred + ) + obs2pred_sqr_dist = obs2pred_sqr_dist.reshape((B, T * N_obs)) + pred2obs_sqr_dist = pred2obs_sqr_dist.reshape((B, T * N_pred)) + + weighted_obs2pred_sqr_dist, w = apply_robust_weighting( + obs2pred_sqr_dist.sqrt(), + robust_loss_type=self.robust_loss, + robust_tuning_const=self.robust_tuning_const, + ) + + loss = torch.sum(weighted_obs2pred_sqr_dist) + loss = 0.5 * loss + return loss + + +def pose_prior_loss(latent_pose_pred, mask=None): + """ + :param latent_pose_pred (B, T, D) + :param mask (optional) (B, T) + """ + # prior is isotropic gaussian so take L2 distance from 0 + loss = latent_pose_pred**2 + if mask is not None: + loss = loss[mask.bool()] + loss = torch.sum(loss) + return loss + + +def shape_prior_loss(betas_pred): + # prior is isotropic gaussian so take L2 distance from 0 + loss = betas_pred**2 + loss = torch.sum(loss) + return loss + + +def joints3d_smooth_loss(joints3d_pred, mask=None): + """ + :param joints3d_pred (B, T, J, 3) + :param mask (optional) (B, T) + """ + # minimize delta steps + B, T, *dims = joints3d_pred.shape + loss = (joints3d_pred[:, 1:, :, :] - joints3d_pred[:, :-1, :, :]) ** 2 + if mask is not None: + mask = mask.bool() + mask = mask[:, 1:] & mask[:, :-1] + loss = loss[mask] + loss = 0.5 * torch.sum(loss) + return loss + + +def motion_prior_loss(latent_motion_pred, cond_prior=None, mask=None): + """ + :param latent_motion_pred (B, T, D) + :param cond_prior (optional) (B, T, D, 2) stacked mean and var of post distribution + :param mask (optional) (B, T) + """ + if mask is not None: + latent_motion_pred = latent_motion_pred[mask.bool()] + + if cond_prior is None: + # assume standard normal + loss = latent_motion_pred**2 + else: + pm, pv = cond_prior[..., 0], cond_prior[..., 1] + if mask is not None: + mask = mask.bool() + pm, pv = pm[mask], pv[mask] + loss = -log_normal(latent_motion_pred, pm, pv) + + return torch.sum(loss) + + +class GMMPriorLoss(nn.Module): + def __init__(self, init_motion_prior=None): + super().__init__() + if init_motion_prior is None: + self.active = False + return + + # build pytorch GMM + self.active = True + self.init_motion_prior = dict() + gmm = build_gmm(*init_motion_prior["gmm"]) + self.init_motion_prior["gmm"] = gmm + + def forward(self, joints, joints_vel, trans_vel, root_orient_vel): + if not self.active: + return torch.tensor(0.0, dtype=torch.float32, device=joints.device) + + # create input + B = joints.size(0) + + joints = joints.reshape((B, -1)) + joints_vel = joints_vel.reshape((B, -1)) + trans_vel = trans_vel.reshape((B, -1)) + root_orient_vel = root_orient_vel.reshape((B, -1)) + init_state = torch.cat([joints, joints_vel, trans_vel, root_orient_vel], dim=-1) + + loss = -self.init_motion_prior["gmm"].log_prob(init_state) + loss = torch.sum(loss) + + return loss + + +def build_gmm(gmm_weights, gmm_means, gmm_covs): + mix = Categorical(gmm_weights) + comp = MultivariateNormal(gmm_means, covariance_matrix=gmm_covs) + gmm_distrib = MixtureSameFamily(mix, comp) + return gmm_distrib + + +def joint_consistency_loss(smpl_joints3d, rollout_joints3d, mask=None): + """ + :param smpl_joints3d (B, T, J, 3) + :param rollout_joints3d (B, T, J, 3) + :param mask (optional) (B, T) + """ + loss = (smpl_joints3d - rollout_joints3d) ** 2 + if mask is not None: + loss = loss[mask.bool()] + loss = 0.5 * torch.sum(loss) + return loss + + +def bone_length_loss(rollout_joints3d, mask=None): + bones = rollout_joints3d[:, :, 1:] + parents = rollout_joints3d[:, :, SMPL_PARENTS[1:]] + bone_lengths = torch.norm(bones - parents, dim=-1) + loss = bone_lengths[:, 1:] - bone_lengths[:, :-1] + if mask is not None: + mask = mask.bool() + mask = mask[:, 1:] & mask[:, :-1] + loss = loss[mask] + loss = 0.5 * torch.sum(loss**2) + return loss + + +def contact_vel_loss(contacts_conf, joints3d, mask=None): + """ + Velocity should be zero at predicted contacts + """ + delta_pos = (joints3d[:, 1:] - joints3d[:, :-1]) ** 2 + loss = delta_pos.sum(dim=-1) * contacts_conf[:, 1:] + if mask is not None: + mask = mask.bool() + mask = mask[:, 1:] & mask[:, :-1] + loss = loss[mask] + loss = 0.5 * torch.sum(loss) + + return loss + + +def contact_height_loss(contacts_conf, joints3d, mask=None): + """ + Contacting joints should be near floor + """ + # won't be exactly on the floor, just near it (since joints are inside the body) + floor_diff = F.relu(torch.torch.abs(joints3d[:, :, :, 2]) - CONTACT_HEIGHT_THRESH) + loss = floor_diff * contacts_conf + if mask is not None: + loss = loss[mask.bool()] + + loss = torch.sum(loss) + return loss + + +def floor_reg_loss(pred_floor_plane, obs_floor_plane): + """ + Pred floor plane shouldn't deviate from the initial observation + :param pred_floor_plane (B, 3) + :param obs_floor_plane (B, 3) + """ + floor_loss = (pred_floor_plane - obs_floor_plane) ** 2 + floor_loss = 0.5 * torch.sum(floor_loss) + + return floor_loss + + +def kl_normal(qm, qv, pm, pv): + """ + Computes the elem-wise KL divergence between two normal distributions KL(q || p) and + sum over the last dimension + ​ + Args: + qm: tensor: (batch, dim): q mean + qv: tensor: (batch, dim): q variance + pm: tensor: (batch, dim): p mean + pv: tensor: (batch, dim): p variance + ​ + Return: + kl: tensor: (batch,): kl between each sample + """ + element_wise = 0.5 * ( + torch.log(pv) - torch.log(qv) + qv / pv + (qm - pm).pow(2) / pv - 1 + ) + kl = element_wise.sum(-1) + return kl + + +def log_normal(x, m, v): + """ + Computes the elem-wise log probability of a Gaussian and then sum over the + last dim. Basically we're assuming all dims are batch dims except for the + last dim. Args: + x: tensor: (batch_1, batch_2, ..., batch_k, dim): Observation + m: tensor: (batch_1, batch_2, ..., batch_k, dim): Mean + v: tensor: (batch_1, batch_2, ..., batch_k, dim): Variance Return: + log_prob: tensor: (batch_1, batch_2, ..., batch_k): log probability of + each sample. Note that the summation dimension is not kept + """ + log_prob = ( + -torch.log(torch.sqrt(v)) + - math.log(math.sqrt(2 * math.pi)) + - ((x - m) ** 2 / (2 * v)) + ) + log_prob = torch.sum(log_prob, dim=-1) + return log_prob + + +def apply_robust_weighting( + res, robust_loss_type="bisquare", robust_tuning_const=4.6851 +): + """ + Returns robustly weighted squared residuals. + - res : torch.Tensor (B x N), take the MAD over each batch dimension independently. + """ + robust_choices = ["none", "bisquare"] + if robust_loss_type not in robust_choices: + print( + "Not a valid robust loss: %s. Please use %s" + % (robust_loss_type, str(robust_choices)) + ) + + w = None + detach_res = ( + res.clone().detach() + ) # don't want gradients flowing through the weights to avoid degeneracy + if robust_loss_type == "none": + w = torch.ones_like(detach_res) + elif robust_loss_type == "bisquare": + w = bisquare_robust_weights(detach_res, tune_const=robust_tuning_const) + + # apply weights to squared residuals + weighted_sqr_res = w * (res**2) + return weighted_sqr_res, w + + +def robust_std(res): + """ + Compute robust estimate of standarad deviation using median absolute deviation (MAD) + of the given residuals independently over each batch dimension. + + - res : (B x N) + + Returns: + - std : B x 1 + """ + B = res.size(0) + med = torch.median(res, dim=-1)[0].reshape((B, 1)) + abs_dev = torch.abs(res - med) + MAD = torch.median(abs_dev, dim=-1)[0].reshape((B, 1)) + std = MAD / 0.67449 + return std + + +def bisquare_robust_weights(res, tune_const=4.6851): + """ + Bisquare (Tukey) loss. + See https://www.mathworks.com/help/curvefit/least-squares-fitting.html + + - residuals + """ + # print(res.size()) + norm_res = res / (robust_std(res) * tune_const) + # NOTE: this should use absolute value, it's ok right now since only used for 3d point cloud residuals + # which are guaranteed positive, but generally this won't work) + outlier_mask = norm_res >= 1.0 + + # print(torch.sum(outlier_mask)) + # print('Outlier frac: %f' % (float(torch.sum(outlier_mask)) / res.size(1))) + + w = (1.0 - norm_res**2) ** 2 + w[outlier_mask] = 0.0 + + return w + + +def gmof(res, sigma): + """ + Geman-McClure error function + - residual + - sigma scaling factor + """ + x_squared = res**2 + sigma_squared = sigma**2 + return (sigma_squared * x_squared) / (sigma_squared + x_squared) diff --git a/slahmr/slahmr/optim/moving_scene.py b/slahmr/slahmr/optim/moving_scene.py new file mode 100644 index 0000000000000000000000000000000000000000..30dd95785db17ea243b1860fb25ee57c81b01455 --- /dev/null +++ b/slahmr/slahmr/optim/moving_scene.py @@ -0,0 +1,726 @@ +import os +import numpy as np + +import torch +import torch.nn as nn +import torch.nn.functional as F + +from body_model import SMPL_JOINTS, KEYPT_VERTS, smpl_to_openpose +from geometry.rotation import batch_rodrigues, rotation_matrix_to_angle_axis +from util.logger import Logger +from util.tensor import ( + detach_all, + scatter_intervals, + select_intervals, + get_scatter_mask, +) + +from .base_scene import BaseSceneModel +from .helpers import compute_world2prior, estimate_floor_planes + + +J_BODY = len(SMPL_JOINTS) - 1 # no root +CONTACT_ORDERING = [ + "hips", + "leftLeg", + "rightLeg", + "leftFoot", + "rightFoot", + "leftToeBase", + "rightToeBase", + "leftHand", + "rightHand", +] +CONTACT_INDS = [SMPL_JOINTS[jname] for jname in CONTACT_ORDERING] +CONTACT_THRESH = 0.5 + + +class MovingSceneModel(BaseSceneModel): + """ + Scene model of moving people in a shared global reference frame + + Parameters: + batch_size: number of sequences to optimize + seq_len: length of the sequences + pose_prior: VPoser model + motion_prior: humor model + init_motion_prior: dict of GMM params to use for prior on initial motion state + shared_floor: (default True) if true, sequences are in the same reference frame + fit_gender: (optional) gender of SMPL model + """ + + def __init__( + self, + batch_size, + seq_len, + body_model, + pose_prior, + motion_prior, + init_motion_prior=None, + fit_gender="neutral", + use_init=False, + opt_cams=False, + opt_scale=True, + cam_graph=False, + est_floor=True, + floor_type="shared", + async_tracks=True, + **kwargs, + ): + super().__init__( + batch_size, + seq_len, + body_model, + pose_prior, + fit_gender=fit_gender, + use_init=use_init, + opt_cams=opt_cams, + opt_scale=opt_scale, + cam_graph=cam_graph, + ) + assert motion_prior is not None + assert motion_prior.model_data_config in [ + "smpl+joints", + "smpl+joints+contacts", + ], "Only smpl+joints motion prior configuration is supported!" + + self.motion_prior = motion_prior + self.init_motion_prior = init_motion_prior + + # need latent dynamics sequence as well + self.latent_motion_dim = self.motion_prior.latent_size + self.cond_prior = self.motion_prior.use_conditional_prior + + # the frame chosen to use for the initial state (first frame by default) + self.async_tracks = async_tracks + self.register_buffer("track_start", torch.zeros(self.batch_size)) + self.register_buffer("track_end", torch.ones(self.batch_size) * self.seq_len) + + self.shared_floor = floor_type == "shared" + self.group_floor = floor_type == "group" + self.floor_type = floor_type + print("FLOOR TYPE", floor_type) + self.est_floor = est_floor + + @property + def is_motion_active(self): + return hasattr(self.params, "latent_motion") + + def initialize(self, obs_data, cam_data, param_dict, data_fps): + """ + we need to also optimize for floor and world scale + """ + Logger.log("Initializing moving scene model with observed data") + + self.params.set_cameras( + cam_data, + opt_scale=self.opt_scale, + opt_cams=self.opt_cams, + opt_focal=self.opt_cams, + **param_dict, + ) + self.init_floor(obs_data, param_dict) + self.init_first_state(obs_data, param_dict, data_fps) + + def init_floor(self, obs_data, param_dict): + if self.est_floor or self.group_floor: + with torch.no_grad(): + smpl_preds = self.pred_smpl( + param_dict["trans"], + param_dict["root_orient"], + self.latent2pose(param_dict["latent_pose"]), + param_dict["betas"], + ) + floor_plane, floor_idcs = estimate_floor_planes( + smpl_preds["joints3d"].detach(), + obs_data["vis_mask"] > 0, + group=self.group_floor, + flatten=self.shared_floor, + ) + if self.group_floor and not self.est_floor: + # don't use the estimated floor as initial plane + floor_plane = obs_data["floor_plane"][: len(floor_plane)] + else: # fixed shared or separate floors + num_floors = 1 if self.shared_floor else self.batch_size + floor_plane = obs_data["floor_plane"][:num_floors] + if self.shared_floor: + floor_idcs = torch.zeros( + self.batch_size, dtype=torch.long, device=floor_plane.device + ) + else: + floor_idcs = torch.arange( + self.batch_size, dtype=torch.long, device=floor_plane.device + ) + + Logger.log(f"ESTIMATED FLOORS: {str(floor_plane.detach().cpu())}") + Logger.log(f"FLOOR IDCS: {str(floor_idcs.detach().cpu())}") + self.params.set_param("floor_plane", floor_plane.float().detach()) + self.params.set_param( + "floor_idcs", floor_idcs.long().detach(), requires_grad=False + ) + + def init_first_state(self, obs_data, param_dict, data_fps): + """ + initialize the latent motion and first state of each track + using per-frame trajectories of trans, rot, latent_pose, betas + and observed data + """ + B, T = self.batch_size, self.seq_len + param_dict = detach_all(param_dict) + + # select the valid segments of each track; pad the shorter tracks with final element + if self.async_tracks and "track_interval" in obs_data: + print("asynchronous tracks") + interval = obs_data["track_interval"] # (B, 2) + start, end = interval[:, 0], interval[:, 1] + self.track_start, self.track_end = start, end + param_dict = select_dict_segments( + param_dict, start, end, names=["trans", "root_orient", "latent_pose"] + ) + + trans = param_dict["trans"] # (B, T, 3) + root_orient = param_dict["root_orient"] # (B, T, 3) + latent_pose = param_dict["latent_pose"] # (B, T, D) + betas = param_dict["betas"] # (B, b) + + Logger.log(f"SEL TRACKS {trans.shape}, {root_orient.shape}") + + # save each track's first appearance + self.params.set_param("trans", trans[:, :1]) + Logger.log(f"INITIAL TRANS {trans[:, :1].detach().cpu()}") + self.params.set_param("root_orient", root_orient[:, :1]) + self.params.set_param("latent_pose", latent_pose[:, :1]) + self.params.set_param("betas", betas) + + # pass the current pose estimates through the motion prior + self.data_fps = data_fps + body_pose = self.latent2pose(latent_pose) + init_latent = self.infer_latent_motion( + trans, root_orient, body_pose, betas, data_fps + ).detach() # (B, T-1, D) + self.params.set_param("latent_motion", init_latent) + + # estimate velocities in prior frame and save initial state + trans_vel, joints_vel, root_orient_vel = self.estimate_prior_velocities( + trans, root_orient, body_pose, betas, data_fps + ) + self.params.set_param("trans_vel", trans_vel[:, :1].detach()) + self.params.set_param("joints_vel", joints_vel[:, :1].detach()) + self.params.set_param("root_orient_vel", root_orient_vel[:, :1].detach()) + + def get_optim_result(self, num_steps=-1): + res = super().get_optim_result() + if not self.is_motion_active: + return res + + num_steps = self.seq_len if num_steps < 0 else num_steps + prior_res, world_res = self.rollout_latent_motion( + self.params.latent_motion[:, : num_steps - 1] + ) + world_res = self.synchronize_preds(world_res, num_steps) + res["world"].update(world_res) + + prior_res = self.synchronize_preds(prior_res, num_steps) + res["prior"] = prior_res + return res + + def estimate_prior_velocities(self, trans, root_orient, body_pose, betas, data_fps): + """ + compute velocities of trajectory in prior frame (not world frame) + Transforms the first of each track into the prior frame + :param trans (B, T, 3) + :param root_orient (B, T, 3) + :param body_pose (B, T, Dp) + :param betas (B, Db) + """ + with torch.no_grad(): + self.update_world2prior(trans, root_orient, body_pose, betas) + trans, root_orient = self.apply_world2prior( + trans, root_orient, body_pose, betas + ) + smpl_results = self.pred_smpl(trans, root_orient, body_pose, betas) + return estimate_velocities( + trans, root_orient, smpl_results["joints3d"], data_fps + ) + + def update_world2prior(self, trans, root_orient, body_pose, betas): + B = trans.shape[0] + smpl_data = self.pred_smpl( + trans[:, :1], root_orient[:, :1], body_pose[:, :1], betas + ) + floor_plane = self.params.floor_plane[self.params.floor_idcs] + R, t, height = compute_world2prior( + floor_plane, + trans[:, 0], + root_orient[:, 0], + smpl_data["joints3d"][:, 0, 0], + ) + self.world2prior_R = R # (B, 3, 3) + self.world2prior_t = t # (B, 3) + self.world2prior_root_height = height # (B) + + def apply_world2prior(self, trans, root_orient, body_pose, betas, inverse=False): + """ + Applies the world2prior tranformation to trans, root_orient + If T=1, this function assumes they are at key_frame_idx, + which we need to compute the offset from the origin + :param trans (B, T, 3) + :param root_orient (B, T, 3) + :param body_pose (B, T, J, 3) + :param betas (B, b) + :param inverse (bool) optional, default False + """ + B, T, _ = trans.size() + # (B, 3, 3), (B, 3), (B) + R, t, root_height = ( + self.world2prior_R, + self.world2prior_t, + self.world2prior_root_height, + ) + R_time = R.unsqueeze(1).expand((B, T, 3, 3)) + t_time = t.unsqueeze(1).expand((B, T, 3)) + root_orient_mat = batch_rodrigues(root_orient.reshape(-1, 3)).reshape( + B, T, 3, 3 + ) + + if inverse: + R_time = R_time.transpose(-1, -2) + + root_orient_mat = torch.matmul(R_time, root_orient_mat) + root_orient = rotation_matrix_to_angle_axis( + root_orient_mat.reshape(B * T, 3, 3) + ).reshape(B, T, 3) + + if inverse: + # transform so first frame is at origin + trans = trans - trans[:, :1, :] + + # rotates to world frame + trans = torch.matmul(R_time, trans[..., None])[..., 0] + # translate to world frame + trans = trans - t_time + + return trans, root_orient + + # first transform so the trans of key frame is at origin + trans = trans + t_time + # then rotate to canonical frame + trans = torch.matmul(R_time, trans[..., None])[..., 0] + # compute the root height after transforming + cur_smpl_data = self.pred_smpl(trans, root_orient, body_pose, betas) + cur_root_height = cur_smpl_data["joints3d"][:, 0, 0, 2:3] + # then apply floor offset so the root joint is at root_height + height_diff = root_height - cur_root_height + trans_offset = torch.cat( + [torch.zeros((B, 2)).to(height_diff), height_diff], axis=1 + ) + trans = trans + trans_offset.reshape((B, 1, 3)) + + return trans, root_orient + + def convert_prior_rot_inputs(self, root_orient, body_pose): + # convert rots + # body pose and root orient are both in aa + B, T = root_orient.shape[:2] + if ( + self.motion_prior.in_rot_rep == "mat" + or self.motion_prior.in_rot_rep == "6d" + ): + root_orient_in = batch_rodrigues(root_orient.reshape(-1, 3)).reshape( + (B, T, 9) + ) + body_pose_in = batch_rodrigues(body_pose.reshape(-1, 3)).reshape( + (B, T, J_BODY * 9) + ) + if self.motion_prior.in_rot_rep == "6d": + root_orient_in = root_orient[:, :, :6] + body_pose_in = body_pose.reshape((B, T, J_BODY, 9))[:, :, :, :6].reshape( + (B, T, J_BODY * 6) + ) + return root_orient_in, body_pose_in + + def convert_prior_rot_outputs(self, out_dict): + keys = ["root_orient", "pose_body"] + for k in keys: + out = out_dict[k] + B, T = out.shape[:2] + out_dict[k] = rotation_matrix_to_angle_axis( + out.reshape((-1, 3, 3)) + ).reshape((B, T, -1)) + return out_dict + + def infer_latent_motion( + self, trans, root_orient, body_pose, betas, data_fps, full_forward_pass=False + ): + """ + By default, gets a sequence of z's from the current SMPL optim params. + + If full_forward_pass is true, also samples from the posterior and feeds + through the motion prior decoder to get all terms needed to calculate the ELBO. + """ + B, T, _ = trans.size() + h = 1.0 / data_fps + + # need to first transform into canonical coordinate frame + self.update_world2prior(trans, root_orient, body_pose, betas) + trans, root_orient = self.apply_world2prior( + trans, root_orient, body_pose, betas + ) + + smpl_results = self.pred_smpl(trans, root_orient, body_pose, betas) + joints = smpl_results["joints3d"] # (B, T, len(SMPL_JOINTS), 3) + trans_vel, joints_vel, root_orient_vel = estimate_velocities( + trans, root_orient, joints, data_fps + ) + + root_orient_in, body_pose_in = self.convert_prior_rot_inputs( + root_orient, body_pose + ) + joints_in = joints.reshape((B, T, -1)) + joints_vel_in = joints_vel.reshape((B, T, -1)) + + seq_dict = { + "trans": trans, + "trans_vel": trans_vel, + "root_orient": root_orient_in, + "root_orient_vel": root_orient_vel, + "pose_body": body_pose_in, + "joints": joints_in, + "joints_vel": joints_vel_in, + } + + infer_results = self.motion_prior.infer_global_seq( + seq_dict, full_forward_pass=full_forward_pass + ) + if full_forward_pass: + # return both the given motion and the one from the forward pass + # make sure rotations are matrix + # NOTE: assumes seq_dict is same thing we want to compute loss on + # Need to change if multiple future steps. + if self.motion_prior.in_rot_rep != "mat": + seq_dict["trans"] = batch_rodrigues(root_orient.reshape(-1, 3)).reshape( + (B, T, 9) + ) + seq_dict["pose_body"] = batch_rodrigues( + body_pose.reshape(-1, 3) + ).reshape((B, T, J_BODY * 9)) + # do not need initial step anymore since output will be T-1 + for k, v in seq_dict.items(): + seq_dict[k] = v[:, 1:] + for k in infer_results.keys(): + if k != "posterior_distrib" and k != "prior_distrib": + infer_results[k] = infer_results[k][ + :, :, 0 + ] # only want first output step + infer_results = (seq_dict, infer_results) + else: + prior_z, posterior_z = infer_results + infer_results = posterior_z[0] # mean of the approximate posterior + + return infer_results + + def rollout_smpl_steps(self, num_steps=-1): + # rollout motion given initial state + num_steps = self.seq_len if num_steps < 0 else num_steps + latent_motion = self.params.latent_motion[:, : num_steps - 1] + + # roll out tracks from their first appearances + # NOTE rolled out tracks are unsynced in time + res, world_res = self.rollout_latent_motion( + latent_motion, return_prior=self.cond_prior + ) + + # get the smpl predictions for the unsynced tracks + preds = self.pred_smpl( + res["trans"], res["root_orient"], res["pose_body"], res["betas"] + ) + world_preds = self.pred_smpl( + world_res["trans"], + world_res["root_orient"], + world_res["pose_body"], + world_res["betas"], + ) + + # pass along relevant results + preds["joints3d_rollout"] = res["joints"] + preds["latent_pose"] = self.pose2latent(res["pose_body"]) + preds["joints3d_init"] = preds["joints3d"][:, :1] + + if "contacts" in res: + preds["contacts"] = res["contacts"] + if "contacts_conf" in res: + preds["contacts_conf"] = res["contacts_conf"] + + # synchronize the tracklets to the same timesteps + preds = self.synchronize_preds(preds, num_steps) + world_preds = self.synchronize_preds(world_preds, num_steps) + + # pass along unsynchronized motion latents + preds["latent_motion"] = latent_motion + if "cond_prior" in res: + preds["cond_prior"] = res["cond_prior"] + + return preds, world_preds + + def rollout_latent_motion( + self, + latent_motion, + return_prior=False, + return_vel=False, + num_steps=-1, + canonicalize_input=False, + ): + """ + From the stored initial state, rolls out a sequence from the latent_motion vector + NOTE: the stored initial states are not at the same time step, but we return all + predicted sequences starting from time 0. + + If latent_motion is None, samples num_steps into the future sequence from the prior. + using the mean of the prior rather than random samples. + + If canonicalize_input is True, transform the initial state into the local canonical + frame before roll out + """ + # get the first frame state + # NOTE: first states do not occur at same time step + trans, root_orient, betas = ( + self.params.trans, + self.params.root_orient, + self.params.betas, + ) + trans_vel, root_orient_vel, joints_vel = ( + self.params.trans_vel, + self.params.root_orient_vel, + self.params.joints_vel, + ) + body_pose = self.latent2pose(self.params.latent_pose) + + B = trans.size(0) + is_sampling = latent_motion is None + Tm1 = num_steps if latent_motion is None else latent_motion.size(1) + if is_sampling and Tm1 <= 0: + Logger.log("num_steps must be positive to sample!") + exit() + + # need to first transform initial state into canonical coordinate frame + self.update_world2prior(trans, root_orient, body_pose, betas) + trans, root_orient = self.apply_world2prior( + trans, root_orient, body_pose, betas + ) + + smpl_results = self.pred_smpl(trans, root_orient, body_pose, betas) + joints = smpl_results["joints3d"] # (B, T, len(SMPL_JOINTS), 3) + + # update to correct rotations for input + root_orient_in, body_pose_in = self.convert_prior_rot_inputs( + root_orient, body_pose + ) + joints_in = joints.reshape((B, 1, -1)) + joints_vel_in = joints_vel.reshape((B, 1, -1)) + + rollout_in_dict = { + "trans": trans, + "root_orient": root_orient_in, + "pose_body": body_pose_in, + "joints": joints_in, + "trans_vel": trans_vel, + "root_orient_vel": root_orient_vel, + "joints_vel": joints_vel_in, + } + + roll_output = self.motion_prior.roll_out( + None, + rollout_in_dict, + Tm1, + z_seq=latent_motion, + return_prior=return_prior, + return_z=is_sampling, + canonicalize_input=canonicalize_input, + gender=[self.fit_gender] * B, + betas=betas.reshape((B, 1, -1)), + ) + + pred_dict = prior_out = None + if return_prior: + pred_dict, prior_out = roll_output + else: + pred_dict = roll_output + + pred_dict = self.convert_prior_rot_outputs(pred_dict) + + # concat with initial state + trans_out = torch.cat([trans, pred_dict["trans"]], dim=1) + root_orient_out = torch.cat([root_orient, pred_dict["root_orient"]], dim=1) + body_pose_out = torch.cat([body_pose, pred_dict["pose_body"]], dim=1) + joints_out = torch.cat( + [joints, pred_dict["joints"].reshape((B, Tm1, -1, 3))], dim=1 + ) + out_dict = { + "trans": trans_out, + "root_orient": root_orient_out, + "pose_body": body_pose_out, + "joints": joints_out, + "betas": betas, + } + if return_vel: + out_dict["trans_vel"] = torch.cat( + [trans_vel, pred_dict["trans_vel"]], dim=1 + ) + out_dict["root_orient_vel"] = torch.cat( + [root_orient_vel, pred_dict["root_orient_vel"]], dim=1 + ) + out_dict["joints_vel"] = torch.cat( + [joints_vel, pred_dict["joints_vel"].reshape((B, Tm1, -1, 3))], + dim=1, + ) + + if return_prior: # return the mean and var of distribution stacked + pm, pv = prior_out + out_dict["cond_prior"] = torch.stack([pm, pv], dim=-1) + + if self.motion_prior.model_data_config == "smpl+joints+contacts": + pred_contacts = pred_dict["contacts"] + # get binary classification + contact_conf = torch.sigmoid(pred_contacts) + pred_contacts = (contact_conf > CONTACT_THRESH).to(torch.float) + # expand to full body + full_contact_conf = torch.zeros((B, Tm1, len(SMPL_JOINTS))).to(contact_conf) + full_contact_conf[:, :, CONTACT_INDS] = ( + full_contact_conf[:, :, CONTACT_INDS] + contact_conf + ) + full_contacts = torch.zeros((B, Tm1, len(SMPL_JOINTS))).to(pred_contacts) + full_contacts[:, :, CONTACT_INDS] = ( + full_contacts[:, :, CONTACT_INDS] + pred_contacts + ) + # repeat first entry for t0 + full_contact_conf = torch.cat( + [full_contact_conf[:, 0:1], full_contact_conf], dim=1 + ) + full_contacts = torch.cat([full_contacts[:, 0:1], full_contacts], dim=1) + out_dict["contacts_conf"] = full_contact_conf + out_dict["contacts"] = full_contacts + + if is_sampling: + out_dict["z"] = pred_dict["z"] + + cam_dict = { + "trans": out_dict["trans"], + "root_orient": out_dict["root_orient"], + "pose_body": out_dict["pose_body"], + "betas": out_dict["betas"], + } + + # also must return trans and root orient in camera frame + cam_dict["trans"], cam_dict["root_orient"] = self.apply_world2prior( + out_dict["trans"], + out_dict["root_orient"], + out_dict["pose_body"], + out_dict["betas"], + inverse=True, + ) + return out_dict, cam_dict + + def synchronize_preds(self, pred_dict, seg_len): + """ + synchronize predictions in time, scatter predictions into [0, seq_len) + """ + if not self.async_tracks: + # predictions are already synchronized + return pred_dict, None + + # return time-synchronized predictions + start = self.track_start + end = torch.clip(start + seg_len, max=self.track_end) + T = end.max() + pred_dict = scatter_dict_segments(pred_dict, start, end, T) + pred_mask = get_scatter_mask(start, end, T) + pred_dict["track_mask"] = pred_mask + return pred_dict + + +def scatter_dict_segments(data_dict, start, end, T=None, names=None): + """ + the tracks as they are stored are synchronized by time step + Uses the start and end to synchronize output predictions + """ + sync_dict = data_dict.copy() + min_len = (end - start).min() + if names is None: + names = data_dict.keys() + for name in names: + val = data_dict[name] + if not isinstance(val, torch.Tensor) or val.ndim < 3 or val.shape[1] < min_len: + continue + sync_dict[name] = scatter_intervals(val, start, end, T) + return sync_dict + + +def select_dict_segments(data_dict, start, end, names=None): + out_data_dict = data_dict.copy() + min_len = (end - start).min() + if names is None: + names = data_dict.keys() + for name in names: + val = data_dict[name] + if not isinstance(val, torch.Tensor) or val.ndim < 3 or val.shape[1] < min_len: + continue + # only select for time-series observations + out_data_dict[name] = select_intervals(val, start, end) + return out_data_dict + + +def estimate_velocities(trans, root_orient, joints3d, data_fps): + """ + Estimates velocity inputs to the motion prior. + - trans (B, T, 3) root translation + - root_orient (B, T, 3) aa root orientation + - joints3d (B, T, len(SMPL_JOINTS), 3) joints3d of SMPL prediction + """ + B, T, _ = trans.size() + h = 1.0 / data_fps + trans_vel = estimate_linear_velocity(trans, h) + joints_vel = estimate_linear_velocity(joints3d, h) + root_orient_mat = batch_rodrigues(root_orient.reshape((-1, 3))).reshape( + (B, T, 3, 3) + ) + root_orient_vel = estimate_angular_velocity(root_orient_mat, h) + return trans_vel, joints_vel, root_orient_vel + + +def estimate_linear_velocity(data_seq, h): + """ + Given some batched data sequences of T timesteps in the shape (B, T, ...), estimates + the velocity for the middle T-2 steps using a second order central difference scheme. + The first and last frames are with forward and backward first-order + differences, respectively + - h : step size + """ + # first steps is forward diff (t+1 - t) / h + init_vel = (data_seq[:, 1:2] - data_seq[:, :1]) / h + # middle steps are second order (t+1 - t-1) / 2h + middle_vel = (data_seq[:, 2:] - data_seq[:, 0:-2]) / (2 * h) + # last step is backward diff (t - t-1) / h + final_vel = (data_seq[:, -1:] - data_seq[:, -2:-1]) / h + + vel_seq = torch.cat([init_vel, middle_vel, final_vel], dim=1) + return vel_seq + + +def estimate_angular_velocity(rot_seq, h): + """ + Given a batch of sequences of T rotation matrices, estimates angular velocity at T-2 steps. + Input sequence should be of shape (B, T, ..., 3, 3) + """ + # see https://en.wikipedia.org/wiki/Angular_velocity#Calculation_from_the_orientation_matrix + dRdt = estimate_linear_velocity(rot_seq, h) + R = rot_seq + RT = R.transpose(-1, -2) + # compute skew-symmetric angular velocity tensor + w_mat = torch.matmul(dRdt, RT) + # pull out angular velocity vector + # average symmetric entries + w_x = (-w_mat[..., 1, 2] + w_mat[..., 2, 1]) / 2.0 + w_y = (w_mat[..., 0, 2] - w_mat[..., 2, 0]) / 2.0 + w_z = (-w_mat[..., 0, 1] + w_mat[..., 1, 0]) / 2.0 + w = torch.stack([w_x, w_y, w_z], axis=-1) + return w diff --git a/slahmr/slahmr/optim/optimizers.py b/slahmr/slahmr/optim/optimizers.py new file mode 100644 index 0000000000000000000000000000000000000000..762eaa64e18fc444dd58e8b0319fdb0f8c500f9d --- /dev/null +++ b/slahmr/slahmr/optim/optimizers.py @@ -0,0 +1,616 @@ +import os +import glob +import numpy as np +import matplotlib.pyplot as plt + +import torch +import torch.nn as nn +import torch.nn.functional as F +import torch.optim as optim + +from body_model import OP_IGNORE_JOINTS +from geometry.mesh import save_mesh_scenes +from util.logger import Logger, log_cur_stats +from util.tensor import move_to, detach_all +from vis.output import prep_result_vis, animate_scene + +from .losses import RootLoss, SMPLLoss, MotionLoss +from .output import save_camera_json + + +LINE_SEARCH = "strong_wolfe" + + +""" +Optimization happens in multiple stages +Stage 1: fit root orients and trans of each frame indendpently +Stage 2: fit SMPL poses and betas of each frame independently +Stage 3: fit poses and roots in same global coordinate frame +""" + + +class StageOptimizer(object): + def __init__( + self, + name, + model, + param_names, + lr=1.0, + lbfgs_max_iter=20, + save_every=10, + vis_every=-1, + save_meshes=True, + max_chunk_steps=10, + **kwargs, + ): + Logger.log(f"INITIALIZING OPTIMIZER {name} for {param_names}") + self.name = name + self.model = model + + self.set_opt_vars(param_names) + + self.optim = torch.optim.LBFGS( + self.opt_params, max_iter=lbfgs_max_iter, lr=lr, line_search_fn=LINE_SEARCH + ) + # LBFGS computes losses multiple times per iteration, + # save a dict mapping iteration to list of stats_dicts + self.loss_dicts = {} + + self.save_every = save_every + self.vis_every = vis_every + self.save_meshes = save_meshes + self.max_chunk_steps = max_chunk_steps + + self.cur_step = 0 + + self.add_chunk = 0 + self.cur_loss = 0 + self.prev_loss = np.inf + self.last_updated = 0 + self.reached_max = False + self.reached_max_iter = -1 + + def set_opt_vars(self, param_names): + Logger.log("Set param names:") + Logger.log(param_names) + + self.param_names = param_names + self.model.params.set_require_grads(self.param_names) + self.opt_params = [ + getattr(self.model.params, name) for name in self.param_names + ] + + def forward_pass(self, obs_data): + raise NotImplementedError + + def load_checkpoint(self, out_dir, device=None): + if device is None: + device = torch.device("cpu") + + param_path = os.path.join(out_dir, f"{self.name}_params.pth") + if os.path.isfile(param_path): + param_dict = torch.load(param_path, map_location=device) + self.model.params.load_dict(param_dict) + Logger.log(f"Params loaded from {param_path}") + + optim_path = os.path.join(out_dir, f"{self.name}_optim.pth") + if os.path.isfile(optim_path): + optim_dict = torch.load(optim_path) + self.optim.load_state_dict(optim_dict["optim"]) + self.cur_step = optim_dict["cur_step"] + Logger.log(f"Optimizer loaded from {optim_path} at iter {self.cur_step}") + + def save_checkpoint(self, out_dir): + param_path = os.path.join(out_dir, f"{self.name}_params.pth") + param_dict = self.model.params.get_dict() + if "world_scale" in param_dict: + print("WORLD_SCALE", param_dict["world_scale"].detach().cpu()) + if "floor_plane" in param_dict: + print("FLOOR PLANE", param_dict["floor_plane"].detach().cpu()) + if "cam_f" in param_dict: + print("CAM_F", param_dict["cam_f"].detach().cpu()) + torch.save(param_dict, param_path) + Logger.log(f"Model saved at {param_path}") + + optim_path = os.path.join(out_dir, f"{self.name}_optim.pth") + torch.save( + {"optim": self.optim.state_dict(), "cur_step": self.cur_step}, + optim_path, + ) + Logger.log(f"Optimizer saved at {optim_path}") + + def save_results(self, out_dir, seq_name): + """ + pred dict will be a dictionary of trajectories. + each trajectory will have params and lists of trimesh sequences + """ + os.makedirs(out_dir, exist_ok=True) + + with torch.no_grad(): + pred_dict = self.model.get_optim_result() + pred_dict = move_to(detach_all(pred_dict), "cpu") + + i = self.cur_step + for name, results in pred_dict.items(): + # save parameters of trajectory + out_path = f"{out_dir}/{seq_name}_{i:06d}_{name}_results.npz" + Logger.log(f"saving params to {out_path}") + np.savez(out_path, **results) + + # also save the cameras + with torch.no_grad(): + cam_R, cam_t = self.model.params.get_extrinsics() + intrins = self.model.params.get_intrinsics() + save_camera_json( + f"{out_dir}/{seq_name}_cameras_{self.cur_step:06d}.json", + cam_R.detach().cpu(), + cam_t.detach().cpu(), + intrins.detach().cpu(), + ) + + # plot losses + self.plot_losses(out_dir) + + def save_mesh_scenes(self, scene_dict, out_dir): + # save the meshes + os.makedirs(out_dir, exist_ok=True) + i = self.cur_step + for name, scene in scene_dict.items(): + scene_dir = f"{out_dir}/{i:06d}_{name}" + mesh_seqs = scene["meshes"] + Logger.log(f"saving {len(mesh_seqs)} meshes to {scene_dir}") + save_mesh_scenes(scene_dir, mesh_seqs) + + def vis_result(self, res_dir, obs_data, vis=None, num_steps=-1): + if vis is None or self.vis_every < 0: + return + + # check which results are saved + seq_name = obs_data["seq_name"][0] + res_pre = f"{res_dir}/{seq_name}_opt_{self.cur_step:06d}" + with torch.no_grad(): + pred_dict = self.model.get_optim_result(num_steps=num_steps) + + res_dict = detach_all(pred_dict["world"]) + scene_dict = move_to( + prep_result_vis( + res_dict, + obs_data["vis_mask"], + obs_data["track_id"], + self.model.body_model, + ), + "cpu", + ) + animate_scene(vis, scene_dict, res_pre, render_views=["src_cam", "above"]) + + def log_losses(self, stats_dict): + stats_dict = move_to(detach_all(stats_dict), "cpu") + log_cur_stats( + stats_dict, + iter=self.cur_step, + to_stdout=(self.cur_step % self.save_every == 0), + ) + for loss_name, loss_val in stats_dict.items(): + loss_dict = self.loss_dicts.get(loss_name, {}) + loss_series = loss_dict.get(self.cur_step, []) + loss_series.append(loss_val) + loss_dict[self.cur_step] = loss_series + self.loss_dicts[loss_name] = loss_dict + + def record_current_losses(self, writer): + """ + record the mean of current step's loss values in tensorboard + """ + if len(self.loss_dicts) < 1: + return + + for loss_name, loss_dict in self.loss_dicts.items(): + loss_mean = np.mean(loss_dict[self.cur_step]) + writer.add_scalar(f"{self.name}/{loss_name}", loss_mean, self.cur_step) + + def plot_losses(self, res_dir): + """ + plot a box plot for each BFGS iteration + """ + if len(self.loss_dicts) < 1: + return + for loss_name, loss_dict in self.loss_dicts.items(): + # times (list len T) + # loss vals (list len T of loss value lists) + times, loss_vals = zip(*loss_dict.items()) + plt.figure() + plt.boxplot(loss_vals, labels=times, showfliers=False) + plt.savefig(f"{res_dir}/{loss_name}.png") + + def run(self, obs_data, num_iters, out_dir, vis=None, writer=None): + self.cur_step = 0 + self.loss.cur_step = 0 + res_dir = os.path.join(out_dir, self.name) + os.makedirs(res_dir, exist_ok=True) + seq_name = obs_data["seq_name"][0] + print("SEQ NAME", seq_name) + + # try to load from checkpoint if exists + device = obs_data["joints2d"].device + self.load_checkpoint(out_dir, device=device) + + if self.cur_step >= num_iters: + Logger.log(f"Checkpoint at {self.cur_step} >= {num_iters}, skipping") + return + + Logger.log(f"OPTIMIZING {self.name} FOR {num_iters} ITERATIONS") + + # save initial results and vis + self.save_results(res_dir, seq_name) + + for i in range(self.cur_step, num_iters): + Logger.log("ITER: %d" % (i)) + + if (i + 1) % self.save_every == 0: # save before + self.save_checkpoint(out_dir) + self.save_results(res_dir, seq_name) + else: + self.save_checkpoint(out_dir) + + if (i + 1) % self.vis_every == 0: # render + self.vis_result(res_dir, obs_data, vis) + + self.cur_step = i + self.loss.cur_step = i + + self.optim_step(obs_data, writer) + + # early termination in case of nans + if np.isnan(self.cur_loss): + # we need to backtrack + self.load_checkpoint(out_dir, device=device) + return + + # termination for the last chunk + if self.reached_max and self.reached_max_iter < 0: + self.reached_max_iter = i - 1 + if self.reached_max and i - self.reached_max_iter >= self.max_chunk_steps: + break + + # termination for middle chunks + loss_change = self.prev_loss - self.cur_loss + if self.last_updated == i - 1 and loss_change == 0: + break + if ( + (self.cur_loss < 0 and loss_change < 100) + or (i - self.last_updated >= self.max_chunk_steps) + or (loss_change < 20 and i - self.last_updated > 5) + ): + self.add_chunk = self.add_chunk + 1 + self.last_updated = i + self.prev_loss = self.cur_loss + + # final save and vis step + self.cur_step = num_iters + self.save_checkpoint(out_dir) + self.save_results(res_dir, seq_name) + self.vis_result(res_dir, obs_data, vis) + + def optim_step(self, obs_data, writer=None): + def closure(): + self.optim.zero_grad() + loss, stats_dict, preds = self.forward_pass(obs_data) + stats_dict["total"] = loss + self.log_losses(move_to(detach_all(stats_dict), "cpu")) + self.cur_loss = stats_dict["total"].detach().cpu().item() + loss_keys = stats_dict.keys() + if "motion_prior" in loss_keys and "pose_prior" in loss_keys: + self.cur_loss = ( + self.cur_loss + - 0.04 * stats_dict["pose_prior"].detach().cpu().item() + ) + loss.backward() + return loss + + self.optim.step(closure) + if writer is not None: + self.record_current_losses(writer) + + +class RootOptimizer(StageOptimizer): + name = "root_fit" + stage = 0 + + def __init__( + self, + model, + all_loss_weights, + use_chamfer=False, + robust_loss_type="none", + robust_tuning_const=4.6851, + joints2d_sigma=100, + **kwargs, + ): + param_names = ["trans", "root_orient"] + super().__init__(self.name, model, param_names, **kwargs) + + self.loss = RootLoss( + all_loss_weights[self.stage], + ignore_op_joints=OP_IGNORE_JOINTS, + joints2d_sigma=joints2d_sigma, + use_chamfer=use_chamfer, + robust_loss=robust_loss_type, + robust_tuning_const=robust_tuning_const, + ) + + def forward_pass(self, obs_data): + """ + Takes in observed data, predicts the smpl parameters and returns loss + """ + # Use current params to go through SMPL and get joints3d, verts3d, points3d + pred_data = self.model.pred_params_smpl() + pred_data["cameras"] = self.model.params.get_cameras() + + # compute data losses only + vis_mask = obs_data["vis_mask"] >= 0 + loss, stats_dict = self.loss(obs_data, pred_data, vis_mask) + return loss, stats_dict, pred_data + + +class SMPLOptimizer(StageOptimizer): + name = "smpl_fit" + stage = 0 + + def __init__( + self, + model, + all_loss_weights, + use_chamfer=False, + robust_loss_type="none", + robust_tuning_const=4.6851, + joints2d_sigma=100, + **kwargs, + ): + param_names = ["trans", "root_orient", "betas", "latent_pose"] + if model.opt_scale: + param_names += ["world_scale"] + + super().__init__(self.name, model, param_names, **kwargs) + + self.loss = SMPLLoss( + all_loss_weights[self.stage], + ignore_op_joints=OP_IGNORE_JOINTS, + joints2d_sigma=joints2d_sigma, + use_chamfer=use_chamfer, + robust_loss=robust_loss_type, + robust_tuning_const=robust_tuning_const, + ) + + def forward_pass(self, obs_data): + """ + Takes in observed data, predicts the smpl parameters and returns loss + """ + # Use current params to go through SMPL and get joints3d, verts3d, points3d + pred_data = self.model.pred_params_smpl() + pred_data["cameras"] = self.model.params.get_cameras() + pred_data.update(self.model.params.get_vars()) + + # compute data losses only + vis_mask = obs_data["vis_mask"] >= 0 + loss, stats_dict = self.loss(obs_data, pred_data, self.model.seq_len, vis_mask) + return loss, stats_dict, pred_data + + +class SmoothOptimizer(StageOptimizer): + name = "smooth_fit" + stage = 1 + + def __init__( + self, + model, + all_loss_weights, + use_chamfer=False, + robust_loss_type="none", + robust_tuning_const=4.6851, + joints2d_sigma=100, + **kwargs, + ): + param_names = ["trans", "root_orient", "betas", "latent_pose"] + if model.opt_scale: + param_names += ["world_scale"] + if model.opt_cams: + param_names += ["cam_f", "delta_cam_R"] + + super().__init__(self.name, model, param_names, **kwargs) + + self.loss = SMPLLoss( + all_loss_weights[self.stage], + ignore_op_joints=OP_IGNORE_JOINTS, + joints2d_sigma=joints2d_sigma, + use_chamfer=use_chamfer, + robust_loss=robust_loss_type, + robust_tuning_const=robust_tuning_const, + ) + + def forward_pass(self, obs_data): + """ + Takes in observed data, predicts the smpl parameters and returns loss + """ + # Use current params to go through SMPL and get joints3d, verts3d, points3d + pred_data = self.model.pred_params_smpl() + pred_data["cameras"] = self.model.params.get_cameras() + pred_data.update(self.model.params.get_vars()) + + # camera predictions + # pts_ij, target, weight = self.model.params.get_reprojected_points() + # pred_data["bg2d_err"] = ( + # (weight * (pts_ij - target) ** 2).sum(dim=(-1, -2)).mean() + # ) + pred_data["cam_R"], pred_data["cam_t"] = self.model.params.get_extrinsics() + + # compute data losses only + vis_mask = obs_data["vis_mask"] >= 0 + loss, stats_dict = self.loss(obs_data, pred_data, self.model.seq_len, vis_mask) + return loss, stats_dict, pred_data + + +class MotionOptimizer(StageOptimizer): + name = "motion_fit" + stage = 2 + + def __init__(self, model, all_loss_weights, opt_cams=False, **kwargs): + self.opt_cams = opt_cams and model.opt_cams + param_names = [ + "trans", + "root_orient", + "latent_pose", + "trans_vel", + "root_orient_vel", + "joints_vel", + "betas", + "latent_motion", + "floor_plane", + ] + if model.opt_scale: + param_names += ["world_scale"] + + if self.opt_cams: + Logger.log(f"{self.name} OPTIMIZING CAMERAS") + param_names += ["delta_cam_R", "cam_f"] + + super().__init__(self.name, model, param_names, **kwargs) + self.set_loss(model, all_loss_weights[self.stage], **kwargs) + + def set_loss( + self, + model, + loss_weights, + use_chamfer=False, + robust_loss_type="none", + robust_tuning_const=4.6851, + joints2d_sigma=100, + **kwargs, + ): + self.loss = MotionLoss( + loss_weights, + init_motion_prior=model.init_motion_prior, + ignore_op_joints=OP_IGNORE_JOINTS, + joints2d_sigma=joints2d_sigma, + use_chamfer=use_chamfer, + robust_loss=robust_loss_type, + robust_tuning_const=robust_tuning_const, + ) + + def get_motion_scale(self): + return 1.0 + + def forward_pass(self, obs_data, num_steps=-1): + p = self.model.params + param_names = [ + "betas", + "joints_vel", + "trans_vel", + "root_orient_vel", + ] + param_dict = p.get_vars(param_names) + param_dict["floor_plane"] = p.floor_plane[p.floor_idcs] + + preds, world_preds = self.model.rollout_smpl_steps(num_steps) + preds.update(param_dict) + world_preds.update(param_dict) + + # track mask is the length of the sequence that contains num_steps of each track + track_mask = world_preds.get("track_mask", None) + T = track_mask.shape[1] if track_mask is not None else num_steps + world_preds["cameras"] = p.get_cameras(np.arange(T)) + if self.opt_cams: + cam_R, cam_t = p.get_extrinsics() + world_preds["cam_R"], world_preds["cam_t"] = cam_R[:T], cam_t[:T] + + obs_data = slice_dict(obs_data, 0, T) + motion_scale = self.get_motion_scale() + loss, stats_dict = self.loss( + obs_data, + preds, + world_preds, + self.model.seq_len, + valid_mask=track_mask, + init_motion_scale=motion_scale, + ) + return loss, stats_dict, (preds, world_preds) + + +def slice_dict(d, start, end): + out = d.copy() + for k, v in d.items(): + if not isinstance(v, torch.Tensor) or v.ndim < 3 or v.shape[1] < end: + continue + out[k] = v[:, start:end] + return out + + +class MotionOptimizerChunks(MotionOptimizer): + """ + Incrementally optimize sequence in chunks (with all variables) + :param chunk_size (int) number of frames per chunk + :param init_steps (int) number of optimization steps to spend on first chunk + :param chunk_steps (int) number of opt steps to spend on subsequent chunks + """ + + name = "motion_chunks" + stage = 2 + + def __init__(self, *args, chunk_size=20, init_steps=20, chunk_steps=10, **kwargs): + self.chunk_size = chunk_size + self.init_steps = init_steps + self.chunk_steps = chunk_steps + super().__init__(*args, **kwargs) + + @property + def num_iters(self): + num_chunks = int(np.ceil(self.model.seq_len / self.chunk_size)) + 1 + return self.init_steps + self.chunk_steps * num_chunks + + @property + def end_idx(self): + if self.cur_step < self.init_steps and self.add_chunk == 0: + return self.chunk_size + chunk_idx = max( + (self.cur_step - self.init_steps) // self.chunk_steps + 1, self.add_chunk + ) + if int(np.ceil(self.model.seq_len / self.chunk_size)) == self.add_chunk: + self.reached_max = True + return min(self.chunk_size * (chunk_idx + 1), self.model.seq_len) + + @property + def start_idx(self): + return 0 + + def get_motion_scale(self): + num_frames = self.end_idx - self.start_idx + return max(1.0, float(self.model.seq_len) / num_frames) + + def forward_pass(self, obs_data): + return super().forward_pass(obs_data, num_steps=self.end_idx) + + def vis_result(self, res_dir, obs_data, vis=None, **kwargs): + print("start, end", self.start_idx, self.end_idx) + return super().vis_result(res_dir, obs_data, vis=vis, num_steps=self.end_idx) + + +class MotionOptimizerFreeze(MotionOptimizer): + """ + Only optimizing a subset of parameters + """ + + name = "motion_freeze" + stage = 2 + + def __init__(self, model, all_loss_weights, no_contacts=True, **kwargs): + loss_weights = all_loss_weights[self.stage].copy() + + if no_contacts: + loss_weights["contact_height"] = 0.0 + loss_weights["contact_vel"] = 0.0 + + param_names = ["latent_motion", "betas", "trans", "floor_plane"] + if model.optim_scale: + param_names += ["world_scale"] + + StageOptimizer.__init__(self, self.name, model, param_names, **kwargs) + self.set_loss(model, loss_weights, **kwargs) diff --git a/slahmr/slahmr/optim/output.py b/slahmr/slahmr/optim/output.py new file mode 100644 index 0000000000000000000000000000000000000000..ee4a61d5dafe2c5d077fef3e4fed0a5dff6fef08 --- /dev/null +++ b/slahmr/slahmr/optim/output.py @@ -0,0 +1,180 @@ +import os +import imageio +import glob +import json +import subprocess + +import numpy as np +import torch + +from util.tensor import move_to, detach_all, to_torch +from util.logger import Logger + + +def get_results_paths(res_dir): + """ + get the iterations of all saved results in res_dir + :param res_dir (str) result dir + returns a dict of iter to result path + """ + res_files = sorted(glob.glob(f"{res_dir}/*_results.npz")) + print(f"found {len(res_files)} results in {res_dir}") + + path_dict = {} + for res_file in res_files: + it, name, _ = os.path.basename(res_file).split("_")[-3:] + assert name in ["world", "prior"] + if it not in path_dict: + path_dict[it] = {} + path_dict[it][name] = res_file + return path_dict + + +def load_result(res_path_dict): + """ + load all saved results for a given iteration + :param res_path_dict (dict) paths to relevant results + returns dict of results + """ + res_dict = {} + for name, path in res_path_dict.items(): + res = np.load(path) + res_dict[name] = to_torch({k: res[k] for k in res.files}) + return res_dict + + +def save_initial_predictions(model, out_dir, seq_name): + os.makedirs(out_dir, exist_ok=True) + with torch.no_grad(): + pred_dict = model.get_optim_result() + pred_dict = move_to(detach_all(pred_dict), "cpu") + + for name, results in pred_dict.items(): + out_path = f"{out_dir}/{seq_name}_{0:06d}_init_{name}_results.npz" + Logger.log(f"saving initial results to {out_path}") + np.savez(out_path, **results) + + +def save_input_poses(dataset, out_dir, seq_name, name="phalp"): + os.makedirs(out_dir, exist_ok=True) + dataset.load_data(interp_input=False) + d = dataset.data_dict + res = { + "pose_body": np.stack(d["init_body_pose"], axis=0), + "trans": np.stack(d["init_trans"], axis=0), + "root_orient": np.stack(d["init_root_orient"], axis=0), + } + print({k: v.shape for k, v in res.items()}) + out_path = f"{out_dir}/{seq_name}_{0:06d}_{name}_world_results.npz" + Logger.log(f"saving inputs to {out_path}") + np.savez(out_path, **res) + + +def save_input_frames_ffmpeg(dataset, out_dir, name="input", fps=30, overwrite=False): + vid_path = f"{out_dir}/{name}.mp4" + if not overwrite and os.path.isfile(vid_path): + return + + list_path = f"{out_dir}/src_paths.txt" + with open(list_path, "w") as f: + f.write("\n".join([f"file '{p}'" for p in dataset.sel_img_paths])) + + filter_str = f"-framerate {fps} -vf 'format=yuv420p'" + cmd = ( + f"ffmpeg -loglevel error -f concat -safe 0 " + f"-i {list_path} -c:v libx264 {filter_str} {vid_path} -y" + ) + print(cmd) + subprocess.call(cmd, shell=True, stdin=subprocess.PIPE) + print(f"SAVED {len(dataset.sel_img_paths)} INPUT FRAMES TO {vid_path}") + return vid_path + + +def save_input_frames(dataset, vid_path, fps=30, overwrite=False): + if not overwrite and os.path.isfile(vid_path): + return + + writer = imageio.get_writer(vid_path, fps=fps) + for path in dataset.sel_img_paths: + writer.append_data(imageio.imread(path)) + writer.close() + print(f"SAVED {len(dataset.sel_img_paths)} INPUT FRAMES TO {vid_path}") + return vid_path + + +def load_track_info(path): + assert os.path.isfile(path) + + with open(path, "r") as f: + track_info = json.load(f) + + meta = track_info["meta"] + tracks = track_info["tracks"] + track_ids, idcs, vis_masks = map( + torch.as_tensor, + zip( + *[ + (int(tid), info["index"], info["vis_mask"]) + for tid, info in tracks.items() + ] + ), + ) + track_ids = track_ids[idcs] + vis_masks = vis_masks[idcs] + data_interval = meta["data_interval"] + seq_interval = meta["seq_interval"] + return track_ids, vis_masks, data_interval, seq_interval + + +def save_track_info(dataset, out_dir): + # track indices are relative to the entire sequence + track_ids = dataset.track_ids + track_dict = {} + for i, (tid, mask) in enumerate(zip(dataset.track_ids, dataset.track_vis_masks)): + track_dict[int(tid)] = {"index": i, "vis_mask": mask.tolist()} + + out_dict = { + "tracks": track_dict, + "meta": { + "seq_interval": (int(dataset.start_idx), int(dataset.end_idx)), + "data_interval": (int(dataset.data_start), int(dataset.data_end)), + }, + } + + with open(f"{out_dir}/track_info.json", "w") as f: + json.dump(out_dict, f) + print("SAVED TRACK INFO") + + +def load_camera_json(path): + assert os.path.isfile(path) + + with open(path, "r") as f: + cam_data = json.load(f) + R = torch.as_tensor(cam_data["rotation"]).reshape(-1, 3, 3) + t = torch.as_tensor(cam_data["translation"]) + intrins = torch.as_tensor(cam_data["intrinsics"]) + return R.float(), t.float(), intrins.float() + + +def save_camera_json(path, cam_R, cam_t, intrins): + """ + :param path + :param cam_R (N, 3, 3) + :param cam_t (N, 3) + :param intrins (N, 4) + """ + N = len(cam_R) + T = torch.tensor([[1, 0, 0], [0, -1, 0], [0, 0, -1]], dtype=torch.float32) + cam_R = torch.einsum("ij,bjk->bik", T, cam_R) + cam_t = torch.einsum("ij,bj->bi", T, cam_t) + with open(path, "w") as f: + json.dump( + { + "rotation": cam_R.reshape(N, 9).tolist(), + "translation": cam_t.tolist(), + "intrinsics": intrins.tolist(), + }, + f, + indent=1, + ) diff --git a/slahmr/slahmr/optim/params.py b/slahmr/slahmr/optim/params.py new file mode 100644 index 0000000000000000000000000000000000000000..eb19c427be933c198bcc9f1d84995893a4927dd2 --- /dev/null +++ b/slahmr/slahmr/optim/params.py @@ -0,0 +1,161 @@ +import numpy as np + +import torch +import torch.nn as nn +import torch.nn.functional as F + +from body_model import SMPL_JOINTS +from geometry.camera import invert_camera, compose_cameras +from geometry.rotation import batch_rodrigues +from util.logger import Logger +from util.tensor import detach_all + +J_BODY = len(SMPL_JOINTS) - 1 # no root + + +class Params(nn.Module): + def __init__(self, batch_size): + super().__init__() + self.batch_size = batch_size + self.param_names = set() + + def set_param(self, name, val, requires_grad=False): + print("SETTING PARAM", name, val.shape) + with torch.no_grad(): + setattr( + self, name, nn.Parameter(val.contiguous(), requires_grad=requires_grad) + ) + self.param_names.add(name) + + def get_param(self, name): + if name not in self.param_names: + raise ValueError(f"{name} not stored as opt param") + return getattr(self, name) + + def load_dict(self, param_dict): + for name, val in param_dict.items(): + self.set_param(name, val, requires_grad=False) + + def get_dict(self): + return {name: self.get_param_item(name) for name in self.param_names} + + def get_vars(self, names=None): + if names is None: + names = self.param_names + return {name: self.get_param(name) for name in names} + + def get_param_item(self, name): + with torch.no_grad(): + param = self.get_param(name) + return param.detach() + + def _set_param_grad(self, name, val: bool): + if name not in self.param_names: + raise ValueError(f"{name} not stored as param") + param = getattr(self, name) + assert isinstance(param, torch.Tensor) + param.requires_grad = val + + def set_require_grads(self, names): + """ + set parameters in names to True, set all others to False + """ + for name in self.param_names: + self._set_param_grad(name, False) + + for name in names: + self._set_param_grad(name, True) + + Logger.log("Set parameter grads:") + Logger.log( + {name: getattr(self, name).requires_grad for name in self.param_names} + ) + + +class CameraParams(Params): + """ + Parameter container with cameras + """ + + def set_cameras( + self, cam_data, opt_scale=True, opt_cams=False, opt_focal=False, **kwargs + ): + self.opt_scale = opt_scale + self.opt_cams = opt_cams + self.opt_focal = opt_focal + + # (T, 3, 3), (T, 3) + cam_R, cam_t = cam_data["cam_R"], cam_data["cam_t"] + intrins = cam_data["intrins"] # (T, 4) + + T = cam_R.shape[0] + device = cam_R.device + + # assume focal length and center are same for all timesteps + self.cam_center = intrins[:, 2:] # (T, 2) + cam_f = intrins[:, :2] # (T, 2) + if self.opt_focal: + self.set_param("cam_f", cam_f) + else: + self.cam_f = cam_f + + self._cam_R = cam_R # (T, 3, 3) + self._cam_t = cam_t # (T, 3) + + world_scale = torch.ones(1, 1, device=device) + if self.opt_scale: + if "world_scale" in kwargs: + world_scale = kwargs["world_scale"] + self.set_param("world_scale", world_scale) + else: + self.world_scale = world_scale + + if self.opt_cams: + init_delta_R = torch.zeros(T, 3, device=device) + init_delta_t = torch.zeros(T, 3, device=device) + if "delta_cam_R" in kwargs: + print("setting delta_cam_R from kwargs") + init_delta_R = kwargs["delta_cam_R"] + if "delta_cam_t" in kwargs: + print("setting delta_cam_t from kwargs") + init_delta_t = kwargs["delta_cam_t"] + + self.set_param("delta_cam_R", init_delta_R) + self.set_param("delta_cam_t", init_delta_t) + + @property + def intrins(self): # (4,) + return torch.cat([self.cam_f[0], self.cam_center[0]], dim=-1).detach().cpu() + + def get_extrinsics(self): + """ + returns (T, 3, 3), (T, 3) + """ + cam_R, cam_t = self._cam_R, self._cam_t + if self.opt_cams: + dR = batch_rodrigues(self.delta_cam_R) + cam_R = torch.matmul(cam_R, dR) + cam_t = cam_t + self.delta_cam_t + return cam_R, cam_t * self.world_scale + + def get_intrinsics(self): + """ + returns (T, 4) + """ + return torch.cat([self.cam_f, self.cam_center], axis=-1) + + def get_cameras(self, idcs=None): + """ + returns cam_R (B, T, 3, 3) cam_t (B, T, 3), cam_f (T, 2), cam_center (T, 2) + """ + if idcs is None: + idcs = np.arange(self._cam_R.shape[0]) + + cam_R, cam_t = self.get_extrinsics() + cam_R, cam_t = cam_R[None, idcs], cam_t[None, idcs] + cam_f, cam_center = self.cam_f[idcs], self.cam_center[idcs] + + B = self.batch_size + cam_R = cam_R.repeat(B, 1, 1, 1) + cam_t = cam_t.repeat(B, 1, 1) + return cam_R, cam_t, cam_f, cam_center diff --git a/slahmr/slahmr/preproc/__init__.py b/slahmr/slahmr/preproc/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/slahmr/preproc/datasets.py b/slahmr/slahmr/preproc/datasets.py new file mode 100644 index 0000000000000000000000000000000000000000..3455bf2122c782719032737ea2ed904fe39de998 --- /dev/null +++ b/slahmr/slahmr/preproc/datasets.py @@ -0,0 +1,137 @@ +import os +import glob +import pandas as pd +from copy import deepcopy +import warnings + + +def update_args(args): + args = deepcopy(args) + if args.type == "egobody": + if args.root is None: + warnings.warn( + "args.root flag is set to None, using root directory in source" + ) + args.root = "/path/to/egobody" + if args.seqs is None: + args.seqs = get_egobody_seqs(args.root, args.split) + args.img_dirs = [ + glob.glob(f"{args.root}/egocentric_color/{seq}/**/PV")[0] + for seq in args.seqs + ] + return args + + if args.type == "3dpw": + if args.root is None: + warnings.warn( + "args.root flag is set to None, using root directory in source" + ) + args.root = "/path/to/3DPW" + if args.split == "val": + args.split = "validation" + if args.seqs is None: + args.seqs = get_3dpw_seqs(args.root, args.split) + args.img_name = "imageFiles" + + elif args.type == "posetrack": + if args.root is None: + warnings.warn( + "args.root flag is set to None, using root directory in source" + ) + args.root = "/path/to/posetrack/posetrack2018/posetrack_data" + args.img_name = f"images/{args.split}" + + elif args.type == "davis": + if args.root is None: + warnings.warn( + "args.root flag is set to None, using root directory in source" + ) + args.root = "/path/to/DAVIS" + args.img_name = "JPEGImages/Full-Resolution" + args.split = "" + + else: + assert args.root is not None + args.img_name = args.img_name if args.img_name is not None else "images" + args.split = "" + + args.img_dirs, args.seqs = get_all_img_dirs( + f"{args.root}/{args.img_name}", args.seqs + ) + return args + + +def isimage(f): + ext = os.path.splitext(f)[-1].lower() + return ext in [".png", ".jpg"] + + +def get_all_img_dirs(data_root, seqs=None): + """ + returns all image directories in root, recursively searching, and the sequence names + """ + seqs = seqs if seqs is not None else [] + img_dirs = [] + + def get_name(p): + return p.removeprefix(f"{data_root}/") + + for root, _, files in os.walk(data_root): + num_imgs = len([f for f in files if isimage(f)]) + if num_imgs > 0: + name = get_name(root) + if len(seqs) == 0 or name in seqs: + img_dirs.append(root) + img_dirs = sorted(img_dirs) + seqs = [get_name(d) for d in img_dirs] + return img_dirs, seqs + + +def get_custom_seqs(data_root): + img_dir = f"{data_root}/images" + if not os.path.isdir(img_dir): + return [] + return sorted(os.listdir(img_dir)) + + +def get_egobody_seqs(data_root, split): + split_file = f"{data_root}/data_splits.csv" + df = pd.read_csv(split_file) + if split not in df.columns: + print(f"{split} not in {split_file}") + return [] + return sorted(df[split].dropna().tolist()) + + +def get_3dpw_seqs(data_root, split): + split_dir = f"{data_root}/sequenceFiles/{split}" + if not os.path.isdir(split_dir): + return [] + seq_files = sorted(os.listdir(split_dir)) + return [os.path.splitext(f)[0] for f in seq_files] + + +def get_posetrack_seqs(data_root, split): + split_dir = f"{data_root}/images/{split}" + if not os.path.isdir(split_dir): + return [] + return sorted(os.listdir(split_dir)) + + +def get_davis_seqs(data_root): + img_root = f"{data_root}/JPEGImages/Full-Resolution" + if not os.path.isdir(img_root): + return [] + return sorted(os.listdir(img_root)) + + +def get_img_dir(data_type, data_root, seq, img_name): + if data_type == "posetrack": + return f"{data_root}/{img_name}/{seq}" + if data_type == "3dpw": + return f"{data_root}/imageFiles/{seq}" + if data_type == "davis": + return f"{data_root}/JPEGImages/Full-Resolution/{seq}" + if data_type == "custom": + return f"{data_root}/images/{seq}" # custom sequence + return None diff --git a/slahmr/slahmr/preproc/export_3dpw.py b/slahmr/slahmr/preproc/export_3dpw.py new file mode 100644 index 0000000000000000000000000000000000000000..45b0f3f36c30897bee30c16b649b2b2f4b463075 --- /dev/null +++ b/slahmr/slahmr/preproc/export_3dpw.py @@ -0,0 +1,78 @@ +import os +import glob +import pickle +import numpy as np +import json + + +def export_cameras(seq_data, cam_dir): + os.makedirs(cam_dir, exist_ok=True) + K = seq_data["cam_intrinsics"] # (3, 3) + # fx, fy, cx, cy + intrins = K[0, 0], K[1, 1], K[0, 2], K[1, 2] + out_path = os.path.join(cam_dir, "intrinsics.txt") + np.savetxt(out_path, intrins) + return out_path + + +def export_keypoints(seq_data, img_dir, kp_dir): + kps_all = seq_data["poses2d"] # M list of (T, 3, 18) + M = len(kps_all) + T = len(kps_all[0]) + img_files = sorted(glob.glob(f"{img_dir}/*.jpg")) + img_names = [os.path.splitext(os.path.basename(x))[0] for x in img_files] + assert T == len(img_names), f"{T}, {len(img_names)}" + os.makedirs(kp_dir, exist_ok=True) + for t, name in enumerate(img_names): + people = [] + for m in range(M): + kps = kps_all[m][t].T # (18, 3) + people.append({"pose_keypoints_2d": kps.tolist()}) + out_dict = {"people": people} + + kp_path = f"{kp_dir}/{name}_keypoints.json" + with open(kp_path, "w") as f: + json.dump(out_dict, f, indent=1) + return kp_dir + + +def export_seq(data_root, split, seq_name, out_root): + print(f"Exporting sequence {seq_name}") + data_path = f"{data_root}/sequenceFiles/{split}/{seq_name}.pkl" + with open(data_path, "rb") as f: + data = pickle.load(f, encoding="latin1") + + cam_dir = f"{out_root}/cameras_gt/{seq_name}" + int_path = export_cameras(data, cam_dir) + + kp_dir = f"{out_root}/keypoints_gt/{seq_name}" + img_dir = f"{data_root}/imageFiles/{seq_name}" + kp_dir = export_keypoints(data, img_dir, kp_dir) + + return int_path, _, kp_dir + + +def main(args): + if not (args.cameras or args.keypoints): + print("Please specify if you want to export cameras or keypoints") + return + + src_dir = f"{args.data_root}/sequenceFiles/{args.split}" + out_root = f"{args.data_root}/slahmr" + data_files = sorted(glob.glob(f"{src_dir}/*.pkl")) + print(f"FOUND {len(data_files)} data files in {src_dir}") + + for path in data_files: + seq_name = os.path.splitext(os.path.basename(path))[0] + export_seq(args.data_root, args.split, seq_name, out_root) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--data_root", default="/path/to/3DPW") + parser.add_argument("--split", default="test") + args = parser.parse_args() + + main(args) diff --git a/slahmr/slahmr/preproc/export_egobody.py b/slahmr/slahmr/preproc/export_egobody.py new file mode 100644 index 0000000000000000000000000000000000000000..8faccb257862913f4b88879c773d003c3959856b --- /dev/null +++ b/slahmr/slahmr/preproc/export_egobody.py @@ -0,0 +1,104 @@ +import os +import glob +import numpy as np + + +def read_camera_params(path): + out_dict = {} + with open(path, "r") as f: + header = np.fromstring(f.readline().strip(), sep=",") + for row in f.readlines(): + tokens = row.strip().split(",") + out_dict[tokens[0]] = [float(x) for x in tokens[1:]] + return out_dict, header + + +def export_cameras(img_dir, cam_dir): + cam_path = glob.glob(f"{img_dir}/*pv.txt") + assert len(cam_path) == 1, f"no camera path found in {img_dir}" + cam_path = cam_path[0] + cam_dict, cam_meta = read_camera_params(cam_path) + + cx, cy, w, h = cam_meta + + extrins = [] + intrins = [] + + img_files = sorted(glob.glob(f"{img_dir}/PV/*.jpg")) + for img_file in img_files: + # get the timestamps of each image file and get corresponding parameters + ts = os.path.basename(img_file).split("_")[0] + data = cam_dict[ts] + fx, fy = data[:2] + c2w = data[2:] + assert len(c2w) == 16 + + intrins.append([fx, fy, cx, cy, w, h]) + extrins.append(c2w) + + intrins = np.array(intrins) + extrins = np.array(extrins) + + os.makedirs(cam_dir, exist_ok=True) + int_path = os.path.join(cam_dir, "intrinsics.txt") + ext_path = os.path.join(cam_dir, "cam2world.txt") + np.savetxt(int_path, intrins) + np.savetxt(ext_path, extrins.reshape(-1, 16)) + print(f"intrinsics and extrinsics saved to {cam_dir}") + return int_path, ext_path + + +def export_keypoints(img_dir, out_path): + kp_file = f"{img_dir}/keypoints.npz" + valid_file = f"{img_dir}/valid_frame.npz" + img_paths = sorted(glob.glob(f"{img_dir}/PV/*.jpg")) + img_names = [os.path.basename(x) for x in img_paths] + + kp_dict = {} + valid_dict = {} + kp_data = np.load(kp_file) + valid_data = np.load(valid_file) + + zeros = np.zeros_like(kp_data["keypoints"][0]) + print(zeros.shape) + for img_path, kps in zip(kp_data["imgname"], kp_data["keypoints"]): + img_name = os.path.basename(img_path) + kp_dict[img_name] = kps + + for img_path, valid in zip(valid_data["imgname"], valid_data["valid"]): + img_name = os.path.basename(img_path) + valid_dict[img_name] = valid + + kps = np.stack([kp_dict.get(name, zeros) for name in img_names], axis=0) + valid = np.stack([valid_dict.get(name, False) for name in img_names], axis=0) + np.savez(out_path, img_names=img_names, keypoints=kps, valid=valid) + print(f"keypoints saved to {out_path}") + + +def export_seq(img_dir, out_root): + kp_root = f"{out_root}/keypoints_gt" + cam_root = f"{out_root}/cameras_gt" + os.makedirs(kp_root, exist_ok=True) + os.makedirs(cam_root, exist_ok=True) + + seq_name = img_dir.strip("/").split("/")[-2] + kp_path = f"{kp_root}/{seq_name}.npz" + cam_dir = f"{cam_root}/{seq_name}" + export_keypoints(img_dir, kp_path) + int_path, ext_path = export_cameras(img_dir, cam_dir) + return int_path, ext_path, kp_path + + +if __name__=="__main__": + import argparse + parser = argparse.ArgumentParser() + parser.add_argument("--data_root", default="/path/to/egobody") + args = parser.parse_args() + + + img_root = f"{args.data_root}/egocentric_color" + img_dirs = glob.glob(f"{img_root}/**/**") + out_root = f"{args.data_root}/slahmr" + + for img_dir in img_dirs: + export_seq(img_dir, out_root) diff --git a/slahmr/slahmr/preproc/export_phalp.py b/slahmr/slahmr/preproc/export_phalp.py new file mode 100644 index 0000000000000000000000000000000000000000..16567af4f1d0d122ea8dd6486f27e3dfe368b65b --- /dev/null +++ b/slahmr/slahmr/preproc/export_phalp.py @@ -0,0 +1,125 @@ +import os +import joblib +import json + +import cv2 +import numpy as np + + +def export_phalp_predictions(res_path, target_dir): + """ + exports phalp output results into a directory for each track + of JSON files with each frame's SMPL prediction + """ + os.makedirs(target_dir, exist_ok=True) + print(f"exporting phalp predictions from {res_path} to {target_dir}") + + tracklet_data = joblib.load(res_path) + for frame, track_data in tracklet_data.items(): + name = os.path.splitext(frame.split("/")[-1])[0] + track_dicts = unpack_frame(track_data) + for tid, pred_dict in track_dicts.items(): + track_dir = os.path.join(target_dir, f"{tid:03d}") + os.makedirs(track_dir, exist_ok=True) + pred_path = os.path.join(track_dir, f"{name}_smpl.json") + with open(pred_path, "w") as f: + json.dump(pred_dict, f, indent=1) + + +def export_vitpose_keypoints(res_path, target_dir): + """ + exports each track of each frame into its own json of keypoints + """ + os.makedirs(target_dir, exist_ok=True) + print(f"exporting keypoints from {res_path} to {target_dir}") + + tracklet_data = joblib.load(res_path) + for frame, track_data in tracklet_data.items(): + name = os.path.splitext(frame.split("/")[-1])[0] + tids = track_data["tid"] + valid_tids = track_data["tracked_ids"] + kps_all = track_data["extra_data"] + # mask_paths = track_data["mask_name"] + for i, tid in enumerate(tids): + if tid not in valid_tids: + continue + track_dir = os.path.join(target_dir, f"{tid:03d}") + os.makedirs(track_dir, exist_ok=True) + kp_path = os.path.join(track_dir, f"{name}_keypoints.json") + kp_dict = { + "people": [ + { + "pose_keypoints_2d": kps_all[i].tolist(), + # "mask_path": mask_paths[i], + } + ], + } + with open(kp_path, "w") as f: + json.dump(kp_dict, f, indent=1) + + +def export_shot_changes(res_path, target_path): + """ + Exports the phalp output of shot changes into a JSON file + dict with the shot index for each frame in the sequence + """ + os.makedirs(os.path.dirname(target_path), exist_ok=True) + print(f"exporting shot changes to {target_path}") + + tracklet_data = joblib.load(res_path) + frames = sorted(tracklet_data.keys()) + shots = np.cumsum([tracklet_data[frame]["shot"] for frame in frames]) + shots = shots.astype(int).tolist() + shot_dict = {frame.split("/")[-1]: shot for frame, shot in zip(frames, shots)} + with open(target_path, "w") as f: + json.dump(shot_dict, f, indent=1) + + +def unpack_frame(track_data): + """ + Unpack one frame of track data from the phalp output into JSON files for each track. + Track data contains body pose, global translation and rotation, + and keypoints for all tracks in the frame. + Each track is unpacked into folders with a JSON for each frame. + """ + out_dict = {} + for i, tid in enumerate(track_data["tid"]): + if tid not in track_data["tracked_ids"]: + continue + cam = track_data["camera_bbox"][i].squeeze() # (3,) + H, W = track_data["size"][i] + focal = 0.5 * (H + W) + + # every tracklet has its own bounding box + cx, cy = track_data["center"][i] # (2,) + bbox = track_data["bbox"][i] # (4,) + scale = max(bbox[-2:]) + + tz = 2 * focal / (scale * cam[0] + 1e-6) + tx = cam[1] + tz / focal * (cx - W / 2) + ty = cam[2] + tz / focal * (cy - H / 2) + cam_trans = np.array([tx, ty, tz]) + + smpl = track_data["smpl"][i] + betas = smpl["betas"].squeeze() # (10,) + body_pose = smpl["body_pose"].squeeze() # (23, 3, 3) + body_pose_aa = np.stack( + [cv2.Rodrigues(x)[0].squeeze() for x in body_pose], axis=0 + ) # (23, 3) + global_orient = smpl["global_orient"].squeeze() # (3, 3) + global_orient_aa = cv2.Rodrigues(global_orient)[0].squeeze() # (3,) + + out_dict[tid] = { + "betas": betas.tolist(), + "body_pose": body_pose_aa.tolist(), + "global_orient": global_orient_aa.tolist(), + "cam_trans": cam_trans.tolist(), + } + + return out_dict + + +def export_sequence_results(phalp_res_path, track_dir, shot_path): + export_phalp_predictions(phalp_res_path, track_dir) + export_vitpose_keypoints(phalp_res_path, track_dir) + export_shot_changes(phalp_res_path, shot_path) diff --git a/slahmr/slahmr/preproc/extract_frames.py b/slahmr/slahmr/preproc/extract_frames.py new file mode 100644 index 0000000000000000000000000000000000000000..04be354e58805af2e6066cebd1f0aaf4cdab3c0c --- /dev/null +++ b/slahmr/slahmr/preproc/extract_frames.py @@ -0,0 +1,89 @@ +import argparse +import imageio +import os +import subprocess + + +def video_to_frames( + path, + out_dir, + fps=30, + ext="jpg", + down_scale=1, + start_sec=0, + end_sec=-1, + overwrite=False, + **kwargs, +): + """ + :param path + :param out_dir + :param fps + :param down_scale (optional int) + """ + os.makedirs(out_dir, exist_ok=True) + + arg_str = f"-copyts -qscale:v 2 -vf fps={fps}" + if down_scale != 1: + arg_str = f"{arg_str},scale='iw/{down_scale}:ih/{down_scale}'" + if start_sec > 0: + arg_str = f"{arg_str} -ss {start_sec}" + if end_sec > start_sec: + arg_str = f"{arg_str} -to {end_sec}" + + yn = "-y" if overwrite else "-n" + cmd = f"ffmpeg -i {path} {arg_str} {out_dir}/%06d.{ext} {yn}" + print(cmd) + + return subprocess.call(cmd, shell=True, stdin=subprocess.PIPE) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser() + parser.add_argument("--data_root", type=str, required=True, help="path to video") + parser.add_argument( + "--out_root", type=str, required=True, help="output dir for frames" + ) + parser.add_argument( + "--seqs", + nargs="*", + default=None, + help="[optional] sequences to run, default runs all available", + ) + parser.add_argument("--fps", type=int, default=30, help="fps to extract frames") + parser.add_argument( + "--ext", type=str, default="jpg", help="output filetype for frames" + ) + parser.add_argument( + "--down_scale", type=int, default=1, help="scale to extract frames" + ) + parser.add_argument( + "-ss", "--start_sec", type=float, default=0, help="seconds to start_sec" + ) + parser.add_argument( + "-es", "--end_sec", type=float, default=-1, help="seconds to end_sec" + ) + parser.add_argument( + "-y", "--overwrite", action="store_true", help="overwrite if already exist" + ) + args = parser.parse_args() + seqs_all = os.listdir(args.data_root) + if args.seqs is None: + args.seqs = seqs_all + + for seq in args.seqs: + path = os.path.join(args.data_root, seq) + print(f"EXTRACTING FRAMES FROM {path}") + assert os.path.isfile(path) + seq_name = os.path.splitext(os.path.basename(path.rstrip("/")))[0] + out_dir = os.path.join(args.out_root, seq_name) + video_to_frames( + path, + out_dir, + args.fps, + args.ext, + args.down_scale, + args.start_sec, + args.end_sec, + args.overwrite, + ) diff --git a/slahmr/slahmr/preproc/launch_phalp.py b/slahmr/slahmr/preproc/launch_phalp.py new file mode 100644 index 0000000000000000000000000000000000000000..626e5265e9d1a7ac3fdd556f3fdbb64394600618 --- /dev/null +++ b/slahmr/slahmr/preproc/launch_phalp.py @@ -0,0 +1,116 @@ +import os +import subprocess +import multiprocessing as mp +from concurrent import futures + +from preproc.datasets import update_args +from preproc.export_phalp import export_sequence_results + + +def launch_phalp(gpus, seq, img_dir, res_dir, overwrite=False): + """ + run phalp using GPU pool + """ + cur_proc = mp.current_process() + print("PROCESS", cur_proc.name, cur_proc._identity) + # 1-indexed processes + worker_id = cur_proc._identity[0] - 1 if len(cur_proc._identity) > 0 else 0 + gpu = gpus[worker_id % len(gpus)] + + PHALP_DIR = os.path.abspath(f"{__file__}/../") + print("PHALP DIR", PHALP_DIR) + + cmd_args = [ + f"cd {PHALP_DIR};", + f"CUDA_VISIBLE_DEVICES={gpu}", + "python track.py", + f"video.source={img_dir}", + f"video.output_dir={res_dir}", + f"overwrite={overwrite}", + "detect_shots=True", + "video.extract_video=False", + "render.enable=False", + ] + + cmd = " ".join(cmd_args) + print(cmd) + return subprocess.call(cmd, shell=True) + + +def process_seq( + gpus, + out_root, + seq, + img_dir, + out_name="phalp_out", + track_name="track_preds", + shot_name="shot_idcs", + overwrite=False, +): + """ + Run and export PHALP results + """ + name = os.path.basename(seq) + res_root = f"{out_root}/{out_name}/{seq}" + os.makedirs(res_root, exist_ok=True) + res_dir = os.path.join(res_root, "results") + res_path = f"{res_root}/{name}.pkl" + if overwrite or not os.path.isfile(res_path): + res = launch_phalp(gpus, seq, img_dir, res_root, overwrite) + os.rename(f"{res_dir}/demo_{name}.pkl", res_path) + assert res == 0, "PHALP FAILED" + + # export the PHALP predictions + track_dir = f"{out_root}/{track_name}/{seq}" + shot_path = f"{out_root}/{shot_name}/{seq}.json" + + export_sequence_results(res_path, track_dir, shot_path) + return 0 + + +def get_out_dir(src_root, src_dir, src_token, out_token): + """ + :param src_root (str) root of all data + :param src_dir (str) img input dir + :param src_token (str) parent name of image input dir + :param out_token (str) name of output dir + """ + src_suffix = src_dir.removeprefix(src_root) + out_dir = f"{out_root}/{src_suffix}" + return out_dir.replace(src_token, out_token) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--type", default="posetrack", help="dataset to process") + parser.add_argument("--root", default=None, help="root dir of data, default None") + parser.add_argument("--split", default="val", help="split of dataset, default val") + parser.add_argument( + "--img_name", default=None, help="input image directory name, default None" + ) + parser.add_argument("--seqs", nargs="*", default=None) + parser.add_argument("--gpus", nargs="*", default=[0]) + parser.add_argument("-y", "--overwrite", action="store_true") + + args = parser.parse_args() + args = update_args(args) + + out_root = f"{args.root}/slahmr/{args.split}" + + print(f"running phalp on {len(args.img_dirs)} image directories") + if len(args.gpus) > 1: + with futures.ProcessPoolExecutor(max_workers=len(args.gpus)) as exe: + for img_dir, seq in zip(args.img_dirs, args.seqs): + exe.submit( + process_seq, + args.gpus, + out_root, + seq, + img_dir, + overwrite=args.overwrite, + ) + else: + for img_dir, seq in zip(args.img_dirs, args.seqs): + process_seq(args.gpus, out_root, seq, img_dir, overwrite=args.overwrite) diff --git a/slahmr/slahmr/preproc/launch_slam.py b/slahmr/slahmr/preproc/launch_slam.py new file mode 100644 index 0000000000000000000000000000000000000000..036fb3f1ee3b56b6819c703e47ee1c5750b34750 --- /dev/null +++ b/slahmr/slahmr/preproc/launch_slam.py @@ -0,0 +1,204 @@ +import os +import glob +import json +import numpy as np + +import subprocess +from concurrent import futures +import multiprocessing as mp + +from preproc import export_3dpw +from preproc import export_egobody +from preproc.datasets import update_args + + +SRC_DIR = os.path.abspath(f"{__file__}/../") + + +def isimage(path): + ext = os.path.splitext(path)[-1].lower() + return ext == ".png" or ext == ".jpg" or ext == ".jpeg" + + +def split_frames_equal(img_dir, seq_len=-1): + """ + split the sequence into subsequences of seq_len + returns start and end indices for each subsequence + """ + if seq_len == -1: # don't split + return [(0, -1)] + + image_list = sorted(list(filter(isimage, os.listdir(img_dir)))) + num_imgs = len(image_list) + splits = list(range(0, num_imgs, seq_len)) + splits[-1] = num_imgs # add remainder to last subseq + return list(zip(splits[:-1], splits[1:])) + + +def split_frames_shots(img_dir, shot_path, pad_shot=0, min_len=0): + """ + split the sequence into subsequences according by shots in the video + returns start and end indices for each subsequence + """ + if shot_path is None or not os.path.isfile(shot_path): + print(f"{shot_path} DOES NOT EXIST, USING WHOLE SEQUENCE") + return [(0, -1)], [0] + + image_list = sorted(list(filter(isimage, os.listdir(img_dir)))) + num_frames = len(image_list) + + with open(shot_path, "r") as f: + shot_dict = json.load(f) + + shot_idcs = np.array([shot_dict[name] for name in image_list]) + subseqs = [] + for i in np.unique(shot_idcs): + idcs = np.where(shot_idcs == i)[0] + start, end = idcs.min(), idcs.max() + 1 + if pad_shot > 0: + if start > 0: + start = start + pad_shot + if end < num_frames: + end = end - pad_shot + if (end - start) < min_len: # this shot is too short + continue + subseqs.append((start, end)) + return subseqs, np.unique(shot_idcs) + + +def split_sequence(args, img_dir, seq): + if args.type == "posetrack": # split posetrack by shot changes + shot_path = f"{args.root}/slahmr/{args.split}/shot_idcs/{seq}.json" + subseqs, idcs = split_frames_shots(img_dir, shot_path) + return subseqs, idcs + subseqs = split_frames_equal(img_dir, args.seq_len) + return subseqs, [None for _ in subseqs] + + +def get_out_dir(args, seq, shot_idx=None, start=0, end=-1): + if "egobody" in args.type or "3dpw" in args.type: + if args.use_intrins: + out_name = "cameras_intrins" + else: + out_name = "cameras_default" + else: + out_name = "cameras" + + if args.seq_len > 0: + out_name = f"{out_name}_split" + + out_dir = f"{args.root}/slahmr/{args.split}/{out_name}/{seq}" + + if args.seq_len > 0: + return f"{out_dir}/{start}-{end}" + + if args.type == "posetrack" and shot_idx is not None: + return f"{out_dir}/shot-{shot_idx}" + + return out_dir + + +def get_intrins_path(data_type, data_root, seq): + if "posetrack" in data_type: + # no intrinsics for posetrack + return None + if "egobody" in data_type or "3dpw" in data_type: + return f"{data_root}/slahmr/cameras_gt/{seq}/intrinsics.txt" + raise NotImplementedError + + +def get_command(img_dir, out_dir, start=0, end=-1, intrins_path=None, overwrite=False): + cmd_args = [ + f"python {SRC_DIR}/run_slam.py", + "-i", + img_dir, + "--map_dir", + out_dir, + "--disable_vis", + ] + if start != 0: + cmd_args += ["--start", str(start)] + if end != -1: + cmd_args += ["--end", str(end)] + + if intrins_path is not None: + cmd_args += ["--intrins_path", intrins_path] + + if overwrite: + cmd_args.append("--overwrite") + + cmd = " ".join(cmd_args) + return cmd + + +def check_intrins(data_type, data_root, intrins_path, img_dir): + assert intrins_path is not None + out_name = intrins_path.split(data_root)[1].strip("/").split("/")[0] + out_root = f"{data_root}/{out_name}" + if "egobody" in data_type: + if not os.path.isfile(intrins_path): + img_root = os.path.dirname(img_dir) + intrins_path = export_egobody.export_seq(img_root, out_root)[0] + return intrins_path + if "3dpw" in data_type: + if not os.path.isfile(intrins_path): + intrins_path = export_3dpw.export_seq(data_root, split, seq, out_root)[0] + return intrins_path + + +def get_slam_command(args, img_dir, seq, shot_idx=None, start=0, end=-1): + out_dir = get_out_dir(args, seq, shot_idx, start, end) + intrins_path = None + if args.use_intrins: + intrins_path = get_intrins_path(args.type, args.root, seq) + if intrins_path is not None: + intrins_path = check_intrins(args.type, args.root, intrins_path, img_dir) + return get_command( + img_dir, + out_dir, + start=start, + end=end, + intrins_path=intrins_path, + overwrite=args.overwrite, + ) + + +def launch_job(gpus, cmd): + cur_proc = mp.current_process() + print(cur_proc.name, cur_proc._identity) + worker_id = cur_proc._identity[0] - 1 + gpu = gpus[worker_id % len(gpus)] + cmd = f"CUDA_VISIBLE_DEVICES={gpu} {cmd}" + print(cmd) + subprocess.call(cmd, shell=True) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--type", default="posetrack", help="dataset to process") + parser.add_argument( + "--root", default=None, help="root of data to process, default None" + ) + parser.add_argument( + "--split", default="val", help="split of dataset to process, default val" + ) + parser.add_argument("--gpus", nargs="*", default=[0]) + parser.add_argument("--seqs", nargs="*", default=None) + parser.add_argument("--seq_len", type=int, default=-1) + parser.add_argument( + "--use_intrins", action="store_true", help="use GT intrinsics if available" + ) + parser.add_argument("-y", "--overwrite", action="store_true") + args = parser.parse_args() + args = update_args(args) + + print(f"Running SLAM on {len(args.seqs)} sequences") + with futures.ProcessPoolExecutor(max_workers=len(args.gpus)) as ex: + for img_dir, seq in zip(args.img_dirs, args.seqs): + subseqs, shot_idcs = split_sequence(args, img_dir, seq) + for shot, (start, end) in zip(shot_idcs, subseqs): + cmd = get_slam_command(args, img_dir, seq, shot, start, end) + print(cmd) + ex.submit(launch_job, args.gpus, cmd) diff --git a/slahmr/slahmr/preproc/run_slam.py b/slahmr/slahmr/preproc/run_slam.py new file mode 100644 index 0000000000000000000000000000000000000000..dbfde492887966f5145d4af29a6d91289d30d9ee --- /dev/null +++ b/slahmr/slahmr/preproc/run_slam.py @@ -0,0 +1,414 @@ +import os + +ROOT_DIR = os.path.abspath(f"{__file__}/../../../") +SRC_DIR = os.path.join(ROOT_DIR, "third-party/DROID-SLAM") +print("PROJ SRC", ROOT_DIR) +print("DROID SRC", SRC_DIR) + +import sys + +sys.path.append(SRC_DIR) +sys.path.append(f"{SRC_DIR}/droid_slam") + +import glob +import shutil +import argparse +from tqdm import tqdm + +import json + +import cv2 +import trimesh +import numpy as np +import torch + +from lietorch import SE3 +from droid import Droid +import droid_backends + + +def get_image(image): + return image.permute(1, 2, 0).cpu().numpy()[..., ::-1] + + +def show_image(image): + image = image.permute(1, 2, 0).cpu().numpy() + cv2.imshow("image", image / 255.0) + cv2.waitKey(1) + + +def get_hwf(test_path): + test_img = cv2.imread(test_path) + H, W, _ = test_img.shape + F = 0.5 * (H + W) + return H, W, F + + +def isimage(path): + ext = os.path.splitext(path)[-1].lower() + return ext == ".png" or ext == ".jpg" or ext == ".jpeg" + + +def get_image_files(img_dir, stride, start=0, end=-1): + image_list = sorted(list(filter(isimage, os.listdir(img_dir)))) + end = len(image_list) + 1 + end if end < 0 else end + return [os.path.join(img_dir, name) for name in image_list[start:end:stride]] + + +def load_intrins(intrins_path, image_files, start=0, end=-1): + N = len(image_files) + H, W, F = get_hwf(image_files[0]) + # intrinsics for default FOV + default = torch.tensor([F, F, W / 2, H / 2, W, H])[None].repeat(N, 1) + if intrins_path is None: + return default + assert os.path.isfile(intrins_path), f"{intrins_path} DOES NOT EXIST" + assert intrins_path.endswith(".txt"), f"{intrins_path} INCORRECT EXT" + + print(f"LOADING INTRINSICS FROM {intrins_path}") + intrins = torch.from_numpy(np.loadtxt(intrins_path).astype(np.float32)) + print(intrins.shape, N) + if intrins.ndim < 2: # assume intrins is same for all frames + intrins = intrins[None].repeat(N, 1) + else: + end = N + 1 + end if end < 0 else end + intrins = intrins[start:end] + print(intrins.shape) + if intrins.shape[1] == 4: # fx, fy, cx, cy, adding on W and H + ones = torch.ones_like(intrins[:, :1]) + intrins = torch.cat([intrins, ones * W, ones * H], dim=-1) + return intrins + + +def image_stream(image_files, intrins_all): + """image generator""" + + N = len(image_files) + + assert intrins_all.shape[0] == N + assert intrins_all.shape[1] >= 4 + + for t, imfile in enumerate(image_files): + image = cv2.imread(imfile) + if image is None: + print(imfile, "is none, exiting") + sys.exit(1) + + h0, w0, _ = image.shape + h1 = int(h0 * np.sqrt((384 * 512) / (h0 * w0))) + w1 = int(w0 * np.sqrt((384 * 512) / (h0 * w0))) + + image = cv2.resize(image, (w1, h1)) + image = image[: h1 - h1 % 8, : w1 - w1 % 8] + image = torch.as_tensor(image).permute(2, 0, 1) + + fx, fy, cx, cy = intrins_all[t, :4] + sx, sy = w1 / w0, h1 / h0 + frame_intrins = torch.as_tensor([fx * sx, fy * sy, cx * sx, cy * sy]) + yield t, image[None], frame_intrins + + +def unpack_video(video, depth_filter_thresh=0.005): + """ + extract the video of keyframe disps and poses + returns: + (T) timestamps + (T, 7) world2cam pose for each keyframe + (T, H, W) disps + (T, H, W, 3) images + (T, H, W) mask of valid pixels + (4) intrinsics (fx, fy, cx, cy) + """ + with torch.no_grad(): + with video.get_lock(): + # dirty frames have disparity normalized over all previous frames + # should probably change this in visualizer + t = video.counter.value + + print(f"{t} keyframes in map") + + # normalization happens after all frames have been processed + if t < 1: + print("no keyframes") + return + + # taken from visualization.py#80 + tstamps = video.tstamp[:t] + dirty_index = torch.arange(t, device=video.poses.device) + + poses = torch.index_select(video.poses, 0, dirty_index) # (T, 7) + disps = torch.index_select(video.disps, 0, dirty_index) # (T, H, W) + images = torch.index_select(video.images, 0, dirty_index) # (T, 3, H, W) + + images = images[:, [2, 1, 0], 3::8, 3::8].permute(0, 2, 3, 1) / 255.0 + intrins = video.intrinsics[0] # (4,) + + # get mask of static points + thresh = depth_filter_thresh * torch.ones_like(disps.mean(dim=[1, 2])) + count = droid_backends.depth_filter( + video.poses, video.disps, intrins, dirty_index, thresh + ) + disp_mean = disps.mean(dim=(1, 2), keepdim=True).clamp_min(0.2) + valid = (count >= 2) & (disps > 0.5 * disp_mean) # (T, H, W) + return { + "tstamps": tstamps.cpu(), + "w2c": poses.cpu(), + "disps": disps.cpu(), + "images": images.cpu(), + "valid": valid.cpu(), + "intrins": intrins.cpu(), + } + + +def get_keyframe_map(video_dict): + """ + :param video_dict (dict) unpacked droid slam video + :returns + (T, 4, 4) camera to world matrix + (N, 3) valid points in world + (N, 3) colors of valid points + """ + poses = video_dict["w2c"] + images = video_dict["images"] + valid = video_dict["valid"] + t = len(poses) + c2w = SE3(poses).inv() + + # `iproj` only has a cuda backend; if we pass in CPU tensors, it will silently + # return zeros + points = droid_backends.iproj( + c2w.data.cuda(), + video_dict["disps"].cuda(), + video_dict["intrins"].cuda(), + ) + valid_pts = torch.cat([points[i, valid[i]] for i in range(t)], dim=0) + valid_rgb = torch.cat([images[i, valid[i]] for i in range(t)], dim=0) + return ( + c2w.matrix().detach().cpu(), + valid_pts.detach().cpu(), + valid_rgb.detach().cpu(), + ) + + +def get_frame_cameras(droid, img_paths, intrins_all): + N = len(img_paths) + + t = droid.video.counter.value + print(f"{t} keyframes in map") + + if t > 1: + with torch.no_grad(): + # localize all frames and get edges into keyframe graph + # returns 7D tensor (3D trans, 4D quat) + c2w = droid.terminate(image_stream(img_paths, intrins_all)) + c2w = torch.from_numpy(c2w.astype(np.float32)) + return SE3(c2w).inv().matrix() + + return torch.eye(4)[None].repeat(N, 1, 1) + + +def save_camera_json(path, extrins, intrins, yup=False): + """ + :param path + :param extrins (N, 4, 4) + :param intrins (N, 4) + """ + N = extrins.shape[0] + if yup: + T = torch.tensor( + [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]], + dtype=torch.float32, + ) + extrins = torch.matmul(T[None], extrins) + with open(path, "w") as f: + json.dump( + { + "rotation": extrins[:, :3, :3].reshape((N, 9)).tolist(), + "translation": extrins[:, :3, 3].tolist(), + "intrinsics": intrins.tolist(), + }, + f, + indent=1, + ) + + +def save_pcl(path, points, colors, yup=False): + assert len(points) == len(colors) + if yup: + T = torch.tensor( + [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]], + dtype=torch.float32, + ) + points = torch.einsum("ij,...j->...i", T, points) # (*, 3) + points = points.reshape(-1, 3).numpy() + colors = colors.reshape(-1, 3).numpy() + obj = trimesh.Trimesh(vertices=points, vertex_colors=colors) + with open(path, "wb") as f: + f.write(trimesh.exchange.ply.export_ply(obj)) + + +def save_keyframe_map(out_dir, kf_nodes): + """ + Saves everything with x right y up z back + (converts from x right y down z forward) + :param out_dir + :param kf_nodes (dict) + """ + c2w, points, colors = get_keyframe_map(kf_nodes) + intrins = kf_nodes["intrins"].detach().cpu() + + print("c2w", c2w.shape) + print("points", points.shape) + print("colors", colors.shape) + + os.makedirs(out_dir, exist_ok=True) + save_pcl(f"{out_dir}/map_points.ply", points, colors) + save_camera_json(f"{out_dir}/map_cameras.json", c2w, intrins) + print(f"saved {len(c2w)} keyframes to {out_dir}") + + +def save_cameras(map_dir, frame_w2c, intrins): + os.makedirs(map_dir, exist_ok=True) + print("SAVING CAMERA INTRINS AND EXTRINS IN", map_dir) + + # save all camera extrinsics and intrinsic + W, H = intrins[0, 4], intrins[0, 5] + focal = intrins[:, :2].mean() + print("INTRINS", intrins[0]) + np.savez( + f"{map_dir}/cameras.npz", + height=H, + width=W, + focal=focal, + intrins=intrins[:, :4], + w2c=frame_w2c, + ) + + # save visualization + frame_intrins = torch.tensor([focal, focal, W / 2, H / 2, W, H]) + frame_c2w = torch.linalg.inv(frame_w2c) + save_camera_json(f"{map_dir}/frame_cameras.json", frame_c2w, intrins) + + +def main(args): + args.stereo = False + torch.multiprocessing.set_start_method("spawn") + + droid = None + + img_paths = get_image_files( + args.img_dir, args.stride, start=args.start, end=args.end + ) + if args.map_dir is not None: + os.makedirs(args.map_dir, exist_ok=True) + camera_file = os.path.join(args.map_dir, "cameras.npz") + if os.path.isfile(camera_file) and not args.overwrite: + print(glob.glob(f"{args.map_dir}/*.npz"), "already exist, skipping") + return + + intrins_all = load_intrins( + args.intrins_path, img_paths, start=args.start, end=args.end + ) + print("intrins shape", intrins_all.shape, "num images", len(img_paths)) + + for t, image, intrinsics in tqdm(image_stream(img_paths, intrins_all)): + if t < args.t0: + continue + + if not args.disable_vis: + show_image(image[0]) + + if droid is None: + args.image_size = [image.shape[2], image.shape[3]] + droid = Droid(args) + + droid.track(t, image, intrinsics=intrinsics) + + if args.map_dir is None: + return + + # save cameras + frame_w2c = get_frame_cameras(droid, img_paths, intrins_all) + save_cameras(args.map_dir, frame_w2c, intrins_all) + + # save keyframe cameras and points + kf_nodes = unpack_video(droid.video) + save_keyframe_map(args.map_dir, kf_nodes) + + +def get_slam_parser(): + parser = argparse.ArgumentParser() + parser.add_argument("--stride", default=1, type=int, help="frame stride") + parser.add_argument("--t0", default=0, type=int, help="starting frame") + parser.add_argument("--weights", default=f"{ROOT_DIR}/_DATA/droid.pth") + parser.add_argument("--buffer", type=int, default=512) + parser.add_argument("--image_size", default=[240, 320]) + parser.add_argument("--disable_vis", action="store_true") + + parser.add_argument( + "--beta", + type=float, + default=0.3, + help="weight for translation / rotation components of flow", + ) + parser.add_argument( + "--filter_thresh", + type=float, + default=1.0, + help="how much motion before considering new keyframe", + ) + parser.add_argument("--warmup", type=int, default=8, help="number of warmup frames") + parser.add_argument( + "--keyframe_thresh", + type=float, + default=4.0, + help="threshold to create a new keyframe", + ) + parser.add_argument( + "--frontend_thresh", + type=float, + default=16.0, + help="add edges between frames whithin this distance", + ) + parser.add_argument( + "--frontend_window", type=int, default=25, help="frontend optimization window" + ) + parser.add_argument( + "--frontend_radius", + type=int, + default=2, + help="force edges between frames within radius", + ) + parser.add_argument( + "--frontend_nms", type=int, default=1, help="non-maximal supression of edges" + ) + + parser.add_argument("--backend_thresh", type=float, default=22.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=3) + parser.add_argument("--upsample", action="store_true") + return parser + + +if __name__ == "__main__": + parser = get_slam_parser() + parser.add_argument( + "-i", "--img_dir", required=True, type=str, help="path to image directory" + ) + parser.add_argument( + "-o", "--map_dir", type=str, default=None, help="path to output directory" + ) + parser.add_argument( + "-y", "--overwrite", action="store_true", help="overwrite existing cameras" + ) + parser.add_argument( + "-g", "--save_graph", action="store_true", help="save the frame graph" + ) + parser.add_argument( + "--intrins_path", default=None, help="path to camera intrinsics" + ) + parser.add_argument("--start", default=0, type=int, help="start frame") + parser.add_argument("--end", default=-1, type=int, help="end frame") + + args = parser.parse_args() + main(args) diff --git a/slahmr/slahmr/preproc/track.py b/slahmr/slahmr/preproc/track.py new file mode 100644 index 0000000000000000000000000000000000000000..1bcf3dc894cfc5d3886fcdda45ba8c579bde569a --- /dev/null +++ b/slahmr/slahmr/preproc/track.py @@ -0,0 +1,107 @@ +import warnings +from dataclasses import dataclass +from typing import Optional +import numpy as np + +import hydra +from hydra.core.config_store import ConfigStore +from omegaconf import DictConfig + +from phalp.configs.base import FullConfig +from phalp.models.hmar.hmr import HMR2018Predictor +from phalp.trackers.PHALP import PHALP +from phalp.utils import get_pylogger + +from vitpose_model import ViTPoseModel + +warnings.filterwarnings("ignore") + +log = get_pylogger(__name__) + + +class HMR2Predictor(HMR2018Predictor): + def __init__(self, cfg) -> None: + super().__init__(cfg) + # Setup our new model + from hmr2.models import download_models, load_hmr2 + + # Download and load checkpoints + download_models() + model, _ = load_hmr2() + + self.model = model + self.model.eval() + + def forward(self, x): + hmar_out = self.hmar_old(x) + batch = { + "img": x[:, :3, :, :], + "mask": (x[:, 3, :, :]).clip(0, 1), + } + model_out = self.model(batch) + + # Overriding the SMPL params with the HMR2 params + out = hmar_out | { + "pose_smpl": model_out["pred_smpl_params"], + "pred_cam": model_out["pred_cam"], + } + return out + + +class PHALP_Prime_HMR2(PHALP): + def __init__(self, cfg): + super().__init__(cfg) + + def setup_hmr(self): + # initialize vitpose model + self.ViTPose = ViTPoseModel("cuda") + self.HMAR = HMR2Predictor(self.cfg) + + def run_additional_models( + self, + image_frame, + pred_bbox, + pred_masks, + pred_scores, + pred_classes, + frame_name, + t_, + measurments, + gt_tids, + gt_annots, + ): + vitposes_out = self.ViTPose.predict_pose( + image_frame[:, :, ::-1], + [np.concatenate([pred_bbox, pred_scores[:, None]], axis=1)], + ) + vitposes_list = [] + for vitpose in vitposes_out: + vitpose_2d = np.zeros([25, 3]) + vitpose_2d[ + [0, 16, 15, 18, 17, 5, 2, 6, 3, 7, 4, 12, 9, 13, 10, 14, 11] + ] = vitpose["keypoints"] + vitposes_list.append(vitpose_2d) + return vitposes_list + + +@dataclass +class Human4DConfig(FullConfig): + # override defaults if needed + pass + + +cs = ConfigStore.instance() +cs.store(name="config", node=Human4DConfig) + + +@hydra.main(version_base="1.2", config_name="config") +def main(cfg: DictConfig) -> Optional[float]: + """Main function for running the PHALP tracker.""" + + phalp_tracker = PHALP_Prime_HMR2(cfg) + + phalp_tracker.track() + + +if __name__ == "__main__": + main() diff --git a/slahmr/slahmr/preproc/vitpose_model.py b/slahmr/slahmr/preproc/vitpose_model.py new file mode 100644 index 0000000000000000000000000000000000000000..8abe91f66f2d886c717e595236a75a08abde1d91 --- /dev/null +++ b/slahmr/slahmr/preproc/vitpose_model.py @@ -0,0 +1,110 @@ +from __future__ import annotations + +import os + +import numpy as np +import torch +import torch.nn as nn + +from mmpose.apis import ( + inference_top_down_pose_model, + init_pose_model, + process_mmdet_results, + vis_pose_result, +) + +os.environ["PYOPENGL_PLATFORM"] = "egl" + +# project root directory +# ROOT_DIR = os.path.abspath(f"{__file__}/../../../../") +ROOT_DIR = os.path.abspath(f"{__file__}/../../../") +VIT_DIR = os.path.join(ROOT_DIR, "third-party/ViTPose") + + +class ViTPoseModel(object): + MODEL_DICT = { + "ViTPose-B (multi-task train, COCO)": { + "config": f"{VIT_DIR}/configs/body/2d_kpt_sview_rgb_img/topdown_heatmap/coco/ViTPose_base_coco_256x192.py", + "model": f"{ROOT_DIR}/_DATA/vitpose_ckpts/vitpose-b-multi-coco.pth", + }, + "ViTPose-L (multi-task train, COCO)": { + "config": f"{VIT_DIR}/configs/body/2d_kpt_sview_rgb_img/topdown_heatmap/coco/ViTPose_large_coco_256x192.py", + "model": f"{ROOT_DIR}/_DATA/vitpose_ckpts/vitpose-l-multi-coco.pth", + }, + "ViTPose-G (multi-task train, COCO)": { + "config": f"{VIT_DIR}/configs/body/2d_kpt_sview_rgb_img/topdown_heatmap/coco/ViTPose_huge_coco_256x192.py", + "model": f"{ROOT_DIR}/_DATA/vitpose_ckpts/vitpose-h-multi-coco.pth", + }, + } + + def __init__(self, device: str | torch.device): + self.device = torch.device(device) + self.model_name = "ViTPose-G (multi-task train, COCO)" + self.model = self._load_model(self.model_name) + + def _load_all_models_once(self) -> None: + for name in self.MODEL_DICT: + self._load_model(name) + + def _load_model(self, name: str) -> nn.Module: + dic = self.MODEL_DICT[name] + ckpt_path = dic["model"] + model = init_pose_model(dic["config"], ckpt_path, device=self.device) + return model + + def set_model(self, name: str) -> None: + if name == self.model_name: + return + self.model_name = name + self.model = self._load_model(name) + + def predict_pose_and_visualize( + self, + image: np.ndarray, + det_results: list[np.ndarray], + box_score_threshold: float, + kpt_score_threshold: float, + vis_dot_radius: int, + vis_line_thickness: int, + ) -> tuple[list[dict[str, np.ndarray]], np.ndarray]: + out = self.predict_pose(image, det_results, box_score_threshold) + vis = self.visualize_pose_results( + image, out, kpt_score_threshold, vis_dot_radius, vis_line_thickness + ) + return out, vis + + def predict_pose( + self, + image: np.ndarray, + det_results: list[np.ndarray], + box_score_threshold: float = 0.5, + ) -> list[dict[str, np.ndarray]]: + image = image[:, :, ::-1] # RGB -> BGR + person_results = process_mmdet_results(det_results, 1) + out, _ = inference_top_down_pose_model( + self.model, + image, + person_results=person_results, + bbox_thr=box_score_threshold, + format="xyxy", + ) + return out + + def visualize_pose_results( + self, + image: np.ndarray, + pose_results: list[np.ndarray], + kpt_score_threshold: float = 0.3, + vis_dot_radius: int = 4, + vis_line_thickness: int = 1, + ) -> np.ndarray: + image = image[:, :, ::-1] # RGB -> BGR + vis = vis_pose_result( + self.model, + image, + pose_results, + kpt_score_thr=kpt_score_threshold, + radius=vis_dot_radius, + thickness=vis_line_thickness, + ) + return vis[:, :, ::-1] # BGR -> RGB diff --git a/slahmr/slahmr/run_opt.py b/slahmr/slahmr/run_opt.py new file mode 100644 index 0000000000000000000000000000000000000000..bf6f7debefd715207772c8c6a5aabcd914e50622 --- /dev/null +++ b/slahmr/slahmr/run_opt.py @@ -0,0 +1,189 @@ +import os +import glob +import json +import subprocess + +import torch +from torch.utils.data import DataLoader +from torch.utils.tensorboard import SummaryWriter + +from data import get_dataset_from_cfg, expand_source_paths + +from humor.humor_model import HumorModel +from optim.base_scene import BaseSceneModel +from optim.moving_scene import MovingSceneModel +from optim.optimizers import ( + RootOptimizer, + SmoothOptimizer, + SMPLOptimizer, + MotionOptimizer, + MotionOptimizerChunks, +) +from optim.output import ( + save_track_info, + save_camera_json, + save_input_poses, + save_initial_predictions, +) +from vis.viewer import init_viewer + +from util.loaders import ( + load_vposer, + load_state, + load_gmm, + load_smpl_body_model, + resolve_cfg_paths, +) +from util.logger import Logger +from util.tensor import get_device, move_to, detach_all, to_torch + +from run_vis import run_vis + +import hydra +from omegaconf import DictConfig, OmegaConf + + +N_STAGES = 3 + + +def run_opt(cfg, dataset, out_dir, device): + args = cfg.data + B = len(dataset) + T = dataset.seq_len + loader = DataLoader(dataset, batch_size=B, shuffle=False) + + obs_data = move_to(next(iter(loader)), device) + cam_data = move_to(dataset.get_camera_data(), device) + print("OBS DATA", obs_data.keys()) + print("CAM DATA", cam_data.keys()) + + # save cameras + cam_R, cam_t = dataset.cam_data.cam2world() + intrins = dataset.cam_data.intrins + save_camera_json(f"cameras.json", cam_R, cam_t, intrins) + + # check whether the cameras are static + # if static, cannot optimize scale + cfg.model.opt_scale &= not dataset.cam_data.is_static + Logger.log(f"OPT SCALE {cfg.model.opt_scale}") + + # loss weights for all stages + all_loss_weights = cfg.optim.loss_weights + assert all(len(wts) == N_STAGES for wts in all_loss_weights.values()) + stage_loss_weights = [ + {k: wts[i] for k, wts in all_loss_weights.items()} for i in range(N_STAGES) + ] + max_loss_weights = {k: max(wts) for k, wts in all_loss_weights.items()} + + # load models + cfg = resolve_cfg_paths(cfg) + paths = cfg.paths + Logger.log(f"Loading pose prior from {paths.vposer}") + pose_prior, _ = load_vposer(paths.vposer) + pose_prior = pose_prior.to(device) + + Logger.log(f"Loading body model from {paths.smpl}") + body_model, fit_gender = load_smpl_body_model(paths.smpl, B * T, device=device) + + margs = cfg.model + base_model = BaseSceneModel( + B, T, body_model, pose_prior, fit_gender=fit_gender, **margs + ) + base_model.initialize(obs_data, cam_data) + base_model.to(device) + + # save initial results for later visualization + save_input_poses(dataset, os.path.join(out_dir, "phalp"), args.seq) + save_initial_predictions(base_model, os.path.join(out_dir, "init"), args.seq) + + opts = cfg.optim.options + vis_scale = 0.25 + vis = None + if opts.vis_every > 0: + vis = init_viewer( + dataset.img_size, + cam_data["intrins"][0], + vis_scale=vis_scale, + bg_paths=dataset.sel_img_paths, + fps=cfg.fps, + ) + print("OPTIMIZER OPTIONS:", opts) + + writer = SummaryWriter(out_dir) + + optim = RootOptimizer(base_model, stage_loss_weights, **opts) + optim.run(obs_data, cfg.optim.root.num_iters, out_dir, vis, writer) + + optim = SMPLOptimizer(base_model, stage_loss_weights, **opts) + optim.run(obs_data, cfg.optim.smpl.num_iters, out_dir, vis, writer) + + args = cfg.optim.smooth + optim = SmoothOptimizer( + base_model, stage_loss_weights, opt_scale=args.opt_scale, **opts + ) + optim.run(obs_data, args.num_iters, out_dir, vis, writer) + + # now optimize motion model + Logger.log(f"Loading motion prior from {paths.humor}") + motion_prior = HumorModel(**cfg.humor) + load_state(paths.humor, motion_prior, map_location="cpu") + motion_prior.to(device) + motion_prior.eval() + + Logger.log(f"Loading GMM motion prior from {paths.init_motion_prior}") + init_motion_prior = load_gmm(paths.init_motion_prior, device=device) + + model = MovingSceneModel( + B, + T, + body_model, + pose_prior, + motion_prior, + init_motion_prior, + fit_gender=fit_gender, + **margs, + ).to(device) + + # initialize motion model with base model predictions + base_params = base_model.params.get_dict() + model.initialize(obs_data, cam_data, base_params, cfg.fps) + model.to(device) + + if "motion_chunks" in cfg.optim: + args = cfg.optim.motion_chunks + optim = MotionOptimizerChunks(model, stage_loss_weights, **args, **opts) + optim.run(obs_data, optim.num_iters, out_dir, vis, writer) + + if "motion_refine" in cfg.optim: + args = cfg.optim.motion_refine + optim = MotionOptimizer(model, stage_loss_weights, **args, **opts) + optim.run(obs_data, args.num_iters, out_dir, vis, writer) + + +@hydra.main(version_base=None, config_path="confs", config_name="config.yaml") +def main(cfg: DictConfig): + OmegaConf.register_new_resolver("eval", eval) + + out_dir = os.getcwd() + print("out_dir", out_dir) + Logger.init(f"{out_dir}/opt_log.txt") + + # make sure we get all necessary inputs + cfg.data.sources = expand_source_paths(cfg.data.sources) + print("SOURCES", cfg.data.sources) + + dataset = get_dataset_from_cfg(cfg) + save_track_info(dataset, out_dir) + + if cfg.run_opt: + device = get_device(0) + run_opt(cfg, dataset, out_dir, device) + + if cfg.run_vis: + run_vis( + cfg, dataset, out_dir, 0, **cfg.get("vis", dict()) + ) + + +if __name__ == "__main__": + main() diff --git a/slahmr/slahmr/run_vis.py b/slahmr/slahmr/run_vis.py new file mode 100644 index 0000000000000000000000000000000000000000..e6f8dd86ab75196658394aa11cb5a0f8850e138b --- /dev/null +++ b/slahmr/slahmr/run_vis.py @@ -0,0 +1,292 @@ +import os +import glob + +import imageio +import numpy as np +import torch +from torch.utils.data import DataLoader + +from omegaconf import DictConfig, OmegaConf + +from data import get_dataset_from_cfg, expand_source_paths +from optim.output import ( + get_results_paths, + load_result, + save_input_frames, + save_input_poses, +) +from util.loaders import load_config_from_log, resolve_cfg_paths, load_smpl_body_model +from util.tensor import get_device, move_to, detach_all, to_torch +from vis.output import prep_result_vis, animate_scene, make_video_grid_2x2 +from vis.tools import vis_keypoints +from vis.viewer import init_viewer + + +def run_vis( + cfg, + dataset, + out_dir, + dev_id, + phases=["motion_chunks"], + render_views=["src_cam", "above", "side"], + make_grid=False, + overwrite=False, + save_dir=None, + render_kps=True, + render_layers=False, + save_frames=False, + **kwargs, +): + save_dir = out_dir if save_dir is None else save_dir + print("OUT_DIR", out_dir) + print("SAVE_DIR", save_dir) + print("VISUALIZING PHASES", phases) + print("RENDERING VIEWS", render_views) + print("OVERWRITE", overwrite) + + # save input frames + inp_vid_path = save_input_frames( + dataset, + f"{save_dir}/{dataset.seq_name}_input.mp4", + fps=cfg.fps, + overwrite=True, + ) + + if render_kps: + render_keypoints_2d(dataset, save_dir, overwrite=overwrite) + + if len(render_views) < 1: + return + + out_ext = "/" if render_layers or save_frames else ".mp4" + phase_results = {} + phase_max_iters = {} + for phase in phases: + res_dir = os.path.join(out_dir, phase) + if phase == "input": + res = get_input_dict(dataset) + it = f"{0:06d}" + + elif os.path.isdir(res_dir): + res_path_dict = get_results_paths(res_dir) + it = sorted(res_path_dict.keys())[-1] + res = load_result(res_path_dict[it])["world"] + + else: + print(f"{res_dir} does not exist, skipping") + continue + + out_name = f"{save_dir}/{dataset.seq_name}_{phase}_final_{it}" + phase_max_iters[phase] = it + + out_paths = [f"{out_name}_{view}{out_ext}" for view in render_views] + if not overwrite and all(os.path.exists(p) for p in out_paths): + print("FOUND OUT PATHS", out_paths) + continue + + phase_results[phase] = out_name, res + + if len(phase_results) > 0: + out_names, res_dicts = zip(*phase_results.values()) + render_results( + cfg, + dataset, + dev_id, + res_dicts, + out_names, + render_views=render_views, + render_layers=render_layers, + save_frames=save_frames, + **kwargs, + ) + + if make_grid: + for phase, it in phase_max_iters.items(): + grid_path = f"{save_dir}/{dataset.seq_name}_{phase}_grid.mp4" + vid_paths = [ + inp_vid_path, + f"{save_dir}/{dataset.seq_name}_{phase}_final_{it}_src_cam.mp4", + f"{save_dir}/{dataset.seq_name}_{phase}_final_{it}_above.mp4", + f"{save_dir}/{dataset.seq_name}_{phase}_final_{it}_side.mp4", + ] + make_video_grid_2x2( + grid_path, + vid_paths, + overwrite=True, + ) + + +def get_input_dict(dataset): + dataset.load_data(interp_input=False) + d = dataset.data_dict + input_params = { + "pose_body": np.stack(d["init_body_pose"], axis=0), + "trans": np.stack(d["init_trans"], axis=0), + "root_orient": np.stack(d["init_root_orient"], axis=0), + } + input_params = to_torch(input_params) + print({k: v.shape for k, v in input_params.items()}) + return input_params + + +def render_keypoints_2d(dataset, save_dir, overwrite=False): + """ + render 2d keypoints for each track + """ + dataset.load_data() + out_dir = f"{save_dir}/{dataset.seq_name}_joints2d" + B, T = dataset.n_tracks, dataset.seq_len + if not overwrite and (os.path.isdir(out_dir) and len(os.listdir(out_dir)) >= B * T): + print(f"Keypoints already rendered in {out_dir}") + return + + os.makedirs(out_dir, exist_ok=True) + for i, tid in enumerate(dataset.track_ids): + joints2d = dataset.data_dict["joints2d"][i] # (T, J, 3) + for t, sel_img_name in enumerate(dataset.sel_img_names): + img = vis_keypoints(joints2d[t : t + 1], dataset.img_size) + out_path = f"{out_dir}/{sel_img_name}_{tid}.png" + imageio.imwrite(out_path, img) + + +def render_results(cfg, dataset, dev_id, res_dicts, out_names, **kwargs): + """ + render results for all selected phases + """ + assert len(res_dicts) == len(out_names) + if len(res_dicts) < 1: + print("no results to render, skipping") + return + + B = len(dataset) + T = dataset.seq_len + loader = DataLoader(dataset, batch_size=B, shuffle=False) + + device = get_device(dev_id) + obs_data = move_to(next(iter(loader)), device) + cam_data = dataset.get_camera_data() + + # load models + cfg = resolve_cfg_paths(cfg) + body_model, _ = load_smpl_body_model(cfg.paths.smpl, B * T, device=device) + vis = init_viewer( + dataset.img_size, + cam_data["intrins"][0], + vis_scale=1.0, + bg_paths=dataset.sel_img_paths, + fps=cfg.fps, + ) + + save_paths_all = [] + for res_dict, out_name in zip(res_dicts, out_names): + res_dict = move_to(res_dict, device) + scene_dict = prep_result_vis( + res_dict, + obs_data["vis_mask"], + obs_data["track_id"], + body_model, + ) + print(kwargs) + save_paths = animate_scene( + vis, scene_dict, out_name, seq_name=dataset.seq_name, **kwargs + ) + save_paths_all.append(save_paths) + + vis.close() + + return save_paths_all + + +def visualize_log(log_dir, dev_id, phases, save_dir=None, **kwargs): + print(log_dir) + cfg = load_config_from_log(log_dir) + + # make sure we get all necessary inputs + cfg.data.sources = expand_source_paths(cfg.data.sources) + print("SOURCES", cfg.data.sources) + # cfg.data.track_ids = "001" + dataset = get_dataset_from_cfg(cfg) + if len(dataset) < 1: + print(f"No tracks in dataset, skipping") + return + + run_vis(cfg, dataset, log_dir, dev_id, phases=phases, save_dir=save_dir, **kwargs) + + +def launch_vis(i, args): + log_dir = args.log_dirs[i] + dev_id = args.gpus[i % len(args.gpus)] + os.environ["EGL_DEVICE_ID"] = str(dev_id) + os.environ["PYOPENGL_PLATFORM"] = "egl" + + if args.save_root is not None: + path_name = log_dir.split(args.log_root)[-1].strip("/") + exp_name = "-".join(path_name.split("/")[:2]) + save_dir = f"{args.save_root}/{exp_name}" + os.makedirs(save_dir, exist_ok=True) + + visualize_log( + log_dir, + dev_id, + phases=args.phases, + save_dir=save_dir, + overwrite=args.overwrite, + accumulate=args.accumulate, + render_kps=args.render_kps, + render_layers=args.render_layers, + render_views=args.render_views, + save_frames=args.save_frames, + make_grid=args.grid, + ) + + +def main(args): + """ + visualize all runs in root + """ + OmegaConf.register_new_resolver("eval", eval) + log_dirs = [] + for root, subd, files in os.walk(args.log_root): + if ".hydra" in subd: + log_dirs.append(root) + args.log_dirs = log_dirs + print(f"FOUND {len(args.log_dirs)} TO RENDER") + + if len(args.gpus) > 1: + from torch.multiprocessing import Pool + + torch.multiprocessing.set_start_method("spawn") + + with Pool(processes=len(args.gpus)) as pool: + res = pool.starmap( + launch_vis, [(i, args) for i in range(len(args.log_dirs))] + ) + return + + for i in range(len(args.log_dirs)): + launch_vis(i, args) + + +if __name__ == "__main__": + import argparse + + parser = argparse.ArgumentParser() + parser.add_argument("--log_root", required=True) + parser.add_argument("--save_root", default=None) + parser.add_argument("--phases", nargs="*", default=["motion_chunks"]) + parser.add_argument("--gpus", nargs="*", default=[0]) + parser.add_argument( + "-rv", + "--render_views", + nargs="*", + default=["src_cam", "front", "above", "side"], + ) + parser.add_argument("-g", "--grid", action="store_true") + parser.add_argument("-rl", "--render_layers", action="store_true") + parser.add_argument("-kp", "--render_kps", action="store_true") + parser.add_argument("-sf", "--save_frames", action="store_true") + parser.add_argument("-ra", "--accumulate", action="store_true") + parser.add_argument("-y", "--overwrite", action="store_true") + args = parser.parse_args() + + main(args) diff --git a/slahmr/slahmr/slahmr.egg-info/PKG-INFO b/slahmr/slahmr/slahmr.egg-info/PKG-INFO new file mode 100644 index 0000000000000000000000000000000000000000..cfca7e5488eabfdf293bc84a08f3df59bb694676 --- /dev/null +++ b/slahmr/slahmr/slahmr.egg-info/PKG-INFO @@ -0,0 +1,11 @@ +Metadata-Version: 2.1 +Name: slahmr +Version: 0.0.0 +Summary: UNKNOWN +Home-page: UNKNOWN +License: UNKNOWN +Platform: UNKNOWN +License-File: LICENSE + +UNKNOWN + diff --git a/slahmr/slahmr/slahmr.egg-info/SOURCES.txt b/slahmr/slahmr/slahmr.egg-info/SOURCES.txt new file mode 100644 index 0000000000000000000000000000000000000000..e3058de5d7167600cbeb64cd7b7ffdf62d02ebf5 --- /dev/null +++ b/slahmr/slahmr/slahmr.egg-info/SOURCES.txt @@ -0,0 +1,61 @@ +LICENSE +README.md +setup.py +slahmr/body_model/__init__.py +slahmr/body_model/body_model.py +slahmr/body_model/specs.py +slahmr/body_model/utils.py +slahmr/data/__init__.py +slahmr/data/dataset.py +slahmr/data/tools.py +slahmr/data/vidproc.py +slahmr/eval/__init__.py +slahmr/eval/associate.py +slahmr/eval/egobody_utils.py +slahmr/eval/run_eval.py +slahmr/eval/split_3dpw.py +slahmr/eval/split_egobody.py +slahmr/eval/tools.py +slahmr/geometry/__init__.py +slahmr/geometry/camera.py +slahmr/geometry/mesh.py +slahmr/geometry/pcl.py +slahmr/geometry/plane.py +slahmr/geometry/rotation.py +slahmr/humor/__init__.py +slahmr/humor/amass_utils.py +slahmr/humor/humor_model.py +slahmr/humor/transforms.py +slahmr/optim/__init__.py +slahmr/optim/base_scene.py +slahmr/optim/helpers.py +slahmr/optim/losses.py +slahmr/optim/moving_scene.py +slahmr/optim/optimizers.py +slahmr/optim/output.py +slahmr/optim/params.py +slahmr/preproc/__init__.py +slahmr/preproc/datasets.py +slahmr/preproc/export_3dpw.py +slahmr/preproc/export_egobody.py +slahmr/preproc/export_phalp.py +slahmr/preproc/extract_frames.py +slahmr/preproc/launch_phalp.py +slahmr/preproc/launch_slam.py +slahmr/preproc/run_slam.py +slahmr/preproc/track.py +slahmr/preproc/vitpose_model.py +slahmr/slahmr.egg-info/PKG-INFO +slahmr/slahmr.egg-info/SOURCES.txt +slahmr/slahmr.egg-info/dependency_links.txt +slahmr/slahmr.egg-info/top_level.txt +slahmr/util/__init__.py +slahmr/util/loaders.py +slahmr/util/logger.py +slahmr/util/tensor.py +slahmr/vis/__init__.py +slahmr/vis/fig_specs.py +slahmr/vis/output.py +slahmr/vis/render.py +slahmr/vis/tools.py +slahmr/vis/viewer.py \ No newline at end of file diff --git a/slahmr/slahmr/slahmr.egg-info/dependency_links.txt b/slahmr/slahmr/slahmr.egg-info/dependency_links.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b137891791fe96927ad78e64b0aad7bded08bdc --- /dev/null +++ b/slahmr/slahmr/slahmr.egg-info/dependency_links.txt @@ -0,0 +1 @@ + diff --git a/slahmr/slahmr/slahmr.egg-info/top_level.txt b/slahmr/slahmr/slahmr.egg-info/top_level.txt new file mode 100644 index 0000000000000000000000000000000000000000..56fa9cb6fb03a39456e5f815036129a536d29b27 --- /dev/null +++ b/slahmr/slahmr/slahmr.egg-info/top_level.txt @@ -0,0 +1,9 @@ +body_model +data +eval +geometry +humor +optim +preproc +util +vis diff --git a/slahmr/slahmr/util/__init__.py b/slahmr/slahmr/util/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..80b0ce9ef3d5793faf351d3081d996df4ca93e8b --- /dev/null +++ b/slahmr/slahmr/util/__init__.py @@ -0,0 +1,3 @@ +from . import loaders +from . import logger +from . import tensor diff --git a/slahmr/slahmr/util/loaders.py b/slahmr/slahmr/util/loaders.py new file mode 100644 index 0000000000000000000000000000000000000000..e3bdb9314e1aceea374f78f6c7d26ecea71d8803 --- /dev/null +++ b/slahmr/slahmr/util/loaders.py @@ -0,0 +1,216 @@ +""" +Utilities for loading input and models (reading pre-processed data) +""" + +import os +import importlib +import glob +from omegaconf import OmegaConf + +import numpy as np +import torch + +from body_model import BodyModel + + +ROOT_DIR = os.path.abspath(f"{__file__}/../../../") + + +def load_config_from_log(log_dir): + hydra_dir = f"{log_dir}/.hydra" + cfg_path = f"{hydra_dir}/config.yaml" + assert os.path.isdir(hydra_dir), f"{hydra_dir} does not exist" + assert os.path.isfile(cfg_path), f"{cfg_path} does not exist" + return OmegaConf.load(cfg_path) + + +def resolve_cfg_paths(cfg): + paths = cfg.paths + for name, rel_path in paths.items(): + if rel_path.startswith("/"): # absolute path + continue + paths[name] = os.path.join(ROOT_DIR, rel_path) + print("RESOLVED PATHS", paths) + return cfg + + +def load_smpl_body_model( + path, + batch_size, + num_betas=16, + model_type="smplh", + use_vtx_selector=True, + device=None, +): + """ + Load SMPL model + """ + if device is None: + device = torch.device("cpu") + fit_gender = path.split("/")[-2] + return ( + BodyModel( + bm_path=path, + num_betas=num_betas, + batch_size=batch_size, + use_vtx_selector=use_vtx_selector, + model_type=model_type, + ).to(device), + fit_gender, + ) + + +def expid2model(expr_dir): + """ " + Reading VPoser models (https://github.com/nghorbani/human_body_prior). + """ + from configer import Configer + + if not os.path.exists(expr_dir): + raise ValueError("Could not find the experiment directory: %s" % expr_dir) + + best_model_fname = sorted( + glob.glob(os.path.join(expr_dir, "snapshots", "*.pt")), key=os.path.getmtime + )[-1] + try_num = os.path.basename(best_model_fname).split("_")[0] + + print(("Found Trained Model: %s" % best_model_fname)) + + default_ps_fname = glob.glob(os.path.join(expr_dir, "*.ini"))[0] + if not os.path.exists(default_ps_fname): + raise ValueError( + "Could not find the appropriate vposer_settings: %s" % default_ps_fname + ) + ps = Configer( + default_ps_fname=default_ps_fname, + work_dir=expr_dir, + best_model_fname=best_model_fname, + ) + + return ps, best_model_fname + + +def load_vposer(expr_dir, vp_model="snapshot"): + """ + :param expr_dir: + :param vp_model: either 'snapshot' to use the experiment folder's code or a VPoser imported module, e.g. + from human_body_prior.train.vposer_smpl import VPoser, then pass VPoser to this function + :param if True will load the model definition used for training, and not the one in current repository + :return: + """ + ps, trained_model_fname = expid2model(expr_dir) + if vp_model == "snapshot": + + vposer_path = sorted( + glob.glob(os.path.join(expr_dir, "vposer_*.py")), key=os.path.getmtime + )[-1] + + spec = importlib.util.spec_from_file_location("VPoser", vposer_path) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + + vposer_pt = getattr(module, "VPoser")( + num_neurons=ps.num_neurons, latentD=ps.latentD, data_shape=ps.data_shape + ) + else: + vposer_pt = vp_model( + num_neurons=ps.num_neurons, latentD=ps.latentD, data_shape=ps.data_shape + ) + + vposer_pt.load_state_dict(torch.load(trained_model_fname, map_location="cpu")) + vposer_pt.eval() + + return vposer_pt, ps + + +def load_state( + load_path, + model, + optimizer=None, + is_parallel=False, + map_location=None, + ignore_keys=None, +): + """ + Load Humor model checkpoint + """ + if not os.path.exists(load_path): + print("Could not find checkpoint at path " + load_path) + + full_checkpoint_dict = torch.load(load_path, map_location=map_location) + model_state_dict = full_checkpoint_dict["model"] + optim_state_dict = full_checkpoint_dict["optim"] + + # load model weights + for k, v in model_state_dict.items(): + if k.split(".")[0] == "module" and not is_parallel: + # then it was trained with Data parallel + print("Loading weights trained with DataParallel...") + model_state_dict = { + ".".join(k.split(".")[1:]): v + for k, v in model_state_dict.items() + if k.split(".")[0] == "module" + } + break + + if ignore_keys is not None: + model_state_dict = { + k: v + for k, v in model_state_dict.items() + if k.split(".")[0] not in ignore_keys + } + + # overwrite entries in the existing state dict + missing_keys, unexpected_keys = model.load_state_dict( + model_state_dict, strict=False + ) + if ignore_keys is not None: + missing_keys = [k for k in missing_keys if k.split(".")[0] not in ignore_keys] + unexpected_keys = [ + k for k in unexpected_keys if k.split(".")[0] not in ignore_keys + ] + if len(missing_keys) > 0: + print( + "WARNING: The following keys could not be found in the given state dict - ignoring..." + ) + print(missing_keys) + if len(unexpected_keys) > 0: + print( + "WARNING: The following keys were found in the given state dict but not in the current model - ignoring..." + ) + print(unexpected_keys) + + # load optimizer weights + if optimizer is not None: + optimizer.load_state_dict(optim_state_dict) + + min_train_loss = float("Inf") + if "min_train_loss" in full_checkpoint_dict.keys(): + min_train_loss = full_checkpoint_dict["min_train_loss"] + + return ( + full_checkpoint_dict["epoch"], + full_checkpoint_dict["min_val_loss"], + min_train_loss, + ) + + +def load_gmm(path, device=None): + """ + Load motion prior GMM for first frame motion prior + """ + if device is None: + device = torch.device("cpu") + + gmm_path = os.path.join(path, "prior_gmm.npz") + if not os.path.isfile(gmm_path): + raise ValueError(f"Init motion prior path {gmm_path} does not exist") + + res = np.load(gmm_path) + return { + "gmm": ( + torch.from_numpy(res["weights"]).to(device), + torch.from_numpy(res["means"]).to(device), + torch.from_numpy(res["covariances"]).to(device), + ) + } diff --git a/slahmr/slahmr/util/logger.py b/slahmr/slahmr/util/logger.py new file mode 100644 index 0000000000000000000000000000000000000000..ad43a9c6e7f897d13000266135ddb341f6847f08 --- /dev/null +++ b/slahmr/slahmr/util/logger.py @@ -0,0 +1,37 @@ +import datetime + + +class Logger(object): + """ + Static logging class + """ + + log_file = None + + @staticmethod + def init(log_path): + Logger.log_file = log_path + + @staticmethod + def log(write_str, to_stdout=True): + if to_stdout: + print(write_str) + if not Logger.log_file: + print("Logger must be initialized before logging!") + return + time_str = datetime.datetime.now().strftime("%Y-%m-%d_%H:%M:%S") + with open(Logger.log_file, "a") as f: + f.write(time_str + " ") + f.write(str(write_str) + "\n") + + +def log_cur_stats(stats_dict, iter=None, to_stdout=True): + loss = stats_dict.pop("total", 0) + Logger.log(f"LOSS: {loss:.04f}", to_stdout=to_stdout) + for k, v in stats_dict.items(): + Logger.log(f"{k}: {v:.04f}", to_stdout=to_stdout) + if to_stdout: + if iter is not None: + print("======= iter %d =======" % iter) + else: + print("========") diff --git a/slahmr/slahmr/util/tensor.py b/slahmr/slahmr/util/tensor.py new file mode 100644 index 0000000000000000000000000000000000000000..ceb85666a485ca08157dc93d140fde84204572d5 --- /dev/null +++ b/slahmr/slahmr/util/tensor.py @@ -0,0 +1,139 @@ +import torch +import numpy as np + + +def move_to(obj, device): + if isinstance(obj, torch.Tensor): + return obj.to(device) + if isinstance(obj, dict): + return {k: move_to(v, device) for k, v in obj.items()} + if isinstance(obj, (list, tuple)): + return [move_to(x, device) for x in obj] + return obj # otherwise do nothing + + +def detach_all(obj): + if isinstance(obj, torch.Tensor): + return obj.detach() + if isinstance(obj, dict): + return {k: detach_all(v) for k, v in obj.items()} + if isinstance(obj, (list, tuple)): + return [detach_all(x) for x in obj] + return obj # otherwise do nothing + + +def to_torch(obj): + if isinstance(obj, np.ndarray): + return torch.from_numpy(obj).float() + if isinstance(obj, dict): + return {k: to_torch(v) for k, v in obj.items()} + if isinstance(obj, (list, tuple)): + return [to_torch(x) for x in obj] + return obj + + +def to_np(obj): + if isinstance(obj, torch.Tensor): + return obj.numpy() + if isinstance(obj, dict): + return {k: to_np(v) for k, v in obj.items()} + if isinstance(obj, (list, tuple)): + return [to_np(x) for x in obj] + return obj + + +def get_device(i=0): + device = f"cuda:{i}" if torch.cuda.is_available() else "cpu" + return torch.device(device) + + +def scatter_intervals(tensor, start, end, T=None): + """ + Scatter the tensor contents into intervals from start to end + output tensor indexed from 0 to end.max() + :param tensor (B, S, *) + :param start (B) start indices + :param end (B) end indices + :param T (int, optional) max length + returns (B, T, *) scattered tensor + """ + assert isinstance(tensor, torch.Tensor) and tensor.ndim >= 2 + if T is not None: + end = torch.where(end < 0, T + 1 + end, end) + assert torch.all(end <= T) + else: + T = end.max() + + B, S, *dims = tensor.shape + start, end = start.long(), end.long() + # get idcs that go past the last time step so we don't have repeat indices in scatter + idcs = time_segment_idcs(start, end, clip=False) # (B, S) + # mask out the extra padding + mask = idcs >= end[:, None] + tensor[mask] = 0 + + idcs = idcs.reshape(B, S, *(1,) * len(dims)).repeat(1, 1, *dims) + output = torch.zeros( + B, idcs.max() + 1, *dims, device=tensor.device, dtype=tensor.dtype + ) + output.scatter_(1, idcs, tensor) + # slice out the extra segments + return output[:, :T] + + +def get_scatter_mask(start, end, T): + """ + get the mask of selected intervals + """ + B = start.shape[0] + start, end = start.long(), end.long() + assert torch.all(end <= T) + idcs = time_segment_idcs(start, end, clip=True) + mask = torch.zeros(B, T, device=start.device, dtype=torch.bool) + mask.scatter_(1, idcs, 1) + return mask + + +def select_intervals(series, start, end): + """ + Select slices of a tensor from start to end + will pad uneven sequences to all the max segment length + :param series (B, T, *) + :param start (B) + :param end (B) + returns (B, S, *) selected segments, S = max(end - start) + """ + B, T, *dims = series.shape + assert torch.all(end <= T) + sel = time_segment_idcs(start, end, clip=True) + S = sel.shape[1] + sel = sel.reshape(B, S, *(1,) * len(dims)).repeat(1, 1, *dims) + return torch.gather(series, 1, sel) + + +def get_select_mask(start, end): + """ + get the mask of unpadded elementes for the selected time segments + e.g. sel[mask] are the unpadded elements + :param start (B) + :param end (B) + """ + idcs = time_segment_idcs(start, end, clip=False) + return idcs < end[:, None] # (B, S) + + +def time_segment_idcs(start, end, clip=True): + """ + :param start (B) + :param end (B) + returns (B, S) long tensor of indices, where S = max(end - start) + """ + start, end = start.long(), end.long() + S = (end - start).max() + seg = torch.arange(S, dtype=torch.int64, device=start.device) + idcs = start[:, None] + seg[None, :] # (B, S) + if clip: + # clip at the lengths of each track + imax = end[:, None] - 1 + idcs = idcs.clamp(max=imax) + return idcs diff --git a/slahmr/slahmr/vis/__init__.py b/slahmr/slahmr/vis/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..081baee392d8fcf73e096f6bb8ae8001db3f2f6f --- /dev/null +++ b/slahmr/slahmr/vis/__init__.py @@ -0,0 +1,4 @@ +from . import viewer + +# from . import render +from . import tools diff --git a/slahmr/slahmr/vis/colors.txt b/slahmr/slahmr/vis/colors.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a58958aa274acfd91c5a5be8bc7275e9c84fd6d --- /dev/null +++ b/slahmr/slahmr/vis/colors.txt @@ -0,0 +1,98 @@ +241 91 181 +0 187 249 +254 228 64 +0 245 212 +222 158 54 +255 133 141 +93 169 233 +155 93 229 +24 242 178 +252 116 186 +138 225 252 +178 171 242 +24 231 98 +232 93 117 +207 250 231 +253 208 242 +109 157 197 +166 189 219 +253 146 207 +167 201 87 +117 68 177 +255 229 50 +251 202 239 +58 134 255 +255 0 110 +251 86 7 +188 51 209 +122 229 130 +0 48 73 +214 40 40 +229 179 179 +0 187 249 +255 190 11 +204 213 174 +0 245 212 +255 153 200 +144 251 146 +189 211 147 +230 0 86 +0 95 57 +0 174 126 +255 116 163 +189 198 255 +90 219 255 +158 0 142 +255 147 126 +164 36 0 +0 21 68 +145 208 203 +95 173 78 +107 104 130 +0 125 181 +106 130 108 +252 246 189 +208 244 222 +169 222 249 +228 193 249 +122 204 174 +194 140 159 +0 143 156 +235 0 0 +255 2 157 +104 61 59 +150 138 232 +152 255 82 +167 87 64 +1 255 254 +255 238 232 +254 137 0 +1 208 255 +187 136 0 +165 255 210 +255 166 254 +119 77 0 +122 71 130 +38 52 0 +0 71 84 +67 0 44 +181 0 255 +255 177 103 +255 219 102 +126 45 210 +229 111 254 +222 255 116 +0 255 120 +0 155 255 +0 100 1 +0 118 255 +133 169 0 +0 185 23 +120 130 49 +0 255 198 +255 110 65 +232 94 190 +1 0 103 +149 0 58 +98 14 0 +0 0 0 diff --git a/slahmr/slahmr/vis/colors_phalp.txt b/slahmr/slahmr/vis/colors_phalp.txt new file mode 100644 index 0000000000000000000000000000000000000000..85ab59fbdb6775a5c9ff66d72763f8cfae38a412 --- /dev/null +++ b/slahmr/slahmr/vis/colors_phalp.txt @@ -0,0 +1,65 @@ +213 255 0 +255 0 86 +158 0 142 +14 76 161 +255 229 2 +0 95 57 +0 255 0 +149 0 58 +255 147 126 +164 36 0 +0 21 68 +145 208 203 +98 14 0 +107 104 130 +0 0 255 +0 125 181 +106 130 108 +0 174 126 +194 140 159 +190 153 112 +0 143 156 +95 173 78 +255 0 0 +255 0 246 +255 2 157 +104 61 59 +255 116 163 +150 138 232 +152 255 82 +167 87 64 +1 255 254 +255 238 232 +254 137 0 +189 198 255 +1 208 255 +187 136 0 +117 68 177 +165 255 210 +255 166 254 +119 77 0 +122 71 130 +38 52 0 +0 71 84 +67 0 44 +181 0 255 +255 177 103 +255 219 102 +144 251 146 +126 45 210 +189 211 147 +229 111 254 +222 255 116 +0 255 120 +0 155 255 +0 100 1 +0 118 255 +133 169 0 +0 185 23 +120 130 49 +0 255 198 +255 110 65 +232 94 190 + +0 0 0 +1 0 103 \ No newline at end of file diff --git a/slahmr/slahmr/vis/fig_specs.py b/slahmr/slahmr/vis/fig_specs.py new file mode 100644 index 0000000000000000000000000000000000000000..cb3b55c60bd973427caf3574558a0c6be56b16ce --- /dev/null +++ b/slahmr/slahmr/vis/fig_specs.py @@ -0,0 +1,245 @@ +import torch +import numpy as np + + +def get_seq_figure_skip(seq_name=None): + if seq_name == "017437_mpii_test": + return 15 + if seq_name == "012968_mpii_test": + return 15 + if seq_name == "recording_20211002_S03_S18_04-all-100-200": + return 11 + return 10 + + +def get_seq_static_lookat_points(seq_name=None, bounds=None): + if seq_name == "002276_mpii_test": + top_source = torch.tensor([-0.5, -3.0, -2.0]) + top_target = torch.tensor([0.0, 0.0, 4.0]) + + side_source = torch.tensor([6.0, -2.0, 2.0]) + side_target = torch.tensor([2.0, 0.0, 6.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "002374_mpii_test": + top_source = torch.tensor([-4.0, 0.0, 0.0]) + top_target = torch.tensor([-2.0, 2.0, 3.0]) + + side_source = torch.tensor([-7.0, 1.0, 7.0]) + side_target = torch.tensor([0.0, 1.0, 8.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "003742_mpii_test": + top_source = torch.tensor([3.0, -2.0, -6]) + top_target = torch.tensor([3.0, 1.0, 2.0]) + + side_source = torch.tensor([-5.0, -1.0, -2]) + side_target = torch.tensor([2.0, 0.0, 5]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "003747_mpii_test": + top_source = torch.tensor([-5.0, -2.0, -5]) + top_target = torch.tensor([-3.0, 2.0, 1.0]) + + side_source = torch.tensor([-9.0, -1.0, -4]) + side_target = torch.tensor([-3.0, 2.0, 3]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "003943_mpii_test": + top_source = torch.tensor([0, -1, -2]) + top_target = torch.tensor([0, 1, 3]) + + side_source = torch.tensor([6, 0, 1]) + side_target = torch.tensor([0, 0, 5]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "006537_mpii_test": + top_source = torch.tensor([0, -4, -1]) + top_target = torch.tensor([1.0, 0.0, 5.0]) + + side_source = torch.tensor([5, -2, 0]) + side_target = torch.tensor([1.0, 1.0, 7.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "007684_mpii_test": + top_source = torch.tensor([-2, -4, -6]) + top_target = torch.tensor([0.5, 0.0, 4.0]) + + side_source = torch.tensor([-8, -3, -2]) + side_target = torch.tensor([1.0, 0.0, 5.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "009039_mpii_test": + top_source = torch.tensor([-2.0, -3.0, -1.5]) + top_target = torch.tensor([1.0, 0.0, 3.0]) + + side_source = torch.tensor([6, -2, -1.5]) + side_target = torch.tensor([2.0, 0.0, 6.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "009607_mpii_test": + top_source = torch.tensor([0, -3, -1]) + top_target = torch.tensor([0, 0, 5]) + + side_source = torch.tensor([-6, -0.5, 2]) + side_target = torch.tensor([-1.0, 0.5, 7]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "012968_mpii_test": + top_source = torch.tensor([-0.5, -3, -4]) + top_target = torch.tensor([0.0, 0.5, 2.0]) + + side_source = torch.tensor([7, -4, 0]) + side_target = torch.tensor([0, 0.5, 2.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "014531_mpii_test": + top_source = torch.tensor([0, -2, -2]) + top_target = torch.tensor([0, 0, 2]) + + side_source = torch.tensor([-2, 0, -2]) + side_target = torch.tensor([0, 0, 2]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "015933_mpii_test": + top_source = torch.tensor([0.0, 0.5, -5.0]) + top_target = torch.tensor([0.0, 2.0, -2.0]) + + side_source = torch.tensor([5.0, 1.5, -3.0]) + side_target = torch.tensor([0.0, 2.5, 1.5]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "016195_mpii_test": + top_source = torch.tensor([0, -1, -2]) + top_target = torch.tensor([0, 1, 1]) + + side_source = torch.tensor([-3, 0, 1]) + side_target = torch.tensor([0, 1, 2]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "018061_mpii_test": + top_source = torch.tensor([4, -1, 2]) + top_target = torch.tensor([1, 1, 3]) + + side_source = torch.tensor([-3, 0, 4]) + side_target = torch.tensor([1, 1, 3]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "018713_mpii_test": + top_source = torch.tensor([0, -1, -1]) + top_target = torch.tensor([0, 0.5, 2]) + + side_source = torch.tensor([3, 0, 1]) + side_target = torch.tensor([0, 0, 3]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "022691_mpii_test": + top_source = torch.tensor([0, -4, -4]) + top_target = torch.tensor([-2.0, 0.0, 1.0]) + + side_source = torch.tensor([-5, -2, -5]) + side_target = torch.tensor([-3.5, 0.0, 1.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "023390_mpii_test": + top_source = torch.tensor([0.0, -1.5, -1.0]) + top_target = torch.tensor([0.0, 0.0, 2.0]) + + side_source = torch.tensor([4.0, -0.5, 0]) + side_target = torch.tensor([1.0, 0.5, 4]) + # top_source = torch.tensor([0.0, -3.0, -2.0]) + # top_target = torch.tensor([0.0, 0.5, 2.0]) + + # side_source = torch.tensor([5.0, -0.5, -3]) + # side_target = torch.tensor([1.0, 0.5, 4]) + return (top_source, top_target), (side_source, side_target) + + if seq_name=="024165_mpii_test": + top_source = torch.tensor([0, -3, -3]) + top_target = torch.tensor([0, 0, 3]) + + side_source = torch.tensor([-4, -1, -2]) + side_target = torch.tensor([0, 0, 3]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "024154_mpii_test": + top_source = torch.tensor([-1, -0.5, 1]) + top_target = torch.tensor([-1, 1, 8]) + + side_source = torch.tensor([-4, 1, 3]) + side_target = torch.tensor([-1, 1, 8]) + return (top_source, top_target), (side_source, side_target) + +# if seq_name == "024159_mpii_test": +# top_source = torch.tensor([-4.0, -2.0, -6.0]) +# top_target = torch.tensor([-4.0, 0.0, 0.0]) + +# side_source = torch.tensor([-12, -1, -2]) +# side_target = torch.tensor([-10.0, 0.0, 0.0]) +# return (top_source, top_target), (side_source, side_target) + + if seq_name == "023962_mpii_test": + top_source = torch.tensor([0, -0.5, -2]) + top_target = torch.tensor([0, 0.5, 2]) + + side_source = torch.tensor([3, 0.5, 0]) + side_target = torch.tensor([0, 0, 2]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "017437_mpii_test": + top_source = torch.tensor([0, -8, -6]) + top_target = torch.tensor([-2.0, -1.0, 2.0]) + + side_source = torch.tensor([-5, -1, -7]) + side_target = torch.tensor([-3.0, -1.0, 1.0]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "recording_20211002_S03_S18_04-all-100-200": + top_source = torch.tensor([1.0, -1, -4.5]) + top_target = torch.tensor([1.0, 0.0, 1]) + + side_source = torch.tensor([1.0, 0.5, -4.5]) + side_target = torch.tensor([1.0, 0.5, 1]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "recording_20211002_S03_S18_04-all-100-500": + top_source = torch.tensor([0.0, -0.5, -3]) + top_target = torch.tensor([0.0, 1.0, 1]) + + side_source = torch.tensor([-2.0, 0.5, -3]) + side_target = torch.tensor([0.0, 1.0, 2]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "recording_20211002_S03_S18_01-all-700-862": + top_source = torch.tensor([0.5, -2.0, -2]) + top_target = torch.tensor([0.5, -0.5, 2]) + + side_source = torch.tensor([2.0, -0.5, -2]) + side_target = torch.tensor([0.5, -0.5, 1]) + return (top_source, top_target), (side_source, side_target) + + if seq_name == "recording_20220315_S21_S30_02-all-0-100": + top_source = torch.tensor([0.0, -1, -2]) + top_target = torch.tensor([0.0, 0.5, 1]) + + side_source = torch.tensor([-2.0, 0.0, -1]) + side_target = torch.tensor([0.0, 0.5, 1]) + return (top_source, top_target), (side_source, side_target) + + if bounds is not None: + # (3), (3), (3) + bb_min, bb_max, center = bounds + print("SCENE BOUNDS", bb_min, bb_max, center) + length = torch.abs(bb_max - bb_min).max() + print(length) + top_source = center + torch.tensor([0.0, -2.0, -0.9 * length]) + + side_source = center + torch.tensor([0.5 * length, -0.5, -0.7 * length]) + return (top_source, center), (side_source, center) + + top_source = torch.tensor([0.0, -2.0, -3.0]) + top_target = torch.tensor([0.0, 0.0, 1.0]) + + side_source = torch.tensor([3.0, -1.0, -1.0]) + side_target = torch.tensor([0.0, 0.0, 1.0]) + return (top_source, top_target), (side_source, side_target) diff --git a/slahmr/slahmr/vis/output.py b/slahmr/slahmr/vis/output.py new file mode 100644 index 0000000000000000000000000000000000000000..cc67994d74cec5b6ed7881f1e81e8d788003ca8f --- /dev/null +++ b/slahmr/slahmr/vis/output.py @@ -0,0 +1,267 @@ +import os +import imageio +import numpy as np +import torch +import subprocess + +from body_model import run_smpl +from geometry import camera as cam_util +from geometry.mesh import make_batch_mesh +from geometry.plane import parse_floor_plane, get_plane_transform + +from util.tensor import detach_all, to_torch, move_to + +from .fig_specs import get_seq_figure_skip, get_seq_static_lookat_points +from .tools import smpl_to_geometry + + +def prep_result_vis(res, vis_mask, track_ids, body_model): + """ + :param res (dict) with (B, T, *) tensor elements, B tracks and T frames + :param vis_mask (B, T) with visibility of each track in each frame + :param track_ids (B,) index of each track + """ + print("RESULT FIELDS", res.keys()) + res = detach_all(res) + with torch.no_grad(): + world_smpl = run_smpl( + body_model, + res["trans"], + res["root_orient"], + res["pose_body"], + res.get("betas", None), + ) + T_w2c = None + floor_plane = None + if "cam_R" in res and "cam_t" in res: + T_w2c = cam_util.make_4x4_pose(res["cam_R"][0], res["cam_t"][0]) + if "floor_plane" in res: + floor_plane = res["floor_plane"][0] + return build_scene_dict( + world_smpl, + vis_mask, + track_ids, + T_w2c=T_w2c, + floor_plane=floor_plane, + ) + + +def build_scene_dict( + world_smpl, vis_mask, track_ids, T_w2c=None, floor_plane=None, **kwargs +): + scene_dict = {} + + # first get the geometry of the people + # lists of length T with (B, V, 3), (F, 3), (B, 3) + scene_dict["geometry"] = smpl_to_geometry( + world_smpl["vertices"], world_smpl["faces"], vis_mask, track_ids + ) + + if T_w2c is None: + T_w2c = torch.eye(4)[None] + + T_c2w = torch.linalg.inv(T_w2c) + # rotate the camera slightly down and translate back and up + T = cam_util.make_4x4_pose( + cam_util.rotx(-np.pi / 10), torch.tensor([0, -1, -2]) + ).to(T_c2w.device) + + scene_dict["cameras"] = { + "src_cam": T_c2w, + "front": torch.einsum("ij,...jk->...ik", T, T_c2w), + } + + if floor_plane is not None: + # compute the ground transform + # use the first appearance of a track as the reference point + tid, sid = torch.where(vis_mask > 0) + idx = tid[torch.argmin(sid)] + root = world_smpl["joints"][idx, 0, 0].detach().cpu() + floor = parse_floor_plane(floor_plane.detach().cpu()) + R, t = get_plane_transform(torch.tensor([0.0, 1.0, 0.0]), floor, root) + scene_dict["ground"] = cam_util.make_4x4_pose(R, t) + + return scene_dict + + +def render_scene_dict(renderer, scene_dict, out_name, fps=30, **kwargs): + # lists of T (B, V, 3), (B, 3), (F, 3) + verts, colors, faces, bounds = scene_dict["geometry"] + print("NUM VERTS", len(verts)) + + # add a top view + scene_dict["cameras"]["above"] = cam_util.make_4x4_pose( + torch.eye(3), torch.tensor([0, 0, -10]) + )[None] + + for cam_name, cam_poses in scene_dict["cameras"].items(): + print("rendering scene for", cam_name) + # cam_poses are (T, 4, 4) + render_bg = cam_name == "src_cam" + ground_pose = scene_dict.get("ground", None) + frames = renderer.render_video( + cam_poses[None], verts, faces, colors, render_bg, ground_pose=ground_pose + ) + imageio.mimwrite(f"{out_name}_{cam_name}.mp4", frames, fps=fps) + + +def animate_scene( + vis, + scene, + out_name, + seq_name=None, + accumulate=False, + render_views=["src_cam", "front", "above", "side"], + render_bg=True, + render_cam=True, + render_ground=True, + debug=False, + **kwargs, +): + if len(render_views) < 1: + return + + scene = build_pyrender_scene( + vis, + scene, + seq_name, + render_views=render_views, + render_cam=render_cam, + accumulate=accumulate, + debug=debug, + ) + + print("RENDERING VIEWS", scene["cameras"].keys()) + render_ground = render_ground and "ground" in scene + save_paths = [] + for cam_name, cam_poses in scene["cameras"].items(): + is_src = cam_name == "src_cam" + show_bg = is_src and render_bg + show_ground = render_ground and not is_src + show_cam = render_cam and not is_src + vis_name = f"{out_name}_{cam_name}" + print(f"{cam_name} has {len(cam_poses)} poses") + skip = 10 if debug else 1 + vis.set_camera_seq(cam_poses[::skip]) + save_path = vis.animate( + vis_name, + render_bg=show_bg, + render_ground=show_ground, + render_cam=show_cam, + **kwargs, + ) + save_paths.append(save_path) + + return save_paths + + +def build_pyrender_scene( + vis, + scene, + seq_name, + render_views=["src_cam", "front", "above", "side"], + render_cam=True, + accumulate=False, + debug=False, +): + """ + :param vis (viewer object) + :param scene (scene dict with geometry, cameras, etc) + :param accumulate (optional bool, default False) whether to render entire trajectory together + :param render_views (list str) camera views to render + """ + if len(render_views) < 1: + return + + assert all(view in ["src_cam", "front", "above", "side"] for view in render_views) + + scene = move_to(detach_all(scene), "cpu") + src_cams = scene["cameras"]["src_cam"] + verts, colors, faces, bounds = scene["geometry"] + T = len(verts) + print(f"{T} mesh frames") + + # set camera views + if not "cameras" in scene: + scene["cameras"] = {} + + # remove default views from source camera perspective if desired + if "src_cam" not in render_views: + scene["cameras"].pop("src_cam", None) + if "front" not in render_views: + scene["cameras"].pop("front", None) + + # add static viewpoints if desired + top_pose, side_pose, _skip = get_static_views(seq_name, bounds) + if "above" in render_views: + scene["cameras"]["above"] = top_pose[None] + if "side" in render_views: + scene["cameras"]["side"] = side_pose[None] + + # accumulate meshes if possible (can only accumulate for static camera) + moving_cam = "src_cam" in render_views or "front" in render_views + accumulate = accumulate and not moving_cam + skip = _skip if accumulate else 1 + + vis.clear_meshes() + + if "ground" in scene: + vis.set_ground(scene["ground"]) + + if debug: + skip = 10 + times = list(range(0, T, skip)) + for t in times: + meshes = make_batch_mesh(verts[t], faces[t], colors[t]) + if accumulate: + vis.add_static_meshes(meshes) + else: + vis.add_mesh_frame(meshes, debug=debug) + + # add camera markers + if render_cam: + if accumulate: + vis.add_camera_markers_static(src_cams[::skip]) + else: + vis.add_camera_markers(src_cams[::skip]) + + return scene + + +def get_static_views(seq_name=None, bounds=None): + print("STATIC VIEWS FOR SEQ NAME", seq_name) + up = torch.tensor([0.0, 1.0, 0.0]) + + skip = get_seq_figure_skip(seq_name) + top_vp, side_vp = get_seq_static_lookat_points(seq_name, bounds) + top_source, top_target = top_vp + side_source, side_target = side_vp + top_pose = cam_util.lookat_matrix(top_source, top_target, up) + side_pose = cam_util.lookat_matrix(side_source, side_target, up) + return top_pose, side_pose, skip + + +def make_video_grid_2x2(out_path, vid_paths, overwrite=False): + if os.path.isfile(out_path) and not overwrite: + print(f"{out_path} already exists, skipping.") + return + + if any(not os.path.isfile(v) for v in vid_paths): + print("not all inputs exist!", vid_paths) + return + + # resize each input by half and then tile + # so the output video is the same resolution + v1, v2, v3, v4 = vid_paths + cmd = ( + f"ffmpeg -i {v1} -i {v2} -i {v3} -i {v4} " + f"-filter_complex '[0:v]scale=iw/2:ih/2[v0];" + f"[1:v]scale=iw/2:ih/2[v1];" + f"[2:v]scale=iw/2:ih/2[v2];" + f"[3:v]scale=iw/2:ih/2[v3];" + f"[v0][v1][v2][v3]xstack=inputs=4:layout=0_0|w0_0|0_h0|w0_h0[v]' " + f"-map '[v]' {out_path} -y" + ) + + print(cmd) + subprocess.call(cmd, shell=True, stdin=subprocess.PIPE) diff --git a/slahmr/slahmr/vis/render.py b/slahmr/slahmr/vis/render.py new file mode 100644 index 0000000000000000000000000000000000000000..4449e93500fba00e3c7047ab7f17ea9d4dc1ba78 --- /dev/null +++ b/slahmr/slahmr/vis/render.py @@ -0,0 +1,254 @@ +import torch +import torch.nn as nn +import numpy as np + +from pytorch3d.renderer import ( + RasterizationSettings, + MeshRenderer, + MeshRasterizer, + HardPhongShader, + PointLights, + PerspectiveCameras, +) +from pytorch3d.structures import Meshes +from pytorch3d.structures.meshes import join_meshes_as_scene +from pytorch3d.renderer import TexturesAtlas, TexturesVertex +from pytorch3d.transforms import euler_angles_to_matrix + +from .tools import get_colors, read_image, transform_torch3d, checkerboard_geometry + + +def init_renderer(img_size, intrins, device, vis_scale=1.0, bg_paths=None): + img_size = int(vis_scale * img_size[0]), int(vis_scale * img_size[1]) + renderer = RenderBase(device, img_size, intrins=vis_scale * intrins) + if bg_paths is not None: + bg_imgs = [ + torch.from_numpy(read_image(p, scale=vis_scale)).float() / 255 + for p in bg_paths + ] + print(bg_imgs[0].shape) + renderer.set_bg_seq(bg_imgs) + print("RENDERER", renderer) + return renderer + + +class RenderBase(nn.Module): + def __init__( + self, + device, + img_size, + intrins=None, + blur_radius: float = 0.0, # rasterizer settings + faces_per_pixel: int = 3, + ): + """ + Uses Pytorch3D to render results. + We use the PyTorch3D coordinate system, which assumes: + +X:left, +Y: up and +Z: from us to scene (right-handed) + https://pytorch3d.org/docs/cameras + """ + super().__init__() + self.device = device + W, H = img_size + self.img_size = (H, W) + if intrins is not None: + intrins = intrins.to(device) + self.cam_f, self.cam_center = intrins[:2], intrins[2:] + cx, cy = self.cam_center.detach().cpu() + else: + self.cam_f = torch.tensor([0.5 * (H + W), 0.5 * (H + W)], device=device) + self.cam_center = torch.tensor([0.5 * W, 0.5 * H], device=device) + print("cam_f", self.cam_f, "cam_center", self.cam_center) + print("img_size", self.img_size) + self.blur_radius = blur_radius + self.faces_per_pixel = faces_per_pixel + + self.light_loc = [[0, 0, -0.5]] + self.cameras = self.make_cameras() + self.bg_imgs = None + self.set_ground() + self.build_renderer() + + def build_renderer(self): + self.lights = PointLights(device=self.device, location=self.light_loc) + + self.rasterizer = RasterizationSettings( + image_size=self.img_size, + blur_radius=self.blur_radius, + faces_per_pixel=self.faces_per_pixel, + max_faces_per_bin=100000, + ) + self.renderer = MeshRenderer( + rasterizer=MeshRasterizer( + cameras=self.cameras, raster_settings=self.rasterizer + ), + shader=HardPhongShader( + cameras=self.cameras, lights=self.lights, device=self.device + ), + ) + + def make_cameras(self, cam_poses=None): + device = self.device + if cam_poses is None: + cam_poses = torch.eye(4, device=device)[None] + cam_poses = cam_poses.to(device) + cam_R, cam_t = transform_torch3d(cam_poses) + Nc = len(cam_poses) + focal = self.cam_f[None].repeat(Nc, 1) + ppt = self.cam_center[None].repeat(Nc, 1) + img_size = [self.img_size for _ in range(Nc)] + return PerspectiveCameras( + device=self.device, + in_ndc=False, + focal_length=focal, + principal_point=ppt, + image_size=img_size, + R=cam_R, + T=cam_t, + ) + + def render_frame(self, cam_poses, verts, faces, colors): + """ + :param cam_poses (C, 4, 4) + :param verts (B, V, 3) + :param faces (F, 3) + :param colors (B, 4) + """ + with torch.no_grad(): + cameras = self.make_cameras(cam_poses) + mesh = build_meshes(verts, faces, colors) + image = self.renderer(mesh, cameras=cameras) + return image + + def render_with_ground(self, cam_poses, verts, faces, colors, ground_pose): + """ + :param cam_poses (C, 4, 4) + :param verts (B, V, 3) + :param faces (F, 3) + :param colors (B, 3) + :param ground_pose (4, 4) + """ + with torch.no_grad(): + self.set_ground_pose(ground_pose) + cameras = self.make_cameras(cam_poses) + # (B, V, 3), (B, F, 3), (B, V, 3) + verts, faces, colors = prep_shared_geometry(verts, faces, colors) + # (V, 3), (F, 3), (V, 3) + gv, gf, gc = self.ground_geometry + verts = list(torch.unbind(verts, dim=0)) + [gv] + faces = list(torch.unbind(faces, dim=0)) + [gf] + colors = list(torch.unbind(colors, dim=0)) + [gc[..., :3]] + mesh = create_meshes(verts, faces, colors) + + image = self.renderer(mesh, cameras=cameras) + return image + + def set_bg_seq(self, bg_imgs): + self.bg_imgs = bg_imgs + + def set_ground(self, pose=None): + device = self.device + v, f, vc, fc = map(torch.from_numpy, checkerboard_geometry(up="y")) + v, f, vc = v.to(device), f.to(device), vc.to(device) + self.ground_geometry = [v, f, vc] + if pose is not None: + self.set_ground_pose(pose) + + def set_ground_pose(self, pose): + """ + :param pose (4, 4) + """ + if self.ground_geometry is None: + return + v = self.ground_geometry[0] + pose = pose.to(self.device) + # R, t = pose[:3, :3], pose[:3, 3] + R, t = transform_torch3d(pose) + self.ground_geometry[0] = torch.einsum("ij,vj->vi", R, v) + t[None] + + def composite_bg(self, frames, fac=1.0): + T = len(frames) + if self.bg_imgs is None: + return frames + + out_frames = [] + for bg, frame in zip(self.bg_imgs, frames): + alpha = fac * frame[..., 3:] + out = alpha * frame[..., :3] + (1 - alpha) * bg + out_frames.append(out) + return out_frames + + def render_video( + self, + cam_poses, + verts, + faces, + colors, + render_bg=False, + fac=1.0, + ground_pose=None, + ): + """ + :param cam_poses (C, T, 4, 4) + :param verts list of T (B, V, 3) + :param faces list of T (F, 3) + :param colors list of T (B, 4) + :param render_bg (optional default False) + :param fac (optional float, default 1) + :param ground_pose (optional, default None) (4, 4) + returns list of T (H, W, 4) + """ + T = len(verts) + print(f"rendering video with {T} frames") + if cam_poses.shape[1] == 1: + cam_poses = cam_poses.expand(-1, T, -1, -1) + + if render_bg: # don't render ground on source frame + ground_pose = None + + frames = [] + for t in range(T): + if ground_pose is None: + # (H, W, 4) + frame = self.render_frame( + cam_poses[:, t], verts[t], faces[t], colors[t] + ) + else: + # (H, W, 4) + frame = self.render_with_ground( + cam_poses[:, t], verts[t], faces[t], colors[t], ground_pose + ) + frames.append(frame.cpu()[0]) + + if render_bg and self.bg_imgs is not None: + frames = self.composite_bg(frames, fac=fac) + + return [(255 * f).byte() for f in frames] + + +def build_meshes(verts, faces, colors): + return create_meshes(*prep_shared_geometry(verts, faces, colors)) + + +def prep_shared_geometry(verts, faces, colors): + """ + :param verts (B, V, 3) + :param faces (F, 3) + :param colors (B, 4) + """ + B, V, _ = verts.shape + F, _ = faces.shape + colors = colors.unsqueeze(1).expand(B, V, -1)[..., :3] + faces = faces.unsqueeze(0).expand(B, F, -1) + return verts, faces, colors + + +def create_meshes(verts, faces, colors): + """ + :param verts (B, V, 3) + :param faces (B, F, 3) + :param colors (B, V, 3) + """ + textures = TexturesVertex(verts_features=colors) + meshes = Meshes(verts=verts, faces=faces, textures=textures) + return join_meshes_as_scene(meshes) diff --git a/slahmr/slahmr/vis/tools.py b/slahmr/slahmr/vis/tools.py new file mode 100644 index 0000000000000000000000000000000000000000..50bb504c600bd0715505b67ee062383d9b82f728 --- /dev/null +++ b/slahmr/slahmr/vis/tools.py @@ -0,0 +1,816 @@ +import os +import cv2 +import numpy as np +import torch +from PIL import Image + + +def read_image(path, scale=1): + im = Image.open(path) + if scale == 1: + return np.array(im) + W, H = im.size + w, h = int(scale * W), int(scale * H) + return np.array(im.resize((w, h), Image.ANTIALIAS)) + + +def transform_torch3d(T_c2w): + """ + :param T_c2w (*, 4, 4) + returns (*, 3, 3), (*, 3) + """ + R1 = torch.tensor( + [[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0],], device=T_c2w.device, + ) + R2 = torch.tensor( + [[1.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0],], device=T_c2w.device, + ) + cam_R, cam_t = T_c2w[..., :3, :3], T_c2w[..., :3, 3] + cam_R = torch.einsum("...ij,jk->...ik", cam_R, R1) + cam_t = torch.einsum("ij,...j->...i", R2, cam_t) + return cam_R, cam_t + + +def transform_pyrender(T_c2w): + """ + :param T_c2w (*, 4, 4) + """ + T_vis = torch.tensor( + [ + [1.0, 0.0, 0.0, 0.0], + [0.0, -1.0, 0.0, 0.0], + [0.0, 0.0, -1.0, 0.0], + [0.0, 0.0, 0.0, 1.0], + ], + device=T_c2w.device, + ) + return torch.einsum( + "...ij,jk->...ik", torch.einsum("ij,...jk->...ik", T_vis, T_c2w), T_vis + ) + + +def smpl_to_geometry(verts, faces, vis_mask=None, track_ids=None): + """ + :param verts (B, T, V, 3) + :param faces (F, 3) + :param vis_mask (optional) (B, T) visibility of each person + :param track_ids (optional) (B,) + returns list of T verts (B, V, 3), faces (F, 3), colors (B, 3) + where B is different depending on the visibility of the people + """ + B, T = verts.shape[:2] + device = verts.device + + # (B, 3) + colors = ( + track_to_colors(track_ids) + if track_ids is not None + else torch.ones(B, 3, device) * 0.5 + ) + + # list T (B, V, 3), T (B, 3), T (F, 3) + return filter_visible_meshes(verts, colors, faces, vis_mask) + + +def filter_visible_meshes(verts, colors, faces, vis_mask=None, vis_opacity=False): + """ + :param verts (B, T, V, 3) + :param colors (B, 3) + :param faces (F, 3) + :param vis_mask (optional tensor, default None) (B, T) ternary mask + -1 if not in frame + 0 if temporarily occluded + 1 if visible + :param vis_opacity (optional bool, default False) + if True, make occluded people alpha=0.5, otherwise alpha=1 + returns a list of T lists verts (Bi, V, 3), colors (Bi, 4), faces (F, 3) + """ + # import ipdb; ipdb.set_trace() + B, T = verts.shape[:2] + faces = [faces for t in range(T)] + if vis_mask is None: + verts = [verts[:, t] for t in range(T)] + colors = [colors for t in range(T)] + return verts, colors, faces + + # render occluded and visible, but not removed + vis_mask = vis_mask >= 0 + if vis_opacity: + alpha = 0.5 * (vis_mask[..., None] + 1) + else: + alpha = (vis_mask[..., None] >= 0).float() + vert_list = [verts[vis_mask[:, t], t] for t in range(T)] + colors = [ + torch.cat([colors[vis_mask[:, t]], alpha[vis_mask[:, t], t]], dim=-1) + for t in range(T) + ] + bounds = get_bboxes(verts, vis_mask) + return vert_list, colors, faces, bounds + + +def get_bboxes(verts, vis_mask): + """ + return bb_min, bb_max, and mean for each track (B, 3) over entire trajectory + :param verts (B, T, V, 3) + :param vis_mask (B, T) + """ + B, T, *_ = verts.shape + bb_min, bb_max, mean = [], [], [] + for b in range(B): + v = verts[b, vis_mask[b, :T]] # (Tb, V, 3) + bb_min.append(v.amin(dim=(0, 1))) + bb_max.append(v.amax(dim=(0, 1))) + mean.append(v.mean(dim=(0, 1))) + bb_min = torch.stack(bb_min, dim=0) + bb_max = torch.stack(bb_max, dim=0) + mean = torch.stack(mean, dim=0) + # point to a track that's long and close to the camera + zs = mean[:, 2] + counts = vis_mask[:, :T].sum(dim=-1) # (B,) + mask = counts < 0.8 * T + zs[mask] = torch.inf + sel = torch.argmin(zs) + return bb_min.amin(dim=0), bb_max.amax(dim=0), mean[sel] + + +def track_to_colors(track_ids): + """ + :param track_ids (B) + """ + color_map = torch.from_numpy(get_colors()).to(track_ids) + return color_map[track_ids] / 255 # (B, 3) + + +def get_colors(): + # color_file = os.path.abspath(os.path.join(__file__, "../colors_phalp.txt")) + color_file = os.path.abspath(os.path.join(__file__, "../colors.txt")) + RGB_tuples = np.vstack( + [ + np.loadtxt(color_file, skiprows=0), + # np.loadtxt(color_file, skiprows=1), + np.random.uniform(0, 255, size=(10000, 3)), + [[0, 0, 0]], + ] + ) + b = np.where(RGB_tuples == 0) + RGB_tuples[b] = 1 + return RGB_tuples.astype(np.float32) + + +def checkerboard_geometry( + length=12.0, + color0=[0.8, 0.9, 0.9], + color1=[0.6, 0.7, 0.7], + tile_width=0.5, + alpha=1.0, + up="y", +): + assert up == "y" or up == "z" + color0 = np.array(color0 + [alpha]) + color1 = np.array(color1 + [alpha]) + radius = length / 2.0 + num_rows = num_cols = int(length / tile_width) + vertices = [] + vert_colors = [] + faces = [] + face_colors = [] + for i in range(num_rows): + for j in range(num_cols): + u0, v0 = j * tile_width - radius, i * tile_width - radius + us = np.array([u0, u0, u0 + tile_width, u0 + tile_width]) + vs = np.array([v0, v0 + tile_width, v0 + tile_width, v0]) + zs = np.zeros(4) + if up == "y": + cur_verts = np.stack([us, zs, vs], axis=-1) # (4, 3) + else: + cur_verts = np.stack([us, vs, zs], axis=-1) # (4, 3) + + cur_faces = np.array( + [[0, 1, 3], [1, 2, 3], [0, 3, 1], [1, 3, 2]], dtype=np.int + ) + cur_faces += 4 * (i * num_cols + j) # the number of previously added verts + use_color0 = (i % 2 == 0 and j % 2 == 0) or (i % 2 == 1 and j % 2 == 1) + cur_color = color0 if use_color0 else color1 + cur_colors = np.array([cur_color, cur_color, cur_color, cur_color]) + + vertices.append(cur_verts) + faces.append(cur_faces) + vert_colors.append(cur_colors) + face_colors.append(cur_colors) + + vertices = np.concatenate(vertices, axis=0).astype(np.float32) + vert_colors = np.concatenate(vert_colors, axis=0).astype(np.float32) + faces = np.concatenate(faces, axis=0).astype(np.float32) + face_colors = np.concatenate(face_colors, axis=0).astype(np.float32) + + return vertices, faces, vert_colors, face_colors + + +def camera_marker_geometry(radius, height, up): + assert up == "y" or up == "z" + if up == "y": + vertices = np.array( + [ + [-radius, -radius, 0], + [radius, -radius, 0], + [radius, radius, 0], + [-radius, radius, 0], + [0, 0, height], + ] + ) + else: + vertices = np.array( + [ + [-radius, 0, -radius], + [radius, 0, -radius], + [radius, 0, radius], + [-radius, 0, radius], + [0, -height, 0], + ] + ) + + faces = np.array( + [[0, 3, 1], [1, 3, 2], [0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4],] + ) + + face_colors = np.array( + [ + [1.0, 1.0, 1.0, 1.0], + [1.0, 1.0, 1.0, 1.0], + [0.0, 1.0, 0.0, 1.0], + [1.0, 0.0, 0.0, 1.0], + [0.0, 1.0, 0.0, 1.0], + [1.0, 0.0, 0.0, 1.0], + ] + ) + return vertices, faces, face_colors + + +def vis_keypoints( + keypts_list, + img_size, + radius=6, + thickness=3, + kpt_score_thr=0.3, + dataset="TopDownCocoDataset", +): + """ + Visualize keypoints + From ViTPose/mmpose/apis/inference.py + """ + palette = np.array( + [ + [255, 128, 0], + [255, 153, 51], + [255, 178, 102], + [230, 230, 0], + [255, 153, 255], + [153, 204, 255], + [255, 102, 255], + [255, 51, 255], + [102, 178, 255], + [51, 153, 255], + [255, 153, 153], + [255, 102, 102], + [255, 51, 51], + [153, 255, 153], + [102, 255, 102], + [51, 255, 51], + [0, 255, 0], + [0, 0, 255], + [255, 0, 0], + [255, 255, 255], + ] + ) + + if dataset in ( + "TopDownCocoDataset", + "BottomUpCocoDataset", + "TopDownOCHumanDataset", + "AnimalMacaqueDataset", + ): + # show the results + skeleton = [ + [15, 13], + [13, 11], + [16, 14], + [14, 12], + [11, 12], + [5, 11], + [6, 12], + [5, 6], + [5, 7], + [6, 8], + [7, 9], + [8, 10], + [1, 2], + [0, 1], + [0, 2], + [1, 3], + [2, 4], + [3, 5], + [4, 6], + ] + + pose_link_color = palette[ + [0, 0, 0, 0, 7, 7, 7, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16] + ] + pose_kpt_color = palette[ + [16, 16, 16, 16, 16, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0] + ] + + elif dataset == "TopDownCocoWholeBodyDataset": + # show the results + skeleton = [ + [15, 13], + [13, 11], + [16, 14], + [14, 12], + [11, 12], + [5, 11], + [6, 12], + [5, 6], + [5, 7], + [6, 8], + [7, 9], + [8, 10], + [1, 2], + [0, 1], + [0, 2], + [1, 3], + [2, 4], + [3, 5], + [4, 6], + [15, 17], + [15, 18], + [15, 19], + [16, 20], + [16, 21], + [16, 22], + [91, 92], + [92, 93], + [93, 94], + [94, 95], + [91, 96], + [96, 97], + [97, 98], + [98, 99], + [91, 100], + [100, 101], + [101, 102], + [102, 103], + [91, 104], + [104, 105], + [105, 106], + [106, 107], + [91, 108], + [108, 109], + [109, 110], + [110, 111], + [112, 113], + [113, 114], + [114, 115], + [115, 116], + [112, 117], + [117, 118], + [118, 119], + [119, 120], + [112, 121], + [121, 122], + [122, 123], + [123, 124], + [112, 125], + [125, 126], + [126, 127], + [127, 128], + [112, 129], + [129, 130], + [130, 131], + [131, 132], + ] + + pose_link_color = palette[ + [0, 0, 0, 0, 7, 7, 7, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16] + + [16, 16, 16, 16, 16, 16] + + [0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16] + + [0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16] + ] + pose_kpt_color = palette[ + [16, 16, 16, 16, 16, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0] + + [0, 0, 0, 0, 0, 0] + + [19] * (68 + 42) + ] + + elif dataset == "TopDownAicDataset": + skeleton = [ + [2, 1], + [1, 0], + [0, 13], + [13, 3], + [3, 4], + [4, 5], + [8, 7], + [7, 6], + [6, 9], + [9, 10], + [10, 11], + [12, 13], + [0, 6], + [3, 9], + ] + + pose_link_color = palette[[9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 0, 7, 7]] + pose_kpt_color = palette[[9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 0, 0]] + + elif dataset == "TopDownMpiiDataset": + skeleton = [ + [0, 1], + [1, 2], + [2, 6], + [6, 3], + [3, 4], + [4, 5], + [6, 7], + [7, 8], + [8, 9], + [8, 12], + [12, 11], + [11, 10], + [8, 13], + [13, 14], + [14, 15], + ] + + pose_link_color = palette[[16, 16, 16, 16, 16, 16, 7, 7, 0, 9, 9, 9, 9, 9, 9]] + pose_kpt_color = palette[[16, 16, 16, 16, 16, 16, 7, 7, 0, 0, 9, 9, 9, 9, 9, 9]] + + elif dataset == "TopDownMpiiTrbDataset": + skeleton = [ + [12, 13], + [13, 0], + [13, 1], + [0, 2], + [1, 3], + [2, 4], + [3, 5], + [0, 6], + [1, 7], + [6, 7], + [6, 8], + [7, 9], + [8, 10], + [9, 11], + [14, 15], + [16, 17], + [18, 19], + [20, 21], + [22, 23], + [24, 25], + [26, 27], + [28, 29], + [30, 31], + [32, 33], + [34, 35], + [36, 37], + [38, 39], + ] + + pose_link_color = palette[[16] * 14 + [19] * 13] + pose_kpt_color = palette[[16] * 14 + [0] * 26] + + elif dataset in ("OneHand10KDataset", "FreiHandDataset", "PanopticDataset"): + skeleton = [ + [0, 1], + [1, 2], + [2, 3], + [3, 4], + [0, 5], + [5, 6], + [6, 7], + [7, 8], + [0, 9], + [9, 10], + [10, 11], + [11, 12], + [0, 13], + [13, 14], + [14, 15], + [15, 16], + [0, 17], + [17, 18], + [18, 19], + [19, 20], + ] + + pose_link_color = palette[ + [0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16] + ] + pose_kpt_color = palette[ + [0, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16] + ] + + elif dataset == "InterHand2DDataset": + skeleton = [ + [0, 1], + [1, 2], + [2, 3], + [4, 5], + [5, 6], + [6, 7], + [8, 9], + [9, 10], + [10, 11], + [12, 13], + [13, 14], + [14, 15], + [16, 17], + [17, 18], + [18, 19], + [3, 20], + [7, 20], + [11, 20], + [15, 20], + [19, 20], + ] + + pose_link_color = palette[ + [0, 0, 0, 4, 4, 4, 8, 8, 8, 12, 12, 12, 16, 16, 16, 0, 4, 8, 12, 16] + ] + pose_kpt_color = palette[ + [0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16, 0] + ] + + elif dataset == "Face300WDataset": + # show the results + skeleton = [] + + pose_link_color = palette[[]] + pose_kpt_color = palette[[19] * 68] + kpt_score_thr = 0 + + elif dataset == "FaceAFLWDataset": + # show the results + skeleton = [] + + pose_link_color = palette[[]] + pose_kpt_color = palette[[19] * 19] + kpt_score_thr = 0 + + elif dataset == "FaceCOFWDataset": + # show the results + skeleton = [] + + pose_link_color = palette[[]] + pose_kpt_color = palette[[19] * 29] + kpt_score_thr = 0 + + elif dataset == "FaceWFLWDataset": + # show the results + skeleton = [] + + pose_link_color = palette[[]] + pose_kpt_color = palette[[19] * 98] + kpt_score_thr = 0 + + elif dataset == "AnimalHorse10Dataset": + skeleton = [ + [0, 1], + [1, 12], + [12, 16], + [16, 21], + [21, 17], + [17, 11], + [11, 10], + [10, 8], + [8, 9], + [9, 12], + [2, 3], + [3, 4], + [5, 6], + [6, 7], + [13, 14], + [14, 15], + [18, 19], + [19, 20], + ] + + pose_link_color = palette[[4] * 10 + [6] * 2 + [6] * 2 + [7] * 2 + [7] * 2] + pose_kpt_color = palette[ + [4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 7, 7, 7, 4, 4, 7, 7, 7, 4] + ] + + elif dataset == "AnimalFlyDataset": + skeleton = [ + [1, 0], + [2, 0], + [3, 0], + [4, 3], + [5, 4], + [7, 6], + [8, 7], + [9, 8], + [11, 10], + [12, 11], + [13, 12], + [15, 14], + [16, 15], + [17, 16], + [19, 18], + [20, 19], + [21, 20], + [23, 22], + [24, 23], + [25, 24], + [27, 26], + [28, 27], + [29, 28], + [30, 3], + [31, 3], + ] + + pose_link_color = palette[[0] * 25] + pose_kpt_color = palette[[0] * 32] + + elif dataset == "AnimalLocustDataset": + skeleton = [ + [1, 0], + [2, 1], + [3, 2], + [4, 3], + [6, 5], + [7, 6], + [9, 8], + [10, 9], + [11, 10], + [13, 12], + [14, 13], + [15, 14], + [17, 16], + [18, 17], + [19, 18], + [21, 20], + [22, 21], + [24, 23], + [25, 24], + [26, 25], + [28, 27], + [29, 28], + [30, 29], + [32, 31], + [33, 32], + [34, 33], + ] + + pose_link_color = palette[[0] * 26] + pose_kpt_color = palette[[0] * 35] + + elif dataset == "AnimalZebraDataset": + skeleton = [[1, 0], [2, 1], [3, 2], [4, 2], [5, 7], [6, 7], [7, 2], [8, 7]] + + pose_link_color = palette[[0] * 8] + pose_kpt_color = palette[[0] * 9] + + elif dataset in "AnimalPoseDataset": + skeleton = [ + [0, 1], + [0, 2], + [1, 3], + [0, 4], + [1, 4], + [4, 5], + [5, 7], + [6, 7], + [5, 8], + [8, 12], + [12, 16], + [5, 9], + [9, 13], + [13, 17], + [6, 10], + [10, 14], + [14, 18], + [6, 11], + [11, 15], + [15, 19], + ] + + pose_link_color = palette[[0] * 20] + pose_kpt_color = palette[[0] * 20] + else: + NotImplementedError() + + img_w, img_h = img_size + img = 255 * np.ones((img_h, img_w, 3), dtype=np.uint8) + img = imshow_keypoints( + img, + keypts_list, + skeleton, + kpt_score_thr, + pose_kpt_color, + pose_link_color, + radius, + thickness, + ) + alpha = 255 * (img != 255).any(axis=-1, keepdims=True).astype(np.uint8) + return np.concatenate([img, alpha], axis=-1) + + +def imshow_keypoints( + img, + pose_result, + skeleton=None, + kpt_score_thr=0.3, + pose_kpt_color=None, + pose_link_color=None, + radius=4, + thickness=1, + show_keypoint_weight=False, +): + """Draw keypoints and links on an image. + From ViTPose/mmpose/core/visualization/image.py + + Args: + img (H, W, 3) array + pose_result (list[kpts]): The poses to draw. Each element kpts is + a set of K keypoints as an Kx3 numpy.ndarray, where each + keypoint is represented as x, y, score. + kpt_score_thr (float, optional): Minimum score of keypoints + to be shown. Default: 0.3. + pose_kpt_color (np.array[Nx3]`): Color of N keypoints. If None, + the keypoint will not be drawn. + pose_link_color (np.array[Mx3]): Color of M links. If None, the + links will not be drawn. + thickness (int): Thickness of lines. + show_keypoint_weight (bool): If True, opacity indicates keypoint score + """ + img_h, img_w, _ = img.shape + idcs = [0, 16, 15, 18, 17, 5, 2, 6, 3, 7, 4, 12, 9, 13, 10, 14, 11] + for kpts in pose_result: + kpts = np.array(kpts, copy=False)[idcs] + + # draw each point on image + if pose_kpt_color is not None: + assert len(pose_kpt_color) == len(kpts) + for kid, kpt in enumerate(kpts): + x_coord, y_coord, kpt_score = int(kpt[0]), int(kpt[1]), kpt[2] + if kpt_score > kpt_score_thr: + color = tuple(int(c) for c in pose_kpt_color[kid]) + if show_keypoint_weight: + img_copy = img.copy() + cv2.circle( + img_copy, (int(x_coord), int(y_coord)), radius, color, -1 + ) + transparency = max(0, min(1, kpt_score)) + cv2.addWeighted( + img_copy, transparency, img, 1 - transparency, 0, dst=img + ) + else: + cv2.circle(img, (int(x_coord), int(y_coord)), radius, color, -1) + + # draw links + if skeleton is not None and pose_link_color is not None: + assert len(pose_link_color) == len(skeleton) + for sk_id, sk in enumerate(skeleton): + pos1 = (int(kpts[sk[0], 0]), int(kpts[sk[0], 1])) + pos2 = (int(kpts[sk[1], 0]), int(kpts[sk[1], 1])) + if ( + pos1[0] > 0 + and pos1[0] < img_w + and pos1[1] > 0 + and pos1[1] < img_h + and pos2[0] > 0 + and pos2[0] < img_w + and pos2[1] > 0 + and pos2[1] < img_h + and kpts[sk[0], 2] > kpt_score_thr + and kpts[sk[1], 2] > kpt_score_thr + ): + color = tuple(int(c) for c in pose_link_color[sk_id]) + if show_keypoint_weight: + img_copy = img.copy() + X = (pos1[0], pos2[0]) + Y = (pos1[1], pos2[1]) + mX = np.mean(X) + mY = np.mean(Y) + length = ((Y[0] - Y[1]) ** 2 + (X[0] - X[1]) ** 2) ** 0.5 + angle = math.degrees(math.atan2(Y[0] - Y[1], X[0] - X[1])) + stickwidth = 2 + polygon = cv2.ellipse2Poly( + (int(mX), int(mY)), + (int(length / 2), int(stickwidth)), + int(angle), + 0, + 360, + 1, + ) + cv2.fillConvexPoly(img_copy, polygon, color) + transparency = max( + 0, min(1, 0.5 * (kpts[sk[0], 2] + kpts[sk[1], 2])) + ) + cv2.addWeighted( + img_copy, transparency, img, 1 - transparency, 0, dst=img + ) + else: + cv2.line(img, pos1, pos2, color, thickness=thickness) + + return img diff --git a/slahmr/slahmr/vis/viewer.py b/slahmr/slahmr/vis/viewer.py new file mode 100644 index 0000000000000000000000000000000000000000..3070695883c3ab9a9c1ecb04a89cf3b63ce1b6e9 --- /dev/null +++ b/slahmr/slahmr/vis/viewer.py @@ -0,0 +1,608 @@ +import os +import imageio +import numpy as np + +import time +import torch +import trimesh + +os.environ["PYOPENGL_PLATFORM"] = "egl" + +import pyrender +from pyrender.constants import RenderFlags +from pyrender.light import DirectionalLight +from pyrender.node import Node + +from geometry.camera import make_rotation, make_translation +from .tools import ( + read_image, + checkerboard_geometry, + camera_marker_geometry, + transform_pyrender, +) + + +def init_viewer( + img_size, intrins, vis_scale=1.0, bg_paths=None, fps=30, +): + img_size = int(vis_scale * img_size[0]), int(vis_scale * img_size[1]) + intrins = vis_scale * intrins + + platform = os.environ.get("PYOPENGL_PLATFORM", "pyglet") + if platform == "pyglet": + vis = AnimationViewer(img_size, intrins=intrins, fps=fps) + print("VIS", vis) + return vis + + if platform != "egl": + raise NotImplementedError + + vis = OffscreenAnimation(img_size, intrins=intrins, fps=fps) + if bg_paths is not None: + bg_imgs = [ + read_image(p, scale=vis_scale).astype(np.float32) / 255 for p in bg_paths + ] + vis.set_bg_seq(bg_imgs) + print("VIS", vis) + return vis + + +class AnimationBase(object): + """ + Render an animation + IMPORTANT: pyrender uses coordinates with Y UP (i.e. xyz = right up back), + we must keep this in mind because the human prior frame has Z UP (i.e. + xyz = right forward up) + """ + + def __init__(self, img_size, intrins=None): + self.scene = pyrender.Scene( + ambient_light=[0.3, 0.3, 0.3], bg_color=[1.0, 1.0, 1.0, 0.0] + ) + self.scene.bg_color = np.array([1.0, 1.0, 1.0, 0.0]) + + self.viewport_size = img_size + self.camera = make_pyrender_camera(img_size, intrins) + + # set the ground with Z up + self.ground_pose = np.eye(4) + ground = pyrender.Mesh.from_trimesh( + make_checkerboard(up="y", alpha=1.0), smooth=False + ) + self.ground_node = self.scene.add(ground, name="ground", pose=self.ground_pose) + self.cam_node = self.scene.add(self.camera, name="camera") + + self.cam_marker_node = None + self.cam_marker_poses = [] + + self.light_nodes = [] + self.light_poses = [] + + self.bg_seq = [] + + # pyrender nodes, reused between frames + self.anim_nodes = [] + # list of meshes per frame of animation + self.anim_meshes = [] + # list of camera poses per frame of animation + self.anim_cameras = None + # current timestep of animation + self.anim_idx = 0 + + def acquire_lock(self): + pass + + def release_lock(self): + pass + + def close(self): + pass + + def delete(self): + pass + + def clear_meshes(self): + self.anim_meshes = [] + self.anim_idx = 0 + + @property + def anim_len(self): + return len(self.anim_meshes) + + def add_lighting(self, color=np.ones(3), intensity=1.0): + self.light_poses = get_light_poses() + self.light_poses.append(np.eye(4)) + cam_pose = self.scene.get_pose(self.cam_node) + for i, pose in enumerate(self.light_poses): + matrix = cam_pose @ pose + node = Node( + name=f"light-{i:02d}", + light=DirectionalLight(color=color, intensity=intensity), + matrix=matrix, + ) + if self.scene.has_node(node): + continue + self.scene.add_node(node) + self.light_nodes.append(node) + + def add_mesh_frame(self, meshes, debug=False): + """ + :param meshes (list) trimesh meshes for this frame timestep + """ + meshes = [pyrender.Mesh.from_trimesh(m) for m in meshes] + num_nodes = len(meshes) + self.anim_meshes.append(meshes) + + if num_nodes > len(self.anim_nodes): + # need to add a node in the pyrender scene + self.acquire_lock() + for i in range(len(self.anim_nodes), num_nodes): + self.anim_nodes.append(self.scene.add(meshes[i], name=f"mesh_{i:03d}")) + self.release_lock() + + def add_static_meshes(self, meshes, smooth=True): + """ + add all meshes to a single frame (timestep) + """ + meshes = [pyrender.Mesh.from_trimesh(m, smooth=smooth) for m in meshes] + if len(self.anim_meshes) < 1: + self.anim_meshes.append([]) + self.anim_meshes[0].extend(meshes) + num_meshes = len(self.anim_meshes[0]) + num_nodes = len(self.anim_nodes) + if num_meshes > num_nodes: + # need to add a node in the pyrender scene + self.acquire_lock() + self.anim_nodes.extend( + [ + self.scene.add(self.anim_meshes[0][i]) + for i in range(num_nodes, num_meshes) + ] + ) + self.release_lock() + + def set_camera_seq(self, poses): + """ + :param poses (*, 4, 4) + """ + poses = transform_pyrender(poses) + poses = np.asarray(poses) + assert poses.ndim >= 2 and poses.shape[-2:] == (4, 4) + if poses.ndim < 3: + poses = poses[None] + print(f"Adding camera sequence length {len(poses)}") + self.anim_cameras = poses + + def add_camera_markers(self, poses): + """ + Add a single camera marker node that we move around when we animate + """ + print("ADDING CAMERA MARKERS") + if self.cam_marker_node is None: + cam_marker = make_camera_marker(up="y") + self.cam_marker_node = self.scene.add( + pyrender.Mesh.from_trimesh(cam_marker, smooth=False) + ) + poses = transform_pyrender(poses) + poses = np.asarray(poses) + self.cam_marker_poses = poses + + def add_camera_markers_static(self, poses): + """ + Add all camera markers as separate mesh nodes to render in one pass + """ + print("ADDING STATIC CAMERA MARKERS") + poses = transform_pyrender(poses) + poses = np.asarray(poses) + cam_meshes = [make_camera_marker(up="y", transform=pose) for pose in poses] + self.add_static_meshes(cam_meshes, smooth=False) + + def update_camera(self, cam_pose): + self.acquire_lock() + self.scene.set_pose(self.cam_node, pose=cam_pose) + self.release_lock() + + def set_ground(self, pose): + pose = transform_pyrender(pose) + print("Setting ground pose to be", pose) + self.ground_pose = np.asarray(pose) + self.scene.set_pose(self.ground_node, pose=self.ground_pose) + + def set_bg_seq(self, bg_imgs): + pass + + def set_mesh_visibility(self, vis): + self.acquire_lock() + for node in self.anim_nodes: + node.mesh.is_visible = vis + self.release_lock() + + def check_mesh_visibility(self): + for node in self.anim_nodes: + if node.mesh.is_visible: + return True + + if self.ground_node.mesh.is_visible: + return True + + if self.cam_marker_node is not None and self.cam_marker_node.mesh.is_visible: + return True + + return False + + def update_frame(self): + t = self.anim_idx % self.anim_len + + # update camera + if self.anim_cameras is not None: + cam_t = min(t, len(self.anim_cameras) - 1) + cam_pose = self.anim_cameras[cam_t] + self.update_camera(cam_pose) + if self.cam_marker_node is not None and t < len(self.cam_marker_poses): + self.acquire_lock() + self.scene.set_pose(self.cam_marker_node, self.cam_marker_poses[t]) + self.release_lock() + + # update meshes + meshes = self.anim_meshes[t] + self.acquire_lock() + for i, node in enumerate(self.anim_nodes): + if i < len(meshes): + node.mesh = meshes[i] + node.mesh.is_visible = True + else: + node.mesh.is_visible = False + self.release_lock() + + +class OffscreenAnimation(AnimationBase): + def __init__(self, img_size, intrins=None, fps=30, ext="mp4"): + super().__init__(img_size, intrins=intrins) + self.add_lighting(0.9) + + self.fps = fps + self.ext = ext + self.viewer = pyrender.OffscreenRenderer(*self.viewport_size) + + self.bg_seq = [] + + def set_bg_seq(self, bg_imgs): + assert isinstance(bg_imgs, list) + print(f"setting length {len(bg_imgs)} bg sequence") + self.bg_seq = bg_imgs + + def delete(self): + self.viewer.delete() + + def close(self): + self.delete() + + def render( + self, render_bg=True, render_ground=True, render_cam=True, fac=1.0, **kwargs + ): + flags = RenderFlags.RGBA | RenderFlags.SHADOWS_DIRECTIONAL + self.ground_node.mesh.is_visible = render_ground and (not render_bg) + if self.cam_marker_node is not None: + self.cam_marker_node.mesh.is_visible = render_cam + + rgba = np.zeros((*self.viewport_size[::-1], 4)) + if self.check_mesh_visibility(): # if any meshes are visible + rgba, _ = self.viewer.render(self.scene, flags=flags) + + img = rgba + if render_bg and len(self.bg_seq) > 0: + t = min(self.anim_idx, len(self.bg_seq) - 1) + bg = self.bg_seq[t] + rgba = rgba.astype(np.float32) / 255 + alpha = fac * rgba[..., 3:] + img = alpha * rgba[..., :3] + (1 - alpha) * bg + img = (255 * img).astype(np.uint8) + + return img + + def render_mesh_layers(self, render_ground=True, render_cam=True, **kwargs): + # render each mesh in its own layer + flags = RenderFlags.RGBA | RenderFlags.SHADOWS_DIRECTIONAL + render_cam = render_cam and self.cam_marker_node is not None + + # current timestep + t = self.anim_idx % self.anim_len + meshes = self.anim_meshes[t] + layers = [] + + # toggle ground and camera + self.ground_node.mesh.is_visible = False + if self.cam_marker_node is not None: + self.cam_marker_node.mesh.is_visible = False + + # render animation meshes for current timestep + for i in range(len(meshes)): + for j, node in enumerate(self.anim_nodes): + if i == j: + node.mesh.is_visible = True + else: + node.mesh.is_visible = False + rgba, _ = self.viewer.render(self.scene, flags=flags) + layers.append(rgba) + + if not render_ground and not render_cam: + return layers + + # render the ground and camera + for node in self.anim_nodes: + node.mesh.is_visible = False + + if render_cam: + self.cam_marker_node.mesh.is_visible = render_cam + rgba, _ = self.viewer.render(self.scene, flags=flags) + layers.append(rgba) + self.cam_marker_node.mesh.is_visible = False + + if render_ground: + self.ground_node.mesh.is_visible = render_ground + rgba, _ = self.viewer.render(self.scene, flags=flags) + layers.append(rgba) + + return layers + + def render_frames_layers(self): + frames_layers = [] + for t in range(self.anim_len): + self.anim_idx = t + self.update_frame() + layers = self.render_mesh_layers() + frames_layers.append(layers) + return frames_layers + + def animate(self, save_name, save_frames=False, render_layers=False, **kwargs): + if render_layers: + frames_layers = self.render_frames_layers() + os.makedirs(save_name, exist_ok=True) + for t, layers in enumerate(frames_layers): + for l, layer in enumerate(layers): + path = f"{save_name}/{t:06d}_{l:03d}.png" + imageio.imwrite(path, layer) + print(f"saved frame layers to {save_name}") + return save_name + + frames = self.render_frames(**kwargs) + if len(frames) > 1: + if save_frames: + os.makedirs(save_name, exist_ok=True) + for i, frame in enumerate(frames): + path = f"{save_name}/{i:06d}.png" + imageio.imwrite(path, frame) + return save_name + save_path = f"{save_name}.{self.ext}" + imageio.mimwrite(save_path, frames, fps=self.fps) + print("wrote video to", save_path) + return save_path + + save_path = f"{save_name}.png" + imageio.imwrite(save_path, frames[0]) + print("wrote image to", save_path) + return save_path + + def render_frames(self, **kwargs): + print("ANIMATION LENGTH", self.anim_len) + frames = [] + for t in range(self.anim_len): + self.anim_idx = t + self.update_frame() + img = self.render(**kwargs) + frames.append(img) + return frames + + def render_layers(self, save_dir, composite=False, fac=0.4): + os.makedirs(save_dir, exist_ok=True) + + # render all frames + frames = self.render_frames(render_bg=False, render_ground=False) + + # render background + self.set_mesh_visibility(False) + bg_img = self.render(render_bg=False, render_ground=True) / 255 + + # save frames + for t, frame in enumerate(frames): + imageio.imwrite(f"{save_dir}/{t:06d}.png", frame) + imageio.imwrite(f"{save_dir}/background.png", bg_img) + + if composite: + rgba = composite_layers(frames, bg_img, fac=fac) + imageio.imwrite(f"{save_dir}/composite.png", (255 * rgba).astype(np.uint8)) + + +def composite_layers(frames, bg_img, fac=0.4): + # composite front to back + H, W = frames[0].shape[:2] + comp = np.zeros((H, W, 3)) + vis = np.ones((H, W, 1)) + for frame in frames: + frame = frame / 255 + alpha = fac * frame[..., 3:] + comp += vis * alpha * frame[..., :3] + vis *= 1 - alpha + + comp += vis * bg_img[..., 3:] * bg_img[..., :3] + vis *= 1 - bg_img[..., 3:] + return comp + vis + rgba = np.concatenate([comp, 1 - vis], axis=-1) + return rgba + + +class AnimationViewer(AnimationBase): + def __init__(self, img_size, intrins=None, fps=30, num_repeats=1): + super().__init__(img_size, intrins=intrins) + + self.fps = fps + self.ext = "gif" + + def pause_play_callback(_, viewer): + viewer.is_paused = not viewer.is_paused + + def step_callback(_, viewer, step): + viewer.anim_idx = (viewer.anim_idx + step) % viewer.anim_len + + def stop_callback(_, viewer): + viewer.do_animate = False + + def loop_callback(_, viewer): + viewer.num_repeats *= -1 + + registered_keys = { + "p": (pause_play_callback, [self]), + ".": (step_callback, [self, 1]), + ",": (step_callback, [self, -1]), + "l": (loop_callback, [self]), + "s": (stop_callback, [self]), + } + + self.viewer = pyrender.Viewer( + self.scene, + run_in_thread=True, + viewport_size=self.viewport_size, + use_raymond_lighting=True, + registered_keys=registered_keys, + ) + + self.num_repeats = num_repeats + self.do_animate = False + self.is_paused = False + + def acquire_lock(self): + self.viewer.render_lock.acquire() + + def release_lock(self): + self.viewer.render_lock.release() + + def close(self): + self.viewer.close_external() + + def animate(self, save_name=None, **kwargs): + print("===================") + print(f"PLAYING ANIMATION {self.num_repeats} TIMES") + print("VIEWER CONTROLS:") + print("p\tpause/play") + print("l\tloop/unloop") + print(".\tstep forward") + print(",\tstep backward") + print("s\tstop") + print("===================") + + self.anim_idx = 0 + self.do_animate = True + frame_dur = 1 / self.fps + if save_name is not None: + self.viewer.viewer_flags["record"] = True + + # set up initial frame + self.update_frame() + + while self.do_animate: + if self.is_paused: + self.update_frame() + continue + + if ( + self.num_repeats > 0 + and self.anim_idx >= self.num_repeats * self.anim_len + ): + break + + if save_name is not None and self.anim_idx >= self.anim_len: + self.viewer.viewer_flags["record"] = False + + start_time = time.time() + self.update_frame() + render_time = time.time() - start_time + + self.anim_idx += 1 + sleep_time = frame_dur - render_time + if sleep_time > 0: + time.sleep(sleep_time) + + if save_name is not None: + print(f"SAVING RECORDING TO {save_name}") + self.viewer.save_gif(f"{save_name}.{self.ext}") + + +def make_checkerboard( + length=25.0, + color0=[0.8, 0.9, 0.9], + color1=[0.6, 0.7, 0.7], + tile_width=0.5, + alpha=1.0, + up="y", +): + v, f, _, fc = checkerboard_geometry(length, color0, color1, tile_width, alpha, up) + return trimesh.Trimesh(v, f, face_colors=fc, process=False) + + +def make_pyrender_camera(img_size, intrins=None): + if intrins is not None: + print("USING INTRINSICS CAMERA", intrins) + fx, fy, cx, cy = intrins + return pyrender.IntrinsicsCamera(fx, fy, cx, cy) + + W, H = img_size + focal = 0.5 * (H + W) + yfov = 2 * np.arctan(0.5 * H / focal) + print("USING PERSPECTIVE CAMERA", H, W, focal) + return pyrender.PerspectiveCamera(yfov=yfov, aspectRatio=W / H) + + +def make_camera_marker(radius=0.1, height=0.2, up="y", transform=None): + """ + :param radius (default 0.1) radius of pyramid base, diagonal of image plane + :param height (default 0.2) height of pyramid, focal length + :param up (default y) camera up vector + :param transform (default None) (4, 4) cam to world transform + """ + verts, faces, face_colors = camera_marker_geometry(radius, height, up) + if transform is not None: + assert transform.shape == (4, 4) + verts = ( + np.einsum("ij,nj->ni", transform[:3, :3], verts) + transform[None, :3, 3] + ) + return trimesh.Trimesh(verts, faces, face_colors=face_colors, process=False) + + +def get_light_poses(n_lights=5, elevation=np.pi / 3, dist=12): + # get lights in a circle around origin at elevation + thetas = elevation * np.ones(n_lights) + phis = 2 * np.pi * np.arange(n_lights) / n_lights + poses = [] + trans = make_translation(torch.tensor([0, 0, dist])) + for phi, theta in zip(phis, thetas): + rot = make_rotation(rx=-theta, ry=phi, order="xyz") + poses.append((rot @ trans).numpy()) + return poses + + +def get_raymond_light_poses(up="z"): + thetas = np.pi * np.ones(3) / 6 + phis = 2 * np.pi * np.arange(3) / 3 + + poses = [] + + for phi, theta in zip(phis, thetas): + xp = np.sin(theta) * np.cos(phi) + yp = np.sin(theta) * np.sin(phi) + zp = np.cos(theta) + + if up == "y": + z = np.array([xp, zp, -yp]) + else: + z = np.array([xp, yp, zp]) + z = z / np.linalg.norm(z) + x = np.array([-z[1], z[0], 0.0]) + if np.linalg.norm(x) == 0: + x = np.array([1.0, 0.0, 0.0]) + x = x / np.linalg.norm(x) + y = np.cross(z, x) + + matrix = np.eye(4) + matrix[:3, :3] = np.c_[x, y, z] + poses.append(matrix) + return poses diff --git a/slahmr/teaser.png b/slahmr/teaser.png new file mode 100644 index 0000000000000000000000000000000000000000..82b5301d856cafccbd35cef1ae8d2bb5a4e3b4e3 --- /dev/null +++ b/slahmr/teaser.png @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:feac41015dcd35b1330c03ccc65f0b645b0c8396f22cd4d899f182d74247535e +size 4155963 diff --git a/slahmr/third-party/DROID-SLAM/.gitignore b/slahmr/third-party/DROID-SLAM/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..a180f698f4396a8fd6323c75ffe4b1867eff1d85 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/.gitignore @@ -0,0 +1,158 @@ +a# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ +cover/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +.pybuilder/ +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +# For a library or package, you might want to ignore these files since the code is +# intended to run in multiple environments; otherwise, check them in: +# .python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ + +# pytype static type analyzer +.pytype/ + +# Cython debug symbols +cython_debug/ + + + +__pycache__ +build +dist +*.egg-info +*.vscode/ +*.pth +tests +checkpoints +datasets +runs +cache +*.out +*.o +data +figures/*.pdf + + diff --git a/slahmr/third-party/DROID-SLAM/.gitmodules b/slahmr/third-party/DROID-SLAM/.gitmodules new file mode 100644 index 0000000000000000000000000000000000000000..d47acde92d97b1012ceacb1e37136ad293cec25e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/.gitmodules @@ -0,0 +1,6 @@ +[submodule "thirdparty/lietorch"] + path = thirdparty/lietorch + url = https://github.com/princeton-vl/lietorch +[submodule "thirdparty/eigen"] + path = thirdparty/eigen + url = https://gitlab.com/libeigen/eigen.git diff --git a/slahmr/third-party/DROID-SLAM/LICENSE b/slahmr/third-party/DROID-SLAM/LICENSE new file mode 100644 index 0000000000000000000000000000000000000000..cc1e23bde2b18bbab3569b0dd4d8677ac3babedb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/LICENSE @@ -0,0 +1,29 @@ +BSD 3-Clause License + +Copyright (c) 2021, Princeton Vision & Learning Lab +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. + +3. 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/slahmr/third-party/DROID-SLAM/README.md b/slahmr/third-party/DROID-SLAM/README.md new file mode 100644 index 0000000000000000000000000000000000000000..dc73a219e51f1c0912fdca4b54b61dcdc80d01ba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/README.md @@ -0,0 +1,139 @@ +# DROID-SLAM + + + + + +[![IMAGE ALT TEXT HERE](misc/screenshot.png)](https://www.youtube.com/watch?v=GG78CSlSHSA) + + + +[DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://arxiv.org/abs/2108.10869) +Zachary Teed and Jia Deng + +``` +@article{teed2021droid, + title={{DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras}}, + author={Teed, Zachary and Deng, Jia}, + journal={Advances in neural information processing systems}, + year={2021} +} +``` + +**Initial Code Release:** This repo currently provides a single GPU implementation of our monocular, stereo, and RGB-D SLAM systems. It currently contains demos, training, and evaluation scripts. + + +## Requirements + +To run the code you will need ... +* **Inference:** Running the demos will require a GPU with at least 11G of memory. + +* **Training:** Training requires a GPU with at least 24G of memory. We train on 4 x RTX-3090 GPUs. + +## Getting Started +1. Clone the repo using the `--recursive` flag +```Bash +git clone --recursive https://github.com/princeton-vl/DROID-SLAM.git +``` + +2. Creating a new anaconda environment using the provided .yaml file. Use `environment_novis.yaml` to if you do not want to use the visualization +```Bash +conda env create -f environment.yaml +pip install evo --upgrade --no-binary evo +pip install gdown +``` + +3. Compile the extensions (takes about 10 minutes) +```Bash +python setup.py install +``` + + +## Demos + +1. Download the model from google drive: [droid.pth](https://drive.google.com/file/d/1PpqVt1H4maBa_GbPJp4NwxRsd9jk-elh/view?usp=sharing) + +2. Download some sample videos using the provided script. +```Bash +./tools/download_sample_data.sh +``` + +Run the demo on any of the samples (all demos can be run on a GPU with 11G of memory). While running, press the "s" key to increase the filtering threshold (= more points) and "a" to decrease the filtering threshold (= fewer points). To save the reconstruction with full resolution depth maps use the `--reconstruction_path` flag. + + +```Python +python demo.py --imagedir=data/abandonedfactory --calib=calib/tartan.txt --stride=2 +``` + +```Python +python demo.py --imagedir=data/sfm_bench/rgb --calib=calib/eth.txt +``` + +```Python +python demo.py --imagedir=data/Barn --calib=calib/barn.txt --stride=1 --backend_nms=4 +``` + +```Python +python demo.py --imagedir=data/mav0/cam0/data --calib=calib/euroc.txt --t0=150 +``` + +```Python +python demo.py --imagedir=data/rgbd_dataset_freiburg3_cabinet/rgb --calib=calib/tum3.txt +``` + + +**Running on your own data:** All you need is a calibration file. Calibration files are in the form +``` +fx fy cx cy [k1 k2 p1 p2 [ k3 [ k4 k5 k6 ]]] +``` +with parameters in brackets optional. + +## Evaluation +We provide evaluation scripts for TartanAir, EuRoC, and TUM. EuRoC and TUM can be run on a 1080Ti. The TartanAir and ETH will require 24G of memory. + +### TartanAir (Mono + Stereo) +Download the [TartanAir](https://theairlab.org/tartanair-dataset/) dataset using the script `thirdparty/tartanair_tools/download_training.py` and put them in `datasets/TartanAir` +```Bash +./tools/validate_tartanair.sh --plot_curve # monocular eval +./tools/validate_tartanair.sh --plot_curve --stereo # stereo eval +``` + +### EuRoC (Mono + Stereo) +Download the [EuRoC](https://projects.asl.ethz.ch/datasets/doku.php?id=kmavvisualinertialdatasets) sequences (ASL format) and put them in `datasets/EuRoC` +```Bash +./tools/evaluate_euroc.sh # monocular eval +./tools/evaluate_euroc.sh --stereo # stereo eval +``` + +### TUM-RGBD (Mono) +Download the fr1 sequences from [TUM-RGBD](https://vision.in.tum.de/data/datasets/rgbd-dataset/download) and put them in `datasets/TUM-RGBD` +```Bash +./tools/evaluate_tum.sh # monocular eval +``` + +### ETH3D (RGB-D) +Download the [ETH3D](https://www.eth3d.net/slam_datasets) dataset +```Bash +./tools/evaluate_eth3d.sh # RGB-D eval +``` + +## Training + +First download the TartanAir dataset. The download script can be found in `thirdparty/tartanair_tools/download_training.py`. You will only need the `rgb` and `depth` data. + +``` +python download_training.py --rgb --depth +``` + +You can then run the training script. We use 4x3090 RTX GPUs for training which takes approximatly 1 week. If you use a different number of GPUs, adjust the learning rate accordingly. + +**Note:** On the first training run, covisibility is computed between all pairs of frames. This can take several hours, but the results are cached so that future training runs will start immediately. + + +``` +python train.py --datapath= --gpus=4 --lr=0.00025 +``` + + +## Acknowledgements +Data from [TartanAir](https://theairlab.org/tartanair-dataset/) was used to train our model. We additionally use evaluation tools from [evo](https://github.com/MichaelGrupp/evo) and [tartanair_tools](https://github.com/castacks/tartanair_tools). diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/droid_backends.cpython-310-x86_64-linux-gnu.so b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/droid_backends.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..1ad4b5bec72b95a0c298d19f97aafc24f8dbf6e2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/droid_backends.cpython-310-x86_64-linux-gnu.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0bcaa246539d6ca06ac4079f6cd8e881220ab6c03416eab3094c6b122685cde2 +size 2014616 diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/__init__.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..275d68e289eb3ccd5c6980b4e886520ca506863e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/__init__.py @@ -0,0 +1,2 @@ +__all__ = ['groups'] +from .groups import LieGroupParameter, SO3, RxSO3, SE3, Sim3, cat, stack diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/broadcasting.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/broadcasting.py new file mode 100644 index 0000000000000000000000000000000000000000..9015a3354b57a9ebf5269abf148bdd30545e6380 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/broadcasting.py @@ -0,0 +1,31 @@ +import torch +import numpy as np + +def check_broadcastable(x, y): + assert len(x.shape) == len(y.shape) + for (n, m) in zip(x.shape[:-1], y.shape[:-1]): + assert n==m or n==1 or m==1 + +def broadcast_inputs(x, y): + """ Automatic broadcasting of missing dimensions """ + if y is None: + xs, xd = x.shape[:-1], x.shape[-1] + return (x.view(-1, xd).contiguous(), ), x.shape[:-1] + + check_broadcastable(x, y) + + xs, xd = x.shape[:-1], x.shape[-1] + ys, yd = y.shape[:-1], y.shape[-1] + out_shape = [max(n,m) for (n,m) in zip(xs,ys)] + + if x.shape[:-1] == y.shape[-1]: + x1 = x.view(-1, xd) + y1 = y.view(-1, yd) + + else: + x_expand = [m if n==1 else 1 for (n,m) in zip(xs, ys)] + y_expand = [n if m==1 else 1 for (n,m) in zip(xs, ys)] + x1 = x.repeat(x_expand + [1]).reshape(-1, xd).contiguous() + y1 = y.repeat(y_expand + [1]).reshape(-1, yd).contiguous() + + return (x1, y1), tuple(out_shape) diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/gradcheck.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/gradcheck.py new file mode 100644 index 0000000000000000000000000000000000000000..d94dccb6969238e68b5d38a12bfaf5c1c41950f2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/gradcheck.py @@ -0,0 +1,592 @@ +import torch + +TORCH_MAJOR = int(torch.__version__.split('.')[0]) +TORCH_MINOR = int(torch.__version__.split('.')[1]) + +from torch.types import _TensorOrTensors +if TORCH_MAJOR == 1 and TORCH_MINOR < 8: + from torch._six import container_abcs, istuple +else: + import collections.abc as container_abcs + +import torch.testing +from torch.overrides import is_tensor_like +from itertools import product +import warnings +from typing import Callable, Union, Optional, Iterable, List + +def zero_gradients(x): + if isinstance(x, torch.Tensor): + if x.grad is not None: + x.grad.detach_() + x.grad.zero_() + elif isinstance(x, container_abcs.Iterable): + for elem in x: + zero_gradients(elem) + + +def make_jacobian(input, num_out): + if is_tensor_like(input): + if not input.is_floating_point() and not input.is_complex(): + return None + if not input.requires_grad: + return None + return input.new_zeros((input.nelement(), num_out), dtype=input.dtype, layout=torch.strided) + elif isinstance(input, container_abcs.Iterable) and not isinstance(input, str): + jacobians = list(filter( + lambda x: x is not None, (make_jacobian(elem, num_out) for elem in input))) + if not jacobians: + return None + return type(input)(jacobians) # type: ignore + else: + return None + + +def iter_tensors(x: Union[torch.Tensor, Iterable[torch.Tensor]], only_requiring_grad: bool = False) -> Iterable[torch.Tensor]: + if is_tensor_like(x): + # mypy doesn't narrow type of `x` to torch.Tensor + if x.requires_grad or not only_requiring_grad: # type: ignore + yield x # type: ignore + elif isinstance(x, container_abcs.Iterable) and not isinstance(x, str): + for elem in x: + for result in iter_tensors(elem, only_requiring_grad): + yield result + +def get_numerical_jacobian(fn, input, target=None, eps=1e-3, grad_out=1.0): + """ + input: input to `fn` + target: the Tensors wrt whom Jacobians are calculated (default=`input`) + grad_out: grad output value used to calculate gradients. + + Note that `target` may not even be part of `input` to `fn`, so please be + **very careful** in this to not clone `target`. + """ + if target is None: + target = input + output_size = fn(input).numel() + jacobian = make_jacobian(target, output_size) + + # It's much easier to iterate over flattened lists of tensors. + # These are reference to the same objects in jacobian, so any changes + # will be reflected in it as well. + x_tensors = iter_tensors(target, True) + j_tensors = iter_tensors(jacobian) + + def update_jacobians(x, idx, d, d_idx, is_mkldnn=False): + + # compute_jacobian only works for pure real + # or pure imaginary delta + def compute_gradient(delta): + # we currently assume that the norm of delta equals eps + assert(delta == eps or delta == (eps * 1j)) + + def fn_out(): + if not is_mkldnn: + # x is a view into input and so this works + return fn(input).clone() + else: + # convert the dense tensor back to have mkldnn layout + return fn([x.to_mkldnn()]) + + orig = x[idx].item() + x[idx] = orig - delta + outa = fn_out() + x[idx] = orig + delta + outb = fn_out() + x[idx] = orig + r = (outb - outa) / (2 * eps) + return r.detach().reshape(-1) + + # for details on the algorithm used here, refer: + # Section 3.5.3 https://arxiv.org/pdf/1701.00392.pdf + # s = fn(z) where z = x for real valued input + # and z = x + yj for complex valued input + ds_dx = compute_gradient(eps) + if x.is_complex(): # C -> C, C -> R + ds_dy = compute_gradient(eps * 1j) + # conjugate wirtinger derivative + conj_w_d = 0.5 * (ds_dx + ds_dy * 1j) + # wirtinger derivative + w_d = 0.5 * (ds_dx - ds_dy * 1j) + d[d_idx] = grad_out.conjugate() * conj_w_d + grad_out * w_d.conj() + elif ds_dx.is_complex(): # R -> C + # w_d = conj_w_d = 0.5 * ds_dx + # dL_dz_conj = 0.5 * [grad_out.conj() * ds_dx + grad_out * ds_dx.conj()] + # = 0.5 * [grad_out.conj() * ds_dx + (grad_out.conj() * ds_dx).conj()] + # = 0.5 * 2 * real(grad_out.conj() * ds_dx) + # = real(grad_out.conj() * ds_dx) + d[d_idx] = torch.real(grad_out.conjugate() * ds_dx) + else: # R -> R + d[d_idx] = ds_dx * grad_out + + # TODO: compare structure + for x_tensor, d_tensor in zip(x_tensors, j_tensors): + if x_tensor.is_sparse: + def get_stride(size): + dim = len(size) + tmp = 1 + stride = [0] * dim + for i in reversed(range(dim)): + stride[i] = tmp + tmp *= size[i] + return stride + + x_nnz = x_tensor._nnz() + x_size = list(x_tensor.size()) + x_indices = x_tensor._indices().t() + x_values = x_tensor._values() + x_stride = get_stride(x_size) + + # Use .data here to get around the version check + x_values = x_values.data + + for i in range(x_nnz): + x_value = x_values[i] + for x_idx in product(*[range(m) for m in x_values.size()[1:]]): + indices = x_indices[i].tolist() + list(x_idx) + d_idx = sum(indices[k] * x_stride[k] for k in range(len(x_size))) + update_jacobians(x_value, x_idx, d_tensor, d_idx) + elif x_tensor.layout == torch._mkldnn: # type: ignore + # Use .data here to get around the version check + x_tensor = x_tensor.data + if len(input) != 1: + raise ValueError('gradcheck currently only supports functions with 1 input, but got: ', + len(input)) + for d_idx, x_idx in enumerate(product(*[range(m) for m in x_tensor.size()])): + # this is really inefficient, but without indexing implemented, there's + # not really a better way than converting back and forth + x_tensor_dense = x_tensor.to_dense() + update_jacobians(x_tensor_dense, x_idx, d_tensor, d_idx, is_mkldnn=True) + else: + # Use .data here to get around the version check + x_tensor = x_tensor.data + for d_idx, x_idx in enumerate(product(*[range(m) for m in x_tensor.size()])): + update_jacobians(x_tensor, x_idx, d_tensor, d_idx) + + return jacobian + + +def get_analytical_jacobian(input, output, nondet_tol=0.0, grad_out=1.0): + # it is easier to call to_dense() on the sparse output than + # to modify analytical jacobian + if output.is_sparse: + raise ValueError('Sparse output is not supported at gradcheck yet. ' + 'Please call to_dense() on the output of fn for gradcheck.') + if output.layout == torch._mkldnn: # type: ignore + raise ValueError('MKLDNN output is not supported at gradcheck yet. ' + 'Please call to_dense() on the output of fn for gradcheck.') + diff_input_list = list(iter_tensors(input, True)) + jacobian = make_jacobian(input, output.numel()) + jacobian_reentrant = make_jacobian(input, output.numel()) + grad_output = torch.zeros_like(output, memory_format=torch.legacy_contiguous_format) + flat_grad_output = grad_output.view(-1) + reentrant = True + correct_grad_sizes = True + correct_grad_types = True + + for i in range(flat_grad_output.numel()): + flat_grad_output.zero_() + flat_grad_output[i] = grad_out + for jacobian_c in (jacobian, jacobian_reentrant): + grads_input = torch.autograd.grad(output, diff_input_list, grad_output, + retain_graph=True, allow_unused=True) + for jacobian_x, d_x, x in zip(jacobian_c, grads_input, diff_input_list): + if d_x is not None and d_x.size() != x.size(): + correct_grad_sizes = False + elif d_x is not None and d_x.dtype != x.dtype: + correct_grad_types = False + elif jacobian_x.numel() != 0: + if d_x is None: + jacobian_x[:, i].zero_() + else: + d_x_dense = d_x.to_dense() if not d_x.layout == torch.strided else d_x + assert jacobian_x[:, i].numel() == d_x_dense.numel() + jacobian_x[:, i] = d_x_dense.contiguous().view(-1) + + for jacobian_x, jacobian_reentrant_x in zip(jacobian, jacobian_reentrant): + if jacobian_x.numel() != 0 and (jacobian_x - jacobian_reentrant_x).abs().max() > nondet_tol: + reentrant = False + + return jacobian, reentrant, correct_grad_sizes, correct_grad_types + + +def _as_tuple(x): + if TORCH_MAJOR == 1 and TORCH_MINOR < 8: + b_tuple = istuple(x) + else: + b_tuple = isinstance(x, tuple) + + if b_tuple: + return x + elif isinstance(x, list): + return tuple(x) + else: + return x, + + + +def _differentiable_outputs(x): + return tuple(o for o in _as_tuple(x) if o.requires_grad) + + +# Note [VarArg of Tensors] +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# 'func' accepts a vararg of tensors, which isn't expressable in the type system at the moment. +# If https://mypy.readthedocs.io/en/latest/additional_features.html?highlight=callable#extended-callable-types is accepted, +# the '...' first argument of Callable can be replaced with VarArg(Tensor). +# For now, we permit any input. +# the '...' first argument of Callable can be replaced with VarArg(Tensor). +# For now, we permit any input. + +def gradcheck( + func: Callable[..., Union[_TensorOrTensors]], # See Note [VarArg of Tensors] + inputs: _TensorOrTensors, + eps: float = 1e-6, + atol: float = 1e-5, + rtol: float = 1e-3, + raise_exception: bool = True, + check_sparse_nnz: bool = False, + nondet_tol: float = 0.0, + check_undefined_grad: bool = True, + check_grad_dtypes: bool = False +) -> bool: + r"""Check gradients computed via small finite differences against analytical + gradients w.r.t. tensors in :attr:`inputs` that are of floating point or complex type + and with ``requires_grad=True``. + + The check between numerical and analytical gradients uses :func:`~torch.allclose`. + + For complex functions, no notion of Jacobian exists. Gradcheck verifies if the numerical and + analytical values of Wirtinger and Conjugate Wirtinger derivative are consistent. The gradient + computation is done under the assumption that the overall function has a real valued output. + For functions with complex output, gradcheck compares the numerical and analytical gradients + for two values of :attr:`grad_output`: 1 and 1j. For more details, check out + :ref:`complex_autograd-doc`. + + .. note:: + The default values are designed for :attr:`input` of double precision. + This check will likely fail if :attr:`input` is of less precision, e.g., + ``FloatTensor``. + + .. warning:: + If any checked tensor in :attr:`input` has overlapping memory, i.e., + different indices pointing to the same memory address (e.g., from + :func:`torch.expand`), this check will likely fail because the numerical + gradients computed by point perturbation at such indices will change + values at all other indices that share the same memory address. + + Args: + func (function): a Python function that takes Tensor inputs and returns + a Tensor or a tuple of Tensors + inputs (tuple of Tensor or Tensor): inputs to the function + eps (float, optional): perturbation for finite differences + atol (float, optional): absolute tolerance + rtol (float, optional): relative tolerance + raise_exception (bool, optional): indicating whether to raise an exception if + the check fails. The exception gives more information about the + exact nature of the failure. This is helpful when debugging gradchecks. + check_sparse_nnz (bool, optional): if True, gradcheck allows for SparseTensor input, + and for any SparseTensor at input, gradcheck will perform check at nnz positions only. + nondet_tol (float, optional): tolerance for non-determinism. When running + identical inputs through the differentiation, the results must either match + exactly (default, 0.0) or be within this tolerance. + check_undefined_grad (bool, options): if True, check if undefined output grads + are supported and treated as zeros, for ``Tensor`` outputs. + + Returns: + True if all differences satisfy allclose condition + """ + def fail_test(msg): + if raise_exception: + raise RuntimeError(msg) + return False + + tupled_inputs = _as_tuple(inputs) + if not check_sparse_nnz and any(t.is_sparse for t in tupled_inputs if isinstance(t, torch.Tensor)): + return fail_test('gradcheck expects all tensor inputs are dense when check_sparse_nnz is set to False.') + + # Make sure that gradients are saved for at least one input + any_input_requiring_grad = False + for idx, inp in enumerate(tupled_inputs): + if is_tensor_like(inp) and inp.requires_grad: + if not (inp.dtype == torch.float64 or inp.dtype == torch.complex128): + warnings.warn( + f'Input #{idx} requires gradient and ' + 'is not a double precision floating point or complex. ' + 'This check will likely fail if all the inputs are ' + 'not of double precision floating point or complex. ') + content = inp._values() if inp.is_sparse else inp + # TODO: To cover more problematic cases, replace stride = 0 check with + # "any overlap in memory" once we have a proper function to check it. + if content.layout is not torch._mkldnn: # type: ignore + if not all(st > 0 or sz <= 1 for st, sz in zip(content.stride(), content.size())): + raise RuntimeError( + 'The {}th input has a dimension with stride 0. gradcheck only ' + 'supports inputs that are non-overlapping to be able to ' + 'compute the numerical gradients correctly. You should call ' + '.contiguous on the input before passing it to gradcheck.') + any_input_requiring_grad = True + inp.retain_grad() + if not any_input_requiring_grad: + raise ValueError( + 'gradcheck expects at least one input tensor to require gradient, ' + 'but none of the them have requires_grad=True.') + + func_out = func(*tupled_inputs) + output = _differentiable_outputs(func_out) + + if not output: + for i, o in enumerate(func_out): + def fn(input): + return _as_tuple(func(*input))[i] + numerical = get_numerical_jacobian(fn, tupled_inputs, eps=eps) + for n in numerical: + if torch.ne(n, 0).sum() > 0: + return fail_test('Numerical gradient for function expected to be zero') + return True + + for i, o in enumerate(output): + if not o.requires_grad: + continue + + def fn(input): + return _as_tuple(func(*input))[i] + + analytical, reentrant, correct_grad_sizes, correct_grad_types = get_analytical_jacobian(tupled_inputs, + o, + nondet_tol=nondet_tol) + numerical = get_numerical_jacobian(fn, tupled_inputs, eps=eps) + + return analytical, numerical + + out_is_complex = o.is_complex() + + if out_is_complex: + # analytical vjp with grad_out = 1.0j + analytical_with_imag_grad_out, reentrant_with_imag_grad_out, \ + correct_grad_sizes_with_imag_grad_out, correct_grad_types_with_imag_grad_out \ + = get_analytical_jacobian(tupled_inputs, o, nondet_tol=nondet_tol, grad_out=1j) + numerical_with_imag_grad_out = get_numerical_jacobian(fn, tupled_inputs, eps=eps, grad_out=1j) + + if not correct_grad_types and check_grad_dtypes: + return fail_test('Gradient has dtype mismatch') + + if out_is_complex and not correct_grad_types_with_imag_grad_out and check_grad_dtypes: + return fail_test('Gradient (calculated using complex valued grad output) has dtype mismatch') + + if not correct_grad_sizes: + return fail_test('Analytical gradient has incorrect size') + + if out_is_complex and not correct_grad_sizes_with_imag_grad_out: + return fail_test('Analytical gradient (calculated using complex valued grad output) has incorrect size') + + def checkIfNumericalAnalyticAreClose(a, n, j, error_str=''): + if not torch.allclose(a, n, rtol, atol): + return fail_test(error_str + 'Jacobian mismatch for output %d with respect to input %d,\n' + 'numerical:%s\nanalytical:%s\n' % (i, j, n, a)) + + inp_tensors = iter_tensors(tupled_inputs, True) + + for j, (a, n, inp) in enumerate(zip(analytical, numerical, inp_tensors)): + if a.numel() != 0 or n.numel() != 0: + if o.is_complex(): + # C -> C, R -> C + a_with_imag_grad_out = analytical_with_imag_grad_out[j] + n_with_imag_grad_out = numerical_with_imag_grad_out[j] + checkIfNumericalAnalyticAreClose(a_with_imag_grad_out, n_with_imag_grad_out, j, + "Gradients failed to compare equal for grad output = 1j. ") + if inp.is_complex(): + # C -> R, C -> C + checkIfNumericalAnalyticAreClose(a, n, j, + "Gradients failed to compare equal for grad output = 1. ") + else: + # R -> R, R -> C + checkIfNumericalAnalyticAreClose(a, n, j) + + + def not_reentrant_error(error_str=''): + error_msg = "Backward" + error_str + " is not reentrant, i.e., running backward with same \ + input and grad_output multiple times gives different values, \ + although analytical gradient matches numerical gradient. \ + The tolerance for nondeterminism was {}.".format(nondet_tol) + return fail_test(error_msg) + + if not reentrant: + return not_reentrant_error() + + if out_is_complex and not reentrant_with_imag_grad_out: + return not_reentrant_error(' (calculated using complex valued grad output)') + + # check if the backward multiplies by grad_output + output = _differentiable_outputs(func(*tupled_inputs)) + if any([o.requires_grad for o in output]): + diff_input_list: List[torch.Tensor] = list(iter_tensors(tupled_inputs, True)) + if not diff_input_list: + raise RuntimeError("no Tensors requiring grad found in input") + grads_input = torch.autograd.grad(output, diff_input_list, + [torch.zeros_like(o, memory_format=torch.legacy_contiguous_format) for o in output], + allow_unused=True) + for gi, di in zip(grads_input, diff_input_list): + if gi is None: + continue + if isinstance(gi, torch.Tensor) and gi.layout != torch.strided: + if gi.layout != di.layout: + return fail_test('grad is incorrect layout (' + str(gi.layout) + ' is not ' + str(di.layout) + ')') + if gi.layout == torch.sparse_coo: + if gi.sparse_dim() != di.sparse_dim(): + return fail_test('grad is sparse tensor, but has incorrect sparse_dim') + if gi.dense_dim() != di.dense_dim(): + return fail_test('grad is sparse tensor, but has incorrect dense_dim') + gi = gi.to_dense() + di = di.to_dense() + if not gi.eq(0).all(): + return fail_test('backward not multiplied by grad_output') + if gi.dtype != di.dtype or gi.device != di.device or gi.is_sparse != di.is_sparse: + return fail_test("grad is incorrect type") + if gi.size() != di.size(): + return fail_test('grad is incorrect size') + + if check_undefined_grad: + def warn_bc_breaking(): + warnings.warn(( + 'Backwards compatibility: New undefined gradient support checking ' + 'feature is enabled by default, but it may break existing callers ' + 'of this function. If this is true for you, you can call this ' + 'function with "check_undefined_grad=False" to disable the feature')) + + def check_undefined_grad_support(output_to_check): + grads_output = [torch.zeros_like(o, memory_format=torch.legacy_contiguous_format) for o in output_to_check] + try: + grads_input = torch.autograd.grad(output_to_check, + diff_input_list, + grads_output, + allow_unused=True) + except RuntimeError: + warn_bc_breaking() + return fail_test(( + 'Expected backward function to handle undefined output grads. ' + 'Please look at "Notes about undefined output gradients" in ' + '"tools/autograd/derivatives.yaml"')) + + for gi, i in zip(grads_input, diff_input_list): + if (gi is not None) and (not gi.eq(0).all()): + warn_bc_breaking() + return fail_test(( + 'Expected all input grads to be undefined or zero when all output grads are undefined ' + 'or zero. Please look at "Notes about undefined output gradients" in ' + '"tools/autograd/derivatives.yaml"')) + return True + + # All backward functions must work properly if all output grads are undefined + outputs_to_check = [[ + torch._C._functions.UndefinedGrad()(o) for o in _differentiable_outputs(func(*tupled_inputs)) + # This check filters out Tensor-likes that aren't instances of Tensor. + if isinstance(o, torch.Tensor) + ]] + + # If there are multiple output grads, we should be able to undef one at a time without error + if len(outputs_to_check[0]) > 1: + for undef_grad_idx in range(len(output)): + output_to_check = _differentiable_outputs(func(*tupled_inputs)) + outputs_to_check.append([ + torch._C._functions.UndefinedGrad()(o) if idx == undef_grad_idx else o + for idx, o in enumerate(output_to_check)]) + + for output_to_check in outputs_to_check: + if not check_undefined_grad_support(output_to_check): + return False + + return True + + +def gradgradcheck( + func: Callable[..., _TensorOrTensors], # See Note [VarArg of Tensors] + inputs: _TensorOrTensors, + grad_outputs: Optional[_TensorOrTensors] = None, + eps: float = 1e-6, + atol: float = 1e-5, + rtol: float = 1e-3, + gen_non_contig_grad_outputs: bool = False, + raise_exception: bool = True, + nondet_tol: float = 0.0, + check_undefined_grad: bool = True, + check_grad_dtypes: bool = False +) -> bool: + r"""Check gradients of gradients computed via small finite differences + against analytical gradients w.r.t. tensors in :attr:`inputs` and + :attr:`grad_outputs` that are of floating point or complex type and with + ``requires_grad=True``. + + This function checks that backpropagating through the gradients computed + to the given :attr:`grad_outputs` are correct. + + The check between numerical and analytical gradients uses :func:`~torch.allclose`. + + .. note:: + The default values are designed for :attr:`input` and + :attr:`grad_outputs` of double precision. This check will likely fail if + they are of less precision, e.g., ``FloatTensor``. + + .. warning:: + If any checked tensor in :attr:`input` and :attr:`grad_outputs` has + overlapping memory, i.e., different indices pointing to the same memory + address (e.g., from :func:`torch.expand`), this check will likely fail + because the numerical gradients computed by point perturbation at such + indices will change values at all other indices that share the same + memory address. + + Args: + func (function): a Python function that takes Tensor inputs and returns + a Tensor or a tuple of Tensors + inputs (tuple of Tensor or Tensor): inputs to the function + grad_outputs (tuple of Tensor or Tensor, optional): The gradients with + respect to the function's outputs. + eps (float, optional): perturbation for finite differences + atol (float, optional): absolute tolerance + rtol (float, optional): relative tolerance + gen_non_contig_grad_outputs (bool, optional): if :attr:`grad_outputs` is + ``None`` and :attr:`gen_non_contig_grad_outputs` is ``True``, the + randomly generated gradient outputs are made to be noncontiguous + raise_exception (bool, optional): indicating whether to raise an exception if + the check fails. The exception gives more information about the + exact nature of the failure. This is helpful when debugging gradchecks. + nondet_tol (float, optional): tolerance for non-determinism. When running + identical inputs through the differentiation, the results must either match + exactly (default, 0.0) or be within this tolerance. Note that a small amount + of nondeterminism in the gradient will lead to larger inaccuracies in + the second derivative. + check_undefined_grad (bool, options): if True, check if undefined output grads + are supported and treated as zeros + + Returns: + True if all differences satisfy allclose condition + """ + tupled_inputs = _as_tuple(inputs) + + if grad_outputs is None: + # If grad_outputs is not specified, create random Tensors of the same + # shape, type, and device as the outputs + def randn_like(x): + y = torch.testing.randn_like( + x if (x.is_floating_point() or x.is_complex()) else x.double(), memory_format=torch.legacy_contiguous_format) + if gen_non_contig_grad_outputs: + y = torch.testing.make_non_contiguous(y) + return y.requires_grad_() + outputs = _as_tuple(func(*tupled_inputs)) + tupled_grad_outputs = tuple(randn_like(x) for x in outputs) + else: + tupled_grad_outputs = _as_tuple(grad_outputs) + + num_outputs = len(tupled_grad_outputs) + + def new_func(*args): + input_args = args[:-num_outputs] + grad_outputs = args[-num_outputs:] + outputs = _differentiable_outputs(func(*input_args)) + input_args = tuple(x for x in input_args if isinstance(x, torch.Tensor) and x.requires_grad) + grad_inputs = torch.autograd.grad(outputs, input_args, grad_outputs, create_graph=True) + return grad_inputs + + return gradcheck(new_func, tupled_inputs + tupled_grad_outputs, eps, atol, rtol, raise_exception, + nondet_tol=nondet_tol, check_undefined_grad=check_undefined_grad, + check_grad_dtypes=check_grad_dtypes) diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/group_ops.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/group_ops.py new file mode 100644 index 0000000000000000000000000000000000000000..f2564c2854cf409e3544f44c4f6c24a91000336f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/group_ops.py @@ -0,0 +1,102 @@ +import lietorch_backends +import torch +import torch.nn.functional as F + + + +class GroupOp(torch.autograd.Function): + """ group operation base class """ + + @classmethod + def forward(cls, ctx, group_id, *inputs): + ctx.group_id = group_id + ctx.save_for_backward(*inputs) + out = cls.forward_op(ctx.group_id, *inputs) + return out + + @classmethod + def backward(cls, ctx, grad): + error_str = "Backward operation not implemented for {}".format(cls) + assert cls.backward_op is not None, error_str + + inputs = ctx.saved_tensors + grad = grad.contiguous() + grad_inputs = cls.backward_op(ctx.group_id, grad, *inputs) + return (None, ) + tuple(grad_inputs) + + +class Exp(GroupOp): + """ exponential map """ + forward_op, backward_op = lietorch_backends.expm, lietorch_backends.expm_backward + +class Log(GroupOp): + """ logarithm map """ + forward_op, backward_op = lietorch_backends.logm, lietorch_backends.logm_backward + +class Inv(GroupOp): + """ group inverse """ + forward_op, backward_op = lietorch_backends.inv, lietorch_backends.inv_backward + +class Mul(GroupOp): + """ group multiplication """ + forward_op, backward_op = lietorch_backends.mul, lietorch_backends.mul_backward + +class Adj(GroupOp): + """ adjoint operator """ + forward_op, backward_op = lietorch_backends.adj, lietorch_backends.adj_backward + +class AdjT(GroupOp): + """ adjoint operator """ + forward_op, backward_op = lietorch_backends.adjT, lietorch_backends.adjT_backward + +class Act3(GroupOp): + """ action on point """ + forward_op, backward_op = lietorch_backends.act, lietorch_backends.act_backward + +class Act4(GroupOp): + """ action on point """ + forward_op, backward_op = lietorch_backends.act4, lietorch_backends.act4_backward + +class Jinv(GroupOp): + """ adjoint operator """ + forward_op, backward_op = lietorch_backends.Jinv, None + +class ToMatrix(GroupOp): + """ convert to matrix representation """ + forward_op, backward_op = lietorch_backends.as_matrix, None + + + + +### conversion operations to/from Euclidean embeddings ### + +class FromVec(torch.autograd.Function): + """ convert vector into group object """ + + @classmethod + def forward(cls, ctx, group_id, *inputs): + ctx.group_id = group_id + ctx.save_for_backward(*inputs) + return inputs[0] + + @classmethod + def backward(cls, ctx, grad): + inputs = ctx.saved_tensors + J = lietorch_backends.projector(ctx.group_id, *inputs) + return None, torch.matmul(grad.unsqueeze(-2), torch.linalg.pinv(J)).squeeze(-2) + +class ToVec(torch.autograd.Function): + """ convert group object to vector """ + + @classmethod + def forward(cls, ctx, group_id, *inputs): + ctx.group_id = group_id + ctx.save_for_backward(*inputs) + return inputs[0] + + @classmethod + def backward(cls, ctx, grad): + inputs = ctx.saved_tensors + J = lietorch_backends.projector(ctx.group_id, *inputs) + return None, torch.matmul(grad.unsqueeze(-2), J).squeeze(-2) + diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/groups.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/groups.py new file mode 100644 index 0000000000000000000000000000000000000000..7fed370de8be8b1b57484b87fb09bf0e68c53a38 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/groups.py @@ -0,0 +1,321 @@ +import torch +import numpy as np + +# group operations implemented in cuda +from .group_ops import Exp, Log, Inv, Mul, Adj, AdjT, Jinv, Act3, Act4, ToMatrix, ToVec, FromVec +from .broadcasting import broadcast_inputs + + +class LieGroupParameter(torch.Tensor): + """ Wrapper class for LieGroup """ + + from torch._C import _disabled_torch_function_impl + __torch_function__ = _disabled_torch_function_impl + + def __new__(cls, group, requires_grad=True): + data = torch.zeros(group.tangent_shape, + device=group.data.device, + dtype=group.data.dtype, + requires_grad=True) + + return torch.Tensor._make_subclass(cls, data, requires_grad) + + def __init__(self, group): + self.group = group + + def retr(self): + return self.group.retr(self) + + def log(self): + return self.retr().log() + + def inv(self): + return self.retr().inv() + + def adj(self, a): + return self.retr().adj(a) + + def __mul__(self, other): + if isinstance(other, LieGroupParameter): + return self.retr() * other.retr() + else: + return self.retr() * other + + def add_(self, update, alpha): + self.group = self.group.exp(alpha*update) * self.group + + def __getitem__(self, index): + return self.retr().__getitem__(index) + + +class LieGroup: + """ Base class for Lie Group """ + + def __init__(self, data): + self.data = data + + def __repr__(self): + return "{}: size={}, device={}, dtype={}".format( + self.group_name, self.shape, self.device, self.dtype) + + @property + def shape(self): + return self.data.shape[:-1] + + @property + def device(self): + return self.data.device + + @property + def dtype(self): + return self.data.dtype + + def vec(self): + return self.apply_op(ToVec, self.data) + + @property + def tangent_shape(self): + return self.data.shape[:-1] + (self.manifold_dim,) + + @classmethod + def Identity(cls, *batch_shape, **kwargs): + """ Construct identity element with batch shape """ + + if isinstance(batch_shape[0], tuple): + batch_shape = batch_shape[0] + + elif isinstance(batch_shape[0], list): + batch_shape = tuple(batch_shape[0]) + + numel = np.prod(batch_shape) + data = cls.id_elem.reshape(1,-1) + + if 'device' in kwargs: + data = data.to(kwargs['device']) + + if 'dtype' in kwargs: + data = data.type(kwargs['dtype']) + + data = data.repeat(numel, 1) + return cls(data).view(batch_shape) + + @classmethod + def IdentityLike(cls, G): + return cls.Identity(G.shape, device=G.data.device, dtype=G.data.dtype) + + @classmethod + def InitFromVec(cls, data): + return cls(cls.apply_op(FromVec, data)) + + @classmethod + def Random(cls, *batch_shape, sigma=1.0, **kwargs): + """ Construct random element with batch_shape by random sampling in tangent space""" + + if isinstance(batch_shape[0], tuple): + batch_shape = batch_shape[0] + + elif isinstance(batch_shape[0], list): + batch_shape = tuple(batch_shape[0]) + + tangent_shape = batch_shape + (cls.manifold_dim,) + xi = torch.randn(tangent_shape, **kwargs) + return cls.exp(sigma * xi) + + @classmethod + def apply_op(cls, op, x, y=None): + """ Apply group operator """ + inputs, out_shape = broadcast_inputs(x, y) + + data = op.apply(cls.group_id, *inputs) + return data.view(out_shape + (-1,)) + + @classmethod + def exp(cls, x): + """ exponential map: x -> X """ + return cls(cls.apply_op(Exp, x)) + + def quaternion(self): + """ extract quaternion """ + return self.apply_op(Quat, self.data) + + def log(self): + """ logarithm map """ + return self.apply_op(Log, self.data) + + def inv(self): + """ group inverse """ + return self.__class__(self.apply_op(Inv, self.data)) + + def mul(self, other): + """ group multiplication """ + return self.__class__(self.apply_op(Mul, self.data, other.data)) + + def retr(self, a): + """ retraction: Exp(a) * X """ + dX = self.__class__.apply_op(Exp, a) + return self.__class__(self.apply_op(Mul, dX, self.data)) + + def adj(self, a): + """ adjoint operator: b = A(X) * a """ + return self.apply_op(Adj, self.data, a) + + def adjT(self, a): + """ transposed adjoint operator: b = a * A(X) """ + return self.apply_op(AdjT, self.data, a) + + def Jinv(self, a): + return self.apply_op(Jinv, self.data, a) + + def act(self, p): + """ action on a point cloud """ + + # action on point + if p.shape[-1] == 3: + return self.apply_op(Act3, self.data, p) + + # action on homogeneous point + elif p.shape[-1] == 4: + return self.apply_op(Act4, self.data, p) + + def matrix(self): + """ convert element to 4x4 matrix """ + I = torch.eye(4, dtype=self.dtype, device=self.device) + I = I.view([1] * (len(self.data.shape) - 1) + [4, 4]) + return self.__class__(self.data[...,None,:]).act(I).transpose(-1,-2) + + def translation(self): + """ extract translation component """ + p = torch.as_tensor([0.0, 0.0, 0.0, 1.0], dtype=self.dtype, device=self.device) + p = p.view([1] * (len(self.data.shape) - 1) + [4,]) + return self.apply_op(Act4, self.data, p) + + def detach(self): + return self.__class__(self.data.detach()) + + def view(self, dims): + data_reshaped = self.data.view(dims + (self.embedded_dim,)) + return self.__class__(data_reshaped) + + def __mul__(self, other): + # group multiplication + if isinstance(other, LieGroup): + return self.mul(other) + + # action on point + elif isinstance(other, torch.Tensor): + return self.act(other) + + def __getitem__(self, index): + return self.__class__(self.data[index]) + + def __setitem__(self, index, item): + self.data[index] = item.data + + def to(self, *args, **kwargs): + return self.__class__(self.data.to(*args, **kwargs)) + + def cpu(self): + return self.__class__(self.data.cpu()) + + def cuda(self): + return self.__class__(self.data.cuda()) + + def float(self, device): + return self.__class__(self.data.float()) + + def double(self, device): + return self.__class__(self.data.double()) + + def unbind(self, dim=0): + return [self.__class__(x) for x in self.data.unbind(dim=dim)] + + +class SO3(LieGroup): + group_name = 'SO3' + group_id = 1 + manifold_dim = 3 + embedded_dim = 4 + + # unit quaternion + id_elem = torch.as_tensor([0.0, 0.0, 0.0, 1.0]) + + def __init__(self, data): + if isinstance(data, SE3): + data = data.data[..., 3:7] + + super(SO3, self).__init__(data) + + +class RxSO3(LieGroup): + group_name = 'RxSO3' + group_id = 2 + manifold_dim = 4 + embedded_dim = 5 + + # unit quaternion + id_elem = torch.as_tensor([0.0, 0.0, 0.0, 1.0, 1.0]) + + def __init__(self, data): + if isinstance(data, Sim3): + data = data.data[..., 3:8] + + super(RxSO3, self).__init__(data) + + +class SE3(LieGroup): + group_name = 'SE3' + group_id = 3 + manifold_dim = 6 + embedded_dim = 7 + + # translation, unit quaternion + id_elem = torch.as_tensor([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]) + + def __init__(self, data): + if isinstance(data, SO3): + translation = torch.zeros_like(data.data[...,:3]) + data = torch.cat([translation, data.data], -1) + + super(SE3, self).__init__(data) + + def scale(self, s): + t, q = self.data.split([3,4], -1) + t = t * s.unsqueeze(-1) + return SE3(torch.cat([t, q], dim=-1)) + + +class Sim3(LieGroup): + group_name = 'Sim3' + group_id = 4 + manifold_dim = 7 + embedded_dim = 8 + + # translation, unit quaternion, scale + id_elem = torch.as_tensor([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0]) + + def __init__(self, data): + + if isinstance(data, SO3): + scale = torch.ones_like(SO3.data[...,:1]) + translation = torch.zeros_like(SO3.data[...,:3]) + data = torch.cat([translation, SO3.data, scale], -1) + + elif isinstance(data, SE3): + scale = torch.ones_like(data.data[...,:1]) + data = torch.cat([data.data, scale], -1) + + elif isinstance(data, Sim3): + data = data.data + + super(Sim3, self).__init__(data) + + +def cat(group_list, dim): + """ Concatenate groups along dimension """ + data = torch.cat([X.data for X in group_list], dim=dim) + return group_list[0].__class__(data) + +def stack(group_list, dim): + """ Concatenate groups along dimension """ + data = torch.stack([X.data for X in group_list], dim=dim) + return group_list[0].__class__(data) diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/run_tests.py b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/run_tests.py new file mode 100644 index 0000000000000000000000000000000000000000..79a05cf8567e8fcc196ab436c351aeb900ec3400 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch/run_tests.py @@ -0,0 +1,302 @@ +import torch +import lietorch + +from lietorch import SO3, RxSO3, SE3, Sim3 +from gradcheck import gradcheck, get_analytical_jacobian + + +### forward tests ### + +def make_homogeneous(p): + return torch.cat([p, torch.ones_like(p[...,:1])], dim=-1) + +def matv(A, b): + return torch.matmul(A, b[...,None])[..., 0] + +def test_exp_log(Group, device='cuda'): + """ check Log(Exp(x)) == x """ + a = .2*torch.randn(2,3,4,5,6,7,Group.manifold_dim, device=device).double() + b = Group.exp(a).log() + assert torch.allclose(a,b,atol=1e-8), "should be identity" + print("\t-", Group, "Passed exp-log test") + +def test_inv(Group, device='cuda'): + """ check X * X^{-1} == 0 """ + X = Group.exp(.1*torch.randn(2,3,4,5,Group.manifold_dim, device=device).double()) + a = (X * X.inv()).log() + assert torch.allclose(a, torch.zeros_like(a), atol=1e-8), "should be 0" + print("\t-", Group, "Passed inv test") + +def test_adj(Group, device='cuda'): + """ check X * Exp(a) == Exp(Adj(X,a)) * X 0 """ + X = Group.exp(torch.randn(2,3,4,5, Group.manifold_dim, device=device).double()) + a = torch.randn(2,3,4,5, Group.manifold_dim, device=device).double() + + b = X.adj(a) + Y1 = X * Group.exp(a) + Y2 = Group.exp(b) * X + + c = (Y1 * Y2.inv()).log() + assert torch.allclose(c, torch.zeros_like(c), atol=1e-8), "should be 0" + print("\t-", Group, "Passed adj test") + + +def test_act(Group, device='cuda'): + X = Group.exp(torch.randn(1, Group.manifold_dim, device=device).double()) + p = torch.randn(1,3,device=device).double() + + p1 = X.act(p) + p2 = matv(X.matrix(), make_homogeneous(p)) + + assert torch.allclose(p1, p2[...,:3], atol=1e-8), "should be 0" + print("\t-", Group, "Passed act test") + + +### backward tests ### +def test_exp_log_grad(Group, device='cuda', tol=1e-8): + + D = Group.manifold_dim + + def fn(a): + return Group.exp(a).log() + + a = torch.zeros(1, Group.manifold_dim, requires_grad=True, device=device).double() + analytical, reentrant, correct_grad_sizes, correct_grad_types = \ + get_analytical_jacobian((a,), fn(a)) + + assert torch.allclose(analytical[0], torch.eye(D, device=device).double(), atol=tol) + + a = .2 * torch.randn(1, Group.manifold_dim, requires_grad=True, device=device).double() + analytical, reentrant, correct_grad_sizes, correct_grad_types = \ + get_analytical_jacobian((a,), fn(a)) + + assert torch.allclose(analytical[0], torch.eye(D, device=device).double(), atol=tol) + + print("\t-", Group, "Passed eye-grad test") + + +def test_inv_log_grad(Group, device='cuda', tol=1e-8): + + D = Group.manifold_dim + X = Group.exp(.2*torch.randn(1,D,device=device).double()) + + def fn(a): + return (Group.exp(a) * X).inv().log() + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + analytical, numerical = gradcheck(fn, [a], eps=1e-4) + + # assert torch.allclose(analytical[0], numerical[0], atol=tol) + if not torch.allclose(analytical[0], numerical[0], atol=tol): + print(analytical[0]) + print(numerical[0]) + + print("\t-", Group, "Passed inv-grad test") + + +def test_adj_grad(Group, device='cuda'): + D = Group.manifold_dim + X = Group.exp(.5*torch.randn(1,Group.manifold_dim, device=device).double()) + + def fn(a, b): + return (Group.exp(a) * X).adj(b) + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + b = torch.randn(1, D, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a, b], eps=1e-4) + assert torch.allclose(analytical[0], numerical[0], atol=1e-8) + assert torch.allclose(analytical[1], numerical[1], atol=1e-8) + + print("\t-", Group, "Passed adj-grad test") + + +def test_adjT_grad(Group, device='cuda'): + D = Group.manifold_dim + X = Group.exp(.5*torch.randn(1,Group.manifold_dim, device=device).double()) + + def fn(a, b): + return (Group.exp(a) * X).adjT(b) + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + b = torch.randn(1, D, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a, b], eps=1e-4) + + assert torch.allclose(analytical[0], numerical[0], atol=1e-8) + assert torch.allclose(analytical[1], numerical[1], atol=1e-8) + + print("\t-", Group, "Passed adjT-grad test") + + +def test_act_grad(Group, device='cuda'): + D = Group.manifold_dim + X = Group.exp(5*torch.randn(1,D, device=device).double()) + + def fn(a, b): + return (X*Group.exp(a)).act(b) + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + b = torch.randn(1, 3, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a, b], eps=1e-4) + + assert torch.allclose(analytical[0], numerical[0], atol=1e-8) + assert torch.allclose(analytical[1], numerical[1], atol=1e-8) + + print("\t-", Group, "Passed act-grad test") + + +def test_matrix_grad(Group, device='cuda'): + D = Group.manifold_dim + X = Group.exp(torch.randn(1, D, device=device).double()) + + def fn(a): + return (Group.exp(a) * X).matrix() + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + analytical, numerical = gradcheck(fn, [a], eps=1e-4) + assert torch.allclose(analytical[0], numerical[0], atol=1e-6) + + print("\t-", Group, "Passed matrix-grad test") + + +def extract_translation_grad(Group, device='cuda'): + """ prototype function """ + + D = Group.manifold_dim + X = Group.exp(5*torch.randn(1,D, device=device).double()) + + def fn(a): + return (Group.exp(a)*X).translation() + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a], eps=1e-4) + + assert torch.allclose(analytical[0], numerical[0], atol=1e-8) + print("\t-", Group, "Passed translation grad test") + + +def test_vec_grad(Group, device='cuda', tol=1e-6): + + D = Group.manifold_dim + X = Group.exp(5*torch.randn(1,D, device=device).double()) + + def fn(a): + return (Group.exp(a)*X).vec() + + a = torch.zeros(1, D, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a], eps=1e-4) + + assert torch.allclose(analytical[0], numerical[0], atol=tol) + print("\t-", Group, "Passed tovec grad test") + + +def test_fromvec_grad(Group, device='cuda', tol=1e-6): + + def fn(a): + if Group == SO3: + a = a / a.norm(dim=-1, keepdim=True) + + elif Group == RxSO3: + q, s = a.split([4, 1], dim=-1) + q = q / q.norm(dim=-1, keepdim=True) + a = torch.cat([q, s.exp()], dim=-1) + + elif Group == SE3: + t, q = a.split([3, 4], dim=-1) + q = q / q.norm(dim=-1, keepdim=True) + a = torch.cat([t, q], dim=-1) + + elif Group == Sim3: + t, q, s = a.split([3, 4, 1], dim=-1) + q = q / q.norm(dim=-1, keepdim=True) + a = torch.cat([t, q, s.exp()], dim=-1) + + return Group.InitFromVec(a).vec() + + D = Group.embedded_dim + a = torch.randn(1, 2, D, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a], eps=1e-4) + + assert torch.allclose(analytical[0], numerical[0], atol=tol) + print("\t-", Group, "Passed fromvec grad test") + + + +def scale(device='cuda'): + + def fn(a, s): + X = SE3.exp(a) + X.scale(s) + return X.log() + + s = torch.rand(1, requires_grad=True, device=device).double() + a = torch.randn(1, 6, requires_grad=True, device=device).double() + + analytical, numerical = gradcheck(fn, [a, s], eps=1e-3) + print(analytical[1]) + print(numerical[1]) + + + assert torch.allclose(analytical[0], numerical[0], atol=1e-8) + assert torch.allclose(analytical[1], numerical[1], atol=1e-8) + + print("\t-", "Passed se3-to-sim3 test") + + +if __name__ == '__main__': + + + print("Testing lietorch forward pass (CPU) ...") + for Group in [SO3, RxSO3, SE3, Sim3]: + test_exp_log(Group, device='cpu') + test_inv(Group, device='cpu') + test_adj(Group, device='cpu') + test_act(Group, device='cpu') + + print("Testing lietorch backward pass (CPU)...") + for Group in [SO3, RxSO3, SE3, Sim3]: + if Group == Sim3: + tol = 1e-3 + else: + tol = 1e-8 + + test_exp_log_grad(Group, device='cpu', tol=tol) + test_inv_log_grad(Group, device='cpu', tol=tol) + test_adj_grad(Group, device='cpu') + test_adjT_grad(Group, device='cpu') + test_act_grad(Group, device='cpu') + test_matrix_grad(Group, device='cpu') + extract_translation_grad(Group, device='cpu') + test_vec_grad(Group, device='cpu') + test_fromvec_grad(Group, device='cpu') + + print("Testing lietorch forward pass (GPU) ...") + for Group in [SO3, RxSO3, SE3, Sim3]: + test_exp_log(Group, device='cuda') + test_inv(Group, device='cuda') + test_adj(Group, device='cuda') + test_act(Group, device='cuda') + + print("Testing lietorch backward pass (GPU)...") + for Group in [SO3, RxSO3, SE3, Sim3]: + if Group == Sim3: + tol = 1e-3 + else: + tol = 1e-8 + + test_exp_log_grad(Group, device='cuda', tol=tol) + test_inv_log_grad(Group, device='cuda', tol=tol) + test_adj_grad(Group, device='cuda') + test_adjT_grad(Group, device='cuda') + test_act_grad(Group, device='cuda') + test_matrix_grad(Group, device='cuda') + extract_translation_grad(Group, device='cuda') + test_vec_grad(Group, device='cuda') + test_fromvec_grad(Group, device='cuda') + + diff --git a/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch_backends.cpython-310-x86_64-linux-gnu.so b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch_backends.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..44345fb301180c3dfb3520219aeff7d2f69b1999 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/lib.linux-x86_64-3.10/lietorch_backends.cpython-310-x86_64-linux-gnu.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2df6031d9476f91493e2d4058ad31d8b84d246358d3ec7726920fec4ad91ed75 +size 10597176 diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/altcorr_kernel.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/altcorr_kernel.o new file mode 100644 index 0000000000000000000000000000000000000000..82e13deaa7dc053cc46ccdaeb932354245a472c9 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/altcorr_kernel.o differ diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/correlation_kernels.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/correlation_kernels.o new file mode 100644 index 0000000000000000000000000000000000000000..912c0dc763dc2bd957e7fd3bb0a2be35a03110a8 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/correlation_kernels.o differ diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid.o new file mode 100644 index 0000000000000000000000000000000000000000..19e7f4ddde535c301c0e39daf98a627522955db0 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid.o differ diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid_kernels.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid_kernels.o new file mode 100644 index 0000000000000000000000000000000000000000..9318f5ed7147a73a050172d28273f22b1ebda159 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/src/droid_kernels.o @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0a8643d3884a569f4b296535af36d4a8bfa5584dfdcf88b4f7737a4a252023df +size 1288240 diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch.o new file mode 100644 index 0000000000000000000000000000000000000000..d1be61001b9162f9451341ed16bb41d6138e653f Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch.o differ diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_cpu.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_cpu.o new file mode 100644 index 0000000000000000000000000000000000000000..3cb92fcb8ee77cef76c872c78d3ddf4fe6817ba3 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_cpu.o differ diff --git a/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_gpu.o b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_gpu.o new file mode 100644 index 0000000000000000000000000000000000000000..d649beaf0c5ae86d6d34f603198d5be3bf85e8b1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/build/temp.linux-x86_64-3.10/thirdparty/lietorch/lietorch/src/lietorch_gpu.o @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:53482c79c008366f26a3d0ea05a0d30247db006d8a466f2f049a243264dcfe45 +size 10221200 diff --git a/slahmr/third-party/DROID-SLAM/calib/barn.txt b/slahmr/third-party/DROID-SLAM/calib/barn.txt new file mode 100644 index 0000000000000000000000000000000000000000..e095d388b20f1ff18046620f19e08260774a1636 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/calib/barn.txt @@ -0,0 +1 @@ +1161.545689 1161.545689 960.000000 540.000000 -0.025158 0.0 0.0 0.0 \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/calib/eth.txt b/slahmr/third-party/DROID-SLAM/calib/eth.txt new file mode 100644 index 0000000000000000000000000000000000000000..25ffe5e59b63165568cbfafd61451f94b460a096 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/calib/eth.txt @@ -0,0 +1 @@ +726.21081542969 726.21081542969 359.2048034668 202.47247314453 \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/calib/euroc.txt b/slahmr/third-party/DROID-SLAM/calib/euroc.txt new file mode 100644 index 0000000000000000000000000000000000000000..3d88c2a90516fe0c384b93e35c8213de168962c6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/calib/euroc.txt @@ -0,0 +1 @@ +458.654 457.296 367.215 248.375 -0.28340811 0.07395907 0.00019359 1.76187114e-05 \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/calib/tartan.txt b/slahmr/third-party/DROID-SLAM/calib/tartan.txt new file mode 100644 index 0000000000000000000000000000000000000000..1216bf09961db241430661c84e5c23f79dcf7096 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/calib/tartan.txt @@ -0,0 +1 @@ +320.0 320.0 320.0 240.0 \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/calib/tum3.txt b/slahmr/third-party/DROID-SLAM/calib/tum3.txt new file mode 100644 index 0000000000000000000000000000000000000000..8c15af136bd689a5f4eda58ec998eda7a3c14440 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/calib/tum3.txt @@ -0,0 +1 @@ +535.4 539.2 320.1 247.6 \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_01_easy.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_01_easy.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b19535dbe9e8967f5e5fa2835ef2f7a7134a77d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_01_easy.txt @@ -0,0 +1,3639 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403636580863555584.0000000000 4.6650211767 -1.8472146877 0.7812067206 0.4502123789 0.6912148472 0.4743667630 -0.307419945794 +1403636580913555456.0000000000 4.6629522096 -1.8453728663 0.8207579572 0.4591252838 0.6879037538 0.4717034923 -0.305758425422 +1403636580963555584.0000000000 4.6609846259 -1.8447596485 0.8600052598 0.4660445575 0.6843175905 0.4693424141 -0.306968409074 +1403636581013555456.0000000000 4.6596583694 -1.8446723346 0.8972069305 0.4713357532 0.6806165727 0.4677468540 -0.309542516151 +1403636581063555584.0000000000 4.6584695461 -1.8448832918 0.9323025417 0.4752778607 0.6776230401 0.4653955749 -0.313599951262 +1403636581113555456.0000000000 4.6567707371 -1.8438028560 0.9652596168 0.4796463782 0.6751678155 0.4622955238 -0.316813227926 +1403636581163555584.0000000000 4.6556223951 -1.8430375195 0.9955650996 0.4841999557 0.6731014856 0.4573074353 -0.321488262013 +1403636581213555456.0000000000 4.6551355257 -1.8415718393 1.0225625975 0.4891932100 0.6703409953 0.4529863730 -0.325785664578 +1403636581263555584.0000000000 4.6553100964 -1.8405548393 1.0461137821 0.4942368675 0.6673200214 0.4481619213 -0.33100574038 +1403636581313555456.0000000000 4.6569095013 -1.8399190938 1.0639175259 0.4993648206 0.6632089510 0.4461463972 -0.334278410279 +1403636581363555584.0000000000 4.6586259151 -1.8398263352 1.0738669267 0.5030624088 0.6608493236 0.4440118006 -0.336243818246 +1403636581413555456.0000000000 4.6607757299 -1.8391279976 1.0744901898 0.5056788647 0.6598235611 0.4441487866 -0.334146089982 +1403636581463555584.0000000000 4.6631142052 -1.8386877869 1.0659636925 0.5056610717 0.6600755252 0.4462786578 -0.33082101091 +1403636581513555456.0000000000 4.6656575418 -1.8384611738 1.0492260766 0.5036646983 0.6617892103 0.4492946439 -0.326329949369 +1403636581563555584.0000000000 4.6671015434 -1.8384954213 1.0261007203 0.4994425698 0.6655796249 0.4503608598 -0.323629384298 +1403636581613555456.0000000000 4.6685127859 -1.8387733808 0.9986153796 0.4942885324 0.6689230252 0.4523267921 -0.321902634829 +1403636581663555584.0000000000 4.6697485696 -1.8389791244 0.9680789477 0.4899133836 0.6721475922 0.4528350304 -0.321158724061 +1403636581713555456.0000000000 4.6714020867 -1.8384458341 0.9361128152 0.4878424601 0.6728077815 0.4555164101 -0.319130417483 +1403636581763555584.0000000000 4.6731657492 -1.8384989389 0.9033135722 0.4854743284 0.6740080915 0.4555485216 -0.320161386783 +1403636581813555456.0000000000 4.6759169156 -1.8397860467 0.8702705074 0.4830638064 0.6737530482 0.4575230503 -0.32152581156 +1403636581863555584.0000000000 4.6786374123 -1.8412498240 0.8369674237 0.4807839480 0.6747606350 0.4584005004 -0.321580257632 +1403636581913555456.0000000000 4.6789098604 -1.8380702615 0.8001037439 0.4760575121 0.6774496252 0.4593379990 -0.321620666457 +1403636581963555584.0000000000 4.6811060719 -1.8394680876 0.7678572354 0.4720695674 0.6817977012 0.4597941574 -0.317634303746 +1403636582013555456.0000000000 4.6827184977 -1.8407854533 0.7374569596 0.4669531920 0.6867695511 0.4605834784 -0.313313197384 +1403636582063555584.0000000000 4.6845440892 -1.8424677579 0.7100893352 0.4619379613 0.6910211345 0.4629213875 -0.307907292103 +1403636582113555456.0000000000 4.6864177192 -1.8444039956 0.6874845691 0.4561609730 0.6942993902 0.4664731512 -0.303757012541 +1403636582163555584.0000000000 4.6880835090 -1.8470605446 0.6715031647 0.4501768467 0.6971475546 0.4692614176 -0.301860589863 +1403636582213555456.0000000000 4.6891591032 -1.8492694573 0.6629683725 0.4455292949 0.6988377916 0.4723171530 -0.300076482574 +1403636582263555584.0000000000 4.6889563220 -1.8505991866 0.6629868294 0.4426625338 0.6999479389 0.4740794436 -0.298950573031 +1403636582313555456.0000000000 4.6875128361 -1.8515523631 0.6724144801 0.4412190252 0.6999608359 0.4750752271 -0.299473084755 +1403636582363555584.0000000000 4.6853306676 -1.8524845822 0.6904417901 0.4422588509 0.6989095844 0.4741915863 -0.301786085126 +1403636582413555456.0000000000 4.6828575878 -1.8532336282 0.7145279947 0.4465133834 0.6960274321 0.4722736895 -0.305170729931 +1403636582463555584.0000000000 4.6800233910 -1.8534587651 0.7424402375 0.4517663182 0.6928928083 0.4693560191 -0.30904963568 +1403636582513555456.0000000000 4.6769995062 -1.8528007494 0.7726710934 0.4575838376 0.6895306911 0.4678377566 -0.310309992018 +1403636582563555584.0000000000 4.6739380479 -1.8519962549 0.8046517355 0.4620053163 0.6877136221 0.4654997802 -0.311305342493 +1403636582613555456.0000000000 4.6713172136 -1.8505469065 0.8369736729 0.4661899190 0.6862379573 0.4645350754 -0.309760535102 +1403636582663555584.0000000000 4.6689739902 -1.8491169488 0.8698644611 0.4691330559 0.6859808668 0.4624915396 -0.308943363836 +1403636582713555456.0000000000 4.6669567150 -1.8475400173 0.9022681926 0.4710961986 0.6855959864 0.4606653507 -0.30953828463 +1403636582763555584.0000000000 4.6641369394 -1.8450330233 0.9350271380 0.4737627358 0.6856172229 0.4571780902 -0.310589902665 +1403636582813555456.0000000000 4.6612415428 -1.8419590174 0.9669980498 0.4776873060 0.6856278521 0.4522216783 -0.311808979778 +1403636582863555584.0000000000 4.6653702485 -1.8363505927 1.0041399424 0.4834769855 0.6850957447 0.4460955667 -0.312877884166 +1403636582913555456.0000000000 4.6641805171 -1.8331189909 1.0350233718 0.4895439457 0.6834682530 0.4399560652 -0.315684229999 +1403636582963555584.0000000000 4.6637638722 -1.8303675678 1.0625889369 0.4959597210 0.6801382405 0.4358630400 -0.318526826597 +1403636583013555456.0000000000 4.6639959243 -1.8285458661 1.0843242503 0.5021823857 0.6768995387 0.4317727617 -0.321235347017 +1403636583063555584.0000000000 4.6648170828 -1.8273142000 1.0986794807 0.5061262630 0.6737316664 0.4307271681 -0.323103627829 +1403636583113555456.0000000000 4.6654470081 -1.8261826713 1.1052410223 0.5084066605 0.6724466649 0.4301129087 -0.323018631324 +1403636583163555584.0000000000 4.6661069801 -1.8250725751 1.1027189760 0.5100860128 0.6720337484 0.4305561025 -0.320631163869 +1403636583213555456.0000000000 4.6666013839 -1.8247096993 1.0920801805 0.5101775382 0.6719095514 0.4320376564 -0.318747388683 +1403636583263555584.0000000000 4.6668634644 -1.8249769341 1.0744048486 0.5088293669 0.6722225028 0.4336299058 -0.318079686248 +1403636583313555456.0000000000 4.6666349144 -1.8250098419 1.0518366810 0.5070194545 0.6729730472 0.4347805994 -0.317811863932 +1403636583363555584.0000000000 4.6668029281 -1.8244978174 1.0244160706 0.5052845853 0.6735835375 0.4364386898 -0.317007848266 +1403636583413555456.0000000000 4.6672885335 -1.8241092349 0.9941015029 0.5024233379 0.6744031252 0.4378102114 -0.317920482255 +1403636583463555584.0000000000 4.6689841537 -1.8240200649 0.9608636054 0.4998679042 0.6743663623 0.4413905962 -0.317074800936 +1403636583513555456.0000000000 4.6703067821 -1.8240759622 0.9269100812 0.4972410854 0.6751430874 0.4436488596 -0.316399753402 +1403636583563555584.0000000000 4.6722037704 -1.8239806715 0.8920071943 0.4948060459 0.6762473714 0.4465779937 -0.313726895884 +1403636583613555456.0000000000 4.6732636189 -1.8238805333 0.8565259278 0.4926548717 0.6789277436 0.4483135698 -0.30880939034 +1403636583663555584.0000000000 4.6752087142 -1.8255498139 0.8220253431 0.4851658170 0.6826178392 0.4515209690 -0.307856834023 +1403636583713555456.0000000000 4.6764493059 -1.8232040641 0.7864114095 0.4759844081 0.6886564815 0.4534392572 -0.305914912558 +1403636583763555584.0000000000 4.6786366552 -1.8246669943 0.7559865394 0.4658695444 0.6949291473 0.4557504203 -0.303859510766 +1403636583813555456.0000000000 4.6809242484 -1.8259930800 0.7279563774 0.4577797685 0.7005852291 0.4574316187 -0.300623243508 +1403636583863555584.0000000000 4.6830458322 -1.8272134384 0.7025755972 0.4524292242 0.7040305696 0.4597177548 -0.297167192081 +1403636583913555456.0000000000 4.6855251521 -1.8281195739 0.6803458162 0.4501109680 0.7050454916 0.4631802370 -0.292873759971 +1403636583963555584.0000000000 4.6880728302 -1.8296851333 0.6629059159 0.4483426769 0.7044111762 0.4670810604 -0.290910676758 +1403636584013555456.0000000000 4.6902219140 -1.8320161297 0.6513369776 0.4466859126 0.7033166757 0.4699862637 -0.291427968986 +1403636584063555584.0000000000 4.6916948854 -1.8345220098 0.6463336748 0.4453099975 0.7016740826 0.4724190425 -0.293551930994 +1403636584113555456.0000000000 4.6918607229 -1.8361070450 0.6486878322 0.4439107379 0.7008058549 0.4736256936 -0.295792347624 +1403636584163555584.0000000000 4.6908446926 -1.8367976958 0.6583222756 0.4430081785 0.7000682159 0.4748158010 -0.296981820848 +1403636584213555456.0000000000 4.6889777125 -1.8366758613 0.6748990768 0.4431002416 0.6994101452 0.4755525928 -0.29721600917 +1403636584263555584.0000000000 4.6866021931 -1.8363575563 0.6969871283 0.4440428391 0.6987608564 0.4750926837 -0.298070737513 +1403636584313555456.0000000000 4.6837139879 -1.8357602929 0.7228081469 0.4456393630 0.6978102217 0.4744741210 -0.298899249085 +1403636584363555584.0000000000 4.6801901939 -1.8341942481 0.7519309042 0.4479319739 0.6967025718 0.4743605819 -0.298235664365 +1403636584413555456.0000000000 4.6760637521 -1.8313713890 0.7838519410 0.4521471385 0.6954956156 0.4741846913 -0.294953712322 +1403636584463555584.0000000000 4.6714600354 -1.8283532070 0.8177506288 0.4568685890 0.6938928378 0.4732049525 -0.293020297887 +1403636584513555456.0000000000 4.6668379937 -1.8259003161 0.8532490850 0.4615255360 0.6918373027 0.4712917763 -0.293665435305 +1403636584563555584.0000000000 4.6618533916 -1.8236463385 0.8896899896 0.4667655039 0.6898115461 0.4676187188 -0.296011366453 +1403636584613555456.0000000000 4.6568416420 -1.8214077035 0.9265069909 0.4736645233 0.6871386158 0.4628562927 -0.298741517615 +1403636584663555584.0000000000 4.6523076412 -1.8195301305 0.9621520884 0.4820276179 0.6842863300 0.4566016147 -0.301523729818 +1403636584713555456.0000000000 4.6489145088 -1.8183096693 0.9961487540 0.4908042037 0.6803424653 0.4511525478 -0.304477818735 +1403636584763555584.0000000000 4.6525036096 -1.8166405777 1.0340973124 0.4990939432 0.6771809676 0.4453446850 -0.30659302766 +1403636584813555456.0000000000 4.6515909950 -1.8163605710 1.0634597879 0.5053986819 0.6738785533 0.4414352014 -0.309184137264 +1403636584863555584.0000000000 4.6513760915 -1.8168893670 1.0886058076 0.5095288260 0.6720477406 0.4369287630 -0.31277062842 +1403636584913555456.0000000000 4.6518471565 -1.8179891609 1.1082838877 0.5119105860 0.6703709419 0.4343925575 -0.315995978054 +1403636584963555584.0000000000 4.6519556539 -1.8190238704 1.1206167439 0.5128476353 0.6709422637 0.4309292448 -0.317999634677 +1403636585013555456.0000000000 4.6516828441 -1.8191398689 1.1251993987 0.5129705162 0.6722676954 0.4292822415 -0.317228864343 +1403636585063555584.0000000000 4.6513861861 -1.8191915968 1.1220375000 0.5121904424 0.6742091061 0.4281709448 -0.315868127535 +1403636585113555456.0000000000 4.6510004787 -1.8192327659 1.1122594751 0.5105815009 0.6756291927 0.4285789214 -0.314883840622 +1403636585163555584.0000000000 4.6506428649 -1.8187672629 1.0961943748 0.5095224841 0.6780822333 0.4279188482 -0.312212719781 +1403636585213555456.0000000000 4.6503011901 -1.8176555914 1.0754269348 0.5087223016 0.6802987878 0.4279425484 -0.308642761923 +1403636585263555584.0000000000 4.6502647486 -1.8157203093 1.0510134723 0.5089165880 0.6813985318 0.4297244526 -0.303375744206 +1403636585313555456.0000000000 4.6504151953 -1.8137223477 1.0248494234 0.5089202249 0.6822685972 0.4314116089 -0.298987942471 +1403636585363555584.0000000000 4.6511899976 -1.8119147545 0.9972690536 0.5088115661 0.6820577213 0.4349718695 -0.294461419885 +1403636585413555456.0000000000 4.6518912110 -1.8105774675 0.9700667580 0.5072549248 0.6829156940 0.4374481896 -0.291475003248 +1403636585463555584.0000000000 4.6539702308 -1.8106399458 0.9432271776 0.5033301282 0.6832765043 0.4419151158 -0.290694050665 +1403636585513555456.0000000000 4.6570390131 -1.8114432298 0.9172675251 0.4989648481 0.6843453764 0.4459658513 -0.289516745038 +1403636585563555584.0000000000 4.6596565139 -1.8089960762 0.8908350399 0.4927810636 0.6847824984 0.4514672547 -0.290546160269 +1403636585613555456.0000000000 4.6655216091 -1.8112623344 0.8694285472 0.4855779594 0.6857208176 0.4565357582 -0.292533941794 +1403636585663555584.0000000000 4.6714178742 -1.8136417811 0.8518317050 0.4775005869 0.6877435286 0.4605467610 -0.29478587022 +1403636585713555456.0000000000 4.6778477371 -1.8167346017 0.8380386496 0.4687953561 0.6903170345 0.4641579515 -0.297070197077 +1403636585763555584.0000000000 4.6835295380 -1.8190340095 0.8280330012 0.4606025100 0.6938915761 0.4666767018 -0.297611599905 +1403636585813555456.0000000000 4.6890187011 -1.8218858198 0.8215145495 0.4517456824 0.6978372188 0.4686499068 -0.298858360018 +1403636585863555584.0000000000 4.6943946621 -1.8244561567 0.8178795983 0.4425492394 0.7022359594 0.4710053076 -0.298611500517 +1403636585913555456.0000000000 4.6993281037 -1.8268945198 0.8166444294 0.4338545190 0.7067633639 0.4731523331 -0.297292235768 +1403636585963555584.0000000000 4.7034842739 -1.8285060584 0.8162651209 0.4256271985 0.7124372098 0.4747634370 -0.293043322664 +1403636586013555456.0000000000 4.7065861324 -1.8295895707 0.8165071578 0.4177798263 0.7195056521 0.4753900368 -0.285964938893 +1403636586063555584.0000000000 4.7090442780 -1.8299897497 0.8169467747 0.4116981315 0.7269789708 0.4755500403 -0.275424007038 +1403636586113555456.0000000000 4.7109837893 -1.8314937514 0.8183447701 0.4061476518 0.7341370690 0.4744391002 -0.266447722875 +1403636586163555584.0000000000 4.7126469004 -1.8338590515 0.8204599966 0.4008796213 0.7404896955 0.4731409435 -0.259052480548 +1403636586213555456.0000000000 4.7148760456 -1.8370008843 0.8228286286 0.3948421782 0.7456146013 0.4728380473 -0.254131268501 +1403636586263555584.0000000000 4.7180969722 -1.8402173055 0.8248392724 0.3876990803 0.7501049370 0.4740964552 -0.249528671158 +1403636586313555456.0000000000 4.7217253199 -1.8429728235 0.8266929934 0.3797864590 0.7552838913 0.4745784866 -0.245119867093 +1403636586363555584.0000000000 4.7264149675 -1.8453593331 0.8280296877 0.3717215183 0.7602664663 0.4754879888 -0.240268985885 +1403636586413555456.0000000000 4.7315551107 -1.8476762787 0.8292004826 0.3632955508 0.7653962041 0.4758828922 -0.23605182993 +1403636586463555584.0000000000 4.7376047549 -1.8493863844 0.8299690782 0.3559766013 0.7688271433 0.4783408812 -0.231031349318 +1403636586513555456.0000000000 4.7436274893 -1.8500039870 0.8310796936 0.3496836676 0.7713520074 0.4810950648 -0.226461811055 +1403636586563555584.0000000000 4.7489406699 -1.8495423132 0.8328969621 0.3442502495 0.7728255974 0.4839240554 -0.223718283495 +1403636586613555456.0000000000 4.7531478303 -1.8475940208 0.8352072697 0.3408524234 0.7734462976 0.4858696795 -0.222555846256 +1403636586663555584.0000000000 4.7558890355 -1.8439621864 0.8377280404 0.3401650254 0.7739896418 0.4854777456 -0.222573916649 +1403636586713555456.0000000000 4.7577051072 -1.8396698827 0.8400314352 0.3416201363 0.7728831266 0.4852889042 -0.224593042008 +1403636586763555584.0000000000 4.7584996648 -1.8354887618 0.8416954725 0.3432075023 0.7713499160 0.4847282291 -0.228618593624 +1403636586813555456.0000000000 4.7584585267 -1.8305573568 0.8429445970 0.3455016627 0.7694334290 0.4844295621 -0.232225749499 +1403636586863555584.0000000000 4.7578824973 -1.8265586530 0.8430461638 0.3481874445 0.7674314294 0.4845733392 -0.23452757524 +1403636586913555456.0000000000 4.7567351010 -1.8241079353 0.8426152179 0.3503363930 0.7649684040 0.4861146409 -0.236178552253 +1403636586963555584.0000000000 4.7550759602 -1.8224303278 0.8422723406 0.3514481525 0.7629840399 0.4873674739 -0.23835372102 +1403636587013555456.0000000000 4.7530738720 -1.8205942346 0.8422103039 0.3521605810 0.7605111731 0.4902579723 -0.239275576292 +1403636587063555584.0000000000 4.7510119171 -1.8190298553 0.8421867146 0.3514025669 0.7597607016 0.4919317578 -0.239338793458 +1403636587113555456.0000000000 4.7491116635 -1.8168321332 0.8423070713 0.3497359580 0.7592773918 0.4945150296 -0.237986317599 +1403636587163555584.0000000000 4.7475883481 -1.8135587879 0.8419777677 0.3482283854 0.7592764119 0.4963870299 -0.236296928661 +1403636587213555456.0000000000 4.7463112024 -1.8090096242 0.8417106568 0.3468751072 0.7593277210 0.4974254120 -0.235938618336 +1403636587263555584.0000000000 4.7453167642 -1.8028301048 0.8412297611 0.3460923814 0.7600734511 0.4970699408 -0.235435525131 +1403636587313555456.0000000000 4.7446476217 -1.7947835778 0.8407569168 0.3455707014 0.7609522120 0.4962291516 -0.235136663301 +1403636587363555584.0000000000 4.7443405282 -1.7847863735 0.8403218392 0.3452134783 0.7620613973 0.4951757373 -0.234288434126 +1403636587413555456.0000000000 4.7445378063 -1.7733340651 0.8399805614 0.3446315529 0.7632595367 0.4940203525 -0.233683255014 +1403636587463555584.0000000000 4.7456917159 -1.7604937879 0.8396706039 0.3435018344 0.7648740152 0.4924440615 -0.233394680479 +1403636587513555456.0000000000 4.7477660688 -1.7462569108 0.8395622392 0.3422783833 0.7664556596 0.4908735618 -0.233311758018 +1403636587563555584.0000000000 4.7508131006 -1.7305946001 0.8395723038 0.3415782636 0.7677661090 0.4893586340 -0.233211533032 +1403636587613555456.0000000000 4.7540624486 -1.7135179557 0.8398714950 0.3421310537 0.7690824477 0.4870127492 -0.232974489629 +1403636587663555584.0000000000 4.7574207178 -1.6955372677 0.8406219479 0.3440929278 0.7698874848 0.4840781077 -0.233541652603 +1403636587713555456.0000000000 4.7605786877 -1.6766215509 0.8417113848 0.3471651751 0.7706559336 0.4802666798 -0.234328166254 +1403636587763555584.0000000000 4.7638285412 -1.6576357947 0.8429028634 0.3505226985 0.7716270534 0.4757617019 -0.235321760963 +1403636587813555456.0000000000 4.7674884349 -1.6387311953 0.8435518674 0.3536141351 0.7726676353 0.4719018638 -0.235054035902 +1403636587863555584.0000000000 4.7715497460 -1.6202338642 0.8433813290 0.3550658974 0.7743131786 0.4685209643 -0.234212330928 +1403636587913555456.0000000000 4.7761071969 -1.6025125556 0.8421281731 0.3551598200 0.7762995432 0.4663335769 -0.231848046262 +1403636587963555584.0000000000 4.7809546733 -1.5855564437 0.8401033114 0.3540669140 0.7792985862 0.4644360902 -0.227221152458 +1403636588013555456.0000000000 4.7859073871 -1.5695677517 0.8377432281 0.3521334752 0.7827247992 0.4631933468 -0.22089777696 +1403636588063555584.0000000000 4.7901350152 -1.5551825669 0.8351697747 0.3495298414 0.7863842787 0.4610102164 -0.216560006829 +1403636588113555456.0000000000 4.7939409087 -1.5428546361 0.8325896612 0.3469799047 0.7883446561 0.4604592656 -0.214697260513 +1403636588163555584.0000000000 4.7974896458 -1.5318369422 0.8300698883 0.3459545552 0.7889869057 0.4609082232 -0.213022811502 +1403636588213555456.0000000000 4.8003105905 -1.5227593932 0.8277060855 0.3454976473 0.7888808076 0.4613381439 -0.213226555786 +1403636588263555584.0000000000 4.8023183677 -1.5157529310 0.8257453613 0.3457184162 0.7885322490 0.4612105909 -0.214430547592 +1403636588313555456.0000000000 4.8035735536 -1.5109040302 0.8243949507 0.3461829938 0.7880095020 0.4607025370 -0.216683021973 +1403636588363555584.0000000000 4.8044289687 -1.5081916164 0.8232321834 0.3467232883 0.7870751209 0.4607712174 -0.219056158647 +1403636588413555456.0000000000 4.8049455602 -1.5076406879 0.8223916205 0.3472667827 0.7869306377 0.4597322255 -0.220889641848 +1403636588463555584.0000000000 4.8049884994 -1.5089909839 0.8218451380 0.3474363479 0.7870523005 0.4591107734 -0.221481281736 +1403636588513555456.0000000000 4.8049498711 -1.5120692044 0.8220159868 0.3481366995 0.7873002306 0.4590950389 -0.219524328279 +1403636588563555584.0000000000 4.8041627372 -1.5172627608 0.8233462880 0.3489303818 0.7872560003 0.4590802674 -0.218451108436 +1403636588613555456.0000000000 4.8028727345 -1.5249997312 0.8253557679 0.3491683479 0.7871204764 0.4589704416 -0.218789748706 +1403636588663555584.0000000000 4.8013396082 -1.5347174991 0.8275065820 0.3493042577 0.7865586623 0.4595161198 -0.219446899987 +1403636588713555456.0000000000 4.7997567933 -1.5467168693 0.8288361341 0.3479283270 0.7863475610 0.4602670446 -0.220811322667 +1403636588763555584.0000000000 4.7979965020 -1.5600724199 0.8294046699 0.3461914446 0.7855602373 0.4626992353 -0.221260061568 +1403636588813555456.0000000000 4.7955148294 -1.5746774243 0.8297162606 0.3443070002 0.7851342534 0.4646239695 -0.221678733178 +1403636588863555584.0000000000 4.7921442500 -1.5908513052 0.8299138420 0.3427341695 0.7846385385 0.4660879547 -0.222795133292 +1403636588913555456.0000000000 4.7881713556 -1.6087257249 0.8307052896 0.3416512571 0.7837157499 0.4674878159 -0.224764729928 +1403636588963555584.0000000000 4.7840572809 -1.6277942478 0.8320276616 0.3413826710 0.7822167620 0.4693180256 -0.226573166988 +1403636589013555456.0000000000 4.7797551436 -1.6479092732 0.8339192838 0.3418921369 0.7802110011 0.4710770341 -0.229056736267 +1403636589063555584.0000000000 4.7753651255 -1.6690392400 0.8364197160 0.3429152997 0.7777733626 0.4729017549 -0.232037979435 +1403636589113555456.0000000000 4.7707166218 -1.6905054192 0.8392234960 0.3443340335 0.7750139977 0.4751224329 -0.234618947609 +1403636589163555584.0000000000 4.7654678661 -1.7125016326 0.8423898498 0.3455908031 0.7729639316 0.4763620973 -0.237008247776 +1403636589213555456.0000000000 4.7599001703 -1.7352075788 0.8454893617 0.3459768803 0.7714522679 0.4776571807 -0.238757228852 +1403636589263555584.0000000000 4.7543559135 -1.7584695243 0.8479939057 0.3453021119 0.7703959083 0.4794168722 -0.239616482343 +1403636589313555456.0000000000 4.7488313013 -1.7819333445 0.8497698640 0.3437769170 0.7691084243 0.4824127352 -0.239932523549 +1403636589363555584.0000000000 4.7431729102 -1.8058054022 0.8505887302 0.3413806940 0.7684371170 0.4851321405 -0.240021718232 +1403636589413555456.0000000000 4.7372869246 -1.8291327636 0.8510235217 0.3397116757 0.7673445853 0.4882345674 -0.239593973281 +1403636589463555584.0000000000 4.7313202372 -1.8522555895 0.8513019022 0.3395284258 0.7661858152 0.4903016982 -0.239340739099 +1403636589513555456.0000000000 4.7252038469 -1.8756346388 0.8512711040 0.3398586519 0.7652381581 0.4910565591 -0.240354142492 +1403636589563555584.0000000000 4.7192969066 -1.8991976327 0.8512545720 0.3401500736 0.7640218185 0.4918624151 -0.242156876461 +1403636589613555456.0000000000 4.7133701468 -1.9223268063 0.8509610971 0.3410354383 0.7626654886 0.4928651210 -0.243146364976 +1403636589663555584.0000000000 4.7075078683 -1.9453384153 0.8506575803 0.3416563391 0.7612578099 0.4939957134 -0.244388477707 +1403636589713555456.0000000000 4.7019129612 -1.9681060183 0.8501632065 0.3418041623 0.7601968692 0.4950607715 -0.24532726545 +1403636589763555584.0000000000 4.6964483738 -1.9906131216 0.8490846544 0.3400522715 0.7590841245 0.4969582986 -0.247362474985 +1403636589813555456.0000000000 4.6914986044 -2.0119008104 0.8474656337 0.3370377257 0.7580756652 0.4998927581 -0.248664608978 +1403636589863555584.0000000000 4.6871413950 -2.0315932342 0.8454034911 0.3331518913 0.7573721347 0.5033389317 -0.249092727314 +1403636589913555456.0000000000 4.6830814481 -2.0497554569 0.8431293516 0.3290731235 0.7566236810 0.5066815447 -0.250010593881 +1403636589963555584.0000000000 4.6793020940 -2.0664974687 0.8411348214 0.3253692166 0.7558338939 0.5090581087 -0.252408081792 +1403636590013555456.0000000000 4.6758580526 -2.0815914201 0.8395818704 0.3235960746 0.7541796534 0.5109795140 -0.255731435746 +1403636590063555584.0000000000 4.6727460747 -2.0941126360 0.8393601866 0.3242607991 0.7519972115 0.5120989549 -0.25905557027 +1403636590113555456.0000000000 4.6702240535 -2.1043635999 0.8396018943 0.3256924275 0.7496127680 0.5128082122 -0.26274108574 +1403636590163555584.0000000000 4.6684665841 -2.1118275356 0.8404063538 0.3268679606 0.7475747727 0.5130488737 -0.266589851135 +1403636590213555456.0000000000 4.6679247438 -2.1160599839 0.8413290603 0.3281320038 0.7461431715 0.5134049112 -0.268356391341 +1403636590263555584.0000000000 4.6686342322 -2.1172292147 0.8421886513 0.3289345834 0.7454550204 0.5139064550 -0.268326308784 +1403636590313555456.0000000000 4.6706060580 -2.1154571054 0.8430208154 0.3291244564 0.7454695788 0.5146192970 -0.266681792655 +1403636590363555584.0000000000 4.6735435774 -2.1107657346 0.8438248855 0.3294392575 0.7465146670 0.5140731928 -0.264413275111 +1403636590413555456.0000000000 4.6776477245 -2.1031678525 0.8447008489 0.3303351527 0.7473671028 0.5135193069 -0.261952327528 +1403636590463555584.0000000000 4.6823357763 -2.0925531482 0.8458037808 0.3323947984 0.7485165334 0.5118629116 -0.259293380015 +1403636590513555456.0000000000 4.6879548842 -2.0796935281 0.8473214212 0.3351442992 0.7489249610 0.5105330331 -0.257188109271 +1403636590563555584.0000000000 4.6940305695 -2.0647190861 0.8488526245 0.3382938706 0.7493527911 0.5088750983 -0.255095640676 +1403636590613555456.0000000000 4.7005423887 -2.0482001941 0.8504590613 0.3408769167 0.7496959123 0.5072905575 -0.253801609473 +1403636590663555584.0000000000 4.7070899847 -2.0302202493 0.8515405866 0.3430142226 0.7506476546 0.5053226471 -0.252028498359 +1403636590713555456.0000000000 4.7138344811 -2.0111221807 0.8521930946 0.3440696872 0.7519263433 0.5037170330 -0.249983950167 +1403636590763555584.0000000000 4.7204115577 -1.9909448082 0.8521838723 0.3437615503 0.7541412468 0.5016788964 -0.247825062022 +1403636590813555456.0000000000 4.7269833116 -1.9701599448 0.8516531930 0.3415017658 0.7562903250 0.5005710782 -0.246637555791 +1403636590863555584.0000000000 4.7334582645 -1.9483136461 0.8505312816 0.3390021481 0.7587777867 0.4992459934 -0.245127011976 +1403636590913555456.0000000000 4.7399492419 -1.9255651421 0.8493804814 0.3372037561 0.7607196898 0.4984041816 -0.243294990097 +1403636590963555584.0000000000 4.7464487749 -1.9023273464 0.8480242972 0.3368774538 0.7618719487 0.4976608866 -0.241657519723 +1403636591013555456.0000000000 4.7524687676 -1.8791621561 0.8466576861 0.3368824654 0.7621368701 0.4973073012 -0.241543047803 +1403636591063555584.0000000000 4.7580921190 -1.8566201566 0.8455438929 0.3368633044 0.7619326147 0.4969655395 -0.242913682888 +1403636591113555456.0000000000 4.7632994502 -1.8342652596 0.8447768437 0.3366467210 0.7618408182 0.4966395740 -0.244165285159 +1403636591163555584.0000000000 4.7681349660 -1.8126848956 0.8439912894 0.3361452511 0.7626493906 0.4954139357 -0.244820974358 +1403636591213555456.0000000000 4.7726068559 -1.7918720401 0.8430217296 0.3354661626 0.7635368515 0.4946564984 -0.244517644992 +1403636591263555584.0000000000 4.7768136263 -1.7723244195 0.8412935093 0.3346668353 0.7647730393 0.4937966806 -0.243485412183 +1403636591313555456.0000000000 4.7804912757 -1.7543826935 0.8389357170 0.3341694325 0.7660943386 0.4929436501 -0.241737073396 +1403636591363555584.0000000000 4.7836043364 -1.7386222818 0.8360897169 0.3338791529 0.7677665102 0.4914869930 -0.239791227254 +1403636591413555456.0000000000 4.7859225789 -1.7251636771 0.8326651620 0.3339898378 0.7691785324 0.4898258208 -0.238507523521 +1403636591463555584.0000000000 4.7871977869 -1.7136998588 0.8287076702 0.3339233825 0.7703503672 0.4881014611 -0.238353624041 +1403636591513555456.0000000000 4.7876629575 -1.7029213966 0.8245774257 0.3359151199 0.7708511729 0.4866152356 -0.236970702698 +1403636591563555584.0000000000 4.7869408391 -1.6927615709 0.8203660689 0.3411000161 0.7717997595 0.4823907331 -0.235106552135 +1403636591613555456.0000000000 4.7850710618 -1.6833601847 0.8162035550 0.3490361004 0.7726953037 0.4761710195 -0.233188611516 +1403636591663555584.0000000000 4.7824380097 -1.6756786015 0.8127739948 0.3589114800 0.7718437391 0.4700637450 -0.233409227532 +1403636591713555456.0000000000 4.7798052135 -1.6698702366 0.8101889772 0.3694591934 0.7695358289 0.4650829613 -0.234547120209 +1403636591763555584.0000000000 4.7770767156 -1.6647931150 0.8088478593 0.3801603528 0.7669861016 0.4602422405 -0.235345503921 +1403636591813555456.0000000000 4.7740880248 -1.6599454219 0.8086649063 0.3908352831 0.7646857142 0.4545533178 -0.236399706395 +1403636591863555584.0000000000 4.7714344318 -1.6558985047 0.8089574150 0.3993565219 0.7630300797 0.4493477478 -0.237457506389 +1403636591913555456.0000000000 4.7687261108 -1.6515643632 0.8095493640 0.4050129363 0.7629791753 0.4444044159 -0.23734366352 +1403636591963555584.0000000000 4.7661345485 -1.6472811918 0.8098285185 0.4057523693 0.7655028102 0.4398975615 -0.236348466661 +1403636592013555456.0000000000 4.7629917589 -1.6411997725 0.8097257265 0.4038065067 0.7694486067 0.4365123725 -0.23312249022 +1403636592063555584.0000000000 4.7583776976 -1.6331986621 0.8092288308 0.4019354176 0.7741046495 0.4318940894 -0.229515592735 +1403636592113555456.0000000000 4.7527302135 -1.6239376150 0.8083801399 0.4000626087 0.7785308781 0.4275606871 -0.225901394003 +1403636592163555584.0000000000 4.7461987541 -1.6138200479 0.8072981311 0.3976897518 0.7829489679 0.4236103144 -0.222234282882 +1403636592213555456.0000000000 4.7390292262 -1.6035596005 0.8060268666 0.3946803647 0.7866888571 0.4213893959 -0.218584145871 +1403636592263555584.0000000000 4.7308101897 -1.5935966209 0.8050252847 0.3915656074 0.7894479064 0.4206791214 -0.215586305095 +1403636592313555456.0000000000 4.7213498754 -1.5846030313 0.8042990035 0.3881487485 0.7912255523 0.4212991562 -0.214031996234 +1403636592363555584.0000000000 4.7097299869 -1.5768854694 0.8038933731 0.3839119692 0.7930532428 0.4213402099 -0.214826863929 +1403636592413555456.0000000000 4.6966546147 -1.5709030270 0.8039499493 0.3799568233 0.7930835620 0.4239163959 -0.216670638129 +1403636592463555584.0000000000 4.6815491783 -1.5666388845 0.8045032425 0.3776620832 0.7915445494 0.4271059377 -0.220020670138 +1403636592513555456.0000000000 4.6650349469 -1.5644524706 0.8054925437 0.3773674631 0.7877598718 0.4315804826 -0.225314156725 +1403636592563555584.0000000000 4.6474890994 -1.5644492382 0.8063014029 0.3788015680 0.7825429724 0.4366122903 -0.231312724316 +1403636592613555456.0000000000 4.6291730460 -1.5666147784 0.8067428039 0.3805310158 0.7762107023 0.4429017596 -0.23776274519 +1403636592663555584.0000000000 4.6105931194 -1.5710328014 0.8064470579 0.3818688515 0.7699885123 0.4497376706 -0.242960693853 +1403636592713555456.0000000000 4.5920816671 -1.5780832550 0.8062099706 0.3814146575 0.7641671250 0.4571009768 -0.248254226673 +1403636592763555584.0000000000 4.5741769819 -1.5885630571 0.8057611235 0.3786479243 0.7583267032 0.4657221977 -0.254301386423 +1403636592813555456.0000000000 4.5570980841 -1.6027212719 0.8057368262 0.3738582104 0.7526678581 0.4747139181 -0.261472426539 +1403636592863555584.0000000000 4.5417636608 -1.6210738202 0.8050294324 0.3668101216 0.7471132297 0.4844081616 -0.269482633092 +1403636592913555456.0000000000 4.5285871811 -1.6427167964 0.8038901316 0.3594348249 0.7415777435 0.4945029911 -0.276289429284 +1403636592963555584.0000000000 4.5180296435 -1.6676968784 0.8031655251 0.3518132462 0.7361559071 0.5043618674 -0.282703072272 +1403636593013555456.0000000000 4.5107419585 -1.6962029704 0.8025571633 0.3440283121 0.7302957890 0.5144158382 -0.28929038421 +1403636593063555584.0000000000 4.5062370641 -1.7271022165 0.8024841614 0.3369055728 0.7242880708 0.5241853852 -0.295179788353 +1403636593113555456.0000000000 4.5051370686 -1.7595824328 0.8027441095 0.3312077120 0.7175805626 0.5340250046 -0.300327957829 +1403636593163555584.0000000000 4.5074224034 -1.7937948740 0.8038072324 0.3247071812 0.7118188113 0.5416774007 -0.307351297108 +1403636593213555456.0000000000 4.5122724580 -1.8281423911 0.8056972066 0.3185986450 0.7074561457 0.5468730895 -0.314532238916 +1403636593263555584.0000000000 4.5204919200 -1.8620667406 0.8078788928 0.3118930717 0.7036429667 0.5510986312 -0.322334586972 +1403636593313555456.0000000000 4.5313092892 -1.8934092104 0.8096830434 0.3063518089 0.7011621248 0.5549440728 -0.326431187291 +1403636593363555584.0000000000 4.5449803061 -1.9213287294 0.8105821638 0.3026967955 0.6994614551 0.5584048709 -0.327585596415 +1403636593413555456.0000000000 4.5612901390 -1.9457003594 0.8105210704 0.3001282996 0.6988421575 0.5604241829 -0.327822174306 +1403636593463555584.0000000000 4.5800874198 -1.9654016168 0.8094285641 0.2996677342 0.6988335422 0.5617504182 -0.325986804998 +1403636593513555456.0000000000 4.6008204976 -1.9808813153 0.8074544749 0.3001493370 0.7010467609 0.5604332715 -0.323045449855 +1403636593563555584.0000000000 4.6227026011 -1.9925036361 0.8050550940 0.2996571944 0.7046390940 0.5577373072 -0.320341082544 +1403636593613555456.0000000000 4.6454805325 -1.9999243363 0.8019040360 0.2987069332 0.7101411755 0.5535577439 -0.316302866114 +1403636593663555584.0000000000 4.6688277608 -2.0033993661 0.7987307572 0.2969339180 0.7171059006 0.5478565329 -0.312157964827 +1403636593713555456.0000000000 4.6926886604 -2.0025222776 0.7951515153 0.2966532173 0.7251295011 0.5410937216 -0.305616851138 +1403636593763555584.0000000000 4.7161043171 -1.9973961831 0.7918563205 0.2982590768 0.7345396602 0.5315194948 -0.298295218508 +1403636593813555456.0000000000 4.7387520135 -1.9876737329 0.7890007325 0.3029021928 0.7440212790 0.5199925898 -0.290327925879 +1403636593863555584.0000000000 4.7604676582 -1.9746355485 0.7869630077 0.3102185001 0.7535392485 0.5057519461 -0.283121974127 +1403636593913555456.0000000000 4.7806380295 -1.9582612030 0.7859340459 0.3198183286 0.7623086407 0.4903063799 -0.276046059218 +1403636593963555584.0000000000 4.7995886731 -1.9390944066 0.7854697939 0.3308205249 0.7702916180 0.4744559940 -0.268514642658 +1403636594013555456.0000000000 4.8169717055 -1.9174665481 0.7856712704 0.3419420415 0.7774920759 0.4591612142 -0.260293471927 +1403636594063555584.0000000000 4.8321556968 -1.8937177246 0.7860895418 0.3519064025 0.7847264810 0.4441236597 -0.251237753416 +1403636594113555456.0000000000 4.8446011363 -1.8684513844 0.7865152378 0.3592370771 0.7918096812 0.4301993915 -0.242723370638 +1403636594163555584.0000000000 4.8537941714 -1.8412857086 0.7863612166 0.3642885822 0.7988611627 0.4175715611 -0.23398432206 +1403636594213555456.0000000000 4.8597488282 -1.8124985247 0.7855689184 0.3681700560 0.8046364982 0.4077076357 -0.225356161245 +1403636594263555584.0000000000 4.8621204035 -1.7821695553 0.7842658997 0.3715740674 0.8091404072 0.3999511864 -0.217401845487 +1403636594313555456.0000000000 4.8609515874 -1.7505268802 0.7830390339 0.3748997233 0.8120270308 0.3947752690 -0.21027312165 +1403636594363555584.0000000000 4.8563482567 -1.7180246594 0.7817171859 0.3787913645 0.8137034441 0.3908877053 -0.203986786714 +1403636594413555456.0000000000 4.8482621722 -1.6849214355 0.7807462137 0.3838286950 0.8135897285 0.3884194652 -0.199693779518 +1403636594463555584.0000000000 4.8373677926 -1.6525075407 0.7797515942 0.3898527510 0.8117686905 0.3875338846 -0.197139326242 +1403636594513555456.0000000000 4.8238787693 -1.6217267731 0.7789731072 0.3958723045 0.8089049646 0.3874927598 -0.19699552745 +1403636594563555584.0000000000 4.8074061461 -1.5945646221 0.7787025538 0.4005880949 0.8068604365 0.3855890657 -0.19956574532 +1403636594613555456.0000000000 4.7891721508 -1.5717682741 0.7784316228 0.4036758242 0.8049374020 0.3847563557 -0.202692265627 +1403636594663555584.0000000000 4.7691339566 -1.5549168154 0.7783973288 0.4054991513 0.8036488860 0.3836595687 -0.206214067589 +1403636594713555456.0000000000 4.7478245140 -1.5444706424 0.7780560732 0.4063912687 0.8015084842 0.3854446503 -0.209434257072 +1403636594763555584.0000000000 4.7253906361 -1.5409260240 0.7771418212 0.4060465331 0.7984682756 0.3894736298 -0.214207650258 +1403636594813555456.0000000000 4.7019042185 -1.5443846014 0.7754365893 0.4050821689 0.7935922724 0.3969188293 -0.220397786991 +1403636594863555584.0000000000 4.6777527253 -1.5547124993 0.7736433277 0.4037886093 0.7878767121 0.4056598931 -0.227255575581 +1403636594913555456.0000000000 4.6539969519 -1.5721225021 0.7719341352 0.4025344894 0.7802776839 0.4172094006 -0.234667929045 +1403636594963555584.0000000000 4.6310839858 -1.5959316687 0.7704119126 0.4001254581 0.7715646396 0.4307999380 -0.242897176246 +1403636595013555456.0000000000 4.6106436806 -1.6261585567 0.7694813190 0.3951562682 0.7621679860 0.4453176715 -0.254251167596 +1403636595063555584.0000000000 4.5929550469 -1.6604745924 0.7683136977 0.3888882761 0.7526206469 0.4610589035 -0.264107474474 +1403636595113555456.0000000000 4.5780810793 -1.6975031330 0.7668994531 0.3806768121 0.7439505790 0.4761140345 -0.273748291252 +1403636595163555584.0000000000 4.5661362165 -1.7349900096 0.7656129745 0.3721267320 0.7359237291 0.4900364045 -0.282492977757 +1403636595213555456.0000000000 4.5578485580 -1.7724770000 0.7647700631 0.3626688399 0.7287919367 0.5022739671 -0.291641025174 +1403636595263555584.0000000000 4.5535165417 -1.8078835197 0.7640233797 0.3538635871 0.7217192282 0.5137281338 -0.299975535587 +1403636595313555456.0000000000 4.5535423527 -1.8403252456 0.7632688223 0.3459580163 0.7154788778 0.5237784718 -0.306690624054 +1403636595363555584.0000000000 4.5576744852 -1.8685700710 0.7626902237 0.3402668524 0.7100811737 0.5320434656 -0.311340563747 +1403636595413555456.0000000000 4.5652762054 -1.8914598282 0.7623060338 0.3359190845 0.7067927934 0.5371009167 -0.314841104631 +1403636595463555584.0000000000 4.5765292204 -1.9083836667 0.7620722586 0.3327639439 0.7044298307 0.5410369493 -0.316742467538 +1403636595513555456.0000000000 4.5907220285 -1.9188035221 0.7615660325 0.3299896387 0.7042280375 0.5426668028 -0.317304980475 +1403636595563555584.0000000000 4.6082229645 -1.9230428172 0.7606451177 0.3276592119 0.7036100892 0.5452891262 -0.316594459871 +1403636595613555456.0000000000 4.6277376883 -1.9210150091 0.7593785522 0.3264340955 0.7046940686 0.5457670273 -0.31461945743 +1403636595663555584.0000000000 4.6490635716 -1.9134716096 0.7573018261 0.3268299334 0.7066845055 0.5451660627 -0.310762237769 +1403636595713555456.0000000000 4.6710363170 -1.9011367998 0.7548533207 0.3290153054 0.7105055026 0.5416225859 -0.30590167376 +1403636595763555584.0000000000 4.6932435929 -1.8835662082 0.7519915717 0.3338148131 0.7144901068 0.5374834950 -0.298635313327 +1403636595813555456.0000000000 4.7154233917 -1.8631187811 0.7484574557 0.3405444935 0.7204212766 0.5301850308 -0.289700647689 +1403636595863555584.0000000000 4.7376307386 -1.8412214086 0.7445289751 0.3476045365 0.7266911714 0.5219872624 -0.280393162307 +1403636595913555456.0000000000 4.7577238099 -1.8174984859 0.7412019774 0.3535139528 0.7343340326 0.5119153974 -0.27152171125 +1403636595963555584.0000000000 4.7787964881 -1.7957527572 0.7381714151 0.3584695735 0.7420841731 0.5020043913 -0.262301803279 +1403636596013555456.0000000000 4.8001091760 -1.7767532536 0.7355964222 0.3623926392 0.7498018396 0.4927505050 -0.252320661519 +1403636596063555584.0000000000 4.8207743677 -1.7619701677 0.7337531840 0.3655628156 0.7577449624 0.4827607337 -0.24316347137 +1403636596113555456.0000000000 4.8402078927 -1.7527941841 0.7324605648 0.3676662407 0.7648289205 0.4736251796 -0.235663843132 +1403636596163555584.0000000000 4.8575705428 -1.7500789714 0.7324483155 0.3689255847 0.7701586476 0.4663183697 -0.230860885739 +1403636596213555456.0000000000 4.8725635232 -1.7540648631 0.7339983821 0.3702940054 0.7734693779 0.4607928124 -0.228686368445 +1403636596263555584.0000000000 4.8855796513 -1.7652061145 0.7372013986 0.3709063893 0.7756161844 0.4564547226 -0.229122393231 +1403636596313555456.0000000000 4.8970816434 -1.7816100155 0.7421524962 0.3719095759 0.7766535766 0.4531668396 -0.230504457204 +1403636596363555584.0000000000 4.9085249781 -1.8024304215 0.7481415014 0.3737336429 0.7767649601 0.4511088960 -0.231214456295 +1403636596413555456.0000000000 4.9198567021 -1.8258300095 0.7548410069 0.3764091164 0.7755466866 0.4508012570 -0.231563686049 +1403636596463555584.0000000000 4.9309566265 -1.8503111064 0.7613373314 0.3790925397 0.7733111273 0.4518472259 -0.232621648367 +1403636596513555456.0000000000 4.9410086036 -1.8741211449 0.7670717725 0.3816310470 0.7705954547 0.4538627392 -0.233557280376 +1403636596563555584.0000000000 4.9528404232 -1.8982914172 0.7722777576 0.3837026182 0.7678196394 0.4564516822 -0.234258754159 +1403636596613555456.0000000000 4.9607860090 -1.9188948242 0.7760385846 0.3843081290 0.7669827589 0.4577533503 -0.233466442493 +1403636596663555584.0000000000 4.9664827170 -1.9363265195 0.7791538865 0.3834135905 0.7669947018 0.4588082711 -0.23282636531 +1403636596713555456.0000000000 4.9700348980 -1.9497721948 0.7805526402 0.3822369441 0.7668656050 0.4602152734 -0.232409045756 +1403636596763555584.0000000000 4.9704532453 -1.9579943695 0.7809780360 0.3826175820 0.7653054255 0.4625981833 -0.23219455737 +1403636596813555456.0000000000 4.9671332644 -1.9608840645 0.7802965231 0.3848840958 0.7635133086 0.4633403057 -0.232867819772 +1403636596863555584.0000000000 4.9598599362 -1.9583417812 0.7790356275 0.3884375061 0.7608445365 0.4649163632 -0.232561110949 +1403636596913555456.0000000000 4.9483350049 -1.9514204795 0.7773905575 0.3915306838 0.7590691523 0.4652541167 -0.232500220723 +1403636596963555584.0000000000 4.9331187131 -1.9402062244 0.7753194311 0.3932928341 0.7578172142 0.4670216747 -0.230053411027 +1403636597013555456.0000000000 4.9141022421 -1.9260576319 0.7732655795 0.3920738224 0.7588989188 0.4673282377 -0.227936102947 +1403636597063555584.0000000000 4.8927871530 -1.9096943325 0.7705571454 0.3884589809 0.7603381004 0.4696159503 -0.224602876912 +1403636597113555456.0000000000 4.8689940353 -1.8918894538 0.7682629367 0.3827953608 0.7619087960 0.4721567572 -0.223675423313 +1403636597163555584.0000000000 4.8436149289 -1.8731612337 0.7667574463 0.3774473878 0.7614586075 0.4771710930 -0.223656000452 +1403636597213555456.0000000000 4.8164996177 -1.8535885056 0.7669588540 0.3730985347 0.7596822644 0.4825022873 -0.225547962245 +1403636597263555584.0000000000 4.7879242454 -1.8340398774 0.7686979893 0.3706652073 0.7564548623 0.4880462269 -0.228460556182 +1403636597313555456.0000000000 4.7584647315 -1.8151681591 0.7706954079 0.3697703031 0.7518540665 0.4940113381 -0.232245954658 +1403636597363555584.0000000000 4.7277815929 -1.7977079228 0.7733798008 0.3688777527 0.7471780596 0.4991835753 -0.237633980829 +1403636597413555456.0000000000 4.6976677745 -1.7817141448 0.7752114698 0.3688027584 0.7415620561 0.5057138367 -0.241503121509 +1403636597463555584.0000000000 4.6686156506 -1.7684506486 0.7768884024 0.3678637599 0.7360413137 0.5121159380 -0.246285819111 +1403636597513555456.0000000000 4.6423714956 -1.7587064731 0.7778880767 0.3669570831 0.7294258646 0.5197457353 -0.251286246689 +1403636597563555584.0000000000 4.6190501761 -1.7533505699 0.7785429563 0.3650109521 0.7231882134 0.5259968577 -0.259023393744 +1403636597613555456.0000000000 4.5998806727 -1.7528249966 0.7787960085 0.3628020078 0.7167402207 0.5314873867 -0.268662086967 +1403636597663555584.0000000000 4.5854088461 -1.7568856979 0.7785472320 0.3606573608 0.7101786780 0.5365258091 -0.278769742861 +1403636597713555456.0000000000 4.5758718065 -1.7650057989 0.7780790567 0.3589182523 0.7037251012 0.5411887872 -0.288207159399 +1403636597763555584.0000000000 4.5715364302 -1.7762828003 0.7775143842 0.3582576108 0.6977732517 0.5452854534 -0.295681835326 +1403636597813555456.0000000000 4.5723314367 -1.7895676300 0.7770863608 0.3582941692 0.6924045777 0.5487869012 -0.301718620908 +1403636597863555584.0000000000 4.5780636277 -1.8033476096 0.7762773138 0.3592695575 0.6876179642 0.5524513594 -0.304802256844 +1403636597913555456.0000000000 4.5884773433 -1.8172830236 0.7753417817 0.3596098646 0.6830967383 0.5567396162 -0.306758196506 +1403636597963555584.0000000000 4.6024198057 -1.8307104919 0.7739600773 0.3594036401 0.6800789291 0.5607314782 -0.30643414158 +1403636598013555456.0000000000 4.6195667089 -1.8436825160 0.7724331106 0.3578916372 0.6785900970 0.5642143681 -0.305108510429 +1403636598063555584.0000000000 4.6383701789 -1.8558066878 0.7701823999 0.3552828012 0.6791726023 0.5663347565 -0.30292515742 +1403636598113555456.0000000000 4.6591958187 -1.8669257829 0.7673543527 0.3505399407 0.6814443237 0.5678673301 -0.300469763934 +1403636598163555584.0000000000 4.6801317450 -1.8758627671 0.7635639445 0.3457690823 0.6846761957 0.5696308132 -0.295267650409 +1403636598213555456.0000000000 4.7002986453 -1.8824364727 0.7583545182 0.3402130742 0.6889354685 0.5713446081 -0.288423860194 +1403636598263555584.0000000000 4.7185687794 -1.8866589209 0.7518052368 0.3353299901 0.6922040250 0.5742056235 -0.280526803407 +1403636598313555456.0000000000 4.7333936471 -1.8883970936 0.7447562511 0.3317921050 0.6957912694 0.5749745682 -0.274212972733 +1403636598363555584.0000000000 4.7442382396 -1.8871408818 0.7373948164 0.3312725706 0.6977974614 0.5758862402 -0.267754038636 +1403636598413555456.0000000000 4.7503971269 -1.8836071259 0.7295451922 0.3321737139 0.6999049914 0.5748631497 -0.263298283101 +1403636598463555584.0000000000 4.7520201417 -1.8779432568 0.7216418038 0.3340982436 0.6998653807 0.5748741639 -0.26093391536 +1403636598513555456.0000000000 4.7486815764 -1.8705995546 0.7142478454 0.3365802246 0.6991399510 0.5738843345 -0.261866095484 +1403636598563555584.0000000000 4.7411586547 -1.8618854587 0.7078568109 0.3395180429 0.6960487833 0.5739790096 -0.266067071023 +1403636598613555456.0000000000 4.7301407887 -1.8522951093 0.7017266880 0.3431196446 0.6926230476 0.5730375301 -0.272342087349 +1403636598663555584.0000000000 4.7168177861 -1.8422280517 0.6957537920 0.3467566621 0.6879292920 0.5728980611 -0.279823011987 +1403636598713555456.0000000000 4.7021788659 -1.8323347622 0.6886909372 0.3506993472 0.6825168570 0.5724473399 -0.28893727838 +1403636598763555584.0000000000 4.6871660174 -1.8228408052 0.6806113702 0.3551549382 0.6760428590 0.5719285606 -0.299547565831 +1403636598813555456.0000000000 4.6724516179 -1.8138834237 0.6712697882 0.3600774067 0.6702155753 0.5701491522 -0.309976270254 +1403636598863555584.0000000000 4.6580709204 -1.8047936655 0.6608956087 0.3663987992 0.6648482982 0.5672354902 -0.319331424833 +1403636598913555456.0000000000 4.6445070156 -1.7963543463 0.6496794413 0.3725039268 0.6610830344 0.5633738425 -0.326833229131 +1403636598963555584.0000000000 4.6321309874 -1.7882201558 0.6378752586 0.3793277127 0.6572492913 0.5607602074 -0.331182495455 +1403636599013555456.0000000000 4.6215230230 -1.7814599682 0.6263009866 0.3844347681 0.6536769447 0.5588624459 -0.335543033898 +1403636599063555584.0000000000 4.6119495377 -1.7760258676 0.6167549835 0.3888094898 0.6502030354 0.5558281959 -0.342225379017 +1403636599113555456.0000000000 4.6039993707 -1.7716039257 0.6088991742 0.3926851476 0.6457717077 0.5528698272 -0.350873525026 +1403636599163555584.0000000000 4.5968767071 -1.7680019620 0.6032731692 0.3979136339 0.6403235077 0.5486142320 -0.361487164149 +1403636599213555456.0000000000 4.5893836651 -1.7643208047 0.5983657116 0.4085623471 0.6333845752 0.5431482744 -0.369987486806 +1403636599263555584.0000000000 4.5818007281 -1.7613407876 0.5944577446 0.4180766006 0.6278016916 0.5359105289 -0.379311082149 +1403636599313555456.0000000000 4.5752402722 -1.7586180838 0.5906441193 0.4262871872 0.6230355848 0.5295321413 -0.386912917166 +1403636599363555584.0000000000 4.5691015807 -1.7560441010 0.5864334174 0.4328055706 0.6200008491 0.5244860219 -0.391398387734 +1403636599413555456.0000000000 4.5637228300 -1.7535825879 0.5814665487 0.4384594984 0.6179885265 0.5217914208 -0.391889222355 +1403636599463555584.0000000000 4.5590786946 -1.7512657409 0.5761095859 0.4425657732 0.6176170767 0.5204463161 -0.3896412645 +1403636599513555456.0000000000 4.5551288757 -1.7496124921 0.5713649768 0.4433558655 0.6208182711 0.5180168667 -0.386883414699 +1403636599563555584.0000000000 4.5520437942 -1.7481826904 0.5669755422 0.4429252875 0.6245997277 0.5162033718 -0.383700988694 +1403636599613555456.0000000000 4.5503211842 -1.7470296772 0.5624172430 0.4415626770 0.6277078997 0.5156074278 -0.38099104372 +1403636599663555584.0000000000 4.5492624984 -1.7458243040 0.5579106016 0.4411685692 0.6294838944 0.5158010581 -0.378245408181 +1403636599713555456.0000000000 4.5489139221 -1.7449309663 0.5547480871 0.4419832251 0.6295318662 0.5144072961 -0.379111582335 +1403636599763555584.0000000000 4.5492823107 -1.7438739231 0.5547388953 0.4475683248 0.6245168614 0.5118632745 -0.384261984277 +1403636599813555456.0000000000 4.5494052102 -1.7430067414 0.5551080720 0.4527040293 0.6210877149 0.5083926064 -0.388389070405 +1403636599863555584.0000000000 4.5498055193 -1.7426737029 0.5547960405 0.4563427016 0.6186223907 0.5053367975 -0.392036219607 +1403636599913555456.0000000000 4.5508115056 -1.7424333874 0.5545740340 0.4567201023 0.6179861898 0.5039811042 -0.39433851443 +1403636599963555584.0000000000 4.5507886264 -1.7419330534 0.5542800026 0.4561294071 0.6196777300 0.5027479822 -0.393941545503 +1403636600013555456.0000000000 4.5510742463 -1.7416402280 0.5538744895 0.4557039787 0.6207606727 0.5019175723 -0.393787787535 +1403636600063555584.0000000000 4.5514154806 -1.7408821566 0.5529716943 0.4545034790 0.6215130504 0.5007047366 -0.395528611515 +1403636600113555456.0000000000 4.5519075401 -1.7403229153 0.5533039684 0.4553260885 0.6207351754 0.4983051767 -0.398820694007 +1403636600163555584.0000000000 4.5523268689 -1.7399078825 0.5530417321 0.4564386244 0.6198649914 0.4988535167 -0.398216452951 +1403636600213555456.0000000000 4.5522755897 -1.7404205471 0.5530334958 0.4555465458 0.6204681854 0.4983041635 -0.398985634121 +1403636600263555584.0000000000 4.5523832956 -1.7406496117 0.5529116434 0.4553510479 0.6204803801 0.4982925353 -0.399204296498 +1403636600313555456.0000000000 4.5526672279 -1.7409019294 0.5528985970 0.4550639829 0.6206683918 0.4980454492 -0.399547555875 +1403636600363555584.0000000000 4.5527538435 -1.7410206842 0.5528866195 0.4549011374 0.6208368577 0.4976767155 -0.399930541655 +1403636600413555456.0000000000 4.5528600609 -1.7410814619 0.5528518902 0.4548535409 0.6207990297 0.4977147331 -0.399996081766 +1403636600463555584.0000000000 4.5529499924 -1.7411518009 0.5528859139 0.4545271309 0.6210265220 0.4974074093 -0.400396073076 +1403636600513555456.0000000000 4.5530310567 -1.7409346072 0.5529241383 0.4548870787 0.6209038949 0.4973554098 -0.400242045928 +1403636600563555584.0000000000 4.5529996575 -1.7408561313 0.5528509035 0.4549473620 0.6207845479 0.4976680769 -0.39996990907 +1403636600613555456.0000000000 4.5529781603 -1.7409970789 0.5529271632 0.4546283883 0.6210261831 0.4973394785 -0.400366021931 +1403636600663555584.0000000000 4.5530353683 -1.7408625279 0.5529115653 0.4546853147 0.6210408813 0.4974134611 -0.400186627815 +1403636600713555456.0000000000 4.5530698183 -1.7408680574 0.5529114686 0.4545973484 0.6210863096 0.4974580836 -0.40016059514 +1403636600763555584.0000000000 4.5530014951 -1.7409086917 0.5528931063 0.4544718570 0.6211671355 0.4973134305 -0.400357431438 +1403636600813555456.0000000000 4.5530619822 -1.7407676905 0.5528446800 0.4547305763 0.6210240793 0.4975034354 -0.400049406564 +1403636600863555584.0000000000 4.5530661333 -1.7408964414 0.5528607810 0.4544357117 0.6212108515 0.4973347869 -0.400304098963 +1403636600913555456.0000000000 4.5530180506 -1.7408048214 0.5528081712 0.4546584626 0.6210876748 0.4974787659 -0.400063320148 +1403636600963555584.0000000000 4.5530305884 -1.7409024471 0.5528496323 0.4544004623 0.6212963865 0.4972681967 -0.400294092627 +1403636601013555456.0000000000 4.5530842127 -1.7407578433 0.5528035271 0.4546561688 0.6211264957 0.4975139990 -0.399961829789 +1403636601063555584.0000000000 4.5530333731 -1.7409142030 0.5529096183 0.4543715906 0.6213449170 0.4972424819 -0.400283482014 +1403636601113555456.0000000000 4.5530084569 -1.7407824594 0.5528429205 0.4546010688 0.6212012617 0.4974563223 -0.399980084665 +1403636601163555584.0000000000 4.5529956058 -1.7408944086 0.5529085107 0.4544039745 0.6213383488 0.4972633228 -0.400231023261 +1403636601213555456.0000000000 4.5529703156 -1.7408358576 0.5528981228 0.4545989202 0.6212072520 0.4974423006 -0.399990661686 +1403636601263555584.0000000000 4.5528859286 -1.7409502884 0.5529569997 0.4543474249 0.6213829019 0.4972389449 -0.400256340906 +1403636601313555456.0000000000 4.5529148926 -1.7408267896 0.5529865690 0.4545422236 0.6212501614 0.4974191340 -0.400017260986 +1403636601363555584.0000000000 4.5528168299 -1.7408348288 0.5529341618 0.4543882773 0.6213907944 0.4972431195 -0.400192521392 +1403636601413555456.0000000000 4.5527128810 -1.7407785435 0.5528959037 0.4544899911 0.6213390866 0.4973342636 -0.400044019731 +1403636601463555584.0000000000 4.5526162841 -1.7408136894 0.5529418873 0.4543821670 0.6214319721 0.4972067801 -0.400180669459 +1403636601513555456.0000000000 4.5525749391 -1.7407089160 0.5529810505 0.4545098146 0.6213606023 0.4972322588 -0.400114872414 +1403636601563555584.0000000000 4.5524635454 -1.7407169509 0.5530815531 0.4544383133 0.6214537874 0.4970908206 -0.400227092498 +1403636601613555456.0000000000 4.5524345451 -1.7406901166 0.5530799430 0.4544604522 0.6214267812 0.4971582448 -0.400160133764 +1403636601663555584.0000000000 4.5523640938 -1.7406311061 0.5531053078 0.4545233540 0.6214200934 0.4970992995 -0.400172306163 +1403636601713555456.0000000000 4.5523912595 -1.7406550895 0.5530823701 0.4544853876 0.6214382250 0.4970964468 -0.400190813914 +1403636601763555584.0000000000 4.5523315329 -1.7406652895 0.5531021109 0.4545149605 0.6214381514 0.4970877952 -0.400168087928 +1403636601813555456.0000000000 4.5522990837 -1.7407251571 0.5529933268 0.4544164791 0.6214646051 0.4971137684 -0.400206583436 +1403636601863555584.0000000000 4.5522130801 -1.7407139876 0.5529802971 0.4544895917 0.6214550053 0.4970967558 -0.400159596672 +1403636601913555456.0000000000 4.5521804455 -1.7407122089 0.5529776684 0.4544384779 0.6214954168 0.4970579135 -0.400203132486 +1403636601963555584.0000000000 4.5521663366 -1.7407008422 0.5529809905 0.4544885623 0.6214703418 0.4971101369 -0.400120322892 +1403636602013555456.0000000000 4.5521681429 -1.7407017651 0.5530561897 0.4544566301 0.6215073270 0.4970197569 -0.40021141313 +1403636602063555584.0000000000 4.5522190798 -1.7406549249 0.5531457067 0.4544773185 0.6214793993 0.4971181886 -0.400109022397 +1403636602113555456.0000000000 4.5521604270 -1.7406794513 0.5531518204 0.4543847778 0.6215787018 0.4969961661 -0.400211446603 +1403636602163555584.0000000000 4.5521610921 -1.7405777461 0.5531264728 0.4544688544 0.6215057530 0.4971329053 -0.400059413055 +1403636602213555456.0000000000 4.5521280731 -1.7405922614 0.5531625901 0.4543662347 0.6216029295 0.4969795821 -0.400215464334 +1403636602263555584.0000000000 4.5521983867 -1.7404546359 0.5531190175 0.4544970188 0.6215125968 0.4971533577 -0.399991363465 +1403636602313555456.0000000000 4.5521764693 -1.7405207023 0.5531401195 0.4543387486 0.6216223297 0.4970232007 -0.400162365367 +1403636602363555584.0000000000 4.5521866140 -1.7405095795 0.5530968926 0.4544184144 0.6215588394 0.4971408942 -0.400024305649 +1403636602413555456.0000000000 4.5521559812 -1.7405918608 0.5531039909 0.4543358095 0.6216042182 0.4970474940 -0.400163662581 +1403636602463555584.0000000000 4.5521247506 -1.7406040738 0.5531106324 0.4543992169 0.6215757527 0.4970627879 -0.400116883148 +1403636602513555456.0000000000 4.5521781136 -1.7406531826 0.5531575247 0.4543472270 0.6216441463 0.4970201170 -0.40012267618 +1403636602563555584.0000000000 4.5521716707 -1.7406538115 0.5531108464 0.4543516504 0.6216385135 0.4970286672 -0.400115783593 +1403636602613555456.0000000000 4.5522103068 -1.7406365521 0.5530839684 0.4543354789 0.6216456209 0.4970578900 -0.400086801445 +1403636602663555584.0000000000 4.5522072331 -1.7406206665 0.5530573057 0.4543448772 0.6216592572 0.4970463083 -0.400069328824 +1403636602713555456.0000000000 4.5522085139 -1.7406360220 0.5530639548 0.4543328506 0.6216786433 0.4970086038 -0.400099703969 +1403636602763555584.0000000000 4.5522071578 -1.7406304751 0.5531229316 0.4543350582 0.6217175076 0.4969698992 -0.400084884639 +1403636602813555456.0000000000 4.5522641083 -1.7406303317 0.5530452363 0.4543777873 0.6216941230 0.4969745427 -0.400066929196 +1403636602863555584.0000000000 4.5523119252 -1.7406432951 0.5530235396 0.4543523268 0.6217220399 0.4969356243 -0.400100804214 +1403636602913555456.0000000000 4.5524057726 -1.7406169042 0.5529970450 0.4543837098 0.6216922888 0.4969769127 -0.40006010877 +1403636602963555584.0000000000 4.5524365729 -1.7406096015 0.5530382597 0.4543753446 0.6217302425 0.4968994069 -0.400106899669 +1403636603013555456.0000000000 4.5524239646 -1.7405699912 0.5530398839 0.4544295553 0.6217108466 0.4969431427 -0.400021143655 +1403636603063555584.0000000000 4.5523964990 -1.7406046912 0.5531227653 0.4543475098 0.6217620839 0.4968835913 -0.400108670224 +1403636603113555456.0000000000 4.5523660212 -1.7405649180 0.5530715286 0.4544800476 0.6217199008 0.4969166788 -0.399982581562 +1403636603163555584.0000000000 4.5523851464 -1.7406110123 0.5531625638 0.4544067247 0.6217936896 0.4968549519 -0.400027865144 +1403636603213555456.0000000000 4.5523830740 -1.7406168178 0.5531249129 0.4544290031 0.6217673914 0.4969041895 -0.399982272818 +1403636603263555584.0000000000 4.5523610131 -1.7406355881 0.5531358103 0.4544000467 0.6217688604 0.4968838201 -0.400038186932 +1403636603313555456.0000000000 4.5523296489 -1.7406115495 0.5531225684 0.4544430186 0.6217487756 0.4969078697 -0.399990714798 +1403636603363555584.0000000000 4.5523022283 -1.7405916273 0.5531416785 0.4544317395 0.6217535280 0.4968677792 -0.400045940504 +1403636603413555456.0000000000 4.5522665874 -1.7405082942 0.5531517936 0.4544706813 0.6217399271 0.4968724404 -0.400017050824 +1403636603463555584.0000000000 4.5522517518 -1.7404873179 0.5531472700 0.4544605322 0.6217631083 0.4968620759 -0.400005424158 +1403636603513555456.0000000000 4.5522704463 -1.7404567395 0.5531990676 0.4544330852 0.6218157816 0.4968639968 -0.399952339161 +1403636603563555584.0000000000 4.5522656150 -1.7404269514 0.5531511341 0.4544283625 0.6218072872 0.4968781975 -0.399953269503 +1403636603613555456.0000000000 4.5522578907 -1.7404486785 0.5531977624 0.4544184523 0.6218262188 0.4968807192 -0.399931962522 +1403636603663555584.0000000000 4.5522364649 -1.7404564705 0.5531549009 0.4544573047 0.6218162300 0.4968775917 -0.399907230816 +1403636603713555456.0000000000 4.5522653240 -1.7404760644 0.5531700167 0.4544396772 0.6218340759 0.4968731072 -0.399905085176 +1403636603763555584.0000000000 4.5522843244 -1.7404873545 0.5531931407 0.4544018274 0.6218763212 0.4968581021 -0.399901046301 +1403636603813555456.0000000000 4.5523174076 -1.7405024716 0.5531298088 0.4543957343 0.6218735129 0.4968971869 -0.399863772233 +1403636603863555584.0000000000 4.5522919847 -1.7405224511 0.5531350049 0.4544751800 0.6218258769 0.4968313093 -0.399929418437 +1403636603913555456.0000000000 4.5523263678 -1.7405617539 0.5531104648 0.4543765491 0.6218815368 0.4968358499 -0.399949301843 +1403636603963555584.0000000000 4.5522990358 -1.7405128030 0.5531173935 0.4545197998 0.6218064645 0.4968676368 -0.399863756678 +1403636604013555456.0000000000 4.5523025636 -1.7405878009 0.5531436678 0.4543944295 0.6218781910 0.4967772940 -0.400006922636 +1403636604063555584.0000000000 4.5523030188 -1.7405585616 0.5531754971 0.4544444979 0.6218604756 0.4968169471 -0.399928329077 +1403636604113555456.0000000000 4.5522822514 -1.7405931292 0.5531171553 0.4544156554 0.6218707618 0.4967637089 -0.400011231432 +1403636604163555584.0000000000 4.5523132509 -1.7405641017 0.5530996225 0.4544884247 0.6218107091 0.4968342865 -0.399934251566 +1403636604213555456.0000000000 4.5522829945 -1.7405843164 0.5531089768 0.4544422710 0.6218601376 0.4967744609 -0.39998415783 +1403636604263555584.0000000000 4.5522598624 -1.7405701632 0.5531249364 0.4544599719 0.6218543465 0.4967785781 -0.399967936256 +1403636604313555456.0000000000 4.5522330237 -1.7405813931 0.5531562618 0.4544412844 0.6218837934 0.4967442924 -0.39998596776 +1403636604363555584.0000000000 4.5522259910 -1.7405659848 0.5531736139 0.4544634060 0.6218651071 0.4967899866 -0.399933132343 +1403636604413555456.0000000000 4.5522297808 -1.7405755036 0.5532096342 0.4544021598 0.6218898856 0.4967824224 -0.399973589247 +1403636604463555584.0000000000 4.5522522208 -1.7405556012 0.5532257620 0.4544613236 0.6218553398 0.4967898244 -0.399950887128 +1403636604513555456.0000000000 4.5522156666 -1.7405453057 0.5532308536 0.4544561682 0.6218764672 0.4967540415 -0.399968339971 +1403636604563555584.0000000000 4.5522075131 -1.7405156663 0.5532578629 0.4544309094 0.6219148521 0.4967176035 -0.39998260932 +1403636604613555456.0000000000 4.5521712011 -1.7404802432 0.5531797107 0.4544750632 0.6219110128 0.4967021982 -0.39995754193 +1403636604663555584.0000000000 4.5521758353 -1.7404646113 0.5531595713 0.4544464608 0.6219140884 0.4967168566 -0.399967055176 +1403636604713555456.0000000000 4.5521774978 -1.7404399814 0.5531286958 0.4544569988 0.6219082069 0.4967208775 -0.399959233268 +1403636604763555584.0000000000 4.5521933104 -1.7404372781 0.5531112207 0.4544592850 0.6219182102 0.4967226850 -0.399938835718 +1403636604813555456.0000000000 4.5522444512 -1.7404386551 0.5531647181 0.4544648830 0.6218982456 0.4967539590 -0.399924675889 +1403636604863555584.0000000000 4.5522327420 -1.7404788768 0.5531279113 0.4544703684 0.6219195322 0.4967372688 -0.399906070971 +1403636604913555456.0000000000 4.5522376778 -1.7405161816 0.5531429434 0.4544536894 0.6219149550 0.4967671727 -0.39989499761 +1403636604963555584.0000000000 4.5522840322 -1.7405617450 0.5531446775 0.4544334587 0.6219075230 0.4967737026 -0.399921433251 +1403636605013555456.0000000000 4.5523380598 -1.7405841976 0.5531513281 0.4544374630 0.6219186143 0.4967666061 -0.399908450145 +1403636605063555584.0000000000 4.5523731773 -1.7405837599 0.5531286246 0.4543845289 0.6219450042 0.4967666387 -0.399927516285 +1403636605113555456.0000000000 4.5523899158 -1.7405219047 0.5530913015 0.4544638483 0.6218915873 0.4967846045 -0.399898138135 +1403636605163555584.0000000000 4.5523726820 -1.7405114011 0.5531042233 0.4543935147 0.6219544237 0.4967199961 -0.399960590814 +1403636605213555456.0000000000 4.5523329092 -1.7404816447 0.5531104802 0.4544273393 0.6219399830 0.4967470529 -0.399911010491 +1403636605263555584.0000000000 4.5522991840 -1.7404840177 0.5531245916 0.4544034294 0.6219655899 0.4966969401 -0.399960595467 +1403636605313555456.0000000000 4.5523000819 -1.7404347632 0.5531524147 0.4544532196 0.6219373051 0.4967240532 -0.399914334203 +1403636605363555584.0000000000 4.5522691708 -1.7404546249 0.5530937101 0.4543995118 0.6219886382 0.4966588806 -0.399976466715 +1403636605413555456.0000000000 4.5522569708 -1.7404551099 0.5530941012 0.4544642180 0.6219587678 0.4966930769 -0.399906930643 +1403636605463555584.0000000000 4.5522355438 -1.7404688381 0.5531212871 0.4544014168 0.6220023783 0.4966589285 -0.399952875358 +1403636605513555456.0000000000 4.5522162740 -1.7404734276 0.5531110936 0.4544282244 0.6219966693 0.4966791791 -0.399906145579 +1403636605563555584.0000000000 4.5522065908 -1.7404920205 0.5531730624 0.4543930345 0.6220543574 0.4966311268 -0.399916079298 +1403636605613555456.0000000000 4.5521956966 -1.7405052437 0.5531450523 0.4544434587 0.6220026178 0.4966739835 -0.39988603426 +1403636605663555584.0000000000 4.5522049941 -1.7405431546 0.5531762948 0.4544145043 0.6220209019 0.4966553870 -0.399913593665 +1403636605713555456.0000000000 4.5522241911 -1.7405598098 0.5531799771 0.4544032024 0.6220368220 0.4966663443 -0.399888064467 +1403636605763555584.0000000000 4.5522536074 -1.7405479013 0.5531746363 0.4543970719 0.6220730003 0.4966567070 -0.399850720579 +1403636605813555456.0000000000 4.5522914541 -1.7405206820 0.5531682934 0.4544490743 0.6220508825 0.4966438056 -0.399842054876 +1403636605863555584.0000000000 4.5523200552 -1.7405105384 0.5531500247 0.4544229035 0.6220902762 0.4966213689 -0.399838378581 +1403636605913555456.0000000000 4.5523537459 -1.7405084060 0.5531387582 0.4544139048 0.6220812379 0.4966538832 -0.399822281553 +1403636605963555584.0000000000 4.5523678586 -1.7405133835 0.5531505090 0.4543951073 0.6221074073 0.4966307014 -0.399831723065 +1403636606013555456.0000000000 4.5523863899 -1.7405099779 0.5531729664 0.4543931887 0.6221043638 0.4966492237 -0.399815631555 +1403636606063555584.0000000000 4.5523942836 -1.7405405380 0.5531240851 0.4544058155 0.6221045251 0.4966363891 -0.399816972691 +1403636606113555456.0000000000 4.5524052429 -1.7405616013 0.5531182362 0.4544218288 0.6221100851 0.4966234984 -0.399806133518 +1403636606163555584.0000000000 4.5524392816 -1.7405792807 0.5530717905 0.4544313693 0.6221323407 0.4966122611 -0.399774615678 +1403636606213555456.0000000000 4.5524804006 -1.7405939104 0.5530472107 0.4544469034 0.6221211604 0.4966063307 -0.399781723027 +1403636606263555584.0000000000 4.5525188582 -1.7405574888 0.5530331053 0.4544648694 0.6221312969 0.4965968763 -0.399757269161 +1403636606313555456.0000000000 4.5525407420 -1.7405250932 0.5530969185 0.4544287624 0.6221809191 0.4965605079 -0.399766263986 +1403636606363555584.0000000000 4.5525433124 -1.7405334512 0.5530413600 0.4544800136 0.6221649254 0.4965526312 -0.399742676239 +1403636606413555456.0000000000 4.5525782784 -1.7405763412 0.5530245433 0.4544820788 0.6221750683 0.4965386606 -0.3997418955 +1403636606463555584.0000000000 4.5526175111 -1.7406126879 0.5530385391 0.4544754786 0.6221790322 0.4965370762 -0.399745197794 +1403636606513555456.0000000000 4.5526271006 -1.7406359311 0.5530781227 0.4544653011 0.6222067846 0.4964879448 -0.399774596544 +1403636606563555584.0000000000 4.5526335209 -1.7406028467 0.5530954244 0.4544781808 0.6222148324 0.4964819162 -0.399754915378 +1403636606613555456.0000000000 4.5526361585 -1.7405570480 0.5530809072 0.4545252828 0.6221906788 0.4964697390 -0.399754080219 +1403636606663555584.0000000000 4.5526277038 -1.7405579556 0.5530550874 0.4545395701 0.6221963057 0.4964642688 -0.399735870511 +1403636606713555456.0000000000 4.5526227142 -1.7405479434 0.5531188933 0.4545277952 0.6221909993 0.4964672702 -0.39975379091 +1403636606763555584.0000000000 4.5525895310 -1.7405447186 0.5530415633 0.4545501929 0.6222061067 0.4964644830 -0.399708268651 +1403636606813555456.0000000000 4.5526140816 -1.7405580062 0.5530216738 0.4545287108 0.6221898767 0.4964921909 -0.399723545386 +1403636606863555584.0000000000 4.5526437629 -1.7405560042 0.5530145313 0.4545146105 0.6221950974 0.4964860127 -0.399739125969 +1403636606913555456.0000000000 4.5526728988 -1.7405578439 0.5529934992 0.4545101723 0.6222097002 0.4965072911 -0.399695011489 +1403636606963555584.0000000000 4.5526789480 -1.7405553093 0.5529819476 0.4545234105 0.6222147836 0.4964895112 -0.399694130079 +1403636607013555456.0000000000 4.5526281684 -1.7405606088 0.5529963232 0.4545219617 0.6222243714 0.4964720272 -0.399702569669 +1403636607063555584.0000000000 4.5526323435 -1.7405616735 0.5530932632 0.4544994913 0.6222308327 0.4964787231 -0.399709745674 +1403636607113555456.0000000000 4.5525669479 -1.7405474075 0.5530441347 0.4545080996 0.6222130247 0.4964918859 -0.399711328961 +1403636607163555584.0000000000 4.5525267252 -1.7405196086 0.5530753668 0.4545177849 0.6222147738 0.4964923775 -0.3996969822 +1403636607213555456.0000000000 4.5524808238 -1.7404728587 0.5530903720 0.4544952953 0.6222344099 0.4965042749 -0.399677208133 +1403636607263555584.0000000000 4.5524057362 -1.7404233820 0.5530995015 0.4545204333 0.6222391915 0.4964891624 -0.399659950393 +1403636607313555456.0000000000 4.5523440016 -1.7404066930 0.5531542950 0.4544565395 0.6222689667 0.4965129776 -0.399656664992 +1403636607363555584.0000000000 4.5522619485 -1.7403708673 0.5530495367 0.4544997376 0.6222450162 0.4965357871 -0.399616491692 +1403636607413555456.0000000000 4.5522197919 -1.7403880480 0.5530404174 0.4544767427 0.6222704641 0.4965161754 -0.399627385717 +1403636607463555584.0000000000 4.5521733940 -1.7404048340 0.5531228519 0.4544811665 0.6222489818 0.4965137967 -0.399658758967 +1403636607513555456.0000000000 4.5521237492 -1.7404004949 0.5530864324 0.4544931897 0.6222347638 0.4965177178 -0.399662351482 +1403636607563555584.0000000000 4.5521035781 -1.7403686690 0.5531071493 0.4545214722 0.6222216663 0.4965286987 -0.399636935989 +1403636607613555456.0000000000 4.5521202532 -1.7403395001 0.5531377380 0.4545397120 0.6222280405 0.4965166467 -0.399621239957 +1403636607663555584.0000000000 4.5521421379 -1.7403379545 0.5531551280 0.4545458377 0.6222457440 0.4965238104 -0.399577803628 +1403636607713555456.0000000000 4.5521754478 -1.7403545818 0.5531716305 0.4545035977 0.6222771758 0.4965219172 -0.399579256015 +1403636607763555584.0000000000 4.5521844275 -1.7403579444 0.5531802548 0.4545087529 0.6222820465 0.4965228643 -0.399564629688 +1403636607813555456.0000000000 4.5522010450 -1.7403502360 0.5531530039 0.4545047786 0.6222751689 0.4965314961 -0.399569135169 +1403636607863555584.0000000000 4.5522164680 -1.7403638739 0.5531178988 0.4544965304 0.6223008071 0.4964976350 -0.399580664981 +1403636607913555456.0000000000 4.5522436960 -1.7403940567 0.5530804052 0.4544979799 0.6223193015 0.4964662947 -0.39958915338 +1403636607963555584.0000000000 4.5522971869 -1.7404159360 0.5530475322 0.4545329125 0.6223224117 0.4964785534 -0.399529339848 +1403636608013555456.0000000000 4.5523489023 -1.7404537276 0.5530478107 0.4545313353 0.6223335923 0.4964729626 -0.399520665884 +1403636608063555584.0000000000 4.5524053084 -1.7404586825 0.5531122621 0.4545095973 0.6223619090 0.4964533220 -0.399525692901 +1403636608113555456.0000000000 4.5524358836 -1.7404557762 0.5530708186 0.4545267866 0.6223679413 0.4964366426 -0.399517466116 +1403636608163555584.0000000000 4.5524602795 -1.7404697302 0.5530862765 0.4545232329 0.6223735884 0.4964106232 -0.399545041754 +1403636608213555456.0000000000 4.5524883079 -1.7404933403 0.5530787010 0.4545235187 0.6223821626 0.4964096271 -0.399532597717 +1403636608263555584.0000000000 4.5525107351 -1.7405220697 0.5530680805 0.4544887358 0.6223884433 0.4963956183 -0.399579785333 +1403636608313555456.0000000000 4.5525316576 -1.7405074659 0.5530494768 0.4545159680 0.6223742420 0.4964040739 -0.399560424895 +1403636608363555584.0000000000 4.5525439489 -1.7404900078 0.5530289410 0.4544803300 0.6223924453 0.4964085123 -0.399567094095 +1403636608413555456.0000000000 4.5525264911 -1.7404847014 0.5530150206 0.4544864585 0.6223958262 0.4964005461 -0.399564753741 +1403636608463555584.0000000000 4.5525052503 -1.7405035023 0.5529940038 0.4544568172 0.6224016242 0.4964021824 -0.399587403231 +1403636608513555456.0000000000 4.5524828315 -1.7405218098 0.5530436665 0.4544528984 0.6224237085 0.4963732802 -0.399593364414 +1403636608563555584.0000000000 4.5524246353 -1.7405475189 0.5529902116 0.4544960023 0.6223877101 0.4963703081 -0.399604103468 +1403636608613555456.0000000000 4.5523994445 -1.7405401485 0.5530152508 0.4545193781 0.6223827983 0.4963681027 -0.399587905183 +1403636608663555584.0000000000 4.5524088298 -1.7405298788 0.5530367242 0.4545334143 0.6223969492 0.4963569705 -0.399563725538 +1403636608713555456.0000000000 4.5523949957 -1.7405196164 0.5530740057 0.4545732491 0.6223885344 0.4963512737 -0.399538591945 +1403636608763555584.0000000000 4.5523802117 -1.7405071737 0.5531207263 0.4545548742 0.6224055283 0.4963502576 -0.399534286845 +1403636608813555456.0000000000 4.5523677817 -1.7404881890 0.5531949590 0.4545209972 0.6224301748 0.4963572514 -0.399525743341 +1403636608863555584.0000000000 4.5523099468 -1.7404855899 0.5531275717 0.4545266926 0.6224329684 0.4963587593 -0.399513038019 +1403636608913555456.0000000000 4.5523261353 -1.7404640522 0.5531192247 0.4545225194 0.6224273856 0.4963615473 -0.399523019908 +1403636608963555584.0000000000 4.5523754111 -1.7404141182 0.5531206912 0.4545194428 0.6224437499 0.4963178464 -0.399555314908 +1403636609013555456.0000000000 4.5524271705 -1.7403534350 0.5530917950 0.4545202555 0.6224441320 0.4963342113 -0.399533466141 +1403636609063555584.0000000000 4.5524462172 -1.7403421933 0.5530720253 0.4545118545 0.6224305661 0.4963474418 -0.399547721226 +1403636609113555456.0000000000 4.5524322051 -1.7403625550 0.5530568736 0.4545238075 0.6224211083 0.4963535039 -0.39954132647 +1403636609163555584.0000000000 4.5524367844 -1.7403913552 0.5530746726 0.4545359978 0.6224073134 0.4963258478 -0.399583302772 +1403636609213555456.0000000000 4.5524514197 -1.7403999765 0.5530770565 0.4545381721 0.6224014358 0.4963123647 -0.399606731036 +1403636609263555584.0000000000 4.5524797414 -1.7404072239 0.5531031827 0.4545320590 0.6224166924 0.4962980651 -0.399607681215 +1403636609313555456.0000000000 4.5524911206 -1.7403915812 0.5530355612 0.4545485607 0.6224020140 0.4963290653 -0.399573269725 +1403636609363555584.0000000000 4.5524911133 -1.7404045985 0.5530398578 0.4545288307 0.6224207822 0.4963429825 -0.399549190543 +1403636609413555456.0000000000 4.5524639390 -1.7404274648 0.5530522222 0.4545412489 0.6224390366 0.4963260638 -0.399527642605 +1403636609463555584.0000000000 4.5524651949 -1.7404628816 0.5530502843 0.4545463587 0.6224303240 0.4963429965 -0.399514366904 +1403636609513555456.0000000000 4.5524785851 -1.7404918731 0.5530338728 0.4545544170 0.6224439078 0.4963371493 -0.399491298832 +1403636609563555584.0000000000 4.5525140105 -1.7405046491 0.5530780935 0.4545491375 0.6224445643 0.4962986731 -0.39954408147 +1403636609613555456.0000000000 4.5525129961 -1.7404916882 0.5530226186 0.4545576544 0.6224479372 0.4963037124 -0.399522877194 +1403636609663555584.0000000000 4.5525337986 -1.7404955098 0.5530597065 0.4545158915 0.6224916121 0.4962799351 -0.399531880046 +1403636609713555456.0000000000 4.5525187939 -1.7404805891 0.5531025879 0.4545787545 0.6224436286 0.4962978194 -0.399512903003 +1403636609763555584.0000000000 4.5525067005 -1.7405264144 0.5531737626 0.4545448921 0.6224741066 0.4962484692 -0.399565244395 +1403636609813555456.0000000000 4.5525532383 -1.7405537311 0.5531536043 0.4544180430 0.6225261489 0.4963391805 -0.399515774381 +1403636609863555584.0000000000 4.5525359474 -1.7405529554 0.5531441782 0.4545176990 0.6224816289 0.4963041669 -0.399515277382 +1403636609913555456.0000000000 4.5525578152 -1.7405890887 0.5530854436 0.4544429067 0.6225118571 0.4962994347 -0.399559136365 +1403636609963555584.0000000000 4.5525605900 -1.7405679326 0.5530223199 0.4544235288 0.6225329090 0.4963144142 -0.399529768453 +1403636610013555456.0000000000 4.5525037701 -1.7405671894 0.5530541232 0.4544382547 0.6225344318 0.4962768693 -0.399557283737 +1403636610063555584.0000000000 4.5524695429 -1.7405972018 0.5530766567 0.4544185950 0.6225285790 0.4962952823 -0.399565891501 +1403636610113555456.0000000000 4.5524102730 -1.7406343415 0.5530970312 0.4544171713 0.6225396025 0.4962531452 -0.399602669681 +1403636610163555584.0000000000 4.5523887633 -1.7406161602 0.5531541881 0.4544325256 0.6225391745 0.4962557145 -0.399582684419 +1403636610213555456.0000000000 4.5523609210 -1.7405955928 0.5531374592 0.4544089356 0.6225671440 0.4962271059 -0.3996014638 +1403636610263555584.0000000000 4.5523746449 -1.7405021383 0.5531065732 0.4544366866 0.6225718674 0.4962873823 -0.399487674336 +1403636610313555456.0000000000 4.5523988303 -1.7404953874 0.5531472852 0.4544185832 0.6225947592 0.4962055132 -0.399574280669 +1403636610363555584.0000000000 4.5524220625 -1.7404619784 0.5531150278 0.4544077317 0.6226277809 0.4961953654 -0.399547768334 +1403636610413555456.0000000000 4.5523908678 -1.7404280912 0.5530577686 0.4544630212 0.6225986114 0.4962301296 -0.399487158668 +1403636610463555584.0000000000 4.5523738348 -1.7404161500 0.5530369308 0.4544146958 0.6226389956 0.4961898280 -0.399529247883 +1403636610513555456.0000000000 4.5524025955 -1.7404060994 0.5529687003 0.4544340323 0.6226189800 0.4962602571 -0.399450964927 +1403636610563555584.0000000000 4.5523471726 -1.7404099707 0.5530176729 0.4544132431 0.6226488632 0.4962118850 -0.39948812604 +1403636610613555456.0000000000 4.5523632225 -1.7404521047 0.5529389160 0.4544624999 0.6226341005 0.4962663124 -0.399387481364 +1403636610663555584.0000000000 4.5523657946 -1.7405163865 0.5529105854 0.4544434545 0.6226495002 0.4962490650 -0.399406574913 +1403636610713555456.0000000000 4.5524126214 -1.7405964429 0.5528604504 0.4544354432 0.6226453738 0.4962954120 -0.399364533345 +1403636610763555584.0000000000 4.5525100984 -1.7406857857 0.5526964190 0.4543521265 0.6226658913 0.4963950241 -0.39930353493 +1403636610813555456.0000000000 4.5526128627 -1.7406625923 0.5526178748 0.4543633743 0.6226544378 0.4964469406 -0.399244048709 +1403636610863555584.0000000000 4.5529663554 -1.7407403755 0.5526093004 0.4541953778 0.6226400008 0.4964741736 -0.399423814027 +1403636610913555456.0000000000 4.5529696687 -1.7406396233 0.5525691681 0.4543580559 0.6225639691 0.4965182066 -0.399302556808 +1403636610963555584.0000000000 4.5530296143 -1.7408030436 0.5525676238 0.4541343847 0.6226542139 0.4965295069 -0.39940222742 +1403636611013555456.0000000000 4.5528717867 -1.7407821164 0.5526204991 0.4543535130 0.6225740851 0.4964199486 -0.399414106405 +1403636611063555584.0000000000 4.5529814063 -1.7408040353 0.5525821234 0.4541909156 0.6226219133 0.4965421211 -0.39937261698 +1403636611113555456.0000000000 4.5529400605 -1.7407611470 0.5525821210 0.4542889022 0.6225638488 0.4964768780 -0.399432794282 +1403636611163555584.0000000000 4.5530717237 -1.7407183837 0.5525652062 0.4542395910 0.6225763821 0.4965233080 -0.399411625983 +1403636611213555456.0000000000 4.5530908670 -1.7406470473 0.5525546501 0.4543114271 0.6225167853 0.4965767849 -0.399356326881 +1403636611263555584.0000000000 4.5529963137 -1.7406971671 0.5526270925 0.4542444397 0.6225691539 0.4964750230 -0.399477395129 +1403636611313555456.0000000000 4.5529104723 -1.7406607264 0.5526979134 0.4542929824 0.6225715120 0.4964704998 -0.399424137372 +1403636611363555584.0000000000 4.5529118619 -1.7410264897 0.5528186706 0.4536706420 0.6227396647 0.4963077805 -0.400071050659 +1403636611413555456.0000000000 4.5528913883 -1.7408179752 0.5528872994 0.4541088033 0.6225371479 0.4963794203 -0.399800156751 +1403636611463555584.0000000000 4.5531094679 -1.7405198706 0.5526727204 0.4534888343 0.6230702296 0.4960089007 -0.400133148573 +1403636611513555456.0000000000 4.5531657307 -1.7399876159 0.5526289442 0.4547551104 0.6224478421 0.4964602375 -0.399103628213 +1403636611563555584.0000000000 4.5530658620 -1.7402708032 0.5526058769 0.4540785355 0.6228531604 0.4961733989 -0.399598026021 +1403636611613555456.0000000000 4.5529321174 -1.7401933144 0.5525138234 0.4544685995 0.6224980251 0.4964229342 -0.399398011084 +1403636611663555584.0000000000 4.5528787886 -1.7403703959 0.5524727992 0.4540875792 0.6228236157 0.4960419746 -0.399796915532 +1403636611713555456.0000000000 4.5529125595 -1.7400956871 0.5523862383 0.4547655743 0.6224195701 0.4962589386 -0.399386050106 +1403636611763555584.0000000000 4.5529063991 -1.7402987721 0.5524162902 0.4542507262 0.6226873842 0.4960513534 -0.399812148449 +1403636611813555456.0000000000 4.5529282253 -1.7403505985 0.5524117862 0.4542037530 0.6228068296 0.4958854931 -0.399885210388 +1403636611863555584.0000000000 4.5528693212 -1.7400178686 0.5524584169 0.4549053090 0.6224321032 0.4960466514 -0.399471095821 +1403636611913555456.0000000000 4.5529395365 -1.7401223348 0.5524512320 0.4545227531 0.6225118755 0.4962723568 -0.399501914491 +1403636611963555584.0000000000 4.5527844653 -1.7403214067 0.5525528116 0.4542236719 0.6226089853 0.4961061655 -0.399896961637 +1403636612013555456.0000000000 4.5527069526 -1.7403654156 0.5526629111 0.4540430093 0.6226494389 0.4959170230 -0.400273566785 +1403636612063555584.0000000000 4.5528706201 -1.7400622373 0.5525453279 0.4544883617 0.6224683864 0.4963975242 -0.399453294998 +1403636612113555456.0000000000 4.5527740540 -1.7404884692 0.5526815345 0.4536551067 0.6228807271 0.4958296687 -0.400461713029 +1403636612163555584.0000000000 4.5525609628 -1.7404563837 0.5526375705 0.4539222151 0.6226227091 0.4959155023 -0.400453991497 +1403636612213555456.0000000000 4.5527261119 -1.7403851494 0.5525271114 0.4536689527 0.6228624572 0.4959716345 -0.400298611667 +1403636612263555584.0000000000 4.5528364578 -1.7394015939 0.5522875429 0.4557111256 0.6215933197 0.4971607115 -0.398472510892 +1403636612313555456.0000000000 4.5527936949 -1.7403768317 0.5525738799 0.4536276514 0.6228508873 0.4958023754 -0.400573002834 +1403636612363555584.0000000000 4.5528511498 -1.7396516923 0.5521753291 0.4552494880 0.6217794562 0.4971776079 -0.398688647665 +1403636612413555456.0000000000 4.5528813839 -1.7403025214 0.5524460571 0.4539483645 0.6226404205 0.4960287976 -0.40025644414 +1403636612463555584.0000000000 4.5529301236 -1.7397804011 0.5522328740 0.4551985086 0.6218342373 0.4969753203 -0.398913562222 +1403636612513555456.0000000000 4.5527992257 -1.7403464978 0.5524174683 0.4540956692 0.6225802869 0.4961185772 -0.400071577327 +1403636612563555584.0000000000 4.5528224479 -1.7398827020 0.5523008389 0.4550431647 0.6219988099 0.4967390240 -0.399128476512 +1403636612613555456.0000000000 4.5528920707 -1.7400758788 0.5524689816 0.4544007584 0.6224652825 0.4962034878 -0.399798726342 +1403636612663555584.0000000000 4.5529009952 -1.7397932220 0.5524042428 0.4549185566 0.6220992146 0.4967051276 -0.399156222785 +1403636612713555456.0000000000 4.5528756217 -1.7400623617 0.5525733012 0.4543466939 0.6224507004 0.4962602435 -0.39981242864 +1403636612763555584.0000000000 4.5530071539 -1.7397531048 0.5524680370 0.4548551480 0.6221965765 0.4966537952 -0.399140604704 +1403636612813555456.0000000000 4.5529114615 -1.7400360192 0.5525877828 0.4545291560 0.6224205808 0.4963312526 -0.399563705395 +1403636612863555584.0000000000 4.5528417071 -1.7399597198 0.5524609283 0.4546458348 0.6223088455 0.4964707362 -0.399431688473 +1403636612913555456.0000000000 4.5528434404 -1.7398790772 0.5524547047 0.4546777810 0.6223534517 0.4964498179 -0.399351818502 +1403636612963555584.0000000000 4.5527940290 -1.7399040845 0.5525111676 0.4545565817 0.6224399405 0.4963053379 -0.399534536734 +1403636613013555456.0000000000 4.5526866753 -1.7397963926 0.5525337238 0.4548022630 0.6223345513 0.4963580430 -0.399353604018 +1403636613063555584.0000000000 4.5525913595 -1.7399643645 0.5526940709 0.4544346266 0.6225467445 0.4961011390 -0.399760404458 +1403636613113555456.0000000000 4.5525166088 -1.7397500219 0.5525145956 0.4548122842 0.6222956416 0.4965056973 -0.399219254458 +1403636613163555584.0000000000 4.5523336285 -1.7399858387 0.5526510943 0.4544796773 0.6225685043 0.4959995600 -0.399801346677 +1403636613213555456.0000000000 4.5523964670 -1.7397871835 0.5525578164 0.4548879418 0.6223332581 0.4963600764 -0.399255495566 +1403636613263555584.0000000000 4.5524601252 -1.7399400514 0.5526564763 0.4544904763 0.6225700486 0.4960520439 -0.399721542159 +1403636613313555456.0000000000 4.5523735429 -1.7398035904 0.5527040020 0.4548769886 0.6223270470 0.4962169442 -0.3994555246 +1403636613363555584.0000000000 4.5523217839 -1.7400071346 0.5527283745 0.4544465939 0.6225979194 0.4959912180 -0.399803496246 +1403636613413555456.0000000000 4.5523223833 -1.7398452023 0.5526625099 0.4548255323 0.6223782370 0.4962620565 -0.399378312627 +1403636613463555584.0000000000 4.5523426338 -1.7399891840 0.5527487831 0.4545276546 0.6225888742 0.4959517198 -0.399774432028 +1403636613513555456.0000000000 4.5524078971 -1.7398304341 0.5527422641 0.4547905558 0.6224120951 0.4961727839 -0.399476285505 +1403636613563555584.0000000000 4.5525131840 -1.7399301368 0.5527136562 0.4545245725 0.6225783936 0.4959724835 -0.399768498626 +1403636613613555456.0000000000 4.5525909723 -1.7398116593 0.5526578890 0.4547845829 0.6224203175 0.4961408400 -0.399509947794 +1403636613663555584.0000000000 4.5525782838 -1.7399714092 0.5527006686 0.4545061175 0.6225958421 0.4959516182 -0.39978819253 +1403636613713555456.0000000000 4.5525806774 -1.7399013605 0.5527252767 0.4546978377 0.6224882823 0.4960147704 -0.399659307894 +1403636613763555584.0000000000 4.5525737690 -1.7398957553 0.5527584221 0.4546391202 0.6225411620 0.4959425099 -0.399733409831 +1403636613813555456.0000000000 4.5525241395 -1.7398844781 0.5527570328 0.4546405024 0.6225423591 0.4959728581 -0.39969231759 +1403636613863555584.0000000000 4.5524974555 -1.7399056640 0.5527649712 0.4545624123 0.6225763837 0.4959953076 -0.399700281019 +1403636613913555456.0000000000 4.5524797903 -1.7398851507 0.5528022026 0.4545639415 0.6225711162 0.4960129740 -0.399684823264 +1403636613963555584.0000000000 4.5524129638 -1.7399047620 0.5527267654 0.4545355694 0.6225860988 0.4960054636 -0.399703072051 +1403636614013555456.0000000000 4.5523655416 -1.7398941607 0.5527218570 0.4545002739 0.6225979818 0.4959669951 -0.399772427538 +1403636614063555584.0000000000 4.5523364585 -1.7398290501 0.5527849872 0.4545680665 0.6225748614 0.4959486665 -0.399754093173 +1403636614113555456.0000000000 4.5522824660 -1.7398494820 0.5527226954 0.4545446681 0.6225718361 0.4959323204 -0.399805686774 +1403636614163555584.0000000000 4.5522745002 -1.7398773675 0.5527053237 0.4545894735 0.6225363471 0.4959748663 -0.399757225143 +1403636614213555456.0000000000 4.5523096261 -1.7399151104 0.5527073923 0.4545186793 0.6225807067 0.4959546242 -0.399793752614 +1403636614263555584.0000000000 4.5523809734 -1.7398669319 0.5527400092 0.4546067474 0.6225500391 0.4959895112 -0.399698084566 +1403636614313555456.0000000000 4.5523760889 -1.7399445037 0.5527961682 0.4545259629 0.6225975252 0.4958809909 -0.399850614053 +1403636614363555584.0000000000 4.5522598730 -1.7398886462 0.5527845777 0.4546638992 0.6225190172 0.4959526325 -0.39972715482 +1403636614413555456.0000000000 4.5522140850 -1.7399713512 0.5528044760 0.4544446891 0.6226605659 0.4958542427 -0.399877999231 +1403636614463555584.0000000000 4.5521955073 -1.7398463234 0.5527894539 0.4546576928 0.6225142886 0.4959795451 -0.399708185687 +1403636614513555456.0000000000 4.5521684369 -1.7399026453 0.5528025766 0.4545084784 0.6225906450 0.4958387198 -0.399933614144 +1403636614563555584.0000000000 4.5522269804 -1.7397931202 0.5528286752 0.4545512759 0.6225721785 0.4959558921 -0.39976839935 +1403636614613555456.0000000000 4.5522188412 -1.7398398499 0.5527848153 0.4544357988 0.6226572888 0.4958622886 -0.399883228255 +1403636614663555584.0000000000 4.5521776893 -1.7398140407 0.5527334004 0.4545432658 0.6225903175 0.4959503809 -0.399756095287 +1403636614713555456.0000000000 4.5521242341 -1.7399025275 0.5527619604 0.4544439375 0.6226591445 0.4958527513 -0.399882915844 +1403636614763555584.0000000000 4.5521733668 -1.7398840744 0.5527680124 0.4545035278 0.6226129882 0.4959436959 -0.39977426215 +1403636614813555456.0000000000 4.5522058483 -1.7398434313 0.5528871323 0.4544516925 0.6226695111 0.4958811785 -0.399822705553 +1403636614863555584.0000000000 4.5522533605 -1.7398562108 0.5527953356 0.4544705683 0.6226329792 0.4959515290 -0.399770880066 +1403636614913555456.0000000000 4.5522557059 -1.7398449460 0.5527787388 0.4544735565 0.6226672028 0.4958817451 -0.399800745086 +1403636614963555584.0000000000 4.5522683954 -1.7398141891 0.5527724521 0.4545638210 0.6226313262 0.4958805935 -0.399755426914 +1403636615013555456.0000000000 4.5522324882 -1.7398473954 0.5527972150 0.4545259087 0.6226539399 0.4958114424 -0.399849075195 +1403636615063555584.0000000000 4.5522437133 -1.7398314836 0.5528024219 0.4544829254 0.6226797518 0.4958326895 -0.399831391035 +1403636615113555456.0000000000 4.5522776803 -1.7398477660 0.5526933526 0.4545117009 0.6226382394 0.4959036297 -0.399775345162 +1403636615163555584.0000000000 4.5522942125 -1.7398622886 0.5526991967 0.4544766014 0.6226402409 0.4959011789 -0.399815169744 +1403636615213555456.0000000000 4.5522705152 -1.7398525592 0.5527198383 0.4545400828 0.6226024475 0.4959269464 -0.399769895503 +1403636615263555584.0000000000 4.5522073638 -1.7398700774 0.5527572798 0.4545253727 0.6226060730 0.4958827168 -0.399835834721 +1403636615313555456.0000000000 4.5521732599 -1.7398611887 0.5527350058 0.4545268608 0.6226178090 0.4959430620 -0.399741011158 +1403636615363555584.0000000000 4.5521396955 -1.7398789108 0.5527581492 0.4545244483 0.6226383217 0.4958746895 -0.399796621464 +1403636615413555456.0000000000 4.5521896547 -1.7398467210 0.5527668906 0.4545772593 0.6226112455 0.4958928614 -0.399756203628 +1403636615463555584.0000000000 4.5522241315 -1.7398110681 0.5527787213 0.4545411325 0.6226279015 0.4958783622 -0.399789325876 +1403636615513555456.0000000000 4.5522301860 -1.7397620263 0.5528212290 0.4545585367 0.6226377959 0.4958598881 -0.399777041944 +1403636615563555584.0000000000 4.5521768819 -1.7397951875 0.5527425559 0.4545514144 0.6226586229 0.4958426323 -0.399774104991 +1403636615613555456.0000000000 4.5521708482 -1.7397945299 0.5527367846 0.4545737326 0.6226477477 0.4958850954 -0.399712992197 +1403636615663555584.0000000000 4.5521826103 -1.7398566131 0.5527502112 0.4545329073 0.6226796904 0.4958401436 -0.399765420262 +1403636615713555456.0000000000 4.5522462841 -1.7398990533 0.5526983048 0.4545234166 0.6226778115 0.4959034110 -0.399700655221 +1403636615763555584.0000000000 4.5522952950 -1.7399336791 0.5526725319 0.4545097612 0.6226898089 0.4958434229 -0.399771908492 +1403636615813555456.0000000000 4.5523119499 -1.7398476331 0.5527546313 0.4545783198 0.6226782397 0.4958069625 -0.399757197504 +1403636615863555584.0000000000 4.5522962767 -1.7398756885 0.5527367608 0.4545125066 0.6227325698 0.4957827269 -0.399777457588 +1403636615913555456.0000000000 4.5522519304 -1.7398625111 0.5527472121 0.4545827059 0.6226966727 0.4958322223 -0.399692162354 +1403636615963555584.0000000000 4.5522193649 -1.7399183080 0.5527636031 0.4545430185 0.6227141940 0.4958113636 -0.399735873695 +1403636616013555456.0000000000 4.5522023265 -1.7399318616 0.5527610378 0.4545523380 0.6227323787 0.4958089721 -0.399699912184 +1403636616063555584.0000000000 4.5522132989 -1.7399272176 0.5527832906 0.4545142611 0.6227542920 0.4957912490 -0.399731054203 +1403636616113555456.0000000000 4.5521656194 -1.7398950951 0.5528185640 0.4545767550 0.6227501382 0.4957319898 -0.399739957303 +1403636616163555584.0000000000 4.5521005040 -1.7398949977 0.5528055721 0.4545376568 0.6227719122 0.4957287401 -0.399754524893 +1403636616213555456.0000000000 4.5520745459 -1.7398592999 0.5527916925 0.4545738399 0.6227667265 0.4957378984 -0.399710100708 +1403636616263555584.0000000000 4.5520684168 -1.7398075609 0.5527798290 0.4545861829 0.6227698743 0.4957297528 -0.399701261007 +1403636616313555456.0000000000 4.5520775240 -1.7397350258 0.5528470993 0.4545855813 0.6227718246 0.4957157923 -0.399716220614 +1403636616363555584.0000000000 4.5520838655 -1.7397390687 0.5527709277 0.4545805382 0.6227788216 0.4956883071 -0.399745138605 +1403636616413555456.0000000000 4.5521153426 -1.7397054696 0.5527263724 0.4545684506 0.6227762222 0.4957044314 -0.399742939284 +1403636616463555584.0000000000 4.5521205787 -1.7397037555 0.5526927092 0.4545682657 0.6227841950 0.4956867435 -0.39975266172 +1403636616513555456.0000000000 4.5521146609 -1.7397061709 0.5526834544 0.4546101915 0.6227909707 0.4956389703 -0.39975366382 +1403636616563555584.0000000000 4.5521193373 -1.7397116404 0.5527632258 0.4545911247 0.6228384416 0.4956294433 -0.39971319713 +1403636616613555456.0000000000 4.5521522581 -1.7397554013 0.5527196015 0.4545820781 0.6228234012 0.4956730720 -0.399692820633 +1403636616663555584.0000000000 4.5521826501 -1.7397641773 0.5527327098 0.4545798770 0.6228230610 0.4956567396 -0.399716107512 +1403636616713555456.0000000000 4.5522146353 -1.7397772233 0.5527407282 0.4545538834 0.6228351732 0.4956635736 -0.39971832077 +1403636616763555584.0000000000 4.5522265138 -1.7397925001 0.5527879379 0.4545340573 0.6228555320 0.4956414086 -0.399736627049 +1403636616813555456.0000000000 4.5522556864 -1.7398356834 0.5528629054 0.4544924670 0.6228705933 0.4956440441 -0.399757180045 +1403636616863555584.0000000000 4.5522837818 -1.7399017674 0.5528079411 0.4545093748 0.6228509686 0.4956611858 -0.399747280143 +1403636616913555456.0000000000 4.5523315566 -1.7399221779 0.5528267595 0.4545199272 0.6228786854 0.4956207519 -0.399742228537 +1403636616963555584.0000000000 4.5523946791 -1.7399261771 0.5528318388 0.4545097198 0.6228879835 0.4956015550 -0.399763146436 +1403636617013555456.0000000000 4.5524222339 -1.7399442773 0.5528207979 0.4545197884 0.6228683471 0.4956316730 -0.399744954849 +1403636617063555584.0000000000 4.5524174814 -1.7399557602 0.5528050965 0.4545604447 0.6228636514 0.4955993519 -0.399746114597 +1403636617113555456.0000000000 4.5524179064 -1.7399489856 0.5527713582 0.4545512557 0.6228734933 0.4956257006 -0.399708559051 +1403636617163555584.0000000000 4.5523983560 -1.7399456357 0.5527396705 0.4545338118 0.6228756224 0.4956394442 -0.39970803637 +1403636617213555456.0000000000 4.5523773227 -1.7399201744 0.5527807041 0.4545252403 0.6228791941 0.4956097807 -0.399748997249 +1403636617263555584.0000000000 4.5523415310 -1.7398897964 0.5527037807 0.4545585045 0.6228739800 0.4956160162 -0.399711565385 +1403636617313555456.0000000000 4.5523175945 -1.7398570538 0.5526933818 0.4545510959 0.6228864354 0.4956074407 -0.399711213972 +1403636617363555584.0000000000 4.5522902787 -1.7398081822 0.5526560646 0.4545445200 0.6228953671 0.4956052833 -0.399707448195 +1403636617413555456.0000000000 4.5522563441 -1.7397494556 0.5527383435 0.4545020688 0.6229371453 0.4955998454 -0.399697354999 +1403636617463555584.0000000000 4.5522309713 -1.7397548961 0.5526624040 0.4545121617 0.6229141710 0.4956249771 -0.399690520969 +1403636617513555456.0000000000 4.5522255484 -1.7397402053 0.5526695585 0.4545087862 0.6229239529 0.4956105421 -0.399697013736 +1403636617563555584.0000000000 4.5522206614 -1.7397288861 0.5527611883 0.4544627241 0.6229664882 0.4956000975 -0.399696047419 +1403636617613555456.0000000000 4.5522451432 -1.7397754258 0.5527212972 0.4544861687 0.6229353526 0.4956341240 -0.399675723621 +1403636617663555584.0000000000 4.5522413710 -1.7398224826 0.5527576677 0.4544633046 0.6229566031 0.4955955080 -0.39971648438 +1403636617713555456.0000000000 4.5522424631 -1.7398503963 0.5527619006 0.4544974081 0.6229227555 0.4956019861 -0.399722426347 +1403636617763555584.0000000000 4.5522760366 -1.7399069591 0.5527702790 0.4544668908 0.6229587754 0.4955454774 -0.399771045873 +1403636617813555456.0000000000 4.5523209146 -1.7399074376 0.5527615684 0.4544863532 0.6229623996 0.4955712773 -0.39971128657 +1403636617863555584.0000000000 4.5523454693 -1.7399205220 0.5527444542 0.4545006976 0.6229894057 0.4955331437 -0.399700162324 +1403636617913555456.0000000000 4.5524056176 -1.7399260822 0.5527248422 0.4544908218 0.6230046133 0.4955448038 -0.399673231784 +1403636617963555584.0000000000 4.5524557116 -1.7399278237 0.5526976214 0.4544785114 0.6230303959 0.4955153909 -0.399683507078 +1403636618013555456.0000000000 4.5524648404 -1.7399218773 0.5527406298 0.4544890725 0.6230417978 0.4955056853 -0.399665756531 +1403636618063555584.0000000000 4.5524414678 -1.7399973010 0.5526778412 0.4544984686 0.6230659007 0.4954717340 -0.399659587842 +1403636618113555456.0000000000 4.5524521198 -1.7399826567 0.5526737394 0.4545281377 0.6230391181 0.4954929805 -0.399641258668 +1403636618163555584.0000000000 4.5524292386 -1.7399748167 0.5526992998 0.4545371171 0.6230488916 0.4954583429 -0.399658752385 +1403636618213555456.0000000000 4.5523978496 -1.7399521194 0.5526843910 0.4545325112 0.6230310144 0.4955367235 -0.399594678419 +1403636618263555584.0000000000 4.5523379692 -1.7399450869 0.5526899177 0.4545304381 0.6230419596 0.4955002990 -0.399625138152 +1403636618313555456.0000000000 4.5522738012 -1.7398967320 0.5527524665 0.4544936021 0.6230776372 0.4955087979 -0.399600869508 +1403636618363555584.0000000000 4.5522283361 -1.7399067232 0.5527076828 0.4545250274 0.6230699616 0.4954573179 -0.399640924511 +1403636618413555456.0000000000 4.5522253746 -1.7398221413 0.5527872257 0.4545331880 0.6230760205 0.4954493076 -0.399632127535 +1403636618463555584.0000000000 4.5522455392 -1.7397752529 0.5527988518 0.4545622438 0.6230521346 0.4954474221 -0.399638656811 +1403636618513555456.0000000000 4.5523185097 -1.7397814525 0.5528721981 0.4544130680 0.6228552140 0.4956896519 -0.399814850854 +1403636618563555584.0000000000 4.5523275745 -1.7397510113 0.5529160596 0.4544824088 0.6228840241 0.4956102751 -0.399789554485 +1403636618613555456.0000000000 4.5523155320 -1.7397602317 0.5528735720 0.4544501115 0.6229314745 0.4955790206 -0.399791081126 +1403636618663555584.0000000000 4.5523019219 -1.7397772202 0.5528220362 0.4545020500 0.6229906801 0.4955097935 -0.399725585513 +1403636618713555456.0000000000 4.5522724593 -1.7396948526 0.5527752421 0.4545778468 0.6232460649 0.4952577943 -0.399553551952 +1403636618763555584.0000000000 4.5522995650 -1.7397464051 0.5527855609 0.4545253433 0.6231229822 0.4953421346 -0.399700676814 +1403636618813555456.0000000000 4.5522957449 -1.7397978032 0.5526986622 0.4544491458 0.6231708053 0.4953370854 -0.399719017792 +1403636618863555584.0000000000 4.5523353272 -1.7398427536 0.5526817020 0.4544976844 0.6230901022 0.4953478195 -0.399776333807 +1403636618913555456.0000000000 4.5523497152 -1.7399731466 0.5527284802 0.4542819678 0.6230272035 0.4954599985 -0.399980483629 +1403636618963555584.0000000000 4.5523643703 -1.7398764076 0.5527689176 0.4543623907 0.6229865211 0.4954842380 -0.39992247039 +1403636619013555456.0000000000 4.5523895121 -1.7398825173 0.5527824245 0.4542625186 0.6230639605 0.4954131020 -0.400003404668 +1403636619063555584.0000000000 4.5524496610 -1.7398525074 0.5527874054 0.4542653313 0.6230995224 0.4954710281 -0.399873047786 +1403636619113555456.0000000000 4.5524186673 -1.7399152363 0.5527491500 0.4542930965 0.6232051932 0.4952868064 -0.399905050072 +1403636619163555584.0000000000 4.5524044054 -1.7399407113 0.5526928166 0.4544085918 0.6232730512 0.4952591618 -0.39970226182 +1403636619213555456.0000000000 4.5523676462 -1.7399310872 0.5526772501 0.4544430156 0.6233689424 0.4951110707 -0.399697053783 +1403636619263555584.0000000000 4.5523353508 -1.7398954644 0.5526645250 0.4545151434 0.6233775051 0.4950842520 -0.399634900894 +1403636619313555456.0000000000 4.5522894020 -1.7399385781 0.5526969430 0.4544992850 0.6233156304 0.4951929263 -0.399614802719 +1403636619363555584.0000000000 4.5522406874 -1.7401321758 0.5527933104 0.4543100006 0.6231440833 0.4953892906 -0.39985413038 +1403636619413555456.0000000000 4.5521585046 -1.7401670063 0.5528793196 0.4543924181 0.6231038558 0.4953660811 -0.399851923719 +1403636619463555584.0000000000 4.5521307193 -1.7400761935 0.5529456919 0.4543601620 0.6232217334 0.4952713339 -0.399822235561 +1403636619513555456.0000000000 4.5520567905 -1.7399569626 0.5529350464 0.4544080669 0.6233038307 0.4952133475 -0.39971162575 +1403636619563555584.0000000000 4.5520985614 -1.7398555803 0.5529137115 0.4544063750 0.6234423593 0.4951014452 -0.399636122046 +1403636619613555456.0000000000 4.5521590302 -1.7397616807 0.5528845152 0.4545202900 0.6233164480 0.4951750336 -0.399611808866 +1403636619663555584.0000000000 4.5522095010 -1.7397647315 0.5529259612 0.4544869916 0.6233207691 0.4951242565 -0.39970584678 +1403636619713555456.0000000000 4.5523048166 -1.7397646397 0.5528599048 0.4545646075 0.6233514666 0.4951252539 -0.399568454257 +1403636619763555584.0000000000 4.5523206373 -1.7398074788 0.5528506687 0.4545152826 0.6233957444 0.4950324648 -0.399670442305 +1403636619813555456.0000000000 4.5522901186 -1.7397963712 0.5528244763 0.4545593069 0.6233703076 0.4950638444 -0.399621178105 +1403636619863555584.0000000000 4.5522360669 -1.7398271770 0.5528146670 0.4544939053 0.6234198908 0.4949692806 -0.399735338693 +1403636619913555456.0000000000 4.5521857794 -1.7397992870 0.5528349429 0.4545614205 0.6233906983 0.4949533353 -0.399723839855 +1403636619963555584.0000000000 4.5521854161 -1.7398150824 0.5528566417 0.4544812432 0.6233715358 0.4950051367 -0.399780743053 +1403636620013555456.0000000000 4.5521397620 -1.7398293131 0.5528269409 0.4544591178 0.6234008941 0.4950041490 -0.39976133877 +1403636620063555584.0000000000 4.5521321382 -1.7398162528 0.5527976761 0.4545065581 0.6234058479 0.4949879433 -0.399719743638 +1403636620113555456.0000000000 4.5520825646 -1.7398277632 0.5527498482 0.4545854909 0.6233262278 0.4950042940 -0.399733903995 +1403636620163555584.0000000000 4.5520957584 -1.7398042182 0.5527025584 0.4545711490 0.6233046824 0.4950481938 -0.399729444955 +1403636620213555456.0000000000 4.5521197496 -1.7397798004 0.5527145513 0.4545666903 0.6233053324 0.4950402058 -0.399743394243 +1403636620263555584.0000000000 4.5521419444 -1.7397763868 0.5527292475 0.4545117225 0.6233477411 0.4950498599 -0.39972781246 +1403636620313555456.0000000000 4.5521322462 -1.7397749057 0.5527712764 0.4545805657 0.6233674073 0.4949564045 -0.399734589966 +1403636620363555584.0000000000 4.5520788717 -1.7397453875 0.5528070424 0.4545954934 0.6233466649 0.4949955724 -0.39970145863 +1403636620413555456.0000000000 4.5520393289 -1.7397715176 0.5528031084 0.4545529754 0.6233244756 0.4950226672 -0.399750859512 +1403636620463555584.0000000000 4.5520091375 -1.7397422904 0.5528479405 0.4546065059 0.6233207619 0.4950102839 -0.399711109924 +1403636620513555456.0000000000 4.5520146769 -1.7398345765 0.5528244894 0.4545469442 0.6233726166 0.4949427944 -0.399781548704 +1403636620563555584.0000000000 4.5520801959 -1.7398757126 0.5528120694 0.4545618693 0.6233841249 0.4949493757 -0.399738483692 +1403636620613555456.0000000000 4.5521124946 -1.7399319503 0.5527695394 0.4544963176 0.6234193109 0.4949440878 -0.399764693291 +1403636620663555584.0000000000 4.5521627686 -1.7399243860 0.5527183780 0.4545418243 0.6233856553 0.4949958415 -0.399701353084 +1403636620713555456.0000000000 4.5521622391 -1.7399541202 0.5527234920 0.4545402467 0.6233816255 0.4949567428 -0.399757846561 +1403636620763555584.0000000000 4.5521677815 -1.7399397288 0.5527335800 0.4545045692 0.6234063176 0.4949782194 -0.399733313673 +1403636620813555456.0000000000 4.5521500719 -1.7398668528 0.5528021538 0.4544337364 0.6234148357 0.4949664356 -0.399815144172 +1403636620863555584.0000000000 4.5522205457 -1.7398050369 0.5527997808 0.4544529808 0.6234008272 0.4949691070 -0.399811805677 +1403636620913555456.0000000000 4.5522624988 -1.7397542153 0.5528468227 0.4544290569 0.6234238085 0.4949266065 -0.399855775819 +1403636620963555584.0000000000 4.5522702572 -1.7396805681 0.5528783663 0.4544090303 0.6234671296 0.4949273007 -0.399810127972 +1403636621013555456.0000000000 4.5522925549 -1.7396144030 0.5528776371 0.4543599346 0.6235022620 0.4949553903 -0.399776363374 +1403636621063555584.0000000000 4.5522846752 -1.7393929325 0.5528632673 0.4547418175 0.6233085135 0.4951244323 -0.399434816926 +1403636621113555456.0000000000 4.5523497476 -1.7396874406 0.5529551550 0.4543390277 0.6234698342 0.4949282385 -0.39988429894 +1403636621163555584.0000000000 4.5523345662 -1.7396619903 0.5528776082 0.4546379520 0.6232438056 0.4951933406 -0.399568575881 +1403636621213555456.0000000000 4.5522510870 -1.7398489492 0.5529095394 0.4544388082 0.6233818752 0.4949693932 -0.399857108416 +1403636621263555584.0000000000 4.5521834486 -1.7397986257 0.5528325838 0.4546357898 0.6232732482 0.4951692109 -0.399555014065 +1403636621313555456.0000000000 4.5520241043 -1.7399208947 0.5528681417 0.4544211204 0.6234070675 0.4950003007 -0.399799669666 +1403636621363555584.0000000000 4.5519182844 -1.7398390814 0.5528444824 0.4546023969 0.6232864317 0.4951234641 -0.399629128292 +1403636621413555456.0000000000 4.5518894010 -1.7399705580 0.5528238595 0.4543472120 0.6234547458 0.4949834312 -0.399830206105 +1403636621463555584.0000000000 4.5519125391 -1.7399130917 0.5527865447 0.4545537345 0.6233200159 0.4950933176 -0.399669447246 +1403636621513555456.0000000000 4.5519711924 -1.7399692703 0.5528020089 0.4544016312 0.6234104343 0.4950240425 -0.399787175071 +1403636621563555584.0000000000 4.5520647505 -1.7398141791 0.5527547442 0.4544989733 0.6233605804 0.4951186116 -0.399637123582 +1403636621613555456.0000000000 4.5520911581 -1.7399106081 0.5528107538 0.4543680896 0.6234610130 0.4950149348 -0.399757699966 +1403636621663555584.0000000000 4.5520914033 -1.7398349079 0.5528718074 0.4545172747 0.6233735393 0.4951004162 -0.39961863743 +1403636621713555456.0000000000 4.5520754544 -1.7398657965 0.5529358193 0.4543639072 0.6234457098 0.4950379803 -0.399757782874 +1403636621763555584.0000000000 4.5520567773 -1.7398147382 0.5529481498 0.4544150732 0.6234032057 0.4951036616 -0.399684561406 +1403636621813555456.0000000000 4.5520885998 -1.7397790118 0.5529774622 0.4543638429 0.6234401688 0.4950668225 -0.399730778681 +1403636621863555584.0000000000 4.5520735763 -1.7398114764 0.5529208274 0.4543812867 0.6234401678 0.4951018397 -0.399667576522 +1403636621913555456.0000000000 4.5520416587 -1.7398046351 0.5528814291 0.4543712287 0.6234738258 0.4950734466 -0.399661678902 +1403636621963555584.0000000000 4.5520240373 -1.7397686037 0.5528758333 0.4543561762 0.6234765846 0.4950182261 -0.399742879104 +1403636622013555456.0000000000 4.5520287666 -1.7396993227 0.5528361678 0.4544160490 0.6234685261 0.4950826760 -0.399607551614 +1403636622063555584.0000000000 4.5520422565 -1.7397587573 0.5528382674 0.4543838868 0.6234852182 0.4950029071 -0.399716884844 +1403636622113555456.0000000000 4.5520563982 -1.7397344090 0.5527833573 0.4543757049 0.6235088679 0.4950524776 -0.399627895489 +1403636622163555584.0000000000 4.5520252871 -1.7397722116 0.5527513205 0.4543277453 0.6235109538 0.4950675479 -0.39966049766 +1403636622213555456.0000000000 4.5520172557 -1.7397641326 0.5527217562 0.4542814080 0.6235324902 0.4950507852 -0.399700332885 +1403636622263555584.0000000000 4.5520727341 -1.7397478853 0.5527029950 0.4542844236 0.6235136771 0.4951035423 -0.399660905396 +1403636622313555456.0000000000 4.5520986898 -1.7396452264 0.5527490343 0.4542825250 0.6235677913 0.4950547346 -0.399639095778 +1403636622363555584.0000000000 4.5522582393 -1.7396393394 0.5527608185 0.4542847653 0.6235607233 0.4951111946 -0.39957762865 +1403636622413555456.0000000000 4.5523383228 -1.7397006483 0.5528110495 0.4542287574 0.6236017987 0.4950773841 -0.399619089051 +1403636622463555584.0000000000 4.5523023588 -1.7397181518 0.5527835435 0.4542284389 0.6236004857 0.4950933241 -0.399601751637 +1403636622513555456.0000000000 4.5522459453 -1.7397166045 0.5527357593 0.4542316419 0.6236122115 0.4950593083 -0.399621954357 +1403636622563555584.0000000000 4.5521985377 -1.7397089257 0.5527177403 0.4542122252 0.6236474508 0.4950427764 -0.399609510723 +1403636622613555456.0000000000 4.5521590580 -1.7398056569 0.5527059304 0.4542615698 0.6236195610 0.4950440664 -0.399595347275 +1403636622663555584.0000000000 4.5521091829 -1.7398885960 0.5527221610 0.4542302373 0.6236013534 0.4950216687 -0.399687116372 +1403636622713555456.0000000000 4.5520860564 -1.7399810353 0.5527264437 0.4542182737 0.6236505524 0.4949415187 -0.399723205933 +1403636622763555584.0000000000 4.5521395371 -1.7400370724 0.5527223563 0.4542584808 0.6236144775 0.4949631821 -0.399706973132 +1403636622813555456.0000000000 4.5522343466 -1.7401155153 0.5527664924 0.4542194016 0.6237034758 0.4948843463 -0.399710136456 +1403636622863555584.0000000000 4.5522994423 -1.7400282694 0.5528697999 0.4543275681 0.6237161977 0.4947430844 -0.399742224643 +1403636622913555456.0000000000 4.5522943219 -1.7398302606 0.5529741659 0.4544136188 0.6237299169 0.4946101217 -0.39978754521 +1403636622963555584.0000000000 4.5522620668 -1.7397556231 0.5531004600 0.4543097911 0.6238520162 0.4944801699 -0.399875777151 +1403636623013555456.0000000000 4.5521948672 -1.7395984539 0.5531658184 0.4545318272 0.6237436629 0.4944626727 -0.399814114699 +1403636623063555584.0000000000 4.5521102616 -1.7394549923 0.5531876237 0.4544537657 0.6238083738 0.4944348916 -0.399836248415 +1403636623113555456.0000000000 4.5520229210 -1.7394326984 0.5531996779 0.4544187782 0.6238649731 0.4944103467 -0.399818056779 +1403636623163555584.0000000000 4.5518916185 -1.7394102508 0.5531606871 0.4544667341 0.6238507719 0.4944013711 -0.399796806305 +1403636623213555456.0000000000 4.5517569108 -1.7393807965 0.5531542296 0.4543699590 0.6239163324 0.4944644236 -0.399726511824 +1403636623263555584.0000000000 4.5514946095 -1.7393954839 0.5531545307 0.4542951504 0.6239710906 0.4944114837 -0.39979154469 +1403636623313555456.0000000000 4.5511164727 -1.7392227163 0.5532097031 0.4544427622 0.6239173817 0.4944035192 -0.399717446268 +1403636623363555584.0000000000 4.5510370084 -1.7394238969 0.5532224036 0.4542508554 0.6240632336 0.4942837110 -0.399856041422 +1403636623413555456.0000000000 4.5509671326 -1.7394003526 0.5531610678 0.4543586262 0.6239787026 0.4943618767 -0.399768873571 +1403636623463555584.0000000000 4.5511507935 -1.7397688911 0.5532591546 0.4543601444 0.6240084360 0.4942495770 -0.399859583708 +1403636623513555456.0000000000 4.5519195198 -1.7398577152 0.5531719187 0.4543426440 0.6240532197 0.4942577288 -0.399799497702 +1403636623563555584.0000000000 4.5527691886 -1.7399041621 0.5530238599 0.4542247525 0.6241522734 0.4942383225 -0.399802819493 +1403636623613555456.0000000000 4.5533527552 -1.7399257415 0.5529427710 0.4542233093 0.6242627340 0.4941621118 -0.399726195553 +1403636623663555584.0000000000 4.5531872607 -1.7399467165 0.5530190838 0.4541118943 0.6243044625 0.4942461750 -0.399683679939 +1403636623713555456.0000000000 4.5528620816 -1.7398343590 0.5531281497 0.4542675430 0.6243345120 0.4941003161 -0.399640205837 +1403636623763555584.0000000000 4.5525544985 -1.7397498509 0.5531824417 0.4543416952 0.6244208346 0.4939075512 -0.399659325233 +1403636623813555456.0000000000 4.5522311300 -1.7396029301 0.5531053568 0.4541903840 0.6247495068 0.4939088713 -0.399315884496 +1403636623863555584.0000000000 4.5518590688 -1.7393986405 0.5530997592 0.4543718281 0.6248111293 0.4935831257 -0.399415814176 +1403636623913555456.0000000000 4.5516298600 -1.7393233632 0.5529620784 0.4544136881 0.6248707921 0.4936493738 -0.399192922021 +1403636623963555584.0000000000 4.5516086760 -1.7393923080 0.5529251971 0.4543417904 0.6251143612 0.4933579752 -0.399253655254 +1403636624013555456.0000000000 4.5518177847 -1.7393429406 0.5528717367 0.4544919050 0.6249310212 0.4935350094 -0.399151000885 +1403636624063555584.0000000000 4.5516984649 -1.7391797671 0.5530666282 0.4544759413 0.6251184182 0.4933208734 -0.399140448732 +1403636624113555456.0000000000 4.5517153002 -1.7392552214 0.5528865257 0.4545134606 0.6256044199 0.4932183457 -0.398462404025 +1403636624163555584.0000000000 4.5522748794 -1.7393469590 0.5528770108 0.4544302721 0.6259317524 0.4928397354 -0.398511686589 +1403636624213555456.0000000000 4.5528147157 -1.7393815679 0.5527455711 0.4543872934 0.6259782184 0.4929857840 -0.398307010415 +1403636624263555584.0000000000 4.5531016295 -1.7392781178 0.5530864850 0.4541387432 0.6261372600 0.4930612026 -0.398247139308 +1403636624313555456.0000000000 4.5528619569 -1.7386595074 0.5530765306 0.4533277163 0.6274473872 0.4939853487 -0.395957362926 +1403636624363555584.0000000000 4.5534909221 -1.7377989698 0.5527341264 0.4512179597 0.6299120613 0.4955242820 -0.392516030026 +1403636624413555456.0000000000 4.5552965448 -1.7363218991 0.5527251963 0.4499151991 0.6320398088 0.4964306358 -0.389433713971 +1403636624463555584.0000000000 4.5579678594 -1.7345876076 0.5525880490 0.4473350331 0.6350103148 0.4972520402 -0.386514782014 +1403636624513555456.0000000000 4.5613595305 -1.7325364470 0.5524676700 0.4452834740 0.6378552324 0.4982134964 -0.382944698685 +1403636624563555584.0000000000 4.5650630006 -1.7302414806 0.5526202787 0.4440473782 0.6400445046 0.4987226081 -0.380053572832 +1403636624613555456.0000000000 4.5691567352 -1.7272143975 0.5525287762 0.4448264341 0.6401008858 0.4995130914 -0.3780039299 +1403636624663555584.0000000000 4.5731111551 -1.7232928182 0.5521983897 0.4476299131 0.6387731386 0.4995026071 -0.376952893336 +1403636624713555456.0000000000 4.5779273680 -1.7187019617 0.5505251614 0.4501924318 0.6371227319 0.5014952160 -0.374037360634 +1403636624763555584.0000000000 4.5836048757 -1.7136813767 0.5497518667 0.4532153767 0.6350557777 0.5018149981 -0.37347247462 +1403636624813555456.0000000000 4.5908470114 -1.7079737600 0.5485635984 0.4546655105 0.6338443897 0.5068934816 -0.366850870936 +1403636624863555584.0000000000 4.5989077776 -1.7022666669 0.5491991577 0.4554647367 0.6328920948 0.5117363492 -0.360728954971 +1403636624913555456.0000000000 4.6078426887 -1.6963527191 0.5515010530 0.4550570457 0.6328195658 0.5183111217 -0.351875067865 +1403636624963555584.0000000000 4.6173539512 -1.6910116939 0.5563574259 0.4545779335 0.6326355696 0.5244803125 -0.343586292448 +1403636625013555456.0000000000 4.6267163386 -1.6864382153 0.5638534058 0.4529389757 0.6332771100 0.5291163109 -0.337405269368 +1403636625063555584.0000000000 4.6355114341 -1.6828128953 0.5734297724 0.4503208476 0.6347001911 0.5330154000 -0.332056297979 +1403636625113555456.0000000000 4.6431623404 -1.6806254043 0.5852157513 0.4468529788 0.6365332934 0.5354363414 -0.329326139368 +1403636625163555584.0000000000 4.6492504624 -1.6795576726 0.5990037871 0.4428093192 0.6393273442 0.5343422891 -0.331147658654 +1403636625213555456.0000000000 4.6537747628 -1.6789129543 0.6140146194 0.4415703417 0.6399931874 0.5322428156 -0.334876004958 +1403636625263555584.0000000000 4.6569786727 -1.6784689594 0.6291469351 0.4422727144 0.6395042705 0.5293769541 -0.339395307285 +1403636625313555456.0000000000 4.6586487304 -1.6781472544 0.6411315237 0.4431970413 0.6385954328 0.5271060663 -0.343411488751 +1403636625363555584.0000000000 4.6598476947 -1.6780514403 0.6477681780 0.4435728768 0.6377257155 0.5260046486 -0.346219763259 +1403636625413555456.0000000000 4.6606881793 -1.6777490571 0.6489171935 0.4422911386 0.6381698311 0.5266791633 -0.346015713892 +1403636625463555584.0000000000 4.6609299183 -1.6774022530 0.6465019729 0.4400990512 0.6391150783 0.5283404099 -0.344530336921 +1403636625513555456.0000000000 4.6596660883 -1.6769793117 0.6421830273 0.4387079088 0.6397693501 0.5289805499 -0.34410772613 +1403636625563555584.0000000000 4.6573510743 -1.6768713585 0.6379646469 0.4378898720 0.6397617148 0.5300041344 -0.343588454 +1403636625613555456.0000000000 4.6537443915 -1.6767410750 0.6362767877 0.4381019147 0.6390551278 0.5309013604 -0.343247726198 +1403636625663555584.0000000000 4.6490864741 -1.6768178856 0.6384918972 0.4392372539 0.6378882490 0.5309517399 -0.343888741478 +1403636625713555456.0000000000 4.6426625753 -1.6772080071 0.6457309903 0.4406629672 0.6363508995 0.5299851596 -0.346394879703 +1403636625763555584.0000000000 4.6352749594 -1.6776601339 0.6566435178 0.4440339170 0.6337400099 0.5285068664 -0.349124580285 +1403636625813555456.0000000000 4.6271037834 -1.6783727237 0.6719136449 0.4469201598 0.6314550302 0.5265686433 -0.352494509897 +1403636625863555584.0000000000 4.6181759662 -1.6793381693 0.6913617983 0.4499252992 0.6290406555 0.5239995498 -0.356790625847 +1403636625913555456.0000000000 4.6094451343 -1.6807375892 0.7136427772 0.4514945905 0.6277249627 0.5222061489 -0.359742608019 +1403636625963555584.0000000000 4.6007692679 -1.6821815627 0.7378674690 0.4528097991 0.6265849493 0.5209148396 -0.361942422204 +1403636626013555456.0000000000 4.5923143225 -1.6837200111 0.7623325161 0.4537802860 0.6256569960 0.5197941530 -0.363937925929 +1403636626063555584.0000000000 4.5851656038 -1.6858043941 0.7864844554 0.4523073881 0.6264429488 0.5175857636 -0.367548957116 +1403636626113555456.0000000000 4.5780819695 -1.6878329569 0.8099583750 0.4499447132 0.6278451213 0.5151898143 -0.37140236127 +1403636626163555584.0000000000 4.5713098479 -1.6894646242 0.8325207479 0.4477576326 0.6292470267 0.5126370257 -0.375186036196 +1403636626213555456.0000000000 4.5649343935 -1.6904430904 0.8529497426 0.4456737363 0.6305120154 0.5105066318 -0.378434271683 +1403636626263555584.0000000000 4.5593044940 -1.6905181723 0.8702228937 0.4444559048 0.6312603574 0.5092130585 -0.38035689937 +1403636626313555456.0000000000 4.5539501323 -1.6897740406 0.8837290221 0.4438997328 0.6314014056 0.5088427888 -0.381266715662 +1403636626363555584.0000000000 4.5493393253 -1.6881923201 0.8933219222 0.4440970283 0.6312533025 0.5088788750 -0.381234033383 +1403636626413555456.0000000000 4.5452861151 -1.6857164458 0.8993672257 0.4453597483 0.6301832160 0.5095782569 -0.380596648579 +1403636626463555584.0000000000 4.5415062650 -1.6823101165 0.9030547003 0.4474318708 0.6285081338 0.5108161923 -0.379274392069 +1403636626513555456.0000000000 4.5382667889 -1.6781904783 0.9059293721 0.4512746029 0.6254663389 0.5114411740 -0.378907663285 +1403636626563555584.0000000000 4.5358761547 -1.6735412656 0.9078343793 0.4554502278 0.6220560676 0.5122152779 -0.378479653138 +1403636626613555456.0000000000 4.5344689610 -1.6686462321 0.9087993663 0.4591259124 0.6187579281 0.5130548350 -0.378307757373 +1403636626663555584.0000000000 4.5342220734 -1.6636868758 0.9087494333 0.4620735311 0.6159542975 0.5139667012 -0.378056325513 +1403636626713555456.0000000000 4.5353128313 -1.6589986173 0.9073204632 0.4620700009 0.6152685357 0.5152013053 -0.377496434735 +1403636626763555584.0000000000 4.5376387277 -1.6546029690 0.9046515279 0.4603654617 0.6155898290 0.5170353280 -0.376546509376 +1403636626813555456.0000000000 4.5407613839 -1.6503838321 0.9011286546 0.4583268978 0.6163669404 0.5187732718 -0.375369873713 +1403636626863555584.0000000000 4.5449942422 -1.6462744727 0.8962213302 0.4558098877 0.6175532755 0.5208231745 -0.373642234048 +1403636626913555456.0000000000 4.5497424381 -1.6423701188 0.8907051235 0.4531190605 0.6190088802 0.5229402282 -0.371543592261 +1403636626963555584.0000000000 4.5550121831 -1.6385377337 0.8842901303 0.4504872056 0.6207104700 0.5252571985 -0.368625372698 +1403636627013555456.0000000000 4.5606353814 -1.6348877428 0.8772892197 0.4478202355 0.6223618353 0.5272477153 -0.366241217489 +1403636627063555584.0000000000 4.5661762138 -1.6312908985 0.8708234949 0.4455135510 0.6240504657 0.5288401120 -0.363877490451 +1403636627113555456.0000000000 4.5718491752 -1.6278814048 0.8658734379 0.4423456963 0.6259893790 0.5309071052 -0.361393453121 +1403636627163555584.0000000000 4.5764573434 -1.6244467307 0.8650501782 0.4427761805 0.6255280180 0.5304077472 -0.362396984524 +1403636627213555456.0000000000 4.5812738321 -1.6211963365 0.8668987551 0.4447141519 0.6240983103 0.5296963267 -0.363527748144 +1403636627263555584.0000000000 4.5849878996 -1.6178273788 0.8718033303 0.4473480427 0.6222137192 0.5282722248 -0.36559304252 +1403636627313555456.0000000000 4.5892726065 -1.6148162295 0.8791543534 0.4487018387 0.6209346947 0.5267563500 -0.368285911277 +1403636627363555584.0000000000 4.5931130746 -1.6116221732 0.8886566638 0.4490636633 0.6207018166 0.5257776479 -0.369633529462 +1403636627413555456.0000000000 4.5975123311 -1.6086131097 0.9002876890 0.4487049289 0.6208029195 0.5252884111 -0.370593722347 +1403636627463555584.0000000000 4.6023053534 -1.6053579685 0.9141604751 0.4488746915 0.6212131831 0.5238359363 -0.371754763637 +1403636627513555456.0000000000 4.6066870365 -1.6016423740 0.9275362130 0.4482391842 0.6233944147 0.5222811500 -0.371057189367 +1403636627563555584.0000000000 4.6111431328 -1.5972957724 0.9376288215 0.4484652295 0.6261063165 0.5199183995 -0.369533051568 +1403636627613555456.0000000000 4.6162076742 -1.5925635415 0.9433384231 0.4491026294 0.6290983624 0.5176199731 -0.366894592763 +1403636627663555584.0000000000 4.6217976244 -1.5879445167 0.9445586326 0.4485653204 0.6323821403 0.5164739657 -0.363506017267 +1403636627713555456.0000000000 4.6278248546 -1.5831226926 0.9417806699 0.4474262609 0.6368316746 0.5154394194 -0.358576859461 +1403636627763555584.0000000000 4.6335299926 -1.5777648391 0.9367053317 0.4459027376 0.6421901936 0.5143656954 -0.352406633357 +1403636627813555456.0000000000 4.6383782478 -1.5720809955 0.9307656747 0.4448899844 0.6474726889 0.5128580882 -0.346162678801 +1403636627863555584.0000000000 4.6425271022 -1.5658307256 0.9242866554 0.4442484493 0.6529698236 0.5107800382 -0.339672603053 +1403636627913555456.0000000000 4.6458401288 -1.5595605042 0.9186753001 0.4434043906 0.6575745998 0.5094549787 -0.333832018909 +1403636627963555584.0000000000 4.6479161086 -1.5533032921 0.9150234202 0.4439834312 0.6606114866 0.5079335684 -0.329354925039 +1403636628013555456.0000000000 4.6479675928 -1.5466755083 0.9136778644 0.4452562578 0.6628172670 0.5060359777 -0.326109988572 +1403636628063555584.0000000000 4.6452228570 -1.5395965834 0.9157912074 0.4480546951 0.6634022587 0.5032743924 -0.325360291458 +1403636628113555456.0000000000 4.6416778715 -1.5327515892 0.9217112973 0.4532296839 0.6621048363 0.4990219860 -0.327379133187 +1403636628163555584.0000000000 4.6367265964 -1.5258751686 0.9300939238 0.4593496180 0.6597804149 0.4936240252 -0.331697232944 +1403636628213555456.0000000000 4.6313079866 -1.5189908631 0.9400232097 0.4645510090 0.6576117305 0.4884844852 -0.336336259923 +1403636628263555584.0000000000 4.6258576854 -1.5123129207 0.9513394598 0.4673539927 0.6568872512 0.4835462247 -0.340972774913 +1403636628313555456.0000000000 4.6210837035 -1.5056807051 0.9637446647 0.4682011495 0.6569458659 0.4793680057 -0.345566387185 +1403636628363555584.0000000000 4.6168341265 -1.4985161352 0.9763914288 0.4682169580 0.6573002604 0.4771499914 -0.34793265693 +1403636628413555456.0000000000 4.6131469925 -1.4909324514 0.9885422358 0.4674564061 0.6580810924 0.4756758569 -0.349494296539 +1403636628463555584.0000000000 4.6100934181 -1.4828988159 0.9993454349 0.4667358842 0.6584848949 0.4750201049 -0.350586875807 +1403636628513555456.0000000000 4.6076273048 -1.4742631852 1.0085651219 0.4656313704 0.6589568665 0.4748696223 -0.351371764464 +1403636628563555584.0000000000 4.6058281164 -1.4651617052 1.0161132291 0.4643304745 0.6595653460 0.4747290179 -0.35214077354 +1403636628613555456.0000000000 4.6045496353 -1.4554496202 1.0220571396 0.4630137938 0.6597553839 0.4750127160 -0.35313450683 +1403636628663555584.0000000000 4.6037395399 -1.4447741597 1.0263645111 0.4626541472 0.6595195477 0.4753853335 -0.353544750976 +1403636628713555456.0000000000 4.6032179208 -1.4326995933 1.0288017643 0.4637738446 0.6592067537 0.4760148612 -0.351809790755 +1403636628763555584.0000000000 4.6032415628 -1.4195140948 1.0289739160 0.4646204676 0.6602704300 0.4769488715 -0.347405461036 +1403636628813555456.0000000000 4.6035073280 -1.4055964476 1.0275347885 0.4652583467 0.6623285512 0.4776996637 -0.341553205726 +1403636628863555584.0000000000 4.6030261610 -1.3909173781 1.0249833245 0.4651772416 0.6651376077 0.4780970028 -0.335597009279 +1403636628913555456.0000000000 4.6016131998 -1.3757953979 1.0240277508 0.4645646564 0.6682628880 0.4780497718 -0.330261726911 +1403636628963555584.0000000000 4.6013220905 -1.3610882044 1.0251619645 0.4640783560 0.6707691562 0.4780212455 -0.325876828568 +1403636629013555456.0000000000 4.6013494877 -1.3466378650 1.0288630187 0.4633063195 0.6732855821 0.4774143772 -0.32265971508 +1403636629063555584.0000000000 4.6017304031 -1.3322837815 1.0350733711 0.4634121929 0.6752656612 0.4760922893 -0.320314780098 +1403636629113555456.0000000000 4.6016701125 -1.3174775468 1.0425141789 0.4645932164 0.6764486932 0.4749538251 -0.317787936771 +1403636629163555584.0000000000 4.6005117021 -1.3020025315 1.0494556735 0.4658447437 0.6787086752 0.4719966137 -0.315535109949 +1403636629213555456.0000000000 4.5980978800 -1.2858579601 1.0552675342 0.4683889330 0.6808662948 0.4678599643 -0.313272963703 +1403636629263555584.0000000000 4.5950022060 -1.2695882646 1.0600022222 0.4711787609 0.6826293235 0.4635283465 -0.311687750688 +1403636629313555456.0000000000 4.5905620499 -1.2530391739 1.0633264641 0.4736832583 0.6843525966 0.4586267301 -0.311363480147 +1403636629363555584.0000000000 4.5857851190 -1.2364859972 1.0654735288 0.4757062428 0.6858277848 0.4540076890 -0.311802563357 +1403636629413555456.0000000000 4.5806187951 -1.2198216592 1.0665245257 0.4773454101 0.6873272868 0.4486149100 -0.313794873798 +1403636629463555584.0000000000 4.5753622114 -1.2024276162 1.0661659476 0.4797076490 0.6893553542 0.4418115225 -0.315392367783 +1403636629513555456.0000000000 4.5703732243 -1.1844413986 1.0639106051 0.4815198627 0.6923993832 0.4350145644 -0.315410913928 +1403636629563555584.0000000000 4.5657547108 -1.1655862920 1.0594802360 0.4823507580 0.6965752839 0.4290987465 -0.313041348443 +1403636629613555456.0000000000 4.5615434658 -1.1455173024 1.0526671501 0.4832675401 0.7015182445 0.4244114630 -0.306919447747 +1403636629663555584.0000000000 4.5577421867 -1.1245873063 1.0441343220 0.4830544514 0.7075692670 0.4201282907 -0.299159403558 +1403636629713555456.0000000000 4.5535337088 -1.1026265617 1.0341525111 0.4833134155 0.7135849307 0.4155143832 -0.290779102615 +1403636629763555584.0000000000 4.5493349430 -1.0796932507 1.0230341633 0.4841624639 0.7195743318 0.4102701318 -0.281918265645 +1403636629813555456.0000000000 4.5444462928 -1.0556061756 1.0110605682 0.4857903466 0.7252992860 0.4037302478 -0.273771021036 +1403636629863555584.0000000000 4.5381727452 -1.0304068226 0.9983626190 0.4875318200 0.7309067274 0.3965381079 -0.26616838526 +1403636629913555456.0000000000 4.5309665366 -1.0045341316 0.9860461864 0.4895290900 0.7357345860 0.3894466249 -0.259590476167 +1403636629963555584.0000000000 4.5235467132 -0.9784963024 0.9753583794 0.4919791036 0.7393913040 0.3833311033 -0.253602694166 +1403636630013555456.0000000000 4.5160259691 -0.9527325429 0.9669350543 0.4941849066 0.7421702667 0.3777841264 -0.249486927762 +1403636630063555584.0000000000 4.5078515992 -0.9266882603 0.9605933180 0.4972645579 0.7435969913 0.3727992087 -0.246601346348 +1403636630113555456.0000000000 4.4979687881 -0.8995044279 0.9565521963 0.5022468055 0.7431666599 0.3677720779 -0.245347020929 +1403636630163555584.0000000000 4.4872963155 -0.8717980882 0.9551274862 0.5085481275 0.7413464928 0.3624128365 -0.245847748682 +1403636630213555456.0000000000 4.4763730415 -0.8437234056 0.9552693595 0.5148006918 0.7391249432 0.3579743581 -0.246026268829 +1403636630263555584.0000000000 4.4651923125 -0.8154212107 0.9575109204 0.5199334792 0.7371428710 0.3539854069 -0.24694917845 +1403636630313555456.0000000000 4.4544060227 -0.7873374008 0.9606009167 0.5232388265 0.7359206527 0.3516765879 -0.246911929503 +1403636630363555584.0000000000 4.4441732187 -0.7596482546 0.9647220387 0.5232912410 0.7365344940 0.3511242045 -0.245753960869 +1403636630413555456.0000000000 4.4340958509 -0.7320183676 0.9701457465 0.5227687668 0.7372732783 0.3512402983 -0.244481456175 +1403636630463555584.0000000000 4.4244437085 -0.7046308090 0.9766705608 0.5212353289 0.7382869161 0.3529032220 -0.242292132239 +1403636630513555456.0000000000 4.4142919652 -0.6773862526 0.9854112994 0.5206539673 0.7384395584 0.3543395297 -0.240977099802 +1403636630563555584.0000000000 4.4039551876 -0.6502473614 0.9951609874 0.5203840087 0.7380780811 0.3570063751 -0.238720920292 +1403636630613555456.0000000000 4.3932845709 -0.6233001496 1.0050760998 0.5208800457 0.7369867533 0.3594664933 -0.237314862016 +1403636630663555584.0000000000 4.3822518852 -0.5967800032 1.0136744033 0.5202545319 0.7365183013 0.3621560136 -0.236048799488 +1403636630713555456.0000000000 4.3706949021 -0.5705854768 1.0210640743 0.5197540873 0.7359961217 0.3641428856 -0.235723050537 +1403636630763555584.0000000000 4.3584307322 -0.5448038313 1.0274116438 0.5189817048 0.7358816993 0.3644812386 -0.237254170511 +1403636630813555456.0000000000 4.3456561880 -0.5194611466 1.0321670842 0.5173888327 0.7361593988 0.3650159347 -0.239042888981 +1403636630863555584.0000000000 4.3324789369 -0.4943694517 1.0355365113 0.5162913160 0.7363358947 0.3649608722 -0.24094872684 +1403636630913555456.0000000000 4.3193030331 -0.4695409701 1.0374328082 0.5153272589 0.7363550671 0.3647773328 -0.24322115213 +1403636630963555584.0000000000 4.3059276756 -0.4447013852 1.0379114729 0.5144959401 0.7364219005 0.3645580494 -0.2451002666 +1403636631013555456.0000000000 4.2923812005 -0.4194706542 1.0372618014 0.5141701115 0.7364296089 0.3643878035 -0.24601230911 +1403636631063555584.0000000000 4.2787513064 -0.3942237322 1.0357968988 0.5145065072 0.7356904202 0.3644974417 -0.247354552733 +1403636631113555456.0000000000 4.2649282030 -0.3688956979 1.0337398926 0.5156287375 0.7347644335 0.3640491095 -0.248428014142 +1403636631163555584.0000000000 4.2510007824 -0.3437296120 1.0310779588 0.5165752583 0.7339099752 0.3638466610 -0.249282486367 +1403636631213555456.0000000000 4.2369928288 -0.3187944765 1.0282416900 0.5178074051 0.7326859576 0.3635930203 -0.250692828731 +1403636631263555584.0000000000 4.2232823726 -0.2937613962 1.0250979102 0.5189554728 0.7317043004 0.3636378813 -0.251120539291 +1403636631313555456.0000000000 4.2096436657 -0.2690262434 1.0214980718 0.5186569625 0.7316444780 0.3637314394 -0.251775203417 +1403636631363555584.0000000000 4.1962275265 -0.2442037895 1.0167668604 0.5188652921 0.7312886306 0.3642261684 -0.251664549868 +1403636631413555456.0000000000 4.1825621495 -0.2196333996 1.0105173458 0.5186682782 0.7311754154 0.3644797210 -0.252032263767 +1403636631463555584.0000000000 4.1692549523 -0.1953226997 1.0027400061 0.5188035045 0.7308184929 0.3652411741 -0.251686588444 +1403636631513555456.0000000000 4.1561253245 -0.1712952379 0.9938366906 0.5189297203 0.7304045181 0.3662876235 -0.251106675064 +1403636631563555584.0000000000 4.1428988269 -0.1476314468 0.9843897388 0.5196020663 0.7296971931 0.3671937034 -0.250448564074 +1403636631613555456.0000000000 4.1298980265 -0.1245896228 0.9753138680 0.5196166595 0.7292555237 0.3683971658 -0.249936865273 +1403636631663555584.0000000000 4.1166082841 -0.1017077882 0.9668121000 0.5191369050 0.7290726221 0.3696612548 -0.249600765688 +1403636631713555456.0000000000 4.1033110735 -0.0789919745 0.9591549030 0.5189777859 0.7288517181 0.3704839905 -0.249356859869 +1403636631763555584.0000000000 4.0913653079 -0.0576115073 0.9532766432 0.5187329428 0.7287060920 0.3713559719 -0.248994593584 +1403636631813555456.0000000000 4.0782422090 -0.0360883841 0.9498847383 0.5189171266 0.7281741735 0.3718845433 -0.24937777614 +1403636631863555584.0000000000 4.0639981507 -0.0139513752 0.9480164808 0.5189567532 0.7279837027 0.3728187881 -0.248454760942 +1403636631913555456.0000000000 4.0499541232 0.0076922925 0.9475092457 0.5186088950 0.7280209960 0.3738125902 -0.247577040119 +1403636631963555584.0000000000 4.0356787810 0.0291220057 0.9474479517 0.5185198519 0.7280199126 0.3742191673 -0.247152149233 +1403636632013555456.0000000000 4.0212238376 0.0499184584 0.9480144811 0.5187423709 0.7279735727 0.3739491272 -0.247230419533 +1403636632063555584.0000000000 4.0062464100 0.0705598513 0.9492768531 0.5200100462 0.7272035770 0.3735248246 -0.247474675262 +1403636632113555456.0000000000 3.9919200484 0.0902089112 0.9501803754 0.5217502472 0.7259096168 0.3738797371 -0.247074583677 +1403636632163555584.0000000000 3.9776925843 0.1092379864 0.9512848112 0.5243417211 0.7243773682 0.3745842501 -0.245009851768 +1403636632213555456.0000000000 3.9628700281 0.1275378101 0.9519888511 0.5246947561 0.7243180715 0.3749477133 -0.243870778348 +1403636632263555584.0000000000 3.9475235626 0.1449998603 0.9519158405 0.5250213262 0.7244910867 0.3737054921 -0.244559762547 +1403636632313555456.0000000000 3.9321315025 0.1617461217 0.9500035343 0.5249216093 0.7249128661 0.3727811975 -0.24493431667 +1403636632363555584.0000000000 3.9168121194 0.1775297608 0.9465582782 0.5248939907 0.7251515136 0.3719135863 -0.245605099892 +1403636632413555456.0000000000 3.9016557831 0.1926050297 0.9409483699 0.5242747921 0.7259571494 0.3716055621 -0.245013195142 +1403636632463555584.0000000000 3.8863977670 0.2066073881 0.9337239115 0.5209149682 0.7285840370 0.3706503212 -0.245827655672 +1403636632513555456.0000000000 3.8708421559 0.2197312237 0.9253922007 0.5163845154 0.7310966851 0.3705567317 -0.248057206824 +1403636632563555584.0000000000 3.8550468287 0.2323557819 0.9158863797 0.5094985741 0.7345597346 0.3711514898 -0.251156865025 +1403636632613555456.0000000000 3.8388998430 0.2449654974 0.9057648476 0.5026817291 0.7370768084 0.3728597341 -0.254959754548 +1403636632663555584.0000000000 3.8224172241 0.2578943750 0.8951592278 0.4967624597 0.7378869228 0.3762160145 -0.259251727589 +1403636632713555456.0000000000 3.8050073556 0.2715116712 0.8850159391 0.4919255391 0.7368262815 0.3810964717 -0.264313779629 +1403636632763555584.0000000000 3.7874250823 0.2857775902 0.8763018604 0.4880013293 0.7341219431 0.3873983830 -0.269892882581 +1403636632813555456.0000000000 3.7698036488 0.3007060268 0.8696312556 0.4861714128 0.7288621407 0.3959689528 -0.274965316975 +1403636632863555584.0000000000 3.7512520919 0.3168949375 0.8649268028 0.4870017189 0.7211038095 0.4058197851 -0.279551290014 +1403636632913555456.0000000000 3.7324894964 0.3338206553 0.8624593941 0.4888077057 0.7123320869 0.4156638175 -0.28438286807 +1403636632963555584.0000000000 3.7132921023 0.3514313745 0.8610659319 0.4897524949 0.7048805013 0.4247828133 -0.28782900146 +1403636633013555456.0000000000 3.6934990184 0.3694831351 0.8612466837 0.4905270610 0.6981905513 0.4327385014 -0.290947668684 +1403636633063555584.0000000000 3.6737357112 0.3874076925 0.8622445331 0.4898734102 0.6932044119 0.4397403958 -0.29346221146 +1403636633113555456.0000000000 3.6536713355 0.4052321858 0.8636073835 0.4890006133 0.6890723339 0.4451769972 -0.296437447054 +1403636633163555584.0000000000 3.6333376424 0.4229104531 0.8635649165 0.4878767897 0.6859161203 0.4498689382 -0.298518428869 +1403636633213555456.0000000000 3.6125005924 0.4401798599 0.8620614432 0.4866161217 0.6836630261 0.4531290061 -0.30080512081 +1403636633263555584.0000000000 3.5915374494 0.4570804472 0.8588930555 0.4841271100 0.6830015007 0.4555027919 -0.30273271698 +1403636633313555456.0000000000 3.5701937667 0.4736746621 0.8545789127 0.4815760097 0.6829789120 0.4570790789 -0.304471785661 +1403636633363555584.0000000000 3.5486766359 0.4900717037 0.8490022443 0.4784272846 0.6838171239 0.4576507832 -0.306687520332 +1403636633413555456.0000000000 3.5265193375 0.5065225653 0.8422910852 0.4756079433 0.6852429843 0.4577815174 -0.307693384636 +1403636633463555584.0000000000 3.5042941797 0.5229004609 0.8344009547 0.4730210002 0.6866357607 0.4576222657 -0.308811151614 +1403636633513555456.0000000000 3.4814934699 0.5397143371 0.8255054466 0.4715173161 0.6878507670 0.4573836122 -0.308760383383 +1403636633563555584.0000000000 3.4581125464 0.5569008170 0.8161265953 0.4699662914 0.6894778091 0.4568140561 -0.308339024076 +1403636633613555456.0000000000 3.4342860709 0.5747715109 0.8069153800 0.4685625674 0.6910308056 0.4566395908 -0.307255317659 +1403636633663555584.0000000000 3.4094481423 0.5933393831 0.7989179597 0.4681722457 0.6923079779 0.4562265023 -0.305584343132 +1403636633713555456.0000000000 3.3840091823 0.6123958017 0.7930242498 0.4688060188 0.6929344325 0.4549431558 -0.305105742293 +1403636633763555584.0000000000 3.3580765071 0.6318993492 0.7885886409 0.4693836260 0.6935022052 0.4534242630 -0.305188696853 +1403636633813555456.0000000000 3.3311728788 0.6521814028 0.7862915374 0.4697410504 0.6943430399 0.4520049645 -0.30483208583 +1403636633863555584.0000000000 3.3037452214 0.6726886590 0.7858409231 0.4702787426 0.6950215738 0.4497943822 -0.305725252368 +1403636633913555456.0000000000 3.2758405952 0.6933926103 0.7869670799 0.4696963622 0.6964735160 0.4465747531 -0.308027529265 +1403636633963555584.0000000000 3.2473835105 0.7144619044 0.7880473369 0.4694489671 0.6976718136 0.4428304711 -0.311083399804 +1403636634013555456.0000000000 3.2187340442 0.7362366578 0.7879237306 0.4696119503 0.6986249562 0.4393810903 -0.313579406672 +1403636634063555584.0000000000 3.1899985222 0.7590444218 0.7865409954 0.4694355318 0.6997651992 0.4373352464 -0.314160516077 +1403636634113555456.0000000000 3.1613901608 0.7824639300 0.7854029174 0.4690171600 0.6999287172 0.4374560787 -0.314252881555 +1403636634163555584.0000000000 3.1330226582 0.8070752556 0.7855601271 0.4686659286 0.6999566906 0.4386316096 -0.313073776699 +1403636634213555456.0000000000 3.1044363998 0.8329352869 0.7873908314 0.4689310567 0.6993245007 0.4410976331 -0.310615171789 +1403636634263555584.0000000000 3.0751018090 0.8600249613 0.7912901532 0.4709072854 0.6974465506 0.4435951352 -0.308282327894 +1403636634313555456.0000000000 3.0450012199 0.8877696901 0.7968404193 0.4744497495 0.6944913785 0.4448925580 -0.307652031064 +1403636634363555584.0000000000 3.0146134005 0.9158994088 0.8024438272 0.4786879509 0.6909924951 0.4454872015 -0.308104480041 +1403636634413555456.0000000000 2.9840685175 0.9443366517 0.8069752640 0.4829180106 0.6874490465 0.4460005805 -0.308686711139 +1403636634463555584.0000000000 2.9536904621 0.9727780632 0.8096518531 0.4856641859 0.6849910415 0.4466543530 -0.308897168231 +1403636634513555456.0000000000 2.9234334515 1.0008986871 0.8107987197 0.4883096893 0.6824116659 0.4468788525 -0.310108459647 +1403636634563555584.0000000000 2.8934993897 1.0288476550 0.8103360268 0.4899960225 0.6805309790 0.4472763243 -0.311007032599 +1403636634613555456.0000000000 2.8640995593 1.0560840675 0.8081143000 0.4908669502 0.6785598786 0.4489926739 -0.311467024098 +1403636634663555584.0000000000 2.8351198105 1.0824104828 0.8045527171 0.4906004533 0.6762414273 0.4517678437 -0.312912995121 +1403636634713555456.0000000000 2.8066813922 1.1083148634 0.8007555586 0.4903848768 0.6735722813 0.4553108976 -0.313871057946 +1403636634763555584.0000000000 2.7787982298 1.1333738725 0.7974643051 0.4881086589 0.6723503959 0.4590962081 -0.314524329639 +1403636634813555456.0000000000 2.7511734464 1.1577828771 0.7954512592 0.4853823839 0.6717780588 0.4621474191 -0.315496345753 +1403636634863555584.0000000000 2.7237880463 1.1817928385 0.7947971491 0.4827242005 0.6713205601 0.4649412070 -0.316442294696 +1403636634913555456.0000000000 2.6965363702 1.2051772714 0.7958360897 0.4804168028 0.6704206964 0.4678875046 -0.317517036636 +1403636634963555584.0000000000 2.6692927468 1.2281634544 0.7983192876 0.4778137229 0.6699076712 0.4711969262 -0.317633774931 +1403636635013555456.0000000000 2.6415726676 1.2508608635 0.8027077982 0.4770932817 0.6683102749 0.4738290501 -0.31816569306 +1403636635063555584.0000000000 2.6138720333 1.2729973296 0.8065500011 0.4756060739 0.6675277391 0.4764781260 -0.318078882413 +1403636635113555456.0000000000 2.5859536367 1.2948515620 0.8091160256 0.4742094991 0.6670276953 0.4786568866 -0.317941802217 +1403636635163555584.0000000000 2.5580355290 1.3162912887 0.8101457551 0.4729044853 0.6666991128 0.4800425415 -0.318485163115 +1403636635213555456.0000000000 2.5299572464 1.3375238269 0.8095524073 0.4711437001 0.6668822683 0.4813730925 -0.318702996496 +1403636635263555584.0000000000 2.5012433409 1.3584044970 0.8079119684 0.4690734603 0.6673548035 0.4816354201 -0.320366941378 +1403636635313555456.0000000000 2.4722348077 1.3789458396 0.8050819817 0.4666580155 0.6683518613 0.4817018828 -0.321713198705 +1403636635363555584.0000000000 2.4424538237 1.3993510004 0.8022183405 0.4632618156 0.6703019916 0.4808368121 -0.323851339907 +1403636635413555456.0000000000 2.4126230119 1.4200226613 0.8003312607 0.4614283186 0.6710765054 0.4808136238 -0.324897660435 +1403636635463555584.0000000000 2.3816675772 1.4412015701 0.7996034669 0.4609429565 0.6713582999 0.4800273003 -0.326164705143 +1403636635513555456.0000000000 2.3495144143 1.4626769755 0.8011948509 0.4591345257 0.6726763969 0.4787079584 -0.327933900315 +1403636635563555584.0000000000 2.3181733345 1.4842711176 0.8046607965 0.4586625388 0.6730262802 0.4783169716 -0.328446611246 +1403636635613555456.0000000000 2.2877478815 1.5060312547 0.8088499573 0.4586860085 0.6731553418 0.4774207588 -0.329451742191 +1403636635663555584.0000000000 2.2569098701 1.5285591819 0.8142578938 0.4592228539 0.6732285444 0.4762882887 -0.330192615746 +1403636635713555456.0000000000 2.2253801236 1.5517105499 0.8209870471 0.4600242832 0.6730399695 0.4753286619 -0.33084365123 +1403636635763555584.0000000000 2.1924252245 1.5757238966 0.8304166752 0.4613537716 0.6725102731 0.4728236904 -0.333647100728 +1403636635813555456.0000000000 2.1597114959 1.6000653244 0.8421379213 0.4622566168 0.6722958137 0.4690667765 -0.338102821967 +1403636635863555584.0000000000 2.1267318904 1.6255970928 0.8558872465 0.4624574524 0.6726788358 0.4659867079 -0.341310235288 +1403636635913555456.0000000000 2.0952093585 1.6517783151 0.8704858518 0.4598788337 0.6748167449 0.4642315715 -0.342961903399 +1403636635963555584.0000000000 2.0637451062 1.6794665025 0.8853578583 0.4573712791 0.6769377480 0.4646984949 -0.341499790998 +1403636636013555456.0000000000 2.0329358432 1.7080227412 0.8996171100 0.4549881988 0.6788594789 0.4673110430 -0.337277239092 +1403636636063555584.0000000000 2.0019803811 1.7377701109 0.9124339516 0.4547550182 0.6793101631 0.4706472717 -0.332004098577 +1403636636113555456.0000000000 1.9707573203 1.7682012877 0.9242194047 0.4554065999 0.6789778952 0.4738081436 -0.327260889385 +1403636636163555584.0000000000 1.9387412704 1.7993177091 0.9369306465 0.4586994008 0.6767337753 0.4753413431 -0.325079781883 +1403636636213555456.0000000000 1.9063869861 1.8309210565 0.9514210684 0.4642372874 0.6728646751 0.4759017987 -0.324429265047 +1403636636263555584.0000000000 1.8737262281 1.8627096351 0.9680498677 0.4702039683 0.6687546454 0.4755266068 -0.324884439037 +1403636636313555456.0000000000 1.8411176677 1.8942084201 0.9863334061 0.4748255017 0.6655393572 0.4745615625 -0.32617392647 +1403636636363555584.0000000000 1.8085141232 1.9255409868 1.0056009363 0.4801828900 0.6618310070 0.4729275794 -0.328243225362 +1403636636413555456.0000000000 1.7763259780 1.9563596241 1.0243374388 0.4863781994 0.6572621632 0.4705298658 -0.331729319507 +1403636636463555584.0000000000 1.7450725284 1.9865696579 1.0412706968 0.4912362385 0.6536181456 0.4685243414 -0.334597099934 +1403636636513555456.0000000000 1.7150638895 2.0162234838 1.0552809418 0.4946933128 0.6511587195 0.4688861622 -0.333791275 +1403636636563555584.0000000000 1.6864328304 2.0449943950 1.0670193311 0.4972553843 0.6492688110 0.4702143285 -0.331791469412 +1403636636613555456.0000000000 1.6587449424 2.0729640267 1.0770647896 0.4997453960 0.6474034179 0.4720650306 -0.329056166178 +1403636636663555584.0000000000 1.6323628070 2.0997889023 1.0847712774 0.5016437365 0.6459575798 0.4745033235 -0.325482661216 +1403636636713555456.0000000000 1.6069405644 2.1250999948 1.0905471141 0.5034960565 0.6446171280 0.4763493531 -0.322570570921 +1403636636763555584.0000000000 1.5823666208 2.1487081089 1.0941130671 0.5049878888 0.6433939961 0.4785239205 -0.319446796035 +1403636636813555456.0000000000 1.5586838769 2.1705170362 1.0953786358 0.5070948392 0.6415697468 0.4812910062 -0.31559792694 +1403636636863555584.0000000000 1.5358245332 2.1901973902 1.0945876847 0.5080495941 0.6405545348 0.4840987404 -0.311807484391 +1403636636913555456.0000000000 1.5134813412 2.2071625686 1.0925112830 0.5046480387 0.6427651440 0.4842206450 -0.312591896252 +1403636636963555584.0000000000 1.4915245382 2.2219287597 1.0894210743 0.5002491860 0.6455214929 0.4827195352 -0.31628247569 +1403636637013555456.0000000000 1.4701778511 2.2348963868 1.0850964405 0.4947338763 0.6490596234 0.4807903960 -0.320625314028 +1403636637063555584.0000000000 1.4494024539 2.2467681796 1.0797718958 0.4903312293 0.6518192625 0.4787496076 -0.324816483244 +1403636637113555456.0000000000 1.4295925285 2.2576293518 1.0729385735 0.4859857847 0.6544755294 0.4777672439 -0.327441688066 +1403636637163555584.0000000000 1.4103713509 2.2681203439 1.0649524045 0.4819231408 0.6570343560 0.4779564348 -0.328045100306 +1403636637213555456.0000000000 1.3919828690 2.2780067438 1.0561029544 0.4783582788 0.6592891648 0.4791832500 -0.32694734632 +1403636637263555584.0000000000 1.3740673308 2.2874768862 1.0480915698 0.4756877788 0.6607194281 0.4802479109 -0.326393809073 +1403636637313555456.0000000000 1.3547764701 2.2972811492 1.0416713284 0.4735716382 0.6617736050 0.4813981274 -0.325640050075 +1403636637363555584.0000000000 1.3345270701 2.3070607665 1.0376069755 0.4726581414 0.6622446053 0.4825299201 -0.324331990844 +1403636637413555456.0000000000 1.3127467160 2.3167117276 1.0361276818 0.4712498315 0.6625723338 0.4830193920 -0.324982716297 +1403636637463555584.0000000000 1.2905201413 2.3263370878 1.0374462945 0.4701016945 0.6628033426 0.4845552978 -0.323886228834 +1403636637513555456.0000000000 1.2692292742 2.3353254985 1.0403917671 0.4692141515 0.6630864854 0.4846415834 -0.324464063584 +1403636637563555584.0000000000 1.2488302385 2.3438578964 1.0440792914 0.4677347201 0.6636696833 0.4853715263 -0.324316611604 +1403636637613555456.0000000000 1.2289759788 2.3519260923 1.0492488254 0.4667304304 0.6638842231 0.4852811800 -0.325457554803 +1403636637663555584.0000000000 1.2094499589 2.3598922905 1.0561913973 0.4656202481 0.6644052253 0.4854782489 -0.32569057547 +1403636637713555456.0000000000 1.1879959514 2.3685293772 1.0656366951 0.4660479151 0.6637527001 0.4856972775 -0.326082579464 +1403636637763555584.0000000000 1.1650838067 2.3776815401 1.0762372344 0.4667534246 0.6628353423 0.4857951548 -0.326792927106 +1403636637813555456.0000000000 1.1423818106 2.3866535622 1.0887212674 0.4683614818 0.6614762728 0.4854305554 -0.32778626996 +1403636637863555584.0000000000 1.1198428876 2.3952838770 1.1031781680 0.4693496870 0.6605118725 0.4851840691 -0.328681238563 +1403636637913555456.0000000000 1.0963294171 2.4039334870 1.1191317005 0.4704453417 0.6594234132 0.4847392809 -0.329954197164 +1403636637963555584.0000000000 1.0731821325 2.4124327528 1.1330464862 0.4720688619 0.6580958778 0.4839807988 -0.331396124893 +1403636638013555456.0000000000 1.0501392217 2.4209088189 1.1426049601 0.4730704558 0.6572342349 0.4834688053 -0.33242355301 +1403636638063555584.0000000000 1.0272659064 2.4291732729 1.1478287498 0.4740117413 0.6562570931 0.4830734803 -0.333585835306 +1403636638113555456.0000000000 1.0043581755 2.4374349077 1.1488681260 0.4752055765 0.6552871071 0.4822879970 -0.334927985263 +1403636638163555584.0000000000 0.9818552240 2.4453315088 1.1471185318 0.4758756010 0.6546083173 0.4817643057 -0.336055824209 +1403636638213555456.0000000000 0.9599034624 2.4530803150 1.1434875703 0.4760193809 0.6542273532 0.4819373752 -0.336345782959 +1403636638263555584.0000000000 0.9383424794 2.4607545804 1.1386399590 0.4765514529 0.6538038138 0.4819483174 -0.336400215804 +1403636638313555456.0000000000 0.9174543360 2.4679539813 1.1323503804 0.4742083549 0.6551862279 0.4819502998 -0.337018325049 +1403636638363555584.0000000000 0.8971173428 2.4749281370 1.1240507497 0.4680558701 0.6594084602 0.4819170127 -0.337431738278 +1403636638413555456.0000000000 0.8774790694 2.4819680892 1.1138898395 0.4586154338 0.6659590208 0.4828184582 -0.336239204917 +1403636638463555584.0000000000 0.8572480226 2.4897004094 1.1026327597 0.4495805902 0.6719619442 0.4842351499 -0.334455913366 +1403636638513555456.0000000000 0.8359993806 2.4983389284 1.0911969324 0.4414069690 0.6773500619 0.4849191835 -0.333481883917 +1403636638563555584.0000000000 0.8152277241 2.5080909091 1.0809195218 0.4373996041 0.6800418004 0.4857938749 -0.332007601178 +1403636638613555456.0000000000 0.7931153109 2.5196814385 1.0724419897 0.4369972153 0.6801101720 0.4876491848 -0.329669319583 +1403636638663555584.0000000000 0.7690969613 2.5329992820 1.0670028835 0.4406924789 0.6773260198 0.4899576351 -0.327049106079 +1403636638713555456.0000000000 0.7434235985 2.5477686683 1.0648256088 0.4446150077 0.6747176007 0.4908554815 -0.325782980713 +1403636638763555584.0000000000 0.7168791084 2.5632650451 1.0650040487 0.4491720220 0.6714107642 0.4909726592 -0.326186953074 +1403636638813555456.0000000000 0.6888215133 2.5794706815 1.0679644070 0.4533927073 0.6683458119 0.4901177304 -0.327923068875 +1403636638863555584.0000000000 0.6600027602 2.5959995387 1.0731678308 0.4563433456 0.6663964676 0.4884547961 -0.330270209147 +1403636638913555456.0000000000 0.6318077100 2.6123363085 1.0788792291 0.4574979456 0.6653543133 0.4866779253 -0.333382459883 +1403636638963555584.0000000000 0.6029152050 2.6293367712 1.0865539719 0.4578995439 0.6649444974 0.4847307778 -0.336471241261 +1403636639013555456.0000000000 0.5732395978 2.6467148673 1.0949595105 0.4554703176 0.6665307652 0.4821099893 -0.340372571021 +1403636639063555584.0000000000 0.5428709665 2.6646927367 1.1032683079 0.4529256277 0.6681675074 0.4790335320 -0.34487306803 +1403636639113555456.0000000000 0.5125047648 2.6835688324 1.1090470486 0.4506378634 0.6696000134 0.4765232926 -0.348549694939 +1403636639163555584.0000000000 0.4824620418 2.7034669428 1.1111945944 0.4481251479 0.6712890919 0.4746825023 -0.351043200956 +1403636639213555456.0000000000 0.4526082374 2.7244937220 1.1094023149 0.4462568080 0.6725154403 0.4731751713 -0.353104943643 +1403636639263555584.0000000000 0.4226401182 2.7469939323 1.1032314031 0.4449002835 0.6733887339 0.4728843368 -0.353541729873 +1403636639313555456.0000000000 0.3931427448 2.7714196008 1.0939547188 0.4472270655 0.6719253273 0.4751826510 -0.350293811889 +1403636639363555584.0000000000 0.3640604441 2.7971550323 1.0831208969 0.4502007151 0.6698839861 0.4784256251 -0.345953295438 +1403636639413555456.0000000000 0.3347371219 2.8240501047 1.0711768924 0.4531326465 0.6678586729 0.4817961330 -0.341332805421 +1403636639463555584.0000000000 0.3053603486 2.8517334713 1.0582869220 0.4562896056 0.6655629091 0.4850801396 -0.336931844793 +1403636639513555456.0000000000 0.2758253439 2.8799404465 1.0446697790 0.4605006550 0.6625588564 0.4879523462 -0.332952573803 +1403636639563555584.0000000000 0.2462575652 2.9082864864 1.0301998980 0.4655615114 0.6588662307 0.4909543982 -0.328803205505 +1403636639613555456.0000000000 0.2163027908 2.9360793992 1.0150961427 0.4694061470 0.6558699787 0.4932242563 -0.325917586514 +1403636639663555584.0000000000 0.1858413348 2.9629682634 1.0009374196 0.4723960429 0.6534673312 0.4932157921 -0.32643622365 +1403636639713555456.0000000000 0.1554934909 2.9888659834 0.9883279989 0.4744790733 0.6518837739 0.4913389104 -0.329398283984 +1403636639763555584.0000000000 0.1253406952 3.0140787144 0.9770596211 0.4754243312 0.6511465946 0.4886221356 -0.333508959618 +1403636639813555456.0000000000 0.0960810032 3.0387496642 0.9671627859 0.4757587226 0.6509089477 0.4869602862 -0.335917935305 +1403636639863555584.0000000000 0.0670085991 3.0629467801 0.9592516969 0.4751917151 0.6512117393 0.4852646638 -0.338576890229 +1403636639913555456.0000000000 0.0393882900 3.0863673024 0.9531666746 0.4742816592 0.6515068630 0.4842553204 -0.340723494698 +1403636639963555584.0000000000 0.0122031369 3.1096744118 0.9483778705 0.4742804582 0.6514625559 0.4837945848 -0.34146359231 +1403636640013555456.0000000000 -0.0144513598 3.1326018022 0.9451245174 0.4743335717 0.6508777928 0.4839840124 -0.342235645964 +1403636640063555584.0000000000 -0.0411017010 3.1552571968 0.9438476090 0.4741189652 0.6491998629 0.4858751974 -0.343039410853 +1403636640113555456.0000000000 -0.0675111659 3.1777737360 0.9448589462 0.4742529735 0.6461170228 0.4896344633 -0.343329291217 +1403636640163555584.0000000000 -0.0931672111 3.1996438395 0.9477943982 0.4729858638 0.6435551967 0.4927303975 -0.345453089193 +1403636640213555456.0000000000 -0.1177240329 3.2211343705 0.9528114860 0.4716118432 0.6410624088 0.4956931657 -0.34772049533 +1403636640263555584.0000000000 -0.1410360532 3.2423399320 0.9583781630 0.4697639635 0.6392752293 0.4993561815 -0.348270589812 +1403636640313555456.0000000000 -0.1637442860 3.2630183079 0.9633380345 0.4681029019 0.6380663596 0.5013890986 -0.349799893895 +1403636640363555584.0000000000 -0.1858909481 3.2834051203 0.9670537428 0.4672437695 0.6361742148 0.5036924566 -0.351083376752 +1403636640413555456.0000000000 -0.2074983529 3.3034311606 0.9689890041 0.4665717943 0.6346251355 0.5056744174 -0.351930506979 +1403636640463555584.0000000000 -0.2286422483 3.3231429341 0.9694744533 0.4661938047 0.6331685821 0.5073589576 -0.352629793498 +1403636640513555456.0000000000 -0.2488775779 3.3424062328 0.9679121787 0.4645767789 0.6328900680 0.5089177771 -0.353017385468 +1403636640563555584.0000000000 -0.2689215975 3.3615209285 0.9654833527 0.4642876205 0.6317801352 0.5102094206 -0.353521163823 +1403636640613555456.0000000000 -0.2887728580 3.3802616568 0.9620676417 0.4637957117 0.6312359526 0.5107689449 -0.354330064821 +1403636640663555584.0000000000 -0.3079137109 3.3986270096 0.9574470226 0.4638612003 0.6303994235 0.5113119658 -0.354949894154 +1403636640713555456.0000000000 -0.3265782412 3.4165920720 0.9515329714 0.4629879066 0.6303902733 0.5120228261 -0.355081578319 +1403636640763555584.0000000000 -0.3446962167 3.4340745924 0.9453464721 0.4615608998 0.6308223112 0.5128840384 -0.35492916265 +1403636640813555456.0000000000 -0.3630965646 3.4512698498 0.9404890892 0.4608183194 0.6308922545 0.5139207134 -0.354269586781 +1403636640863555584.0000000000 -0.3806364685 3.4678172620 0.9363165715 0.4597694724 0.6312021515 0.5150981514 -0.353369170458 +1403636640913555456.0000000000 -0.3985178338 3.4841592622 0.9344515522 0.4592173225 0.6313353436 0.5155964288 -0.353122439501 +1403636640963555584.0000000000 -0.4162785208 3.5002263195 0.9348310966 0.4591464288 0.6313923961 0.5159450899 -0.352602982546 +1403636641013555456.0000000000 -0.4327900333 3.5157255753 0.9358634927 0.4598232427 0.6310707861 0.5157541675 -0.352576072706 +1403636641063555584.0000000000 -0.4493414328 3.5307221717 0.9362910937 0.4603502117 0.6309958038 0.5146721965 -0.353602189423 +1403636641113555456.0000000000 -0.4656780993 3.5453296774 0.9351928219 0.4611521169 0.6307711552 0.5143262567 -0.353461421403 +1403636641163555584.0000000000 -0.4821528424 3.5595164549 0.9324841255 0.4613074569 0.6309468967 0.5143531597 -0.352905470106 +1403636641213555456.0000000000 -0.4984318624 3.5732703920 0.9287173687 0.4621346517 0.6307855343 0.5136553135 -0.353128011199 +1403636641263555584.0000000000 -0.5145394998 3.5863203700 0.9237983787 0.4621104411 0.6310131328 0.5124103162 -0.354558929216 +1403636641313555456.0000000000 -0.5302379856 3.5988893259 0.9174828368 0.4603538497 0.6327435859 0.5105208325 -0.356480528455 +1403636641363555584.0000000000 -0.5455479854 3.6112196869 0.9102982186 0.4580481846 0.6347412097 0.5083626284 -0.358974783653 +1403636641413555456.0000000000 -0.5607078132 3.6236865009 0.9022251305 0.4560349927 0.6363039008 0.5065470241 -0.361330241872 +1403636641463555584.0000000000 -0.5756394491 3.6367426897 0.8932130298 0.4559707816 0.6366166921 0.5059578150 -0.361685669069 +1403636641513555456.0000000000 -0.5896981328 3.6500071645 0.8844236725 0.4571464755 0.6360730337 0.5062435218 -0.360757109969 +1403636641563555584.0000000000 -0.6019799180 3.6630378360 0.8761719023 0.4579701862 0.6355116160 0.5072482986 -0.359287430933 +1403636641613555456.0000000000 -0.6140811981 3.6760502894 0.8696091878 0.4594274703 0.6348207390 0.5079942651 -0.357590346012 +1403636641663555584.0000000000 -0.6257743557 3.6890264572 0.8645401271 0.4601052792 0.6345633685 0.5087525728 -0.356094486249 +1403636641713555456.0000000000 -0.6364401107 3.7017347022 0.8620771787 0.4614550585 0.6337088266 0.5089262560 -0.355621172028 +1403636641763555584.0000000000 -0.6466354338 3.7142579494 0.8621488431 0.4616069320 0.6339711694 0.5091937019 -0.354572094984 +1403636641813555456.0000000000 -0.6567830590 3.7264353588 0.8646444445 0.4623469770 0.6334918646 0.5090045044 -0.354736162323 +1403636641863555584.0000000000 -0.6679600326 3.7386554912 0.8683581161 0.4630559118 0.6331245819 0.5087244937 -0.354868815029 +1403636641913555456.0000000000 -0.6796442722 3.7509819474 0.8732189229 0.4636259027 0.6337102136 0.5078180588 -0.354377209795 +1403636641963555584.0000000000 -0.6900217871 3.7631336906 0.8810750724 0.4645314634 0.6352871663 0.5054480492 -0.353755572954 +1403636642013555456.0000000000 -0.7002312115 3.7753762088 0.8897423528 0.4669128223 0.6367838810 0.5023540198 -0.352333853121 +1403636642063555584.0000000000 -0.7099659843 3.7875448050 0.8995046447 0.4689779407 0.6391185188 0.4986271444 -0.350653933353 +1403636642113555456.0000000000 -0.7195717536 3.7995640769 0.9085509981 0.4713674363 0.6408290112 0.4957567558 -0.348390811511 +1403636642163555584.0000000000 -0.7285694343 3.8111597260 0.9164675687 0.4734052136 0.6424203927 0.4931400598 -0.346405000287 +1403636642213555456.0000000000 -0.7366496383 3.8221907189 0.9228217047 0.4750069520 0.6438158123 0.4905337678 -0.345320456967 +1403636642263555584.0000000000 -0.7441631220 3.8327668367 0.9276991776 0.4761503768 0.6454694530 0.4880397953 -0.344190589896 +1403636642313555456.0000000000 -0.7510735910 3.8431651277 0.9307675668 0.4774108254 0.6475336452 0.4849850816 -0.342882709801 +1403636642363555584.0000000000 -0.7572249389 3.8536049319 0.9316500950 0.4793928659 0.6499262677 0.4812944950 -0.340784295079 +1403636642413555456.0000000000 -0.7628839116 3.8637833594 0.9310086793 0.4812967925 0.6520169558 0.4775208564 -0.339412902706 +1403636642463555584.0000000000 -0.7678728200 3.8736719158 0.9285281413 0.4825870521 0.6541042586 0.4747761934 -0.337409131977 +1403636642513555456.0000000000 -0.7720721478 3.8830368553 0.9244516312 0.4827013845 0.6564707069 0.4727674001 -0.33546470719 +1403636642563555584.0000000000 -0.7753294809 3.8919579673 0.9185059819 0.4817608669 0.6593095211 0.4722195823 -0.332003145456 +1403636642613555456.0000000000 -0.7782315688 3.9002891190 0.9112214956 0.4794619078 0.6625501613 0.4717390895 -0.329553932073 +1403636642663555584.0000000000 -0.7810180002 3.9084844199 0.9024201208 0.4769390281 0.6657122302 0.4717569992 -0.326805330113 +1403636642713555456.0000000000 -0.7839211561 3.9166723068 0.8928735590 0.4748239739 0.6683751972 0.4720060608 -0.324078799146 +1403636642763555584.0000000000 -0.7872597624 3.9249199368 0.8838435242 0.4725338784 0.6706004444 0.4725010940 -0.322101682521 +1403636642813555456.0000000000 -0.7911614698 3.9332062314 0.8772903026 0.4706043348 0.6725295295 0.4725836365 -0.320780764009 +1403636642863555584.0000000000 -0.7948925838 3.9412699007 0.8729747322 0.4692763883 0.6737988907 0.4724638987 -0.320238334107 +1403636642913555456.0000000000 -0.7996488916 3.9496487417 0.8703576896 0.4679566256 0.6747218924 0.4729779471 -0.319466470925 +1403636642963555584.0000000000 -0.8040753261 3.9580077953 0.8697968664 0.4672652511 0.6753768271 0.4726933452 -0.319515770999 +1403636643013555456.0000000000 -0.8090000323 3.9665918298 0.8715027068 0.4674858030 0.6751428389 0.4723420224 -0.320206472309 +1403636643063555584.0000000000 -0.8154511570 3.9761193799 0.8745442868 0.4698605585 0.6735137068 0.4710202332 -0.322102906198 +1403636643113555456.0000000000 -0.8223452866 3.9859530651 0.8773593160 0.4725921320 0.6715805448 0.4693515224 -0.324569556503 +1403636643163555584.0000000000 -0.8292052189 3.9959342681 0.8787608882 0.4743150879 0.6702707644 0.4679646254 -0.326758946585 +1403636643213555456.0000000000 -0.8358778610 4.0061773874 0.8785258368 0.4758250771 0.6692030213 0.4668724701 -0.328310689599 +1403636643263555584.0000000000 -0.8421029582 4.0163267816 0.8765322018 0.4763272205 0.6686402791 0.4666248087 -0.329080300327 +1403636643313555456.0000000000 -0.8479080301 4.0266926567 0.8732379015 0.4761532894 0.6686032206 0.4670462030 -0.328809401788 +1403636643363555584.0000000000 -0.8528661781 4.0368849518 0.8696554519 0.4748443534 0.6693014028 0.4681068928 -0.32777188591 +1403636643413555456.0000000000 -0.8582540864 4.0473642472 0.8679592441 0.4728255548 0.6705055871 0.4688182617 -0.327211995308 +1403636643463555584.0000000000 -0.8640558882 4.0581839684 0.8684388551 0.4698111505 0.6722830726 0.4699659855 -0.326258985431 +1403636643513555456.0000000000 -0.8708555623 4.0698461839 0.8699660456 0.4669976992 0.6738252835 0.4716994668 -0.324610920027 +1403636643563555584.0000000000 -0.8792153813 4.0823519297 0.8740314384 0.4645693288 0.6750035779 0.4733413517 -0.32325450236 +1403636643613555456.0000000000 -0.8880110825 4.0955229282 0.8789001429 0.4623312508 0.6763080377 0.4751837583 -0.321025931284 +1403636643663555584.0000000000 -0.8967481175 4.1085143138 0.8858849505 0.4600416789 0.6770391352 0.4772939422 -0.319640666722 +1403636643713555456.0000000000 -0.9063071986 4.1222009480 0.8944783423 0.4581156539 0.6777923304 0.4790958064 -0.318111321372 +1403636643763555584.0000000000 -0.9160009327 4.1355943082 0.9047350709 0.4572369414 0.6780409518 0.4802243256 -0.31714262449 +1403636643813555456.0000000000 -0.9264782902 4.1495152597 0.9142406432 0.4558005678 0.6786447451 0.4821856695 -0.314935124246 +1403636643863555584.0000000000 -0.9382335471 4.1639312942 0.9228036058 0.4537305012 0.6797584583 0.4834240579 -0.313621190058 +1403636643913555456.0000000000 -0.9513014138 4.1785240449 0.9302460253 0.4525571239 0.6802738625 0.4845152792 -0.312513144978 +1403636643963555584.0000000000 -0.9658425683 4.1938194365 0.9359420841 0.4515201167 0.6807895549 0.4857384125 -0.310987718152 +1403636644013555456.0000000000 -0.9819655575 4.2095817615 0.9402168867 0.4512546040 0.6809728727 0.4863406888 -0.310028972025 +1403636644063555584.0000000000 -0.9994703652 4.2255565500 0.9431952389 0.4506367932 0.6812445553 0.4866940434 -0.30977612003 +1403636644113555456.0000000000 -1.0184152351 4.2419782788 0.9446633889 0.4501351705 0.6816532130 0.4870527419 -0.309041828958 +1403636644163555584.0000000000 -1.0391328375 4.2589905339 0.9452151971 0.4511423184 0.6809305607 0.4868150554 -0.309540436584 +1403636644213555456.0000000000 -1.0617861107 4.2763350699 0.9453073978 0.4536513536 0.6794586353 0.4838050867 -0.313797785724 +1403636644263555584.0000000000 -1.0859868602 4.2941307854 0.9447680545 0.4558670409 0.6783434728 0.4785400648 -0.320990311874 +1403636644313555456.0000000000 -1.1112237647 4.3124300029 0.9432344473 0.4583349721 0.6768968639 0.4724650799 -0.329418331715 +1403636644363555584.0000000000 -1.1367035768 4.3318418248 0.9398759597 0.4607198505 0.6756077879 0.4667274464 -0.33683353004 +1403636644413555456.0000000000 -1.1618792511 4.3522162706 0.9343946384 0.4628053242 0.6741952824 0.4627850782 -0.342201584369 +1403636644463555584.0000000000 -1.1865894882 4.3737656003 0.9268259756 0.4649188961 0.6728683876 0.4594333372 -0.346438395254 +1403636644513555456.0000000000 -1.2105572302 4.3961327129 0.9175642090 0.4655366033 0.6723303031 0.4552152026 -0.352174323018 +1403636644563555584.0000000000 -1.2335188821 4.4196976444 0.9058891606 0.4651669341 0.6722940868 0.4524680547 -0.356248570175 +1403636644613555456.0000000000 -1.2553012999 4.4447552136 0.8922259065 0.4656915839 0.6720549569 0.4511331407 -0.357704309501 +1403636644663555584.0000000000 -1.2757220351 4.4712751030 0.8762864712 0.4685678760 0.6701984239 0.4528607178 -0.355239902776 +1403636644713555456.0000000000 -1.2948560802 4.4988806746 0.8584251796 0.4728265384 0.6674606694 0.4560695640 -0.350616417464 +1403636644763555584.0000000000 -1.3126911805 4.5271312861 0.8383063340 0.4770537003 0.6646462715 0.4608260532 -0.343954138632 +1403636644813555456.0000000000 -1.3296526562 4.5558645672 0.8171083502 0.4816922643 0.6617723687 0.4647032308 -0.337758496363 +1403636644863555584.0000000000 -1.3458569710 4.5840574568 0.7942282693 0.4837317518 0.6608210872 0.4679921903 -0.332118040438 +1403636644913555456.0000000000 -1.3616838473 4.6117748400 0.7720971103 0.4832124279 0.6617460866 0.4694439325 -0.328968479635 +1403636644963555584.0000000000 -1.3771975749 4.6388869715 0.7516810781 0.4814440556 0.6633573586 0.4702144384 -0.327210968671 +1403636645013555456.0000000000 -1.3917777331 4.6652130150 0.7328445394 0.4767347469 0.6669745836 0.4726163414 -0.323268742346 +1403636645063555584.0000000000 -1.4060770878 4.6909879447 0.7158018691 0.4683246857 0.6732431132 0.4751214801 -0.318865612013 +1403636645113555456.0000000000 -1.4198674691 4.7164990283 0.7010433134 0.4599070918 0.6792521404 0.4778354488 -0.314285348979 +1403636645163555584.0000000000 -1.4334848736 4.7422389555 0.6877467007 0.4534538884 0.6836550641 0.4816158425 -0.308288022227 +1403636645213555456.0000000000 -1.4501444998 4.7688494070 0.6773543846 0.4467184721 0.6883479031 0.4834368772 -0.304809049646 +1403636645263555584.0000000000 -1.4697715453 4.7967575746 0.6698817321 0.4437563629 0.6903483308 0.4851021030 -0.301952682191 +1403636645313555456.0000000000 -1.4915929239 4.8253754297 0.6644902351 0.4441648651 0.6901835945 0.4847164572 -0.302347704807 +1403636645363555584.0000000000 -1.5158532950 4.8550651965 0.6604814707 0.4475669798 0.6881353391 0.4834368490 -0.304043363414 +1403636645413555456.0000000000 -1.5421502649 4.8855135088 0.6567743398 0.4516423700 0.6858156902 0.4818247773 -0.30581185825 +1403636645463555584.0000000000 -1.5700337758 4.9162216896 0.6524068771 0.4544591019 0.6842423570 0.4801895616 -0.307729274523 +1403636645513555456.0000000000 -1.5991708929 4.9472958972 0.6466053378 0.4568771931 0.6827202802 0.4792736382 -0.308954736457 +1403636645563555584.0000000000 -1.6297351606 4.9787252261 0.6389218255 0.4580944440 0.6821183943 0.4788519240 -0.30913558735 +1403636645613555456.0000000000 -1.6617127585 5.0106847300 0.6302524329 0.4597963609 0.6813019800 0.4779926204 -0.309738556591 +1403636645663555584.0000000000 -1.6947050280 5.0428743173 0.6210631790 0.4611502509 0.6802730514 0.4780715996 -0.30986540174 +1403636645713555456.0000000000 -1.7289150515 5.0758430202 0.6125744589 0.4622109672 0.6796441194 0.4777446336 -0.310169240615 +1403636645763555584.0000000000 -1.7647320188 5.1088717877 0.6057430999 0.4624051810 0.6793659339 0.4772195302 -0.311295512964 +1403636645813555456.0000000000 -1.8018087109 5.1421241113 0.6013571796 0.4622205415 0.6794550469 0.4766216671 -0.312289603735 +1403636645863555584.0000000000 -1.8398404173 5.1757340538 0.6000887444 0.4614380124 0.6801283936 0.4765062702 -0.312157177412 +1403636645913555456.0000000000 -1.8779089477 5.2090070801 0.6022814393 0.4604294755 0.6807244833 0.4760999580 -0.312965982046 +1403636645963555584.0000000000 -1.9179857737 5.2432308565 0.6078999853 0.4634184375 0.6798585594 0.4728091397 -0.315415929199 +1403636646013555456.0000000000 -1.9582655433 5.2779073990 0.6154118259 0.4664896615 0.6800841586 0.4681450754 -0.317353306861 +1403636646063555584.0000000000 -1.9970615247 5.3101616193 0.6244279252 0.4686418904 0.6821276987 0.4617552293 -0.31915308145 +1403636646113555456.0000000000 -2.0361687145 5.3444130922 0.6341222266 0.4719066528 0.6849393831 0.4542162205 -0.319139119541 +1403636646163555584.0000000000 -2.0752377644 5.3775455838 0.6438781043 0.4760064355 0.6886208751 0.4453444666 -0.31762787936 +1403636646213555456.0000000000 -2.1150980380 5.4120933899 0.6528517486 0.4799855574 0.6930665048 0.4351326460 -0.316120649301 +1403636646263555584.0000000000 -2.1538383923 5.4474701169 0.6603305732 0.4847417480 0.6980238614 0.4237728104 -0.313376342179 +1403636646313555456.0000000000 -2.1920105732 5.4832279260 0.6672452387 0.4904870819 0.7028016584 0.4113147491 -0.310342437648 +1403636646363555584.0000000000 -2.2289344499 5.5201741097 0.6723377004 0.4961611224 0.7076182735 0.3984392808 -0.307159012739 +1403636646413555456.0000000000 -2.2639413515 5.5581079358 0.6751401636 0.5031802606 0.7117138362 0.3873575562 -0.300378368752 +1403636646463555584.0000000000 -2.2976888297 5.5964125863 0.6773131635 0.5117126618 0.7134910976 0.3778826110 -0.293743659817 +1403636646513555456.0000000000 -2.3300434418 5.6351241166 0.6800853583 0.5199615872 0.7142407068 0.3705189583 -0.286733085339 +1403636646563555584.0000000000 -2.3603193970 5.6735154550 0.6832907710 0.5260840288 0.7155637075 0.3641897001 -0.280303473884 +1403636646613555456.0000000000 -2.3891870506 5.7117433345 0.6870798466 0.5290092860 0.7180258933 0.3594318123 -0.274584712085 +1403636646663555584.0000000000 -2.4167434469 5.7499225307 0.6928479065 0.5307033948 0.7206468678 0.3570050516 -0.267524562873 +1403636646713555456.0000000000 -2.4431989584 5.7873778839 0.7013292439 0.5311380952 0.7234739589 0.3540515678 -0.262916796721 +1403636646763555584.0000000000 -2.4685768976 5.8241690389 0.7122984811 0.5318821873 0.7254476140 0.3513718162 -0.259547577421 +1403636646813555456.0000000000 -2.4929936159 5.8602053644 0.7255091621 0.5331741279 0.7263638829 0.3493221912 -0.257089217574 +1403636646863555584.0000000000 -2.5160323106 5.8957580740 0.7405543292 0.5343659405 0.7272217902 0.3472803789 -0.254946754842 +1403636646913555456.0000000000 -2.5378936076 5.9301461399 0.7558706061 0.5339025605 0.7283815590 0.3462828787 -0.253961667023 +1403636646963555584.0000000000 -2.5587868901 5.9640242037 0.7703050323 0.5333097102 0.7295701286 0.3458406606 -0.252393379328 +1403636647013555456.0000000000 -2.5788150563 5.9972631961 0.7833601673 0.5325411709 0.7306120131 0.3459028919 -0.250912688017 +1403636647063555584.0000000000 -2.5981184916 6.0298151598 0.7947102643 0.5310957866 0.7317073490 0.3468993085 -0.249404271578 +1403636647113555456.0000000000 -2.6162972730 6.0618269439 0.8041864550 0.5284070332 0.7337526592 0.3481243420 -0.247391359958 +1403636647163555584.0000000000 -2.6343704975 6.0936204980 0.8124808421 0.5260145865 0.7353084696 0.3491024022 -0.246490612455 +1403636647213555456.0000000000 -2.6516460755 6.1249107943 0.8196213176 0.5247710789 0.7360176699 0.3503323410 -0.245276487448 +1403636647263555584.0000000000 -2.6689399086 6.1562064942 0.8259653077 0.5243772296 0.7359755419 0.3503875880 -0.246164702846 +1403636647313555456.0000000000 -2.6860578143 6.1873835272 0.8311156263 0.5242667183 0.7355472707 0.3500453157 -0.248159016715 +1403636647363555584.0000000000 -2.7028954857 6.2186860938 0.8351448824 0.5247534015 0.7347231005 0.3496485485 -0.250123421139 +1403636647413555456.0000000000 -2.7191326534 6.2498052119 0.8377115697 0.5254465927 0.7337684009 0.3492986151 -0.251952950958 +1403636647463555584.0000000000 -2.7345478082 6.2803431122 0.8391325486 0.5258884401 0.7328086775 0.3487770344 -0.254533634386 +1403636647513555456.0000000000 -2.7492254679 6.3107447397 0.8397010915 0.5272938523 0.7310882681 0.3480447630 -0.257557722711 +1403636647563555584.0000000000 -2.7623856305 6.3403373827 0.8406283381 0.5289317716 0.7291532988 0.3465671409 -0.261644538635 +1403636647613555456.0000000000 -2.7743137663 6.3699510796 0.8426944700 0.5310204684 0.7271580524 0.3438436799 -0.266514451184 +1403636647663555584.0000000000 -2.7849960562 6.4002410668 0.8450739938 0.5318129446 0.7270459934 0.3427456307 -0.266654360625 +1403636647713555456.0000000000 -2.7944416927 6.4306745138 0.8484598646 0.5317333311 0.7275962616 0.3430295946 -0.264941582031 +1403636647763555584.0000000000 -2.8030223754 6.4615368651 0.8530735463 0.5309956824 0.7287315603 0.3437718575 -0.262325767487 +1403636647813555456.0000000000 -2.8106300316 6.4925374692 0.8583515472 0.5315564216 0.7292097663 0.3440706308 -0.259453826922 +1403636647863555584.0000000000 -2.8166213643 6.5230834585 0.8623949270 0.5312503889 0.7310711236 0.3428476528 -0.256443996898 +1403636647913555456.0000000000 -2.8215136078 6.5537490800 0.8647920702 0.5327022308 0.7324453426 0.3400904971 -0.253161227452 +1403636647963555584.0000000000 -2.8255394679 6.5844088228 0.8651273135 0.5343064774 0.7345161265 0.3355954823 -0.249756522294 +1403636648013555456.0000000000 -2.8283663416 6.6150635738 0.8628164576 0.5360822281 0.7374376920 0.3300739864 -0.244648030142 +1403636648063555584.0000000000 -2.8297910581 6.6456712683 0.8582549867 0.5381416499 0.7409942724 0.3228818072 -0.238910844029 +1403636648113555456.0000000000 -2.8303736001 6.6763140974 0.8516492976 0.5403932755 0.7451020540 0.3141826695 -0.232566736745 +1403636648163555584.0000000000 -2.8302166144 6.7069674769 0.8437324513 0.5432125012 0.7492050324 0.3044895160 -0.225606144879 +1403636648213555456.0000000000 -2.8294676576 6.7375239068 0.8350691593 0.5462543018 0.7530039783 0.2947169384 -0.218479227236 +1403636648263555584.0000000000 -2.8275955757 6.7678532732 0.8251181732 0.5491194312 0.7570765792 0.2839306310 -0.211391343882 +1403636648313555456.0000000000 -2.8246051185 6.7974768710 0.8139588887 0.5516428588 0.7613032580 0.2730148958 -0.203888136967 +1403636648363555584.0000000000 -2.8208101052 6.8267662213 0.8018241067 0.5549167368 0.7647554858 0.2622595434 -0.196052018568 +1403636648413555456.0000000000 -2.8158127276 6.8554247733 0.7885667660 0.5574840423 0.7686261454 0.2513602712 -0.187732270192 +1403636648463555584.0000000000 -2.8098211374 6.8835896665 0.7742925324 0.5596785251 0.7726818763 0.2399142981 -0.179342678099 +1403636648513555456.0000000000 -2.8033725187 6.9116462496 0.7600009391 0.5619602780 0.7762275756 0.2286066878 -0.17149454563 +1403636648563555584.0000000000 -2.7963567385 6.9391885155 0.7474769365 0.5640239165 0.7791546260 0.2183828669 -0.164632966914 +1403636648613555456.0000000000 -2.7883424127 6.9656803428 0.7361555104 0.5658037766 0.7815409544 0.2099031889 -0.158115382727 +1403636648663555584.0000000000 -2.7792721192 6.9906660618 0.7266463706 0.5662929458 0.7841545499 0.2034271446 -0.151760792612 +1403636648713555456.0000000000 -2.7695954230 7.0148217657 0.7183202709 0.5658554171 0.7868925468 0.1989343082 -0.145027265449 +1403636648763555584.0000000000 -2.7600963417 7.0387469792 0.7119974284 0.5642742324 0.7898958169 0.1949500764 -0.140191500793 +1403636648813555456.0000000000 -2.7504378012 7.0621030256 0.7070647741 0.5591814688 0.7948557323 0.1928435906 -0.135394975309 +1403636648863555584.0000000000 -2.7408728428 7.0854691597 0.7050885778 0.5540588930 0.7994424421 0.1911362637 -0.13182357001 +1403636648913555456.0000000000 -2.7314989573 7.1091127220 0.7050930172 0.5492967434 0.8034288420 0.1910206888 -0.127617710122 +1403636648963555584.0000000000 -2.7223597714 7.1327662233 0.7083747943 0.5459632298 0.8060889186 0.1909723490 -0.125197320267 +1403636649013555456.0000000000 -2.7138342835 7.1578293982 0.7140567600 0.5455138707 0.8067003766 0.1908320882 -0.123418934384 +1403636649063555584.0000000000 -2.7055321051 7.1826664732 0.7226968876 0.5484850078 0.8047963246 0.1904199305 -0.12331797211 +1403636649113555456.0000000000 -2.6983594656 7.2088222415 0.7334707054 0.5543680149 0.8007040394 0.1899539083 -0.124365019808 +1403636649163555584.0000000000 -2.6917672692 7.2352690699 0.7460957418 0.5605936150 0.7962721952 0.1888442342 -0.126582958076 +1403636649213555456.0000000000 -2.6840845753 7.2591214291 0.7603490772 0.5662130103 0.7920924133 0.1888843810 -0.127730679084 +1403636649263555584.0000000000 -2.6769794594 7.2839889011 0.7755671989 0.5704614905 0.7887489074 0.1891287852 -0.129147789416 +1403636649313555456.0000000000 -2.6694414557 7.3078289372 0.7918106701 0.5716784097 0.7875218356 0.1900119540 -0.12995619123 +1403636649363555584.0000000000 -2.6617130237 7.3309461914 0.8090844814 0.5707459815 0.7877285191 0.1917077546 -0.130310942157 +1403636649413555456.0000000000 -2.6537917907 7.3533652291 0.8278558797 0.5686344292 0.7887654671 0.1934456217 -0.130700862003 +1403636649463555584.0000000000 -2.6458074173 7.3752733263 0.8478664417 0.5655072778 0.7904070624 0.1959046630 -0.13068878097 +1403636649513555456.0000000000 -2.6378843508 7.3966772926 0.8701952529 0.5653163590 0.7899204648 0.1974402106 -0.132137945877 +1403636649563555584.0000000000 -2.6300599443 7.4178556560 0.8949604558 0.5668787844 0.7882267429 0.1979560132 -0.134760760083 +1403636649613555456.0000000000 -2.6221878237 7.4390102761 0.9208864270 0.5685937519 0.7867944510 0.1969110141 -0.137410660437 +1403636649663555584.0000000000 -2.6137256054 7.4596961282 0.9463308935 0.5712511268 0.7852419072 0.1939140386 -0.13951574444 +1403636649713555456.0000000000 -2.6041551067 7.4796420935 0.9697952057 0.5728046066 0.7850661056 0.1898975200 -0.139660389442 +1403636649763555584.0000000000 -2.5938558637 7.4993149997 0.9912696895 0.5748739438 0.7848397550 0.1862749481 -0.137288569813 +1403636649813555456.0000000000 -2.5831094313 7.5183599980 1.0108616969 0.5763539897 0.7848867057 0.1834506459 -0.134591226884 +1403636649863555584.0000000000 -2.5718298598 7.5365251377 1.0287273568 0.5782376342 0.7845977869 0.1806676976 -0.131934583086 +1403636649913555456.0000000000 -2.5604222157 7.5541238073 1.0447733190 0.5794136455 0.7846681884 0.1783526808 -0.129483523213 +1403636649963555584.0000000000 -2.5486639611 7.5712178445 1.0582850057 0.5804610495 0.7847434503 0.1764943331 -0.126855971976 +1403636650013555456.0000000000 -2.5364871204 7.5875685925 1.0692418123 0.5809885606 0.7851008205 0.1748549085 -0.124477930183 +1403636650063555584.0000000000 -2.5239232151 7.6029982428 1.0776167409 0.5819313050 0.7851580274 0.1724152569 -0.123108925487 +1403636650113555456.0000000000 -2.5104473998 7.6172030257 1.0835627274 0.5826802555 0.7857647708 0.1686672412 -0.120866896135 +1403636650163555584.0000000000 -2.4960664581 7.6308010037 1.0874705142 0.5837657293 0.7865930139 0.1634599734 -0.117344964819 +1403636650213555456.0000000000 -2.4803607776 7.6431612326 1.0890477352 0.5844312613 0.7882617918 0.1569678650 -0.111555088437 +1403636650263555584.0000000000 -2.4640659841 7.6546398464 1.0892057525 0.5851180811 0.7902718123 0.1485560216 -0.105063801033 +1403636650313555456.0000000000 -2.4474917909 7.6658560021 1.0877304386 0.5853769076 0.7927369598 0.1384490132 -0.0986603235073 +1403636650363555584.0000000000 -2.4303132277 7.6768937327 1.0849881662 0.5851319148 0.7956405051 0.1277635615 -0.0908476812971 +1403636650413555456.0000000000 -2.4125690730 7.6870072303 1.0811673324 0.5846012294 0.7986009632 0.1171143705 -0.0822321618401 +1403636650463555584.0000000000 -2.3942341619 7.6958378937 1.0762388427 0.5833086186 0.8019432920 0.1062202292 -0.0731797421816 +1403636650513555456.0000000000 -2.3756274396 7.7034157238 1.0701239749 0.5814734531 0.8053420066 0.0956346967 -0.0645513789887 +1403636650563555584.0000000000 -2.3571361533 7.7098631059 1.0628156168 0.5792008081 0.8085917447 0.0859520452 -0.0576026060359 +1403636650613555456.0000000000 -2.3389612181 7.7158456424 1.0545495052 0.5776178213 0.8109432649 0.0780538090 -0.051344683741 +1403636650663555584.0000000000 -2.3210403988 7.7214499219 1.0455824809 0.5765416882 0.8126303358 0.0712763251 -0.0463821588244 +1403636650713555456.0000000000 -2.3031416932 7.7268053220 1.0363000497 0.5757273990 0.8139516820 0.0658449272 -0.0410495672089 +1403636650763555584.0000000000 -2.2855922869 7.7315257844 1.0284419000 0.5754894415 0.8146821380 0.0606685811 -0.037739104649 +1403636650813555456.0000000000 -2.2682943822 7.7361279024 1.0225984661 0.5762069413 0.8145941982 0.0566193023 -0.034872736455 +1403636650863555584.0000000000 -2.2512860927 7.7408895549 1.0196967899 0.5783323589 0.8133947594 0.0536290943 -0.0323197823674 +1403636650913555456.0000000000 -2.2343261644 7.7451979865 1.0189235780 0.5820085200 0.8109836157 0.0514083841 -0.0304768073095 +1403636650963555584.0000000000 -2.2175860020 7.7488313981 1.0195052412 0.5851868148 0.8088298879 0.0496577754 -0.0297440684959 +1403636651013555456.0000000000 -2.2009359721 7.7518709563 1.0213527061 0.5879798930 0.8068837026 0.0489275532 -0.0287128989419 +1403636651063555584.0000000000 -2.1845603633 7.7542055909 1.0249147117 0.5895383060 0.8057746852 0.0487106569 -0.0282668427559 +1403636651113555456.0000000000 -2.1683307164 7.7555269874 1.0299096102 0.5908652214 0.8047858852 0.0486830278 -0.0287738055023 +1403636651163555584.0000000000 -2.1520521220 7.7561275932 1.0361147888 0.5906898040 0.8048912741 0.0491467623 -0.0286389258524 +1403636651213555456.0000000000 -2.1358807082 7.7552261256 1.0435984086 0.5890878442 0.8059834153 0.0500779957 -0.0292991539535 +1403636651263555584.0000000000 -2.1196345217 7.7530050654 1.0525902575 0.5870887691 0.8073627359 0.0511934435 -0.0295198439451 +1403636651313555456.0000000000 -2.1035287758 7.7501386861 1.0625451425 0.5846265246 0.8090324062 0.0527217775 -0.0299801053175 +1403636651363555584.0000000000 -2.0877443828 7.7468750740 1.0724333974 0.5820418508 0.8107749412 0.0539023589 -0.0310775544573 +1403636651413555456.0000000000 -2.0719813445 7.7434170174 1.0812361811 0.5807445667 0.8115755692 0.0554825350 -0.0316627856351 +1403636651463555584.0000000000 -2.0562563683 7.7395618342 1.0882424576 0.5797403343 0.8121420778 0.0569085952 -0.032981844006 +1403636651513555456.0000000000 -2.0405107027 7.7356494773 1.0933948743 0.5802425613 0.8116380534 0.0584588851 -0.0338348785009 +1403636651563555584.0000000000 -2.0250053190 7.7315870698 1.0972379159 0.5822362833 0.8100676276 0.0592684188 -0.0357575671221 +1403636651613555456.0000000000 -2.0095404580 7.7274081528 1.0997852367 0.5853158577 0.8077033067 0.0604562415 -0.0369561619328 +1403636651663555584.0000000000 -1.9941173238 7.7227188756 1.1010950483 0.5880210607 0.8056171944 0.0609128802 -0.0387529269272 +1403636651713555456.0000000000 -1.9785679553 7.7172106051 1.1011412325 0.5895897977 0.8044019671 0.0603772265 -0.0409382020336 +1403636651763555584.0000000000 -1.9625511617 7.7113821884 1.1002709199 0.5908390184 0.8035712944 0.0575959926 -0.0431871611713 +1403636651813555456.0000000000 -1.9459169931 7.7050377423 1.0986913140 0.5917807211 0.8031083760 0.0522532704 -0.0456301473253 +1403636651863555584.0000000000 -1.9282956884 7.6979912269 1.0960659231 0.5933104720 0.8023340302 0.0459029436 -0.0462137164623 +1403636651913555456.0000000000 -1.9092351051 7.6899490200 1.0918942249 0.5941015554 0.8022379392 0.0381788895 -0.0447213947523 +1403636651963555584.0000000000 -1.8886747779 7.6809115622 1.0865516735 0.5950030023 0.8021196391 0.0294428826 -0.0413355590856 +1403636652013555456.0000000000 -1.8667710229 7.6720806632 1.0802134651 0.5961708307 0.8018245512 0.0203170135 -0.0352838300481 +1403636652063555584.0000000000 -1.8432345635 7.6626174527 1.0718752304 0.5954403530 0.8028971997 0.0104972574 -0.0263947024566 +1403636652113555456.0000000000 -1.8182300679 7.6523636280 1.0626742467 0.5938644028 0.8044338106 0.0007354339 -0.0145180772041 +1403636652163555584.0000000000 -1.7921821666 7.6411353442 1.0529401054 0.5916697014 0.8061094742 -0.0105921620 -0.00151199683156 +1403636652213555456.0000000000 -1.7654266956 7.6294722983 1.0426251857 0.5881684854 0.8083011846 -0.0238305858 0.0117953817899 +1403636652263555584.0000000000 -1.7383766350 7.6155282723 1.0307271186 0.5842461911 0.8103226902 -0.0380949625 0.0241308896381 +1403636652313555456.0000000000 -1.7111931753 7.5992398955 1.0170558366 0.5780672898 0.8134594831 -0.0530162150 0.0362099261813 +1403636652363555584.0000000000 -1.6839952973 7.5829016181 1.0023520998 0.5722364222 0.8159338629 -0.0677422996 0.0469935028132 +1403636652413555456.0000000000 -1.6569224374 7.5674772228 0.9881859596 0.5677942669 0.8172348268 -0.0807958765 0.0566474604081 +1403636652463555584.0000000000 -1.6304089790 7.5526645616 0.9747915859 0.5642973568 0.8178893224 -0.0923973933 0.0639395897223 +1403636652513555456.0000000000 -1.6041301216 7.5381050396 0.9624804252 0.5607177900 0.8186803818 -0.1023898671 0.0698162406794 +1403636652563555584.0000000000 -1.5779719782 7.5245355448 0.9524132975 0.5564589153 0.8199995156 -0.1111753446 0.0747951385495 +1403636652613555456.0000000000 -1.5517826196 7.5117399072 0.9444445051 0.5519622130 0.8217258249 -0.1177928370 0.0789254811385 +1403636652663555584.0000000000 -1.5251625833 7.5004659122 0.9384492924 0.5473049606 0.8237365469 -0.1225092632 0.0831075317917 +1403636652713555456.0000000000 -1.4981882171 7.4902705871 0.9352712623 0.5446674658 0.8246107642 -0.1250372476 0.0878642475179 +1403636652763555584.0000000000 -1.4715884059 7.4815501417 0.9350540523 0.5432087067 0.8249807187 -0.1279550268 0.0892111301855 +1403636652813555456.0000000000 -1.4445152469 7.4743139010 0.9368670297 0.5428761013 0.8247719590 -0.1292593154 0.0912621699442 +1403636652863555584.0000000000 -1.4173340585 7.4691264684 0.9407383918 0.5435138876 0.8240738670 -0.1305422554 0.0919436526829 +1403636652913555456.0000000000 -1.3899879733 7.4652997862 0.9466757234 0.5452493366 0.8228460427 -0.1303029903 0.09299828812 +1403636652963555584.0000000000 -1.3625025132 7.4625947032 0.9540621988 0.5472368107 0.8215464681 -0.1294019535 0.0940659782227 +1403636653013555456.0000000000 -1.3349686890 7.4610709845 0.9609873406 0.5491475678 0.8203636896 -0.1285279012 0.0944507505135 +1403636653063555584.0000000000 -1.3075184232 7.4603030099 0.9654248203 0.5514162169 0.8190387233 -0.1264490007 0.0955320661704 +1403636653113555456.0000000000 -1.2799756244 7.4611150499 0.9654917649 0.5546108264 0.8171407676 -0.1250771973 0.095097275635 +1403636653163555584.0000000000 -1.2522717058 7.4633439699 0.9624381733 0.5582479947 0.8149605961 -0.1229489578 0.0952993025643 +1403636653213555456.0000000000 -1.2249885726 7.4659092390 0.9588664110 0.5631779168 0.8119029261 -0.1206514641 0.0953283630438 +1403636653263555584.0000000000 -1.1979078821 7.4688620879 0.9556018853 0.5683952635 0.8086480666 -0.1182790321 0.0950010494232 +1403636653313555456.0000000000 -1.1712151725 7.4715489544 0.9531788496 0.5725720256 0.8060848868 -0.1152833773 0.095384347595 +1403636653363555584.0000000000 -1.1452129689 7.4741498812 0.9522538602 0.5750309686 0.8047798368 -0.1128244047 0.0945486814675 +1403636653413555456.0000000000 -1.1199363877 7.4760424645 0.9532777710 0.5762658005 0.8043354406 -0.1104665944 0.0935914399863 +1403636653463555584.0000000000 -1.0953415046 7.4775621367 0.9562879494 0.5762965690 0.8047005707 -0.1086505572 0.0923813425052 +1403636653513555456.0000000000 -1.0713319048 7.4786837019 0.9617555395 0.5762318024 0.8051552253 -0.1065843828 0.0912235852662 +1403636653563555584.0000000000 -1.0479853100 7.4790548541 0.9686410990 0.5759119354 0.8057695195 -0.1050861267 0.0895423361592 +1403636653613555456.0000000000 -1.0249603421 7.4796421985 0.9773964730 0.5774072810 0.8049823113 -0.1041233229 0.0881058680212 +1403636653663555584.0000000000 -1.0022986944 7.4799594859 0.9864346150 0.5795271095 0.8037522371 -0.1025044248 0.0873127349506 +1403636653713555456.0000000000 -0.9800324817 7.4797008893 0.9942199455 0.5816844293 0.8023914369 -0.1011092803 0.0871098164274 +1403636653763555584.0000000000 -0.9583879122 7.4788324053 1.0004134960 0.5838000592 0.8010007130 -0.1004543579 0.0865116789741 +1403636653813555456.0000000000 -0.9374142991 7.4770737556 1.0044795943 0.5850510095 0.8002359720 -0.0991924562 0.0865942374718 +1403636653863555584.0000000000 -0.9169000941 7.4746125617 1.0067440619 0.5862179618 0.7994296842 -0.0984283787 0.0870203166617 +1403636653913555456.0000000000 -0.8970359792 7.4711818662 1.0070754740 0.5864836806 0.7992800178 -0.0981034348 0.0869716135494 +1403636653963555584.0000000000 -0.8780602583 7.4667231402 1.0056030073 0.5854343441 0.8001260119 -0.0989781325 0.0852544606696 +1403636654013555456.0000000000 -0.8595776960 7.4615281768 1.0024068296 0.5840202920 0.8012011436 -0.1004319410 0.0831291237094 +1403636654063555584.0000000000 -0.8415114265 7.4555092840 0.9976687017 0.5832578873 0.8017964025 -0.1017752942 0.0810836311429 +1403636654113555456.0000000000 -0.8234527282 7.4489421018 0.9917878697 0.5832918765 0.8015915843 -0.1035801895 0.080577063757 +1403636654163555584.0000000000 -0.8052985387 7.4417808013 0.9866273826 0.5841448872 0.8005189001 -0.1065192380 0.0812274168943 +1403636654213555456.0000000000 -0.7869401743 7.4341946925 0.9828203518 0.5845984520 0.7994747798 -0.1100062319 0.0835664728024 +1403636654263555584.0000000000 -0.7683833662 7.4252814857 0.9799165345 0.5835133778 0.7993007164 -0.1135702480 0.0879335061023 +1403636654313555456.0000000000 -0.7496619439 7.4156207367 0.9792428886 0.5820792840 0.7990984095 -0.1184571126 0.0927003319431 +1403636654363555584.0000000000 -0.7312159639 7.4049151656 0.9802398092 0.5796922798 0.7993563317 -0.1244447121 0.0974670681336 +1403636654413555456.0000000000 -0.7126870855 7.3939107955 0.9832671069 0.5769755562 0.7995066566 -0.1312419513 0.103265986148 +1403636654463555584.0000000000 -0.6945547105 7.3820888683 0.9883674399 0.5745669708 0.7992132429 -0.1388679353 0.108842477942 +1403636654513555456.0000000000 -0.6764732507 7.3697240979 0.9954814861 0.5725137150 0.7983051365 -0.1466792789 0.115853978649 +1403636654563555584.0000000000 -0.6587373102 7.3568195914 1.0040646830 0.5703074193 0.7972457123 -0.1551091423 0.122840854746 +1403636654613555456.0000000000 -0.6419053094 7.3434609879 1.0130132204 0.5671357937 0.7971151846 -0.1635389180 0.12735539325 +1403636654663555584.0000000000 -0.6257977593 7.3300438183 1.0213274257 0.5640543441 0.7971125689 -0.1723136614 0.129469113818 +1403636654713555456.0000000000 -0.6100570369 7.3164648442 1.0282443027 0.5614781073 0.7969610848 -0.1787338508 0.132851702989 +1403636654763555584.0000000000 -0.5946442840 7.3027775541 1.0335863309 0.5590413044 0.7969717842 -0.1840677178 0.135749292373 +1403636654813555456.0000000000 -0.5792514550 7.2893888799 1.0372070858 0.5573528511 0.7965473481 -0.1883706417 0.139235853467 +1403636654863555584.0000000000 -0.5642612211 7.2760249629 1.0392426167 0.5557970717 0.7962864002 -0.1918109252 0.142218680203 +1403636654913555456.0000000000 -0.5493475593 7.2631869975 1.0396473626 0.5555161391 0.7952978437 -0.1946294634 0.144991486285 +1403636654963555584.0000000000 -0.5344979348 7.2509071753 1.0388382985 0.5579486691 0.7926163090 -0.1959494497 0.148514250501 +1403636655013555456.0000000000 -0.5201613864 7.2388391690 1.0369369066 0.5618920940 0.7890316272 -0.1973583550 0.150851071318 +1403636655063555584.0000000000 -0.5063122794 7.2267494601 1.0339366549 0.5654975969 0.7858810100 -0.1984748640 0.152352336236 +1403636655113555456.0000000000 -0.4930727670 7.2143288642 1.0300052490 0.5681753663 0.7834943050 -0.1994593030 0.15339300372 +1403636655163555584.0000000000 -0.4803598530 7.2013923234 1.0253896172 0.5706946701 0.7813105596 -0.1998272211 0.154694811748 +1403636655213555456.0000000000 -0.4683971540 7.1878680635 1.0205303272 0.5729535093 0.7795319405 -0.2005987578 0.154319047132 +1403636655263555584.0000000000 -0.4565446521 7.1733463680 1.0149960420 0.5745768142 0.7777147198 -0.2028230221 0.154544883122 +1403636655313555456.0000000000 -0.4448570162 7.1576208365 1.0088845325 0.5754390566 0.7761074462 -0.2054818123 0.155898521383 +1403636655363555584.0000000000 -0.4335078080 7.1408035454 1.0027191503 0.5760993005 0.7742787987 -0.2096211087 0.157037984512 +1403636655413555456.0000000000 -0.4230134098 7.1226635239 0.9972398369 0.5765071186 0.7726118538 -0.2137451417 0.158188115409 +1403636655463555584.0000000000 -0.4124648725 7.1037826428 0.9933570270 0.5763630653 0.7710824110 -0.2174786823 0.161060719034 +1403636655513555456.0000000000 -0.4023341867 7.0832438829 0.9915048820 0.5749719184 0.7700377263 -0.2224695924 0.164184267399 +1403636655563555584.0000000000 -0.3933419463 7.0605510516 0.9904128777 0.5706107738 0.7709748563 -0.2286833282 0.1664483438 +1403636655613555456.0000000000 -0.3846918708 7.0361227619 0.9889840237 0.5641510258 0.7729537869 -0.2362398351 0.168721082835 +1403636655663555584.0000000000 -0.3760969389 7.0112912623 0.9866845681 0.5582011623 0.7745040667 -0.2443092230 0.169905611196 +1403636655713555456.0000000000 -0.3676454964 6.9860715645 0.9820617415 0.5527549841 0.7759659610 -0.2513040844 0.170836214401 +1403636655763555584.0000000000 -0.3584766362 6.9609823830 0.9744137969 0.5481414228 0.7766042221 -0.2575967062 0.173409341638 +1403636655813555456.0000000000 -0.3486523739 6.9360621365 0.9634725843 0.5447924820 0.7759256474 -0.2647622287 0.176185991275 +1403636655863555584.0000000000 -0.3380174136 6.9109024425 0.9493934274 0.5415444945 0.7746474810 -0.2728616798 0.179436184704 +1403636655913555456.0000000000 -0.3264828758 6.8856980535 0.9335208629 0.5387986482 0.7724337856 -0.2817509164 0.183462488401 +1403636655963555584.0000000000 -0.3139650780 6.8606002632 0.9178006679 0.5367813428 0.7694120808 -0.2904919498 0.188375335622 +1403636656013555456.0000000000 -0.3009272358 6.8353074471 0.9034728750 0.5356357579 0.7663560179 -0.2979439633 0.192411494875 +1403636656063555584.0000000000 -0.2870779570 6.8095857377 0.8915071477 0.5343506681 0.7635838026 -0.3041345506 0.197259511953 +1403636656113555456.0000000000 -0.2727073619 6.7833433016 0.8811718567 0.5320177658 0.7621660742 -0.3085441832 0.20213970198 +1403636656163555584.0000000000 -0.2576329067 6.7571684033 0.8740454600 0.5300377518 0.7609669683 -0.3121498066 0.206280762778 +1403636656213555456.0000000000 -0.2424835160 6.7302317876 0.8693022401 0.5267868992 0.7611123689 -0.3142100418 0.210892328978 +1403636656263555584.0000000000 -0.2271223617 6.7034211144 0.8679335482 0.5249446341 0.7607826547 -0.3164697778 0.213283293086 +1403636656313555456.0000000000 -0.2111770138 6.6769475636 0.8686770184 0.5228396397 0.7610152529 -0.3181769794 0.215076511565 +1403636656363555584.0000000000 -0.1947525679 6.6513224064 0.8723980581 0.5217636197 0.7608927332 -0.3198517827 0.215638148046 +1403636656413555456.0000000000 -0.1774485442 6.6265766180 0.8781675645 0.5206175388 0.7612899260 -0.3202344495 0.216436882619 +1403636656463555584.0000000000 -0.1590484333 6.6025975689 0.8859783716 0.5204271739 0.7611842499 -0.3207141888 0.216556005302 +1403636656513555456.0000000000 -0.1400287633 6.5789420425 0.8948565109 0.5197246713 0.7617748964 -0.3200088109 0.217208733923 +1403636656563555584.0000000000 -0.1202773196 6.5559346116 0.9039012595 0.5203168064 0.7616562154 -0.3185455653 0.218355108337 +1403636656613555456.0000000000 -0.1010305557 6.5347472557 0.9129498146 0.5217883371 0.7610718097 -0.3169130835 0.219254941151 +1403636656663555584.0000000000 -0.0808536718 6.5137526076 0.9211237888 0.5255358613 0.7589610332 -0.3151143194 0.220211657917 +1403636656713555456.0000000000 -0.0602682093 6.4932092041 0.9286269031 0.5322093259 0.7549094418 -0.3127348066 0.221499230049 +1403636656763555584.0000000000 -0.0397275393 6.4724190983 0.9343313796 0.5383520268 0.7511546064 -0.3102779170 0.222870964254 +1403636656813555456.0000000000 -0.0192721863 6.4512288370 0.9377310175 0.5423493167 0.7488556017 -0.3072866176 0.225049863521 +1403636656863555584.0000000000 0.0008600032 6.4295971221 0.9391207711 0.5446857395 0.7477120134 -0.3044786967 0.227017429746 +1403636656913555456.0000000000 0.0202129406 6.4073949111 0.9389771256 0.5472800638 0.7464358188 -0.3023737686 0.227789824811 +1403636656963555584.0000000000 0.0384085647 6.3845088269 0.9370241603 0.5492696366 0.7456057939 -0.3011422360 0.227350434489 +1403636657013555456.0000000000 0.0556832257 6.3607016470 0.9333353092 0.5512937380 0.7446937123 -0.3007208440 0.225994387888 +1403636657063555584.0000000000 0.0722025721 6.3360796767 0.9278633873 0.5530571329 0.7438987763 -0.3006747908 0.224359284567 +1403636657113555456.0000000000 0.0877056983 6.3102160182 0.9211946948 0.5544212956 0.7433818301 -0.3010215925 0.222230696758 +1403636657163555584.0000000000 0.1024016080 6.2835935300 0.9146575269 0.5557092289 0.7428207977 -0.3017461314 0.219894946567 +1403636657213555456.0000000000 0.1162346526 6.2551634655 0.9092629796 0.5560386935 0.7429704594 -0.3026754393 0.217263541011 +1403636657263555584.0000000000 0.1297085602 6.2257319402 0.9048319715 0.5543294936 0.7444510985 -0.3037844496 0.215003215522 +1403636657313555456.0000000000 0.1427198827 6.1951008097 0.9015602572 0.5523619886 0.7459850961 -0.3045183326 0.213707873166 +1403636657363555584.0000000000 0.1554030821 6.1630912422 0.8997132544 0.5500489989 0.7476538915 -0.3060706520 0.211614066769 +1403636657413555456.0000000000 0.1679943254 6.1306024749 0.8978303931 0.5467109039 0.7499685282 -0.3085483678 0.208452150164 +1403636657463555584.0000000000 0.1806735586 6.0972747742 0.8950278562 0.5427744952 0.7527346085 -0.3106304548 0.205657912665 +1403636657513555456.0000000000 0.1938247437 6.0635304085 0.8912565815 0.5395876305 0.7549464108 -0.3125751175 0.202972662525 +1403636657563555584.0000000000 0.2077623539 6.0293655549 0.8862194989 0.5368733774 0.7567305283 -0.3134720827 0.202141380017 +1403636657613555456.0000000000 0.2223636036 5.9950871942 0.8802127617 0.5356129190 0.7575355069 -0.3138089727 0.201947234378 +1403636657663555584.0000000000 0.2376258649 5.9608638941 0.8733351604 0.5352458484 0.7577752439 -0.3138874952 0.201898989434 +1403636657713555456.0000000000 0.2536556506 5.9267339941 0.8657515206 0.5358293736 0.7571634035 -0.3142944429 0.202013529152 +1403636657763555584.0000000000 0.2707140545 5.8925915500 0.8571205881 0.5360421436 0.7562127485 -0.3160065882 0.202338665333 +1403636657813555456.0000000000 0.2883694154 5.8581497970 0.8473307247 0.5356544737 0.7555450752 -0.3184866791 0.201970689387 +1403636657863555584.0000000000 0.3065945932 5.8234836829 0.8367898854 0.5351107446 0.7550043292 -0.3222458008 0.199455753799 +1403636657913555456.0000000000 0.3257224461 5.7882788085 0.8266065673 0.5336230939 0.7551785638 -0.3261316190 0.196443115369 +1403636657963555584.0000000000 0.3460355578 5.7520997518 0.8177996767 0.5320555671 0.7555236803 -0.3289280290 0.194697698471 +1403636658013555456.0000000000 0.3686776167 5.7160887083 0.8110529911 0.5307220895 0.7559052819 -0.3297652392 0.195438367507 +1403636658063555584.0000000000 0.3923798071 5.6788869729 0.8063557893 0.5284501666 0.7570385682 -0.3293476707 0.197896789945 +1403636658113555456.0000000000 0.4172957488 5.6409142670 0.8038878469 0.5270745461 0.7576931330 -0.3267734141 0.20325519651 +1403636658163555584.0000000000 0.4433875916 5.6028673141 0.8028607418 0.5249908439 0.7587491569 -0.3248051046 0.207812354587 +1403636658213555456.0000000000 0.4704982935 5.5649022581 0.8027404743 0.5237228370 0.7591970460 -0.3231784417 0.211872438387 +1403636658263555584.0000000000 0.4983700837 5.5269948295 0.8017356333 0.5219060342 0.7601415277 -0.3206589063 0.216741355424 +1403636658313555456.0000000000 0.5264950995 5.4895836388 0.7996233544 0.5204951720 0.7608019055 -0.3195529119 0.219433755288 +1403636658363555584.0000000000 0.5549374815 5.4527292454 0.7963276612 0.5191756034 0.7613671525 -0.3188781753 0.221570443024 +1403636658413555456.0000000000 0.5836632474 5.4166872274 0.7921574405 0.5178054776 0.7620897661 -0.3182700989 0.223160972991 +1403636658463555584.0000000000 0.6127130191 5.3813679071 0.7870254726 0.5162013826 0.7629246573 -0.3171194004 0.225648810562 +1403636658513555456.0000000000 0.6421109285 5.3471011268 0.7815057026 0.5147256928 0.7637799689 -0.3155195643 0.228352851413 +1403636658563555584.0000000000 0.6717005559 5.3137431259 0.7753920880 0.5132978882 0.7645449653 -0.3131234337 0.232271369951 +1403636658613555456.0000000000 0.7011112797 5.2817000622 0.7687555285 0.5123476135 0.7650800164 -0.3111886442 0.235189538891 +1403636658663555584.0000000000 0.7300957334 5.2509225594 0.7616299200 0.5119074257 0.7652650503 -0.3101571714 0.236902341207 +1403636658713555456.0000000000 0.7587183907 5.2217037803 0.7538569088 0.5122476181 0.7649248861 -0.3089926523 0.238779892766 +1403636658763555584.0000000000 0.7869634687 5.1937878632 0.7453399484 0.5129851809 0.7643084706 -0.3071677255 0.241509325717 +1403636658813555456.0000000000 0.8148302926 5.1671201791 0.7361719624 0.5143141409 0.7632102073 -0.3044817114 0.245523993636 +1403636658863555584.0000000000 0.8417592550 5.1421226859 0.7266402395 0.5163520509 0.7616609985 -0.3028466750 0.248066471428 +1403636658913555456.0000000000 0.8674661285 5.1185146728 0.7168027674 0.5197758749 0.7592495242 -0.3032713947 0.247789549924 +1403636658963555584.0000000000 0.8919125337 5.0959849945 0.7061927903 0.5236097204 0.7566499668 -0.3048815805 0.245684574825 +1403636659013555456.0000000000 0.9152718694 5.0742519330 0.6945188096 0.5268402853 0.7544774159 -0.3064477752 0.243501342408 +1403636659063555584.0000000000 0.9380281701 5.0529559171 0.6820868124 0.5310841094 0.7515003244 -0.3070469813 0.242732532912 +1403636659113555456.0000000000 0.9595319038 5.0316256810 0.6682362982 0.5334296858 0.7499058413 -0.3073937115 0.242080783228 +1403636659163555584.0000000000 0.9801414586 5.0104194452 0.6532765563 0.5356494384 0.7483308791 -0.3077275277 0.24162852311 +1403636659213555456.0000000000 0.9995122975 4.9891124594 0.6377345767 0.5371404488 0.7473843511 -0.3076627196 0.241330522151 +1403636659263555584.0000000000 1.0174157328 4.9676735921 0.6227982069 0.5374220363 0.7472434828 -0.3079875723 0.240724713158 +1403636659313555456.0000000000 1.0340777431 4.9459161005 0.6087758181 0.5356320200 0.7486350469 -0.3082814743 0.240013412816 +1403636659363555584.0000000000 1.0498684058 4.9242713422 0.5961872122 0.5330575024 0.7505099839 -0.3090084101 0.238952434185 +1403636659413555456.0000000000 1.0646909282 4.9025328847 0.5847680639 0.5292654529 0.7533307336 -0.3092577292 0.238181743847 +1403636659463555584.0000000000 1.0790937822 4.8814675811 0.5749925633 0.5251948770 0.7563158834 -0.3097154813 0.237134869432 +1403636659513555456.0000000000 1.0933234190 4.8609048352 0.5679908446 0.5235513648 0.7573181412 -0.3093229035 0.238080958486 +1403636659563555584.0000000000 1.1069117962 4.8410271472 0.5618533657 0.5234323088 0.7573640212 -0.3105076823 0.236650241121 +1403636659613555456.0000000000 1.1199602741 4.8213764960 0.5554924150 0.5241757533 0.7566354434 -0.3097265904 0.23835273155 +1403636659663555584.0000000000 1.1325709352 4.8023474285 0.5481956329 0.5253706279 0.7554742508 -0.3096318375 0.239525541138 +1403636659713555456.0000000000 1.1445395174 4.7838203093 0.5394631770 0.5264732967 0.7543699860 -0.3094628136 0.240799831872 +1403636659763555584.0000000000 1.1556949444 4.7658876612 0.5292093822 0.5276589851 0.7531227371 -0.3096599010 0.241853021657 +1403636659813555456.0000000000 1.1660660676 4.7484438360 0.5174201530 0.5277480887 0.7527015741 -0.3097855720 0.242806908116 +1403636659863555584.0000000000 1.1752624831 4.7313892474 0.5047806869 0.5279028371 0.7521947083 -0.3108542260 0.242675432607 +1403636659913555456.0000000000 1.1835859680 4.7143428578 0.4900883967 0.5264846488 0.7529174939 -0.3117039026 0.242424914252 +1403636659963555584.0000000000 1.1910792530 4.6973814346 0.4741069603 0.5228140861 0.7550016996 -0.3128566043 0.242401753377 +1403636660013555456.0000000000 1.1978637473 4.6810978242 0.4572765632 0.5194119850 0.7571234687 -0.3141991582 0.241358927579 +1403636660063555584.0000000000 1.2041428010 4.6653814209 0.4395670005 0.5156222272 0.7593482969 -0.3159047622 0.24026665196 +1403636660113555456.0000000000 1.2101641804 4.6502658839 0.4210941802 0.5122862241 0.7613045921 -0.3168893631 0.239915139449 +1403636660163555584.0000000000 1.2158464409 4.6360617681 0.4020576595 0.5095201970 0.7629950992 -0.3176947582 0.239369355148 +1403636660213555456.0000000000 1.2218317761 4.6230399015 0.3826448603 0.5087876577 0.7634248251 -0.3181616869 0.238936804912 +1403636660263555584.0000000000 1.2277143022 4.6110685596 0.3628924492 0.5058749999 0.7651568642 -0.3190472086 0.238399530984 +1403636660313555456.0000000000 1.2337577361 4.6004897360 0.3442352152 0.5025967318 0.7672358611 -0.3196914404 0.23778780773 +1403636660363555584.0000000000 1.2398321995 4.5909394738 0.3264080824 0.4966461335 0.7710739742 -0.3209115373 0.236227283798 +1403636660413555456.0000000000 1.2465239764 4.5834608882 0.3108847784 0.4914233625 0.7743491912 -0.3225166883 0.234242170694 +1403636660463555584.0000000000 1.2539113708 4.5779746265 0.2982632357 0.4887604942 0.7760492239 -0.3232721680 0.233143489575 +1403636660513555456.0000000000 1.2619122194 4.5745840197 0.2865840517 0.4883989282 0.7763871050 -0.3227430765 0.233509007891 +1403636660563555584.0000000000 1.2708851785 4.5735862414 0.2751844545 0.4914478850 0.7744305573 -0.3214512853 0.235383430626 +1403636660613555456.0000000000 1.2808300142 4.5746369155 0.2632275240 0.4969663696 0.7709539601 -0.3192527294 0.238185040817 +1403636660663555584.0000000000 1.2911342956 4.5773111618 0.2500576733 0.5032955417 0.7668675002 -0.3161861688 0.242144877064 +1403636660713555456.0000000000 1.3013718206 4.5813730596 0.2352536348 0.5091386212 0.7629933508 -0.3128655074 0.246443066885 +1403636660763555584.0000000000 1.3110843640 4.5864628359 0.2189903724 0.5139317421 0.7597020557 -0.3089207201 0.25158485593 +1403636660813555456.0000000000 1.3199730317 4.5922475866 0.2011676662 0.5167875757 0.7576728767 -0.3049877584 0.256602573622 +1403636660863555584.0000000000 1.3275060147 4.5986683671 0.1819141172 0.5184599660 0.7564329449 -0.3011893936 0.261330083757 +1403636660913555456.0000000000 1.3335748739 4.6060682123 0.1616220831 0.5199923987 0.7552505530 -0.2990892141 0.264102535836 +1403636660963555584.0000000000 1.3379209926 4.6144681385 0.1404959918 0.5216645954 0.7542454923 -0.2993951854 0.263329280935 +1403636661013555456.0000000000 1.3406355877 4.6239094840 0.1184663689 0.5237754052 0.7530355053 -0.3009696181 0.260795210057 +1403636661063555584.0000000000 1.3420704971 4.6340609741 0.0957447548 0.5259643861 0.7516524292 -0.3027794670 0.258272500518 +1403636661113555456.0000000000 1.3421825954 4.6447669957 0.0720645708 0.5280106753 0.7503918599 -0.3044481723 0.255789158719 +1403636661163555584.0000000000 1.3410065033 4.6558432323 0.0476907857 0.5294280405 0.7494698244 -0.3062027971 0.25345764809 +1403636661213555456.0000000000 1.3387852182 4.6672751443 0.0245445004 0.5317099411 0.7479270814 -0.3072026791 0.252024072997 +1403636661263555584.0000000000 1.3349333548 4.6781029429 0.0024559697 0.5317479056 0.7479409670 -0.3085148912 0.250293900801 +1403636661313555456.0000000000 1.3296310216 4.6884595500 -0.0174585418 0.5329496941 0.7471648391 -0.3089781064 0.249483178992 +1403636661363555584.0000000000 1.3233849359 4.6985753914 -0.0357505029 0.5333406483 0.7469320794 -0.3092462106 0.249012053818 +1403636661413555456.0000000000 1.3163373537 4.7086916519 -0.0522292471 0.5334976151 0.7468818596 -0.3089844706 0.249151318404 +1403636661463555584.0000000000 1.3085527223 4.7189433478 -0.0666428350 0.5336221563 0.7468406882 -0.3094737846 0.248399592273 +1403636661513555456.0000000000 1.2997015540 4.7287815485 -0.0792023630 0.5328194806 0.7475502821 -0.3099189847 0.247431202132 +1403636661563555584.0000000000 1.2897286004 4.7385170703 -0.0895823989 0.5327447121 0.7478582135 -0.3109143941 0.245404571709 +1403636661613555456.0000000000 1.2786071166 4.7477409541 -0.0984664658 0.5319266893 0.7486122011 -0.3122466710 0.243178506301 +1403636661663555584.0000000000 1.2668582558 4.7567627583 -0.1050932792 0.5329898975 0.7480725041 -0.3126321590 0.242013286791 +1403636661713555456.0000000000 1.2548989182 4.7658011053 -0.1103485407 0.5340637484 0.7474545631 -0.3122498123 0.242048845217 +1403636661763555584.0000000000 1.2419459218 4.7746713324 -0.1132466111 0.5367719787 0.7456163734 -0.3146121812 0.238644593616 +1403636661813555456.0000000000 1.2283870895 4.7828300698 -0.1145541754 0.5391893982 0.7442072855 -0.3168364939 0.234616591933 +1403636661863555584.0000000000 1.2145915663 4.7900221174 -0.1141504515 0.5413185114 0.7429914591 -0.3178231208 0.232220638282 +1403636661913555456.0000000000 1.2010029618 4.7962441698 -0.1118724898 0.5424879082 0.7422073099 -0.3183034108 0.231339830563 +1403636661963555584.0000000000 1.1870564441 4.8013255514 -0.1079495280 0.5432529899 0.7420204752 -0.3182321637 0.230239208874 +1403636662013555456.0000000000 1.1732126912 4.8054494397 -0.1021762650 0.5435943898 0.7418309338 -0.3178312463 0.230597710021 +1403636662063555584.0000000000 1.1591278333 4.8083721698 -0.0948019636 0.5439251340 0.7416501807 -0.3171049175 0.231397772921 +1403636662113555456.0000000000 1.1448974004 4.8103456569 -0.0868223370 0.5439374253 0.7417699666 -0.3163717542 0.231987730663 +1403636662163555584.0000000000 1.1304600902 4.8110821796 -0.0799296162 0.5418769648 0.7431933449 -0.3148836547 0.234267563069 +1403636662213555456.0000000000 1.1154739301 4.8107848249 -0.0746072483 0.5391090014 0.7450451455 -0.3127485378 0.237608013148 +1403636662263555584.0000000000 1.1000463835 4.8097503253 -0.0709919245 0.5362507459 0.7468635174 -0.3101169030 0.241779921419 +1403636662313555456.0000000000 1.0839545444 4.8083241678 -0.0686218368 0.5336630188 0.7483762590 -0.3089205309 0.244345785329 +1403636662363555584.0000000000 1.0672533682 4.8067816904 -0.0676188399 0.5307964713 0.7501189835 -0.3079145491 0.246506079217 +1403636662413555456.0000000000 1.0499653735 4.8054880425 -0.0679131012 0.5275867676 0.7520393373 -0.3082471475 0.24712898226 +1403636662463555584.0000000000 1.0318132581 4.8043134603 -0.0701111857 0.5232071942 0.7548660290 -0.3093193539 0.246481332919 +1403636662513555456.0000000000 1.0129015436 4.8034805204 -0.0733682788 0.5191362140 0.7575229191 -0.3106960767 0.245203112497 +1403636662563555584.0000000000 0.9936965320 4.8035584501 -0.0773390661 0.5167793501 0.7589441936 -0.3130815741 0.242740071632 +1403636662613555456.0000000000 0.9738976737 4.8042930721 -0.0817854430 0.5166600702 0.7589531506 -0.3171424047 0.237640868039 +1403636662663555584.0000000000 0.9543306654 4.8058354204 -0.0865935057 0.5189581750 0.7570445563 -0.3229368992 0.230819651431 +1403636662713555456.0000000000 0.9355371682 4.8078520917 -0.0920785880 0.5223303357 0.7545260074 -0.3275132365 0.22493688995 +1403636662763555584.0000000000 0.9178427043 4.8098597144 -0.0986369243 0.5256230999 0.7520149115 -0.3307741945 0.220867294971 +1403636662813555456.0000000000 0.9011614519 4.8113987981 -0.1065759601 0.5279013731 0.7499997142 -0.3335320077 0.218121454061 +1403636662863555584.0000000000 0.8852845938 4.8123356186 -0.1164552833 0.5272509993 0.7503493790 -0.3350362313 0.216177975114 +1403636662913555456.0000000000 0.8705391415 4.8123500518 -0.1280284751 0.5239073701 0.7524778717 -0.3351870441 0.216674330649 +1403636662963555584.0000000000 0.8567973708 4.8120521656 -0.1401608756 0.5210217633 0.7542994381 -0.3362209368 0.215694602347 +1403636663013555456.0000000000 0.8442221540 4.8116854114 -0.1515998189 0.5188952451 0.7555307540 -0.3388716654 0.212336993559 +1403636663063555584.0000000000 0.8331889199 4.8111694487 -0.1613071847 0.5176964162 0.7560083894 -0.3421996036 0.208185415465 +1403636663113555456.0000000000 0.8239278431 4.8102489054 -0.1695388714 0.5172143456 0.7561232143 -0.3449226323 0.204439192154 +1403636663163555584.0000000000 0.8169022065 4.8091163618 -0.1761759650 0.5153629343 0.7572130876 -0.3464035920 0.202568352412 +1403636663213555456.0000000000 0.8126503404 4.8073257342 -0.1821949574 0.5133079350 0.7584217604 -0.3447066850 0.206127869394 +1403636663263555584.0000000000 0.8107693986 4.8049941151 -0.1892329698 0.5095494456 0.7612400546 -0.3385494640 0.215074875718 +1403636663313555456.0000000000 0.8101095582 4.8029745447 -0.1976142782 0.5052366733 0.7642187567 -0.3334645750 0.222501624906 +1403636663363555584.0000000000 0.8105038750 4.8014229550 -0.2076845226 0.5006090179 0.7672496969 -0.3290478694 0.229010946231 +1403636663413555456.0000000000 0.8114196922 4.8008733234 -0.2197156522 0.4953896532 0.7707200142 -0.3255249279 0.233694827769 +1403636663463555584.0000000000 0.8130197275 4.8020938793 -0.2327670287 0.4910843297 0.7735921160 -0.3234668027 0.236136923786 +1403636663513555456.0000000000 0.8155710269 4.8050279773 -0.2470909558 0.4867509002 0.7762074320 -0.3220314522 0.238477100702 +1403636663563555584.0000000000 0.8185417532 4.8100718779 -0.2619052341 0.4840318899 0.7779317711 -0.3210339226 0.239734247808 +1403636663613555456.0000000000 0.8223277132 4.8176092796 -0.2776501905 0.4825345585 0.7789766956 -0.3208570020 0.239596518909 +1403636663663555584.0000000000 0.8271948162 4.8275255840 -0.2939281731 0.4811608025 0.7798975071 -0.3203922825 0.239985303311 +1403636663713555456.0000000000 0.8332989735 4.8398449536 -0.3099995877 0.4799024653 0.7807990306 -0.3175195586 0.243367679816 +1403636663763555584.0000000000 0.8399866447 4.8546388363 -0.3249779507 0.4795845545 0.7811984359 -0.3139361541 0.247329233845 +1403636663813555456.0000000000 0.8471856349 4.8723286291 -0.3385016411 0.4806200100 0.7807177572 -0.3087605178 0.253280738085 +1403636663863555584.0000000000 0.8544487328 4.8934945912 -0.3502383087 0.4823699302 0.7798902674 -0.3034760732 0.258829469316 +1403636663913555456.0000000000 0.8613177069 4.9182866247 -0.3599839869 0.4851164138 0.7784043650 -0.2999938576 0.262206779095 +1403636663963555584.0000000000 0.8676759117 4.9461668330 -0.3677387746 0.4892833431 0.7760281823 -0.2948541058 0.26728847097 +1403636664013555456.0000000000 0.8727800488 4.9767226934 -0.3733129206 0.4938365709 0.7732532455 -0.2903192425 0.271881586203 +1403636664063555584.0000000000 0.8756128593 5.0093953894 -0.3775427560 0.4977425588 0.7711539502 -0.2884710760 0.272687309164 +1403636664113555456.0000000000 0.8765278610 5.0449157434 -0.3795995751 0.5023793663 0.7688987303 -0.2883686315 0.270653370795 +1403636664163555584.0000000000 0.8760528105 5.0814163925 -0.3794816137 0.5076373873 0.7661655186 -0.2893883440 0.267486574347 +1403636664213555456.0000000000 0.8737117762 5.1200589327 -0.3781737151 0.5135188202 0.7632110870 -0.2904760442 0.263497487217 +1403636664263555584.0000000000 0.8700119365 5.1578228467 -0.3768512400 0.5190868755 0.7603715374 -0.2910595966 0.260131220696 +1403636664313555456.0000000000 0.8647005278 5.1961749543 -0.3789561574 0.5235117434 0.7582184470 -0.2918007396 0.256695480306 +1403636664363555584.0000000000 0.8579525354 5.2340981807 -0.3854631438 0.5264258442 0.7571008339 -0.2918068714 0.254013597323 +1403636664413555456.0000000000 0.8501591688 5.2720722111 -0.3963545289 0.5292450867 0.7560563434 -0.2915246839 0.251578620757 +1403636664463555584.0000000000 0.8408904666 5.3097407123 -0.4101196356 0.5308675695 0.7558601485 -0.2911091424 0.249219836297 +1403636664513555456.0000000000 0.8305896121 5.3475239012 -0.4251424528 0.5335005171 0.7549769909 -0.2903233404 0.247182725008 +1403636664563555584.0000000000 0.8191841434 5.3855773192 -0.4405084639 0.5356806421 0.7545774545 -0.2899125284 0.244151266135 +1403636664613555456.0000000000 0.8060778870 5.4238932902 -0.4545582824 0.5392462351 0.7533202412 -0.2917371004 0.237931873538 +1403636664663555584.0000000000 0.7921616493 5.4617206327 -0.4678727219 0.5413657643 0.7529085627 -0.2916048875 0.234560002959 +1403636664713555456.0000000000 0.7775282882 5.4994757401 -0.4795010306 0.5423600370 0.7532679150 -0.2925754589 0.229853517246 +1403636664763555584.0000000000 0.7625694422 5.5362431420 -0.4900951329 0.5401274466 0.7556403243 -0.2902103593 0.230321490546 +1403636664813555456.0000000000 0.7466076663 5.5722468465 -0.4988219830 0.5381819006 0.7577636205 -0.2873043418 0.231539958921 +1403636664863555584.0000000000 0.7302292131 5.6088971293 -0.5053449753 0.5378537418 0.7588939031 -0.2855694452 0.230745505145 +1403636664913555456.0000000000 0.7132452036 5.6455540962 -0.5099946327 0.5384920873 0.7591993883 -0.2851437413 0.228769769646 +1403636664963555584.0000000000 0.6956457027 5.6819786135 -0.5139938418 0.5362867992 0.7614382224 -0.2847217290 0.227028278976 +1403636665013555456.0000000000 0.6775342465 5.7188156092 -0.5157809689 0.5341738383 0.7636126310 -0.2855802084 0.223602336414 +1403636665063555584.0000000000 0.6585797573 5.7545162504 -0.5157977861 0.5303394011 0.7667619723 -0.2859710674 0.221442421702 +1403636665113555456.0000000000 0.6390300269 5.7899512295 -0.5137024189 0.5276753586 0.7691854110 -0.2864688221 0.218742161733 +1403636665163555584.0000000000 0.6198226437 5.8257664295 -0.5096484851 0.5253772015 0.7710477903 -0.2867858818 0.217296938187 +1403636665213555456.0000000000 0.6002239552 5.8616710461 -0.5042183001 0.5262213310 0.7709580670 -0.2887463812 0.21293261168 +1403636665263555584.0000000000 0.5810500479 5.8978067748 -0.4975816642 0.5306956271 0.7680542718 -0.2914377606 0.208611645439 +1403636665313555456.0000000000 0.5634745786 5.9346280768 -0.4902979320 0.5351347973 0.7651168177 -0.2922715023 0.206892176971 +1403636665363555584.0000000000 0.5462980044 5.9709613760 -0.4838788945 0.5371929252 0.7638195324 -0.2923735927 0.206206608193 +1403636665413555456.0000000000 0.5301764200 6.0068941331 -0.4775421133 0.5374111109 0.7636168658 -0.2910104802 0.208306218137 +1403636665463555584.0000000000 0.5146226643 6.0420410248 -0.4718815854 0.5351695283 0.7650007989 -0.2886193959 0.212288006886 +1403636665513555456.0000000000 0.4987402027 6.0756433604 -0.4666189648 0.5319307003 0.7668967006 -0.2858714456 0.217248008629 +1403636665563555584.0000000000 0.4824735804 6.1090783788 -0.4603511665 0.5298623774 0.7678888786 -0.2829530209 0.222553631769 +1403636665613555456.0000000000 0.4655310754 6.1423808550 -0.4535394377 0.5267337402 0.7697390662 -0.2812017040 0.225785160323 +1403636665663555584.0000000000 0.4480743475 6.1763270331 -0.4464924938 0.5254808202 0.7701265037 -0.2805107659 0.228229678362 +1403636665713555456.0000000000 0.4303132637 6.2111718725 -0.4389116990 0.5259588724 0.7693112480 -0.2799969330 0.230497691596 +1403636665763555584.0000000000 0.4122337431 6.2469146678 -0.4305386748 0.5278339876 0.7675306559 -0.2793976588 0.23286245306 +1403636665813555456.0000000000 0.3931455426 6.2830039992 -0.4218812978 0.5300937122 0.7654610790 -0.2803438631 0.233403751502 +1403636665863555584.0000000000 0.3728205219 6.3200294587 -0.4118958709 0.5353238365 0.7616666361 -0.2845193716 0.228781670405 +1403636665913555456.0000000000 0.3520077240 6.3569731010 -0.4017916237 0.5394082661 0.7585769529 -0.2896942231 0.222883346504 +1403636665963555584.0000000000 0.3307722809 6.3932876695 -0.3924046944 0.5424062571 0.7561541327 -0.2946341395 0.217294969431 +1403636666013555456.0000000000 0.3095001841 6.4287853182 -0.3849280861 0.5435516339 0.7550241593 -0.2985669440 0.212950510937 +1403636666063555584.0000000000 0.2885435550 6.4632995432 -0.3793099549 0.5441850928 0.7544033541 -0.3005586798 0.210719349173 +1403636666113555456.0000000000 0.2680872998 6.4964420492 -0.3755361802 0.5441598335 0.7542426560 -0.2998711948 0.212333129701 +1403636666163555584.0000000000 0.2481030914 6.5284332632 -0.3734916975 0.5435577770 0.7544394315 -0.2975370437 0.216420412522 +1403636666213555456.0000000000 0.2279415219 6.5597574353 -0.3724960081 0.5441109271 0.7540199439 -0.2959680849 0.218632376177 +1403636666263555584.0000000000 0.2075773373 6.5905543953 -0.3728076150 0.5444649643 0.7538147204 -0.2955922975 0.218966809381 +1403636666313555456.0000000000 0.1872184184 6.6204786526 -0.3745063957 0.5460544123 0.7526395613 -0.2961674323 0.218273043499 +1403636666363555584.0000000000 0.1665814850 6.6496003060 -0.3773733760 0.5480427570 0.7515020752 -0.2969899810 0.216080352407 +1403636666413555456.0000000000 0.1456865758 6.6775681241 -0.3803741374 0.5484780103 0.7513972611 -0.2987771708 0.212852602768 +1403636666463555584.0000000000 0.1248423032 6.7042720759 -0.3828342366 0.5480128774 0.7520435460 -0.3000329637 0.209982408179 +1403636666513555456.0000000000 0.1042747835 6.7294854850 -0.3838648497 0.5470231959 0.7532078040 -0.3001123803 0.208269504352 +1403636666563555584.0000000000 0.0837296702 6.7523660970 -0.3832191118 0.5442934031 0.7554406565 -0.2990330553 0.20888594393 +1403636666613555456.0000000000 0.0636027175 6.7744365317 -0.3803046172 0.5408072308 0.7583879308 -0.2973212942 0.209702964988 +1403636666663555584.0000000000 0.0437119664 6.7956990869 -0.3759489031 0.5372059294 0.7613439166 -0.2945755555 0.212109575648 +1403636666713555456.0000000000 0.0234923819 6.8160592460 -0.3706504215 0.5326117920 0.7649854892 -0.2927851434 0.21306980142 +1403636666763555584.0000000000 0.0035336821 6.8366656744 -0.3642696082 0.5283820160 0.7683573671 -0.2915504885 0.213161239821 +1403636666813555456.0000000000 -0.0164937780 6.8575707182 -0.3570980275 0.5254186625 0.7708065289 -0.2918450338 0.211232100554 +1403636666863555584.0000000000 -0.0360413568 6.8789243458 -0.3509005325 0.5220340368 0.7734255569 -0.2941065103 0.206868878754 +1403636666913555456.0000000000 -0.0553633201 6.9008405453 -0.3457962002 0.5197862439 0.7751649236 -0.3000238877 0.197299945853 +1403636666963555584.0000000000 -0.0736380363 6.9226483777 -0.3422566161 0.5182512238 0.7761951980 -0.3057036550 0.188366554826 +1403636667013555456.0000000000 -0.0894770356 6.9450182171 -0.3400493191 0.5189355678 0.7757487684 -0.3080401073 0.184474976749 +1403636667063555584.0000000000 -0.1031710677 6.9674160722 -0.3388768364 0.5207858503 0.7746470098 -0.3080905818 0.18380506426 +1403636667113555456.0000000000 -0.1145278883 6.9896799238 -0.3385988072 0.5254834778 0.7717369446 -0.3036521839 0.189959348642 +1403636667163555584.0000000000 -0.1239865793 7.0123812573 -0.3394433213 0.5309163776 0.7683265571 -0.2969949496 0.198987691834 +1403636667213555456.0000000000 -0.1331307316 7.0345553787 -0.3413811866 0.5353726255 0.7653919066 -0.2915406277 0.206289708089 +1403636667263555584.0000000000 -0.1418404139 7.0566288263 -0.3443717285 0.5382568024 0.7634478174 -0.2857564027 0.213939999057 +1403636667313555456.0000000000 -0.1512013852 7.0784373461 -0.3487988074 0.5397454554 0.7625128821 -0.2818097548 0.218705761629 +1403636667363555584.0000000000 -0.1614257887 7.0999621721 -0.3541284391 0.5411388695 0.7616479960 -0.2799337226 0.220676607592 +1403636667413555456.0000000000 -0.1722859033 7.1212013716 -0.3603714749 0.5404822635 0.7621871467 -0.2790880811 0.221493835418 +1403636667463555584.0000000000 -0.1842680050 7.1419225588 -0.3670368079 0.5376997404 0.7643969504 -0.2789457056 0.220829311134 +1403636667513555456.0000000000 -0.1970236831 7.1625460089 -0.3741539575 0.5346121314 0.7667772857 -0.2797048423 0.21910651348 +1403636667563555584.0000000000 -0.2100215738 7.1836223934 -0.3811679423 0.5308124722 0.7696518872 -0.2825165825 0.214612377338 +1403636667613555456.0000000000 -0.2233535950 7.2049644153 -0.3866692846 0.5278432613 0.7717515501 -0.2862760587 0.209349121496 +1403636667663555584.0000000000 -0.2363116670 7.2266392902 -0.3897037168 0.5260179746 0.7731703633 -0.2892210937 0.204606545919 +1403636667713555456.0000000000 -0.2487364560 7.2484697427 -0.3904679465 0.5258818913 0.7732947519 -0.2915696922 0.201123289557 +1403636667763555584.0000000000 -0.2603485209 7.2702511168 -0.3892872672 0.5266342778 0.7727574096 -0.2926316471 0.199672337986 +1403636667813555456.0000000000 -0.2709151759 7.2924393982 -0.3870188622 0.5278706588 0.7717866396 -0.2931963685 0.199333489642 +1403636667863555584.0000000000 -0.2812372132 7.3143840543 -0.3844733483 0.5284608295 0.7712078352 -0.2939965454 0.198830726857 +1403636667913555456.0000000000 -0.2911763768 7.3357551323 -0.3820778080 0.5290572943 0.7705697310 -0.2949420689 0.198317535583 +1403636667963555584.0000000000 -0.3002675892 7.3570692707 -0.3810198649 0.5280491873 0.7710899683 -0.2953132208 0.198429882146 +1403636668013555456.0000000000 -0.3084847343 7.3787268540 -0.3811483920 0.5284383585 0.7706028871 -0.2954911849 0.19902022829 +1403636668063555584.0000000000 -0.3157126988 7.4004145196 -0.3836473414 0.5279667942 0.7705222464 -0.2945290823 0.201987998945 +1403636668113555456.0000000000 -0.3221516435 7.4224255106 -0.3882050179 0.5274114216 0.7704688461 -0.2934665874 0.205164108912 +1403636668163555584.0000000000 -0.3281454713 7.4445490006 -0.3942703376 0.5263485864 0.7706613592 -0.2925001912 0.208523075942 +1403636668213555456.0000000000 -0.3338328844 7.4670240111 -0.4021131376 0.5240264038 0.7716871840 -0.2922045982 0.210977939699 +1403636668263555584.0000000000 -0.3391662418 7.4898750810 -0.4108972889 0.5220522967 0.7724725229 -0.2918722486 0.213443649139 +1403636668313555456.0000000000 -0.3442086236 7.5132585527 -0.4205590223 0.5205697411 0.7727008841 -0.2922364771 0.215727443313 +1403636668363555584.0000000000 -0.3494305485 7.5372992396 -0.4310014547 0.5200920160 0.7724512167 -0.2928266041 0.21697002708 +1403636668413555456.0000000000 -0.3546760046 7.5617323634 -0.4421085481 0.5205152869 0.7715792067 -0.2931827620 0.218570885472 +1403636668463555584.0000000000 -0.3597005990 7.5866721786 -0.4538440126 0.5216192638 0.7701969877 -0.2935106030 0.220366671127 +1403636668513555456.0000000000 -0.3647260039 7.6121865878 -0.4661437054 0.5219320378 0.7694558166 -0.2938321152 0.221782285742 +1403636668563555584.0000000000 -0.3701831517 7.6382436799 -0.4786007048 0.5218649119 0.7689576822 -0.2948485752 0.22231827286 +1403636668613555456.0000000000 -0.3758253642 7.6647018444 -0.4910554419 0.5216409815 0.7686670093 -0.2953057947 0.223240235804 +1403636668663555584.0000000000 -0.3813442011 7.6919880112 -0.5035503533 0.5209756327 0.7685345801 -0.2958877557 0.224475890363 +1403636668713555456.0000000000 -0.3867729640 7.7197853058 -0.5163737372 0.5201348499 0.7686219934 -0.2942979070 0.228185694311 +1403636668763555584.0000000000 -0.3921188055 7.7487388394 -0.5290171539 0.5200264253 0.7682506790 -0.2913158596 0.233449097333 +1403636668813555456.0000000000 -0.3980092776 7.7786124805 -0.5409468844 0.5209086588 0.7670451801 -0.2887463640 0.238582057272 +1403636668863555584.0000000000 -0.4051470039 7.8093213844 -0.5517121286 0.5212581190 0.7665376565 -0.2847408173 0.244197996533 +1403636668913555456.0000000000 -0.4133321946 7.8415866354 -0.5601342903 0.5228786583 0.7650009231 -0.2814626498 0.249299565095 +1403636668963555584.0000000000 -0.4233396817 7.8754893208 -0.5659291847 0.5258394031 0.7629295814 -0.2821146063 0.248681975244 +1403636669013555456.0000000000 -0.4359477590 7.9093830702 -0.5692776396 0.5292930727 0.7607249921 -0.2847883402 0.245034550607 +1403636669063555584.0000000000 -0.4499605432 7.9435643691 -0.5709455138 0.5326763499 0.7584292945 -0.2874256594 0.241717607444 +1403636669113555456.0000000000 -0.4653004121 7.9770982976 -0.5701998004 0.5355889896 0.7564035713 -0.2902059032 0.238282616684 +1403636669163555584.0000000000 -0.4815289808 8.0100275151 -0.5699699303 0.5368689883 0.7553484271 -0.2921008400 0.236426610867 +1403636669213555456.0000000000 -0.4986089765 8.0424523412 -0.5708653616 0.5382302416 0.7542287478 -0.2931308365 0.235630039969 +1403636669263555584.0000000000 -0.5164208834 8.0733836737 -0.5725117912 0.5388349390 0.7536559052 -0.2935541416 0.235553923623 +1403636669313555456.0000000000 -0.5351829738 8.1042081910 -0.5762489468 0.5384225340 0.7537279069 -0.2934900870 0.23634505723 +1403636669363555584.0000000000 -0.5547895561 8.1344191612 -0.5811850902 0.5379283994 0.7539753497 -0.2943846224 0.235567194922 +1403636669413555456.0000000000 -0.5751025172 8.1646736510 -0.5871490963 0.5390170775 0.7531466151 -0.2944058076 0.235703175132 +1403636669463555584.0000000000 -0.5963678022 8.1947326878 -0.5939652930 0.5413386037 0.7514685585 -0.2944432932 0.235691893684 +1403636669513555456.0000000000 -0.6185292228 8.2243868427 -0.6020275402 0.5435940065 0.7500249582 -0.2934543099 0.23633172899 +1403636669563555584.0000000000 -0.6416652003 8.2534758598 -0.6109922097 0.5464339777 0.7480263573 -0.2924273220 0.237387316939 +1403636669613555456.0000000000 -0.6659282918 8.2816979705 -0.6200130215 0.5506318833 0.7450298220 -0.2905406278 0.239418539443 +1403636669663555584.0000000000 -0.6918498786 8.3086734041 -0.6281371173 0.5547383242 0.7422315087 -0.2890651367 0.240414487683 +1403636669713555456.0000000000 -0.7189613556 8.3349071272 -0.6347786635 0.5588455750 0.7393180664 -0.2876007227 0.241632456831 +1403636669763555584.0000000000 -0.7475797212 8.3599841611 -0.6401227585 0.5613268350 0.7377062310 -0.2874520578 0.240983434106 +1403636669813555456.0000000000 -0.7785923481 8.3837168686 -0.6434089395 0.5645647122 0.7360342152 -0.2920486690 0.232868835812 +1403636669863555584.0000000000 -0.8113838907 8.4059523348 -0.6442256534 0.5683148004 0.7339468608 -0.2995814879 0.220434174523 +1403636669913555456.0000000000 -0.8455670156 8.4253525535 -0.6432631461 0.5686062613 0.7341471168 -0.3081639091 0.206760575526 +1403636669963555584.0000000000 -0.8789157853 8.4424883003 -0.6415459626 0.5678655801 0.7347885415 -0.3145035328 0.196728264609 +1403636670013555456.0000000000 -0.9114033665 8.4565879150 -0.6387163520 0.5656824699 0.7363868664 -0.3186156026 0.190320319395 +1403636670063555584.0000000000 -0.9431383527 8.4677350252 -0.6346826013 0.5643107226 0.7374905035 -0.3215434534 0.185124210228 +1403636670113555456.0000000000 -0.9738756374 8.4762324587 -0.6291252929 0.5634859399 0.7387094464 -0.3231530957 0.179900044457 +1403636670163555584.0000000000 -1.0029699478 8.4821313752 -0.6217863876 0.5664083818 0.7374022826 -0.3235298077 0.175350740612 +1403636670213555456.0000000000 -1.0303969828 8.4856771180 -0.6132320252 0.5723596510 0.7339710080 -0.3247467426 0.168019470652 +1403636670263555584.0000000000 -1.0560433601 8.4860285258 -0.6055157431 0.5784116629 0.7304468248 -0.3252635952 0.161527019255 +1403636670313555456.0000000000 -1.0799093051 8.4830662750 -0.5995790212 0.5830750803 0.7279366628 -0.3256131122 0.155266760279 +1403636670363555584.0000000000 -1.1018073481 8.4763240300 -0.5957680373 0.5852222175 0.7277223701 -0.3251648557 0.14900645895 +1403636670413555456.0000000000 -1.1216969828 8.4656896578 -0.5934479245 0.5860667482 0.7290953623 -0.3232638452 0.142990229444 +1403636670463555584.0000000000 -1.1393884756 8.4508962582 -0.5913505013 0.5865511103 0.7311640192 -0.3210461544 0.135226990097 +1403636670513555456.0000000000 -1.1542798463 8.4316936343 -0.5877283868 0.5873680135 0.7335198423 -0.3170880537 0.128072729027 +1403636670563555584.0000000000 -1.1662185028 8.4083566531 -0.5829266657 0.5882849336 0.7365493365 -0.3111659548 0.120795944944 +1403636670613555456.0000000000 -1.1747916685 8.3808284996 -0.5761513152 0.5891843723 0.7398380962 -0.3041324198 0.114038756718 +1403636670663555584.0000000000 -1.1794913149 8.3496394321 -0.5671586726 0.5902415846 0.7433141043 -0.2956598520 0.108093783458 +1403636670713555456.0000000000 -1.1808771212 8.3142870487 -0.5568745668 0.5917783514 0.7465679712 -0.2863669629 0.102120564448 +1403636670763555584.0000000000 -1.1785137152 8.2757922080 -0.5454721205 0.5936507569 0.7495087083 -0.2770128462 0.0952856653 +1403636670813555456.0000000000 -1.1731249075 8.2340149334 -0.5342260623 0.5960456374 0.7518657841 -0.2683258444 0.086189803059 +1403636670863555584.0000000000 -1.1648071297 8.1886600052 -0.5237129169 0.5989535487 0.7536927133 -0.2599720267 0.0749432164576 +1403636670913555456.0000000000 -1.1529650941 8.1403572586 -0.5140183510 0.6025257488 0.7548805648 -0.2512934562 0.0630051891056 +1403636670963555584.0000000000 -1.1373895716 8.0882028728 -0.5034454014 0.6073940013 0.7549668131 -0.2422294764 0.0492190923729 +1403636671013555456.0000000000 -1.1176199766 8.0317885169 -0.4916223927 0.6117030467 0.7559392426 -0.2301406043 0.037557241527 +1403636671063555584.0000000000 -1.0928070153 7.9707989441 -0.4774355025 0.6149241599 0.7579438806 -0.2157458670 0.0290357081719 +1403636671113555456.0000000000 -1.0627900345 7.9058832620 -0.4616909056 0.6162698452 0.7615747089 -0.1991270853 0.0237454122259 +1403636671163555584.0000000000 -1.0281879581 7.8363036204 -0.4444207879 0.6158765534 0.7661955849 -0.1824057123 0.0191977281621 +1403636671213555456.0000000000 -0.9885767214 7.7636010067 -0.4251955921 0.6138550179 0.7713699779 -0.1671326179 0.0153968283419 +1403636671263555584.0000000000 -0.9446539989 7.6863361326 -0.4049279200 0.6100921899 0.7774577480 -0.1521197809 0.0143715759697 +1403636671313555456.0000000000 -0.8965365585 7.6065179482 -0.3856607167 0.6033823757 0.7855009030 -0.1362929813 0.0185003585052 +1403636671363555584.0000000000 -0.8449402045 7.5238738359 -0.3662825770 0.5952475210 0.7943118920 -0.1184222620 0.0269290690704 +1403636671413555456.0000000000 -0.7914289363 7.4404064295 -0.3474736065 0.5868906250 0.8026929481 -0.0997027456 0.0360941527838 +1403636671463555584.0000000000 -0.7371884665 7.3566087817 -0.3294536451 0.5781919839 0.8106169354 -0.0829941414 0.0413060078004 +1403636671513555456.0000000000 -0.6827488579 7.2730100638 -0.3120281532 0.5696956967 0.8177818951 -0.0694937054 0.0430140687711 +1403636671563555584.0000000000 -0.6283810731 7.1901205890 -0.2954420072 0.5618019414 0.8240748195 -0.0594293831 0.0418021413999 +1403636671613555456.0000000000 -0.5739470447 7.1086675418 -0.2803650388 0.5538418579 0.8300588727 -0.0513145415 0.0403519773989 +1403636671663555584.0000000000 -0.5197200482 7.0292764596 -0.2662585024 0.5466259672 0.8352465266 -0.0457139663 0.0383865206957 +1403636671713555456.0000000000 -0.4655402791 6.9524727491 -0.2530202092 0.5407597622 0.8393652018 -0.0414364076 0.0364412085667 +1403636671763555584.0000000000 -0.4115185877 6.8780291956 -0.2410436391 0.5361118621 0.8425400093 -0.0383795284 0.0351769226202 +1403636671813555456.0000000000 -0.3576385081 6.8063341120 -0.2300760474 0.5311999719 0.8457611160 -0.0348947315 0.0360150284867 +1403636671863555584.0000000000 -0.3043414288 6.7377335917 -0.2187672898 0.5263571423 0.8488517732 -0.0335086823 0.0357210589168 +1403636671913555456.0000000000 -0.2512518951 6.6728321879 -0.2069755319 0.5200179287 0.8527489001 -0.0328245636 0.0363760254981 +1403636671963555584.0000000000 -0.1984877270 6.6121670142 -0.1932107126 0.5137276301 0.8564948011 -0.0314731218 0.0388589809867 +1403636672013555456.0000000000 -0.1463942446 6.5559606356 -0.1774533058 0.5072978488 0.8602114490 -0.0298883605 0.0423301497938 +1403636672063555584.0000000000 -0.0948512935 6.5052528065 -0.1594677712 0.5045281790 0.8616219391 -0.0267432112 0.0484123048689 +1403636672113555456.0000000000 -0.0444545397 6.4599048509 -0.1394551711 0.5044756068 0.8613076166 -0.0220634359 0.0562739410962 +1403636672163555584.0000000000 0.0039749984 6.4193826789 -0.1168795204 0.5056615553 0.8602465774 -0.0191025656 0.0625884136242 +1403636672213555456.0000000000 0.0501910236 6.3832367508 -0.0933607230 0.5062032533 0.8595923906 -0.0169086533 0.0676260736374 +1403636672263555584.0000000000 0.0941688948 6.3524831312 -0.0697212344 0.5072071718 0.8587390656 -0.0164411912 0.0709773858289 +1403636672313555456.0000000000 0.1361852518 6.3260865907 -0.0473956069 0.5091916597 0.8572248478 -0.0145606966 0.075348523865 +1403636672363555584.0000000000 0.1761068013 6.3041972808 -0.0266606896 0.5134267915 0.8541890803 -0.0110226977 0.0814398239591 +1403636672413555456.0000000000 0.2134081632 6.2858575936 -0.0088343534 0.5190630146 0.8502096827 -0.0067749650 0.087585285804 +1403636672463555584.0000000000 0.2476109755 6.2712752180 0.0063040919 0.5283580902 0.8440411769 -0.0038929612 0.0917445644821 +1403636672513555456.0000000000 0.2779019508 6.2595526235 0.0189213861 0.5410137195 0.8363166384 -0.0067230461 0.0885067022816 +1403636672563555584.0000000000 0.3050961864 6.2497743901 0.0279464908 0.5541159112 0.8281998569 -0.0104306732 0.0832571620145 +1403636672613555456.0000000000 0.3297230083 6.2411189462 0.0314480175 0.5646988642 0.8216739206 -0.0157917308 0.0756160187502 +1403636672663555584.0000000000 0.3524365332 6.2329127917 0.0304051305 0.5728248459 0.8164994890 -0.0207108271 0.0690749018137 +1403636672713555456.0000000000 0.3734909982 6.2244281283 0.0235638196 0.5749186429 0.8154025859 -0.0254399991 0.062769287354 +1403636672763555584.0000000000 0.3932226654 6.2153017011 0.0114583814 0.5717393478 0.8179077844 -0.0291029129 0.0573933340383 +1403636672813555456.0000000000 0.4112238455 6.2057004619 -0.0029788177 0.5671503017 0.8213922638 -0.0304792917 0.0522139543306 +1403636672863555584.0000000000 0.4281191117 6.1968483478 -0.0166133234 0.5647184635 0.8233338785 -0.0278946165 0.0493586053424 +1403636672913555456.0000000000 0.4436427780 6.1887436073 -0.0283865838 0.5640219349 0.8241725158 -0.0232675093 0.0455800858902 +1403636672963555584.0000000000 0.4575454317 6.1804715461 -0.0392823731 0.5633320825 0.8249784123 -0.0166009548 0.0423319314502 +1403636673013555456.0000000000 0.4700690103 6.1731533229 -0.0481677102 0.5628899253 0.8255873936 -0.0088114272 0.0385064440126 +1403636673063555584.0000000000 0.4813085820 6.1665683623 -0.0555215703 0.5618790446 0.8264462376 -0.0002907377 0.035755712855 +1403636673113555456.0000000000 0.4912381951 6.1608285948 -0.0612713587 0.5600989950 0.8277828536 0.0073061738 0.0318006751592 +1403636673163555584.0000000000 0.5000419896 6.1567634561 -0.0643016107 0.5549657516 0.8312934923 0.0134896693 0.0279673571002 +1403636673213555456.0000000000 0.5077018364 6.1533097355 -0.0655514293 0.5479263985 0.8359431033 0.0190581643 0.0247502772206 +1403636673263555584.0000000000 0.5141258199 6.1514904025 -0.0656351875 0.5408939919 0.8404134339 0.0248371919 0.0228487086829 +1403636673313555456.0000000000 0.5192028564 6.1515029363 -0.0634985725 0.5349878680 0.8441401700 0.0283460797 0.0202941918019 +1403636673363555584.0000000000 0.5226815035 6.1542833568 -0.0599238700 0.5309970871 0.8465743596 0.0317312082 0.0186300187226 +1403636673413555456.0000000000 0.5248782427 6.1600662180 -0.0561499863 0.5303510653 0.8469108000 0.0343969845 0.0169319778741 +1403636673463555584.0000000000 0.5256923480 6.1686000690 -0.0533181253 0.5310082966 0.8464555264 0.0362668750 0.0150978358342 +1403636673513555456.0000000000 0.5253865453 6.1796946683 -0.0521317429 0.5322413218 0.8456160293 0.0380774823 0.014241197516 +1403636673563555584.0000000000 0.5237178637 6.1931757689 -0.0517634646 0.5352559194 0.8436642366 0.0395230195 0.0130264148497 +1403636673613555456.0000000000 0.5208217803 6.2093102308 -0.0521991055 0.5413357700 0.8397094292 0.0410163517 0.0127010831006 +1403636673663555584.0000000000 0.5164332428 6.2272868969 -0.0535835851 0.5477829838 0.8354806363 0.0419858651 0.011962280522 +1403636673713555456.0000000000 0.5105179921 6.2469237482 -0.0556043241 0.5542936096 0.8311579748 0.0426257480 0.0108655834474 +1403636673763555584.0000000000 0.5034116738 6.2671598175 -0.0575637881 0.5617360133 0.8260787005 0.0438636087 0.0110732011597 +1403636673813555456.0000000000 0.4946925097 6.2867560458 -0.0589955785 0.5671713973 0.8223769937 0.0438849628 0.00931646151464 +1403636673863555584.0000000000 0.4849846529 6.3060834781 -0.0598997775 0.5702591980 0.8201880985 0.0447741855 0.00955000276225 +1403636673913555456.0000000000 0.4740062058 6.3260400514 -0.0604090860 0.5698273323 0.8203798375 0.0463732843 0.0111018953613 +1403636673963555584.0000000000 0.4613678876 6.3466439742 -0.0590798841 0.5697978673 0.8203831073 0.0466574272 0.0111817758691 +1403636674013555456.0000000000 0.4472267526 6.3675196024 -0.0583227522 0.5687614459 0.8211536980 0.0459723095 0.0101768700157 +1403636674063555584.0000000000 0.4316857166 6.3892135873 -0.0584936066 0.5684934537 0.8213615746 0.0456337494 0.00989534327142 +1403636674113555456.0000000000 0.4147056460 6.4111611954 -0.0597868091 0.5682501255 0.8216024989 0.0446145684 0.00840647874983 +1403636674163555584.0000000000 0.3965208683 6.4331870413 -0.0625523810 0.5691519895 0.8210228766 0.0439433987 0.00751177258882 +1403636674213555456.0000000000 0.3772194094 6.4553958816 -0.0668185103 0.5708280552 0.8199459034 0.0425344243 0.00590505430936 +1403636674263555584.0000000000 0.3568567613 6.4775172269 -0.0727476222 0.5727789195 0.8187407250 0.0397777615 0.00237996901715 +1403636674313555456.0000000000 0.3353770754 6.4991490913 -0.0803740495 0.5738470267 0.8181895842 0.0353997828 -0.00349994893157 +1403636674363555584.0000000000 0.3132235285 6.5198556904 -0.0896610407 0.5736212997 0.8184400157 0.0318187826 -0.0101049639804 +1403636674413555456.0000000000 0.2904890640 6.5401235912 -0.1003619433 0.5736532006 0.8183584331 0.0296561590 -0.0182206640301 +1403636674463555584.0000000000 0.2678184889 6.5600462214 -0.1124524791 0.5743345243 0.8176696927 0.0298188860 -0.0258256060926 +1403636674513555456.0000000000 0.2455220206 6.5794552227 -0.1261927850 0.5752739542 0.8166691263 0.0319873653 -0.0329882453151 +1403636674563555584.0000000000 0.2241496495 6.5984313314 -0.1418533670 0.5755278363 0.8161107468 0.0358530643 -0.0380199462 +1403636674613555456.0000000000 0.2037402476 6.6172372217 -0.1587741571 0.5762103972 0.8152686684 0.0401780243 -0.0412832025376 +1403636674663555584.0000000000 0.1841452503 6.6362092857 -0.1767008408 0.5772254084 0.8141861135 0.0451619526 -0.0432689094346 +1403636674713555456.0000000000 0.1652351375 6.6548009555 -0.1961540834 0.5760584569 0.8146572870 0.0483255161 -0.0464198606476 +1403636674763555584.0000000000 0.1473002236 6.6732096991 -0.2173153114 0.5717337630 0.8173564475 0.0515844288 -0.0488670509747 +1403636674813555456.0000000000 0.1305182615 6.6912408456 -0.2384324843 0.5648876017 0.8217930227 0.0542943150 -0.051091610488 +1403636674863555584.0000000000 0.1145491378 6.7105081820 -0.2583329142 0.5578687077 0.8263260741 0.0566300168 -0.052542987076 +1403636674913555456.0000000000 0.0996183616 6.7305955958 -0.2766269199 0.5518385647 0.8301482738 0.0586460768 -0.0537464381025 +1403636674963555584.0000000000 0.0855944227 6.7525945545 -0.2931469592 0.5460881303 0.8337925101 0.0606586309 -0.0538361833257 +1403636675013555456.0000000000 0.0721999911 6.7768410070 -0.3067625193 0.5414413233 0.8367071576 0.0615613346 -0.0545218117567 +1403636675063555584.0000000000 0.0596348261 6.8030726832 -0.3181076959 0.5373026072 0.8392958634 0.0637242244 -0.0531750431888 +1403636675113555456.0000000000 0.0479876798 6.8319740568 -0.3272427497 0.5356527045 0.8403546062 0.0666291440 -0.0494051928506 +1403636675163555584.0000000000 0.0368787304 6.8630285926 -0.3345254189 0.5339199013 0.8413955819 0.0716170364 -0.043058261796 +1403636675213555456.0000000000 0.0255870353 6.8973102092 -0.3392216052 0.5352526937 0.8403888788 0.0773543149 -0.0356005091594 +1403636675263555584.0000000000 0.0133756326 6.9347000033 -0.3424898788 0.5363762640 0.8395195273 0.0815089415 -0.0293897786303 +1403636675313555456.0000000000 -0.0001348093 6.9744386986 -0.3437376409 0.5378968299 0.8383897023 0.0846798697 -0.0244750294062 +1403636675363555584.0000000000 -0.0151570641 7.0157658997 -0.3424861948 0.5431987619 0.8347703309 0.0873481682 -0.0215382745994 +1403636675413555456.0000000000 -0.0321766717 7.0552252077 -0.3391446393 0.5508274077 0.8294616689 0.0902000018 -0.0211297526956 +1403636675463555584.0000000000 -0.0512443202 7.0969490347 -0.3368505127 0.5570716105 0.8248715552 0.0933599962 -0.0232819531553 +1403636675513555456.0000000000 -0.0717319405 7.1390011418 -0.3363158635 0.5627194688 0.8203612620 0.0987853615 -0.0244059738535 +1403636675563555584.0000000000 -0.0936869861 7.1764578226 -0.3355581411 0.5681312447 0.8158886167 0.1044526838 -0.0253434565252 +1403636675613555456.0000000000 -0.1170924027 7.2158392482 -0.3371515934 0.5725906874 0.8119980063 0.1099967922 -0.0264546428983 +1403636675663555584.0000000000 -0.1423118103 7.2544898629 -0.3399918078 0.5755650007 0.8090879240 0.1151208996 -0.0291348531253 +1403636675713555456.0000000000 -0.1692371561 7.2922740407 -0.3438977854 0.5785321821 0.8060814529 0.1199011473 -0.0340135352253 +1403636675763555584.0000000000 -0.1980125733 7.3292914539 -0.3487323882 0.5819527112 0.8026309535 0.1240346425 -0.04159329172 +1403636675813555456.0000000000 -0.2286518505 7.3652438627 -0.3545641857 0.5834631386 0.8005565682 0.1251241733 -0.0549898919563 +1403636675863555584.0000000000 -0.2602182791 7.4004113289 -0.3617503665 0.5840597626 0.7988363635 0.1254913020 -0.0706158001801 +1403636675913555456.0000000000 -0.2918196527 7.4342028765 -0.3709619447 0.5810418936 0.7993158322 0.1263285250 -0.0867503427995 +1403636675963555584.0000000000 -0.3229233914 7.4670036810 -0.3817971461 0.5766125261 0.8003968409 0.1290930826 -0.10108346941 +1403636676013555456.0000000000 -0.3529159110 7.4991366235 -0.3942906527 0.5717436185 0.8015230763 0.1349169555 -0.111657547675 +1403636676063555584.0000000000 -0.3814426206 7.5311092600 -0.4080977657 0.5680111659 0.8016949340 0.1432846383 -0.118819445476 +1403636676113555456.0000000000 -0.4085191055 7.5628710945 -0.4234440047 0.5645291408 0.8016556570 0.1544598234 -0.121643823378 +1403636676163555584.0000000000 -0.4345517080 7.5947761883 -0.4397637325 0.5630852697 0.7998652762 0.1691261885 -0.120610328246 +1403636676213555456.0000000000 -0.4602097095 7.6264443144 -0.4567482769 0.5618561244 0.7976128060 0.1838683173 -0.119682701497 +1403636676263555584.0000000000 -0.4854546745 7.6578997079 -0.4748071357 0.5607549307 0.7947716797 0.2008918850 -0.11633716267 +1403636676313555456.0000000000 -0.5114559998 7.6886814713 -0.4929900801 0.5578141525 0.7928229683 0.2160957878 -0.116523486183 +1403636676363555584.0000000000 -0.5385531829 7.7195173985 -0.5097534160 0.5580969478 0.7882373514 0.2316150652 -0.116465171757 +1403636676413555456.0000000000 -0.5670523079 7.7495374378 -0.5247850804 0.5569055143 0.7845710823 0.2459414443 -0.117546887861 +1403636676463555584.0000000000 -0.5975682929 7.7784160609 -0.5371127760 0.5544572025 0.7818589300 0.2571965366 -0.122978720852 +1403636676513555456.0000000000 -0.6293955828 7.8051067150 -0.5476676273 0.5509607748 0.7800215092 0.2661549395 -0.131035178455 +1403636676563555584.0000000000 -0.6636156717 7.8316904353 -0.5556974552 0.5482891795 0.7779438893 0.2717032870 -0.142687085867 +1403636676613555456.0000000000 -0.6995100423 7.8583591988 -0.5612865226 0.5456224920 0.7761194904 0.2765637736 -0.153124498422 +1403636676663555584.0000000000 -0.7366736706 7.8854813904 -0.5645180351 0.5439572492 0.7742148165 0.2797446871 -0.16261869195 +1403636676713555456.0000000000 -0.7743899378 7.9124465008 -0.5659638649 0.5423659391 0.7728173290 0.2815441917 -0.171246699967 +1403636676763555584.0000000000 -0.8124275057 7.9395348691 -0.5658056379 0.5414717330 0.7714496772 0.2822749787 -0.178870328236 +1403636676813555456.0000000000 -0.8507275452 7.9664340409 -0.5640534280 0.5394680613 0.7708885414 0.2831625592 -0.185806438705 +1403636676863555584.0000000000 -0.8889906011 7.9930073759 -0.5601460855 0.5364231671 0.7710091268 0.2839793125 -0.192745589422 +1403636676913555456.0000000000 -0.9261427920 8.0194759789 -0.5562894249 0.5357501634 0.7699383818 0.2850428101 -0.197274547547 +1403636676963555584.0000000000 -0.9628443169 8.0457019625 -0.5538073945 0.5349562952 0.7693303742 0.2857522767 -0.200744050684 +1403636677013555456.0000000000 -0.9989261307 8.0726005366 -0.5553844849 0.5355576446 0.7681538529 0.2876872950 -0.20088227348 +1403636677063555584.0000000000 -1.0344081613 8.1000561026 -0.5611277831 0.5374485843 0.7663759556 0.2911423174 -0.197618483137 +1403636677113555456.0000000000 -1.0699031468 8.1279776272 -0.5705583920 0.5394962960 0.7647023543 0.2943266047 -0.193767658996 +1403636677163555584.0000000000 -1.1052486579 8.1557064809 -0.5832900409 0.5410753974 0.7635187996 0.2970030628 -0.189909551063 +1403636677213555456.0000000000 -1.1406516033 8.1830216205 -0.5978534925 0.5437153525 0.7616216439 0.2985054109 -0.187618247479 +1403636677263555584.0000000000 -1.1764109826 8.2094550690 -0.6125430499 0.5470126567 0.7588875291 0.2999311111 -0.186837362851 +1403636677313555456.0000000000 -1.2125640529 8.2341744556 -0.6260377924 0.5499760344 0.7557538386 0.3014336397 -0.188415121045 +1403636677363555584.0000000000 -1.2488761035 8.2576997012 -0.6380394045 0.5541415994 0.7508734459 0.3040969441 -0.191418924483 +1403636677413555456.0000000000 -1.2856718032 8.2792597508 -0.6469106062 0.5581696824 0.7456313367 0.3069167469 -0.195659464151 +1403636677463555584.0000000000 -1.3221854654 8.2990719632 -0.6536051708 0.5617113104 0.7402075995 0.3096848402 -0.201664109895 +1403636677513555456.0000000000 -1.3578665614 8.3165058534 -0.6584613809 0.5631677528 0.7357985126 0.3126893873 -0.208968844796 +1403636677563555584.0000000000 -1.3926289457 8.3319249445 -0.6616589643 0.5631425326 0.7319563892 0.3167836692 -0.216236997746 +1403636677613555456.0000000000 -1.4264848431 8.3453504848 -0.6632999743 0.5607944200 0.7293777342 0.3211516942 -0.224453399775 +1403636677663555584.0000000000 -1.4593055950 8.3572597691 -0.6631851258 0.5566101483 0.7278484308 0.3264134358 -0.232112200388 +1403636677713555456.0000000000 -1.4907461963 8.3672571463 -0.6614468068 0.5515103916 0.7262887787 0.3319386999 -0.241158863353 +1403636677763555584.0000000000 -1.5204717677 8.3757257913 -0.6587220875 0.5449323930 0.7254729979 0.3389856408 -0.248649053169 +1403636677813555456.0000000000 -1.5484987263 8.3826233861 -0.6549954247 0.5352788647 0.7261501308 0.3461479044 -0.2576124083 +1403636677863555584.0000000000 -1.5746247174 8.3885833946 -0.6507535440 0.5245517760 0.7269598849 0.3531123636 -0.267743195533 +1403636677913555456.0000000000 -1.5993814832 8.3947521025 -0.6457685405 0.5142424167 0.7269448812 0.3615118488 -0.276432740003 +1403636677963555584.0000000000 -1.6229351854 8.4014792315 -0.6398967215 0.5058435481 0.7252586041 0.3703353778 -0.284559255558 +1403636678013555456.0000000000 -1.6451949962 8.4094206950 -0.6347239997 0.4990368796 0.7224152854 0.3807049809 -0.290072517999 +1403636678063555584.0000000000 -1.6665179454 8.4188056367 -0.6303560812 0.4951988972 0.7178470655 0.3902628910 -0.295243151782 +1403636678113555456.0000000000 -1.6869304626 8.4296417189 -0.6277403346 0.4945854837 0.7119616133 0.4002848978 -0.297099076247 +1403636678163555584.0000000000 -1.7066309826 8.4417269995 -0.6266226090 0.4948396291 0.7061952804 0.4092419556 -0.29823311206 +1403636678213555456.0000000000 -1.7255633295 8.4545885854 -0.6273779160 0.4951407438 0.7010353936 0.4182458796 -0.297414533995 +1403636678263555584.0000000000 -1.7439498812 8.4676889619 -0.6284519387 0.4952355515 0.6959965465 0.4261510292 -0.297868857416 +1403636678313555456.0000000000 -1.7619302655 8.4804984801 -0.6288052844 0.4942073176 0.6913473381 0.4332199252 -0.300197404511 +1403636678363555584.0000000000 -1.7796874219 8.4927983658 -0.6272780886 0.4914938857 0.6875844775 0.4385071455 -0.305569681024 +1403636678413555456.0000000000 -1.7970526438 8.5050121252 -0.6246693301 0.4877085209 0.6843510915 0.4448594245 -0.309683830011 +1403636678463555584.0000000000 -1.8142358622 8.5171543530 -0.6202913307 0.4844994818 0.6804858236 0.4514188501 -0.313720126694 +1403636678513555456.0000000000 -1.8310835914 8.5291053200 -0.6144325185 0.4808667802 0.6765907293 0.4585455386 -0.317376926984 +1403636678563555584.0000000000 -1.8479280895 8.5407808741 -0.6065860936 0.4777823675 0.6719868319 0.4650131589 -0.322366978944 +1403636678613555456.0000000000 -1.8641028900 8.5519307125 -0.5972507131 0.4743870276 0.6662794598 0.4727216469 -0.327967794265 +1403636678663555584.0000000000 -1.8797390387 8.5632182285 -0.5888691219 0.4725461566 0.6589116235 0.4822956392 -0.331551683299 +1403636678713555456.0000000000 -1.8951686907 8.5744105877 -0.5817949291 0.4718016065 0.6501705314 0.4935154350 -0.333352725395 +1403636678763555584.0000000000 -1.9104541173 8.5851756030 -0.5761127777 0.4710902737 0.6404833219 0.5058794071 -0.33457599111 +1403636678813555456.0000000000 -1.9256455081 8.5952683974 -0.5726589664 0.4706486738 0.6304971921 0.5186164171 -0.334664202669 +1403636678863555584.0000000000 -1.9409721767 8.6043836092 -0.5707573770 0.4697934905 0.6214836223 0.5302206618 -0.334541825809 +1403636678913555456.0000000000 -1.9567544496 8.6121488514 -0.5705207551 0.4697696404 0.6124283317 0.5407926621 -0.334352090033 +1403636678963555584.0000000000 -1.9725193679 8.6176329234 -0.5714749498 0.4671790279 0.6053919248 0.5496123110 -0.336408502916 +1403636679013555456.0000000000 -1.9885999905 8.6208312505 -0.5729118004 0.4641209790 0.5988892511 0.5562133864 -0.341394274473 +1403636679063555584.0000000000 -2.0048029115 8.6216991178 -0.5753499766 0.4597402537 0.5932012670 0.5615212745 -0.348489618659 +1403636679113555456.0000000000 -2.0209292015 8.6205166351 -0.5786951044 0.4553061033 0.5872629417 0.5661147751 -0.356837008947 +1403636679163555584.0000000000 -2.0368278634 8.6171635541 -0.5830490783 0.4487467590 0.5826909440 0.5690237295 -0.367844539744 +1403636679213555456.0000000000 -2.0522761074 8.6119206562 -0.5876681998 0.4415252711 0.5776743051 0.5709653946 -0.38124316425 +1403636679263555584.0000000000 -2.0670243229 8.6055380705 -0.5918207694 0.4340179310 0.5723157426 0.5735423032 -0.39386844588 +1403636679313555456.0000000000 -2.0809386052 8.5984500062 -0.5948580727 0.4259860025 0.5670496473 0.5770408158 -0.404987061614 +1403636679363555584.0000000000 -2.0939398977 8.5911829167 -0.5966528369 0.4192243857 0.5600049732 0.5822747517 -0.414248063351 +1403636679413555456.0000000000 -2.1060557014 8.5840097921 -0.5967805347 0.4122493966 0.5533863977 0.5883715923 -0.421465063001 +1403636679463555584.0000000000 -2.1168541742 8.5770364104 -0.5949821703 0.4056416793 0.5462785092 0.5948131933 -0.428055934953 +1403636679513555456.0000000000 -2.1267116500 8.5703749245 -0.5917946228 0.3994588301 0.5393987216 0.6017353998 -0.432892793841 +1403636679563555584.0000000000 -2.1358039980 8.5642140959 -0.5871898915 0.3940098830 0.5334761219 0.6079748673 -0.436492840896 +1403636679613555456.0000000000 -2.1448862669 8.5583748922 -0.5805383746 0.3888213461 0.5287273394 0.6129070367 -0.440011733682 +1403636679663555584.0000000000 -2.1523979795 8.5532485610 -0.5729287809 0.3837296820 0.5253189462 0.6179051754 -0.441570753233 +1403636679713555456.0000000000 -2.1589031502 8.5487825086 -0.5638876293 0.3802788893 0.5218168963 0.6221993664 -0.442677130167 +1403636679763555584.0000000000 -2.1645910309 8.5452527912 -0.5532771758 0.3793919747 0.5178323908 0.6258307914 -0.442997929053 +1403636679813555456.0000000000 -2.1699172242 8.5420102952 -0.5401771311 0.3804252226 0.5134942157 0.6268546748 -0.445705684424 +1403636679863555584.0000000000 -2.1757797559 8.5388633398 -0.5246868521 0.3827414225 0.5095798557 0.6271539906 -0.44778928778 +1403636679913555456.0000000000 -2.1813332472 8.5359968562 -0.5078764968 0.3877270586 0.5040846737 0.6278031801 -0.448809020426 +1403636679963555584.0000000000 -2.1861887931 8.5327864196 -0.4899163933 0.3903154706 0.5012812544 0.6292715744 -0.447647431584 +1403636680013555456.0000000000 -2.1898420382 8.5295859762 -0.4709292737 0.3956471879 0.4972843052 0.6316838836 -0.444012492796 +1403636680063555584.0000000000 -2.1914470535 8.5260629832 -0.4507950811 0.4010279884 0.4935404561 0.6342084876 -0.439743066943 +1403636680113555456.0000000000 -2.1915342048 8.5215366092 -0.4306292411 0.4075759413 0.4890890010 0.6366736543 -0.435109709189 +1403636680163555584.0000000000 -2.1899764987 8.5154485753 -0.4113712519 0.4108322849 0.4874541460 0.6377546962 -0.432289528739 +1403636680213555456.0000000000 -2.1866604584 8.5071277209 -0.3930116603 0.4107178753 0.4881546958 0.6370015450 -0.432717981493 +1403636680263555584.0000000000 -2.1819838825 8.4970849684 -0.3757491232 0.4123857571 0.4876672615 0.6352119843 -0.434309065537 +1403636680313555456.0000000000 -2.1756922102 8.4859768263 -0.3610628552 0.4155320051 0.4864871716 0.6354912207 -0.432220190343 +1403636680363555584.0000000000 -2.1676719091 8.4734368342 -0.3486978655 0.4186188038 0.4854053611 0.6381191671 -0.426548779349 +1403636680413555456.0000000000 -2.1579152561 8.4590114656 -0.3378257626 0.4203968582 0.4855360440 0.6405662877 -0.42094662689 +1403636680463555584.0000000000 -2.1468203209 8.4423528178 -0.3280180826 0.4212611666 0.4862310460 0.6422537659 -0.416687532209 +1403636680513555456.0000000000 -2.1345442918 8.4232792151 -0.3195756769 0.4219646381 0.4871766178 0.6434868806 -0.412952081641 +1403636680563555584.0000000000 -2.1210902938 8.4015086130 -0.3121092308 0.4204303884 0.4897545364 0.6430646711 -0.412124509503 +1403636680613555456.0000000000 -2.1065734864 8.3771113245 -0.3055282056 0.4184895987 0.4925263046 0.6411655051 -0.413752450322 +1403636680663555584.0000000000 -2.0912363585 8.3506533005 -0.3003540878 0.4176477420 0.4944943843 0.6399839980 -0.414084713377 +1403636680713555456.0000000000 -2.0748953525 8.3218136269 -0.2962178034 0.4145054672 0.4978886656 0.6386557499 -0.415223948588 +1403636680763555584.0000000000 -2.0575364112 8.2906144747 -0.2925623589 0.4079561707 0.5038908266 0.6357277644 -0.418946305834 +1403636680813555456.0000000000 -2.0396455848 8.2577642158 -0.2892844063 0.4012953895 0.5096725206 0.6324079900 -0.423386426706 +1403636680863555584.0000000000 -2.0211713930 8.2237484900 -0.2867392035 0.3930255409 0.5165162961 0.6285492409 -0.428564687935 +1403636680913555456.0000000000 -2.0022544014 8.1891864247 -0.2856615449 0.3835017241 0.5240011406 0.6256367643 -0.432351560085 +1403636680963555584.0000000000 -1.9829767328 8.1549934614 -0.2870045830 0.3747634770 0.5304942630 0.6258496922 -0.43178737367 +1403636681013555456.0000000000 -1.9645134948 8.1214722221 -0.2905319140 0.3692104329 0.5347742916 0.6281161374 -0.427983914657 +1403636681063555584.0000000000 -1.9467058170 8.0885125648 -0.2957226311 0.3644344478 0.5381639843 0.6311905936 -0.423279451154 +1403636681113555456.0000000000 -1.9302818614 8.0562378057 -0.3017663776 0.3622256143 0.5396483664 0.6343854082 -0.418482256244 +1403636681163555584.0000000000 -1.9157685823 8.0242743947 -0.3077209942 0.3634925759 0.5387692316 0.6354013605 -0.416972389211 +1403636681213555456.0000000000 -1.9033447183 7.9924011153 -0.3136243272 0.3697890783 0.5342335495 0.6353363807 -0.417370621361 +1403636681263555584.0000000000 -1.8922987048 7.9600813198 -0.3184351089 0.3773607854 0.5285859357 0.6338847673 -0.419983151993 +1403636681313555456.0000000000 -1.8815465977 7.9270513142 -0.3218683907 0.3822494324 0.5247965193 0.6318974916 -0.423296048671 +1403636681363555584.0000000000 -1.8716831712 7.8934648356 -0.3234506868 0.3864433321 0.5217796840 0.6293917381 -0.426935068255 +1403636681413555456.0000000000 -1.8613173214 7.8594077728 -0.3232598979 0.3883439709 0.5198926426 0.6270769738 -0.430900300935 +1403636681463555584.0000000000 -1.8506213842 7.8251168667 -0.3213265091 0.3884781833 0.5193387454 0.6250242070 -0.434415364954 +1403636681513555456.0000000000 -1.8394128222 7.7907143224 -0.3181831721 0.3884947403 0.5187530378 0.6240130374 -0.436548796491 +1403636681563555584.0000000000 -1.8278670613 7.7563033928 -0.3148054005 0.3881825615 0.5179542436 0.6243778273 -0.43725282074 +1403636681613555456.0000000000 -1.8160117802 7.7223477341 -0.3125297391 0.3894505799 0.5163684106 0.6258904583 -0.435836029529 +1403636681663555584.0000000000 -1.8037433271 7.6882999399 -0.3112474222 0.3899925247 0.5152656702 0.6266125243 -0.435618943679 +1403636681713555456.0000000000 -1.7910055885 7.6541129830 -0.3111906155 0.3906376952 0.5139143019 0.6275630479 -0.435268770185 +1403636681763555584.0000000000 -1.7782709907 7.6197257792 -0.3120140854 0.3911156064 0.5129013087 0.6279821588 -0.435429946369 +1403636681813555456.0000000000 -1.7649926114 7.5848593532 -0.3135362328 0.3912688235 0.5119956356 0.6284234232 -0.435721445552 +1403636681863555584.0000000000 -1.7512056347 7.5495648032 -0.3144670564 0.3909711859 0.5114062477 0.6284050270 -0.436706198423 +1403636681913555456.0000000000 -1.7370191160 7.5141150578 -0.3141129020 0.3908972420 0.5106682961 0.6281898332 -0.437943798964 +1403636681963555584.0000000000 -1.7221995482 7.4784277308 -0.3119331272 0.3896896505 0.5106370118 0.6281291815 -0.439141833335 +1403636682013555456.0000000000 -1.7076475852 7.4424493021 -0.3078110037 0.3884183636 0.5108134467 0.6279977553 -0.440249493878 +1403636682063555584.0000000000 -1.6922677646 7.4063467624 -0.3014886061 0.3867379147 0.5113588661 0.6277991130 -0.441377581125 +1403636682113555456.0000000000 -1.6759081983 7.3705790546 -0.2934158218 0.3859626097 0.5112982843 0.6275881042 -0.442425247808 +1403636682163555584.0000000000 -1.6586599026 7.3347612959 -0.2844611977 0.3846402438 0.5117951211 0.6275182449 -0.443100992076 +1403636682213555456.0000000000 -1.6407683724 7.2991189153 -0.2761039089 0.3822608765 0.5131249897 0.6285971981 -0.442091540151 +1403636682263555584.0000000000 -1.6226267377 7.2636792759 -0.2690718091 0.3788577766 0.5154819999 0.6296123067 -0.440832662315 +1403636682313555456.0000000000 -1.6042607226 7.2286133635 -0.2642563264 0.3753914200 0.5179348603 0.6321022673 -0.437345956884 +1403636682363555584.0000000000 -1.5864483299 7.1936534702 -0.2608018216 0.3714745847 0.5208541395 0.6341706982 -0.434217829991 +1403636682413555456.0000000000 -1.5695255535 7.1588681656 -0.2583792084 0.3695060380 0.5225963221 0.6351781704 -0.432327496107 +1403636682463555584.0000000000 -1.5536437094 7.1243544469 -0.2561688646 0.3707273563 0.5222517966 0.6341071041 -0.433269510578 +1403636682513555456.0000000000 -1.5384011428 7.0901689618 -0.2549382346 0.3746650561 0.5204109095 0.6325885900 -0.434315849158 +1403636682563555584.0000000000 -1.5234403394 7.0559307168 -0.2546969836 0.3787535453 0.5184073617 0.6310013510 -0.435473138347 +1403636682613555456.0000000000 -1.5084069425 7.0214580104 -0.2556688543 0.3823136734 0.5164873621 0.6296798282 -0.436555121197 +1403636682663555584.0000000000 -1.4932685282 6.9868803357 -0.2574758365 0.3854983157 0.5152747764 0.6280196906 -0.437577674976 +1403636682713555456.0000000000 -1.4777349930 6.9520725305 -0.2588366595 0.3862715237 0.5154366396 0.6261113909 -0.439435896109 +1403636682763555584.0000000000 -1.4620920575 6.9174251993 -0.2589357793 0.3871896631 0.5156664520 0.6240365081 -0.441305689516 +1403636682813555456.0000000000 -1.4459066124 6.8830812917 -0.2575648990 0.3887213672 0.5156804007 0.6221227806 -0.442642823176 +1403636682863555584.0000000000 -1.4293731473 6.8489553636 -0.2551547918 0.3910880374 0.5145342259 0.6219034065 -0.442199989184 +1403636682913555456.0000000000 -1.4121647692 6.8149342411 -0.2515453384 0.3934909099 0.5140083605 0.6222715840 -0.440157227497 +1403636682963555584.0000000000 -1.3939397340 6.7804595431 -0.2462001019 0.3954143516 0.5131968731 0.6229854378 -0.438366974357 +1403636683013555456.0000000000 -1.3746772654 6.7457849452 -0.2400528675 0.3972988119 0.5120124456 0.6243514955 -0.436098749936 +1403636683063555584.0000000000 -1.3552009752 6.7103629578 -0.2338382485 0.3982028605 0.5115904280 0.6237528208 -0.436625851712 +1403636683113555456.0000000000 -1.3347631681 6.6743060585 -0.2292864459 0.3971868899 0.5120848515 0.6242134896 -0.436313188774 +1403636683163555584.0000000000 -1.3137376626 6.6377059890 -0.2263713416 0.3954485643 0.5130228450 0.6238997857 -0.437237979735 +1403636683213555456.0000000000 -1.2919593156 6.6005626122 -0.2250625684 0.3928985323 0.5143373685 0.6240877064 -0.437724056287 +1403636683263555584.0000000000 -1.2697021426 6.5630909240 -0.2249258558 0.3913835542 0.5149629074 0.6241266861 -0.438289855213 +1403636683313555456.0000000000 -1.2467812352 6.5251448230 -0.2260035396 0.3895519448 0.5154047972 0.6241648332 -0.439346603863 +1403636683363555584.0000000000 -1.2235257108 6.4871560269 -0.2282128934 0.3879779462 0.5157524035 0.6242556065 -0.440201668952 +1403636683413555456.0000000000 -1.1999062247 6.4494169809 -0.2316589285 0.3868871618 0.5157201435 0.6245584029 -0.440769621163 +1403636683463555584.0000000000 -1.1761258642 6.4116069410 -0.2361539176 0.3851543983 0.5159147260 0.6248530357 -0.441640995281 +1403636683513555456.0000000000 -1.1521902307 6.3743032599 -0.2417387220 0.3850125352 0.5153895385 0.6253266839 -0.441707493314 +1403636683563555584.0000000000 -1.1280755960 6.3371469050 -0.2479972072 0.3843749297 0.5152322590 0.6253923507 -0.44235284609 +1403636683613555456.0000000000 -1.1034627258 6.3004561103 -0.2555213686 0.3832460763 0.5155146083 0.6263473522 -0.441651591125 +1403636683663555584.0000000000 -1.0785724440 6.2641475406 -0.2639040642 0.3812064325 0.5162738218 0.6273975082 -0.441038959083 +1403636683713555456.0000000000 -1.0535013768 6.2282602614 -0.2723424674 0.3792604694 0.5170597959 0.6287543632 -0.439862040371 +1403636683763555584.0000000000 -1.0284495983 6.1925297151 -0.2794209501 0.3765667005 0.5184953568 0.6294893691 -0.4394351138 +1403636683813555456.0000000000 -1.0033769235 6.1573120465 -0.2851032177 0.3747222158 0.5190925843 0.6314371400 -0.437508043412 +1403636683863555584.0000000000 -0.9780488648 6.1222568694 -0.2886246262 0.3712729355 0.5205536261 0.6319493500 -0.437973000007 +1403636683913555456.0000000000 -0.9538593025 6.0876845267 -0.2913929992 0.3719707980 0.5192675440 0.6334622827 -0.436720138739 +1403636683963555584.0000000000 -0.9306017024 6.0529953763 -0.2914949678 0.3711798269 0.5191856688 0.6333278436 -0.437684383952 +1403636684013555456.0000000000 -0.9080895244 6.0186485018 -0.2891212384 0.3715127299 0.5181965390 0.6327256596 -0.439441552601 +1403636684063555584.0000000000 -0.8867669458 5.9845248532 -0.2844457432 0.3723245166 0.5167777978 0.6323278218 -0.440995110899 +1403636684113555456.0000000000 -0.8644527246 5.9508562238 -0.2779619075 0.3730052603 0.5153486196 0.6322801657 -0.442159098146 +1403636684163555584.0000000000 -0.8422622827 5.9173008033 -0.2704336647 0.3730277831 0.5142529442 0.6324770422 -0.443133132896 +1403636684213555456.0000000000 -0.8200323092 5.8839141164 -0.2608164104 0.3731055798 0.5132440776 0.6321919877 -0.444641466683 +1403636684263555584.0000000000 -0.7980004133 5.8506041519 -0.2498382849 0.3729434168 0.5123139413 0.6317683750 -0.446448601501 +1403636684313555456.0000000000 -0.7759393568 5.8177491160 -0.2390442926 0.3741437933 0.5106289923 0.6315527134 -0.447678036402 +1403636684363555584.0000000000 -0.7535268672 5.7854121009 -0.2296304536 0.3747283416 0.5094202732 0.6311061642 -0.449193349034 +1403636684413555456.0000000000 -0.7309631890 5.7536175398 -0.2220482960 0.3750861691 0.5084366198 0.6309489205 -0.450228863111 +1403636684463555584.0000000000 -0.7081760380 5.7222485585 -0.2162809543 0.3743309567 0.5084489039 0.6304819471 -0.451495915121 +1403636684513555456.0000000000 -0.6850946452 5.6910823629 -0.2118716614 0.3723794651 0.5090625474 0.6294522173 -0.45384883272 +1403636684563555584.0000000000 -0.6620649587 5.6607920081 -0.2088938155 0.3718874484 0.5090941243 0.6284037278 -0.455666164228 +1403636684613555456.0000000000 -0.6385024080 5.6310383280 -0.2074979233 0.3706708598 0.5095768925 0.6275241975 -0.457326891699 +1403636684663555584.0000000000 -0.6146670463 5.6020853385 -0.2077303627 0.3703614940 0.5093028098 0.6272730745 -0.45822647426 +1403636684713555456.0000000000 -0.5905734237 5.5739065140 -0.2093614768 0.3704102921 0.5090329145 0.6267691955 -0.459175438227 +1403636684763555584.0000000000 -0.5659141390 5.5466781337 -0.2127269423 0.3709391242 0.5084790965 0.6268324770 -0.459275756267 +1403636684813555456.0000000000 -0.5407239528 5.5202705970 -0.2176365493 0.3710761742 0.5083641372 0.6266358498 -0.459560538688 +1403636684863555584.0000000000 -0.5148200495 5.4949114134 -0.2245061248 0.3714695924 0.5079538176 0.6273927368 -0.458662855354 +1403636684913555456.0000000000 -0.4884852606 5.4704824579 -0.2322345888 0.3741488434 0.5062006904 0.6283108106 -0.457164116335 +1403636684963555584.0000000000 -0.4614716496 5.4467604804 -0.2401005234 0.3772158475 0.5041307883 0.6311140119 -0.453051273857 +1403636685013555456.0000000000 -0.4337393855 5.4234470489 -0.2468535409 0.3792891240 0.5031873761 0.6327444451 -0.450085205418 +1403636685063555584.0000000000 -0.4062388325 5.4000178207 -0.2518426283 0.3805691232 0.5027917916 0.6338334967 -0.447909204289 +1403636685113555456.0000000000 -0.3781959822 5.3762121903 -0.2540879870 0.3805198026 0.5034582253 0.6346859888 -0.445991245245 +1403636685163555584.0000000000 -0.3494897613 5.3524410515 -0.2545812962 0.3789084000 0.5054365381 0.6349956664 -0.444682846537 +1403636685213555456.0000000000 -0.3199835006 5.3291472043 -0.2540157137 0.3797046438 0.5059851158 0.6364145379 -0.441338851658 +1403636685263555584.0000000000 -0.2902366187 5.3056645345 -0.2523179234 0.3807781372 0.5064379821 0.6377757646 -0.437916264373 +1403636685313555456.0000000000 -0.2609498330 5.2816774200 -0.2486064340 0.3819818021 0.5068597081 0.6385847269 -0.435192699552 +1403636685363555584.0000000000 -0.2316084770 5.2570772729 -0.2435745066 0.3830326902 0.5071917116 0.6387788665 -0.433594379185 +1403636685413555456.0000000000 -0.2025681857 5.2319606920 -0.2384998950 0.3834331870 0.5081720193 0.6378724574 -0.433426946565 +1403636685463555584.0000000000 -0.1733442814 5.2062910852 -0.2345987346 0.3824494638 0.5098588606 0.6368259437 -0.433853739502 +1403636685513555456.0000000000 -0.1443248375 5.1802484665 -0.2321393162 0.3817531550 0.5112573832 0.6355472590 -0.434695408708 +1403636685563555584.0000000000 -0.1151859389 5.1540994378 -0.2315533976 0.3808710098 0.5126196340 0.6349876400 -0.434682736891 +1403636685613555456.0000000000 -0.0861546711 5.1274845068 -0.2321706119 0.3799920764 0.5138824053 0.6335845604 -0.436006307572 +1403636685663555584.0000000000 -0.0572206585 5.1009725763 -0.2344835794 0.3811823782 0.5136596472 0.6332936280 -0.435652317904 +1403636685713555456.0000000000 -0.0281611169 5.0743211802 -0.2383367434 0.3824924236 0.5129632467 0.6331222637 -0.43557370522 +1403636685763555584.0000000000 0.0007815645 5.0472844815 -0.2435206242 0.3834086283 0.5123542590 0.6332257936 -0.435334390243 +1403636685813555456.0000000000 0.0294616413 5.0200415620 -0.2497551414 0.3858239184 0.5107774768 0.6335377773 -0.434598847138 +1403636685863555584.0000000000 0.0583224696 4.9925515658 -0.2570717693 0.3879105534 0.5093609933 0.6337199118 -0.43413805918 +1403636685913555456.0000000000 0.0874473034 4.9641715773 -0.2651390077 0.3870059264 0.5099884116 0.6334433451 -0.434612196628 +1403636685963555584.0000000000 0.1169832412 4.9351884848 -0.2738550005 0.3842949479 0.5116280489 0.6328296934 -0.435982467333 +1403636686013555456.0000000000 0.1468151775 4.9060391733 -0.2822620735 0.3813708515 0.5136165486 0.6325217019 -0.43665846069 +1403636686063555584.0000000000 0.1769898246 4.8766162919 -0.2891591583 0.3776721506 0.5158309075 0.6326068517 -0.437139328619 +1403636686113555456.0000000000 0.2065941531 4.8472171100 -0.2940515181 0.3751554157 0.5175069430 0.6324310476 -0.437579647697 +1403636686163555584.0000000000 0.2352008455 4.8180016715 -0.2964852928 0.3750409879 0.5177234700 0.6319383714 -0.43813304006 +1403636686213555456.0000000000 0.2638533856 4.7890713729 -0.2976553404 0.3739901562 0.5186975706 0.6318635903 -0.437986982116 +1403636686263555584.0000000000 0.2921594092 4.7603492262 -0.2974484681 0.3725553949 0.5198586845 0.6316855409 -0.438089948785 +1403636686313555456.0000000000 0.3199978939 4.7319332972 -0.2954193013 0.3714959700 0.5208539107 0.6317263681 -0.437748493802 +1403636686363555584.0000000000 0.3472938398 4.7038343520 -0.2916338076 0.3703954309 0.5215907783 0.6317580931 -0.437757919964 +1403636686413555456.0000000000 0.3739146220 4.6763056806 -0.2873536734 0.3701711298 0.5219587647 0.6322394086 -0.436813132625 +1403636686463555584.0000000000 0.4002154987 4.6491645564 -0.2840224561 0.3689518602 0.5227690703 0.6327038538 -0.436202770881 +1403636686513555456.0000000000 0.4260633472 4.6225744390 -0.2822507655 0.3675139932 0.5236124425 0.6330195810 -0.435946883106 +1403636686563555584.0000000000 0.4509585347 4.5964187207 -0.2817875601 0.3678837767 0.5233792044 0.6332983310 -0.435509999028 +1403636686613555456.0000000000 0.4754168606 4.5707330962 -0.2833864969 0.3682437460 0.5225414328 0.6343837347 -0.434631190387 +1403636686663555584.0000000000 0.4992214492 4.5450339032 -0.2864220255 0.3686037065 0.5222081112 0.6346122212 -0.434393053442 +1403636686713555456.0000000000 0.5222865941 4.5192207542 -0.2903815341 0.3686203000 0.5219810524 0.6345107843 -0.434799861898 +1403636686763555584.0000000000 0.5445768209 4.4934806925 -0.2944509796 0.3690932811 0.5212607854 0.6338704299 -0.436194476723 +1403636686813555456.0000000000 0.5659836552 4.4680401337 -0.2976636865 0.3701211432 0.5205062430 0.6331440997 -0.437278103062 +1403636686863555584.0000000000 0.5869725016 4.4427665894 -0.2994394599 0.3700104768 0.5200987361 0.6324034535 -0.438925305456 +1403636686913555456.0000000000 0.6075341982 4.4179032557 -0.2993100906 0.3699896070 0.5198219486 0.6315593957 -0.440483327897 +1403636686963555584.0000000000 0.6278584379 4.3934716920 -0.2974534411 0.3700178239 0.5195448234 0.6310267607 -0.441548653887 +1403636687013555456.0000000000 0.6475764105 4.3693631807 -0.2940803345 0.3701181037 0.5190007724 0.6305868021 -0.442731377456 +1403636687063555584.0000000000 0.6668375491 4.3457174664 -0.2888518829 0.3696696870 0.5193942298 0.6299543044 -0.443544282923 +1403636687113555456.0000000000 0.6860469713 4.3225876259 -0.2822276547 0.3694595751 0.5192354020 0.6300398203 -0.443783781191 +1403636687163555584.0000000000 0.7051663041 4.2997923230 -0.2756075728 0.3694956521 0.5188067172 0.6301612384 -0.444082612668 +1403636687213555456.0000000000 0.7238763094 4.2775000545 -0.2695053770 0.3705182782 0.5181072626 0.6296069856 -0.444832680487 +1403636687263555584.0000000000 0.7425760792 4.2557840046 -0.2649645122 0.3708681415 0.5175481969 0.6297733889 -0.444956361982 +1403636687313555456.0000000000 0.7611450031 4.2344676501 -0.2618799502 0.3712583084 0.5169430814 0.6296423338 -0.445519528839 +1403636687363555584.0000000000 0.7795489920 4.2138367829 -0.2604569990 0.3728398003 0.5157699320 0.6293494239 -0.445972155125 +1403636687413555456.0000000000 0.7978777046 4.1934571062 -0.2604127521 0.3739140490 0.5146293087 0.6293564510 -0.44638034919 +1403636687463555584.0000000000 0.8161104603 4.1731759306 -0.2616554412 0.3745211367 0.5139973758 0.6292282756 -0.446780027577 +1403636687513555456.0000000000 0.8343078222 4.1530508422 -0.2645089101 0.3747488527 0.5137585257 0.6289330647 -0.447279191181 +1403636687563555584.0000000000 0.8528107294 4.1331198963 -0.2692761676 0.3735970117 0.5141819876 0.6286572314 -0.44814310432 +1403636687613555456.0000000000 0.8713724083 4.1134126821 -0.2754660096 0.3734661656 0.5139367515 0.6279182081 -0.449567306064 +1403636687663555584.0000000000 0.8903380323 4.0942771347 -0.2835606718 0.3726943145 0.5140079136 0.6277461526 -0.450366051823 +1403636687713555456.0000000000 0.9094360502 4.0756577154 -0.2930256493 0.3725434588 0.5137706340 0.6267114330 -0.452198945921 +1403636687763555584.0000000000 0.9287913759 4.0574189112 -0.3045383262 0.3716963337 0.5139848513 0.6269011338 -0.452389629144 +1403636687813555456.0000000000 0.9480858930 4.0398316630 -0.3174589985 0.3719784514 0.5135900556 0.6274123825 -0.451897099722 +1403636687863555584.0000000000 0.9674048793 4.0227065150 -0.3315117129 0.3716598826 0.5136295229 0.6276718878 -0.451753966274 +1403636687913555456.0000000000 0.9868370211 4.0062636886 -0.3471206128 0.3722338186 0.5131082781 0.6284447073 -0.45079832427 +1403636687963555584.0000000000 1.0063574068 3.9903255977 -0.3639356746 0.3736563952 0.5119203701 0.6297342301 -0.449169491799 +1403636688013555456.0000000000 1.0257994046 3.9745034599 -0.3814515293 0.3750586459 0.5109476394 0.6303600915 -0.448229491437 +1403636688063555584.0000000000 1.0453891520 3.9590280118 -0.3995510721 0.3773099748 0.5090532877 0.6321368601 -0.44598758196 +1403636688113555456.0000000000 1.0654617242 3.9437038430 -0.4164908820 0.3790255559 0.5079083831 0.6332271817 -0.444288238308 +1403636688163555584.0000000000 1.0859429586 3.9281338071 -0.4316217081 0.3792669415 0.5076192593 0.6338618279 -0.443506998576 +1403636688213555456.0000000000 1.1062527125 3.9122108640 -0.4448527180 0.3790978899 0.5077281707 0.6339458569 -0.44340674893 +1403636688263555584.0000000000 1.1268716302 3.8959053988 -0.4562919827 0.3786156418 0.5079280551 0.6331802110 -0.444682029198 +1403636688313555456.0000000000 1.1476107548 3.8792129244 -0.4663416478 0.3763431068 0.5094084429 0.6326508995 -0.445669993993 +1403636688363555584.0000000000 1.1685916840 3.8625605765 -0.4756247783 0.3745930031 0.5105144678 0.6319392288 -0.446886866318 +1403636688413555456.0000000000 1.1896517992 3.8460671014 -0.4858090561 0.3732707410 0.5112748573 0.6324288723 -0.44643106489 +1403636688463555584.0000000000 1.2105312041 3.8300442908 -0.4968837146 0.3747206876 0.5104792344 0.6329883606 -0.445332564304 +1403636688513555456.0000000000 1.2317126870 3.8140117505 -0.5091952923 0.3759316564 0.5094403714 0.6344049768 -0.443481931009 +1403636688563555584.0000000000 1.2527863608 3.7980938249 -0.5225824941 0.3786794559 0.5076160735 0.6363285680 -0.440469914037 +1403636688613555456.0000000000 1.2739698675 3.7818643359 -0.5372711466 0.3812266557 0.5055605514 0.6385987829 -0.437340096892 +1403636688663555584.0000000000 1.2950114788 3.7648122384 -0.5525300435 0.3828772290 0.5039587011 0.6399800517 -0.435724900094 +1403636688713555456.0000000000 1.3161120478 3.7470488253 -0.5685379605 0.3836172826 0.5029000358 0.6408007050 -0.435090554879 +1403636688763555584.0000000000 1.3375685108 3.7285971117 -0.5851564364 0.3835920860 0.5020076936 0.6420399055 -0.434315722547 +1403636688813555456.0000000000 1.3589611367 3.7090113986 -0.6005248475 0.3818149670 0.5023027189 0.6419788462 -0.43562882204 +1403636688863555584.0000000000 1.3803418485 3.6886017075 -0.6145207741 0.3802346715 0.5012081243 0.6438217477 -0.435552026625 +1403636688913555456.0000000000 1.4019749447 3.6669751958 -0.6263961827 0.3766011912 0.5004889519 0.6453838390 -0.437220827702 +1403636688963555584.0000000000 1.4234516699 3.6446539428 -0.6363600093 0.3725047025 0.5001402843 0.6469972600 -0.438741938028 +1403636689013555456.0000000000 1.4445880474 3.6217110178 -0.6442729724 0.3686400489 0.4996987821 0.6484031278 -0.440430500161 +1403636689063555584.0000000000 1.4654857166 3.5983118660 -0.6497444566 0.3645347989 0.4992432790 0.6496676372 -0.442495751263 +1403636689113555456.0000000000 1.4856228455 3.5744366635 -0.6539279368 0.3601696784 0.4990053938 0.6508740419 -0.444560908379 +1403636689163555584.0000000000 1.5052284905 3.5503623765 -0.6562789595 0.3560217114 0.4987731031 0.6523961783 -0.445929544966 +1403636689213555456.0000000000 1.5244571222 3.5263780405 -0.6567816405 0.3532348368 0.4977398503 0.6543428374 -0.446447804978 +1403636689263555584.0000000000 1.5430858975 3.5025119158 -0.6553743848 0.3505213735 0.4970347949 0.6555157125 -0.44764978509 +1403636689313555456.0000000000 1.5605173543 3.4787351030 -0.6520303548 0.3481145686 0.4963131098 0.6571261868 -0.447967318933 +1403636689363555584.0000000000 1.5759262058 3.4547528384 -0.6465969672 0.3470571034 0.4951075304 0.6579098554 -0.448970514075 +1403636689413555456.0000000000 1.5901217889 3.4308804718 -0.6392563511 0.3464722353 0.4936049470 0.6590012480 -0.449475807654 +1403636689463555584.0000000000 1.6036621659 3.4070678966 -0.6297648505 0.3455642556 0.4929040624 0.6591984657 -0.450653207373 +1403636689513555456.0000000000 1.6166276748 3.3834852085 -0.6182616557 0.3444206026 0.4925406477 0.6600414425 -0.450692193283 +1403636689563555584.0000000000 1.6294727133 3.3601917083 -0.6055305739 0.3423716601 0.4929887769 0.6608816681 -0.450532055376 +1403636689613555456.0000000000 1.6424174110 3.3374621018 -0.5913153111 0.3400923620 0.4940172250 0.6618518470 -0.449706903817 +1403636689663555584.0000000000 1.6544924045 3.3148320397 -0.5769855920 0.3364988088 0.4961978946 0.6622708967 -0.449392323509 +1403636689713555456.0000000000 1.6635062847 3.2918392252 -0.5645889532 0.3319764958 0.4992961599 0.6624918639 -0.448998308681 +1403636689763555584.0000000000 1.6723047964 3.2696244877 -0.5530446297 0.3263221368 0.5036603072 0.6622288117 -0.44865706166 +1403636689813555456.0000000000 1.6789530882 3.2478944515 -0.5426428947 0.3225112544 0.5066522903 0.6614497548 -0.449192797534 +1403636689863555584.0000000000 1.6834994314 3.2267831078 -0.5329364998 0.3206364034 0.5086283217 0.6594658378 -0.451214290491 +1403636689913555456.0000000000 1.6861475839 3.2063784716 -0.5237141209 0.3175154472 0.5113954662 0.6558134853 -0.455595533853 +1403636689963555584.0000000000 1.6867809657 3.1874285496 -0.5156534700 0.3168878178 0.5128800471 0.6527895184 -0.458695991734 +1403636690013555456.0000000000 1.6857620919 3.1702718646 -0.5091470316 0.3179478698 0.5130173688 0.6515198728 -0.459613083797 +1403636690063555584.0000000000 1.6832800686 3.1549111780 -0.5040128696 0.3197705237 0.5125858772 0.6514831995 -0.458881435161 +1403636690113555456.0000000000 1.6794694303 3.1411853465 -0.5006610654 0.3225722411 0.5112400340 0.6539055487 -0.45495967989 +1403636690163555584.0000000000 1.6739869775 3.1287007934 -0.4977294655 0.3267181092 0.5091525755 0.6563053362 -0.450868315292 +1403636690213555456.0000000000 1.6669855527 3.1169056225 -0.4936379979 0.3299751751 0.5074874770 0.6582839045 -0.447476418932 +1403636690263555584.0000000000 1.6581521747 3.1053120386 -0.4870585345 0.3319309028 0.5065948590 0.6588211873 -0.446248997525 +1403636690313555456.0000000000 1.6477125032 3.0941609059 -0.4791385911 0.3342564153 0.5052406532 0.6595522619 -0.444966678503 +1403636690363555584.0000000000 1.6356560084 3.0832753261 -0.4696137028 0.3360495792 0.5045444708 0.6597681935 -0.44408500102 +1403636690413555456.0000000000 1.6226130190 3.0725497271 -0.4593183186 0.3369449247 0.5041707899 0.6598155817 -0.443760442588 +1403636690463555584.0000000000 1.6081973342 3.0618290820 -0.4487361439 0.3369267342 0.5043259033 0.6587552111 -0.44517112542 +1403636690513555456.0000000000 1.5927408814 3.0510881387 -0.4386273598 0.3353640764 0.5055587944 0.6563560143 -0.448484140321 +1403636690563555584.0000000000 1.5761800104 3.0408253030 -0.4298764067 0.3339534684 0.5066312747 0.6543113263 -0.45130535194 +1403636690613555456.0000000000 1.5586505776 3.0308480109 -0.4223107191 0.3297144543 0.5097190823 0.6516692031 -0.454754972957 +1403636690663555584.0000000000 1.5398475685 3.0217621148 -0.4159908614 0.3269575851 0.5117348538 0.6487527533 -0.458634976952 +1403636690713555456.0000000000 1.5198847353 3.0134512054 -0.4114611021 0.3228887370 0.5144522083 0.6437043149 -0.465538982169 +1403636690763555584.0000000000 1.4991315107 3.0065283628 -0.4108838719 0.3179588405 0.5178822216 0.6380359663 -0.472874492837 +1403636690813555456.0000000000 1.4775495138 3.0015777091 -0.4145148776 0.3147260969 0.5199528558 0.6332799243 -0.47911694714 +1403636690863555584.0000000000 1.4549955187 2.9991248718 -0.4214993567 0.3139891619 0.5202696965 0.6285939134 -0.485386383318 +1403636690913555456.0000000000 1.4317669929 2.9993793868 -0.4302282184 0.3149798769 0.5193520296 0.6238097199 -0.491856259347 +1403636690963555584.0000000000 1.4078781302 3.0026604598 -0.4383703382 0.3167556692 0.5177748469 0.6180363178 -0.499606008601 +1403636691013555456.0000000000 1.3832170823 3.0094513427 -0.4449660312 0.3201817970 0.5149268269 0.6123231464 -0.50734046188 +1403636691063555584.0000000000 1.3591596632 3.0204602155 -0.4495734191 0.3241853134 0.5115197185 0.6078680542 -0.513563909144 +1403636691113555456.0000000000 1.3364396554 3.0356361982 -0.4532284917 0.3277410810 0.5081834666 0.6060643522 -0.516741085109 +1403636691163555584.0000000000 1.3151777265 3.0552783601 -0.4541423955 0.3343883028 0.5030203781 0.6049062754 -0.518886654336 +1403636691213555456.0000000000 1.2953992085 3.0790701144 -0.4543118633 0.3430180368 0.4965658827 0.6066523213 -0.51743010309 +1403636691263555584.0000000000 1.2783248537 3.1066838702 -0.4530017437 0.3531069714 0.4891883520 0.6101099524 -0.51359134438 +1403636691313555456.0000000000 1.2649405888 3.1374114682 -0.4504492253 0.3609641175 0.4832411812 0.6146091833 -0.508368388528 +1403636691363555584.0000000000 1.2540989643 3.1700467359 -0.4460675477 0.3656728612 0.4793071267 0.6195227203 -0.502732171127 +1403636691413555456.0000000000 1.2459111814 3.2037960783 -0.4401683035 0.3640605472 0.4792957641 0.6256058958 -0.496339351247 +1403636691463555584.0000000000 1.2392166453 3.2384942316 -0.4318704322 0.3603781296 0.4808908343 0.6318581624 -0.489516978016 +1403636691513555456.0000000000 1.2339646200 3.2737581087 -0.4207328347 0.3551207515 0.4833244333 0.6365731584 -0.48483126754 +1403636691563555584.0000000000 1.2293458029 3.3096460180 -0.4066371372 0.3519318685 0.4843295630 0.6397428261 -0.481972977217 +1403636691613555456.0000000000 1.2264294620 3.3476641146 -0.3941064490 0.3498888450 0.4844527299 0.6434646588 -0.478368666959 +1403636691663555584.0000000000 1.2225280443 3.3852846031 -0.3773813302 0.3516194558 0.4825536744 0.6475489924 -0.473482852918 +1403636691713555456.0000000000 1.2191774519 3.4233237793 -0.3609737491 0.3537766187 0.4803696647 0.6520957306 -0.467822880343 +1403636691763555584.0000000000 1.2163239835 3.4609068432 -0.3450738577 0.3566449079 0.4777695547 0.6547887335 -0.464534580748 +1403636691813555456.0000000000 1.2141845789 3.4978641725 -0.3305308882 0.3565804126 0.4774279239 0.6560087732 -0.463212128836 +1403636691863555584.0000000000 1.2128757483 3.5342549473 -0.3176511919 0.3550410230 0.4782006650 0.6561225390 -0.463436306117 +1403636691913555456.0000000000 1.2120924319 3.5704448251 -0.3063196310 0.3534842591 0.4793193828 0.6549397771 -0.465140512365 +1403636691963555584.0000000000 1.2112992802 3.6065402807 -0.2954877610 0.3536818991 0.4790376885 0.6518211333 -0.469639454746 +1403636692013555456.0000000000 1.2109486641 3.6428004371 -0.2856858016 0.3545745556 0.4785362855 0.6488219759 -0.473613715599 +1403636692063555584.0000000000 1.2114286461 3.6792044751 -0.2766158741 0.3535142298 0.4793913326 0.6476579403 -0.475132436149 +1403636692113555456.0000000000 1.2127098601 3.7165473457 -0.2676233842 0.3543368795 0.4791513349 0.6485347714 -0.473563115492 +1403636692163555584.0000000000 1.2136564699 3.7538542949 -0.2573027502 0.3579706184 0.4771069905 0.6505059910 -0.470178595484 +1403636692213555456.0000000000 1.2152367559 3.7906760427 -0.2451216169 0.3591915702 0.4764919160 0.6522403211 -0.467460622221 +1403636692263555584.0000000000 1.2177695250 3.8270556442 -0.2314657972 0.3593611013 0.4768016710 0.6532533984 -0.465596137214 +1403636692313555456.0000000000 1.2214490039 3.8628156394 -0.2145809072 0.3584320701 0.4778287276 0.6532319817 -0.465289303813 +1403636692363555584.0000000000 1.2266720535 3.8983959439 -0.1957440596 0.3562975776 0.4796789390 0.6524520020 -0.466118586546 +1403636692413555456.0000000000 1.2318483907 3.9338275857 -0.1759578604 0.3558596062 0.4805941742 0.6529929174 -0.464750933554 +1403636692463555584.0000000000 1.2367876183 3.9687952763 -0.1543779716 0.3572422899 0.4800806488 0.6542290524 -0.462476879428 +1403636692513555456.0000000000 1.2421154100 4.0034512368 -0.1316015605 0.3604041397 0.4786414014 0.6556391358 -0.459509073355 +1403636692563555584.0000000000 1.2478665471 4.0370230190 -0.1069727537 0.3610132214 0.4787962144 0.6554721591 -0.459107708104 +1403636692613555456.0000000000 1.2534928247 4.0694321403 -0.0800445558 0.3601289851 0.4798255975 0.6550136302 -0.459381817624 +1403636692663555584.0000000000 1.2599270454 4.1016880774 -0.0521052083 0.3598690472 0.4808493328 0.6543573264 -0.459450408062 +1403636692713555456.0000000000 1.2666129057 4.1340213271 -0.0252144364 0.3606370710 0.4809890165 0.6561505696 -0.456132545597 +1403636692763555584.0000000000 1.2735761395 4.1664754494 -0.0001338090 0.3640293546 0.4791328746 0.6602923877 -0.449364306699 +1403636692813555456.0000000000 1.2806595288 4.1980987589 0.0233416754 0.3681627834 0.4767877792 0.6651032578 -0.441324410156 +1403636692863555584.0000000000 1.2876279619 4.2279514217 0.0459995191 0.3712657245 0.4747849964 0.6684669756 -0.435766992145 +1403636692913555456.0000000000 1.2947243490 4.2559097074 0.0677217667 0.3733564182 0.4733608671 0.6711374675 -0.431403493535 +1403636692963555584.0000000000 1.3016676071 4.2810399563 0.0890180102 0.3725436728 0.4739557114 0.6717452683 -0.430506085946 +1403636693013555456.0000000000 1.3084110661 4.3035685283 0.1098916952 0.3693770514 0.4761196533 0.6711210067 -0.431818554446 +1403636693063555584.0000000000 1.3148162916 4.3242147701 0.1299077615 0.3673687083 0.4775910143 0.6692137043 -0.434856382331 +1403636693113555456.0000000000 1.3208472829 4.3430159564 0.1486801493 0.3660367513 0.4782645547 0.6670859662 -0.438493359137 +1403636693163555584.0000000000 1.3269019026 4.3601838613 0.1655619466 0.3639790975 0.4793544426 0.6652251305 -0.441830352808 +1403636693213555456.0000000000 1.3328702808 4.3762548392 0.1801216111 0.3614932104 0.4806980404 0.6653916940 -0.442160543598 +1403636693263555584.0000000000 1.3387082082 4.3911295471 0.1930676482 0.3574731600 0.4831055863 0.6660185232 -0.441861131071 +1403636693313555456.0000000000 1.3443665320 4.4048912453 0.2044998172 0.3523309144 0.4862644251 0.6667980412 -0.441350436531 +1403636693363555584.0000000000 1.3495588662 4.4177702840 0.2146686016 0.3477902982 0.4889380123 0.6676169182 -0.440759774882 +1403636693413555456.0000000000 1.3539088236 4.4297531096 0.2239068239 0.3435127720 0.4913524384 0.6683222249 -0.440360262052 +1403636693463555584.0000000000 1.3572244883 4.4410576788 0.2321159235 0.3394067067 0.4934408399 0.6698245100 -0.438924083264 +1403636693513555456.0000000000 1.3593233519 4.4519523736 0.2393373741 0.3344088863 0.4968537511 0.6715056363 -0.436333848373 +1403636693563555584.0000000000 1.3598401630 4.4623545115 0.2454605106 0.3300331015 0.4993836974 0.6740378406 -0.432859173587 +1403636693613555456.0000000000 1.3584095470 4.4720022272 0.2510481848 0.3272582812 0.5006786212 0.6762422351 -0.43002252857 +1403636693663555584.0000000000 1.3546158841 4.4811647416 0.2562284150 0.3255538881 0.5015662920 0.6774384536 -0.428395917496 +1403636693713555456.0000000000 1.3483167907 4.4892553472 0.2614207807 0.3257618379 0.5011145138 0.6769127074 -0.429595921287 +1403636693763555584.0000000000 1.3395640374 4.4966373151 0.2664201554 0.3288119763 0.4986197431 0.6748832912 -0.433351565436 +1403636693813555456.0000000000 1.3290166447 4.5035675110 0.2705721448 0.3323233430 0.4961493656 0.6728638854 -0.436636226666 +1403636693863555584.0000000000 1.3166470203 4.5099653381 0.2743633515 0.3360448703 0.4934352365 0.6698645329 -0.441448774024 +1403636693913555456.0000000000 1.3030314524 4.5155826397 0.2777691240 0.3395445271 0.4908304175 0.6656580751 -0.447989221452 +1403636693963555584.0000000000 1.2882755706 4.5209892626 0.2800207879 0.3443042908 0.4874231983 0.6625790911 -0.452616978446 +1403636694013555456.0000000000 1.2730394282 4.5256822863 0.2818209220 0.3476033110 0.4846900894 0.6586200027 -0.458766986063 +1403636694063555584.0000000000 1.2578102468 4.5304664672 0.2824028736 0.3509151383 0.4822140735 0.6559219539 -0.46270351576 +1403636694113555456.0000000000 1.2433203182 4.5353526517 0.2823353898 0.3520770538 0.4809471043 0.6547136581 -0.464845842092 +1403636694163555584.0000000000 1.2291570027 4.5402748149 0.2831717484 0.3536268905 0.4796166305 0.6534725953 -0.466786329455 +1403636694213555456.0000000000 1.2158819750 4.5454319833 0.2856973818 0.3544052878 0.4789137911 0.6527200860 -0.467968975453 +1403636694263555584.0000000000 1.2032128793 4.5507580174 0.2886738908 0.3545574689 0.4784216439 0.6534553168 -0.46733059063 +1403636694313555456.0000000000 1.1908952312 4.5557423432 0.2937092246 0.3534194356 0.4787955086 0.6545411602 -0.466289001712 +1403636694363555584.0000000000 1.1794311253 4.5608139051 0.3000131203 0.3511338469 0.4804791540 0.6552485124 -0.465289362883 +1403636694413555456.0000000000 1.1682797448 4.5659351969 0.3061866012 0.3494368578 0.4812551972 0.6570986222 -0.463150859128 +1403636694463555584.0000000000 1.1571774684 4.5711643974 0.3120169176 0.3484286006 0.4822317399 0.6580713571 -0.461510723916 +1403636694513555456.0000000000 1.1459030325 4.5762987351 0.3169402758 0.3484148226 0.4824461357 0.6591314823 -0.459780954953 +1403636694563555584.0000000000 1.1345721769 4.5811852219 0.3205294765 0.3478351414 0.4828167497 0.6596658755 -0.459063866252 +1403636694613555456.0000000000 1.1232774493 4.5860632181 0.3227155913 0.3477303874 0.4832665326 0.6599386696 -0.458277196035 +1403636694663555584.0000000000 1.1116616321 4.5907030120 0.3231450966 0.3481856835 0.4832982652 0.6601325414 -0.457618339218 +1403636694713555456.0000000000 1.0999534794 4.5951759700 0.3223985956 0.3493820717 0.4827302209 0.6596773232 -0.457962368587 +1403636694763555584.0000000000 1.0883802714 4.5991893788 0.3208687207 0.3494049137 0.4832752299 0.6575222776 -0.460462498973 +1403636694813555456.0000000000 1.0770227336 4.6033229493 0.3177346606 0.3507252593 0.4831818366 0.6561810083 -0.461468947611 +1403636694863555584.0000000000 1.0661991648 4.6068965400 0.3133521110 0.3465308273 0.4863494605 0.6538096961 -0.46466490001 +1403636694913555456.0000000000 1.0552097096 4.6109688130 0.3076007212 0.3436652719 0.4889991046 0.6517085615 -0.466958250109 +1403636694963555584.0000000000 1.0443067872 4.6154985563 0.3013781489 0.3404071953 0.4918318401 0.6498515907 -0.468953401228 +1403636695013555456.0000000000 1.0333775755 4.6210224963 0.2943688416 0.3388218668 0.4933250850 0.6491840501 -0.469457316689 +1403636695063555584.0000000000 1.0220297286 4.6275350881 0.2871806293 0.3396884079 0.4933914343 0.6502973366 -0.467215209556 +1403636695113555456.0000000000 1.0108283118 4.6350418853 0.2815479222 0.3424308517 0.4922493248 0.6510420878 -0.465377173883 +1403636695163555584.0000000000 0.9995526052 4.6429750256 0.2776419223 0.3438686754 0.4921183150 0.6514369355 -0.463900654485 +1403636695213555456.0000000000 0.9876473458 4.6513366581 0.2757127628 0.3467415055 0.4911392786 0.6520177575 -0.461979849392 +1403636695263555584.0000000000 0.9757714898 4.6600133989 0.2756869153 0.3496327053 0.4899537767 0.6523700675 -0.460560053814 +1403636695313555456.0000000000 0.9643806437 4.6689200140 0.2776944587 0.3518232682 0.4892957628 0.6524231563 -0.459515037424 +1403636695363555584.0000000000 0.9528354719 4.6777322716 0.2816100633 0.3537682704 0.4889605880 0.6523057598 -0.458544163613 +1403636695413555456.0000000000 0.9417542484 4.6864775706 0.2868133805 0.3545783911 0.4890101959 0.6521023207 -0.458154729554 +1403636695463555584.0000000000 0.9308809214 4.6951906829 0.2928845130 0.3560376891 0.4886090660 0.6518829928 -0.457762939029 +1403636695513555456.0000000000 0.9202230490 4.7038518086 0.2985716985 0.3583354873 0.4875657414 0.6523551157 -0.456407854215 +1403636695563555584.0000000000 0.9094431000 4.7117832928 0.3039107086 0.3600311798 0.4869143150 0.6520838089 -0.456156448679 +1403636695613555456.0000000000 0.8992429830 4.7196352605 0.3076300004 0.3620823269 0.4860805416 0.6523429278 -0.45505032705 +1403636695663555584.0000000000 0.8894337126 4.7270733893 0.3099246487 0.3645662069 0.4849358513 0.6528562854 -0.453549745358 +1403636695713555456.0000000000 0.8800309746 4.7336775008 0.3111217786 0.3653522864 0.4848383719 0.6525928358 -0.453400540937 +1403636695763555584.0000000000 0.8713324067 4.7395374132 0.3113735720 0.3632114386 0.4870496588 0.6514516651 -0.454390590605 +1403636695813555456.0000000000 0.8631407424 4.7453027606 0.3102750090 0.3628547576 0.4875682484 0.6514225717 -0.454161052006 +1403636695863555584.0000000000 0.8554175583 4.7508146678 0.3081688428 0.3623641311 0.4882719916 0.6508602319 -0.45460274667 +1403636695913555456.0000000000 0.8481448120 4.7560428785 0.3047177990 0.3620811310 0.4890216653 0.6510878668 -0.453695553212 +1403636695963555584.0000000000 0.8413586356 4.7608763299 0.3002449894 0.3601259137 0.4906475505 0.6513765906 -0.453081498897 +1403636696013555456.0000000000 0.8347453336 4.7654842756 0.2948184553 0.3580095951 0.4926843434 0.6515363419 -0.452318099012 +1403636696063555584.0000000000 0.8282484460 4.7699868075 0.2882111069 0.3564350307 0.4942471385 0.6529915568 -0.449750888431 +1403636696113555456.0000000000 0.8211086591 4.7742972189 0.2808767171 0.3561058626 0.4950732247 0.6551706772 -0.445917593817 +1403636696163555584.0000000000 0.8137296170 4.7783349347 0.2731460296 0.3576383092 0.4944239601 0.6569647065 -0.442760840487 +1403636696213555456.0000000000 0.8063520721 4.7818276917 0.2647117693 0.3584475114 0.4942137631 0.6582989412 -0.440352860696 +1403636696263555584.0000000000 0.7986324654 4.7845516529 0.2563086269 0.3612993352 0.4925391044 0.6576471946 -0.440872077101 +1403636696313555456.0000000000 0.7906763414 4.7861977587 0.2477634797 0.3628287118 0.4915532251 0.6556544058 -0.44367561689 +1403636696363555584.0000000000 0.7820478448 4.7870712436 0.2399401237 0.3667896319 0.4892955370 0.6514366226 -0.449094166233 +1403636696413555456.0000000000 0.7737217546 4.7871031959 0.2332192938 0.3695114005 0.4876630537 0.6463192819 -0.455979667043 +1403636696463555584.0000000000 0.7662470504 4.7868681169 0.2271582859 0.3697572000 0.4878595270 0.6422153891 -0.461337283357 +1403636696513555456.0000000000 0.7599216695 4.7869599045 0.2221090557 0.3706147208 0.4877162415 0.6410481465 -0.46242282648 +1403636696563555584.0000000000 0.7546943322 4.7867548565 0.2187162987 0.3693833699 0.4891512216 0.6406746859 -0.462409942841 +1403636696613555456.0000000000 0.7517347846 4.7868217861 0.2166596604 0.3688574587 0.4896188687 0.6409190645 -0.461995986313 +1403636696663555584.0000000000 0.7497324647 4.7868969564 0.2159624325 0.3670322962 0.4912977156 0.6408948444 -0.461700819272 +1403636696713555456.0000000000 0.7484514189 4.7873139120 0.2164608063 0.3665619453 0.4916698623 0.6409631170 -0.461583545463 +1403636696763555584.0000000000 0.7478712757 4.7879209672 0.2163477940 0.3654237633 0.4925673764 0.6416175730 -0.460618869566 +1403636696813555456.0000000000 0.7478359339 4.7889263452 0.2148068892 0.3661806722 0.4923249929 0.6421474156 -0.459537281727 +1403636696863555584.0000000000 0.7486218769 4.7899512155 0.2122023186 0.3660284892 0.4923478055 0.6429732315 -0.458478142503 +1403636696913555456.0000000000 0.7498550647 4.7910674353 0.2081617053 0.3671948717 0.4916074787 0.6437827686 -0.457202099605 +1403636696963555584.0000000000 0.7514844262 4.7922540017 0.2026489359 0.3715442540 0.4885119022 0.6461636384 -0.453633708139 +1403636697013555456.0000000000 0.7535534717 4.7929685144 0.1966726752 0.3762062792 0.4852504566 0.6487492834 -0.449583359511 +1403636697063555584.0000000000 0.7562423680 4.7929856201 0.1911065667 0.3806311159 0.4821317035 0.6509230894 -0.446058410583 +1403636697113555456.0000000000 0.7598491610 4.7922100358 0.1866811992 0.3853617734 0.4789221080 0.6536937429 -0.44137785242 +1403636697163555584.0000000000 0.7647029128 4.7899164480 0.1844070949 0.3891309401 0.4763814967 0.6554314048 -0.438232192622 +1403636697213555456.0000000000 0.7702743352 4.7852666658 0.1853380157 0.3916857823 0.4746051796 0.6561235967 -0.43684550735 +1403636697263555584.0000000000 0.7773420948 4.7784661995 0.1880746255 0.3929580097 0.4741849704 0.6560113633 -0.436327523458 +1403636697313555456.0000000000 0.7859712156 4.7692735141 0.1928087333 0.3896864903 0.4765918251 0.6560904862 -0.436520269249 +1403636697363555584.0000000000 0.7954172680 4.7578363712 0.1999732135 0.3846094345 0.4807723857 0.6546002908 -0.438670668355 +1403636697413555456.0000000000 0.8053029772 4.7447232229 0.2087788307 0.3786745768 0.4850928487 0.6534300611 -0.440817023616 +1403636697463555584.0000000000 0.8158298400 4.7305084001 0.2195158681 0.3732289741 0.4888265548 0.6528749706 -0.442157217488 +1403636697513555456.0000000000 0.8265790272 4.7155361395 0.2323939299 0.3694169942 0.4920510537 0.6521901120 -0.442792166522 +1403636697563555584.0000000000 0.8370359665 4.7001443837 0.2472112648 0.3683245655 0.4948581135 0.6510279375 -0.442283943339 +1403636697613555456.0000000000 0.8470175247 4.6845750741 0.2619619314 0.3702863904 0.4972513268 0.6491964117 -0.440650798395 +1403636697663555584.0000000000 0.8563599602 4.6687728069 0.2754233776 0.3739665744 0.5007759189 0.6461768990 -0.437981615376 +1403636697713555456.0000000000 0.8656184240 4.6525211883 0.2873647461 0.3773378815 0.5067626944 0.6416894836 -0.434789950805 +1403636697763555584.0000000000 0.8748588202 4.6360977683 0.2972374082 0.3817359085 0.5137701290 0.6370785232 -0.429475151867 +1403636697813555456.0000000000 0.8839199938 4.6191960958 0.3059308881 0.3869225130 0.5207928334 0.6311114003 -0.4251637261 +1403636697863555584.0000000000 0.8928698200 4.6015645773 0.3131287087 0.3913424265 0.5275228517 0.6251637617 -0.421593426407 +1403636697913555456.0000000000 0.9019905454 4.5830557090 0.3188825499 0.3949302409 0.5340439148 0.6197123160 -0.418071581487 +1403636697963555584.0000000000 0.9111218287 4.5638125312 0.3234398385 0.3978287164 0.5400915842 0.6142536653 -0.415602968953 +1403636698013555456.0000000000 0.9203036150 4.5439443026 0.3263874150 0.4000699135 0.5452179434 0.6100094660 -0.413001101587 +1403636698063555584.0000000000 0.9293747196 4.5235298927 0.3282552073 0.4029933252 0.5487006642 0.6061416511 -0.411237473706 +1403636698113555456.0000000000 0.9386625231 4.5023412637 0.3288615312 0.4042102629 0.5525490944 0.6028946583 -0.40966033816 +1403636698163555584.0000000000 0.9477096083 4.4807644173 0.3280571216 0.4053422533 0.5556686627 0.5999652188 -0.408621745904 +1403636698213555456.0000000000 0.9565239363 4.4590768469 0.3260749567 0.4071113878 0.5582208091 0.5970750579 -0.407616512665 +1403636698263555584.0000000000 0.9653292450 4.4373172227 0.3226908771 0.4088029005 0.5619045965 0.5937241894 -0.405752387306 +1403636698313555456.0000000000 0.9737880974 4.4157564604 0.3180179752 0.4119539769 0.5656473230 0.5903470700 -0.402277719724 +1403636698363555584.0000000000 0.9819657296 4.3938018953 0.3127515534 0.4158023973 0.5698713976 0.5857046916 -0.399130267967 +1403636698413555456.0000000000 0.9900513978 4.3717996947 0.3064877646 0.4192847733 0.5753223164 0.5809298758 -0.394620058444 +1403636698463555584.0000000000 0.9980158222 4.3498190840 0.2992254476 0.4223660847 0.5816374305 0.5755195459 -0.389976976384 +1403636698513555456.0000000000 1.0056761315 4.3276803897 0.2910960859 0.4268046438 0.5874726494 0.5700181812 -0.384438493693 +1403636698563555584.0000000000 1.0127834476 4.3054349572 0.2827183834 0.4310894223 0.5941414033 0.5632358662 -0.379372194508 +1403636698613555456.0000000000 1.0195764094 4.2829624929 0.2734787304 0.4353682382 0.6012088606 0.5558840174 -0.374159541126 +1403636698663555584.0000000000 1.0261831247 4.2604625880 0.2633027365 0.4389900229 0.6091863968 0.5477357712 -0.369005716335 +1403636698713555456.0000000000 1.0323882726 4.2376281812 0.2521531109 0.4431967732 0.6170249428 0.5391705127 -0.363527163108 +1403636698763555584.0000000000 1.0380682598 4.2146843405 0.2400688044 0.4475046303 0.6251577957 0.5301800205 -0.357528295708 +1403636698813555456.0000000000 1.0433093219 4.1916301192 0.2269901073 0.4519346195 0.6333997683 0.5208813501 -0.351059043988 +1403636698863555584.0000000000 1.0481821000 4.1682798533 0.2133326002 0.4556719096 0.6421748530 0.5103971315 -0.345643366939 +1403636698913555456.0000000000 1.0523492799 4.1452724122 0.2002386579 0.4607341707 0.6497317381 0.5005390378 -0.339165688356 +1403636698963555584.0000000000 1.0563715927 4.1220597776 0.1889329792 0.4644670494 0.6579410800 0.4902110877 -0.333282139845 +1403636699013555456.0000000000 1.0602350321 4.0988526118 0.1789958297 0.4685114636 0.6652752593 0.4801156482 -0.327711461819 +1403636699063555584.0000000000 1.0631300226 4.0759730359 0.1709765083 0.4723235706 0.6726823638 0.4696069832 -0.322301355054 +1403636699113555456.0000000000 1.0660208339 4.0532080492 0.1650211203 0.4764882317 0.6798310696 0.4584879456 -0.317139536521 +1403636699163555584.0000000000 1.0690302099 4.0307565534 0.1610414923 0.4790585142 0.6879941063 0.4457688374 -0.313778892455 +1403636699213555456.0000000000 1.0725755137 4.0091891073 0.1583687992 0.4819597879 0.6958668343 0.4342189019 -0.308120199017 +1403636699263555584.0000000000 1.0761111871 3.9886513502 0.1573468044 0.4848155376 0.7039778987 0.4216390114 -0.302637665828 +1403636699313555456.0000000000 1.0792608944 3.9691042908 0.1575740476 0.4862504955 0.7127067725 0.4091470928 -0.296998600352 +1403636699363555584.0000000000 1.0820603867 3.9511369867 0.1596402242 0.4889148697 0.7200540182 0.3975000939 -0.290651228191 +1403636699413555456.0000000000 1.0850075625 3.9342706787 0.1627156206 0.4907421310 0.7276485595 0.3853044940 -0.285026632986 +1403636699463555584.0000000000 1.0880647680 3.9186511897 0.1662678046 0.4928055380 0.7342960550 0.3743587899 -0.278939960845 +1403636699513555456.0000000000 1.0911396163 3.9043997666 0.1693968658 0.4957474152 0.7400193529 0.3640097455 -0.272218226587 +1403636699563555584.0000000000 1.0944304981 3.8914724715 0.1714890453 0.4981977124 0.7457903414 0.3530035010 -0.266428854161 +1403636699613555456.0000000000 1.0979070132 3.8796940717 0.1722822374 0.5005860613 0.7511366617 0.3422479048 -0.260909337546 +1403636699663555584.0000000000 1.1016194124 3.8696967818 0.1716765808 0.5032313001 0.7562528928 0.3311406303 -0.25531491073 +1403636699713555456.0000000000 1.1056541499 3.8616029400 0.1699713747 0.5071160837 0.7602528995 0.3208793000 -0.248767524667 +1403636699763555584.0000000000 1.1103370745 3.8550188346 0.1668303150 0.5116953218 0.7628819705 0.3136455505 -0.240427671802 +1403636699813555456.0000000000 1.1154571924 3.8494472301 0.1623917120 0.5169840224 0.7641573959 0.3080080689 -0.232211163397 +1403636699863555584.0000000000 1.1207813885 3.8445863433 0.1574802881 0.5220514283 0.7645317294 0.3030719448 -0.226055164188 +1403636699913555456.0000000000 1.1262365333 3.8403402640 0.1525083196 0.5260250111 0.7647877338 0.2984919262 -0.222035987905 +1403636699963555584.0000000000 1.1318420929 3.8364294126 0.1468797930 0.5286795352 0.7651374821 0.2942423063 -0.220190934753 +1403636700013555456.0000000000 1.1375024614 3.8330168797 0.1399713783 0.5298113686 0.7660152322 0.2910713952 -0.218627584377 +1403636700063555584.0000000000 1.1439131091 3.8297643922 0.1320651138 0.5306652885 0.7665329629 0.2890071137 -0.217477485256 +1403636700113555456.0000000000 1.1505869423 3.8268268449 0.1234555119 0.5310003476 0.7668858570 0.2871378301 -0.217891210935 +1403636700163555584.0000000000 1.1579857822 3.8247173193 0.1137126599 0.5319090064 0.7668543917 0.2861836073 -0.21703938316 +1403636700213555456.0000000000 1.1651007238 3.8235705093 0.1031688137 0.5320925041 0.7668938260 0.2857053912 -0.21708029885 +1403636700263555584.0000000000 1.1730759029 3.8228480613 0.0915438892 0.5318144966 0.7674354338 0.2848766835 -0.216936560809 +1403636700313555456.0000000000 1.1818149722 3.8229545591 0.0780876071 0.5307068872 0.7691650794 0.2830969369 -0.215850422375 +1403636700363555584.0000000000 1.1906834771 3.8243254201 0.0631839395 0.5291663404 0.7716346618 0.2797220609 -0.215217335461 +1403636700413555456.0000000000 1.2003108699 3.8267569470 0.0466027733 0.5286824392 0.7739563898 0.2753392446 -0.213716366887 +1403636700463555584.0000000000 1.2102576171 3.8307446120 0.0289028371 0.5313088015 0.7744244734 0.2714016358 -0.210520413569 +1403636700513555456.0000000000 1.2207335559 3.8354717805 0.0102018827 0.5347323014 0.7739561794 0.2679192856 -0.208020322687 +1403636700563555584.0000000000 1.2317842702 3.8411162518 -0.0093812589 0.5385931113 0.7732760835 0.2650126272 -0.204278893843 +1403636700613555456.0000000000 1.2435513858 3.8475248216 -0.0291874935 0.5430865360 0.7725076673 0.2611560011 -0.200216036671 +1403636700663555584.0000000000 1.2562897620 3.8545388632 -0.0500259263 0.5470537792 0.7725421383 0.2572627244 -0.194233616652 +1403636700713555456.0000000000 1.2693717875 3.8615896644 -0.0707010084 0.5500206208 0.7731794385 0.2523496869 -0.18971164467 +1403636700763555584.0000000000 1.2828968404 3.8682240360 -0.0899882140 0.5527126577 0.7734875426 0.2486624729 -0.185452727131 +1403636700813555456.0000000000 1.2969133313 3.8744590631 -0.1076138401 0.5537813476 0.7745602411 0.2458638204 -0.181476262217 +1403636700863555584.0000000000 1.3113852759 3.8801382822 -0.1238967043 0.5525677339 0.7768479580 0.2438066374 -0.178141721727 +1403636700913555456.0000000000 1.3259136899 3.8858919615 -0.1379760782 0.5513590798 0.7788130581 0.2423752359 -0.175235928338 +1403636700963555584.0000000000 1.3406753765 3.8913442998 -0.1502560243 0.5490985653 0.7811824678 0.2418147649 -0.172540827181 +1403636701013555456.0000000000 1.3555705038 3.8966969833 -0.1607927148 0.5468399470 0.7832305847 0.2413728193 -0.171041180895 +1403636701063555584.0000000000 1.3704634810 3.9021206536 -0.1696475826 0.5432405227 0.7859006027 0.2422043880 -0.169076939791 +1403636701113555456.0000000000 1.3853031000 3.9077330014 -0.1765239387 0.5392031229 0.7886572976 0.2431402136 -0.167816851569 +1403636701163555584.0000000000 1.3994178208 3.9144025422 -0.1807751521 0.5379572145 0.7892510356 0.2448619169 -0.166515704568 +1403636701213555456.0000000000 1.4129383614 3.9220265976 -0.1825798861 0.5358969350 0.7902473807 0.2466790529 -0.165749802746 +1403636701263555584.0000000000 1.4259276614 3.9303680801 -0.1816887474 0.5352186869 0.7902512277 0.2477656622 -0.166301325959 +1403636701313555456.0000000000 1.4384495473 3.9393280929 -0.1794648028 0.5341254672 0.7904340957 0.2496413661 -0.166141848788 +1403636701363555584.0000000000 1.4501495584 3.9490283084 -0.1757051908 0.5343226566 0.7898488426 0.2501921527 -0.167457431245 +1403636701413555456.0000000000 1.4613826584 3.9595654627 -0.1715018845 0.5358323915 0.7882229684 0.2517542137 -0.167952422512 +1403636701463555584.0000000000 1.4715294011 3.9705139770 -0.1666666146 0.5379714873 0.7860512794 0.2528556718 -0.169629225845 +1403636701513555456.0000000000 1.4811443939 3.9821707317 -0.1614728130 0.5416023149 0.7829617213 0.2536020539 -0.171242149276 +1403636701563555584.0000000000 1.4903463977 3.9938456223 -0.1563711234 0.5447609142 0.7800576274 0.2544283918 -0.173239250132 +1403636701613555456.0000000000 1.4992616009 4.0055321523 -0.1517425647 0.5466444633 0.7779995382 0.2556899045 -0.174697515786 +1403636701663555584.0000000000 1.5077434173 4.0172975769 -0.1475397644 0.5486291195 0.7758726118 0.2573996502 -0.17542291637 +1403636701713555456.0000000000 1.5162621338 4.0291034355 -0.1436509425 0.5499093483 0.7748743528 0.2570775995 -0.176296777605 +1403636701763555584.0000000000 1.5246863634 4.0411790442 -0.1406633938 0.5503291135 0.7751128020 0.2555134700 -0.176212592524 +1403636701813555456.0000000000 1.5333700641 4.0534976386 -0.1394987144 0.5500501548 0.7766353234 0.2523023409 -0.175002658497 +1403636701863555584.0000000000 1.5424744881 4.0664482146 -0.1401054115 0.5508606571 0.7781701626 0.2482978647 -0.171323976141 +1403636701913555456.0000000000 1.5515441556 4.0795771620 -0.1422795899 0.5505841373 0.7808854727 0.2421893194 -0.168580307087 +1403636701963555584.0000000000 1.5607682384 4.0930670662 -0.1456888060 0.5518729792 0.7828721519 0.2354700268 -0.164624648957 +1403636702013555456.0000000000 1.5701317607 4.1066640268 -0.1504314079 0.5526990951 0.7855166279 0.2277705372 -0.160024747937 +1403636702063555584.0000000000 1.5797535978 4.1201890555 -0.1564202768 0.5541465253 0.7880003645 0.2189095357 -0.155098901321 +1403636702113555456.0000000000 1.5896467603 4.1341001726 -0.1640726632 0.5560435647 0.7903733477 0.2090461516 -0.149750565759 +1403636702163555584.0000000000 1.5999687775 4.1482941545 -0.1731206520 0.5584164376 0.7924504174 0.1989525986 -0.143566297429 +1403636702213555456.0000000000 1.6103483107 4.1626966979 -0.1835435969 0.5596452980 0.7948346147 0.1900823980 -0.137490937063 +1403636702263555584.0000000000 1.6208321880 4.1766463436 -0.1955605054 0.5599910761 0.7972206099 0.1829027156 -0.131893481489 +1403636702313555456.0000000000 1.6315732985 4.1902126691 -0.2089755169 0.5591895520 0.7999873605 0.1773097354 -0.126049695326 +1403636702363555584.0000000000 1.6420714588 4.2037891011 -0.2232961675 0.5585523639 0.8021856965 0.1731225746 -0.120606547491 +1403636702413555456.0000000000 1.6524567497 4.2173089415 -0.2387705285 0.5585798149 0.8036079781 0.1704991266 -0.114598672232 +1403636702463555584.0000000000 1.6623767448 4.2308284337 -0.2552344938 0.5574029787 0.8056648114 0.1677442672 -0.109854411619 +1403636702513555456.0000000000 1.6718131424 4.2445690758 -0.2725426595 0.5573858146 0.8066089668 0.1660718917 -0.105466369848 +1403636702563555584.0000000000 1.6804833390 4.2581149889 -0.2911378132 0.5571953988 0.8074161622 0.1646267371 -0.102520563326 +1403636702613555456.0000000000 1.6886325658 4.2720166730 -0.3110484893 0.5560251532 0.8087910453 0.1636275583 -0.0995946599357 +1403636702663555584.0000000000 1.6960899045 4.2861172946 -0.3320512983 0.5545660402 0.8101573676 0.1633106422 -0.0971142671766 +1403636702713555456.0000000000 1.7027649431 4.3004630249 -0.3540078311 0.5540611233 0.8107268344 0.1635317322 -0.0948453700228 +1403636702763555584.0000000000 1.7084170872 4.3148691045 -0.3767452541 0.5532298811 0.8114596562 0.1627573252 -0.0947627461797 +1403636702813555456.0000000000 1.7132872135 4.3298182144 -0.4006939626 0.5518535077 0.8123809617 0.1638553833 -0.0929854425743 +1403636702863555584.0000000000 1.7171080277 4.3453762894 -0.4251676026 0.5508491491 0.8130340143 0.1643164217 -0.0924176396115 +1403636702913555456.0000000000 1.7197106465 4.3616785249 -0.4488332292 0.5497149712 0.8137710935 0.1643219463 -0.092673382514 +1403636702963555584.0000000000 1.7214564856 4.3789413260 -0.4707861167 0.5499626078 0.8134896810 0.1646679845 -0.0930597858599 +1403636703013555456.0000000000 1.7222134986 4.3971871137 -0.4906731063 0.5509140397 0.8128109675 0.1633514006 -0.0956471221245 +1403636703063555584.0000000000 1.7224770528 4.4160741535 -0.5089034508 0.5526289296 0.8115692427 0.1626169109 -0.0975313837691 +1403636703113555456.0000000000 1.7217910407 4.4359379286 -0.5245656430 0.5546440101 0.8101738484 0.1600380679 -0.101863507943 +1403636703163555584.0000000000 1.7206876436 4.4561352793 -0.5373135583 0.5585801411 0.8073894980 0.1564463507 -0.107865489407 +1403636703213555456.0000000000 1.7195306008 4.4765646928 -0.5484081291 0.5603813430 0.8059516860 0.1534258452 -0.113468675431 +1403636703263555584.0000000000 1.7184997774 4.4982229401 -0.5578523484 0.5621585677 0.8045923274 0.1492742694 -0.119691787223 +1403636703313555456.0000000000 1.7184668191 4.5199329044 -0.5657943001 0.5636780762 0.8033233846 0.1460611772 -0.124918768406 +1403636703363555584.0000000000 1.7198255768 4.5417214792 -0.5726539918 0.5653483749 0.8020292740 0.1455522132 -0.126272767487 +1403636703413555456.0000000000 1.7227161363 4.5638748720 -0.5783109721 0.5671074426 0.8008419356 0.1475648376 -0.123555499345 +1403636703463555584.0000000000 1.7269148266 4.5859264791 -0.5829020283 0.5674026558 0.8006830855 0.1514485772 -0.118423608934 +1403636703513555456.0000000000 1.7316539597 4.6072559557 -0.5857747654 0.5672356487 0.8007674667 0.1560436038 -0.112541445069 +1403636703563555584.0000000000 1.7367625542 4.6285835454 -0.5865343888 0.5670689476 0.8008315021 0.1594754515 -0.108024507776 +1403636703613555456.0000000000 1.7412244157 4.6487239857 -0.5851250690 0.5651300434 0.8020697623 0.1616801086 -0.105696135071 +1403636703663555584.0000000000 1.7454586713 4.6689240678 -0.5826859025 0.5637270368 0.8029200104 0.1630198193 -0.10467006915 +1403636703713555456.0000000000 1.7495216696 4.6887552568 -0.5805559135 0.5628327887 0.8034235207 0.1638576746 -0.104309927135 +1403636703763555584.0000000000 1.7531421262 4.7085462659 -0.5788326453 0.5634153256 0.8028579806 0.1637718479 -0.105645708455 +1403636703813555456.0000000000 1.7562623028 4.7281600390 -0.5782886322 0.5642917439 0.8021127196 0.1629599519 -0.107861331876 +1403636703863555584.0000000000 1.7592017038 4.7477240413 -0.5788621023 0.5654778212 0.8011214331 0.1617894614 -0.110740477312 +1403636703913555456.0000000000 1.7619814575 4.7671686114 -0.5805603660 0.5663428568 0.8002684846 0.1608494472 -0.113813779787 +1403636703963555584.0000000000 1.7650402086 4.7864882533 -0.5835478825 0.5668404791 0.7997570577 0.1607305763 -0.115092144935 +1403636704013555456.0000000000 1.7681961621 4.8053578359 -0.5873679680 0.5667930551 0.7995391194 0.1599461610 -0.117898494062 +1403636704063555584.0000000000 1.7718234905 4.8240730495 -0.5923830212 0.5668132697 0.7992665405 0.1597404379 -0.119911246678 +1403636704113555456.0000000000 1.7762059489 4.8426067058 -0.5992372897 0.5653064449 0.8001143336 0.1605738112 -0.120256923571 +1403636704163555584.0000000000 1.7810966780 4.8611897410 -0.6075658883 0.5631175533 0.8014530607 0.1622275277 -0.11938945454 +1403636704213555456.0000000000 1.7863390487 4.8800118053 -0.6172327460 0.5604603705 0.8031227700 0.1643628136 -0.117740625924 +1403636704263555584.0000000000 1.7916952833 4.8993642541 -0.6274988316 0.5579622959 0.8047191523 0.1663660020 -0.115877158123 +1403636704313555456.0000000000 1.7970814058 4.9192641041 -0.6367977405 0.5565295616 0.8055558765 0.1684827970 -0.113877671303 +1403636704363555584.0000000000 1.8022680079 4.9398916099 -0.6445406813 0.5553279189 0.8062563551 0.1704205031 -0.111885854202 +1403636704413555456.0000000000 1.8068224332 4.9610326605 -0.6499816307 0.5539615244 0.8070582987 0.1710613682 -0.111899688352 +1403636704463555584.0000000000 1.8113834280 4.9820637617 -0.6532816871 0.5525814928 0.8078756774 0.1729185658 -0.109953413821 +1403636704513555456.0000000000 1.8153102247 5.0037249535 -0.6546410024 0.5510459605 0.8088089208 0.1746648941 -0.108021543357 +1403636704563555584.0000000000 1.8184615533 5.0258705447 -0.6539402182 0.5491566861 0.8100391678 0.1752674303 -0.107446770728 +1403636704613555456.0000000000 1.8209446931 5.0486550820 -0.6528848656 0.5476449753 0.8109486430 0.1763434828 -0.106537578062 +1403636704663555584.0000000000 1.8224853087 5.0721866074 -0.6524577139 0.5463711857 0.8117755338 0.1770282222 -0.105640990176 +1403636704713555456.0000000000 1.8235174042 5.0959511354 -0.6541303014 0.5431652731 0.8137703426 0.1789994451 -0.103481951781 +1403636704763555584.0000000000 1.8236445040 5.1204186136 -0.6571694771 0.5411377420 0.8149330766 0.1804890984 -0.102360686383 +1403636704813555456.0000000000 1.8226581846 5.1459457494 -0.6619059372 0.5380681254 0.8168212371 0.1812253544 -0.102191633838 +1403636704863555584.0000000000 1.8203087730 5.1724412072 -0.6682968650 0.5348766346 0.8187428748 0.1821044800 -0.102005142449 +1403636704913555456.0000000000 1.8168307094 5.2004013382 -0.6759035688 0.5322505803 0.8202109382 0.1829885722 -0.102364637742 +1403636704963555584.0000000000 1.8123526166 5.2300595468 -0.6849620436 0.5299260981 0.8215248549 0.1843001262 -0.101531802206 +1403636705013555456.0000000000 1.8068493573 5.2612730533 -0.6950530523 0.5284542564 0.8222815029 0.1855502076 -0.100798557596 +1403636705063555584.0000000000 1.7998615361 5.2944090122 -0.7055309011 0.5285431334 0.8220090010 0.1872044705 -0.0994879115025 +1403636705113555456.0000000000 1.7911371480 5.3298853043 -0.7161909181 0.5325956854 0.8192930734 0.1870669316 -0.100531880082 +1403636705163555584.0000000000 1.7810291267 5.3665752709 -0.7262336153 0.5399199880 0.8144006025 0.1866217291 -0.10203134551 +1403636705213555456.0000000000 1.7694387856 5.4045047800 -0.7352386813 0.5476873403 0.8091086296 0.1864237509 -0.103092132672 +1403636705263555584.0000000000 1.7567266869 5.4431094940 -0.7427255181 0.5537900858 0.8048274407 0.1865168684 -0.103830579573 +1403636705313555456.0000000000 1.7430650484 5.4814950704 -0.7482783575 0.5575260084 0.8022072884 0.1861328461 -0.104798759304 +1403636705363555584.0000000000 1.7287711548 5.5195535589 -0.7528906058 0.5599844422 0.8004661635 0.1857285279 -0.10571782956 +1403636705413555456.0000000000 1.7137014377 5.5573136120 -0.7565828493 0.5585288025 0.8014453018 0.1859797781 -0.10555816986 +1403636705463555584.0000000000 1.6978754133 5.5948486303 -0.7597879577 0.5564950419 0.8029180354 0.1857099089 -0.105582794058 +1403636705513555456.0000000000 1.6812049702 5.6322808070 -0.7638681853 0.5532286578 0.8052403952 0.1858032287 -0.104895749782 +1403636705563555584.0000000000 1.6637411950 5.6697383862 -0.7692707869 0.5504689361 0.8070985782 0.1865706168 -0.103765314359 +1403636705613555456.0000000000 1.6453685778 5.7074662607 -0.7758635873 0.5490894805 0.8081036320 0.1861739253 -0.103964089576 +1403636705663555584.0000000000 1.6263140995 5.7455783811 -0.7840694385 0.5479691886 0.8089526730 0.1861882757 -0.103243727008 +1403636705713555456.0000000000 1.6061472730 5.7847276547 -0.7927361488 0.5495981501 0.8079172412 0.1854829562 -0.103959982088 +1403636705763555584.0000000000 1.5850720705 5.8244868188 -0.8022298948 0.5515989951 0.8066587445 0.1842414427 -0.105334274312 +1403636705813555456.0000000000 1.5632015411 5.8644048443 -0.8114581654 0.5538008722 0.8051826306 0.1824681006 -0.108124546465 +1403636705863555584.0000000000 1.5407904231 5.9048303507 -0.8197138871 0.5568525772 0.8030901277 0.1806932612 -0.110956746137 +1403636705913555456.0000000000 1.5179941266 5.9452596779 -0.8260506285 0.5592352625 0.8014729232 0.1775134448 -0.115698105139 +1403636705963555584.0000000000 1.4949964712 5.9857926784 -0.8302874863 0.5611080652 0.8001108630 0.1743800938 -0.120714245153 +1403636706013555456.0000000000 1.4722255302 6.0256933028 -0.8321257793 0.5619340341 0.7993330603 0.1703304253 -0.12761013371 +1403636706063555584.0000000000 1.4505190659 6.0649716236 -0.8321150237 0.5617872543 0.7991416402 0.1665429497 -0.13428017617 +1403636706113555456.0000000000 1.4296405008 6.1051107626 -0.8314355358 0.5628741930 0.7981156851 0.1633736711 -0.139617475724 +1403636706163555584.0000000000 1.4108036455 6.1453511115 -0.8325036839 0.5647510998 0.7966320605 0.1650489625 -0.138536621043 +1403636706213555456.0000000000 1.3934802512 6.1859218476 -0.8358811358 0.5666980789 0.7951579897 0.1692218625 -0.133944092905 +1403636706263555584.0000000000 1.3771467614 6.2262961624 -0.8415152566 0.5671370890 0.7947265765 0.1731637066 -0.129535792765 +1403636706313555456.0000000000 1.3614912201 6.2662482581 -0.8492271349 0.5676634087 0.7941624015 0.1784134964 -0.123421872725 +1403636706363555584.0000000000 1.3462718376 6.3058410542 -0.8591954624 0.5667258520 0.7945993107 0.1824497384 -0.118936272872 +1403636706413555456.0000000000 1.3311552042 6.3448529001 -0.8700991464 0.5659279916 0.7949470752 0.1859317614 -0.114952321142 +1403636706463555584.0000000000 1.3158738036 6.3835920924 -0.8815041499 0.5644177554 0.7957934877 0.1887111254 -0.111952818279 +1403636706513555456.0000000000 1.2999342256 6.4223998496 -0.8914699016 0.5635773495 0.7962366637 0.1906143048 -0.109790406321 +1403636706563555584.0000000000 1.2838897051 6.4604351967 -0.8998971240 0.5624054611 0.7970726566 0.1916100292 -0.107985527464 +1403636706613555456.0000000000 1.2671243758 6.4980683319 -0.9060427161 0.5616534101 0.7975254609 0.1920039287 -0.107856744874 +1403636706663555584.0000000000 1.2499129400 6.5353837477 -0.9113455724 0.5607430193 0.7982422066 0.1923166771 -0.106728354308 +1403636706713555456.0000000000 1.2313342267 6.5735526915 -0.9146960337 0.5589303154 0.7995343385 0.1926652565 -0.105933201095 +1403636706763555584.0000000000 1.2117444121 6.6114894501 -0.9153141268 0.5564435902 0.8014190358 0.1918286795 -0.106300600806 +1403636706813555456.0000000000 1.1918973112 6.6491699666 -0.9154255289 0.5542450858 0.8030949295 0.1919429189 -0.104922995515 +1403636706863555584.0000000000 1.1713101704 6.6868676050 -0.9146021527 0.5527538024 0.8043712874 0.1913929022 -0.104013570697 +1403636706913555456.0000000000 1.1497891238 6.7246433670 -0.9125260328 0.5521378941 0.8050771030 0.1901044721 -0.104186821963 +1403636706963555584.0000000000 1.1274600550 6.7630907233 -0.9097878813 0.5525025312 0.8051636773 0.1892609975 -0.103114890569 +1403636707013555456.0000000000 1.1040193026 6.8016522151 -0.9059376733 0.5547305305 0.8039707776 0.1876273703 -0.10344562431 +1403636707063555584.0000000000 1.0800110132 6.8403256891 -0.9020574022 0.5573020153 0.8025060393 0.1866349455 -0.102790650592 +1403636707113555456.0000000000 1.0554691156 6.8789189863 -0.8980584223 0.5593790326 0.8014417938 0.1850586238 -0.102661846258 +1403636707163555584.0000000000 1.0303960904 6.9172031163 -0.8943119536 0.5598452654 0.8015117153 0.1838025317 -0.101827689479 +1403636707213555456.0000000000 1.0048589248 6.9552151246 -0.8903402552 0.5597270030 0.8020705597 0.1824721917 -0.100460931141 +1403636707263555584.0000000000 0.9786960530 6.9931783531 -0.8851373541 0.5597222792 0.8024780169 0.1814498744 -0.0990754544833 +1403636707313555456.0000000000 0.9518769911 7.0309264465 -0.8782499974 0.5593077001 0.8031069655 0.1810871265 -0.0969615964087 +1403636707363555584.0000000000 0.9240757244 7.0683419656 -0.8692689440 0.5588544147 0.8037347251 0.1802445404 -0.0959382117174 +1403636707413555456.0000000000 0.8953743019 7.1058186350 -0.8581598112 0.5582220011 0.8044320410 0.1793636557 -0.0954251951302 +1403636707463555584.0000000000 0.8655567565 7.1436579175 -0.8447846310 0.5577221000 0.8049042045 0.1794198019 -0.0942539944096 +1403636707513555456.0000000000 0.8349640691 7.1809379096 -0.8293776594 0.5572445687 0.8054189206 0.1782332582 -0.0949302832204 +1403636707563555584.0000000000 0.8033766580 7.2184724795 -0.8123327701 0.5568561684 0.8058433900 0.1770068289 -0.0958969293197 +1403636707613555456.0000000000 0.7711552679 7.2556961861 -0.7959595365 0.5552780267 0.8070760517 0.1755839158 -0.0972874520942 +1403636707663555584.0000000000 0.7380489880 7.2931935129 -0.7810065448 0.5526518487 0.8090256683 0.1717306012 -0.102771604757 +1403636707713555456.0000000000 0.7049819733 7.3312133142 -0.7691026397 0.5511762416 0.8100549975 0.1695482951 -0.106155674881 +1403636707763555584.0000000000 0.6718851219 7.3699197767 -0.7604122608 0.5495707378 0.8110978565 0.1677906286 -0.109263792311 +1403636707813555456.0000000000 0.6387020610 7.4097607978 -0.7547748678 0.5498949918 0.8108773710 0.1666592221 -0.110986894695 +1403636707863555584.0000000000 0.6056446347 7.4500398901 -0.7520660051 0.5508022934 0.8100858754 0.1664532956 -0.112565574162 +1403636707913555456.0000000000 0.5730500071 7.4905963022 -0.7522115078 0.5523158013 0.8088393054 0.1664453796 -0.114114719576 +1403636707963555584.0000000000 0.5405956984 7.5316709124 -0.7550862311 0.5536942553 0.8076086359 0.1676597192 -0.114372992443 +1403636708013555456.0000000000 0.5081558418 7.5733495297 -0.7604211504 0.5551701612 0.8062685716 0.1693134024 -0.114236834654 +1403636708063555584.0000000000 0.4759256993 7.6152157780 -0.7679840237 0.5567098197 0.8048475419 0.1714943944 -0.11350895828 +1403636708113555456.0000000000 0.4437313057 7.6574015906 -0.7767780563 0.5587380012 0.8030328992 0.1737307215 -0.112994005363 +1403636708163555584.0000000000 0.4115021538 7.6996109695 -0.7868471286 0.5605115242 0.8014364640 0.1757643960 -0.112397964998 +1403636708213555456.0000000000 0.3792022924 7.7414174567 -0.7979767974 0.5613883183 0.8005176830 0.1758978596 -0.114343947151 +1403636708263555584.0000000000 0.3469434442 7.7828174953 -0.8099879724 0.5620930544 0.7998251895 0.1745155291 -0.11779386452 +1403636708313555456.0000000000 0.3148760485 7.8240804610 -0.8224172496 0.5628897139 0.7990992938 0.1710944384 -0.123782800835 +1403636708363555584.0000000000 0.2835554109 7.8643980045 -0.8348923262 0.5626035490 0.7990942288 0.1662785955 -0.13144233986 +1403636708413555456.0000000000 0.2537191945 7.9048929139 -0.8464947137 0.5626520979 0.7988436311 0.1625982719 -0.137234368016 +1403636708463555584.0000000000 0.2251386078 7.9462443387 -0.8569848869 0.5628848736 0.7984593456 0.1598763615 -0.141643360434 +1403636708513555456.0000000000 0.1980585850 7.9889574303 -0.8655207782 0.5634591399 0.7979884811 0.1586577618 -0.143373276012 +1403636708563555584.0000000000 0.1727794150 8.0322633491 -0.8726010976 0.5650077093 0.7968707603 0.1590105416 -0.143104603244 +1403636708613555456.0000000000 0.1497950082 8.0757992732 -0.8786242967 0.5671972733 0.7955594050 0.1612339928 -0.139198009387 +1403636708663555584.0000000000 0.1284941669 8.1191481255 -0.8854620508 0.5685976596 0.7948316212 0.1652379263 -0.132799936268 +1403636708713555456.0000000000 0.1084186032 8.1622908974 -0.8930087862 0.5719153873 0.7927410182 0.1692558823 -0.125805064134 +1403636708763555584.0000000000 0.0890995699 8.2048677017 -0.9020037110 0.5740758390 0.7913786684 0.1734426843 -0.118635448193 +1403636708813555456.0000000000 0.0702433234 8.2467257488 -0.9119642889 0.5774536370 0.7891172931 0.1766854652 -0.112354088956 +1403636708863555584.0000000000 0.0512961292 8.2871294525 -0.9228834933 0.5781406746 0.7889069468 0.1776583573 -0.108704635463 +1403636708913555456.0000000000 0.0322231949 8.3265668455 -0.9330545158 0.5804747915 0.7876183051 0.1774089606 -0.105983406981 +1403636708963555584.0000000000 0.0130170232 8.3645183584 -0.9421307969 0.5822361066 0.7868090310 0.1769291167 -0.103095842125 +1403636709013555456.0000000000 -0.0067319939 8.4008164800 -0.9486713028 0.5844759211 0.7855684033 0.1751389085 -0.102939516562 +1403636709063555584.0000000000 -0.0262473660 8.4353254505 -0.9539041165 0.5869868416 0.7841386629 0.1749698506 -0.0997925673144 +1403636709113555456.0000000000 -0.0463237504 8.4679283239 -0.9573066848 0.5879974040 0.7838382491 0.1731755952 -0.0993320961694 +1403636709163555584.0000000000 -0.0666865868 8.4989391727 -0.9590188908 0.5875649706 0.7845650434 0.1725940813 -0.0971410368932 +1403636709213555456.0000000000 -0.0873373853 8.5278059745 -0.9588837528 0.5851681191 0.7867427777 0.1713295910 -0.0962301692087 +1403636709263555584.0000000000 -0.1081781438 8.5551233368 -0.9577030954 0.5824759629 0.7889472901 0.1716525022 -0.0939113653745 +1403636709313555456.0000000000 -0.1297923292 8.5809884801 -0.9547333274 0.5795821128 0.7912300625 0.1713733719 -0.0931167551508 +1403636709363555584.0000000000 -0.1519925241 8.6057290555 -0.9519213732 0.5768546746 0.7932958940 0.1712344551 -0.0927311727862 +1403636709413555456.0000000000 -0.1745190100 8.6296207303 -0.9502673818 0.5759108774 0.7940075798 0.1724597856 -0.0902011471309 +1403636709463555584.0000000000 -0.1980334941 8.6525421233 -0.9501361850 0.5750771907 0.7946277804 0.1720602516 -0.0908195200303 +1403636709513555456.0000000000 -0.2220352070 8.6746878258 -0.9523484999 0.5743933545 0.7950830934 0.1730386742 -0.0892903477865 +1403636709563555584.0000000000 -0.2469285333 8.6956978068 -0.9561257976 0.5734124210 0.7957500033 0.1731371403 -0.0894631674442 +1403636709613555456.0000000000 -0.2725472974 8.7160464810 -0.9612511236 0.5720405065 0.7966884818 0.1736295848 -0.0889375582639 +1403636709663555584.0000000000 -0.2989717241 8.7357949437 -0.9675316305 0.5712059193 0.7971766236 0.1741618095 -0.0888869654233 +1403636709713555456.0000000000 -0.3262759332 8.7552043236 -0.9741277590 0.5708081255 0.7972639225 0.1751786200 -0.0886609995179 +1403636709763555584.0000000000 -0.3547182955 8.7736950856 -0.9807805967 0.5700822233 0.7975760443 0.1753924902 -0.0900898808492 +1403636709813555456.0000000000 -0.3837861099 8.7915084340 -0.9872602048 0.5705471693 0.7969776416 0.1767616083 -0.0897658082634 +1403636709863555584.0000000000 -0.4141287130 8.8086819100 -0.9922827298 0.5704088997 0.7969147246 0.1766487212 -0.0914102733022 +1403636709913555456.0000000000 -0.4451997785 8.8256337837 -0.9956028913 0.5709584952 0.7963286090 0.1776122137 -0.0912197604577 +1403636709963555584.0000000000 -0.4770589551 8.8416420442 -0.9972248102 0.5715565743 0.7956500573 0.1784582882 -0.0917426185794 +1403636710013555456.0000000000 -0.5096959416 8.8568914114 -0.9973144727 0.5714104932 0.7955436127 0.1787255574 -0.0930461370226 +1403636710063555584.0000000000 -0.5428766464 8.8713178052 -0.9964362166 0.5718681191 0.7949791096 0.1794624890 -0.0936391198366 +1403636710113555456.0000000000 -0.5770788349 8.8854608606 -0.9958336764 0.5724504720 0.7942607281 0.1803206711 -0.094524115794 +1403636710163555584.0000000000 -0.6119402267 8.8989324274 -0.9969214348 0.5727635366 0.7937215342 0.1814679460 -0.0949602120926 +1403636710213555456.0000000000 -0.6475389065 8.9119016367 -1.0000627611 0.5731473512 0.7930811477 0.1826227294 -0.0957775843372 +1403636710263555584.0000000000 -0.6839131255 8.9239648429 -1.0055629613 0.5730486382 0.7928103900 0.1827306910 -0.0983688892122 +1403636710313555456.0000000000 -0.7210737027 8.9350281979 -1.0125859081 0.5727623253 0.7927484688 0.1802604511 -0.104877803937 +1403636710363555584.0000000000 -0.7586583794 8.9450938691 -1.0211309300 0.5711026371 0.7934642130 0.1774132118 -0.113052523034 +1403636710413555456.0000000000 -0.7963246566 8.9542654686 -1.0309173567 0.5694629407 0.7936898541 0.1763255491 -0.121151456557 +1403636710463555584.0000000000 -0.8337151953 8.9627421874 -1.0421107931 0.5671084740 0.7940155647 0.1768270921 -0.129071457965 +1403636710513555456.0000000000 -0.8707071809 8.9709030011 -1.0543917998 0.5650601787 0.7937362876 0.1785311926 -0.137172568424 +1403636710563555584.0000000000 -0.9066699791 8.9790010305 -1.0678008488 0.5634090889 0.7930342857 0.1816570894 -0.143762032847 +1403636710613555456.0000000000 -0.9415038580 8.9872507456 -1.0823183003 0.5625331822 0.7917602206 0.1854264224 -0.14929572638 +1403636710663555584.0000000000 -0.9752677884 8.9954592166 -1.0979665772 0.5615163924 0.7902124149 0.1908044770 -0.154458188282 +1403636710713555456.0000000000 -1.0077315271 9.0038152743 -1.1143872028 0.5613849376 0.7878472531 0.1977133805 -0.158281637629 +1403636710763555584.0000000000 -1.0390251963 9.0121444409 -1.1303113219 0.5610747528 0.7852526280 0.2053789944 -0.162458919698 +1403636710813555456.0000000000 -1.0689576092 9.0204987790 -1.1447630968 0.5618959643 0.7815531432 0.2161133582 -0.163531727942 +1403636710863555584.0000000000 -1.0977616926 9.0282381525 -1.1578701224 0.5615603027 0.7783147356 0.2275148763 -0.164660802204 +1403636710913555456.0000000000 -1.1260456788 9.0358676784 -1.1693151966 0.5608707811 0.7751748866 0.2386307715 -0.16608195868 +1403636710963555584.0000000000 -1.1537557718 9.0434722280 -1.1787902629 0.5608970346 0.7717145956 0.2486002098 -0.167478462011 +1403636711013555456.0000000000 -1.1809500944 9.0509167922 -1.1869050626 0.5602221729 0.7689195000 0.2595850052 -0.165920295908 +1403636711063555584.0000000000 -1.2081549502 9.0575067756 -1.1928016150 0.5598319249 0.7665080665 0.2660532071 -0.168134740105 +1403636711113555456.0000000000 -1.2353011934 9.0639138459 -1.1976875059 0.5601159539 0.7639797125 0.2727653981 -0.167940926132 +1403636711163555584.0000000000 -1.2626478129 9.0693586824 -1.2012924967 0.5607471886 0.7617248745 0.2770975283 -0.168981554571 +1403636711213555456.0000000000 -1.2903871261 9.0739990474 -1.2045801657 0.5611213654 0.7600344623 0.2804289985 -0.169852895682 +1403636711263555584.0000000000 -1.3179355224 9.0772205717 -1.2073980241 0.5612826260 0.7588944126 0.2826480198 -0.170737169853 +1403636711313555456.0000000000 -1.3458433295 9.0790294699 -1.2087335934 0.5611997157 0.7581978716 0.2825817898 -0.174179213965 +1403636711363555584.0000000000 -1.3736599958 9.0798125067 -1.2094870135 0.5613180721 0.7577278287 0.2817229778 -0.177208135617 +1403636711413555456.0000000000 -1.4021481024 9.0801527825 -1.2077740072 0.5642470870 0.7554229456 0.2794207955 -0.181343368096 +1403636711463555584.0000000000 -1.4297345297 9.0788966108 -1.2048040740 0.5690191455 0.7518943771 0.2764927869 -0.18553650997 +1403636711513555456.0000000000 -1.4565685477 9.0764645549 -1.2019070275 0.5736582960 0.7485934706 0.2740541232 -0.188197536736 +1403636711563555584.0000000000 -1.4829636927 9.0732620760 -1.1986613265 0.5783700800 0.7454182808 0.2731555010 -0.187685133905 +1403636711613555456.0000000000 -1.5086929746 9.0682162919 -1.1952860310 0.5814337278 0.7435045014 0.2726538285 -0.186536233317 +1403636711663555584.0000000000 -1.5335364572 9.0611236332 -1.1920016949 0.5831763119 0.7426441637 0.2724495888 -0.184814114335 +1403636711713555456.0000000000 -1.5574094660 9.0519623284 -1.1885387814 0.5834709534 0.7429657142 0.2729679537 -0.18180233866 +1403636711763555584.0000000000 -1.5806254013 9.0404274379 -1.1842116940 0.5829393358 0.7438965540 0.2722215553 -0.180817788465 +1403636711813555456.0000000000 -1.6031491207 9.0268096749 -1.1797511731 0.5806147031 0.7461523085 0.2708077497 -0.181125541608 +1403636711863555584.0000000000 -1.6249298932 9.0109012947 -1.1745627566 0.5766779309 0.7495167895 0.2687932325 -0.182804114801 +1403636711913555456.0000000000 -1.6462563919 8.9934130915 -1.1684215725 0.5717581605 0.7535800358 0.2659924718 -0.18562796253 +1403636711963555584.0000000000 -1.6665686405 8.9747600932 -1.1612574452 0.5670341681 0.7574108890 0.2631002777 -0.188624604189 +1403636712013555456.0000000000 -1.6857522218 8.9547718083 -1.1528981588 0.5627958763 0.7607862138 0.2596646236 -0.19245628523 +1403636712063555584.0000000000 -1.7039972268 8.9345042550 -1.1432397072 0.5592943156 0.7634824525 0.2564489058 -0.196260979431 +1403636712113555456.0000000000 -1.7210682484 8.9143748330 -1.1324131184 0.5580910941 0.7644210994 0.2542854433 -0.198830648771 +1403636712163555584.0000000000 -1.7368847957 8.8944415942 -1.1207806815 0.5580369532 0.7642864322 0.2535727947 -0.200404207151 +1403636712213555456.0000000000 -1.7511091220 8.8742914006 -1.1089630170 0.5590590684 0.7625549230 0.2580177097 -0.19846865988 +1403636712263555584.0000000000 -1.7643433522 8.8535038086 -1.0959770764 0.5601541688 0.7599023693 0.2649605603 -0.196396531942 +1403636712313555456.0000000000 -1.7769343571 8.8321004957 -1.0814527057 0.5619351203 0.7559907747 0.2728644789 -0.195580789845 +1403636712363555584.0000000000 -1.7888204509 8.8097078347 -1.0660960491 0.5628501036 0.7522133126 0.2815102318 -0.19526106279 +1403636712413555456.0000000000 -1.8000799495 8.7864316098 -1.0494956249 0.5634773902 0.7488250438 0.2885721712 -0.196164182444 +1403636712463555584.0000000000 -1.8107378119 8.7622451091 -1.0316886894 0.5644583080 0.7451535839 0.2950431620 -0.197692912071 +1403636712513555456.0000000000 -1.8211174754 8.7370112227 -1.0126337235 0.5644632747 0.7422306994 0.3007441591 -0.20006936594 +1403636712563555584.0000000000 -1.8311293385 8.7106307182 -0.9927586974 0.5641623957 0.7398582955 0.3049354022 -0.203334439689 +1403636712613555456.0000000000 -1.8407661305 8.6829020173 -0.9732833129 0.5647992818 0.7368667930 0.3078601023 -0.207969367994 +1403636712663555584.0000000000 -1.8498286513 8.6542408036 -0.9550616211 0.5654679714 0.7340869799 0.3093214795 -0.213734652479 +1403636712713555456.0000000000 -1.8579175483 8.6245879666 -0.9385779032 0.5660590289 0.7316760238 0.3105003664 -0.218670744634 +1403636712763555584.0000000000 -1.8651425244 8.5940747445 -0.9240222116 0.5654904603 0.7302507417 0.3121542940 -0.222517618158 +1403636712813555456.0000000000 -1.8712263148 8.5628189848 -0.9114554568 0.5640070952 0.7299958858 0.3138205078 -0.224763636343 +1403636712863555584.0000000000 -1.8760297061 8.5307401144 -0.9004726529 0.5616429525 0.7307846642 0.3156133282 -0.2256085005 +1403636712913555456.0000000000 -1.8796563477 8.4978134396 -0.8907068974 0.5594069528 0.7317250839 0.3172099193 -0.225876359582 +1403636712963555584.0000000000 -1.8819184162 8.4639405307 -0.8828137676 0.5570951450 0.7329973628 0.3190837482 -0.224823102002 +1403636713013555456.0000000000 -1.8834984824 8.4298595248 -0.8760062487 0.5563211783 0.7333802170 0.3209545941 -0.22281910246 +1403636713063555584.0000000000 -1.8843607299 8.3946330994 -0.8677417394 0.5560767518 0.7333533788 0.3205648145 -0.224075138478 +1403636713113555456.0000000000 -1.8837692735 8.3576634824 -0.8580461537 0.5552412285 0.7334738303 0.3201596952 -0.226320763312 +1403636713163555584.0000000000 -1.8821019563 8.3198974553 -0.8473535255 0.5536732012 0.7341738567 0.3206202221 -0.227238657918 +1403636713213555456.0000000000 -1.8793860338 8.2816084602 -0.8345048206 0.5519534054 0.7353279762 0.3205014528 -0.22785746535 +1403636713263555584.0000000000 -1.8758144243 8.2428711904 -0.8198463834 0.5496917534 0.7368535685 0.3210207674 -0.227665240381 +1403636713313555456.0000000000 -1.8713782784 8.2039118928 -0.8031691548 0.5489096280 0.7375002509 0.3214683925 -0.226825203504 +1403636713363555584.0000000000 -1.8664752610 8.1644208229 -0.7844266040 0.5472475531 0.7387825294 0.3218527461 -0.226122311372 +1403636713413555456.0000000000 -1.8618088022 8.1246907434 -0.7630944501 0.5461517228 0.7396877217 0.3206566626 -0.227507527024 +1403636713463555584.0000000000 -1.8563145798 8.0847323252 -0.7411879522 0.5450538884 0.7406789812 0.3197391593 -0.228205555618 +1403636713513555456.0000000000 -1.8494806256 8.0441315328 -0.7183226341 0.5435684777 0.7419149208 0.3185729615 -0.22936178525 +1403636713563555584.0000000000 -1.8422500380 8.0035551501 -0.6956324994 0.5426051983 0.7428473244 0.3168830819 -0.230960091394 +1403636713613555456.0000000000 -1.8340126751 7.9631964033 -0.6741947029 0.5398298411 0.7452533916 0.3148903050 -0.232433260917 +1403636713663555584.0000000000 -1.8252919720 7.9233444735 -0.6543917234 0.5375677030 0.7472490353 0.3132503118 -0.233482517816 +1403636713713555456.0000000000 -1.8158776494 7.8843316109 -0.6360745848 0.5356692092 0.7489766512 0.3112502090 -0.234980385766 +1403636713763555584.0000000000 -1.8057745363 7.8464651399 -0.6194826891 0.5340118483 0.7506464350 0.3091735774 -0.23616302525 +1403636713813555456.0000000000 -1.7948161988 7.8094846304 -0.6044188813 0.5327136219 0.7519203164 0.3078108050 -0.236821754185 +1403636713863555584.0000000000 -1.7829829990 7.7741329500 -0.5908536128 0.5327504007 0.7523957119 0.3069649429 -0.236326526358 +1403636713913555456.0000000000 -1.7701615907 7.7396149541 -0.5786674383 0.5333557325 0.7525256119 0.3073628211 -0.234019149255 +1403636713963555584.0000000000 -1.7564789036 7.7057186386 -0.5678557001 0.5341160812 0.7524529419 0.3080476209 -0.231605797117 +1403636714013555456.0000000000 -1.7420583565 7.6721555639 -0.5584945618 0.5341608999 0.7529985215 0.3083556990 -0.229307920985 +1403636714063555584.0000000000 -1.7269156523 7.6393121039 -0.5502487293 0.5368805752 0.7517244934 0.3099191259 -0.22498815387 +1403636714113555456.0000000000 -1.7114514555 7.6065517725 -0.5431311384 0.5373155929 0.7520142062 0.3096950361 -0.223283612947 +1403636714163555584.0000000000 -1.6955402065 7.5740820758 -0.5369855146 0.5382256144 0.7519582175 0.3095689791 -0.221447678371 +1403636714213555456.0000000000 -1.6792371259 7.5418568550 -0.5315498193 0.5395893190 0.7515255891 0.3083152517 -0.221346699113 +1403636714263555584.0000000000 -1.6627031613 7.5097059160 -0.5269081060 0.5397365443 0.7518763212 0.3059767896 -0.223035119831 +1403636714313555456.0000000000 -1.6457267485 7.4777827073 -0.5232350702 0.5393629181 0.7526046700 0.3038819811 -0.224342583819 +1403636714363555584.0000000000 -1.6279597640 7.4461732796 -0.5210182490 0.5385353551 0.7536637203 0.3029761837 -0.22400022343 +1403636714413555456.0000000000 -1.6094786801 7.4150238386 -0.5203531502 0.5361224082 0.7557676027 0.3034560789 -0.222041668083 +1403636714463555584.0000000000 -1.5906206283 7.3840264459 -0.5208402267 0.5324553841 0.7579576881 0.3052400483 -0.220952302458 +1403636714513555456.0000000000 -1.5715786422 7.3535140570 -0.5221544708 0.5285163453 0.7595948262 0.3082336053 -0.220631405957 +1403636714563555584.0000000000 -1.5526696369 7.3235395861 -0.5241657400 0.5241801836 0.7607077172 0.3116779266 -0.222296590412 +1403636714613555456.0000000000 -1.5340782695 7.2944252651 -0.5272015035 0.5201537707 0.7607136054 0.3169289062 -0.22430098927 +1403636714663555584.0000000000 -1.5157857615 7.2664705722 -0.5298793271 0.5173061369 0.7591823799 0.3236445473 -0.226474461602 +1403636714713555456.0000000000 -1.4978895688 7.2394138650 -0.5313641569 0.5141290787 0.7569757355 0.3312436682 -0.230079678699 +1403636714763555584.0000000000 -1.4801427611 7.2134124814 -0.5312602303 0.5113359430 0.7536763729 0.3403325242 -0.233840226013 +1403636714813555456.0000000000 -1.4629686453 7.1884835422 -0.5291355287 0.5097484373 0.7486341352 0.3509932722 -0.237712400292 +1403636714863555584.0000000000 -1.4462492844 7.1645936462 -0.5251263734 0.5084466748 0.7428042343 0.3622842547 -0.241813910156 +1403636714913555456.0000000000 -1.4302078174 7.1415016538 -0.5193520697 0.5060710277 0.7372946145 0.3734362648 -0.246645742801 +1403636714963555584.0000000000 -1.4150730767 7.1191748615 -0.5113266619 0.5026026801 0.7323379156 0.3840529473 -0.252140946827 +1403636715013555456.0000000000 -1.4007156994 7.0978708723 -0.5013383223 0.4999003406 0.7274489638 0.3936067703 -0.256887845008 +1403636715063555584.0000000000 -1.3873947592 7.0774847712 -0.4894024963 0.4970921022 0.7230834673 0.4022456445 -0.261243531524 +1403636715113555456.0000000000 -1.3744646272 7.0579187143 -0.4762147859 0.4948206808 0.7191997508 0.4103970097 -0.263587759062 +1403636715163555584.0000000000 -1.3628150762 7.0390625519 -0.4618393303 0.4923090689 0.7163536005 0.4159715444 -0.267276961225 +1403636715213555456.0000000000 -1.3522649307 7.0213728174 -0.4470684616 0.4910055961 0.7135995491 0.4208162064 -0.269449268841 +1403636715263555584.0000000000 -1.3429027608 7.0042495287 -0.4331429745 0.4900143011 0.7113078298 0.4236424776 -0.272862982447 +1403636715313555456.0000000000 -1.3346887524 6.9878304350 -0.4206847271 0.4896723771 0.7092902447 0.4247980853 -0.276902326961 +1403636715363555584.0000000000 -1.3275102075 6.9719967153 -0.4099513333 0.4897390468 0.7075307045 0.4259201656 -0.279549603369 +1403636715413555456.0000000000 -1.3216860257 6.9566518736 -0.4003766445 0.4900426502 0.7062063576 0.4241840744 -0.284953772416 +1403636715463555584.0000000000 -1.3163385559 6.9419061982 -0.3929989360 0.4905999763 0.7051561546 0.4221389501 -0.289594833434 +1403636715513555456.0000000000 -1.3113270128 6.9274327138 -0.3875504345 0.4898714736 0.7052091426 0.4184881616 -0.295928476396 +1403636715563555584.0000000000 -1.3061942198 6.9136405543 -0.3838222796 0.4878343426 0.7063862005 0.4137953464 -0.303000992101 +1403636715613555456.0000000000 -1.3005285949 6.9012574151 -0.3830674301 0.4867366529 0.7071085797 0.4120033301 -0.30551291811 +1403636715663555584.0000000000 -1.2945403802 6.8906352235 -0.3833623964 0.4901490930 0.7050542778 0.4107191437 -0.306532407679 +1403636715713555456.0000000000 -1.2880718174 6.8814287431 -0.3850905417 0.4968476918 0.7008779062 0.4104738482 -0.305652992427 +1403636715763555584.0000000000 -1.2807627272 6.8729673502 -0.3874082321 0.5032484515 0.6970371676 0.4106013227 -0.303787321895 +1403636715813555456.0000000000 -1.2726909498 6.8648257744 -0.3894223586 0.5089238367 0.6937660242 0.4104237873 -0.302055536213 +1403636715863555584.0000000000 -1.2643810231 6.8568289387 -0.3896668047 0.5134799105 0.6910151416 0.4097794936 -0.301524828515 +1403636715913555456.0000000000 -1.2546535554 6.8486351344 -0.3879120744 0.5184195878 0.6881400777 0.4095319263 -0.299979942263 +1403636715963555584.0000000000 -1.2437396506 6.8397607113 -0.3844998889 0.5211337266 0.6869943180 0.4082019563 -0.299715880421 +1403636716013555456.0000000000 -1.2310559949 6.8300352423 -0.3807014914 0.5225125666 0.6866423501 0.4072190928 -0.299458697023 +1403636716063555584.0000000000 -1.2176269923 6.8200331961 -0.3761650877 0.5226833970 0.6873632682 0.4065700583 -0.298386648056 +1403636716113555456.0000000000 -1.2028346533 6.8092997510 -0.3702142768 0.5212825010 0.6891895860 0.4051375167 -0.298573041541 +1403636716163555584.0000000000 -1.1866260456 6.7979944954 -0.3635004232 0.5175107723 0.6928722051 0.4049657723 -0.296839066089 +1403636716213555456.0000000000 -1.1690517152 6.7860232802 -0.3554212847 0.5125753082 0.6975033316 0.4048493396 -0.294707767214 +1403636716263555584.0000000000 -1.1506249130 6.7741767569 -0.3476319334 0.5101832715 0.7004248099 0.4045910509 -0.292274180693 +1403636716313555456.0000000000 -1.1315558301 6.7622841525 -0.3409698489 0.5078960614 0.7031172249 0.4043885046 -0.290064986178 +1403636716363555584.0000000000 -1.1121637943 6.7508208968 -0.3358702839 0.5063037739 0.7053340602 0.4037399505 -0.288365054069 +1403636716413555456.0000000000 -1.0927404056 6.7395677096 -0.3321431565 0.5063202904 0.7062369211 0.4027729050 -0.287477237046 +1403636716463555584.0000000000 -1.0730490655 6.7285078080 -0.3304684999 0.5061629208 0.7071519139 0.4024027714 -0.286019715871 +1403636716513555456.0000000000 -1.0535792316 6.7177525683 -0.3300928158 0.5068807668 0.7075015106 0.4013516213 -0.285360082962 +1403636716563555584.0000000000 -1.0339964790 6.7069782347 -0.3314333806 0.5082679805 0.7063979295 0.4023423261 -0.284229269791 +1403636716613555456.0000000000 -1.0143047592 6.6958680432 -0.3341804107 0.5083350651 0.7053741576 0.4041807749 -0.284043413149 +1403636716663555584.0000000000 -0.9944373826 6.6843126890 -0.3382418534 0.5080526759 0.7035369151 0.4066539868 -0.285571046747 +1403636716713555456.0000000000 -0.9743304644 6.6723049032 -0.3436521860 0.5069556771 0.7014010898 0.4103026726 -0.287548551576 +1403636716763555584.0000000000 -0.9539965884 6.6600646195 -0.3502436475 0.5056188729 0.6989207813 0.4138246077 -0.290875387122 +1403636716813555456.0000000000 -0.9330903832 6.6472709429 -0.3573847396 0.5034015314 0.6959386698 0.4187811861 -0.294751733193 +1403636716863555584.0000000000 -0.9120641500 6.6341988647 -0.3641103814 0.5004708731 0.6927514159 0.4244289565 -0.299139502311 +1403636716913555456.0000000000 -0.8906583196 6.6206654210 -0.3696769619 0.4971430298 0.6887797277 0.4310800253 -0.304304627746 +1403636716963555584.0000000000 -0.8687529236 6.6068095872 -0.3738167860 0.4931130981 0.6841262702 0.4397383748 -0.308935075117 +1403636717013555456.0000000000 -0.8466047621 6.5931504735 -0.3759624117 0.4897815459 0.6786721088 0.4477263466 -0.314736913271 +1403636717063555584.0000000000 -0.8245162559 6.5796264184 -0.3764274552 0.4857024462 0.6732913616 0.4565682627 -0.319870751398 +1403636717113555456.0000000000 -0.8024385504 6.5660861240 -0.3750743898 0.4822222470 0.6677137624 0.4646821077 -0.325100868695 +1403636717163555584.0000000000 -0.7805664322 6.5531026219 -0.3722875872 0.4796848292 0.6627685888 0.4718644350 -0.328609521116 +1403636717213555456.0000000000 -0.7589915378 6.5403970197 -0.3686046109 0.4772828417 0.6584045037 0.4782047786 -0.331699846692 +1403636717263555584.0000000000 -0.7370935685 6.5280866054 -0.3647721306 0.4764761686 0.6538995357 0.4843961060 -0.332785622311 +1403636717313555456.0000000000 -0.7150239720 6.5159166549 -0.3610439972 0.4766501456 0.6495606563 0.4906840276 -0.331820399491 +1403636717363555584.0000000000 -0.6930458269 6.5037598840 -0.3567960404 0.4787403950 0.6446126875 0.4965497698 -0.32972783229 +1403636717413555456.0000000000 -0.6712554027 6.4910036589 -0.3527840816 0.4805639977 0.6404477832 0.5014094589 -0.327831413568 +1403636717463555584.0000000000 -0.6494908946 6.4773358573 -0.3490016719 0.4814377133 0.6376715052 0.5045466857 -0.327147400551 +1403636717513555456.0000000000 -0.6280823175 6.4623406940 -0.3466826635 0.4809751575 0.6366295802 0.5061307354 -0.327410070238 +1403636717563555584.0000000000 -0.6072309901 6.4459688887 -0.3455358651 0.4798162623 0.6365116819 0.5058401560 -0.329780184106 +1403636717613555456.0000000000 -0.5867546955 6.4284959830 -0.3460880474 0.4773446490 0.6377683043 0.5048134510 -0.332501211642 +1403636717663555584.0000000000 -0.5665060424 6.4103963286 -0.3484616744 0.4769853314 0.6379528028 0.5038883665 -0.334062463039 +1403636717713555456.0000000000 -0.5465410300 6.3914119207 -0.3525414692 0.4765750906 0.6383414248 0.5028251038 -0.335504580264 +1403636717763555584.0000000000 -0.5264704489 6.3716339129 -0.3584785136 0.4773606063 0.6370509697 0.5050157747 -0.333544571134 +1403636717813555456.0000000000 -0.5064612075 6.3504340159 -0.3643616884 0.4768429707 0.6357727395 0.5070646752 -0.333615377581 +1403636717863555584.0000000000 -0.4866051851 6.3278688860 -0.3693693179 0.4760819490 0.6333609409 0.5106905163 -0.33375903435 +1403636717913555456.0000000000 -0.4671223288 6.3038152603 -0.3728270620 0.4748276511 0.6302117412 0.5148650100 -0.335090860081 +1403636717963555584.0000000000 -0.4477426174 6.2782772352 -0.3746781448 0.4736396843 0.6262905458 0.5195303403 -0.336918131491 +1403636718013555456.0000000000 -0.4286071093 6.2507909247 -0.3743488616 0.4711004329 0.6220630626 0.5245882894 -0.340454189171 +1403636718063555584.0000000000 -0.4098570998 6.2218115956 -0.3723349607 0.4674659766 0.6179820428 0.5298700308 -0.344690449487 +1403636718113555456.0000000000 -0.3913178061 6.1910210580 -0.3683998858 0.4621315087 0.6141454043 0.5342440079 -0.351913669933 +1403636718163555584.0000000000 -0.3732639905 6.1592541391 -0.3644400346 0.4560678879 0.6106147560 0.5388875856 -0.358820110106 +1403636718213555456.0000000000 -0.3556405114 6.1268985091 -0.3615553192 0.4506037951 0.6072974553 0.5429257311 -0.365209078715 +1403636718263555584.0000000000 -0.3376015143 6.0942335114 -0.3608824105 0.4455499507 0.6044768429 0.5467181217 -0.37039476693 +1403636718313555456.0000000000 -0.3195415138 6.0612414434 -0.3623557881 0.4405045845 0.6022051113 0.5499342790 -0.375335854602 +1403636718363555584.0000000000 -0.3016202871 6.0279076961 -0.3658535157 0.4362815743 0.5989061043 0.5537381351 -0.379926234907 +1403636718413555456.0000000000 -0.2838461020 5.9941098347 -0.3708725149 0.4312279247 0.5959721383 0.5578178952 -0.384316123936 +1403636718463555584.0000000000 -0.2665397801 5.9599955747 -0.3770339036 0.4259860608 0.5928852771 0.5612012172 -0.389969380768 +1403636718513555456.0000000000 -0.2491698373 5.9259441823 -0.3847716475 0.4215995801 0.5887235732 0.5653601909 -0.395001522699 +1403636718563555584.0000000000 -0.2320809016 5.8921977335 -0.3935000762 0.4165780230 0.5859971290 0.5682283027 -0.400233321494 +1403636718613555456.0000000000 -0.2154687418 5.8589646684 -0.4031859304 0.4114489776 0.5839153541 0.5708218873 -0.404864139067 +1403636718663555584.0000000000 -0.1992276984 5.8265165512 -0.4135541223 0.4054067962 0.5830674441 0.5720551702 -0.410402932996 +1403636718713555456.0000000000 -0.1833865069 5.7953762642 -0.4254270608 0.4001211175 0.5821407732 0.5738650751 -0.414359852208 +1403636718763555584.0000000000 -0.1681753601 5.7657664222 -0.4381328070 0.3976032354 0.5798799490 0.5757501452 -0.417328027046 +1403636718813555456.0000000000 -0.1529330531 5.7379211720 -0.4524979214 0.3976402448 0.5765757316 0.5793318285 -0.416914012605 +1403636718863555584.0000000000 -0.1384237724 5.7113500860 -0.4664287807 0.3998094667 0.5723521051 0.5835211735 -0.414811400824 +1403636718913555456.0000000000 -0.1244828453 5.6855740953 -0.4790272888 0.4022077970 0.5685137138 0.5867534006 -0.413208775528 +1403636718963555584.0000000000 -0.1103621876 5.6604685797 -0.4898795601 0.4050310841 0.5649012779 0.5893859418 -0.411655898486 +1403636719013555456.0000000000 -0.0969516269 5.6355540647 -0.4980913644 0.4068741923 0.5622528838 0.5913378807 -0.410663605833 +1403636719063555584.0000000000 -0.0833983769 5.6106933090 -0.5038178389 0.4086199042 0.5600462241 0.5918363594 -0.411227095956 +1403636719113555456.0000000000 -0.0697651557 5.5858654397 -0.5077583905 0.4107874666 0.5579698122 0.5917625396 -0.411995682832 +1403636719163555584.0000000000 -0.0569057114 5.5606823295 -0.5092322868 0.4126040081 0.5564101352 0.5904693888 -0.414139583774 +1403636719213555456.0000000000 -0.0437590411 5.5353731033 -0.5091770721 0.4143068201 0.5553249866 0.5887724540 -0.416306396276 +1403636719263555584.0000000000 -0.0302700658 5.5100611491 -0.5096988593 0.4161537133 0.5543546553 0.5869795601 -0.418284591075 +1403636719313555456.0000000000 -0.0161423252 5.4846257929 -0.5113672830 0.4161583740 0.5548402448 0.5844830189 -0.421122442016 +1403636719363555584.0000000000 -0.0013810136 5.4595847656 -0.5148835759 0.4174997678 0.5544207051 0.5827964568 -0.42268181356 +1403636719413555456.0000000000 0.0142803556 5.4346554162 -0.5201866023 0.4179143046 0.5546982701 0.5813409903 -0.423910505026 +1403636719463555584.0000000000 0.0306705050 5.4101713964 -0.5270651728 0.4179706251 0.5554165181 0.5799482292 -0.424821255862 +1403636719513555456.0000000000 0.0478346207 5.3862165182 -0.5357434516 0.4176897481 0.5564122052 0.5789752765 -0.42512158429 +1403636719563555584.0000000000 0.0658979343 5.3627111300 -0.5459238658 0.4162291026 0.5583760482 0.5794729842 -0.423297275601 +1403636719613555456.0000000000 0.0848870620 5.3394803233 -0.5556400812 0.4139508799 0.5608668229 0.5792312773 -0.422568578305 +1403636719663555584.0000000000 0.1039071671 5.3169973476 -0.5637412121 0.4126487108 0.5629806513 0.5802161767 -0.41967012759 +1403636719713555456.0000000000 0.1235482899 5.2950124878 -0.5696666105 0.4110009386 0.5655013260 0.5807107181 -0.417206832029 +1403636719763555584.0000000000 0.1437412186 5.2734898738 -0.5733577518 0.4100856801 0.5676194130 0.5806387654 -0.415327053229 +1403636719813555456.0000000000 0.1634927065 5.2524471679 -0.5747745837 0.4092552746 0.5696783952 0.5803972342 -0.413661331099 +1403636719863555584.0000000000 0.1834292123 5.2319831135 -0.5740897303 0.4093143573 0.5710462297 0.5795257642 -0.412938069248 +1403636719913555456.0000000000 0.2036365792 5.2119290525 -0.5722590665 0.4092319121 0.5724313462 0.5786896193 -0.41227408433 +1403636719963555584.0000000000 0.2237975948 5.1922747303 -0.5706536336 0.4084203292 0.5740568534 0.5785199060 -0.411055084186 +1403636720013555456.0000000000 0.2437608892 5.1733930296 -0.5699219783 0.4091902931 0.5747185349 0.5781693113 -0.409856263934 +1403636720063555584.0000000000 0.2632888405 5.1547727054 -0.5706036120 0.4087805469 0.5754748036 0.5779243143 -0.409549388711 +1403636720113555456.0000000000 0.2824348672 5.1366990051 -0.5728241385 0.4090847197 0.5757857813 0.5779489908 -0.408773030195 +1403636720163555584.0000000000 0.3015346745 5.1190783567 -0.5769652692 0.4086011557 0.5764575439 0.5782359384 -0.407903168927 +1403636720213555456.0000000000 0.3201833736 5.1018305790 -0.5821636130 0.4080436529 0.5768732750 0.5779298087 -0.408307161428 +1403636720263555584.0000000000 0.3384832105 5.0849116068 -0.5882602339 0.4080198272 0.5768472760 0.5777973723 -0.408555060381 +1403636720313555456.0000000000 0.3563610234 5.0683476285 -0.5952544644 0.4075944285 0.5770778558 0.5774603338 -0.409130166561 +1403636720363555584.0000000000 0.3739975765 5.0523268716 -0.6032551608 0.4076063429 0.5767317651 0.5777811637 -0.409153354072 +1403636720413555456.0000000000 0.3914934061 5.0367115841 -0.6120759387 0.4070663842 0.5765686423 0.5779600990 -0.409667772052 +1403636720463555584.0000000000 0.4087690048 5.0216263934 -0.6206848246 0.4059971750 0.5767156737 0.5782177739 -0.410157934854 +1403636720513555456.0000000000 0.4260117041 5.0072264131 -0.6279096700 0.4052090924 0.5767880354 0.5785111081 -0.410421797043 +1403636720563555584.0000000000 0.4429544668 4.9934803340 -0.6334447755 0.4043441738 0.5766638192 0.5786194247 -0.411295745323 +1403636720613555456.0000000000 0.4596057324 4.9805370499 -0.6376476887 0.4043880620 0.5761051537 0.5797853708 -0.410392581555 +1403636720663555584.0000000000 0.4759102621 4.9679958282 -0.6394946490 0.4034540743 0.5759161512 0.5799530066 -0.411339162704 +1403636720713555456.0000000000 0.4924554620 4.9563673658 -0.6394531870 0.4045209506 0.5752972399 0.5793777644 -0.41196758649 +1403636720763555584.0000000000 0.5083114581 4.9454625544 -0.6375643362 0.4044401940 0.5765861328 0.5784284015 -0.411578844608 +1403636720813555456.0000000000 0.5232064615 4.9355863589 -0.6347867448 0.4058032202 0.5785095055 0.5767981393 -0.409822406615 +1403636720863555584.0000000000 0.5373355170 4.9265577429 -0.6322640629 0.4083709353 0.5807218987 0.5748299140 -0.406897807237 +1403636720913555456.0000000000 0.5511785224 4.9182057375 -0.6307150474 0.4109563941 0.5842645222 0.5713278305 -0.404146409515 +1403636720963555584.0000000000 0.5644278065 4.9104720966 -0.6306587638 0.4142692249 0.5877156153 0.5669372326 -0.40193723277 +1403636721013555456.0000000000 0.5775661345 4.9029463159 -0.6321815661 0.4168085612 0.5913400495 0.5619933454 -0.400937712003 +1403636721063555584.0000000000 0.5903374959 4.8959726910 -0.6351472680 0.4201487938 0.5948608181 0.5567270237 -0.399588061948 +1403636721113555456.0000000000 0.6029910551 4.8897486136 -0.6397742187 0.4232511893 0.5991247423 0.5513567510 -0.397383576838 +1403636721163555584.0000000000 0.6153764012 4.8844558576 -0.6452772103 0.4283536405 0.6029605065 0.5453188127 -0.39443526557 +1403636721213555456.0000000000 0.6281218745 4.8794867613 -0.6505206026 0.4321360451 0.6074039264 0.5394058323 -0.39161238079 +1403636721263555584.0000000000 0.6411898071 4.8750485993 -0.6540508276 0.4363672587 0.6107827137 0.5331873465 -0.390178607407 +1403636721313555456.0000000000 0.6541818209 4.8712321869 -0.6561087404 0.4391070675 0.6143817471 0.5290652154 -0.387053032583 +1403636721363555584.0000000000 0.6682087160 4.8679539355 -0.6561615125 0.4419727921 0.6174998382 0.5252720628 -0.383983412284 +1403636721413555456.0000000000 0.6826820062 4.8651281207 -0.6541110973 0.4450289972 0.6194893023 0.5221784602 -0.381460157358 +1403636721463555584.0000000000 0.6976776284 4.8623198052 -0.6509319913 0.4466148074 0.6219519627 0.5196014440 -0.379111209741 +1403636721513555456.0000000000 0.7131288446 4.8600095910 -0.6473779144 0.4488435581 0.6244783904 0.5173377817 -0.375403542778 +1403636721563555584.0000000000 0.7287052199 4.8581290535 -0.6444587371 0.4507639298 0.6275946672 0.5144275421 -0.371888581807 +1403636721613555456.0000000000 0.7445331153 4.8564776601 -0.6430173172 0.4531403548 0.6303933722 0.5119356892 -0.367681744634 +1403636721663555584.0000000000 0.7606291578 4.8547649832 -0.6431502389 0.4546886247 0.6330085691 0.5099309904 -0.364045039848 +1403636721713555456.0000000000 0.7768018800 4.8531131137 -0.6442363092 0.4571906338 0.6340828917 0.5078998521 -0.361874772581 +1403636721763555584.0000000000 0.7934298933 4.8513648094 -0.6470531017 0.4590421041 0.6350871957 0.5071783565 -0.358768330994 +1403636721813555456.0000000000 0.8104049740 4.8492512840 -0.6509610951 0.4600836558 0.6358918796 0.5059047904 -0.357805659742 +1403636721863555584.0000000000 0.8274104357 4.8470461454 -0.6560616722 0.4606501437 0.6364805787 0.5046143184 -0.357852354653 +1403636721913555456.0000000000 0.8443480187 4.8446214380 -0.6622150436 0.4611878224 0.6366757452 0.5042428334 -0.357335910542 +1403636721963555584.0000000000 0.8613842541 4.8422438249 -0.6690552403 0.4628692797 0.6354943178 0.5054851212 -0.355504984645 +1403636722013555456.0000000000 0.8784471722 4.8397526716 -0.6750416993 0.4646964842 0.6340902437 0.5071487053 -0.353251937257 +1403636722063555584.0000000000 0.8954568760 4.8368447556 -0.6791935091 0.4661471276 0.6326678303 0.5088729041 -0.351406658188 +1403636722113555456.0000000000 0.9126188322 4.8332254736 -0.6810870331 0.4659464424 0.6320697818 0.5098844955 -0.351282656902 +1403636722163555584.0000000000 0.9299963074 4.8289191761 -0.6810891709 0.4645533279 0.6325010325 0.5098593763 -0.352386245305 +1403636722213555456.0000000000 0.9473590064 4.8241541319 -0.6790892045 0.4633481114 0.6326670229 0.5099583576 -0.353529969371 +1403636722263555584.0000000000 0.9647768752 4.8188579539 -0.6759219120 0.4617231573 0.6331213892 0.5100580230 -0.354696836433 +1403636722313555456.0000000000 0.9819960050 4.8131903417 -0.6726395302 0.4605546418 0.6331487274 0.5097421228 -0.356616150936 +1403636722363555584.0000000000 0.9993358627 4.8075065559 -0.6707618682 0.4597764404 0.6335194692 0.5097442421 -0.356958701554 +1403636722413555456.0000000000 1.0166166606 4.8021227150 -0.6703316310 0.4601787882 0.6342310918 0.5091335024 -0.356047022022 +1403636722463555584.0000000000 1.0338645953 4.7968248526 -0.6711172588 0.4614753463 0.6351309566 0.5074944542 -0.35510357883 +1403636722513555456.0000000000 1.0511292557 4.7913743951 -0.6730541069 0.4621908175 0.6365471321 0.5055647303 -0.354389193238 +1403636722563555584.0000000000 1.0684950881 4.7857760174 -0.6760707491 0.4629273633 0.6377920772 0.5042058078 -0.353123244582 +1403636722613555456.0000000000 1.0856061600 4.7800370396 -0.6798341141 0.4642800089 0.6381838075 0.5038005953 -0.351212843352 +1403636722663555584.0000000000 1.1026887258 4.7740908652 -0.6841172550 0.4649618212 0.6389881827 0.5031548723 -0.349771041892 +1403636722713555456.0000000000 1.1195713441 4.7678857968 -0.6886300246 0.4661668100 0.6391876224 0.5024753896 -0.348778112152 +1403636722763555584.0000000000 1.1363517920 4.7613774164 -0.6934387138 0.4670351530 0.6394729156 0.5025063863 -0.347044504015 +1403636722813555456.0000000000 1.1530245649 4.7545745617 -0.6969453334 0.4672834446 0.6398261855 0.5027629265 -0.345684935411 +1403636722863555584.0000000000 1.1698859280 4.7472014465 -0.6978851691 0.4681162759 0.6397223119 0.5027793892 -0.344725110292 +1403636722913555456.0000000000 1.1866977476 4.7391614058 -0.6971615174 0.4675594296 0.6404519751 0.5021433229 -0.345052938762 +1403636722963555584.0000000000 1.2035094456 4.7306317493 -0.6947114184 0.4666071406 0.6411639893 0.5017658643 -0.345568419425 +1403636723013555456.0000000000 1.2212584081 4.7215071303 -0.6911256318 0.4658280521 0.6416253737 0.5007923590 -0.347171598657 +1403636723063555584.0000000000 1.2375824740 4.7123793324 -0.6848919862 0.4651072362 0.6420844807 0.4994413445 -0.349229325592 +1403636723113555456.0000000000 1.2539424209 4.7032463416 -0.6788632763 0.4646844078 0.6423335768 0.4989398766 -0.350049963312 +1403636723163555584.0000000000 1.2702830057 4.6941981748 -0.6734926169 0.4647207784 0.6424136534 0.4986978791 -0.350199545168 +1403636723213555456.0000000000 1.2866240631 4.6850370286 -0.6692958266 0.4644245516 0.6427734494 0.4983970576 -0.350360530973 +1403636723263555584.0000000000 1.3030353643 4.6758972648 -0.6665346802 0.4645948921 0.6427460692 0.4992022551 -0.349036080328 +1403636723313555456.0000000000 1.3193631632 4.6669164603 -0.6649801606 0.4661832676 0.6419267763 0.4999211538 -0.347393170551 +1403636723363555584.0000000000 1.3355858242 4.6578382940 -0.6641976079 0.4673647957 0.6424149919 0.4992306391 -0.345892895201 +1403636723413555456.0000000000 1.3517811846 4.6489606566 -0.6645889147 0.4702243685 0.6429693503 0.4978127425 -0.343018849661 +1403636723463555584.0000000000 1.3677535726 4.6401744230 -0.6651846859 0.4746372105 0.6433116911 0.4952748650 -0.33995940137 +1403636723513555456.0000000000 1.3835577094 4.6309615789 -0.6655357415 0.4792014926 0.6444095174 0.4900047807 -0.33911298734 +1403636723563555584.0000000000 1.3982146170 4.6212672253 -0.6637126611 0.4840593775 0.6451209893 0.4828402097 -0.341131587682 +1403636723613555456.0000000000 1.4136572768 4.6109083060 -0.6605120592 0.4887947478 0.6454361368 0.4761133053 -0.343231712338 +1403636723663555584.0000000000 1.4304365748 4.6001927506 -0.6562631070 0.4904234771 0.6477152762 0.4719193267 -0.342406020911 +1403636723713555456.0000000000 1.4478954367 4.5887684297 -0.6513482348 0.4893564471 0.6514231151 0.4705466065 -0.33876848133 +1403636723763555584.0000000000 1.4665899828 4.5765727303 -0.6455011403 0.4875554721 0.6557195348 0.4692342658 -0.334874240691 +1403636723813555456.0000000000 1.4858073909 4.5637647465 -0.6401766367 0.4846607561 0.6601700515 0.4679847560 -0.332068852503 +1403636723863555584.0000000000 1.5054059010 4.5508401548 -0.6355269257 0.4827834929 0.6635706444 0.4668507208 -0.329612656634 +1403636723913555456.0000000000 1.5250198112 4.5377031338 -0.6324209293 0.4807017918 0.6668396185 0.4658956578 -0.327401812158 +1403636723963555584.0000000000 1.5446282126 4.5245346029 -0.6310260845 0.4780226319 0.6704050512 0.4652792857 -0.324910167586 +1403636724013555456.0000000000 1.5640600590 4.5117955302 -0.6311464322 0.4763267910 0.6738305958 0.4646480986 -0.321196607771 +1403636724063555584.0000000000 1.5828569335 4.4997467928 -0.6324006798 0.4754114606 0.6776537498 0.4626364311 -0.317390723204 +1403636724113555456.0000000000 1.6013498081 4.4882986134 -0.6353223872 0.4749595718 0.6819979206 0.4600477602 -0.312487279471 +1403636724163555584.0000000000 1.6190471743 4.4775773648 -0.6388711176 0.4775895417 0.6849063635 0.4558248676 -0.308277785496 +1403636724213555456.0000000000 1.6359594936 4.4672691012 -0.6437899201 0.4788133889 0.6893426292 0.4504840879 -0.304316553629 +1403636724263555584.0000000000 1.6518308153 4.4577884592 -0.6494681611 0.4818164213 0.6931957924 0.4444006092 -0.299734262576 +1403636724313555456.0000000000 1.6668899449 4.4487438081 -0.6556383051 0.4860919522 0.6963811825 0.4380217670 -0.294796191137 +1403636724363555584.0000000000 1.6807113922 4.4401675526 -0.6617927002 0.4906499566 0.6994396161 0.4307843405 -0.290640147652 +1403636724413555456.0000000000 1.6947681924 4.4314739078 -0.6664950335 0.4959828311 0.7018857540 0.4233060526 -0.286652063354 +1403636724463555584.0000000000 1.7084515563 4.4225462889 -0.6696304550 0.4997595850 0.7043905717 0.4168135711 -0.283444397923 +1403636724513555456.0000000000 1.7216966767 4.4135600747 -0.6708702462 0.5043865870 0.7054636276 0.4115409803 -0.280266413317 +1403636724563555584.0000000000 1.7351872410 4.4039346937 -0.6709390621 0.5078256192 0.7065662515 0.4067907264 -0.27820599838 +1403636724613555456.0000000000 1.7480347140 4.3943783304 -0.6694177642 0.5097802335 0.7082074487 0.4032776344 -0.275560288734 +1403636724663555584.0000000000 1.7604826348 4.3843944639 -0.6651330322 0.5114841917 0.7092274469 0.4005082868 -0.273812823713 +1403636724713555456.0000000000 1.7727179522 4.3739593825 -0.6589211009 0.5121762960 0.7105119941 0.3982884148 -0.272423359197 +1403636724763555584.0000000000 1.7845807151 4.3632435992 -0.6505391263 0.5123168005 0.7117328428 0.3967628340 -0.271195704306 +1403636724813555456.0000000000 1.7964077715 4.3520460337 -0.6402090628 0.5119692974 0.7127595457 0.3960120155 -0.270251275982 +1403636724863555584.0000000000 1.8078968596 4.3405431710 -0.6277908677 0.5110303861 0.7137706873 0.3954783519 -0.270141118067 +1403636724913555456.0000000000 1.8190289521 4.3286376280 -0.6134354534 0.5095656293 0.7147599566 0.3948378022 -0.271227181094 +1403636724963555584.0000000000 1.8298889575 4.3165284739 -0.5971756258 0.5077225836 0.7157902927 0.3941813802 -0.272915874444 +1403636725013555456.0000000000 1.8403011946 4.3044558820 -0.5789537369 0.5060056784 0.7164842919 0.3933971653 -0.27540367314 +1403636725063555584.0000000000 1.8506610265 4.2925893805 -0.5586379887 0.5050165447 0.7167065986 0.3926546421 -0.277690967 +1403636725113555456.0000000000 1.8610531426 4.2811010443 -0.5367737116 0.5036261393 0.7171593152 0.3924697608 -0.279303983651 +1403636725163555584.0000000000 1.8711224606 4.2703105920 -0.5142566804 0.5018828415 0.7179168592 0.3924369168 -0.280539236342 +1403636725213555456.0000000000 1.8812447830 4.2602391430 -0.4922907551 0.5021073233 0.7173839128 0.3932047141 -0.280425766121 +1403636725263555584.0000000000 1.8912273669 4.2504437458 -0.4713423747 0.5013789089 0.7174004792 0.3937392528 -0.280936190266 +1403636725313555456.0000000000 1.9012548528 4.2415640080 -0.4519694927 0.5019717900 0.7168804174 0.3951732453 -0.279186130262 +1403636725363555584.0000000000 1.9111346337 4.2331793310 -0.4338669197 0.5023020181 0.7164620622 0.3960210494 -0.27846386544 +1403636725413555456.0000000000 1.9208164334 4.2252223671 -0.4172451779 0.5033635106 0.7156096431 0.3969950684 -0.27734983415 +1403636725463555584.0000000000 1.9302190360 4.2174700484 -0.4021853135 0.5037507634 0.7153179826 0.3974079838 -0.2768072372 +1403636725513555456.0000000000 1.9396033191 4.2100706510 -0.3886963532 0.5043755761 0.7148332432 0.3982988665 -0.275638759137 +1403636725563555584.0000000000 1.9489922970 4.2028742194 -0.3769832022 0.5043307320 0.7150235716 0.3987973996 -0.27450398693 +1403636725613555456.0000000000 1.9580155648 4.1960001349 -0.3665409980 0.5051321150 0.7145235373 0.3993983786 -0.273456753697 +1403636725663555584.0000000000 1.9665440495 4.1891816150 -0.3574897743 0.5063990856 0.7137183580 0.3988466263 -0.274020875669 +1403636725713555456.0000000000 1.9746968407 4.1824192996 -0.3499839538 0.5064303663 0.7138339685 0.3983365382 -0.274403629451 +1403636725763555584.0000000000 1.9825921458 4.1755826019 -0.3442024321 0.5061074761 0.7139887651 0.3986011630 -0.274212287836 +1403636725813555456.0000000000 1.9903327090 4.1688716763 -0.3398345952 0.5064208627 0.7136584465 0.3987343537 -0.274299921023 +1403636725863555584.0000000000 1.9978584034 4.1621863345 -0.3369600588 0.5049360510 0.7145003609 0.3991092195 -0.274300290873 +1403636725913555456.0000000000 2.0048572330 4.1557069760 -0.3348849501 0.5040102318 0.7149248249 0.3983173331 -0.276042538688 +1403636725963555584.0000000000 2.0117221494 4.1494471512 -0.3343331950 0.5031765216 0.7151959688 0.3985561554 -0.276516012659 +1403636726013555456.0000000000 2.0183608582 4.1434618625 -0.3346928555 0.5033346467 0.7148207216 0.3981864746 -0.277728465887 +1403636726063555584.0000000000 2.0247772164 4.1378545509 -0.3363711005 0.5038159993 0.7141134593 0.3989011250 -0.277649596762 +1403636726113555456.0000000000 2.0311345389 4.1325044756 -0.3392936085 0.5044828990 0.7133569924 0.3996953078 -0.277240810449 +1403636726163555584.0000000000 2.0372376509 4.1273135368 -0.3431694166 0.5060555316 0.7119045799 0.3999184585 -0.2777856991 +1403636726213555456.0000000000 2.0434301501 4.1220995253 -0.3484905366 0.5065401158 0.7111892409 0.4002398617 -0.278271500275 +1403636726263555584.0000000000 2.0498460341 4.1167953841 -0.3543721824 0.5069655069 0.7104848131 0.4011504164 -0.277984979196 +1403636726313555456.0000000000 2.0561445196 4.1112705545 -0.3592081149 0.5070192493 0.7099508316 0.4015785965 -0.278632245873 +1403636726363555584.0000000000 2.0626502677 4.1057389645 -0.3627260654 0.5080567338 0.7088376676 0.4020187569 -0.278941634244 +1403636726413555456.0000000000 2.0684455920 4.1002429897 -0.3636118315 0.5081966014 0.7081803689 0.4025603353 -0.279574598126 +1403636726463555584.0000000000 2.0738259843 4.0946763906 -0.3621350598 0.5082088259 0.7076255801 0.4026086922 -0.28088443983 +1403636726513555456.0000000000 2.0789212661 4.0890728005 -0.3589682648 0.5072433532 0.7078932495 0.4016826331 -0.28327087779 +1403636726563555584.0000000000 2.0836249429 4.0833479583 -0.3532716122 0.5048263772 0.7090831487 0.3984017651 -0.289184112069 +1403636726613555456.0000000000 2.0894858187 4.0773652266 -0.3461052999 0.5013097917 0.7110488953 0.3941643225 -0.296196637491 +1403636726663555584.0000000000 2.0953734868 4.0725164333 -0.3375940865 0.4993941802 0.7118556271 0.3899695625 -0.302969898199 +1403636726713555456.0000000000 2.1030387143 4.0688494646 -0.3286142659 0.4989248575 0.7119675971 0.3897178606 -0.303802758982 +1403636726763555584.0000000000 2.1116634184 4.0665865416 -0.3179012436 0.5011789983 0.7103248381 0.3913933465 -0.301777209736 +1403636726813555456.0000000000 2.1206515253 4.0654796005 -0.3051526639 0.5037927207 0.7082239289 0.3946060665 -0.298157363591 +1403636726863555584.0000000000 2.1308846477 4.0643883590 -0.2905738347 0.5062562136 0.7053040533 0.3988580931 -0.295233907507 +1403636726913555456.0000000000 2.1420556813 4.0632552477 -0.2746590205 0.5075779569 0.7030767216 0.4026781168 -0.293083734512 +1403636726963555584.0000000000 2.1539548769 4.0619022492 -0.2572878335 0.5082472414 0.7012856431 0.4057615583 -0.291960179284 +1403636727013555456.0000000000 2.1655448575 4.0608239334 -0.2383168784 0.5085450582 0.7000522674 0.4075453088 -0.291917056471 +1403636727063555584.0000000000 2.1777223389 4.0597041250 -0.2185999223 0.5093980861 0.6986438235 0.4094974413 -0.291070856224 +1403636727113555456.0000000000 2.1901421965 4.0584104836 -0.1999374174 0.5096261825 0.6976754924 0.4116101910 -0.290012261925 +1403636727163555584.0000000000 2.2031353565 4.0569007286 -0.1827413365 0.5100917925 0.6967404683 0.4140277372 -0.287993256567 +1403636727213555456.0000000000 2.2161680592 4.0547433342 -0.1671251229 0.5106798359 0.6958329156 0.4161483943 -0.28608245794 +1403636727263555584.0000000000 2.2290259009 4.0519665628 -0.1530320665 0.5112909402 0.6949947927 0.4181054662 -0.284168315841 +1403636727313555456.0000000000 2.2418682268 4.0484698935 -0.1403980781 0.5120636543 0.6942137047 0.4199756649 -0.281919468983 +1403636727363555584.0000000000 2.2546362854 4.0441163880 -0.1284364873 0.5111925316 0.6946426186 0.4212213595 -0.280582241737 +1403636727413555456.0000000000 2.2669932891 4.0390415452 -0.1170833468 0.5114379374 0.6943114760 0.4219535157 -0.279853606562 +1403636727463555584.0000000000 2.2791355078 4.0333100573 -0.1063885662 0.5119939309 0.6938497467 0.4225184923 -0.279128764939 +1403636727513555456.0000000000 2.2910091474 4.0265211577 -0.0951043146 0.5121463095 0.6937414043 0.4210922990 -0.281265528041 +1403636727563555584.0000000000 2.3026544505 4.0187891556 -0.0828021762 0.5114490659 0.6942749641 0.4188391741 -0.28456260028 +1403636727613555456.0000000000 2.3146659358 4.0104661136 -0.0695425251 0.5119444435 0.6939418387 0.4177532357 -0.286076642537 +1403636727663555584.0000000000 2.3267228099 4.0013651468 -0.0552565055 0.5111051688 0.6945211530 0.4166114139 -0.287831208106 +1403636727713555456.0000000000 2.3384228346 3.9923133623 -0.0394496883 0.5102205678 0.6952285560 0.4172424529 -0.286776851584 +1403636727763555584.0000000000 2.3497393086 3.9828960703 -0.0216202882 0.5102600404 0.6951711137 0.4180102315 -0.285725848129 +1403636727813555456.0000000000 2.3611225229 3.9727246108 -0.0023261319 0.5104489573 0.6948772663 0.4191062910 -0.284494927221 +1403636727863555584.0000000000 2.3727819937 3.9621407647 0.0181182554 0.5122027891 0.6937451850 0.4217199819 -0.280210952763 +1403636727913555456.0000000000 2.3843620278 3.9505266395 0.0385266604 0.5143691249 0.6921982336 0.4239272993 -0.276715835454 +1403636727963555584.0000000000 2.3955039393 3.9377978467 0.0581163399 0.5148673671 0.6918226445 0.4245317511 -0.275800317731 +1403636728013555456.0000000000 2.4062215041 3.9238927610 0.0763559010 0.5140781154 0.6925351778 0.4238667130 -0.276506290095 +1403636728063555584.0000000000 2.4165258539 3.9091032550 0.0930055961 0.5131450876 0.6932916422 0.4230073305 -0.277657372037 +1403636728113555456.0000000000 2.4264213529 3.8932897972 0.1085171508 0.5126060767 0.6937762578 0.4207017312 -0.280926267259 +1403636728163555584.0000000000 2.4363001720 3.8771309806 0.1223932286 0.5127468683 0.6939752189 0.4192113297 -0.282402028345 +1403636728213555456.0000000000 2.4460927997 3.8602238727 0.1347776611 0.5126101074 0.6941011052 0.4178958681 -0.284284324117 +1403636728263555584.0000000000 2.4557922103 3.8429510515 0.1455425255 0.5125441647 0.6942547413 0.4169980486 -0.285344460021 +1403636728313555456.0000000000 2.4655972851 3.8249873623 0.1547449311 0.5117416690 0.6949325440 0.4162073749 -0.286287695547 +1403636728363555584.0000000000 2.4754973965 3.8066148783 0.1622201878 0.5117135133 0.6950868399 0.4163447511 -0.285763212287 +1403636728413555456.0000000000 2.4852483157 3.7873159382 0.1684655614 0.5094578516 0.6966565873 0.4145570251 -0.288556354564 +1403636728463555584.0000000000 2.4949295518 3.7678775604 0.1734938709 0.5069655886 0.6985572396 0.4111287230 -0.293218089723 +1403636728513555456.0000000000 2.5051506736 3.7484224945 0.1770632503 0.5033007989 0.7012190556 0.4074811290 -0.298226879099 +1403636728563555584.0000000000 2.5160969231 3.7292822333 0.1788583866 0.5010280989 0.7023617306 0.4062923769 -0.30097399863 +1403636728613555456.0000000000 2.5275513150 3.7106864355 0.1797407131 0.4997914626 0.7021317743 0.4062249406 -0.303645785472 +1403636728663555584.0000000000 2.5400730696 3.6927047968 0.1796616597 0.5001370488 0.6998837271 0.4106776089 -0.302274052157 +1403636728713555456.0000000000 2.5531245050 3.6749905313 0.1805268454 0.5012038838 0.6960791374 0.4165375356 -0.3012722736 +1403636728763555584.0000000000 2.5663417091 3.6572190351 0.1833067367 0.5011949895 0.6918926195 0.4234382179 -0.301310904582 +1403636728813555456.0000000000 2.5798857340 3.6393404556 0.1878460107 0.5007492675 0.6872059580 0.4311814996 -0.301795720414 +1403636728863555584.0000000000 2.5938948914 3.6208290208 0.1944077253 0.4998532142 0.6829368783 0.4377146769 -0.303561931196 +1403636728913555456.0000000000 2.6081169636 3.6023289930 0.2018205723 0.4997668177 0.6782532363 0.4433995370 -0.305945298831 +1403636728963555584.0000000000 2.6223303961 3.5835655878 0.2090382270 0.4989247590 0.6747894231 0.4476175989 -0.308823257676 +1403636729013555456.0000000000 2.6367265107 3.5644314989 0.2153511633 0.4984216629 0.6713441355 0.4513039178 -0.311765410811 +1403636729063555584.0000000000 2.6512749214 3.5451171039 0.2203622394 0.4985486020 0.6679452003 0.4545181040 -0.314184331091 +1403636729113555456.0000000000 2.6660310953 3.5254993561 0.2237970637 0.4979075440 0.6654933081 0.4570513838 -0.316718750728 +1403636729163555584.0000000000 2.6812431785 3.5056897121 0.2257011249 0.4970078889 0.6639056055 0.4595657351 -0.317823599639 +1403636729213555456.0000000000 2.6967200498 3.4853537120 0.2261267234 0.4945428453 0.6639012775 0.4618197059 -0.318410155518 +1403636729263555584.0000000000 2.7121048611 3.4643882772 0.2258285191 0.4921081286 0.6641072254 0.4626652061 -0.320518470588 +1403636729313555456.0000000000 2.7277242071 3.4434415523 0.2241065463 0.4914357893 0.6635300415 0.4638197426 -0.321076307724 +1403636729363555584.0000000000 2.7435520873 3.4218609481 0.2219596893 0.4906313863 0.6632941582 0.4641258163 -0.322349079495 +1403636729413555456.0000000000 2.7596434441 3.4002877091 0.2198572897 0.4910442242 0.6624319374 0.4645520575 -0.322879054848 +1403636729463555584.0000000000 2.7764318866 3.3782413651 0.2191375701 0.4910293021 0.6620412826 0.4648755695 -0.323237172 +1403636729513555456.0000000000 2.7940317499 3.3555885084 0.2199877068 0.4907076055 0.6618932077 0.4650937244 -0.323714774159 +1403636729563555584.0000000000 2.8118924152 3.3327724297 0.2223849633 0.4899219126 0.6622185134 0.4652280490 -0.324046327722 +1403636729613555456.0000000000 2.8293129147 3.3099321090 0.2270401346 0.4892264531 0.6625544113 0.4656455569 -0.32381066216 +1403636729663555584.0000000000 2.8474409906 3.2868463185 0.2334388485 0.4886934631 0.6629283871 0.4656996315 -0.323772305736 +1403636729713555456.0000000000 2.8656146311 3.2635683895 0.2408330628 0.4881526840 0.6632560263 0.4650123340 -0.324902954609 +1403636729763555584.0000000000 2.8836041509 3.2404614833 0.2483400529 0.4872399329 0.6641345796 0.4657146325 -0.323469301679 +1403636729813555456.0000000000 2.9018526761 3.2170805059 0.2552354961 0.4857333713 0.6655242654 0.4659182718 -0.32258442012 +1403636729863555584.0000000000 2.9205536528 3.1937726957 0.2609108409 0.4842642725 0.6667749600 0.4669190960 -0.320758203162 +1403636729913555456.0000000000 2.9393066282 3.1701348149 0.2654633770 0.4821977219 0.6684876539 0.4663576056 -0.321123336568 +1403636729963555584.0000000000 2.9579005431 3.1467036123 0.2684435853 0.4815590523 0.6689629762 0.4674324967 -0.319525079798 +1403636730013555456.0000000000 2.9758979636 3.1231177834 0.2706437120 0.4800790018 0.6701269168 0.4674218287 -0.319328829729 +1403636730063555584.0000000000 2.9936313507 3.0994314055 0.2719238797 0.4793438021 0.6704628579 0.4678118925 -0.319156871824 +1403636730113555456.0000000000 3.0108944327 3.0757225068 0.2721126608 0.4786847386 0.6705494289 0.4683455882 -0.319181444546 +1403636730163555584.0000000000 3.0278517048 3.0520563711 0.2714571230 0.4782717752 0.6708316507 0.4677788891 -0.320037367097 +1403636730213555456.0000000000 3.0447454680 3.0286477563 0.2693408726 0.4778459388 0.6710102019 0.4686817492 -0.318976465706 +1403636730263555584.0000000000 3.0612732014 3.0053273417 0.2664458769 0.4777519569 0.6707821139 0.4690411935 -0.319068616628 +1403636730313555456.0000000000 3.0775132701 2.9821510831 0.2629042168 0.4770667142 0.6711309048 0.4680617560 -0.320794095117 +1403636730363555584.0000000000 3.0938829619 2.9591755890 0.2578261781 0.4765031417 0.6712429415 0.4684051619 -0.320896048182 +1403636730413555456.0000000000 3.1101006074 2.9364504787 0.2519538615 0.4758959228 0.6714332188 0.4693870641 -0.319962946809 +1403636730463555584.0000000000 3.1254474348 2.9140235200 0.2470376384 0.4730795678 0.6730992002 0.4706568034 -0.318771646557 +1403636730513555456.0000000000 3.1411286220 2.8918170713 0.2436013503 0.4710516460 0.6743269835 0.4726720329 -0.316187626985 +1403636730563555584.0000000000 3.1555981715 2.8698287498 0.2426751659 0.4677225516 0.6764384485 0.4738181904 -0.314901512585 +1403636730613555456.0000000000 3.1685007361 2.8485453715 0.2434320315 0.4654062761 0.6778558142 0.4746670574 -0.314005856644 +1403636730663555584.0000000000 3.1796119183 2.8281967666 0.2464529616 0.4640857182 0.6787343755 0.4749402645 -0.313649229151 +1403636730713555456.0000000000 3.1889323455 2.8085490453 0.2528899575 0.4631550322 0.6790899038 0.4754038261 -0.313553058833 +1403636730763555584.0000000000 3.1964289752 2.7896146283 0.2616980439 0.4627108063 0.6794349425 0.4760531237 -0.31247446619 +1403636730813555456.0000000000 3.2035101879 2.7709297130 0.2718761987 0.4624792610 0.6793174584 0.4765849741 -0.312261887489 +1403636730863555584.0000000000 3.2102752831 2.7527580091 0.2830901574 0.4609589805 0.6804703166 0.4757169165 -0.313321531076 +1403636730913555456.0000000000 3.2158802245 2.7349466149 0.2943182452 0.4587468773 0.6821764373 0.4740595457 -0.315363533309 +1403636730963555584.0000000000 3.2206774217 2.7179267850 0.3048520926 0.4571064277 0.6834832845 0.4710180909 -0.31944682114 +1403636731013555456.0000000000 3.2244053310 2.7017356003 0.3139138807 0.4555436109 0.6848980488 0.4677069544 -0.323488618249 +1403636731063555584.0000000000 3.2269278006 2.6866234486 0.3226171933 0.4559215740 0.6849091769 0.4622891106 -0.330641370634 +1403636731113555456.0000000000 3.2289575854 2.6732387436 0.3301913318 0.4585880445 0.6834915013 0.4577370014 -0.336174375263 +1403636731163555584.0000000000 3.2310016912 2.6612907997 0.3360068376 0.4612126881 0.6819107669 0.4546982126 -0.339897187067 +1403636731213555456.0000000000 3.2332427009 2.6510640041 0.3401208233 0.4648970608 0.6797178226 0.4539249097 -0.340303659941 +1403636731263555584.0000000000 3.2359499723 2.6423175468 0.3429537517 0.4694012917 0.6768993702 0.4545017686 -0.338965798308 +1403636731313555456.0000000000 3.2391618017 2.6347913132 0.3443592983 0.4735548953 0.6744307902 0.4560984657 -0.335950978556 +1403636731363555584.0000000000 3.2426503667 2.6277998881 0.3447962236 0.4761687375 0.6728732868 0.4576755712 -0.333223565858 +1403636731413555456.0000000000 3.2466499659 2.6213485944 0.3436153645 0.4781914250 0.6716246694 0.4603865756 -0.32908580252 +1403636731463555584.0000000000 3.2506410675 2.6149900601 0.3420014882 0.4794112200 0.6708219409 0.4608847917 -0.328249926887 +1403636731513555456.0000000000 3.2550416525 2.6085953102 0.3393084129 0.4782473375 0.6716749293 0.4605980158 -0.328605753839 +1403636731563555584.0000000000 3.2595804416 2.6021535545 0.3360431166 0.4756614363 0.6732815737 0.4589178248 -0.331409943409 +1403636731613555456.0000000000 3.2642765103 2.5963694358 0.3320411784 0.4743107632 0.6742548863 0.4573234810 -0.333563909806 +1403636731663555584.0000000000 3.2694245712 2.5912388531 0.3269577291 0.4728679175 0.6751462781 0.4562171867 -0.335319719566 +1403636731713555456.0000000000 3.2747594557 2.5873597526 0.3205983452 0.4733600205 0.6749184759 0.4563121404 -0.334954582604 +1403636731763555584.0000000000 3.2806388748 2.5842768770 0.3129275990 0.4747298033 0.6739676543 0.4579670022 -0.332664154693 +1403636731813555456.0000000000 3.2869962233 2.5817136322 0.3044217520 0.4757615960 0.6731923144 0.4589500859 -0.33140282168 +1403636731863555584.0000000000 3.2936284545 2.5796468198 0.2948901156 0.4768156821 0.6722982445 0.4603848939 -0.32970839418 +1403636731913555456.0000000000 3.3003142001 2.5777858990 0.2846914314 0.4777094569 0.6712829158 0.4614441442 -0.329001859369 +1403636731963555584.0000000000 3.3070057890 2.5760583662 0.2738866938 0.4782945995 0.6706973306 0.4614757208 -0.329301572867 +1403636732013555456.0000000000 3.3137030216 2.5745471937 0.2620351191 0.4786274204 0.6701909864 0.4619357958 -0.329203819323 +1403636732063555584.0000000000 3.3204964437 2.5733673133 0.2493857889 0.4800069276 0.6689752603 0.4620574512 -0.329497135518 +1403636732113555456.0000000000 3.3274765581 2.5724277979 0.2354835755 0.4797235144 0.6690398277 0.4618453273 -0.330075676732 +1403636732163555584.0000000000 3.3346865218 2.5716519295 0.2205400824 0.4801992933 0.6683500813 0.4626145417 -0.329703796452 +1403636732213555456.0000000000 3.3420189811 2.5713714134 0.2065260770 0.4814158492 0.6672894293 0.4624737034 -0.330275144951 +1403636732263555584.0000000000 3.3499431559 2.5712879573 0.1935951605 0.4827562746 0.6660351579 0.4633633985 -0.32960265268 +1403636732313555456.0000000000 3.3587361474 2.5706764966 0.1823642500 0.4826574438 0.6657820859 0.4628083115 -0.331035455477 +1403636732363555584.0000000000 3.3681199869 2.5706317166 0.1721309624 0.4835653691 0.6650208547 0.4643680080 -0.329050375862 +1403636732413555456.0000000000 3.3777529695 2.5705542385 0.1646938104 0.4868411417 0.6626522680 0.4659626908 -0.326736048338 +1403636732463555584.0000000000 3.3877282378 2.5704383060 0.1595513531 0.4919895165 0.6587892926 0.4686434166 -0.322980389028 +1403636732513555456.0000000000 3.3990925811 2.5693620036 0.1563754065 0.4980574770 0.6541161964 0.4718437123 -0.31848746039 +1403636732563555584.0000000000 3.4107393643 2.5669177530 0.1545919201 0.5029592341 0.6502369362 0.4738614449 -0.315720234882 +1403636732613555456.0000000000 3.4224106535 2.5627964966 0.1542177878 0.5072683787 0.6467287672 0.4753113729 -0.313846765882 +1403636732663555584.0000000000 3.4343171548 2.5562721415 0.1557023696 0.5085195931 0.6454430182 0.4745488597 -0.315617669571 +1403636732713555456.0000000000 3.4465813494 2.5475375349 0.1589030849 0.5076969530 0.6458455050 0.4722981924 -0.319471133318 +1403636732763555584.0000000000 3.4596249555 2.5368994357 0.1635309422 0.5053585401 0.6473489365 0.4702339312 -0.323159635972 +1403636732813555456.0000000000 3.4720597152 2.5245708150 0.1702049750 0.5032488865 0.6486198337 0.4678201078 -0.32737931567 +1403636732863555584.0000000000 3.4856260825 2.5114267302 0.1761295618 0.5023024988 0.6491939178 0.4669534712 -0.328928430751 +1403636732913555456.0000000000 3.5002940716 2.4970472847 0.1806631861 0.5009261925 0.6499864767 0.4669484578 -0.329468765722 +1403636732963555584.0000000000 3.5159569336 2.4815108145 0.1834954197 0.4988795548 0.6512653264 0.4674051035 -0.32940117424 +1403636733013555456.0000000000 3.5323285844 2.4651578219 0.1847597981 0.4966387012 0.6525990932 0.4685050068 -0.328584057142 +1403636733063555584.0000000000 3.5492515169 2.4480708876 0.1857549095 0.4947509731 0.6538071198 0.4696325492 -0.327418682046 +1403636733113555456.0000000000 3.5667503513 2.4302786131 0.1882706931 0.4918237222 0.6556849974 0.4710400134 -0.326048947734 +1403636733163555584.0000000000 3.5847043346 2.4121410699 0.1931956411 0.4931477318 0.6546327878 0.4725315748 -0.323998670642 +1403636733213555456.0000000000 3.6028566558 2.3930005974 0.1998866346 0.4921493571 0.6550590352 0.4733101514 -0.323518425022 +1403636733263555584.0000000000 3.6212424282 2.3731248712 0.2084251632 0.4919306588 0.6547746838 0.4743906319 -0.32284341208 +1403636733313555456.0000000000 3.6407183312 2.3521040661 0.2183115307 0.4905264551 0.6555025783 0.4740443485 -0.324009447895 +1403636733363555584.0000000000 3.6610663181 2.3304898235 0.2289875554 0.4879541128 0.6570502654 0.4741862331 -0.324550687653 +1403636733413555456.0000000000 3.6810264315 2.3085613132 0.2408584670 0.4851607820 0.6585747625 0.4747164647 -0.32487316896 +1403636733463555584.0000000000 3.7007282091 2.2863408863 0.2545477265 0.4826550235 0.6603984391 0.4740929429 -0.325812693636 +1403636733513555456.0000000000 3.7199489335 2.2641117114 0.2688184806 0.4809435731 0.6614269618 0.4748185311 -0.325199963338 +1403636733563555584.0000000000 3.7392416503 2.2416461239 0.2823707681 0.4794508069 0.6624326488 0.4749763890 -0.325126651432 +1403636733613555456.0000000000 3.7586606551 2.2192104972 0.2948734182 0.4788156698 0.6624907402 0.4762243275 -0.324117206294 +1403636733663555584.0000000000 3.7778867861 2.1965517959 0.3059850931 0.4771110924 0.6637285116 0.4758077585 -0.324709786327 +1403636733713555456.0000000000 3.7969196717 2.1740520171 0.3153365753 0.4763341167 0.6640797747 0.4764834473 -0.324140997906 +1403636733763555584.0000000000 3.8154888837 2.1517010325 0.3231217792 0.4764432012 0.6638154415 0.4771447234 -0.323548835025 +1403636733813555456.0000000000 3.8338082001 2.1291965413 0.3290682922 0.4747737375 0.6648649862 0.4776960791 -0.323033905923 +1403636733863555584.0000000000 3.8519231705 2.1066962308 0.3338389274 0.4740799224 0.6651963154 0.4781474831 -0.322702763601 +1403636733913555456.0000000000 3.8694416067 2.0843907299 0.3374601809 0.4756070771 0.6640288786 0.4785832640 -0.322213618615 +1403636733963555584.0000000000 3.8865797541 2.0622243541 0.3399685843 0.4786553413 0.6618801388 0.4793163990 -0.32102887066 +1403636734013555456.0000000000 3.9030955182 2.0397835424 0.3420050904 0.4814202671 0.6599045880 0.4787860867 -0.321751992052 +1403636734063555584.0000000000 3.9195427589 2.0170484655 0.3431597015 0.4832907826 0.6588879807 0.4777075954 -0.322633075972 +1403636734113555456.0000000000 3.9355354269 1.9939495502 0.3442882013 0.4841457015 0.6587232987 0.4759255151 -0.324316912219 +1403636734163555584.0000000000 3.9518775792 1.9704469761 0.3458065303 0.4845370081 0.6586515599 0.4753362135 -0.324742197016 +1403636734213555456.0000000000 3.9679566718 1.9464793154 0.3489806412 0.4838110116 0.6590369304 0.4746047632 -0.326109718152 +1403636734263555584.0000000000 3.9845297454 1.9220679141 0.3542898266 0.4833473555 0.6589120666 0.4741484904 -0.327709370494 +1403636734313555456.0000000000 4.0015608205 1.8974105013 0.3604913523 0.4815696060 0.6599047821 0.4740239091 -0.328508335814 +1403636734363555584.0000000000 4.0184480605 1.8728842419 0.3685492827 0.4798858794 0.6607981946 0.4742863385 -0.328797441824 +1403636734413555456.0000000000 4.0354330012 1.8482350466 0.3787048486 0.4778514072 0.6618628716 0.4744282205 -0.32941377528 +1403636734463555584.0000000000 4.0524834611 1.8237963362 0.3896301069 0.4762494848 0.6625849491 0.4753524623 -0.328949312136 +1403636734513555456.0000000000 4.0693656011 1.7995162067 0.4003943680 0.4746923757 0.6632658240 0.4760191968 -0.328863679165 +1403636734563555584.0000000000 4.0860867831 1.7753887854 0.4099786062 0.4728513350 0.6641804135 0.4770231542 -0.32821472191 +1403636734613555456.0000000000 4.1025780360 1.7514052349 0.4183317488 0.4710838152 0.6649761273 0.4779082950 -0.327857363432 +1403636734663555584.0000000000 4.1188732008 1.7278032926 0.4250330298 0.4701258855 0.6653054268 0.4792623990 -0.326585201369 +1403636734713555456.0000000000 4.1347104497 1.7044154418 0.4302947225 0.4697205395 0.6650751431 0.4803379135 -0.326056985102 +1403636734763555584.0000000000 4.1501999032 1.6814236967 0.4342089290 0.4703119175 0.6640974538 0.4812806514 -0.32580700835 +1403636734813555456.0000000000 4.1653601162 1.6584806052 0.4364028533 0.4692637075 0.6643919755 0.4819107032 -0.325786663233 +1403636734863555584.0000000000 4.1799809551 1.6357266476 0.4371689304 0.4688558966 0.6641299948 0.4823664712 -0.326233176672 +1403636734913555456.0000000000 4.1939133347 1.6132328491 0.4366787025 0.4681906115 0.6641207487 0.4826116448 -0.326844278968 +1403636734963555584.0000000000 4.2073133077 1.5911326598 0.4351238356 0.4676095624 0.6643355190 0.4825276350 -0.327363249178 +1403636735013555456.0000000000 4.2201850888 1.5694609588 0.4323708493 0.4681749731 0.6637368634 0.4831365807 -0.326870945725 +1403636735063555584.0000000000 4.2323856126 1.5478750629 0.4290659071 0.4681394549 0.6636560444 0.4826869958 -0.327748942862 +1403636735113555456.0000000000 4.2448568179 1.5264318204 0.4250351048 0.4678043139 0.6639971875 0.4821855631 -0.328274186797 +1403636735163555584.0000000000 4.2571950780 1.5053645048 0.4218345724 0.4670504226 0.6645451768 0.4816238207 -0.329062465128 +1403636735213555456.0000000000 4.2688526604 1.4848243755 0.4196415888 0.4660924966 0.6654810997 0.4813146429 -0.32898161808 +1403636735263555584.0000000000 4.2795698508 1.4646966153 0.4195651799 0.4646607638 0.6668025663 0.4807451590 -0.329163795539 +1403636735313555456.0000000000 4.2895803800 1.4451371460 0.4217900216 0.4632946841 0.6682880265 0.4801259621 -0.328980561388 +1403636735363555584.0000000000 4.2982422527 1.4263355160 0.4271343544 0.4623783384 0.6695837084 0.4794152469 -0.328671493714 +1403636735413555456.0000000000 4.3058934706 1.4083836426 0.4360782164 0.4639936461 0.6693245551 0.4781950257 -0.328700553222 +1403636735463555584.0000000000 4.3135273880 1.3908531047 0.4475845878 0.4647238249 0.6699640869 0.4762262499 -0.329224008319 +1403636735513555456.0000000000 4.3205586713 1.3741874648 0.4601061744 0.4664960137 0.6700077380 0.4750986154 -0.328256615867 +1403636735563555584.0000000000 4.3274145006 1.3582708539 0.4742018463 0.4683471846 0.6699580398 0.4736636480 -0.327795497505 +1403636735613555456.0000000000 4.3336534250 1.3429011586 0.4892545467 0.4700821888 0.6698471400 0.4726141466 -0.327052615373 +1403636735663555584.0000000000 4.3397347150 1.3280050527 0.5036238584 0.4713176928 0.6702319272 0.4716288752 -0.325906428808 +1403636735713555456.0000000000 4.3456287858 1.3131687020 0.5164859618 0.4709211652 0.6714195285 0.4707878934 -0.325250414886 +1403636735763555584.0000000000 4.3510695968 1.2989467639 0.5278756525 0.4715802898 0.6717990637 0.4706620724 -0.323690070814 +1403636735813555456.0000000000 4.3559536993 1.2849457000 0.5382942379 0.4716361788 0.6724689748 0.4694707935 -0.323947475444 +1403636735863555584.0000000000 4.3606175857 1.2715031082 0.5472927671 0.4724331649 0.6722947388 0.4690091955 -0.323816403952 +1403636735913555456.0000000000 4.3649119744 1.2584165363 0.5550112360 0.4727500847 0.6721872635 0.4686749533 -0.324060840455 +1403636735963555584.0000000000 4.3687611291 1.2459367762 0.5614495500 0.4733222357 0.6719389746 0.4687683628 -0.323605156965 +1403636736013555456.0000000000 4.3722363250 1.2333619280 0.5680614615 0.4738683185 0.6703737969 0.4700242628 -0.32422982833 +1403636736063555584.0000000000 4.3754542277 1.2207600754 0.5756847389 0.4736828989 0.6681964964 0.4723236632 -0.325650595966 +1403636736113555456.0000000000 4.3785143715 1.2079582824 0.5855165758 0.4731887229 0.6652473728 0.4743404670 -0.329453315283 +1403636736163555584.0000000000 4.3816645915 1.1950674908 0.5968809447 0.4725511307 0.6613210424 0.4777879248 -0.333269570549 +1403636736213555456.0000000000 4.3851459660 1.1821664959 0.6102902860 0.4713912379 0.6573959599 0.4812897841 -0.337610717386 +1403636736263555584.0000000000 4.3886656352 1.1694185906 0.6242089613 0.4699061157 0.6538641615 0.4852366680 -0.340874282843 +1403636736313555456.0000000000 4.3921987744 1.1571423025 0.6378114642 0.4687076771 0.6505340642 0.4891430990 -0.343303908274 +1403636736363555584.0000000000 4.3957346276 1.1449946691 0.6499377522 0.4677079661 0.6475450667 0.4928170112 -0.345059471008 +1403636736413555456.0000000000 4.3993388211 1.1329179725 0.6605766165 0.4665199739 0.6451814385 0.4959701476 -0.346574144969 +1403636736463555584.0000000000 4.4027891786 1.1212609079 0.6696146292 0.4673872604 0.6418177990 0.4999357725 -0.345952720941 +1403636736513555456.0000000000 4.4059543324 1.1095295087 0.6766763004 0.4692033347 0.6381671989 0.5036786697 -0.344816842165 +1403636736563555584.0000000000 4.4091771428 1.0975066218 0.6819512930 0.4707117557 0.6350320939 0.5069818028 -0.34370646539 +1403636736613555456.0000000000 4.4124472457 1.0851917894 0.6860119742 0.4720106594 0.6325504786 0.5096031284 -0.34262294282 +1403636736663555584.0000000000 4.4159766011 1.0718367516 0.6892071599 0.4725088014 0.6309894661 0.5107826529 -0.343058023869 +1403636736713555456.0000000000 4.4194054234 1.0578245726 0.6915313743 0.4730816396 0.6296098255 0.5118649303 -0.343190214169 +1403636736763555584.0000000000 4.4229920135 1.0429491576 0.6924966923 0.4725367358 0.6292442688 0.5130598761 -0.342826847093 +1403636736813555456.0000000000 4.4266074283 1.0271271870 0.6929763793 0.4732202464 0.6279111532 0.5137762152 -0.343255273473 +1403636736863555584.0000000000 4.4303484664 1.0104024570 0.6928146235 0.4722555917 0.6278926618 0.5135837945 -0.344901648765 +1403636736913555456.0000000000 4.4344768097 0.9929471185 0.6916073540 0.4715828641 0.6275561379 0.5149573182 -0.344386202583 +1403636736963555584.0000000000 4.4383802152 0.9744271843 0.6900808443 0.4699823434 0.6279238141 0.5146518202 -0.346354997816 +1403636737013555456.0000000000 4.4424549598 0.9548892034 0.6880143002 0.4673496647 0.6289393918 0.5138675077 -0.349227313988 +1403636737063555584.0000000000 4.4464217166 0.9349429912 0.6854603285 0.4653585367 0.6293114021 0.5131484879 -0.3522601608 +1403636737113555456.0000000000 4.4505204911 0.9144548867 0.6824821519 0.4630390412 0.6298773892 0.5117992687 -0.35624546234 +1403636737163555584.0000000000 4.4548676415 0.8941185033 0.6782272690 0.4616612212 0.6297434191 0.5122520466 -0.35761709104 +1403636737213555456.0000000000 4.4594323063 0.8736122217 0.6731379411 0.4603305305 0.6296014301 0.5125848255 -0.359102545976 +1403636737263555584.0000000000 4.4644361683 0.8529012091 0.6671412041 0.4579550158 0.6302359972 0.5125137020 -0.361122550656 +1403636737313555456.0000000000 4.4696077680 0.8324856789 0.6603722131 0.4563773129 0.6303495317 0.5144111225 -0.360222727207 +1403636737363555584.0000000000 4.4744082979 0.8121508401 0.6550788452 0.4540194176 0.6310379331 0.5153370253 -0.360673322838 +1403636737413555456.0000000000 4.4804035354 0.7918709502 0.6512559266 0.4521897073 0.6312770854 0.5171044792 -0.36002314892 +1403636737463555584.0000000000 4.4863632921 0.7718242431 0.6494244840 0.4501236723 0.6317863933 0.5186844013 -0.359445579499 +1403636737513555456.0000000000 4.4915891728 0.7522150307 0.6498654315 0.4491412474 0.6316790431 0.5204777359 -0.358268967091 +1403636737563555584.0000000000 4.4963555989 0.7327828563 0.6519092282 0.4473106601 0.6324011273 0.5205051759 -0.359244136274 +1403636737613555456.0000000000 4.5004896690 0.7136854909 0.6556789037 0.4451715343 0.6334933177 0.5202134962 -0.360397613549 +1403636737663555584.0000000000 4.5049998499 0.6948063281 0.6605595157 0.4420659399 0.6352139151 0.5193938844 -0.362368568908 +1403636737713555456.0000000000 4.5096485476 0.6765917193 0.6665654855 0.4392563847 0.6370604028 0.5185859150 -0.363698392279 +1403636737763555584.0000000000 4.5133755649 0.6592482245 0.6743162169 0.4374499706 0.6381754996 0.5177746004 -0.365073990006 +1403636737813555456.0000000000 4.5164526756 0.6428761043 0.6835337118 0.4356110120 0.6395751129 0.5166823852 -0.366368713065 +1403636737863555584.0000000000 4.5193410732 0.6275443887 0.6951189903 0.4348062735 0.6403483074 0.5158411590 -0.367158614832 +1403636737913555456.0000000000 4.5218321659 0.6134136181 0.7082532905 0.4345532914 0.6406624010 0.5155388159 -0.36733479866 +1403636737963555584.0000000000 4.5236740581 0.6006432594 0.7236361469 0.4345816927 0.6409225190 0.5149219969 -0.36771240678 +1403636738013555456.0000000000 4.5250046086 0.5891986174 0.7409929128 0.4353017992 0.6410027041 0.5144197727 -0.367423698856 +1403636738063555584.0000000000 4.5265702860 0.5788918724 0.7594874378 0.4358580442 0.6412205486 0.5144282555 -0.366370772963 +1403636738113555456.0000000000 4.5275903455 0.5699972135 0.7779911065 0.4387505378 0.6397265795 0.5150212488 -0.364692997416 +1403636738163555584.0000000000 4.5282066797 0.5615779891 0.7956642342 0.4404920440 0.6391298227 0.5145926748 -0.36424470901 +1403636738213555456.0000000000 4.5287900463 0.5540129053 0.8117852136 0.4425399578 0.6383873632 0.5143928789 -0.363345464192 +1403636738263555584.0000000000 4.5293393086 0.5469667833 0.8261765335 0.4431133962 0.6386995396 0.5138470205 -0.362870025871 +1403636738313555456.0000000000 4.5296079533 0.5403865335 0.8388418404 0.4437509270 0.6388231453 0.5137693010 -0.361982332633 +1403636738363555584.0000000000 4.5295004693 0.5342991199 0.8501385976 0.4439053284 0.6395538263 0.5131211368 -0.361421722606 +1403636738413555456.0000000000 4.5289860758 0.5286929615 0.8599236977 0.4439788168 0.6401024597 0.5127461158 -0.360892050355 +1403636738463555584.0000000000 4.5281833793 0.5239669568 0.8681031552 0.4447092929 0.6410508970 0.5119236036 -0.359474082961 +1403636738513555456.0000000000 4.5269218744 0.5202049133 0.8748798049 0.4450979188 0.6435578271 0.5097889671 -0.357542130308 +1403636738563555584.0000000000 4.5252770367 0.5173995916 0.8797115882 0.4456720334 0.6470944290 0.5069024801 -0.35453506764 +1403636738613555456.0000000000 4.5230143779 0.5154342474 0.8829038293 0.4461881552 0.6516494065 0.5027149983 -0.351492263997 +1403636738663555584.0000000000 4.5201007041 0.5145552291 0.8846495577 0.4485145840 0.6561074461 0.4972753069 -0.347958268034 +1403636738713555456.0000000000 4.5167743472 0.5146713674 0.8849952759 0.4513848705 0.6610608785 0.4902357422 -0.344846532156 +1403636738763555584.0000000000 4.5132744139 0.5155861236 0.8838616514 0.4561831495 0.6654090451 0.4816931020 -0.342198030776 +1403636738813555456.0000000000 4.5098538030 0.5172613570 0.8813354252 0.4606796986 0.6705520165 0.4720710801 -0.339533656333 +1403636738863555584.0000000000 4.5063910395 0.5201451284 0.8775259524 0.4654516289 0.6757719900 0.4614449996 -0.337276609141 +1403636738913555456.0000000000 4.5034420626 0.5240044918 0.8718529648 0.4697398719 0.6816609127 0.4511575029 -0.3333763045 +1403636738963555584.0000000000 4.5007586789 0.5287883900 0.8648752973 0.4731983417 0.6882479403 0.4399664364 -0.329890340683 +1403636739013555456.0000000000 4.4983702508 0.5347246421 0.8564501199 0.4767762480 0.6949769150 0.4280907614 -0.326235799755 +1403636739063555584.0000000000 4.4965632368 0.5421200856 0.8465251924 0.4800539961 0.7020320582 0.4164958159 -0.321294857509 +1403636739113555456.0000000000 4.4953276531 0.5511430400 0.8353140077 0.4852561781 0.7078169841 0.4063693275 -0.313664674966 +1403636739163555584.0000000000 4.4949736107 0.5612889424 0.8223539632 0.4908269445 0.7131274619 0.3979310611 -0.303626422287 +1403636739213555456.0000000000 4.4952136884 0.5725352693 0.8087066815 0.4971420128 0.7178761696 0.3886709819 -0.294004238355 +1403636739263555584.0000000000 4.4963175839 0.5846670824 0.7939249031 0.5034119675 0.7224612487 0.3802554728 -0.282899117216 +1403636739313555456.0000000000 4.4979381992 0.5972791589 0.7784905114 0.5100827123 0.7263553045 0.3720437934 -0.27167446316 +1403636739363555584.0000000000 4.4999756722 0.6101913395 0.7630685794 0.5165487371 0.7300480265 0.3643513054 -0.259721788527 +1403636739413555456.0000000000 4.5027022897 0.6228130755 0.7492495677 0.5215081541 0.7341208349 0.3562086887 -0.24942176137 +1403636739463555584.0000000000 4.5056447243 0.6353320699 0.7373791800 0.5261215469 0.7380996190 0.3476118063 -0.239939789135 +1403636739513555456.0000000000 4.5085014655 0.6472960884 0.7279320675 0.5289649484 0.7428465211 0.3381193309 -0.232487521227 +1403636739563555584.0000000000 4.5111530849 0.6588031152 0.7216192519 0.5317033347 0.7467137926 0.3282188747 -0.227996592286 +1403636739613555456.0000000000 4.5138701838 0.6696958974 0.7168832038 0.5331574425 0.7503754456 0.3198235373 -0.22448326707 +1403636739663555584.0000000000 4.5167672038 0.6803844161 0.7136261516 0.5341900539 0.7534409791 0.3142141457 -0.219629569659 +1403636739713555456.0000000000 4.5196038313 0.6906301779 0.7115104999 0.5358091738 0.7551598274 0.3091810624 -0.216908356381 +1403636739763555584.0000000000 4.5220223460 0.7005459765 0.7090666492 0.5355693313 0.7575486009 0.3039206582 -0.216605268041 +1403636739813555456.0000000000 4.5246852537 0.7102934030 0.7050721347 0.5358175822 0.7589404663 0.3004307047 -0.215986756312 +1403636739863555584.0000000000 4.5273264002 0.7201864176 0.6996969197 0.5357345316 0.7601749475 0.2981700173 -0.214981863404 +1403636739913555456.0000000000 4.5300583673 0.7303779955 0.6932360804 0.5359597589 0.7606876615 0.2970340482 -0.214177946332 +1403636739963555584.0000000000 4.5330095924 0.7407708176 0.6852897296 0.5364855136 0.7607010590 0.2966436746 -0.213353516063 +1403636740013555456.0000000000 4.5363116302 0.7510405752 0.6762776039 0.5364078280 0.7608428504 0.2972533428 -0.212191539038 +1403636740063555584.0000000000 4.5397413024 0.7613660885 0.6661264921 0.5366385080 0.7604480251 0.2987241805 -0.21095444255 +1403636740113555456.0000000000 4.5434821368 0.7714459360 0.6548929176 0.5380531839 0.7591132961 0.3007855894 -0.209221901686 +1403636740163555584.0000000000 4.5475384080 0.7817653671 0.6425917750 0.5392828203 0.7577994194 0.3036408282 -0.206679285627 +1403636740213555456.0000000000 4.5515786989 0.7917567675 0.6293329954 0.5411545363 0.7558461372 0.3066475786 -0.204488746153 +1403636740263555584.0000000000 4.5554459078 0.8012370665 0.6152906563 0.5421795656 0.7545103893 0.3093361261 -0.202648839757 +1403636740313555456.0000000000 4.5588533568 0.8099864711 0.6013216628 0.5428733266 0.7534893683 0.3093190496 -0.204607059287 +1403636740363555584.0000000000 4.5619416865 0.8179724186 0.5860728607 0.5422702428 0.7531741259 0.3092610117 -0.207435162247 +1403636740413555456.0000000000 4.5646825191 0.8255544503 0.5697702376 0.5412954774 0.7533830365 0.3079828425 -0.211091864098 +1403636740463555584.0000000000 4.5675216250 0.8327643864 0.5518775223 0.5397435173 0.7539487949 0.3077345078 -0.213395461367 +1403636740513555456.0000000000 4.5704219573 0.8398007100 0.5343034894 0.5400543666 0.7531047668 0.3068063882 -0.216897052889 +1403636740563555584.0000000000 4.5738013468 0.8466264024 0.5173162495 0.5401583140 0.7525058880 0.3073964439 -0.217879119238 +1403636740613555456.0000000000 4.5773589618 0.8532476546 0.5019218403 0.5400702559 0.7519553574 0.3081552451 -0.218923740423 +1403636740663555584.0000000000 4.5810125434 0.8596725859 0.4882051997 0.5383242700 0.7527268962 0.3082587162 -0.220421786706 +1403636740713555456.0000000000 4.5851392693 0.8659954758 0.4760367020 0.5360661579 0.7539158511 0.3088613621 -0.221017245395 +1403636740763555584.0000000000 4.5897974573 0.8725341938 0.4647516281 0.5342521768 0.7546748679 0.3108462954 -0.220034169921 +1403636740813555456.0000000000 4.5946459313 0.8791998068 0.4539093755 0.5334555241 0.7548136313 0.3113830568 -0.220731007728 +1403636740863555584.0000000000 4.5995587552 0.8859207585 0.4421677206 0.5338506979 0.7542111889 0.3115550609 -0.221590520979 +1403636740913555456.0000000000 4.6049151289 0.8929185518 0.4286365468 0.5358348994 0.7524279819 0.3134045809 -0.220251359285 +1403636740963555584.0000000000 4.6104520991 0.9000320765 0.4136163940 0.5390051847 0.7499603589 0.3156557082 -0.217702422679 +1403636741013555456.0000000000 4.6162489554 0.9068165004 0.3966662153 0.5424208414 0.7472482544 0.3196146623 -0.212711411823 +1403636741063555584.0000000000 4.6220421494 0.9133135760 0.3781232722 0.5464395898 0.7446812298 0.3220546341 -0.207688356325 +1403636741113555456.0000000000 4.6273230997 0.9190440608 0.3581610248 0.5489603256 0.7438525783 0.3211322780 -0.205426295066 +1403636741163555584.0000000000 4.6327910768 0.9237814948 0.3367473237 0.5508911523 0.7442887302 0.3174728217 -0.204362990324 +1403636741213555456.0000000000 4.6379912593 0.9274411920 0.3140799850 0.5514707393 0.7459984926 0.3117384437 -0.205390884555 +1403636741263555584.0000000000 4.6429836053 0.9298426555 0.2900902431 0.5505866550 0.7485647340 0.3055750915 -0.207675318127 +1403636741313555456.0000000000 4.6482770247 0.9310764912 0.2648156373 0.5487622002 0.7513001689 0.3009360765 -0.209393365943 +1403636741363555584.0000000000 4.6541914482 0.9314062804 0.2392915202 0.5445669517 0.7557088197 0.2971693242 -0.209860448036 +1403636741413555456.0000000000 4.6603600165 0.9314353813 0.2150367316 0.5411878508 0.7593776002 0.2946093330 -0.208965813798 +1403636741463555584.0000000000 4.6666425570 0.9312780896 0.1922182061 0.5378070107 0.7627965679 0.2932405859 -0.207159296152 +1403636741513555456.0000000000 4.6730796152 0.9313241201 0.1706483612 0.5324237041 0.7673877483 0.2932973924 -0.204004124236 +1403636741563555584.0000000000 4.6791101651 0.9315789732 0.1516284577 0.5279793070 0.7710829491 0.2908048843 -0.205186393714 +1403636741613555456.0000000000 4.6857200679 0.9325584842 0.1336499856 0.5263767226 0.7726256110 0.2924591380 -0.201109083864 +1403636741663555584.0000000000 4.6917964966 0.9341710196 0.1178468523 0.5252309873 0.7736246996 0.2926896205 -0.199925036515 +1403636741713555456.0000000000 4.6973278504 0.9367830286 0.1042896634 0.5259511184 0.7732224727 0.2928976137 -0.199282253635 +1403636741763555584.0000000000 4.7019838821 0.9405721421 0.0927916745 0.5283313040 0.7714848585 0.2933529157 -0.199050780425 +1403636741813555456.0000000000 4.7062897112 0.9450284506 0.0820254413 0.5308912512 0.7694321481 0.2943718083 -0.198680364796 +1403636741863555584.0000000000 4.7105656981 0.9497543891 0.0705494828 0.5340591250 0.7668088649 0.2959976226 -0.197915191976 +1403636741913555456.0000000000 4.7147052756 0.9545800952 0.0571553099 0.5362903050 0.7646964117 0.2983602708 -0.196502558264 +1403636741963555584.0000000000 4.7184904388 0.9595216387 0.0419504092 0.5389163847 0.7620991038 0.3018739975 -0.194026225023 +1403636742013555456.0000000000 4.7217393901 0.9642898487 0.0250383804 0.5393316540 0.7610611205 0.3055567795 -0.191160645513 +1403636742063555584.0000000000 4.7242753158 0.9685289667 0.0079998390 0.5374603910 0.7615066075 0.3084024336 -0.190084070559 +1403636742113555456.0000000000 4.7258567816 0.9722762844 -0.0080774593 0.5329238429 0.7638592367 0.3103348154 -0.190272295618 +1403636742163555584.0000000000 4.7262915938 0.9759056945 -0.0221532619 0.5289800805 0.7659548930 0.3106943367 -0.192255573142 +1403636742213555456.0000000000 4.7255675656 0.9800036377 -0.0346709098 0.5266621715 0.7669070361 0.3109251681 -0.194437894815 +1403636742263555584.0000000000 4.7237597397 0.9844757530 -0.0446512506 0.5242612765 0.7679333896 0.3099723624 -0.198357146605 +1403636742313555456.0000000000 4.7216869182 0.9892373550 -0.0530539532 0.5249603740 0.7666668670 0.3099323601 -0.201445905603 +1403636742363555584.0000000000 4.7193371022 0.9941193626 -0.0599344521 0.5270024689 0.7648962903 0.3086457080 -0.204792309122 +1403636742413555456.0000000000 4.7161656233 0.9998318635 -0.0645148005 0.5297678712 0.7623399893 0.3083946882 -0.207548692159 +1403636742463555584.0000000000 4.7128530721 1.0059672081 -0.0673784360 0.5313596652 0.7608133632 0.3080235176 -0.209622148365 +1403636742513555456.0000000000 4.7095483351 1.0122183921 -0.0696813916 0.5327209058 0.7593907533 0.3083416095 -0.210854386019 +1403636742563555584.0000000000 4.7055480304 1.0191834381 -0.0714456081 0.5331934437 0.7586047361 0.3087193634 -0.211933859238 +1403636742613555456.0000000000 4.7014776375 1.0263709508 -0.0721231952 0.5348351940 0.7571056625 0.3090015604 -0.212744839329 +1403636742663555584.0000000000 4.6974466798 1.0336141873 -0.0739483134 0.5367942492 0.7554882614 0.3087384007 -0.213939292358 +1403636742713555456.0000000000 4.6934529954 1.0406735521 -0.0778205112 0.5383899754 0.7539120780 0.3086376500 -0.215628416391 +1403636742763555584.0000000000 4.6895206631 1.0476436709 -0.0842391492 0.5397774157 0.7525262323 0.3087888666 -0.216781104082 +1403636742813555456.0000000000 4.6859750204 1.0543514015 -0.0924751785 0.5406799275 0.7516463044 0.3087797734 -0.217596187185 +1403636742863555584.0000000000 4.6828091958 1.0605309865 -0.1024754911 0.5410069826 0.7510009054 0.3085977337 -0.219263593698 +1403636742913555456.0000000000 4.6804243767 1.0662046945 -0.1144856256 0.5409521681 0.7507493568 0.3085130333 -0.22037663958 +1403636742963555584.0000000000 4.6787133270 1.0717232359 -0.1284644861 0.5408698316 0.7512176681 0.3075432927 -0.220338293329 +1403636743013555456.0000000000 4.6772293143 1.0773916083 -0.1448426130 0.5397929428 0.7529920688 0.3065758658 -0.218260765705 +1403636743063555584.0000000000 4.6762811966 1.0829664337 -0.1631229546 0.5359382073 0.7572250255 0.3050590971 -0.215219529803 +1403636743113555456.0000000000 4.6756417773 1.0885080713 -0.1819003230 0.5295116676 0.7633851283 0.3036793586 -0.211280351494 +1403636743163555584.0000000000 4.6749392029 1.0944740957 -0.2002809876 0.5211680049 0.7705482959 0.3033758692 -0.206403285553 +1403636743213555456.0000000000 4.6736743693 1.1015243754 -0.2174045044 0.5152906798 0.7756793606 0.3031136510 -0.202284847395 +1403636743263555584.0000000000 4.6719243954 1.1097147085 -0.2337294968 0.5096719356 0.7804891852 0.3038742531 -0.196803425298 +1403636743313555456.0000000000 4.6687740727 1.1191128335 -0.2466981915 0.5068014435 0.7832544272 0.3024462699 -0.195425313177 +1403636743363555584.0000000000 4.6643838100 1.1301583450 -0.2574785887 0.5049226313 0.7851524751 0.3008261027 -0.195172700657 +1403636743413555456.0000000000 4.6584327502 1.1433927528 -0.2658249082 0.5048389806 0.7857852685 0.2992786628 -0.195221406157 +1403636743463555584.0000000000 4.6506907502 1.1587124415 -0.2724940249 0.5078534829 0.7842278030 0.2976698507 -0.196123055395 +1403636743513555456.0000000000 4.6424746101 1.1753314265 -0.2797230025 0.5110417598 0.7825020848 0.2964618741 -0.196563384994 +1403636743563555584.0000000000 4.6336098046 1.1930884361 -0.2879675253 0.5154041007 0.7798912289 0.2951001444 -0.197596024399 +1403636743613555456.0000000000 4.6238233649 1.2121929274 -0.2980770952 0.5204358042 0.7765418652 0.2953260962 -0.197260746585 +1403636743663555584.0000000000 4.6134687714 1.2320460882 -0.3100520210 0.5240407794 0.7741290535 0.2956192079 -0.196760651435 +1403636743713555456.0000000000 4.6025745235 1.2526680534 -0.3234088434 0.5288628705 0.7709745652 0.2953837995 -0.196597800004 +1403636743763555584.0000000000 4.5910906868 1.2740992832 -0.3380998253 0.5341728820 0.7681228081 0.2937427308 -0.19586192055 +1403636743813555456.0000000000 4.5793828996 1.2954686929 -0.3542689768 0.5369851893 0.7675526279 0.2904704658 -0.1952864009 +1403636743863555584.0000000000 4.5673137157 1.3166756966 -0.3713838289 0.5391943399 0.7675354304 0.2854325428 -0.19669034138 +1403636743913555456.0000000000 4.5552715007 1.3379234002 -0.3900412287 0.5428130267 0.7663217282 0.2831156833 -0.194808974905 +1403636743963555584.0000000000 4.5432001693 1.3590547136 -0.4102040884 0.5458557054 0.7652490411 0.2809825579 -0.193608512673 +1403636744013555456.0000000000 4.5307883625 1.3800340701 -0.4317919903 0.5472297892 0.7652146871 0.2787061740 -0.19315514223 +1403636744063555584.0000000000 4.5182819016 1.4011686822 -0.4547429536 0.5497824063 0.7648583460 0.2768208917 -0.190003184748 +1403636744113555456.0000000000 4.5056543067 1.4220315982 -0.4793359247 0.5512181140 0.7656432454 0.2734232522 -0.18758661112 +1403636744163555584.0000000000 4.4931466529 1.4421912320 -0.5043404841 0.5528480202 0.7663046901 0.2696593434 -0.185526351167 +1403636744213555456.0000000000 4.4810941821 1.4609399802 -0.5310142017 0.5539770236 0.7670187239 0.2654420718 -0.185289614163 +1403636744263555584.0000000000 4.4691720193 1.4790051202 -0.5586888185 0.5551234719 0.7674918219 0.2609755029 -0.186241835071 +1403636744313555456.0000000000 4.4577330375 1.4961891820 -0.5879932628 0.5554027097 0.7683518145 0.2580443965 -0.1859473279 +1403636744363555584.0000000000 4.4463266661 1.5129865938 -0.6186808910 0.5548768858 0.7695846543 0.2545877328 -0.187179560206 +1403636744413555456.0000000000 4.4353499494 1.5291775519 -0.6506667522 0.5541850169 0.7705325949 0.2516556316 -0.189282673286 +1403636744463555584.0000000000 4.4248155045 1.5449273867 -0.6836603726 0.5532619844 0.7715046064 0.2487086435 -0.191900571792 +1403636744513555456.0000000000 4.4148621518 1.5601592751 -0.7175955591 0.5516809134 0.7725015188 0.2453890515 -0.196656519291 +1403636744563555584.0000000000 4.4058697218 1.5760718484 -0.7530724295 0.5525007244 0.7717878027 0.2442873861 -0.198520049945 +1403636744613555456.0000000000 4.3974740781 1.5918455963 -0.7898421827 0.5524463775 0.7715623589 0.2425456019 -0.20165851675 +1403636744663555584.0000000000 4.3904330728 1.6080126841 -0.8276252795 0.5534128136 0.7706786536 0.2420586801 -0.202968632939 +1403636744713555456.0000000000 4.3849663856 1.6244344148 -0.8669019185 0.5558203610 0.7689036844 0.2432404268 -0.20170509456 +1403636744763555584.0000000000 4.3811198314 1.6406735977 -0.9068053662 0.5582070087 0.7672993866 0.2461048705 -0.197709330877 +1403636744813555456.0000000000 4.3785756909 1.6563514389 -0.9453417837 0.5592432459 0.7666461611 0.2484774973 -0.194318267319 +1403636744863555584.0000000000 4.3774600442 1.6709988057 -0.9821538072 0.5590569713 0.7667919379 0.2511177526 -0.190854135879 +1403636744913555456.0000000000 4.3774192655 1.6848432365 -1.0172714797 0.5571695823 0.7681096686 0.2541917998 -0.186965565068 +1403636744963555584.0000000000 4.3778625512 1.6978141431 -1.0494783893 0.5552522782 0.7691555052 0.2562383951 -0.185571013873 +1403636745013555456.0000000000 4.3785588573 1.7104770083 -1.0792355649 0.5517367718 0.7712615904 0.2581666663 -0.184640369803 +1403636745063555584.0000000000 4.3788866863 1.7234831939 -1.1066466425 0.5488921136 0.7726858903 0.2606108353 -0.183727937957 +1403636745113555456.0000000000 4.3791450250 1.7362227873 -1.1322739075 0.5447935872 0.7748320493 0.2630189808 -0.183456420936 +1403636745163555584.0000000000 4.3791824778 1.7489482884 -1.1555717228 0.5421954388 0.7758941249 0.2635806367 -0.185843108756 +1403636745213555456.0000000000 4.3789195575 1.7625594693 -1.1779382042 0.5416671041 0.7753320525 0.2663618075 -0.185764216835 +1403636745263555584.0000000000 4.3782627836 1.7765297710 -1.1994977801 0.5406002201 0.7750615016 0.2687793589 -0.186517363967 +1403636745313555456.0000000000 4.3772727717 1.7908911466 -1.2200319277 0.5411471476 0.7736737527 0.2711809871 -0.187215280494 +1403636745363555584.0000000000 4.3754829502 1.8060424069 -1.2373287298 0.5444561958 0.7702861277 0.2729675592 -0.188985300963 +1403636745413555456.0000000000 4.3739967043 1.8210960839 -1.2514635003 0.5483457480 0.7668119917 0.2737367532 -0.190747214983 +1403636745463555584.0000000000 4.3727556479 1.8357617277 -1.2631870472 0.5519003713 0.7638471510 0.2745851762 -0.191171366034 +1403636745513555456.0000000000 4.3712129977 1.8500564969 -1.2729016339 0.5540259395 0.7622935010 0.2735937673 -0.192640409179 +1403636745563555584.0000000000 4.3699356617 1.8637693885 -1.2812193882 0.5552538720 0.7616950380 0.2725785339 -0.192911247979 +1403636745613555456.0000000000 4.3689130469 1.8769101491 -1.2880505319 0.5564758439 0.7615474973 0.2708612737 -0.192390786985 +1403636745663555584.0000000000 4.3682348249 1.8892087117 -1.2932103878 0.5575026511 0.7617654808 0.2690106664 -0.19114760686 +1403636745713555456.0000000000 4.3673116470 1.9011059074 -1.2960020448 0.5588067425 0.7618946072 0.2673475415 -0.189147889622 +1403636745763555584.0000000000 4.3665158186 1.9124989607 -1.2974343731 0.5599157874 0.7623837218 0.2659765820 -0.185800510098 +1403636745813555456.0000000000 4.3657428467 1.9230026278 -1.2974039914 0.5599851281 0.7635828656 0.2645699698 -0.182648828782 +1403636745863555584.0000000000 4.3646596522 1.9331587853 -1.2953750980 0.5610111370 0.7641981501 0.2633364387 -0.178666201235 +1403636745913555456.0000000000 4.3634521647 1.9423848846 -1.2920669369 0.5623093841 0.7647027476 0.2613751200 -0.175273816905 +1403636745963555584.0000000000 4.3622760269 1.9505329431 -1.2875003758 0.5637857370 0.7649840028 0.2607145091 -0.170214755544 +1403636746013555456.0000000000 4.3601674493 1.9578528855 -1.2807991227 0.5647520907 0.7655305859 0.2596946884 -0.166062238204 +1403636746063555584.0000000000 4.3579752123 1.9636304591 -1.2725240810 0.5656286236 0.7660060018 0.2588671897 -0.16213217881 +1403636746113555456.0000000000 4.3552009987 1.9682237227 -1.2626454004 0.5659027729 0.7667929220 0.2586135101 -0.157802784524 +1403636746163555584.0000000000 4.3516817163 1.9713118779 -1.2507321324 0.5671415872 0.7666979011 0.2573157258 -0.155927437586 +1403636746213555456.0000000000 4.3476924886 1.9725314795 -1.2368191323 0.5691099633 0.7658710314 0.2560552517 -0.154890674236 +1403636746263555584.0000000000 4.3425774506 1.9727469004 -1.2212779084 0.5726714498 0.7638776969 0.2536065125 -0.15563422394 +1403636746313555456.0000000000 4.3365043378 1.9719312578 -1.2055059857 0.5793925089 0.7592842801 0.2511027491 -0.157286719462 +1403636746363555584.0000000000 4.3301149278 1.9688692423 -1.1915035984 0.5835380790 0.7564562679 0.2484012658 -0.15985629888 +1403636746413555456.0000000000 4.3235406609 1.9639015265 -1.1798292528 0.5856996771 0.7549540727 0.2472437897 -0.160843852586 +1403636746463555584.0000000000 4.3168789939 1.9566369070 -1.1710823193 0.5829482737 0.7570253622 0.2462059179 -0.162685454895 +1403636746513555456.0000000000 4.3104942134 1.9474005849 -1.1648815348 0.5780044862 0.7605546506 0.2464543535 -0.163486051512 +1403636746563555584.0000000000 4.3040029243 1.9364579556 -1.1608803870 0.5697086441 0.7663071158 0.2472584561 -0.164525745594 +1403636746613555456.0000000000 4.2975031965 1.9245830877 -1.1593170120 0.5597051596 0.7730528487 0.2489893205 -0.164692882838 +1403636746663555584.0000000000 4.2905398932 1.9122036037 -1.1587657641 0.5488870710 0.7800440191 0.2503455412 -0.1660765534 +1403636746713555456.0000000000 4.2828258900 1.8999094157 -1.1590081372 0.5382966774 0.7867186758 0.2505494349 -0.168924222302 +1403636746763555584.0000000000 4.2745172947 1.8883749244 -1.1599551435 0.5308175374 0.7911448171 0.2500823335 -0.172573018956 +1403636746813555456.0000000000 4.2654363348 1.8788232047 -1.1608337063 0.5269798608 0.7931048840 0.2488653092 -0.177039337731 +1403636746863555584.0000000000 4.2562748724 1.8704753943 -1.1623035494 0.5249998581 0.7938904517 0.2476456884 -0.181065492851 +1403636746913555456.0000000000 4.2470450512 1.8639077449 -1.1638461638 0.5249931846 0.7933405072 0.2472455594 -0.184018012873 +1403636746963555584.0000000000 4.2383836664 1.8588271957 -1.1652200232 0.5259755129 0.7921839685 0.2481777458 -0.184938169015 +1403636747013555456.0000000000 4.2297467460 1.8556305402 -1.1643759849 0.5277925239 0.7905727838 0.2485940940 -0.186093260579 +1403636747063555584.0000000000 4.2214234015 1.8543625263 -1.1609791793 0.5326100282 0.7870155961 0.2515046181 -0.183516855716 +1403636747113555456.0000000000 4.2131421767 1.8542637011 -1.1552246449 0.5378751929 0.7833420396 0.2542010427 -0.180131495938 +1403636747163555584.0000000000 4.2041134485 1.8553500487 -1.1476080808 0.5425554583 0.7800956847 0.2551907783 -0.178779092774 +1403636747213555456.0000000000 4.1944770452 1.8578023084 -1.1384115868 0.5472165132 0.7768707588 0.2575967480 -0.175128031146 +1403636747263555584.0000000000 4.1841283339 1.8607251826 -1.1266303642 0.5507150297 0.7745364807 0.2586937434 -0.172869150723 +1403636747313555456.0000000000 4.1735354653 1.8631548203 -1.1125624925 0.5524573008 0.7734758751 0.2596094162 -0.170672061111 +1403636747363555584.0000000000 4.1630618539 1.8646362585 -1.0977353959 0.5536396923 0.7728577769 0.2595060179 -0.169795684533 +1403636747413555456.0000000000 4.1516752685 1.8662058246 -1.0830667830 0.5547795559 0.7724286372 0.2589638032 -0.168853171487 +1403636747463555584.0000000000 4.1402245793 1.8672314197 -1.0705636184 0.5554627462 0.7724105505 0.2584016525 -0.167546008649 +1403636747513555456.0000000000 4.1282254485 1.8677608939 -1.0595847575 0.5543770951 0.7737323897 0.2569708292 -0.16724299228 +1403636747563555584.0000000000 4.1157098625 1.8679234190 -1.0498589124 0.5534368807 0.7747750504 0.2562968986 -0.166562721141 +1403636747613555456.0000000000 4.1026923534 1.8677945018 -1.0409958577 0.5524988022 0.7759285500 0.2548289739 -0.166559757816 +1403636747663555584.0000000000 4.0893472283 1.8673788747 -1.0310714469 0.5520621597 0.7766760302 0.2540610061 -0.165694662494 +1403636747713555456.0000000000 4.0757402061 1.8664542004 -1.0196635311 0.5519944239 0.7772560157 0.2527711598 -0.165172585175 +1403636747763555584.0000000000 4.0618490114 1.8653250859 -1.0065184687 0.5516581491 0.7780088855 0.2519800210 -0.163955876858 +1403636747813555456.0000000000 4.0470805009 1.8643029610 -0.9909187056 0.5515038797 0.7785803253 0.2507889651 -0.163588027295 +1403636747863555584.0000000000 4.0313625290 1.8635466047 -0.9728025680 0.5519161695 0.7787888364 0.2487640157 -0.164295327583 +1403636747913555456.0000000000 4.0148316114 1.8625085191 -0.9523611144 0.5504606740 0.7803476875 0.2436683534 -0.169340681707 +1403636747963555584.0000000000 3.9978329316 1.8617712317 -0.9307943916 0.5503366171 0.7809048687 0.2372797738 -0.176112188161 +1403636748013555456.0000000000 3.9812842971 1.8612956213 -0.9102657094 0.5488204591 0.7823168187 0.2316780103 -0.18193899668 +1403636748063555584.0000000000 3.9659411555 1.8612685499 -0.8917541546 0.5477050928 0.7834728468 0.2273618441 -0.185731046247 +1403636748113555456.0000000000 3.9516226930 1.8618308774 -0.8753581393 0.5468518417 0.7843614562 0.2254319039 -0.186843854263 +1403636748163555584.0000000000 3.9380821840 1.8629535223 -0.8605518702 0.5453550250 0.7856902667 0.2229967152 -0.188550169796 +1403636748213555456.0000000000 3.9258658027 1.8649235853 -0.8479683329 0.5454093516 0.7860026874 0.2234881421 -0.186497895375 +1403636748263555584.0000000000 3.9148893913 1.8677834699 -0.8376237782 0.5465017715 0.7854521463 0.2269649352 -0.181349546035 +1403636748313555456.0000000000 3.9047062846 1.8716897689 -0.8289263825 0.5484311491 0.7843237381 0.2311966740 -0.174950411232 +1403636748363555584.0000000000 3.8948547830 1.8762548241 -0.8212164630 0.5506475507 0.7828013839 0.2360390685 -0.168210660911 +1403636748413555456.0000000000 3.8847930145 1.8812332542 -0.8136944788 0.5528164953 0.7810957481 0.2403376696 -0.162853183566 +1403636748463555584.0000000000 3.8742510739 1.8861431592 -0.8048209015 0.5543050104 0.7799707584 0.2418437418 -0.16094463658 +1403636748513555456.0000000000 3.8635199382 1.8906906106 -0.7945387944 0.5559987704 0.7786074092 0.2436706197 -0.158935517716 +1403636748563555584.0000000000 3.8524490161 1.8946387074 -0.7827942096 0.5563169281 0.7784199328 0.2436061014 -0.158839387475 +1403636748613555456.0000000000 3.8409486975 1.8982057838 -0.7689016933 0.5559803668 0.7787683552 0.2410058629 -0.162240114545 +1403636748663555584.0000000000 3.8294659219 1.9016907113 -0.7537796053 0.5555939508 0.7791548229 0.2384325085 -0.165478284661 +1403636748713555456.0000000000 3.8179346914 1.9052797877 -0.7380064554 0.5547723486 0.7798979760 0.2348638214 -0.169781546757 +1403636748763555584.0000000000 3.8069946948 1.9087724900 -0.7232230797 0.5537373297 0.7807742092 0.2317341721 -0.173395147885 +1403636748813555456.0000000000 3.7964167300 1.9126038592 -0.7098397162 0.5527613718 0.7817003668 0.2289541032 -0.176009718668 +1403636748863555584.0000000000 3.7863622866 1.9168549248 -0.6978678136 0.5526989265 0.7820729191 0.2267280208 -0.177426746622 +1403636748913555456.0000000000 3.7768792811 1.9215253028 -0.6871712142 0.5526756209 0.7825782512 0.2240088510 -0.178720377849 +1403636748963555584.0000000000 3.7683920995 1.9267914031 -0.6776671334 0.5529367321 0.7829919193 0.2219914294 -0.17861811201 +1403636749013555456.0000000000 3.7607715979 1.9325097601 -0.6690325958 0.5532683400 0.7833400404 0.2200237295 -0.178499533706 +1403636749063555584.0000000000 3.7538466516 1.9384320933 -0.6608581550 0.5528090097 0.7840872360 0.2169291389 -0.180419383158 +1403636749113555456.0000000000 3.7479456502 1.9447746461 -0.6530548791 0.5524274931 0.7846851501 0.2133650166 -0.183216947283 +1403636749163555584.0000000000 3.7433518423 1.9517761356 -0.6462621813 0.5526424440 0.7848644843 0.2114952889 -0.183966880731 +1403636749213555456.0000000000 3.7402518683 1.9595424559 -0.6392859165 0.5534586680 0.7847523093 0.2114311027 -0.18205549917 +1403636749263555584.0000000000 3.7389862591 1.9678424209 -0.6311095123 0.5560296877 0.7835438493 0.2140174562 -0.176313785496 +1403636749313555456.0000000000 3.7386590725 1.9764158496 -0.6212601653 0.5585072772 0.7822206078 0.2164638464 -0.171300745313 +1403636749363555584.0000000000 3.7390508720 1.9851977417 -0.6095239999 0.5598620119 0.7815727675 0.2189759951 -0.166577460534 +1403636749413555456.0000000000 3.7401056957 1.9934329365 -0.5959961041 0.5613178563 0.7807172592 0.2213052202 -0.162563294967 +1403636749463555584.0000000000 3.7415794301 2.0015024988 -0.5812621415 0.5629957788 0.7796146080 0.2238051464 -0.158581437981 +1403636749513555456.0000000000 3.7432055123 2.0090090899 -0.5657410140 0.5638805611 0.7789625146 0.2263767053 -0.154950640253 +1403636749563555584.0000000000 3.7448553797 2.0161549099 -0.5499235106 0.5646539801 0.7782584046 0.2296435994 -0.150809666988 +1403636749613555456.0000000000 3.7462809362 2.0233133730 -0.5343772557 0.5664805394 0.7767623140 0.2321943957 -0.147735806867 +1403636749663555584.0000000000 3.7470373833 2.0295909482 -0.5202940482 0.5667109155 0.7763722707 0.2334171830 -0.146973651224 +1403636749713555456.0000000000 3.7469711800 2.0350829666 -0.5074684216 0.5672302240 0.7757576957 0.2333956313 -0.148244223313 +1403636749763555584.0000000000 3.7463757331 2.0399606512 -0.4958466739 0.5689935158 0.7742042883 0.2328440844 -0.150458403639 +1403636749813555456.0000000000 3.7455792718 2.0441179820 -0.4856802053 0.5717434299 0.7718656160 0.2320410497 -0.153264061034 +1403636749863555584.0000000000 3.7445861901 2.0474645286 -0.4769527394 0.5745089220 0.7694845680 0.2307351119 -0.156825719239 +1403636749913555456.0000000000 3.7437793975 2.0498353148 -0.4700798405 0.5764353026 0.7675808677 0.2306698199 -0.15916465591 +1403636749963555584.0000000000 3.7432234222 2.0510304229 -0.4644800146 0.5782376543 0.7656566903 0.2308841588 -0.161565939889 +1403636750013555456.0000000000 3.7431053063 2.0507978558 -0.4604085697 0.5788855927 0.7645246709 0.2316279978 -0.163529718296 +1403636750063555584.0000000000 3.7435320525 2.0489857745 -0.4574627803 0.5787817399 0.7640327122 0.2323565477 -0.165154918332 +1403636750113555456.0000000000 3.7445677688 2.0457522664 -0.4550637574 0.5770718115 0.7647104076 0.2336800192 -0.166131771669 +1403636750163555584.0000000000 3.7462235702 2.0412385209 -0.4519057227 0.5751347712 0.7656533393 0.2351298013 -0.166460011966 +1403636750213555456.0000000000 3.7487165153 2.0349815705 -0.4475469902 0.5732094426 0.7665392524 0.2361513666 -0.167573988268 +1403636750263555584.0000000000 3.7514298030 2.0281199752 -0.4420321093 0.5705214010 0.7680126231 0.2382879637 -0.166975411688 +1403636750313555456.0000000000 3.7537289357 2.0210605404 -0.4337304715 0.5680966377 0.7691993762 0.2395429606 -0.167981248469 +1403636750363555584.0000000000 3.7568978479 2.0129143886 -0.4234484641 0.5658633588 0.7702260358 0.2420732263 -0.167185723235 +1403636750413555456.0000000000 3.7595445015 2.0047056743 -0.4100535789 0.5637635066 0.7712643541 0.2424197168 -0.168981317418 +1403636750463555584.0000000000 3.7626768884 1.9955795376 -0.3948753240 0.5626817192 0.7713344485 0.2446332614 -0.169076961537 +1403636750513555456.0000000000 3.7659049503 1.9860299498 -0.3762574121 0.5625325429 0.7706803301 0.2461581036 -0.170338354253 +1403636750563555584.0000000000 3.7691963556 1.9760872083 -0.3556799976 0.5617242240 0.7705183564 0.2481665067 -0.170823720606 +1403636750613555456.0000000000 3.7725301387 1.9658208527 -0.3333482118 0.5607084698 0.7705368841 0.2497470496 -0.171771165902 +1403636750663555584.0000000000 3.7759943390 1.9560745964 -0.3097471983 0.5609543059 0.7698056451 0.2518798325 -0.17113177821 +1403636750713555456.0000000000 3.7793993726 1.9460183673 -0.2842902025 0.5599956094 0.7699600256 0.2532728043 -0.171520736489 +1403636750763555584.0000000000 3.7829420708 1.9354426533 -0.2579497174 0.5588595405 0.7702750225 0.2546428002 -0.171783142331 +1403636750813555456.0000000000 3.7862145718 1.9248860793 -0.2300733525 0.5583606193 0.7702841463 0.2560180107 -0.171319966494 +1403636750863555584.0000000000 3.7895967572 1.9135844361 -0.2001642003 0.5577396976 0.7703802693 0.2570015660 -0.17143764309 +1403636750913555456.0000000000 3.7934068970 1.9014959375 -0.1690612324 0.5567141434 0.7709075100 0.2588127984 -0.169667053232 +1403636750963555584.0000000000 3.7969475779 1.8890582442 -0.1381948362 0.5564001977 0.7709500120 0.2603951802 -0.168075129354 +1403636751013555456.0000000000 3.8000542663 1.8767752937 -0.1080832433 0.5557451183 0.7714330736 0.2612757221 -0.166653453145 +1403636751063555584.0000000000 3.8025341194 1.8643323360 -0.0788771547 0.5556656836 0.7715547149 0.2614074500 -0.166147871098 +1403636751113555456.0000000000 3.8043003962 1.8516476717 -0.0515528460 0.5553149119 0.7719147494 0.2609425061 -0.166379015553 +1403636751163555584.0000000000 3.8053865412 1.8387419126 -0.0260396114 0.5530413080 0.7737791605 0.2602613784 -0.166358460103 +1403636751213555456.0000000000 3.8059421379 1.8259432734 -0.0020657473 0.5498634148 0.7762034765 0.2613464142 -0.16387934566 +1403636751263555584.0000000000 3.8056548775 1.8130852521 0.0214017172 0.5457217620 0.7793384858 0.2610366847 -0.1633374796 +1403636751313555456.0000000000 3.8048429713 1.8003500892 0.0447682960 0.5432813634 0.7812944913 0.2598976798 -0.163943509043 +1403636751363555584.0000000000 3.8032229404 1.7881929728 0.0682936844 0.5419294135 0.7825849730 0.2570962650 -0.166657676986 +1403636751413555456.0000000000 3.8008390453 1.7768258094 0.0918979348 0.5424619640 0.7825616957 0.2536790854 -0.170232581244 +1403636751463555584.0000000000 3.7981233581 1.7661688233 0.1154787206 0.5431542562 0.7823969630 0.2493531942 -0.175104057096 +1403636751513555456.0000000000 3.7953995887 1.7560824978 0.1386774497 0.5443538048 0.7814612914 0.2465035489 -0.179536028774 +1403636751563555584.0000000000 3.7929713423 1.7464923128 0.1612407820 0.5459685024 0.7795990435 0.2454072152 -0.18417118242 +1403636751613555456.0000000000 3.7910099380 1.7372465406 0.1827668344 0.5453381983 0.7789707609 0.2454571278 -0.188577839495 +1403636751663555584.0000000000 3.7899861622 1.7286361084 0.2034311300 0.5439987559 0.7787941338 0.2464360879 -0.191870543158 +1403636751713555456.0000000000 3.7898002143 1.7205526554 0.2226430554 0.5405425335 0.7800686662 0.2485493100 -0.193726317186 +1403636751763555584.0000000000 3.7906140134 1.7133296237 0.2408841681 0.5363823402 0.7819324886 0.2509628709 -0.194661772764 +1403636751813555456.0000000000 3.7920768403 1.7072452749 0.2583919079 0.5319655189 0.7840062667 0.2534241822 -0.195251234082 +1403636751863555584.0000000000 3.7941948749 1.7029906372 0.2752447000 0.5287257700 0.7855272329 0.2577083790 -0.192308132537 +1403636751913555456.0000000000 3.7966833210 1.7000656186 0.2923488824 0.5278789410 0.7853646525 0.2624127723 -0.188906652209 +1403636751963555584.0000000000 3.7989777730 1.6986201788 0.3092535813 0.5278423504 0.7847502473 0.2668696863 -0.1852837637 +1403636752013555456.0000000000 3.8007696518 1.6986257069 0.3258752144 0.5283052031 0.7839634125 0.2704908484 -0.182015606841 +1403636752063555584.0000000000 3.8018853880 1.6995708934 0.3425577869 0.5296914599 0.7826907319 0.2723720310 -0.180653403541 +1403636752113555456.0000000000 3.8022455287 1.7016533911 0.3590816421 0.5317519069 0.7810124280 0.2732463662 -0.180543402255 +1403636752163555584.0000000000 3.8017370378 1.7043984785 0.3756332709 0.5354572827 0.7777833214 0.2741569092 -0.182144427604 +1403636752213555456.0000000000 3.8006664453 1.7075354470 0.3915974371 0.5392547284 0.7739930614 0.2756749009 -0.184776697186 +1403636752263555584.0000000000 3.7994844945 1.7103918451 0.4079148174 0.5419878121 0.7702646395 0.2780466102 -0.188763553816 +1403636752313555456.0000000000 3.7979480990 1.7134208331 0.4255957212 0.5451503809 0.7656913107 0.2809905306 -0.193835499019 +1403636752363555584.0000000000 3.7964412693 1.7160858804 0.4444697200 0.5472978685 0.7611787830 0.2852023925 -0.199327616639 +1403636752413555456.0000000000 3.7952449384 1.7182274872 0.4646152057 0.5475791810 0.7574089833 0.2907742777 -0.204790116924 +1403636752463555584.0000000000 3.7944121286 1.7198174362 0.4860912529 0.5458263604 0.7544684796 0.2976842950 -0.210321083342 +1403636752513555456.0000000000 3.7939998661 1.7210980312 0.5082418401 0.5441023877 0.7510407270 0.3058529610 -0.215277458871 +1403636752563555584.0000000000 3.7939567914 1.7221326464 0.5295554166 0.5409745765 0.7482883859 0.3145828872 -0.220110440768 +1403636752613555456.0000000000 3.7940395006 1.7229782259 0.5495122827 0.5379354210 0.7451010315 0.3236968267 -0.225100644435 +1403636752663555584.0000000000 3.7946377287 1.7234717461 0.5675175993 0.5337101792 0.7425466782 0.3332015752 -0.229683664155 +1403636752713555456.0000000000 3.7951429844 1.7239715033 0.5844205855 0.5307618553 0.7388678880 0.3417070273 -0.235801621094 +1403636752763555584.0000000000 3.7957597746 1.7243889515 0.5996069568 0.5272996364 0.7352151805 0.3507148777 -0.241687414605 +1403636752813555456.0000000000 3.7966831890 1.7246682466 0.6126312866 0.5246800572 0.7307813329 0.3607165799 -0.246075252859 +1403636752863555584.0000000000 3.7978693723 1.7243714227 0.6240510412 0.5209506318 0.7267651567 0.3705973475 -0.251158221522 +1403636752913555456.0000000000 3.7990900960 1.7240883936 0.6340239791 0.5198852022 0.7206389973 0.3809716553 -0.255459214027 +1403636752963555584.0000000000 3.8002368789 1.7234399305 0.6418147316 0.5177993321 0.7148728527 0.3918360829 -0.259432342488 +1403636753013555456.0000000000 3.8013105990 1.7222682489 0.6479889328 0.5151946527 0.7092151863 0.4025891553 -0.263647987561 +1403636753063555584.0000000000 3.8022700177 1.7205509945 0.6524749731 0.5123038582 0.7034129535 0.4133071822 -0.268201690636 +1403636753113555456.0000000000 3.8028042313 1.7181149732 0.6553748910 0.5091482273 0.6974754134 0.4236616665 -0.27350854214 +1403636753163555584.0000000000 3.8028916928 1.7149136019 0.6568278402 0.5056346748 0.6915090217 0.4338080201 -0.279212195803 +1403636753213555456.0000000000 3.8025476701 1.7110098252 0.6566805440 0.5021093955 0.6852803713 0.4439876547 -0.284871778486 +1403636753263555584.0000000000 3.8017308388 1.7064078495 0.6547390170 0.4991048362 0.6784892721 0.4545841582 -0.28965481727 +1403636753313555456.0000000000 3.8003117742 1.7009728936 0.6512488324 0.4970031872 0.6708375211 0.4655243195 -0.293686840077 +1403636753363555584.0000000000 3.7983018369 1.6944894691 0.6471461956 0.4944868889 0.6643177063 0.4735215733 -0.299903353495 +1403636753413555456.0000000000 3.7955129177 1.6870959901 0.6435405969 0.4913452532 0.6594500737 0.4793509498 -0.306476931058 +1403636753463555584.0000000000 3.7915705655 1.6788705930 0.6409441987 0.4872825272 0.6565023364 0.4828939663 -0.313646039761 +1403636753513555456.0000000000 3.7874274351 1.6699895412 0.6399214524 0.4837157213 0.6544773656 0.4853826510 -0.319502990558 +1403636753563555584.0000000000 3.7834586560 1.6604508210 0.6409956320 0.4803657299 0.6531268714 0.4869320520 -0.324917269695 +1403636753613555456.0000000000 3.7796239192 1.6505977992 0.6435160232 0.4790068349 0.6513828430 0.4876993654 -0.329244852451 +1403636753663555584.0000000000 3.7767050789 1.6402412550 0.6475202502 0.4774568208 0.6507326158 0.4881888044 -0.33204478344 +1403636753713555456.0000000000 3.7733276444 1.6300193266 0.6509354121 0.4761642337 0.6506448628 0.4882879885 -0.333921735456 +1403636753763555584.0000000000 3.7697369114 1.6198683838 0.6540564332 0.4768163276 0.6496598231 0.4884744456 -0.33463565251 +1403636753813555456.0000000000 3.7663818975 1.6093904816 0.6557309852 0.4775116027 0.6490384629 0.4886810040 -0.334548381149 +1403636753863555584.0000000000 3.7635969469 1.5985374323 0.6558891010 0.4782707226 0.6489118700 0.4882115931 -0.334394888268 +1403636753913555456.0000000000 3.7609340628 1.5871868624 0.6545697207 0.4777928439 0.6499057822 0.4872336208 -0.334574164222 +1403636753963555584.0000000000 3.7587690586 1.5755324086 0.6520952088 0.4786494195 0.6500331198 0.4865790871 -0.334054588912 +1403636754013555456.0000000000 3.7568444276 1.5636187427 0.6500572474 0.4799251457 0.6501311605 0.4857796160 -0.333195878517 +1403636754063555584.0000000000 3.7546070913 1.5513250977 0.6499628034 0.4823034647 0.6494885931 0.4834721628 -0.334368962598 +1403636754113555456.0000000000 3.7524776794 1.5386888509 0.6517590549 0.4848776324 0.6485618777 0.4812193088 -0.335692045244 +1403636754163555584.0000000000 3.7510750554 1.5254396936 0.6550116015 0.4873326015 0.6478607734 0.4795327879 -0.335904240986 +1403636754213555456.0000000000 3.7506008423 1.5115516359 0.6589700938 0.4903553387 0.6467754166 0.4784506547 -0.33513903579 +1403636754263555584.0000000000 3.7515891468 1.4967015797 0.6646585429 0.4922023665 0.6464959223 0.4776694311 -0.334083473715 +1403636754313555456.0000000000 3.7526575765 1.4812110744 0.6717982357 0.4932178390 0.6467463711 0.4771648079 -0.332819832367 +1403636754363555584.0000000000 3.7541992935 1.4650577576 0.6804245053 0.4943023625 0.6463978885 0.4774985274 -0.331406246961 +1403636754413555456.0000000000 3.7566082537 1.4474345579 0.6903114959 0.4938299462 0.6463080137 0.4778340891 -0.331801927199 +1403636754463555584.0000000000 3.7599823155 1.4284366702 0.7004717643 0.4926799381 0.6456784528 0.4791750047 -0.332801936763 +1403636754513555456.0000000000 3.7641202773 1.4084064670 0.7098178718 0.4913701185 0.6444826253 0.4816213303 -0.333524281848 +1403636754563555584.0000000000 3.7689954313 1.3872026632 0.7174122410 0.4894240232 0.6426712423 0.4858513804 -0.333745765429 +1403636754613555456.0000000000 3.7743632751 1.3647607786 0.7234160124 0.4868330131 0.6403601933 0.4906233747 -0.334994245421 +1403636754663555584.0000000000 3.7801960651 1.3411745415 0.7282887995 0.4842199441 0.6371052497 0.4952843514 -0.338114415335 +1403636754713555456.0000000000 3.7865998579 1.3165570845 0.7319984738 0.4804450546 0.6340267879 0.5003204517 -0.341850884778 +1403636754763555584.0000000000 3.7932869658 1.2910067418 0.7349467215 0.4773574126 0.6296357632 0.5055436898 -0.346575077112 +1403636754813555456.0000000000 3.8004765492 1.2651519677 0.7364334000 0.4744417623 0.6253615355 0.5110950149 -0.350156893238 +1403636754863555584.0000000000 3.8079563666 1.2386915481 0.7368334631 0.4709782601 0.6220612065 0.5152924817 -0.354532075009 +1403636754913555456.0000000000 3.8158620533 1.2119568973 0.7359372526 0.4693979273 0.6182332309 0.5194142322 -0.357298353557 +1403636754963555584.0000000000 3.8241193936 1.1846239796 0.7340929168 0.4664778591 0.6157670966 0.5227461042 -0.360507697944 +1403636755013555456.0000000000 3.8325543553 1.1570479360 0.7311694862 0.4653213237 0.6126447409 0.5268268913 -0.361380566455 +1403636755063555584.0000000000 3.8413660499 1.1287609704 0.7282884101 0.4634545721 0.6110655973 0.5284693627 -0.3640450908 +1403636755113555456.0000000000 3.8508232726 1.1000812350 0.7264119891 0.4620596300 0.6094014402 0.5307337257 -0.36531150446 +1403636755163555584.0000000000 3.8616448763 1.0706122350 0.7255615442 0.4599529426 0.6088431319 0.5320723074 -0.366950120645 +1403636755213555456.0000000000 3.8732552171 1.0406134692 0.7261627725 0.4586396216 0.6080828348 0.5331284597 -0.368319167224 +1403636755263555584.0000000000 3.8850152752 1.0103293458 0.7284660436 0.4563544981 0.6087025711 0.5348312419 -0.367664649727 +1403636755313555456.0000000000 3.8967147668 0.9796252885 0.7323395491 0.4525126231 0.6105709080 0.5372497192 -0.365784405864 +1403636755363555584.0000000000 3.9091615849 0.9485989863 0.7381112207 0.4480347146 0.6132313017 0.5397026938 -0.363226193272 +1403636755413555456.0000000000 3.9209784977 0.9177267710 0.7453273975 0.4449905703 0.6151216074 0.5421633690 -0.360093990277 +1403636755463555584.0000000000 3.9316509666 0.8867207583 0.7538958141 0.4425901179 0.6168740726 0.5431798696 -0.358519170011 +1403636755513555456.0000000000 3.9414021842 0.8557192416 0.7624644466 0.4426214806 0.6172369524 0.5436059064 -0.35720776598 +1403636755563555584.0000000000 3.9504133171 0.8245195319 0.7698480451 0.4436440516 0.6169886933 0.5440086025 -0.355752088282 +1403636755613555456.0000000000 3.9585982166 0.7930069655 0.7760352974 0.4455667754 0.6161235710 0.5434711244 -0.355669974784 +1403636755663555584.0000000000 3.9660531847 0.7608764807 0.7808527722 0.4459611715 0.6165511038 0.5417276788 -0.357091713628 +1403636755713555456.0000000000 3.9733764389 0.7285360530 0.7839729945 0.4465039988 0.6167382768 0.5407634451 -0.357551357815 +1403636755763555584.0000000000 3.9803681223 0.6958432796 0.7860267708 0.4470307072 0.6169571497 0.5390587490 -0.359086462304 +1403636755813555456.0000000000 3.9869545226 0.6629868795 0.7869126408 0.4485977006 0.6163705915 0.5371507927 -0.360993660343 +1403636755863555584.0000000000 3.9936898754 0.6298368101 0.7863423903 0.4493620511 0.6161204224 0.5358615791 -0.36238341598 +1403636755913555456.0000000000 4.0001280793 0.5965322338 0.7851547883 0.4511168292 0.6150744881 0.5346429780 -0.363777221094 +1403636755963555584.0000000000 4.0065599767 0.5628665248 0.7842524628 0.4510326168 0.6152455901 0.5336514525 -0.36504598296 +1403636756013555456.0000000000 4.0133469525 0.5290418117 0.7845548808 0.4514977820 0.6149510641 0.5328509125 -0.366135011645 +1403636756063555584.0000000000 4.0195508967 0.4952061889 0.7862562708 0.4518114959 0.6147395729 0.5322307246 -0.367004203487 +1403636756113555456.0000000000 4.0256623290 0.4615044266 0.7894359800 0.4530526688 0.6138280657 0.5325311266 -0.36656375182 +1403636756163555584.0000000000 4.0310498999 0.4275254003 0.7947199056 0.4540000647 0.6130005477 0.5324335684 -0.366917926863 +1403636756213555456.0000000000 4.0375830304 0.3933802974 0.8012706531 0.4545299114 0.6125439283 0.5318458956 -0.367875575189 +1403636756263555584.0000000000 4.0445058898 0.3589267427 0.8082922911 0.4543293282 0.6124507364 0.5317191236 -0.368461301377 +1403636756313555456.0000000000 4.0518016354 0.3243222031 0.8147784421 0.4541873052 0.6122668259 0.5318181923 -0.368798909855 +1403636756363555584.0000000000 4.0590532859 0.2897366126 0.8203795063 0.4545854305 0.6115108481 0.5321159221 -0.369133058032 +1403636756413555456.0000000000 4.0665565158 0.2551521452 0.8246860546 0.4552802609 0.6106972118 0.5325164153 -0.369046158263 +1403636756463555584.0000000000 4.0744641186 0.2203324267 0.8275211186 0.4550718257 0.6104256925 0.5325204146 -0.369746014736 +1403636756513555456.0000000000 4.0827225908 0.1853534589 0.8286596371 0.4546415112 0.6102649615 0.5326027690 -0.370421467382 +1403636756563555584.0000000000 4.0911573586 0.1503665728 0.8285146739 0.4547558468 0.6097551273 0.5330113906 -0.370532943266 +1403636756613555456.0000000000 4.0996917760 0.1149377470 0.8273851959 0.4548173808 0.6093809507 0.5328619002 -0.371287223575 +1403636756663555584.0000000000 4.1086507440 0.0792555006 0.8262883650 0.4544415494 0.6091430632 0.5329413078 -0.372023076081 +1403636756713555456.0000000000 4.1182492033 0.0435463999 0.8262136093 0.4549524593 0.6082724778 0.5328052464 -0.373016651 +1403636756763555584.0000000000 4.1286238251 0.0076629447 0.8275306857 0.4551375962 0.6077107377 0.5328171933 -0.373688729163 +1403636756813555456.0000000000 4.1399173319 -0.0283927048 0.8297660797 0.4548999537 0.6073941839 0.5326714934 -0.374699102874 +1403636756863555584.0000000000 4.1515841363 -0.0645413678 0.8335549646 0.4543089244 0.6073399463 0.5329225973 -0.37514676607 +1403636756913555456.0000000000 4.1639311440 -0.1007491430 0.8389654591 0.4542019236 0.6071630256 0.5333759966 -0.374918283254 +1403636756963555584.0000000000 4.1770178314 -0.1372351304 0.8465935520 0.4532970159 0.6073718222 0.5334455771 -0.37557569314 +1403636757013555456.0000000000 4.1908147976 -0.1735293107 0.8542301997 0.4534817278 0.6068730031 0.5338723714 -0.375552621886 +1403636757063555584.0000000000 4.2048618239 -0.2102109725 0.8615417068 0.4518065629 0.6077356227 0.5333290534 -0.376946101419 +1403636757113555456.0000000000 4.2191577932 -0.2467584662 0.8678170546 0.4521174460 0.6072866338 0.5334180275 -0.377171005558 +1403636757163555584.0000000000 4.2336197371 -0.2833564208 0.8724584564 0.4514136172 0.6076788433 0.5337405564 -0.376925971577 +1403636757213555456.0000000000 4.2486672537 -0.3198312373 0.8757966452 0.4515038625 0.6075562185 0.5334567109 -0.377417065211 +1403636757263555584.0000000000 4.2642005223 -0.3561960718 0.8775401009 0.4515839182 0.6072166540 0.5341289551 -0.376916647661 +1403636757313555456.0000000000 4.2802201344 -0.3922616954 0.8772612036 0.4524117966 0.6064719206 0.5356912554 -0.374900326283 +1403636757363555584.0000000000 4.2965546439 -0.4287125978 0.8759040128 0.4514136206 0.6069425250 0.5361197366 -0.374729425792 +1403636757413555456.0000000000 4.3132827953 -0.4651635372 0.8728395203 0.4511088370 0.6068713793 0.5377647516 -0.372849860013 +1403636757463555584.0000000000 4.3300330482 -0.5017769520 0.8694534215 0.4507499599 0.6068928795 0.5396231979 -0.370556757686 +1403636757513555456.0000000000 4.3473304957 -0.5388922697 0.8670159988 0.4494568786 0.6062685714 0.5425136900 -0.368925235998 +1403636757563555584.0000000000 4.3647088937 -0.5767839213 0.8662540411 0.4461685978 0.6061766097 0.5462082543 -0.367613986538 +1403636757613555456.0000000000 4.3821722177 -0.6150808770 0.8660949506 0.4412645481 0.6063947226 0.5510776501 -0.365902258355 +1403636757663555584.0000000000 4.3992701433 -0.6537305827 0.8681596885 0.4360701464 0.6069411231 0.5558896351 -0.363939574832 +1403636757713555456.0000000000 4.4155342356 -0.6926717553 0.8716949346 0.4304449919 0.6075586876 0.5604265902 -0.36264526344 +1403636757763555584.0000000000 4.4303509920 -0.7317082094 0.8775425366 0.4254266097 0.6080233887 0.5641155279 -0.362068266752 +1403636757813555456.0000000000 4.4434222528 -0.7708308889 0.8856891056 0.4213463695 0.6079284292 0.5674658010 -0.361763495403 +1403636757863555584.0000000000 4.4544799593 -0.8098118558 0.8968320403 0.4179032972 0.6078443978 0.5693311613 -0.362965633372 +1403636757913555456.0000000000 4.4639797227 -0.8487440339 0.9109348426 0.4162998113 0.6068322919 0.5704406981 -0.364755324327 +1403636757963555584.0000000000 4.4718440129 -0.8877540417 0.9265045379 0.4158533514 0.6052927985 0.5698131124 -0.368781283688 +1403636758013555456.0000000000 4.4774812932 -0.9261075748 0.9427973061 0.4201074858 0.6010428345 0.5676937170 -0.374140421687 +1403636758063555584.0000000000 4.4821256104 -0.9642346529 0.9576117040 0.4232867681 0.5974830426 0.5655532983 -0.379462504796 +1403636758113555456.0000000000 4.4861601058 -1.0021931888 0.9709943503 0.4259609969 0.5946765616 0.5629924463 -0.384651168586 +1403636758163555584.0000000000 4.4899472875 -1.0399107564 0.9826718366 0.4285184698 0.5921315445 0.5610405863 -0.388568675545 +1403636758213555456.0000000000 4.4940557799 -1.0771396827 0.9925995608 0.4307359132 0.5898720566 0.5593937581 -0.391913451204 +1403636758263555584.0000000000 4.4987163671 -1.1141589327 1.0007585959 0.4311673001 0.5891743241 0.5582241287 -0.394149968014 +1403636758313555456.0000000000 4.5035789068 -1.1509163370 1.0071156749 0.4313897921 0.5888078249 0.5568732798 -0.396358856262 +1403636758363555584.0000000000 4.5090472965 -1.1872166182 1.0106521476 0.4296487361 0.5898791137 0.5570630208 -0.396390445997 +1403636758413555456.0000000000 4.5154520095 -1.2233969301 1.0116286631 0.4241510202 0.5936730843 0.5584607537 -0.39467678888 +1403636758463555584.0000000000 4.5219836333 -1.2592573654 1.0107094857 0.4164495377 0.5990127136 0.5603381087 -0.392141244408 +1403636758513555456.0000000000 4.5282187778 -1.2948508190 1.0086220309 0.4062315899 0.6060073291 0.5619783749 -0.389758025707 +1403636758563555584.0000000000 4.5335239762 -1.3295123306 1.0061120241 0.3955794282 0.6131925300 0.5629242311 -0.388108421903 +1403636758613555456.0000000000 4.5375125105 -1.3624872660 1.0031879135 0.3868710276 0.6189582474 0.5634554208 -0.386961864827 +1403636758663555584.0000000000 4.5388640273 -1.3931918983 1.0005299283 0.3850973543 0.6204556732 0.5632555927 -0.386623748136 +1403636758713555456.0000000000 4.5375209273 -1.4217437232 0.9985674354 0.3898006402 0.6178669370 0.5609203416 -0.389440983338 +1403636758763555584.0000000000 4.5344010068 -1.4481180448 0.9961461210 0.3979166217 0.6132370667 0.5588393160 -0.391537074916 +1403636758813555456.0000000000 4.5302264644 -1.4733775912 0.9935356933 0.4036921330 0.6095609898 0.5559636785 -0.395439565198 +1403636758863555584.0000000000 4.5254542206 -1.4970994617 0.9901379713 0.4110316380 0.6046402841 0.5542119587 -0.397884687121 +1403636758913555456.0000000000 4.5209620773 -1.5193952049 0.9852844006 0.4179217326 0.6001536985 0.5545643105 -0.397008046699 +1403636758963555584.0000000000 4.5167580852 -1.5410610618 0.9799748347 0.4222611802 0.5972503489 0.5538566079 -0.397781817561 +1403636759013555456.0000000000 4.5131996880 -1.5621284293 0.9737090942 0.4248124495 0.5954579145 0.5539510705 -0.39762100835 +1403636759063555584.0000000000 4.5099098320 -1.5832208565 0.9674450074 0.4249970668 0.5951673879 0.5520479060 -0.400495172339 +1403636759113555456.0000000000 4.5070092452 -1.6040300386 0.9609519953 0.4216080945 0.5974384786 0.5483191395 -0.405783193645 +1403636759163555584.0000000000 4.5044887965 -1.6243321692 0.9542778370 0.4154717024 0.6012949009 0.5433008947 -0.413100283876 +1403636759213555456.0000000000 4.5024370804 -1.6430010213 0.9468304074 0.4093375157 0.6050778487 0.5385191966 -0.419905549126 +1403636759263555584.0000000000 4.5009292361 -1.6594039540 0.9381353440 0.4040787693 0.6082627178 0.5344635270 -0.425541481681 +1403636759313555456.0000000000 4.4999593478 -1.6729919892 0.9276381561 0.4026579937 0.6089008495 0.5336037456 -0.427051915209 +1403636759363555584.0000000000 4.4995955138 -1.6834415159 0.9152817902 0.4071991151 0.6057527384 0.5365052458 -0.423573632149 +1403636759413555456.0000000000 4.4999385564 -1.6914721477 0.9014617555 0.4119145197 0.6025592452 0.5405587404 -0.418383834084 +1403636759463555584.0000000000 4.5008636836 -1.6978320245 0.8870342425 0.4171490127 0.5988190673 0.5439426835 -0.414160334762 +1403636759513555456.0000000000 4.5026902807 -1.7028643193 0.8714864228 0.4218594655 0.5955505623 0.5476487395 -0.409188192871 +1403636759563555584.0000000000 4.5051838763 -1.7072793785 0.8559124071 0.4250228866 0.5927542036 0.5502395664 -0.406490368273 +1403636759613555456.0000000000 4.5083630008 -1.7108597988 0.8416829343 0.4285546848 0.5898204224 0.5531941281 -0.403024823278 +1403636759663555584.0000000000 4.5130499497 -1.7141039963 0.8302865887 0.4302462911 0.5882089877 0.5551501123 -0.400882362555 +1403636759713555456.0000000000 4.5179299881 -1.7173071791 0.8215431749 0.4309786121 0.5872863115 0.5566740230 -0.399332262988 +1403636759763555584.0000000000 4.5233150203 -1.7208138190 0.8158563303 0.4307056815 0.5869845713 0.5564447190 -0.400388565772 +1403636759813555456.0000000000 4.5285109484 -1.7239590716 0.8125894137 0.4322844151 0.5857482337 0.5568668009 -0.399910686465 +1403636759863555584.0000000000 4.5342468533 -1.7270646300 0.8105433868 0.4313744836 0.5864644504 0.5569554094 -0.399720121136 +1403636759913555456.0000000000 4.5409822916 -1.7302096025 0.8074970667 0.4282554653 0.5885625145 0.5591527134 -0.396912668209 +1403636759963555584.0000000000 4.5483068245 -1.7332243609 0.8036736603 0.4251121527 0.5908237579 0.5615807204 -0.393489566795 +1403636760013555456.0000000000 4.5557640694 -1.7363938348 0.7994937678 0.4220465372 0.5931026340 0.5630795377 -0.391212755759 +1403636760063555584.0000000000 4.5630048130 -1.7394996547 0.7948027719 0.4185285224 0.5957528213 0.5637719739 -0.389966169437 +1403636760113555456.0000000000 4.5699698469 -1.7423413367 0.7891481849 0.4162243298 0.5975439771 0.5657829420 -0.386766292759 +1403636760163555584.0000000000 4.5760908295 -1.7452926285 0.7835387650 0.4142028387 0.5990400050 0.5671929333 -0.384550721297 +1403636760213555456.0000000000 4.5805851978 -1.7479959844 0.7788471060 0.4162818269 0.5977080296 0.5650905294 -0.387462573087 +1403636760263555584.0000000000 4.5843196243 -1.7502537943 0.7740566520 0.4207558444 0.5949114057 0.5618789226 -0.391582705337 +1403636760313555456.0000000000 4.5878189959 -1.7524358043 0.7689416320 0.4241743783 0.5925144717 0.5583845046 -0.396496459786 +1403636760363555584.0000000000 4.5915270411 -1.7539392881 0.7623680081 0.4275045226 0.5902524198 0.5572726030 -0.397855765316 +1403636760413555456.0000000000 4.5955914091 -1.7553140765 0.7550704147 0.4308228412 0.5877542999 0.5565779798 -0.398945503632 +1403636760463555584.0000000000 4.6002863620 -1.7566217786 0.7468985013 0.4325062754 0.5865587107 0.5567847401 -0.398594974707 +1403636760513555456.0000000000 4.6060707537 -1.7579746694 0.7382911988 0.4325121074 0.5865253611 0.5582719484 -0.396552278286 +1403636760563555584.0000000000 4.6125129986 -1.7597615641 0.7294771130 0.4297837098 0.5881763444 0.5609224396 -0.393319930129 +1403636760613555456.0000000000 4.6190802690 -1.7615460193 0.7205953782 0.4269430373 0.5899965579 0.5636945529 -0.389707782269 +1403636760663555584.0000000000 4.6254977990 -1.7634839800 0.7121056476 0.4256873172 0.5906299543 0.5664455909 -0.386116507754 +1403636760713555456.0000000000 4.6317294230 -1.7656811177 0.7041994755 0.4244442309 0.5911141141 0.5688045024 -0.383265752447 +1403636760763555584.0000000000 4.6371647915 -1.7681674869 0.6971826205 0.4256320442 0.5900160168 0.5698039029 -0.382154386522 +1403636760813555456.0000000000 4.6418871815 -1.7712528560 0.6905736658 0.4275811492 0.5883822443 0.5693850845 -0.383120504685 +1403636760863555584.0000000000 4.6463224855 -1.7746998066 0.6840983001 0.4307902858 0.5858968881 0.5689066529 -0.384043990211 +1403636760913555456.0000000000 4.6509499800 -1.7787905315 0.6777571849 0.4332348358 0.5837034742 0.5685577889 -0.38514915529 +1403636760963555584.0000000000 4.6557782595 -1.7836339018 0.6711544243 0.4330139400 0.5837144141 0.5687764434 -0.385058135835 +1403636761013555456.0000000000 4.6609271796 -1.7894886413 0.6645128356 0.4296373324 0.5858384105 0.5695839256 -0.384420695563 +1403636761063555584.0000000000 4.6659382567 -1.7956574474 0.6575054976 0.4254220545 0.5887364661 0.5705327369 -0.383272546916 +1403636761113555456.0000000000 4.6704479782 -1.8024086877 0.6504253726 0.4199942097 0.5922601755 0.5722132186 -0.381319788134 +1403636761163555584.0000000000 4.6742712300 -1.8093721481 0.6429026730 0.4145311681 0.5958215829 0.5747783177 -0.377876219852 +1403636761213555456.0000000000 4.6771664400 -1.8164665742 0.6357590376 0.4105954400 0.5980249487 0.5780411693 -0.373692322621 +1403636761263555584.0000000000 4.6787531162 -1.8238579659 0.6297835013 0.4069710447 0.6004041007 0.5792112152 -0.372026683006 +1403636761313555456.0000000000 4.6783914995 -1.8312127338 0.6248345004 0.4065737167 0.6005951417 0.5799857103 -0.370944557176 +1403636761363555584.0000000000 4.6759852647 -1.8386432036 0.6212310412 0.4079752390 0.5995275735 0.5788021618 -0.372975804164 +1403636761413555456.0000000000 4.6720079491 -1.8460109327 0.6191515748 0.4124125232 0.5966263163 0.5760608887 -0.376970558463 +1403636761463555584.0000000000 4.6670085420 -1.8533245744 0.6179948691 0.4177837114 0.5931647384 0.5731441920 -0.380943695129 +1403636761513555456.0000000000 4.6613529742 -1.8608318940 0.6177802568 0.4220414344 0.5904594260 0.5698651801 -0.38534707786 +1403636761563555584.0000000000 4.6556095404 -1.8684222818 0.6181589713 0.4258885661 0.5881543837 0.5670456954 -0.388783396777 +1403636761613555456.0000000000 4.6499134445 -1.8762092956 0.6190411172 0.4284683625 0.5867048169 0.5644912676 -0.391844266245 +1403636761663555584.0000000000 4.6447391411 -1.8842178370 0.6202782547 0.4276282856 0.5876465826 0.5615519214 -0.395556548315 +1403636761713555456.0000000000 4.6398658449 -1.8922985134 0.6222686191 0.4250510796 0.5898554922 0.5576866922 -0.400484246187 +1403636761763555584.0000000000 4.6354523869 -1.8999387685 0.6244137135 0.4218939072 0.5922292229 0.5547646584 -0.404359063692 +1403636761813555456.0000000000 4.6314373911 -1.9068070033 0.6270354835 0.4192468296 0.5943523439 0.5522283777 -0.407456999013 +1403636761863555584.0000000000 4.6279896241 -1.9126570836 0.6298910022 0.4175134575 0.5956509547 0.5508213646 -0.409241099104 +1403636761913555456.0000000000 4.6252223207 -1.9168292074 0.6325958983 0.4178276964 0.5956690132 0.5515443057 -0.407918278278 +1403636761963555584.0000000000 4.6228831689 -1.9196366142 0.6354585651 0.4197610749 0.5946374824 0.5532060413 -0.405178948509 +1403636762013555456.0000000000 4.6205844255 -1.9212906778 0.6383167401 0.4256335931 0.5907517464 0.5568299571 -0.399735934502 +1403636762063555584.0000000000 4.6184727639 -1.9226147022 0.6415230003 0.4316675744 0.5869165766 0.5603431274 -0.393963979208 +1403636762113555456.0000000000 4.6171653892 -1.9238031618 0.6448626708 0.4390891466 0.5817316305 0.5653706156 -0.386193084263 +1403636762163555584.0000000000 4.6163425234 -1.9260091585 0.6485812144 0.4433184346 0.5788322505 0.5693945265 -0.379752372539 +1403636762213555456.0000000000 4.6160979062 -1.9298100955 0.6523218399 0.4422542738 0.5798602210 0.5724969970 -0.374727193989 +1403636762263555584.0000000000 4.6157990791 -1.9353059562 0.6556403698 0.4370819415 0.5837376640 0.5749405011 -0.371016355716 +1403636762313555456.0000000000 4.6146644188 -1.9420462023 0.6576024338 0.4307303524 0.5884730423 0.5766760666 -0.36826017474 +1403636762363555584.0000000000 4.6136050924 -1.9495607641 0.6574803399 0.4245345347 0.5929500810 0.5778253811 -0.366467541901 +1403636762413555456.0000000000 4.6105858049 -1.9579484608 0.6555296062 0.4198470028 0.5964182810 0.5772138037 -0.367202877382 +1403636762463555584.0000000000 4.6063367822 -1.9672802646 0.6521215536 0.4144238873 0.6003904806 0.5741345411 -0.371690248984 +1403636762513555456.0000000000 4.6003152754 -1.9773819195 0.6483332017 0.4088785752 0.6045631397 0.5660916742 -0.383225700106 +1403636762563555584.0000000000 4.5935815995 -1.9870368859 0.6425383094 0.4046877865 0.6076417455 0.5577300103 -0.394888009648 +1403636762613555456.0000000000 4.5864396718 -1.9957258291 0.6347560171 0.4008246534 0.6102372604 0.5493906385 -0.406349615036 +1403636762663555584.0000000000 4.5789525221 -2.0024570552 0.6244682677 0.4004289446 0.6102942535 0.5435098790 -0.414481116572 +1403636762713555456.0000000000 4.5716951912 -2.0065929182 0.6104925102 0.4055113263 0.6066729508 0.5434930556 -0.414878046608 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_02_easy.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_02_easy.txt new file mode 100644 index 0000000000000000000000000000000000000000..702c7f2a1f8e0477c8f3038f62c84566ea65eb5d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_02_easy.txt @@ -0,0 +1,3000 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403636859551666432.0000000000 4.6007251330 -1.8992266135 0.7254218941 0.4553496982 0.6652088523 0.4806972609 -0.345085465526 +1403636859601666560.0000000000 4.5986132409 -1.8957845851 0.7476130289 0.4578604366 0.6661437955 0.4802166833 -0.340599767178 +1403636859651666432.0000000000 4.5960790067 -1.8926073207 0.7705000109 0.4624068450 0.6658715875 0.4786942508 -0.33711534057 +1403636859701666560.0000000000 4.5932628122 -1.8903267716 0.7940387527 0.4673689069 0.6646097000 0.4756961562 -0.337006555515 +1403636859751666432.0000000000 4.5905739813 -1.8879864657 0.8175848138 0.4738624301 0.6620928672 0.4732541966 -0.33633004313 +1403636859801666560.0000000000 4.5883869808 -1.8860577519 0.8402761439 0.4802112544 0.6594949047 0.4715534337 -0.33481484585 +1403636859851666432.0000000000 4.5867636625 -1.8844915355 0.8622409401 0.4858023464 0.6571830669 0.4706510208 -0.332556932742 +1403636859901666560.0000000000 4.5860565127 -1.8839241257 0.8831788284 0.4889187907 0.6559270013 0.4698856203 -0.33155043196 +1403636859951666432.0000000000 4.5860467146 -1.8836141293 0.9021344939 0.4907032984 0.6555303130 0.4687546958 -0.331299436868 +1403636860001666560.0000000000 4.5867605505 -1.8827386843 0.9170741102 0.4917685232 0.6558961233 0.4678833602 -0.330225917025 +1403636860051666432.0000000000 4.5873967418 -1.8810180258 0.9263528689 0.4918892338 0.6571993132 0.4671897297 -0.328432338196 +1403636860101666560.0000000000 4.5882292257 -1.8787878358 0.9278415538 0.4904044646 0.6598095820 0.4659323709 -0.327202998673 +1403636860151666432.0000000000 4.5891755842 -1.8764623463 0.9211182081 0.4880116279 0.6621457515 0.4658908619 -0.326118628134 +1403636860201666560.0000000000 4.5907776864 -1.8745791881 0.9060767797 0.4846225920 0.6647731418 0.4664992160 -0.3249555273 +1403636860251666432.0000000000 4.5928801063 -1.8739484164 0.8847568274 0.4791198408 0.6681090846 0.4675566709 -0.324754043478 +1403636860301666560.0000000000 4.5953053145 -1.8738760549 0.8587300054 0.4722389992 0.6726900331 0.4689491326 -0.323365363228 +1403636860351666432.0000000000 4.5979561124 -1.8734197831 0.8294532968 0.4646976572 0.6783317812 0.4709599194 -0.319560379929 +1403636860401666560.0000000000 4.6009032293 -1.8736109762 0.7999149085 0.4561419063 0.6848722254 0.4727842984 -0.315213583874 +1403636860451666432.0000000000 4.6041696804 -1.8742072936 0.7707819998 0.4474409662 0.6912571226 0.4749813310 -0.310407647084 +1403636860501666560.0000000000 4.6072545695 -1.8750770763 0.7434868878 0.4380260768 0.6975416711 0.4770071398 -0.306647944227 +1403636860551666432.0000000000 4.6100552722 -1.8762165399 0.7195651896 0.4291716999 0.7023640488 0.4793990700 -0.304422283426 +1403636860601666560.0000000000 4.6129975649 -1.8770004728 0.6991733468 0.4222902498 0.7063530274 0.4813475007 -0.301729894501 +1403636860651666432.0000000000 4.6157729415 -1.8779571913 0.6826182664 0.4171681133 0.7080534120 0.4834497069 -0.301508726102 +1403636860701666560.0000000000 4.6179924359 -1.8784334210 0.6685783310 0.4146381379 0.7078010246 0.4860098444 -0.301475298033 +1403636860751666432.0000000000 4.6201836764 -1.8786693575 0.6611674105 0.4152340195 0.7063254235 0.4885342181 -0.300032369776 +1403636860801666560.0000000000 4.6219347314 -1.8786362172 0.6597550726 0.4168594273 0.7039402596 0.4914868648 -0.298558186167 +1403636860851666432.0000000000 4.6229967627 -1.8783765721 0.6651911615 0.4182496400 0.7017227154 0.4942209594 -0.297318200996 +1403636860901666560.0000000000 4.6233121159 -1.8778027308 0.6775860961 0.4188659597 0.6997897782 0.4965897029 -0.29705932271 +1403636860951666432.0000000000 4.6230756935 -1.8769846469 0.6963656488 0.4193750601 0.6978553397 0.4985029024 -0.297686647473 +1403636861001666560.0000000000 4.6218727666 -1.8755941006 0.7202896893 0.4218198496 0.6954813115 0.4990660434 -0.298842507218 +1403636861051666432.0000000000 4.6197797471 -1.8738751236 0.7478137832 0.4257000318 0.6928182829 0.4976826447 -0.301818314487 +1403636861101666560.0000000000 4.6167828148 -1.8717432087 0.7775421884 0.4317269700 0.6893374233 0.4949858023 -0.305638341397 +1403636861151666432.0000000000 4.6133092988 -1.8692395931 0.8080543505 0.4392490650 0.6850481124 0.4913280599 -0.31042886491 +1403636861201666560.0000000000 4.6095237190 -1.8664509270 0.8393565887 0.4477734366 0.6795519629 0.4878967506 -0.315697386712 +1403636861251666432.0000000000 4.6061386731 -1.8637047544 0.8704068236 0.4564913913 0.6738085647 0.4840230040 -0.321433289142 +1403636861301666560.0000000000 4.6031024282 -1.8611831738 0.9009661133 0.4642180279 0.6686707404 0.4795039649 -0.327806362227 +1403636861351666432.0000000000 4.6077357258 -1.8616316080 0.9331627599 0.4713334528 0.6644234483 0.4750385865 -0.332753059946 +1403636861401666560.0000000000 4.6062444069 -1.8593691560 0.9571163232 0.4769946456 0.6614985834 0.4700324423 -0.337587374418 +1403636861451666432.0000000000 4.6051334750 -1.8570311073 0.9741852060 0.4822384764 0.6586561201 0.4666316457 -0.340401343322 +1403636861501666560.0000000000 4.6042096483 -1.8551822270 0.9830963842 0.4855708053 0.6572228518 0.4637325399 -0.342390489819 +1403636861551666432.0000000000 4.6034989209 -1.8533161351 0.9830590642 0.4873767661 0.6571633930 0.4625637647 -0.34151855937 +1403636861601666560.0000000000 4.6031617789 -1.8520765419 0.9745049976 0.4858029561 0.6584391783 0.4632666480 -0.34034886387 +1403636861651666432.0000000000 4.6031376316 -1.8516556825 0.9584918130 0.4818493410 0.6608222260 0.4649882842 -0.339000138342 +1403636861701666560.0000000000 4.6032778567 -1.8518703248 0.9365410985 0.4775263089 0.6632593451 0.4675277426 -0.336858242086 +1403636861751666432.0000000000 4.6038124948 -1.8525121201 0.9110132842 0.4733446022 0.6654518903 0.4705064829 -0.334278804038 +1403636861801666560.0000000000 4.6047365188 -1.8536311372 0.8835868833 0.4697508807 0.6674682305 0.4735087436 -0.331073618754 +1403636861851666432.0000000000 4.6060475251 -1.8557537263 0.8554024216 0.4647905089 0.6697266650 0.4761673344 -0.329697811114 +1403636861901666560.0000000000 4.6075257592 -1.8586579808 0.8267914316 0.4581952473 0.6728868043 0.4794124363 -0.327786790216 +1403636861951666432.0000000000 4.6090950028 -1.8618925170 0.7980015929 0.4501117017 0.6775435472 0.4825424943 -0.324787528822 +1403636862001666560.0000000000 4.6105810039 -1.8654619496 0.7695507435 0.4413105570 0.6826352331 0.4855388788 -0.321723682784 +1403636862051666432.0000000000 4.6119951176 -1.8693284349 0.7429237139 0.4332730880 0.6875698012 0.4875018915 -0.319161566512 +1403636862101666560.0000000000 4.6144829334 -1.8721934567 0.7155465186 0.4272987511 0.6913625638 0.4888715353 -0.316919871088 +1403636862151666432.0000000000 4.6154803373 -1.8751953647 0.6944550621 0.4220300027 0.6940244316 0.4897533259 -0.316800323321 +1403636862201666560.0000000000 4.6169867540 -1.8772280629 0.6776676886 0.4190724282 0.6946189528 0.4923527314 -0.315391182776 +1403636862251666432.0000000000 4.6184128837 -1.8779953780 0.6672518363 0.4181567945 0.6944725973 0.4958284949 -0.311459163331 +1403636862301666560.0000000000 4.6196143191 -1.8784104477 0.6641775135 0.4169055298 0.6944860532 0.4991105506 -0.30784340074 +1403636862351666432.0000000000 4.6201439888 -1.8780276390 0.6695560814 0.4149744404 0.6947221134 0.5022835601 -0.304743538316 +1403636862401666560.0000000000 4.6200793584 -1.8774882495 0.6837827021 0.4132492350 0.6950986885 0.5036570197 -0.303961329092 +1403636862451666432.0000000000 4.6195601867 -1.8765777957 0.7049616054 0.4135075890 0.6945451336 0.5037784180 -0.304673328003 +1403636862501666560.0000000000 4.6182124321 -1.8746441523 0.7306395871 0.4167667004 0.6930499321 0.5029454122 -0.305013477344 +1403636862551666432.0000000000 4.6155579611 -1.8713553217 0.7596185636 0.4227409001 0.6915330872 0.5005217050 -0.304220550841 +1403636862601666560.0000000000 4.6121870579 -1.8670209054 0.7907733128 0.4315275036 0.6889792999 0.4981414344 -0.301573621545 +1403636862651666432.0000000000 4.6087701156 -1.8633713658 0.8235490459 0.4395552418 0.6865649089 0.4946406207 -0.301248189535 +1403636862701666560.0000000000 4.6054156116 -1.8604541513 0.8574274173 0.4467628632 0.6838331508 0.4916302072 -0.301786191434 +1403636862751666432.0000000000 4.6020178316 -1.8588818680 0.8918010380 0.4499755866 0.6836111397 0.4863475882 -0.306045428938 +1403636862801666560.0000000000 4.5989975726 -1.8567762240 0.9261958768 0.4525228628 0.6837250026 0.4829582069 -0.307399658111 +1403636862851666432.0000000000 4.5963534149 -1.8552814098 0.9598407326 0.4535619001 0.6854364221 0.4777748645 -0.310144632336 +1403636862901666560.0000000000 4.5946748158 -1.8539609999 0.9910915600 0.4551999578 0.6859042825 0.4738763912 -0.312681114706 +1403636862951666432.0000000000 4.5936622849 -1.8533794838 1.0175920982 0.4567245995 0.6858315849 0.4695055422 -0.317178535151 +1403636863001666560.0000000000 4.5986771696 -1.8574039087 1.0372940235 0.4595558310 0.6834106687 0.4676459553 -0.321038247943 +1403636863051666432.0000000000 4.5993688698 -1.8565030888 1.0463283558 0.4645850564 0.6795983619 0.4674563267 -0.322166687476 +1403636863101666560.0000000000 4.5998857062 -1.8550831824 1.0459570323 0.4702874606 0.6759457806 0.4679087655 -0.320918047607 +1403636863151666432.0000000000 4.6003077330 -1.8540553534 1.0370488107 0.4750632127 0.6726024496 0.4692419429 -0.3189559337 +1403636863201666560.0000000000 4.6007316073 -1.8537473846 1.0199693059 0.4776842972 0.6708214239 0.4710373392 -0.316133127821 +1403636863251666432.0000000000 4.6008997402 -1.8543502862 0.9964592282 0.4780714938 0.6703119607 0.4727500812 -0.314065093275 +1403636863301666560.0000000000 4.6011523059 -1.8546846716 0.9678042050 0.4791518280 0.6699282465 0.4747451744 -0.310204270971 +1403636863351666432.0000000000 4.6015910639 -1.8554167734 0.9362818716 0.4790965549 0.6706145724 0.4754250931 -0.307755693893 +1403636863401666560.0000000000 4.6016933434 -1.8555208614 0.9036997322 0.4797514466 0.6719267730 0.4756174054 -0.303547434377 +1403636863451666432.0000000000 4.6024121966 -1.8565444601 0.8702294426 0.4784338737 0.6740969896 0.4752569132 -0.301372101535 +1403636863501666560.0000000000 4.6036072180 -1.8579943372 0.8356191279 0.4739294749 0.6784074808 0.4744137184 -0.30014291038 +1403636863551666432.0000000000 4.6057745030 -1.8608701082 0.8018806550 0.4660129986 0.6822275226 0.4753033774 -0.302463538106 +1403636863601666560.0000000000 4.6087707123 -1.8634885357 0.7696588864 0.4575196366 0.6865844832 0.4765366728 -0.303628603653 +1403636863651666432.0000000000 4.6119661555 -1.8661785498 0.7394207873 0.4489926459 0.6908923950 0.4780410308 -0.304220438597 +1403636863701666560.0000000000 4.6154802010 -1.8667938983 0.7103942970 0.4409229411 0.6950934211 0.4792491265 -0.304552738795 +1403636863751666432.0000000000 4.6174843619 -1.8680799155 0.6882941743 0.4341365175 0.6997062462 0.4793820405 -0.303528437555 +1403636863801666560.0000000000 4.6195019504 -1.8688424769 0.6726648754 0.4280777609 0.7032738759 0.4811403093 -0.3010968097 +1403636863851666432.0000000000 4.6215597678 -1.8692760797 0.6654059853 0.4235692582 0.7058081948 0.4832636160 -0.298127746439 +1403636863901666560.0000000000 4.6233373459 -1.8693198020 0.6673085009 0.4200181663 0.7071055476 0.4854387349 -0.296539574351 +1403636863951666432.0000000000 4.6245645262 -1.8689966766 0.6787760340 0.4172509404 0.7073661363 0.4872435550 -0.296864481014 +1403636864001666560.0000000000 4.6250386263 -1.8682235276 0.6989575322 0.4170752233 0.7062784153 0.4884910546 -0.297650042406 +1403636864051666432.0000000000 4.6251040047 -1.8675570508 0.7256468433 0.4186719202 0.7039610500 0.4891252664 -0.299848523589 +1403636864101666560.0000000000 4.6244962067 -1.8659413273 0.7573005591 0.4229968054 0.7004905981 0.4906243263 -0.299456833173 +1403636864151666432.0000000000 4.6230858401 -1.8638721106 0.7919484387 0.4286783760 0.6976143998 0.4906465460 -0.298051952016 +1403636864201666560.0000000000 4.6207807065 -1.8617681674 0.8282647684 0.4340882282 0.6954946497 0.4896426645 -0.296824297338 +1403636864251666432.0000000000 4.6182364869 -1.8605461014 0.8636726224 0.4376463472 0.6941709529 0.4884199916 -0.296712444345 +1403636864301666560.0000000000 4.6156671321 -1.8601742527 0.8976967209 0.4390144745 0.6930696448 0.4876973197 -0.298449464785 +1403636864351666432.0000000000 4.6133314965 -1.8602235507 0.9294722134 0.4403643713 0.6922698613 0.4863190373 -0.300558569428 +1403636864401666560.0000000000 4.6107541253 -1.8601698146 0.9590796834 0.4433457812 0.6912573751 0.4832725799 -0.303406284116 +1403636864451666432.0000000000 4.6102646170 -1.8613458704 0.9883650269 0.4486352807 0.6897373740 0.4780933009 -0.30727111068 +1403636864501666560.0000000000 4.6073560571 -1.8611338473 1.0126726216 0.4554033423 0.6874101400 0.4711870777 -0.313141873547 +1403636864551666432.0000000000 4.6044125314 -1.8615760590 1.0317990062 0.4608107711 0.6845809246 0.4642904356 -0.321615892509 +1403636864601666560.0000000000 4.6020921742 -1.8614447524 1.0433393592 0.4673694879 0.6811406626 0.4597171796 -0.325995819425 +1403636864651666432.0000000000 4.6007829464 -1.8610639022 1.0462176933 0.4729466334 0.6777672697 0.4577123976 -0.327799284864 +1403636864701666560.0000000000 4.6006136076 -1.8605461792 1.0398161657 0.4771092877 0.6749334077 0.4591788902 -0.325555478273 +1403636864751666432.0000000000 4.6009141963 -1.8600430034 1.0254970228 0.4786789898 0.6737737828 0.4619672846 -0.32168547122 +1403636864801666560.0000000000 4.6014584088 -1.8604207395 1.0045794062 0.4770841788 0.6742334460 0.4649869123 -0.318727341169 +1403636864851666432.0000000000 4.6019694521 -1.8614000303 0.9788185957 0.4743795336 0.6758045818 0.4673132670 -0.316022998854 +1403636864901666560.0000000000 4.6020668840 -1.8623091705 0.9502380908 0.4716856867 0.6782182411 0.4684912154 -0.313127148995 +1403636864951666432.0000000000 4.6022315190 -1.8624225956 0.9202050304 0.4696744380 0.6806755764 0.4701876768 -0.308237295929 +1403636865001666560.0000000000 4.6024896216 -1.8624733206 0.8889463027 0.4677547385 0.6836834550 0.4714060559 -0.302586794811 +1403636865051666432.0000000000 4.6028551023 -1.8629713670 0.8579407473 0.4637943775 0.6863577039 0.4737499708 -0.298946220854 +1403636865101666560.0000000000 4.6024287002 -1.8618899588 0.8269197611 0.4590908843 0.6899103199 0.4749157196 -0.296166118502 +1403636865151666432.0000000000 4.6021476723 -1.8630780572 0.7988339533 0.4516057656 0.6950300917 0.4727538541 -0.299147451159 +1403636865201666560.0000000000 4.6021535673 -1.8647125017 0.7736766357 0.4438953585 0.6991923615 0.4706949338 -0.30419275398 +1403636865251666432.0000000000 4.6026679869 -1.8662974002 0.7516140347 0.4369393258 0.7026605250 0.4683982965 -0.309766441081 +1403636865301666560.0000000000 4.6031522602 -1.8673036223 0.7323388248 0.4329717245 0.7043907800 0.4671990553 -0.313199868383 +1403636865351666432.0000000000 4.6034053786 -1.8675669036 0.7168912801 0.4322565029 0.7054426232 0.4660260347 -0.31356778529 +1403636865401666560.0000000000 4.6036327784 -1.8677777196 0.7049569619 0.4321339477 0.7054104097 0.4674771282 -0.31164328914 +1403636865451666432.0000000000 4.6039002864 -1.8678287899 0.6980747046 0.4316561887 0.7051880540 0.4709399745 -0.307568339868 +1403636865501666560.0000000000 4.6041133467 -1.8677045895 0.6971970521 0.4302445103 0.7057337377 0.4752217850 -0.301651799081 +1403636865551666432.0000000000 4.6041891707 -1.8676791218 0.7039513666 0.4272273069 0.7063248418 0.4800466311 -0.296879231471 +1403636865601666560.0000000000 4.6039002134 -1.8683121231 0.7181467814 0.4243769042 0.7069287193 0.4832867714 -0.294261661848 +1403636865651666432.0000000000 4.6034689728 -1.8699719340 0.7387578851 0.4222607256 0.7066385267 0.4850260126 -0.295140033185 +1403636865701666560.0000000000 4.6027489077 -1.8718506741 0.7644667069 0.4227515885 0.7048576449 0.4854053606 -0.298057764265 +1403636865751666432.0000000000 4.6013277300 -1.8733188685 0.7935373579 0.4258001222 0.7026374992 0.4836672818 -0.301762756338 +1403636865801666560.0000000000 4.5993107087 -1.8740261457 0.8252349965 0.4304004575 0.6997478919 0.4809957889 -0.306188479455 +1403636865851666432.0000000000 4.5970330412 -1.8740379559 0.8584234819 0.4356613211 0.6969826126 0.4770992322 -0.311112156154 +1403636865901666560.0000000000 4.5949050929 -1.8737209323 0.8926101641 0.4420836269 0.6931392916 0.4730412118 -0.316783839876 +1403636865951666432.0000000000 4.5931217645 -1.8736252397 0.9270066687 0.4492073659 0.6887684780 0.4677508285 -0.324067722055 +1403636866001666560.0000000000 4.5915631538 -1.8732675916 0.9608775817 0.4578036844 0.6836263220 0.4621269072 -0.330922287048 +1403636866051666432.0000000000 4.5904025890 -1.8730808592 0.9930424367 0.4677131228 0.6783340007 0.4553565380 -0.337280064062 +1403636866101666560.0000000000 4.5901513337 -1.8735641894 1.0273479234 0.4774954548 0.6727722934 0.4500708334 -0.34177737893 +1403636866151666432.0000000000 4.5904434574 -1.8734759403 1.0526136161 0.4858408966 0.6676313272 0.4465366475 -0.344720258467 +1403636866201666560.0000000000 4.5914709725 -1.8736507815 1.0709095460 0.4913836921 0.6639849067 0.4449046643 -0.346014378876 +1403636866251666432.0000000000 4.5923488271 -1.8736736473 1.0819070600 0.4946192785 0.6623942051 0.4443855143 -0.34511911141 +1403636866301666560.0000000000 4.5933931274 -1.8737311276 1.0841122563 0.4957429355 0.6624976244 0.4458926570 -0.341343782759 +1403636866351666432.0000000000 4.5938220699 -1.8736707574 1.0784456656 0.4953760010 0.6645123626 0.4474379220 -0.335894691159 +1403636866401666560.0000000000 4.5940682385 -1.8733462804 1.0654141151 0.4934520512 0.6667654923 0.4504649348 -0.330166918237 +1403636866451666432.0000000000 4.5937714431 -1.8731061043 1.0461796668 0.4906306646 0.6694745087 0.4525894964 -0.325957329839 +1403636866501666560.0000000000 4.5940448919 -1.8730587132 1.0215876891 0.4876354676 0.6714458917 0.4554436702 -0.322402122297 +1403636866551666432.0000000000 4.5942675219 -1.8722176928 0.9936692700 0.4848155443 0.6737349357 0.4575753023 -0.318841601914 +1403636866601666560.0000000000 4.5946494235 -1.8707478695 0.9649446974 0.4816283656 0.6766043229 0.4592965793 -0.315098968462 +1403636866651666432.0000000000 4.5958591200 -1.8687256109 0.9370524879 0.4789084718 0.6795805519 0.4613515563 -0.309792980282 +1403636866701666560.0000000000 4.5978922247 -1.8668804355 0.9117119458 0.4753250040 0.6824895153 0.4634831295 -0.305708342607 +1403636866751666432.0000000000 4.6015158853 -1.8660924682 0.8895830837 0.4709397711 0.6839581582 0.4669325114 -0.303958878142 +1403636866801666560.0000000000 4.6033423276 -1.8632665820 0.8690730324 0.4661705699 0.6852476843 0.4699662787 -0.30373065019 +1403636866851666432.0000000000 4.6074047632 -1.8641178197 0.8512700491 0.4594071567 0.6866047768 0.4730247793 -0.306213165942 +1403636866901666560.0000000000 4.6111841270 -1.8653321237 0.8349255348 0.4513618833 0.6894195331 0.4754878279 -0.308033250052 +1403636866951666432.0000000000 4.6149711122 -1.8671148651 0.8203436099 0.4420679918 0.6930775352 0.4779602565 -0.309472800118 +1403636867001666560.0000000000 4.6186500634 -1.8685315810 0.8080771037 0.4348771143 0.6967425367 0.4800791251 -0.308148935791 +1403636867051666432.0000000000 4.6218337476 -1.8695309191 0.7982844983 0.4300093128 0.7002314424 0.4812318047 -0.305260328355 +1403636867101666560.0000000000 4.6252020132 -1.8708405982 0.7909811085 0.4262056437 0.7019312716 0.4834752347 -0.303138477628 +1403636867151666432.0000000000 4.6291915463 -1.8726119010 0.7863605468 0.4220533661 0.7034250745 0.4846817293 -0.303558465466 +1403636867201666560.0000000000 4.6341609494 -1.8752345323 0.7836058241 0.4176737434 0.7033281044 0.4872277521 -0.30575699375 +1403636867251666432.0000000000 4.6396981965 -1.8786072029 0.7822552228 0.4127417128 0.7023302318 0.4908673362 -0.308910638197 +1403636867301666560.0000000000 4.6444193349 -1.8807740737 0.7826198014 0.4089471707 0.7017714019 0.4936582302 -0.31077429548 +1403636867351666432.0000000000 4.6485814474 -1.8824326131 0.7839531887 0.4057187447 0.7023748095 0.4956589298 -0.310457972325 +1403636867401666560.0000000000 4.6519627794 -1.8833581917 0.7859830078 0.4038588200 0.7033612186 0.4975804224 -0.307562632506 +1403636867451666432.0000000000 4.6554979869 -1.8848997888 0.7886318977 0.4008279334 0.7054298784 0.4994560702 -0.30372567939 +1403636867501666560.0000000000 4.6591316787 -1.8862301594 0.7911233635 0.3965688821 0.7085861410 0.5019780504 -0.29775298401 +1403636867551666432.0000000000 4.6639430627 -1.8876559000 0.7920193817 0.3890932501 0.7127257266 0.5072288216 -0.288699504532 +1403636867601666560.0000000000 4.6692752520 -1.8890454551 0.7916886599 0.3766868470 0.7190832961 0.5136083389 -0.277907730709 +1403636867651666432.0000000000 4.6752201245 -1.8908323357 0.7900856900 0.3588475163 0.7277994679 0.5206778823 -0.265388276799 +1403636867701666560.0000000000 4.6814488293 -1.8928706937 0.7878380380 0.3365457290 0.7384865020 0.5276455837 -0.250927871356 +1403636867751666432.0000000000 4.6878839406 -1.8946102031 0.7848777057 0.3130332755 0.7493642023 0.5343561380 -0.234365054044 +1403636867801666560.0000000000 4.6934708234 -1.8955364388 0.7823180832 0.2919964031 0.7591988596 0.5394973455 -0.21748058851 +1403636867851666432.0000000000 4.6973363415 -1.8959656328 0.7805743707 0.2753882138 0.7676747155 0.5413291664 -0.204449496364 +1403636867901666560.0000000000 4.6991888999 -1.8961209462 0.7804776358 0.2655086407 0.7726732638 0.5419972759 -0.196774342844 +1403636867951666432.0000000000 4.6990759334 -1.8962982821 0.7817667503 0.2622644916 0.7757448384 0.5400016897 -0.194513385761 +1403636868001666560.0000000000 4.6984038463 -1.8966255629 0.7839051416 0.2643808444 0.7757511447 0.5383538545 -0.196183735358 +1403636868051666432.0000000000 4.6973113624 -1.8968363375 0.7867013794 0.2700139669 0.7744610019 0.5359291333 -0.200206339293 +1403636868101666560.0000000000 4.6969586084 -1.8972769229 0.7891071170 0.2764521504 0.7720694073 0.5343701442 -0.204772038803 +1403636868151666432.0000000000 4.6970838904 -1.8979207387 0.7909805579 0.2816996712 0.7700375874 0.5329554275 -0.208916063157 +1403636868201666560.0000000000 4.6982987353 -1.8992019099 0.7922385979 0.2838364955 0.7688919534 0.5321691722 -0.212221535006 +1403636868251666432.0000000000 4.7000449496 -1.9006804415 0.7929331205 0.2843325942 0.7683498987 0.5322866066 -0.213223773296 +1403636868301666560.0000000000 4.7022204985 -1.9033286159 0.7934165753 0.2828702218 0.7697160149 0.5307839661 -0.213986156827 +1403636868351666432.0000000000 4.7047542625 -1.9067680006 0.7937126267 0.2803578158 0.7712124184 0.5301683596 -0.213430108673 +1403636868401666560.0000000000 4.7070062142 -1.9106831371 0.7940293365 0.2793559911 0.7725607255 0.5286565394 -0.213617459413 +1403636868451666432.0000000000 4.7090450698 -1.9152362935 0.7944519722 0.2811129308 0.7729376000 0.5267071391 -0.214761673234 +1403636868501666560.0000000000 4.7107859852 -1.9193775563 0.7955680843 0.2860892049 0.7720092182 0.5250716409 -0.215533073589 +1403636868551666432.0000000000 4.7122792259 -1.9232154184 0.7975305979 0.2922375845 0.7713258832 0.5223136050 -0.216430298684 +1403636868601666560.0000000000 4.7136704758 -1.9269405613 0.8002109444 0.2964074398 0.7716700879 0.5189822221 -0.217543922549 +1403636868651666432.0000000000 4.7156823815 -1.9302054981 0.8028646077 0.2979467620 0.7723474867 0.5170744317 -0.21758014349 +1403636868701666560.0000000000 4.7185711173 -1.9334508064 0.8046495887 0.2972288544 0.7731723387 0.5169083323 -0.21602156995 +1403636868751666432.0000000000 4.7220382845 -1.9370810504 0.8056269252 0.2943779915 0.7729659936 0.5195962645 -0.214207592677 +1403636868801666560.0000000000 4.7253353479 -1.9407050980 0.8055895174 0.2913403507 0.7727671684 0.5225771707 -0.21181313503 +1403636868851666432.0000000000 4.7279278748 -1.9436216336 0.8054732117 0.2900713501 0.7721071078 0.5253846831 -0.208997992052 +1403636868901666560.0000000000 4.7291070632 -1.9460863554 0.8057007639 0.2917331762 0.7709059373 0.5268570096 -0.207406559838 +1403636868951666432.0000000000 4.7292803179 -1.9487880709 0.8062013518 0.2940740494 0.7698171096 0.5266611277 -0.20863874946 +1403636869001666560.0000000000 4.7287855213 -1.9512584435 0.8072544915 0.2954288958 0.7680320609 0.5270584783 -0.212268418021 +1403636869051666432.0000000000 4.7284314926 -1.9533680030 0.8082154465 0.2957934991 0.7670122035 0.5267209439 -0.216248775184 +1403636869101666560.0000000000 4.7278452735 -1.9552951297 0.8091407973 0.2959285342 0.7657842723 0.5270709771 -0.219538005995 +1403636869151666432.0000000000 4.7277724991 -1.9574218397 0.8090922049 0.2954868324 0.7651970512 0.5271457509 -0.221987301444 +1403636869201666560.0000000000 4.7277042587 -1.9588006531 0.8084137432 0.2949316180 0.7641535584 0.5287216343 -0.222571591415 +1403636869251666432.0000000000 4.7268588133 -1.9595881150 0.8076613676 0.2946332215 0.7638158803 0.5293944524 -0.222526581621 +1403636869301666560.0000000000 4.7263147428 -1.9599684772 0.8067899455 0.2945278483 0.7632059773 0.5303843918 -0.222401393492 +1403636869351666432.0000000000 4.7254542368 -1.9604215401 0.8062275171 0.2941011420 0.7630582169 0.5304387098 -0.223341556683 +1403636869401666560.0000000000 4.7247911017 -1.9604755076 0.8056957209 0.2940906679 0.7625940748 0.5309582251 -0.223705876776 +1403636869451666432.0000000000 4.7242368462 -1.9601679316 0.8052719962 0.2938416204 0.7625000088 0.5310294703 -0.224184166139 +1403636869501666560.0000000000 4.7240979940 -1.9587520390 0.8048602450 0.2940660466 0.7625897204 0.5308159554 -0.224090383694 +1403636869551666432.0000000000 4.7243481140 -1.9557266868 0.8044280776 0.2943858038 0.7626499012 0.5306148485 -0.223941977599 +1403636869601666560.0000000000 4.7250378133 -1.9506692237 0.8039665233 0.2940890861 0.7631812470 0.5301771040 -0.223558117614 +1403636869651666432.0000000000 4.7263205438 -1.9431546696 0.8035143800 0.2931878596 0.7635951184 0.5306221317 -0.222269042873 +1403636869701666560.0000000000 4.7280658668 -1.9330313776 0.8027992700 0.2920125027 0.7650086963 0.5301462107 -0.220080412743 +1403636869751666432.0000000000 4.7298872088 -1.9204828333 0.8023792916 0.2909959206 0.7663842868 0.5295681159 -0.21802318622 +1403636869801666560.0000000000 4.7313439001 -1.9054514263 0.8020899451 0.2913935817 0.7678369221 0.5277372403 -0.216817081325 +1403636869851666432.0000000000 4.7323028588 -1.8879392063 0.8021962635 0.2936763007 0.7691094814 0.5248250962 -0.216294832137 +1403636869901666560.0000000000 4.7329511542 -1.8683075909 0.8024931325 0.2971895878 0.7704056578 0.5209026822 -0.216365124383 +1403636869951666432.0000000000 4.7338095196 -1.8471559032 0.8027012223 0.3007038411 0.7715729209 0.5169018014 -0.216944590414 +1403636870001666560.0000000000 4.7348089959 -1.8242698804 0.8025449486 0.3033150787 0.7730698798 0.5132955555 -0.216542367063 +1403636870051666432.0000000000 4.7361907145 -1.8003947070 0.8020857984 0.3042303625 0.7754859358 0.5096192766 -0.21529896156 +1403636870101666560.0000000000 4.7376655515 -1.7753018969 0.8014834307 0.3038680838 0.7784985942 0.5065212008 -0.212227235766 +1403636870151666432.0000000000 4.7396343229 -1.7493527947 0.8010059090 0.3031969521 0.7813128026 0.5044533750 -0.207722664324 +1403636870201666560.0000000000 4.7417609140 -1.7228919442 0.8009205315 0.3030370150 0.7828858779 0.5039150943 -0.20329251708 +1403636870251666432.0000000000 4.7438572047 -1.6967621091 0.8012535403 0.3032630293 0.7841768574 0.5025147054 -0.201437737702 +1403636870301666560.0000000000 4.7455792580 -1.6706242761 0.8018071436 0.3053655799 0.7847984147 0.5002312826 -0.201524129788 +1403636870351666432.0000000000 4.7472820917 -1.6445492496 0.8021316272 0.3091299354 0.7852369635 0.4969709653 -0.202142162254 +1403636870401666560.0000000000 4.7490962756 -1.6185031724 0.8017348136 0.3140968211 0.7848879451 0.4947819687 -0.201208608215 +1403636870451666432.0000000000 4.7512785756 -1.5938277817 0.8006200928 0.3176168350 0.7849413400 0.4931031683 -0.199589339318 +1403636870501666560.0000000000 4.7535955884 -1.5724820096 0.7988668053 0.3166250910 0.7872759553 0.4900269626 -0.199546230036 +1403636870551666432.0000000000 4.7557398936 -1.5536079687 0.7969184773 0.3134944655 0.7907906427 0.4866789254 -0.19878381018 +1403636870601666560.0000000000 4.7586458931 -1.5350916338 0.7941908433 0.3120455713 0.7932323716 0.4859517021 -0.193030850827 +1403636870651666432.0000000000 4.7612524313 -1.5182584107 0.7918273086 0.3117082543 0.7954729306 0.4846005803 -0.187678071182 +1403636870701666560.0000000000 4.7629171111 -1.5033458321 0.7901393714 0.3137736454 0.7962983159 0.4829172977 -0.185056680718 +1403636870751666432.0000000000 4.7630112479 -1.4909236941 0.7890290679 0.3166812084 0.7958900782 0.4811172949 -0.186542607267 +1403636870801666560.0000000000 4.7626969492 -1.4816893773 0.7871951459 0.3192632673 0.7960084274 0.4772312225 -0.191551324481 +1403636870851666432.0000000000 4.7625906668 -1.4742091451 0.7851753815 0.3220309070 0.7952289261 0.4747250565 -0.196324147266 +1403636870901666560.0000000000 4.7633142484 -1.4685189352 0.7829934631 0.3255698622 0.7935294847 0.4737338309 -0.199728513734 +1403636870951666432.0000000000 4.7636144305 -1.4647366637 0.7810501005 0.3271812682 0.7926702570 0.4723743344 -0.203687922148 +1403636871001666560.0000000000 4.7642332877 -1.4630650334 0.7790125769 0.3267484225 0.7929423879 0.4710270156 -0.206425261184 +1403636871051666432.0000000000 4.7643921733 -1.4628477445 0.7765956958 0.3234907439 0.7949313854 0.4693297854 -0.207767619104 +1403636871101666560.0000000000 4.7650466000 -1.4628216236 0.7740215901 0.3199273563 0.7973107159 0.4694083404 -0.203955678712 +1403636871151666432.0000000000 4.7655398251 -1.4633833413 0.7723315492 0.3173018418 0.7995109370 0.4702229831 -0.197464297938 +1403636871201666560.0000000000 4.7653331591 -1.4660005258 0.7722324850 0.3154095120 0.8017320095 0.4694748801 -0.193225157653 +1403636871251666432.0000000000 4.7644264521 -1.4702297013 0.7735669294 0.3151647724 0.8025907037 0.4688459215 -0.191579827968 +1403636871301666560.0000000000 4.7628230337 -1.4767333868 0.7754878394 0.3157291732 0.8023125652 0.4683890568 -0.192928298656 +1403636871351666432.0000000000 4.7612179201 -1.4853516085 0.7772088991 0.3166222703 0.8011385912 0.4695369191 -0.193552001499 +1403636871401666560.0000000000 4.7593484473 -1.4964929337 0.7787963772 0.3174036471 0.7996389578 0.4717033169 -0.193205700678 +1403636871451666432.0000000000 4.7566135049 -1.5103945809 0.7803170332 0.3176289758 0.7981183075 0.4737136280 -0.19420195593 +1403636871501666560.0000000000 4.7529664259 -1.5268147252 0.7815879688 0.3175074664 0.7971421971 0.4749744783 -0.195326832336 +1403636871551666432.0000000000 4.7489291865 -1.5456435864 0.7829397879 0.3165558820 0.7967236501 0.4758560968 -0.196430074187 +1403636871601666560.0000000000 4.7445038632 -1.5666149410 0.7844393524 0.3152202813 0.7964560375 0.4770579278 -0.196747777801 +1403636871651666432.0000000000 4.7398642161 -1.5899573016 0.7865797077 0.3124943812 0.7963308801 0.4782170317 -0.198778423846 +1403636871701666560.0000000000 4.7349189764 -1.6151077149 0.7890790697 0.3091773729 0.7958368788 0.4799167408 -0.201824023315 +1403636871751666432.0000000000 4.7293157126 -1.6415371464 0.7915383177 0.3063374953 0.7949434206 0.4815931020 -0.205646252426 +1403636871801666560.0000000000 4.7234438703 -1.6682906001 0.7931673839 0.3044907642 0.7936863507 0.4838309957 -0.207978169178 +1403636871851666432.0000000000 4.7173127771 -1.6952681921 0.7939612034 0.3041076146 0.7914719983 0.4872463053 -0.209001609222 +1403636871901666560.0000000000 4.7101759640 -1.7230292598 0.7945608249 0.3039061082 0.7894422414 0.4894395367 -0.211827676872 +1403636871951666432.0000000000 4.7024517584 -1.7514981132 0.7951071154 0.3039212982 0.7871240199 0.4913759729 -0.215910340242 +1403636872001666560.0000000000 4.6938273208 -1.7804665791 0.7953930544 0.3037711157 0.7845028027 0.4929361888 -0.222018863127 +1403636872051666432.0000000000 4.6851114679 -1.8092885137 0.7952875049 0.3035540602 0.7818373983 0.4944385107 -0.228288795682 +1403636872101666560.0000000000 4.6768588947 -1.8373226642 0.7945147531 0.3034019581 0.7788126425 0.4970168664 -0.233178803254 +1403636872151666432.0000000000 4.6692519614 -1.8640385503 0.7934424820 0.3031732545 0.7765822568 0.4992983685 -0.236023548257 +1403636872201666560.0000000000 4.6624771224 -1.8895778266 0.7915747963 0.3017751338 0.7749568691 0.5021344750 -0.237138332191 +1403636872251666432.0000000000 4.6564790587 -1.9142292647 0.7895975974 0.2984626707 0.7735254366 0.5059157227 -0.237965784766 +1403636872301666560.0000000000 4.6514548334 -1.9378467129 0.7870815385 0.2939432053 0.7725761929 0.5099549956 -0.238053188651 +1403636872351666432.0000000000 4.6469754019 -1.9591353141 0.7845438008 0.2895534736 0.7713650896 0.5143950581 -0.237807503474 +1403636872401666560.0000000000 4.6431364332 -1.9775770784 0.7822905078 0.2856914421 0.7705608978 0.5177978510 -0.237700837697 +1403636872451666432.0000000000 4.6396256221 -1.9922541351 0.7806850257 0.2834063424 0.7697555565 0.5201766561 -0.237851791593 +1403636872501666560.0000000000 4.6370690365 -2.0031091653 0.7799989676 0.2822911694 0.7686589460 0.5220189156 -0.238686765849 +1403636872551666432.0000000000 4.6356188761 -2.0100644165 0.7800167459 0.2825787571 0.7671119667 0.5236251311 -0.239802415978 +1403636872601666560.0000000000 4.6352346425 -2.0135981458 0.7806477623 0.2838123083 0.7650389085 0.5251596522 -0.241605839916 +1403636872651666432.0000000000 4.6357053941 -2.0141613109 0.7815877430 0.2859913445 0.7634292555 0.5257579367 -0.242823628672 +1403636872701666560.0000000000 4.6365266467 -2.0121645926 0.7825305402 0.2882444845 0.7619636546 0.5264668114 -0.24322664888 +1403636872751666432.0000000000 4.6377481879 -2.0077502468 0.7832129646 0.2899112349 0.7618650586 0.5260978362 -0.242351346564 +1403636872801666560.0000000000 4.6394918815 -2.0002913461 0.7834249764 0.2908292856 0.7623829306 0.5259631885 -0.23990272614 +1403636872851666432.0000000000 4.6415255683 -1.9897607115 0.7834091743 0.2903787992 0.7641624113 0.5242819650 -0.238462540571 +1403636872901666560.0000000000 4.6440262130 -1.9753575976 0.7828753460 0.2901195617 0.7661140741 0.5223438381 -0.236763130754 +1403636872951666432.0000000000 4.6470946777 -1.9570807139 0.7818518814 0.2909066904 0.7680716481 0.5201751471 -0.234215834632 +1403636873001666560.0000000000 4.6510701183 -1.9359747110 0.7806278054 0.2921609853 0.7698297031 0.5179288045 -0.231848960271 +1403636873051666432.0000000000 4.6553729718 -1.9121834111 0.7792782816 0.2940868495 0.7713627557 0.5156029340 -0.229490824408 +1403636873101666560.0000000000 4.6600359668 -1.8865763630 0.7780943831 0.2953221140 0.7728805150 0.5133454990 -0.227852928711 +1403636873151666432.0000000000 4.6649892424 -1.8594916672 0.7771898470 0.2955529640 0.7751675782 0.5105719653 -0.226008715409 +1403636873201666560.0000000000 4.6699659319 -1.8305560175 0.7765295264 0.2959531420 0.7776596332 0.5075612877 -0.223693477467 +1403636873251666432.0000000000 4.6752675832 -1.8007911502 0.7760517891 0.2964004410 0.7802673309 0.5042881012 -0.221411792699 +1403636873301666560.0000000000 4.6806328728 -1.7703302452 0.7756723071 0.2971212618 0.7828775539 0.5008273720 -0.219074496312 +1403636873351666432.0000000000 4.6864103360 -1.7397134879 0.7750029354 0.2978777139 0.7851165751 0.4978322764 -0.216849845578 +1403636873401666560.0000000000 4.6924579624 -1.7093251840 0.7740601911 0.2985507743 0.7871544978 0.4951421724 -0.214684561437 +1403636873451666432.0000000000 4.6988556216 -1.6799904468 0.7727049024 0.2984977527 0.7894175627 0.4921018137 -0.213435723893 +1403636873501666560.0000000000 4.7056812636 -1.6513560270 0.7708646061 0.2985928621 0.7912302458 0.4903212020 -0.21067064297 +1403636873551666432.0000000000 4.7126074351 -1.6240067469 0.7686479312 0.2987480441 0.7938446607 0.4877558955 -0.206529531284 +1403636873601666560.0000000000 4.7196263561 -1.5987212179 0.7659166191 0.2989457988 0.7963940441 0.4853183789 -0.20212374204 +1403636873651666432.0000000000 4.7261739985 -1.5753099955 0.7628411493 0.2995267576 0.7984168643 0.4833773956 -0.197890186156 +1403636873701666560.0000000000 4.7322424048 -1.5548693496 0.7596719971 0.2987783767 0.8007449775 0.4810084198 -0.195371089733 +1403636873751666432.0000000000 4.7380590658 -1.5374163463 0.7567329307 0.2975899054 0.8020720936 0.4800016070 -0.19421395972 +1403636873801666560.0000000000 4.7433929139 -1.5233651141 0.7543856707 0.2965752255 0.8023735198 0.4805183552 -0.19324073249 +1403636873851666432.0000000000 4.7473140105 -1.5128922865 0.7524233107 0.2961985886 0.8031177203 0.4794979860 -0.193261493676 +1403636873901666560.0000000000 4.7501409119 -1.5053727731 0.7505890570 0.2964579850 0.8036037620 0.4785175672 -0.193273367774 +1403636873951666432.0000000000 4.7516837754 -1.5002145498 0.7489467781 0.2977456376 0.8040200135 0.4771598780 -0.192919164465 +1403636874001666560.0000000000 4.7523948669 -1.4977480681 0.7475243801 0.2987460633 0.8047012477 0.4756013432 -0.192379972704 +1403636874051666432.0000000000 4.7520120604 -1.4969810963 0.7464560935 0.2993803171 0.8051908376 0.4746391581 -0.191720657246 +1403636874101666560.0000000000 4.7512892477 -1.4983226380 0.7458627755 0.2990083640 0.8053126353 0.4746684338 -0.191717071838 +1403636874151666432.0000000000 4.7499563898 -1.5013177988 0.7459429511 0.2981937157 0.8055327819 0.4748142036 -0.191700071099 +1403636874201666560.0000000000 4.7484409511 -1.5064390011 0.7465621724 0.2972470171 0.8053233529 0.4759116162 -0.191328621935 +1403636874251666432.0000000000 4.7461256223 -1.5142682404 0.7474388694 0.2961734616 0.8050932633 0.4770685937 -0.191080284212 +1403636874301666560.0000000000 4.7430165466 -1.5252699846 0.7483232007 0.2946583933 0.8035588038 0.4804491079 -0.191411427855 +1403636874351666432.0000000000 4.7385856570 -1.5398894782 0.7491955773 0.2925761158 0.8027031676 0.4825670970 -0.192862225564 +1403636874401666560.0000000000 4.7329397504 -1.5576853880 0.7502398720 0.2901878120 0.8011644199 0.4856090408 -0.195219019227 +1403636874451666432.0000000000 4.7262196508 -1.5783466657 0.7514169058 0.2885785527 0.7998173901 0.4875911563 -0.19816514747 +1403636874501666560.0000000000 4.7188758282 -1.6009044913 0.7526456642 0.2888594821 0.7977899938 0.4897357116 -0.20062466991 +1403636874551666432.0000000000 4.7110781019 -1.6250012301 0.7540670647 0.2903558212 0.7957268832 0.4912913182 -0.202842463641 +1403636874601666560.0000000000 4.7032705837 -1.6516539431 0.7552682181 0.2909450498 0.7934722066 0.4935620685 -0.20530299533 +1403636874651666432.0000000000 4.6952184506 -1.6805435836 0.7561570072 0.2905102991 0.7911484564 0.4960322633 -0.208901603141 +1403636874701666560.0000000000 4.6871292157 -1.7101922225 0.7564927856 0.2898655118 0.7886201896 0.4990650623 -0.212109040861 +1403636874751666432.0000000000 4.6785149099 -1.7397372571 0.7561329169 0.2886823804 0.7867638068 0.5015078188 -0.214837387964 +1403636874801666560.0000000000 4.6701623258 -1.7688424743 0.7550638204 0.2870628710 0.7849474428 0.5041711971 -0.217402447344 +1403636874851666432.0000000000 4.6617451749 -1.7972848353 0.7535332802 0.2840449713 0.7842850337 0.5054682360 -0.220719964231 +1403636874901666560.0000000000 4.6541701486 -1.8241393524 0.7518874554 0.2804248296 0.7832303275 0.5078263107 -0.223661814169 +1403636874951666432.0000000000 4.6466820976 -1.8481997350 0.7505211176 0.2780309881 0.7825948501 0.5090275355 -0.226130578073 +1403636875001666560.0000000000 4.6398310284 -1.8690430664 0.7492841153 0.2782207027 0.7808519792 0.5104541485 -0.22869190935 +1403636875051666432.0000000000 4.6321599967 -1.8865792452 0.7482049686 0.2821818748 0.7801953869 0.5080774586 -0.231356529682 +1403636875101666560.0000000000 4.6240108076 -1.9008370834 0.7470729800 0.2896948104 0.7797309558 0.5034581153 -0.233723082932 +1403636875151666432.0000000000 4.6162800739 -1.9132718653 0.7458245554 0.2995429138 0.7811876520 0.4947707879 -0.234993111807 +1403636875201666560.0000000000 4.6101718259 -1.9247104290 0.7444021620 0.3089408672 0.7829547024 0.4855275652 -0.236221205448 +1403636875251666432.0000000000 4.6052055622 -1.9351081341 0.7426415531 0.3165545745 0.7869071232 0.4741760460 -0.23606663942 +1403636875301666560.0000000000 4.6019272583 -1.9451215864 0.7407528689 0.3213733592 0.7921456298 0.4623432448 -0.235506240425 +1403636875351666432.0000000000 4.6005623877 -1.9552906894 0.7392888194 0.3228900860 0.7987394257 0.4499543104 -0.23515620496 +1403636875401666560.0000000000 4.6021050697 -1.9654309488 0.7380583071 0.3216706069 0.8055171937 0.4388223516 -0.234744573955 +1403636875451666432.0000000000 4.6073189827 -1.9753416509 0.7373038215 0.3188841037 0.8115486022 0.4296609747 -0.234719495468 +1403636875501666560.0000000000 4.6164117931 -1.9844448361 0.7366874875 0.3149465816 0.8169163851 0.4225613040 -0.234303680882 +1403636875551666432.0000000000 4.6291816069 -1.9920973704 0.7363460352 0.3108901742 0.8219812252 0.4157475074 -0.234196872354 +1403636875601666560.0000000000 4.6453737625 -1.9978787450 0.7360560158 0.3075847222 0.8257377576 0.4110900561 -0.233567463663 +1403636875651666432.0000000000 4.6636619441 -2.0010118358 0.7361848520 0.3065090960 0.8292190551 0.4055436038 -0.232340952538 +1403636875701666560.0000000000 4.6836857808 -2.0014975489 0.7358422795 0.3080128281 0.8321027761 0.4000633357 -0.229526458715 +1403636875751666432.0000000000 4.7042089056 -1.9991039850 0.7355022787 0.3115466077 0.8352315218 0.3929824226 -0.225592180167 +1403636875801666560.0000000000 4.7259299275 -1.9954523528 0.7345447703 0.3145650928 0.8385170437 0.3861836880 -0.220907512223 +1403636875851666432.0000000000 4.7477669137 -1.9899797682 0.7338142238 0.3165453695 0.8426216007 0.3788971491 -0.214999575485 +1403636875901666560.0000000000 4.7696405440 -1.9828344209 0.7333259964 0.3178566684 0.8474472031 0.3706636305 -0.208347904413 +1403636875951666432.0000000000 4.7910429038 -1.9734437112 0.7338516522 0.3199141069 0.8524532870 0.3613068735 -0.201086302144 +1403636876001666560.0000000000 4.8117583490 -1.9615367897 0.7350632728 0.3234714591 0.8571738446 0.3504555065 -0.194422615146 +1403636876051666432.0000000000 4.8315560439 -1.9462047426 0.7368206296 0.3298842535 0.8608124113 0.3399514037 -0.186041433563 +1403636876101666560.0000000000 4.8495180571 -1.9284980416 0.7391678810 0.3372910810 0.8640134402 0.3284218314 -0.178478577075 +1403636876151666432.0000000000 4.8649521047 -1.9086185042 0.7412791954 0.3445111657 0.8665648258 0.3176426823 -0.171699113842 +1403636876201666560.0000000000 4.8777927856 -1.8871058529 0.7431965245 0.3498476535 0.8690997174 0.3077182647 -0.166077602655 +1403636876251666432.0000000000 4.8880773100 -1.8638498513 0.7440633832 0.3531367205 0.8719491738 0.2987535169 -0.160453828711 +1403636876301666560.0000000000 4.8954501289 -1.8385610474 0.7443426182 0.3538567398 0.8748475399 0.2921268315 -0.155206649169 +1403636876351666432.0000000000 4.9000503849 -1.8111369702 0.7434369576 0.3533692734 0.8781515228 0.2855725017 -0.149761162935 +1403636876401666560.0000000000 4.9016076958 -1.7813552865 0.7424174736 0.3523732058 0.8807872637 0.2813880536 -0.144456509767 +1403636876451666432.0000000000 4.9001544312 -1.7495575342 0.7409538566 0.3534656439 0.8825264590 0.2774983411 -0.138577625845 +1403636876501666560.0000000000 4.8956163027 -1.7164819330 0.7397949311 0.3569315964 0.8821682961 0.2767331097 -0.133408091681 +1403636876551666432.0000000000 4.8872871833 -1.6833115630 0.7394776635 0.3625131304 0.8801791893 0.2768031119 -0.13133492395 +1403636876601666560.0000000000 4.8758342403 -1.6504467312 0.7396359771 0.3691386979 0.8765962564 0.2800519158 -0.129948256966 +1403636876651666432.0000000000 4.8606738750 -1.6191769330 0.7405299502 0.3755518206 0.8723503581 0.2842432779 -0.131039847855 +1403636876701666560.0000000000 4.8423219309 -1.5913350487 0.7420325425 0.3798335148 0.8680243925 0.2902268433 -0.134270378087 +1403636876751666432.0000000000 4.8212119666 -1.5671396485 0.7438900216 0.3825952492 0.8634925963 0.2980263774 -0.138497977261 +1403636876801666560.0000000000 4.7978457869 -1.5473570534 0.7454979286 0.3848386498 0.8582765942 0.3080976603 -0.142605515867 +1403636876851666432.0000000000 4.7724287620 -1.5327779104 0.7466505132 0.3863724974 0.8525534752 0.3196794326 -0.147220669561 +1403636876901666560.0000000000 4.7446872296 -1.5233545349 0.7475823726 0.3879286759 0.8459856140 0.3319407097 -0.153736946268 +1403636876951666432.0000000000 4.7152813261 -1.5192708665 0.7477712573 0.3890283748 0.8387767180 0.3447876429 -0.161963027277 +1403636877001666560.0000000000 4.6848175583 -1.5205845403 0.7477747188 0.3887923369 0.8310958083 0.3585020320 -0.172036534729 +1403636877051666432.0000000000 4.6544466440 -1.5271249637 0.7473696181 0.3873048070 0.8225558046 0.3743949573 -0.182278223287 +1403636877101666560.0000000000 4.6244334289 -1.5388238869 0.7473225805 0.3844052467 0.8137113740 0.3905893144 -0.193768918022 +1403636877151666432.0000000000 4.5959867890 -1.5554996331 0.7471241226 0.3804964089 0.8038783123 0.4088927954 -0.204472060882 +1403636877201666560.0000000000 4.5688313154 -1.5768879308 0.7473307857 0.3747229789 0.7946857671 0.4257481042 -0.216323305149 +1403636877251666432.0000000000 4.5437266946 -1.6019463533 0.7478406485 0.3686817743 0.7853355882 0.4423894516 -0.22718568669 +1403636877301666560.0000000000 4.5220996921 -1.6309386048 0.7485494878 0.3626118088 0.7763923333 0.4576256120 -0.23728973863 +1403636877351666432.0000000000 4.5039115289 -1.6623153087 0.7490570616 0.3565204331 0.7667140420 0.4736932194 -0.246287418448 +1403636877401666560.0000000000 4.4895155610 -1.6953149933 0.7495668744 0.3498529283 0.7575426500 0.4887887731 -0.254593003176 +1403636877451666432.0000000000 4.4791147832 -1.7295527022 0.7494510127 0.3424812236 0.7491243214 0.5027785330 -0.262170000591 +1403636877501666560.0000000000 4.4726511682 -1.7638325967 0.7487436736 0.3341020948 0.7420828934 0.5152075157 -0.268793573728 +1403636877551666432.0000000000 4.4704588791 -1.7979082818 0.7476103847 0.3250061084 0.7372748809 0.5249114369 -0.274344241671 +1403636877601666560.0000000000 4.4727295206 -1.8308014688 0.7460862683 0.3155118410 0.7338878588 0.5334105584 -0.278090030552 +1403636877651666432.0000000000 4.4793859212 -1.8620211134 0.7445209908 0.3070796690 0.7315683487 0.5401172069 -0.280683506632 +1403636877701666560.0000000000 4.4896053906 -1.8912683646 0.7433020289 0.2984543931 0.7309187280 0.5442866001 -0.283610446274 +1403636877751666432.0000000000 4.5031617611 -1.9179412464 0.7424548367 0.2914836640 0.7316969529 0.5463496319 -0.284884050913 +1403636877801666560.0000000000 4.5197609021 -1.9419270625 0.7414331889 0.2863813619 0.7338029763 0.5466765999 -0.284013384664 +1403636877851666432.0000000000 4.5382118514 -1.9632039756 0.7401758811 0.2821441767 0.7379482945 0.5443919039 -0.281894365253 +1403636877901666560.0000000000 4.5585141034 -1.9810142517 0.7382938933 0.2794076286 0.7424770652 0.5416874226 -0.277909915113 +1403636877951666432.0000000000 4.5803878635 -1.9954508304 0.7358691376 0.2775276680 0.7482998281 0.5376627442 -0.271927442923 +1403636878001666560.0000000000 4.6034677757 -2.0065175743 0.7330423081 0.2772203496 0.7542670443 0.5325376168 -0.265770183074 +1403636878051666432.0000000000 4.6271833335 -2.0133046362 0.7296257031 0.2790741005 0.7605952910 0.5262135146 -0.258286249843 +1403636878101666560.0000000000 4.6506092905 -2.0159600048 0.7262266582 0.2822415451 0.7677405228 0.5173489992 -0.251523781802 +1403636878151666432.0000000000 4.6740547652 -2.0142001792 0.7227373423 0.2872369253 0.7749692169 0.5070354726 -0.244607218155 +1403636878201666560.0000000000 4.6974904331 -2.0086056794 0.7197505004 0.2922061062 0.7815539351 0.4964346174 -0.239461288443 +1403636878251666432.0000000000 4.7206570990 -1.9988924164 0.7166515701 0.2976040344 0.7881165014 0.4853364228 -0.233993110449 +1403636878301666560.0000000000 4.7428798143 -1.9861057975 0.7140103893 0.3016535757 0.7947897629 0.4733103566 -0.230849863301 +1403636878351666432.0000000000 4.7640859408 -1.9699015027 0.7116899869 0.3056675102 0.8015083379 0.4607088255 -0.227813817759 +1403636878401666560.0000000000 4.7840559419 -1.9500432190 0.7098480669 0.3099383153 0.8081117906 0.4484066089 -0.223215339109 +1403636878451666432.0000000000 4.8024701437 -1.9271642386 0.7086608972 0.3142413014 0.8145944784 0.4362751714 -0.217605641072 +1403636878501666560.0000000000 4.8186859546 -1.9012981280 0.7086800804 0.3193006798 0.8201348755 0.4255069337 -0.210641190735 +1403636878551666432.0000000000 4.8318358433 -1.8732704795 0.7099556952 0.3243384852 0.8256409703 0.4142047196 -0.203852852536 +1403636878601666560.0000000000 4.8420119970 -1.8432189908 0.7121408183 0.3299692950 0.8300890282 0.4044655711 -0.19616337961 +1403636878651666432.0000000000 4.8490346096 -1.8118977563 0.7151024526 0.3357765247 0.8338123133 0.3951213379 -0.189447301523 +1403636878701666560.0000000000 4.8532716384 -1.7794108648 0.7184487714 0.3423805916 0.8363939404 0.3875190142 -0.18179582154 +1403636878751666432.0000000000 4.8546058677 -1.7468719969 0.7223010785 0.3492848463 0.8376968835 0.3813925484 -0.175509975454 +1403636878801666560.0000000000 4.8531587076 -1.7151696236 0.7261584404 0.3552725591 0.8386903046 0.3754108237 -0.171600393858 +1403636878851666432.0000000000 4.8494038085 -1.6837791704 0.7298038957 0.3596090472 0.8392240410 0.3714564612 -0.168536167203 +1403636878901666560.0000000000 4.8439297662 -1.6543357560 0.7324308616 0.3612112559 0.8401263204 0.3683510475 -0.167426701025 +1403636878951666432.0000000000 4.8363066444 -1.6263784177 0.7347369082 0.3613044907 0.8409690626 0.3666980308 -0.166621292083 +1403636879001666560.0000000000 4.8267266197 -1.6006878925 0.7364605096 0.3602762971 0.8416732940 0.3664029297 -0.165939594343 +1403636879051666432.0000000000 4.8145587740 -1.5773235951 0.7386524459 0.3598501260 0.8420261889 0.3657509874 -0.166511258575 +1403636879101666560.0000000000 4.7996691963 -1.5562572300 0.7416087602 0.3616336024 0.8408718897 0.3655738243 -0.168853136394 +1403636879151666432.0000000000 4.7825678239 -1.5382825890 0.7452973280 0.3653952612 0.8381901451 0.3657469568 -0.173645464204 +1403636879201666560.0000000000 4.7636040717 -1.5230292486 0.7492062613 0.3709765534 0.8343326881 0.3667422862 -0.178228667335 +1403636879251666432.0000000000 4.7436811319 -1.5115078839 0.7530908921 0.3766519882 0.8295517821 0.3696729787 -0.182534953961 +1403636879301666560.0000000000 4.7226916288 -1.5043169806 0.7567765138 0.3813428831 0.8245598262 0.3733262875 -0.187899392008 +1403636879351666432.0000000000 4.7017461568 -1.5013419212 0.7604367578 0.3848073337 0.8183966299 0.3805506233 -0.193213600123 +1403636879401666560.0000000000 4.6807333244 -1.5030002132 0.7636767256 0.3867463489 0.8121524806 0.3887057156 -0.199357659905 +1403636879451666432.0000000000 4.6599416707 -1.5095378028 0.7667657379 0.3864717223 0.8049544228 0.3998887079 -0.206826029272 +1403636879501666560.0000000000 4.6400171163 -1.5204753008 0.7696665110 0.3847623579 0.7978767145 0.4116401328 -0.214250035073 +1403636879551666432.0000000000 4.6220233454 -1.5356904322 0.7723700051 0.3813171920 0.7909234539 0.4245749650 -0.220846979293 +1403636879601666560.0000000000 4.6047280977 -1.5546014801 0.7756283960 0.3765856767 0.7850542502 0.4356409859 -0.228232302096 +1403636879651666432.0000000000 4.5893289840 -1.5769565263 0.7794171871 0.3713424925 0.7797359456 0.4452406583 -0.236383934661 +1403636879701666560.0000000000 4.5761887309 -1.6025747929 0.7833672955 0.3654378458 0.7749742822 0.4540411231 -0.244370008973 +1403636879751666432.0000000000 4.5652680374 -1.6305212501 0.7871171731 0.3589459628 0.7707823526 0.4623089142 -0.251640276259 +1403636879801666560.0000000000 4.5575855253 -1.6600676351 0.7897108110 0.3523181210 0.7669274784 0.4707680605 -0.257043999438 +1403636879851666432.0000000000 4.5531960325 -1.6900453883 0.7913997585 0.3454702798 0.7642395705 0.4779943327 -0.260978126666 +1403636879901666560.0000000000 4.5526196207 -1.7196643304 0.7922262912 0.3392398860 0.7622791601 0.4847446130 -0.262429880278 +1403636879951666432.0000000000 4.5561809459 -1.7483073619 0.7931107706 0.3331263547 0.7614456985 0.4897159461 -0.263449373189 +1403636880001666560.0000000000 4.5638500742 -1.7744586045 0.7938068691 0.3280064514 0.7609142417 0.4940526289 -0.263312142841 +1403636880051666432.0000000000 4.5752528155 -1.7967326260 0.7944914592 0.3237156949 0.7605525976 0.4974334380 -0.263301860829 +1403636880101666560.0000000000 4.5900925669 -1.8144614296 0.7950980104 0.3213960317 0.7608082541 0.4991989741 -0.262060633289 +1403636880151666432.0000000000 4.6077968843 -1.8271269265 0.7958372092 0.3210367508 0.7612722386 0.4996064891 -0.260371541248 +1403636880201666560.0000000000 4.6277319666 -1.8350366095 0.7963532436 0.3232824053 0.7636123014 0.4959947629 -0.257631393052 +1403636880251666432.0000000000 4.6493225109 -1.8386029651 0.7969344535 0.3279864112 0.7665588318 0.4902651847 -0.253875008767 +1403636880301666560.0000000000 4.6724044403 -1.8389872646 0.7971888035 0.3342248436 0.7710556477 0.4815175923 -0.248812681188 +1403636880351666432.0000000000 4.6960229389 -1.8370321241 0.7977248364 0.3412537476 0.7758723863 0.4717853120 -0.242871445815 +1403636880401666560.0000000000 4.7201022919 -1.8341828623 0.7993307350 0.3490542044 0.7805418938 0.4618510791 -0.235815807764 +1403636880451666432.0000000000 4.7446119068 -1.8318839654 0.8019117982 0.3567338989 0.7855048475 0.4512151420 -0.228315473879 +1403636880501666560.0000000000 4.7688466420 -1.8318043534 0.8059085539 0.3631999371 0.7897828573 0.4419880163 -0.221303948262 +1403636880551666432.0000000000 4.7923106809 -1.8344199041 0.8098312177 0.3681882659 0.7946352837 0.4327370296 -0.213847679518 +1403636880601666560.0000000000 4.8148298802 -1.8403438519 0.8140691102 0.3706794926 0.7986930883 0.4263565193 -0.207138077002 +1403636880651666432.0000000000 4.8356971957 -1.8501899842 0.8175468061 0.3704140438 0.8030413047 0.4211829427 -0.201303323286 +1403636880701666560.0000000000 4.8543099873 -1.8636503573 0.8209593906 0.3678601578 0.8068582186 0.4181899588 -0.196915915298 +1403636880751666432.0000000000 4.8699430742 -1.8799941805 0.8238359851 0.3644000978 0.8102587416 0.4159765968 -0.194053629939 +1403636880801666560.0000000000 4.8821704551 -1.8985779582 0.8260619631 0.3606862549 0.8120803557 0.4158313786 -0.193688373324 +1403636880851666432.0000000000 4.8906670784 -1.9185530978 0.8279059080 0.3572631501 0.8124373045 0.4171075186 -0.19578045271 +1403636880901666560.0000000000 4.8950298092 -1.9389075652 0.8294376070 0.3551600146 0.8107139765 0.4201196903 -0.200258977789 +1403636880951666432.0000000000 4.8953622048 -1.9588630526 0.8306356086 0.3552156697 0.8074264864 0.4236529787 -0.205918553532 +1403636881001666560.0000000000 4.8918958466 -1.9774893814 0.8318309624 0.3573926673 0.8027126914 0.4278345121 -0.211850057103 +1403636881051666432.0000000000 4.8850778331 -1.9949564108 0.8329984009 0.3607210773 0.7967946345 0.4328571206 -0.218250608243 +1403636881101666560.0000000000 4.8754051548 -2.0114084591 0.8341141403 0.3637256755 0.7898978890 0.4393667848 -0.225214978094 +1403636881151666432.0000000000 4.8634858293 -2.0269736756 0.8350322450 0.3644760212 0.7829487169 0.4467329291 -0.233619833838 +1403636881201666560.0000000000 4.8494651877 -2.0408566987 0.8363225198 0.3633726529 0.7757994538 0.4549879148 -0.243066904308 +1403636881251666432.0000000000 4.8341964936 -2.0522234792 0.8377117349 0.3608608630 0.7685970222 0.4641619916 -0.25217394908 +1403636881301666560.0000000000 4.8171703972 -2.0599066874 0.8395188680 0.3584682464 0.7616641330 0.4732291517 -0.259658303859 +1403636881351666432.0000000000 4.7993214092 -2.0634489470 0.8410943969 0.3568287917 0.7551040358 0.4820964544 -0.264715162256 +1403636881401666560.0000000000 4.7800200984 -2.0624434603 0.8424439191 0.3559417279 0.7497433735 0.4892043298 -0.268084844555 +1403636881451666432.0000000000 4.7597522453 -2.0565665739 0.8432806791 0.3570169368 0.7441889872 0.4960233763 -0.269596862746 +1403636881501666560.0000000000 4.7389233755 -2.0464263751 0.8438347997 0.3596530106 0.7393917239 0.5007334858 -0.270583752015 +1403636881551666432.0000000000 4.7185420426 -2.0318977053 0.8438816802 0.3635888457 0.7339129909 0.5059946744 -0.270451959868 +1403636881601666560.0000000000 4.6985480033 -2.0139126065 0.8436648834 0.3669806890 0.7296835849 0.5093793902 -0.270960655082 +1403636881651666432.0000000000 4.6800652366 -1.9922043424 0.8426220166 0.3697609229 0.7249459610 0.5142688077 -0.270661794297 +1403636881701666560.0000000000 4.6625705815 -1.9673419006 0.8408841612 0.3718542449 0.7218718465 0.5177424047 -0.269384966486 +1403636881751666432.0000000000 4.6463412059 -1.9400186843 0.8382847100 0.3725547330 0.7201321853 0.5208146489 -0.267141737631 +1403636881801666560.0000000000 4.6312283800 -1.9108363370 0.8351252574 0.3737216215 0.7204076430 0.5214610310 -0.26348315056 +1403636881851666432.0000000000 4.6177672716 -1.8809510611 0.8317034778 0.3743842685 0.7226795309 0.5193928785 -0.260387697203 +1403636881901666560.0000000000 4.6071900756 -1.8512606103 0.8277503954 0.3741690231 0.7261871525 0.5158672644 -0.257935509782 +1403636881951666432.0000000000 4.5997575121 -1.8218080153 0.8237045709 0.3739026962 0.7300574187 0.5117071223 -0.255673150917 +1403636882001666560.0000000000 4.5953554319 -1.7932318160 0.8195094967 0.3740698639 0.7341685068 0.5063632205 -0.254292409489 +1403636882051666432.0000000000 4.5943013411 -1.7654161714 0.8148150002 0.3754100642 0.7374489713 0.5012606593 -0.252930919237 +1403636882101666560.0000000000 4.5964638357 -1.7398811998 0.8090051936 0.3770686990 0.7406298576 0.4959402998 -0.251654185984 +1403636882151666432.0000000000 4.6015148880 -1.7171347803 0.8022650893 0.3794154057 0.7429502065 0.4914384835 -0.250114289075 +1403636882201666560.0000000000 4.6090389149 -1.6978619230 0.7947223460 0.3829700772 0.7450053521 0.4866422462 -0.247952151752 +1403636882251666432.0000000000 4.6184138308 -1.6828804577 0.7871347793 0.3872485454 0.7461803314 0.4824409061 -0.245976115393 +1403636882301666560.0000000000 4.6292144954 -1.6728062839 0.7793864423 0.3908982315 0.7465662036 0.4792655633 -0.245238651459 +1403636882351666432.0000000000 4.6406385665 -1.6680182964 0.7719478889 0.3928716390 0.7462825131 0.4772774304 -0.246820866872 +1403636882401666560.0000000000 4.6517246672 -1.6678653633 0.7642921177 0.3936204836 0.7449294820 0.4776445348 -0.248995341535 +1403636882451666432.0000000000 4.6611100659 -1.6721372660 0.7571558558 0.3925798817 0.7437752710 0.4779083555 -0.253540897168 +1403636882501666560.0000000000 4.6684460982 -1.6792558542 0.7500613516 0.3910863064 0.7418928368 0.4794525748 -0.258402299017 +1403636882551666432.0000000000 4.6722676651 -1.6880292244 0.7441090869 0.3894396007 0.7393516742 0.4812333677 -0.264783581756 +1403636882601666560.0000000000 4.6725206088 -1.6968691599 0.7385312855 0.3901884811 0.7353764017 0.4833601058 -0.270808982662 +1403636882651666432.0000000000 4.6685770642 -1.7053073519 0.7337861495 0.3931284711 0.7297825946 0.4847615096 -0.279058504177 +1403636882701666560.0000000000 4.6611005243 -1.7133040137 0.7292287611 0.3983627387 0.7217204025 0.4857777291 -0.290597293477 +1403636882751666432.0000000000 4.6512387304 -1.7206851401 0.7240887280 0.4040580436 0.7110540774 0.4878265152 -0.305228582252 +1403636882801666560.0000000000 4.6397936976 -1.7270745346 0.7173936723 0.4104036093 0.6989610349 0.4907111103 -0.31972637578 +1403636882851666432.0000000000 4.6275533636 -1.7327368885 0.7092381348 0.4157435622 0.6865797816 0.4942927022 -0.333826629387 +1403636882901666560.0000000000 4.6150389938 -1.7379527239 0.6996030601 0.4191024103 0.6756201558 0.4983822005 -0.34569604723 +1403636882951666432.0000000000 4.6030746092 -1.7433117910 0.6888609825 0.4182713131 0.6665664714 0.5038644217 -0.356172559912 +1403636883001666560.0000000000 4.5919682469 -1.7487077001 0.6769816987 0.4146333772 0.6593517977 0.5106835548 -0.364055869663 +1403636883051666432.0000000000 4.5813542992 -1.7537375662 0.6649294818 0.4092547863 0.6533062381 0.5184443814 -0.370022840581 +1403636883101666560.0000000000 4.5708562969 -1.7578223748 0.6529217700 0.4072101494 0.6473518927 0.5248746122 -0.373660357479 +1403636883151666432.0000000000 4.5607361046 -1.7612778066 0.6411034821 0.4074851051 0.6411225203 0.5303586812 -0.376347541879 +1403636883201666560.0000000000 4.5508915658 -1.7643524241 0.6295596500 0.4103832691 0.6345582773 0.5343217130 -0.378710538804 +1403636883251666432.0000000000 4.5417925717 -1.7672984484 0.6184928568 0.4132010530 0.6285386230 0.5373008105 -0.381460257729 +1403636883301666560.0000000000 4.5338093922 -1.7703704335 0.6086132042 0.4142078343 0.6239597074 0.5389856728 -0.385487480996 +1403636883351666432.0000000000 4.5268484060 -1.7725878020 0.5998536893 0.4147486467 0.6208127346 0.5401865929 -0.388295703574 +1403636883401666560.0000000000 4.5208172853 -1.7744016621 0.5924298303 0.4143130291 0.6185245694 0.5407373082 -0.391631503465 +1403636883451666432.0000000000 4.5157845899 -1.7755970532 0.5864153917 0.4149705026 0.6155127178 0.5413910124 -0.394764927354 +1403636883501666560.0000000000 4.5119302439 -1.7764049060 0.5819536848 0.4160585718 0.6115364395 0.5420015323 -0.398939578043 +1403636883551666432.0000000000 4.5084927920 -1.7771442840 0.5785258031 0.4182114438 0.6066737100 0.5425058772 -0.403402492616 +1403636883601666560.0000000000 4.5055328022 -1.7778265959 0.5752534457 0.4199040220 0.6019582167 0.5433501016 -0.407550714437 +1403636883651666432.0000000000 4.5029645826 -1.7784436591 0.5721486965 0.4198979672 0.5981838489 0.5449063651 -0.411021694384 +1403636883701666560.0000000000 4.5009793547 -1.7785291658 0.5693963309 0.4203584066 0.5945698077 0.5481675825 -0.411458205902 +1403636883751666432.0000000000 4.4993025189 -1.7788555869 0.5675504883 0.4195209942 0.5928627718 0.5497884092 -0.412611892999 +1403636883801666560.0000000000 4.4979446083 -1.7789014121 0.5655666677 0.4188217758 0.5916677651 0.5509686648 -0.413462339632 +1403636883851666432.0000000000 4.4968474875 -1.7793590984 0.5639894287 0.4158482152 0.5915845537 0.5502999946 -0.417454061739 +1403636883901666560.0000000000 4.4960639403 -1.7792716531 0.5619652182 0.4143570483 0.5900967472 0.5511505904 -0.419913196045 +1403636883951666432.0000000000 4.4951040922 -1.7790311131 0.5602715542 0.4145124208 0.5888229064 0.5520449076 -0.420372998578 +1403636884001666560.0000000000 4.4944257252 -1.7789186226 0.5598006276 0.4157608683 0.5859956879 0.5522572828 -0.422804739441 +1403636884051666432.0000000000 4.4942680488 -1.7787953411 0.5594766388 0.4163311302 0.5834626556 0.5518657440 -0.426243967961 +1403636884101666560.0000000000 4.4943921125 -1.7782967043 0.5588809494 0.4160348221 0.5815562119 0.5510216093 -0.430212256104 +1403636884151666432.0000000000 4.4947255599 -1.7774049393 0.5584312850 0.4187939455 0.5794220162 0.5515205448 -0.429775344808 +1403636884201666560.0000000000 4.4948769770 -1.7772173874 0.5585259050 0.4213750572 0.5771154961 0.5509250029 -0.431117624923 +1403636884251666432.0000000000 4.4951409369 -1.7772810782 0.5586735112 0.4241221055 0.5756372776 0.5499551918 -0.431638102114 +1403636884301666560.0000000000 4.4956007153 -1.7778734692 0.5587626133 0.4245910928 0.5753820607 0.5490892032 -0.43261869475 +1403636884351666432.0000000000 4.4958724807 -1.7783662780 0.5588680967 0.4244614492 0.5752506287 0.5485869196 -0.433556898191 +1403636884401666560.0000000000 4.4960433935 -1.7785288488 0.5587852824 0.4242925645 0.5753875043 0.5483443024 -0.433847398975 +1403636884451666432.0000000000 4.4960861241 -1.7783030274 0.5587038416 0.4248246745 0.5749379073 0.5487478875 -0.433412222619 +1403636884501666560.0000000000 4.4962008481 -1.7782721337 0.5586806623 0.4249389754 0.5749524323 0.5487651040 -0.433259077713 +1403636884551666432.0000000000 4.4962118417 -1.7784055406 0.5586892115 0.4245875496 0.5751112858 0.5486582925 -0.433527968874 +1403636884601666560.0000000000 4.4963469607 -1.7785153186 0.5587416245 0.4246811030 0.5749885856 0.5485684173 -0.433712783733 +1403636884651666432.0000000000 4.4962549299 -1.7784331844 0.5586394407 0.4244048486 0.5752923116 0.5486118066 -0.433525508307 +1403636884701666560.0000000000 4.4964074679 -1.7784989048 0.5585892252 0.4244151744 0.5752036317 0.5486693428 -0.433560254296 +1403636884751666432.0000000000 4.4964693091 -1.7785383096 0.5585538527 0.4242002301 0.5754111614 0.5485403159 -0.433658485349 +1403636884801666560.0000000000 4.4964395667 -1.7783654351 0.5584732732 0.4244839754 0.5752077578 0.5487117244 -0.433433770573 +1403636884851666432.0000000000 4.4964201543 -1.7784905763 0.5584947015 0.4241263494 0.5754150708 0.5484817040 -0.43379967309 +1403636884901666560.0000000000 4.4963965080 -1.7783132301 0.5584154397 0.4244232061 0.5752405992 0.5486807789 -0.433488867212 +1403636884951666432.0000000000 4.4964013725 -1.7784403755 0.5584413683 0.4241409412 0.5754136958 0.5485151869 -0.433744890894 +1403636885001666560.0000000000 4.4963782995 -1.7783970777 0.5583646532 0.4242397419 0.5753235931 0.5486529042 -0.433593583056 +1403636885051666432.0000000000 4.4963991809 -1.7784560949 0.5584154685 0.4241745464 0.5753760777 0.5485903713 -0.433666839705 +1403636885101666560.0000000000 4.4963633138 -1.7784608377 0.5584066591 0.4241709936 0.5754033619 0.5485203443 -0.433722689242 +1403636885151666432.0000000000 4.4963032472 -1.7783716154 0.5583937035 0.4242410642 0.5754154403 0.5485972744 -0.433540795126 +1403636885201666560.0000000000 4.4962876866 -1.7784945357 0.5584829153 0.4240899966 0.5755011516 0.5484619694 -0.433745971134 +1403636885251666432.0000000000 4.4962087081 -1.7784227979 0.5584950945 0.4242180225 0.5754547231 0.5485340494 -0.433591198783 +1403636885301666560.0000000000 4.4961704557 -1.7784886722 0.5585439700 0.4241187037 0.5754889593 0.5484768261 -0.433715291595 +1403636885351666432.0000000000 4.4960522370 -1.7785020430 0.5585722438 0.4241423069 0.5755236317 0.5484931562 -0.433625541791 +1403636885401666560.0000000000 4.4960207799 -1.7784905073 0.5586257650 0.4242044468 0.5755188657 0.5484142899 -0.433670830425 +1403636885451666432.0000000000 4.4959589427 -1.7784783087 0.5586561497 0.4242262069 0.5755126465 0.5483743996 -0.433708239388 +1403636885501666560.0000000000 4.4959063310 -1.7784490676 0.5586330869 0.4242030477 0.5755355909 0.5483956029 -0.433673633802 +1403636885551666432.0000000000 4.4959278907 -1.7784395323 0.5587007106 0.4241717321 0.5755781723 0.5484011928 -0.433640681846 +1403636885601666560.0000000000 4.4959991345 -1.7783776619 0.5587273498 0.4242288452 0.5755298429 0.5483780259 -0.433678253532 +1403636885651666432.0000000000 4.4960457113 -1.7783339233 0.5587104029 0.4242408143 0.5755038247 0.5484827910 -0.433568572699 +1403636885701666560.0000000000 4.4959670036 -1.7783726535 0.5587321023 0.4240510336 0.5756716974 0.5483802850 -0.433661020512 +1403636885751666432.0000000000 4.4960075245 -1.7783402265 0.5587307591 0.4242172223 0.5755234502 0.5484264279 -0.433636898516 +1403636885801666560.0000000000 4.4959469532 -1.7783030036 0.5587519064 0.4240653026 0.5756993530 0.5483659490 -0.433628481561 +1403636885851666432.0000000000 4.4959334394 -1.7782675008 0.5587308914 0.4242458586 0.5755567624 0.5483948459 -0.433604609981 +1403636885901666560.0000000000 4.4959174031 -1.7782567593 0.5586974765 0.4239818020 0.5757841047 0.5483373820 -0.433633730084 +1403636885951666432.0000000000 4.4959948865 -1.7781597605 0.5586868683 0.4242737143 0.5755916357 0.5484535325 -0.433456810924 +1403636886001666560.0000000000 4.4959066106 -1.7782928771 0.5587164202 0.4239863473 0.5757971437 0.5482785325 -0.433686381401 +1403636886051666432.0000000000 4.4959198594 -1.7782701206 0.5586415698 0.4241229388 0.5757221934 0.5483771715 -0.433527584632 +1403636886101666560.0000000000 4.4959336924 -1.7782958591 0.5586941458 0.4240848186 0.5757902986 0.5483050828 -0.433565606292 +1403636886151666432.0000000000 4.4959644001 -1.7783140034 0.5587057631 0.4240987450 0.5757954012 0.5482611280 -0.433600790978 +1403636886201666560.0000000000 4.4959559004 -1.7782856432 0.5586676522 0.4241569941 0.5757936681 0.5483161776 -0.43347648782 +1403636886251666432.0000000000 4.4960025804 -1.7783602329 0.5587702154 0.4240653100 0.5758425653 0.5482047160 -0.433642182275 +1403636886301666560.0000000000 4.4960161237 -1.7783035711 0.5587696293 0.4241852516 0.5757873225 0.5483110328 -0.433463773404 +1403636886351666432.0000000000 4.4959818422 -1.7783917333 0.5587215737 0.4239994691 0.5758928548 0.5482226732 -0.433617078191 +1403636886401666560.0000000000 4.4960000503 -1.7783698866 0.5587158908 0.4241089952 0.5758272316 0.5482598854 -0.433550063458 +1403636886451666432.0000000000 4.4960175438 -1.7783482461 0.5586786704 0.4240970127 0.5758457641 0.5482793874 -0.433512506336 +1403636886501666560.0000000000 4.4960472550 -1.7783836351 0.5587394618 0.4240918241 0.5758247484 0.5482412414 -0.433593732786 +1403636886551666432.0000000000 4.4960346522 -1.7783647667 0.5588095886 0.4240834089 0.5758645822 0.5482294646 -0.433563950757 +1403636886601666560.0000000000 4.4960374917 -1.7783564382 0.5587763374 0.4240940124 0.5758461447 0.5482333002 -0.433573217314 +1403636886651666432.0000000000 4.4960104069 -1.7783398283 0.5587881598 0.4240760552 0.5758668022 0.5482129130 -0.433589122949 +1403636886701666560.0000000000 4.4959966067 -1.7783117683 0.5587447942 0.4240787535 0.5758795426 0.5482278186 -0.433550714614 +1403636886751666432.0000000000 4.4959702089 -1.7783190647 0.5587330490 0.4240119125 0.5759116040 0.5482149013 -0.433589834346 +1403636886801666560.0000000000 4.4960188551 -1.7783092168 0.5587266606 0.4240785110 0.5758491384 0.5482320447 -0.433585990843 +1403636886851666432.0000000000 4.4960105212 -1.7783168603 0.5587176064 0.4240155564 0.5758989703 0.5482437141 -0.433566619891 +1403636886901666560.0000000000 4.4960291781 -1.7783520087 0.5587436588 0.4239836098 0.5758767714 0.5482419551 -0.433629567106 +1403636886951666432.0000000000 4.4960097564 -1.7783231488 0.5587500070 0.4240405186 0.5758610501 0.5482488281 -0.433586106964 +1403636887001666560.0000000000 4.4960106822 -1.7783142133 0.5588009162 0.4240455203 0.5758635069 0.5482630552 -0.43355996184 +1403636887051666432.0000000000 4.4959527214 -1.7783157701 0.5587445275 0.4239974994 0.5758880501 0.5482263071 -0.433620791077 +1403636887101666560.0000000000 4.4959575228 -1.7782710517 0.5587618589 0.4240262514 0.5758660427 0.5482424326 -0.433601515349 +1403636887151666432.0000000000 4.4959735657 -1.7782725543 0.5588188078 0.4239476441 0.5759321085 0.5481999905 -0.433644291923 +1403636887201666560.0000000000 4.4959860579 -1.7782869277 0.5588619261 0.4239741921 0.5758903189 0.5482257162 -0.433641313961 +1403636887251666432.0000000000 4.4959948606 -1.7783014468 0.5588800112 0.4239473410 0.5759147911 0.5482107573 -0.433653976204 +1403636887301666560.0000000000 4.4960092481 -1.7783012204 0.5589624656 0.4239424399 0.5759519800 0.5481817203 -0.433646083812 +1403636887351666432.0000000000 4.4960146391 -1.7782996024 0.5589224270 0.4239713344 0.5759379473 0.5481466831 -0.433680760836 +1403636887401666560.0000000000 4.4960072705 -1.7782539657 0.5588557074 0.4239950166 0.5759353853 0.5482253933 -0.43356150199 +1403636887451666432.0000000000 4.4960477678 -1.7782983364 0.5588554588 0.4239348283 0.5759641185 0.5481596197 -0.433665339818 +1403636887501666560.0000000000 4.4960598854 -1.7782356115 0.5587850312 0.4239823347 0.5759348648 0.5482480445 -0.43354595256 +1403636887551666432.0000000000 4.4960863664 -1.7782705267 0.5587815032 0.4238999071 0.5759660704 0.5482167424 -0.433624673895 +1403636887601666560.0000000000 4.4960567015 -1.7782610277 0.5587679900 0.4239651178 0.5759526290 0.5481824756 -0.433622095341 +1403636887651666432.0000000000 4.4960257239 -1.7782841282 0.5587511885 0.4239730158 0.5759581353 0.5481912064 -0.433596021161 +1403636887701666560.0000000000 4.4960101117 -1.7783349267 0.5587600310 0.4239283172 0.5759741481 0.5481716370 -0.433643193289 +1403636887751666432.0000000000 4.4960225383 -1.7783300959 0.5587480280 0.4239540713 0.5759628385 0.5482338679 -0.433554356687 +1403636887801666560.0000000000 4.4960452727 -1.7783661202 0.5587615265 0.4238735579 0.5759952392 0.5481747897 -0.433664722222 +1403636887851666432.0000000000 4.4960539517 -1.7782968838 0.5587566272 0.4239865456 0.5759329134 0.5482154937 -0.433585586518 +1403636887901666560.0000000000 4.4960454382 -1.7783196341 0.5587725877 0.4238470299 0.5760420353 0.5481717756 -0.433632301844 +1403636887951666432.0000000000 4.4960270400 -1.7782722986 0.5587715727 0.4238916752 0.5760149143 0.5482086898 -0.433578019088 +1403636888001666560.0000000000 4.4960162495 -1.7782601031 0.5587671830 0.4238032643 0.5760996203 0.5481844154 -0.433582595794 +1403636888051666432.0000000000 4.4960395227 -1.7782488035 0.5588034255 0.4238233360 0.5760655362 0.5482066305 -0.433580174993 +1403636888101666560.0000000000 4.4960410095 -1.7782456676 0.5587546666 0.4237878710 0.5760755003 0.5481778045 -0.433638043838 +1403636888151666432.0000000000 4.4960709236 -1.7782353251 0.5587847354 0.4237944071 0.5760785535 0.5481766764 -0.433629025844 +1403636888201666560.0000000000 4.4960569559 -1.7782720445 0.5587393946 0.4237597427 0.5760843048 0.5481521213 -0.433686299207 +1403636888251666432.0000000000 4.4960503051 -1.7782855519 0.5587216336 0.4237458282 0.5760795762 0.5481586972 -0.433697864515 +1403636888301666560.0000000000 4.4960550489 -1.7783079412 0.5587061699 0.4237564172 0.5760715550 0.5481415570 -0.433719835651 +1403636888351666432.0000000000 4.4960762868 -1.7783306997 0.5586879259 0.4237102984 0.5760910584 0.5481227596 -0.433762741452 +1403636888401666560.0000000000 4.4960753296 -1.7783239099 0.5586594913 0.4237399085 0.5760935818 0.5481734636 -0.433666379441 +1403636888451666432.0000000000 4.4961267120 -1.7783553602 0.5586958472 0.4236109040 0.5761822419 0.5481110716 -0.433753477598 +1403636888501666560.0000000000 4.4961295979 -1.7783434029 0.5586529312 0.4236919129 0.5761424069 0.5481492482 -0.433679019001 +1403636888551666432.0000000000 4.4961594095 -1.7784308500 0.5587055890 0.4236303054 0.5761790495 0.5481019820 -0.433750255971 +1403636888601666560.0000000000 4.4960883561 -1.7784949781 0.5587853346 0.4237314303 0.5761648052 0.5480582774 -0.433725623841 +1403636888651666432.0000000000 4.4959795021 -1.7785860182 0.5588813618 0.4237306680 0.5762176869 0.5479659078 -0.433772823239 +1403636888701666560.0000000000 4.4958964409 -1.7787304751 0.5589841204 0.4238460246 0.5760118381 0.5480324409 -0.433849459493 +1403636888751666432.0000000000 4.4958566841 -1.7788145144 0.5590413407 0.4239511171 0.5760206443 0.5479302678 -0.433864136898 +1403636888801666560.0000000000 4.4958630717 -1.7788107987 0.5589672118 0.4238346080 0.5759634910 0.5480830746 -0.433860836537 +1403636888851666432.0000000000 4.4957971002 -1.7787091340 0.5588960313 0.4238755278 0.5762300098 0.5479053787 -0.433691374886 +1403636888901666560.0000000000 4.4958405252 -1.7785869046 0.5589347489 0.4237199293 0.5764240286 0.5477942713 -0.433725946947 +1403636888951666432.0000000000 4.4959090695 -1.7784231352 0.5589580599 0.4239366470 0.5762913859 0.5477844206 -0.433702878045 +1403636889001666560.0000000000 4.4960566698 -1.7783918951 0.5590175549 0.4236947849 0.5762450969 0.5477477609 -0.434046896064 +1403636889051666432.0000000000 4.4960920303 -1.7781451442 0.5589900198 0.4239229088 0.5762974503 0.5477065283 -0.433806610193 +1403636889101666560.0000000000 4.4960495185 -1.7780782555 0.5590414269 0.4238300524 0.5765351452 0.5475632979 -0.433762317173 +1403636889151666432.0000000000 4.4959760557 -1.7781795194 0.5590216196 0.4238612121 0.5764483930 0.5476302156 -0.43376268861 +1403636889201666560.0000000000 4.4960101496 -1.7782765921 0.5589170164 0.4237844670 0.5766141095 0.5475709011 -0.433692290143 +1403636889251666432.0000000000 4.4960106070 -1.7782880186 0.5588375382 0.4237503811 0.5767146312 0.5474850884 -0.433700272757 +1403636889301666560.0000000000 4.4959355176 -1.7782752629 0.5587928196 0.4237924510 0.5766970190 0.5474623164 -0.433711331232 +1403636889351666432.0000000000 4.4959217155 -1.7783375225 0.5587673360 0.4238088407 0.5765984344 0.5475065330 -0.433770571029 +1403636889401666560.0000000000 4.4959831602 -1.7784603139 0.5587439474 0.4236938485 0.5763970856 0.5477367075 -0.433859910121 +1403636889451666432.0000000000 4.4960750518 -1.7784668384 0.5587297884 0.4237514098 0.5765254125 0.5475992346 -0.43380671926 +1403636889501666560.0000000000 4.4961541221 -1.7783707038 0.5586130736 0.4238749870 0.5764728515 0.5476894910 -0.433641866429 +1403636889551666432.0000000000 4.4961254256 -1.7783691200 0.5586309051 0.4238408912 0.5765654498 0.5475851530 -0.43368384942 +1403636889601666560.0000000000 4.4961302437 -1.7782232126 0.5586312674 0.4241003205 0.5765882537 0.5475244744 -0.433476474255 +1403636889651666432.0000000000 4.4961589682 -1.7783162678 0.5587076387 0.4239466464 0.5765521520 0.5474669399 -0.433747399792 +1403636889701666560.0000000000 4.4961853431 -1.7783316236 0.5587119376 0.4241909634 0.5763577056 0.5476098650 -0.433586505177 +1403636889751666432.0000000000 4.4961438838 -1.7784486897 0.5587428771 0.4241533926 0.5764471486 0.5474963725 -0.433647675594 +1403636889801666560.0000000000 4.4962239225 -1.7785943962 0.5587372735 0.4241212191 0.5762709615 0.5477127233 -0.433640108021 +1403636889851666432.0000000000 4.4962033336 -1.7785565165 0.5587596810 0.4241394840 0.5764655538 0.5475302492 -0.433594037804 +1403636889901666560.0000000000 4.4962311688 -1.7785319742 0.5588196674 0.4241105525 0.5765976524 0.5474458450 -0.433553264611 +1403636889951666432.0000000000 4.4962757307 -1.7784851353 0.5588400484 0.4240347708 0.5763498273 0.5477128004 -0.433619739044 +1403636890001666560.0000000000 4.4963013033 -1.7783990646 0.5588335319 0.4239182464 0.5765085238 0.5476604608 -0.433588816687 +1403636890051666432.0000000000 4.4962670555 -1.7782678384 0.5588327785 0.4239892106 0.5767658688 0.5474862956 -0.433397090459 +1403636890101666560.0000000000 4.4962144553 -1.7782811654 0.5589471259 0.4241484123 0.5769087492 0.5471379656 -0.433491021798 +1403636890151666432.0000000000 4.4961978250 -1.7784154958 0.5590965296 0.4243022046 0.5765725868 0.5471804470 -0.433734077356 +1403636890201666560.0000000000 4.4962978536 -1.7787109299 0.5591579566 0.4241065621 0.5762705167 0.5474231873 -0.434020471265 +1403636890251666432.0000000000 4.4963402660 -1.7789309953 0.5590936170 0.4239303586 0.5760828204 0.5478011593 -0.433964889154 +1403636890301666560.0000000000 4.4964234201 -1.7790786849 0.5589357824 0.4236121857 0.5762890508 0.5479623119 -0.433798283463 +1403636890351666432.0000000000 4.4964703703 -1.7790946134 0.5587609406 0.4235746396 0.5766108346 0.5478571734 -0.433540064751 +1403636890401666560.0000000000 4.4965200742 -1.7789934589 0.5586413265 0.4238257653 0.5768894244 0.5474882483 -0.433390044612 +1403636890451666432.0000000000 4.4964716988 -1.7788808140 0.5585694689 0.4242068262 0.5769500489 0.5470365025 -0.433506948738 +1403636890501666560.0000000000 4.4965284741 -1.7787575077 0.5585746198 0.4244339185 0.5766929890 0.5469491913 -0.433736818205 +1403636890551666432.0000000000 4.4966768972 -1.7787299123 0.5585956599 0.4243355451 0.5763787881 0.5471330308 -0.434018760447 +1403636890601666560.0000000000 4.4968180894 -1.7786753673 0.5585182110 0.4241590210 0.5761181045 0.5475603466 -0.433998526914 +1403636890651666432.0000000000 4.4969060222 -1.7786175538 0.5585043691 0.4237722516 0.5762206884 0.5478370598 -0.433890945882 +1403636890701666560.0000000000 4.4969516672 -1.7784873335 0.5584964472 0.4236524290 0.5764643213 0.5478655798 -0.433648258643 +1403636890751666432.0000000000 4.4969324329 -1.7783951356 0.5585959557 0.4237156947 0.5767378230 0.5476474034 -0.433498344958 +1403636890801666560.0000000000 4.4968607154 -1.7783412751 0.5588190475 0.4239873184 0.5768395320 0.5472851190 -0.433554963907 +1403636890851666432.0000000000 4.4968426809 -1.7783628611 0.5589749146 0.4241901517 0.5767073319 0.5472146971 -0.433621313832 +1403636890901666560.0000000000 4.4969245621 -1.7785908707 0.5590311522 0.4240376937 0.5765475488 0.5473738276 -0.433782031731 +1403636890951666432.0000000000 4.4969487347 -1.7787032348 0.5589661840 0.4239570355 0.5765112651 0.5475429500 -0.433695643455 +1403636891001666560.0000000000 4.4969531446 -1.7788866142 0.5589510476 0.4237303589 0.5765275633 0.5475592915 -0.433874836819 +1403636891051666432.0000000000 4.4969088240 -1.7788529148 0.5588418105 0.4237834723 0.5765049243 0.5476837658 -0.433695899859 +1403636891101666560.0000000000 4.4968868441 -1.7789144686 0.5588159180 0.4237790774 0.5765112370 0.5476279497 -0.433762280338 +1403636891151666432.0000000000 4.4968925645 -1.7789416641 0.5587984826 0.4238192191 0.5764738627 0.5476177322 -0.433785632005 +1403636891201666560.0000000000 4.4969270483 -1.7789229969 0.5587548229 0.4238333756 0.5764660732 0.5476429761 -0.433750281637 +1403636891251666432.0000000000 4.4969310296 -1.7789268030 0.5587348244 0.4237655731 0.5764763507 0.5476520908 -0.433791359424 +1403636891301666560.0000000000 4.4968622645 -1.7788752075 0.5586748663 0.4237430070 0.5764961297 0.5477048329 -0.433720523369 +1403636891351666432.0000000000 4.4968808794 -1.7788699121 0.5586122935 0.4237664322 0.5764603358 0.5476787780 -0.43377810957 +1403636891401666560.0000000000 4.4968684782 -1.7788043169 0.5585822748 0.4238393025 0.5764526432 0.5476578706 -0.433743533183 +1403636891451666432.0000000000 4.4968753021 -1.7787916854 0.5585824304 0.4237843633 0.5764750161 0.5476565754 -0.433769114434 +1403636891501666560.0000000000 4.4968759756 -1.7787786511 0.5585968178 0.4237558866 0.5764521170 0.5477005807 -0.433771805539 +1403636891551666432.0000000000 4.4968975008 -1.7787708262 0.5586598581 0.4236919957 0.5764923218 0.5477282152 -0.433745890949 +1403636891601666560.0000000000 4.4969217764 -1.7787771289 0.5586470358 0.4236603529 0.5764982844 0.5477547280 -0.433735393416 +1403636891651666432.0000000000 4.4968849870 -1.7788085418 0.5586468820 0.4236428143 0.5765563248 0.5477156747 -0.433724693764 +1403636891701666560.0000000000 4.4968466429 -1.7788283462 0.5586131517 0.4236803472 0.5765267666 0.5477136767 -0.433729845781 +1403636891751666432.0000000000 4.4968268604 -1.7788403147 0.5586236141 0.4236756185 0.5765155253 0.5477250366 -0.433735061577 +1403636891801666560.0000000000 4.4968216797 -1.7788454516 0.5586565905 0.4236486314 0.5765259637 0.5477025512 -0.433775939578 +1403636891851666432.0000000000 4.4968481947 -1.7787838529 0.5586792154 0.4237154884 0.5764577901 0.5477848424 -0.433697322473 +1403636891901666560.0000000000 4.4969005501 -1.7787949854 0.5587497653 0.4236215936 0.5765091503 0.5477064885 -0.43381971775 +1403636891951666432.0000000000 4.4969268969 -1.7787585083 0.5587477185 0.4236840467 0.5765030485 0.5477395117 -0.433725132847 +1403636892001666560.0000000000 4.4969319960 -1.7787700164 0.5588038555 0.4236561283 0.5765497171 0.5476927768 -0.433749387126 +1403636892051666432.0000000000 4.4969600046 -1.7787842396 0.5587862593 0.4236781943 0.5765265314 0.5476959904 -0.433754594624 +1403636892101666560.0000000000 4.4969705256 -1.7787609318 0.5587620792 0.4236514464 0.5765363710 0.5477062725 -0.433754658611 +1403636892151666432.0000000000 4.4969778344 -1.7787766580 0.5587433216 0.4236202947 0.5765592968 0.5476693348 -0.433801248059 +1403636892201666560.0000000000 4.4969660940 -1.7787269294 0.5586902062 0.4236528987 0.5765635950 0.5477146455 -0.433706478565 +1403636892251666432.0000000000 4.4969548981 -1.7787174866 0.5586579100 0.4236458046 0.5765615879 0.5477110547 -0.433720610691 +1403636892301666560.0000000000 4.4968679121 -1.7785820950 0.5586185205 0.4237999129 0.5765468526 0.5478224556 -0.433448864001 +1403636892351666432.0000000000 4.4968883808 -1.7787319257 0.5586535350 0.4237097080 0.5766063533 0.5476524924 -0.433672623411 +1403636892401666560.0000000000 4.4968038639 -1.7787404490 0.5586821633 0.4237567615 0.5767210592 0.5475558158 -0.433596189546 +1403636892451666432.0000000000 4.4967942064 -1.7788086962 0.5587260988 0.4239224452 0.5765520446 0.5475756660 -0.433633935843 +1403636892501666560.0000000000 4.4967871114 -1.7788640501 0.5587300004 0.4237864823 0.5766492846 0.5475644260 -0.433651725798 +1403636892551666432.0000000000 4.4968265158 -1.7788860322 0.5587287362 0.4237537761 0.5766681012 0.5476161366 -0.433593363975 +1403636892601666560.0000000000 4.4969167496 -1.7789562158 0.5587657848 0.4237507660 0.5766416830 0.5475824212 -0.433674013216 +1403636892651666432.0000000000 4.4969326298 -1.7789191576 0.5587440981 0.4236754388 0.5767200789 0.5475878794 -0.433636469236 +1403636892701666560.0000000000 4.4970173888 -1.7788885031 0.5587098152 0.4237457757 0.5766487960 0.5475782867 -0.433674651869 +1403636892751666432.0000000000 4.4970345537 -1.7788101242 0.5587322681 0.4236779223 0.5767107235 0.5476128642 -0.433614933531 +1403636892801666560.0000000000 4.4970713939 -1.7788190969 0.5587777653 0.4237266867 0.5765906325 0.5476592125 -0.433668449872 +1403636892851666432.0000000000 4.4970120838 -1.7788012640 0.5587508667 0.4236282991 0.5767002531 0.5476713570 -0.433603467441 +1403636892901666560.0000000000 4.4969385632 -1.7787639879 0.5587266026 0.4235725174 0.5767419995 0.5476992184 -0.433567243537 +1403636892951666432.0000000000 4.4968896367 -1.7787569580 0.5587387599 0.4236052071 0.5766897646 0.5477095963 -0.433591676724 +1403636893001666560.0000000000 4.4968689753 -1.7787160685 0.5587411650 0.4236729550 0.5766439586 0.5476963885 -0.433603088321 +1403636893051666432.0000000000 4.4968710865 -1.7787290150 0.5587646650 0.4235882096 0.5767133268 0.5476486810 -0.433653882175 +1403636893101666560.0000000000 4.4968930400 -1.7787207539 0.5587432239 0.4236890084 0.5766474142 0.5476608734 -0.433627664812 +1403636893151666432.0000000000 4.4968906499 -1.7787264296 0.5587789700 0.4236440469 0.5766942623 0.5476070129 -0.433677309481 +1403636893201666560.0000000000 4.4968848957 -1.7787023719 0.5587569766 0.4236476853 0.5767216041 0.5476140603 -0.433628494384 +1403636893251666432.0000000000 4.4968921655 -1.7787345512 0.5586923463 0.4236210452 0.5767056167 0.5476479464 -0.433632988298 +1403636893301666560.0000000000 4.4968909695 -1.7787772878 0.5586402184 0.4236296380 0.5767453920 0.5476027932 -0.433628716188 +1403636893351666432.0000000000 4.4969583110 -1.7788147809 0.5586715524 0.4236129859 0.5767271077 0.5475965111 -0.433677233082 +1403636893401666560.0000000000 4.4970003252 -1.7788080955 0.5586804547 0.4235846446 0.5767806292 0.5476194549 -0.433604759281 +1403636893451666432.0000000000 4.4970334467 -1.7788202883 0.5587246642 0.4236269191 0.5767439822 0.5475838576 -0.433657158793 +1403636893501666560.0000000000 4.4969900903 -1.7788144574 0.5587677109 0.4235695074 0.5767999822 0.5476194926 -0.433593754796 +1403636893551666432.0000000000 4.4969472185 -1.7787969946 0.5588062092 0.4235800143 0.5767738212 0.5476529143 -0.433576078872 +1403636893601666560.0000000000 4.4968973413 -1.7788005415 0.5587641896 0.4235743426 0.5768242948 0.5476233639 -0.433551796844 +1403636893651666432.0000000000 4.4968882671 -1.7788287858 0.5587406464 0.4236269309 0.5766807323 0.5476928938 -0.433603563739 +1403636893701666560.0000000000 4.4968736445 -1.7788489696 0.5587062800 0.4235379539 0.5767553182 0.5477102387 -0.433569370409 +1403636893751666432.0000000000 4.4968767565 -1.7788576084 0.5587094654 0.4235583784 0.5767052487 0.5477184780 -0.433605609966 +1403636893801666560.0000000000 4.4968380409 -1.7788355298 0.5587210753 0.4234083216 0.5768308074 0.5477196654 -0.433583649355 +1403636893851666432.0000000000 4.4968414973 -1.7788564127 0.5587005925 0.4234503898 0.5767577905 0.5477764315 -0.433567987292 +1403636893901666560.0000000000 4.4968551226 -1.7788685720 0.5586884525 0.4233528690 0.5768453339 0.5477071775 -0.433634243025 +1403636893951666432.0000000000 4.4969079337 -1.7788684068 0.5586858724 0.4232924134 0.5768396211 0.5477372544 -0.433662869522 +1403636894001666560.0000000000 4.4969159521 -1.7788500369 0.5586720795 0.4232923918 0.5768973670 0.5476732598 -0.433666899305 +1403636894051666432.0000000000 4.4969273254 -1.7788104543 0.5586556231 0.4232864622 0.5768660255 0.5476851960 -0.433699303267 +1403636894101666560.0000000000 4.4969598108 -1.7787951992 0.5586206277 0.4232736653 0.5769634283 0.5476600809 -0.433613932508 +1403636894151666432.0000000000 4.4969678180 -1.7788012703 0.5586301925 0.4232418650 0.5769307096 0.5476646510 -0.433682729719 +1403636894201666560.0000000000 4.4969743614 -1.7788039829 0.5586509482 0.4232787316 0.5769364641 0.5476490869 -0.433658747616 +1403636894251666432.0000000000 4.4969487758 -1.7788319878 0.5586892804 0.4232000875 0.5770036043 0.5476165020 -0.433687321994 +1403636894301666560.0000000000 4.4969097620 -1.7788107883 0.5587179365 0.4232923788 0.5769637522 0.5476023967 -0.433668082502 +1403636894351666432.0000000000 4.4969317263 -1.7788768978 0.5587416383 0.4232109660 0.5769993081 0.5476308743 -0.433664273715 +1403636894401666560.0000000000 4.4968981845 -1.7788723546 0.5587784236 0.4232391974 0.5769969461 0.5476575316 -0.43360619693 +1403636894451666432.0000000000 4.4969103767 -1.7788815798 0.5587773842 0.4231894939 0.5770415268 0.5476201383 -0.433642609491 +1403636894501666560.0000000000 4.4969733675 -1.7788772624 0.5587689763 0.4231756378 0.5769660970 0.5476784966 -0.433682795222 +1403636894551666432.0000000000 4.4969784788 -1.7788524103 0.5587154451 0.4232191511 0.5770109092 0.5476271743 -0.433645522182 +1403636894601666560.0000000000 4.4970485727 -1.7788831329 0.5586750430 0.4231914429 0.5770495955 0.5476243086 -0.43362470368 +1403636894651666432.0000000000 4.4970613003 -1.7788842636 0.5586489470 0.4231860847 0.5770335644 0.5476349682 -0.433637803831 +1403636894701666560.0000000000 4.4970690626 -1.7789108301 0.5586775932 0.4231782395 0.5770221037 0.5475909001 -0.43371635377 +1403636894751666432.0000000000 4.4970317914 -1.7788956179 0.5586753885 0.4231855373 0.5770175622 0.5476122690 -0.433688294533 +1403636894801666560.0000000000 4.4970072512 -1.7788424075 0.5586910793 0.4231496150 0.5770788975 0.5475838969 -0.433677559147 +1403636894851666432.0000000000 4.4969395950 -1.7788027043 0.5587268915 0.4231707246 0.5770874966 0.5475944928 -0.43363213746 +1403636894901666560.0000000000 4.4968590890 -1.7787365963 0.5587447945 0.4233252487 0.5771302480 0.5475138005 -0.433526295608 +1403636894951666432.0000000000 4.4967861572 -1.7787693425 0.5587532566 0.4232041476 0.5771690681 0.5475034719 -0.433605886149 +1403636895001666560.0000000000 4.4966858485 -1.7787388004 0.5587608175 0.4232107428 0.5771458296 0.5475646799 -0.433553087682 +1403636895051666432.0000000000 4.4966843266 -1.7788167302 0.5587295380 0.4230933659 0.5771688718 0.5475987252 -0.433593972786 +1403636895101666560.0000000000 4.4966849485 -1.7788129386 0.5587031548 0.4231104575 0.5771640219 0.5475994683 -0.433582812007 +1403636895151666432.0000000000 4.4967016418 -1.7787861334 0.5586469208 0.4232945682 0.5770042663 0.5476640110 -0.433534215834 +1403636895201666560.0000000000 4.4966735697 -1.7788531016 0.5586493457 0.4231585148 0.5771644583 0.5475405678 -0.433609716242 +1403636895251666432.0000000000 4.4966865421 -1.7788488204 0.5586071111 0.4232387404 0.5771053696 0.5476194095 -0.433510488166 +1403636895301666560.0000000000 4.4967368125 -1.7788903261 0.5586478142 0.4231362116 0.5771572479 0.5475415871 -0.433639790693 +1403636895351666432.0000000000 4.4968365540 -1.7788944647 0.5585756587 0.4232244567 0.5771351092 0.5476071526 -0.433500324604 +1403636895401666560.0000000000 4.4969079582 -1.7789257471 0.5585699258 0.4231606253 0.5771792921 0.5475620283 -0.433560809094 +1403636895451666432.0000000000 4.4969287999 -1.7788840880 0.5585740867 0.4232207123 0.5771486528 0.5475909327 -0.43350643795 +1403636895501666560.0000000000 4.4969464724 -1.7788850716 0.5586093053 0.4231905336 0.5771471618 0.5475354915 -0.433607900489 +1403636895551666432.0000000000 4.4969309071 -1.7787803648 0.5586600739 0.4231961012 0.5772170377 0.5475351614 -0.433509859534 +1403636895601666560.0000000000 4.4969461220 -1.7787364447 0.5586869366 0.4230935285 0.5772448093 0.5475466420 -0.433558497922 +1403636895651666432.0000000000 4.4969343765 -1.7786271726 0.5587507343 0.4232155792 0.5771108869 0.5476353115 -0.433505666996 +1403636895701666560.0000000000 4.4968554633 -1.7785561240 0.5588116560 0.4231201088 0.5771854407 0.5475741621 -0.433576841577 +1403636895751666432.0000000000 4.4968291560 -1.7785555765 0.5588186949 0.4231939737 0.5770966750 0.5476347611 -0.433546372097 +1403636895801666560.0000000000 4.4966498367 -1.7785880412 0.5588131852 0.4232583636 0.5770901489 0.5475990743 -0.433537278103 +1403636895851666432.0000000000 4.4964508444 -1.7786548511 0.5587868716 0.4232135331 0.5770778356 0.5476149720 -0.433577351207 +1403636895901666560.0000000000 4.4962131704 -1.7785920462 0.5587884179 0.4231790791 0.5770420379 0.5477121596 -0.433535862103 +1403636895951666432.0000000000 4.4961032219 -1.7786159343 0.5588369283 0.4231782260 0.5769800965 0.5477673809 -0.433549367134 +1403636896001666560.0000000000 4.4959721339 -1.7786363841 0.5588696455 0.4231259534 0.5770566414 0.5477811010 -0.433481170982 +1403636896051666432.0000000000 4.4960216622 -1.7786107612 0.5587666530 0.4229101019 0.5771899502 0.5479339905 -0.433321069362 +1403636896101666560.0000000000 4.4960655541 -1.7786080496 0.5586550594 0.4224988188 0.5774097866 0.5481121073 -0.43320411386 +1403636896151666432.0000000000 4.4960989118 -1.7785492965 0.5585246660 0.4221099551 0.5776650936 0.5483393519 -0.432955171561 +1403636896201666560.0000000000 4.4961790306 -1.7784924266 0.5583963047 0.4216217167 0.5780106874 0.5485031804 -0.432762099098 +1403636896251666432.0000000000 4.4963420034 -1.7784910306 0.5583762940 0.4216118917 0.5779806813 0.5485600742 -0.43273963272 +1403636896301666560.0000000000 4.4964610989 -1.7785716134 0.5585297430 0.4217704493 0.5778230348 0.5485991512 -0.432746114748 +1403636896351666432.0000000000 4.4967323274 -1.7788083705 0.5586978412 0.4220534890 0.5776598225 0.5484497871 -0.432877364855 +1403636896401666560.0000000000 4.4968601812 -1.7788215445 0.5587691658 0.4222547110 0.5774314549 0.5484594367 -0.432973579091 +1403636896451666432.0000000000 4.4965440374 -1.7786206381 0.5588387896 0.4224756401 0.5772673547 0.5484410985 -0.433000111155 +1403636896501666560.0000000000 4.4967366844 -1.7784847745 0.5588625087 0.4224638245 0.5772393665 0.5483737582 -0.433134219361 +1403636896551666432.0000000000 4.4969060610 -1.7784091402 0.5587553496 0.4224935641 0.5772270868 0.5483826927 -0.433110264203 +1403636896601666560.0000000000 4.4970139841 -1.7785320261 0.5586938278 0.4225131245 0.5772194509 0.5483892463 -0.433093061297 +1403636896651666432.0000000000 4.4971391893 -1.7786785743 0.5586640084 0.4223238401 0.5772766262 0.5484067466 -0.433179305974 +1403636896701666560.0000000000 4.4972433006 -1.7786149587 0.5584978770 0.4221278724 0.5773823838 0.5486396130 -0.432934426016 +1403636896751666432.0000000000 4.4971151890 -1.7785005695 0.5584526320 0.4216110135 0.5776483910 0.5488166781 -0.432858803224 +1403636896801666560.0000000000 4.4972503063 -1.7785728886 0.5586771743 0.4217538376 0.5774629883 0.5488467375 -0.432928927584 +1403636896851666432.0000000000 4.4969301591 -1.7786470531 0.5590212793 0.4219141777 0.5773839169 0.5486070476 -0.433181886181 +1403636896901666560.0000000000 4.4965633847 -1.7784368157 0.5591464766 0.4218540210 0.5772892474 0.5490414868 -0.432816075985 +1403636896951666432.0000000000 4.4962011650 -1.7784838441 0.5591981933 0.4218103982 0.5772672153 0.5489192946 -0.433042905637 +1403636897001666560.0000000000 4.4958355601 -1.7785677978 0.5593232009 0.4222392976 0.5768524117 0.5487389080 -0.433406139193 +1403636897051666432.0000000000 4.4954892659 -1.7784776512 0.5595318920 0.4222409083 0.5762976226 0.5491297454 -0.433647539142 +1403636897101666560.0000000000 4.4957107318 -1.7785105985 0.5595978671 0.4217841977 0.5752188165 0.5501718064 -0.434203163477 +1403636897151666432.0000000000 4.4966524414 -1.7789148047 0.5593607666 0.4212359788 0.5737690515 0.5515820074 -0.434863903824 +1403636897201666560.0000000000 4.4977702970 -1.7791473476 0.5586435164 0.4200528620 0.5735398840 0.5524690919 -0.435184440273 +1403636897251666432.0000000000 4.4993885290 -1.7788967576 0.5581102646 0.4196554478 0.5738237241 0.5527293241 -0.434863119845 +1403636897301666560.0000000000 4.5016471633 -1.7777761594 0.5576082950 0.4198824459 0.5748521558 0.5521067047 -0.434075934861 +1403636897351666432.0000000000 4.5048683235 -1.7757633205 0.5574508411 0.4202078765 0.5766613981 0.5513829366 -0.432277491542 +1403636897401666560.0000000000 4.5093941628 -1.7725946613 0.5567827577 0.4204275421 0.5791394714 0.5518938432 -0.428078661418 +1403636897451666432.0000000000 4.5150469448 -1.7689489615 0.5562726949 0.4202885475 0.5819531648 0.5523764951 -0.423754950924 +1403636897501666560.0000000000 4.5212583281 -1.7647825211 0.5553393708 0.4206658372 0.5844639668 0.5534026576 -0.418554206121 +1403636897551666432.0000000000 4.5279701049 -1.7603179160 0.5547507573 0.4199789027 0.5878039317 0.5544023371 -0.413209762558 +1403636897601666560.0000000000 4.5360594383 -1.7557650928 0.5544658084 0.4181306823 0.5914299160 0.5574175639 -0.405786947002 +1403636897651666432.0000000000 4.5446051153 -1.7507336168 0.5555563978 0.4166178148 0.5945377723 0.5612772322 -0.397394391497 +1403636897701666560.0000000000 4.5535390882 -1.7453109014 0.5580489219 0.4143312863 0.5976875953 0.5661484983 -0.38803994833 +1403636897751666432.0000000000 4.5623565088 -1.7399938449 0.5625478365 0.4119462094 0.5997221383 0.5706862653 -0.380724131076 +1403636897801666560.0000000000 4.5705345969 -1.7347018096 0.5688082187 0.4097336128 0.6014086817 0.5745199395 -0.374636895174 +1403636897851666432.0000000000 4.5778506063 -1.7297628200 0.5767842429 0.4071899473 0.6029849597 0.5776444077 -0.370043812779 +1403636897901666560.0000000000 4.5838487942 -1.7252022246 0.5865702897 0.4053026042 0.6037283553 0.5800434980 -0.36713950004 +1403636897951666432.0000000000 4.5876163429 -1.7209918967 0.5980951309 0.4072715045 0.6016952541 0.5798019437 -0.368676618265 +1403636898001666560.0000000000 4.5894980539 -1.7171077856 0.6088640409 0.4108116643 0.5984699993 0.5782473492 -0.372421051476 +1403636898051666432.0000000000 4.5904323927 -1.7137448555 0.6175987990 0.4137589731 0.5953866872 0.5764569151 -0.376849611913 +1403636898101666560.0000000000 4.5911386404 -1.7108729277 0.6242356858 0.4150165122 0.5930758125 0.5751323951 -0.381110355822 +1403636898151666432.0000000000 4.5915194377 -1.7079882971 0.6300324530 0.4159187738 0.5911989727 0.5745448389 -0.383918710716 +1403636898201666560.0000000000 4.5914623356 -1.7052948036 0.6361357964 0.4162759034 0.5894882339 0.5745465811 -0.386153104951 +1403636898251666432.0000000000 4.5908422600 -1.7028255896 0.6428736125 0.4160488500 0.5881218339 0.5753788424 -0.38724055904 +1403636898301666560.0000000000 4.5896540345 -1.7005680589 0.6505466633 0.4156243177 0.5871405108 0.5761058951 -0.388103651955 +1403636898351666432.0000000000 4.5879663244 -1.6985689683 0.6590353098 0.4148313679 0.5861616034 0.5773423532 -0.388594027388 +1403636898401666560.0000000000 4.5857445808 -1.6969476326 0.6685360337 0.4139994347 0.5851016219 0.5782347687 -0.389750063885 +1403636898451666432.0000000000 4.5830174788 -1.6956606676 0.6786539101 0.4125534328 0.5843978119 0.5794613486 -0.390516847251 +1403636898501666560.0000000000 4.5797398032 -1.6946537955 0.6893403540 0.4109817537 0.5838678508 0.5803720971 -0.391612767753 +1403636898551666432.0000000000 4.5758153488 -1.6936842887 0.7002960713 0.4101406380 0.5831390222 0.5810391033 -0.392590242155 +1403636898601666560.0000000000 4.5714648865 -1.6927367435 0.7108320344 0.4096804034 0.5821866939 0.5824458729 -0.392399573969 +1403636898651666432.0000000000 4.5666723838 -1.6919977559 0.7211511538 0.4094647214 0.5812995952 0.5834465328 -0.392453265893 +1403636898701666560.0000000000 4.5614315004 -1.6915923140 0.7309432659 0.4088473193 0.5807417284 0.5846022360 -0.392202932238 +1403636898751666432.0000000000 4.5556089545 -1.6915227524 0.7404021488 0.4077693976 0.5805911935 0.5850817068 -0.392832509912 +1403636898801666560.0000000000 4.5492491975 -1.6915585715 0.7494613996 0.4071025297 0.5801498820 0.5852139018 -0.393977580461 +1403636898851666432.0000000000 4.5423405317 -1.6918833024 0.7579723509 0.4055674843 0.5806426510 0.5851655785 -0.394905524505 +1403636898901666560.0000000000 4.5349542633 -1.6923480621 0.7659715862 0.4036133298 0.5814583641 0.5851315999 -0.395756821306 +1403636898951666432.0000000000 4.5268989286 -1.6928364251 0.7735937021 0.4009499807 0.5826921113 0.5843593076 -0.397785389494 +1403636899001666560.0000000000 4.5179365822 -1.6929334040 0.7804216111 0.3986318754 0.5847867657 0.5825362560 -0.399710616523 +1403636899051666432.0000000000 4.5078642272 -1.6921940807 0.7865051680 0.3981195368 0.5869944561 0.5796726062 -0.401145874301 +1403636899101666560.0000000000 4.4967866273 -1.6903492796 0.7921849961 0.3995967986 0.5896880590 0.5756809103 -0.401474633327 +1403636899151666432.0000000000 4.4851574754 -1.6872779423 0.7975921558 0.4035841550 0.5920128594 0.5713810583 -0.400205310302 +1403636899201666560.0000000000 4.4729169205 -1.6831517971 0.8029582060 0.4094870258 0.5942233918 0.5660427463 -0.39851542718 +1403636899251666432.0000000000 4.4602615619 -1.6782980849 0.8084868396 0.4166848997 0.5969756255 0.5582014779 -0.398001139321 +1403636899301666560.0000000000 4.4477734716 -1.6726653146 0.8136159215 0.4240480639 0.6006902656 0.5498764886 -0.396220003934 +1403636899351666432.0000000000 4.4356313317 -1.6661303626 0.8181519037 0.4325092166 0.6049221317 0.5410230326 -0.392809203558 +1403636899401666560.0000000000 4.4233435514 -1.6588593745 0.8227982903 0.4405370947 0.6100387369 0.5321820825 -0.388023245182 +1403636899451666432.0000000000 4.4126504598 -1.6515126830 0.8271297082 0.4459054537 0.6164118875 0.5236512848 -0.383398021939 +1403636899501666560.0000000000 4.4033537715 -1.6444892362 0.8309369107 0.4464481346 0.6249053828 0.5160564124 -0.379292901193 +1403636899551666432.0000000000 4.3953962108 -1.6373818479 0.8340691258 0.4453107429 0.6330087887 0.5105624819 -0.37459867554 +1403636899601666560.0000000000 4.3879583345 -1.6299278458 0.8370782782 0.4441703240 0.6399605352 0.5059340944 -0.370396988085 +1403636899651666432.0000000000 4.3806205739 -1.6217757985 0.8403130870 0.4435726251 0.6454489879 0.5016133466 -0.367454732902 +1403636899701666560.0000000000 4.3733243566 -1.6126111200 0.8435356898 0.4436588275 0.6496274605 0.4985764707 -0.36410508111 +1403636899751666432.0000000000 4.3659601115 -1.6024969708 0.8464215730 0.4438654358 0.6532375904 0.4962555504 -0.360547575374 +1403636899801666560.0000000000 4.3585497880 -1.5914114964 0.8487406983 0.4450565971 0.6553794156 0.4951076159 -0.356750466936 +1403636899851666432.0000000000 4.3511730815 -1.5794058203 0.8501875251 0.4477196699 0.6558671053 0.4949830159 -0.352671591348 +1403636899901666560.0000000000 4.3434284980 -1.5666495732 0.8510160623 0.4508687268 0.6554982365 0.4949889044 -0.349321396015 +1403636899951666432.0000000000 4.3354454341 -1.5534762712 0.8513081788 0.4546976944 0.6541395316 0.4942901887 -0.347891778046 +1403636900001666560.0000000000 4.3272299668 -1.5399982362 0.8509197901 0.4590004686 0.6520761911 0.4936609533 -0.347007311148 +1403636900051666432.0000000000 4.3190261490 -1.5265696637 0.8505078976 0.4624856685 0.6501609690 0.4922046492 -0.348040664534 +1403636900101666560.0000000000 4.3112056142 -1.5132269826 0.8508012244 0.4661203028 0.6477275869 0.4909090122 -0.349555686842 +1403636900151666432.0000000000 4.3040490419 -1.4999572453 0.8530599568 0.4693254504 0.6455206304 0.4896332014 -0.351135394732 +1403636900201666560.0000000000 4.2976044839 -1.4868243518 0.8574117039 0.4710565482 0.6438080030 0.4898355592 -0.351678985133 +1403636900251666432.0000000000 4.2922091513 -1.4739603047 0.8639186222 0.4713243661 0.6431603741 0.4906927489 -0.351309978806 +1403636900301666560.0000000000 4.2877511560 -1.4614486643 0.8727449565 0.4705740044 0.6429764465 0.4921870148 -0.350561461168 +1403636900351666432.0000000000 4.2838144631 -1.4494091958 0.8838379133 0.4669854219 0.6444455395 0.4941610090 -0.349884923161 +1403636900401666560.0000000000 4.2808266601 -1.4375583972 0.8964033219 0.4637309467 0.6455887625 0.4967453135 -0.348443470852 +1403636900451666432.0000000000 4.2777599963 -1.4257497054 0.9092415972 0.4603346762 0.6466536176 0.4994567799 -0.347093661236 +1403636900501666560.0000000000 4.2748114089 -1.4139741122 0.9216649979 0.4583209746 0.6466425463 0.5018547144 -0.346319429407 +1403636900551666432.0000000000 4.2716156841 -1.4021882637 0.9331421244 0.4563043259 0.6469763207 0.5032500172 -0.346334264524 +1403636900601666560.0000000000 4.2682323035 -1.3903977999 0.9435029693 0.4545343519 0.6470523496 0.5047036652 -0.346404373774 +1403636900651666432.0000000000 4.2646541769 -1.3784973940 0.9521392130 0.4515684500 0.6480318694 0.5067608337 -0.345447664011 +1403636900701666560.0000000000 4.2606971089 -1.3665366226 0.9591032822 0.4475758893 0.6500092400 0.5086400031 -0.34416443528 +1403636900751666432.0000000000 4.2560175561 -1.3544515519 0.9645607454 0.4436230092 0.6515982197 0.5107692488 -0.343122660711 +1403636900801666560.0000000000 4.2504433838 -1.3420892026 0.9688692980 0.4403754505 0.6530224808 0.5112473604 -0.343885502258 +1403636900851666432.0000000000 4.2437654578 -1.3293060213 0.9723858478 0.4396431932 0.6530226199 0.5099882270 -0.346680442086 +1403636900901666560.0000000000 4.2364098668 -1.3163190211 0.9748677763 0.4374117420 0.6539699082 0.5072206196 -0.351740771148 +1403636900951666432.0000000000 4.2282322129 -1.3023557521 0.9760761528 0.4373580475 0.6535737051 0.5050782091 -0.355605614305 +1403636901001666560.0000000000 4.2194957425 -1.2871416241 0.9759657754 0.4378157977 0.6533047630 0.5030863436 -0.358349472825 +1403636901051666432.0000000000 4.2104701909 -1.2709630798 0.9743878106 0.4373241194 0.6533860607 0.5018302202 -0.360556098728 +1403636901101666560.0000000000 4.2012771275 -1.2536216887 0.9719924065 0.4369794626 0.6534835458 0.5003176148 -0.36289184192 +1403636901151666432.0000000000 4.1920452873 -1.2350170820 0.9687120226 0.4369008093 0.6535443359 0.4995670703 -0.363909640186 +1403636901201666560.0000000000 4.1824116420 -1.2151766160 0.9656710777 0.4374016468 0.6532203772 0.4990280983 -0.36462843459 +1403636901251666432.0000000000 4.1728790105 -1.1939037413 0.9638162765 0.4387509977 0.6523594814 0.4997472214 -0.363562076854 +1403636901301666560.0000000000 4.1643891435 -1.1716860312 0.9635279970 0.4406712375 0.6510632005 0.5007334119 -0.362203836984 +1403636901351666432.0000000000 4.1563292559 -1.1486116066 0.9639677462 0.4419750250 0.6502718897 0.5013693215 -0.361155576222 +1403636901401666560.0000000000 4.1468355619 -1.1243583287 0.9658963651 0.4434768775 0.6493922972 0.5023206612 -0.359571768642 +1403636901451666432.0000000000 4.1363461853 -1.0990898411 0.9703451668 0.4454141688 0.6482278977 0.5033769494 -0.357796670934 +1403636901501666560.0000000000 4.1262015133 -1.0732575170 0.9759785274 0.4475788039 0.6468562426 0.5045802635 -0.355877750504 +1403636901551666432.0000000000 4.1159981049 -1.0470458563 0.9811983648 0.4492196675 0.6459443212 0.5056025724 -0.354010823293 +1403636901601666560.0000000000 4.1056948614 -1.0207966443 0.9854108856 0.4505170049 0.6450907591 0.5059170940 -0.35346885981 +1403636901651666432.0000000000 4.0954176311 -0.9945270852 0.9881376609 0.4523586549 0.6439472191 0.5055734681 -0.353693503957 +1403636901701666560.0000000000 4.0854061490 -0.9682098215 0.9890672973 0.4532027102 0.6435496641 0.5048572322 -0.354359010675 +1403636901751666432.0000000000 4.0755448357 -0.9419507020 0.9882462511 0.4528346945 0.6436526894 0.5039475769 -0.355933694081 +1403636901801666560.0000000000 4.0658539429 -0.9153355013 0.9857184986 0.4531768057 0.6435707998 0.5039389042 -0.355658529112 +1403636901851666432.0000000000 4.0563498376 -0.8886791461 0.9819119376 0.4534281395 0.6433570387 0.5042957179 -0.35521890709 +1403636901901666560.0000000000 4.0471371392 -0.8621102783 0.9769683591 0.4535767854 0.6430867802 0.5045231266 -0.355195590733 +1403636901951666432.0000000000 4.0383234904 -0.8355215615 0.9706712144 0.4538106591 0.6428393915 0.5050478474 -0.354598468954 +1403636902001666560.0000000000 4.0295996741 -0.8091661337 0.9640499042 0.4546082199 0.6420338391 0.5055071884 -0.354381712849 +1403636902051666432.0000000000 4.0208375390 -0.7827905614 0.9581900477 0.4547825053 0.6414697911 0.5061632741 -0.354243023946 +1403636902101666560.0000000000 4.0126755109 -0.7567091270 0.9540572045 0.4554230618 0.6408065013 0.5060783122 -0.354741602603 +1403636902151666432.0000000000 4.0032496717 -0.7304972620 0.9515974773 0.4556068065 0.6403310870 0.5068039861 -0.354327893978 +1403636902201666560.0000000000 3.9946626289 -0.7046875358 0.9507031768 0.4554163116 0.6402740395 0.5071726672 -0.35414830672 +1403636902251666432.0000000000 3.9861410300 -0.6789751917 0.9507586259 0.4546955618 0.6409824337 0.5064269504 -0.354859422458 +1403636902301666560.0000000000 3.9778605308 -0.6533469242 0.9506603482 0.4537544792 0.6419593305 0.5054019526 -0.355758284417 +1403636902351666432.0000000000 3.9700953032 -0.6277573832 0.9473535537 0.4531276469 0.6427814420 0.5047854181 -0.355948079125 +1403636902401666560.0000000000 3.9622659141 -0.6018601194 0.9405725449 0.4527400637 0.6437503528 0.5042124514 -0.355502070086 +1403636902451666432.0000000000 3.9547979033 -0.5757220261 0.9300124435 0.4529466530 0.6444195046 0.5040195376 -0.354298091076 +1403636902501666560.0000000000 3.9475100801 -0.5494260151 0.9164866356 0.4536656875 0.6446420513 0.5043790737 -0.35245683384 +1403636902551666432.0000000000 3.9397281032 -0.5228152095 0.9017730888 0.4561097675 0.6439957942 0.5044426833 -0.350386752529 +1403636902601666560.0000000000 3.9317292226 -0.4963924240 0.8871397820 0.4576791500 0.6438514040 0.5053367999 -0.347303734309 +1403636902651666432.0000000000 3.9235981591 -0.4701979942 0.8737952238 0.4602775948 0.6429938663 0.5056639075 -0.344974544293 +1403636902701666560.0000000000 3.9151195663 -0.4444699080 0.8625549249 0.4620157190 0.6427484277 0.5050715357 -0.343974821661 +1403636902751666432.0000000000 3.9068754417 -0.4194270513 0.8533808228 0.4633613311 0.6426720199 0.5041838129 -0.343609712522 +1403636902801666560.0000000000 3.8986791780 -0.3950898642 0.8463258260 0.4631010555 0.6433002708 0.5033171106 -0.344055315678 +1403636902851666432.0000000000 3.8904414220 -0.3713638874 0.8413665632 0.4639461850 0.6425125554 0.5025477988 -0.345510149629 +1403636902901666560.0000000000 3.8825060604 -0.3483523053 0.8385763246 0.4645230144 0.6415522536 0.5018863078 -0.347475479743 +1403636902951666432.0000000000 3.8749463802 -0.3257886863 0.8378530003 0.4648173862 0.6407233794 0.5019190628 -0.348562193807 +1403636903001666560.0000000000 3.8684680816 -0.3037889573 0.8381525423 0.4634810457 0.6410446329 0.5026453540 -0.348704383526 +1403636903051666432.0000000000 3.8616331026 -0.2822272145 0.8402339068 0.4629958823 0.6407199779 0.5028673864 -0.349624247742 +1403636903101666560.0000000000 3.8545779191 -0.2611579965 0.8445813681 0.4616197090 0.6407776943 0.5037291203 -0.350097363613 +1403636903151666432.0000000000 3.8463832877 -0.2401495702 0.8521016890 0.4605234420 0.6407221506 0.5045703853 -0.350431179312 +1403636903201666560.0000000000 3.8383633950 -0.2194208253 0.8617340741 0.4593899315 0.6407108707 0.5052373824 -0.350978145087 +1403636903251666432.0000000000 3.8318107122 -0.1991470570 0.8732010990 0.4578752184 0.6408168550 0.5067219662 -0.35062357552 +1403636903301666560.0000000000 3.8258087907 -0.1788752909 0.8854551895 0.4573623554 0.6404152899 0.5082225534 -0.349853924643 +1403636903351666432.0000000000 3.8197951069 -0.1587307817 0.8976027510 0.4569280873 0.6401749264 0.5095139643 -0.348981814471 +1403636903401666560.0000000000 3.8138099654 -0.1386494954 0.9081140444 0.4573357501 0.6391839116 0.5111974103 -0.347800440678 +1403636903451666432.0000000000 3.8078466907 -0.1188297318 0.9166790280 0.4570299802 0.6388763527 0.5124375741 -0.346941401147 +1403636903501666560.0000000000 3.8017057353 -0.0992893816 0.9239325733 0.4571693695 0.6384411615 0.5127136490 -0.347150925347 +1403636903551666432.0000000000 3.7955175990 -0.0802274995 0.9294525610 0.4571158723 0.6380230951 0.5132714510 -0.34716570538 +1403636903601666560.0000000000 3.7893183205 -0.0615729813 0.9331983224 0.4562226255 0.6382958991 0.5136228161 -0.347319541588 +1403636903651666432.0000000000 3.7832105002 -0.0435238379 0.9347110205 0.4533797871 0.6400474275 0.5141464798 -0.347043882768 +1403636903701666560.0000000000 3.7769306993 -0.0258099644 0.9345817190 0.4504850163 0.6417889289 0.5140371080 -0.347758641077 +1403636903751666432.0000000000 3.7703587112 -0.0081605303 0.9331880683 0.4478024650 0.6434134830 0.5145850443 -0.347410815072 +1403636903801666560.0000000000 3.7631673068 0.0095185998 0.9324999749 0.4449795809 0.6451831645 0.5136738217 -0.349100360467 +1403636903851666432.0000000000 3.7545246520 0.0277538468 0.9328926317 0.4420455246 0.6470395251 0.5125794594 -0.350995591067 +1403636903901666560.0000000000 3.7450240118 0.0467279770 0.9356490849 0.4420945081 0.6470544006 0.5115861740 -0.352352998005 +1403636903951666432.0000000000 3.7349267618 0.0657771629 0.9403925271 0.4414357183 0.6473496516 0.5098536532 -0.355136857456 +1403636904001666560.0000000000 3.7244489160 0.0855147683 0.9469709754 0.4420539123 0.6469972347 0.5086180698 -0.356778048566 +1403636904051666432.0000000000 3.7139521284 0.1058106360 0.9558864194 0.4427181694 0.6464846313 0.5070379591 -0.35912498104 +1403636904101666560.0000000000 3.7027610851 0.1269940541 0.9661599615 0.4429111560 0.6464907082 0.5059482855 -0.360410605453 +1403636904151666432.0000000000 3.6913185811 0.1489279912 0.9781296293 0.4418697645 0.6472303664 0.5053390185 -0.361215227242 +1403636904201666560.0000000000 3.6802608893 0.1715915004 0.9914772693 0.4417989235 0.6473877432 0.5039008114 -0.363024507999 +1403636904251666432.0000000000 3.6702128946 0.1952258835 1.0060822257 0.4429661405 0.6470163752 0.5035942755 -0.362689418509 +1403636904301666560.0000000000 3.6601617859 0.2193259938 1.0198771503 0.4430292304 0.6472049116 0.5027504673 -0.36344582951 +1403636904351666432.0000000000 3.6501198841 0.2441862665 1.0325926968 0.4441165650 0.6467674569 0.5023470747 -0.363455293072 +1403636904401666560.0000000000 3.6401113583 0.2697488069 1.0440356075 0.4457329027 0.6462737195 0.5020422024 -0.362775531028 +1403636904451666432.0000000000 3.6302208003 0.2958298266 1.0541519868 0.4475768119 0.6452746763 0.5029332376 -0.361045354611 +1403636904501666560.0000000000 3.6206011835 0.3221558532 1.0632015465 0.4481480443 0.6453839667 0.5026144074 -0.360585112596 +1403636904551666432.0000000000 3.6111183211 0.3491218014 1.0707092636 0.4494110620 0.6451117941 0.5030115099 -0.358942741104 +1403636904601666560.0000000000 3.6016949585 0.3763903999 1.0771792575 0.4508885334 0.6444516791 0.5036016283 -0.357445049966 +1403636904651666432.0000000000 3.5923456666 0.4039940422 1.0829041792 0.4519874758 0.6443453706 0.5042151296 -0.355377922926 +1403636904701666560.0000000000 3.5830170967 0.4317747104 1.0884543701 0.4533200655 0.6441196279 0.5044794305 -0.353710796261 +1403636904751666432.0000000000 3.5737496645 0.4596825605 1.0936958139 0.4545215399 0.6438882150 0.5045298791 -0.35251629387 +1403636904801666560.0000000000 3.5645299437 0.4876398643 1.0984016005 0.4557829347 0.6436510902 0.5048312494 -0.350885451731 +1403636904851666432.0000000000 3.5555183287 0.5155306982 1.1023497943 0.4567569014 0.6436456574 0.5050699194 -0.349281802008 +1403636904901666560.0000000000 3.5465442956 0.5432751485 1.1048910785 0.4579669596 0.6434333040 0.5057850544 -0.347046576134 +1403636904951666432.0000000000 3.5376529819 0.5705839007 1.1059948188 0.4589512232 0.6434222997 0.5060765810 -0.345337535064 +1403636905001666560.0000000000 3.5287412585 0.5976420516 1.1057800674 0.4599587461 0.6434362582 0.5057174911 -0.344496085019 +1403636905051666432.0000000000 3.5198013752 0.6241875022 1.1049851464 0.4601825965 0.6439869358 0.5048832582 -0.34439178264 +1403636905101666560.0000000000 3.5108219105 0.6506337596 1.1041233233 0.4623225611 0.6432829852 0.5050703753 -0.342562062062 +1403636905151666432.0000000000 3.5016625623 0.6764270834 1.1045828732 0.4630751434 0.6435668885 0.5039188557 -0.342708124195 +1403636905201666560.0000000000 3.4920970819 0.7022848733 1.1058444592 0.4643520460 0.6433260714 0.5041564108 -0.34107925289 +1403636905251666432.0000000000 3.4822869798 0.7275315261 1.1085395627 0.4645215330 0.6439043439 0.5042227611 -0.339656220888 +1403636905301666560.0000000000 3.4723309045 0.7521501222 1.1125068279 0.4649792623 0.6443130245 0.5045278144 -0.337796827366 +1403636905351666432.0000000000 3.4622895507 0.7758535264 1.1181008125 0.4637061420 0.6458964399 0.5045513184 -0.336485318937 +1403636905401666560.0000000000 3.4524090859 0.7986385011 1.1251539551 0.4627804076 0.6467783184 0.5056923447 -0.334346158474 +1403636905451666432.0000000000 3.4421487535 0.8203769122 1.1337060069 0.4625933451 0.6458675400 0.5075200581 -0.333595426228 +1403636905501666560.0000000000 3.4316907122 0.8409424517 1.1435161027 0.4618103705 0.6442095126 0.5103665767 -0.333543464805 +1403636905551666432.0000000000 3.4207041155 0.8607759781 1.1528992735 0.4616350626 0.6421864915 0.5130689987 -0.333541274444 +1403636905601666560.0000000000 3.4093332640 0.8799173713 1.1610464589 0.4616462710 0.6401564608 0.5156100183 -0.333509722881 +1403636905651666432.0000000000 3.3974446786 0.8981624918 1.1676221828 0.4601074652 0.6392830103 0.5170832042 -0.335027331856 +1403636905701666560.0000000000 3.3852185076 0.9156332290 1.1723248337 0.4581533029 0.6390735690 0.5179344778 -0.336785393376 +1403636905751666432.0000000000 3.3720928254 0.9324827171 1.1756031915 0.4565631305 0.6386495882 0.5181609118 -0.339390749495 +1403636905801666560.0000000000 3.3583995634 0.9488837685 1.1764464810 0.4547412845 0.6387430002 0.5185762659 -0.341022580264 +1403636905851666432.0000000000 3.3445773556 0.9647045658 1.1752436496 0.4532440761 0.6386623653 0.5192377069 -0.342158434623 +1403636905901666560.0000000000 3.3305659792 0.9798718018 1.1724232263 0.4515363253 0.6387653757 0.5200291982 -0.343020953781 +1403636905951666432.0000000000 3.3160439022 0.9945971873 1.1680419007 0.4493949237 0.6393369623 0.5210022471 -0.343291581269 +1403636906001666560.0000000000 3.3009839682 1.0091085540 1.1624633252 0.4474174936 0.6397434874 0.5226188516 -0.342659295441 +1403636906051666432.0000000000 3.2852372679 1.0235873711 1.1556991111 0.4465263118 0.6395317747 0.5249722820 -0.34061336603 +1403636906101666560.0000000000 3.2683696875 1.0375053519 1.1485355042 0.4456603740 0.6394026290 0.5262635831 -0.339996691377 +1403636906151666432.0000000000 3.2505072982 1.0508234969 1.1421190482 0.4450152006 0.6390509643 0.5270858219 -0.340229147146 +1403636906201666560.0000000000 3.2312570460 1.0640996927 1.1378336606 0.4461262140 0.6378938096 0.5267672960 -0.34143682388 +1403636906251666432.0000000000 3.2107727061 1.0768553898 1.1363148619 0.4479978448 0.6360122995 0.5252292844 -0.344848495381 +1403636906301666560.0000000000 3.1892078274 1.0891668355 1.1370717448 0.4505666379 0.6339525473 0.5230034170 -0.34865641884 +1403636906351666432.0000000000 3.1679050804 1.1008379184 1.1392956498 0.4515940920 0.6331425009 0.5203371086 -0.352764288271 +1403636906401666560.0000000000 3.1467626576 1.1121653291 1.1429117611 0.4515882371 0.6330758958 0.5178317004 -0.35655757509 +1403636906451666432.0000000000 3.1256918925 1.1230649695 1.1481783911 0.4488300875 0.6351125121 0.5138989873 -0.362065574679 +1403636906501666560.0000000000 3.1048709215 1.1342678040 1.1540975937 0.4453163257 0.6376801063 0.5105128054 -0.366652597892 +1403636906551666432.0000000000 3.0845749330 1.1459768130 1.1591019181 0.4416471129 0.6401567273 0.5089064210 -0.369000605366 +1403636906601666560.0000000000 3.0648082735 1.1585311004 1.1624051153 0.4385299098 0.6425070113 0.5090330115 -0.368458480437 +1403636906651666432.0000000000 3.0451109453 1.1720890333 1.1643176891 0.4386065092 0.6425074062 0.5100772082 -0.366919343676 +1403636906701666560.0000000000 3.0254793988 1.1865148709 1.1647533382 0.4414745313 0.6406390615 0.5118047364 -0.36433191322 +1403636906751666432.0000000000 3.0059876314 1.2017816701 1.1635724586 0.4446239198 0.6385752482 0.5137771352 -0.361336792485 +1403636906801666560.0000000000 2.9866807926 1.2174989102 1.1610285979 0.4469915901 0.6368045103 0.5161337920 -0.35816817669 +1403636906851666432.0000000000 2.9671375030 1.2331231260 1.1573708121 0.4481172659 0.6356762686 0.5178413035 -0.356296199717 +1403636906901666560.0000000000 2.9476799615 1.2485604889 1.1533357362 0.4491771392 0.6343806963 0.5199183371 -0.354239964619 +1403636906951666432.0000000000 2.9280144214 1.2635576870 1.1504670205 0.4499347142 0.6332318888 0.5213248964 -0.353265453006 +1403636907001666560.0000000000 2.9080838727 1.2781061892 1.1492423573 0.4502990938 0.6321485480 0.5227822078 -0.352587156183 +1403636907051666432.0000000000 2.8876292039 1.2923931073 1.1498253640 0.4500902414 0.6315871933 0.5234648120 -0.352846967585 +1403636907101666560.0000000000 2.8672894673 1.3064643939 1.1515720970 0.4492521706 0.6315846559 0.5244884654 -0.352399147679 +1403636907151666432.0000000000 2.8470327834 1.3203194615 1.1530135464 0.4483684166 0.6315909853 0.5263871423 -0.350678152546 +1403636907201666560.0000000000 2.8264955956 1.3337285916 1.1531255355 0.4458914483 0.6327510211 0.5277723799 -0.349661660044 +1403636907251666432.0000000000 2.8053560643 1.3469187169 1.1513724333 0.4431852868 0.6341750010 0.5288835815 -0.348842409824 +1403636907301666560.0000000000 2.7836120575 1.3598644750 1.1477809880 0.4408029339 0.6350840766 0.5300391085 -0.34845305646 +1403636907351666432.0000000000 2.7610665915 1.3724207701 1.1443571640 0.4385506857 0.6361457075 0.5295712171 -0.350066080669 +1403636907401666560.0000000000 2.7379593891 1.3849107266 1.1417924282 0.4358543346 0.6376068816 0.5286734214 -0.352126223272 +1403636907451666432.0000000000 2.7140200826 1.3975257517 1.1410024661 0.4337745589 0.6387465985 0.5281218517 -0.353453992341 +1403636907501666560.0000000000 2.6894218065 1.4105192184 1.1419420669 0.4318373994 0.6396876226 0.5264081968 -0.356665973035 +1403636907551666432.0000000000 2.6642566956 1.4239825051 1.1453474089 0.4288342718 0.6417581279 0.5246861052 -0.359099100089 +1403636907601666560.0000000000 2.6387274478 1.4381976296 1.1508496596 0.4285609375 0.6416343652 0.5240656666 -0.360549637908 +1403636907651666432.0000000000 2.6123083325 1.4534124817 1.1577440899 0.4277533344 0.6422226984 0.5231133622 -0.36184181745 +1403636907701666560.0000000000 2.5848765937 1.4695141612 1.1669163606 0.4268891699 0.6427879759 0.5222484669 -0.363105760861 +1403636907751666432.0000000000 2.5575704127 1.4865189786 1.1777722328 0.4268257175 0.6426920733 0.5219741604 -0.363743978171 +1403636907801666560.0000000000 2.5297742581 1.5044425845 1.1893796084 0.4261586339 0.6432509054 0.5210747262 -0.364826289012 +1403636907851666432.0000000000 2.5020044701 1.5232959863 1.1990027193 0.4262004007 0.6432770543 0.5204242914 -0.36565886662 +1403636907901666560.0000000000 2.4730434884 1.5430595471 1.2053053813 0.4274501680 0.6422986195 0.5202448069 -0.366175064889 +1403636907951666432.0000000000 2.4425864170 1.5639705427 1.2079505820 0.4313715968 0.6393926898 0.5207249776 -0.365979550642 +1403636908001666560.0000000000 2.4115080399 1.5858522863 1.2077723170 0.4352910180 0.6364487898 0.5219184388 -0.364768160557 +1403636908051666432.0000000000 2.3803326549 1.6082713336 1.2061023225 0.4397886770 0.6327284177 0.5240214101 -0.362825344688 +1403636908101666560.0000000000 2.3490361530 1.6307138185 1.2052051980 0.4423810884 0.6301780060 0.5246299006 -0.36323287394 +1403636908151666432.0000000000 2.3179660232 1.6533081842 1.2054973963 0.4438832637 0.6283773370 0.5254867362 -0.363281241858 +1403636908201666560.0000000000 2.2877862802 1.6755924638 1.2076194934 0.4456313724 0.6261616551 0.5259682959 -0.364268600625 +1403636908251666432.0000000000 2.2585694965 1.6977008583 1.2101448092 0.4460447545 0.6248909323 0.5271146735 -0.364287689511 +1403636908301666560.0000000000 2.2296970602 1.7194971493 1.2124169211 0.4460025383 0.6240517354 0.5278122674 -0.364767566656 +1403636908351666432.0000000000 2.2010679885 1.7411178815 1.2132858992 0.4455390014 0.6234385816 0.5292657497 -0.364276130715 +1403636908401666560.0000000000 2.1726202381 1.7623125798 1.2129302193 0.4445557557 0.6232491096 0.5298594520 -0.364937924398 +1403636908451666432.0000000000 2.1441401873 1.7833405416 1.2110611773 0.4433871808 0.6231228173 0.5309882525 -0.364934566884 +1403636908501666560.0000000000 2.1152182107 1.8042084951 1.2079571444 0.4422373244 0.6230282832 0.5319455785 -0.365096985272 +1403636908551666432.0000000000 2.0861550505 1.8248996244 1.2040110117 0.4414900695 0.6227170326 0.5327307856 -0.365387364162 +1403636908601666560.0000000000 2.0571179633 1.8454979560 1.1999744180 0.4407537859 0.6222900924 0.5337149658 -0.36556733494 +1403636908651666432.0000000000 2.0287080075 1.8658181113 1.1969357566 0.4401481942 0.6216537923 0.5351884188 -0.365225253802 +1403636908701666560.0000000000 2.0006024242 1.8859335905 1.1956252910 0.4384863614 0.6221868589 0.5360554400 -0.365044913325 +1403636908751666432.0000000000 1.9721301014 1.9058966371 1.1963035756 0.4358633783 0.6233535214 0.5371047710 -0.364653215815 +1403636908801666560.0000000000 1.9431896227 1.9257638008 1.1994385561 0.4334753466 0.6244214889 0.5376182770 -0.364915766218 +1403636908851666432.0000000000 1.9134915649 1.9457184671 1.2050093611 0.4302871900 0.6263407977 0.5380694160 -0.364734756908 +1403636908901666560.0000000000 1.8828267683 1.9659619134 1.2127718265 0.4289178595 0.6269647846 0.5392342188 -0.363553415522 +1403636908951666432.0000000000 1.8521413957 1.9860283924 1.2222929421 0.4274497602 0.6274841135 0.5395497251 -0.363918238019 +1403636909001666560.0000000000 1.8202198606 2.0063154094 1.2334737906 0.4268521525 0.6276627659 0.5393846982 -0.364555674087 +1403636909051666432.0000000000 1.7878501498 2.0268341396 1.2448164123 0.4259877524 0.6283126375 0.5385755033 -0.365642026555 +1403636909101666560.0000000000 1.7547029095 2.0476084805 1.2550734331 0.4246420835 0.6293082099 0.5381807248 -0.366076201614 +1403636909151666432.0000000000 1.7213652438 2.0686774554 1.2642447074 0.4241413117 0.6297413446 0.5374202543 -0.367027869303 +1403636909201666560.0000000000 1.6874195656 2.0903754725 1.2714474092 0.4241075920 0.6300201427 0.5375681229 -0.366371237224 +1403636909251666432.0000000000 1.6532035787 2.1124569401 1.2773231924 0.4238452192 0.6304057146 0.5375323744 -0.366063944647 +1403636909301666560.0000000000 1.6183216206 2.1349600156 1.2819555926 0.4235334714 0.6310207834 0.5370644503 -0.366051834812 +1403636909351666432.0000000000 1.5825856336 2.1578661031 1.2857010573 0.4248844363 0.6305206340 0.5364812951 -0.36620317562 +1403636909401666560.0000000000 1.5461163714 2.1811608534 1.2880739977 0.4261664826 0.6299911347 0.5361855484 -0.366057860114 +1403636909451666432.0000000000 1.5086840862 2.2050849383 1.2894599297 0.4291895759 0.6285071131 0.5355983113 -0.365936559591 +1403636909501666560.0000000000 1.4707628996 2.2292562920 1.2895240813 0.4320250394 0.6270334490 0.5349309701 -0.366104187909 +1403636909551666432.0000000000 1.4329099221 2.2533779225 1.2877334757 0.4329320184 0.6267591273 0.5340567645 -0.36677818363 +1403636909601666560.0000000000 1.3949956655 2.2776245984 1.2843806663 0.4332030046 0.6273424103 0.5325479917 -0.367653768626 +1403636909651666432.0000000000 1.3568979115 2.3017190059 1.2802065834 0.4326214246 0.6281948325 0.5300237111 -0.370519663455 +1403636909701666560.0000000000 1.3188379283 2.3264677119 1.2744640704 0.4338731648 0.6280206791 0.5280908875 -0.372107670042 +1403636909751666432.0000000000 1.2806035535 2.3518344897 1.2674848274 0.4375594265 0.6259577889 0.5263628699 -0.373712087053 +1403636909801666560.0000000000 1.2426337291 2.3779378547 1.2584632634 0.4425430527 0.6228399348 0.5268616872 -0.372347720185 +1403636909851666432.0000000000 1.2051762198 2.4043468521 1.2479587333 0.4491543742 0.6186253581 0.5283387311 -0.369352405758 +1403636909901666560.0000000000 1.1685264795 2.4304861085 1.2357637752 0.4548815893 0.6146859125 0.5312521201 -0.364712425879 +1403636909951666432.0000000000 1.1324367368 2.4559288725 1.2226711832 0.4616562126 0.6099374526 0.5335150257 -0.360848392774 +1403636910001666560.0000000000 1.0970915171 2.4800706137 1.2088555072 0.4672435013 0.6060631219 0.5342993821 -0.359019739103 +1403636910051666432.0000000000 1.0629607454 2.5021212274 1.1946109872 0.4697770806 0.6040842550 0.5343352909 -0.358995131396 +1403636910101666560.0000000000 1.0299808478 2.5222125654 1.1810115132 0.4675179755 0.6056484060 0.5332688564 -0.360889564217 +1403636910151666432.0000000000 0.9978375216 2.5407095186 1.1686624694 0.4632648828 0.6083403173 0.5326455207 -0.362762258165 +1403636910201666560.0000000000 0.9656519653 2.5580974446 1.1574470485 0.4569100262 0.6126921700 0.5323032905 -0.363998268878 +1403636910251666432.0000000000 0.9332845104 2.5747208464 1.1491958114 0.4532482022 0.6149535076 0.5325304964 -0.364430406473 +1403636910301666560.0000000000 0.9016769651 2.5905985845 1.1429711973 0.4491907682 0.6175591514 0.5324996273 -0.365092447528 +1403636910351666432.0000000000 0.8711796977 2.6060804338 1.1384520862 0.4458777788 0.6196239287 0.5329371645 -0.365016673669 +1403636910401666560.0000000000 0.8406290248 2.6213119469 1.1358100376 0.4443699059 0.6201455565 0.5335639276 -0.365053983087 +1403636910451666432.0000000000 0.8102415514 2.6363511279 1.1347688938 0.4436576971 0.6201300803 0.5346610478 -0.364340630891 +1403636910501666560.0000000000 0.7797280441 2.6511059849 1.1355509843 0.4428224714 0.6199787857 0.5348989484 -0.365263848662 +1403636910551666432.0000000000 0.7491400418 2.6658736110 1.1357178765 0.4426896472 0.6196587468 0.5360291442 -0.364309854903 +1403636910601666560.0000000000 0.7184783494 2.6804341960 1.1352776875 0.4429296893 0.6191451756 0.5365539863 -0.364118609279 +1403636910651666432.0000000000 0.6879571828 2.6946716675 1.1331336719 0.4426536609 0.6191436688 0.5370312278 -0.363753095207 +1403636910701666560.0000000000 0.6575025004 2.7085072253 1.1295497831 0.4426288870 0.6188663560 0.5371279465 -0.364112168077 +1403636910751666432.0000000000 0.6270906520 2.7219722608 1.1243280789 0.4418910365 0.6192301100 0.5370141070 -0.364557583347 +1403636910801666560.0000000000 0.5966110012 2.7351640260 1.1177149521 0.4413412410 0.6196684996 0.5367712788 -0.364836201451 +1403636910851666432.0000000000 0.5662419839 2.7481239520 1.1102076866 0.4403258254 0.6201964966 0.5364572243 -0.365627022608 +1403636910901666560.0000000000 0.5358521261 2.7607468845 1.1018718756 0.4388041846 0.6212413110 0.5357948902 -0.366652364927 +1403636910951666432.0000000000 0.5049106180 2.7732815314 1.0935274064 0.4394023815 0.6207052419 0.5338685546 -0.36964160506 +1403636911001666560.0000000000 0.4737709943 2.7858555122 1.0870412659 0.4424740762 0.6183982229 0.5295570797 -0.375991527916 +1403636911051666432.0000000000 0.4431843363 2.7988623115 1.0810968216 0.4467908827 0.6153350021 0.5259052590 -0.381004463097 +1403636911101666560.0000000000 0.4128580206 2.8124575920 1.0764695151 0.4494702114 0.6132579584 0.5241093232 -0.383667333524 +1403636911151666432.0000000000 0.3839742538 2.8263070981 1.0721161373 0.4485420297 0.6138641425 0.5249817430 -0.382589900244 +1403636911201666560.0000000000 0.3562800910 2.8404932386 1.0690891721 0.4470483780 0.6150039710 0.5276857655 -0.378768525979 +1403636911251666432.0000000000 0.3295300918 2.8545807404 1.0675114442 0.4439344658 0.6171458428 0.5302719487 -0.375319676098 +1403636911301666560.0000000000 0.3033384802 2.8688921624 1.0677385209 0.4425396117 0.6182093837 0.5326399530 -0.371847455835 +1403636911351666432.0000000000 0.2779315948 2.8832318608 1.0697993148 0.4425081742 0.6184799824 0.5346531984 -0.368530846138 +1403636911401666560.0000000000 0.2531553954 2.8969135258 1.0749576451 0.4425104808 0.6184080987 0.5348740085 -0.368328240624 +1403636911451666432.0000000000 0.2291477059 2.9104402486 1.0815401755 0.4433024931 0.6181901968 0.5352467433 -0.367198453109 +1403636911501666560.0000000000 0.2034080310 2.9230785138 1.0894016913 0.4428780978 0.6186435555 0.5355465562 -0.366509246627 +1403636911551666432.0000000000 0.1784462259 2.9354760585 1.0966219314 0.4430538371 0.6185076177 0.5359713694 -0.365904790165 +1403636911601666560.0000000000 0.1537730474 2.9475536971 1.1026644861 0.4427150015 0.6188908923 0.5359628904 -0.365679191388 +1403636911651666432.0000000000 0.1279649413 2.9580847546 1.1079662973 0.4433360473 0.6186042255 0.5360339476 -0.365307498288 +1403636911701666560.0000000000 0.1033026639 2.9692010552 1.1117647605 0.4428607462 0.6189590787 0.5357887378 -0.365642512282 +1403636911751666432.0000000000 0.0781521033 2.9799729993 1.1144670241 0.4424499321 0.6195815316 0.5348860639 -0.366406443528 +1403636911801666560.0000000000 0.0530352072 2.9904526296 1.1160994286 0.4401627200 0.6214560341 0.5330349426 -0.368677267443 +1403636911851666432.0000000000 0.0281562325 3.0009956779 1.1159901642 0.4379705025 0.6230702306 0.5313556087 -0.370980516872 +1403636911901666560.0000000000 0.0033514088 3.0117742619 1.1139510333 0.4331888400 0.6267731352 0.5295996247 -0.372863384338 +1403636911951666432.0000000000 -0.0218156112 3.0233677189 1.1104181294 0.4296633282 0.6294873047 0.5280180466 -0.374609263272 +1403636912001666560.0000000000 -0.0469672406 3.0360178188 1.1051234898 0.4295434495 0.6299018044 0.5282582278 -0.373710297703 +1403636912051666432.0000000000 -0.0723195443 3.0494331476 1.0985567489 0.4312264473 0.6291008401 0.5291707509 -0.371825497421 +1403636912101666560.0000000000 -0.0975940943 3.0631064024 1.0910906171 0.4311448103 0.6295818601 0.5287380192 -0.37172159065 +1403636912151666432.0000000000 -0.1233632880 3.0775591605 1.0842428884 0.4327169244 0.6283601305 0.5289798604 -0.371617971852 +1403636912201666560.0000000000 -0.1493845432 3.0928054647 1.0797272276 0.4345527636 0.6273060795 0.5294251420 -0.370621096621 +1403636912251666432.0000000000 -0.1752987487 3.1085967481 1.0773532702 0.4365877382 0.6261187192 0.5295032279 -0.370125421857 +1403636912301666560.0000000000 -0.2012913954 3.1247840627 1.0767170279 0.4389907776 0.6245460957 0.5302360595 -0.368888862342 +1403636912351666432.0000000000 -0.2269528190 3.1407924203 1.0773344017 0.4396044405 0.6244223024 0.5301451565 -0.368498083041 +1403636912401666560.0000000000 -0.2526043105 3.1569251754 1.0787713711 0.4395806546 0.6247344697 0.5300283339 -0.368165256055 +1403636912451666432.0000000000 -0.2784227198 3.1730517299 1.0800493256 0.4383630406 0.6257406081 0.5285907503 -0.369970748462 +1403636912501666560.0000000000 -0.3041484245 3.1895145450 1.0801516241 0.4362239749 0.6274837336 0.5267046103 -0.372229850132 +1403636912551666432.0000000000 -0.3298344014 3.2067186762 1.0783412183 0.4364678519 0.6278052272 0.5260898684 -0.372271220021 +1403636912601666560.0000000000 -0.3554058153 3.2242133033 1.0751608936 0.4355183914 0.6288350654 0.5253554376 -0.372681976274 +1403636912651666432.0000000000 -0.3811066844 3.2420359420 1.0709385119 0.4346195143 0.6298128147 0.5233724540 -0.374863936239 +1403636912701666560.0000000000 -0.4067642586 3.2602952357 1.0652458456 0.4326101546 0.6315317014 0.5219139549 -0.376326969484 +1403636912751666432.0000000000 -0.4323861589 3.2793481145 1.0587251650 0.4309190654 0.6328989699 0.5198314715 -0.37884415561 +1403636912801666560.0000000000 -0.4578511752 3.2991611771 1.0508813659 0.4302850473 0.6334533383 0.5188040899 -0.380044684855 +1403636912851666432.0000000000 -0.4830226552 3.3201921928 1.0419093903 0.4310731596 0.6331091229 0.5188130117 -0.379712823597 +1403636912901666560.0000000000 -0.5080769648 3.3425785544 1.0317265040 0.4333373250 0.6318056720 0.5196820437 -0.378114968005 +1403636912951666432.0000000000 -0.5329659036 3.3657338334 1.0206855834 0.4370086031 0.6293359780 0.5199697028 -0.377612520801 +1403636913001666560.0000000000 -0.5572819009 3.3894169381 1.0084987883 0.4413348811 0.6264001624 0.5207612612 -0.376369589689 +1403636913051666432.0000000000 -0.5810983354 3.4134083517 0.9957779193 0.4445419088 0.6242518880 0.5209857964 -0.375853524106 +1403636913101666560.0000000000 -0.6040378210 3.4375025943 0.9830134302 0.4473679115 0.6222369713 0.5212492011 -0.375476195892 +1403636913151666432.0000000000 -0.6256337959 3.4616980581 0.9712909616 0.4497167207 0.6204388673 0.5217721579 -0.374919055686 +1403636913201666560.0000000000 -0.6464502147 3.4859125854 0.9610614343 0.4519394379 0.6188541804 0.5215344673 -0.37519601175 +1403636913251666432.0000000000 -0.6670446340 3.5100502683 0.9526490792 0.4519595813 0.6186675913 0.5221412909 -0.374635049809 +1403636913301666560.0000000000 -0.6871552414 3.5342591246 0.9466199537 0.4518810960 0.6186755662 0.5227881319 -0.373813573774 +1403636913351666432.0000000000 -0.7069461957 3.5581566717 0.9423179633 0.4484369979 0.6209070638 0.5230957620 -0.373830845104 +1403636913401666560.0000000000 -0.7261229460 3.5820343949 0.9399091000 0.4453435257 0.6229730293 0.5230282970 -0.374185982355 +1403636913451666432.0000000000 -0.7447277347 3.6058399050 0.9398838714 0.4412311515 0.6255782124 0.5223165407 -0.375702545087 +1403636913501666560.0000000000 -0.7627267808 3.6303530343 0.9396517173 0.4399040392 0.6269013127 0.5220566598 -0.37541447024 +1403636913551666432.0000000000 -0.7808234581 3.6553793636 0.9386889317 0.4406000068 0.6266024071 0.5227713595 -0.374100471958 +1403636913601666560.0000000000 -0.7983651832 3.6807202004 0.9360269219 0.4414329334 0.6262310962 0.5237084774 -0.372425845121 +1403636913651666432.0000000000 -0.8156321725 3.7061304973 0.9320004562 0.4419628381 0.6262091133 0.5242973382 -0.371003096072 +1403636913701666560.0000000000 -0.8326606695 3.7316631408 0.9266659822 0.4429171775 0.6258487138 0.5248410545 -0.369702081096 +1403636913751666432.0000000000 -0.8495229116 3.7571702995 0.9204919638 0.4441844333 0.6250564840 0.5252062548 -0.369002670728 +1403636913801666560.0000000000 -0.8662145285 3.7824964815 0.9147438876 0.4442570552 0.6250124391 0.5252007297 -0.368997714608 +1403636913851666432.0000000000 -0.8824890778 3.8079303988 0.9094568937 0.4453719821 0.6244008683 0.5255967737 -0.368124143152 +1403636913901666560.0000000000 -0.8989088722 3.8331804284 0.9060205211 0.4457560044 0.6240262370 0.5254925904 -0.368443180806 +1403636913951666432.0000000000 -0.9153278008 3.8584827554 0.9049691269 0.4465246338 0.6231919449 0.5258096237 -0.368472238892 +1403636914001666560.0000000000 -0.9309854800 3.8837179367 0.9064253650 0.4466335090 0.6230793693 0.5260256620 -0.368222230693 +1403636914051666432.0000000000 -0.9463645403 3.9087584060 0.9093314612 0.4459962685 0.6234611203 0.5258443766 -0.368607177913 +1403636914101666560.0000000000 -0.9621696776 3.9336171304 0.9133195340 0.4450074968 0.6241133453 0.5244558369 -0.370670925642 +1403636914151666432.0000000000 -0.9777830377 3.9584930906 0.9168514876 0.4438181959 0.6249353969 0.5235317608 -0.37201566372 +1403636914201666560.0000000000 -0.9930381769 3.9836619226 0.9190999363 0.4434292341 0.6253627855 0.5234183868 -0.371920815921 +1403636914251666432.0000000000 -1.0079804505 4.0091542235 0.9201560935 0.4439760677 0.6254370451 0.5229742299 -0.371768353658 +1403636914301666560.0000000000 -1.0222378630 4.0346952127 0.9193469494 0.4437263621 0.6255135442 0.5243799154 -0.369953275235 +1403636914351666432.0000000000 -1.0364313930 4.0604173878 0.9178733724 0.4453100232 0.6245086964 0.5245811647 -0.369462410823 +1403636914401666560.0000000000 -1.0501280643 4.0862530918 0.9155532856 0.4470179074 0.6235051069 0.5256044666 -0.367636120059 +1403636914451666432.0000000000 -1.0635232869 4.1117168918 0.9141016572 0.4478094027 0.6229730101 0.5261411535 -0.366806289725 +1403636914501666560.0000000000 -1.0768470379 4.1368357830 0.9145440600 0.4488311477 0.6224468135 0.5267893002 -0.365518259938 +1403636914551666432.0000000000 -1.0900498599 4.1616665984 0.9168318216 0.4491577275 0.6223512082 0.5269784702 -0.365006851221 +1403636914601666560.0000000000 -1.1037427958 4.1861934117 0.9211186129 0.4496123698 0.6221014389 0.5269901154 -0.364856046757 +1403636914651666432.0000000000 -1.1174816380 4.2106008746 0.9279201100 0.4510690759 0.6212468800 0.5265876277 -0.365095156338 +1403636914701666560.0000000000 -1.1302166349 4.2343401670 0.9361894536 0.4510802395 0.6213557935 0.5261326314 -0.365551705903 +1403636914751666432.0000000000 -1.1429642486 4.2578764495 0.9449815697 0.4523042662 0.6210375600 0.5258998016 -0.364914508534 +1403636914801666560.0000000000 -1.1554121241 4.2808578240 0.9533418142 0.4526730706 0.6209679051 0.5255897013 -0.365022489633 +1403636914851666432.0000000000 -1.1673899565 4.3033253100 0.9602766188 0.4527498851 0.6212064333 0.5256313033 -0.364461029137 +1403636914901666560.0000000000 -1.1789433543 4.3255357100 0.9654220449 0.4522076421 0.6220692884 0.5257830732 -0.363442167083 +1403636914951666432.0000000000 -1.1899889902 4.3474050940 0.9688340710 0.4514366879 0.6229707943 0.5262888819 -0.362121967023 +1403636915001666560.0000000000 -1.2009446887 4.3689249449 0.9707082340 0.4504075008 0.6241790877 0.5264782252 -0.361046019366 +1403636915051666432.0000000000 -1.2117932190 4.3900464890 0.9711034003 0.4494748980 0.6249935905 0.5270521623 -0.359960200773 +1403636915101666560.0000000000 -1.2228410939 4.4110974445 0.9704657825 0.4492158523 0.6255302505 0.5273839059 -0.358863817483 +1403636915151666432.0000000000 -1.2335916422 4.4317430962 0.9683987509 0.4483234106 0.6264752972 0.5277942913 -0.357726162969 +1403636915201666560.0000000000 -1.2447336898 4.4519030348 0.9647941128 0.4470998840 0.6275609866 0.5286768556 -0.356047306066 +1403636915251666432.0000000000 -1.2561523133 4.4715985241 0.9595428595 0.4443872241 0.6296561811 0.5298626265 -0.35397554398 +1403636915301666560.0000000000 -1.2679629807 4.4908169042 0.9531884881 0.4420594096 0.6314259504 0.5315873467 -0.351140485113 +1403636915351666432.0000000000 -1.2804229410 4.5098647674 0.9459504594 0.4393157518 0.6333268654 0.5332437675 -0.348639980815 +1403636915401666560.0000000000 -1.2936337181 4.5287331155 0.9383582949 0.4380479511 0.6340518159 0.5341818314 -0.347479579729 +1403636915451666432.0000000000 -1.3080477720 4.5473899646 0.9312249546 0.4377576764 0.6342645081 0.5339747616 -0.34777536496 +1403636915501666560.0000000000 -1.3237904470 4.5657508607 0.9261409072 0.4383321867 0.6339666477 0.5312147562 -0.351798332156 +1403636915551666432.0000000000 -1.3407888125 4.5839334943 0.9235187692 0.4393241466 0.6333302282 0.5269329189 -0.358090512661 +1403636915601666560.0000000000 -1.3584843565 4.6020842608 0.9221991353 0.4395767195 0.6331361182 0.5230337029 -0.363794872246 +1403636915651666432.0000000000 -1.3770952499 4.6207429538 0.9228837254 0.4391904970 0.6331448040 0.5194846003 -0.369290014138 +1403636915701666560.0000000000 -1.3952116568 4.6402023125 0.9249493561 0.4390376966 0.6331084468 0.5166912915 -0.373429651668 +1403636915751666432.0000000000 -1.4121804350 4.6604926916 0.9285004078 0.4402498716 0.6320525879 0.5158906694 -0.374895177271 +1403636915801666560.0000000000 -1.4283855875 4.6812629308 0.9331649998 0.4398731181 0.6320843803 0.5152775239 -0.376125045069 +1403636915851666432.0000000000 -1.4446496119 4.7025385161 0.9402989732 0.4403028300 0.6315416119 0.5150705081 -0.376816907874 +1403636915901666560.0000000000 -1.4600907422 4.7244748402 0.9498355385 0.4407430716 0.6309643239 0.5152373637 -0.377041146031 +1403636915951666432.0000000000 -1.4752774215 4.7468028752 0.9594951320 0.4419214693 0.6300046549 0.5164491554 -0.375605936673 +1403636916001666560.0000000000 -1.4901634884 4.7700671810 0.9681228188 0.4452274512 0.6275494417 0.5186501215 -0.372768381718 +1403636916051666432.0000000000 -1.5048416291 4.7937327027 0.9751571489 0.4476673035 0.6257456391 0.5209515154 -0.369656460926 +1403636916101666560.0000000000 -1.5191744076 4.8174177222 0.9805217035 0.4506890896 0.6233559786 0.5236066407 -0.366255039907 +1403636916151666432.0000000000 -1.5329918834 4.8407732367 0.9847463323 0.4520678906 0.6219491109 0.5256322962 -0.364039304144 +1403636916201666560.0000000000 -1.5465063295 4.8637025011 0.9882595183 0.4526468787 0.6213242937 0.5268161765 -0.362672912507 +1403636916251666432.0000000000 -1.5595815985 4.8859202966 0.9927794982 0.4521986310 0.6215387365 0.5264858802 -0.36334365979 +1403636916301666560.0000000000 -1.5723077707 4.9076278198 0.9985114119 0.4514111536 0.6218521819 0.5263863513 -0.363930272676 +1403636916351666432.0000000000 -1.5844243152 4.9290267859 1.0057012513 0.4508225970 0.6219263133 0.5264606592 -0.364425330018 +1403636916401666560.0000000000 -1.5969070002 4.9506241434 1.0134400414 0.4512024847 0.6221196308 0.5271644804 -0.362603217613 +1403636916451666432.0000000000 -1.6094587726 4.9724308186 1.0209382890 0.4544928480 0.6218073629 0.5266034261 -0.359834248156 +1403636916501666560.0000000000 -1.6220562615 4.9938351834 1.0273334397 0.4560354599 0.6244771668 0.5236183413 -0.35760838935 +1403636916551666432.0000000000 -1.6346225120 5.0152856159 1.0324158196 0.4596782027 0.6269709736 0.5203309685 -0.353353974517 +1403636916601666560.0000000000 -1.6472978463 5.0362008240 1.0362541542 0.4625208709 0.6305583863 0.5159548630 -0.349658611701 +1403636916651666432.0000000000 -1.6598924003 5.0565344819 1.0387537760 0.4653083248 0.6340500024 0.5118565760 -0.345646644613 +1403636916701666560.0000000000 -1.6723211896 5.0759798774 1.0402225049 0.4676791730 0.6370644392 0.5078531145 -0.342797761825 +1403636916751666432.0000000000 -1.6847308707 5.0945141312 1.0405218724 0.4699484836 0.6395445769 0.5041959378 -0.340466757835 +1403636916801666560.0000000000 -1.6968572659 5.1122723063 1.0393040595 0.4712464450 0.6423296290 0.5003966970 -0.339031829572 +1403636916851666432.0000000000 -1.7086280150 5.1292127826 1.0368595009 0.4724846068 0.6443911932 0.4978585482 -0.337127798296 +1403636916901666560.0000000000 -1.7203018112 5.1456075817 1.0333127953 0.4744370374 0.6457078265 0.4960213424 -0.334564983708 +1403636916951666432.0000000000 -1.7320174963 5.1610515322 1.0287551553 0.4760172083 0.6465156030 0.4943079205 -0.33329397272 +1403636917001666560.0000000000 -1.7435498131 5.1755773717 1.0227107455 0.4766311026 0.6477584762 0.4926962301 -0.332388587908 +1403636917051666432.0000000000 -1.7549130994 5.1892071808 1.0156751647 0.4763494051 0.6492776688 0.4909346515 -0.332434837153 +1403636917101666560.0000000000 -1.7661638087 5.2021022246 1.0076148287 0.4759535266 0.6506314636 0.4892417769 -0.332850451109 +1403636917151666432.0000000000 -1.7772519854 5.2142793114 0.9986338633 0.4749681298 0.6522276866 0.4874330573 -0.333786361613 +1403636917201666560.0000000000 -1.7882448086 5.2262969658 0.9885008038 0.4750186484 0.6540605417 0.4847084077 -0.334095571593 +1403636917251666432.0000000000 -1.7989127721 5.2384204234 0.9767722195 0.4761854634 0.6564983307 0.4814504529 -0.332359455498 +1403636917301666560.0000000000 -1.8093956099 5.2505930901 0.9638472161 0.4790449149 0.6590281276 0.4767928614 -0.329949183584 +1403636917351666432.0000000000 -1.8191101048 5.2628347580 0.9496784212 0.4824427729 0.6624783935 0.4715938290 -0.325531272738 +1403636917401666560.0000000000 -1.8291128465 5.2753588076 0.9343545612 0.4870354145 0.6664960787 0.4651257241 -0.319746060172 +1403636917451666432.0000000000 -1.8388564014 5.2872569308 0.9175512629 0.4907161648 0.6713655640 0.4571152518 -0.315454547723 +1403636917501666560.0000000000 -1.8484784959 5.2988552748 0.8999094660 0.4937887402 0.6758547262 0.4512161047 -0.309511059614 +1403636917551666432.0000000000 -1.8577440151 5.3095426232 0.8834598714 0.4963503897 0.6796795120 0.4449534438 -0.306085746861 +1403636917601666560.0000000000 -1.8672699594 5.3197945758 0.8688859928 0.4981267444 0.6833540697 0.4390260093 -0.303567331928 +1403636917651666432.0000000000 -1.8754596600 5.3290772349 0.8560842033 0.5007098655 0.6857639796 0.4341173317 -0.300931117074 +1403636917701666560.0000000000 -1.8835020631 5.3376795560 0.8448261081 0.5021593419 0.6882279937 0.4298584606 -0.298998207062 +1403636917751666432.0000000000 -1.8914444403 5.3460679086 0.8354022780 0.5041299249 0.6903198663 0.4258982707 -0.296516718094 +1403636917801666560.0000000000 -1.8989411670 5.3539433714 0.8279213294 0.5060015299 0.6920242684 0.4227658539 -0.293826303176 +1403636917851666432.0000000000 -1.9061089576 5.3613900861 0.8227378288 0.5080152615 0.6933421730 0.4200492501 -0.291128412983 +1403636917901666560.0000000000 -1.9129636486 5.3681340322 0.8200893062 0.5096614727 0.6944308892 0.4175301462 -0.289274092128 +1403636917951666432.0000000000 -1.9190476095 5.3740971631 0.8185181724 0.5108071993 0.6953212635 0.4159864845 -0.287331847202 +1403636918001666560.0000000000 -1.9247065079 5.3793963556 0.8165371755 0.5107391503 0.6968765747 0.4147613206 -0.285449832528 +1403636918051666432.0000000000 -1.9299871067 5.3840681633 0.8134599502 0.5108756563 0.6979327683 0.4139979687 -0.283728032912 +1403636918101666560.0000000000 -1.9350015063 5.3881879572 0.8089120148 0.5113336703 0.6982985387 0.4143202251 -0.281524030064 +1403636918151666432.0000000000 -1.9398443425 5.3917075657 0.8032164689 0.5113829053 0.6987584529 0.4147079646 -0.279716736709 +1403636918201666560.0000000000 -1.9447671096 5.3946540041 0.7973707592 0.5114328428 0.6989244423 0.4157868510 -0.277601091112 +1403636918251666432.0000000000 -1.9495994117 5.3969824148 0.7927414194 0.5114502774 0.6989352770 0.4167259556 -0.276129625855 +1403636918301666560.0000000000 -1.9544136570 5.3984406441 0.7900361587 0.5115603720 0.6987697398 0.4175336402 -0.275122692213 +1403636918351666432.0000000000 -1.9589556810 5.3989378344 0.7886973668 0.5095172482 0.6999790730 0.4195018723 -0.272836306846 +1403636918401666560.0000000000 -1.9635282219 5.3983788989 0.7887269934 0.5044830831 0.7032122839 0.4217620847 -0.270381298634 +1403636918451666432.0000000000 -1.9688844053 5.3973676631 0.7905524334 0.5003999981 0.7057361650 0.4241424127 -0.267655601499 +1403636918501666560.0000000000 -1.9753810231 5.3960280571 0.7947937877 0.4972682282 0.7074969249 0.4260674812 -0.265779818741 +1403636918551666432.0000000000 -1.9832648261 5.3944388312 0.8013967920 0.4955073049 0.7082575080 0.4270910119 -0.265399850661 +1403636918601666560.0000000000 -1.9924933465 5.3928077032 0.8099615749 0.4948728279 0.7080666542 0.4284990019 -0.264822776214 +1403636918651666432.0000000000 -2.0035445952 5.3911510279 0.8212232797 0.4950583682 0.7071781498 0.4290137208 -0.266014104789 +1403636918701666560.0000000000 -2.0158126508 5.3886655733 0.8343378209 0.4952533119 0.7063650395 0.4285678784 -0.268518456682 +1403636918751666432.0000000000 -2.0289566053 5.3857776527 0.8495523781 0.4943551443 0.7064490326 0.4260142119 -0.273961031675 +1403636918801666560.0000000000 -2.0433628782 5.3827585495 0.8666234671 0.4922948043 0.7074597280 0.4215407492 -0.281868685278 +1403636918851666432.0000000000 -2.0584775771 5.3802424361 0.8853605518 0.4915221839 0.7077382474 0.4157596982 -0.290957710393 +1403636918901666560.0000000000 -2.0728079736 5.3774325429 0.9037831887 0.4924069756 0.7074707165 0.4109036575 -0.296949052671 +1403636918951666432.0000000000 -2.0873051919 5.3767070380 0.9231163468 0.4935273830 0.7083700367 0.4040198045 -0.302341877379 +1403636919001666560.0000000000 -2.1010320611 5.3769444205 0.9425126321 0.4945434604 0.7097605930 0.3985306644 -0.304696530986 +1403636919051666432.0000000000 -2.1144147193 5.3786181063 0.9626818717 0.4955330490 0.7110380040 0.3931978742 -0.307029943153 +1403636919101666560.0000000000 -2.1269695729 5.3818264102 0.9834604166 0.4965207443 0.7121378659 0.3896638610 -0.307390445355 +1403636919151666432.0000000000 -2.1378258757 5.3862848288 1.0044915473 0.4978720944 0.7129918741 0.3866523373 -0.307027580406 +1403636919201666560.0000000000 -2.1471378939 5.3918665159 1.0256960980 0.4994827987 0.7134789335 0.3843691025 -0.306145616196 +1403636919251666432.0000000000 -2.1548700294 5.3985471485 1.0469019147 0.5003684646 0.7143240633 0.3830434756 -0.304384999589 +1403636919301666560.0000000000 -2.1613587482 5.4063401076 1.0677595195 0.5021401013 0.7145654031 0.3814951544 -0.302841626234 +1403636919351666432.0000000000 -2.1664716033 5.4152595294 1.0870933520 0.5040234027 0.7151128828 0.3795213635 -0.300894514818 +1403636919401666560.0000000000 -2.1703117181 5.4251698362 1.1046404772 0.5062181867 0.7153332431 0.3789962104 -0.297327044327 +1403636919451666432.0000000000 -2.1730401746 5.4360066207 1.1203179579 0.5090956478 0.7149566172 0.3793725143 -0.292805656339 +1403636919501666560.0000000000 -2.1746936219 5.4473876630 1.1344924523 0.5128187292 0.7135956625 0.3811192065 -0.287308774346 +1403636919551666432.0000000000 -2.1753847336 5.4591285703 1.1471618202 0.5163024439 0.7122713608 0.3831227415 -0.281634976435 +1403636919601666560.0000000000 -2.1754884905 5.4710382292 1.1586663748 0.5191320284 0.7112131294 0.3844707204 -0.277236517902 +1403636919651666432.0000000000 -2.1750509513 5.4825542030 1.1689105907 0.5220522119 0.7098997804 0.3848437259 -0.274588959282 +1403636919701666560.0000000000 -2.1739828277 5.4934500462 1.1773262221 0.5235029257 0.7092761389 0.3855537235 -0.272434160581 +1403636919751666432.0000000000 -2.1723458939 5.5038191928 1.1843602412 0.5236026790 0.7095314514 0.3850851123 -0.27224035391 +1403636919801666560.0000000000 -2.1702263113 5.5137177254 1.1901463632 0.5243675177 0.7092545543 0.3839711483 -0.273061972617 +1403636919851666432.0000000000 -2.1677123511 5.5231751143 1.1942065027 0.5241726363 0.7095012497 0.3831981967 -0.27387983885 +1403636919901666560.0000000000 -2.1647187482 5.5321215641 1.1964837073 0.5240726194 0.7096620287 0.3822994385 -0.274908773778 +1403636919951666432.0000000000 -2.1612132141 5.5406111569 1.1974460218 0.5236714712 0.7099500280 0.3807180316 -0.277115370211 +1403636920001666560.0000000000 -2.1567461816 5.5487177541 1.1967590115 0.5231281762 0.7101319681 0.3792574219 -0.279666421012 +1403636920051666432.0000000000 -2.1513562042 5.5566216856 1.1945946070 0.5224161665 0.7103926329 0.3774355874 -0.282782661043 +1403636920101666560.0000000000 -2.1449126445 5.5643141863 1.1910794105 0.5215051357 0.7107702949 0.3758190843 -0.285653631465 +1403636920151666432.0000000000 -2.1372280234 5.5719730774 1.1862698144 0.5203134866 0.7113243124 0.3742792732 -0.288455583974 +1403636920201666560.0000000000 -2.1283081871 5.5797450981 1.1801356643 0.5195395154 0.7115116436 0.3732791274 -0.290676049894 +1403636920251666432.0000000000 -2.1179643488 5.5878239614 1.1723518414 0.5198372987 0.7110649985 0.3742711216 -0.289960132469 +1403636920301666560.0000000000 -2.1063540229 5.5962442226 1.1634232877 0.5222713974 0.7091806850 0.3774607994 -0.286039662298 +1403636920351666432.0000000000 -2.0936965785 5.6045289087 1.1536062922 0.5249284420 0.7071627093 0.3805950555 -0.281990136497 +1403636920401666560.0000000000 -2.0801018091 5.6123970447 1.1437574917 0.5266724513 0.7058046931 0.3832623827 -0.278506391909 +1403636920451666432.0000000000 -2.0654055829 5.6195547776 1.1348920975 0.5270446826 0.7053057026 0.3863968526 -0.274709374966 +1403636920501666560.0000000000 -2.0503095123 5.6259620831 1.1277791645 0.5265133235 0.7055470892 0.3883983261 -0.272275164721 +1403636920551666432.0000000000 -2.0344101065 5.6314479392 1.1227268525 0.5250426954 0.7065605770 0.3901648312 -0.269951335485 +1403636920601666560.0000000000 -2.0178354915 5.6358272705 1.1198202237 0.5228461079 0.7080386495 0.3915614236 -0.268314870614 +1403636920651666432.0000000000 -2.0015160719 5.6398727261 1.1186808883 0.5201826689 0.7100160577 0.3925894101 -0.266759711726 +1403636920701666560.0000000000 -1.9849019065 5.6432826701 1.1199537503 0.5176572333 0.7119346840 0.3938165336 -0.264742388702 +1403636920751666432.0000000000 -1.9687939019 5.6463792376 1.1228281456 0.5154337270 0.7135984643 0.3946500379 -0.263356511832 +1403636920801666560.0000000000 -1.9523605797 5.6487886284 1.1274833505 0.5128524885 0.7157014786 0.3952053783 -0.261851919018 +1403636920851666432.0000000000 -1.9367696706 5.6510861689 1.1343278174 0.5110199609 0.7170832108 0.3954959866 -0.261214840507 +1403636920901666560.0000000000 -1.9214208910 5.6529261750 1.1431961072 0.5098845918 0.7179944975 0.3954563599 -0.260990176212 +1403636920951666432.0000000000 -1.9067375606 5.6547556512 1.1530203198 0.5096739008 0.7184565725 0.3953671078 -0.260264324136 +1403636921001666560.0000000000 -1.8928624358 5.6564205377 1.1625911285 0.5095769737 0.7186682087 0.3951522429 -0.260196115911 +1403636921051666432.0000000000 -1.8795922195 5.6579947979 1.1709062387 0.5094669512 0.7189393430 0.3949388567 -0.259986434528 +1403636921101666560.0000000000 -1.8670012007 5.6594884169 1.1780706592 0.5099921556 0.7188365809 0.3941301795 -0.260467604179 +1403636921151666432.0000000000 -1.8550097634 5.6609558514 1.1835805464 0.5104448377 0.7187204788 0.3939549572 -0.260166163633 +1403636921201666560.0000000000 -1.8435764770 5.6623698941 1.1878701205 0.5121983057 0.7176669205 0.3931657743 -0.260821319525 +1403636921251666432.0000000000 -1.8326676701 5.6636268770 1.1910295382 0.5156651123 0.7152628725 0.3916253444 -0.262903223298 +1403636921301666560.0000000000 -1.8218566710 5.6646404514 1.1927790245 0.5194913859 0.7127222615 0.3898948405 -0.264835215506 +1403636921351666432.0000000000 -1.8110864912 5.6649604307 1.1931609716 0.5215677389 0.7113831474 0.3873879614 -0.268014325448 +1403636921401666560.0000000000 -1.8000802108 5.6645425681 1.1921883070 0.5222235427 0.7110211299 0.3845871242 -0.271706216777 +1403636921451666432.0000000000 -1.7887616286 5.6638051809 1.1900518952 0.5226373497 0.7108404269 0.3821000521 -0.274873859029 +1403636921501666560.0000000000 -1.7766005464 5.6624307429 1.1864984555 0.5202457529 0.7125965596 0.3796750792 -0.278203763676 +1403636921551666432.0000000000 -1.7636954530 5.6608578153 1.1813588227 0.5177111548 0.7145215335 0.3783124423 -0.279846090433 +1403636921601666560.0000000000 -1.7498022970 5.6592380690 1.1746760364 0.5134738783 0.7177209769 0.3774272333 -0.280659685825 +1403636921651666432.0000000000 -1.7350024387 5.6580921087 1.1662402745 0.5084274815 0.7214513343 0.3781166284 -0.279351541282 +1403636921701666560.0000000000 -1.7196657319 5.6575093286 1.1558520844 0.5018233518 0.7263280739 0.3811315874 -0.274516968011 +1403636921751666432.0000000000 -1.7044166592 5.6574934981 1.1451569513 0.4952894755 0.7310501810 0.3835009260 -0.270519884622 +1403636921801666560.0000000000 -1.6896119067 5.6588129143 1.1342592583 0.4923862801 0.7332516517 0.3868889130 -0.264980632318 +1403636921851666432.0000000000 -1.6758908422 5.6612842970 1.1240488123 0.4922728899 0.7336229493 0.3881040412 -0.262373823435 +1403636921901666560.0000000000 -1.6631404718 5.6647528653 1.1138634796 0.4940077047 0.7328060272 0.3885161769 -0.26078131561 +1403636921951666432.0000000000 -1.6515438522 5.6692750349 1.1040168763 0.4988349362 0.7301258216 0.3873159873 -0.260895222281 +1403636922001666560.0000000000 -1.6407170996 5.6746184166 1.0938343902 0.5045854071 0.7269788128 0.3860706542 -0.260470387315 +1403636922051666432.0000000000 -1.6301089659 5.6805062935 1.0832262018 0.5108469230 0.7239747863 0.3842325864 -0.259347738737 +1403636922101666560.0000000000 -1.6197282862 5.6862530383 1.0729094116 0.5153202213 0.7222748166 0.3815711490 -0.259167160372 +1403636922151666432.0000000000 -1.6091999183 5.6913625886 1.0637120093 0.5193600602 0.7208896592 0.3794563830 -0.258062163897 +1403636922201666560.0000000000 -1.5987618032 5.6961540759 1.0562304455 0.5212278694 0.7211859987 0.3776264621 -0.256145502633 +1403636922251666432.0000000000 -1.5883494724 5.7006703578 1.0500039664 0.5198411673 0.7236404252 0.3774986918 -0.252199194223 +1403636922301666560.0000000000 -1.5779211863 5.7046707136 1.0458378350 0.5186809161 0.7258659717 0.3774710162 -0.248202196413 +1403636922351666432.0000000000 -1.5682325781 5.7084376589 1.0435981029 0.5168869644 0.7283708403 0.3766318970 -0.245870289533 +1403636922401666560.0000000000 -1.5589195827 5.7118853250 1.0411084231 0.5151879926 0.7308209167 0.3762212439 -0.242774989837 +1403636922451666432.0000000000 -1.5502495937 5.7152249883 1.0375963940 0.5131746815 0.7337191784 0.3753301889 -0.239656343257 +1403636922501666560.0000000000 -1.5424350504 5.7188889941 1.0329188143 0.5124491655 0.7365869946 0.3729996455 -0.236022703643 +1403636922551666432.0000000000 -1.5355648974 5.7228026501 1.0268919840 0.5117448789 0.7398934347 0.3697837256 -0.232238843644 +1403636922601666560.0000000000 -1.5299903474 5.7270678568 1.0201466179 0.5130403048 0.7419523525 0.3658573401 -0.229008207207 +1403636922651666432.0000000000 -1.5258962451 5.7315547925 1.0131807522 0.5162478681 0.7426667471 0.3605415727 -0.227912298493 +1403636922701666560.0000000000 -1.5226805688 5.7363502115 1.0054890147 0.5224486485 0.7408341109 0.3566651001 -0.225836747028 +1403636922751666432.0000000000 -1.5205476605 5.7407783755 0.9980920842 0.5294021288 0.7381650566 0.3507650990 -0.227617179954 +1403636922801666560.0000000000 -1.5188103193 5.7444788351 0.9910707794 0.5337179049 0.7371547653 0.3443101811 -0.230648106697 +1403636922851666432.0000000000 -1.5168481467 5.7471178436 0.9851598700 0.5361773821 0.7369399616 0.3379901602 -0.234938203502 +1403636922901666560.0000000000 -1.5144319917 5.7492293696 0.9808228381 0.5385902918 0.7364700231 0.3325972498 -0.23856125459 +1403636922951666432.0000000000 -1.5111785814 5.7505490995 0.9783097106 0.5394628562 0.7368018009 0.3276432901 -0.242389784105 +1403636923001666560.0000000000 -1.5071522645 5.7515887683 0.9771348374 0.5396872295 0.7374532898 0.3230774604 -0.246010760605 +1403636923051666432.0000000000 -1.5020344083 5.7531071535 0.9763164929 0.5390925714 0.7390037149 0.3203992971 -0.246164577589 +1403636923101666560.0000000000 -1.4957530446 5.7549412381 0.9751136947 0.5402524372 0.7396356344 0.3182163057 -0.244550230253 +1403636923151666432.0000000000 -1.4883236673 5.7568326361 0.9722343697 0.5401320440 0.7420575430 0.3150117350 -0.241610398633 +1403636923201666560.0000000000 -1.4798994348 5.7590233634 0.9677284300 0.5401749613 0.7447281725 0.3123458963 -0.236708684543 +1403636923251666432.0000000000 -1.4701019498 5.7611193952 0.9615931736 0.5392463828 0.7483436517 0.3103839066 -0.229906389784 +1403636923301666560.0000000000 -1.4594795842 5.7632072801 0.9539729293 0.5386099375 0.7515751755 0.3093862842 -0.222068048209 +1403636923351666432.0000000000 -1.4485648338 5.7651213572 0.9451883807 0.5370404371 0.7550616321 0.3089016873 -0.214590885557 +1403636923401666560.0000000000 -1.4374361435 5.7665475212 0.9353717721 0.5342739388 0.7589829108 0.3083266893 -0.20840094083 +1403636923451666432.0000000000 -1.4266211889 5.7679577327 0.9246767102 0.5313381384 0.7628089922 0.3075202754 -0.20306034662 +1403636923501666560.0000000000 -1.4163327170 5.7693755180 0.9129814522 0.5274780148 0.7668514171 0.3073658932 -0.198070835063 +1403636923551666432.0000000000 -1.4069718953 5.7709944311 0.9019190436 0.5227798288 0.7711539561 0.3070196408 -0.194323870648 +1403636923601666560.0000000000 -1.3985772540 5.7734043947 0.8930039724 0.5193190326 0.7743144233 0.3070629249 -0.190937886107 +1403636923651666432.0000000000 -1.3916999461 5.7768222548 0.8867748982 0.5172804806 0.7763951637 0.3063743459 -0.189119576767 +1403636923701666560.0000000000 -1.3862970811 5.7816521829 0.8826254531 0.5159398490 0.7777510012 0.3070130048 -0.186151731786 +1403636923751666432.0000000000 -1.3828002149 5.7875393964 0.8819361301 0.5162777501 0.7779119506 0.3062751400 -0.185757423829 +1403636923801666560.0000000000 -1.3807445893 5.7945719198 0.8831718627 0.5172347927 0.7775438570 0.3062431893 -0.184685756282 +1403636923851666432.0000000000 -1.3801453143 5.8023240868 0.8852440766 0.5185947600 0.7766756551 0.3069898650 -0.183280180164 +1403636923901666560.0000000000 -1.3809458232 5.8103091424 0.8867132897 0.5174006342 0.7775107517 0.3065890243 -0.183784615655 +1403636923951666432.0000000000 -1.3830475578 5.8195517552 0.8871943070 0.5179021038 0.7771846637 0.3073216282 -0.182523495047 +1403636924001666560.0000000000 -1.3866277329 5.8291670055 0.8864595597 0.5180522377 0.7767917508 0.3080436691 -0.182552876952 +1403636924051666432.0000000000 -1.3916662779 5.8397935281 0.8843622113 0.5185016140 0.7764611029 0.3083458581 -0.182173169804 +1403636924101666560.0000000000 -1.3982223653 5.8512487635 0.8811987997 0.5193664272 0.7757602522 0.3086478082 -0.182184181154 +1403636924151666432.0000000000 -1.4061900522 5.8633986806 0.8769621371 0.5206333597 0.7746040703 0.3091508880 -0.182633971211 +1403636924201666560.0000000000 -1.4153297767 5.8762626998 0.8715615518 0.5215952158 0.7737570774 0.3096819381 -0.182580155843 +1403636924251666432.0000000000 -1.4256779278 5.8894961833 0.8654628419 0.5217424838 0.7733639943 0.3105984631 -0.182267681156 +1403636924301666560.0000000000 -1.4376952961 5.9031020837 0.8609146442 0.5231313670 0.7722909281 0.3096500787 -0.184437317171 +1403636924351666432.0000000000 -1.4509601016 5.9166976753 0.8578363378 0.5223621554 0.7727000579 0.3084772705 -0.186853345571 +1403636924401666560.0000000000 -1.4656321428 5.9308470034 0.8567380621 0.5223933225 0.7725940881 0.3054843296 -0.192049254155 +1403636924451666432.0000000000 -1.4811525041 5.9457964441 0.8578054015 0.5236678670 0.7716437818 0.3023089983 -0.197350218116 +1403636924501666560.0000000000 -1.4974195479 5.9618708498 0.8610809599 0.5258480736 0.7699854209 0.2993010380 -0.202546645896 +1403636924551666432.0000000000 -1.5142144235 5.9789279088 0.8664808296 0.5279613848 0.7683472826 0.2960840951 -0.207926520785 +1403636924601666560.0000000000 -1.5312888404 5.9968589297 0.8725076594 0.5293481260 0.7669927553 0.2925641020 -0.214287006114 +1403636924651666432.0000000000 -1.5477603523 6.0155690665 0.8776084668 0.5304986904 0.7659677060 0.2896767174 -0.218979478955 +1403636924701666560.0000000000 -1.5633901523 6.0349302125 0.8814822701 0.5320563071 0.7644866857 0.2878518741 -0.222749841844 +1403636924751666432.0000000000 -1.5781660716 6.0547253825 0.8840145129 0.5335438489 0.7628459365 0.2857951841 -0.227416251072 +1403636924801666560.0000000000 -1.5917794362 6.0751614856 0.8847584638 0.5350666825 0.7611587512 0.2839110241 -0.231809256041 +1403636924851666432.0000000000 -1.6039367244 6.0964124067 0.8837823633 0.5371636551 0.7592596776 0.2824645178 -0.234933492217 +1403636924901666560.0000000000 -1.6143855224 6.1185549734 0.8806190439 0.5391157442 0.7581885126 0.2809618549 -0.235721933175 +1403636924951666432.0000000000 -1.6231645793 6.1416614221 0.8753789022 0.5404085711 0.7585226966 0.2782355888 -0.234918820435 +1403636925001666560.0000000000 -1.6299937755 6.1655955795 0.8677394472 0.5411845742 0.7600209982 0.2754678524 -0.231527107055 +1403636925051666432.0000000000 -1.6346607988 6.1897948400 0.8578904858 0.5421988503 0.7613474585 0.2748302689 -0.225474560666 +1403636925101666560.0000000000 -1.6378488913 6.2143690265 0.8465890777 0.5441984860 0.7617903027 0.2748671390 -0.219024195899 +1403636925151666432.0000000000 -1.6396960374 6.2390321052 0.8331528469 0.5450168237 0.7628794874 0.2771428664 -0.210150853394 +1403636925201666560.0000000000 -1.6408965587 6.2638079617 0.8188944097 0.5462927602 0.7634078461 0.2796306228 -0.201443281143 +1403636925251666432.0000000000 -1.6417715476 6.2883766546 0.8036090858 0.5451503356 0.7653949313 0.2819217260 -0.193653946986 +1403636925301666560.0000000000 -1.6425596347 6.3125942775 0.7874240835 0.5422796327 0.7683532514 0.2840519656 -0.186763384665 +1403636925351666432.0000000000 -1.6437260543 6.3369062229 0.7702209516 0.5384063916 0.7719160193 0.2857935848 -0.180516601666 +1403636925401666560.0000000000 -1.6453152762 6.3610032110 0.7524055072 0.5334995497 0.7759630894 0.2872919223 -0.175279393218 +1403636925451666432.0000000000 -1.6480272413 6.3853593270 0.7350712655 0.5296570983 0.7792019384 0.2877557943 -0.171768158356 +1403636925501666560.0000000000 -1.6518183156 6.4100136080 0.7188581254 0.5261583193 0.7820698748 0.2882508942 -0.168628455294 +1403636925551666432.0000000000 -1.6571063853 6.4349992727 0.7045104210 0.5225954258 0.7848791765 0.2886142483 -0.166013598513 +1403636925601666560.0000000000 -1.6639798882 6.4601820336 0.6922415960 0.5189494621 0.7876100093 0.2890593913 -0.163727204303 +1403636925651666432.0000000000 -1.6725847051 6.4855842507 0.6826251250 0.5157283087 0.7900964879 0.2884752664 -0.162953589182 +1403636925701666560.0000000000 -1.6833774570 6.5123672999 0.6750567457 0.5142076189 0.7912754603 0.2890095992 -0.161081104148 +1403636925751666432.0000000000 -1.6962386610 6.5402185396 0.6702271703 0.5136121140 0.7918347415 0.2895149185 -0.159315568688 +1403636925801666560.0000000000 -1.7111420256 6.5688894835 0.6684089520 0.5141517611 0.7915792793 0.2895338569 -0.158809183502 +1403636925851666432.0000000000 -1.7287250092 6.5991507371 0.6687673434 0.5173664333 0.7895403036 0.2891234954 -0.15926608883 +1403636925901666560.0000000000 -1.7484347067 6.6302366254 0.6716204649 0.5233411471 0.7857419559 0.2871852159 -0.162013191686 +1403636925951666432.0000000000 -1.7698226657 6.6619713023 0.6756927650 0.5307982334 0.7807312599 0.2859445648 -0.164157366975 +1403636926001666560.0000000000 -1.7925066691 6.6941503055 0.6802284541 0.5393170855 0.7749602986 0.2841071709 -0.166903362017 +1403636926051666432.0000000000 -1.8162921078 6.7260668944 0.6840288780 0.5471491293 0.7695455771 0.2805523831 -0.172388501385 +1403636926101666560.0000000000 -1.8404386294 6.7570812172 0.6860045897 0.5528344331 0.7655172424 0.2770085167 -0.177830601664 +1403636926151666432.0000000000 -1.8647011999 6.7875598242 0.6859223663 0.5571428620 0.7623067137 0.2733704388 -0.183708760647 +1403636926201666560.0000000000 -1.8887244347 6.8172220831 0.6838565037 0.5593714883 0.7604352718 0.2697370370 -0.189957011926 +1403636926251666432.0000000000 -1.9120334219 6.8466094560 0.6796224085 0.5607348811 0.7592231213 0.2670452198 -0.19453404773 +1403636926301666560.0000000000 -1.9344092746 6.8753614278 0.6733165409 0.5611762320 0.7585641881 0.2648049131 -0.198846592 +1403636926351666432.0000000000 -1.9555144509 6.9031379178 0.6655199878 0.5611541841 0.7581877343 0.2624110442 -0.203464456643 +1403636926401666560.0000000000 -1.9755549759 6.9304970943 0.6559298053 0.5606760358 0.7580706625 0.2610329998 -0.206961413162 +1403636926451666432.0000000000 -1.9938065220 6.9571440075 0.6450384709 0.5602837851 0.7579721352 0.2607686587 -0.2087103953 +1403636926501666560.0000000000 -2.0102190865 6.9830033111 0.6332117620 0.5587916185 0.7586846450 0.2606471899 -0.210267874397 +1403636926551666432.0000000000 -2.0246583541 7.0084601048 0.6214349493 0.5577597100 0.7591348405 0.2629806096 -0.208469659214 +1403636926601666560.0000000000 -2.0379039687 7.0337121588 0.6110948078 0.5566097279 0.7596862745 0.2656816867 -0.206096134065 +1403636926651666432.0000000000 -2.0496358275 7.0582974587 0.6031727505 0.5566049659 0.7595071421 0.2683696556 -0.203267166651 +1403636926701666560.0000000000 -2.0602694629 7.0821504733 0.5971629028 0.5551323778 0.7603617901 0.2703313438 -0.201491825698 +1403636926751666432.0000000000 -2.0690639960 7.1047393777 0.5934204907 0.5524166980 0.7626920342 0.2710090579 -0.199225358078 +1403636926801666560.0000000000 -2.0770138148 7.1270642373 0.5919108252 0.5498535774 0.7656137513 0.2684917183 -0.198516559658 +1403636926851666432.0000000000 -2.0844123460 7.1497868806 0.5921733247 0.5470208153 0.7692362648 0.2653754119 -0.196518923382 +1403636926901666560.0000000000 -2.0907096929 7.1728136099 0.5940564941 0.5454651476 0.7725335145 0.2597802766 -0.195381548739 +1403636926951666432.0000000000 -2.0963153088 7.1965523056 0.5954216933 0.5444727222 0.7759217613 0.2533618759 -0.193138900562 +1403636927001666560.0000000000 -2.1009211560 7.2208626403 0.5962493431 0.5455497849 0.7783453823 0.2460639175 -0.189753646877 +1403636927051666432.0000000000 -2.1048402831 7.2459686412 0.5957603080 0.5468980512 0.7808604062 0.2383696157 -0.185309130965 +1403636927101666560.0000000000 -2.1075653869 7.2713687907 0.5935624836 0.5487342286 0.7832324247 0.2308775915 -0.179257504687 +1403636927151666432.0000000000 -2.1093132009 7.2972222228 0.5902151951 0.5504696020 0.7859069463 0.2217046826 -0.173725423443 +1403636927201666560.0000000000 -2.1099598158 7.3236275116 0.5853449826 0.5526973233 0.7883441091 0.2126800750 -0.166752571746 +1403636927251666432.0000000000 -2.1094689939 7.3504508737 0.5787911903 0.5550191616 0.7907795744 0.2031778106 -0.159185967634 +1403636927301666560.0000000000 -2.1080241914 7.3771205026 0.5706337413 0.5569856499 0.7931357357 0.1949381805 -0.150671153123 +1403636927351666432.0000000000 -2.1061347565 7.4036027796 0.5611123219 0.5575659584 0.7957980424 0.1886026451 -0.142319077717 +1403636927401666560.0000000000 -2.1036649808 7.4298686266 0.5498874221 0.5554861809 0.7997432549 0.1852558441 -0.13238618255 +1403636927451666432.0000000000 -2.1012384075 7.4557361631 0.5379523840 0.5514780283 0.8044636136 0.1824182629 -0.124233071588 +1403636927501666560.0000000000 -2.0990344510 7.4816768332 0.5254364446 0.5469435975 0.8091117053 0.1802420467 -0.11706303481 +1403636927551666432.0000000000 -2.0972869304 7.5078603738 0.5127251100 0.5417923547 0.8138371634 0.1784698833 -0.110808919053 +1403636927601666560.0000000000 -2.0963866186 7.5349067902 0.5014054528 0.5377691387 0.8175844868 0.1764008700 -0.10603156885 +1403636927651666432.0000000000 -2.0965179698 7.5635003465 0.4921810823 0.5361380771 0.8194815312 0.1751920818 -0.101556470719 +1403636927701666560.0000000000 -2.0978484042 7.5931982802 0.4853651696 0.5342942290 0.8213593584 0.1738795354 -0.0983076213067 +1403636927751666432.0000000000 -2.1006093892 7.6242424071 0.4809770292 0.5335474106 0.8223680446 0.1722980378 -0.0967023577288 +1403636927801666560.0000000000 -2.1047009119 7.6567595187 0.4790362013 0.5335362584 0.8227961026 0.1703433733 -0.096585556059 +1403636927851666432.0000000000 -2.1099479358 7.6909769113 0.4784828626 0.5339229881 0.8227746091 0.1694288177 -0.0962396031574 +1403636927901666560.0000000000 -2.1163656311 7.7267946276 0.4780212275 0.5347899646 0.8223911626 0.1683142647 -0.0966580456216 +1403636927951666432.0000000000 -2.1236611055 7.7640516760 0.4766719065 0.5361226624 0.8216290981 0.1679269963 -0.0964294560387 +1403636928001666560.0000000000 -2.1318225616 7.8023432146 0.4744124476 0.5370603055 0.8210778319 0.1672184610 -0.0971360307181 +1403636928051666432.0000000000 -2.1406688309 7.8418035490 0.4713242769 0.5389908241 0.8197847722 0.1673451889 -0.0971463151543 +1403636928101666560.0000000000 -2.1504777597 7.8826146690 0.4677016734 0.5428606497 0.8171629784 0.1671552479 -0.0980107380439 +1403636928151666432.0000000000 -2.1611687367 7.9245760182 0.4633307845 0.5471662101 0.8141978925 0.1668659529 -0.099230459885 +1403636928201666560.0000000000 -2.1727845745 7.9674491099 0.4586249611 0.5528587812 0.8102776192 0.1654225292 -0.102140759442 +1403636928251666432.0000000000 -2.1848789996 8.0105498803 0.4530224406 0.5583381048 0.8063907405 0.1634066955 -0.106258111285 +1403636928301666560.0000000000 -2.1968839127 8.0535148946 0.4459926230 0.5626931187 0.8032088064 0.1618678501 -0.10968530733 +1403636928351666432.0000000000 -2.2088080475 8.0959743722 0.4379168229 0.5675925501 0.7995812973 0.1606556748 -0.112686290695 +1403636928401666560.0000000000 -2.2203152334 8.1378903613 0.4280217515 0.5704540419 0.7973479214 0.1606005886 -0.114131193059 +1403636928451666432.0000000000 -2.2312229937 8.1791153026 0.4175261101 0.5727498643 0.7955576525 0.1604679538 -0.11530676638 +1403636928501666560.0000000000 -2.2414506221 8.2196463347 0.4076717089 0.5747881889 0.7940018192 0.1616385531 -0.114248094446 +1403636928551666432.0000000000 -2.2511362361 8.2590001516 0.3988915663 0.5747673475 0.7939012178 0.1627774798 -0.11343211493 +1403636928601666560.0000000000 -2.2603964229 8.2974880721 0.3911861907 0.5730948849 0.7949612619 0.1644305221 -0.112077867486 +1403636928651666432.0000000000 -2.2692269252 8.3350648621 0.3850308844 0.5701719298 0.7969507125 0.1664030193 -0.109925280887 +1403636928701666560.0000000000 -2.2781179875 8.3721150192 0.3808353301 0.5661747946 0.7996595234 0.1682462857 -0.108092256399 +1403636928751666432.0000000000 -2.2871405747 8.4088253683 0.3783964333 0.5620838731 0.8024297295 0.1700576446 -0.106059635586 +1403636928801666560.0000000000 -2.2962978763 8.4451613452 0.3780039375 0.5595003548 0.8041324447 0.1716708892 -0.104208781707 +1403636928851666432.0000000000 -2.3060120521 8.4817095171 0.3796427630 0.5570875578 0.8057595182 0.1726217399 -0.102989254678 +1403636928901666560.0000000000 -2.3161876158 8.5184412023 0.3835323939 0.5568662120 0.8058909766 0.1730892140 -0.102371283629 +1403636928951666432.0000000000 -2.3271779524 8.5556453478 0.3902894242 0.5595408530 0.8040146020 0.1734552475 -0.101920707918 +1403636929001666560.0000000000 -2.3392667839 8.5928784512 0.4003037829 0.5647122172 0.8004834721 0.1704262184 -0.106213119565 +1403636929051666432.0000000000 -2.3515803562 8.6299753757 0.4124657753 0.5696894536 0.7970470605 0.1664674649 -0.111617619029 +1403636929101666560.0000000000 -2.3640931392 8.6689108817 0.4252821587 0.5731089802 0.7945690220 0.1629157936 -0.116895723731 +1403636929151666432.0000000000 -2.3755906800 8.7051645690 0.4394737422 0.5753439272 0.7929260971 0.1597866294 -0.121308709996 +1403636929201666560.0000000000 -2.3864544286 8.7410443764 0.4541324354 0.5756840203 0.7926061990 0.1574176248 -0.12483194063 +1403636929251666432.0000000000 -2.3963853831 8.7759395634 0.4682985029 0.5744088915 0.7934273116 0.1557489183 -0.127553130278 +1403636929301666560.0000000000 -2.4055477947 8.8103044590 0.4814701714 0.5729282720 0.7943533811 0.1540982506 -0.13042097302 +1403636929351666432.0000000000 -2.4135098696 8.8443606374 0.4930402495 0.5718824762 0.7949243910 0.1535218327 -0.1321994437 +1403636929401666560.0000000000 -2.4197638760 8.8783192541 0.5028564881 0.5719018440 0.7948311012 0.1547505400 -0.131240511223 +1403636929451666432.0000000000 -2.4247591944 8.9117906103 0.5112409924 0.5714120055 0.7950546759 0.1557004562 -0.130895951833 +1403636929501666560.0000000000 -2.4282597931 8.9449453999 0.5177413198 0.5712112800 0.7951435725 0.1589049415 -0.127332604721 +1403636929551666432.0000000000 -2.4307665020 8.9773683868 0.5226186957 0.5712610057 0.7950552436 0.1621764652 -0.123478002388 +1403636929601666560.0000000000 -2.4327399123 9.0096133743 0.5262870307 0.5719519780 0.7944460485 0.1652189965 -0.120121163837 +1403636929651666432.0000000000 -2.4340621935 9.0412618626 0.5284525070 0.5722813380 0.7941126015 0.1688355428 -0.115645171915 +1403636929701666560.0000000000 -2.4353430976 9.0721534693 0.5298440307 0.5731597128 0.7933522228 0.1707962988 -0.113616981533 +1403636929751666432.0000000000 -2.4363414462 9.1020521059 0.5297308935 0.5738067277 0.7927753294 0.1727370756 -0.111422704129 +1403636929801666560.0000000000 -2.4373995214 9.1310675805 0.5282257468 0.5733226874 0.7930471309 0.1739402237 -0.110100603598 +1403636929851666432.0000000000 -2.4384933272 9.1588523030 0.5258567669 0.5738373146 0.7926619994 0.1735922148 -0.110740390443 +1403636929901666560.0000000000 -2.4399187143 9.1859028659 0.5232003612 0.5740579229 0.7924244487 0.1730281834 -0.112170593238 +1403636929951666432.0000000000 -2.4412803118 9.2119192165 0.5216550336 0.5741431088 0.7922987492 0.1719278196 -0.114294389107 +1403636930001666560.0000000000 -2.4427151175 9.2371173106 0.5217704613 0.5740627066 0.7923893110 0.1699257444 -0.117031748166 +1403636930051666432.0000000000 -2.4440009766 9.2622119602 0.5237198281 0.5738232362 0.7925352940 0.1686572522 -0.119035426302 +1403636930101666560.0000000000 -2.4447440018 9.2868122180 0.5280327333 0.5725083187 0.7934630484 0.1685779818 -0.119298281293 +1403636930151666432.0000000000 -2.4450137247 9.3105256513 0.5344951822 0.5716220018 0.7941998557 0.1663795218 -0.121707563604 +1403636930201666560.0000000000 -2.4448849853 9.3342673905 0.5420628493 0.5709391869 0.7946678843 0.1661049890 -0.12223146527 +1403636930251666432.0000000000 -2.4440831319 9.3571334283 0.5508323502 0.5694398418 0.7956916662 0.1656485200 -0.123181194616 +1403636930301666560.0000000000 -2.4425209421 9.3795973359 0.5607604605 0.5678915311 0.7968598542 0.1649286772 -0.123742123617 +1403636930351666432.0000000000 -2.4403040572 9.4022039425 0.5729974209 0.5677828532 0.7969530639 0.1650967810 -0.123415956895 +1403636930401666560.0000000000 -2.4372422613 9.4247724249 0.5852409525 0.5691701448 0.7960442644 0.1660778796 -0.121560739564 +1403636930451666432.0000000000 -2.4334819885 9.4469148495 0.5958951555 0.5700426117 0.7954761334 0.1685925280 -0.117667759459 +1403636930501666560.0000000000 -2.4295384966 9.4684738987 0.6054553250 0.5712192928 0.7946790228 0.1695409591 -0.115972554212 +1403636930551666432.0000000000 -2.4253381089 9.4895477992 0.6132749071 0.5726675197 0.7936309084 0.1706618101 -0.114352261286 +1403636930601666560.0000000000 -2.4211581131 9.5098524151 0.6193428689 0.5726550209 0.7935884237 0.1710008725 -0.114203075456 +1403636930651666432.0000000000 -2.4169241899 9.5295727745 0.6240170226 0.5731820965 0.7932282317 0.1698539402 -0.115762237933 +1403636930701666560.0000000000 -2.4127351795 9.5482605508 0.6273448194 0.5722370273 0.7938663299 0.1678759855 -0.118906216656 +1403636930751666432.0000000000 -2.4082775854 9.5664181493 0.6295562881 0.5714144836 0.7944104433 0.1655833457 -0.122391548832 +1403636930801666560.0000000000 -2.4034709517 9.5844291286 0.6304991395 0.5701680823 0.7952294768 0.1624699040 -0.12697230978 +1403636930851666432.0000000000 -2.3977385059 9.6025368666 0.6299368923 0.5701749474 0.7952147139 0.1607736480 -0.129173999772 +1403636930901666560.0000000000 -2.3910639401 9.6205265509 0.6282042728 0.5697524162 0.7957400211 0.1573923160 -0.131938098681 +1403636930951666432.0000000000 -2.3830297865 9.6387160412 0.6252152155 0.5691008767 0.7968129595 0.1523344922 -0.134192034763 +1403636931001666560.0000000000 -2.3735972665 9.6570928277 0.6209495251 0.5686716502 0.7980347418 0.1460903073 -0.13568613513 +1403636931051666432.0000000000 -2.3621007482 9.6756731184 0.6151990433 0.5689480598 0.7990912305 0.1408309323 -0.133857980987 +1403636931101666560.0000000000 -2.3490725342 9.6949941496 0.6103295119 0.5718749132 0.7983579580 0.1375414559 -0.129096872143 +1403636931151666432.0000000000 -2.3342810618 9.7137925866 0.6066273146 0.5765189591 0.7962524375 0.1361418608 -0.12277352852 +1403636931201666560.0000000000 -2.3178670835 9.7317311300 0.6037972891 0.5802020184 0.7947037070 0.1361239300 -0.115247176008 +1403636931251666432.0000000000 -2.3005327723 9.7488314875 0.6036752059 0.5851406653 0.7920500362 0.1352557916 -0.109421263399 +1403636931301666560.0000000000 -2.2824943186 9.7650694928 0.6056497897 0.5892265276 0.7897492479 0.1340756583 -0.105508020667 +1403636931351666432.0000000000 -2.2635251658 9.7799276456 0.6085822154 0.5916325069 0.7885818000 0.1342738881 -0.10040042041 +1403636931401666560.0000000000 -2.2438776191 9.7930919423 0.6132061278 0.5932560083 0.7879112733 0.1341537552 -0.0961556235602 +1403636931451666432.0000000000 -2.2234089044 9.8043169442 0.6182643341 0.5936145061 0.7880359887 0.1360868599 -0.0900081396055 +1403636931501666560.0000000000 -2.2028948923 9.8141239648 0.6251424854 0.5943201018 0.7877958654 0.1384196816 -0.0836736685226 +1403636931551666432.0000000000 -2.1823272517 9.8220190965 0.6331875695 0.5948482948 0.7875831058 0.1411359417 -0.0771297842612 +1403636931601666560.0000000000 -2.1624917504 9.8283436200 0.6414795551 0.5949245387 0.7875995564 0.1436918476 -0.0714449782566 +1403636931651666432.0000000000 -2.1435558424 9.8332041763 0.6492322029 0.5961172177 0.7867061391 0.1459273999 -0.066655138227 +1403636931701666560.0000000000 -2.1259603219 9.8361243765 0.6559362233 0.5962142929 0.7867473757 0.1457977444 -0.0655751595446 +1403636931751666432.0000000000 -2.1096299727 9.8367251497 0.6608860622 0.5932933245 0.7891755340 0.1429344482 -0.069099574463 +1403636931801666560.0000000000 -2.0939196851 9.8356096939 0.6641773357 0.5893225026 0.7923765423 0.1395614034 -0.0732189716392 +1403636931851666432.0000000000 -2.0788557934 9.8334734750 0.6658912201 0.5856683876 0.7952197589 0.1367242075 -0.0769712015819 +1403636931901666560.0000000000 -2.0640399693 9.8304423703 0.6659658544 0.5820810195 0.7979621229 0.1346656790 -0.0793932748559 +1403636931951666432.0000000000 -2.0494025231 9.8268749803 0.6645952487 0.5794303464 0.7999591052 0.1333004485 -0.0809746511321 +1403636932001666560.0000000000 -2.0347524236 9.8227821228 0.6618787122 0.5785761057 0.8006685762 0.1314831504 -0.0830162765034 +1403636932051666432.0000000000 -2.0200051807 9.8185624123 0.6578081448 0.5800606532 0.7996758416 0.1307578539 -0.0833700819747 +1403636932101666560.0000000000 -2.0056352384 9.8137284997 0.6523823849 0.5813401241 0.7987888276 0.1294161915 -0.0850383341731 +1403636932151666432.0000000000 -1.9912142942 9.8083767093 0.6459238372 0.5829860551 0.7976923148 0.1281473326 -0.0859796001045 +1403636932201666560.0000000000 -1.9762948516 9.8023749357 0.6393542705 0.5856055489 0.7958687806 0.1283854152 -0.0847125151842 +1403636932251666432.0000000000 -1.9610089679 9.7959250277 0.6342169866 0.5890746097 0.7934517468 0.1297629738 -0.0811603372862 +1403636932301666560.0000000000 -1.9457510056 9.7883409747 0.6304122688 0.5922951761 0.7911724790 0.1318701771 -0.0764381400772 +1403636932351666432.0000000000 -1.9307533102 9.7794005488 0.6284626641 0.5945814668 0.7895761882 0.1338596250 -0.0715815839517 +1403636932401666560.0000000000 -1.9162796505 9.7687487949 0.6284338972 0.5963541779 0.7883629245 0.1352815021 -0.0674129735871 +1403636932451666432.0000000000 -1.9024151755 9.7562907550 0.6303676951 0.5977716710 0.7875822805 0.1348943739 -0.0647046257087 +1403636932501666560.0000000000 -1.8890064034 9.7418362223 0.6341464949 0.5979234527 0.7880697832 0.1323820827 -0.0625183623105 +1403636932551666432.0000000000 -1.8761168668 9.7255193407 0.6396048045 0.5967936284 0.7898408598 0.1278163262 -0.0604298606177 +1403636932601666560.0000000000 -1.8637278668 9.7071686855 0.6477426567 0.5960254326 0.7916283490 0.1212632418 -0.0580815543358 +1403636932651666432.0000000000 -1.8520320951 9.6878574269 0.6577188789 0.5946027458 0.7940583887 0.1126290927 -0.0568642017651 +1403636932701666560.0000000000 -1.8410390557 9.6678712534 0.6698303708 0.5946302556 0.7952588116 0.1042124617 -0.0558394538086 +1403636932751666432.0000000000 -1.8303920425 9.6468542368 0.6829305934 0.5946238516 0.7962995222 0.0975462181 -0.0530498013854 +1403636932801666560.0000000000 -1.8199818838 9.6241325284 0.6978054496 0.5948434342 0.7970107273 0.0912840436 -0.0510138484268 +1403636932851666432.0000000000 -1.8093349205 9.5995969528 0.7138859774 0.5943362638 0.7981943538 0.0858557618 -0.0477385308393 +1403636932901666560.0000000000 -1.7992576925 9.5741430092 0.7286320971 0.5926889194 0.8000574475 0.0812662354 -0.04498582518 +1403636932951666432.0000000000 -1.7894092046 9.5479704029 0.7411038068 0.5912061273 0.8016616660 0.0776481560 -0.0422451438731 +1403636933001666560.0000000000 -1.7799422673 9.5213752564 0.7498831333 0.5894888306 0.8034296172 0.0737518564 -0.0395529065242 +1403636933051666432.0000000000 -1.7704459474 9.4941026578 0.7548538708 0.5885395527 0.8047216051 0.0690806425 -0.035667886466 +1403636933101666560.0000000000 -1.7612888713 9.4660136392 0.7562245619 0.5878220259 0.8057829609 0.0641770006 -0.03256375817 +1403636933151666432.0000000000 -1.7524138316 9.4371995526 0.7550737192 0.5863081279 0.8073026897 0.0602811879 -0.0295182114766 +1403636933201666560.0000000000 -1.7438114780 9.4070366076 0.7514427186 0.5805052474 0.8118132550 0.0564810917 -0.0279782607104 +1403636933251666432.0000000000 -1.7352690997 9.3763804060 0.7457573431 0.5722928912 0.8178567406 0.0544979828 -0.0249232497314 +1403636933301666560.0000000000 -1.7271620667 9.3460060098 0.7388306522 0.5634581172 0.8241475572 0.0528468303 -0.0224269202469 +1403636933351666432.0000000000 -1.7200338927 9.3166551001 0.7317299155 0.5565826476 0.8289319061 0.0510439918 -0.0219581945552 +1403636933401666560.0000000000 -1.7134578682 9.2891856214 0.7244611154 0.5529701458 0.8314361816 0.0496559441 -0.0217297249431 +1403636933451666432.0000000000 -1.7073644677 9.2634955857 0.7172459290 0.5540513930 0.8307831555 0.0484061492 -0.0219828823413 +1403636933501666560.0000000000 -1.7016545283 9.2393036343 0.7094418494 0.5564988115 0.8291748593 0.0478639096 -0.0220719651338 +1403636933551666432.0000000000 -1.6963978521 9.2163533809 0.7017834249 0.5604603520 0.8265126751 0.0478033986 -0.0218134544269 +1403636933601666560.0000000000 -1.6915777785 9.1943527693 0.6956620188 0.5642986970 0.8238885953 0.0475247430 -0.0227147929589 +1403636933651666432.0000000000 -1.6868706533 9.1725267796 0.6909287221 0.5682451105 0.8211406858 0.0479926947 -0.0228510332996 +1403636933701666560.0000000000 -1.6824317089 9.1515863156 0.6876754653 0.5718007251 0.8186360105 0.0483262200 -0.0233150059906 +1403636933751666432.0000000000 -1.6783120891 9.1312809843 0.6865280247 0.5755105546 0.8159732668 0.0493960848 -0.0231356043785 +1403636933801666560.0000000000 -1.6745417310 9.1109802159 0.6872186004 0.5787083349 0.8136547067 0.0498272726 -0.0240816190329 +1403636933851666432.0000000000 -1.6711127474 9.0905402382 0.6898241899 0.5813695659 0.8117298355 0.0490548311 -0.0264144945093 +1403636933901666560.0000000000 -1.6675686105 9.0698194848 0.6938074739 0.5833292691 0.8103564250 0.0478956185 -0.0274852325087 +1403636933951666432.0000000000 -1.6637302742 9.0490975180 0.6988946819 0.5836742315 0.8102477230 0.0454391977 -0.0275372140963 +1403636934001666560.0000000000 -1.6595902715 9.0285411226 0.7047428208 0.5837744361 0.8104312415 0.0411141345 -0.0267999713464 +1403636934051666432.0000000000 -1.6547885548 9.0077515734 0.7091622408 0.5840037348 0.8106025611 0.0354748820 -0.0245898021318 +1403636934101666560.0000000000 -1.6491295673 8.9866900050 0.7101835701 0.5838924935 0.8110780035 0.0288695275 -0.0197123967653 +1403636934151666432.0000000000 -1.6427914846 8.9655877666 0.7073222338 0.5842079308 0.8112236272 0.0211054558 -0.0131103047893 +1403636934201666560.0000000000 -1.6360759137 8.9442017582 0.7009616387 0.5845724530 0.8112255972 0.0123216416 -0.00602120036884 +1403636934251666432.0000000000 -1.6291086201 8.9224422379 0.6921764871 0.5845964624 0.8113180184 0.0026785254 0.00169550883371 +1403636934301666560.0000000000 -1.6220627575 8.9002086046 0.6819953848 0.5848872489 0.8110245511 -0.0078836081 0.009161457206 +1403636934351666432.0000000000 -1.6150114657 8.8778591863 0.6714755628 0.5853782997 0.8103560330 -0.0203401201 0.015544308635 +1403636934401666560.0000000000 -1.6079066894 8.8547299741 0.6609395884 0.5848532279 0.8101630153 -0.0342394090 0.0202547118353 +1403636934451666432.0000000000 -1.6004239779 8.8313994692 0.6513343521 0.5831223974 0.8105531142 -0.0485666562 0.0247628454371 +1403636934501666560.0000000000 -1.5920880781 8.8078074720 0.6435637584 0.5829142929 0.8095769996 -0.0619752112 0.0309044021461 +1403636934551666432.0000000000 -1.5829102096 8.7837234931 0.6373712433 0.5816215582 0.8091267177 -0.0748218369 0.0378419126166 +1403636934601666560.0000000000 -1.5728159891 8.7593183085 0.6332673377 0.5808166979 0.8081156472 -0.0862257054 0.0465423665561 +1403636934651666432.0000000000 -1.5621854177 8.7346896204 0.6318115320 0.5798248762 0.8070767207 -0.0978110995 0.0535095197343 +1403636934701666560.0000000000 -1.5510475750 8.7087365428 0.6323469567 0.5762685403 0.8080038243 -0.1062192124 0.0613340705868 +1403636934751666432.0000000000 -1.5393384842 8.6828084619 0.6345131624 0.5726333563 0.8091091655 -0.1122951583 0.0694492253742 +1403636934801666560.0000000000 -1.5274727675 8.6561872894 0.6386768453 0.5685960601 0.8107258157 -0.1162496574 0.0768647466725 +1403636934851666432.0000000000 -1.5153572966 8.6294761619 0.6444437364 0.5645564537 0.8124626093 -0.1190395012 0.0837264367835 +1403636934901666560.0000000000 -1.5035039728 8.6031614726 0.6526173907 0.5611441871 0.8139562085 -0.1215617787 0.088403765719 +1403636934951666432.0000000000 -1.4919896923 8.5773523186 0.6627740218 0.5588788500 0.8148536717 -0.1236475013 0.0915380806381 +1403636935001666560.0000000000 -1.4806867480 8.5521879916 0.6750778693 0.5573502742 0.8154611957 -0.1243841372 0.094404960807 +1403636935051666432.0000000000 -1.4695885739 8.5280667001 0.6897881333 0.5584859762 0.8144214372 -0.1242603292 0.0968013821054 +1403636935101666560.0000000000 -1.4580132971 8.5046630127 0.7061386824 0.5617753653 0.8121299486 -0.1243186007 0.0969446805323 +1403636935151666432.0000000000 -1.4473248409 8.4822204610 0.7242341028 0.5658217668 0.8094168346 -0.1243113345 0.0961083151835 +1403636935201666560.0000000000 -1.4370122803 8.4601166322 0.7422661428 0.5696029259 0.8069630793 -0.1252086880 0.0931980687975 +1403636935251666432.0000000000 -1.4266673756 8.4379732668 0.7585933414 0.5716138334 0.8057909729 -0.1250201317 0.0912606163814 +1403636935301666560.0000000000 -1.4163746053 8.4157664288 0.7734122627 0.5733798804 0.8048136145 -0.1252479915 0.0884505476165 +1403636935351666432.0000000000 -1.4059632337 8.3932256125 0.7864172539 0.5746565452 0.8042174841 -0.1249527720 0.0859703324679 +1403636935401666560.0000000000 -1.3953034488 8.3703753270 0.7974573382 0.5746043482 0.8045518791 -0.1245792025 0.0837026830288 +1403636935451666432.0000000000 -1.3843398535 8.3474221715 0.8067387344 0.5749145626 0.8046347909 -0.1237330886 0.0820135462551 +1403636935501666560.0000000000 -1.3730639006 8.3244005578 0.8146858064 0.5754554944 0.8045218039 -0.1226355287 0.0809701682788 +1403636935551666432.0000000000 -1.3613741301 8.3011095289 0.8204582196 0.5755123092 0.8047515362 -0.1215141779 0.0799678151649 +1403636935601666560.0000000000 -1.3495566956 8.2775505302 0.8244763512 0.5758645209 0.8047094638 -0.1208686023 0.0788258420972 +1403636935651666432.0000000000 -1.3375113675 8.2534091999 0.8265028699 0.5760392190 0.8048054252 -0.1200532498 0.0778091447649 +1403636935701666560.0000000000 -1.3250096557 8.2290388944 0.8269800162 0.5763692985 0.8047631856 -0.1187431561 0.077812015894 +1403636935751666432.0000000000 -1.3120480132 8.2047067085 0.8253994918 0.5734659838 0.8069814606 -0.1178493207 0.0776480866724 +1403636935801666560.0000000000 -1.2985793325 8.1802538503 0.8217939496 0.5696096809 0.8098969659 -0.1160870984 0.0783294427795 +1403636935851666432.0000000000 -1.2846500223 8.1560967174 0.8165525922 0.5656813120 0.8127462152 -0.1151058052 0.0787330712547 +1403636935901666560.0000000000 -1.2702842525 8.1322653910 0.8098748462 0.5612459397 0.8159221677 -0.1143538367 0.0787223692569 +1403636935951666432.0000000000 -1.2557966792 8.1087760651 0.8013178534 0.5547856048 0.8204275329 -0.1150253074 0.0766862085765 +1403636936001666560.0000000000 -1.2407196999 8.0861950190 0.7916656835 0.5485201449 0.8246642790 -0.1152979082 0.0759003948502 +1403636936051666432.0000000000 -1.2251625126 8.0649521279 0.7815301537 0.5439507362 0.8277203609 -0.1155322175 0.0751592142816 +1403636936101666560.0000000000 -1.2089916583 8.0456149727 0.7710084310 0.5413788589 0.8294489222 -0.1152865555 0.0750494949762 +1403636936151666432.0000000000 -1.1918906000 8.0287966439 0.7602019667 0.5410556688 0.8296574383 -0.1145367070 0.0762144418878 +1403636936201666560.0000000000 -1.1740776785 8.0138289292 0.7497450773 0.5421187440 0.8289113941 -0.1137116138 0.0779925449651 +1403636936251666432.0000000000 -1.1554856615 8.0007890396 0.7402071419 0.5443856517 0.8273801336 -0.1128017938 0.0797629744861 +1403636936301666560.0000000000 -1.1364945320 7.9890298888 0.7329973235 0.5489005744 0.8243031539 -0.1124338710 0.0811855558678 +1403636936351666432.0000000000 -1.1173304619 7.9778787884 0.7270855317 0.5533533225 0.8212001532 -0.1129411471 0.0816988749338 +1403636936401666560.0000000000 -1.0978417387 7.9680454598 0.7225822492 0.5571303377 0.8185157061 -0.1127358968 0.083237270717 +1403636936451666432.0000000000 -1.0786948805 7.9588433887 0.7203419827 0.5617696416 0.8152396937 -0.1141004034 0.0823420279885 +1403636936501666560.0000000000 -1.0592426429 7.9501032451 0.7196622646 0.5655425275 0.8124836524 -0.1134450978 0.0846296275615 +1403636936551666432.0000000000 -1.0397191606 7.9423273830 0.7206729368 0.5680177656 0.8105911499 -0.1144786868 0.0848082302044 +1403636936601666560.0000000000 -1.0198140736 7.9353286953 0.7216531937 0.5695889932 0.8092685669 -0.1152564389 0.0858412416101 +1403636936651666432.0000000000 -1.0001064265 7.9285502781 0.7211607443 0.5698523268 0.8088453027 -0.1166859193 0.0861510199983 +1403636936701666560.0000000000 -0.9805742215 7.9218168318 0.7190231125 0.5700679701 0.8085169306 -0.1174267795 0.0867976604134 +1403636936751666432.0000000000 -0.9610119196 7.9150818864 0.7153588761 0.5702068677 0.8082510446 -0.1175579647 0.0881731359776 +1403636936801666560.0000000000 -0.9413943932 7.9083470467 0.7104117186 0.5702345911 0.8080515951 -0.1179181194 0.0893333524373 +1403636936851666432.0000000000 -0.9217776458 7.9016506228 0.7048454827 0.5691042908 0.8086783901 -0.1173911088 0.0915363052184 +1403636936901666560.0000000000 -0.9023785882 7.8954527564 0.7004598487 0.5692912626 0.8083884059 -0.1171823558 0.0931876548742 +1403636936951666432.0000000000 -0.8833301585 7.8895575170 0.6975751217 0.5687140963 0.8086660515 -0.1170359464 0.0944779396151 +1403636937001666560.0000000000 -0.8646365609 7.8836852772 0.6969612189 0.5684870278 0.8087331980 -0.1163149975 0.0961453847473 +1403636937051666432.0000000000 -0.8463779229 7.8775114168 0.6982501277 0.5681121218 0.8088713675 -0.1159979544 0.0975715250614 +1403636937101666560.0000000000 -0.8289012063 7.8710259093 0.7014873906 0.5676913182 0.8090750626 -0.1169577663 0.0971853444321 +1403636937151666432.0000000000 -0.8119987999 7.8649525250 0.7063311391 0.5679474066 0.8088341399 -0.1184314051 0.095901406168 +1403636937201666560.0000000000 -0.7956291767 7.8596098307 0.7125306591 0.5681737577 0.8085774446 -0.1207549920 0.0938047391332 +1403636937251666432.0000000000 -0.7791885063 7.8541233796 0.7177642175 0.5678214552 0.8087210902 -0.1220152284 0.0930659835287 +1403636937301666560.0000000000 -0.7626415225 7.8488517081 0.7216121106 0.5678276260 0.8086362629 -0.1223039304 0.0933859206739 +1403636937351666432.0000000000 -0.7463097123 7.8437464225 0.7240874990 0.5685472200 0.8080532056 -0.1229841869 0.0931609647466 +1403636937401666560.0000000000 -0.7299610669 7.8385417916 0.7246680733 0.5683464751 0.8080733009 -0.1233430568 0.0937353451168 +1403636937451666432.0000000000 -0.7138336226 7.8333906498 0.7238258269 0.5682424575 0.8080643745 -0.1239494372 0.0936430092069 +1403636937501666560.0000000000 -0.6978316691 7.8283051982 0.7214173983 0.5684609321 0.8078202837 -0.1241531545 0.0941517510232 +1403636937551666432.0000000000 -0.6818989512 7.8233859704 0.7176693098 0.5688811651 0.8074009527 -0.1243028785 0.0950090307839 +1403636937601666560.0000000000 -0.6661438690 7.8183380507 0.7124727384 0.5687164092 0.8074011835 -0.1244164857 0.0958410814586 +1403636937651666432.0000000000 -0.6502140131 7.8130477901 0.7057827104 0.5682104897 0.8076059447 -0.1229760109 0.0989261248173 +1403636937701666560.0000000000 -0.6345151883 7.8080074707 0.6976294284 0.5676650525 0.8078042734 -0.1209058989 0.102909705972 +1403636937751666432.0000000000 -0.6193158126 7.8032840599 0.6880470996 0.5675584937 0.8076870793 -0.1180099960 0.107668839386 +1403636937801666560.0000000000 -0.6050804871 7.7990164927 0.6774714156 0.5675410965 0.8075052692 -0.1168708727 0.110333780237 +1403636937851666432.0000000000 -0.5918220659 7.7953113929 0.6663235903 0.5701655955 0.8054868387 -0.1166687086 0.111761168919 +1403636937901666560.0000000000 -0.5792428076 7.7918805588 0.6542182703 0.5741492250 0.8024020696 -0.1153109735 0.114921562407 +1403636937951666432.0000000000 -0.5677083096 7.7883701077 0.6411760021 0.5776145039 0.7996339820 -0.1142686459 0.117854386058 +1403636938001666560.0000000000 -0.5576085372 7.7844823673 0.6274262567 0.5813154236 0.7966677047 -0.1133299822 0.120620320273 +1403636938051666432.0000000000 -0.5492233214 7.7798844008 0.6126755625 0.5848775755 0.7937917779 -0.1134290167 0.12225666939 +1403636938101666560.0000000000 -0.5423697296 7.7744721671 0.5970702724 0.5881347484 0.7909679150 -0.1154309036 0.123056823032 +1403636938151666432.0000000000 -0.5371609464 7.7679961442 0.5808217922 0.5909563754 0.7882932396 -0.1195731490 0.122746050047 +1403636938201666560.0000000000 -0.5339054568 7.7604626472 0.5651316251 0.5926288757 0.7866338926 -0.1250405257 0.119845741113 +1403636938251666432.0000000000 -0.5316583471 7.7520928363 0.5507666030 0.5939046793 0.7852040625 -0.1302959108 0.117280807347 +1403636938301666560.0000000000 -0.5306720107 7.7422742982 0.5383172110 0.5949427152 0.7840055946 -0.1368107085 0.112522101226 +1403636938351666432.0000000000 -0.5309102500 7.7304258623 0.5276123559 0.5944231574 0.7839982205 -0.1457844543 0.103705318768 +1403636938401666560.0000000000 -0.5313728915 7.7159067706 0.5184661237 0.5928956398 0.7846167108 -0.1545656895 0.0946616347995 +1403636938451666432.0000000000 -0.5312936662 7.6992656153 0.5103298270 0.5896530452 0.7863314536 -0.1631446495 0.0858833781726 +1403636938501666560.0000000000 -0.5295503765 7.6815009951 0.5043016687 0.5865424475 0.7879716572 -0.1690449214 0.0805756746415 +1403636938551666432.0000000000 -0.5260510915 7.6618861952 0.4996942491 0.5820262363 0.7907908460 -0.1725710279 0.0781955137471 +1403636938601666560.0000000000 -0.5204656431 7.6411384910 0.4966548675 0.5790447868 0.7925262935 -0.1750062566 0.077343513167 +1403636938651666432.0000000000 -0.5130961705 7.6192096473 0.4951908408 0.5768814254 0.7937795168 -0.1769783454 0.0761614397979 +1403636938701666560.0000000000 -0.5034508273 7.5963828832 0.4955654904 0.5758994331 0.7943219863 -0.1770632168 0.0777241422682 +1403636938751666432.0000000000 -0.4916261696 7.5726011584 0.4969496172 0.5747355371 0.7950721118 -0.1762657789 0.0804349090246 +1403636938801666560.0000000000 -0.4780272567 7.5477907274 0.4990253815 0.5734766659 0.7959931298 -0.1743928450 0.0843005729285 +1403636938851666432.0000000000 -0.4626020982 7.5222739670 0.5017043839 0.5723524509 0.7968927364 -0.1713464895 0.0895266396479 +1403636938901666560.0000000000 -0.4459670594 7.4956866663 0.5042011054 0.5694948798 0.7990999745 -0.1672402444 0.0956321767416 +1403636938951666432.0000000000 -0.4285203083 7.4687594293 0.5067122109 0.5664180769 0.8013322574 -0.1643571712 0.100119407205 +1403636939001666560.0000000000 -0.4104378930 7.4419700198 0.5084702959 0.5645384413 0.8026819995 -0.1610505517 0.105169747458 +1403636939051666432.0000000000 -0.3920576262 7.4154065749 0.5089468320 0.5626632364 0.8040588322 -0.1591627039 0.107548642605 +1403636939101666560.0000000000 -0.3732880423 7.3894618281 0.5086485709 0.5630760448 0.8038249820 -0.1578694423 0.109032129534 +1403636939151666432.0000000000 -0.3545116083 7.3638161333 0.5071906685 0.5645543797 0.8029563312 -0.1567796837 0.109360017445 +1403636939201666560.0000000000 -0.3353330396 7.3385512075 0.5044072734 0.5660367667 0.8020319855 -0.1560855874 0.109473112337 +1403636939251666432.0000000000 -0.3162837815 7.3136287884 0.5002062128 0.5670358281 0.8014917460 -0.1554589525 0.109150652189 +1403636939301666560.0000000000 -0.2971705455 7.2888519622 0.4950190022 0.5686908867 0.8005278563 -0.1546550197 0.108755007276 +1403636939351666432.0000000000 -0.2779214381 7.2639814974 0.4889014802 0.5695403337 0.8001932210 -0.1534626286 0.108461232569 +1403636939401666560.0000000000 -0.2585240217 7.2390217359 0.4830772792 0.5700567995 0.8001485316 -0.1521623876 0.107908204507 +1403636939451666432.0000000000 -0.2390868386 7.2137185691 0.4786443964 0.5712455999 0.7996316444 -0.1505441027 0.107722657755 +1403636939501666560.0000000000 -0.2195656511 7.1882712370 0.4762971925 0.5738101067 0.7981131838 -0.1489523100 0.107566336066 +1403636939551666432.0000000000 -0.2001340257 7.1625123878 0.4757594025 0.5770411439 0.7960575666 -0.1471015386 0.108060197741 +1403636939601666560.0000000000 -0.1807969174 7.1359736307 0.4775086527 0.5807319094 0.7936323478 -0.1452603741 0.108616617975 +1403636939651666432.0000000000 -0.1618551518 7.1089677890 0.4815360402 0.5843620157 0.7911797492 -0.1448259120 0.107615492633 +1403636939701666560.0000000000 -0.1433533431 7.0805877283 0.4860191516 0.5863942690 0.7897755198 -0.1452974852 0.106231023764 +1403636939751666432.0000000000 -0.1249327384 7.0510661149 0.4903293611 0.5874265793 0.7890646973 -0.1447298518 0.10658417955 +1403636939801666560.0000000000 -0.1067302069 7.0207137834 0.4934921761 0.5877783280 0.7888239006 -0.1443032097 0.107005021908 +1403636939851666432.0000000000 -0.0887839645 6.9893184290 0.4947282610 0.5866643795 0.7896326971 -0.1442810735 0.107182467073 +1403636939901666560.0000000000 -0.0714236354 6.9571541642 0.4945684991 0.5858731601 0.7901902899 -0.1458702499 0.105232201727 +1403636939951666432.0000000000 -0.0538442914 6.9240486088 0.4928139733 0.5851619953 0.7903270041 -0.1489014659 0.103908706582 +1403636940001666560.0000000000 -0.0357389270 6.8902091862 0.4892902905 0.5841569901 0.7902640203 -0.1525944577 0.104681997658 +1403636940051666432.0000000000 -0.0174624806 6.8553589618 0.4843645351 0.5821134854 0.7907896146 -0.1564447236 0.106398891108 +1403636940101666560.0000000000 0.0009107363 6.8196799928 0.4779967585 0.5802576113 0.7911204441 -0.1603885935 0.108189863384 +1403636940151666432.0000000000 0.0191444193 6.7831136011 0.4703310892 0.5777727213 0.7919515633 -0.1648547986 0.108693603034 +1403636940201666560.0000000000 0.0374023925 6.7458921840 0.4617703835 0.5758252078 0.7925498916 -0.1685330706 0.109025701531 +1403636940251666432.0000000000 0.0560712708 6.7083047206 0.4523644536 0.5745681053 0.7926897642 -0.1716868529 0.109718069028 +1403636940301666560.0000000000 0.0751169381 6.6701686721 0.4421646714 0.5740579196 0.7923425615 -0.1740230059 0.111205951499 +1403636940351666432.0000000000 0.0946270627 6.6315945957 0.4310347132 0.5739686677 0.7917338296 -0.1758159118 0.113164820982 +1403636940401666560.0000000000 0.1143021750 6.5924164422 0.4190433912 0.5738909670 0.7911317515 -0.1784406449 0.11366022167 +1403636940451666432.0000000000 0.1341305014 6.5526019503 0.4067284289 0.5738509028 0.7905718918 -0.1803168056 0.114791440703 +1403636940501666560.0000000000 0.1540976719 6.5123373146 0.3951691616 0.5731407012 0.7905559843 -0.1820484787 0.115712245296 +1403636940551666432.0000000000 0.1744974572 6.4719181326 0.3851608494 0.5710424807 0.7915268274 -0.1842569493 0.115953194882 +1403636940601666560.0000000000 0.1951746556 6.4314902762 0.3760659265 0.5667417306 0.7942482127 -0.1854629551 0.116520726208 +1403636940651666432.0000000000 0.2165953175 6.3908933830 0.3689794958 0.5628938530 0.7966124272 -0.1857465181 0.118563831391 +1403636940701666560.0000000000 0.2386430946 6.3515822554 0.3638727473 0.5590258626 0.7990755220 -0.1852876115 0.12098304082 +1403636940751666432.0000000000 0.2609990690 6.3121770027 0.3609376648 0.5554757309 0.8013698877 -0.1851308986 0.122391036833 +1403636940801666560.0000000000 0.2837518311 6.2730859200 0.3599594608 0.5527141552 0.8031486491 -0.1847575348 0.123789997628 +1403636940851666432.0000000000 0.3068036803 6.2342682011 0.3611363234 0.5508350133 0.8042851407 -0.1844498041 0.125237655513 +1403636940901666560.0000000000 0.3298638561 6.1956786509 0.3639514868 0.5489913595 0.8055376578 -0.1831028462 0.127243533377 +1403636940951666432.0000000000 0.3532713974 6.1577977946 0.3685309501 0.5480292187 0.8061451644 -0.1821557823 0.128892281873 +1403636941001666560.0000000000 0.3770237609 6.1216906969 0.3758326738 0.5502258261 0.8047006207 -0.1818998245 0.128922089758 +1403636941051666432.0000000000 0.4010028072 6.0864374908 0.3845140205 0.5513122936 0.8040023779 -0.1811494353 0.129691222864 +1403636941101666560.0000000000 0.4250581643 6.0515586049 0.3946018558 0.5534776456 0.8024808610 -0.1806339406 0.130607591762 +1403636941151666432.0000000000 0.4490739913 6.0171556620 0.4054565623 0.5552725026 0.8013341046 -0.1802256818 0.130594043714 +1403636941201666560.0000000000 0.4728690738 5.9830872429 0.4166729401 0.5566350395 0.8005141071 -0.1794467950 0.130894785495 +1403636941251666432.0000000000 0.4963783683 5.9494218359 0.4281484495 0.5589723271 0.7990549631 -0.1791680323 0.130230256271 +1403636941301666560.0000000000 0.5198550396 5.9160148601 0.4386867498 0.5614897321 0.7975204591 -0.1778829512 0.130568195717 +1403636941351666432.0000000000 0.5432186704 5.8828298031 0.4477635137 0.5631972862 0.7966724427 -0.1762664668 0.13058318616 +1403636941401666560.0000000000 0.5661330261 5.8497905078 0.4554970174 0.5644675993 0.7961406440 -0.1747703451 0.13035233341 +1403636941451666432.0000000000 0.5886883555 5.8168168811 0.4619986525 0.5659387392 0.7954714866 -0.1731056927 0.130279993363 +1403636941501666560.0000000000 0.6110031304 5.7839110881 0.4668888721 0.5668144671 0.7953024693 -0.1716468872 0.129432176875 +1403636941551666432.0000000000 0.6331266025 5.7507985085 0.4702283414 0.5669223050 0.7956003674 -0.1698552693 0.12949263661 +1403636941601666560.0000000000 0.6548824701 5.7180607820 0.4722701596 0.5664715520 0.7963046092 -0.1687441750 0.128585977582 +1403636941651666432.0000000000 0.6762831721 5.6854922900 0.4733453151 0.5665323050 0.7965552785 -0.1676704561 0.128169628823 +1403636941701666560.0000000000 0.6972554286 5.6529348473 0.4729480844 0.5658643917 0.7973327186 -0.1665225727 0.127782075633 +1403636941751666432.0000000000 0.7180856538 5.6206296910 0.4722410433 0.5657853185 0.7976487946 -0.1655183797 0.127463876943 +1403636941801666560.0000000000 0.7385452289 5.5884934436 0.4724910073 0.5652960322 0.7982764576 -0.1652365773 0.126063344147 +1403636941851666432.0000000000 0.7584150487 5.5558652195 0.4749251497 0.5651602835 0.7986188751 -0.1646970542 0.125206336046 +1403636941901666560.0000000000 0.7780974923 5.5232434818 0.4782637077 0.5638202558 0.7997325995 -0.1647955326 0.124003713128 +1403636941951666432.0000000000 0.7977343866 5.4914874659 0.4839319911 0.5631389429 0.8003908711 -0.1644686110 0.123284469982 +1403636942001666560.0000000000 0.8170444391 5.4597210539 0.4911568128 0.5630027215 0.8005880423 -0.1655897182 0.12110642983 +1403636942051666432.0000000000 0.8363664642 5.4282045216 0.4992429210 0.5636239175 0.8002634016 -0.1667427475 0.118757836633 +1403636942101666560.0000000000 0.8559959115 5.3963796163 0.5081004915 0.5638837461 0.8000560413 -0.1671898892 0.118291980331 +1403636942151666432.0000000000 0.8755200544 5.3647116837 0.5170166489 0.5646087851 0.7995416120 -0.1680525823 0.117083133466 +1403636942201666560.0000000000 0.8951423704 5.3327535202 0.5248172089 0.5654787207 0.7988610427 -0.1687686952 0.116498834601 +1403636942251666432.0000000000 0.9150010310 5.3007848568 0.5310996573 0.5656463424 0.7986272915 -0.1700229489 0.115459350128 +1403636942301666560.0000000000 0.9350810730 5.2687322984 0.5358342311 0.5663639406 0.7979600513 -0.1713563030 0.114580368322 +1403636942351666432.0000000000 0.9552530860 5.2367345932 0.5392414597 0.5672664893 0.7971160449 -0.1731185978 0.113334426666 +1403636942401666560.0000000000 0.9756418915 5.2046843300 0.5408823373 0.5675736593 0.7966606521 -0.1753910895 0.111489517111 +1403636942451666432.0000000000 0.9966790306 5.1724394510 0.5407344838 0.5673495085 0.7965705942 -0.1772602506 0.110311500707 +1403636942501666560.0000000000 1.0180787885 5.1401283171 0.5392103611 0.5665418693 0.7968139962 -0.1793268986 0.109360090106 +1403636942551666432.0000000000 1.0400409101 5.1073483591 0.5361394032 0.5645048805 0.7980478402 -0.1808592658 0.108368863768 +1403636942601666560.0000000000 1.0628332384 5.0744487561 0.5318797772 0.5628725874 0.7989196245 -0.1818144602 0.108836510225 +1403636942651666432.0000000000 1.0862533919 5.0413077531 0.5264125127 0.5604347972 0.8004367053 -0.1823867830 0.109311391304 +1403636942701666560.0000000000 1.1105595244 5.0083420606 0.5197598809 0.5578238620 0.8021001414 -0.1815273225 0.111873738086 +1403636942751666432.0000000000 1.1354488865 4.9756453635 0.5123880773 0.5562048181 0.8030689779 -0.1812103892 0.113486615493 +1403636942801666560.0000000000 1.1609986887 4.9435362780 0.5055687713 0.5553685224 0.8034822949 -0.1807649720 0.115351770846 +1403636942851666432.0000000000 1.1872127294 4.9122997692 0.5006346923 0.5563824121 0.8026077042 -0.1797834462 0.118056754128 +1403636942901666560.0000000000 1.2138069353 4.8815058171 0.4979939471 0.5584920506 0.8009308718 -0.1788041099 0.120935761095 +1403636942951666432.0000000000 1.2406450267 4.8508047456 0.4970036422 0.5594273491 0.8000860153 -0.1776675241 0.123845306971 +1403636943001666560.0000000000 1.2673834311 4.8206467953 0.4986970433 0.5608768629 0.7989127052 -0.1776293017 0.124913831391 +1403636943051666432.0000000000 1.2941321011 4.7903465915 0.5024664203 0.5626707265 0.7975295389 -0.1766385175 0.127071327232 +1403636943101666560.0000000000 1.3209958457 4.7604694699 0.5079481220 0.5639987927 0.7963257251 -0.1768316856 0.128457216011 +1403636943151666432.0000000000 1.3475080942 4.7309765426 0.5141047545 0.5655088757 0.7950109817 -0.1780492066 0.128279891293 +1403636943201666560.0000000000 1.3737608828 4.7012328687 0.5193049959 0.5664499899 0.7941657228 -0.1783848133 0.128895586008 +1403636943251666432.0000000000 1.3997166212 4.6713752236 0.5231793601 0.5663737560 0.7940114255 -0.1788880446 0.129482401225 +1403636943301666560.0000000000 1.4254963972 4.6413067866 0.5255139991 0.5667019857 0.7934827248 -0.1789521996 0.131187404769 +1403636943351666432.0000000000 1.4509452318 4.6108686057 0.5263125138 0.5667923082 0.7930898820 -0.1791780003 0.132853914992 +1403636943401666560.0000000000 1.4758565507 4.5804832913 0.5260002848 0.5675949603 0.7921995332 -0.1800293633 0.133586260455 +1403636943451666432.0000000000 1.5002431785 4.5499960183 0.5240056385 0.5674827995 0.7919975628 -0.1806657248 0.134398767323 +1403636943501666560.0000000000 1.5243087679 4.5197140500 0.5208050099 0.5678263644 0.7915204815 -0.1807589315 0.135627268295 +1403636943551666432.0000000000 1.5477223077 4.4889780599 0.5158683256 0.5677993920 0.7913045598 -0.1810311895 0.136633277117 +1403636943601666560.0000000000 1.5707783253 4.4580466116 0.5097771787 0.5682439332 0.7907839940 -0.1806967391 0.138232397263 +1403636943651666432.0000000000 1.5933593203 4.4267193260 0.5023381866 0.5682744835 0.7905967557 -0.1801223900 0.139917139716 +1403636943701666560.0000000000 1.6153737269 4.3952722630 0.4940273863 0.5693138155 0.7897034498 -0.1807330114 0.139949345819 +1403636943751666432.0000000000 1.6366954239 4.3633321043 0.4838951342 0.5690526787 0.7896918446 -0.1809613982 0.140779301706 +1403636943801666560.0000000000 1.6571944425 4.3312347781 0.4722906734 0.5686915524 0.7898551680 -0.1805545100 0.141840758311 +1403636943851666432.0000000000 1.6763359394 4.2988646796 0.4595303387 0.5679581982 0.7908408180 -0.1801571342 0.139777297088 +1403636943901666560.0000000000 1.6943305854 4.2661776462 0.4448927977 0.5651259165 0.7938207440 -0.1782322201 0.136801317997 +1403636943951666432.0000000000 1.7113777318 4.2330982193 0.4286419370 0.5599729372 0.7988406176 -0.1756365049 0.132044671876 +1403636944001666560.0000000000 1.7282100283 4.2001964231 0.4113896280 0.5536256966 0.8045628785 -0.1728212472 0.127710528835 +1403636944051666432.0000000000 1.7450183707 4.1678433405 0.3942707480 0.5472493419 0.8101253887 -0.1700451591 0.123691779296 +1403636944101666560.0000000000 1.7619057060 4.1364065088 0.3782805455 0.5400679872 0.8159665250 -0.1673689394 0.120469238685 +1403636944151666432.0000000000 1.7790690396 4.1067345254 0.3645277332 0.5355071240 0.8199166811 -0.1648052420 0.117507396713 +1403636944201666560.0000000000 1.7967681771 4.0793799663 0.3528802455 0.5325527778 0.8225826134 -0.1619074085 0.116324434498 +1403636944251666432.0000000000 1.8145305542 4.0542169081 0.3435416933 0.5316567147 0.8238371105 -0.1604705320 0.113502253164 +1403636944301666560.0000000000 1.8330959195 4.0312517550 0.3372280251 0.5328584122 0.8235771721 -0.1582092707 0.11292643972 +1403636944351666432.0000000000 1.8522155628 4.0109487654 0.3327051815 0.5365489738 0.8216591577 -0.1564911822 0.111812061629 +1403636944401666560.0000000000 1.8719380346 3.9928339687 0.3302045306 0.5410629361 0.8190673304 -0.1548968967 0.111294918453 +1403636944451666432.0000000000 1.8921516016 3.9759470111 0.3290273574 0.5463913839 0.8158302475 -0.1513767138 0.113853210181 +1403636944501666560.0000000000 1.9124055379 3.9604947716 0.3297832489 0.5525136377 0.8119544017 -0.1480354102 0.116379753961 +1403636944551666432.0000000000 1.9324403888 3.9454602207 0.3317514540 0.5582714258 0.8081346188 -0.1431953728 0.121435324939 +1403636944601666560.0000000000 1.9515668605 3.9308942102 0.3349662830 0.5624749840 0.8052675779 -0.1383855389 0.126552214127 +1403636944651666432.0000000000 1.9692751078 3.9165408829 0.3389181478 0.5648944671 0.8036982253 -0.1334382867 0.130987126853 +1403636944701666560.0000000000 1.9851411456 3.9027990016 0.3443566158 0.5671324222 0.8026149426 -0.1285367649 0.132847166503 +1403636944751666432.0000000000 1.9988785701 3.8892557132 0.3512291317 0.5687011039 0.8022935750 -0.1273487944 0.1291756882 +1403636944801666560.0000000000 2.0110943422 3.8758495541 0.3596456141 0.5702178997 0.8019829827 -0.1269892605 0.124693905304 +1403636944851666432.0000000000 2.0221250290 3.8625851889 0.3697844983 0.5718740535 0.8014774905 -0.1266119724 0.120678530085 +1403636944901666560.0000000000 2.0319782720 3.8492877828 0.3809858476 0.5724043323 0.8016714123 -0.1268738185 0.116530086986 +1403636944951666432.0000000000 2.0408180030 3.8360700350 0.3921537891 0.5736289970 0.8012697207 -0.1271140024 0.112954144895 +1403636945001666560.0000000000 2.0489548025 3.8226925760 0.4010736973 0.5742020974 0.8012129403 -0.1263741451 0.111262532166 +1403636945051666432.0000000000 2.0565644481 3.8101761954 0.4070680504 0.5746881085 0.8011597948 -0.1255607036 0.110050311112 +1403636945101666560.0000000000 2.0632489844 3.7969973641 0.4094588714 0.5753187905 0.8009704221 -0.1245966691 0.109226106345 +1403636945151666432.0000000000 2.0690380015 3.7828029174 0.4085871224 0.5752781601 0.8012076618 -0.1240373536 0.108333079747 +1403636945201666560.0000000000 2.0741250363 3.7681616191 0.4061232152 0.5753951728 0.8013029831 -0.1231435604 0.10802586725 +1403636945251666432.0000000000 2.0785761506 3.7531873638 0.4030228381 0.5757903329 0.8011650267 -0.1226045669 0.107555626051 +1403636945301666560.0000000000 2.0824634119 3.7382886151 0.4007244265 0.5757807307 0.8012545707 -0.1225653657 0.106983149415 +1403636945351666432.0000000000 2.0856026563 3.7229982629 0.4000585067 0.5758712459 0.8012231172 -0.1222950579 0.10704084905 +1403636945401666560.0000000000 2.0880022505 3.7072384288 0.4011553358 0.5751715099 0.8016937863 -0.1220325603 0.10757723505 +1403636945451666432.0000000000 2.0894662628 3.6912721740 0.4042265800 0.5754581043 0.8014299396 -0.1222726973 0.107737689013 +1403636945501666560.0000000000 2.0901166016 3.6748919878 0.4079586470 0.5752881462 0.8014545536 -0.1228429670 0.107813509198 +1403636945551666432.0000000000 2.0899436015 3.6578878924 0.4106592996 0.5738508758 0.8023777327 -0.1242654415 0.106973110764 +1403636945601666560.0000000000 2.0891706764 3.6403935026 0.4116419790 0.5704105949 0.8046726698 -0.1257425316 0.106407064472 +1403636945651666432.0000000000 2.0877964859 3.6225954015 0.4105631242 0.5647041237 0.8085125423 -0.1266367212 0.106676438074 +1403636945701666560.0000000000 2.0858142845 3.6047812745 0.4078847293 0.5576594747 0.8132183782 -0.1280451573 0.10628366427 +1403636945751666432.0000000000 2.0836984182 3.5877345999 0.4037311786 0.5509840072 0.8175827913 -0.1285984844 0.106945935187 +1403636945801666560.0000000000 2.0812447140 3.5718418473 0.3979773810 0.5443274764 0.8218929619 -0.1295154089 0.106889272263 +1403636945851666432.0000000000 2.0787494948 3.5576274809 0.3916584251 0.5409083866 0.8239621513 -0.1303158356 0.107341853525 +1403636945901666560.0000000000 2.0759424826 3.5452613704 0.3849952278 0.5404275071 0.8241053020 -0.1320902344 0.106492867186 +1403636945951666432.0000000000 2.0733285505 3.5347616544 0.3777748917 0.5437363067 0.8217394826 -0.1318082474 0.108266511035 +1403636946001666560.0000000000 2.0703843889 3.5258096124 0.3696718128 0.5500103099 0.8174059542 -0.1315879372 0.109639316918 +1403636946051666432.0000000000 2.0670455854 3.5177158453 0.3604128134 0.5558994497 0.8131955690 -0.1314424333 0.111407607674 +1403636946101666560.0000000000 2.0631028578 3.5102554569 0.3488277105 0.5583469678 0.8113317090 -0.1318426516 0.112281060929 +1403636946151666432.0000000000 2.0587421577 3.5031334084 0.3356212856 0.5602643286 0.8097970964 -0.1325470686 0.112977074521 +1403636946201666560.0000000000 2.0540040024 3.4965572946 0.3209406950 0.5613812423 0.8088084283 -0.1338637043 0.112962541925 +1403636946251666432.0000000000 2.0490276797 3.4904563313 0.3047743863 0.5634105275 0.8071604043 -0.1337550349 0.114761708805 +1403636946301666560.0000000000 2.0434972750 3.4843616334 0.2872862311 0.5659900998 0.8051617578 -0.1341571092 0.115635724451 +1403636946351666432.0000000000 2.0378097366 3.4785655998 0.2676982735 0.5676008678 0.8036935697 -0.1343211314 0.117744360829 +1403636946401666560.0000000000 2.0310549072 3.4729341875 0.2469607893 0.5695117536 0.8022032170 -0.1356955043 0.117102908738 +1403636946451666432.0000000000 2.0238547896 3.4670247963 0.2242739935 0.5695700989 0.8018806698 -0.1370614079 0.117437065034 +1403636946501666560.0000000000 2.0160041700 3.4610807445 0.2005408255 0.5701064491 0.8012857282 -0.1379232424 0.117885527732 +1403636946551666432.0000000000 2.0075556953 3.4552258935 0.1767248353 0.5707050122 0.8006120130 -0.1386763080 0.118680560355 +1403636946601666560.0000000000 1.9983442507 3.4486351513 0.1537666351 0.5706217045 0.8004398392 -0.1393780471 0.119418148213 +1403636946651666432.0000000000 1.9883157102 3.4416690045 0.1316903431 0.5693182763 0.8011763213 -0.1406219165 0.119242102619 +1403636946701666560.0000000000 1.9770895008 3.4348705791 0.1119346797 0.5688270881 0.8014966085 -0.1456493907 0.113248335377 +1403636946751666432.0000000000 1.9654541221 3.4277263306 0.0945483122 0.5685598470 0.8015629562 -0.1524330763 0.104884149867 +1403636946801666560.0000000000 1.9540138336 3.4206001588 0.0794355135 0.5691042850 0.8009116514 -0.1595190121 0.0959923130563 +1403636946851666432.0000000000 1.9436098902 3.4127064376 0.0651264770 0.5687707058 0.8008621250 -0.1647487594 0.0893173397608 +1403636946901666560.0000000000 1.9346109745 3.4045188052 0.0506525913 0.5681519326 0.8010158957 -0.1682994417 0.0851599329562 +1403636946951666432.0000000000 1.9266622188 3.3959349518 0.0356097741 0.5673425204 0.8011634749 -0.1739981282 0.0773576267964 +1403636947001666560.0000000000 1.9207360379 3.3865178855 0.0193921979 0.5676218336 0.8005102755 -0.1785535738 0.0714658954937 +1403636947051666432.0000000000 1.9174169749 3.3765459505 0.0018480713 0.5668255058 0.8007774054 -0.1810256362 0.0685135897989 +1403636947101666560.0000000000 1.9167546775 3.3660966019 -0.0166580263 0.5653509998 0.8019329073 -0.1799287814 0.070053499664 +1403636947151666432.0000000000 1.9191756120 3.3550617473 -0.0351995602 0.5627841147 0.8041136292 -0.1753388148 0.0770169565408 +1403636947201666560.0000000000 1.9236615434 3.3431179948 -0.0528211532 0.5563272841 0.8089494760 -0.1699686579 0.0849196891192 +1403636947251666432.0000000000 1.9298242630 3.3307112697 -0.0690767184 0.5484823877 0.8145534774 -0.1638322531 0.093961139696 +1403636947301666560.0000000000 1.9370616731 3.3191019278 -0.0828441504 0.5404099214 0.8200356465 -0.1592720486 0.10065321588 +1403636947351666432.0000000000 1.9450773075 3.3094680905 -0.0936340446 0.5333199325 0.8247230711 -0.1559218158 0.105309510527 +1403636947401666560.0000000000 1.9534330204 3.3015391077 -0.1020970140 0.5277465580 0.8283018227 -0.1542394052 0.107749091945 +1403636947451666432.0000000000 1.9625968231 3.2964018577 -0.1081025275 0.5249609295 0.8300141561 -0.1529521738 0.109991616103 +1403636947501666560.0000000000 1.9720921034 3.2942231786 -0.1106156499 0.5268065341 0.8287461808 -0.1546471698 0.108346187675 +1403636947551666432.0000000000 1.9823624715 3.2943603650 -0.1111192084 0.5308956642 0.8259991635 -0.1569734884 0.105992921831 +1403636947601666560.0000000000 1.9938658622 3.2964633461 -0.1094587376 0.5370292741 0.8218942211 -0.1573902364 0.106384968931 +1403636947651666432.0000000000 2.0060879040 3.2996464549 -0.1068260646 0.5412331064 0.8191341575 -0.1559167166 0.108516975863 +1403636947701666560.0000000000 2.0187494001 3.3042114467 -0.1042526931 0.5434108431 0.8176497056 -0.1548822504 0.110295526265 +1403636947751666432.0000000000 2.0319234131 3.3096363122 -0.1027725881 0.5444240981 0.8169698308 -0.1523411044 0.113819527877 +1403636947801666560.0000000000 2.0447987482 3.3157961841 -0.1018550052 0.5446859359 0.8168387955 -0.1491254400 0.117699687701 +1403636947851666432.0000000000 2.0580031661 3.3231517142 -0.1030034651 0.5447140193 0.8167851631 -0.1445870501 0.123463433897 +1403636947901666560.0000000000 2.0707162746 3.3318682315 -0.1050504793 0.5451961116 0.8163847009 -0.1401495640 0.1289779816 +1403636947951666432.0000000000 2.0825050378 3.3418655994 -0.1081820896 0.5459196675 0.8159124840 -0.1372507343 0.131987768458 +1403636948001666560.0000000000 2.0927967322 3.3529997830 -0.1124327282 0.5447023499 0.8168855065 -0.1384450591 0.129731973169 +1403636948051666432.0000000000 2.1019793667 3.3650484552 -0.1179857213 0.5426570208 0.8184685757 -0.1402839544 0.12630502967 +1403636948101666560.0000000000 2.1103690018 3.3783810287 -0.1247605711 0.5406720121 0.8200179391 -0.1415166025 0.123358850921 +1403636948151666432.0000000000 2.1185971325 3.3926578679 -0.1326079692 0.5397792178 0.8207597423 -0.1405015426 0.123495578376 +1403636948201666560.0000000000 2.1264029458 3.4081941868 -0.1411420583 0.5405678968 0.8204021169 -0.1388763733 0.124258072372 +1403636948251666432.0000000000 2.1334988233 3.4249819876 -0.1505248458 0.5409748053 0.8203344007 -0.1374162639 0.124557221652 +1403636948301666560.0000000000 2.1399727504 3.4431057834 -0.1605483203 0.5419255149 0.8198366374 -0.1356032641 0.125683646778 +1403636948351666432.0000000000 2.1457724276 3.4624337229 -0.1714474507 0.5427526180 0.8194948445 -0.1336610415 0.126421997848 +1403636948401666560.0000000000 2.1509328581 3.4828870267 -0.1830054363 0.5429620986 0.8195034036 -0.1312350163 0.127998834025 +1403636948451666432.0000000000 2.1550456761 3.5044658932 -0.1951747179 0.5433346452 0.8194705811 -0.1285655981 0.129330263224 +1403636948501666560.0000000000 2.1586147367 3.5272041416 -0.2080767355 0.5441528801 0.8188926087 -0.1231105551 0.134745425958 +1403636948551666432.0000000000 2.1607720951 3.5509864290 -0.2214405144 0.5455335322 0.8177669535 -0.1166442923 0.141578544053 +1403636948601666560.0000000000 2.1609204161 3.5761132616 -0.2349010223 0.5471336817 0.8164050440 -0.1107882400 0.147829307996 +1403636948651666432.0000000000 2.1584395350 3.6023294638 -0.2473560970 0.5488811762 0.8149942754 -0.1058491247 0.152675303177 +1403636948701666560.0000000000 2.1526057326 3.6302556994 -0.2575203689 0.5521707757 0.8129816594 -0.1046244911 0.152387570811 +1403636948751666432.0000000000 2.1433495948 3.6592209566 -0.2656654166 0.5550056316 0.8116636499 -0.1071595486 0.14726744207 +1403636948801666560.0000000000 2.1310534481 3.6888825404 -0.2714504900 0.5585807605 0.8101157824 -0.1127397730 0.137803108409 +1403636948851666432.0000000000 2.1168034354 3.7194016968 -0.2749340682 0.5622664731 0.8082437993 -0.1176399998 0.129457346396 +1403636948901666560.0000000000 2.1008211082 3.7500102029 -0.2765934518 0.5661417779 0.8061522444 -0.1224897034 0.120823502335 +1403636948951666432.0000000000 2.0834972391 3.7806472162 -0.2768012518 0.5703347635 0.8036792671 -0.1280803813 0.111415030815 +1403636949001666560.0000000000 2.0658804516 3.8107885372 -0.2775388260 0.5746783863 0.8009351375 -0.1322752513 0.103686622846 +1403636949051666432.0000000000 2.0486786831 3.8402012733 -0.2800551811 0.5766879200 0.7997002543 -0.1344955795 0.0991034073421 +1403636949101666560.0000000000 2.0320484284 3.8688710752 -0.2841160679 0.5780654531 0.7988915565 -0.1336920784 0.098686580272 +1403636949151666432.0000000000 2.0156051815 3.8964347270 -0.2895051980 0.5781044017 0.7990105071 -0.1322254512 0.0994682884801 +1403636949201666560.0000000000 1.9992420607 3.9230645547 -0.2959124587 0.5779743346 0.7992531262 -0.1309899735 0.0999086367951 +1403636949251666432.0000000000 1.9829119951 3.9488061117 -0.3038781617 0.5769826488 0.8000707605 -0.1290539642 0.101601552523 +1403636949301666560.0000000000 1.9658269196 3.9734596697 -0.3124812491 0.5770056574 0.8001570518 -0.1290610151 0.100779056187 +1403636949351666432.0000000000 1.9484525507 3.9976119042 -0.3219005889 0.5780595424 0.7995574268 -0.1300749586 0.0981610504538 +1403636949401666560.0000000000 1.9311250160 4.0207802058 -0.3326903456 0.5784173529 0.7993934355 -0.1310403155 0.096082969087 +1403636949451666432.0000000000 1.9140460848 4.0430871378 -0.3447883383 0.5790635343 0.7990113761 -0.1315784217 0.094622212801 +1403636949501666560.0000000000 1.8969581572 4.0643264751 -0.3571585520 0.5799890522 0.7983809250 -0.1332004894 0.0919686221983 +1403636949551666432.0000000000 1.8799828573 4.0845514430 -0.3692398909 0.5800503909 0.7983989805 -0.1346854146 0.089221359338 +1403636949601666560.0000000000 1.8636886048 4.1040802157 -0.3795362128 0.5806804393 0.7979921520 -0.1356927443 0.0872137136082 +1403636949651666432.0000000000 1.8481944870 4.1226326302 -0.3886778979 0.5784316799 0.7996164275 -0.1365884754 0.085871700852 +1403636949701666560.0000000000 1.8333181442 4.1396861354 -0.3965303703 0.5753276183 0.8018624603 -0.1361316144 0.0865038150435 +1403636949751666432.0000000000 1.8193632084 4.1563179099 -0.4022235798 0.5713121082 0.8047527804 -0.1352087099 0.0877156891498 +1403636949801666560.0000000000 1.8058039420 4.1721414788 -0.4058854146 0.5677394001 0.8073492308 -0.1339505150 0.0889744491211 +1403636949851666432.0000000000 1.7924213736 4.1867597237 -0.4085650105 0.5629617663 0.8106858587 -0.1351004074 0.087237423959 +1403636949901666560.0000000000 1.7799526647 4.2010336052 -0.4103601231 0.5593108937 0.8132038034 -0.1345633055 0.0881113788652 +1403636949951666432.0000000000 1.7680264098 4.2153721916 -0.4108408425 0.5559231132 0.8155237383 -0.1350845651 0.0873079885353 +1403636950001666560.0000000000 1.7572115063 4.2308960415 -0.4098763982 0.5537165759 0.8169748867 -0.1358834903 0.0865197383602 +1403636950051666432.0000000000 1.7473771427 4.2473681854 -0.4076459268 0.5510317540 0.8187041252 -0.1366430563 0.0861175744405 +1403636950101666560.0000000000 1.7382815321 4.2646615832 -0.4050017429 0.5488571360 0.8201193814 -0.1375825026 0.0850358719851 +1403636950151666432.0000000000 1.7304192284 4.2826591226 -0.4031824841 0.5477479901 0.8208098827 -0.1370534051 0.0863692071337 +1403636950201666560.0000000000 1.7235848065 4.3013630715 -0.4029776833 0.5466298201 0.8214893205 -0.1357345350 0.0890352294784 +1403636950251666432.0000000000 1.7174372903 4.3208413604 -0.4040476265 0.5469625046 0.8212552086 -0.1343835028 0.0911755178881 +1403636950301666560.0000000000 1.7121135333 4.3411205517 -0.4063343562 0.5477303829 0.8206560182 -0.1330630093 0.0938582072655 +1403636950351666432.0000000000 1.7071275070 4.3624177377 -0.4092851681 0.5498852371 0.8191356391 -0.1317449676 0.0963654208049 +1403636950401666560.0000000000 1.7023823394 4.3845800328 -0.4132525729 0.5521521511 0.8175663982 -0.1299999392 0.0990616092637 +1403636950451666432.0000000000 1.6979123745 4.4075583269 -0.4180600318 0.5556708504 0.8151133085 -0.1287040981 0.101269222503 +1403636950501666560.0000000000 1.6937476757 4.4310162291 -0.4245522133 0.5579148056 0.8134592951 -0.1252125480 0.10647470457 +1403636950551666432.0000000000 1.6892124562 4.4548582640 -0.4318513557 0.5604485637 0.8115942611 -0.1218295420 0.111219267707 +1403636950601666560.0000000000 1.6840613750 4.4790694751 -0.4390885457 0.5622865830 0.8102075710 -0.1190056157 0.115044139044 +1403636950651666432.0000000000 1.6776061409 4.5033078748 -0.4450109153 0.5631567115 0.8095485413 -0.1177788333 0.116678292367 +1403636950701666560.0000000000 1.6698410091 4.5276023204 -0.4496281327 0.5650377810 0.8083699339 -0.1185003668 0.115013125266 +1403636950751666432.0000000000 1.6612765367 4.5522119963 -0.4523521257 0.5669273017 0.8071744759 -0.1196608104 0.112889727093 +1403636950801666560.0000000000 1.6516499906 4.5770716587 -0.4532174385 0.5693686004 0.8056590810 -0.1217108798 0.109175564471 +1403636950851666432.0000000000 1.6411016953 4.6010978087 -0.4529734434 0.5703115574 0.8051982339 -0.1233802600 0.105725318706 +1403636950901666560.0000000000 1.6303163212 4.6251396885 -0.4511110611 0.5713597856 0.8045573796 -0.1239282063 0.10429390239 +1403636950951666432.0000000000 1.6191924724 4.6486924780 -0.4480075081 0.5715972260 0.8044827483 -0.1241240139 0.103331253817 +1403636951001666560.0000000000 1.6078621437 4.6724951369 -0.4426859389 0.5725967363 0.8038830080 -0.1246534714 0.101816497076 +1403636951051666432.0000000000 1.5961105855 4.6956494221 -0.4347058096 0.5737468508 0.8031432142 -0.1264516604 0.0989217179471 +1403636951101666560.0000000000 1.5839086156 4.7172949910 -0.4263040277 0.5733651903 0.8035040282 -0.1293292719 0.0943799482073 +1403636951151666432.0000000000 1.5717890788 4.7383653753 -0.4187770949 0.5710803637 0.8051683726 -0.1325891135 0.089393718614 +1403636951201666560.0000000000 1.5604334554 4.7589441646 -0.4132783846 0.5673864031 0.8077468614 -0.1335416149 0.0882287631836 +1403636951251666432.0000000000 1.5497763413 4.7792392470 -0.4098204803 0.5636413847 0.8103442563 -0.1334379534 0.0885713743352 +1403636951301666560.0000000000 1.5397326410 4.7997946436 -0.4086408707 0.5584584545 0.8138972422 -0.1329559008 0.0895441919118 +1403636951351666432.0000000000 1.5301924217 4.8205751433 -0.4091743767 0.5538400506 0.8170414004 -0.1326038572 0.0901152899689 +1403636951401666560.0000000000 1.5211860825 4.8420702784 -0.4108430213 0.5495483567 0.8199398637 -0.1317957089 0.0912420664873 +1403636951451666432.0000000000 1.5129374568 4.8643318196 -0.4133836734 0.5471216392 0.8215207509 -0.1307298198 0.0931197188044 +1403636951501666560.0000000000 1.5050387150 4.8871875546 -0.4166854668 0.5456223230 0.8224915033 -0.1305660552 0.0935762413045 +1403636951551666432.0000000000 1.4976053897 4.9109291031 -0.4206867497 0.5452344424 0.8226977804 -0.1300863301 0.0946853297887 +1403636951601666560.0000000000 1.4905076716 4.9354120923 -0.4254791409 0.5447759765 0.8229800939 -0.1287717559 0.0966474795145 +1403636951651666432.0000000000 1.4836623333 4.9610557086 -0.4305976768 0.5458148768 0.8222297366 -0.1278658397 0.098360091629 +1403636951701666560.0000000000 1.4769526867 4.9875607117 -0.4354373384 0.5479100631 0.8207764939 -0.1268244339 0.100180201982 +1403636951751666432.0000000000 1.4704284085 5.0156595343 -0.4387990771 0.5507619101 0.8188449149 -0.1261615378 0.10118097705 +1403636951801666560.0000000000 1.4642501970 5.0454510945 -0.4392860923 0.5537297586 0.8167898276 -0.1256982071 0.102165027001 +1403636951851666432.0000000000 1.4582831971 5.0760048282 -0.4377996481 0.5561706544 0.8150986724 -0.1232445766 0.105352417191 +1403636951901666560.0000000000 1.4518259585 5.1064530699 -0.4352111983 0.5581447543 0.8136770127 -0.1219109267 0.107433133604 +1403636951951666432.0000000000 1.4451517653 5.1371135251 -0.4321627954 0.5591698838 0.8128259362 -0.1194902862 0.111198515971 +1403636952001666560.0000000000 1.4377145127 5.1686642085 -0.4294011203 0.5599090158 0.8122690763 -0.1180391982 0.113082223649 +1403636952051666432.0000000000 1.4292691275 5.2005575766 -0.4274225393 0.5607585561 0.8115764738 -0.1175918008 0.114305018948 +1403636952101666560.0000000000 1.4198920338 5.2327877070 -0.4264383054 0.5626682499 0.8102576265 -0.1179445841 0.113912661183 +1403636952151666432.0000000000 1.4096303060 5.2650914441 -0.4271084474 0.5640371863 0.8093717703 -0.1192871682 0.112026610063 +1403636952201666560.0000000000 1.3987466477 5.2974664243 -0.4291802489 0.5667914187 0.8074959107 -0.1206464592 0.110191985586 +1403636952251666432.0000000000 1.3873073166 5.3297121407 -0.4328532978 0.5693684941 0.8057723890 -0.1226074726 0.10732093274 +1403636952301666560.0000000000 1.3752318859 5.3617429122 -0.4378125100 0.5719230615 0.8040878986 -0.1256406179 0.10276720439 +1403636952351666432.0000000000 1.3630577038 5.3933044556 -0.4441166561 0.5745377618 0.8022877130 -0.1281489460 0.0990890182286 +1403636952401666560.0000000000 1.3511373506 5.4240416290 -0.4522408854 0.5762669204 0.8010578361 -0.1298603319 0.096742306673 +1403636952451666432.0000000000 1.3393994671 5.4540204501 -0.4620931816 0.5778437906 0.8000087714 -0.1290340985 0.0971221949825 +1403636952501666560.0000000000 1.3278266347 5.4833672263 -0.4736509801 0.5782326793 0.7997266244 -0.1279642154 0.0985365639956 +1403636952551666432.0000000000 1.3161540854 5.5119215843 -0.4863790962 0.5777982652 0.8000608771 -0.1263613113 0.100421992612 +1403636952601666560.0000000000 1.3043300054 5.5395910943 -0.4986533447 0.5782190340 0.7997847466 -0.1245118627 0.102488554617 +1403636952651666432.0000000000 1.2921241588 5.5657769017 -0.5093083395 0.5787962022 0.7993579430 -0.1237567701 0.103470271796 +1403636952701666560.0000000000 1.2794964220 5.5910044908 -0.5183245048 0.5783877687 0.7997107762 -0.1229097484 0.104035845771 +1403636952751666432.0000000000 1.2663730967 5.6154581469 -0.5264539777 0.5766501317 0.8009769919 -0.1228206032 0.104046064206 +1403636952801666560.0000000000 1.2527617695 5.6382985276 -0.5341987606 0.5726270119 0.8038763240 -0.1227634625 0.103972559884 +1403636952851666432.0000000000 1.2386932217 5.6609580382 -0.5405495245 0.5694679754 0.8061354519 -0.1233398543 0.10314619998 +1403636952901666560.0000000000 1.2243384185 5.6834620589 -0.5466968054 0.5663593305 0.8083345632 -0.1247055813 0.10139457862 +1403636952951666432.0000000000 1.2097961679 5.7061286747 -0.5539818676 0.5625604760 0.8109929530 -0.1270840301 0.0983147509833 +1403636953001666560.0000000000 1.1952992930 5.7290437442 -0.5621465709 0.5601758518 0.8125775393 -0.1307111669 0.0939965350427 +1403636953051666432.0000000000 1.1810726184 5.7521294288 -0.5716636770 0.5584881630 0.8136751652 -0.1338237369 0.0900827660722 +1403636953101666560.0000000000 1.1674139480 5.7755273689 -0.5822433183 0.5580209954 0.8139203865 -0.1368243887 0.0861699477927 +1403636953151666432.0000000000 1.1547399678 5.7990596161 -0.5945800253 0.5570756052 0.8145276731 -0.1382705013 0.0842182191727 +1403636953201666560.0000000000 1.1431284320 5.8229636610 -0.6084088777 0.5567126358 0.8147213620 -0.1389366839 0.0836465259961 +1403636953251666432.0000000000 1.1326443798 5.8467963922 -0.6232828943 0.5561493900 0.8151290094 -0.1385471714 0.0840668499884 +1403636953301666560.0000000000 1.1232454069 5.8713467456 -0.6370811886 0.5562443824 0.8151101800 -0.1380329545 0.0844658808166 +1403636953351666432.0000000000 1.1149389342 5.8964303390 -0.6496284765 0.5559943004 0.8153743188 -0.1369234711 0.0853640510048 +1403636953401666560.0000000000 1.1076620008 5.9222214562 -0.6599690976 0.5575560396 0.8143882406 -0.1345427688 0.0883249669142 +1403636953451666432.0000000000 1.1010693478 5.9476656259 -0.6690241424 0.5589787686 0.8134747440 -0.1320972006 0.0913887670488 +1403636953501666560.0000000000 1.0949493649 5.9728833275 -0.6762559158 0.5602346531 0.8127142682 -0.1287476247 0.0951667007729 +1403636953551666432.0000000000 1.0888482141 5.9981348335 -0.6818943013 0.5618074717 0.8117072920 -0.1268714087 0.0969911465031 +1403636953601666560.0000000000 1.0829894915 6.0239651222 -0.6871978676 0.5609782270 0.8123198962 -0.1244676636 0.0997377346677 +1403636953651666432.0000000000 1.0771299403 6.0502849638 -0.6908690138 0.5591768269 0.8136611995 -0.1218003489 0.102183187005 +1403636953701666560.0000000000 1.0707776943 6.0764884198 -0.6927070985 0.5563733772 0.8156680432 -0.1193780501 0.104322526678 +1403636953751666432.0000000000 1.0640757968 6.1038328411 -0.6923782185 0.5545016054 0.8170080874 -0.1169167524 0.106565603104 +1403636953801666560.0000000000 1.0568616501 6.1319781980 -0.6895575613 0.5532658796 0.8178327630 -0.1133744094 0.11042047565 +1403636953851666432.0000000000 1.0489050636 6.1611680339 -0.6847374170 0.5536205893 0.8176718740 -0.1111160672 0.112116765813 +1403636953901666560.0000000000 1.0395775977 6.1912082421 -0.6778307666 0.5542131522 0.8174691982 -0.1115348893 0.110235477516 +1403636953951666432.0000000000 1.0293868817 6.2224263144 -0.6694453295 0.5547804739 0.8172284154 -0.1123333248 0.10834005266 +1403636954001666560.0000000000 1.0183092929 6.2540574927 -0.6612538167 0.5552751771 0.8170479650 -0.1136664815 0.105745125144 +1403636954051666432.0000000000 1.0067794768 6.2860716934 -0.6540069912 0.5560702563 0.8166024034 -0.1145837082 0.10400460876 +1403636954101666560.0000000000 0.9949032968 6.3182871447 -0.6484236142 0.5565112075 0.8163092734 -0.1149560182 0.10353530731 +1403636954151666432.0000000000 0.9824101337 6.3505272728 -0.6438121300 0.5573617066 0.8157781862 -0.1156039678 0.102418755991 +1403636954201666560.0000000000 0.9696031318 6.3833241425 -0.6403713801 0.5574816495 0.8157091261 -0.1159301084 0.101946270491 +1403636954251666432.0000000000 0.9565315053 6.4170335383 -0.6377167637 0.5559182103 0.8167640939 -0.1161945716 0.101735834362 +1403636954301666560.0000000000 0.9430547157 6.4513863454 -0.6342573302 0.5553928514 0.8170864300 -0.1164088753 0.101771902725 +1403636954351666432.0000000000 0.9289758087 6.4861560662 -0.6294225842 0.5546993891 0.8174809246 -0.1176991829 0.100898106482 +1403636954401666560.0000000000 0.9146131837 6.5212479427 -0.6235461154 0.5522677106 0.8190264131 -0.1181608157 0.101163887503 +1403636954451666432.0000000000 0.8996754728 6.5567826344 -0.6156221237 0.5517367397 0.8192737812 -0.1193723466 0.1006344093 +1403636954501666560.0000000000 0.8845172572 6.5926886574 -0.6067862097 0.5504616337 0.8199480408 -0.1206216879 0.100636020677 +1403636954551666432.0000000000 0.8695593179 6.6297640602 -0.5972149117 0.5502811791 0.8198389399 -0.1210262153 0.102016624614 +1403636954601666560.0000000000 0.8546071038 6.6678023936 -0.5889629222 0.5498211131 0.8198602033 -0.1211898814 0.104110534127 +1403636954651666432.0000000000 0.8394987787 6.7067694525 -0.5836532153 0.5509676266 0.8187853391 -0.1216971398 0.105901128907 +1403636954701666560.0000000000 0.8242382232 6.7465525904 -0.5825632202 0.5528195283 0.8171822757 -0.1230538143 0.107058190861 +1403636954751666432.0000000000 0.8087568032 6.7868120821 -0.5853956804 0.5560320446 0.8146503582 -0.1245534539 0.107979611052 +1403636954801666560.0000000000 0.7928198704 6.8274682718 -0.5907839354 0.5590156602 0.8122342107 -0.1264198125 0.10860529302 +1403636954851666432.0000000000 0.7767425030 6.8685172572 -0.5980007701 0.5618439626 0.8098523099 -0.1277052926 0.11028125866 +1403636954901666560.0000000000 0.7600081065 6.9095587479 -0.6069082961 0.5643721641 0.8077364946 -0.1301182770 0.110068386502 +1403636954951666432.0000000000 0.7429265586 6.9501827682 -0.6175118646 0.5665573038 0.8057876484 -0.1323425320 0.110474166265 +1403636955001666560.0000000000 0.7255045185 6.9901708610 -0.6296083779 0.5676472445 0.8045587372 -0.1333204583 0.11263880168 +1403636955051666432.0000000000 0.7077383225 7.0295567679 -0.6422117670 0.5672217758 0.8044029444 -0.1346351737 0.114318546967 +1403636955101666560.0000000000 0.6896007857 7.0681506788 -0.6539722999 0.5660515331 0.8047182100 -0.1354599639 0.116896803252 +1403636955151666432.0000000000 0.6711174399 7.1068284736 -0.6639930540 0.5654538188 0.8046520224 -0.1359437424 0.119651161916 +1403636955201666560.0000000000 0.6521679298 7.1456973090 -0.6722362711 0.5646679717 0.8046858423 -0.1375056362 0.121338275104 +1403636955251666432.0000000000 0.6326487279 7.1849075636 -0.6775710029 0.5649707079 0.8039677865 -0.1400890266 0.121733159584 +1403636955301666560.0000000000 0.6126814086 7.2239834314 -0.6818027130 0.5651361014 0.8033055423 -0.1418121030 0.123331748135 +1403636955351666432.0000000000 0.5922234883 7.2627559501 -0.6840553931 0.5650463475 0.8027975580 -0.1428578367 0.1258186969 +1403636955401666560.0000000000 0.5709728095 7.3013047171 -0.6851041835 0.5652013461 0.8022196536 -0.1449697760 0.126391573195 +1403636955451666432.0000000000 0.5492907650 7.3396453642 -0.6865569161 0.5647482989 0.8020675510 -0.1457593984 0.128456997821 +1403636955501666560.0000000000 0.5270520036 7.3780610392 -0.6892962930 0.5642557990 0.8020546224 -0.1470351710 0.129245636201 +1403636955551666432.0000000000 0.5045662263 7.4168521083 -0.6937777176 0.5638568826 0.8019848717 -0.1479653397 0.130353134791 +1403636955601666560.0000000000 0.4812853133 7.4552847071 -0.6994893177 0.5639020414 0.8016396041 -0.1492660488 0.130797857258 +1403636955651666432.0000000000 0.4574954965 7.4931826446 -0.7064709517 0.5633640784 0.8016971941 -0.1499288308 0.131999507257 +1403636955701666560.0000000000 0.4331442200 7.5307671885 -0.7134237132 0.5633791374 0.8014662187 -0.1507226411 0.132433127765 +1403636955751666432.0000000000 0.4081765061 7.5680232199 -0.7195584587 0.5629607290 0.8015931964 -0.1516300883 0.132408011285 +1403636955801666560.0000000000 0.3829214403 7.6054920221 -0.7240239143 0.5629404646 0.8014158828 -0.1514999098 0.133710110055 +1403636955851666432.0000000000 0.3570068854 7.6428698346 -0.7265406782 0.5624783560 0.8016077094 -0.1532187642 0.132541275041 +1403636955901666560.0000000000 0.3305272208 7.6800898140 -0.7266251200 0.5630577554 0.8011648333 -0.1556682374 0.129877918727 +1403636955951666432.0000000000 0.3035472720 7.7167738835 -0.7247881159 0.5630728057 0.8010463419 -0.1596637820 0.125623446559 +1403636956001666560.0000000000 0.2765628168 7.7522738013 -0.7202000458 0.5645249424 0.7999009208 -0.1644566821 0.120100399667 +1403636956051666432.0000000000 0.2500781779 7.7875376780 -0.7136021502 0.5659432783 0.7986474941 -0.1695692321 0.114527993978 +1403636956101666560.0000000000 0.2242113422 7.8217886598 -0.7053093810 0.5672791071 0.7974607338 -0.1741403385 0.10920593011 +1403636956151666432.0000000000 0.1995839087 7.8547700813 -0.6970812252 0.5669420628 0.7974500856 -0.1768441445 0.106659303374 +1403636956201666560.0000000000 0.1759804632 7.8869711390 -0.6897089442 0.5676206065 0.7966678625 -0.1795448180 0.104359102866 +1403636956251666432.0000000000 0.1537197283 7.9185809084 -0.6845454281 0.5674969643 0.7964833140 -0.1809669243 0.103983163541 +1403636956301666560.0000000000 0.1328326875 7.9493520264 -0.6818730988 0.5663406191 0.7971817122 -0.1795036370 0.107415385826 +1403636956351666432.0000000000 0.1133669406 7.9793165932 -0.6814246196 0.5654650672 0.7976551173 -0.1755449999 0.114802110297 +1403636956401666560.0000000000 0.0944542256 8.0086216009 -0.6827326158 0.5636134528 0.7989028395 -0.1717960011 0.120748759009 +1403636956451666432.0000000000 0.0758853502 8.0378163463 -0.6849249091 0.5634591234 0.7989297180 -0.1678475181 0.126697800386 +1403636956501666560.0000000000 0.0571008550 8.0669846587 -0.6885753916 0.5637021024 0.7989357232 -0.1641799216 0.13033266386 +1403636956551666432.0000000000 0.0373765565 8.0963504583 -0.6923950132 0.5674728275 0.7970626146 -0.1605510093 0.129958269724 +1403636956601666560.0000000000 0.0166903759 8.1250614219 -0.6974174943 0.5714229208 0.7955213925 -0.1575900868 0.125646027703 +1403636956651666432.0000000000 -0.0048540902 8.1529149963 -0.7035161461 0.5756092361 0.7941818180 -0.1548945427 0.118139442935 +1403636956701666560.0000000000 -0.0271784477 8.1797310503 -0.7108520029 0.5789885065 0.7937774135 -0.1523304365 0.107168863657 +1403636956751666432.0000000000 -0.0494325723 8.2048719328 -0.7185728703 0.5801604325 0.7951915806 -0.1478662453 0.0960197699418 +1403636956801666560.0000000000 -0.0711240677 8.2286684633 -0.7249666104 0.5810279493 0.7969722085 -0.1417853778 0.0844909907855 +1403636956851666432.0000000000 -0.0921100476 8.2507751419 -0.7296874271 0.5807781431 0.7997044366 -0.1333142367 0.0734634385454 +1403636956901666560.0000000000 -0.1117934195 8.2712985622 -0.7329409112 0.5798296956 0.8029545221 -0.1217934366 0.0650224451952 +1403636956951666432.0000000000 -0.1300761118 8.2911280853 -0.7340019089 0.5804399410 0.8049393539 -0.1082117280 0.0587565601779 +1403636957001666560.0000000000 -0.1473978894 8.3096283897 -0.7335954934 0.5805888013 0.8071036610 -0.0931761074 0.0530898977649 +1403636957051666432.0000000000 -0.1637500676 8.3268353065 -0.7312730630 0.5813050642 0.8085846236 -0.0769196924 0.0485663441733 +1403636957101666560.0000000000 -0.1796564231 8.3435576380 -0.7265997851 0.5816863476 0.8099704093 -0.0609227396 0.0433283843967 +1403636957151666432.0000000000 -0.1952314863 8.3592640750 -0.7208650234 0.5810488099 0.8117109705 -0.0452305266 0.0382332368465 +1403636957201666560.0000000000 -0.2104987928 8.3742613230 -0.7135538645 0.5808085401 0.8127722924 -0.0313616008 0.0328495136827 +1403636957251666432.0000000000 -0.2255692253 8.3889157125 -0.7047973539 0.5809826363 0.8132304450 -0.0202934659 0.0265253648202 +1403636957301666560.0000000000 -0.2402942432 8.4031808400 -0.6968443670 0.5800549565 0.8142278471 -0.0111995931 0.021067260524 +1403636957351666432.0000000000 -0.2547686072 8.4172180886 -0.6900030147 0.5798802542 0.8145322787 -0.0032352809 0.0162969537273 +1403636957401666560.0000000000 -0.2692854435 8.4309078645 -0.6849906506 0.5796379452 0.8147962063 0.0024974637 0.0109889630233 +1403636957451666432.0000000000 -0.2836123491 8.4444058919 -0.6820012316 0.5794540915 0.8149406471 0.0073424100 0.00712646973656 +1403636957501666560.0000000000 -0.2981133407 8.4579840288 -0.6809361544 0.5795723269 0.8148489596 0.0103028668 0.00330786282423 +1403636957551666432.0000000000 -0.3126737575 8.4711922279 -0.6817727259 0.5792738487 0.8150284027 0.0130471793 -0.000531128747991 +1403636957601666560.0000000000 -0.3272221370 8.4841214759 -0.6843297647 0.5797056091 0.8146481550 0.0163699310 -0.00467073350419 +1403636957651666432.0000000000 -0.3418195687 8.4965913614 -0.6889535296 0.5796094890 0.8145844440 0.0205385567 -0.00912093398717 +1403636957701666560.0000000000 -0.3563928616 8.5084656440 -0.6953059587 0.5797068451 0.8142989691 0.0254607897 -0.0144537495722 +1403636957751666432.0000000000 -0.3711242525 8.5197129989 -0.7031783285 0.5789202513 0.8145035452 0.0314938037 -0.0210584372392 +1403636957801666560.0000000000 -0.3859645609 8.5303131210 -0.7122232161 0.5776831580 0.8147678988 0.0396412980 -0.0293940049756 +1403636957851666432.0000000000 -0.4006011630 8.5400939034 -0.7221304343 0.5765514515 0.8146300856 0.0494830113 -0.0389573986409 +1403636957901666560.0000000000 -0.4150287540 8.5491977278 -0.7329240907 0.5753859021 0.8141193347 0.0612873278 -0.0488327353202 +1403636957951666432.0000000000 -0.4287815700 8.5572736471 -0.7431877598 0.5742092307 0.8131945115 0.0746582816 -0.0585199698338 +1403636958001666560.0000000000 -0.4419593706 8.5646841733 -0.7519526592 0.5730249452 0.8117981157 0.0883837988 -0.069386854823 +1403636958051666432.0000000000 -0.4544137836 8.5724860109 -0.7587121790 0.5710077109 0.8106589758 0.1018648261 -0.0800360934329 +1403636958101666560.0000000000 -0.4659612898 8.5807058237 -0.7637787867 0.5695827475 0.8088506582 0.1163003224 -0.0883761366657 +1403636958151666432.0000000000 -0.4765706330 8.5895045871 -0.7669398010 0.5677510875 0.8073711279 0.1289178316 -0.0958684367491 +1403636958201666560.0000000000 -0.4867341681 8.5991648001 -0.7677163607 0.5656285776 0.8061141401 0.1395364183 -0.10379736693 +1403636958251666432.0000000000 -0.4959135170 8.6085928955 -0.7649300246 0.5644953617 0.8041473467 0.1498549028 -0.110614372923 +1403636958301666560.0000000000 -0.5042344733 8.6176425183 -0.7605420533 0.5640132759 0.8016440767 0.1600442164 -0.116797464125 +1403636958351666432.0000000000 -0.5118695650 8.6268113458 -0.7546836647 0.5620246893 0.8002203206 0.1702205530 -0.121657924117 +1403636958401666560.0000000000 -0.5185035327 8.6364794784 -0.7471000708 0.5609767733 0.7985017148 0.1794653839 -0.124467856122 +1403636958451666432.0000000000 -0.5247034015 8.6462168906 -0.7375512049 0.5599665589 0.7971668156 0.1862436616 -0.127576719972 +1403636958501666560.0000000000 -0.5303284652 8.6559572913 -0.7290439648 0.5584148784 0.7965418993 0.1922674278 -0.129333145094 +1403636958551666432.0000000000 -0.5358593634 8.6662800155 -0.7216796877 0.5577806127 0.7957028623 0.1967129610 -0.130544069417 +1403636958601666560.0000000000 -0.5414933855 8.6769693375 -0.7154176898 0.5576659663 0.7948445053 0.1993191229 -0.132298033535 +1403636958651666432.0000000000 -0.5470406964 8.6881970796 -0.7100422829 0.5574412506 0.7943172134 0.2016124126 -0.132935517145 +1403636958701666560.0000000000 -0.5526245918 8.6999441474 -0.7053368059 0.5580511123 0.7935277146 0.2030639917 -0.132882419912 +1403636958751666432.0000000000 -0.5578627034 8.7114785422 -0.7017531696 0.5582293513 0.7932504709 0.2039301614 -0.132461960756 +1403636958801666560.0000000000 -0.5633867736 8.7232938654 -0.6989356662 0.5582124194 0.7932209176 0.2039085365 -0.132743283927 +1403636958851666432.0000000000 -0.5692647786 8.7353927324 -0.6971275672 0.5580108777 0.7934742729 0.2035511908 -0.132624851861 +1403636958901666560.0000000000 -0.5749484503 8.7477258149 -0.6969993594 0.5576033989 0.7940581680 0.2037189642 -0.130570513386 +1403636958951666432.0000000000 -0.5808351509 8.7605466828 -0.6978629846 0.5582478686 0.7939924571 0.2034360560 -0.12864317476 +1403636959001666560.0000000000 -0.5869687339 8.7732102465 -0.7001925555 0.5582722946 0.7943749766 0.2024468097 -0.127733045501 +1403636959051666432.0000000000 -0.5933122072 8.7859599904 -0.7041054259 0.5581996945 0.7948405181 0.2014695130 -0.126695253062 +1403636959101666560.0000000000 -0.5997534686 8.7984093628 -0.7095629220 0.5572074702 0.7959531978 0.2001814094 -0.126117982062 +1403636959151666432.0000000000 -0.6066539598 8.8111353703 -0.7162752480 0.5569476704 0.7965289319 0.1986495298 -0.12605283562 +1403636959201666560.0000000000 -0.6138151643 8.8240767180 -0.7244255842 0.5572816418 0.7966605311 0.1978748454 -0.124958854987 +1403636959251666432.0000000000 -0.6211064225 8.8369872960 -0.7338955841 0.5580919810 0.7964162547 0.1975998644 -0.123323896878 +1403636959301666560.0000000000 -0.6286047721 8.8501020981 -0.7448686714 0.5593000865 0.7959059972 0.1984877686 -0.119664792349 +1403636959351666432.0000000000 -0.6364145723 8.8628995092 -0.7572719032 0.5603377586 0.7953498424 0.2001586311 -0.115657887608 +1403636959401666560.0000000000 -0.6450234920 8.8754695037 -0.7708690819 0.5612073162 0.7950158327 0.2002431084 -0.113573198607 +1403636959451666432.0000000000 -0.6544678860 8.8877643491 -0.7858112931 0.5628194749 0.7940276206 0.2006236422 -0.111823658152 +1403636959501666560.0000000000 -0.6646595032 8.8995689139 -0.8017148742 0.5648574583 0.7927935644 0.2002930494 -0.110892336834 +1403636959551666432.0000000000 -0.6759958831 8.9105713367 -0.8167305041 0.5670979441 0.7914846415 0.1972177368 -0.114267880035 +1403636959601666560.0000000000 -0.6877594009 8.9210697252 -0.8307791658 0.5693301130 0.7901643969 0.1938988377 -0.11792662537 +1403636959651666432.0000000000 -0.6993998368 8.9309730065 -0.8438745486 0.5695549830 0.7901715414 0.1924755626 -0.119118488368 +1403636959701666560.0000000000 -0.7108404445 8.9402415006 -0.8552379614 0.5680256574 0.7915804406 0.1909378192 -0.119540820709 +1403636959751666432.0000000000 -0.7232860448 8.9506007019 -0.8638385468 0.5667363140 0.7927854782 0.1894923571 -0.119974091101 +1403636959801666560.0000000000 -0.7357453147 8.9606707462 -0.8700815022 0.5652359170 0.7940123100 0.1891626852 -0.119458311554 +1403636959851666432.0000000000 -0.7479225160 8.9694635189 -0.8742559467 0.5644035955 0.7947924363 0.1882147360 -0.119702872847 +1403636959901666560.0000000000 -0.7597940029 8.9778219131 -0.8772153975 0.5631800770 0.7959092363 0.1877555581 -0.118762531261 +1403636959951666432.0000000000 -0.7715228556 8.9854199089 -0.8780930683 0.5624855202 0.7964937422 0.1875807624 -0.118411214629 +1403636960001666560.0000000000 -0.7833899862 8.9929871178 -0.8768191020 0.5622891678 0.7967505097 0.1868242327 -0.118811713301 +1403636960051666432.0000000000 -0.7952004607 9.0007206071 -0.8745664205 0.5623495369 0.7967599544 0.1869000995 -0.118342411088 +1403636960101666560.0000000000 -0.8074463651 9.0087918077 -0.8708016691 0.5626466305 0.7965790859 0.1865846175 -0.118645310527 +1403636960151666432.0000000000 -0.8195455713 9.0170326506 -0.8665276728 0.5629969650 0.7963947509 0.1874493378 -0.116844186425 +1403636960201666560.0000000000 -0.8318998419 9.0251088252 -0.8630625852 0.5631398406 0.7962414564 0.1884309570 -0.115615040404 +1403636960251666432.0000000000 -0.8439941429 9.0329872529 -0.8610123222 0.5644942895 0.7951537982 0.1922351474 -0.110101237633 +1403636960301666560.0000000000 -0.8568443187 9.0407783455 -0.8604741945 0.5648714502 0.7947986629 0.1945534146 -0.106603466237 +1403636960351666432.0000000000 -0.8704452710 9.0483519783 -0.8608641956 0.5659575294 0.7938954022 0.1966230981 -0.1037377591 +1403636960401666560.0000000000 -0.8849683529 9.0558832710 -0.8618664956 0.5682476894 0.7921725997 0.1973806742 -0.10294661344 +1403636960451666432.0000000000 -0.9006323142 9.0626419299 -0.8638543679 0.5706917129 0.7899788215 0.1988998744 -0.103359906822 +1403636960501666560.0000000000 -0.9171575328 9.0684890057 -0.8667515302 0.5729422520 0.7875602508 0.2015532522 -0.104222424018 +1403636960551666432.0000000000 -0.9346397777 9.0732216799 -0.8708511103 0.5747092519 0.7853183127 0.2047921756 -0.105093236242 +1403636960601666560.0000000000 -0.9530310651 9.0768027033 -0.8759692067 0.5762546801 0.7831795029 0.2081866131 -0.105918572808 +1403636960651666432.0000000000 -0.9724074338 9.0792808975 -0.8819408547 0.5771107671 0.7816937328 0.2099971929 -0.108624351067 +1403636960701666560.0000000000 -0.9927718321 9.0804591509 -0.8886565289 0.5758715300 0.7819446843 0.2093887644 -0.114415195783 +1403636960751666432.0000000000 -1.0136680843 9.0802055616 -0.8964792353 0.5729344050 0.7834697106 0.2081028873 -0.120890729674 +1403636960801666560.0000000000 -1.0348144728 9.0787836456 -0.9054501147 0.5694995096 0.7848494612 0.2087004636 -0.126987197026 +1403636960851666432.0000000000 -1.0563087637 9.0764814846 -0.9152436475 0.5664520342 0.7852156217 0.2114752584 -0.133591674148 +1403636960901666560.0000000000 -1.0779176856 9.0734300015 -0.9256039300 0.5633707502 0.7848105789 0.2170118446 -0.139970040817 +1403636960951666432.0000000000 -1.0995170364 9.0695438914 -0.9354152484 0.5606313961 0.7834604030 0.2245804849 -0.146443984093 +1403636961001666560.0000000000 -1.1213006336 9.0652539055 -0.9437962437 0.5591990951 0.7803060615 0.2344257146 -0.153177696717 +1403636961051666432.0000000000 -1.1430710410 9.0605699934 -0.9506762054 0.5573745215 0.7769437682 0.2446741502 -0.160706515141 +1403636961101666560.0000000000 -1.1646948628 9.0551428977 -0.9560409201 0.5549124934 0.7736679577 0.2547442872 -0.169160763743 +1403636961151666432.0000000000 -1.1859248216 9.0491451363 -0.9596144141 0.5526355786 0.7697871669 0.2652017707 -0.178015886106 +1403636961201666560.0000000000 -1.2064211258 9.0427181855 -0.9622890080 0.5493791568 0.7662269177 0.2765900346 -0.185948394747 +1403636961251666432.0000000000 -1.2267981449 9.0362223782 -0.9631243394 0.5461589684 0.7625290190 0.2869494850 -0.194730248178 +1403636961301666560.0000000000 -1.2470734133 9.0304570492 -0.9621690575 0.5438380117 0.7583521095 0.2980982174 -0.200698150969 +1403636961351666432.0000000000 -1.2671109849 9.0249388355 -0.9591564650 0.5424548162 0.7540569898 0.3074539768 -0.206428875637 +1403636961401666560.0000000000 -1.2867542698 9.0192745345 -0.9536621982 0.5404860286 0.7506451688 0.3154758686 -0.211852920239 +1403636961451666432.0000000000 -1.3050841851 9.0128399385 -0.9463801380 0.5388356523 0.7477136176 0.3220160190 -0.216532143774 +1403636961501666560.0000000000 -1.3232420751 9.0064747963 -0.9373913910 0.5365517010 0.7456894735 0.3274200716 -0.221032979273 +1403636961551666432.0000000000 -1.3415762529 9.0002371830 -0.9264778142 0.5348526491 0.7429952746 0.3331907940 -0.225553896813 +1403636961601666560.0000000000 -1.3594398161 8.9935163132 -0.9137429118 0.5326522389 0.7402828185 0.3392060737 -0.230655978789 +1403636961651666432.0000000000 -1.3768772386 8.9864174463 -0.8995685712 0.5303377923 0.7373297065 0.3452495184 -0.236409602134 +1403636961701666560.0000000000 -1.3945178935 8.9796174420 -0.8832608655 0.5287998666 0.7336606808 0.3518848798 -0.241432677636 +1403636961751666432.0000000000 -1.4114532108 8.9723868921 -0.8659281889 0.5267999890 0.7300077198 0.3589009574 -0.246496660112 +1403636961801666560.0000000000 -1.4280194934 8.9650501540 -0.8491366300 0.5249330260 0.7260878804 0.3661417828 -0.25136010625 +1403636961851666432.0000000000 -1.4441414369 8.9573103364 -0.8341077013 0.5216977209 0.7228267623 0.3745084561 -0.255139914657 +1403636961901666560.0000000000 -1.4600710596 8.9493243193 -0.8202507889 0.5199859922 0.7181780911 0.3824317637 -0.259962965587 +1403636961951666432.0000000000 -1.4760703778 8.9408315510 -0.8077574678 0.5174050633 0.7135815021 0.3898772337 -0.266625547976 +1403636962001666560.0000000000 -1.4917305544 8.9321043200 -0.7972503403 0.5138999771 0.7094860814 0.3982500842 -0.271906572802 +1403636962051666432.0000000000 -1.5070641572 8.9229519316 -0.7880021880 0.5098943669 0.7054572043 0.4066526964 -0.277437293887 +1403636962101666560.0000000000 -1.5220215009 8.9134549188 -0.7795489735 0.5063100779 0.7008173974 0.4153119732 -0.282879913449 +1403636962151666432.0000000000 -1.5367199297 8.9035693093 -0.7705967459 0.5027703076 0.6958189485 0.4238644415 -0.288785290245 +1403636962201666560.0000000000 -1.5511141752 8.8935329337 -0.7602642397 0.4993271824 0.6905984417 0.4320870990 -0.295037109763 +1403636962251666432.0000000000 -1.5654017531 8.8832863413 -0.7484534554 0.4972294412 0.6839555446 0.4406261172 -0.301357463218 +1403636962301666560.0000000000 -1.5791831123 8.8725004430 -0.7352817274 0.4938270972 0.6779513806 0.4499010279 -0.306766668178 +1403636962351666432.0000000000 -1.5924478096 8.8609380457 -0.7208314719 0.4896298643 0.6723152456 0.4582098246 -0.313526016701 +1403636962401666560.0000000000 -1.6057682247 8.8492072181 -0.7045380943 0.4862991762 0.6656280897 0.4672686985 -0.3195501852 +1403636962451666432.0000000000 -1.6188443996 8.8371450796 -0.6866924753 0.4824397005 0.6592759312 0.4762886095 -0.325202002431 +1403636962501666560.0000000000 -1.6316304099 8.8249475237 -0.6673946387 0.4798067188 0.6518045352 0.4862908329 -0.329328994037 +1403636962551666432.0000000000 -1.6440533192 8.8121919408 -0.6474939997 0.4769973359 0.6439742492 0.4968007502 -0.33310617308 +1403636962601666560.0000000000 -1.6562005812 8.7988355554 -0.6273977428 0.4741007125 0.6360483959 0.5073028238 -0.336622633544 +1403636962651666432.0000000000 -1.6680899557 8.7850888386 -0.6084956658 0.4720055682 0.6281285451 0.5171264397 -0.339478305289 +1403636962701666560.0000000000 -1.6797553841 8.7706704950 -0.5909303783 0.4707153896 0.6204044185 0.5262978897 -0.341373564981 +1403636962751666432.0000000000 -1.6914853223 8.7551536319 -0.5748111507 0.4697086930 0.6136959255 0.5336236112 -0.343506763233 +1403636962801666560.0000000000 -1.7030760052 8.7386442413 -0.5604619453 0.4676144497 0.6093548619 0.5390847773 -0.345558940901 +1403636962851666432.0000000000 -1.7148422113 8.7209393081 -0.5475437821 0.4667514679 0.6052304271 0.5430151532 -0.347812795583 +1403636962901666560.0000000000 -1.7264437996 8.7016833669 -0.5361914000 0.4641939917 0.6036788468 0.5445085472 -0.351576776878 +1403636962951666432.0000000000 -1.7378225638 8.6810358229 -0.5261139657 0.4617071160 0.6030844721 0.5441075706 -0.356458426933 +1403636963001666560.0000000000 -1.7491987335 8.6595896897 -0.5167373885 0.4615806755 0.6014942488 0.5417931208 -0.362778393726 +1403636963051666432.0000000000 -1.7601897850 8.6374867162 -0.5086065675 0.4627425091 0.5997065652 0.5389169526 -0.36849684411 +1403636963101666560.0000000000 -1.7702209658 8.6146547578 -0.5021628911 0.4636736079 0.5986993995 0.5362987324 -0.372759284349 +1403636963151666432.0000000000 -1.7792593576 8.5913029639 -0.4973689839 0.4638179461 0.5987241570 0.5346397978 -0.374916768514 +1403636963201666560.0000000000 -1.7873140055 8.5673772361 -0.4941014128 0.4632746851 0.6000113680 0.5337525545 -0.374794790467 +1403636963251666432.0000000000 -1.7943731180 8.5427673620 -0.4922741976 0.4599834275 0.6034802963 0.5328531368 -0.374558824549 +1403636963301666560.0000000000 -1.8004943360 8.5178116421 -0.4913533431 0.4565781719 0.6070212230 0.5314579350 -0.374985427823 +1403636963351666432.0000000000 -1.8061093407 8.4926175410 -0.4912223108 0.4535003113 0.6107917269 0.5295064802 -0.375358257417 +1403636963401666560.0000000000 -1.8113503337 8.4675533869 -0.4919820692 0.4520743789 0.6133449237 0.5280773937 -0.374928028753 +1403636963451666432.0000000000 -1.8157674664 8.4427613129 -0.4936893051 0.4519191577 0.6149268300 0.5275522899 -0.373259494357 +1403636963501666560.0000000000 -1.8190904465 8.4181972755 -0.4953331370 0.4532737915 0.6155894993 0.5272908549 -0.370886495452 +1403636963551666432.0000000000 -1.8215083906 8.3935554967 -0.4958740995 0.4543416212 0.6162881217 0.5264467627 -0.369616623313 +1403636963601666560.0000000000 -1.8224806168 8.3689375783 -0.4955240113 0.4556795490 0.6169037679 0.5260498245 -0.367501662422 +1403636963651666432.0000000000 -1.8233031951 8.3442286377 -0.4938731410 0.4567726791 0.6177594302 0.5253923057 -0.365643174557 +1403636963701666560.0000000000 -1.8249160362 8.3194078988 -0.4898888638 0.4580097103 0.6185516816 0.5246148718 -0.363868326126 +1403636963751666432.0000000000 -1.8262151738 8.2940523189 -0.4833982006 0.4588235278 0.6193872889 0.5236327007 -0.362834881871 +1403636963801666560.0000000000 -1.8261985471 8.2681265130 -0.4757972247 0.4593911318 0.6203266380 0.5229091046 -0.361553202981 +1403636963851666432.0000000000 -1.8260589760 8.2418980332 -0.4664480959 0.4603581001 0.6206503000 0.5219898262 -0.361095896144 +1403636963901666560.0000000000 -1.8256378564 8.2155306449 -0.4548950671 0.4616682394 0.6208267053 0.5211862374 -0.360279814341 +1403636963951666432.0000000000 -1.8242398237 8.1886360610 -0.4420648876 0.4620528331 0.6213126636 0.5201538928 -0.3604409538 +1403636964001666560.0000000000 -1.8228338617 8.1613864482 -0.4275537972 0.4626575141 0.6213321765 0.5199422978 -0.359936602837 +1403636964051666432.0000000000 -1.8209374338 8.1337420508 -0.4114687592 0.4630467039 0.6215260618 0.5193711320 -0.359926008758 +1403636964101666560.0000000000 -1.8182487447 8.1057472328 -0.3944560880 0.4636152804 0.6210163056 0.5196915175 -0.359611382738 +1403636964151666432.0000000000 -1.8150892153 8.0775746133 -0.3775036528 0.4644309559 0.6203449805 0.5197445515 -0.359640923093 +1403636964201666560.0000000000 -1.8114894079 8.0491985695 -0.3616428114 0.4655137129 0.6193840576 0.5194059151 -0.360385720607 +1403636964251666432.0000000000 -1.8070529996 8.0203914152 -0.3477810620 0.4654278445 0.6190903619 0.5197234208 -0.360543494427 +1403636964301666560.0000000000 -1.8021936022 7.9914375816 -0.3357932104 0.4659352471 0.6184046811 0.5210680798 -0.359121222027 +1403636964351666432.0000000000 -1.7971544101 7.9618390862 -0.3251209967 0.4662599482 0.6176551594 0.5213426077 -0.359590948442 +1403636964401666560.0000000000 -1.7918195789 7.9318645979 -0.3159917048 0.4666054342 0.6169874775 0.5220919500 -0.359201638522 +1403636964451666432.0000000000 -1.7860023101 7.9013866003 -0.3083851537 0.4667347777 0.6160884884 0.5231148557 -0.359088386641 +1403636964501666560.0000000000 -1.7798282419 7.8705985525 -0.3020706732 0.4676013381 0.6145582066 0.5246032011 -0.358411328896 +1403636964551666432.0000000000 -1.7729688766 7.8388475737 -0.2970625426 0.4674040223 0.6128402475 0.5273281743 -0.357610552883 +1403636964601666560.0000000000 -1.7657398946 7.8063938112 -0.2931344006 0.4695819751 0.6080470092 0.5313910694 -0.356924550137 +1403636964651666432.0000000000 -1.7580352799 7.7724056296 -0.2902815780 0.4687117903 0.6044498470 0.5355471251 -0.35796496607 +1403636964701666560.0000000000 -1.7497356626 7.7374171847 -0.2889324057 0.4675395461 0.5999114016 0.5410344053 -0.358880001447 +1403636964751666432.0000000000 -1.7410506846 7.7013907751 -0.2888285085 0.4665047027 0.5943600649 0.5471534368 -0.360184108723 +1403636964801666560.0000000000 -1.7318074448 7.6638528839 -0.2896466676 0.4650742786 0.5881442610 0.5533500795 -0.36276153753 +1403636964851666432.0000000000 -1.7218706671 7.6243454548 -0.2901436535 0.4608720011 0.5826428466 0.5586422899 -0.368840214536 +1403636964901666560.0000000000 -1.7109246255 7.5829734796 -0.2891236578 0.4561387590 0.5764368478 0.5632746871 -0.377332240795 +1403636964951666432.0000000000 -1.6986944543 7.5404210791 -0.2868282069 0.4528850480 0.5684448690 0.5693891073 -0.384137486821 +1403636965001666560.0000000000 -1.6855476785 7.4960113761 -0.2828065592 0.4476973513 0.5609371323 0.5758972631 -0.391483023336 +1403636965051666432.0000000000 -1.6713178528 7.4502079903 -0.2770679362 0.4409284333 0.5548911559 0.5813665052 -0.399613448807 +1403636965101666560.0000000000 -1.6561900598 7.4038465070 -0.2698875178 0.4352949924 0.5490697316 0.5887558117 -0.402997882891 +1403636965151666432.0000000000 -1.6403501236 7.3568420650 -0.2608555394 0.4288296666 0.5448489124 0.5944230149 -0.407315674927 +1403636965201666560.0000000000 -1.6236902171 7.3095023775 -0.2504915232 0.4218995546 0.5422674835 0.6012046599 -0.408043746532 +1403636965251666432.0000000000 -1.6065757403 7.2615644709 -0.2384347069 0.4149251558 0.5406400833 0.6079691554 -0.407331463835 +1403636965301666560.0000000000 -1.5893747415 7.2132292001 -0.2259702217 0.4062335513 0.5418433991 0.6152361318 -0.403564783818 +1403636965351666432.0000000000 -1.5722436530 7.1643019211 -0.2120022317 0.3978215082 0.5435557341 0.6225051449 -0.398462741311 +1403636965401666560.0000000000 -1.5560480305 7.1147601894 -0.1963744852 0.3895485793 0.5462013125 0.6289352749 -0.392882234954 +1403636965451666432.0000000000 -1.5410741440 7.0645943661 -0.1781340501 0.3820208655 0.5492758095 0.6331959626 -0.389125964762 +1403636965501666560.0000000000 -1.5286945909 7.0137148449 -0.1571269694 0.3757373510 0.5524182035 0.6342155218 -0.389135250846 +1403636965551666432.0000000000 -1.5195098220 6.9628138232 -0.1332005033 0.3737879558 0.5534063804 0.6320895080 -0.393048083746 +1403636965601666560.0000000000 -1.5137051174 6.9113699698 -0.1052075608 0.3749268701 0.5531151862 0.6257576163 -0.402393884833 +1403636965651666432.0000000000 -1.5101069189 6.8597625048 -0.0747742056 0.3780984858 0.5514388572 0.6183661560 -0.413013339885 +1403636965701666560.0000000000 -1.5074497374 6.8081353242 -0.0444365051 0.3798927306 0.5510254493 0.6107619391 -0.423110294352 +1403636965751666432.0000000000 -1.5052161072 6.7572607776 -0.0159030263 0.3816795498 0.5506976744 0.6047399224 -0.430514133277 +1403636965801666560.0000000000 -1.5028823529 6.7076343081 0.0097878556 0.3857524405 0.5487951992 0.6015075989 -0.433828874551 +1403636965851666432.0000000000 -1.5001996219 6.6593953669 0.0325668382 0.3916108691 0.5457704878 0.6010031721 -0.433094318805 +1403636965901666560.0000000000 -1.4967953630 6.6123394927 0.0530198197 0.3968894858 0.5432273945 0.6016214213 -0.43062094632 +1403636965951666432.0000000000 -1.4927927543 6.5659210619 0.0714910854 0.4007213774 0.5413987662 0.6026185701 -0.427972677354 +1403636966001666560.0000000000 -1.4884239458 6.5197948639 0.0885166783 0.4049427545 0.5394070157 0.6033553220 -0.425468908876 +1403636966051666432.0000000000 -1.4835842074 6.4732760098 0.1041000441 0.4081044855 0.5379232964 0.6039243500 -0.423514622617 +1403636966101666560.0000000000 -1.4781636069 6.4264099592 0.1182994186 0.4097670261 0.5376051417 0.6035154362 -0.4228957486 +1403636966151666432.0000000000 -1.4723535606 6.3794530928 0.1308804003 0.4120902207 0.5369924533 0.6033730550 -0.421617968838 +1403636966201666560.0000000000 -1.4657498721 6.3322880401 0.1415793445 0.4123796870 0.5374756509 0.6030009175 -0.42125148297 +1403636966251666432.0000000000 -1.4586262869 6.2850989684 0.1508287908 0.4134439914 0.5374156351 0.6017022564 -0.422140848177 +1403636966301666560.0000000000 -1.4511790093 6.2381653161 0.1579283837 0.4142273147 0.5376594140 0.6013978856 -0.421495752576 +1403636966351666432.0000000000 -1.4431802114 6.1905932482 0.1640614463 0.4132345203 0.5391900028 0.5991180615 -0.423755732067 +1403636966401666560.0000000000 -1.4343505387 6.1433583742 0.1687219672 0.4083321904 0.5433643668 0.5949046904 -0.429078543514 +1403636966451666432.0000000000 -1.4246780573 6.0964062775 0.1722055190 0.4026709981 0.5481475644 0.5899716564 -0.435113501892 +1403636966501666560.0000000000 -1.4146618184 6.0517359759 0.1737460096 0.3976816752 0.5523703608 0.5853725377 -0.440539739263 +1403636966551666432.0000000000 -1.4040255128 6.0088359523 0.1734734131 0.3948383734 0.5551563601 0.5823869852 -0.443541964386 +1403636966601666560.0000000000 -1.3928491934 5.9682155285 0.1710801342 0.3956155485 0.5556254020 0.5814967656 -0.44343010951 +1403636966651666432.0000000000 -1.3808007016 5.9297276290 0.1665767188 0.3993200722 0.5543062675 0.5829146984 -0.439884639563 +1403636966701666560.0000000000 -1.3677451786 5.8925541374 0.1607418519 0.4032353934 0.5527885141 0.5853346585 -0.434982084341 +1403636966751666432.0000000000 -1.3538851470 5.8562178238 0.1557375716 0.4077679448 0.5506707789 0.5870521161 -0.431111133518 +1403636966801666560.0000000000 -1.3391064418 5.8201777279 0.1527140944 0.4100187754 0.5498897577 0.5871936840 -0.429778356392 +1403636966851666432.0000000000 -1.3230795992 5.7841412662 0.1514663141 0.4101061964 0.5505085234 0.5867081914 -0.429565794169 +1403636966901666560.0000000000 -1.3064769995 5.7484296083 0.1525469578 0.4096057107 0.5515647666 0.5855465104 -0.430272883433 +1403636966951666432.0000000000 -1.2889931430 5.7131697934 0.1555184220 0.4078070078 0.5532723280 0.5839745330 -0.431922354423 +1403636967001666560.0000000000 -1.2708386796 5.6789558991 0.1589284243 0.4081321046 0.5535759772 0.5834961616 -0.431872726728 +1403636967051666432.0000000000 -1.2519109331 5.6459311512 0.1611925149 0.4097953802 0.5531095974 0.5837873941 -0.430499475174 +1403636967101666560.0000000000 -1.2320423911 5.6134828045 0.1620681053 0.4119046131 0.5519340005 0.5851019072 -0.428204632123 +1403636967151666432.0000000000 -1.2115352916 5.5815155408 0.1612640030 0.4139276291 0.5510563482 0.5860765033 -0.42604594963 +1403636967201666560.0000000000 -1.1902223796 5.5497281460 0.1589699753 0.4150658336 0.5505148152 0.5866494616 -0.424848445111 +1403636967251666432.0000000000 -1.1681376112 5.5180987889 0.1554774358 0.4153332115 0.5507224399 0.5863488598 -0.424733012925 +1403636967301666560.0000000000 -1.1454540081 5.4868666944 0.1506175337 0.4163752545 0.5503971901 0.5869259213 -0.423335025103 +1403636967351666432.0000000000 -1.1220315169 5.4559405613 0.1460384458 0.4180871011 0.5494786085 0.5870666190 -0.422645501046 +1403636967401666560.0000000000 -1.0978208090 5.4250807299 0.1426638794 0.4191738436 0.5490605324 0.5871429368 -0.422005915071 +1403636967451666432.0000000000 -1.0732832564 5.3941796546 0.1413780516 0.4198176622 0.5490356963 0.5870959836 -0.421463214075 +1403636967501666560.0000000000 -1.0477599224 5.3631320621 0.1423936420 0.4194974928 0.5494597272 0.5861950818 -0.422482174555 +1403636967551666432.0000000000 -1.0213887793 5.3326037159 0.1453267410 0.4207758655 0.5490870088 0.5862735433 -0.421585649909 +1403636967601666560.0000000000 -0.9934245760 5.3019530437 0.1497608000 0.4215290902 0.5489864622 0.5860685446 -0.421249037311 +1403636967651666432.0000000000 -0.9646853247 5.2712393299 0.1537462704 0.4221239225 0.5490348224 0.5861147855 -0.420525404802 +1403636967701666560.0000000000 -0.9351872156 5.2405235412 0.1548196595 0.4228382741 0.5490463711 0.5864210220 -0.419364115383 +1403636967751666432.0000000000 -0.9057128310 5.2095700074 0.1524199541 0.4231504210 0.5491217102 0.5859809017 -0.419565789084 +1403636967801666560.0000000000 -0.8753754981 5.1784443830 0.1454080844 0.4231291762 0.5492857563 0.5857335736 -0.419717808589 +1403636967851666432.0000000000 -0.8442732900 5.1472145371 0.1340608659 0.4232156959 0.5491911409 0.5855655438 -0.419988761041 +1403636967901666560.0000000000 -0.8122726933 5.1156815947 0.1202319198 0.4240180253 0.5487421467 0.5853055316 -0.420128796064 +1403636967951666432.0000000000 -0.7797788754 5.0838280998 0.1042589808 0.4245844358 0.5481721361 0.5852863096 -0.42032761265 +1403636968001666560.0000000000 -0.7465887353 5.0517583925 0.0864640289 0.4241776020 0.5485172988 0.5850453271 -0.420623465986 +1403636968051666432.0000000000 -0.7125895914 5.0195624182 0.0674029363 0.4240313055 0.5482730081 0.5853046974 -0.420728620131 +1403636968101666560.0000000000 -0.6781721120 4.9871314484 0.0477145607 0.4234382107 0.5483426685 0.5840661904 -0.422950451981 +1403636968151666432.0000000000 -0.6425505689 4.9549083784 0.0277820602 0.4217752636 0.5494780618 0.5834006363 -0.424055638043 +1403636968201666560.0000000000 -0.6059842937 4.9228519853 0.0085081398 0.4208302704 0.5500833149 0.5832722863 -0.424386227682 +1403636968251666432.0000000000 -0.5683679769 4.8912493586 -0.0085149060 0.4210768915 0.5499544000 0.5840144661 -0.423286561024 +1403636968301666560.0000000000 -0.5293599764 4.8594274911 -0.0236065428 0.4200828648 0.5505197768 0.5840169881 -0.423535736011 +1403636968351666432.0000000000 -0.4896892561 4.8279782022 -0.0364647076 0.4197666525 0.5507650130 0.5847316615 -0.422543183494 +1403636968401666560.0000000000 -0.4488901305 4.7967086132 -0.0472975084 0.4192291216 0.5511467897 0.5848039998 -0.422478924334 +1403636968451666432.0000000000 -0.4079473363 4.7657120835 -0.0561363804 0.4184507826 0.5518445244 0.5848003005 -0.422344849605 +1403636968501666560.0000000000 -0.3659175387 4.7350114013 -0.0627858210 0.4179498683 0.5523464138 0.5847203375 -0.42229548141 +1403636968551666432.0000000000 -0.3230611366 4.7044214613 -0.0674380249 0.4178798434 0.5523974470 0.5844611110 -0.422656724557 +1403636968601666560.0000000000 -0.2802529733 4.6740183786 -0.0708890041 0.4194746885 0.5513427071 0.5853655792 -0.421199885709 +1403636968651666432.0000000000 -0.2370099702 4.6439340613 -0.0726817639 0.4221228081 0.5496775177 0.5872116498 -0.418150020609 +1403636968701666560.0000000000 -0.1925889771 4.6135892607 -0.0736672770 0.4236017400 0.5486235062 0.5881418383 -0.416728919455 +1403636968751666432.0000000000 -0.1475934577 4.5831080221 -0.0756132167 0.4254765185 0.5471787525 0.5897746780 -0.414404360718 +1403636968801666560.0000000000 -0.1023794487 4.5520307473 -0.0783555557 0.4263960690 0.5466966760 0.5901354310 -0.413581080118 +1403636968851666432.0000000000 -0.0564917776 4.5203406515 -0.0808795207 0.4268485665 0.5464758738 0.5901894238 -0.413329002967 +1403636968901666560.0000000000 -0.0096989166 4.4876605700 -0.0817471376 0.4245120187 0.5484999053 0.5885391608 -0.415402282062 +1403636968951666432.0000000000 0.0371307301 4.4545429831 -0.0808427540 0.4237256943 0.5491406349 0.5880397306 -0.416065348628 +1403636969001666560.0000000000 0.0840347068 4.4209011298 -0.0778740445 0.4225907744 0.5499993249 0.5875814446 -0.416732319346 +1403636969051666432.0000000000 0.1319398869 4.3869053663 -0.0728143146 0.4217660594 0.5506259641 0.5863261815 -0.418504537133 +1403636969101666560.0000000000 0.1807125354 4.3525321865 -0.0663351655 0.4188298557 0.5527154141 0.5854979061 -0.419856433698 +1403636969151666432.0000000000 0.2299696759 4.3185392512 -0.0594937058 0.4161750506 0.5546561696 0.5864119162 -0.418659677138 +1403636969201666560.0000000000 0.2796809697 4.2848399080 -0.0511100271 0.4132371160 0.5568981926 0.5881024266 -0.416215118587 +1403636969251666432.0000000000 0.3298216456 4.2512597343 -0.0412295740 0.4089424113 0.5600007929 0.5898367907 -0.413833029873 +1403636969301666560.0000000000 0.3799567528 4.2181378918 -0.0292854572 0.4058581802 0.5624165953 0.5919673779 -0.410537859914 +1403636969351666432.0000000000 0.4296844428 4.1850359262 -0.0162540539 0.4038445454 0.5639699643 0.5939068641 -0.407580788755 +1403636969401666560.0000000000 0.4783920412 4.1519856556 -0.0013791799 0.4027764479 0.5650686867 0.5955659388 -0.404684722798 +1403636969451666432.0000000000 0.5261833644 4.1190636333 0.0135881378 0.4018328640 0.5660469977 0.5965373563 -0.402820466646 +1403636969501666560.0000000000 0.5729023292 4.0863755796 0.0274456959 0.4013232939 0.5668322994 0.5975015426 -0.400790050721 +1403636969551666432.0000000000 0.6184935078 4.0537502114 0.0399459701 0.4009246222 0.5675197353 0.5979763905 -0.399505987112 +1403636969601666560.0000000000 0.6632144546 4.0211715975 0.0508416848 0.4003661148 0.5684228486 0.5981661807 -0.398496749656 +1403636969651666432.0000000000 0.7068481938 3.9885612792 0.0602271815 0.4007342516 0.5685997304 0.5977677450 -0.398472243984 +1403636969701666560.0000000000 0.7494339813 3.9559112455 0.0681067681 0.4009121042 0.5688539070 0.5974650884 -0.398384469148 +1403636969751666432.0000000000 0.7908198870 3.9232282528 0.0748328860 0.4012898065 0.5689856752 0.5967973639 -0.398816623314 +1403636969801666560.0000000000 0.8313761000 3.8904866080 0.0800392952 0.4014718759 0.5689605749 0.5974959641 -0.397621390112 +1403636969851666432.0000000000 0.8708162499 3.8578179799 0.0839783104 0.4009450264 0.5696227964 0.5975268054 -0.397158246165 +1403636969901666560.0000000000 0.9089278403 3.8252435862 0.0867561902 0.4009495088 0.5697282900 0.5970205761 -0.397763244355 +1403636969951666432.0000000000 0.9458385293 3.7927350422 0.0879453461 0.4019823026 0.5689475289 0.5965805166 -0.39849796091 +1403636970001666560.0000000000 0.9814611927 3.7598844556 0.0882273068 0.4026803034 0.5684068744 0.5945514389 -0.401585339562 +1403636970051666432.0000000000 1.0159324277 3.7271512284 0.0875737681 0.4061916781 0.5657825492 0.5922534190 -0.405134934808 +1403636970101666560.0000000000 1.0499572214 3.6943969096 0.0854367538 0.4091876479 0.5633392819 0.5908716924 -0.407535232032 +1403636970151666432.0000000000 1.0836236261 3.6615532954 0.0826360714 0.4125128567 0.5608214566 0.5891875286 -0.410085958087 +1403636970201666560.0000000000 1.1173795051 3.6287211826 0.0793475595 0.4138859672 0.5596947405 0.5878656469 -0.412133697768 +1403636970251666432.0000000000 1.1511236488 3.5959275627 0.0764095401 0.4160758846 0.5577378768 0.5865881006 -0.414395607276 +1403636970301666560.0000000000 1.1854587156 3.5632661518 0.0726908391 0.4150858309 0.5582788256 0.5873075750 -0.413640324589 +1403636970351666432.0000000000 1.2201406248 3.5306057488 0.0691486110 0.4131826888 0.5594152206 0.5880897932 -0.41289837942 +1403636970401666560.0000000000 1.2549438744 3.4980642226 0.0652069618 0.4103924673 0.5613528467 0.5907052664 -0.409302202005 +1403636970451666432.0000000000 1.2891750121 3.4651599626 0.0617312133 0.4070306546 0.5632910601 0.5931832840 -0.40640228763 +1403636970501666560.0000000000 1.3228464237 3.4322807298 0.0591143612 0.4036763607 0.5655185148 0.5947608658 -0.404343564066 +1403636970551666432.0000000000 1.3557709850 3.3994840351 0.0567295055 0.4011330930 0.5669895381 0.5969109494 -0.40163717946 +1403636970601666560.0000000000 1.3877481208 3.3665761204 0.0557150101 0.3986628065 0.5681715427 0.5988840243 -0.399483404216 +1403636970651666432.0000000000 1.4188083747 3.3336427624 0.0567139192 0.3968592166 0.5689022144 0.6008264613 -0.39731674519 +1403636970701666560.0000000000 1.4485220244 3.3005800265 0.0595744476 0.3946871320 0.5697952957 0.6029576634 -0.394965118806 +1403636970751666432.0000000000 1.4764864780 3.2673079936 0.0650657739 0.3917660422 0.5713275114 0.6044125753 -0.39343319848 +1403636970801666560.0000000000 1.5027885705 3.2341783340 0.0716143953 0.3900592802 0.5719095697 0.6064136047 -0.391197829849 +1403636970851666432.0000000000 1.5274999511 3.2008487848 0.0774705466 0.3872166268 0.5732749374 0.6090584651 -0.387900652419 +1403636970901666560.0000000000 1.5500417729 3.1672061645 0.0824963041 0.3841689456 0.5749262026 0.6107681960 -0.385793071007 +1403636970951666432.0000000000 1.5703294705 3.1337647017 0.0865875771 0.3812530457 0.5766094054 0.6115118459 -0.384994767537 +1403636971001666560.0000000000 1.5879490846 3.0999882274 0.0898283402 0.3791094730 0.5778913153 0.6102925110 -0.387118439497 +1403636971051666432.0000000000 1.6030281766 3.0662636456 0.0919576569 0.3773154977 0.5791621724 0.6075297220 -0.391295067866 +1403636971101666560.0000000000 1.6158060742 3.0328656253 0.0930745104 0.3764359648 0.5800089552 0.6032536591 -0.397455153607 +1403636971151666432.0000000000 1.6266704508 3.0001926076 0.0927455862 0.3764851734 0.5799694776 0.5988912790 -0.404009350384 +1403636971201666560.0000000000 1.6359201198 2.9682520703 0.0910649616 0.3749282218 0.5811410212 0.5935284485 -0.411616232357 +1403636971251666432.0000000000 1.6439643973 2.9379123800 0.0878900245 0.3743617782 0.5816966129 0.5884512094 -0.418577930317 +1403636971301666560.0000000000 1.6512050994 2.9094526954 0.0834580744 0.3733422478 0.5823941467 0.5835868049 -0.425275281419 +1403636971351666432.0000000000 1.6577143693 2.8830966437 0.0775755883 0.3714717213 0.5834653419 0.5800123661 -0.430305252426 +1403636971401666560.0000000000 1.6636986523 2.8590549174 0.0702690140 0.3708081683 0.5836536353 0.5779545920 -0.433380001691 +1403636971451666432.0000000000 1.6688321544 2.8373248654 0.0614899079 0.3721286212 0.5827328325 0.5776358716 -0.433911897883 +1403636971501666560.0000000000 1.6734640894 2.8177725357 0.0510446600 0.3736731225 0.5814322306 0.5793957326 -0.431978638122 +1403636971551666432.0000000000 1.6775099252 2.8002653214 0.0396651097 0.3766578888 0.5791186413 0.5807228902 -0.430710295844 +1403636971601666560.0000000000 1.6807145105 2.7846369201 0.0274345142 0.3821857239 0.5752253366 0.5821606421 -0.429114053911 +1403636971651666432.0000000000 1.6836286040 2.7706269026 0.0140485788 0.3887000227 0.5705723068 0.5834299803 -0.427748749979 +1403636971701666560.0000000000 1.6863505580 2.7578356261 -0.0005049548 0.3949762993 0.5658402898 0.5851180683 -0.425975745344 +1403636971751666432.0000000000 1.6891380712 2.7457172866 -0.0156383208 0.3994256210 0.5622553126 0.5853302787 -0.426282302716 +1403636971801666560.0000000000 1.6920892532 2.7342533165 -0.0312831596 0.4016651864 0.5604137480 0.5842386299 -0.428096639085 +1403636971851666432.0000000000 1.6952826895 2.7233624533 -0.0470810316 0.4031244442 0.5588687518 0.5836385422 -0.42956076735 +1403636971901666560.0000000000 1.6992664504 2.7131413183 -0.0618637140 0.4037206545 0.5580685997 0.5835271303 -0.430192002905 +1403636971951666432.0000000000 1.7040451727 2.7036085307 -0.0753308002 0.4034890511 0.5579603858 0.5836899785 -0.430328714517 +1403636972001666560.0000000000 1.7088940482 2.6948434984 -0.0870318602 0.4034209023 0.5575404952 0.5843620457 -0.430024617201 +1403636972051666432.0000000000 1.7138489689 2.6868994449 -0.0957641681 0.4039846737 0.5570356936 0.5843849991 -0.430118346806 +1403636972101666560.0000000000 1.7207277327 2.6797622091 -0.1038418613 0.4044357434 0.5567646095 0.5851227547 -0.429041094779 +1403636972151666432.0000000000 1.7282959934 2.6730410761 -0.1110104344 0.4036682120 0.5575614041 0.5857508642 -0.427870518224 +1403636972201666560.0000000000 1.7369510493 2.6666354534 -0.1158304600 0.3995525027 0.5603674081 0.5861674626 -0.427497217937 +1403636972251666432.0000000000 1.7462446790 2.6609191078 -0.1193167117 0.3954459406 0.5632805357 0.5869833520 -0.426366146163 +1403636972301666560.0000000000 1.7554271364 2.6561203537 -0.1212853640 0.3919616377 0.5658450198 0.5882411033 -0.424450106033 +1403636972351666432.0000000000 1.7638455665 2.6525556949 -0.1210918383 0.3914720621 0.5663073182 0.5899988872 -0.421837597842 +1403636972401666560.0000000000 1.7709145495 2.6496553725 -0.1186602482 0.3912293469 0.5667137994 0.5907656571 -0.420441441949 +1403636972451666432.0000000000 1.7776858068 2.6475314143 -0.1139222712 0.3924977395 0.5660102323 0.5917999480 -0.418749045437 +1403636972501666560.0000000000 1.7845457932 2.6460138553 -0.1073911718 0.3945605593 0.5647116966 0.5916865463 -0.418723889654 +1403636972551666432.0000000000 1.7897740829 2.6447866753 -0.0990891569 0.3961190064 0.5639069722 0.5913253028 -0.418847282135 +1403636972601666560.0000000000 1.7952096561 2.6441370510 -0.0890006351 0.3982934807 0.5627302863 0.5913822582 -0.418286926572 +1403636972651666432.0000000000 1.8008401797 2.6440571537 -0.0783106037 0.4018869660 0.5604871404 0.5914637438 -0.417745941768 +1403636972701666560.0000000000 1.8066453086 2.6438997810 -0.0684660718 0.4028397420 0.5601679442 0.5912401796 -0.417572827916 +1403636972751666432.0000000000 1.8125517783 2.6438682349 -0.0600341377 0.4036019467 0.5599225497 0.5914492586 -0.416869261835 +1403636972801666560.0000000000 1.8184154109 2.6437219721 -0.0530952258 0.4034262558 0.5602101569 0.5911442338 -0.417085520108 +1403636972851666432.0000000000 1.8243075093 2.6437076810 -0.0480140596 0.4032519226 0.5605229934 0.5912153147 -0.416732902998 +1403636972901666560.0000000000 1.8301613454 2.6439275151 -0.0445036617 0.4039853022 0.5608377499 0.5910441684 -0.415840937068 +1403636972951666432.0000000000 1.8360057930 2.6445033971 -0.0429184205 0.4040052858 0.5631594787 0.5901223158 -0.413988868282 +1403636973001666560.0000000000 1.8414790537 2.6456999218 -0.0432065015 0.4053785655 0.5666150645 0.5884181719 -0.41034088544 +1403636973051666432.0000000000 1.8465694010 2.6468303365 -0.0447621988 0.4062944703 0.5711664805 0.5857516478 -0.40692586805 +1403636973101666560.0000000000 1.8514549945 2.6481457384 -0.0475785380 0.4075207196 0.5756852955 0.5826165481 -0.403820828541 +1403636973151666432.0000000000 1.8560975596 2.6495323328 -0.0516406427 0.4095241213 0.5790409359 0.5798648140 -0.400946861936 +1403636973201666560.0000000000 1.8606613713 2.6507755072 -0.0571149590 0.4105033559 0.5825299107 0.5771562552 -0.398793875431 +1403636973251666432.0000000000 1.8648883701 2.6522279071 -0.0638664021 0.4134916310 0.5840789567 0.5746825829 -0.397009284963 +1403636973301666560.0000000000 1.8690335535 2.6536000983 -0.0718357629 0.4154385951 0.5860166111 0.5724433043 -0.395352967085 +1403636973351666432.0000000000 1.8728721424 2.6549051610 -0.0810204367 0.4167858369 0.5878492759 0.5702840404 -0.394333498761 +1403636973401666560.0000000000 1.8761744126 2.6561659635 -0.0914963312 0.4187828779 0.5888110541 0.5691407056 -0.392429995039 +1403636973451666432.0000000000 1.8790985367 2.6568908898 -0.1027334606 0.4187777806 0.5908144501 0.5674884470 -0.391816690061 +1403636973501666560.0000000000 1.8816320871 2.6577467900 -0.1149304407 0.4203604222 0.5913668861 0.5665444046 -0.390652990682 +1403636973551666432.0000000000 1.8838859448 2.6584764487 -0.1279093945 0.4226910445 0.5911442352 0.5658180269 -0.389526295049 +1403636973601666560.0000000000 1.8858167480 2.6587697468 -0.1414929428 0.4244138063 0.5911298930 0.5639476744 -0.390386207773 +1403636973651666432.0000000000 1.8877425733 2.6589195402 -0.1556741235 0.4264171894 0.5906211654 0.5626733289 -0.390811648423 +1403636973701666560.0000000000 1.8897527132 2.6588168135 -0.1694462964 0.4275024978 0.5903366668 0.5620717275 -0.390921484905 +1403636973751666432.0000000000 1.8916448840 2.6587615524 -0.1811617455 0.4303816423 0.5887887486 0.5610609208 -0.391548329898 +1403636973801666560.0000000000 1.8936080997 2.6584266161 -0.1912633843 0.4319100832 0.5876630705 0.5606056006 -0.392208052101 +1403636973851666432.0000000000 1.8961875424 2.6577359384 -0.1996771423 0.4331784231 0.5867177817 0.5606983595 -0.392091887341 +1403636973901666560.0000000000 1.8991773520 2.6565336167 -0.2058726358 0.4331689732 0.5865513588 0.5602539717 -0.392985535861 +1403636973951666432.0000000000 1.9022585431 2.6548962550 -0.2095480259 0.4322979363 0.5871046742 0.5594159984 -0.394309949915 +1403636974001666560.0000000000 1.9063125142 2.6530706548 -0.2121941843 0.4302571066 0.5893035328 0.5592456443 -0.393502830763 +1403636974051666432.0000000000 1.9105760060 2.6515477354 -0.2139322609 0.4286287666 0.5926759048 0.5575483680 -0.392622553677 +1403636974101666560.0000000000 1.9144756501 2.6505587333 -0.2147351281 0.4276505640 0.5972187815 0.5550291330 -0.390368266778 +1403636974151666432.0000000000 1.9181865192 2.6501427423 -0.2161742530 0.4276051269 0.6030446688 0.5515479467 -0.386375265018 +1403636974201666560.0000000000 1.9215367737 2.6506910627 -0.2186802048 0.4304560314 0.6088966849 0.5465284263 -0.381128733249 +1403636974251666432.0000000000 1.9240204059 2.6519882342 -0.2227078958 0.4355871462 0.6144974607 0.5404615059 -0.374910748623 +1403636974301666560.0000000000 1.9259248803 2.6536485029 -0.2281241758 0.4406898956 0.6210384193 0.5337061357 -0.367779089231 +1403636974351666432.0000000000 1.9278071798 2.6556679463 -0.2344139908 0.4474035623 0.6272178800 0.5254248310 -0.361049207904 +1403636974401666560.0000000000 1.9295878226 2.6575022041 -0.2422709871 0.4528976348 0.6344299384 0.5164771829 -0.354448452179 +1403636974451666432.0000000000 1.9309872201 2.6596882177 -0.2513027194 0.4604372374 0.6408794389 0.5062307760 -0.34785269379 +1403636974501666560.0000000000 1.9324726795 2.6616004812 -0.2615932894 0.4665943700 0.6481104093 0.4954091049 -0.341778305318 +1403636974551666432.0000000000 1.9339787035 2.6636327990 -0.2729813430 0.4733946285 0.6548694497 0.4849676399 -0.334439707249 +1403636974601666560.0000000000 1.9349819491 2.6657320107 -0.2852323502 0.4801920273 0.6617426934 0.4734774083 -0.327614664638 +1403636974651666432.0000000000 1.9360729068 2.6675058920 -0.2981081151 0.4851410788 0.6694097125 0.4631915455 -0.319346775023 +1403636974701666560.0000000000 1.9378849028 2.6686942832 -0.3099452217 0.4883582051 0.6774752071 0.4529077063 -0.312102894699 +1403636974751666432.0000000000 1.9406394240 2.6693281361 -0.3203910637 0.4904948670 0.6858219634 0.4429065827 -0.304789729093 +1403636974801666560.0000000000 1.9430913782 2.6697598394 -0.3286830432 0.4916009406 0.6941639762 0.4332910420 -0.297865342454 +1403636974851666432.0000000000 1.9456269058 2.6697505567 -0.3343982981 0.4911608272 0.7029044041 0.4228612500 -0.293044030451 +1403636974901666560.0000000000 1.9477523803 2.6698861065 -0.3385790935 0.4898440485 0.7118624241 0.4130724442 -0.287534090429 +1403636974951666432.0000000000 1.9495623388 2.6706524755 -0.3403568379 0.4895825861 0.7196219033 0.4029642665 -0.282971743435 +1403636975001666560.0000000000 1.9513725360 2.6721247153 -0.3406544289 0.4895574330 0.7265396635 0.3943990268 -0.27735003999 +1403636975051666432.0000000000 1.9522331761 2.6749495844 -0.3391033628 0.4913935844 0.7318257626 0.3855934482 -0.272545576145 +1403636975101666560.0000000000 1.9525919440 2.6792209920 -0.3365979230 0.4962850732 0.7344506296 0.3784040191 -0.26663420102 +1403636975151666432.0000000000 1.9526594672 2.6840863040 -0.3342747983 0.5017470676 0.7355364053 0.3722202252 -0.262084300417 +1403636975201666560.0000000000 1.9522087381 2.6896818793 -0.3326830585 0.5081757037 0.7351852203 0.3672227620 -0.25769669963 +1403636975251666432.0000000000 1.9514304311 2.6955319890 -0.3321513508 0.5145477631 0.7339098335 0.3635279931 -0.253898314277 +1403636975301666560.0000000000 1.9507065402 2.7011487264 -0.3329167686 0.5196145037 0.7327373381 0.3603717659 -0.251453676252 +1403636975351666432.0000000000 1.9498325362 2.7064655631 -0.3351678444 0.5240120113 0.7313234057 0.3575219049 -0.250510630063 +1403636975401666560.0000000000 1.9493644877 2.7114028081 -0.3398073100 0.5260420842 0.7311001091 0.3569353846 -0.247728656497 +1403636975451666432.0000000000 1.9490165800 2.7157250673 -0.3455277284 0.5266307853 0.7314576269 0.3561960774 -0.246483489226 +1403636975501666560.0000000000 1.9489670722 2.7194819386 -0.3526152911 0.5257767111 0.7323802061 0.3567342002 -0.24478315734 +1403636975551666432.0000000000 1.9489025767 2.7229174763 -0.3594365363 0.5236687694 0.7339250258 0.3579943193 -0.2428273951 +1403636975601666560.0000000000 1.9486303508 2.7261615874 -0.3647973433 0.5215261661 0.7352545160 0.3596663303 -0.240938551301 +1403636975651666432.0000000000 1.9481079122 2.7290256652 -0.3678223854 0.5194760617 0.7360992108 0.3613368060 -0.240287922939 +1403636975701666560.0000000000 1.9472762170 2.7317506269 -0.3687670623 0.5176718075 0.7366998236 0.3631856113 -0.239552669371 +1403636975751666432.0000000000 1.9458173019 2.7343562440 -0.3675495457 0.5157637869 0.7371346211 0.3652040474 -0.23926192801 +1403636975801666560.0000000000 1.9437216074 2.7371390263 -0.3642353720 0.5145588831 0.7375103114 0.3661502237 -0.239252398313 +1403636975851666432.0000000000 1.9401514472 2.7410832493 -0.3595416842 0.5140786311 0.7384709504 0.3659128646 -0.237679599412 +1403636975901666560.0000000000 1.9355747979 2.7456873639 -0.3546638544 0.5140977457 0.7404644991 0.3636544551 -0.234885654623 +1403636975951666432.0000000000 1.9300524568 2.7506984704 -0.3504149744 0.5149284203 0.7428148698 0.3587466089 -0.233185895498 +1403636976001666560.0000000000 1.9240378558 2.7560920650 -0.3470976422 0.5168977951 0.7452555781 0.3517015754 -0.231768838669 +1403636976051666432.0000000000 1.9175913417 2.7619798504 -0.3445186026 0.5202593978 0.7475046123 0.3419854006 -0.231544810737 +1403636976101666560.0000000000 1.9109253216 2.7682156040 -0.3429015384 0.5238704969 0.7499315611 0.3301756975 -0.232693714869 +1403636976151666432.0000000000 1.9043333164 2.7747389147 -0.3419930102 0.5269836380 0.7529504402 0.3169331320 -0.234323002972 +1403636976201666560.0000000000 1.8984214565 2.7819388091 -0.3428816651 0.5297059007 0.7565132431 0.3035141006 -0.234475078686 +1403636976251666432.0000000000 1.8935417259 2.7897062708 -0.3455320969 0.5321625111 0.7604058274 0.2898482228 -0.233610888374 +1403636976301666560.0000000000 1.8899565357 2.7987507437 -0.3495330681 0.5348838854 0.7644103053 0.2774603252 -0.229329200717 +1403636976351666432.0000000000 1.8876627986 2.8084867236 -0.3546429111 0.5378975439 0.7682578912 0.2648380238 -0.224291921675 +1403636976401666560.0000000000 1.8873095971 2.8189835200 -0.3614836398 0.5407186909 0.7721921887 0.2531671972 -0.217368100913 +1403636976451666432.0000000000 1.8883243165 2.8307184946 -0.3694137958 0.5440552343 0.7755820866 0.2422403075 -0.209274849067 +1403636976501666560.0000000000 1.8910972956 2.8430775091 -0.3789968011 0.5472508572 0.7787470316 0.2345614069 -0.19761200977 +1403636976551666432.0000000000 1.8950843039 2.8557774382 -0.3898418949 0.5507164177 0.7808556044 0.2292952041 -0.185471457776 +1403636976601666560.0000000000 1.8999225505 2.8683208440 -0.4020392535 0.5537761377 0.7823303639 0.2253598318 -0.174654336548 +1403636976651666432.0000000000 1.9054648038 2.8804162432 -0.4156228727 0.5563068485 0.7834605467 0.2222555799 -0.165271652726 +1403636976701666560.0000000000 1.9112370446 2.8922684130 -0.4304870158 0.5583624829 0.7843363806 0.2192229269 -0.158079372713 +1403636976751666432.0000000000 1.9168812946 2.9039114915 -0.4466272407 0.5592896879 0.7856128095 0.2156893982 -0.153250259815 +1403636976801666560.0000000000 1.9224632526 2.9150890045 -0.4642181410 0.5586481341 0.7875671598 0.2126169024 -0.14981416433 +1403636976851666432.0000000000 1.9281664908 2.9255429516 -0.4831012182 0.5551104203 0.7911405190 0.2100953796 -0.147678813241 +1403636976901666560.0000000000 1.9339438138 2.9360945337 -0.5009206148 0.5525361055 0.7936901840 0.2078942283 -0.146764211746 +1403636976951666432.0000000000 1.9396750096 2.9469948683 -0.5168048650 0.5495596588 0.7963136082 0.2056996879 -0.146821174246 +1403636977001666560.0000000000 1.9454081421 2.9583855586 -0.5299500276 0.5487218288 0.7971592358 0.2042908264 -0.147332161179 +1403636977051666432.0000000000 1.9510435461 2.9704998704 -0.5411010276 0.5468592430 0.7985024175 0.2039198460 -0.147497640485 +1403636977101666560.0000000000 1.9563831640 2.9839774161 -0.5491558818 0.5458019677 0.7992474656 0.2032983770 -0.148234512527 +1403636977151666432.0000000000 1.9621422806 2.9978981414 -0.5551135983 0.5446505769 0.7998490237 0.2034130251 -0.149065185465 +1403636977201666560.0000000000 1.9679284377 3.0125433206 -0.5590994321 0.5432369950 0.8004853168 0.2038352004 -0.150226615058 +1403636977251666432.0000000000 1.9737806310 3.0281049961 -0.5613778125 0.5427222353 0.8004500217 0.2045047991 -0.151360910346 +1403636977301666560.0000000000 1.9797101493 3.0445824699 -0.5631956580 0.5427173855 0.7999753082 0.2059407741 -0.15193993322 +1403636977351666432.0000000000 1.9855729793 3.0617272626 -0.5652572951 0.5449714358 0.7978709426 0.2068983418 -0.153626720562 +1403636977401666560.0000000000 1.9916108534 3.0793822756 -0.5686883802 0.5473255953 0.7957056615 0.2087101637 -0.154036555834 +1403636977451666432.0000000000 1.9976461120 3.0977067378 -0.5730128525 0.5512378726 0.7924317767 0.2104530878 -0.154590377752 +1403636977501666560.0000000000 2.0038158314 3.1161093814 -0.5787327738 0.5540944861 0.7898830596 0.2120701290 -0.155210544193 +1403636977551666432.0000000000 2.0101035179 3.1347331318 -0.5853309488 0.5575208109 0.7870594438 0.2130797140 -0.155900650625 +1403636977601666560.0000000000 2.0166629712 3.1530198185 -0.5934945975 0.5589830671 0.7856054543 0.2133353542 -0.15763891505 +1403636977651666432.0000000000 2.0236816454 3.1715309401 -0.6030532950 0.5607786115 0.7840259390 0.2145928731 -0.15741846962 +1403636977701666560.0000000000 2.0310827060 3.1901431132 -0.6139529144 0.5605286900 0.7844324114 0.2133860390 -0.157923329815 +1403636977751666432.0000000000 2.0387848837 3.2088119613 -0.6262800055 0.5586946007 0.7863052067 0.2108915567 -0.158458879228 +1403636977801666560.0000000000 2.0469699430 3.2273303758 -0.6396136331 0.5563645767 0.7885942681 0.2073388178 -0.159962973245 +1403636977851666432.0000000000 2.0558765926 3.2456033429 -0.6538690918 0.5536258462 0.7911221387 0.2044021618 -0.160760506271 +1403636977901666560.0000000000 2.0652423493 3.2646052899 -0.6682282096 0.5534575364 0.7917850028 0.2022855338 -0.160753934683 +1403636977951666432.0000000000 2.0752051378 3.2843913104 -0.6815125584 0.5550141906 0.7913028940 0.2011122267 -0.159225784627 +1403636978001666560.0000000000 2.0862780897 3.3037899565 -0.6931711915 0.5568977648 0.7904261487 0.2007334956 -0.157472050546 +1403636978051666432.0000000000 2.0983277044 3.3231825897 -0.7025903874 0.5589477369 0.7894867069 0.2014097206 -0.15402042529 +1403636978101666560.0000000000 2.1104632187 3.3432412025 -0.7104877404 0.5598673535 0.7892433491 0.2021681433 -0.150902366725 +1403636978151666432.0000000000 2.1225061688 3.3635614757 -0.7160225146 0.5595838807 0.7897188619 0.2022811919 -0.149306125504 +1403636978201666560.0000000000 2.1351340451 3.3838101417 -0.7199779249 0.5593024916 0.7902136781 0.2032885570 -0.146344895489 +1403636978251666432.0000000000 2.1483677281 3.4034920320 -0.7225173179 0.5576617878 0.7916148096 0.2039846356 -0.1440471872 +1403636978301666560.0000000000 2.1619060154 3.4226767501 -0.7236019262 0.5571568355 0.7921220958 0.2047944197 -0.142049609758 +1403636978351666432.0000000000 2.1750092319 3.4421307821 -0.7227090841 0.5553575575 0.7936252909 0.2049767691 -0.140432920052 +1403636978401666560.0000000000 2.1878163883 3.4614380293 -0.7195428391 0.5533251392 0.7951395451 0.2058318625 -0.138627697113 +1403636978451666432.0000000000 2.2003676991 3.4806912751 -0.7150587994 0.5503107130 0.7973450060 0.2073398081 -0.135680745134 +1403636978501666560.0000000000 2.2122617692 3.5001179705 -0.7104527021 0.5461622251 0.8003606907 0.2077853849 -0.133995605763 +1403636978551666432.0000000000 2.2235018777 3.5198879886 -0.7064243063 0.5424821966 0.8029768647 0.2087849652 -0.131719624582 +1403636978601666560.0000000000 2.2337756199 3.5401985393 -0.7037769880 0.5383406582 0.8059719916 0.2087389157 -0.130485821131 +1403636978651666432.0000000000 2.2432882367 3.5613861201 -0.7023766374 0.5355533982 0.8079735986 0.2091540141 -0.12890236635 +1403636978701666560.0000000000 2.2516597499 3.5835462341 -0.7023924114 0.5336005652 0.8093514131 0.2095010019 -0.127789111926 +1403636978751666432.0000000000 2.2590061024 3.6066083203 -0.7038070132 0.5316655920 0.8107108097 0.2097613755 -0.126806335787 +1403636978801666560.0000000000 2.2651073847 3.6310138155 -0.7063196347 0.5306234550 0.8114847050 0.2099166808 -0.125961540097 +1403636978851666432.0000000000 2.2696247925 3.6567623972 -0.7093517895 0.5320349075 0.8105445292 0.2097130069 -0.126399676232 +1403636978901666560.0000000000 2.2730372447 3.6840334075 -0.7130739126 0.5354247632 0.8083952566 0.2086722866 -0.127566880369 +1403636978951666432.0000000000 2.2753233604 3.7126511385 -0.7177120431 0.5402679079 0.8051673360 0.2082010830 -0.128329488827 +1403636979001666560.0000000000 2.2766343537 3.7420410030 -0.7232026757 0.5478094883 0.8001251552 0.2069939306 -0.129838411922 +1403636979051666432.0000000000 2.2774378201 3.7714716732 -0.7305918303 0.5543935333 0.7956403860 0.2057802451 -0.131372284425 +1403636979101666560.0000000000 2.2779481957 3.8005697261 -0.7402195024 0.5595068234 0.7920294600 0.2050081651 -0.132714360024 +1403636979151666432.0000000000 2.2780007931 3.8291338047 -0.7513430237 0.5632123146 0.7893847710 0.2044145946 -0.133709556653 +1403636979201666560.0000000000 2.2777751835 3.8569423506 -0.7642260441 0.5637468557 0.7889866842 0.2042967581 -0.133986303435 +1403636979251666432.0000000000 2.2773118480 3.8837873970 -0.7782801786 0.5604527680 0.7912176804 0.2050609480 -0.13348140159 +1403636979301666560.0000000000 2.2765709768 3.9102989301 -0.7911536132 0.5564396733 0.7940121201 0.2062714083 -0.131801931865 +1403636979351666432.0000000000 2.2751533968 3.9368810601 -0.8026427503 0.5520323838 0.7970285310 0.2073141392 -0.130486074584 +1403636979401666560.0000000000 2.2726545975 3.9641262885 -0.8125910698 0.5480985660 0.7996346207 0.2088745136 -0.128622987728 +1403636979451666432.0000000000 2.2693823435 3.9916646220 -0.8202245093 0.5443462101 0.8022063650 0.2092638146 -0.12790937147 +1403636979501666560.0000000000 2.2655062551 4.0191926181 -0.8255593826 0.5414218727 0.8041238433 0.2094051596 -0.128049519776 +1403636979551666432.0000000000 2.2609912842 4.0471858144 -0.8294038307 0.5391395822 0.8057032005 0.2100110878 -0.126752541153 +1403636979601666560.0000000000 2.2551335272 4.0762545026 -0.8307840212 0.5383373141 0.8063063858 0.2096544932 -0.126917067528 +1403636979651666432.0000000000 2.2482066973 4.1064215413 -0.8306170469 0.5372871596 0.8071761763 0.2091120611 -0.126733083397 +1403636979701666560.0000000000 2.2407397380 4.1374031406 -0.8297350176 0.5374043935 0.8072836265 0.2101416919 -0.123814916322 +1403636979751666432.0000000000 2.2318780616 4.1690393735 -0.8273490528 0.5367731207 0.8079280544 0.2096126852 -0.12324527594 +1403636979801666560.0000000000 2.2215772848 4.2021856842 -0.8229712197 0.5392286173 0.8065422647 0.2087754877 -0.123023856859 +1403636979851666432.0000000000 2.2100579684 4.2365791550 -0.8170380842 0.5436466625 0.8039181895 0.2076623516 -0.122638487637 +1403636979901666560.0000000000 2.1972196928 4.2713788049 -0.8108499054 0.5469604960 0.8020176425 0.2056459156 -0.12374035091 +1403636979951666432.0000000000 2.1835759375 4.3066533627 -0.8056729179 0.5509580397 0.7996276990 0.2045866528 -0.123227768598 +1403636980001666560.0000000000 2.1691831456 4.3418876407 -0.8024305138 0.5530510260 0.7984913000 0.2037584482 -0.122591603361 +1403636980051666432.0000000000 2.1544687602 4.3767994051 -0.8007488091 0.5546624909 0.7976614061 0.2031257547 -0.121760954975 +1403636980101666560.0000000000 2.1392304388 4.4116176187 -0.8006276783 0.5559158788 0.7970380231 0.2022233442 -0.121629127306 +1403636980151666432.0000000000 2.1233791372 4.4462231666 -0.8017388524 0.5569936408 0.7965526932 0.2010434567 -0.121833573144 +1403636980201666560.0000000000 2.1068016959 4.4806625620 -0.8043659767 0.5573452379 0.7965570926 0.2000652851 -0.12180708355 +1403636980251666432.0000000000 2.0895960572 4.5147584779 -0.8082031778 0.5576684390 0.7965141162 0.1988974623 -0.12251928103 +1403636980301666560.0000000000 2.0718609402 4.5487585127 -0.8130485983 0.5597415396 0.7953211287 0.1968780465 -0.124067505347 +1403636980351666432.0000000000 2.0540706741 4.5822686522 -0.8192671710 0.5623417938 0.7935981514 0.1959284758 -0.124842754588 +1403636980401666560.0000000000 2.0358028060 4.6152318547 -0.8267006491 0.5647842283 0.7919536293 0.1936470193 -0.12778519644 +1403636980451666432.0000000000 2.0175822890 4.6478353788 -0.8357832808 0.5670503160 0.7903683404 0.1927921036 -0.128852747256 +1403636980501666560.0000000000 1.9992570300 4.6796529359 -0.8458782650 0.5684642711 0.7893703616 0.1907558297 -0.131738446148 +1403636980551666432.0000000000 1.9812409770 4.7104529306 -0.8569658479 0.5690238010 0.7888219232 0.1896315352 -0.13420792939 +1403636980601666560.0000000000 1.9637111758 4.7399241580 -0.8684172420 0.5695678293 0.7883055363 0.1879060232 -0.137325146146 +1403636980651666432.0000000000 1.9469466680 4.7684761990 -0.8793696089 0.5697837810 0.7879845703 0.1868210907 -0.13973059779 +1403636980701666560.0000000000 1.9306666936 4.7971702845 -0.8887290122 0.5704770582 0.7872888883 0.1880101684 -0.139227544055 +1403636980751666432.0000000000 1.9149952359 4.8253257021 -0.8965235066 0.5693075293 0.7879704503 0.1891588029 -0.13860178139 +1403636980801666560.0000000000 1.8999680182 4.8531349419 -0.9027407379 0.5681120744 0.7886496481 0.1926280197 -0.134814129333 +1403636980851666432.0000000000 1.8853132909 4.8797964551 -0.9072372079 0.5654371992 0.7902471335 0.1956124320 -0.132385868676 +1403636980901666560.0000000000 1.8701677715 4.9070346032 -0.9092527846 0.5627268152 0.7919669515 0.1981963054 -0.129788689018 +1403636980951666432.0000000000 1.8551042894 4.9338043125 -0.9099668689 0.5613222290 0.7927025654 0.2010647351 -0.126936875443 +1403636981001666560.0000000000 1.8398488677 4.9595491106 -0.9100944435 0.5601993301 0.7933060031 0.2024054425 -0.125993384129 +1403636981051666432.0000000000 1.8237594122 4.9853959522 -0.9110269289 0.5600529300 0.7933142933 0.2030184300 -0.125605194032 +1403636981101666560.0000000000 1.8071068940 5.0104885166 -0.9125779010 0.5609283360 0.7927092942 0.2019194450 -0.127278885219 +1403636981151666432.0000000000 1.7900410778 5.0350643136 -0.9155526895 0.5609510641 0.7927547211 0.1998714622 -0.130097095953 +1403636981201666560.0000000000 1.7727622611 5.0592126767 -0.9194639471 0.5610221454 0.7928844171 0.1966265847 -0.13388965484 +1403636981251666432.0000000000 1.7553316609 5.0831918030 -0.9239086314 0.5610480474 0.7930950568 0.1916199561 -0.139667862297 +1403636981301666560.0000000000 1.7382785173 5.1071418616 -0.9291255138 0.5615272524 0.7928865894 0.1865051230 -0.145718358957 +1403636981351666432.0000000000 1.7221001363 5.1310852574 -0.9354007809 0.5617048978 0.7928560492 0.1818310003 -0.151011192839 +1403636981401666560.0000000000 1.7071181279 5.1550355764 -0.9434723050 0.5616380411 0.7930754526 0.1796196061 -0.152744343264 +1403636981451666432.0000000000 1.6936629177 5.1789956512 -0.9534340487 0.5617818885 0.7933125720 0.1805325651 -0.149880838616 +1403636981501666560.0000000000 1.6814030342 5.2029566172 -0.9640978135 0.5618291668 0.7937153795 0.1829057998 -0.144600664005 +1403636981551666432.0000000000 1.6702662919 5.2268888595 -0.9745290373 0.5619153288 0.7940766329 0.1866031853 -0.13737800278 +1403636981601666560.0000000000 1.6596428461 5.2506089248 -0.9835691347 0.5608557460 0.7951293581 0.1906089751 -0.129916722335 +1403636981651666432.0000000000 1.6487429362 5.2746470679 -0.9903558472 0.5599862684 0.7960317630 0.1935159456 -0.123694746767 +1403636981701666560.0000000000 1.6376453280 5.2980183423 -0.9947810911 0.5590533546 0.7969482867 0.1950968914 -0.119457013037 +1403636981751666432.0000000000 1.6261622369 5.3211291781 -0.9971370986 0.5584647508 0.7976861583 0.1959197636 -0.115885121014 +1403636981801666560.0000000000 1.6139821421 5.3441721501 -0.9974810013 0.5559266853 0.7997265181 0.1963710769 -0.113231695779 +1403636981851666432.0000000000 1.6010105615 5.3672610694 -0.9957148238 0.5531331965 0.8019416895 0.1966718378 -0.110694994372 +1403636981901666560.0000000000 1.5870776441 5.3904669925 -0.9915469313 0.5499969233 0.8043579617 0.1968044681 -0.108534119891 +1403636981951666432.0000000000 1.5719497008 5.4138208436 -0.9864146489 0.5453527360 0.8078351542 0.1960910843 -0.107429249885 +1403636982001666560.0000000000 1.5558147418 5.4377212952 -0.9815753430 0.5409517255 0.8110002121 0.1956603397 -0.106615749364 +1403636982051666432.0000000000 1.5385878334 5.4623592357 -0.9776358580 0.5362724092 0.8143487169 0.1946257031 -0.106625073166 +1403636982101666560.0000000000 1.5201578982 5.4879808736 -0.9748305046 0.5321904291 0.8171911135 0.1939731834 -0.106519647718 +1403636982151666432.0000000000 1.5004558352 5.5147688532 -0.9727613093 0.5292337054 0.8192702104 0.1927197520 -0.10755047497 +1403636982201666560.0000000000 1.4795986739 5.5428995789 -0.9715962316 0.5276006454 0.8204930855 0.1911111442 -0.109110889135 +1403636982251666432.0000000000 1.4574270117 5.5725208105 -0.9712620376 0.5272921139 0.8207997549 0.1887065774 -0.112430497152 +1403636982301666560.0000000000 1.4343202624 5.6037795510 -0.9719213292 0.5280238256 0.8204281001 0.1859138215 -0.116295412688 +1403636982351666432.0000000000 1.4107482565 5.6367013380 -0.9736105864 0.5310088457 0.8184937262 0.1838608190 -0.119552604189 +1403636982401666560.0000000000 1.3867463927 5.6714499637 -0.9755263489 0.5357189282 0.8153972559 0.1815970299 -0.123105905185 +1403636982451666432.0000000000 1.3629152413 5.7074184020 -0.9765399505 0.5419932590 0.8111374903 0.1799145347 -0.126214259293 +1403636982501666560.0000000000 1.3393651384 5.7445524272 -0.9759746650 0.5478452051 0.8069741350 0.1783492112 -0.129807301488 +1403636982551666432.0000000000 1.3161572798 5.7830272545 -0.9736627449 0.5531447698 0.8031578617 0.1784889671 -0.130805204605 +1403636982601666560.0000000000 1.2934827564 5.8220160465 -0.9707480532 0.5552748436 0.8014727529 0.1791483770 -0.131214074599 +1403636982651666432.0000000000 1.2710880298 5.8615209202 -0.9665647637 0.5546049709 0.8016642020 0.1794514843 -0.132457533949 +1403636982701666560.0000000000 1.2492866992 5.9013326462 -0.9614805486 0.5538700746 0.8019022561 0.1798659123 -0.133525150192 +1403636982751666432.0000000000 1.2284494910 5.9411701281 -0.9568451422 0.5516674766 0.8031626635 0.1821258152 -0.131995904129 +1403636982801666560.0000000000 1.2081551812 5.9812336962 -0.9522070056 0.5497975711 0.8041084619 0.1841178797 -0.131273831412 +1403636982851666432.0000000000 1.1885350372 6.0216841716 -0.9486039551 0.5480700365 0.8051690965 0.1856594618 -0.129817276824 +1403636982901666560.0000000000 1.1693169982 6.0625517406 -0.9463953755 0.5468353513 0.8058804970 0.1878147156 -0.127488649414 +1403636982951666432.0000000000 1.1498614115 6.1039181505 -0.9452019608 0.5477356707 0.8051365221 0.1890297761 -0.126524936253 +1403636983001666560.0000000000 1.1301169063 6.1458515636 -0.9454639567 0.5489200527 0.8042679415 0.1898052173 -0.125753065235 +1403636983051666432.0000000000 1.1101493842 6.1882446084 -0.9471661523 0.5522520549 0.8018973417 0.1899516764 -0.126082044372 +1403636983101666560.0000000000 1.0901762583 6.2305017162 -0.9502274212 0.5550883403 0.7999265352 0.1898499973 -0.12629905502 +1403636983151666432.0000000000 1.0703406970 6.2731342437 -0.9549828227 0.5576945020 0.7980927165 0.1903492422 -0.125666321322 +1403636983201666560.0000000000 1.0507948608 6.3158208423 -0.9611353144 0.5596016564 0.7967488588 0.1915878304 -0.123819810087 +1403636983251666432.0000000000 1.0311974935 6.3585914197 -0.9684579211 0.5614285839 0.7954326296 0.1922654466 -0.122958834151 +1403636983301666560.0000000000 1.0115821726 6.4011298609 -0.9771014169 0.5629138989 0.7944847053 0.1929051919 -0.121283067298 +1403636983351666432.0000000000 0.9919369396 6.4434817312 -0.9867197327 0.5636296445 0.7940512440 0.1926715625 -0.121168951351 +1403636983401666560.0000000000 0.9725031083 6.4854449023 -0.9972692635 0.5649075230 0.7932273898 0.1932949712 -0.119611256203 +1403636983451666432.0000000000 0.9526882860 6.5270127307 -1.0077765254 0.5653133702 0.7930784069 0.1925583011 -0.11986965683 +1403636983501666560.0000000000 0.9329213486 6.5679298630 -1.0177188859 0.5645663488 0.7937499191 0.1922470320 -0.119444473756 +1403636983551666432.0000000000 0.9132342618 6.6082338195 -1.0261764236 0.5634123438 0.7947146725 0.1922695839 -0.11843786271 +1403636983601666560.0000000000 0.8933136872 6.6475692097 -1.0332059807 0.5619113501 0.7959622451 0.1926193455 -0.116608433221 +1403636983651666432.0000000000 0.8730480568 6.6862397296 -1.0388510519 0.5587544134 0.7983446908 0.1928256316 -0.11514137422 +1403636983701666560.0000000000 0.8520994890 6.7251512688 -1.0420139914 0.5566307319 0.8000449037 0.1928019519 -0.113656445578 +1403636983751666432.0000000000 0.8303657079 6.7637976506 -1.0423218348 0.5542855709 0.8018599475 0.1930133230 -0.111955293351 +1403636983801666560.0000000000 0.8078247464 6.8027603498 -1.0407846380 0.5529987291 0.8028972399 0.1935344435 -0.109967481654 +1403636983851666432.0000000000 0.7848009294 6.8411449097 -1.0375918710 0.5508360923 0.8046055721 0.1934429936 -0.108486316799 +1403636983901666560.0000000000 0.7611349110 6.8791765710 -1.0328963452 0.5494561588 0.8056696267 0.1933880528 -0.107682139594 +1403636983951666432.0000000000 0.7364941289 6.9175249387 -1.0268645920 0.5481427277 0.8068524651 0.1924744326 -0.107155225911 +1403636984001666560.0000000000 0.7108731538 6.9560961093 -1.0188597133 0.5469929405 0.8078462517 0.1918853141 -0.106598231604 +1403636984051666432.0000000000 0.6843996923 6.9949867867 -1.0100732953 0.5454507975 0.8091043194 0.1912123653 -0.106167128947 +1403636984101666560.0000000000 0.6570325865 7.0344811300 -1.0013824795 0.5451644732 0.8095436329 0.1905822814 -0.10541915199 +1403636984151666432.0000000000 0.6290584411 7.0746964471 -0.9938876528 0.5466287450 0.8087367796 0.1899241506 -0.105217172436 +1403636984201666560.0000000000 0.6004123438 7.1154571580 -0.9879127492 0.5490032363 0.8073767694 0.1890134304 -0.104938657954 +1403636984251666432.0000000000 0.5708095440 7.1564863409 -0.9835542157 0.5522474710 0.8054351557 0.1873018646 -0.10590067169 +1403636984301666560.0000000000 0.5407140578 7.1978412234 -0.9816252982 0.5551192584 0.8036287749 0.1869477905 -0.105232717128 +1403636984351666432.0000000000 0.5100477449 7.2395409489 -0.9815230178 0.5574045163 0.8022831336 0.1854131437 -0.106131733732 +1403636984401666560.0000000000 0.4788427296 7.2810929730 -0.9836757055 0.5588511905 0.8014514929 0.1848124638 -0.105854638836 +1403636984451666432.0000000000 0.4471200104 7.3225710696 -0.9874334293 0.5608579127 0.8001798895 0.1844888960 -0.105424823536 +1403636984501666560.0000000000 0.4148891313 7.3637605437 -0.9925336869 0.5625466094 0.7991692480 0.1836992013 -0.105472407532 +1403636984551666432.0000000000 0.3821871139 7.4044192424 -0.9987959450 0.5632362649 0.7987435929 0.1835794826 -0.105224314023 +1403636984601666560.0000000000 0.3489012511 7.4445592598 -1.0045989421 0.5639633528 0.7982468933 0.1834565852 -0.105313414633 +1403636984651666432.0000000000 0.3150965088 7.4842773600 -1.0090085758 0.5641363806 0.7981081414 0.1835190007 -0.105329554174 +1403636984701666560.0000000000 0.2809125197 7.5232983427 -1.0116462817 0.5647682727 0.7975768720 0.1839591368 -0.105199654517 +1403636984751666432.0000000000 0.2461453554 7.5618361412 -1.0125243741 0.5650883620 0.7972669657 0.1833056636 -0.106955889288 +1403636984801666560.0000000000 0.2110013852 7.6001267993 -1.0121778765 0.5651730263 0.7972006425 0.1822204327 -0.108840708062 +1403636984851666432.0000000000 0.1757020708 7.6376670310 -1.0107685964 0.5644165481 0.7977077276 0.1808060475 -0.111380046788 +1403636984901666560.0000000000 0.1405715394 7.6745126960 -1.0080330356 0.5637447195 0.7982109035 0.1789879083 -0.114081432956 +1403636984951666432.0000000000 0.1058233351 7.7106449192 -1.0040508546 0.5641152400 0.7979650943 0.1780906455 -0.115366486591 +1403636985001666560.0000000000 0.0715715963 7.7457212721 -0.9990280346 0.5638270776 0.7981589401 0.1778218250 -0.115847880948 +1403636985051666432.0000000000 0.0376573256 7.7806349127 -0.9935460996 0.5635924143 0.7983569052 0.1777402677 -0.115750765605 +1403636985101666560.0000000000 0.0037427125 7.8157809964 -0.9884589326 0.5637417642 0.7982851914 0.1785704129 -0.114230399414 +1403636985151666432.0000000000 -0.0298545751 7.8500499882 -0.9859273577 0.5628495816 0.7989341859 0.1797687609 -0.112194953881 +1403636985201666560.0000000000 -0.0638162288 7.8846993628 -0.9859338464 0.5635481937 0.7984795868 0.1803784185 -0.110938762121 +1403636985251666432.0000000000 -0.0976941671 7.9184845603 -0.9898112782 0.5642053443 0.7980826202 0.1808901043 -0.10961400895 +1403636985301666560.0000000000 -0.1319485036 7.9521766269 -0.9968568660 0.5647086682 0.7977927843 0.1810844855 -0.108808099477 +1403636985351666432.0000000000 -0.1665638172 7.9854911109 -1.0051900648 0.5646615762 0.7975713757 0.1823073572 -0.108633477581 +1403636985401666560.0000000000 -0.2015780981 8.0178926459 -1.0130196817 0.5644769841 0.7970293608 0.1848977269 -0.109191404988 +1403636985451666432.0000000000 -0.2371892094 8.0498180490 -1.0199134204 0.5635431559 0.7964990585 0.1897420882 -0.109573268527 +1403636985501666560.0000000000 -0.2734004380 8.0811559083 -1.0244177726 0.5632096339 0.7952471286 0.1949565536 -0.111215353961 +1403636985551666432.0000000000 -0.3100917971 8.1118124137 -1.0270123431 0.5632530476 0.7937650394 0.1995449915 -0.113423379238 +1403636985601666560.0000000000 -0.3471419612 8.1417057443 -1.0280054300 0.5637738462 0.7921043543 0.2039137530 -0.114668756086 +1403636985651666432.0000000000 -0.3847951310 8.1706866486 -1.0272006234 0.5643650084 0.7904390827 0.2085052265 -0.114994627418 +1403636985701666560.0000000000 -0.4229791798 8.1987067019 -1.0245829589 0.5657046628 0.7884746106 0.2119365086 -0.115624129146 +1403636985751666432.0000000000 -0.4618527624 8.2256137912 -1.0201346820 0.5673437656 0.7863828881 0.2147031896 -0.116728511045 +1403636985801666560.0000000000 -0.5013780959 8.2515125480 -1.0144050362 0.5693415857 0.7841014434 0.2168438069 -0.118380102276 +1403636985851666432.0000000000 -0.5416914755 8.2766392099 -1.0074693872 0.5751297851 0.7792401128 0.2173644494 -0.121504210103 +1403636985901666560.0000000000 -0.5826249862 8.3007613350 -1.0011200191 0.5832025630 0.7726549709 0.2171742102 -0.125357205167 +1403636985951666432.0000000000 -0.6238984353 8.3233129188 -0.9960520907 0.5923583872 0.7652228106 0.2160867468 -0.129815673157 +1403636986001666560.0000000000 -0.6645925431 8.3434549813 -0.9937810553 0.5982347340 0.7602754306 0.2160883985 -0.131917689175 +1403636986051666432.0000000000 -0.7044691897 8.3610797419 -0.9942696782 0.6009172259 0.7579215448 0.2171777335 -0.131480992971 +1403636986101666560.0000000000 -0.7439555701 8.3758164088 -0.9969712801 0.5995889228 0.7586912154 0.2176210399 -0.132370111507 +1403636986151666432.0000000000 -0.7830313832 8.3879844507 -1.0021026575 0.5944865139 0.7625004447 0.2188244228 -0.13150942434 +1403636986201666560.0000000000 -0.8218448499 8.3977562537 -1.0084407815 0.5883270129 0.7671437190 0.2196821831 -0.130773004541 +1403636986251666432.0000000000 -0.8601371145 8.4054058442 -1.0164210595 0.5808315364 0.7727195650 0.2217373096 -0.12795220113 +1403636986301666560.0000000000 -0.8987383905 8.4115634301 -1.0245218409 0.5754397908 0.7766620600 0.2224722264 -0.127166033866 +1403636986351666432.0000000000 -0.9376450556 8.4167236137 -1.0331537093 0.5714391388 0.7795108397 0.2238218487 -0.125395141284 +1403636986401666560.0000000000 -0.9772839208 8.4203758270 -1.0420361369 0.5677620147 0.7821919192 0.2228181951 -0.127177624322 +1403636986451666432.0000000000 -1.0175030054 8.4232582860 -1.0507934057 0.5651975498 0.7841018257 0.2208914520 -0.13016536764 +1403636986501666560.0000000000 -1.0580803455 8.4253510259 -1.0588189453 0.5627661591 0.7858584175 0.2192132461 -0.132914824504 +1403636986551666432.0000000000 -1.0990898781 8.4270144470 -1.0642530192 0.5615190766 0.7867774690 0.2166724982 -0.136859670128 +1403636986601666560.0000000000 -1.1395202648 8.4275136552 -1.0678784592 0.5604095467 0.7875012081 0.2151721789 -0.139584815023 +1403636986651666432.0000000000 -1.1793367347 8.4275171441 -1.0694081558 0.5595460324 0.7880932295 0.2141717838 -0.141236490632 +1403636986701666560.0000000000 -1.2189691760 8.4273577227 -1.0683558481 0.5585542136 0.7887829081 0.2121461153 -0.144335512611 +1403636986751666432.0000000000 -1.2583491018 8.4277238395 -1.0649391407 0.5581445917 0.7889876134 0.2107315672 -0.146851514304 +1403636986801666560.0000000000 -1.2972879107 8.4283775463 -1.0593051745 0.5569520382 0.7898384189 0.2085868755 -0.149837293622 +1403636986851666432.0000000000 -1.3351290991 8.4291273870 -1.0514889347 0.5578917644 0.7891594927 0.2078739677 -0.150905559284 +1403636986901666560.0000000000 -1.3720745410 8.4300457028 -1.0413245108 0.5577308914 0.7893901051 0.2069676927 -0.151538407501 +1403636986951666432.0000000000 -1.4082588515 8.4314718753 -1.0289642971 0.5588392330 0.7886242924 0.2074349102 -0.150801840944 +1403636987001666560.0000000000 -1.4435266441 8.4331369151 -1.0145118778 0.5596517594 0.7882157214 0.2076891534 -0.149569717393 +1403636987051666432.0000000000 -1.4775203399 8.4344550486 -0.9986223771 0.5612819971 0.7873093537 0.2088915338 -0.14652927475 +1403636987101666560.0000000000 -1.5109494161 8.4353643704 -0.9824460256 0.5625199913 0.7866151661 0.2094375304 -0.144719593334 +1403636987151666432.0000000000 -1.5438306230 8.4360270108 -0.9669851317 0.5634091883 0.7861933141 0.2093543278 -0.143669498705 +1403636987201666560.0000000000 -1.5760112234 8.4364835228 -0.9526822070 0.5646704760 0.7855483380 0.2090538346 -0.142679908888 +1403636987251666432.0000000000 -1.6077436854 8.4365836381 -0.9398176891 0.5653265907 0.7853302150 0.2074300966 -0.143649065935 +1403636987301666560.0000000000 -1.6387369727 8.4365213967 -0.9290581177 0.5667210872 0.7845833934 0.2073384537 -0.14236177065 +1403636987351666432.0000000000 -1.6693875429 8.4358945956 -0.9199831258 0.5671282037 0.7843189316 0.2070620233 -0.142599903673 +1403636987401666560.0000000000 -1.6997650290 8.4346923828 -0.9121207298 0.5683764586 0.7831492887 0.2072313222 -0.143807413347 +1403636987451666432.0000000000 -1.7296943045 8.4328402057 -0.9060111742 0.5695841808 0.7816312419 0.2094860316 -0.14402105801 +1403636987501666560.0000000000 -1.7592317617 8.4305121420 -0.9004045481 0.5728708641 0.7786360984 0.2108037287 -0.145281063172 +1403636987551666432.0000000000 -1.7881395643 8.4272526738 -0.8962377818 0.5757417561 0.7760000613 0.2130669194 -0.144733627914 +1403636987601666560.0000000000 -1.8164208338 8.4227713500 -0.8930147536 0.5781951042 0.7736176757 0.2145337595 -0.145538239899 +1403636987651666432.0000000000 -1.8439641744 8.4169458065 -0.8910069546 0.5794443043 0.7722299422 0.2155640638 -0.146414989188 +1403636987701666560.0000000000 -1.8708336651 8.4098400468 -0.8894333042 0.5802633154 0.7711450274 0.2169392425 -0.146857742815 +1403636987751666432.0000000000 -1.8970312355 8.4011631815 -0.8871306104 0.5803474860 0.7705805150 0.2179572286 -0.147976727566 +1403636987801666560.0000000000 -1.9225442762 8.3910438427 -0.8834038209 0.5798498701 0.7704532384 0.2184802305 -0.149807624924 +1403636987851666432.0000000000 -1.9473681216 8.3798795529 -0.8774411237 0.5791688681 0.7705565102 0.2190480676 -0.151076242255 +1403636987901666560.0000000000 -1.9711777560 8.3669836587 -0.8695961395 0.5771592414 0.7716931356 0.2181880859 -0.154178058392 +1403636987951666432.0000000000 -1.9940595803 8.3529838503 -0.8606322050 0.5744027628 0.7733654486 0.2174180982 -0.157151899917 +1403636988001666560.0000000000 -2.0163388474 8.3382936716 -0.8508454694 0.5704750347 0.7759794276 0.2158543395 -0.160689348904 +1403636988051666432.0000000000 -2.0373731814 8.3229765370 -0.8416849726 0.5663197546 0.7789049507 0.2141700517 -0.163463152401 +1403636988101666560.0000000000 -2.0574275520 8.3073599687 -0.8337893448 0.5627051503 0.7813805861 0.2124276124 -0.166378493084 +1403636988151666432.0000000000 -2.0761913843 8.2917209541 -0.8274619775 0.5598170896 0.7834524743 0.2111148521 -0.168040370025 +1403636988201666560.0000000000 -2.0938049086 8.2762998432 -0.8221845934 0.5581782238 0.7846228747 0.2091782923 -0.170436079189 +1403636988251666432.0000000000 -2.1100109158 8.2613573951 -0.8179597869 0.5582028199 0.7846402236 0.2074394604 -0.172389679618 +1403636988301666560.0000000000 -2.1250013298 8.2468716094 -0.8139540054 0.5604427012 0.7830940653 0.2047260283 -0.17537079861 +1403636988351666432.0000000000 -2.1382224142 8.2328755979 -0.8097641637 0.5644230241 0.7803235214 0.2028857367 -0.177085373923 +1403636988401666560.0000000000 -2.1497020558 8.2193002202 -0.8041956735 0.5681671987 0.7776131323 0.2010979480 -0.17906274374 +1403636988451666432.0000000000 -2.1587682537 8.2055339187 -0.7971350098 0.5716791513 0.7750409005 0.2008994675 -0.179259461432 +1403636988501666560.0000000000 -2.1651988540 8.1907570274 -0.7879824987 0.5747822732 0.7727762029 0.2006840685 -0.179354908983 +1403636988551666432.0000000000 -2.1692410640 8.1751463535 -0.7772776260 0.5764032515 0.7715010021 0.2002397361 -0.180137568304 +1403636988601666560.0000000000 -2.1707787674 8.1587209261 -0.7655495494 0.5777025312 0.7704739753 0.1999888165 -0.180649140843 +1403636988651666432.0000000000 -2.1701862511 8.1417020017 -0.7538770315 0.5781748220 0.7700813104 0.1997483659 -0.181077996937 +1403636988701666560.0000000000 -2.1676819188 8.1242106728 -0.7431674611 0.5787015362 0.7696465506 0.1993085475 -0.18172732875 +1403636988751666432.0000000000 -2.1630589620 8.1060738354 -0.7338323242 0.5800983056 0.7686329469 0.1999340172 -0.180874922153 +1403636988801666560.0000000000 -2.1565982312 8.0871374373 -0.7255788026 0.5813557798 0.7676150922 0.1992553298 -0.181906132758 +1403636988851666432.0000000000 -2.1479085958 8.0673549621 -0.7188048500 0.5825031387 0.7666553635 0.1986097653 -0.18298581426 +1403636988901666560.0000000000 -2.1369789629 8.0469565520 -0.7132201369 0.5838954106 0.7655519131 0.1976751698 -0.184176396848 +1403636988951666432.0000000000 -2.1238741453 8.0257020452 -0.7088198496 0.5850745437 0.7645739620 0.1963516019 -0.185904500751 +1403636989001666560.0000000000 -2.1081560547 8.0035946960 -0.7057373664 0.5861847480 0.7637630305 0.1955804372 -0.186552317151 +1403636989051666432.0000000000 -2.0898561733 7.9802012553 -0.7036213325 0.5871511665 0.7629957356 0.1939363117 -0.18836061725 +1403636989101666560.0000000000 -2.0686147387 7.9558666744 -0.7027681761 0.5875952890 0.7627680836 0.1937726575 -0.188065903728 +1403636989151666432.0000000000 -2.0449203945 7.9305511148 -0.7025856858 0.5875652294 0.7628513654 0.1930301677 -0.188584861155 +1403636989201666560.0000000000 -2.0186451228 7.9042617294 -0.7027441085 0.5873122936 0.7632249794 0.1930588533 -0.18783018865 +1403636989251666432.0000000000 -1.9894044704 7.8769468552 -0.7026582099 0.5859403438 0.7645930178 0.1949217266 -0.184599434041 +1403636989301666560.0000000000 -1.9576468878 7.8491839083 -0.7020068086 0.5832613060 0.7672218423 0.1983924753 -0.178374099395 +1403636989351666432.0000000000 -1.9242133062 7.8212713746 -0.6992187972 0.5801056380 0.7700519918 0.2025924625 -0.171620723877 +1403636989401666560.0000000000 -1.8886366466 7.7915753893 -0.6945482781 0.5753330506 0.7740016590 0.2061280554 -0.165603555153 +1403636989451666432.0000000000 -1.8521436980 7.7615420501 -0.6873296825 0.5703049253 0.7779382569 0.2088108518 -0.161128485387 +1403636989501666560.0000000000 -1.8145345621 7.7305047049 -0.6780276263 0.5670390267 0.7804870964 0.2103748035 -0.158269000902 +1403636989551666432.0000000000 -1.7765932646 7.6997361787 -0.6671354291 0.5644690854 0.7825599127 0.2117986853 -0.155293115053 +1403636989601666560.0000000000 -1.7380457878 7.6685079864 -0.6552922335 0.5638223120 0.7830828860 0.2133889279 -0.152809553198 +1403636989651666432.0000000000 -1.6991548708 7.6373950384 -0.6444969975 0.5625986234 0.7839947014 0.2154571639 -0.149710746701 +1403636989701666560.0000000000 -1.6604824347 7.6063438203 -0.6347395002 0.5624399427 0.7841343395 0.2174648327 -0.146641382402 +1403636989751666432.0000000000 -1.6219683219 7.5751205017 -0.6264054113 0.5621577456 0.7843297798 0.2189535407 -0.144446573843 +1403636989801666560.0000000000 -1.5839134548 7.5436928100 -0.6193627160 0.5615825615 0.7847506943 0.2192182676 -0.143995574848 +1403636989851666432.0000000000 -1.5463290533 7.5124024232 -0.6137677928 0.5618516076 0.7845174320 0.2190920369 -0.144408619238 +1403636989901666560.0000000000 -1.5091495834 7.4813176710 -0.6092499599 0.5632139863 0.7835360643 0.2182775646 -0.145657633839 +1403636989951666432.0000000000 -1.4722201168 7.4501769618 -0.6056489744 0.5662648581 0.7813816445 0.2168563715 -0.147513220483 +1403636990001666560.0000000000 -1.4353436663 7.4187183425 -0.6030727449 0.5687216373 0.7795475075 0.2157779292 -0.149336091284 +1403636990051666432.0000000000 -1.3983075676 7.3869453358 -0.5999756379 0.5719040917 0.7772668034 0.2150117139 -0.150173196812 +1403636990101666560.0000000000 -1.3612494371 7.3546286914 -0.5956471670 0.5740058009 0.7756540836 0.2143939119 -0.151371508817 +1403636990151666432.0000000000 -1.3238140486 7.3214180502 -0.5897686446 0.5751176842 0.7747543891 0.2145926230 -0.151477034695 +1403636990201666560.0000000000 -1.2859526756 7.2874545754 -0.5826815843 0.5750853067 0.7747422107 0.2154054918 -0.15050538585 +1403636990251666432.0000000000 -1.2481855150 7.2532289408 -0.5740593710 0.5735334932 0.7757073879 0.2168045072 -0.149442919434 +1403636990301666560.0000000000 -1.2099267790 7.2180160962 -0.5638741795 0.5716297590 0.7769434451 0.2184231129 -0.147951497261 +1403636990351666432.0000000000 -1.1716506467 7.1821584450 -0.5518850810 0.5704211523 0.7776022473 0.2196265297 -0.147372458043 +1403636990401666560.0000000000 -1.1334745859 7.1456175512 -0.5395900533 0.5681484510 0.7789983138 0.2216225574 -0.145782052484 +1403636990451666432.0000000000 -1.0960030755 7.1084555378 -0.5276193303 0.5664925301 0.7798891497 0.2222565294 -0.146496288778 +1403636990501666560.0000000000 -1.0587498756 7.0705519016 -0.5171716001 0.5637404183 0.7815768303 0.2230547328 -0.146904681097 +1403636990551666432.0000000000 -1.0219567171 7.0327129702 -0.5077817798 0.5630891285 0.7817806709 0.2236967603 -0.147341017362 +1403636990601666560.0000000000 -0.9852357333 6.9944072074 -0.4999801709 0.5615196419 0.7826308392 0.2247115349 -0.147273172284 +1403636990651666432.0000000000 -0.9487170623 6.9563973070 -0.4936420165 0.5596896246 0.7836831094 0.2252998838 -0.147743935342 +1403636990701666560.0000000000 -0.9123804958 6.9187925256 -0.4890905174 0.5590568166 0.7838275431 0.2270480389 -0.146693716372 +1403636990751666432.0000000000 -0.8765262670 6.8809111938 -0.4861907822 0.5581222939 0.7842558935 0.2279844510 -0.146510370241 +1403636990801666560.0000000000 -0.8414134511 6.8429446292 -0.4851042984 0.5579820176 0.7841377057 0.2290491958 -0.146015727008 +1403636990851666432.0000000000 -0.8070840031 6.8048194544 -0.4855338008 0.5579901156 0.7839018967 0.2298315323 -0.14602162172 +1403636990901666560.0000000000 -0.7734075995 6.7669030364 -0.4874967090 0.5574591112 0.7841981363 0.2296411204 -0.14675686743 +1403636990951666432.0000000000 -0.7401929869 6.7294755734 -0.4907423714 0.5573696354 0.7842205346 0.2302237440 -0.146062556102 +1403636991001666560.0000000000 -0.7075780864 6.6927424484 -0.4949599993 0.5577945071 0.7838439374 0.2303318314 -0.146291548233 +1403636991051666432.0000000000 -0.6755093614 6.6565126480 -0.5000278173 0.5591373439 0.7828887424 0.2302406135 -0.1464237259 +1403636991101666560.0000000000 -0.6440475510 6.6203062206 -0.5065207917 0.5587051845 0.7832740589 0.2303633911 -0.145818289375 +1403636991151666432.0000000000 -0.6135501156 6.5850418471 -0.5136682605 0.5589554464 0.7832383498 0.2297733220 -0.145981906061 +1403636991201666560.0000000000 -0.5834705043 6.5500678195 -0.5199554001 0.5589306772 0.7833599796 0.2303189858 -0.144557273616 +1403636991251666432.0000000000 -0.5538064296 6.5144574670 -0.5246378386 0.5582703210 0.7839532632 0.2298424291 -0.144651262191 +1403636991301666560.0000000000 -0.5238768544 6.4778521976 -0.5285176909 0.5581873937 0.7840845201 0.2298373100 -0.144267493962 +1403636991351666432.0000000000 -0.4945546043 6.4412486622 -0.5306007936 0.5577618479 0.7846531182 0.2286887891 -0.144646613553 +1403636991401666560.0000000000 -0.4657754261 6.4049615518 -0.5308155694 0.5572109757 0.7851545258 0.2289908587 -0.143567008181 +1403636991451666432.0000000000 -0.4373955271 6.3684397372 -0.5282546832 0.5572092264 0.7853489619 0.2287987598 -0.14281461259 +1403636991501666560.0000000000 -0.4097329134 6.3324230272 -0.5231827363 0.5569891887 0.7858071498 0.2282974722 -0.141952214408 +1403636991551666432.0000000000 -0.3837776709 6.2975123615 -0.5157233820 0.5569386815 0.7860911731 0.2265562602 -0.143360502086 +1403636991601666560.0000000000 -0.3581950199 6.2628537834 -0.5071964385 0.5563093569 0.7869136482 0.2249820984 -0.143770181748 +1403636991651666432.0000000000 -0.3337047950 6.2289616136 -0.4960682954 0.5555251478 0.7878692969 0.2219663782 -0.146235112062 +1403636991701666560.0000000000 -0.3091136132 6.1946687528 -0.4839892254 0.5539267689 0.7894472282 0.2182594234 -0.149335302763 +1403636991751666432.0000000000 -0.2847858447 6.1612725247 -0.4708097034 0.5526478139 0.7907800842 0.2150634791 -0.151640865784 +1403636991801666560.0000000000 -0.2603050660 6.1287495460 -0.4566015121 0.5520677699 0.7916214205 0.2119728405 -0.15370172084 +1403636991851666432.0000000000 -0.2356463177 6.0971192095 -0.4428419412 0.5509870488 0.7928086619 0.2091048575 -0.155379716478 +1403636991901666560.0000000000 -0.2106507248 6.0664888520 -0.4302401299 0.5503555932 0.7936435939 0.2073492565 -0.155707587454 +1403636991951666432.0000000000 -0.1851231345 6.0368985888 -0.4190977944 0.5505742191 0.7938811941 0.2063600834 -0.155036108221 +1403636992001666560.0000000000 -0.1591513216 6.0080510125 -0.4102556550 0.5510737946 0.7939477977 0.2063164770 -0.152964305262 +1403636992051666432.0000000000 -0.1325246206 5.9799540789 -0.4030556025 0.5539243947 0.7923791121 0.2074827139 -0.149177850798 +1403636992101666560.0000000000 -0.1057557524 5.9524233003 -0.3972300647 0.5570643594 0.7905060228 0.2087350909 -0.145633750543 +1403636992151666432.0000000000 -0.0790848133 5.9250893885 -0.3925329948 0.5602787805 0.7884971182 0.2090063680 -0.143792631287 +1403636992201666560.0000000000 -0.0523342613 5.8977746281 -0.3890346933 0.5635527129 0.7864458413 0.2093475824 -0.141721092823 +1403636992251666432.0000000000 -0.0256613061 5.8702067293 -0.3866528885 0.5652227793 0.7854867621 0.2093152247 -0.140431096985 +1403636992301666560.0000000000 0.0009702349 5.8424577877 -0.3853733312 0.5660568327 0.7851452197 0.2092111474 -0.139130665174 +1403636992351666432.0000000000 0.0276093778 5.8144040254 -0.3852861206 0.5655739865 0.7857796074 0.2091174904 -0.137645739607 +1403636992401666560.0000000000 0.0539501251 5.7862725641 -0.3861716804 0.5637212913 0.7873817232 0.2094209906 -0.135614071647 +1403636992451666432.0000000000 0.0799615371 5.7581220963 -0.3864859828 0.5611936633 0.7894643259 0.2094604315 -0.133918176813 +1403636992501666560.0000000000 0.1055246552 5.7301985791 -0.3851786764 0.5596453456 0.7908693809 0.2092966752 -0.132354113005 +1403636992551666432.0000000000 0.1306375504 5.7026544223 -0.3823164980 0.5586985245 0.7918227622 0.2096840931 -0.130020202788 +1403636992601666560.0000000000 0.1550926214 5.6753697105 -0.3770751185 0.5577713635 0.7927595507 0.2092950538 -0.128914628154 +1403636992651666432.0000000000 0.1788765116 5.6485710832 -0.3699086947 0.5573703155 0.7933457613 0.2085669044 -0.128221218447 +1403636992701666560.0000000000 0.2022483136 5.6217859032 -0.3616934173 0.5570834401 0.7937892648 0.2085244224 -0.126784104343 +1403636992751666432.0000000000 0.2248168857 5.5952411261 -0.3535183060 0.5562311620 0.7946015313 0.2081873323 -0.125989426337 +1403636992801666560.0000000000 0.2466503695 5.5691187828 -0.3463100074 0.5564200687 0.7947546836 0.2081548203 -0.124230715998 +1403636992851666432.0000000000 0.2674995996 5.5431836619 -0.3404464793 0.5568275915 0.7946917916 0.2078935454 -0.123240673572 +1403636992901666560.0000000000 0.2875987675 5.5176850246 -0.3362358143 0.5575085814 0.7944737691 0.2080412259 -0.121303174903 +1403636992951666432.0000000000 0.3066717084 5.4924218882 -0.3335411281 0.5583356196 0.7940473901 0.2080578554 -0.120258084965 +1403636993001666560.0000000000 0.3247014948 5.4673813753 -0.3318579332 0.5599992361 0.7931718973 0.2066526886 -0.120722256383 +1403636993051666432.0000000000 0.3419480472 5.4423259225 -0.3309789638 0.5617816041 0.7922353779 0.2044499621 -0.122330488532 +1403636993101666560.0000000000 0.3581074242 5.4169301951 -0.3307629913 0.5632475630 0.7910407529 0.2028690644 -0.125900169818 +1403636993151666432.0000000000 0.3733549383 5.3908732998 -0.3299891641 0.5643724916 0.7896141241 0.2023141209 -0.130622441324 +1403636993201666560.0000000000 0.3883596198 5.3641268978 -0.3284241638 0.5646047499 0.7882464595 0.2039311559 -0.135281480966 +1403636993251666432.0000000000 0.4029868156 5.3371382069 -0.3250183071 0.5644844116 0.7866585605 0.2072737722 -0.139868658798 +1403636993301666560.0000000000 0.4171152980 5.3101535781 -0.3196877838 0.5639953240 0.7848956706 0.2117739724 -0.144913233706 +1403636993351666432.0000000000 0.4312120075 5.2829264270 -0.3120683455 0.5633568807 0.7827297098 0.2176430734 -0.150315398301 +1403636993401666560.0000000000 0.4454484153 5.2552823148 -0.3024650042 0.5624945564 0.7803841368 0.2243036244 -0.155847223502 +1403636993451666432.0000000000 0.4599904829 5.2267692995 -0.2910248551 0.5612316235 0.7778766302 0.2315945888 -0.162144871687 +1403636993501666560.0000000000 0.4749412007 5.1977643900 -0.2783150641 0.5594192820 0.7754729194 0.2398253060 -0.167856011767 +1403636993551666432.0000000000 0.4902793628 5.1685130239 -0.2641079231 0.5583423438 0.7723184373 0.2484168215 -0.173398792753 +1403636993601666560.0000000000 0.5059563537 5.1387515310 -0.2494021428 0.5555770129 0.7703287345 0.2567303350 -0.178933950317 +1403636993651666432.0000000000 0.5218257849 5.1097559640 -0.2348831444 0.5526339868 0.7688443778 0.2640942307 -0.183652488851 +1403636993701666560.0000000000 0.5379613489 5.0811302005 -0.2212151047 0.5501898252 0.7674084552 0.2705363090 -0.187578049556 +1403636993751666432.0000000000 0.5542861345 5.0530386796 -0.2092291846 0.5481717256 0.7661336049 0.2762346851 -0.190371892387 +1403636993801666560.0000000000 0.5705499752 5.0254327471 -0.1988832639 0.5463437515 0.7651943053 0.2806754347 -0.192892407211 +1403636993851666432.0000000000 0.5869841898 4.9984537034 -0.1901585285 0.5460318943 0.7634767695 0.2852456027 -0.193874544644 +1403636993901666560.0000000000 0.6032412858 4.9713308270 -0.1828381802 0.5450765841 0.7624031431 0.2890139565 -0.195202197282 +1403636993951666432.0000000000 0.6192006704 4.9442862787 -0.1766066509 0.5457219287 0.7605995480 0.2905831682 -0.198084139963 +1403636994001666560.0000000000 0.6349745272 4.9172937806 -0.1718905787 0.5479436923 0.7579651213 0.2922878765 -0.199535415941 +1403636994051666432.0000000000 0.6507382412 4.8901305985 -0.1683974533 0.5510445114 0.7549622544 0.2936436809 -0.200387947473 +1403636994101666560.0000000000 0.6665532515 4.8624176096 -0.1657499501 0.5553345137 0.7513248757 0.2938718898 -0.201875757553 +1403636994151666432.0000000000 0.6825345831 4.8340556323 -0.1644066829 0.5585370494 0.7485476546 0.2938985781 -0.20331354875 +1403636994201666560.0000000000 0.6986240909 4.8048830602 -0.1638928381 0.5622042229 0.7454758903 0.2937058199 -0.204765720078 +1403636994251666432.0000000000 0.7150108014 4.7746550723 -0.1645228892 0.5652480485 0.7430542609 0.2928979665 -0.206339017774 +1403636994301666560.0000000000 0.7320019448 4.7432514417 -0.1662085055 0.5678489080 0.7410321924 0.2921308252 -0.207553579627 +1403636994351666432.0000000000 0.7497382294 4.7106205581 -0.1690669238 0.5695189679 0.7397270931 0.2919688227 -0.207860961912 +1403636994401666560.0000000000 0.7682636190 4.6766817660 -0.1725712440 0.5713867068 0.7384132154 0.2912826079 -0.208368896385 +1403636994451666432.0000000000 0.7878853139 4.6411978863 -0.1764839841 0.5716256444 0.7383879168 0.2911267396 -0.208020740568 +1403636994501666560.0000000000 0.8084915138 4.6043507113 -0.1795096370 0.5706174637 0.7392766657 0.2910455005 -0.207745609406 +1403636994551666432.0000000000 0.8298945522 4.5658819995 -0.1808690166 0.5675637964 0.7416220731 0.2896052689 -0.209754203612 +1403636994601666560.0000000000 0.8522472049 4.5264234989 -0.1807554882 0.5647596871 0.7438911013 0.2897702982 -0.209059081145 +1403636994651666432.0000000000 0.8752203175 4.4856391388 -0.1791440142 0.5603313957 0.7474002122 0.2894648080 -0.208882202685 +1403636994701666560.0000000000 0.8985010643 4.4440336586 -0.1754826853 0.5547017966 0.7516792460 0.2878087363 -0.210832538394 +1403636994751666432.0000000000 0.9224325527 4.4019367454 -0.1701414427 0.5485006104 0.7563229962 0.2861720023 -0.212669205433 +1403636994801666560.0000000000 0.9468244017 4.3598382429 -0.1634966462 0.5429035272 0.7605341338 0.2841604160 -0.214700837088 +1403636994851666432.0000000000 0.9717138021 4.3183109195 -0.1562767225 0.5392611134 0.7632184842 0.2816030560 -0.217703274658 +1403636994901666560.0000000000 0.9972696726 4.2775113193 -0.1501980065 0.5363055146 0.7654548910 0.2801771482 -0.218988516653 +1403636994951666432.0000000000 1.0234383792 4.2376662999 -0.1451490652 0.5362174664 0.7656577494 0.2789443473 -0.22006610498 +1403636995001666560.0000000000 1.0503914195 4.1986884130 -0.1417031569 0.5380376776 0.7644997233 0.2785919344 -0.220095807985 +1403636995051666432.0000000000 1.0779918986 4.1604603480 -0.1400930473 0.5413534691 0.7622097807 0.2799508942 -0.21817462835 +1403636995101666560.0000000000 1.1058245124 4.1227154485 -0.1392533748 0.5457423592 0.7590334893 0.2813067436 -0.216563975493 +1403636995151666432.0000000000 1.1341963300 4.0852217724 -0.1384045007 0.5498772192 0.7559904999 0.2827086397 -0.214916804673 +1403636995201666560.0000000000 1.1630952231 4.0477332273 -0.1367358368 0.5524435241 0.7539490393 0.2841927379 -0.213545045635 +1403636995251666432.0000000000 1.1925771794 4.0102124074 -0.1331091842 0.5548760722 0.7519550294 0.2851821833 -0.212949056306 +1403636995301666560.0000000000 1.2227402326 3.9722875136 -0.1272941293 0.5562397007 0.7507218972 0.2865300467 -0.211930556617 +1403636995351666432.0000000000 1.2540669727 3.9334367094 -0.1197139468 0.5563854443 0.7503286716 0.2882292691 -0.210632405806 +1403636995401666560.0000000000 1.2854339312 3.8941469288 -0.1108026204 0.5549297238 0.7510046605 0.2905159708 -0.208914987933 +1403636995451666432.0000000000 1.3171856761 3.8541690580 -0.0999429613 0.5523281515 0.7526652213 0.2922308605 -0.207436259606 +1403636995501666560.0000000000 1.3495367472 3.8133226785 -0.0875676259 0.5493193209 0.7545959655 0.2936140984 -0.206455742757 +1403636995551666432.0000000000 1.3819667060 3.7721675373 -0.0729099188 0.5481723642 0.7552225308 0.2937498101 -0.207019412535 +1403636995601666560.0000000000 1.4143060881 3.7314225475 -0.0576095576 0.5469843504 0.7559775595 0.2947553542 -0.205974102868 +1403636995651666432.0000000000 1.4463003364 3.6904538406 -0.0422009109 0.5456718484 0.7569188591 0.2936728296 -0.207538776786 +1403636995701666560.0000000000 1.4785026280 3.6494668478 -0.0279363419 0.5457038260 0.7569261184 0.2933632546 -0.207865789519 +1403636995751666432.0000000000 1.5104338380 3.6083150349 -0.0152391790 0.5448825643 0.7574920580 0.2926561910 -0.208952451761 +1403636995801666560.0000000000 1.5424979726 3.5671624747 -0.0040476682 0.5430154997 0.7589945625 0.2902814340 -0.211655640642 +1403636995851666432.0000000000 1.5748398070 3.5261287744 0.0055031394 0.5400253824 0.7611648141 0.2879881335 -0.214624199419 +1403636995901666560.0000000000 1.6074667903 3.4859149540 0.0136817958 0.5374472598 0.7630610835 0.2861679371 -0.216785925723 +1403636995951666432.0000000000 1.6404181329 3.4465831600 0.0204170919 0.5351768881 0.7647905830 0.2845859276 -0.218384780497 +1403636996001666560.0000000000 1.6739543926 3.4080408098 0.0256409130 0.5339446948 0.7657569899 0.2840214431 -0.218748977573 +1403636996051666432.0000000000 1.7081506256 3.3707472798 0.0289627285 0.5342794407 0.7656154088 0.2861603447 -0.215617212129 +1403636996101666560.0000000000 1.7428462322 3.3343530752 0.0311950815 0.5345397298 0.7655701022 0.2877051740 -0.213062030233 +1403636996151666432.0000000000 1.7778474790 3.2986657316 0.0335258689 0.5355914302 0.7649213623 0.2895934410 -0.210173186478 +1403636996201666560.0000000000 1.8130790734 3.2632961134 0.0369637826 0.5361240408 0.7645688776 0.2913291674 -0.207684280946 +1403636996251666432.0000000000 1.8480241657 3.2288224557 0.0413577859 0.5369211018 0.7640668510 0.2928901337 -0.205263117032 +1403636996301666560.0000000000 1.8819322503 3.1953762054 0.0486545783 0.5376046102 0.7632098948 0.2946853796 -0.20408935914 +1403636996351666432.0000000000 1.9156579162 3.1617266858 0.0578797139 0.5369078755 0.7628098412 0.2966684572 -0.204545608581 +1403636996401666560.0000000000 1.9488693654 3.1283082372 0.0699397508 0.5365302518 0.7616958853 0.2991165656 -0.206116344382 +1403636996451666432.0000000000 1.9819122043 3.0945665325 0.0837608000 0.5351969286 0.7606379745 0.3030127007 -0.207791777094 +1403636996501666560.0000000000 2.0142423562 3.0610995192 0.0989302345 0.5348760205 0.7582365615 0.3079061498 -0.210187445846 +1403636996551666432.0000000000 2.0463414763 3.0276616518 0.1157009483 0.5340186934 0.7557067835 0.3139628223 -0.212505620253 +1403636996601666560.0000000000 2.0779644155 2.9939170559 0.1337161216 0.5316646089 0.7536369404 0.3202506500 -0.21634145908 +1403636996651666432.0000000000 2.1088316742 2.9604561201 0.1513652900 0.5295149246 0.7507255354 0.3272515033 -0.221204811599 +1403636996701666560.0000000000 2.1394921304 2.9270654577 0.1657142740 0.5267980877 0.7477562040 0.3356396430 -0.22514542919 +1403636996751666432.0000000000 2.1699606798 2.8934568209 0.1758645370 0.5235057509 0.7447577840 0.3434656824 -0.230887195248 +1403636996801666560.0000000000 2.2000514365 2.8599374158 0.1821924855 0.5205392087 0.7409814764 0.3524844331 -0.23609343145 +1403636996851666432.0000000000 2.2296218602 2.8265116882 0.1856845840 0.5166827316 0.7375453792 0.3606537869 -0.242888069849 +1403636996901666560.0000000000 2.2587475290 2.7931726712 0.1871725265 0.5128698538 0.7336281982 0.3693669298 -0.249644249049 +1403636996951666432.0000000000 2.2874058824 2.7600557486 0.1871013927 0.5086041742 0.7297665350 0.3777508279 -0.25703484273 +1403636997001666560.0000000000 2.3152859713 2.7278819330 0.1856002948 0.5052552805 0.7250722743 0.3871324160 -0.262898822957 +1403636997051666432.0000000000 2.3426064478 2.6961769823 0.1829012815 0.5019152007 0.7206429192 0.3953902445 -0.269112372199 +1403636997101666560.0000000000 2.3694792601 2.6651342914 0.1786296848 0.4979538759 0.7170268896 0.4033721391 -0.274235837494 +1403636997151666432.0000000000 2.3959608542 2.6351390390 0.1733756340 0.4947361306 0.7139132647 0.4097840361 -0.278641445738 +1403636997201666560.0000000000 2.4217079640 2.6060867795 0.1668251560 0.4919999412 0.7112337117 0.4150881479 -0.282461492344 +1403636997251666432.0000000000 2.4464676687 2.5781855492 0.1594313886 0.4901276558 0.7085837380 0.4199785950 -0.285134962739 +1403636997301666560.0000000000 2.4705978427 2.5512163705 0.1521215808 0.4885214731 0.7065512189 0.4238287122 -0.287230513823 +1403636997351666432.0000000000 2.4945051378 2.5250508297 0.1457246775 0.4871025038 0.7051431461 0.4267681980 -0.288744176421 +1403636997401666560.0000000000 2.5176594794 2.4999163550 0.1414605442 0.4863276804 0.7038088536 0.4294593947 -0.289314903145 +1403636997451666432.0000000000 2.5403560099 2.4753703020 0.1398296664 0.4860623232 0.7027493258 0.4304074475 -0.290923069141 +1403636997501666560.0000000000 2.5620647617 2.4518673780 0.1394128916 0.4862320940 0.7019084290 0.4317824825 -0.290631718627 +1403636997551666432.0000000000 2.5829944759 2.4289243350 0.1408662725 0.4859171731 0.7017714098 0.4323926884 -0.290582092169 +1403636997601666560.0000000000 2.6030255313 2.4067564403 0.1446335830 0.4851886450 0.7023380973 0.4324582052 -0.290332699942 +1403636997651666432.0000000000 2.6220261744 2.3855281828 0.1504870164 0.4852301846 0.7025744295 0.4323805873 -0.289806602153 +1403636997701666560.0000000000 2.6399671602 2.3649978190 0.1581232257 0.4855576823 0.7027694144 0.4325075415 -0.288593336537 +1403636997751666432.0000000000 2.6563801537 2.3453055846 0.1675128517 0.4859804299 0.7031805052 0.4325289458 -0.286843005566 +1403636997801666560.0000000000 2.6716530837 2.3260739123 0.1784675337 0.4857320703 0.7040649196 0.4324302113 -0.285238597218 +1403636997851666432.0000000000 2.6867463351 2.3071510712 0.1926342877 0.4861270787 0.7043733770 0.4318961702 -0.28461255664 +1403636997901666560.0000000000 2.7001831746 2.2889549068 0.2073169720 0.4865009768 0.7050694808 0.4312367279 -0.283246732 +1403636997951666432.0000000000 2.7126550448 2.2710045017 0.2242082416 0.4866471301 0.7056227466 0.4301170644 -0.283320350652 +1403636998001666560.0000000000 2.7244433535 2.2538804343 0.2431800411 0.4870204563 0.7062002174 0.4293900029 -0.282341200518 +1403636998051666432.0000000000 2.7353518716 2.2370174696 0.2634129676 0.4871740616 0.7069017632 0.4285846086 -0.281543183649 +1403636998101666560.0000000000 2.7455637450 2.2204213594 0.2840885606 0.4870957697 0.7075568487 0.4276921777 -0.281390152903 +1403636998151666432.0000000000 2.7544771196 2.2045985347 0.3049655628 0.4880592169 0.7075585731 0.4264125779 -0.281658267637 +1403636998201666560.0000000000 2.7623724675 2.1890911030 0.3248414972 0.4880911407 0.7081788887 0.4243503783 -0.283154474492 +1403636998251666432.0000000000 2.7696926357 2.1740734429 0.3426960118 0.4877210568 0.7087789896 0.4236965662 -0.283269720363 +1403636998301666560.0000000000 2.7764232185 2.1598585340 0.3589126513 0.4879590295 0.7093531638 0.4234277229 -0.281820932401 +1403636998351666432.0000000000 2.7821385030 2.1461629076 0.3737339184 0.4882944380 0.7095099777 0.4226498174 -0.282012881365 +1403636998401666560.0000000000 2.7867570299 2.1329929878 0.3870801076 0.4882166691 0.7099143540 0.4218931345 -0.282262780271 +1403636998451666432.0000000000 2.7905593372 2.1204121022 0.3994880408 0.4880195718 0.7104626907 0.4210682964 -0.282455576034 +1403636998501666560.0000000000 2.7935918214 2.1085927559 0.4126941458 0.4881597294 0.7107584831 0.4201033141 -0.282905748965 +1403636998551666432.0000000000 2.7961472144 2.0974949736 0.4275539121 0.4907321902 0.7093310735 0.4197063503 -0.282626830242 +1403636998601666560.0000000000 2.7983046078 2.0868043044 0.4436546432 0.4929554442 0.7079414797 0.4184707480 -0.284070456829 +1403636998651666432.0000000000 2.7996847096 2.0772459748 0.4619813594 0.4997191912 0.7035319815 0.4173533536 -0.284850240007 +1403636998701666560.0000000000 2.8010306973 2.0674199831 0.4819940880 0.5045817556 0.7002504369 0.4151552064 -0.287563440163 +1403636998751666432.0000000000 2.8027344140 2.0576590921 0.5029098741 0.5088049740 0.6973973738 0.4136327513 -0.289244444437 +1403636998801666560.0000000000 2.8050443707 2.0480733186 0.5239766856 0.5123049949 0.6953459022 0.4130660609 -0.288814988939 +1403636998851666432.0000000000 2.8079093319 2.0380513627 0.5440866344 0.5150982318 0.6933368583 0.4146124649 -0.286451246329 +1403636998901666560.0000000000 2.8109087381 2.0273953005 0.5630759384 0.5171256195 0.6921056993 0.4149510102 -0.285283111606 +1403636998951666432.0000000000 2.8144057214 2.0160466712 0.5802350338 0.5183220448 0.6915214881 0.4158044881 -0.283278867817 +1403636999001666560.0000000000 2.8181367918 2.0040078679 0.5958857980 0.5187115848 0.6913716193 0.4165719072 -0.281800323062 +1403636999051666432.0000000000 2.8222993475 1.9911226054 0.6100300236 0.5202282373 0.6903753935 0.4174236263 -0.2801819293 +1403636999101666560.0000000000 2.8267912382 1.9771164418 0.6223732811 0.5199649019 0.6906596229 0.4179450980 -0.279191119662 +1403636999151666432.0000000000 2.8312806392 1.9624243672 0.6331776085 0.5199506421 0.6908858770 0.4185745457 -0.27771097286 +1403636999201666560.0000000000 2.8358269483 1.9467211378 0.6423429786 0.5188403577 0.6918209752 0.4191494847 -0.276590185815 +1403636999251666432.0000000000 2.8404109062 1.9302249250 0.6501416144 0.5181301709 0.6924176463 0.4194748793 -0.275934330548 +1403636999301666560.0000000000 2.8448882096 1.9127693034 0.6565581689 0.5163259917 0.6938689215 0.4189900974 -0.276406744246 +1403636999351666432.0000000000 2.8495187609 1.8945520854 0.6616544107 0.5142150347 0.6956078803 0.4178695522 -0.277664567905 +1403636999401666560.0000000000 2.8536753015 1.8757093443 0.6660243933 0.5132147416 0.6963934212 0.4162199886 -0.280013844452 +1403636999451666432.0000000000 2.8577732539 1.8566284838 0.6691565469 0.5120663352 0.6973762240 0.4148715326 -0.281666614812 +1403636999501666560.0000000000 2.8619224420 1.8372542180 0.6711921952 0.5121201258 0.6973602871 0.4141210255 -0.282710776257 +1403636999551666432.0000000000 2.8661534368 1.8176001319 0.6724920812 0.5132550119 0.6967902155 0.4127530826 -0.284055595283 +1403636999601666560.0000000000 2.8705354563 1.7974677966 0.6728760089 0.5138628152 0.6963721178 0.4115620742 -0.285705337327 +1403636999651666432.0000000000 2.8753549820 1.7770100066 0.6724394529 0.5149663243 0.6957079795 0.4105459017 -0.286796364601 +1403636999701666560.0000000000 2.8806866248 1.7561668584 0.6710086044 0.5157805633 0.6953311554 0.4096592311 -0.28751401572 +1403636999751666432.0000000000 2.8865788218 1.7348610063 0.6687954231 0.5158025510 0.6954242875 0.4092806591 -0.287788343999 +1403636999801666560.0000000000 2.8928674031 1.7134887324 0.6661616430 0.5162355459 0.6954601202 0.4086941985 -0.287758812998 +1403636999851666432.0000000000 2.8998382713 1.6915974039 0.6627001439 0.5162920818 0.6955031093 0.4089800404 -0.287146718257 +1403636999901666560.0000000000 2.9073125286 1.6694544040 0.6584912339 0.5169357188 0.6951813650 0.4093395055 -0.286254260293 +1403636999951666432.0000000000 2.9153437367 1.6468963908 0.6540097792 0.5178314938 0.6946711433 0.4099505324 -0.284996680002 +1403637000001666560.0000000000 2.9239648219 1.6239409547 0.6505309368 0.5191997537 0.6937023134 0.4113937167 -0.282778934879 +1403637000051666432.0000000000 2.9330433214 1.5999876836 0.6486809887 0.5197232246 0.6931415654 0.4128346763 -0.281087299961 +1403637000101666560.0000000000 2.9429123126 1.5750797849 0.6485313264 0.5192036113 0.6935480403 0.4134204108 -0.280182600738 +1403637000151666432.0000000000 2.9532377447 1.5490998419 0.6506500946 0.5183761196 0.6940788153 0.4135635606 -0.280189182556 +1403637000201666560.0000000000 2.9637372561 1.5223219416 0.6543530507 0.5168045690 0.6950130675 0.4142373325 -0.27978081739 +1403637000251666432.0000000000 2.9737676376 1.4952398911 0.6589824405 0.5154347772 0.6960249717 0.4141953081 -0.279854383351 +1403637000301666560.0000000000 2.9837921736 1.4678754698 0.6635786851 0.5144290655 0.6966985369 0.4143348570 -0.279822285661 +1403637000351666432.0000000000 2.9936325705 1.4402649364 0.6677354634 0.5141667353 0.6968796754 0.4139715305 -0.280390545833 +1403637000401666560.0000000000 3.0039071144 1.4122338328 0.6709638732 0.5139533007 0.6969890807 0.4128356439 -0.282178945302 +1403637000451666432.0000000000 3.0146786063 1.3842411900 0.6724506593 0.5146683280 0.6965258045 0.4136416590 -0.28083606217 +1403637000501666560.0000000000 3.0255239858 1.3557067152 0.6731182384 0.5150402971 0.6962223545 0.4139056024 -0.28051751785 +1403637000551666432.0000000000 3.0367741844 1.3265790857 0.6736813117 0.5154505347 0.6960267702 0.4142268381 -0.279774208983 +1403637000601666560.0000000000 3.0481577304 1.2967718993 0.6748588590 0.5151898476 0.6961145776 0.4143445714 -0.27986155844 +1403637000651666432.0000000000 3.0596360050 1.2661239417 0.6775524685 0.5152525694 0.6961208822 0.4131866442 -0.281437922188 +1403637000701666560.0000000000 3.0711639769 1.2352481745 0.6817937378 0.5150947394 0.6962728942 0.4124936510 -0.282365816305 +1403637000751666432.0000000000 3.0827318899 1.2042814716 0.6882770110 0.5154115590 0.6960005615 0.4126302517 -0.282259488132 +1403637000801666560.0000000000 3.0942802442 1.1730661458 0.6971735757 0.5157264688 0.6961003963 0.4116252950 -0.282904690887 +1403637000851666432.0000000000 3.1060688285 1.1412463436 0.7062988455 0.5157186656 0.6962286528 0.4107739056 -0.283839249199 +1403637000901666560.0000000000 3.1181824195 1.1091927847 0.7141205665 0.5153218756 0.6966835591 0.4108326572 -0.28335827267 +1403637000951666432.0000000000 3.1304677323 1.0770076108 0.7206018030 0.5153121875 0.6969695279 0.4106562889 -0.282927974836 +1403637001001666560.0000000000 3.1432710743 1.0444392882 0.7255542638 0.5157400836 0.6968883996 0.4099340068 -0.283395191943 +1403637001051666432.0000000000 3.1565817218 1.0114642218 0.7284809675 0.5158820676 0.6968161663 0.4097639000 -0.28356034441 +1403637001101666560.0000000000 3.1701078862 0.9781716477 0.7301961831 0.5157420705 0.6971507162 0.4091862556 -0.283826714484 +1403637001151666432.0000000000 3.1839725536 0.9447193589 0.7308797812 0.5159307982 0.6970890765 0.4090209423 -0.283873386716 +1403637001201666560.0000000000 3.1981320520 0.9111293734 0.7318070249 0.5159918099 0.6972304013 0.4078168402 -0.285144953302 +1403637001251666432.0000000000 3.2131992652 0.8770325743 0.7336683415 0.5153901653 0.6978013505 0.4074302824 -0.285388888757 +1403637001301666560.0000000000 3.2291495995 0.8425669848 0.7375077858 0.5153561447 0.6978289521 0.4071712064 -0.285752351412 +1403637001351666432.0000000000 3.2457434940 0.8079273689 0.7435841510 0.5142345985 0.6987923723 0.4065063790 -0.286364386804 +1403637001401666560.0000000000 3.2623956113 0.7733900186 0.7518491661 0.5125317786 0.7000390471 0.4062237954 -0.286772970453 +1403637001451666432.0000000000 3.2793994323 0.7388944226 0.7612627171 0.5106055573 0.7015485848 0.4070271129 -0.285377780063 +1403637001501666560.0000000000 3.2964712296 0.7045849894 0.7717492169 0.5089481392 0.7031571006 0.4070040658 -0.284410924406 +1403637001551666432.0000000000 3.3139049837 0.6705117624 0.7819005390 0.5079579902 0.7042177170 0.4069633957 -0.283613966047 +1403637001601666560.0000000000 3.3316010776 0.6365323368 0.7911654013 0.5073155093 0.7049527881 0.4069845081 -0.282906611391 +1403637001651666432.0000000000 3.3494728762 0.6026411265 0.7994080002 0.5064250586 0.7057787254 0.4060601587 -0.283769622024 +1403637001701666560.0000000000 3.3674584310 0.5693301410 0.8061305993 0.5073412725 0.7053921414 0.4065065838 -0.282452044281 +1403637001751666432.0000000000 3.3856441896 0.5360889579 0.8116938369 0.5077196114 0.7054535370 0.4060676153 -0.282250235085 +1403637001801666560.0000000000 3.4038384335 0.5028335614 0.8161006821 0.5080397387 0.7053865235 0.4048488984 -0.283589220362 +1403637001851666432.0000000000 3.4225178809 0.4697380783 0.8181233794 0.5072562491 0.7061496034 0.4055373685 -0.282105083293 +1403637001901666560.0000000000 3.4410509912 0.4368847190 0.8190766153 0.5067425717 0.7066054992 0.4057747591 -0.281544808888 +1403637001951666432.0000000000 3.4595102360 0.4043920297 0.8189835323 0.5068010183 0.7067168068 0.4058473280 -0.281055206816 +1403637002001666560.0000000000 3.4779282982 0.3718837682 0.8176495816 0.5059842223 0.7072867563 0.4062973424 -0.280442294937 +1403637002051666432.0000000000 3.4960569004 0.3397380252 0.8155794862 0.5061669773 0.7072739697 0.4067700851 -0.279457726082 +1403637002101666560.0000000000 3.5141533251 0.3077663621 0.8126311380 0.5054777120 0.7079003018 0.4064758298 -0.279547572164 +1403637002151666432.0000000000 3.5322033234 0.2758559506 0.8087011376 0.5056154828 0.7077800739 0.4063545537 -0.279779068466 +1403637002201666560.0000000000 3.5503396063 0.2440809054 0.8036534704 0.5051577454 0.7080953476 0.4064706909 -0.279639425836 +1403637002251666432.0000000000 3.5683921412 0.2126761452 0.7976143928 0.5050255000 0.7082430154 0.4066437028 -0.279252528279 +1403637002301666560.0000000000 3.5864380475 0.1816057416 0.7913566045 0.5059116579 0.7076429338 0.4071514611 -0.278428734603 +1403637002351666432.0000000000 3.6050516974 0.1505695535 0.7856914145 0.5062105942 0.7073469547 0.4076959539 -0.277840114582 +1403637002401666560.0000000000 3.6226499170 0.1200203508 0.7815189365 0.5064230767 0.7070943508 0.4088421614 -0.276407911253 +1403637002451666432.0000000000 3.6400006152 0.0895035324 0.7795206668 0.5073883458 0.7063962539 0.4090798491 -0.276070780877 +1403637002501666560.0000000000 3.6565379970 0.0592982036 0.7794340225 0.5079309409 0.7059600684 0.4095693673 -0.275462292163 +1403637002551666432.0000000000 3.6728039806 0.0292251506 0.7809756477 0.5093741441 0.7048427383 0.4112412760 -0.27315802846 +1403637002601666560.0000000000 3.6885972735 -0.0011059010 0.7859872457 0.5097976498 0.7045607311 0.4110103039 -0.273442978476 +1403637002651666432.0000000000 3.7047395617 -0.0317732713 0.7929003486 0.5098871821 0.7045989224 0.4111638412 -0.272946360431 +1403637002701666560.0000000000 3.7209971621 -0.0626614910 0.8004132312 0.5100700124 0.7047787818 0.4112178687 -0.272057559425 +1403637002751666432.0000000000 3.7365553176 -0.0936749635 0.8077535942 0.5097969602 0.7052457534 0.4108360496 -0.271936071573 +1403637002801666560.0000000000 3.7516968188 -0.1248169448 0.8143692284 0.5104113455 0.7050981603 0.4102927483 -0.271986587022 +1403637002851666432.0000000000 3.7664213867 -0.1562270338 0.8195612975 0.5098252406 0.7058133664 0.4090213132 -0.273143334566 +1403637002901666560.0000000000 3.7809098201 -0.1879269765 0.8231577826 0.5093663470 0.7065517431 0.4071317554 -0.2749077894 +1403637002951666432.0000000000 3.7952897930 -0.2195013104 0.8245022158 0.5092803265 0.7070187004 0.4064176384 -0.274923279236 +1403637003001666560.0000000000 3.8094564540 -0.2511328378 0.8242900593 0.5088394267 0.7076421306 0.4059235101 -0.27486570675 +1403637003051666432.0000000000 3.8232607512 -0.2826758837 0.8227080878 0.5085880069 0.7082334661 0.4050830023 -0.275047919457 +1403637003101666560.0000000000 3.8370154158 -0.3141024832 0.8195869352 0.5083065102 0.7088933130 0.4046016017 -0.274576594802 +1403637003151666432.0000000000 3.8504088536 -0.3453557587 0.8153651460 0.5089539184 0.7087644390 0.4042903236 -0.274168220608 +1403637003201666560.0000000000 3.8637433746 -0.3764448608 0.8099489232 0.5091643845 0.7091357327 0.4033839412 -0.274152399469 +1403637003251666432.0000000000 3.8771329955 -0.4073080879 0.8036961565 0.5098516351 0.7090856558 0.4029380929 -0.273659891415 +1403637003301666560.0000000000 3.8902542206 -0.4383670763 0.7983875838 0.5103647640 0.7090551088 0.4014556089 -0.274958277519 +1403637003351666432.0000000000 3.9035161563 -0.4696199490 0.7941710435 0.5104931731 0.7092281814 0.4003173302 -0.275931408376 +1403637003401666560.0000000000 3.9166691097 -0.5005545595 0.7912764291 0.5117899881 0.7085525956 0.3997983795 -0.276017178781 +1403637003451666432.0000000000 3.9292273750 -0.5311404218 0.7905161484 0.5127342606 0.7080926365 0.3988953855 -0.276750551338 +1403637003501666560.0000000000 3.9420326060 -0.5616315602 0.7918766855 0.5128960274 0.7084002775 0.3977395367 -0.277326473538 +1403637003551666432.0000000000 3.9553482823 -0.5923634977 0.7949678467 0.5123855173 0.7089411156 0.3973633302 -0.277427395939 +1403637003601666560.0000000000 3.9689512872 -0.6229987877 0.7996407216 0.5122412906 0.7093031792 0.3967925061 -0.277585243363 +1403637003651666432.0000000000 3.9826713543 -0.6535559052 0.8060619802 0.5121333974 0.7095944181 0.3963105904 -0.277728394421 +1403637003701666560.0000000000 3.9966995692 -0.6840047467 0.8125711825 0.5118808117 0.7099102230 0.3962444188 -0.277481297554 +1403637003751666432.0000000000 4.0108301266 -0.7141754810 0.8181709223 0.5116329335 0.7100478184 0.3964259755 -0.277327032467 +1403637003801666560.0000000000 4.0251469670 -0.7443461323 0.8227861382 0.5105027190 0.7105616726 0.3961594573 -0.278472202716 +1403637003851666432.0000000000 4.0398945409 -0.7740021909 0.8259112105 0.5094458556 0.7110819568 0.3974016901 -0.277307171906 +1403637003901666560.0000000000 4.0546424266 -0.8032910729 0.8275970935 0.5091681768 0.7108770952 0.3990201443 -0.276015303457 +1403637003951666432.0000000000 4.0694185564 -0.8326286983 0.8273089068 0.5075092484 0.7114796771 0.4009057078 -0.274782905753 +1403637004001666560.0000000000 4.0842299333 -0.8618196441 0.8253984864 0.5065053992 0.7115954989 0.4027672566 -0.27361042308 +1403637004051666432.0000000000 4.0990248776 -0.8907309131 0.8215770871 0.5054513638 0.7118618519 0.4050752742 -0.271450999117 +1403637004101666560.0000000000 4.1132025393 -0.9194230624 0.8167125302 0.5045066482 0.7120467143 0.4058879312 -0.271509679353 +1403637004151666432.0000000000 4.1267971365 -0.9476946582 0.8107443518 0.5045222041 0.7115876275 0.4073681237 -0.270465535301 +1403637004201666560.0000000000 4.1398242468 -0.9759787294 0.8047461290 0.5033417276 0.7120254232 0.4081043757 -0.270402885443 +1403637004251666432.0000000000 4.1519144394 -1.0039801201 0.8005965049 0.5030982102 0.7116460349 0.4091459220 -0.270280828925 +1403637004301666560.0000000000 4.1629954112 -1.0320622682 0.7989875090 0.5021068130 0.7119466758 0.4085203315 -0.272271588418 +1403637004351666432.0000000000 4.1735066616 -1.0595143821 0.7989883694 0.5015405361 0.7123126156 0.4081501581 -0.272912580764 +1403637004401666560.0000000000 4.1828972132 -1.0860782881 0.8012651528 0.5022028503 0.7119746417 0.4064589440 -0.275091863961 +1403637004451666432.0000000000 4.1918195891 -1.1122408007 0.8063601796 0.5036452159 0.7112149530 0.4049535586 -0.276635866446 +1403637004501666560.0000000000 4.2001476445 -1.1379233143 0.8150924084 0.5072620402 0.7091921590 0.4028093976 -0.278345636638 +1403637004551666432.0000000000 4.2089511418 -1.1636359107 0.8265176904 0.5097805806 0.7079878650 0.4012685189 -0.279034976975 +1403637004601666560.0000000000 4.2185424001 -1.1898978949 0.8403613383 0.5097264308 0.7087855947 0.3989978404 -0.280361676916 +1403637004651666432.0000000000 4.2287009536 -1.2166096678 0.8557423643 0.5080795821 0.7107634896 0.3951544129 -0.28376643585 +1403637004701666560.0000000000 4.2390316389 -1.2428527438 0.8707762119 0.5055150612 0.7133656891 0.3910815483 -0.287435451998 +1403637004751666432.0000000000 4.2499222938 -1.2681100771 0.8836285246 0.5041172666 0.7151832933 0.3875110443 -0.290196190614 +1403637004801666560.0000000000 4.2608175889 -1.2926055139 0.8933929422 0.5019627176 0.7173483586 0.3842102588 -0.29296286381 +1403637004851666432.0000000000 4.2729066022 -1.3164401604 0.8986945711 0.5001741837 0.7193315843 0.3827676360 -0.293047427105 +1403637004901666560.0000000000 4.2856162043 -1.3392137904 0.8994652076 0.4975951750 0.7217193532 0.3825353713 -0.291867961289 +1403637004951666432.0000000000 4.2986338119 -1.3605373817 0.8964887533 0.4951866692 0.7240590586 0.3831129780 -0.289401258368 +1403637005001666560.0000000000 4.3119898835 -1.3806245073 0.8901218862 0.4943607240 0.7251275855 0.3850128332 -0.285591627232 +1403637005051666432.0000000000 4.3252887968 -1.3991690010 0.8823539602 0.4958693991 0.7245366412 0.3870744245 -0.281662181443 +1403637005101666560.0000000000 4.3383767113 -1.4164231498 0.8740597308 0.4990709390 0.7227996964 0.3882616491 -0.278821965603 +1403637005151666432.0000000000 4.3512032004 -1.4326477966 0.8647299968 0.5027448785 0.7206404427 0.3904059463 -0.274787438898 +1403637005201666560.0000000000 4.3635991354 -1.4484289294 0.8551274294 0.5044075559 0.7196703430 0.3908100419 -0.27370627701 +1403637005251666432.0000000000 4.3760479494 -1.4636503851 0.8442860115 0.5049485336 0.7194014034 0.3924008455 -0.271127600366 +1403637005301666560.0000000000 4.3883652203 -1.4786408017 0.8325922901 0.5040379441 0.7199551912 0.3938823931 -0.269196831326 +1403637005351666432.0000000000 4.4004763586 -1.4933685844 0.8204537657 0.5030013586 0.7205548033 0.3950095335 -0.267876608067 +1403637005401666560.0000000000 4.4121348776 -1.5076811019 0.8082684418 0.5034605860 0.7197797236 0.3959735104 -0.267674367315 +1403637005451666432.0000000000 4.4231643264 -1.5218899724 0.7963301746 0.5056003911 0.7176178921 0.3966032941 -0.268511885315 +1403637005501666560.0000000000 4.4338916576 -1.5359189399 0.7847220125 0.5081882679 0.7151409986 0.3975511949 -0.268832817588 +1403637005551666432.0000000000 4.4440226541 -1.5501325639 0.7748801826 0.5092080714 0.7138149878 0.3980262392 -0.269722850341 +1403637005601666560.0000000000 4.4541666008 -1.5646887727 0.7674711335 0.5083266087 0.7138065590 0.3980936288 -0.271303737529 +1403637005651666432.0000000000 4.4643349754 -1.5794997399 0.7621594792 0.5045694710 0.7157874005 0.3989210991 -0.271882332925 +1403637005701666560.0000000000 4.4739394288 -1.5941816439 0.7601172306 0.4999151764 0.7185508512 0.3985999904 -0.273655875854 +1403637005751666432.0000000000 4.4832126797 -1.6083325163 0.7612541774 0.4966382622 0.7204757797 0.3983988510 -0.274851674209 +1403637005801666560.0000000000 4.4919089349 -1.6214435720 0.7650844026 0.4962462971 0.7204073861 0.3988663056 -0.275060867674 +1403637005851666432.0000000000 4.5000517639 -1.6335889560 0.7703438350 0.4982081711 0.7187621108 0.3999560477 -0.274234947264 +1403637005901666560.0000000000 4.5075120851 -1.6451409005 0.7757309673 0.5001615412 0.7171768685 0.4007405685 -0.273683701972 +1403637005951666432.0000000000 4.5143811326 -1.6562232994 0.7807303943 0.5024514607 0.7154442940 0.4011712248 -0.27339283138 +1403637006001666560.0000000000 4.5207495527 -1.6669642353 0.7848695993 0.5045333872 0.7140209267 0.4010144963 -0.273509691182 +1403637006051666432.0000000000 4.5266303623 -1.6776106969 0.7882780592 0.5055498823 0.7133390684 0.4000114081 -0.27487736072 +1403637006101666560.0000000000 4.5322322525 -1.6882247465 0.7909930205 0.5058716680 0.7130748594 0.3988874061 -0.276598874974 +1403637006151666432.0000000000 4.5379521099 -1.6987110913 0.7932242181 0.5061907054 0.7128036245 0.3986266890 -0.277089742646 +1403637006201666560.0000000000 4.5435072540 -1.7092487161 0.7952186907 0.5053373994 0.7132778500 0.3986077120 -0.277453984145 +1403637006251666432.0000000000 4.5492181778 -1.7196600193 0.7965758291 0.5027949795 0.7150417524 0.3989458268 -0.277046436911 +1403637006301666560.0000000000 4.5549543873 -1.7298670959 0.7973677805 0.4987460789 0.7178182681 0.3994256785 -0.27649305634 +1403637006351666432.0000000000 4.5605049978 -1.7396597563 0.7973735760 0.4935839394 0.7212727205 0.4008657156 -0.274676601661 +1403637006401666560.0000000000 4.5654017891 -1.7488500386 0.7972711505 0.4894730441 0.7239890676 0.4018829342 -0.273397286524 +1403637006451666432.0000000000 4.5695131918 -1.7573229067 0.7968386207 0.4856764562 0.7264999133 0.4016624519 -0.273831208072 +1403637006501666560.0000000000 4.5727055769 -1.7647855794 0.7960771734 0.4827191272 0.7284222575 0.4000056839 -0.276366987544 +1403637006551666432.0000000000 4.5749497253 -1.7709405587 0.7955970359 0.4834944554 0.7270879539 0.3985836581 -0.280548189148 +1403637006601666560.0000000000 4.5766034495 -1.7756040440 0.7948758212 0.4865867165 0.7235351308 0.3993525148 -0.283280515839 +1403637006651666432.0000000000 4.5778777858 -1.7794427496 0.7935273679 0.4897014895 0.7189445303 0.4017078508 -0.286255159188 +1403637006701666560.0000000000 4.5789027134 -1.7826799715 0.7913527020 0.4923646086 0.7138595113 0.4054067858 -0.289183381835 +1403637006751666432.0000000000 4.5799799885 -1.7855119814 0.7886170125 0.4944734088 0.7082014297 0.4100192072 -0.292969337403 +1403637006801666560.0000000000 4.5814664067 -1.7882678276 0.7849567858 0.4950276617 0.7028886710 0.4149730597 -0.297812844069 +1403637006851666432.0000000000 4.5829844782 -1.7908262622 0.7805209812 0.4923509607 0.6989422389 0.4211725524 -0.302793591896 +1403637006901666560.0000000000 4.5844723628 -1.7932036076 0.7758848311 0.4891936748 0.6943885740 0.4285442629 -0.307999791501 +1403637006951666432.0000000000 4.5862817236 -1.7954826619 0.7706475029 0.4852967830 0.6893680928 0.4382274309 -0.311793816349 +1403637007001666560.0000000000 4.5884818400 -1.7973372933 0.7657540686 0.4824545345 0.6835127871 0.4478811949 -0.315357459437 +1403637007051666432.0000000000 4.5905198262 -1.7987768260 0.7611972682 0.4805397856 0.6775856819 0.4558761724 -0.31958734907 +1403637007101666560.0000000000 4.5924625452 -1.7996672281 0.7562287943 0.4792641328 0.6720648960 0.4631402177 -0.322700798307 +1403637007151666432.0000000000 4.5944750106 -1.8003069278 0.7513719026 0.4781413490 0.6670109577 0.4691881667 -0.32609768021 +1403637007201666560.0000000000 4.5963275793 -1.8007547128 0.7466932404 0.4775003705 0.6624545082 0.4739778676 -0.32938184788 +1403637007251666432.0000000000 4.5978168120 -1.8007553568 0.7420696902 0.4791123594 0.6572229605 0.4778760570 -0.331879197054 +1403637007301666560.0000000000 4.5997941217 -1.8006941219 0.7373829241 0.4821120368 0.6517004088 0.4809411986 -0.333991204341 +1403637007351666432.0000000000 4.6020322373 -1.8011586946 0.7328527824 0.4842926703 0.6475191197 0.4826985214 -0.336424934424 +1403637007401666560.0000000000 4.6048228500 -1.8022414416 0.7276947779 0.4850081152 0.6451432223 0.4847593424 -0.336995149594 +1403637007451666432.0000000000 4.6084652329 -1.8041983091 0.7218862773 0.4832675421 0.6449321730 0.4863622646 -0.337589577013 +1403637007501666560.0000000000 4.6125741152 -1.8065789341 0.7159573075 0.4820981332 0.6448106582 0.4878324398 -0.337372369394 +1403637007551666432.0000000000 4.6171734962 -1.8095859533 0.7097564338 0.4804350534 0.6454350323 0.4891974867 -0.336573316708 +1403637007601666560.0000000000 4.6222358943 -1.8132456715 0.7027236715 0.4760120774 0.6483361925 0.4908440147 -0.334880332178 +1403637007651666432.0000000000 4.6274462289 -1.8174451059 0.6951960451 0.4710134969 0.6519436785 0.4932593734 -0.331377302048 +1403637007701666560.0000000000 4.6325529391 -1.8220921592 0.6879647425 0.4664542811 0.6554768582 0.4949987315 -0.328247997478 +1403637007751666432.0000000000 4.6370823244 -1.8269137328 0.6810748222 0.4632247832 0.6581010740 0.4967604687 -0.324892002678 +1403637007801666560.0000000000 4.6403851750 -1.8316848302 0.6754127016 0.4633146593 0.6586293317 0.4967679752 -0.323679639106 +1403637007851666432.0000000000 4.6423245640 -1.8367942184 0.6704999908 0.4650451396 0.6580640288 0.4952074873 -0.324737273336 +1403637007901666560.0000000000 4.6431775048 -1.8422540990 0.6667795226 0.4675467925 0.6572020851 0.4902071845 -0.330427499539 +1403637007951666432.0000000000 4.6435787696 -1.8478695790 0.6634769951 0.4697686745 0.6565362860 0.4846227387 -0.336776333398 +1403637008001666560.0000000000 4.6443390190 -1.8531732261 0.6599031874 0.4721787574 0.6557111462 0.4808272140 -0.340433993722 +1403637008051666432.0000000000 4.6459553834 -1.8582519500 0.6559524743 0.4740790890 0.6552941587 0.4795975509 -0.340330386739 +1403637008101666560.0000000000 4.6486002254 -1.8632538248 0.6512677010 0.4722275873 0.6576584064 0.4810321653 -0.336295379436 +1403637008151666432.0000000000 4.6517768758 -1.8682854321 0.6464961979 0.4682657528 0.6614407338 0.4837289916 -0.330499021222 +1403637008201666560.0000000000 4.6546248765 -1.8733891281 0.6424744701 0.4639659930 0.6652832290 0.4860688468 -0.325378024355 +1403637008251666432.0000000000 4.6567875559 -1.8783062541 0.6394466222 0.4607861384 0.6682609253 0.4881131136 -0.320700886539 +1403637008301666560.0000000000 4.6580847676 -1.8828857753 0.6374030097 0.4593277542 0.6699766589 0.4900840451 -0.316175456901 +1403637008351666432.0000000000 4.6579226849 -1.8872883360 0.6366728425 0.4590881540 0.6708287400 0.4907215325 -0.313718418326 +1403637008401666560.0000000000 4.6562375899 -1.8916352383 0.6374751095 0.4607380793 0.6704855042 0.4895608487 -0.313846756188 +1403637008451666432.0000000000 4.6528232998 -1.8959263556 0.6400147007 0.4646005275 0.6685551595 0.4856934083 -0.318248741833 +1403637008501666560.0000000000 4.6483731516 -1.9000107118 0.6431242074 0.4683405224 0.6667718031 0.4817366790 -0.322493860159 +1403637008551666432.0000000000 4.6435192916 -1.9040169419 0.6464616578 0.4718203569 0.6650552911 0.4779571492 -0.326563889826 +1403637008601666560.0000000000 4.6386536728 -1.9078544835 0.6487614258 0.4743427023 0.6640978914 0.4746497760 -0.329667380256 +1403637008651666432.0000000000 4.6341830011 -1.9118481430 0.6498053552 0.4758410108 0.6636769174 0.4721600451 -0.331923445417 +1403637008701666560.0000000000 4.6299859816 -1.9160450971 0.6499981904 0.4743138275 0.6653420572 0.4689631906 -0.335290718324 +1403637008751666432.0000000000 4.6261217599 -1.9202933079 0.6494406426 0.4697096015 0.6691042221 0.4656434932 -0.338893150469 +1403637008801666560.0000000000 4.6226133854 -1.9241795236 0.6483600667 0.4631361914 0.6740489189 0.4625431461 -0.342369334333 +1403637008851666432.0000000000 4.6192148074 -1.9269373234 0.6464088153 0.4574045991 0.6781499238 0.4603552772 -0.344915543764 +1403637008901666560.0000000000 4.6159438295 -1.9279564353 0.6426986843 0.4534590308 0.6811033788 0.4595999745 -0.345312841109 +1403637008951666432.0000000000 4.6129251444 -1.9268580187 0.6376971338 0.4525580871 0.6821337568 0.4593233922 -0.344828561727 +1403637009001666560.0000000000 4.6101597221 -1.9236833569 0.6315793110 0.4550955376 0.6808788752 0.4605590122 -0.34231185375 +1403637009051666432.0000000000 4.6074057165 -1.9186704218 0.6241227071 0.4594275593 0.6784626829 0.4629522046 -0.338067984239 +1403637009101666560.0000000000 4.6051362265 -1.9125806328 0.6156220594 0.4638548618 0.6758090257 0.4656761284 -0.333566442279 +1403637009151666432.0000000000 4.6032590527 -1.9057985255 0.6070067916 0.4676886030 0.6734780866 0.4681103941 -0.329495518028 +1403637009201666560.0000000000 4.6013082355 -1.8982076014 0.5979292302 0.4718745652 0.6707750412 0.4711392809 -0.324689107937 +1403637009251666432.0000000000 4.5993501945 -1.8901539949 0.5880608633 0.4762920978 0.6678502535 0.4751085954 -0.318423772768 +1403637009301666560.0000000000 4.5963971217 -1.8819459600 0.5778567796 0.4807000894 0.6646862567 0.4798955593 -0.311158892409 +1403637009351666432.0000000000 4.5915360404 -1.8739406790 0.5676613226 0.4857622496 0.6610301244 0.4834641088 -0.305510502186 +1403637009401666560.0000000000 4.5895305849 -1.8701116859 0.5659240102 0.4775922275 0.6608084534 0.4788104901 -0.325543187245 +1403637009451666432.0000000000 4.5899450099 -1.8645972528 0.5619746351 0.4786989502 0.6539403445 0.4859081047 -0.327265419398 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_03_medium.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_03_medium.txt new file mode 100644 index 0000000000000000000000000000000000000000..134b3f1b263adf6f0889ea90f8f6cc536c2198fc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_03_medium.txt @@ -0,0 +1,2632 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403637132888318976.0000000000 4.6053979055 -1.8480601270 0.5587802567 0.4895050236 0.6601100115 0.4362728530 -0.366477287495 +1403637132938319104.0000000000 4.6053662210 -1.8476316042 0.5586384325 0.4899099547 0.6599110595 0.4365313624 -0.365986337832 +1403637132988318976.0000000000 4.6051003710 -1.8478513267 0.5587431947 0.4890700274 0.6607357371 0.4356430823 -0.366679558852 +1403637133038319104.0000000000 4.6047968101 -1.8477829055 0.5587033690 0.4887768113 0.6611309512 0.4354998430 -0.366528281059 +1403637133088318976.0000000000 4.6051499000 -1.8477694265 0.5588528485 0.4893955558 0.6604729490 0.4357749920 -0.366561904665 +1403637133138319104.0000000000 4.6063243719 -1.8484318468 0.5599004518 0.4889010200 0.6598586575 0.4351928657 -0.369011536929 +1403637133188318976.0000000000 4.6072515488 -1.8482409130 0.5608780200 0.4896561599 0.6595321061 0.4354831222 -0.368250860698 +1403637133238319104.0000000000 4.6076354927 -1.8473726342 0.5614334922 0.4918185750 0.6590826392 0.4363449739 -0.365140559032 +1403637133288318976.0000000000 4.6085067746 -1.8469514190 0.5629914620 0.4929506310 0.6589672768 0.4373750921 -0.362580794201 +1403637133338319104.0000000000 4.6094818850 -1.8465863086 0.5660221937 0.4932197507 0.6595985531 0.4377852569 -0.360566353317 +1403637133388318976.0000000000 4.6103791226 -1.8457527567 0.5707320418 0.4936418435 0.6617783776 0.4366845184 -0.357314624104 +1403637133438319104.0000000000 4.6112912648 -1.8453105006 0.5752269165 0.4926208826 0.6644323523 0.4360973768 -0.354504433258 +1403637133488318976.0000000000 4.6125496520 -1.8458491253 0.5784793980 0.4890660400 0.6669293193 0.4371506124 -0.353438868322 +1403637133538319104.0000000000 4.6130156676 -1.8447260206 0.5805040542 0.4860848641 0.6707209787 0.4369211288 -0.350649113425 +1403637133588318976.0000000000 4.6136365544 -1.8432872877 0.5820662562 0.4832157821 0.6744515058 0.4364201782 -0.348073415023 +1403637133638319104.0000000000 4.6147375699 -1.8413447347 0.5848205072 0.4819642479 0.6771852270 0.4357908061 -0.345278156596 +1403637133688318976.0000000000 4.6164855791 -1.8391579616 0.5894588164 0.4824367058 0.6784087606 0.4359172563 -0.342041699373 +1403637133738319104.0000000000 4.6187189234 -1.8372736579 0.5974728885 0.4832160464 0.6792628233 0.4352790747 -0.340053519936 +1403637133788318976.0000000000 4.6210041406 -1.8357564995 0.6089892343 0.4845211685 0.6802265137 0.4338092129 -0.338143008394 +1403637133838319104.0000000000 4.6221786721 -1.8337028937 0.6243506347 0.4856411473 0.6828295277 0.4314216799 -0.334322966965 +1403637133888318976.0000000000 4.6227641147 -1.8317654725 0.6446973436 0.4854280246 0.6865090394 0.4290718915 -0.330094355643 +1403637133938319104.0000000000 4.6230760421 -1.8305003814 0.6704093499 0.4843362192 0.6897953047 0.4270701975 -0.327432299508 +1403637133988318976.0000000000 4.6233684911 -1.8295591808 0.6998090187 0.4851504172 0.6917059409 0.4256647530 -0.324008459964 +1403637134038319104.0000000000 4.6235429832 -1.8289398578 0.7316844567 0.4869462490 0.6922509104 0.4245044428 -0.321664430057 +1403637134088318976.0000000000 4.6237437222 -1.8282600191 0.7639807038 0.4904573962 0.6918702737 0.4244109890 -0.3172418308 +1403637134138319104.0000000000 4.6237559283 -1.8276892218 0.7964924743 0.4948822888 0.6913999002 0.4238562026 -0.31209552665 +1403637134188318976.0000000000 4.6232054527 -1.8268086752 0.8285776267 0.5004732719 0.6901900938 0.4229472026 -0.30705016258 +1403637134238319104.0000000000 4.6220715746 -1.8262175517 0.8606190965 0.5082183526 0.6876112336 0.4203230587 -0.303699561766 +1403637134288318976.0000000000 4.6212494586 -1.8263979984 0.8905536845 0.5146517118 0.6839715406 0.4173743037 -0.305147895026 +1403637134338319104.0000000000 4.6205884892 -1.8264386079 0.9169776572 0.5210143350 0.6797198203 0.4143225720 -0.307996485136 +1403637134388318976.0000000000 4.6198968317 -1.8262070120 0.9385654264 0.5271649990 0.6756454435 0.4107126479 -0.311312414329 +1403637134438319104.0000000000 4.6189239630 -1.8258017156 0.9532961278 0.5315685162 0.6740078251 0.4055990886 -0.314066463555 +1403637134488318976.0000000000 4.6177309045 -1.8255076214 0.9604144285 0.5326170910 0.6742179989 0.4006189167 -0.318203720737 +1403637134538319104.0000000000 4.6164459594 -1.8244190347 0.9583489602 0.5319367195 0.6758966730 0.3978156915 -0.319295614427 +1403637134588318976.0000000000 4.6153603098 -1.8223670648 0.9471828543 0.5300553983 0.6782338792 0.3977482769 -0.317547458073 +1403637134638319104.0000000000 4.6145104263 -1.8195331785 0.9275437445 0.5273122423 0.6808786497 0.4001811839 -0.313370521264 +1403637134688318976.0000000000 4.6137911415 -1.8165618205 0.9002152264 0.5230933148 0.6839713280 0.4040065681 -0.308764148632 +1403637134738319104.0000000000 4.6130571133 -1.8141540698 0.8669701838 0.5157957128 0.6879888506 0.4090013535 -0.305522530989 +1403637134788318976.0000000000 4.6129908850 -1.8127021451 0.8301368911 0.5065954135 0.6928371580 0.4150389879 -0.301795291562 +1403637134838319104.0000000000 4.6135331999 -1.8125058230 0.7921086124 0.4956165849 0.6993887736 0.4194301128 -0.29882758341 +1403637134888318976.0000000000 4.6146628546 -1.8132512700 0.7550472256 0.4844118979 0.7057365430 0.4236236731 -0.296351191212 +1403637134938319104.0000000000 4.6160672506 -1.8145332193 0.7207002793 0.4751887394 0.7119405437 0.4250167674 -0.294443664507 +1403637134988318976.0000000000 4.6174655878 -1.8164284537 0.6906905574 0.4682039676 0.7158826446 0.4253570422 -0.295581580143 +1403637135038319104.0000000000 4.6188442595 -1.8180498738 0.6654506847 0.4644191283 0.7180702580 0.4253944184 -0.296191773306 +1403637135088318976.0000000000 4.6200466407 -1.8193672981 0.6454853200 0.4619246122 0.7194469680 0.4254383610 -0.296688243485 +1403637135138319104.0000000000 4.6249946604 -1.8163290638 0.6269595431 0.4599997961 0.7201592613 0.4273625674 -0.295181405261 +1403637135188318976.0000000000 4.6271995119 -1.8167547670 0.6182082945 0.4573869567 0.7214685380 0.4301184587 -0.292024711328 +1403637135238319104.0000000000 4.6292041237 -1.8170044863 0.6177347123 0.4527443317 0.7241221315 0.4336630458 -0.287412719908 +1403637135288318976.0000000000 4.6302008957 -1.8164306631 0.6277002027 0.4485160010 0.7270689682 0.4358455519 -0.283271543121 +1403637135338319104.0000000000 4.6299590134 -1.8150397916 0.6484724211 0.4481198015 0.7281251881 0.4359483603 -0.281018471069 +1403637135388318976.0000000000 4.6286500444 -1.8132499867 0.6779538491 0.4525043412 0.7262723546 0.4346268663 -0.280834070618 +1403637135438319104.0000000000 4.6267009335 -1.8108556034 0.7139740376 0.4612194000 0.7215661771 0.4325618197 -0.281973738657 +1403637135488318976.0000000000 4.6243198079 -1.8081818049 0.7546617264 0.4724881845 0.7152913733 0.4301792294 -0.282946986842 +1403637135538319104.0000000000 4.6217619008 -1.8060288152 0.7978074687 0.4831526617 0.7089110654 0.4272300092 -0.285452493664 +1403637135588318976.0000000000 4.6189396991 -1.8037596306 0.8415216744 0.4937508337 0.7033151814 0.4240583698 -0.285888735086 +1403637135638319104.0000000000 4.6157555522 -1.8019727545 0.8844143127 0.5033193201 0.6989459626 0.4192136368 -0.287061195839 +1403637135688318976.0000000000 4.6126968227 -1.8007930745 0.9251317837 0.5118534095 0.6946368321 0.4138894359 -0.290140127407 +1403637135738319104.0000000000 4.6101162084 -1.8006166397 0.9617183164 0.5176792418 0.6913230699 0.4084177584 -0.295424356251 +1403637135788318976.0000000000 4.6081675805 -1.8009212854 0.9920325556 0.5215693680 0.6888372016 0.4032787837 -0.301388331886 +1403637135838319104.0000000000 4.6068213359 -1.8007203630 1.0134570351 0.5242283872 0.6871845592 0.3997701461 -0.305197985008 +1403637135888318976.0000000000 4.6052347528 -1.8001544790 1.0255101079 0.5251571342 0.6868132851 0.3968979817 -0.308171199107 +1403637135938319104.0000000000 4.6098215872 -1.7973442173 1.0300847548 0.5250537672 0.6875873124 0.3956559988 -0.308218364042 +1403637135988318976.0000000000 4.6085748342 -1.7964953384 1.0214660383 0.5230331382 0.6887454043 0.3964574816 -0.30803826012 +1403637136038319104.0000000000 4.6071030637 -1.7962448610 1.0026871473 0.5203071498 0.6900395680 0.3988957183 -0.306607355475 +1403637136088318976.0000000000 4.6051426459 -1.7958806286 0.9750953499 0.5176779980 0.6917390665 0.4019593495 -0.303208238034 +1403637136138319104.0000000000 4.6027425314 -1.7956971852 0.9406012269 0.5137985845 0.6947851473 0.4038580872 -0.300305276435 +1403637136188318976.0000000000 4.6007093846 -1.7955920264 0.9004561802 0.5097945155 0.6978370205 0.4081164445 -0.294234621424 +1403637136238319104.0000000000 4.5992937950 -1.7965662559 0.8585880502 0.5027019946 0.7030101668 0.4108627951 -0.290274307459 +1403637136288318976.0000000000 4.5992336111 -1.7981935956 0.8160344356 0.4940072506 0.7086046818 0.4155222724 -0.284916623619 +1403637136338319104.0000000000 4.6000228140 -1.8000150884 0.7753196021 0.4847270553 0.7151563864 0.4190119236 -0.279320662971 +1403637136388318976.0000000000 4.6021651991 -1.8026941752 0.7375472343 0.4742191298 0.7215049940 0.4222942428 -0.276069435173 +1403637136438319104.0000000000 4.6052952845 -1.8057972380 0.7035188680 0.4639667078 0.7271623332 0.4257866532 -0.27326829515 +1403637136488318976.0000000000 4.6082912359 -1.8051908317 0.6735577727 0.4539873322 0.7324775860 0.4274936546 -0.273168928327 +1403637136538319104.0000000000 4.6112359484 -1.8075169831 0.6543679640 0.4463616467 0.7365994214 0.4281766322 -0.273582426783 +1403637136588318976.0000000000 4.6135593249 -1.8089437468 0.6436059765 0.4421077042 0.7388419894 0.4291019944 -0.272992254191 +1403637136638319104.0000000000 4.6151566969 -1.8094723406 0.6425552224 0.4401834362 0.7396095714 0.4307014743 -0.271500394952 +1403637136688318976.0000000000 4.6161029319 -1.8092715073 0.6524296359 0.4400221324 0.7392584230 0.4328318028 -0.269321624552 +1403637136738319104.0000000000 4.6162547857 -1.8090889168 0.6741899576 0.4401293949 0.7390587944 0.4326306467 -0.270016550939 +1403637136788318976.0000000000 4.6159667275 -1.8086055296 0.7058802929 0.4425035857 0.7374545474 0.4322038959 -0.271203170244 +1403637136838319104.0000000000 4.6154679273 -1.8078540060 0.7454689270 0.4480457786 0.7335649994 0.4310365390 -0.274490207407 +1403637136888318976.0000000000 4.6142489459 -1.8060146288 0.7906119363 0.4572112198 0.7284015922 0.4283753906 -0.277278822962 +1403637136938319104.0000000000 4.6135991836 -1.8031523232 0.8400393682 0.4673753062 0.7235332416 0.4235478636 -0.280476698902 +1403637136988318976.0000000000 4.6120860759 -1.7995734761 0.8891323641 0.4790448485 0.7190715623 0.4176372505 -0.281124969339 +1403637137038319104.0000000000 4.6110723244 -1.7967973249 0.9358381206 0.4896771372 0.7152581838 0.4101656375 -0.28352456972 +1403637137088318976.0000000000 4.6100781065 -1.7947655038 0.9778939160 0.4996758265 0.7115521958 0.4022564128 -0.286718188014 +1403637137138319104.0000000000 4.6091721783 -1.7944176333 1.0129530831 0.5066011189 0.7081465007 0.3942132322 -0.294074424987 +1403637137188318976.0000000000 4.6084851020 -1.7947621619 1.0383180838 0.5114227878 0.7046913088 0.3883448755 -0.30173688719 +1403637137238319104.0000000000 4.6089032287 -1.7935764262 1.0554304751 0.5155704399 0.7007016723 0.3864544960 -0.306361241758 +1403637137288318976.0000000000 4.6085893987 -1.7920748843 1.0592533319 0.5189415931 0.6979726448 0.3853303053 -0.308308880541 +1403637137338319104.0000000000 4.6079347125 -1.7905495697 1.0525208327 0.5217850242 0.6957804252 0.3848075148 -0.309116749788 +1403637137388318976.0000000000 4.6069629664 -1.7898238553 1.0354831076 0.5231158279 0.6940918863 0.3855435768 -0.309745757766 +1403637137438319104.0000000000 4.6053827211 -1.7895896647 1.0099203854 0.5220734496 0.6937871393 0.3866216771 -0.3108414345 +1403637137488318976.0000000000 4.6039024839 -1.7894612886 0.9763892198 0.5200201611 0.6947848987 0.3902321090 -0.307525409718 +1403637137538319104.0000000000 4.6029184280 -1.7902661489 0.9371487831 0.5156916618 0.6970313815 0.3957798397 -0.302601522997 +1403637137588318976.0000000000 4.6027098807 -1.7910245600 0.8938089569 0.5103543351 0.7009861968 0.4022445508 -0.293864128231 +1403637137638319104.0000000000 4.6027640895 -1.7922223506 0.8486589654 0.5028327994 0.7070407454 0.4083193594 -0.283774313357 +1403637137688318976.0000000000 4.6031338874 -1.7941592585 0.8040662059 0.4935538756 0.7142690154 0.4124803257 -0.275833874618 +1403637137738319104.0000000000 4.6040730478 -1.7973877896 0.7622827809 0.4831029631 0.7207737718 0.4162233048 -0.271762501916 +1403637137788318976.0000000000 4.6068480931 -1.8017673451 0.7246399401 0.4736832495 0.7256725620 0.4194325406 -0.270369850077 +1403637137838319104.0000000000 4.6091738784 -1.8019764597 0.6886763717 0.4657426078 0.7290862648 0.4225673255 -0.270099791044 +1403637137888318976.0000000000 4.6137086608 -1.8057517253 0.6621602600 0.4584016318 0.7316163194 0.4264322729 -0.269742510021 +1403637137938319104.0000000000 4.6180165210 -1.8079888722 0.6439120308 0.4522769490 0.7342942248 0.4303427737 -0.266575786474 +1403637137988318976.0000000000 4.6212853029 -1.8086685173 0.6360046146 0.4459154072 0.7373270869 0.4343458589 -0.262396439378 +1403637138038319104.0000000000 4.6232408141 -1.8080207223 0.6403322061 0.4401333985 0.7404689789 0.4369702173 -0.258931094994 +1403637138088318976.0000000000 4.6239510707 -1.8067299708 0.6577479656 0.4364211211 0.7424049532 0.4371662391 -0.259339873435 +1403637138138319104.0000000000 4.6236151691 -1.8050028385 0.6867321415 0.4366071896 0.7408399177 0.4374183400 -0.263050516389 +1403637138188318976.0000000000 4.6226555542 -1.8011972213 0.7240521445 0.4430323159 0.7348377925 0.4400876109 -0.264686003625 +1403637138238319104.0000000000 4.6215663712 -1.7959929853 0.7677582010 0.4563509755 0.7265105197 0.4413291704 -0.262973031318 +1403637138288318976.0000000000 4.6200622500 -1.7910077678 0.8164612948 0.4707861584 0.7185559472 0.4380097174 -0.264924953972 +1403637138338319104.0000000000 4.6179627220 -1.7881925360 0.8654003440 0.4854252036 0.7108564430 0.4319246066 -0.269233399333 +1403637138388318976.0000000000 4.6153082146 -1.7865596586 0.9129140776 0.4998996782 0.7041872097 0.4228167167 -0.274675644253 +1403637138438319104.0000000000 4.6134221377 -1.7854661621 0.9554996658 0.5139815854 0.6974434021 0.4148872455 -0.277964393986 +1403637138488318976.0000000000 4.6122681976 -1.7850822986 0.9911813063 0.5251452312 0.6926053770 0.4069226097 -0.280952429462 +1403637138538319104.0000000000 4.6116463418 -1.7851835169 1.0174078802 0.5331706923 0.6889473100 0.4004179373 -0.284158569263 +1403637138588318976.0000000000 4.6114382299 -1.7850806861 1.0329294054 0.5388064196 0.6859100107 0.3964870903 -0.286379270705 +1403637138638319104.0000000000 4.6117109586 -1.7834255389 1.0417558574 0.5410450450 0.6841337705 0.3943258862 -0.289375774535 +1403637138688318976.0000000000 4.6108372157 -1.7824917609 1.0359858077 0.5406291361 0.6840522799 0.3939362953 -0.290872499166 +1403637138738319104.0000000000 4.6090707865 -1.7816657800 1.0198557965 0.5375466746 0.6858015033 0.3936193727 -0.292888477308 +1403637138788318976.0000000000 4.6066711838 -1.7801544261 0.9944558596 0.5334336878 0.6890013894 0.3939586718 -0.292441705486 +1403637138838319104.0000000000 4.6033788542 -1.7781380217 0.9610849946 0.5284703868 0.6936710240 0.3945469426 -0.289607097228 +1403637138888318976.0000000000 4.6007269923 -1.7765392479 0.9216815247 0.5223512965 0.6984318094 0.3967958157 -0.286173393842 +1403637138938319104.0000000000 4.5990267154 -1.7761592726 0.8785729793 0.5158378189 0.7020789533 0.4007334882 -0.283565088478 +1403637138988318976.0000000000 4.5968594333 -1.7771387420 0.8351769811 0.5074509421 0.7056340907 0.4027091131 -0.287053029148 +1403637139038319104.0000000000 4.5948276362 -1.7789882425 0.7926572400 0.4992907728 0.7084442197 0.4048029895 -0.291461921178 +1403637139088318976.0000000000 4.5932000938 -1.7815889005 0.7528035084 0.4921382289 0.7109912394 0.4060980717 -0.295593939821 +1403637139138319104.0000000000 4.5921892479 -1.7848959040 0.7159766795 0.4865908131 0.7128337015 0.4077465175 -0.298060852917 +1403637139188318976.0000000000 4.5900784810 -1.7848274637 0.6803496891 0.4811438019 0.7145057923 0.4095721892 -0.300387643838 +1403637139238319104.0000000000 4.5891874619 -1.7873791551 0.6515688965 0.4778021957 0.7150272403 0.4122045494 -0.300879572123 +1403637139288318976.0000000000 4.5876205368 -1.7892378221 0.6284410122 0.4761209839 0.7145633737 0.4141871627 -0.301922155199 +1403637139338319104.0000000000 4.5855690468 -1.7901370557 0.6110684049 0.4752611878 0.7137539055 0.4165699017 -0.301913369528 +1403637139388318976.0000000000 4.5834416050 -1.7901543916 0.5984609215 0.4749343646 0.7122644369 0.4198430364 -0.301410925482 +1403637139438319104.0000000000 4.5821142169 -1.7904623653 0.5896852978 0.4740563531 0.7097417050 0.4236037512 -0.303475119709 +1403637139488318976.0000000000 4.5808150597 -1.7908791224 0.5835654871 0.4737142472 0.7069019191 0.4262093516 -0.306969179911 +1403637139538319104.0000000000 4.5792675415 -1.7916232520 0.5789094539 0.4737176254 0.7045936870 0.4272267646 -0.310832172116 +1403637139588318976.0000000000 4.5776538921 -1.7923494401 0.5748803661 0.4753317145 0.7023317423 0.4273457523 -0.313313729272 +1403637139638319104.0000000000 4.5763143843 -1.7929405642 0.5710843527 0.4778123027 0.6994522751 0.4284586428 -0.314460028622 +1403637139688318976.0000000000 4.5751523308 -1.7932548212 0.5672097076 0.4793390353 0.6970903925 0.4293763918 -0.316124956489 +1403637139738319104.0000000000 4.5743470288 -1.7934060763 0.5628305502 0.4799381507 0.6955593709 0.4300776022 -0.317631530487 +1403637139788318976.0000000000 4.5740178443 -1.7930188403 0.5587202042 0.4806082086 0.6948991978 0.4303988978 -0.317628153039 +1403637139838319104.0000000000 4.5742966709 -1.7924376547 0.5565023035 0.4819419151 0.6939591182 0.4284876411 -0.320235966436 +1403637139888318976.0000000000 4.5748699773 -1.7913556857 0.5562343734 0.4868666837 0.6911228074 0.4250878046 -0.323435396592 +1403637139938319104.0000000000 4.5754406806 -1.7902397278 0.5558406510 0.4905187058 0.6901770418 0.4208046141 -0.325531145942 +1403637139988318976.0000000000 4.5763234863 -1.7899050851 0.5552344531 0.4928500139 0.6905532118 0.4160805602 -0.327279838892 +1403637140038319104.0000000000 4.5776038748 -1.7896596184 0.5553856662 0.4955157306 0.6907681193 0.4103715328 -0.329998138108 +1403637140088318976.0000000000 4.5790815363 -1.7888514891 0.5558106535 0.5009223643 0.6888469890 0.4069101409 -0.330137468072 +1403637140138319104.0000000000 4.5805954790 -1.7885592634 0.5566177874 0.5062922358 0.6869618647 0.4028805398 -0.330815415321 +1403637140188318976.0000000000 4.5818357970 -1.7883488120 0.5570570049 0.5085407045 0.6865994823 0.4000592511 -0.331542000943 +1403637140238319104.0000000000 4.5828726037 -1.7872446938 0.5561167791 0.5087047647 0.6881437788 0.3993333127 -0.328953655474 +1403637140288318976.0000000000 4.5835559408 -1.7865413866 0.5556117956 0.5086633693 0.6887897293 0.3981593073 -0.329088820108 +1403637140338319104.0000000000 4.5840692255 -1.7861721429 0.5550176923 0.5081227799 0.6893785694 0.3965219950 -0.330664083281 +1403637140388318976.0000000000 4.5841823424 -1.7864648564 0.5552948805 0.5074671040 0.6898651187 0.3955523324 -0.331815624518 +1403637140438319104.0000000000 4.5844048516 -1.7863636578 0.5552229483 0.5077228178 0.6896040041 0.3961869604 -0.331209526285 +1403637140488318976.0000000000 4.5845039546 -1.7866239341 0.5553548482 0.5073550008 0.6899021751 0.3954468191 -0.332035698661 +1403637140538319104.0000000000 4.5846244421 -1.7866595895 0.5553387105 0.5072983751 0.6899530600 0.3953928437 -0.332080762482 +1403637140588318976.0000000000 4.5846874372 -1.7869921802 0.5554920626 0.5067482819 0.6902636271 0.3948104325 -0.332967004733 +1403637140638319104.0000000000 4.5847767321 -1.7869527512 0.5553979816 0.5067599402 0.6902220202 0.3949170248 -0.332909100646 +1403637140688318976.0000000000 4.5848035289 -1.7870685104 0.5553624631 0.5066412439 0.6902413911 0.3948913559 -0.33308000398 +1403637140738319104.0000000000 4.5848727547 -1.7870614672 0.5553100119 0.5066447136 0.6902211428 0.3949684301 -0.333025295456 +1403637140788318976.0000000000 4.5849395776 -1.7871077417 0.5552952409 0.5065537359 0.6902405531 0.3949923054 -0.333095136809 +1403637140838319104.0000000000 4.5850313453 -1.7871316586 0.5553365629 0.5065091325 0.6902795192 0.3949606711 -0.333119726739 +1403637140888318976.0000000000 4.5850487718 -1.7870985349 0.5553056686 0.5064850552 0.6903162270 0.3949213513 -0.333126885642 +1403637140938319104.0000000000 4.5850596757 -1.7871075915 0.5552811385 0.5065237497 0.6903037210 0.3949491420 -0.333061013841 +1403637140988318976.0000000000 4.5850935392 -1.7871617329 0.5552672601 0.5064320909 0.6903611091 0.3949365863 -0.333096336259 +1403637141038319104.0000000000 4.5850609613 -1.7871524118 0.5552246535 0.5064393168 0.6903515859 0.3949569814 -0.333080904787 +1403637141088318976.0000000000 4.5850559972 -1.7871703933 0.5552287028 0.5064039505 0.6903792960 0.3949265336 -0.3331133435 +1403637141138319104.0000000000 4.5850683876 -1.7871231527 0.5552238794 0.5064282609 0.6903710369 0.3949788277 -0.333031490453 +1403637141188318976.0000000000 4.5850422288 -1.7871457254 0.5552512354 0.5063541575 0.6904090791 0.3949459420 -0.333104298437 +1403637141238319104.0000000000 4.5850213163 -1.7871152640 0.5552459764 0.5063856311 0.6903763821 0.3949970528 -0.333063615633 +1403637141288318976.0000000000 4.5850016712 -1.7871477656 0.5552924619 0.5063408570 0.6904045838 0.3949904753 -0.333081028569 +1403637141338319104.0000000000 4.5849477172 -1.7871490903 0.5552756681 0.5063137203 0.6904007363 0.3950048967 -0.333113151311 +1403637141388318976.0000000000 4.5849076765 -1.7871253732 0.5552671036 0.5063214511 0.6904067585 0.3950113452 -0.333081271107 +1403637141438319104.0000000000 4.5849053116 -1.7871188531 0.5552803752 0.5062764546 0.6904292145 0.3950332898 -0.333077095064 +1403637141488318976.0000000000 4.5848125667 -1.7870660072 0.5552483182 0.5062958297 0.6904306834 0.3950061176 -0.333076824892 +1403637141538319104.0000000000 4.5847680831 -1.7870763443 0.5552889914 0.5062580062 0.6904560798 0.3950267897 -0.333057154872 +1403637141588318976.0000000000 4.5846899187 -1.7870605752 0.5552680280 0.5062620892 0.6904546029 0.3950457031 -0.333031576475 +1403637141638319104.0000000000 4.5846330963 -1.7870410627 0.5552906315 0.5062836995 0.6904637395 0.3950004194 -0.333033494971 +1403637141688318976.0000000000 4.5846033496 -1.7870608824 0.5553376731 0.5062064629 0.6905118452 0.3949696380 -0.333087666709 +1403637141738319104.0000000000 4.5845744633 -1.7870220801 0.5553173764 0.5062355803 0.6905015125 0.3949878530 -0.333043232049 +1403637141788318976.0000000000 4.5845762831 -1.7870535686 0.5553576988 0.5061672456 0.6905393664 0.3950158120 -0.333035450474 +1403637141838319104.0000000000 4.5846022295 -1.7870829674 0.5553637847 0.5061561324 0.6905299680 0.3950129459 -0.333075224917 +1403637141888318976.0000000000 4.5846145774 -1.7870850018 0.5553256254 0.5061600000 0.6905233174 0.3950653451 -0.333020983685 +1403637141938319104.0000000000 4.5845822351 -1.7871530226 0.5553451190 0.5060671100 0.6905697351 0.3950279619 -0.33311023768 +1403637141988318976.0000000000 4.5846068878 -1.7870978732 0.5553623707 0.5061012135 0.6905602637 0.3950315238 -0.333073834222 +1403637142038319104.0000000000 4.5846462210 -1.7870696506 0.5553918772 0.5060751110 0.6905878971 0.3950053628 -0.333087228538 +1403637142088318976.0000000000 4.5847160737 -1.7870494857 0.5553737035 0.5060515352 0.6905948913 0.3950589047 -0.333045044433 +1403637142138319104.0000000000 4.5847637861 -1.7870620909 0.5553419635 0.5059659763 0.6906373860 0.3950627580 -0.333082345719 +1403637142188318976.0000000000 4.5847835562 -1.7870283264 0.5553328616 0.5060323843 0.6906033843 0.3950823813 -0.333028682877 +1403637142238319104.0000000000 4.5847698725 -1.7870705746 0.5553422570 0.5060055408 0.6906191962 0.3950509844 -0.333073923166 +1403637142288318976.0000000000 4.5847799642 -1.7870996139 0.5553753961 0.5060021322 0.6906197109 0.3950645244 -0.333061974245 +1403637142338319104.0000000000 4.5848131264 -1.7870979559 0.5553805519 0.5059908293 0.6906197926 0.3950645457 -0.333078950591 +1403637142388318976.0000000000 4.5848392447 -1.7870770588 0.5553659397 0.5060445355 0.6905874290 0.3951047286 -0.333016792945 +1403637142438319104.0000000000 4.5848019180 -1.7871086671 0.5553513741 0.5059776687 0.6906271745 0.3950677674 -0.333079815976 +1403637142488318976.0000000000 4.5847797353 -1.7870963940 0.5553454756 0.5059810304 0.6906353327 0.3950678080 -0.333057744382 +1403637142538319104.0000000000 4.5847801147 -1.7871083577 0.5553350346 0.5059759267 0.6906265351 0.3950498293 -0.333105062982 +1403637142588318976.0000000000 4.5847819847 -1.7871223642 0.5553458351 0.5059622034 0.6906296306 0.3950629634 -0.333103913204 +1403637142638319104.0000000000 4.5847736962 -1.7871312225 0.5552754560 0.5059239992 0.6906567097 0.3950551074 -0.333115112926 +1403637142688318976.0000000000 4.5848178740 -1.7871205619 0.5552821160 0.5059058950 0.6906561247 0.3950934895 -0.333098299858 +1403637142738319104.0000000000 4.5848049726 -1.7871250885 0.5552461559 0.5058898338 0.6906576176 0.3951035911 -0.333107615649 +1403637142788318976.0000000000 4.5847737929 -1.7871540357 0.5553120497 0.5058534320 0.6906750309 0.3950838158 -0.33315024459 +1403637142838319104.0000000000 4.5847281513 -1.7871294681 0.5553058657 0.5058645144 0.6906806992 0.3950682032 -0.333140180064 +1403637142888318976.0000000000 4.5847706853 -1.7871158269 0.5553822220 0.5058586228 0.6906764468 0.3950594474 -0.333168324697 +1403637142938319104.0000000000 4.5847551482 -1.7871250421 0.5553477943 0.5058343410 0.6906812314 0.3950670153 -0.333186298489 +1403637142988318976.0000000000 4.5848219243 -1.7871638220 0.5553578754 0.5058028999 0.6907039631 0.3950475049 -0.333210040007 +1403637143038319104.0000000000 4.5848712731 -1.7871634144 0.5553719506 0.5058184647 0.6906847267 0.3950301107 -0.333246906506 +1403637143088318976.0000000000 4.5849415497 -1.7871963984 0.5553850390 0.5057657491 0.6907008985 0.3950555031 -0.333263297352 +1403637143138319104.0000000000 4.5849599110 -1.7872419164 0.5553684794 0.5057413446 0.6906933051 0.3951077749 -0.333254102645 +1403637143188318976.0000000000 4.5849917256 -1.7872789062 0.5554254281 0.5057239907 0.6907181228 0.3950833087 -0.333258006971 +1403637143238319104.0000000000 4.5850188248 -1.7873017348 0.5553878783 0.5057311020 0.6907086048 0.3950979600 -0.33324957273 +1403637143288318976.0000000000 4.5850530461 -1.7873405749 0.5553695247 0.5057152388 0.6907100819 0.3950933819 -0.333276010972 +1403637143338319104.0000000000 4.5850876123 -1.7873405077 0.5553387357 0.5056793312 0.6907143165 0.3951324933 -0.33327535124 +1403637143388318976.0000000000 4.5851244963 -1.7873353508 0.5553690050 0.5056659289 0.6907139962 0.3951233393 -0.333307201654 +1403637143438319104.0000000000 4.5851185264 -1.7873044737 0.5552970596 0.5057140047 0.6906918649 0.3951016002 -0.333305893589 +1403637143488318976.0000000000 4.5851230664 -1.7872897953 0.5553192202 0.5056682631 0.6907054469 0.3950879884 -0.333363277391 +1403637143538319104.0000000000 4.5851702620 -1.7873099148 0.5552675300 0.5056119622 0.6907342726 0.3951108007 -0.333361910733 +1403637143588318976.0000000000 4.5851479538 -1.7872789211 0.5552888268 0.5057023486 0.6906677778 0.3950801663 -0.333398886713 +1403637143638319104.0000000000 4.5851671035 -1.7873122888 0.5552871230 0.5055978505 0.6907190500 0.3951076722 -0.333418558129 +1403637143688318976.0000000000 4.5851183055 -1.7873295019 0.5552718056 0.5055763878 0.6907309356 0.3951111491 -0.333422360698 +1403637143738319104.0000000000 4.5850445019 -1.7873622584 0.5552809276 0.5056178847 0.6907058704 0.3951096677 -0.333413115732 +1403637143788318976.0000000000 4.5849802011 -1.7874177324 0.5553396387 0.5056087019 0.6907187898 0.3950767634 -0.333439267338 +1403637143838319104.0000000000 4.5849339446 -1.7874504099 0.5553460759 0.5055966125 0.6907348346 0.3950791973 -0.33342147737 +1403637143888318976.0000000000 4.5848998823 -1.7874493354 0.5554259701 0.5056159608 0.6907103032 0.3950521295 -0.333475024948 +1403637143938319104.0000000000 4.5849030197 -1.7874990067 0.5554936610 0.5055352035 0.6905944584 0.3952381560 -0.333616924171 +1403637143988318976.0000000000 4.5849656112 -1.7874859183 0.5554917507 0.5055095256 0.6906336115 0.3952374595 -0.333575605802 +1403637144038319104.0000000000 4.5849930993 -1.7873672630 0.5554684291 0.5055049723 0.6906848003 0.3951395805 -0.333592478176 +1403637144088318976.0000000000 4.5850573859 -1.7872340208 0.5554937409 0.5055192601 0.6907256161 0.3951047010 -0.333527624369 +1403637144138319104.0000000000 4.5850782979 -1.7870838916 0.5555184693 0.5055054127 0.6908414483 0.3949060244 -0.333544004544 +1403637144188318976.0000000000 4.5851638095 -1.7870516673 0.5555483714 0.5055370971 0.6908290800 0.3949833320 -0.333430042452 +1403637144238319104.0000000000 4.5851212184 -1.7871422864 0.5555607164 0.5054113135 0.6908980656 0.3949403909 -0.333528641669 +1403637144288318976.0000000000 4.5851734716 -1.7872556018 0.5555480046 0.5054048945 0.6909173593 0.3950015604 -0.333425947618 +1403637144338319104.0000000000 4.5851119647 -1.7873000967 0.5555057299 0.5054528941 0.6909440189 0.3948680755 -0.333456050374 +1403637144388318976.0000000000 4.5851567108 -1.7873155445 0.5554446040 0.5054656691 0.6908859621 0.3949210691 -0.333494218833 +1403637144438319104.0000000000 4.5851434678 -1.7873012778 0.5553535958 0.5054665773 0.6908278502 0.3949360497 -0.333595469512 +1403637144488318976.0000000000 4.5851690323 -1.7873009423 0.5553014997 0.5054650311 0.6907425218 0.3950494851 -0.33364018822 +1403637144538319104.0000000000 4.5851538987 -1.7873574337 0.5553461144 0.5054215844 0.6907176705 0.3950634176 -0.333740944062 +1403637144588318976.0000000000 4.5852075919 -1.7871952122 0.5552624735 0.5055077424 0.6910116616 0.3947869058 -0.33332882403 +1403637144638319104.0000000000 4.5852222296 -1.7872437031 0.5553120742 0.5055056555 0.6908642935 0.3948941514 -0.333510373839 +1403637144688318976.0000000000 4.5852293584 -1.7873011374 0.5553639198 0.5054019459 0.6909290463 0.3948951739 -0.333532198901 +1403637144738319104.0000000000 4.5851958002 -1.7873974234 0.5554181463 0.5054969572 0.6906944432 0.3950859286 -0.333648200049 +1403637144788318976.0000000000 4.5850936905 -1.7874682435 0.5554451231 0.5054759485 0.6907253304 0.3950155602 -0.333699401446 +1403637144838319104.0000000000 4.5850209466 -1.7874402738 0.5554080410 0.5054913815 0.6907106188 0.3950898790 -0.333618482351 +1403637144888318976.0000000000 4.5849393893 -1.7874247713 0.5553850972 0.5053848402 0.6907608772 0.3950828060 -0.333684207227 +1403637144938319104.0000000000 4.5849501742 -1.7873486939 0.5553527331 0.5054053928 0.6906561764 0.3952906191 -0.333623682411 +1403637144988318976.0000000000 4.5849532749 -1.7873302735 0.5553562653 0.5051956417 0.6906512929 0.3954599225 -0.333750812541 +1403637145038319104.0000000000 4.5849734991 -1.7872680266 0.5553707089 0.5052444286 0.6906765171 0.3954063137 -0.333688272452 +1403637145088318976.0000000000 4.5849175663 -1.7872999489 0.5554618583 0.5052483502 0.6907441865 0.3952939483 -0.333675392827 +1403637145138319104.0000000000 4.5849021974 -1.7873608989 0.5554501606 0.5052161691 0.6908292175 0.3952434423 -0.333607907744 +1403637145188318976.0000000000 4.5849092976 -1.7874141851 0.5554446614 0.5052282521 0.6909085051 0.3951494405 -0.333536760427 +1403637145238319104.0000000000 4.5849357237 -1.7874594148 0.5554052029 0.5052147482 0.6909459813 0.3950790110 -0.333563013845 +1403637145288318976.0000000000 4.5849748897 -1.7874529766 0.5554042515 0.5051679555 0.6910222381 0.3950306376 -0.333533204534 +1403637145338319104.0000000000 4.5850399116 -1.7874852536 0.5553733603 0.5051509482 0.6909818201 0.3950324054 -0.333640588855 +1403637145388318976.0000000000 4.5851140219 -1.7874726781 0.5553371091 0.5051765025 0.6909644996 0.3950490309 -0.333618082269 +1403637145438319104.0000000000 4.5851510573 -1.7875057588 0.5553179829 0.5051641699 0.6909366225 0.3950642799 -0.333676430073 +1403637145488318976.0000000000 4.5851932462 -1.7875399077 0.5553129059 0.5051566532 0.6909201079 0.3950422254 -0.333748109153 +1403637145538319104.0000000000 4.5851921997 -1.7875612210 0.5552852391 0.5051637386 0.6909293803 0.3950360781 -0.333725464313 +1403637145588318976.0000000000 4.5851839591 -1.7875686368 0.5552812833 0.5051577886 0.6909066653 0.3950669962 -0.333744898019 +1403637145638319104.0000000000 4.5851813375 -1.7876382138 0.5552135077 0.5050901872 0.6909250764 0.3950888917 -0.333783176946 +1403637145688318976.0000000000 4.5851968428 -1.7876476868 0.5551711343 0.5050801829 0.6909153945 0.3951654743 -0.333727694904 +1403637145738319104.0000000000 4.5852023306 -1.7876577535 0.5551943907 0.5050305009 0.6909159906 0.3951553544 -0.333813620189 +1403637145788318976.0000000000 4.5852298165 -1.7876604727 0.5552155389 0.5050303618 0.6908950918 0.3951779522 -0.333830333899 +1403637145838319104.0000000000 4.5852030821 -1.7876729110 0.5552557306 0.5050057453 0.6909329933 0.3951543380 -0.33381708331 +1403637145888318976.0000000000 4.5851783506 -1.7876511510 0.5552921447 0.5050157698 0.6909630701 0.3951269784 -0.333772046263 +1403637145938319104.0000000000 4.5851998215 -1.7876419620 0.5553196471 0.5049782035 0.6909781141 0.3951292576 -0.333795041258 +1403637145988318976.0000000000 4.5852467787 -1.7876032510 0.5553348262 0.5049618236 0.6909495783 0.3952032956 -0.333791240213 +1403637146038319104.0000000000 4.5852464074 -1.7875239278 0.5553567572 0.5048639368 0.6910021847 0.3952190135 -0.333811799432 +1403637146088318976.0000000000 4.5851778157 -1.7873769518 0.5553207702 0.5048712213 0.6910241881 0.3952092108 -0.333766836449 +1403637146138319104.0000000000 4.5850815533 -1.7872608442 0.5553228401 0.5048602237 0.6910159097 0.3952220073 -0.333785458123 +1403637146188318976.0000000000 4.5849804347 -1.7871526668 0.5553692841 0.5049160127 0.6909518035 0.3953256019 -0.333711093437 +1403637146238319104.0000000000 4.5849998291 -1.7869265371 0.5554101817 0.5051949331 0.6908524097 0.3954798100 -0.333311787279 +1403637146288318976.0000000000 4.5848341987 -1.7872195340 0.5556167347 0.5047512858 0.6910027704 0.3952052578 -0.333997178061 +1403637146338319104.0000000000 4.5848028173 -1.7872048302 0.5556257733 0.5050407930 0.6908038427 0.3955320130 -0.333583985053 +1403637146388318976.0000000000 4.5846499352 -1.7874902135 0.5557479668 0.5047206594 0.6909781056 0.3952742198 -0.334012881047 +1403637146438319104.0000000000 4.5847737600 -1.7875190930 0.5556294562 0.5048808846 0.6909271574 0.3955164582 -0.333589098837 +1403637146488318976.0000000000 4.5847693296 -1.7877244829 0.5555604420 0.5046510805 0.6910873479 0.3952476689 -0.333923411489 +1403637146538319104.0000000000 4.5848167572 -1.7876834860 0.5553812464 0.5048104293 0.6910007821 0.3954358493 -0.33363878474 +1403637146588318976.0000000000 4.5848570139 -1.7877758644 0.5553240569 0.5045461897 0.6911504522 0.3952191699 -0.33398503363 +1403637146638319104.0000000000 4.5849128067 -1.7877101491 0.5552129311 0.5046984414 0.6910254730 0.3954360125 -0.333756856065 +1403637146688318976.0000000000 4.5849160404 -1.7877334154 0.5552613563 0.5045922218 0.6910684778 0.3952935199 -0.333997128335 +1403637146738319104.0000000000 4.5849328790 -1.7876499539 0.5552545387 0.5046757868 0.6910158687 0.3954315595 -0.333816268606 +1403637146788318976.0000000000 4.5849629070 -1.7876301013 0.5552926074 0.5045460464 0.6910793256 0.3953655625 -0.333959166393 +1403637146838319104.0000000000 4.5849467893 -1.7875977901 0.5552628686 0.5046101716 0.6910219809 0.3954444508 -0.33388753051 +1403637146888318976.0000000000 4.5849676121 -1.7876188311 0.5552656969 0.5045487746 0.6910535142 0.3954396573 -0.333920727094 +1403637146938319104.0000000000 4.5849971589 -1.7875893999 0.5552673290 0.5045558480 0.6910731929 0.3954619951 -0.333842850425 +1403637146988318976.0000000000 4.5850025499 -1.7875955227 0.5553085124 0.5046401810 0.6910016947 0.3955261789 -0.333787338592 +1403637147038319104.0000000000 4.5850032830 -1.7876397185 0.5553722998 0.5044857561 0.6910505777 0.3955226753 -0.333923695165 +1403637147088318976.0000000000 4.5850146734 -1.7877037362 0.5553826558 0.5045064187 0.6910528380 0.3955356894 -0.333872381357 +1403637147138319104.0000000000 4.5850043080 -1.7877450911 0.5553619021 0.5044667196 0.6911066998 0.3955198912 -0.333839593208 +1403637147188318976.0000000000 4.5850140051 -1.7877520229 0.5553443417 0.5045129084 0.6911011619 0.3954840117 -0.333823764553 +1403637147238319104.0000000000 4.5850262345 -1.7877046105 0.5553718671 0.5045209628 0.6911094576 0.3954654728 -0.333816380028 +1403637147288318976.0000000000 4.5850196881 -1.7876562784 0.5553840362 0.5044448079 0.6911590301 0.3954258456 -0.333875772636 +1403637147338319104.0000000000 4.5849797492 -1.7876113025 0.5554024358 0.5044201471 0.6911717844 0.3954057314 -0.333910447814 +1403637147388318976.0000000000 4.5849687644 -1.7875774719 0.5554084567 0.5043847638 0.6911492764 0.3954234703 -0.33398947131 +1403637147438319104.0000000000 4.5850239685 -1.7874601508 0.5553642295 0.5044201248 0.6911357401 0.3954485749 -0.333934351428 +1403637147488318976.0000000000 4.5850640612 -1.7873580171 0.5553570579 0.5043651030 0.6911565905 0.3954237630 -0.334003679473 +1403637147538319104.0000000000 4.5852578392 -1.7872499164 0.5552870035 0.5044487281 0.6910796015 0.3954835843 -0.333965865921 +1403637147588318976.0000000000 4.5851187715 -1.7873487790 0.5553401634 0.5043187826 0.6911522059 0.3954317605 -0.334073220525 +1403637147638319104.0000000000 4.5850236722 -1.7873796040 0.5553197734 0.5044201028 0.6910836052 0.3955398114 -0.333934227248 +1403637147688318976.0000000000 4.5848843290 -1.7875026254 0.5553332862 0.5043210473 0.6911169843 0.3955030149 -0.334058319047 +1403637147738319104.0000000000 4.5847812405 -1.7875326249 0.5553424935 0.5043863538 0.6910938660 0.3954907665 -0.334022047195 +1403637147788318976.0000000000 4.5846893614 -1.7875935964 0.5553377916 0.5043088445 0.6911356738 0.3954806885 -0.334064506911 +1403637147838319104.0000000000 4.5846293341 -1.7876091121 0.5553480634 0.5043675215 0.6911080752 0.3955012028 -0.334008727631 +1403637147888318976.0000000000 4.5845881204 -1.7876748824 0.5553721525 0.5042980248 0.6911461048 0.3954758149 -0.334065029389 +1403637147938319104.0000000000 4.5845861154 -1.7876863598 0.5553617757 0.5043275687 0.6911164860 0.3955271470 -0.334020930879 +1403637147988318976.0000000000 4.5845896149 -1.7877502013 0.5553632288 0.5042846099 0.6911354756 0.3954931305 -0.334086770781 +1403637148038319104.0000000000 4.5845241373 -1.7877487610 0.5553686845 0.5042870741 0.6911370893 0.3954921656 -0.334080854892 +1403637148088318976.0000000000 4.5844436147 -1.7876994125 0.5554233931 0.5042881476 0.6911640604 0.3954642317 -0.334056502939 +1403637148138319104.0000000000 4.5844631114 -1.7875858040 0.5555223537 0.5043277627 0.6911524362 0.3954710138 -0.334012716833 +1403637148188318976.0000000000 4.5844464755 -1.7875226865 0.5555697512 0.5042660169 0.6911797264 0.3954503029 -0.334073985831 +1403637148238319104.0000000000 4.5845565343 -1.7875566481 0.5555583750 0.5041705018 0.6911549178 0.3955807957 -0.334114978419 +1403637148288318976.0000000000 4.5845881680 -1.7875836197 0.5555161805 0.5041547328 0.6911663341 0.3955667631 -0.334131770342 +1403637148338319104.0000000000 4.5845847123 -1.7876644423 0.5554891360 0.5040540950 0.6911779344 0.3956922806 -0.334110986551 +1403637148388318976.0000000000 4.5844587150 -1.7876658332 0.5555158739 0.5041047737 0.6911281862 0.3956428897 -0.33419591738 +1403637148438319104.0000000000 4.5843971281 -1.7877063062 0.5554934265 0.5039839384 0.6911247603 0.3957380969 -0.334272514781 +1403637148488318976.0000000000 4.5843756044 -1.7876822925 0.5553834055 0.5039189285 0.6911172312 0.3958917754 -0.334204111869 +1403637148538319104.0000000000 4.5843284507 -1.7876335205 0.5553704298 0.5039210314 0.6910283803 0.3959756956 -0.334285237832 +1403637148588318976.0000000000 4.5842395568 -1.7874841743 0.5553654944 0.5038072533 0.6910155793 0.3961129317 -0.334320603696 +1403637148638319104.0000000000 4.5846009625 -1.7877739780 0.5552773128 0.5034556063 0.6909944787 0.3965897120 -0.334328705398 +1403637148688318976.0000000000 4.5847414096 -1.7878965443 0.5553922345 0.5032888525 0.6908118042 0.3967325965 -0.334787438576 +1403637148738319104.0000000000 4.5850582303 -1.7879539267 0.5553434150 0.5031355999 0.6906990319 0.3972346022 -0.334655175112 +1403637148788318976.0000000000 4.5852836241 -1.7880745887 0.5553450027 0.5028514376 0.6907476947 0.3973033130 -0.334900181306 +1403637148838319104.0000000000 4.5858393016 -1.7882351551 0.5553247088 0.5027823749 0.6906510056 0.3976378908 -0.334806182446 +1403637148888318976.0000000000 4.5864260560 -1.7885333350 0.5554372253 0.5024756334 0.6905349650 0.3979806964 -0.335098590253 +1403637148938319104.0000000000 4.5870881353 -1.7887883625 0.5554284476 0.5023325799 0.6903972300 0.3983751321 -0.3351281815 +1403637148988318976.0000000000 4.5868923284 -1.7886137622 0.5554017212 0.5020445962 0.6903815517 0.3985422526 -0.335393215984 +1403637149038319104.0000000000 4.5871243396 -1.7886826908 0.5552496740 0.5019173515 0.6902722943 0.3990307843 -0.33522763181 +1403637149088318976.0000000000 4.5868183672 -1.7887468230 0.5553162359 0.5016746714 0.6902145052 0.3991665873 -0.335548053784 +1403637149138319104.0000000000 4.5864049862 -1.7886194573 0.5552810079 0.5015537634 0.6901734254 0.3993694534 -0.335571907352 +1403637149188318976.0000000000 4.5861038311 -1.7883867959 0.5552709728 0.5014779865 0.6900185618 0.3997799205 -0.335514871022 +1403637149238319104.0000000000 4.5858482333 -1.7881681559 0.5553341594 0.5013029360 0.6900011316 0.3998565719 -0.335720905908 +1403637149288318976.0000000000 4.5855766012 -1.7881070603 0.5554724779 0.5011217472 0.6898665419 0.4001591925 -0.335907382399 +1403637149338319104.0000000000 4.5855192315 -1.7881252509 0.5555123582 0.5008586973 0.6897361929 0.4006195495 -0.336018639589 +1403637149388318976.0000000000 4.5856457018 -1.7881143283 0.5555401516 0.5006144717 0.6895942047 0.4009529478 -0.336276251368 +1403637149438319104.0000000000 4.5858786869 -1.7881601094 0.5556129715 0.5003202366 0.6893287197 0.4015694447 -0.336522745465 +1403637149488318976.0000000000 4.5859917763 -1.7883037553 0.5556320341 0.4999241755 0.6890949603 0.4023709000 -0.336632757273 +1403637149538319104.0000000000 4.5861458398 -1.7883591292 0.5555166689 0.4996176822 0.6888664562 0.4032196910 -0.336539831252 +1403637149588318976.0000000000 4.5866620296 -1.7886239678 0.5552201868 0.4979611795 0.6885948124 0.4060430476 -0.33615605238 +1403637149638319104.0000000000 4.5876986665 -1.7891305042 0.5545367105 0.4942157823 0.6885352564 0.4112958279 -0.335418698306 +1403637149688318976.0000000000 4.5892074567 -1.7900249487 0.5539983799 0.4905189357 0.6871210406 0.4175833356 -0.335976200272 +1403637149738319104.0000000000 4.5905898013 -1.7899966568 0.5534961178 0.4889345298 0.6862904266 0.4206658254 -0.336137976662 +1403637149788318976.0000000000 4.5914855143 -1.7896506952 0.5529646193 0.4851585889 0.6876322134 0.4228942739 -0.336070700545 +1403637149838319104.0000000000 4.5924618822 -1.7891729229 0.5524725682 0.4810658214 0.6893122170 0.4260244253 -0.334555723362 +1403637149888318976.0000000000 4.5940251099 -1.7870997977 0.5518910411 0.4745590746 0.6935792578 0.4286215509 -0.331700262119 +1403637149938319104.0000000000 4.5962935255 -1.7836458056 0.5512632406 0.4699021195 0.6967947657 0.4331643903 -0.325634248154 +1403637149988318976.0000000000 4.5989657387 -1.7793359548 0.5520164192 0.4647654054 0.7001926761 0.4393214717 -0.317364110622 +1403637150038319104.0000000000 4.6021118231 -1.7735442048 0.5545520031 0.4617965060 0.7024313158 0.4459975195 -0.30727910157 +1403637150088318976.0000000000 4.6049942806 -1.7663935157 0.5590819923 0.4592462383 0.7049894162 0.4507965147 -0.298102864693 +1403637150138319104.0000000000 4.6062979825 -1.7578052609 0.5658055294 0.4585466634 0.7063211201 0.4542268989 -0.290729009734 +1403637150188318976.0000000000 4.6056454672 -1.7479694283 0.5748933130 0.4601564953 0.7067304633 0.4548524700 -0.286177012742 +1403637150238319104.0000000000 4.6031100659 -1.7372719315 0.5856839014 0.4627699283 0.7065524735 0.4541048485 -0.283577823908 +1403637150288318976.0000000000 4.5982290042 -1.7259319023 0.5986498428 0.4667768392 0.7055089037 0.4515725100 -0.283652670482 +1403637150338319104.0000000000 4.5916680074 -1.7140500207 0.6125459449 0.4707653961 0.7045040846 0.4487911040 -0.283972677608 +1403637150388318976.0000000000 4.5831289745 -1.7017360229 0.6278230107 0.4764423571 0.7022428135 0.4435311913 -0.288336250901 +1403637150438319104.0000000000 4.5739440174 -1.6890252817 0.6428511196 0.4811452767 0.7004075664 0.4395173156 -0.2911236729 +1403637150488318976.0000000000 4.5644780210 -1.6760013088 0.6572712169 0.4849890460 0.6991188987 0.4367097782 -0.292066705364 +1403637150538319104.0000000000 4.5547253953 -1.6628503538 0.6715308378 0.4876423121 0.6986794749 0.4341148404 -0.292568405891 +1403637150588318976.0000000000 4.5447455775 -1.6496511164 0.6850072472 0.4889130250 0.6987864166 0.4327351818 -0.292235966849 +1403637150638319104.0000000000 4.5343757631 -1.6362930018 0.6983422733 0.4903415721 0.6987517343 0.4311710714 -0.292237341274 +1403637150688318976.0000000000 4.5237845635 -1.6229356899 0.7110204343 0.4911400832 0.6989416590 0.4302486764 -0.291801391915 +1403637150738319104.0000000000 4.5129125630 -1.6094948875 0.7229531398 0.4919263506 0.6989764967 0.4299404017 -0.29084630598 +1403637150788318976.0000000000 4.5016014090 -1.5959765675 0.7344589937 0.4927348753 0.6988941321 0.4295110941 -0.290309412153 +1403637150838319104.0000000000 4.4900105916 -1.5823988108 0.7457970911 0.4945052077 0.6981453742 0.4290066659 -0.289846367357 +1403637150888318976.0000000000 4.4780639198 -1.5691888488 0.7571937446 0.4976717612 0.6961931436 0.4278637574 -0.290810126956 +1403637150938319104.0000000000 4.4661384515 -1.5563773879 0.7676941501 0.5005813975 0.6942639401 0.4265835695 -0.292305155923 +1403637150988318976.0000000000 4.4542720490 -1.5440086648 0.7770698261 0.5033984637 0.6922658919 0.4254546595 -0.293847331694 +1403637151038319104.0000000000 4.4426303316 -1.5321294346 0.7853652287 0.5056584318 0.6904393261 0.4246626513 -0.295406025505 +1403637151088318976.0000000000 4.4313541905 -1.5205930313 0.7928183555 0.5082966493 0.6882280282 0.4240611481 -0.296898703519 +1403637151138319104.0000000000 4.4204719711 -1.5096731835 0.7996174899 0.5112813166 0.6856666374 0.4233681134 -0.298683977017 +1403637151188318976.0000000000 4.4106840154 -1.4995162247 0.8053439133 0.5118428867 0.6846678771 0.4237137053 -0.299522041414 +1403637151238319104.0000000000 4.4019597807 -1.4901801610 0.8113971267 0.5094440923 0.6860058379 0.4248446121 -0.298947759117 +1403637151288318976.0000000000 4.3941527880 -1.4818579268 0.8194728837 0.5059030121 0.6879358477 0.4258253867 -0.299130660155 +1403637151338319104.0000000000 4.3872614612 -1.4740425613 0.8297689662 0.5009574135 0.6908835944 0.4259775965 -0.300440703003 +1403637151388318976.0000000000 4.3807260515 -1.4667036168 0.8430570538 0.4952520284 0.6943919865 0.4248825512 -0.303348009833 +1403637151438319104.0000000000 4.3741794860 -1.4589749822 0.8593595995 0.4908221934 0.6972769109 0.4236978879 -0.305579095941 +1403637151488318976.0000000000 4.3683510668 -1.4505996151 0.8761996639 0.4903340699 0.6971672077 0.4257874807 -0.303702824606 +1403637151538319104.0000000000 4.3627598640 -1.4419393705 0.8925427026 0.4898349027 0.6971396655 0.4269826771 -0.302892469915 +1403637151588318976.0000000000 4.3574068190 -1.4327073577 0.9077603871 0.4904338907 0.6965221159 0.4281891895 -0.301638125596 +1403637151638319104.0000000000 4.3521188966 -1.4231828376 0.9220082924 0.4909066230 0.6957934835 0.4296418551 -0.300482931445 +1403637151688318976.0000000000 4.3468947090 -1.4133699833 0.9351967356 0.4918552951 0.6948137217 0.4306312003 -0.299781637237 +1403637151738319104.0000000000 4.3418261994 -1.4034959511 0.9467986235 0.4916934072 0.6947600598 0.4315047385 -0.298914223886 +1403637151788318976.0000000000 4.3366841225 -1.3934642490 0.9570551000 0.4916948439 0.6944775105 0.4322153620 -0.298541536074 +1403637151838319104.0000000000 4.3315245339 -1.3833650176 0.9659145959 0.4918541766 0.6940970181 0.4328113925 -0.298300346978 +1403637151888318976.0000000000 4.3262728131 -1.3728959569 0.9734606506 0.4924120184 0.6935994243 0.4333908031 -0.297695573693 +1403637151938319104.0000000000 4.3208166132 -1.3624647786 0.9802224204 0.4925080658 0.6934747161 0.4340231245 -0.29690495228 +1403637151988318976.0000000000 4.3151099402 -1.3522820514 0.9876657225 0.4921911028 0.6934431256 0.4342484527 -0.297174748786 +1403637152038319104.0000000000 4.3095795822 -1.3423610664 0.9970607257 0.4916624242 0.6936711282 0.4342132134 -0.297569003472 +1403637152088318976.0000000000 4.3046013086 -1.3327720370 1.0073765091 0.4907026301 0.6941176486 0.4341866766 -0.298150211409 +1403637152138319104.0000000000 4.2994508149 -1.3229940451 1.0185838501 0.4896789497 0.6947803756 0.4341494156 -0.298343829921 +1403637152188318976.0000000000 4.2941903671 -1.3131199124 1.0295469736 0.4887297176 0.6954922768 0.4340976798 -0.29831687915 +1403637152238319104.0000000000 4.2888001070 -1.3031632313 1.0393158208 0.4875350287 0.6962719575 0.4338284805 -0.298844117316 +1403637152288318976.0000000000 4.2831878842 -1.2928429127 1.0471578473 0.4869716026 0.6966575953 0.4339157325 -0.298737326585 +1403637152338319104.0000000000 4.2775834979 -1.2823426763 1.0535500208 0.4853615958 0.6977343697 0.4335445682 -0.29938266153 +1403637152388318976.0000000000 4.2718977411 -1.2712581299 1.0582232485 0.4859201264 0.6971730413 0.4339606675 -0.299181416958 +1403637152438319104.0000000000 4.2659351717 -1.2599398129 1.0614106331 0.4855649884 0.6973915784 0.4341044008 -0.299040127003 +1403637152488318976.0000000000 4.2594197755 -1.2483249988 1.0628767035 0.4856960000 0.6971645364 0.4346797446 -0.298520559265 +1403637152538319104.0000000000 4.2524966574 -1.2364961675 1.0627783560 0.4857505007 0.6970137346 0.4345696059 -0.298944078953 +1403637152588318976.0000000000 4.2452944632 -1.2242201874 1.0610102830 0.4857976912 0.6970556880 0.4349939354 -0.298151383185 +1403637152638319104.0000000000 4.2372613720 -1.2116262490 1.0586766815 0.4864939243 0.6965469471 0.4347633114 -0.298541245149 +1403637152688318976.0000000000 4.2289895571 -1.1987015831 1.0557981823 0.4869660839 0.6962685337 0.4343821861 -0.298975380944 +1403637152738319104.0000000000 4.2201881702 -1.1854337766 1.0535657531 0.4880495981 0.6955918694 0.4334116728 -0.300189711488 +1403637152788318976.0000000000 4.2110318597 -1.1720504597 1.0528905154 0.4886166527 0.6949617607 0.4316472221 -0.30325334883 +1403637152838319104.0000000000 4.2019705154 -1.1581747566 1.0534650783 0.4900115479 0.6940469742 0.4304288113 -0.304825390807 +1403637152888318976.0000000000 4.1941849359 -1.1446202389 1.0560164023 0.4913041557 0.6929057926 0.4297939250 -0.306233524143 +1403637152938319104.0000000000 4.1876723002 -1.1310124490 1.0601920826 0.4929757701 0.6914825677 0.4299913996 -0.306486777773 +1403637152988318976.0000000000 4.1810964971 -1.1170009301 1.0663754886 0.4933816599 0.6911011279 0.4303146208 -0.306240258245 +1403637153038319104.0000000000 4.1755350820 -1.1032208499 1.0735175715 0.4940196406 0.6904472757 0.4306984195 -0.30614706544 +1403637153088318976.0000000000 4.1699292451 -1.0889779374 1.0799679191 0.4942480288 0.6905509137 0.4313016672 -0.30469196481 +1403637153138319104.0000000000 4.1645253009 -1.0748363503 1.0850887751 0.4939627543 0.6907579688 0.4320060426 -0.303685701138 +1403637153188318976.0000000000 4.1591867877 -1.0605794164 1.0885722322 0.4932150890 0.6913457455 0.4325703492 -0.302758697822 +1403637153238319104.0000000000 4.1538044375 -1.0462820247 1.0904592261 0.4933269099 0.6913913248 0.4336738009 -0.300888069402 +1403637153288318976.0000000000 4.1485179733 -1.0321966500 1.0911641308 0.4934633189 0.6912895868 0.4343224047 -0.299961178916 +1403637153338319104.0000000000 4.1431813060 -1.0179360791 1.0908103795 0.4939757035 0.6909430596 0.4347882230 -0.299240528623 +1403637153388318976.0000000000 4.1378586026 -1.0037824341 1.0901650930 0.4942350681 0.6908997835 0.4354649162 -0.297925315206 +1403637153438319104.0000000000 4.1323705458 -0.9898268408 1.0906900451 0.4936900225 0.6911932073 0.4361858600 -0.297092590514 +1403637153488318976.0000000000 4.1273853965 -0.9763155120 1.0928325181 0.4930429246 0.6917395110 0.4372134978 -0.295380230913 +1403637153538319104.0000000000 4.1222210662 -0.9632548805 1.0964450945 0.4915441975 0.6928520363 0.4381000045 -0.293953642009 +1403637153588318976.0000000000 4.1167665833 -0.9504892499 1.1017931375 0.4901903780 0.6938106485 0.4380799761 -0.293983183041 +1403637153638319104.0000000000 4.1106022282 -0.9374724780 1.1087273817 0.4900034794 0.6939377710 0.4385344953 -0.293316308064 +1403637153688318976.0000000000 4.1035724636 -0.9246173812 1.1181050593 0.4906307381 0.6933867120 0.4380359587 -0.294314194875 +1403637153738319104.0000000000 4.0965605325 -0.9120526494 1.1284428359 0.4916928540 0.6927356461 0.4379783562 -0.294160536827 +1403637153788318976.0000000000 4.0892358994 -0.8998004018 1.1386753324 0.4934480992 0.6915843508 0.4368663184 -0.295580579486 +1403637153838319104.0000000000 4.0818326606 -0.8879596951 1.1478327920 0.4938973111 0.6912429429 0.4356421668 -0.297429895066 +1403637153888318976.0000000000 4.0745394669 -0.8760359369 1.1553134811 0.4947838145 0.6907401235 0.4355023942 -0.297329318 +1403637153938319104.0000000000 4.0672393717 -0.8643816477 1.1612863658 0.4961992673 0.6898379722 0.4351196486 -0.297625184741 +1403637153988318976.0000000000 4.0597632116 -0.8531022661 1.1653904703 0.4962511304 0.6898064645 0.4343830860 -0.298685774282 +1403637154038319104.0000000000 4.0525668406 -0.8422624918 1.1672915640 0.4958313495 0.6901074033 0.4345397532 -0.298459792227 +1403637154088318976.0000000000 4.0455705954 -0.8318128041 1.1672285159 0.4935973823 0.6916672331 0.4342195009 -0.299017537732 +1403637154138319104.0000000000 4.0386597205 -0.8215648966 1.1650539400 0.4885146813 0.6951582780 0.4337071388 -0.300010820706 +1403637154188318976.0000000000 4.0317333782 -0.8114574406 1.1614339064 0.4804367811 0.7008714520 0.4313677488 -0.303119732647 +1403637154238319104.0000000000 4.0248031224 -0.8008977393 1.1569882863 0.4736163305 0.7056472185 0.4285259953 -0.306781756106 +1403637154288318976.0000000000 4.0177009538 -0.7891651577 1.1510438160 0.4679429288 0.7095580853 0.4265130918 -0.309262544733 +1403637154338319104.0000000000 4.0104207659 -0.7757680031 1.1438220362 0.4654466588 0.7113247028 0.4254212096 -0.310472815818 +1403637154388318976.0000000000 4.0028227287 -0.7603284584 1.1354502618 0.4673075705 0.7103440339 0.4262708469 -0.308752575874 +1403637154438319104.0000000000 3.9947097458 -0.7432748626 1.1267566851 0.4722957684 0.7072862158 0.4267374486 -0.307535471094 +1403637154488318976.0000000000 3.9863851368 -0.7249353260 1.1176374944 0.4779307728 0.7037328663 0.4270498025 -0.306546400364 +1403637154538319104.0000000000 3.9780989290 -0.7055620436 1.1084531354 0.4823001384 0.7011539069 0.4276436150 -0.304779779222 +1403637154588318976.0000000000 3.9700698721 -0.6854200058 1.0996420430 0.4854719438 0.6996369330 0.4289654204 -0.301353317306 +1403637154638319104.0000000000 3.9620621118 -0.6648650131 1.0910863301 0.4874574729 0.6989814004 0.4313788138 -0.296179899706 +1403637154688318976.0000000000 3.9536640968 -0.6440822274 1.0825476268 0.4878634686 0.6995777951 0.4345613350 -0.289372753906 +1403637154738319104.0000000000 3.9449185845 -0.6233670730 1.0743164117 0.4879870768 0.7011843820 0.4358113629 -0.283332898314 +1403637154788318976.0000000000 3.9352055943 -0.6023488849 1.0667822997 0.4880292962 0.7042596218 0.4344870917 -0.277609002549 +1403637154838319104.0000000000 3.9245340467 -0.5811840225 1.0604563465 0.4875818970 0.7084558619 0.4312354569 -0.272745607001 +1403637154888318976.0000000000 3.9127231791 -0.5600084941 1.0555496707 0.4878850538 0.7119338646 0.4268878526 -0.269972420757 +1403637154938319104.0000000000 3.9000084116 -0.5386394211 1.0508965299 0.4871524372 0.7156499271 0.4242086741 -0.26565896468 +1403637154988318976.0000000000 3.8853572839 -0.5168250679 1.0487220930 0.4881468246 0.7182994769 0.4191362576 -0.264732575949 +1403637155038319104.0000000000 3.8697288306 -0.4947412210 1.0486254599 0.4907509865 0.7200124563 0.4147109719 -0.262221932518 +1403637155088318976.0000000000 3.8523779840 -0.4721760618 1.0513100315 0.4932526505 0.7225889874 0.4081363765 -0.260752135681 +1403637155138319104.0000000000 3.8335536403 -0.4492136961 1.0562899516 0.4990588797 0.7231754559 0.4003828495 -0.260098189766 +1403637155188318976.0000000000 3.8143459015 -0.4267728971 1.0626462975 0.5026563697 0.7245176224 0.3936512160 -0.259710432983 +1403637155238319104.0000000000 3.7947494760 -0.4045605780 1.0709811274 0.5070786436 0.7243053881 0.3891145836 -0.258539735212 +1403637155288318976.0000000000 3.7745959452 -0.3825328136 1.0805809927 0.5100564637 0.7242435381 0.3853421526 -0.258505564436 +1403637155338319104.0000000000 3.7541051631 -0.3602821308 1.0912987275 0.5139318168 0.7236622273 0.3814774731 -0.258189864183 +1403637155388318976.0000000000 3.7334176107 -0.3376222811 1.1013124446 0.5172827851 0.7242331146 0.3760703941 -0.25782935176 +1403637155438319104.0000000000 3.7131141192 -0.3148547759 1.1094578209 0.5203605007 0.7258018907 0.3701336728 -0.255807796993 +1403637155488318976.0000000000 3.6932137471 -0.2921166601 1.1158354949 0.5240416824 0.7276212321 0.3628364492 -0.253569258704 +1403637155538319104.0000000000 3.6738285864 -0.2698872708 1.1198806929 0.5260130462 0.7303512272 0.3559103365 -0.251446202063 +1403637155588318976.0000000000 3.6544095519 -0.2478642860 1.1221735204 0.5267673726 0.7334926026 0.3491357367 -0.250217854036 +1403637155638319104.0000000000 3.6350135809 -0.2259960859 1.1229726023 0.5267525835 0.7366838130 0.3424529913 -0.250109224727 +1403637155688318976.0000000000 3.6165912944 -0.2045521092 1.1219030402 0.5258606049 0.7402743781 0.3366139725 -0.249310053587 +1403637155738319104.0000000000 3.5992884916 -0.1831550561 1.1194741818 0.5266433576 0.7431223160 0.3301024181 -0.247887859381 +1403637155788318976.0000000000 3.5828885458 -0.1612942759 1.1153744292 0.5267296050 0.7470013361 0.3226031799 -0.245910787194 +1403637155838319104.0000000000 3.5672934878 -0.1384551230 1.1101127905 0.5280081304 0.7506024118 0.3141009651 -0.243195430295 +1403637155888318976.0000000000 3.5532549991 -0.1148824687 1.1027959548 0.5280975761 0.7556648067 0.3064725947 -0.236977211529 +1403637155938319104.0000000000 3.5403511370 -0.0902516401 1.0941126167 0.5283873878 0.7607556029 0.2989081744 -0.229590035501 +1403637155988318976.0000000000 3.5281979074 -0.0648323602 1.0850096343 0.5305168248 0.7647393944 0.2899201082 -0.22287190987 +1403637156038319104.0000000000 3.5166559668 -0.0386398777 1.0761886617 0.5334148665 0.7680679037 0.2794531865 -0.217821468372 +1403637156088318976.0000000000 3.5060830339 -0.0119946680 1.0674485468 0.5363505123 0.7712401939 0.2682538149 -0.213439879114 +1403637156138319104.0000000000 3.4969130557 0.0151864595 1.0589385044 0.5398078662 0.7740202913 0.2569096104 -0.20856056279 +1403637156188318976.0000000000 3.4890535867 0.0431767654 1.0497483589 0.5424355507 0.7774396053 0.2451538657 -0.203103214276 +1403637156238319104.0000000000 3.4821390177 0.0723421596 1.0413277468 0.5451889419 0.7806880796 0.2328806894 -0.19764039195 +1403637156288318976.0000000000 3.4770334873 0.1018729939 1.0332101152 0.5477961342 0.7839747458 0.2213635078 -0.190528713565 +1403637156338319104.0000000000 3.4736317373 0.1316235021 1.0249539093 0.5497571951 0.7874993020 0.2089370449 -0.184274759798 +1403637156388318976.0000000000 3.4719175112 0.1623316405 1.0172016514 0.5518465730 0.7908702283 0.1973747161 -0.176161469469 +1403637156438319104.0000000000 3.4717784904 0.1937278944 1.0091901477 0.5536059112 0.7941757255 0.1856137623 -0.16838332297 +1403637156488318976.0000000000 3.4735305615 0.2253343415 1.0009538464 0.5560543530 0.7967382340 0.1739625699 -0.16046422445 +1403637156538319104.0000000000 3.4766740833 0.2575711113 0.9925428219 0.5593199134 0.7984503800 0.1623369655 -0.152594019405 +1403637156588318976.0000000000 3.4814415276 0.2901349258 0.9831621400 0.5614550520 0.8006316323 0.1517518943 -0.143974221941 +1403637156638319104.0000000000 3.4878228597 0.3232693666 0.9731530969 0.5644160992 0.8020661368 0.1408942260 -0.135178386808 +1403637156688318976.0000000000 3.4957955961 0.3564973036 0.9614782789 0.5664968724 0.8037955970 0.1308175859 -0.126018613681 +1403637156738319104.0000000000 3.5052477936 0.3898774103 0.9485303820 0.5691324186 0.8047862379 0.1214544414 -0.116859830728 +1403637156788318976.0000000000 3.5159965703 0.4226587733 0.9335325168 0.5692915873 0.8069611799 0.1147616915 -0.107473238581 +1403637156838319104.0000000000 3.5278524470 0.4554851428 0.9174408744 0.5685460442 0.8093052753 0.1104926416 -0.0978352856353 +1403637156888318976.0000000000 3.5403061711 0.4879701185 0.9005479078 0.5669702584 0.8117800394 0.1068365518 -0.0902432537587 +1403637156938319104.0000000000 3.5533798035 0.5202956805 0.8823737443 0.5659623673 0.8134633030 0.1055554576 -0.0825959972466 +1403637156988318976.0000000000 3.5667038446 0.5521875237 0.8626966788 0.5638789421 0.8156204386 0.1040317509 -0.0773384354172 +1403637157038319104.0000000000 3.5800105388 0.5839305002 0.8420100042 0.5618968255 0.8174420134 0.1026992112 -0.0742521671584 +1403637157088318976.0000000000 3.5932701758 0.6160330429 0.8210737691 0.5602600814 0.8188370754 0.1012200733 -0.0732733374677 +1403637157138319104.0000000000 3.6063519636 0.6488668645 0.8010938862 0.5589575744 0.8198936680 0.0993218823 -0.0739997761594 +1403637157188318976.0000000000 3.6194629886 0.6824228323 0.7827205428 0.5582648440 0.8203707468 0.0981355008 -0.0755091065084 +1403637157238319104.0000000000 3.6330421850 0.7166364951 0.7658515942 0.5579840148 0.8205498377 0.0970214750 -0.0770625497384 +1403637157288318976.0000000000 3.6473847745 0.7516300844 0.7509770296 0.5579308210 0.8204632238 0.0961944696 -0.0793720443881 +1403637157338319104.0000000000 3.6624287468 0.7875462318 0.7380241812 0.5579089602 0.8202705906 0.0954051540 -0.0824112063057 +1403637157388318976.0000000000 3.6778742666 0.8244578852 0.7278231753 0.5572178221 0.8204858232 0.0939400472 -0.0865250270287 +1403637157438319104.0000000000 3.6944990352 0.8621041099 0.7197805869 0.5562271385 0.8208199711 0.0921670316 -0.091494173529 +1403637157488318976.0000000000 3.7123020642 0.9002928980 0.7137243899 0.5554059111 0.8209795846 0.0915157808 -0.0956120153594 +1403637157538319104.0000000000 3.7315901290 0.9392292553 0.7095812163 0.5547081790 0.8210705353 0.0909834590 -0.0993177851272 +1403637157588318976.0000000000 3.7523256109 0.9792737028 0.7072130141 0.5546053328 0.8207702529 0.0912507849 -0.102090210405 +1403637157638319104.0000000000 3.7747384977 1.0201108999 0.7061048079 0.5542214019 0.8207430792 0.0924566983 -0.103301474343 +1403637157688318976.0000000000 3.7987924202 1.0618018089 0.7069952026 0.5538832248 0.8207029574 0.0932967964 -0.104669655161 +1403637157738319104.0000000000 3.8227619121 1.1045831629 0.7099644583 0.5535323666 0.8206912872 0.0942078003 -0.105795182049 +1403637157788318976.0000000000 3.8485986627 1.1486900443 0.7146256233 0.5567503208 0.8183726169 0.0953992264 -0.105803250255 +1403637157838319104.0000000000 3.8748588406 1.1931385568 0.7188258858 0.5604764440 0.8157899563 0.0973328530 -0.104303492625 +1403637157888318976.0000000000 3.9024656642 1.2381244965 0.7218450379 0.5635457937 0.8136750542 0.0984967960 -0.103186364144 +1403637157938319104.0000000000 3.9308715083 1.2834613371 0.7234529796 0.5671720418 0.8111814435 0.1003726054 -0.101123097056 +1403637157988318976.0000000000 3.9602540069 1.3285267373 0.7230994179 0.5694118041 0.8096856978 0.1025786375 -0.098269482937 +1403637158038319104.0000000000 3.9903573560 1.3735073638 0.7219109603 0.5720581758 0.8078823255 0.1057232779 -0.0943301650492 +1403637158088318976.0000000000 4.0211695422 1.4182534800 0.7214225099 0.5737633960 0.8067667509 0.1080731583 -0.0907918911867 +1403637158138319104.0000000000 4.0523239895 1.4629291823 0.7227598615 0.5747936384 0.8060082812 0.1092759840 -0.0895638505401 +1403637158188318976.0000000000 4.0837866604 1.5076893180 0.7258252911 0.5754661515 0.8055406987 0.1104997006 -0.0879358135491 +1403637158238319104.0000000000 4.1163149471 1.5516637784 0.7310613822 0.5767638610 0.8047445309 0.1095131069 -0.0879577631035 +1403637158288318976.0000000000 4.1503031803 1.5940392199 0.7367742629 0.5764726883 0.8053108108 0.1081948812 -0.0862995094403 +1403637158338319104.0000000000 4.1850774443 1.6373433850 0.7439552727 0.5770291510 0.8056011964 0.1050693193 -0.083692947332 +1403637158388318976.0000000000 4.2206427620 1.6799188989 0.7515003113 0.5773550666 0.8062893439 0.0992621233 -0.0818880439214 +1403637158438319104.0000000000 4.2570505369 1.7223176273 0.7579390951 0.5781847998 0.8067952099 0.0928395706 -0.0785152257167 +1403637158488318976.0000000000 4.2942330538 1.7647481884 0.7629207485 0.5791914023 0.8072453048 0.0845027653 -0.0758394354519 +1403637158538319104.0000000000 4.3323036286 1.8070068561 0.7664154209 0.5799195146 0.8079260399 0.0745729941 -0.0734012205143 +1403637158588318976.0000000000 4.3714788138 1.8489111518 0.7680686181 0.5799364640 0.8090699341 0.0631175283 -0.071384291264 +1403637158638319104.0000000000 4.4120895645 1.8903019406 0.7680205785 0.5798765746 0.8101864077 0.0515402383 -0.0684452098321 +1403637158688318976.0000000000 4.4544300616 1.9310989198 0.7663182911 0.5806004508 0.8107272203 0.0402365378 -0.0632891131091 +1403637158738319104.0000000000 4.4982965064 1.9706753824 0.7627149617 0.5807497770 0.8115491567 0.0297325644 -0.056865079473 +1403637158788318976.0000000000 4.5431262558 2.0093440707 0.7577542838 0.5800280691 0.8127680160 0.0210527124 -0.0503227034383 +1403637158838319104.0000000000 4.5887846353 2.0468875129 0.7510961396 0.5775557746 0.8150781318 0.0148179438 -0.043097504614 +1403637158888318976.0000000000 4.6352757940 2.0836915178 0.7448537933 0.5760620124 0.8164608743 0.0090942085 -0.0382294908181 +1403637158938319104.0000000000 4.6831455583 2.1202803127 0.7389959512 0.5750782477 0.8175105825 0.0076217298 -0.0300560438265 +1403637158988318976.0000000000 4.7314854418 2.1569988872 0.7348525958 0.5729668562 0.8192066647 0.0062020897 -0.0238946907759 +1403637159038319104.0000000000 4.7804712629 2.1939912731 0.7323964174 0.5714910302 0.8203915620 0.0054975330 -0.0180406370721 +1403637159088318976.0000000000 4.8296053986 2.2311897053 0.7323089326 0.5709136248 0.8208527339 0.0041859914 -0.0155209421412 +1403637159138319104.0000000000 4.8786809907 2.2679152689 0.7326868579 0.5709262221 0.8208489719 0.0020052095 -0.0156905484701 +1403637159188318976.0000000000 4.9277245046 2.3042235266 0.7323834936 0.5712432456 0.8205716443 -0.0011909299 -0.0184908803475 +1403637159238319104.0000000000 4.9770023097 2.3404853987 0.7304803083 0.5714122346 0.8203693120 -0.0037000499 -0.0216462403125 +1403637159288318976.0000000000 5.0270144248 2.3765456953 0.7270310901 0.5711942091 0.8204288644 -0.0052655320 -0.0246156090223 +1403637159338319104.0000000000 5.0780598389 2.4127113129 0.7223037100 0.5708398850 0.8205910035 -0.0063133525 -0.0270623783299 +1403637159388318976.0000000000 5.1301279485 2.4489676030 0.7161666989 0.5704129596 0.8208255873 -0.0063853485 -0.0288727900714 +1403637159438319104.0000000000 5.1833340610 2.4851065932 0.7088836192 0.5705413623 0.8207422192 -0.0047995542 -0.0290125476667 +1403637159488318976.0000000000 5.2374048258 2.5215269120 0.7008168245 0.5709021610 0.8204525300 -0.0037946696 -0.0302319230864 +1403637159538319104.0000000000 5.2927243603 2.5579998155 0.6912966101 0.5702306314 0.8210485773 0.0004309139 -0.0267595789819 +1403637159588318976.0000000000 5.3486879803 2.5943663329 0.6812234110 0.5691944879 0.8218392188 0.0039170140 -0.0241369081413 +1403637159638319104.0000000000 5.4052789081 2.6309556067 0.6710598879 0.5682258686 0.8225755417 0.0078440693 -0.0206715054178 +1403637159688318976.0000000000 5.4620417395 2.6680891116 0.6619535647 0.5682123953 0.8226001007 0.0108731700 -0.0185882309328 +1403637159738319104.0000000000 5.5193275229 2.7053225242 0.6542540628 0.5683421928 0.8225224362 0.0138223701 -0.015903956535 +1403637159788318976.0000000000 5.5761962544 2.7437282844 0.6485129933 0.5689322082 0.8221046430 0.0153969460 -0.0149342699286 +1403637159838319104.0000000000 5.6326789744 2.7822021303 0.6451104609 0.5698797973 0.8214711452 0.0159745105 -0.0129224350505 +1403637159888318976.0000000000 5.6894766907 2.8208828937 0.6423205949 0.5700729586 0.8214080085 0.0147778113 -0.00934461134237 +1403637159938319104.0000000000 5.7462626903 2.8601039284 0.6396080888 0.5691447317 0.8221579765 0.0092767763 -0.00666914025174 +1403637159988318976.0000000000 5.8029883221 2.8994202252 0.6360706154 0.5683574936 0.8227744057 0.0029888858 -0.00176166601886 +1403637160038319104.0000000000 5.8593713344 2.9395298814 0.6321322017 0.5702467047 0.8214490009 -0.0058329092 0.00249236982486 +1403637160088318976.0000000000 5.9153238108 2.9802132648 0.6275853774 0.5729557060 0.8194050962 -0.0160285297 0.0063350945289 +1403637160138319104.0000000000 5.9709029387 3.0205352664 0.6227804925 0.5759144265 0.8169853291 -0.0273725296 0.0104062469371 +1403637160188318976.0000000000 6.0267225559 3.0608064340 0.6173903898 0.5778013541 0.8150879456 -0.0386897673 0.0167433003026 +1403637160238319104.0000000000 6.0826969950 3.1003129993 0.6103524091 0.5784699014 0.8138062311 -0.0495795150 0.0251766357073 +1403637160288318976.0000000000 6.1389020055 3.1393787643 0.6023223846 0.5788682741 0.8124016935 -0.0619152372 0.0328863639694 +1403637160338319104.0000000000 6.1954601036 3.1779846226 0.5925657939 0.5785611298 0.8111880398 -0.0737517922 0.042445923407 +1403637160388318976.0000000000 6.2523359413 3.2160410551 0.5825095339 0.5776329626 0.8099826284 -0.0873992298 0.0512803747985 +1403637160438319104.0000000000 6.3094945923 3.2526861733 0.5709835910 0.5759353621 0.8089365269 -0.1001754717 0.0623300016316 +1403637160488318976.0000000000 6.3668718480 3.2890696161 0.5585224093 0.5734597097 0.8080299793 -0.1125797878 0.0745473360425 +1403637160538319104.0000000000 6.4241532190 3.3247913053 0.5452235381 0.5695890855 0.8077063451 -0.1248983858 0.087058181775 +1403637160588318976.0000000000 6.4812049059 3.3602413113 0.5312330422 0.5669474925 0.8061484000 -0.1378010820 0.0985198442211 +1403637160638319104.0000000000 6.5382984931 3.3953083351 0.5165116811 0.5632559277 0.8051098287 -0.1494955304 0.11041743514 +1403637160688318976.0000000000 6.5946808872 3.4302314573 0.5013509101 0.5592793683 0.8045618267 -0.1603617174 0.119041903291 +1403637160738319104.0000000000 6.6506295804 3.4655752783 0.4865698767 0.5547455520 0.8047816077 -0.1694749810 0.12594509648 +1403637160788318976.0000000000 6.7060321521 3.5012865594 0.4730379407 0.5507293483 0.8050295643 -0.1760850252 0.132735261006 +1403637160838319104.0000000000 6.7612426296 3.5380337604 0.4620422992 0.5484604974 0.8045496758 -0.1818258497 0.137223402691 +1403637160888318976.0000000000 6.8156768926 3.5757286573 0.4528581140 0.5464370187 0.8042558036 -0.1870813901 0.13992762564 +1403637160938319104.0000000000 6.8698162416 3.6145866091 0.4460048399 0.5435867848 0.8048784246 -0.1915120451 0.141447041514 +1403637160988318976.0000000000 6.9233397633 3.6538752320 0.4427844151 0.5418852038 0.8050952584 -0.1958432901 0.140810001284 +1403637161038319104.0000000000 6.9764213434 3.6939675533 0.4426405450 0.5405602400 0.8053221901 -0.2001748321 0.138494887015 +1403637161088318976.0000000000 7.0298605683 3.7363725427 0.4459526819 0.5409149621 0.8045543569 -0.2044282488 0.135323248458 +1403637161138319104.0000000000 7.0837172161 3.7799849292 0.4525089448 0.5428230400 0.8028516974 -0.2089228583 0.130856939152 +1403637161188318976.0000000000 7.1366461824 3.8234140465 0.4613957559 0.5460600560 0.8002110205 -0.2148318110 0.123806425027 +1403637161238319104.0000000000 7.1905776479 3.8672315759 0.4730344161 0.5516202870 0.7960050412 -0.2200033799 0.11700233429 +1403637161288318976.0000000000 7.2456944786 3.9102220868 0.4857750578 0.5551912632 0.7932006315 -0.2246973377 0.110029659182 +1403637161338319104.0000000000 7.2988950542 3.9502396528 0.4999566032 0.5578372771 0.7912322113 -0.2269833754 0.106055208884 +1403637161388318976.0000000000 7.3564172144 3.9903208982 0.5152999143 0.5585806187 0.7908758079 -0.2260847841 0.106718410943 +1403637161438319104.0000000000 7.4163032574 4.0292795224 0.5313517931 0.5576255368 0.7915188257 -0.2239571331 0.111332438037 +1403637161488318976.0000000000 7.4779574454 4.0676143502 0.5488688249 0.5572627885 0.7911711685 -0.2239398817 0.115573768831 +1403637161538319104.0000000000 7.5414540763 4.1052601759 0.5664388377 0.5546037989 0.7918273180 -0.2255998640 0.1205355806 +1403637161588318976.0000000000 7.6062548446 4.1423322281 0.5839358650 0.5536011071 0.7907927831 -0.2289903433 0.125443258505 +1403637161638319104.0000000000 7.6719230577 4.1783611070 0.6000676218 0.5527847566 0.7894953626 -0.2325855749 0.130499178857 +1403637161688318976.0000000000 7.7387134808 4.2140532023 0.6156147639 0.5539632112 0.7867652359 -0.2359593959 0.135824842206 +1403637161738319104.0000000000 7.8064786890 4.2496531325 0.6301082047 0.5568141294 0.7830626340 -0.2380596886 0.141769253661 +1403637161788318976.0000000000 7.8748317732 4.2845116595 0.6436790978 0.5617497640 0.7779840093 -0.2383581622 0.149544208973 +1403637161838319104.0000000000 7.9433509992 4.3184420095 0.6564618255 0.5684048961 0.7715379586 -0.2387294186 0.157013748157 +1403637161888318976.0000000000 8.0115887271 4.3508403394 0.6680071958 0.5745909175 0.7652567500 -0.2388365441 0.164877194269 +1403637161938319104.0000000000 8.0789544454 4.3815517282 0.6786961207 0.5814625758 0.7585227501 -0.2396172967 0.17066945139 +1403637161988318976.0000000000 8.1451412078 4.4100776992 0.6879620604 0.5872192232 0.7527967483 -0.2396944970 0.176116972016 +1403637162038319104.0000000000 8.2098019468 4.4360544100 0.6957334804 0.5920338680 0.7479082282 -0.2399931459 0.180367600671 +1403637162088318976.0000000000 8.2725979231 4.4592763031 0.7014907111 0.5946248366 0.7449477624 -0.2408713668 0.182907407445 +1403637162138319104.0000000000 8.3334036405 4.4799042018 0.7055904597 0.5966539761 0.7427627085 -0.2427978325 0.182638452158 +1403637162188318976.0000000000 8.3921161998 4.4976144424 0.7077226967 0.5965822289 0.7425398059 -0.2465667381 0.178687225289 +1403637162238319104.0000000000 8.4491532102 4.5125041569 0.7081816962 0.5949229544 0.7437324558 -0.2509042246 0.173135157062 +1403637162288318976.0000000000 8.5050905257 4.5245405476 0.7073267575 0.5931793766 0.7451205983 -0.2544301488 0.167925044538 +1403637162338319104.0000000000 8.5603687437 4.5336253451 0.7047477030 0.5909011196 0.7470174482 -0.2565588968 0.164250818612 +1403637162388318976.0000000000 8.6151849662 4.5399818591 0.7011292250 0.5891996506 0.7484697319 -0.2594790290 0.159083203382 +1403637162438319104.0000000000 8.6696890502 4.5435942222 0.6960783282 0.5864579983 0.7507627730 -0.2627253262 0.152962995404 +1403637162488318976.0000000000 8.7247962992 4.5443571191 0.6896048987 0.5790071272 0.7567493722 -0.2636820717 0.15017622824 +1403637162538319104.0000000000 8.7806547163 4.5422983968 0.6842916168 0.5715957014 0.7626675976 -0.2625980827 0.150528192079 +1403637162588318976.0000000000 8.8375185218 4.5382579266 0.6819061616 0.5679452488 0.7657258495 -0.2604809272 0.152485423411 +1403637162638319104.0000000000 8.8951701431 4.5324840739 0.6821788922 0.5686623996 0.7654610339 -0.2570922389 0.156831315809 +1403637162688318976.0000000000 8.9194554107 4.4925053787 0.6806182852 0.5750452264 0.7604810333 -0.2557792675 0.159901694506 +1403637162738319104.0000000000 8.9778518812 4.4834856797 0.6846979484 0.5842288150 0.7523593431 -0.2576703715 0.161981759009 +1403637162788318976.0000000000 9.0363397523 4.4717462388 0.6875209214 0.5909297477 0.7449550992 -0.2617842302 0.165266300939 +1403637162838319104.0000000000 9.0952141451 4.4573433996 0.6878595705 0.5923261259 0.7406983900 -0.2667035160 0.171420215095 +1403637162888318976.0000000000 9.1539976141 4.4399403037 0.6863521819 0.5926145777 0.7363922586 -0.2730525061 0.178820392295 +1403637162938319104.0000000000 9.2128279079 4.4195590064 0.6830132594 0.5906830901 0.7328865647 -0.2798498859 0.188824817706 +1403637162988318976.0000000000 9.2710095840 4.3961957307 0.6782791620 0.5871622710 0.7298669498 -0.2874429724 0.199777978519 +1403637163038319104.0000000000 9.3288624257 4.3703451895 0.6722828576 0.5828682617 0.7264864719 -0.2966491080 0.210905908825 +1403637163088318976.0000000000 9.3853380747 4.3418130247 0.6655820325 0.5780325539 0.7223989253 -0.3072492449 0.222746629262 +1403637163138319104.0000000000 9.4408231717 4.3109872014 0.6577972679 0.5727875927 0.7176218202 -0.3180836180 0.236127314702 +1403637163188318976.0000000000 9.4943657714 4.2779402707 0.6492801905 0.5672084331 0.7123150720 -0.3304133353 0.248412679914 +1403637163238319104.0000000000 9.5461485638 4.2428729751 0.6401401250 0.5620292856 0.7060333175 -0.3425129948 0.261390292763 +1403637163288318976.0000000000 9.5953329682 4.2059035567 0.6304088865 0.5570192837 0.6996473869 -0.3547417559 0.272729422953 +1403637163338319104.0000000000 9.6418460476 4.1672325912 0.6200509087 0.5525296627 0.6927833334 -0.3678138828 0.281913412901 +1403637163388318976.0000000000 9.6856591511 4.1269807199 0.6091213315 0.5480730746 0.6862277174 -0.3813274141 0.28861189849 +1403637163438319104.0000000000 9.7265386644 4.0846700163 0.5973022195 0.5431909212 0.6800913349 -0.3951989236 0.293661727439 +1403637163488318976.0000000000 9.7648142144 4.0408482831 0.5848519778 0.5384616671 0.6747343671 -0.4087199317 0.296210371819 +1403637163538319104.0000000000 9.8143210951 4.0004925610 0.5676255154 0.5323095735 0.6713543793 -0.4210361308 0.297755590741 +1403637163588318976.0000000000 9.8494024106 3.9540132681 0.5554892071 0.5261559668 0.6692695055 -0.4331886936 0.295948954038 +1403637163638319104.0000000000 9.8830178707 3.9055340532 0.5449772727 0.5181912372 0.6694039176 -0.4439133680 0.293797819187 +1403637163688318976.0000000000 9.9159497951 3.8557165447 0.5376089682 0.5129283522 0.6686826093 -0.4528010280 0.291100158977 +1403637163738319104.0000000000 9.9485262617 3.8042219821 0.5322589544 0.5077155584 0.6686068017 -0.4614450956 0.286807043433 +1403637163788318976.0000000000 9.9820949065 3.7509777848 0.5297651877 0.5042071261 0.6681450372 -0.4669472655 0.285162470369 +1403637163838319104.0000000000 10.0155544818 3.6957776810 0.5304236817 0.5024435311 0.6672318673 -0.4722012893 0.281741150149 +1403637163888318976.0000000000 10.0490907128 3.6385912684 0.5340531223 0.5029158025 0.6650829170 -0.4768813175 0.27807304459 +1403637163938319104.0000000000 10.0837066932 3.5791108959 0.5398934693 0.5048524858 0.6624171066 -0.4794775448 0.27645764339 +1403637163988318976.0000000000 10.1196850799 3.5172285461 0.5471210564 0.5068652547 0.6600606443 -0.4808536915 0.276020446377 +1403637164038319104.0000000000 10.1570646428 3.4530099688 0.5558057058 0.5078565456 0.6592193923 -0.4805567191 0.276725065049 +1403637164088318976.0000000000 10.1955132176 3.3862320365 0.5667072465 0.5096922597 0.6579921161 -0.4791546491 0.278695170064 +1403637164138319104.0000000000 10.2349566889 3.3169146021 0.5792135889 0.5112620934 0.6575710844 -0.4768052913 0.280834568561 +1403637164188318976.0000000000 10.2747739454 3.2446095974 0.5927524646 0.5124831700 0.6576009322 -0.4738703154 0.283494159835 +1403637164238319104.0000000000 10.3148650246 3.1697521892 0.6072159243 0.5119328205 0.6591802003 -0.4707136241 0.286068059967 +1403637164288318976.0000000000 10.3554232013 3.0926794927 0.6227665017 0.5107382319 0.6615945482 -0.4652598376 0.291500250084 +1403637164338319104.0000000000 10.3958879005 3.0137742204 0.6378510072 0.5078357796 0.6652954199 -0.4610463185 0.294823875197 +1403637164388318976.0000000000 10.4361498194 2.9335515771 0.6520979143 0.5061306265 0.6680451443 -0.4583520636 0.29573782306 +1403637164438319104.0000000000 10.4762814754 2.8522707785 0.6642481999 0.5035346933 0.6714342598 -0.4566250594 0.295165042907 +1403637164488318976.0000000000 10.5158305115 2.7700231350 0.6749824966 0.5033609362 0.6730013367 -0.4570844257 0.291154248612 +1403637164538319104.0000000000 10.5542326291 2.6926038091 0.6923535761 0.5056495770 0.6726689425 -0.4585467106 0.285604469895 +1403637164588318976.0000000000 10.5946796962 2.6094473262 0.7000512032 0.5068750210 0.6732634223 -0.4592896602 0.280797231555 +1403637164638319104.0000000000 10.6357302349 2.5249310356 0.7058386309 0.5079090463 0.6737679731 -0.4599173978 0.276660633747 +1403637164688318976.0000000000 10.6775684027 2.4386106494 0.7094393392 0.5070239177 0.6759040447 -0.4578779807 0.276456549737 +1403637164738319104.0000000000 10.7205181387 2.3507148736 0.7115302395 0.5058852913 0.6779885179 -0.4534182670 0.280755261423 +1403637164788318976.0000000000 10.7647090405 2.2615888046 0.7120734843 0.5048626457 0.6789286184 -0.4482319140 0.288544262352 +1403637164838319104.0000000000 10.8091682480 2.1715719739 0.7113170505 0.5044947424 0.6783380393 -0.4449100795 0.29563081802 +1403637164888318976.0000000000 10.8539478723 2.0805653288 0.7090784420 0.5026784430 0.6774328284 -0.4431809900 0.303298130554 +1403637164938319104.0000000000 10.8985586174 1.9883140467 0.7091976801 0.5008219018 0.6756704452 -0.4437898701 0.309350001496 +1403637164988318976.0000000000 10.9425334625 1.8961331662 0.7053848738 0.4986505110 0.6732896096 -0.4463874800 0.314272154586 +1403637165038319104.0000000000 10.9869068408 1.8041120094 0.7005984042 0.4962487457 0.6701293964 -0.4499470338 0.319705241168 +1403637165088318976.0000000000 11.0312119107 1.7122517637 0.6955417302 0.4948519436 0.6653145279 -0.4545832569 0.325318605861 +1403637165138319104.0000000000 11.0754291384 1.6203207794 0.6904447191 0.4947695981 0.6583874998 -0.4594494276 0.332618652941 +1403637165188318976.0000000000 11.1187987822 1.5280639920 0.6841441553 0.4912826859 0.6529128571 -0.4651404048 0.340573820771 +1403637165238319104.0000000000 11.1608855863 1.4347316349 0.6771224087 0.4873410079 0.6472583830 -0.4721983703 0.347252108333 +1403637165288318976.0000000000 11.2010984907 1.3418086226 0.6716345797 0.4805382183 0.6430121183 -0.4802441957 0.353530690372 +1403637165338319104.0000000000 11.2389408272 1.2490012674 0.6683003279 0.4723929625 0.6399775611 -0.4897132209 0.357007803298 +1403637165388318976.0000000000 11.2752445035 1.1565016211 0.6668762585 0.4636365767 0.6380618262 -0.4984043668 0.359876809378 +1403637165438319104.0000000000 11.3110777952 1.0649942935 0.6676548875 0.4558467902 0.6363507840 -0.5070392701 0.360794348788 +1403637165488318976.0000000000 11.3465321021 0.9743771284 0.6715670270 0.4504540571 0.6341104693 -0.5136414797 0.362170519889 +1403637165538319104.0000000000 11.3811637746 0.8841672534 0.6774416211 0.4447951826 0.6326071606 -0.5178220047 0.365822084298 +1403637165588318976.0000000000 11.4156368604 0.7950876214 0.6850102478 0.4397985630 0.6312620163 -0.5220476731 0.368173488652 +1403637165638319104.0000000000 11.4501572101 0.7065921066 0.6931236689 0.4332229588 0.6315655595 -0.5226088816 0.37459680841 +1403637165688318976.0000000000 11.4845522171 0.6195778025 0.7009177056 0.4274759951 0.6321156815 -0.5221308512 0.380885039041 +1403637165738319104.0000000000 11.5188834066 0.5342115267 0.7077353102 0.4219945374 0.6331210899 -0.5209081385 0.386953494702 +1403637165788318976.0000000000 11.5535013001 0.4509265966 0.7133936185 0.4165497746 0.6346890963 -0.5189125392 0.392919601192 +1403637165838319104.0000000000 11.5876316636 0.3699180910 0.7177606971 0.4117623661 0.6361658290 -0.5163857778 0.398861530216 +1403637165888318976.0000000000 11.6206624711 0.2917524395 0.7205935426 0.4081656771 0.6384207540 -0.5135106157 0.402649436214 +1403637165938319104.0000000000 11.6531558898 0.2167251272 0.7219822955 0.4057841643 0.6416168999 -0.5089856403 0.405709974935 +1403637165988318976.0000000000 11.6848866142 0.1448982467 0.7215908382 0.4037316808 0.6458644737 -0.5036616379 0.407657657949 +1403637166038319104.0000000000 11.7171206162 0.0766928524 0.7188747426 0.4033526106 0.6501423087 -0.4981335893 0.408025216248 +1403637166088318976.0000000000 11.7495933763 0.0115760178 0.7122191907 0.4023158461 0.6543982936 -0.4927662563 0.408761849882 +1403637166138319104.0000000000 11.7814675668 -0.0502929542 0.7016797303 0.4028696233 0.6574471407 -0.4883755105 0.408593544354 +1403637166188318976.0000000000 11.8127730156 -0.1088418646 0.6874549230 0.4033976206 0.6602896032 -0.4845392811 0.40805598219 +1403637166238319104.0000000000 11.8439798723 -0.1636092781 0.6709761170 0.4074009191 0.6608125581 -0.4811447260 0.407248090072 +1403637166288318976.0000000000 11.8743654643 -0.2145410518 0.6535592976 0.4142784498 0.6592285097 -0.4783838694 0.406128072843 +1403637166338319104.0000000000 11.9041161174 -0.2615862409 0.6385257774 0.4254190921 0.6550500496 -0.4723191304 0.408463789966 +1403637166388318976.0000000000 11.9323387262 -0.3045218491 0.6260906863 0.4410355362 0.6482783386 -0.4647794635 0.411342803201 +1403637166438319104.0000000000 11.9572752973 -0.3448387774 0.6142965912 0.4552027029 0.6426845547 -0.4578385186 0.41246933615 +1403637166488318976.0000000000 11.9781632824 -0.3833216170 0.6027161848 0.4632103028 0.6407417064 -0.4522546943 0.412737171141 +1403637166538319104.0000000000 11.9949337648 -0.4199733140 0.5922981492 0.4677814624 0.6408866350 -0.4493168996 0.410559555072 +1403637166588318976.0000000000 12.0073686815 -0.4553200665 0.5816557924 0.4664154349 0.6449072380 -0.4484552182 0.406742195752 +1403637166638319104.0000000000 12.0157016326 -0.4891474333 0.5709712608 0.4608794004 0.6514813660 -0.4499147964 0.400922541222 +1403637166688318976.0000000000 12.0205883827 -0.5213632256 0.5600888993 0.4513531495 0.6603998656 -0.4532592426 0.393329900918 +1403637166738319104.0000000000 12.0239462397 -0.5517540009 0.5490372638 0.4418464656 0.6687597858 -0.4530179296 0.390265044697 +1403637166788318976.0000000000 12.0261797531 -0.5795172577 0.5373587081 0.4340134493 0.6757068602 -0.4515454988 0.388792010517 +1403637166838319104.0000000000 12.0277202368 -0.6044034311 0.5249509468 0.4276184204 0.6811856317 -0.4478544773 0.390582883362 +1403637166888318976.0000000000 12.0286153996 -0.6260642418 0.5118125203 0.4232790322 0.6850046190 -0.4416386484 0.395675166165 +1403637166938319104.0000000000 12.0286326311 -0.6437729600 0.4979483440 0.4203515386 0.6878216163 -0.4345497417 0.401711998996 +1403637166988318976.0000000000 12.0274970878 -0.6569817987 0.4846845582 0.4200471752 0.6883035933 -0.4267455482 0.409495752282 +1403637167038319104.0000000000 12.0236310637 -0.6654304474 0.4728917102 0.4195239013 0.6889743248 -0.4188929138 0.416944603974 +1403637167088318976.0000000000 12.0156126856 -0.6690242528 0.4631513275 0.4200907036 0.6891637546 -0.4111767861 0.423687114017 +1403637167138319104.0000000000 12.0031284279 -0.6675017256 0.4559934557 0.4208235490 0.6886564453 -0.4043098784 0.43034098476 +1403637167188318976.0000000000 11.9870288472 -0.6599829858 0.4517372024 0.4223878685 0.6875676844 -0.3984237015 0.436001974851 +1403637167238319104.0000000000 11.9668053534 -0.6462696045 0.4504979041 0.4231059501 0.6868122400 -0.3943474814 0.440182196174 +1403637167288318976.0000000000 11.9418278649 -0.6266876159 0.4513421608 0.4232629047 0.6864204688 -0.3929936974 0.44184998275 +1403637167338319104.0000000000 11.9134253775 -0.6011508938 0.4529697798 0.4225599150 0.6864915848 -0.3946981967 0.440892000089 +1403637167388318976.0000000000 11.8809505438 -0.5703400156 0.4539276743 0.4215408695 0.6870082758 -0.3995950147 0.436631135583 +1403637167438319104.0000000000 11.8448454658 -0.5340400260 0.4536661431 0.4224704543 0.6874462072 -0.4090243029 0.4261872207 +1403637167488318976.0000000000 11.8061035017 -0.4926474378 0.4531093892 0.4275900021 0.6856396829 -0.4207177199 0.4123852757 +1403637167538319104.0000000000 11.7655063116 -0.4473076027 0.4516114405 0.4332535625 0.6833366830 -0.4335679051 0.396687786404 +1403637167588318976.0000000000 11.7239490873 -0.3990076684 0.4495190284 0.4401522037 0.6798325856 -0.4451367658 0.382030041877 +1403637167638319104.0000000000 11.6817561606 -0.3487599118 0.4465846665 0.4474449616 0.6758766422 -0.4547903774 0.368984394702 +1403637167688318976.0000000000 11.6392202670 -0.2974982573 0.4419414605 0.4528382730 0.6736637425 -0.4606612438 0.359034648829 +1403637167738319104.0000000000 11.5964231624 -0.2456971726 0.4349007945 0.4555192736 0.6741337896 -0.4632553562 0.351340717895 +1403637167788318976.0000000000 11.5534866992 -0.1934013469 0.4260685793 0.4564931188 0.6766641929 -0.4638990477 0.34429242812 +1403637167838319104.0000000000 11.5106791947 -0.1408402555 0.4156764043 0.4565976973 0.6808789109 -0.4625522630 0.337591255142 +1403637167888318976.0000000000 11.4686342603 -0.0880890621 0.4054147474 0.4551382545 0.6862556625 -0.4601240027 0.33194613579 +1403637167938319104.0000000000 11.4277144042 -0.0352665820 0.3965268269 0.4533339148 0.6913748916 -0.4565284916 0.328741322699 +1403637167988318976.0000000000 11.3880985681 0.0177234697 0.3893586415 0.4512704905 0.6963729164 -0.4504616847 0.329399417616 +1403637168038319104.0000000000 11.3502371532 0.0718097411 0.3842727558 0.4502737229 0.7003666163 -0.4442301628 0.330756314675 +1403637168088318976.0000000000 11.3131624577 0.1271787976 0.3805191044 0.4512323600 0.7027626420 -0.4404103080 0.329473499594 +1403637168138319104.0000000000 11.2767372582 0.1835578642 0.3753953680 0.4532539209 0.7038453351 -0.4403563295 0.324420915745 +1403637168188318976.0000000000 11.2417450786 0.2404938198 0.3668308342 0.4556537027 0.7042145902 -0.4398934049 0.320866493309 +1403637168238319104.0000000000 11.2080562414 0.2980291578 0.3552069760 0.4594369759 0.7033091750 -0.4378646755 0.320231783865 +1403637168288318976.0000000000 11.1151843572 0.3819259842 0.3874498138 0.4625065910 0.7024825874 -0.4348617635 0.321715890695 +1403637168338319104.0000000000 11.0811723499 0.4421172899 0.3685476767 0.4665676972 0.7005904910 -0.4313868715 0.32464274975 +1403637168388318976.0000000000 11.0469551385 0.5022178308 0.3466484695 0.4718716445 0.6976844243 -0.4270255731 0.328972270985 +1403637168438319104.0000000000 11.0125790421 0.5626546410 0.3232178903 0.4767683909 0.6948210124 -0.4229504767 0.333209478344 +1403637168488318976.0000000000 10.9775368571 0.6233910481 0.2990845763 0.4833753822 0.6907905372 -0.4211914473 0.334296931404 +1403637168538319104.0000000000 10.9415482448 0.6838902969 0.2734887986 0.4868153367 0.6886568847 -0.4211323253 0.333781497088 +1403637168588318976.0000000000 10.9045143154 0.7442796031 0.2482652387 0.4869820821 0.6890086556 -0.4228750169 0.330593775403 +1403637168638319104.0000000000 10.8665402118 0.8040544626 0.2241678492 0.4854388314 0.6903103902 -0.4242733343 0.328348662098 +1403637168688318976.0000000000 10.8268433810 0.8654887562 0.2011233691 0.4823951152 0.6923881674 -0.4254336363 0.32695534797 +1403637168738319104.0000000000 10.7876547018 0.9251852312 0.1811169760 0.4793756754 0.6944641280 -0.4258191682 0.326491305857 +1403637168788318976.0000000000 10.7483198224 0.9850776654 0.1632680282 0.4782905735 0.6949751771 -0.4277380015 0.324480866416 +1403637168838319104.0000000000 10.7097644181 1.0449404685 0.1469951694 0.4753296953 0.6965101377 -0.4271263214 0.326340948168 +1403637168888318976.0000000000 10.6715804051 1.1052783178 0.1315017784 0.4733115028 0.6978056491 -0.4263293279 0.327546640186 +1403637168938319104.0000000000 10.6332452866 1.1654860807 0.1152732560 0.4703188376 0.6992994736 -0.4252321726 0.330087922448 +1403637168988318976.0000000000 10.5949967140 1.2264007335 0.0980363371 0.4686953790 0.6998149724 -0.4249385816 0.331678832519 +1403637169038319104.0000000000 10.5568869376 1.2878021087 0.0798377942 0.4667545520 0.7006999271 -0.4231623781 0.334803527695 +1403637169088318976.0000000000 10.5187999617 1.3500742850 0.0613787837 0.4643285562 0.7023900013 -0.4201141472 0.338454400503 +1403637169138319104.0000000000 10.4802586572 1.4142749570 0.0447210056 0.4650037494 0.7032319930 -0.4170389703 0.339580291464 +1403637169188318976.0000000000 10.4408376059 1.4801377437 0.0301951572 0.4670326764 0.7046697585 -0.4120594744 0.339894101514 +1403637169238319104.0000000000 10.4006834048 1.5476994545 0.0180089638 0.4704615551 0.7066190917 -0.4061998396 0.338167229009 +1403637169288318976.0000000000 10.3594654424 1.6167979750 0.0087570965 0.4755919334 0.7087744828 -0.3993229338 0.334652416744 +1403637169338319104.0000000000 10.3168291932 1.6868989034 0.0014018447 0.4815413983 0.7112607030 -0.3920578408 0.329418796557 +1403637169388318976.0000000000 10.2725645627 1.7580061372 -0.0034860487 0.4872507948 0.7146259635 -0.3833358480 0.323959909385 +1403637169438319104.0000000000 10.2270890241 1.8301721350 -0.0072913074 0.4925580087 0.7191292744 -0.3731893790 0.31775679724 +1403637169488318976.0000000000 10.1803932058 1.9030812633 -0.0090369147 0.4989048966 0.7232112474 -0.3622994491 0.311124581119 +1403637169538319104.0000000000 10.1319817533 1.9761261838 -0.0095521174 0.5045718931 0.7281859931 -0.3487763837 0.305789794294 +1403637169588318976.0000000000 10.0820694787 2.0498859307 -0.0085293757 0.5114764069 0.7327263377 -0.3348941312 0.298914570094 +1403637169638319104.0000000000 10.0308383111 2.1237510378 -0.0061736732 0.5173779079 0.7379343129 -0.3178725539 0.294499727835 +1403637169688318976.0000000000 9.9775804679 2.1980529075 -0.0028295643 0.5242990757 0.7423590796 -0.3033968927 0.286293209144 +1403637169738319104.0000000000 9.9222200901 2.2721574057 -0.0002077874 0.5297952314 0.7475732209 -0.2892747295 0.277076565234 +1403637169788318976.0000000000 9.8652117671 2.3460681005 0.0009219609 0.5345229790 0.7525806688 -0.2760138352 0.267813152441 +1403637169838319104.0000000000 9.8063038920 2.4195417599 0.0002384163 0.5393565880 0.7568808767 -0.2630549934 0.258897431308 +1403637169888318976.0000000000 9.7461752409 2.4926698620 -0.0025724690 0.5421212002 0.7615537716 -0.2486610712 0.253590474903 +1403637169938319104.0000000000 9.6871843958 2.5662695643 -0.0104453323 0.5461343453 0.7649203201 -0.2355586830 0.247277753955 +1403637169988318976.0000000000 9.6239594129 2.6395740616 -0.0168213969 0.5495436043 0.7680155309 -0.2222187083 0.242431056246 +1403637170038319104.0000000000 9.5582507870 2.7127421266 -0.0249110317 0.5521809549 0.7713604663 -0.2104485810 0.236242711528 +1403637170088318976.0000000000 9.4898807810 2.7855292738 -0.0344044153 0.5543742692 0.7748751021 -0.1991804953 0.229270312308 +1403637170138319104.0000000000 9.4189995337 2.8582757268 -0.0448815610 0.5578970516 0.7772045737 -0.1879456016 0.22221696907 +1403637170188318976.0000000000 9.3457205765 2.9308930523 -0.0565999376 0.5619028849 0.7789906779 -0.1767653109 0.214924862531 +1403637170238319104.0000000000 9.2699204884 3.0027577257 -0.0698601389 0.5650151864 0.7810839057 -0.1651213372 0.208328383496 +1403637170288318976.0000000000 9.1915194681 3.0742781713 -0.0843557350 0.5680140210 0.7829908516 -0.1527954821 0.202333731455 +1403637170338319104.0000000000 9.1099482103 3.1454754066 -0.0992816415 0.5729190468 0.7837620436 -0.1418974450 0.193250976442 +1403637170388318976.0000000000 9.0250171420 3.2163981298 -0.1145815923 0.5791969013 0.7839666603 -0.1334162495 0.179240981463 +1403637170438319104.0000000000 8.9374524165 3.2865177756 -0.1301556295 0.5875624787 0.7825023297 -0.1255364422 0.163404526577 +1403637170488318976.0000000000 8.8476663301 3.3552203715 -0.1461999143 0.5966053589 0.7803041461 -0.1178587983 0.145934193943 +1403637170538319104.0000000000 8.7562255390 3.4217678456 -0.1631557663 0.6061652508 0.7771056103 -0.1088115097 0.1297328585 +1403637170588318976.0000000000 8.6634899038 3.4855253251 -0.1811530682 0.6159749219 0.7730605990 -0.0992481131 0.114464046526 +1403637170638319104.0000000000 8.5701072405 3.5465128911 -0.2007452578 0.6240203443 0.7699167650 -0.0886009589 0.0998832067035 +1403637170688318976.0000000000 8.4762871148 3.6037141114 -0.2216205900 0.6319761792 0.7662631359 -0.0766958215 0.0869750904396 +1403637170738319104.0000000000 8.3819656998 3.6566788410 -0.2432363579 0.6374775526 0.7641395536 -0.0638354494 0.0750876018511 +1403637170788318976.0000000000 8.2868874283 3.7049893427 -0.2646052220 0.6404860948 0.7638241525 -0.0512047360 0.0610598182051 +1403637170838319104.0000000000 8.1919380575 3.7479623326 -0.2858261595 0.6382678564 0.7673133646 -0.0378120422 0.0491385136867 +1403637170888318976.0000000000 8.0970479130 3.7864636315 -0.3047722392 0.6368684769 0.7697523338 -0.0230505556 0.0367227394501 +1403637170938319104.0000000000 8.0027169139 3.8206350003 -0.3218378265 0.6336747986 0.7731558918 -0.0076759424 0.0250458876012 +1403637170988318976.0000000000 7.9091326130 3.8500421460 -0.3367676955 0.6298070543 0.7766044057 0.0071869187 0.0133048681795 +1403637171038319104.0000000000 7.8161016428 3.8761363362 -0.3491052193 0.6271907821 0.7785809793 0.0210490904 0.000563287489622 +1403637171088318976.0000000000 7.7240770689 3.8989999352 -0.3599270649 0.6237124607 0.7808214181 0.0334465678 -0.0134909792079 +1403637171138319104.0000000000 7.6339275150 3.9190610000 -0.3693139223 0.6197536942 0.7830845154 0.0462071990 -0.0234285081286 +1403637171188318976.0000000000 7.5455001867 3.9365435799 -0.3764240311 0.6177450135 0.7836498349 0.0568087692 -0.0325084338989 +1403637171238319104.0000000000 7.4586299567 3.9516738468 -0.3805576735 0.6175564562 0.7827547873 0.0644552744 -0.0420057615054 +1403637171288318976.0000000000 7.3738245390 3.9642211756 -0.3827220297 0.6187611555 0.7807613101 0.0721778998 -0.0483400429215 +1403637171338319104.0000000000 7.2908991234 3.9744499926 -0.3826147358 0.6201550068 0.7787190007 0.0794429529 -0.0518970400923 +1403637171388318976.0000000000 7.2099061864 3.9820044874 -0.3813376261 0.6213943370 0.7768972310 0.0874290579 -0.0515357179944 +1403637171438319104.0000000000 7.1304825929 3.9862407925 -0.3778833170 0.6229185321 0.7749689522 0.0948514100 -0.0489779078053 +1403637171488318976.0000000000 7.0516417336 3.9867852967 -0.3727113899 0.6227639250 0.7745188345 0.1000025657 -0.0478033011995 +1403637171538319104.0000000000 6.9727227609 3.9841004216 -0.3661740531 0.6223940728 0.7743755325 0.1039259549 -0.0465569409458 +1403637171588318976.0000000000 6.8942229779 3.9785511443 -0.3596086462 0.6220339577 0.7743947405 0.1065282108 -0.0451473320826 +1403637171638319104.0000000000 6.8155525935 3.9695121582 -0.3540389286 0.6224873517 0.7738186417 0.1093568437 -0.0418961506938 +1403637171688318976.0000000000 6.7367402286 3.9575171777 -0.3494907080 0.6229687046 0.7734262254 0.1102475543 -0.0395896912282 +1403637171738319104.0000000000 6.6577611622 3.9426438436 -0.3460399620 0.6239560920 0.7727458353 0.1102584612 -0.037225542148 +1403637171788318976.0000000000 6.5788071244 3.9246454207 -0.3437400075 0.6250250600 0.7720416557 0.1100817696 -0.0343126838942 +1403637171838319104.0000000000 6.5003370596 3.9040844318 -0.3430021264 0.6264605390 0.7710700499 0.1097616676 -0.0308309502445 +1403637171888318976.0000000000 6.4217131898 3.8799967834 -0.3438334724 0.6278443318 0.7701937239 0.1086508441 -0.0284273951195 +1403637171938319104.0000000000 6.3440814084 3.8531717969 -0.3459681853 0.6284586298 0.7699818627 0.1070232637 -0.0267152140745 +1403637171988318976.0000000000 6.2663377608 3.8232382739 -0.3490124171 0.6299718960 0.7690291161 0.1054212377 -0.0248191772452 +1403637172038319104.0000000000 6.1886386672 3.7894975187 -0.3537774063 0.6307488842 0.7686681819 0.1038117317 -0.0229825042258 +1403637172088318976.0000000000 6.1108291049 3.7529899248 -0.3591853075 0.6319013430 0.7679902872 0.1021116004 -0.0215599757989 +1403637172138319104.0000000000 6.0319854816 3.7132049363 -0.3654709080 0.6308492717 0.7692707774 0.0984889281 -0.0234861339656 +1403637172188318976.0000000000 5.9524286987 3.6698578190 -0.3716885050 0.6281300320 0.7719963669 0.0930139998 -0.0286821920165 +1403637172238319104.0000000000 5.8719765840 3.6231198940 -0.3768848562 0.6213251571 0.7779308332 0.0865132693 -0.0359739091574 +1403637172288318976.0000000000 5.7917878718 3.5734500716 -0.3799941182 0.6139689209 0.7840790747 0.0793519644 -0.044333221868 +1403637172338319104.0000000000 5.7123680912 3.5218686678 -0.3805990078 0.6076563024 0.7891960229 0.0727073621 -0.0513526539526 +1403637172388318976.0000000000 5.6341382290 3.4688080373 -0.3785610189 0.6023933414 0.7933150823 0.0662687043 -0.0581541173966 +1403637172438319104.0000000000 5.5578870593 3.4145475569 -0.3745924570 0.5981780530 0.7965330802 0.0605888758 -0.0636164847058 +1403637172488318976.0000000000 5.4841104766 3.3583837583 -0.3691962463 0.5939497922 0.7996333483 0.0545309105 -0.0695451822669 +1403637172538319104.0000000000 5.4128759209 3.3009127806 -0.3613266939 0.5921466486 0.8009340511 0.0502001098 -0.0731227822515 +1403637172588318976.0000000000 5.3444732889 3.2422568793 -0.3518590620 0.5904859585 0.8021526479 0.0466241489 -0.0755225198458 +1403637172638319104.0000000000 5.2787603932 3.1832950421 -0.3406436885 0.5893862490 0.8029550055 0.0434850350 -0.0774348783228 +1403637172688318976.0000000000 5.2158457559 3.1241931580 -0.3279066358 0.5870275885 0.8046406180 0.0405461186 -0.0794235379736 +1403637172738319104.0000000000 5.1562607689 3.0651701263 -0.3137191899 0.5848849126 0.8062702570 0.0381238255 -0.0799029763543 +1403637172788318976.0000000000 5.1002527194 3.0063129296 -0.2986437986 0.5805245873 0.8096451551 0.0347492515 -0.0791101508219 +1403637172838319104.0000000000 5.0473612360 2.9472559776 -0.2827443745 0.5731704221 0.8152011533 0.0301433420 -0.0775507944336 +1403637172888318976.0000000000 4.9986211373 2.8890626785 -0.2680371427 0.5629319065 0.8227912409 0.0253070930 -0.0740391353268 +1403637172938319104.0000000000 4.9530615834 2.8323309704 -0.2561367808 0.5516082836 0.8309326050 0.0202845904 -0.0697699273868 +1403637172988318976.0000000000 4.9104367735 2.7773043024 -0.2478281052 0.5412361734 0.8381252216 0.0151672402 -0.0661775818823 +1403637173038319104.0000000000 4.8702824544 2.7246513604 -0.2437042341 0.5316744956 0.8445087753 0.0101093899 -0.0634425667718 +1403637173088318976.0000000000 4.8328438522 2.6760893506 -0.2434297087 0.5257235632 0.8485436919 0.0045229038 -0.0597317454362 +1403637173138319104.0000000000 4.7978652803 2.6309334916 -0.2464296723 0.5204069947 0.8520562037 -0.0032798218 -0.0562674721317 +1403637173188318976.0000000000 4.7654356004 2.5890384780 -0.2521744588 0.5176368844 0.8538786420 -0.0130823118 -0.0526514363851 +1403637173238319104.0000000000 4.7359260572 2.5508601147 -0.2599338398 0.5182235160 0.8536514216 -0.0232584378 -0.0467191913828 +1403637173288318976.0000000000 4.7094946323 2.5173735102 -0.2675531900 0.5216944011 0.8514718610 -0.0346002775 -0.0404158701717 +1403637173338319104.0000000000 4.6859675821 2.4871824448 -0.2756307600 0.5268899036 0.8480992806 -0.0454889128 -0.0323326248535 +1403637173388318976.0000000000 4.6657515077 2.4601976948 -0.2837766604 0.5315131918 0.8447466575 -0.0570873042 -0.0252557161297 +1403637173438319104.0000000000 4.6487906576 2.4361937201 -0.2920745160 0.5355652407 0.8415218683 -0.0684551023 -0.0180199108385 +1403637173488318976.0000000000 4.6349249413 2.4140910428 -0.3014241681 0.5388091178 0.8385527473 -0.0800220867 -0.0105114351806 +1403637173538319104.0000000000 4.6239427554 2.3935720844 -0.3117542969 0.5412652689 0.8358402510 -0.0915695028 -0.00424378341757 +1403637173588318976.0000000000 4.6157354269 2.3748324138 -0.3228583496 0.5424925009 0.8335586244 -0.1043155180 0.000422910290121 +1403637173638319104.0000000000 4.6103909940 2.3579761369 -0.3353291513 0.5425760225 0.8316140481 -0.1184205820 0.00242910799291 +1403637173688318976.0000000000 4.6082662150 2.3422734380 -0.3495186267 0.5414843281 0.8302572308 -0.1320994649 0.00416946822616 +1403637173738319104.0000000000 4.6098016102 2.3277443422 -0.3651038152 0.5389038367 0.8296735054 -0.1455710977 0.00579523240639 +1403637173788318976.0000000000 4.6149488209 2.3141152636 -0.3826820356 0.5346463511 0.8301450436 -0.1579417190 0.00817919604704 +1403637173838319104.0000000000 4.6246373361 2.3030593776 -0.4014496858 0.5281808881 0.8317974454 -0.1704137656 0.00985432333683 +1403637173888318976.0000000000 4.6393298705 2.2943928242 -0.4202918533 0.5206070463 0.8344212481 -0.1803629071 0.0133680870262 +1403637173938319104.0000000000 4.6594688424 2.2875767086 -0.4379212137 0.5133707727 0.8378317310 -0.1844363561 0.0217179830033 +1403637173988318976.0000000000 4.6853874109 2.2833884535 -0.4521905381 0.5111423651 0.8388364293 -0.1841640114 0.0342132197426 +1403637174038319104.0000000000 4.7168190746 2.2825664243 -0.4621431863 0.5142370006 0.8372631036 -0.1785824880 0.051566439205 +1403637174088318976.0000000000 4.7522373500 2.2856180908 -0.4666640774 0.5233492723 0.8315656305 -0.1737861084 0.0663515631024 +1403637174138319104.0000000000 4.7906205692 2.2915642981 -0.4665596268 0.5363837228 0.8231432354 -0.1682421183 0.0801392884465 +1403637174188318976.0000000000 4.8304830698 2.2996725868 -0.4623909729 0.5504732995 0.8135208585 -0.1651187272 0.0888749973464 +1403637174238319104.0000000000 4.8712279359 2.3085091030 -0.4554316520 0.5635161915 0.8043131445 -0.1632880917 0.0941640413538 +1403637174288318976.0000000000 4.9125319125 2.3170695064 -0.4465721923 0.5738834548 0.7966999557 -0.1637794712 0.0954109309016 +1403637174338319104.0000000000 4.9539036769 2.3242284191 -0.4375136329 0.5779546548 0.7936698174 -0.1650076251 0.0939634050192 +1403637174388318976.0000000000 4.9954473733 2.3298773103 -0.4266141243 0.5811904526 0.7911838911 -0.1676460944 0.0902246941315 +1403637174438319104.0000000000 5.0377369476 2.3346047683 -0.4140028466 0.5837253314 0.7889134881 -0.1729494791 0.0834788803372 +1403637174488318976.0000000000 5.0836694460 2.3408452449 -0.4005910001 0.5873036006 0.7853239015 -0.1807123564 0.0753916096882 +1403637174538319104.0000000000 5.1296191704 2.3423043871 -0.3852137957 0.5887527671 0.7831821155 -0.1861064644 0.0732143225704 +1403637174588318976.0000000000 5.1776423135 2.3412565947 -0.3685367488 0.5889904772 0.7814592168 -0.1924932021 0.0731988891224 +1403637174638319104.0000000000 5.2289998802 2.3390123754 -0.3524127025 0.5885372438 0.7801711722 -0.1960616749 0.0807259214482 +1403637174688318976.0000000000 5.2829611552 2.3351058432 -0.3367520739 0.5897154433 0.7769866151 -0.2001723892 0.0919701611823 +1403637174738319104.0000000000 5.3386529153 2.3293027152 -0.3226385300 0.5902678405 0.7736231673 -0.2051263691 0.104948769513 +1403637174788318976.0000000000 5.3954308231 2.3215772213 -0.3096818511 0.5906846799 0.7697784282 -0.2106032329 0.119075853148 +1403637174838319104.0000000000 5.4522448034 2.3117134911 -0.2990727057 0.5870432997 0.7683541113 -0.2191569657 0.130316339738 +1403637174888318976.0000000000 5.5087940429 2.2996342031 -0.2903146318 0.5805334984 0.7685132757 -0.2313100106 0.137345845863 +1403637174938319104.0000000000 5.5657783042 2.2862751033 -0.2824837066 0.5737299367 0.7683887652 -0.2444274221 0.143763349043 +1403637174988318976.0000000000 5.6231960138 2.2714151232 -0.2753653084 0.5678946747 0.7674542564 -0.2561678741 0.151286559485 +1403637175038319104.0000000000 5.6810178326 2.2555910597 -0.2691938347 0.5639925410 0.7654675738 -0.2666999171 0.157616501114 +1403637175088318976.0000000000 5.7393396839 2.2391159773 -0.2632501955 0.5635656901 0.7614166675 -0.2748444500 0.164617434559 +1403637175138319104.0000000000 5.7980893790 2.2219391922 -0.2579809152 0.5659696468 0.7556993998 -0.2820561690 0.170414476148 +1403637175188318976.0000000000 5.8567866897 2.2032863052 -0.2534363409 0.5703188869 0.7489268738 -0.2887101650 0.174617712723 +1403637175238319104.0000000000 5.9156236971 2.1830285063 -0.2494431608 0.5760373110 0.7413427270 -0.2944716065 0.178545373895 +1403637175288318976.0000000000 5.9743898880 2.1605182205 -0.2465570354 0.5819765305 0.7340648976 -0.2981271548 0.18322730021 +1403637175338319104.0000000000 6.0330125176 2.1354171460 -0.2450114712 0.5864743664 0.7282108028 -0.3001289803 0.188890019414 +1403637175388318976.0000000000 6.0907695892 2.1076137970 -0.2444748715 0.5900227094 0.7236404021 -0.3017504794 0.192780753942 +1403637175438319104.0000000000 6.1472916399 2.0769503841 -0.2455238817 0.5906653672 0.7219901166 -0.3046732707 0.192402946296 +1403637175488318976.0000000000 6.2029352641 2.0431851073 -0.2480955180 0.5885158053 0.7227199106 -0.3086492799 0.189896550126 +1403637175538319104.0000000000 6.2575677296 2.0060983677 -0.2519598930 0.5849773265 0.7249623934 -0.3128850559 0.185294353692 +1403637175588318976.0000000000 6.3119300343 1.9661067275 -0.2570556963 0.5804843990 0.7283100535 -0.3162366411 0.180545604537 +1403637175638319104.0000000000 6.3666723096 1.9234542777 -0.2626369869 0.5739810873 0.7333504301 -0.3186773424 0.17660014024 +1403637175688318976.0000000000 6.4221896049 1.8780398497 -0.2666176227 0.5693521389 0.7369973586 -0.3201444078 0.173725627106 +1403637175738319104.0000000000 6.4787528818 1.8304115753 -0.2685347981 0.5663811104 0.7395267983 -0.3211273904 0.170850084951 +1403637175788318976.0000000000 6.5365180274 1.7801896548 -0.2683167027 0.5636045175 0.7421068854 -0.3198053790 0.171323781541 +1403637175838319104.0000000000 6.5956462253 1.7279805560 -0.2658763756 0.5621392836 0.7438385518 -0.3168101021 0.174169440282 +1403637175888318976.0000000000 6.6561979009 1.6737735616 -0.2615975710 0.5604024240 0.7457486793 -0.3122309377 0.179777284251 +1403637175938319104.0000000000 6.7176220925 1.6182192013 -0.2550215085 0.5605901475 0.7463568649 -0.3066823595 0.186107622404 +1403637175988318976.0000000000 6.7792558500 1.5613031788 -0.2453193872 0.5630769379 0.7450991340 -0.3022266159 0.190868318773 +1403637176038319104.0000000000 6.8405696931 1.5030515848 -0.2327584793 0.5679004199 0.7420341885 -0.2998416378 0.192274201332 +1403637176088318976.0000000000 6.9019740240 1.4434447163 -0.2186895875 0.5727788928 0.7390305176 -0.2969570463 0.193842066234 +1403637176138319104.0000000000 6.9628224951 1.3821767242 -0.2052818596 0.5763110804 0.7370329817 -0.2930438705 0.196909147808 +1403637176188318976.0000000000 7.0227210169 1.3192874278 -0.1926896214 0.5800701990 0.7348621969 -0.2901193186 0.198310102271 +1403637176238319104.0000000000 7.0819680422 1.2544337815 -0.1819065889 0.5823817294 0.7332402404 -0.2880103082 0.20059993378 +1403637176288318976.0000000000 7.1405608675 1.1876549381 -0.1728180703 0.5833179027 0.7319817004 -0.2881069477 0.20232993189 +1403637176338319104.0000000000 7.1980857847 1.1187645110 -0.1653422494 0.5837671486 0.7308914556 -0.2894842409 0.203008548466 +1403637176388318976.0000000000 7.2548064730 1.0478301512 -0.1594627023 0.5827152100 0.7310836395 -0.2897008278 0.205019819443 +1403637176438319104.0000000000 7.3105353754 0.9748570318 -0.1547903776 0.5801514914 0.7322516036 -0.2916316282 0.205384589272 +1403637176488318976.0000000000 7.3655899805 0.9000169963 -0.1515220020 0.5751938867 0.7345299207 -0.2930893493 0.209084723399 +1403637176538319104.0000000000 7.4194637423 0.8237166392 -0.1485255394 0.5708690719 0.7356708760 -0.2967034519 0.21181106342 +1403637176588318976.0000000000 7.4728003381 0.7465320547 -0.1459374165 0.5671058956 0.7357080094 -0.3027881872 0.213175847165 +1403637176638319104.0000000000 7.5253646620 0.6682405313 -0.1445794853 0.5623536794 0.7363109533 -0.3092374647 0.214421803127 +1403637176688318976.0000000000 7.5774169737 0.5891507630 -0.1443387333 0.5575365416 0.7370249798 -0.3151533556 0.215929494022 +1403637176738319104.0000000000 7.6283724015 0.5091909807 -0.1450726956 0.5529302619 0.7378296897 -0.3210439184 0.216347583675 +1403637176788318976.0000000000 7.6786143892 0.4286072827 -0.1465362547 0.5491090187 0.7383648724 -0.3254699426 0.217637123024 +1403637176838319104.0000000000 7.7281957059 0.3474601892 -0.1487639470 0.5451909818 0.7390826349 -0.3295315188 0.218935219393 +1403637176888318976.0000000000 7.7774811503 0.2658632446 -0.1522233692 0.5397812201 0.7413015545 -0.3334798892 0.218859323057 +1403637176938319104.0000000000 7.8263436283 0.1840384640 -0.1564471856 0.5346112475 0.7436209812 -0.3362902045 0.219379918549 +1403637176988318976.0000000000 7.8749330546 0.1022129498 -0.1619064273 0.5283394039 0.7470590045 -0.3384208336 0.219617069834 +1403637177038319104.0000000000 7.9234056196 0.0208603018 -0.1684510040 0.5210772281 0.7511987502 -0.3418916932 0.217460410833 +1403637177088318976.0000000000 7.9722351939 -0.0600716736 -0.1766664475 0.5107882575 0.7576262165 -0.3445648082 0.215343829789 +1403637177138319104.0000000000 8.0215980878 -0.1399437130 -0.1857187926 0.5014442596 0.7632204645 -0.3482579858 0.21157635103 +1403637177188318976.0000000000 8.0721618009 -0.2184492410 -0.1957569350 0.4933002944 0.7679282644 -0.3512857019 0.208660863689 +1403637177238319104.0000000000 8.1245216636 -0.2950294376 -0.2067787692 0.4865267745 0.7718508810 -0.3534180421 0.206479061238 +1403637177288318976.0000000000 8.1791100965 -0.3694368370 -0.2186004237 0.4826042946 0.7740175020 -0.3549682165 0.204908678966 +1403637177338319104.0000000000 8.2360719018 -0.4415066534 -0.2318436471 0.4786048165 0.7763678124 -0.3559335309 0.203719834941 +1403637177388318976.0000000000 8.2957447393 -0.5112545605 -0.2460765061 0.4758386158 0.7780006722 -0.3556318511 0.204495848912 +1403637177438319104.0000000000 8.3583011048 -0.5787441018 -0.2617988293 0.4724638133 0.7803215781 -0.3527356200 0.20845566031 +1403637177488318976.0000000000 8.4238368900 -0.6436955392 -0.2788758260 0.4681316939 0.7826558699 -0.3498592039 0.214245289045 +1403637177538319104.0000000000 8.4922465987 -0.7055424545 -0.2959733952 0.4655744337 0.7833466315 -0.3478996663 0.220395834271 +1403637177588318976.0000000000 8.5632347129 -0.7641611488 -0.3121980332 0.4624399555 0.7845272493 -0.3436199923 0.229328549177 +1403637177638319104.0000000000 8.6359117787 -0.8190072884 -0.3263861390 0.4617605946 0.7843827709 -0.3388700311 0.238092259506 +1403637177688318976.0000000000 8.7099046398 -0.8689636680 -0.3373327967 0.4626276532 0.7831773407 -0.3346198269 0.246248815352 +1403637177738319104.0000000000 8.7848568898 -0.9142149849 -0.3456040274 0.4637580714 0.7817915922 -0.3299991764 0.254619129548 +1403637177788318976.0000000000 8.8602791700 -0.9544588970 -0.3512960814 0.4673556539 0.7781241864 -0.3293478614 0.260060434401 +1403637177838319104.0000000000 8.9346996116 -0.9911693725 -0.3565034627 0.4689232524 0.7748612302 -0.3341961667 0.260794899316 +1403637177888318976.0000000000 9.0088470576 -1.0244692949 -0.3622020488 0.4696100913 0.7711030448 -0.3403422024 0.262742538976 +1403637177938319104.0000000000 9.0824993895 -1.0548948587 -0.3691049073 0.4689457663 0.7671376143 -0.3471819378 0.266560407891 +1403637177988318976.0000000000 9.1552030885 -1.0828903097 -0.3778421453 0.4653434244 0.7642793930 -0.3526600797 0.273794402737 +1403637178038319104.0000000000 9.2274766046 -1.1083622712 -0.3878201726 0.4606561172 0.7613308519 -0.3556513694 0.285803042495 +1403637178088318976.0000000000 9.2978925144 -1.1306888490 -0.3987934198 0.4548720776 0.7585060809 -0.3568588581 0.300685340078 +1403637178138319104.0000000000 9.3669454811 -1.1493258353 -0.4108053814 0.4498841392 0.7551816888 -0.3610592113 0.311353696207 +1403637178188318976.0000000000 9.4347310104 -1.1638147263 -0.4220781432 0.4446265379 0.7524171651 -0.3650068111 0.320851491139 +1403637178238319104.0000000000 9.5012229227 -1.1738900288 -0.4309470177 0.4420459925 0.7487450979 -0.3666356892 0.330990015517 +1403637178288318976.0000000000 9.5662255577 -1.1790352216 -0.4379804190 0.4410656579 0.7449748760 -0.3667773127 0.340511266306 +1403637178338319104.0000000000 9.6295074214 -1.1791102987 -0.4434095920 0.4412762112 0.7408249241 -0.3654175406 0.350604846185 +1403637178388318976.0000000000 9.6913712932 -1.1737969526 -0.4478088753 0.4388310287 0.7389226134 -0.3637755687 0.359288234119 +1403637178438319104.0000000000 9.7498969605 -1.1632505885 -0.4494378106 0.4385629948 0.7363020529 -0.3626180609 0.366100981092 +1403637178488318976.0000000000 9.8047522037 -1.1477152291 -0.4494274480 0.4370138956 0.7350587945 -0.3635524368 0.369509200772 +1403637178538319104.0000000000 9.8562169782 -1.1267433987 -0.4474717107 0.4375644469 0.7332708140 -0.3657398103 0.370250805918 +1403637178588318976.0000000000 9.9045868465 -1.1008084167 -0.4448846114 0.4382141289 0.7317959668 -0.3678088056 0.370350810372 +1403637178638319104.0000000000 9.9496253955 -1.0696601875 -0.4423415359 0.4431531555 0.7286037810 -0.3724995418 0.366054507551 +1403637178688318976.0000000000 9.9920215601 -1.0341553189 -0.4406143553 0.4501125249 0.7246750949 -0.3771122046 0.360598262411 +1403637178738319104.0000000000 10.0321174726 -0.9953324275 -0.4394409268 0.4593191334 0.7189745946 -0.3813989543 0.355859949636 +1403637178788318976.0000000000 10.0701645578 -0.9535723090 -0.4394923603 0.4686604573 0.7133329307 -0.3847697741 0.351376901101 +1403637178838319104.0000000000 10.1062158892 -0.9098492970 -0.4409295519 0.4768592433 0.7081552595 -0.3873491925 0.347968380168 +1403637178888318976.0000000000 10.1399247290 -0.8643246661 -0.4437125453 0.4845917771 0.7034419554 -0.3917613946 0.341852650476 +1403637178938319104.0000000000 10.1714003450 -0.8179204496 -0.4480790686 0.4910629790 0.6995173240 -0.3951422027 0.336742191625 +1403637178988318976.0000000000 10.2010089016 -0.7710108040 -0.4535532429 0.4963885183 0.6962334480 -0.3967751706 0.333806663719 +1403637179038319104.0000000000 10.2280475945 -0.7240142936 -0.4601836824 0.5012286337 0.6933748933 -0.3979644579 0.331097273158 +1403637179088318976.0000000000 10.3087638808 -0.6681947060 -0.4690911118 0.5017025067 0.6935222818 -0.3990119886 0.328802178208 +1403637179138319104.0000000000 10.3355296826 -0.6210841720 -0.4801972920 0.4989309344 0.6960220590 -0.4003881691 0.326052955917 +1403637179188318976.0000000000 10.3607332818 -0.5736584589 -0.4914433853 0.4975494930 0.6975977633 -0.4010859834 0.323931931984 +1403637179238319104.0000000000 10.3833413819 -0.5262226440 -0.5021165861 0.4937474633 0.7010292137 -0.4005296248 0.323028642096 +1403637179288318976.0000000000 10.4045047679 -0.4784982123 -0.5084567323 0.4912106777 0.7034664050 -0.3995940009 0.322756443138 +1403637179338319104.0000000000 10.4233772439 -0.4309517251 -0.5092628125 0.4891176562 0.7051588180 -0.3981252327 0.324054407373 +1403637179388318976.0000000000 10.4401278541 -0.3827847813 -0.5047961344 0.4872910513 0.7069400735 -0.3971776236 0.32408810383 +1403637179438319104.0000000000 10.4550966015 -0.3339111316 -0.4956695003 0.4862709168 0.7081336020 -0.3962473729 0.324153384517 +1403637179488318976.0000000000 10.4685280344 -0.2842267413 -0.4849944510 0.4860944470 0.7085303910 -0.3966062106 0.323110487763 +1403637179538319104.0000000000 10.4809449952 -0.2339349111 -0.4755264740 0.4865918279 0.7084590503 -0.3964907964 0.322659596878 +1403637179588318976.0000000000 10.4922393270 -0.1834680444 -0.4677225131 0.4871093177 0.7078783413 -0.3960842567 0.323651090135 +1403637179638319104.0000000000 10.5019245410 -0.1325202759 -0.4629247996 0.4878722831 0.7073405021 -0.3964167461 0.323270494934 +1403637179688318976.0000000000 10.5110794389 -0.0792757180 -0.4586065575 0.4883645621 0.7065945136 -0.3957519150 0.324968721033 +1403637179738319104.0000000000 10.5193050995 -0.0270592870 -0.4635859572 0.4875128888 0.7065185400 -0.3943951306 0.328047583232 +1403637179788318976.0000000000 10.5265945347 0.0252073976 -0.4761136307 0.4844763736 0.7077368928 -0.3915113296 0.333331685997 +1403637179838319104.0000000000 10.5330437828 0.0777487484 -0.4958238558 0.4815335596 0.7086836992 -0.3864903329 0.341347430242 +1403637179888318976.0000000000 10.5378015705 0.1312487597 -0.5207045451 0.4793293098 0.7090704434 -0.3811717228 0.349529164489 +1403637179938319104.0000000000 10.5395526076 0.1860847033 -0.5482305359 0.4785221610 0.7086780304 -0.3771809702 0.355705645687 +1403637179988318976.0000000000 10.5379562236 0.2427571658 -0.5776503845 0.4785344452 0.7084780065 -0.3759718838 0.357363738563 +1403637180038319104.0000000000 10.5329244263 0.3014951416 -0.6076796812 0.4799057239 0.7077507979 -0.3792728204 0.353456407402 +1403637180088318976.0000000000 10.5253085676 0.3621738959 -0.6368167225 0.4815406106 0.7073305132 -0.3831372107 0.347862132411 +1403637180138319104.0000000000 10.5146386847 0.4240803016 -0.6643434037 0.4847054708 0.7059924334 -0.3878214601 0.340924926612 +1403637180188318976.0000000000 10.5008210563 0.4865671437 -0.6908125399 0.4870227160 0.7052609355 -0.3927895153 0.333365090518 +1403637180238319104.0000000000 10.4905016959 0.5539982619 -0.7055184744 0.4892631848 0.7044350037 -0.3962463248 0.327691488545 +1403637180288318976.0000000000 10.4742123365 0.6182248068 -0.7256676524 0.4906585545 0.7042288240 -0.3996709034 0.321837094457 +1403637180338319104.0000000000 10.4569281326 0.6827314280 -0.7433516250 0.4916463960 0.7040784058 -0.4017030292 0.31810705135 +1403637180388318976.0000000000 10.4384380129 0.7471005191 -0.7601986481 0.4888386718 0.7065319687 -0.4056251228 0.31195767321 +1403637180438319104.0000000000 10.4191663416 0.8111933275 -0.7760366192 0.4832854277 0.7106360062 -0.4089635128 0.306888428137 +1403637180488318976.0000000000 10.3992182020 0.8750527702 -0.7904189621 0.4761505085 0.7154992827 -0.4130730804 0.301184494876 +1403637180538319104.0000000000 10.3797026118 0.9391066405 -0.8023561068 0.4707260364 0.7190376263 -0.4157488493 0.29758156018 +1403637180588318976.0000000000 10.3620840539 1.0041315519 -0.8111502811 0.4670392612 0.7212470772 -0.4161325283 0.297507480699 +1403637180638319104.0000000000 10.3466079795 1.0700190380 -0.8168484424 0.4661933337 0.7214881457 -0.4108575808 0.305474515322 +1403637180688318976.0000000000 10.3316138085 1.1372665017 -0.8201734991 0.4693565610 0.7189826515 -0.4058832278 0.313092910881 +1403637180738319104.0000000000 10.3161073857 1.2054621804 -0.8214095827 0.4728407929 0.7160561319 -0.4041690184 0.316753224263 +1403637180788318976.0000000000 10.3004777590 1.2742387482 -0.8203779679 0.4756031757 0.7132527517 -0.4015422681 0.322235842724 +1403637180838319104.0000000000 10.2845635511 1.3439860602 -0.8182552708 0.4758619851 0.7120229887 -0.3993543815 0.327253285391 +1403637180888318976.0000000000 10.2682573415 1.4142759059 -0.8144943177 0.4745784107 0.7114053484 -0.3949351120 0.335714193575 +1403637180938319104.0000000000 10.2504008876 1.4860715839 -0.8095626620 0.4723772709 0.7114532582 -0.3926503183 0.341349824609 +1403637180988318976.0000000000 10.2312048291 1.5594691546 -0.8030121318 0.4699945046 0.7114168659 -0.3899940965 0.347700752364 +1403637181038319104.0000000000 10.2101326950 1.6345215658 -0.7945866583 0.4663572149 0.7120653856 -0.3876384558 0.35385062147 +1403637181088318976.0000000000 10.1870294882 1.7124122497 -0.7834447778 0.4661786850 0.7111042312 -0.3887919795 0.354752029945 +1403637181138319104.0000000000 10.1614753612 1.7926036424 -0.7701424462 0.4686568327 0.7087685297 -0.3929471597 0.351568590919 +1403637181188318976.0000000000 10.1336803466 1.8746190001 -0.7548368519 0.4727924309 0.7056697693 -0.3988821861 0.345529297722 +1403637181238319104.0000000000 10.1043788332 1.9580130249 -0.7370192701 0.4783582306 0.7013956662 -0.4041824027 0.340373483133 +1403637181288318976.0000000000 10.0738418742 2.0419926806 -0.7181227137 0.4839085952 0.6970466469 -0.4087261385 0.336008016619 +1403637181338319104.0000000000 10.0429434523 2.1261376048 -0.6974927360 0.4883689364 0.6931911064 -0.4104751994 0.335398245037 +1403637181388318976.0000000000 10.0107874220 2.2098404661 -0.6754739012 0.4912401769 0.6902835116 -0.4100855138 0.337670895514 +1403637181438319104.0000000000 9.9770587797 2.2931105134 -0.6521521877 0.4920981337 0.6889107578 -0.4092950325 0.340174912385 +1403637181488318976.0000000000 9.9413180862 2.3759055777 -0.6273979209 0.4898871738 0.6896907131 -0.4095799207 0.341440427697 +1403637181538319104.0000000000 9.9036415111 2.4584872675 -0.6014094805 0.4866530609 0.6911028500 -0.4108187289 0.341721554716 +1403637181588318976.0000000000 9.8640324916 2.5412238845 -0.5734694822 0.4841826176 0.6919938536 -0.4131742418 0.340585885272 +1403637181638319104.0000000000 9.8226675451 2.6239287693 -0.5438139385 0.4811573183 0.6930657449 -0.4153437819 0.340054482726 +1403637181688318976.0000000000 9.7795151680 2.7067020239 -0.5121693951 0.4800716294 0.6928720168 -0.4174823416 0.339364248836 +1403637181738319104.0000000000 9.7332972855 2.7787347480 -0.4848724291 0.4802461678 0.6919048161 -0.4210065046 0.336726694599 +1403637181788318976.0000000000 9.6898480060 2.8616715273 -0.4542182063 0.4823782980 0.6894654307 -0.4237459938 0.335243091273 +1403637181838319104.0000000000 9.6462712362 2.9445780598 -0.4249935071 0.4848429492 0.6871177209 -0.4257927050 0.333911851404 +1403637181888318976.0000000000 9.6021906948 3.0269782784 -0.3974434182 0.4862540141 0.6855590888 -0.4273006055 0.33313655176 +1403637181938319104.0000000000 9.5576854676 3.1089541494 -0.3717640484 0.4865877382 0.6849847160 -0.4285867225 0.332177261642 +1403637181988318976.0000000000 9.5129672866 3.1905344715 -0.3473759956 0.4875191940 0.6841248860 -0.4288532561 0.332239462673 +1403637182038319104.0000000000 9.4675736975 3.2716608051 -0.3238681076 0.4890879197 0.6830170423 -0.4283698604 0.332836280161 +1403637182088318976.0000000000 9.4216753899 3.3523297786 -0.3007668853 0.4928200098 0.6804626154 -0.4267297106 0.334665237278 +1403637182138319104.0000000000 9.3746920822 3.4322964559 -0.2785340202 0.4963241252 0.6783791269 -0.4263784497 0.334163942822 +1403637182188318976.0000000000 9.3266848652 3.5113398229 -0.2570557944 0.5016464102 0.6753070832 -0.4268739123 0.331797958818 +1403637182238319104.0000000000 9.2775246877 3.5891364713 -0.2367141862 0.5072518492 0.6721613934 -0.4272729894 0.329138899593 +1403637182288318976.0000000000 9.2273994533 3.6653673761 -0.2175278969 0.5124856494 0.6693684611 -0.4280812270 0.325654395885 +1403637182338319104.0000000000 9.1763830282 3.7396070695 -0.1993084759 0.5176680393 0.6665910193 -0.4281515966 0.323051736297 +1403637182388318976.0000000000 9.1242264237 3.8113195847 -0.1823059500 0.5212090450 0.6647305001 -0.4272121843 0.322434866706 +1403637182438319104.0000000000 9.0708529522 3.8810523844 -0.1652120565 0.5268016574 0.6616495914 -0.4265470573 0.320558013175 +1403637182488318976.0000000000 9.0166629655 3.9475322688 -0.1476283163 0.5292590638 0.6601735140 -0.4217656142 0.32583667906 +1403637182538319104.0000000000 8.9607844458 4.0115456730 -0.1291823913 0.5299297867 0.6603137191 -0.4180855969 0.329187860184 +1403637182588318976.0000000000 8.9030780973 4.0729601502 -0.1086267693 0.5295710682 0.6608493057 -0.4145528238 0.333134560105 +1403637182638319104.0000000000 8.8426933440 4.1320320802 -0.0867206441 0.5286312687 0.6619017713 -0.4126923841 0.334843281264 +1403637182688318976.0000000000 8.7796493621 4.1887265577 -0.0628670835 0.5282678046 0.6626274604 -0.4128390479 0.333799185011 +1403637182738319104.0000000000 8.7140049636 4.2430940106 -0.0380414314 0.5297817355 0.6619192519 -0.4132147507 0.332336856805 +1403637182788318976.0000000000 8.6462922651 4.2953150793 -0.0144759171 0.5305693767 0.6614582301 -0.4154492168 0.329197652724 +1403637182838319104.0000000000 8.5765525518 4.3450427400 0.0080671176 0.5320566811 0.6602422822 -0.4180327249 0.32595161882 +1403637182888318976.0000000000 8.5049746007 4.3921354125 0.0285931391 0.5332946943 0.6590661983 -0.4200078096 0.323762189371 +1403637182938319104.0000000000 8.4314248766 4.4363007305 0.0478165589 0.5356312587 0.6569709980 -0.4224848190 0.320928091998 +1403637182988318976.0000000000 8.3560188385 4.4778928288 0.0642885584 0.5379599505 0.6549286539 -0.4254650756 0.317249144078 +1403637183038319104.0000000000 8.2788805388 4.5167394512 0.0767625992 0.5405532370 0.6526347571 -0.4289266804 0.312876932144 +1403637183088318976.0000000000 8.2003776626 4.5524360438 0.0848740072 0.5431865760 0.6503077825 -0.4315685232 0.309510486741 +1403637183138319104.0000000000 8.1212648432 4.5853572882 0.0889355057 0.5452020843 0.6486742074 -0.4344557081 0.305327197417 +1403637183188318976.0000000000 8.0409310676 4.6146534551 0.0883716707 0.5462385071 0.6477498283 -0.4362557969 0.302860583393 +1403637183238319104.0000000000 7.9594319182 4.6402625121 0.0846806426 0.5469827331 0.6471585695 -0.4381236699 0.300072200436 +1403637183288318976.0000000000 7.8809896832 4.6640366011 0.0791530825 0.5472629064 0.6468799491 -0.4395829161 0.298020976711 +1403637183338319104.0000000000 7.8011797355 4.6837711723 0.0724608733 0.5475229454 0.6465308746 -0.4414690038 0.295502235542 +1403637183388318976.0000000000 7.7207131779 4.6997974333 0.0646167409 0.5478462596 0.6461420323 -0.4431801362 0.293183077524 +1403637183438319104.0000000000 7.6459542761 4.7150898289 0.0551740797 0.5481354442 0.6456087158 -0.4436490273 0.293108276028 +1403637183488318976.0000000000 7.5685107974 4.7252213471 0.0453550302 0.5484514038 0.6451031390 -0.4439149113 0.293227811272 +1403637183538319104.0000000000 7.4907716074 4.7315856749 0.0345236611 0.5486499528 0.6448462799 -0.4455810024 0.290884985685 +1403637183588318976.0000000000 7.4127397422 4.7336911895 0.0229325908 0.5493647683 0.6441821185 -0.4465716698 0.289484875867 +1403637183638319104.0000000000 7.3342513793 4.7315785413 0.0105471306 0.5504305398 0.6431531480 -0.4480273089 0.287492225212 +1403637183688318976.0000000000 7.2552298396 4.7252244924 -0.0026692045 0.5514537903 0.6420726643 -0.4489232435 0.286547260091 +1403637183738319104.0000000000 7.1746892198 4.7140506503 -0.0167219073 0.5511365438 0.6421355795 -0.4516732983 0.282668780116 +1403637183788318976.0000000000 7.0931584592 4.6979978774 -0.0303629571 0.5499885575 0.6430806346 -0.4555291932 0.276501425224 +1403637183838319104.0000000000 7.0127533890 4.6774806494 -0.0428828584 0.5482008691 0.6443308622 -0.4592422601 0.270942971302 +1403637183888318976.0000000000 6.9341378518 4.6525967856 -0.0530622510 0.5468479156 0.6451199056 -0.4630414210 0.265274022612 +1403637183938319104.0000000000 6.8562047732 4.6224489061 -0.0616368060 0.5457637207 0.6454788287 -0.4666544092 0.260255077301 +1403637183988318976.0000000000 6.7793578848 4.5870624092 -0.0687280484 0.5440596933 0.6463015474 -0.4700597474 0.255611411887 +1403637184038319104.0000000000 6.7039398905 4.5464260650 -0.0727937836 0.5428690672 0.6467108667 -0.4730826419 0.251497603843 +1403637184088318976.0000000000 6.6304603075 4.5004333528 -0.0744177324 0.5416044169 0.6470634574 -0.4748246677 0.250030143396 +1403637184138319104.0000000000 6.5575485417 4.4480726223 -0.0745646724 0.5395408301 0.6482976968 -0.4749761312 0.251004907816 +1403637184188318976.0000000000 6.4872268959 4.3908123005 -0.0723607920 0.5367002681 0.6503748070 -0.4744906842 0.252634168823 +1403637184238319104.0000000000 6.4192131148 4.3288543222 -0.0697872223 0.5334338837 0.6528862770 -0.4714482647 0.25869738051 +1403637184288318976.0000000000 6.3521362880 4.2630209562 -0.0708604818 0.5275884328 0.6577193230 -0.4667907827 0.266762259184 +1403637184338319104.0000000000 6.2863862046 4.1943635801 -0.0756785491 0.5206358047 0.6631948159 -0.4618635134 0.27530544847 +1403637184388318976.0000000000 6.2214088971 4.1233805245 -0.0845651290 0.5130140503 0.6690513999 -0.4578082328 0.282131938052 +1403637184438319104.0000000000 6.1567135733 4.0503956654 -0.0956321203 0.5058935164 0.6745243208 -0.4546598705 0.287007130158 +1403637184488318976.0000000000 6.0929159148 3.9764373153 -0.1081509590 0.4990807714 0.6798035161 -0.4533731125 0.288510630679 +1403637184538319104.0000000000 6.0298242309 3.9012039578 -0.1222384849 0.4928158549 0.6845860910 -0.4527706377 0.288917231726 +1403637184588318976.0000000000 5.9678347252 3.8255623310 -0.1374429117 0.4861420415 0.6895864709 -0.4531300598 0.287766508653 +1403637184638319104.0000000000 5.9074641452 3.7498415704 -0.1530797165 0.4807349538 0.6936630497 -0.4534331191 0.286572650905 +1403637184688318976.0000000000 5.8486579528 3.6739492566 -0.1688750555 0.4761154024 0.6971102975 -0.4541542793 0.284772272645 +1403637184738319104.0000000000 5.7919399697 3.5981021880 -0.1840853133 0.4721509900 0.7000982992 -0.4554895250 0.281895559867 +1403637184788318976.0000000000 5.7382306342 3.5227106091 -0.1984184112 0.4684894671 0.7027274419 -0.4561124055 0.280451840927 +1403637184838319104.0000000000 5.6882158899 3.4486366335 -0.2107697476 0.4656723410 0.7048570080 -0.4564153163 0.279304364723 +1403637184888318976.0000000000 5.6404570539 3.3748876787 -0.2197356394 0.4638975097 0.7059895115 -0.4570497277 0.278358503524 +1403637184938319104.0000000000 5.5965488064 3.3021121843 -0.2268188441 0.4612628310 0.7080906047 -0.4558541665 0.279358685268 +1403637184988318976.0000000000 5.5563583891 3.2310864471 -0.2310600031 0.4606302107 0.7084595304 -0.4574599191 0.276830860248 +1403637185038319104.0000000000 5.5195057829 3.1606191547 -0.2341155419 0.4574830302 0.7107118150 -0.4565292842 0.277811097381 +1403637185088318976.0000000000 5.4860090982 3.0914259324 -0.2350059641 0.4563973248 0.7114049333 -0.4569927356 0.277059817311 +1403637185138319104.0000000000 5.4558384464 3.0232670708 -0.2325909354 0.4558122267 0.7114058579 -0.4582133398 0.276002635138 +1403637185188318976.0000000000 5.4286078485 2.9557829582 -0.2280490344 0.4550775366 0.7117895506 -0.4581170392 0.276385328405 +1403637185238319104.0000000000 5.4039909715 2.8891071911 -0.2227566943 0.4531266803 0.7129738778 -0.4582478496 0.276321134698 +1403637185288318976.0000000000 5.3838668252 2.8241899129 -0.2158223816 0.4501773895 0.7147122044 -0.4587079567 0.275887283628 +1403637185338319104.0000000000 5.3666544266 2.7601913092 -0.2066759903 0.4461747126 0.7173089241 -0.4580865852 0.276681610732 +1403637185388318976.0000000000 5.3522476351 2.6971680773 -0.1952264451 0.4411706063 0.7204821599 -0.4568774576 0.27845456008 +1403637185438319104.0000000000 5.3398419299 2.6353828137 -0.1816726165 0.4366432265 0.7232287065 -0.4562925329 0.279428086019 +1403637185488318976.0000000000 5.3310827340 2.5757447700 -0.1657363453 0.4339088329 0.7249002128 -0.4551002750 0.281294411351 +1403637185538319104.0000000000 5.3254022979 2.5180146746 -0.1480188195 0.4335732299 0.7248740108 -0.4541340158 0.283432917117 +1403637185588318976.0000000000 5.3245535559 2.4635625298 -0.1281693685 0.4365377612 0.7226591165 -0.4534260987 0.285663013843 +1403637185638319104.0000000000 5.3263332964 2.4110977659 -0.1070712468 0.4428619652 0.7185008729 -0.4518190673 0.288945160563 +1403637185688318976.0000000000 5.3311118430 2.3604259731 -0.0857564781 0.4503890856 0.7133187893 -0.4494823814 0.293754259821 +1403637185738319104.0000000000 5.3378495465 2.3109564570 -0.0656501605 0.4568930544 0.7088631502 -0.4470183866 0.298221952833 +1403637185788318976.0000000000 5.3509184571 2.2648031444 -0.0485089947 0.4608228703 0.7060524857 -0.4438375939 0.303546306146 +1403637185838319104.0000000000 5.3621435762 2.2180581629 -0.0332030615 0.4619962577 0.7050246256 -0.4413714846 0.307718942861 +1403637185888318976.0000000000 5.3744494972 2.1726709581 -0.0191033982 0.4645062919 0.7033202005 -0.4390079527 0.311201892316 +1403637185938319104.0000000000 5.3874482256 2.1287264234 -0.0063805180 0.4663641985 0.7017581160 -0.4380088091 0.313350066445 +1403637185988318976.0000000000 5.4004048270 2.0858750368 0.0054067446 0.4696684127 0.6995340647 -0.4369164798 0.314908977478 +1403637186038319104.0000000000 5.4135112116 2.0440362438 0.0161881672 0.4731914425 0.6970884510 -0.4360560028 0.316247865647 +1403637186088318976.0000000000 5.4264953349 2.0029657494 0.0272482227 0.4755851532 0.6954039055 -0.4350377365 0.317764595322 +1403637186138319104.0000000000 5.4390152764 1.9626378311 0.0395392422 0.4770385871 0.6944828501 -0.4347467309 0.317998486168 +1403637186188318976.0000000000 5.4505213425 1.9226454968 0.0535823750 0.4779583673 0.6939114627 -0.4345511629 0.318131997651 +1403637186238319104.0000000000 5.4622071898 1.8834004598 0.0686379867 0.4772971759 0.6944182960 -0.4345898469 0.317965880299 +1403637186288318976.0000000000 5.4754735603 1.8456549435 0.0859920487 0.4767027304 0.6949820178 -0.4340774994 0.318325660525 +1403637186338319104.0000000000 5.4889464085 1.8091067820 0.1067401672 0.4788055776 0.6934992162 -0.4331838649 0.319618202032 +1403637186388318976.0000000000 5.5014541467 1.7733044620 0.1291570859 0.4804385073 0.6921594857 -0.4335857215 0.319527008492 +1403637186438319104.0000000000 5.5134716739 1.7381720705 0.1537121403 0.4826423892 0.6905456689 -0.4346980418 0.318183305489 +1403637186488318976.0000000000 5.5253002558 1.7036715283 0.1798297644 0.4846993327 0.6889168200 -0.4364143491 0.316232015993 +1403637186538319104.0000000000 5.5369033205 1.6696886413 0.2072924239 0.4877996129 0.6865392484 -0.4384329343 0.313834287851 +1403637186588318976.0000000000 5.5484308053 1.6356248511 0.2347007269 0.4891124264 0.6853043496 -0.4394009627 0.313135396641 +1403637186638319104.0000000000 5.5596226853 1.6014207675 0.2608010584 0.4894624878 0.6847281478 -0.4404918583 0.312315160348 +1403637186688318976.0000000000 5.5705558365 1.5670643771 0.2851590958 0.4891924994 0.6845019670 -0.4422222976 0.310784805276 +1403637186738319104.0000000000 5.5809594279 1.5325044430 0.3074338123 0.4880150440 0.6849733202 -0.4453130762 0.307163037505 +1403637186788318976.0000000000 5.5910328817 1.4976338116 0.3275971060 0.4876425700 0.6848754611 -0.4493623236 0.302032827547 +1403637186838319104.0000000000 5.6015148946 1.4628296525 0.3457777133 0.4884493583 0.6840142490 -0.4543858150 0.295085178733 +1403637186888318976.0000000000 5.6125227406 1.4273558670 0.3618981825 0.4897150127 0.6827474471 -0.4591800069 0.288424775312 +1403637186938319104.0000000000 5.6245136595 1.3911189765 0.3762674982 0.4923847433 0.6803578114 -0.4638983275 0.281902207838 +1403637186988318976.0000000000 5.6377280569 1.3536186630 0.3883484866 0.4942174350 0.6786631211 -0.4674697716 0.276834801943 +1403637187038319104.0000000000 5.6526235129 1.3145959435 0.3989684444 0.4974075804 0.6760439429 -0.4694601104 0.274148665944 +1403637187088318976.0000000000 5.6689730846 1.2737458094 0.4075270463 0.5000029202 0.6740664986 -0.4695479159 0.274146292963 +1403637187138319104.0000000000 5.6866143676 1.2309336873 0.4139974851 0.5013551719 0.6731831428 -0.4679143664 0.276628982049 +1403637187188318976.0000000000 5.7054893252 1.1860747799 0.4182924619 0.5003965365 0.6731830172 -0.4664226252 0.280852036395 +1403637187238319104.0000000000 5.7254494875 1.1390310433 0.4206855717 0.4961634517 0.6745830115 -0.4666019147 0.284679193291 +1403637187288318976.0000000000 5.7463492532 1.0904551740 0.4206851463 0.4878970859 0.6783223148 -0.4676675504 0.288309439838 +1403637187338319104.0000000000 5.7686066238 1.0411667919 0.4199040548 0.4798348286 0.6818729560 -0.4687817462 0.291635874994 +1403637187388318976.0000000000 5.7920498046 0.9913719906 0.4181072150 0.4715860908 0.6859342703 -0.4685891188 0.295846199092 +1403637187438319104.0000000000 5.8170070560 0.9416814323 0.4161835756 0.4648732387 0.6888142763 -0.4689381191 0.299206960312 +1403637187488318976.0000000000 5.8431363547 0.8924639049 0.4141970319 0.4599989253 0.6905225312 -0.4700096343 0.301115536392 +1403637187538319104.0000000000 5.8701596299 0.8436122132 0.4116587412 0.4557483069 0.6920352219 -0.4713448839 0.302017768978 +1403637187588318976.0000000000 5.8986472599 0.7954194519 0.4087111612 0.4531867768 0.6924738041 -0.4727124430 0.302728793178 +1403637187638319104.0000000000 5.9290481326 0.7481829596 0.4052802594 0.4516504273 0.6924006236 -0.4746845011 0.302105763449 +1403637187688318976.0000000000 5.9607622841 0.7014723537 0.4016005522 0.4514346800 0.6915743087 -0.4765922166 0.301316385531 +1403637187738319104.0000000000 5.9939975898 0.6551753192 0.3968877175 0.4502435327 0.6915273750 -0.4784927873 0.300192110772 +1403637187788318976.0000000000 6.0292356791 0.6093922223 0.3918733607 0.4495481608 0.6913535677 -0.4794518013 0.300104424918 +1403637187838319104.0000000000 6.0662381747 0.5641635874 0.3860364453 0.4480995630 0.6918336350 -0.4813449211 0.298127606979 +1403637187888318976.0000000000 6.1056757122 0.5194844493 0.3797298551 0.4463807906 0.6926861159 -0.4812920674 0.298811111649 +1403637187938319104.0000000000 6.1474978940 0.4756006694 0.3729506536 0.4445147668 0.6937328581 -0.4801560169 0.30098429046 +1403637187988318976.0000000000 6.1914933141 0.4327098782 0.3660638024 0.4446262282 0.6935820921 -0.4788955535 0.303167359009 +1403637188038319104.0000000000 6.2380155197 0.3906692483 0.3585338313 0.4444212134 0.6936610600 -0.4768417429 0.306506233432 +1403637188088318976.0000000000 6.2866039296 0.3495664554 0.3504361498 0.4444528881 0.6935765776 -0.4749143847 0.309627983896 +1403637188138319104.0000000000 6.3373908336 0.3094784536 0.3419072813 0.4454989609 0.6929556913 -0.4727396110 0.312826383009 +1403637188188318976.0000000000 6.3907056926 0.2702410915 0.3326298670 0.4460066961 0.6926295104 -0.4681833470 0.319604039276 +1403637188238319104.0000000000 6.4454522758 0.2323634154 0.3229340563 0.4475117261 0.6915043234 -0.4626354230 0.327907747895 +1403637188288318976.0000000000 6.5010104604 0.1963119680 0.3125400663 0.4499024593 0.6898130299 -0.4588022549 0.333535982811 +1403637188338319104.0000000000 6.5572271830 0.1620520296 0.3009765637 0.4521062580 0.6880236946 -0.4575805941 0.335921608456 +1403637188388318976.0000000000 6.6136248166 0.1292166112 0.2892338404 0.4567554897 0.6846957995 -0.4565959703 0.337766494285 +1403637188438319104.0000000000 6.6693930736 0.0974940016 0.2768268190 0.4609641670 0.6816406595 -0.4563771305 0.338523208817 +1403637188488318976.0000000000 6.7245129738 0.0664847501 0.2634222352 0.4642107776 0.6786385390 -0.4566135289 0.339797252226 +1403637188538319104.0000000000 6.7783390364 0.0362424607 0.2494612754 0.4675266283 0.6744675398 -0.4587702099 0.340649796873 +1403637188588318976.0000000000 6.8314380909 0.0067380925 0.2343077708 0.4693832979 0.6704254419 -0.4632159815 0.340058819959 +1403637188638319104.0000000000 6.8822509760 -0.0223314412 0.2187246035 0.4709293798 0.6656146154 -0.4680097174 0.340807287756 +1403637188688318976.0000000000 6.9319307775 -0.0512376479 0.2024032288 0.4730800287 0.6594749382 -0.4756172490 0.339229015143 +1403637188738319104.0000000000 6.9808033325 -0.0802063363 0.1850443307 0.4749955268 0.6524392291 -0.4840022434 0.338295921018 +1403637188788318976.0000000000 7.0287321838 -0.1097750513 0.1667232349 0.4763779437 0.6451786836 -0.4937648941 0.336161791751 +1403637188838319104.0000000000 7.0754790203 -0.1406681627 0.1475330522 0.4758216200 0.6389510732 -0.5027056463 0.335592528522 +1403637188888318976.0000000000 7.1220310776 -0.1727857933 0.1287182618 0.4740645570 0.6340884141 -0.5098685304 0.336494815241 +1403637188938319104.0000000000 7.1681962077 -0.2062720531 0.1106416744 0.4714296163 0.6308209489 -0.5155190676 0.337726425344 +1403637188988318976.0000000000 7.2133288241 -0.2416500692 0.0932473589 0.4659120275 0.6303354861 -0.5192109029 0.340621778472 +1403637189038319104.0000000000 7.2586960428 -0.2784066579 0.0778270047 0.4585131171 0.6320524486 -0.5207381529 0.345119109615 +1403637189088318976.0000000000 7.3038031614 -0.3159754702 0.0649710193 0.4511128418 0.6342168118 -0.5226801187 0.347953636388 +1403637189138319104.0000000000 7.3497677072 -0.3537269729 0.0523476306 0.4423994885 0.6378484772 -0.5253474093 0.348485454822 +1403637189188318976.0000000000 7.3960963176 -0.3913792615 0.0402820082 0.4365905170 0.6398336782 -0.5284436243 0.347489453954 +1403637189238319104.0000000000 7.4433544537 -0.4290666322 0.0261529960 0.4322597936 0.6410137877 -0.5319648142 0.345349433567 +1403637189288318976.0000000000 7.4917956790 -0.4663858222 0.0098956279 0.4319942176 0.6400123981 -0.5350459156 0.342769593827 +1403637189338319104.0000000000 7.5411283754 -0.5037955391 -0.0098283161 0.4353636916 0.6369361540 -0.5368417715 0.341425986268 +1403637189388318976.0000000000 7.5915975939 -0.5415361902 -0.0315479860 0.4403025260 0.6332205796 -0.5358891144 0.34349416322 +1403637189438319104.0000000000 7.6431930489 -0.5797740820 -0.0532950347 0.4459630847 0.6294251167 -0.5332109520 0.347314022352 +1403637189488318976.0000000000 7.6956771320 -0.6184393984 -0.0739237804 0.4501315627 0.6268274562 -0.5303819616 0.350947134556 +1403637189538319104.0000000000 7.7484133500 -0.6579537046 -0.0933000832 0.4518098219 0.6261987519 -0.5269744873 0.355022390459 +1403637189588318976.0000000000 7.8021709621 -0.6978300071 -0.1109393978 0.4524859399 0.6265916334 -0.5232610535 0.358939088156 +1403637189638319104.0000000000 7.8557161168 -0.7382408208 -0.1259533534 0.4520128188 0.6274785209 -0.5203501633 0.362202740082 +1403637189688318976.0000000000 7.9083166028 -0.7789989008 -0.1379214090 0.4523586417 0.6279898891 -0.5172122805 0.365365317733 +1403637189738319104.0000000000 7.9598895088 -0.8198174994 -0.1481285116 0.4507931267 0.6300151169 -0.5162815515 0.365129934321 +1403637189788318976.0000000000 8.0108525073 -0.8607787451 -0.1564897041 0.4494529534 0.6316176377 -0.5159577761 0.364470541619 +1403637189838319104.0000000000 8.0609525645 -0.9020058009 -0.1629889946 0.4468209854 0.6339356184 -0.5151888916 0.364769851726 +1403637189888318976.0000000000 8.1112989286 -0.9427477643 -0.1654622687 0.4472363993 0.6339451326 -0.5143343052 0.365449578644 +1403637189938319104.0000000000 8.1603742884 -0.9833310238 -0.1649304012 0.4487669585 0.6330599650 -0.5139129574 0.365700382728 +1403637189988318976.0000000000 8.2082536216 -1.0241257931 -0.1633370663 0.4487232235 0.6330575705 -0.5124889498 0.367750809071 +1403637190038319104.0000000000 8.2545627122 -1.0649919267 -0.1598475382 0.4501075109 0.6318507360 -0.5116875561 0.369247506386 +1403637190088318976.0000000000 8.3046733435 -1.1055065044 -0.1550787337 0.4505681452 0.6311056356 -0.5104542160 0.371659140258 +1403637190138319104.0000000000 8.3507532329 -1.1456207941 -0.1483385224 0.4512927765 0.6303275101 -0.5104803296 0.372064366761 +1403637190188318976.0000000000 8.3969990862 -1.1852279928 -0.1404223345 0.4516632501 0.6295844026 -0.5099127437 0.37364793897 +1403637190238319104.0000000000 8.4428792988 -1.2241618026 -0.1305781242 0.4530921660 0.6283221746 -0.5105452371 0.373178636682 +1403637190288318976.0000000000 8.4871176592 -1.2635003995 -0.1195084369 0.4534468534 0.6274680527 -0.5106228580 0.374077653359 +1403637190338319104.0000000000 8.5304474341 -1.3026816784 -0.1066686060 0.4533742548 0.6270737658 -0.5110950416 0.374181955483 +1403637190388318976.0000000000 8.5726014575 -1.3415347997 -0.0917614595 0.4536139892 0.6263463949 -0.5121965752 0.373603012143 +1403637190438319104.0000000000 8.6135202518 -1.3800827588 -0.0751676068 0.4547092490 0.6252685839 -0.5132891613 0.372576077782 +1403637190488318976.0000000000 8.6540126976 -1.4186616239 -0.0587140600 0.4553902620 0.6242217767 -0.5132873679 0.373500951406 +1403637190538319104.0000000000 8.6927599705 -1.4573678002 -0.0431599472 0.4537405918 0.6246811391 -0.5131165551 0.374972466565 +1403637190588318976.0000000000 8.7306354353 -1.4957862582 -0.0290301587 0.4524889263 0.6253816323 -0.5117816532 0.377135420129 +1403637190638319104.0000000000 8.7672785287 -1.5340339582 -0.0170143992 0.4501234569 0.6281188701 -0.5084397231 0.37992710694 +1403637190688318976.0000000000 8.8024227443 -1.5715273665 -0.0063089360 0.4491831599 0.6316713699 -0.5039380478 0.381145921188 +1403637190738319104.0000000000 8.8359795322 -1.6076829872 0.0033044776 0.4509567862 0.6349643752 -0.5008183348 0.377676071111 +1403637190788318976.0000000000 8.8684796351 -1.6430038220 0.0119476043 0.4540853552 0.6375592512 -0.4974623487 0.37397313134 +1403637190838319104.0000000000 8.9002681126 -1.6777754551 0.0192868978 0.4575744952 0.6399415282 -0.4947299613 0.36924610669 +1403637190888318976.0000000000 8.9310993497 -1.7121254380 0.0252203478 0.4615877611 0.6415033864 -0.4925469438 0.364427842297 +1403637190938319104.0000000000 8.9610196893 -1.7463531423 0.0296036148 0.4652989888 0.6427154350 -0.4902991545 0.360583499048 +1403637190988318976.0000000000 8.9901348060 -1.7806706588 0.0322967745 0.4684632339 0.6437188363 -0.4882484292 0.357465704283 +1403637191038319104.0000000000 9.0182056274 -1.8152039848 0.0331156662 0.4707876788 0.6450448396 -0.4858936738 0.355223104759 +1403637191088318976.0000000000 9.0456346103 -1.8499802505 0.0328670768 0.4732933255 0.6456643887 -0.4839439824 0.353424881816 +1403637191138319104.0000000000 9.0723974428 -1.8850645076 0.0309756040 0.4748062105 0.6464446030 -0.4823055457 0.352207039023 +1403637191188318976.0000000000 9.0981672292 -1.9204053933 0.0278681544 0.4755897285 0.6473804209 -0.4803432882 0.352112661331 +1403637191238319104.0000000000 9.1230555559 -1.9559830752 0.0235540894 0.4758808545 0.6480246357 -0.4792903453 0.351969101967 +1403637191288318976.0000000000 9.1471923779 -1.9915010947 0.0176385379 0.4755080843 0.6490976537 -0.4778400958 0.352467219149 +1403637191338319104.0000000000 9.1702560590 -2.0271308846 0.0107300923 0.4762834291 0.6491313802 -0.4769714842 0.352534749599 +1403637191388318976.0000000000 9.1926589776 -2.0631167814 0.0029572315 0.4755854186 0.6497563181 -0.4751541615 0.354772828148 +1403637191438319104.0000000000 9.2142460075 -2.0988937046 -0.0043048590 0.4749492284 0.6502878663 -0.4738689758 0.356366545956 +1403637191488318976.0000000000 9.2342453500 -2.1346312052 -0.0096390769 0.4750148144 0.6499996044 -0.4738520339 0.356827255677 +1403637191538319104.0000000000 9.2525841354 -2.1705901723 -0.0138414097 0.4731280301 0.6508870077 -0.4726171801 0.359345198109 +1403637191588318976.0000000000 9.2701925150 -2.2063187519 -0.0158302041 0.4703662808 0.6522155638 -0.4715881129 0.361904783054 +1403637191638319104.0000000000 9.2863078776 -2.2414083741 -0.0158944072 0.4655004413 0.6549470261 -0.4726834060 0.361834395628 +1403637191688318976.0000000000 9.3008259726 -2.2759409477 -0.0144121244 0.4600477151 0.6579083143 -0.4751130962 0.360250323696 +1403637191738319104.0000000000 9.3145161926 -2.3094476501 -0.0105893417 0.4561098260 0.6600707294 -0.4773279066 0.358369262516 +1403637191788318976.0000000000 9.3276424519 -2.3420141248 -0.0052985211 0.4514981984 0.6625388490 -0.4791141619 0.35726918464 +1403637191838319104.0000000000 9.3413508997 -2.3735842468 0.0012633993 0.4469879648 0.6649100488 -0.4777234541 0.360384083628 +1403637191888318976.0000000000 9.3545394997 -2.4037919273 0.0097211530 0.4425396155 0.6672671433 -0.4754788699 0.364462745077 +1403637191938319104.0000000000 9.3677064929 -2.4321765161 0.0197704231 0.4385656988 0.6691363044 -0.4727446652 0.369363256686 +1403637191988318976.0000000000 9.3802388210 -2.4581748489 0.0323725253 0.4351744289 0.6708367720 -0.4705950626 0.373016794285 +1403637192038319104.0000000000 9.3918080605 -2.4817849024 0.0470222938 0.4320671862 0.6721494915 -0.4720454759 0.372432646807 +1403637192088318976.0000000000 9.4024970541 -2.5029755487 0.0631505242 0.4288596114 0.6736670377 -0.4754708362 0.369025256479 +1403637192138319104.0000000000 9.4129389556 -2.5218324022 0.0809345626 0.4256417194 0.6753825208 -0.4780427229 0.36628231244 +1403637192188318976.0000000000 9.4235272377 -2.5384173446 0.1003164212 0.4225876618 0.6769940097 -0.4794991065 0.364937509496 +1403637192238319104.0000000000 9.4349922346 -2.5523359324 0.1214780452 0.4198984387 0.6783773987 -0.4795915572 0.365350987833 +1403637192288318976.0000000000 9.4468707536 -2.5638079817 0.1441496408 0.4164287203 0.6801912054 -0.4776106003 0.368531083525 +1403637192338319104.0000000000 9.4593872160 -2.5723533563 0.1674366533 0.4140378884 0.6814846274 -0.4747260591 0.372540599768 +1403637192388318976.0000000000 9.4724383152 -2.5776776436 0.1904748914 0.4145116423 0.6809362250 -0.4728881371 0.375343530058 +1403637192438319104.0000000000 9.4852253003 -2.5799300653 0.2121226061 0.4153381632 0.6801877146 -0.4747145350 0.373476897994 +1403637192488318976.0000000000 9.4978465547 -2.5791973603 0.2319280035 0.4168264261 0.6790334272 -0.4797635554 0.367418380373 +1403637192538319104.0000000000 9.5105129289 -2.5762258492 0.2503203622 0.4185734226 0.6777392315 -0.4849714131 0.360927350742 +1403637192588318976.0000000000 9.5237044673 -2.5711896707 0.2670204937 0.4200334709 0.6766852624 -0.4901725784 0.354118317058 +1403637192638319104.0000000000 9.5378241688 -2.5646449487 0.2818817068 0.4205459694 0.6762042438 -0.4940250286 0.349038936883 +1403637192688318976.0000000000 9.5535418345 -2.5566710187 0.2950281408 0.4208569121 0.6760230059 -0.4965757092 0.345376490325 +1403637192738319104.0000000000 9.5707306337 -2.5476155475 0.3066522426 0.4216253210 0.6754584467 -0.4978118746 0.343760546121 +1403637192788318976.0000000000 9.5892748738 -2.5373354472 0.3166575814 0.4224365216 0.6750873510 -0.4977911096 0.343523601766 +1403637192838319104.0000000000 9.6093403567 -2.5257943189 0.3266598424 0.4243239166 0.6742223766 -0.4965138967 0.344742441578 +1403637192888318976.0000000000 9.6310817305 -2.5129198825 0.3375275612 0.4269954545 0.6726743499 -0.4946195758 0.347182338396 +1403637192938319104.0000000000 9.6540552685 -2.4985158773 0.3505584968 0.4303339665 0.6709312217 -0.4932520755 0.348376754451 +1403637192988318976.0000000000 9.6774215760 -2.4833012538 0.3647970862 0.4328151980 0.6697933500 -0.4914111189 0.350089966725 +1403637193038319104.0000000000 9.7021154040 -2.4667221771 0.3808224995 0.4353605104 0.6683845395 -0.4917422265 0.349160301265 +1403637193088318976.0000000000 9.7270614852 -2.4490791343 0.3988212206 0.4376875201 0.6669812807 -0.4949306642 0.344396927464 +1403637193138319104.0000000000 9.7518446906 -2.4309432337 0.4180117870 0.4401791968 0.6651426768 -0.5018262411 0.334660899979 +1403637193188318976.0000000000 9.7783349210 -2.4124012890 0.4386882283 0.4427381569 0.6630959054 -0.5094918712 0.323581176496 +1403637193238319104.0000000000 9.8060459549 -2.3950195397 0.4592110205 0.4439991598 0.6619964510 -0.5144408840 0.31618985087 +1403637193288318976.0000000000 9.8357531909 -2.3786759565 0.4767200664 0.4448339048 0.6610638926 -0.5174477700 0.312033864138 +1403637193338319104.0000000000 9.8684638523 -2.3639150487 0.4899345792 0.4426199152 0.6626797584 -0.5138526462 0.317645409871 +1403637193388318976.0000000000 9.9032880044 -2.3497242208 0.4991997785 0.4418897656 0.6633355434 -0.5089992077 0.32502184302 +1403637193438319104.0000000000 9.9392484570 -2.3357474227 0.5058249332 0.4411884850 0.6638646917 -0.5036830905 0.333076171747 +1403637193488318976.0000000000 9.9761600554 -2.3217579468 0.5117084751 0.4402888205 0.6647234794 -0.4989140514 0.339666335981 +1403637193538319104.0000000000 10.0133830141 -2.3076035801 0.5186843928 0.4389367759 0.6658744137 -0.4945968595 0.345426864151 +1403637193588318976.0000000000 10.0509315675 -2.2927562616 0.5268882543 0.4369778579 0.6675810707 -0.4914468337 0.349092932483 +1403637193638319104.0000000000 10.0893205495 -2.2768721154 0.5368677472 0.4358442552 0.6685067121 -0.4892923088 0.35175502504 +1403637193688318976.0000000000 10.1284163476 -2.2598505709 0.5483616351 0.4344407401 0.6696085959 -0.4878450905 0.353401668518 +1403637193738319104.0000000000 10.1686261095 -2.2417467940 0.5618234820 0.4332169103 0.6706708050 -0.4859645760 0.355474627526 +1403637193788318976.0000000000 10.2089161019 -2.2224263338 0.5764464360 0.4324595231 0.6712282686 -0.4851431757 0.356465245714 +1403637193838319104.0000000000 10.2492811546 -2.2020126029 0.5925071255 0.4314875121 0.6721227577 -0.4842515176 0.357169418171 +1403637193888318976.0000000000 10.2898986062 -2.1799904013 0.6094410375 0.4314460003 0.6720543331 -0.4843082620 0.357271366751 +1403637193938319104.0000000000 10.3310104873 -2.1566270458 0.6258615964 0.4334157213 0.6708147027 -0.4839891579 0.357649188818 +1403637193988318976.0000000000 10.3724713833 -2.1324154233 0.6391010946 0.4364639786 0.6687776990 -0.4824951418 0.359769402144 +1403637194038319104.0000000000 10.4136560497 -2.1074408392 0.6482785738 0.4398476349 0.6664379293 -0.4813524902 0.36151670037 +1403637194088318976.0000000000 10.4542852338 -2.0818517852 0.6533176066 0.4422576773 0.6645744416 -0.4809169050 0.362585009155 +1403637194138319104.0000000000 10.4945727032 -2.0555891607 0.6547276251 0.4434504298 0.6635780953 -0.4803248171 0.363736027644 +1403637194188318976.0000000000 10.5353210839 -2.0281523837 0.6537277217 0.4438373992 0.6631926132 -0.4805717145 0.363640960477 +1403637194238319104.0000000000 10.5750931654 -2.0000364673 0.6519466099 0.4432468419 0.6635897614 -0.4822954531 0.36134742528 +1403637194288318976.0000000000 10.6141771276 -1.9711931152 0.6508477272 0.4428318798 0.6637476034 -0.4830721463 0.360527872178 +1403637194338319104.0000000000 10.6528993687 -1.9420638948 0.6498758957 0.4411905495 0.6646424445 -0.4841630771 0.35942653596 +1403637194388318976.0000000000 10.6907102293 -1.9118817378 0.6507974642 0.4401087471 0.6654308059 -0.4847191555 0.358543544949 +1403637194438319104.0000000000 10.7288017918 -1.8807626430 0.6534888156 0.4386575587 0.6663199150 -0.4847629961 0.358611425873 +1403637194488318976.0000000000 10.7675831907 -1.8481491915 0.6582899463 0.4392710640 0.6658166954 -0.4858017197 0.357387394414 +1403637194538319104.0000000000 10.8067220390 -1.8146543513 0.6646529973 0.4385857044 0.6662031209 -0.4863521946 0.356759757267 +1403637194588318976.0000000000 10.8456446693 -1.7803366569 0.6728318716 0.4382047812 0.6663109368 -0.4868982886 0.356281295839 +1403637194638319104.0000000000 10.8841680537 -1.7453175353 0.6831797822 0.4371287894 0.6667174544 -0.4871449013 0.356505403353 +1403637194688318976.0000000000 10.9225771778 -1.7095004186 0.6943999780 0.4345378419 0.6681634577 -0.4885009706 0.355107391376 +1403637194738319104.0000000000 10.9613141129 -1.6727928983 0.7064036726 0.4320696732 0.6694157962 -0.4902508146 0.353344630855 +1403637194788318976.0000000000 10.9998802784 -1.6357347739 0.7180087597 0.4303082957 0.6702142494 -0.4916844353 0.351985861324 +1403637194838319104.0000000000 11.0396053245 -1.5973448347 0.7283063843 0.4292095514 0.6704667373 -0.4930206681 0.350975976359 +1403637194888318976.0000000000 11.0795899839 -1.5581832871 0.7370098911 0.4281028054 0.6709230487 -0.4939600434 0.35013386913 +1403637194938319104.0000000000 11.1205216263 -1.5179456025 0.7454584989 0.4309225495 0.6689081017 -0.4942099160 0.35017747883 +1403637194988318976.0000000000 11.1620188121 -1.4771207868 0.7524421472 0.4343625846 0.6661959848 -0.4936443128 0.35189110155 +1403637195038319104.0000000000 11.2036853852 -1.4357557762 0.7578842957 0.4380388589 0.6635385330 -0.4915382206 0.35528685737 +1403637195088318976.0000000000 11.2451239895 -1.3938143670 0.7617092410 0.4415048651 0.6609741858 -0.4900382185 0.357839522881 +1403637195138319104.0000000000 11.2861310271 -1.3514799527 0.7639928006 0.4447712884 0.6583778180 -0.4884872739 0.360690078855 +1403637195188318976.0000000000 11.3264173311 -1.3086610049 0.7648416910 0.4479412598 0.6561408022 -0.4868512415 0.363047853733 +1403637195238319104.0000000000 11.3660916317 -1.2656497231 0.7644323652 0.4503652299 0.6542773766 -0.4857656476 0.364861631022 +1403637195288318976.0000000000 11.4048903956 -1.2225297844 0.7624452467 0.4520739261 0.6530448717 -0.4846110773 0.366488287006 +1403637195338319104.0000000000 11.4429969327 -1.1792585198 0.7593635597 0.4543082970 0.6515697185 -0.4841614665 0.366944883621 +1403637195388318976.0000000000 11.4801156376 -1.1360783830 0.7552202569 0.4543242189 0.6517352171 -0.4829959019 0.368165275029 +1403637195438319104.0000000000 11.5163513754 -1.0922446495 0.7520010216 0.4563793764 0.6515404793 -0.4822192692 0.366984257227 +1403637195488318976.0000000000 11.5515155126 -1.0478365277 0.7501214487 0.4576744097 0.6533161440 -0.4805386996 0.36441008349 +1403637195538319104.0000000000 11.5859307023 -1.0033533201 0.7493882609 0.4585244029 0.6559475075 -0.4788092161 0.360873903039 +1403637195588318976.0000000000 11.6190424020 -0.9590447141 0.7514783288 0.4596749540 0.6582308463 -0.4759373105 0.35904702481 +1403637195638319104.0000000000 11.6515497081 -0.9145518206 0.7556712620 0.4613096806 0.6599633443 -0.4733203393 0.357224886055 +1403637195688318976.0000000000 11.6832699665 -0.8701036479 0.7618128082 0.4633138278 0.6610842358 -0.4708257007 0.35585262352 +1403637195738319104.0000000000 11.7140551352 -0.8260675697 0.7690214353 0.4645866937 0.6622318442 -0.4679292262 0.355879794065 +1403637195788318976.0000000000 11.7433736446 -0.7823678078 0.7763372191 0.4639377040 0.6644866420 -0.4657858758 0.355334810153 +1403637195838319104.0000000000 11.7722871683 -0.7388895806 0.7848776306 0.4631906241 0.6663977543 -0.4608341793 0.35916617046 +1403637195888318976.0000000000 11.8004385069 -0.6951270345 0.7936288553 0.4606877742 0.6691527731 -0.4567023221 0.362524936933 +1403637195938319104.0000000000 11.8274468223 -0.6508812393 0.8021209556 0.4581972717 0.6716360129 -0.4528203206 0.365942732744 +1403637195988318976.0000000000 11.8531561401 -0.6061207296 0.8091123174 0.4551717496 0.6740968707 -0.4476742775 0.371483281679 +1403637196038319104.0000000000 11.8770666573 -0.5604001971 0.8145729617 0.4527559033 0.6759760544 -0.4426141718 0.377042651166 +1403637196088318976.0000000000 11.8997645498 -0.5129236921 0.8191961655 0.4524873530 0.6760093247 -0.4366454480 0.384197008242 +1403637196138319104.0000000000 11.9207091885 -0.4639979044 0.8227853415 0.4531101889 0.6751383565 -0.4304971752 0.391856528044 +1403637196188318976.0000000000 11.9394039650 -0.4130879818 0.8256598340 0.4549286313 0.6733291253 -0.4239293476 0.399939667643 +1403637196238319104.0000000000 11.9552871052 -0.3599983106 0.8277222653 0.4579194645 0.6705884199 -0.4187612996 0.406521720195 +1403637196288318976.0000000000 11.9679886850 -0.3046945378 0.8286188500 0.4605075133 0.6681195811 -0.4141931739 0.412302159008 +1403637196338319104.0000000000 11.9773295457 -0.2471636144 0.8279034045 0.4619808380 0.6660905784 -0.4101328160 0.417957078886 +1403637196388318976.0000000000 11.9826013899 -0.1874254853 0.8259291127 0.4631241130 0.6642597921 -0.4072824658 0.422369479993 +1403637196438319104.0000000000 11.9828917227 -0.1258979305 0.8226783156 0.4638874969 0.6630074136 -0.4058817041 0.424840678342 +1403637196488318976.0000000000 11.9787424175 -0.0616467462 0.8185545300 0.4648864552 0.6620162061 -0.4068327331 0.424384558955 +1403637196538319104.0000000000 11.9703308011 0.0048144388 0.8128697026 0.4650108542 0.6615069432 -0.4083585100 0.42357619954 +1403637196588318976.0000000000 11.9580336928 0.0740218983 0.8065343721 0.4672540947 0.6599406726 -0.4105166696 0.421459349965 +1403637196638319104.0000000000 11.9415370037 0.1448135979 0.7986486281 0.4670262632 0.6598584370 -0.4136352519 0.418782987934 +1403637196688318976.0000000000 11.9207832401 0.2173857861 0.7898593171 0.4683666785 0.6588880884 -0.4168264920 0.415637843534 +1403637196738319104.0000000000 11.8961814241 0.2914576459 0.7796133819 0.4702231693 0.6575714447 -0.4196950534 0.412729970208 +1403637196788318976.0000000000 11.8678301146 0.3666837233 0.7672015491 0.4712854047 0.6568368302 -0.4233600664 0.408927499627 +1403637196838319104.0000000000 11.8359116179 0.4419513980 0.7560175275 0.4708788036 0.6566415470 -0.4240843783 0.408959009103 +1403637196888318976.0000000000 11.8005363686 0.5186979770 0.7423706716 0.4713924972 0.6554646857 -0.4232855340 0.411077262972 +1403637196938319104.0000000000 11.7615128394 0.5968855749 0.7279700197 0.4730919732 0.6539970088 -0.4244876930 0.410222008047 +1403637196988318976.0000000000 11.7188339089 0.6766747633 0.7144375284 0.4777749111 0.6513124798 -0.4284941095 0.404865392514 +1403637197038319104.0000000000 11.6724270522 0.7574628219 0.7008659336 0.4812790871 0.6509176200 -0.4319872976 0.397572216145 +1403637197088318976.0000000000 11.6230494040 0.8391155558 0.6887263162 0.4841582307 0.6521539152 -0.4336138128 0.390211660325 +1403637197138319104.0000000000 11.5700423306 0.9207474298 0.6777123711 0.4871716366 0.6545146493 -0.4334112819 0.38266046441 +1403637197188318976.0000000000 11.5130220717 1.0021057709 0.6673694358 0.4895278548 0.6588614432 -0.4323093577 0.373326529115 +1403637197238319104.0000000000 11.4559103387 1.0842401015 0.6609301380 0.4927204154 0.6639357753 -0.4280474164 0.364953816009 +1403637197288318976.0000000000 11.3945918485 1.1654637913 0.6553013335 0.4947807643 0.6711368425 -0.4237839681 0.353800059817 +1403637197338319104.0000000000 11.3310288317 1.2462687675 0.6518030124 0.4976106701 0.6786919440 -0.4175682541 0.342633359864 +1403637197388318976.0000000000 11.2658026694 1.3267880607 0.6506577651 0.5023621621 0.6859610063 -0.4091941787 0.331134232773 +1403637197438319104.0000000000 11.1988049039 1.4064121289 0.6511257823 0.5062909464 0.6948298632 -0.3988967397 0.319002084531 +1403637197488318976.0000000000 11.1298426820 1.4846543898 0.6530880741 0.5081607390 0.7057305622 -0.3850656070 0.308936102226 +1403637197538319104.0000000000 11.0598669894 1.5624237687 0.6567214300 0.5113833559 0.7161058217 -0.3698508164 0.298144074122 +1403637197588318976.0000000000 10.9886357989 1.6394403789 0.6612734574 0.5132586297 0.7277559418 -0.3522424438 0.287857827647 +1403637197638319104.0000000000 10.9164773944 1.7161343013 0.6677846105 0.5173912864 0.7375637222 -0.3343041656 0.276670810371 +1403637197688318976.0000000000 10.8437291033 1.7921424390 0.6759038617 0.5228842814 0.7458087466 -0.3164411788 0.265002494434 +1403637197738319104.0000000000 10.7708944640 1.8673548215 0.6855884142 0.5274080526 0.7536882959 -0.2975996076 0.255400024053 +1403637197788318976.0000000000 10.6968480050 1.9415907714 0.6969180651 0.5328983739 0.7600152332 -0.2783013858 0.246869413024 +1403637197838319104.0000000000 10.6212334061 2.0147006617 0.7096906048 0.5386417454 0.7653120838 -0.2577046731 0.240313932133 +1403637197888318976.0000000000 10.5443074807 2.0875520370 0.7243073433 0.5425065294 0.7709043560 -0.2388297778 0.233138320907 +1403637197938319104.0000000000 10.4658187038 2.1602787752 0.7401926178 0.5471157381 0.7751726630 -0.2220111810 0.224683659972 +1403637197988318976.0000000000 10.3856723238 2.2323760422 0.7574009776 0.5507143456 0.7792379675 -0.2057872762 0.217148558751 +1403637198038319104.0000000000 10.3031062372 2.3033376057 0.7766730306 0.5547383019 0.7824146024 -0.1913473504 0.208516181142 +1403637198088318976.0000000000 10.2184781229 2.3736475303 0.7980344177 0.5586165527 0.7850913618 -0.1779729646 0.199761669544 +1403637198138319104.0000000000 10.1320572289 2.4435002581 0.8208715845 0.5617153594 0.7878261673 -0.1647672405 0.191461592712 +1403637198188318976.0000000000 10.0435979973 2.5134996360 0.8458451653 0.5642358208 0.7905928237 -0.1529476440 0.182230469027 +1403637198238319104.0000000000 9.9531819419 2.5825098021 0.8722287287 0.5655033095 0.7938427969 -0.1407809302 0.173782480515 +1403637198288318976.0000000000 9.8609936309 2.6507682958 0.9003984269 0.5694603337 0.7946474495 -0.1268295199 0.167823217325 +1403637198338319104.0000000000 9.7669334138 2.7182538435 0.9283014384 0.5716231895 0.7964003899 -0.1146751659 0.160757439833 +1403637198388318976.0000000000 9.6616363357 2.7901907373 0.9831068128 0.5753927275 0.7962388029 -0.1007345277 0.15741516102 +1403637198438319104.0000000000 9.5633801853 2.8568271399 1.0120159945 0.5788692511 0.7956243522 -0.0896034192 0.154478178261 +1403637198488318976.0000000000 9.4625443556 2.9219344271 1.0384881066 0.5814844004 0.7949592633 -0.0803111461 0.153185448214 +1403637198538319104.0000000000 9.3590424448 2.9859753528 1.0614397590 0.5838787030 0.7939464826 -0.0723751035 0.153285639411 +1403637198588318976.0000000000 9.2525962976 3.0490357856 1.0805605101 0.5859060944 0.7928448773 -0.0658959263 0.154171255722 +1403637198638319104.0000000000 9.1431360014 3.1105401876 1.0951227874 0.5871868884 0.7920297880 -0.0608940463 0.155538702878 +1403637198688318976.0000000000 9.0307029603 3.1705908081 1.1050431844 0.5884229197 0.7914944711 -0.0587613578 0.154408784016 +1403637198738319104.0000000000 8.9145144581 3.2286602077 1.1102875697 0.5892940535 0.7912246245 -0.0578181184 0.152817463998 +1403637198788318976.0000000000 8.7959691584 3.2852023873 1.1110633966 0.5912819202 0.7899477190 -0.0574442008 0.151883033795 +1403637198838319104.0000000000 8.6747735411 3.3406509212 1.1083139232 0.5962051304 0.7865546476 -0.0580329155 0.150011364455 +1403637198888318976.0000000000 8.5510867245 3.3949799652 1.1022026643 0.6016303106 0.7826606874 -0.0597394498 0.148035184736 +1403637198938319104.0000000000 8.4291738570 3.4495329009 1.0948609465 0.6071523303 0.7791376905 -0.0644337460 0.1419816866 +1403637198988318976.0000000000 8.3038647289 3.5014288126 1.0881148642 0.6138443810 0.7748698687 -0.0682489261 0.134587690934 +1403637199038319104.0000000000 8.1759629564 3.5505437506 1.0820426535 0.6176882988 0.7729942130 -0.0712341573 0.125963514871 +1403637199088318976.0000000000 8.0462030204 3.5965213481 1.0767014972 0.6184385439 0.7736441930 -0.0727419073 0.117119789421 +1403637199138319104.0000000000 7.9325191660 3.6463063109 1.0710974185 0.6177480497 0.7754997330 -0.0721836029 0.108522065295 +1403637199188318976.0000000000 7.8064830206 3.6877894269 1.0676439270 0.6160571534 0.7781744758 -0.0696557236 0.100330200515 +1403637199238319104.0000000000 7.6792615049 3.7266282245 1.0658456796 0.6152831017 0.7801969448 -0.0645114810 0.0925078421249 +1403637199288318976.0000000000 7.5505797967 3.7622697928 1.0661847697 0.6153627877 0.7813822239 -0.0569850555 0.0867361699641 +1403637199338319104.0000000000 7.4201659356 3.7943629611 1.0686714948 0.6169556051 0.7814377530 -0.0479229666 0.0801511618935 +1403637199388318976.0000000000 7.2883216117 3.8222698049 1.0725991599 0.6179953597 0.7817784965 -0.0372308093 0.0742831378256 +1403637199438319104.0000000000 7.1547173875 3.8467854644 1.0777126241 0.6195607912 0.7816861752 -0.0259708562 0.0666082880311 +1403637199488318976.0000000000 7.0201250621 3.8682936207 1.0831399327 0.6209090332 0.7815077351 -0.0139980647 0.0593438007499 +1403637199538319104.0000000000 6.8844559638 3.8863939402 1.0877538802 0.6215865817 0.7817077076 -0.0026235049 0.0505598509617 +1403637199588318976.0000000000 6.7481432259 3.9016501395 1.0904976463 0.6230459342 0.7810165223 0.0088023207 0.0418267251338 +1403637199638319104.0000000000 6.6109798453 3.9131667805 1.0914726159 0.6251876026 0.7797153468 0.0176011889 0.0295742736545 +1403637199688318976.0000000000 6.4731227794 3.9219187377 1.0908955583 0.6278716990 0.7776914913 0.0266175325 0.0162659428722 +1403637199738319104.0000000000 6.3353594131 3.9275435532 1.0876779703 0.6292462934 0.7763884839 0.0355528187 0.00245385216821 +1403637199788318976.0000000000 6.1978268268 3.9301824410 1.0811114298 0.6309225908 0.7744905051 0.0429985547 -0.0158828894357 +1403637199838319104.0000000000 6.0610368953 3.9304432122 1.0690340598 0.6332345666 0.7714618607 0.0518239564 -0.0342762113476 +1403637199888318976.0000000000 5.9254532008 3.9282896543 1.0508307724 0.6358736053 0.7674910138 0.0596569338 -0.0553475562962 +1403637199938319104.0000000000 5.7919325319 3.9235795742 1.0282631960 0.6385364690 0.7627542575 0.0684302115 -0.0761211312807 +1403637199988318976.0000000000 5.6612946744 3.9155071896 1.0044357063 0.6434474478 0.7552531943 0.0779148061 -0.0974539762449 +1403637200038319104.0000000000 5.5345329798 3.9032003489 0.9790777833 0.6468413905 0.7482620437 0.0887611874 -0.117565220344 +1403637200088318976.0000000000 5.4124462148 3.8866359694 0.9522438828 0.6497291902 0.7411475134 0.1026372293 -0.13423092783 +1403637200138319104.0000000000 5.2953097088 3.8659147717 0.9248788882 0.6525290083 0.7335400597 0.1177662637 -0.14918438684 +1403637200188318976.0000000000 5.1838808904 3.8404478017 0.8948480896 0.6496376823 0.7310004372 0.1351455289 -0.159200906451 +1403637200238319104.0000000000 5.0777084115 3.8105574460 0.8639987501 0.6449785140 0.7297928820 0.1522917302 -0.167965159272 +1403637200288318976.0000000000 4.9773342753 3.7773108582 0.8312996115 0.6391515113 0.7305472002 0.1724627001 -0.167459699592 +1403637200338319104.0000000000 4.8821991153 3.7400680463 0.7981307828 0.6296306998 0.7348007614 0.1915831706 -0.164100310022 +1403637200388318976.0000000000 4.7812475945 3.6947794588 0.7642388882 0.6188956908 0.7401106476 0.2070983269 -0.162217866574 +1403637200438319104.0000000000 4.6950898509 3.6515545548 0.7345685337 0.6070702700 0.7466388918 0.2194472858 -0.16074495705 +1403637200488318976.0000000000 4.6115999315 3.6062038973 0.7073481608 0.5964744393 0.7526424333 0.2295617802 -0.158268758376 +1403637200538319104.0000000000 4.5310532035 3.5590802091 0.6828083763 0.5873930860 0.7576328041 0.2332735971 -0.162927362965 +1403637200588318976.0000000000 4.4509588608 3.5108228316 0.6618062974 0.5820116906 0.7603355753 0.2336181610 -0.169040704676 +1403637200638319104.0000000000 4.3730914092 3.4615033966 0.6429119734 0.5775312745 0.7628085559 0.2336730109 -0.173140572671 +1403637200688318976.0000000000 4.2975511171 3.4116589253 0.6265386781 0.5748348160 0.7645341746 0.2326488513 -0.175860575852 +1403637200738319104.0000000000 4.2239669720 3.3612714384 0.6117778846 0.5721034156 0.7666050907 0.2309009297 -0.178042347258 +1403637200788318976.0000000000 4.1522437007 3.3103093867 0.5992518976 0.5715882010 0.7675253716 0.2264724419 -0.181388989405 +1403637200838319104.0000000000 4.0822073948 3.2597032233 0.5889794283 0.5722019172 0.7683681435 0.2198086552 -0.184063894034 +1403637200888318976.0000000000 4.0148693489 3.2085863873 0.5810266240 0.5734893574 0.7689931177 0.2142753434 -0.183971788699 +1403637200938319104.0000000000 3.9501488886 3.1572363549 0.5739817666 0.5741657721 0.7702027211 0.2100093250 -0.181707231432 +1403637200988318976.0000000000 3.8882128435 3.1054137011 0.5683417127 0.5747134045 0.7715339072 0.2062926044 -0.178558937499 +1403637201038319104.0000000000 3.8291389508 3.0529833689 0.5642659429 0.5760091811 0.7723621774 0.2026171977 -0.174975316406 +1403637201088318976.0000000000 3.7724433654 3.0005976114 0.5623846723 0.5764201499 0.7736687702 0.1995241962 -0.171366682524 +1403637201138319104.0000000000 3.7180989490 2.9482418756 0.5623402785 0.5766288773 0.7751570515 0.1968794614 -0.166940591376 +1403637201188318976.0000000000 3.6655347287 2.8958044586 0.5647659040 0.5768639074 0.7764028761 0.1927045548 -0.165201576598 +1403637201238319104.0000000000 3.6148911185 2.8427199827 0.5689368742 0.5751522753 0.7788726447 0.1885553479 -0.164329377404 +1403637201288318976.0000000000 3.5669146393 2.7892615870 0.5755260785 0.5735469231 0.7813538572 0.1811041209 -0.16652739791 +1403637201338319104.0000000000 3.5216330448 2.7361025065 0.5823683809 0.5704009702 0.7849200780 0.1701925541 -0.171981681743 +1403637201388318976.0000000000 3.4792875465 2.6834058714 0.5876203845 0.5658101286 0.7897640959 0.1592575490 -0.175409817909 +1403637201438319104.0000000000 3.4404387549 2.6316423043 0.5913450203 0.5604946186 0.7950788513 0.1477410254 -0.178516083738 +1403637201488318976.0000000000 3.4048453625 2.5817185727 0.5932747866 0.5551946723 0.8003953590 0.1363286985 -0.180390218873 +1403637201538319104.0000000000 3.3727747596 2.5334904552 0.5935291770 0.5506531626 0.8049259378 0.1256076660 -0.181928676618 +1403637201588318976.0000000000 3.3446114550 2.4871032439 0.5925181072 0.5477852490 0.8079692496 0.1163689567 -0.183235582029 +1403637201638319104.0000000000 3.3208528763 2.4428304159 0.5904468898 0.5457703829 0.8101856434 0.1083459442 -0.184377516758 +1403637201688318976.0000000000 3.3017813457 2.4010999168 0.5872397549 0.5462956693 0.8107102545 0.1022004517 -0.184024434869 +1403637201738319104.0000000000 3.2874676942 2.3619721144 0.5828886060 0.5506542817 0.8090034301 0.0999860021 -0.179711188855 +1403637201788318976.0000000000 3.2777326890 2.3248135752 0.5774795672 0.5553775758 0.8071140220 0.1004046052 -0.173325182692 +1403637201838319104.0000000000 3.2723459700 2.2892394907 0.5727851898 0.5587765409 0.8056641132 0.0999753028 -0.169348908809 +1403637201888318976.0000000000 3.2713014900 2.2549282803 0.5692977482 0.5616617503 0.8043854634 0.1004409998 -0.165564821409 +1403637201938319104.0000000000 3.2741837918 2.2221677336 0.5674204842 0.5628960633 0.8039608606 0.1007766697 -0.163214642193 +1403637201988318976.0000000000 3.2807682563 2.1905632386 0.5672644107 0.5605102011 0.8055799672 0.1002511535 -0.163764884045 +1403637202038319104.0000000000 3.2910375022 2.1605342142 0.5685279709 0.5562074813 0.8082258939 0.0990152947 -0.166132819094 +1403637202088318976.0000000000 3.3053862893 2.1318961397 0.5710465123 0.5497646712 0.8121006410 0.0983125138 -0.169073962575 +1403637202138319104.0000000000 3.3242705038 2.1046313356 0.5743224845 0.5425009077 0.8166710804 0.0995393668 -0.169802903737 +1403637202188318976.0000000000 3.3477136658 2.0798487128 0.5787718810 0.5371185774 0.8204682055 0.1038865322 -0.165961278438 +1403637202238319104.0000000000 3.3753823179 2.0576446836 0.5830364428 0.5346836074 0.8228469180 0.1121731716 -0.156376370109 +1403637202288318976.0000000000 3.4055613012 2.0393305117 0.5861315443 0.5327985061 0.8247821821 0.1221542817 -0.144701193463 +1403637202338319104.0000000000 3.4376929674 2.0230236031 0.5883375671 0.5311562373 0.8262179190 0.1304961407 -0.134936130184 +1403637202388318976.0000000000 3.4710124641 2.0094970705 0.5893818841 0.5307056577 0.8266600207 0.1377574620 -0.126521131546 +1403637202438319104.0000000000 3.5050274473 1.9987402405 0.5899427048 0.5314844353 0.8261890946 0.1424314573 -0.121033693496 +1403637202488318976.0000000000 3.5392136713 1.9907446094 0.5905513076 0.5343970222 0.8242468911 0.1448453686 -0.11856097281 +1403637202538319104.0000000000 3.5735420082 1.9851362053 0.5916921692 0.5380884078 0.8217538772 0.1462068886 -0.117494580416 +1403637202588318976.0000000000 3.6077320737 1.9821897186 0.5941392889 0.5424003507 0.8188117662 0.1460181395 -0.118439241517 +1403637202638319104.0000000000 3.6424057092 1.9812137468 0.5984891227 0.5479178520 0.8150328283 0.1464028633 -0.118632701407 +1403637202688318976.0000000000 3.6776308828 1.9814358873 0.6045329371 0.5522285215 0.8120649263 0.1473784707 -0.117787103707 +1403637202738319104.0000000000 3.7133450653 1.9826882122 0.6130100696 0.5566458205 0.8089452638 0.1483481893 -0.117242506894 +1403637202788318976.0000000000 3.7498488443 1.9846549126 0.6219180018 0.5597405691 0.8067585455 0.1516632018 -0.113267020044 +1403637202838319104.0000000000 3.7865587818 1.9872503672 0.6307724615 0.5623744719 0.8049508436 0.1546426870 -0.108971244427 +1403637202888318976.0000000000 3.8227269170 1.9907338231 0.6381646236 0.5642067507 0.8036574194 0.1578681234 -0.104322338282 +1403637202938319104.0000000000 3.8583916447 1.9945047624 0.6440126448 0.5657022088 0.8025664219 0.1606928094 -0.100229588296 +1403637202988318976.0000000000 3.8935005761 1.9981763878 0.6484198273 0.5666166271 0.8019139828 0.1627011486 -0.0969943205531 +1403637203038319104.0000000000 3.9279059033 2.0018772530 0.6518971217 0.5673522854 0.8014054967 0.1637224632 -0.0951607538662 +1403637203088318976.0000000000 3.9614828266 2.0054466455 0.6546238466 0.5676329824 0.8012532604 0.1636994179 -0.0948077556057 +1403637203138319104.0000000000 3.9939736673 2.0092034121 0.6566456110 0.5678604149 0.8011902092 0.1622621207 -0.0964354809923 +1403637203188318976.0000000000 4.0263025648 2.0127946062 0.6570079426 0.5679482334 0.8011396671 0.1634060870 -0.0943847905988 +1403637203238319104.0000000000 4.0575761641 2.0162101791 0.6571346613 0.5689749258 0.8005277166 0.1630339748 -0.0940363325251 +1403637203288318976.0000000000 4.0878849564 2.0196811343 0.6564392524 0.5694917070 0.8002403405 0.1631563240 -0.0931375706101 +1403637203338319104.0000000000 4.1173116868 2.0228745602 0.6551593743 0.5699929416 0.7999206409 0.1631062306 -0.0929051796829 +1403637203388318976.0000000000 4.1462325625 2.0257259979 0.6530135556 0.5698360958 0.8001287953 0.1621435577 -0.0937560743493 +1403637203438319104.0000000000 4.1748652327 2.0283571915 0.6494979479 0.5697598064 0.8002512125 0.1625574968 -0.0924490141554 +1403637203488318976.0000000000 4.2023800772 2.0307789454 0.6451331290 0.5697349542 0.8003273976 0.1622982255 -0.0923981847062 +1403637203538319104.0000000000 4.2292076864 2.0329109372 0.6397614585 0.5705458058 0.7997932976 0.1624214949 -0.0918009941667 +1403637203588318976.0000000000 4.2553035498 2.0351025643 0.6334055983 0.5715235425 0.7991515966 0.1628499883 -0.0905397561627 +1403637203638319104.0000000000 4.2806375374 2.0371498260 0.6261243517 0.5720357185 0.7988586268 0.1637118970 -0.0883088096633 +1403637203688318976.0000000000 4.3043617779 2.0387751659 0.6182681652 0.5721820793 0.7988362364 0.1631676615 -0.0885700275616 +1403637203738319104.0000000000 4.3268833203 2.0400087792 0.6097827957 0.5730524208 0.7983709390 0.1622238509 -0.0888717557727 +1403637203788318976.0000000000 4.3485469047 2.0408340524 0.6002805419 0.5731273702 0.7984326831 0.1616718495 -0.088839636835 +1403637203838319104.0000000000 4.3692679033 2.0412425579 0.5899694674 0.5732117205 0.7984602873 0.1610586139 -0.0891606191601 +1403637203888318976.0000000000 4.3890995695 2.0411235081 0.5787853299 0.5738214380 0.7980703732 0.1610003633 -0.088834225795 +1403637203938319104.0000000000 4.4080992071 2.0404279685 0.5666412862 0.5742192329 0.7978493592 0.1608151955 -0.0885841152859 +1403637203988318976.0000000000 4.4262493522 2.0391810808 0.5534972945 0.5740439828 0.7980182474 0.1608705601 -0.0880967966256 +1403637204038319104.0000000000 4.4436171299 2.0377138940 0.5404376257 0.5741546842 0.7980041434 0.1610497927 -0.0871708096091 +1403637204088318976.0000000000 4.4600446898 2.0356761283 0.5284273550 0.5740394556 0.7981952546 0.1601624843 -0.0878123996591 +1403637204138319104.0000000000 4.4759636158 2.0331328469 0.5184182818 0.5742553221 0.7980617504 0.1603081107 -0.0873474511179 +1403637204188318976.0000000000 4.4907108389 2.0307581468 0.5113787171 0.5736569079 0.7985670468 0.1598724505 -0.0874598387864 +1403637204238319104.0000000000 4.5050449009 2.0274261205 0.5059125971 0.5740449310 0.7983183752 0.1601449858 -0.0866820190134 +1403637204288318976.0000000000 4.5184602960 2.0233317633 0.5018381098 0.5727099182 0.7993907812 0.1593888508 -0.0870225417624 +1403637204338319104.0000000000 4.5309839620 2.0188113770 0.5002847880 0.5728423799 0.7993541787 0.1583275985 -0.088413100179 +1403637204388318976.0000000000 4.5427506106 2.0136780012 0.5008024901 0.5735241857 0.7990636977 0.1560804585 -0.0905875593903 +1403637204438319104.0000000000 4.5545895860 2.0083566095 0.5025552053 0.5753939757 0.7979173507 0.1549448864 -0.0907841189183 +1403637204488318976.0000000000 4.5655112427 2.0031373326 0.5069470850 0.5776723601 0.7965177662 0.1517910063 -0.0938806844427 +1403637204538319104.0000000000 4.5762423826 1.9976453613 0.5130318522 0.5789419085 0.7958035208 0.1505225992 -0.0941592801215 +1403637204588318976.0000000000 4.5868327470 1.9915080740 0.5206845340 0.5786228728 0.7963163211 0.1491831869 -0.0939162637896 +1403637204638319104.0000000000 4.5972300910 1.9847131479 0.5300440353 0.5776125205 0.7973189266 0.1480867628 -0.0933628199387 +1403637204688318976.0000000000 4.6075848642 1.9777249406 0.5400064396 0.5768752580 0.7980991484 0.1485588675 -0.090459653445 +1403637204738319104.0000000000 4.6175131425 1.9701209170 0.5501732679 0.5764734032 0.7986132713 0.1475026599 -0.0902121031691 +1403637204788318976.0000000000 4.6271965761 1.9622013173 0.5585669346 0.5750408664 0.7998885850 0.1471086216 -0.0886865658745 +1403637204838319104.0000000000 4.6366692446 1.9535274221 0.5657381011 0.5736173923 0.8011007361 0.1461276829 -0.0885855414342 +1403637204888318976.0000000000 4.6457128411 1.9448784192 0.5710719404 0.5732463361 0.8015329787 0.1460160129 -0.0872516254552 +1403637204938319104.0000000000 4.6544113969 1.9359208275 0.5746776015 0.5716766570 0.8027291801 0.1461304384 -0.086357154863 +1403637204988318976.0000000000 4.6626706806 1.9267949722 0.5764581360 0.5689145800 0.8047663836 0.1461565835 -0.0855892608545 +1403637205038319104.0000000000 4.6704766556 1.9176413015 0.5768741588 0.5662877706 0.8066451689 0.1464547202 -0.0848100657831 +1403637205088318976.0000000000 4.6776615227 1.9088575008 0.5760009853 0.5645648820 0.8078439551 0.1468570495 -0.0841881539892 +1403637205138319104.0000000000 4.6843006053 1.9002913428 0.5742097996 0.5643115026 0.8080378639 0.1467471089 -0.0842177215367 +1403637205188318976.0000000000 4.6904704789 1.8920588987 0.5710986540 0.5644255981 0.8078924926 0.1474096957 -0.0836889853792 +1403637205238319104.0000000000 4.6958420969 1.8837778098 0.5668663532 0.5635544581 0.8081587750 0.1487733662 -0.0845709912115 +1403637205288318976.0000000000 4.7005988745 1.8755580884 0.5619751435 0.5628054063 0.8080763766 0.1513377647 -0.0857876748782 +1403637205338319104.0000000000 4.7042840314 1.8677322343 0.5580577474 0.5633919694 0.8067877349 0.1547752935 -0.087907042455 +1403637205388318976.0000000000 4.7074199275 1.8602942390 0.5553615858 0.5633176014 0.8059919185 0.1582934241 -0.0894063712268 +1403637205438319104.0000000000 4.7098569324 1.8533029259 0.5546320761 0.5641399190 0.8046018619 0.1616359593 -0.0907513761094 +1403637205488318976.0000000000 4.7114476202 1.8465000587 0.5559208118 0.5660352153 0.8024282859 0.1645716956 -0.0928931539442 +1403637205538319104.0000000000 4.7123849980 1.8398576465 0.5586046759 0.5682224937 0.8001008444 0.1670537124 -0.0951572052409 +1403637205588318976.0000000000 4.7128668469 1.8333230903 0.5607722062 0.5695398087 0.7984896854 0.1696313473 -0.0962488165955 +1403637205638319104.0000000000 4.7126554415 1.8266238145 0.5614926451 0.5705528108 0.7972041311 0.1711315803 -0.0982295560297 +1403637205688318976.0000000000 4.7121118210 1.8196044716 0.5601777522 0.5708518786 0.7965373097 0.1727952781 -0.0989860536212 +1403637205738319104.0000000000 4.7109020083 1.8126358636 0.5570150244 0.5703344129 0.7965609475 0.1736155684 -0.100334185758 +1403637205788318976.0000000000 4.7092816660 1.8052975460 0.5522181500 0.5703618810 0.7962661401 0.1745446015 -0.100904612857 +1403637205838319104.0000000000 4.7070808383 1.7976547396 0.5462365034 0.5702541648 0.7961458904 0.1754282434 -0.10092987761 +1403637205888318976.0000000000 4.7042513463 1.7898864730 0.5393232463 0.5700347310 0.7961623785 0.1754382450 -0.10201614887 +1403637205938319104.0000000000 4.7009886733 1.7821205210 0.5319948314 0.5702131839 0.7959523954 0.1755892484 -0.102396899047 +1403637205988318976.0000000000 4.6973415273 1.7739335912 0.5255093820 0.5706706784 0.7954750767 0.1761571933 -0.102581783744 +1403637206038319104.0000000000 4.6931938407 1.7650969591 0.5204501140 0.5707094784 0.7953702849 0.1758645047 -0.103674862101 +1403637206088318976.0000000000 4.6888476139 1.7553919126 0.5170169285 0.5704919674 0.7954701066 0.1752364147 -0.105159039818 +1403637206138319104.0000000000 4.6842253016 1.7447921142 0.5145845096 0.5697105630 0.7959834842 0.1735825156 -0.108209415393 +1403637206188318976.0000000000 4.6790641671 1.7343757656 0.5146113980 0.5688350468 0.7965478489 0.1710240964 -0.112645338786 +1403637206238319104.0000000000 4.6741413504 1.7240229442 0.5166976763 0.5682868805 0.7968750786 0.1699581098 -0.114692508021 +1403637206288318976.0000000000 4.6693936072 1.7138713335 0.5212006501 0.5684120308 0.7967893730 0.1684836657 -0.116823425272 +1403637206338319104.0000000000 4.6648372872 1.7038114381 0.5272518131 0.5686798189 0.7966441949 0.1671593450 -0.118402042718 +1403637206388318976.0000000000 4.6604095281 1.6940466462 0.5351786318 0.5686746987 0.7966036596 0.1672661816 -0.118548391757 +1403637206438319104.0000000000 4.6561575515 1.6847465505 0.5445647946 0.5685449899 0.7967694797 0.1670204754 -0.118402497643 +1403637206488318976.0000000000 4.6522685547 1.6755087465 0.5546488030 0.5687885932 0.7966271166 0.1670918296 -0.118089347023 +1403637206538319104.0000000000 4.6487623973 1.6662307382 0.5641552612 0.5691512761 0.7964629612 0.1667043098 -0.117996819637 +1403637206588318976.0000000000 4.6456115823 1.6569528790 0.5722473415 0.5694948288 0.7963059709 0.1669707331 -0.117018011129 +1403637206638319104.0000000000 4.6430620654 1.6469379241 0.5787881633 0.5697854722 0.7961843366 0.1674006091 -0.115810422236 +1403637206688318976.0000000000 4.6408644127 1.6369396746 0.5836261220 0.5701960145 0.7960220664 0.1678867318 -0.114190280103 +1403637206738319104.0000000000 4.6388414035 1.6267394300 0.5871220155 0.5708463339 0.7956410210 0.1679610088 -0.113485365841 +1403637206788318976.0000000000 4.6371354187 1.6163101811 0.5892321738 0.5719183949 0.7949692976 0.1680449183 -0.112667967619 +1403637206838319104.0000000000 4.6355177594 1.6055826922 0.5909244546 0.5720893774 0.7949451692 0.1679773258 -0.112069354689 +1403637206888318976.0000000000 4.6340425084 1.5945282828 0.5940033799 0.5731541857 0.7943011299 0.1676135641 -0.111739373351 +1403637206938319104.0000000000 4.6329455518 1.5824373190 0.5980421732 0.5744593102 0.7933748505 0.1670955719 -0.112391802592 +1403637206988318976.0000000000 4.6319451012 1.5704400854 0.6027702546 0.5747213463 0.7933248046 0.1666533660 -0.112061519378 +1403637207038319104.0000000000 4.6309031352 1.5590040948 0.6095944930 0.5751392552 0.7931800089 0.1660704764 -0.111807457232 +1403637207088318976.0000000000 4.6301078476 1.5467251917 0.6168523592 0.5744394305 0.7938183637 0.1655881720 -0.111589889813 +1403637207138319104.0000000000 4.6294244808 1.5341392052 0.6233921879 0.5756565793 0.7931634950 0.1645422701 -0.111521362677 +1403637207188318976.0000000000 4.6288848678 1.5209261144 0.6280943271 0.5755601082 0.7934392350 0.1637456901 -0.111229902449 +1403637207238319104.0000000000 4.6283978952 1.5073957700 0.6314141078 0.5769666525 0.7925693690 0.1628180371 -0.111505892441 +1403637207288318976.0000000000 4.6282390664 1.4934214105 0.6323592687 0.5765571545 0.7930501947 0.1621160878 -0.111227740709 +1403637207338319104.0000000000 4.6284702445 1.4790741147 0.6316211134 0.5762131859 0.7934476517 0.1615270566 -0.111032420459 +1403637207388318976.0000000000 4.6291788319 1.4643941824 0.6293110261 0.5763139206 0.7934730409 0.1614713113 -0.110407490403 +1403637207438319104.0000000000 4.6302412663 1.4492665848 0.6257373047 0.5765043351 0.7934803647 0.1610240642 -0.110013241256 +1403637207488318976.0000000000 4.6315571051 1.4335387428 0.6206489929 0.5761203832 0.7939016256 0.1604130196 -0.109878005784 +1403637207538319104.0000000000 4.6332204991 1.4171517967 0.6139171809 0.5742971813 0.7953388966 0.1597850855 -0.109943229454 +1403637207588318976.0000000000 4.6347762960 1.4003752877 0.6065628310 0.5705910502 0.7981242699 0.1578569793 -0.111824314818 +1403637207638319104.0000000000 4.6364833032 1.3833533294 0.5994895890 0.5642089343 0.8026769919 0.1556565483 -0.114668933019 +1403637207688318976.0000000000 4.6389786464 1.3667452293 0.5941175658 0.5593581834 0.8061088685 0.1539457366 -0.11665172511 +1403637207738319104.0000000000 4.6419423263 1.3515746625 0.5905400773 0.5568736061 0.8078672172 0.1538490172 -0.116502472268 +1403637207788318976.0000000000 4.6456802046 1.3374027930 0.5896922097 0.5572372349 0.8076807075 0.1544394011 -0.115269294342 +1403637207838319104.0000000000 4.6502568799 1.3236008704 0.5913342473 0.5588459783 0.8066756607 0.1552997349 -0.113347003484 +1403637207888318976.0000000000 4.6554520729 1.3105289611 0.5949075558 0.5607241409 0.8054860758 0.1567361044 -0.110518835889 +1403637207938319104.0000000000 4.6602979934 1.2991379307 0.6016153057 0.5630199323 0.8039424733 0.1577603070 -0.108612803288 +1403637207988318976.0000000000 4.6654313800 1.2877953848 0.6111197429 0.5646814652 0.8028364907 0.1586215614 -0.106900011232 +1403637208038319104.0000000000 4.6709493239 1.2759987787 0.6224952669 0.5659424054 0.8019894155 0.1596399418 -0.105058365783 +1403637208088318976.0000000000 4.6760357645 1.2649791393 0.6352381046 0.5665424544 0.8016235309 0.1604320152 -0.103396956463 +1403637208138319104.0000000000 4.6809279105 1.2539439202 0.6499142290 0.5667513123 0.8015159988 0.1609895354 -0.1022126364 +1403637208188318976.0000000000 4.6855391880 1.2432980039 0.6658605283 0.5683394975 0.8004651737 0.1615213698 -0.10077980144 +1403637208238319104.0000000000 4.6899556734 1.2324033679 0.6812485762 0.5673386732 0.8012889264 0.1612699075 -0.100274140563 +1403637208288318976.0000000000 4.6935909814 1.2214414741 0.6961132735 0.5666444899 0.8019541347 0.1580210291 -0.103985298138 +1403637208338319104.0000000000 4.6972932916 1.2108528166 0.7094512676 0.5664771553 0.8022322474 0.1546043679 -0.107817175089 +1403637208388318976.0000000000 4.7011747284 1.2005920653 0.7208366224 0.5664881951 0.8023467622 0.1519553005 -0.11063627185 +1403637208438319104.0000000000 4.7054957948 1.1907178405 0.7302873750 0.5674252402 0.8018643331 0.1507770416 -0.110943552824 +1403637208488318976.0000000000 4.7104883919 1.1810413528 0.7373291423 0.5677257565 0.8017610336 0.1506846080 -0.110276286445 +1403637208538319104.0000000000 4.7158919840 1.1719028438 0.7429384432 0.5691048642 0.8008756193 0.1508048189 -0.109434009656 +1403637208588318976.0000000000 4.7221362500 1.1627533687 0.7468617048 0.5698970307 0.8004536459 0.1520423544 -0.106651102302 +1403637208638319104.0000000000 4.7285927716 1.1535807083 0.7496107941 0.5706692254 0.7999236245 0.1530854190 -0.104993736295 +1403637208688318976.0000000000 4.7351979203 1.1444905172 0.7509797900 0.5716035432 0.7993181644 0.1542506538 -0.102793955898 +1403637208738319104.0000000000 4.7417910208 1.1353242527 0.7513379380 0.5729585623 0.7983651788 0.1546852510 -0.10200000141 +1403637208788318976.0000000000 4.7483488293 1.1258549854 0.7504571758 0.5740475666 0.7975799958 0.1549008500 -0.10169202646 +1403637208838319104.0000000000 4.7550118795 1.1162079795 0.7480902466 0.5744706135 0.7973004530 0.1552787178 -0.10091591374 +1403637208888318976.0000000000 4.7618370191 1.1064270066 0.7441051981 0.5745108257 0.7972740669 0.1565307851 -0.0989418350423 +1403637208938319104.0000000000 4.7687969290 1.0965318569 0.7383785903 0.5754593202 0.7965184945 0.1595518711 -0.0945941813425 +1403637208988318976.0000000000 4.7756369360 1.0862783861 0.7309814843 0.5763332062 0.7958096157 0.1632215873 -0.0888020518014 +1403637209038319104.0000000000 4.7819583020 1.0756621345 0.7218664382 0.5771894638 0.7950241253 0.1670097680 -0.0830463751995 +1403637209088318976.0000000000 4.7871419344 1.0643222237 0.7118613677 0.5779231743 0.7940900039 0.1710338740 -0.0785702502782 +1403637209138319104.0000000000 4.7905891677 1.0518124854 0.7026422756 0.5789262664 0.7926141624 0.1747885296 -0.0778211891501 +1403637209188318976.0000000000 4.7917747543 1.0378859196 0.6943355260 0.5766194995 0.7931653142 0.1776897531 -0.082614095675 +1403637209238319104.0000000000 4.7909614948 1.0228093572 0.6882201577 0.5736637995 0.7938497586 0.1797950028 -0.0915759952957 +1403637209288318976.0000000000 4.7892762877 1.0069004644 0.6836180759 0.5687281245 0.7955592784 0.1836401093 -0.0995493101107 +1403637209338319104.0000000000 4.7872389794 0.9903799646 0.6810298111 0.5643399647 0.7967976836 0.1879131142 -0.106407317497 +1403637209388318976.0000000000 4.7850109332 0.9736289386 0.6797757901 0.5597932265 0.7982583139 0.1925565715 -0.111072834897 +1403637209438319104.0000000000 4.7822109085 0.9573798721 0.6799745899 0.5552479807 0.7998776506 0.1971188292 -0.114191028774 +1403637209488318976.0000000000 4.7787997364 0.9414434851 0.6812777988 0.5488821881 0.8027497900 0.2021930277 -0.115927122831 +1403637209538319104.0000000000 4.7747387545 0.9261785385 0.6838172201 0.5414163520 0.8063906208 0.2076020640 -0.116206210783 +1403637209588318976.0000000000 4.7696789759 0.9124810534 0.6879010954 0.5333081099 0.8105394072 0.2126605154 -0.115688523811 +1403637209638319104.0000000000 4.7631152786 0.9005753281 0.6942177832 0.5257774175 0.8143725999 0.2167419712 -0.115664573792 +1403637209688318976.0000000000 4.7553087957 0.8898746322 0.7025797487 0.5201812209 0.8170847949 0.2198186210 -0.116033224594 +1403637209738319104.0000000000 4.7451589948 0.8823712699 0.7124685830 0.5159424042 0.8191202325 0.2219929046 -0.116467293826 +1403637209788318976.0000000000 4.7325146794 0.8785235226 0.7237717024 0.5133380956 0.8203336866 0.2235090001 -0.116534841079 +1403637209838319104.0000000000 4.7180168217 0.8769263958 0.7349707635 0.5109808838 0.8215406892 0.2246494731 -0.116198307231 +1403637209888318976.0000000000 4.7014985746 0.8775475357 0.7453833306 0.5081272501 0.8231997796 0.2245552358 -0.117148481595 +1403637209938319104.0000000000 4.6835484850 0.8802834796 0.7530045068 0.5046148755 0.8253196671 0.2249206352 -0.116713248639 +1403637209988318976.0000000000 4.6643668847 0.8853408013 0.7557112608 0.5003953618 0.8277852161 0.2260026338 -0.115320975777 +1403637210038319104.0000000000 4.6437066622 0.8922873698 0.7542661975 0.4951496141 0.8308552906 0.2272093645 -0.113500001539 +1403637210088318976.0000000000 4.6212254509 0.9021789786 0.7491037781 0.4902251495 0.8338056675 0.2280954520 -0.11144449934 +1403637210138319104.0000000000 4.5967727004 0.9145928776 0.7402672249 0.4851374821 0.8368451755 0.2281313856 -0.11085056002 +1403637210188318976.0000000000 4.5701433141 0.9305086397 0.7285209000 0.4796729964 0.8400161503 0.2287973563 -0.109263230358 +1403637210238319104.0000000000 4.5407756934 0.9501542587 0.7152874096 0.4750234211 0.8426808593 0.2292474067 -0.108108026191 +1403637210288318976.0000000000 4.5085909893 0.9741273034 0.7014398791 0.4713732761 0.8446782073 0.2301395437 -0.10659151546 +1403637210338319104.0000000000 4.4733676119 1.0025342898 0.6875878945 0.4690326178 0.8459915882 0.2301804264 -0.106412440222 +1403637210388318976.0000000000 4.4350826528 1.0352698301 0.6735759783 0.4671955673 0.8470212567 0.2303368649 -0.105963301223 +1403637210438319104.0000000000 4.3934375766 1.0730188982 0.6599679359 0.4687244850 0.8461202163 0.2303264077 -0.106431586345 +1403637210488318976.0000000000 4.3484872757 1.1159719844 0.6472028835 0.4740510389 0.8430812912 0.2301368918 -0.107361818057 +1403637210538319104.0000000000 4.3006068793 1.1630708287 0.6351065135 0.4812723159 0.8389213495 0.2293940681 -0.109390533229 +1403637210588318976.0000000000 4.2503022960 1.2133614167 0.6225614602 0.4873438473 0.8353995339 0.2281573206 -0.112017098088 +1403637210638319104.0000000000 4.1978192952 1.2666478490 0.6095928582 0.4933536633 0.8318329402 0.2266842488 -0.115197108764 +1403637210688318976.0000000000 4.1436876950 1.3226525946 0.5956639341 0.4981693592 0.8288362057 0.2260429303 -0.117313372486 +1403637210738319104.0000000000 4.0877230023 1.3811818508 0.5808124565 0.5009698153 0.8270401166 0.2251547813 -0.119746457822 +1403637210788318976.0000000000 4.0297662600 1.4419376364 0.5655800123 0.5026164682 0.8260644223 0.2218433218 -0.125617660562 +1403637210838319104.0000000000 3.9707160254 1.5048510895 0.5495093384 0.5046118691 0.8248620262 0.2189219101 -0.130547679308 +1403637210888318976.0000000000 3.9108046448 1.5697438171 0.5326664852 0.5065621065 0.8237673534 0.2150402871 -0.136234557918 +1403637210938319104.0000000000 3.8499453326 1.6369948113 0.5154993024 0.5108277822 0.8211759444 0.2104847775 -0.142902777219 +1403637210988318976.0000000000 3.7891842073 1.7063361963 0.4972090738 0.5161189893 0.8179263294 0.2066214595 -0.148071878087 +1403637211038319104.0000000000 3.7287867969 1.7774810910 0.4783253794 0.5216785183 0.8144641537 0.2029209227 -0.152717926618 +1403637211088318976.0000000000 3.6690067170 1.8501975727 0.4586307755 0.5262675279 0.8116322919 0.1988312905 -0.157358284796 +1403637211138319104.0000000000 3.6104839481 1.9243388419 0.4371916345 0.5297454722 0.8095871486 0.1980003600 -0.157271233687 +1403637211188318976.0000000000 3.5528910369 2.0002645263 0.4148261671 0.5340778226 0.8070955411 0.1992837621 -0.153764914969 +1403637211238319104.0000000000 3.4840278010 2.0685834818 0.3982008004 0.5389800048 0.8041640988 0.2000157002 -0.151044285902 +1403637211288318976.0000000000 3.4271998513 2.1458772483 0.3750846235 0.5449615382 0.8006167884 0.2003809857 -0.147909230714 +1403637211338319104.0000000000 3.3711120452 2.2235321436 0.3512594694 0.5508080811 0.7971261897 0.1999998448 -0.145603425849 +1403637211388318976.0000000000 3.3156212466 2.3011712837 0.3267105316 0.5555405968 0.7942434623 0.1992438133 -0.144408693227 +1403637211438319104.0000000000 3.2609545966 2.3781608812 0.3010737905 0.5581142321 0.7927623812 0.1987811150 -0.143256340657 +1403637211488318976.0000000000 3.2068833424 2.4549394262 0.2745998747 0.5594596758 0.7920707072 0.1980182835 -0.142890256478 +1403637211538319104.0000000000 3.1537254665 2.5307788561 0.2479422326 0.5574546865 0.7935722638 0.1975109888 -0.143096974298 +1403637211588318976.0000000000 3.1015542755 2.6063452211 0.2222970442 0.5548943005 0.7955051835 0.1972835354 -0.142628976927 +1403637211638319104.0000000000 3.0502233831 2.6817031813 0.1989932398 0.5524289281 0.7972026544 0.1970874440 -0.142992120791 +1403637211688318976.0000000000 2.9996184533 2.7565532177 0.1776692749 0.5503519872 0.7986185951 0.1962616862 -0.144230302673 +1403637211738319104.0000000000 2.9494469568 2.8318372353 0.1576118715 0.5446490054 0.8024692567 0.1954701696 -0.145574605637 +1403637211788318976.0000000000 2.9000892717 2.9070323797 0.1404334373 0.5387635216 0.8063353886 0.1938326348 -0.148276830451 +1403637211838319104.0000000000 2.8515074188 2.9827337619 0.1252792067 0.5332092027 0.8099406048 0.1913468470 -0.151889917461 +1403637211888318976.0000000000 2.8040181064 3.0601694423 0.1121012222 0.5297100981 0.8122700542 0.1907540038 -0.152438449843 +1403637211938319104.0000000000 2.7581514739 3.1384723549 0.1007790446 0.5289800052 0.8128503010 0.1914927842 -0.150947195514 +1403637211988318976.0000000000 2.7128949797 3.2186128144 0.0914854264 0.5312166670 0.8114536927 0.1928812689 -0.148823967742 +1403637212038319104.0000000000 2.6682652655 3.3006292398 0.0849700863 0.5363911136 0.8082401798 0.1946588640 -0.145397083044 +1403637212088318976.0000000000 2.6241565343 3.3833819078 0.0804746263 0.5439321872 0.8033259482 0.1952424563 -0.143824823539 +1403637212138319104.0000000000 2.5807932504 3.4659310473 0.0779145410 0.5515676970 0.7981504123 0.1951948623 -0.143624373248 +1403637212188318976.0000000000 2.5383552020 3.5481241985 0.0769159038 0.5582413323 0.7937094646 0.1951253005 -0.142541284218 +1403637212238319104.0000000000 2.4968575328 3.6293832625 0.0768414329 0.5631185529 0.7904112613 0.1944632039 -0.142588904563 +1403637212288318976.0000000000 2.4562864494 3.7098227422 0.0778102029 0.5661026796 0.7883824994 0.1945962427 -0.141820636948 +1403637212338319104.0000000000 2.4164526278 3.7893834369 0.0805888985 0.5688206509 0.7865951302 0.1938831462 -0.141846726576 +1403637212388318976.0000000000 2.3776344572 3.8677217326 0.0850197874 0.5702532385 0.7857972922 0.1932414570 -0.141391650287 +1403637212438319104.0000000000 2.3400420144 3.9444219461 0.0907462837 0.5713124401 0.7852871936 0.1929787601 -0.140304374721 +1403637212488318976.0000000000 2.2959630955 4.0220489227 0.0995092380 0.5694980263 0.7867847104 0.1930919733 -0.139130541252 +1403637212538319104.0000000000 2.2595588669 4.0964885847 0.1073101933 0.5665270026 0.7891561437 0.1934375753 -0.1373376884 +1403637212588318976.0000000000 2.2242233965 4.1703835439 0.1158411576 0.5628693381 0.7919984656 0.1932948709 -0.136211716382 +1403637212638319104.0000000000 2.1893076413 4.2436622894 0.1248557655 0.5587277063 0.7951677510 0.1938459867 -0.133997505482 +1403637212688318976.0000000000 2.1549136090 4.3169960013 0.1344310564 0.5550569995 0.7977868479 0.1944027128 -0.132873842054 +1403637212738319104.0000000000 2.1207431414 4.3907567992 0.1443784901 0.5528710310 0.7993957690 0.1956789347 -0.130421555134 +1403637212788318976.0000000000 2.0867475669 4.4647565404 0.1552476759 0.5522038113 0.7998695266 0.1967047747 -0.128790227647 +1403637212838319104.0000000000 2.0528312381 4.5388352759 0.1660957340 0.5502295144 0.8012212491 0.1980385069 -0.126778315269 +1403637212888318976.0000000000 2.0186910588 4.6129817262 0.1778657875 0.5502848591 0.8011306045 0.1993381811 -0.125062455947 +1403637212938319104.0000000000 1.9844848249 4.6869876137 0.1902918033 0.5506557214 0.8007344332 0.2011759646 -0.123007622569 +1403637212988318976.0000000000 1.9501257751 4.7605501943 0.2032022251 0.5509232945 0.8002732247 0.2030832466 -0.121669570554 +1403637213038319104.0000000000 1.9149213658 4.8340349622 0.2166225481 0.5505129652 0.8003455767 0.2037283786 -0.121972049193 +1403637213088318976.0000000000 1.8790170553 4.9071777348 0.2297352458 0.5501585224 0.8003457802 0.2034333281 -0.124044803773 +1403637213138319104.0000000000 1.8429638483 4.9798961216 0.2411653950 0.5487621238 0.8010317009 0.2033105025 -0.125988829901 +1403637213188318976.0000000000 1.8064675836 5.0527507209 0.2508012629 0.5480412877 0.8012653232 0.2029180170 -0.128253292885 +1403637213238319104.0000000000 1.7697474545 5.1252146054 0.2589262078 0.5480915409 0.8010244245 0.2028499722 -0.129643445248 +1403637213288318976.0000000000 1.7328515965 5.1976570729 0.2656819394 0.5476170363 0.8011733625 0.2028182570 -0.130773007151 +1403637213338319104.0000000000 1.6956659667 5.2701778629 0.2715738884 0.5487193019 0.8003520425 0.2027034006 -0.1313585444 +1403637213388318976.0000000000 1.6585600058 5.3427047639 0.2761124220 0.5500456892 0.7993691171 0.2029980038 -0.13134140597 +1403637213438319104.0000000000 1.6213304568 5.4153749983 0.2796218407 0.5520383710 0.7979482989 0.2027873426 -0.131944847805 +1403637213488318976.0000000000 1.5844428558 5.4877227791 0.2816817100 0.5538316296 0.7967587769 0.2027983673 -0.131600911036 +1403637213538319104.0000000000 1.5477699121 5.5603266671 0.2826960341 0.5555728220 0.7954774195 0.2034145822 -0.13106113932 +1403637213588318976.0000000000 1.5112924970 5.6328413698 0.2822109733 0.5590359049 0.7929498801 0.2071926165 -0.125620716247 +1403637213638319104.0000000000 1.4746761558 5.7043797132 0.2800204458 0.5608381356 0.7915220229 0.2104898866 -0.121026775982 +1403637213688318976.0000000000 1.4378564015 5.7747702325 0.2760962381 0.5612454932 0.7909328427 0.2145758820 -0.115697561264 +1403637213738319104.0000000000 1.4003224049 5.8439776068 0.2712594347 0.5619542239 0.7902262992 0.2172823608 -0.11197420242 +1403637213788318976.0000000000 1.3619822200 5.9117351629 0.2645693739 0.5606251652 0.7909184944 0.2196603383 -0.109071972504 +1403637213838319104.0000000000 1.3226065601 5.9782587441 0.2568489117 0.5602849752 0.7908378113 0.2215324426 -0.107608919714 +1403637213888318976.0000000000 1.2820665742 6.0439722589 0.2481307660 0.5601966361 0.7906824357 0.2229593155 -0.106255157137 +1403637213938319104.0000000000 1.2400797183 6.1081810021 0.2384295395 0.5592658446 0.7911813157 0.2238242753 -0.105624498028 +1403637213988318976.0000000000 1.1960761975 6.1720511140 0.2300619108 0.5616685024 0.7892610833 0.2244600577 -0.105892012631 +1403637214038319104.0000000000 1.1500167664 6.2344155078 0.2236306544 0.5640906526 0.7869468985 0.2250450185 -0.108954367644 +1403637214088318976.0000000000 1.1022588914 6.2952802951 0.2186838439 0.5663955649 0.7843040887 0.2255505238 -0.114848254701 +1403637214138319104.0000000000 1.0529909618 6.3548402084 0.2156585325 0.5669724278 0.7826614221 0.2254182298 -0.123166497562 +1403637214188318976.0000000000 1.0031092018 6.4128482681 0.2141196828 0.5678392539 0.7802291469 0.2271686407 -0.131131493549 +1403637214238319104.0000000000 0.9529355642 6.4696660180 0.2143342153 0.5686487532 0.7773985899 0.2309039289 -0.137743978424 +1403637214288318976.0000000000 0.9025625143 6.5251489127 0.2161823616 0.5701814497 0.7734827323 0.2367137967 -0.143471793822 +1403637214338319104.0000000000 0.8520339849 6.5783234304 0.2197809782 0.5718271975 0.7688293592 0.2437865373 -0.149943979169 +1403637214388318976.0000000000 0.8018386966 6.6295486075 0.2243414143 0.5743958813 0.7627596914 0.2537071619 -0.154595280575 +1403637214438319104.0000000000 0.7519265078 6.6781903098 0.2296014464 0.5760635395 0.7565817602 0.2661361838 -0.157817521705 +1403637214488318976.0000000000 0.7022994872 6.7240022864 0.2360623329 0.5771179782 0.7501844444 0.2794788870 -0.161399164655 +1403637214538319104.0000000000 0.6525783920 6.7671658755 0.2440349857 0.5783902175 0.7432962182 0.2930371404 -0.164635119726 +1403637214588318976.0000000000 0.6030786879 6.8075048111 0.2532432160 0.5794947236 0.7367715426 0.3059414970 -0.166593396311 +1403637214638319104.0000000000 0.5531432188 6.8448292829 0.2641192149 0.5817279620 0.7295922282 0.3178004381 -0.168198217072 +1403637214688318976.0000000000 0.5025167123 6.8790387034 0.2765114318 0.5838706551 0.7230689826 0.3280925755 -0.169179095845 +1403637214738319104.0000000000 0.4510779555 6.9099708999 0.2902210943 0.5859978661 0.7171056612 0.3375873007 -0.16852532767 +1403637214788318976.0000000000 0.3988688049 6.9366321675 0.3057077896 0.5876527743 0.7122485360 0.3441447854 -0.170089995373 +1403637214838319104.0000000000 0.3455739551 6.9590597087 0.3222998478 0.5875685537 0.7096381305 0.3485701871 -0.172266488338 +1403637214888318976.0000000000 0.2916613139 6.9771486807 0.3384544978 0.5869345396 0.7081881380 0.3515418864 -0.174343653382 +1403637214938319104.0000000000 0.2368854091 6.9911842285 0.3535260627 0.5868924846 0.7067857986 0.3534203696 -0.176366348433 +1403637214988318976.0000000000 0.1816842458 7.0010434617 0.3674374724 0.5875180923 0.7053819082 0.3541021073 -0.178523254423 +1403637215038319104.0000000000 0.1262601209 7.0068591039 0.3797729173 0.5878506207 0.7045395908 0.3540729499 -0.180798116767 +1403637215088318976.0000000000 0.0706769574 7.0085651104 0.3909365127 0.5894894522 0.7029971579 0.3537129715 -0.182165626728 +1403637215138319104.0000000000 0.0152933640 7.0062386073 0.4005749559 0.5911287581 0.7016794574 0.3529045122 -0.183496963505 +1403637215188318976.0000000000 -0.0407357552 6.9998364718 0.4089296015 0.5924492189 0.7008243425 0.3514654829 -0.185259758688 +1403637215238319104.0000000000 -0.0975768495 6.9894615031 0.4162453513 0.5926082367 0.7008551653 0.3490265093 -0.189203622942 +1403637215288318976.0000000000 -0.1543737457 6.9749217152 0.4219428452 0.5920019076 0.7006823678 0.3479976634 -0.193586123022 +1403637215338319104.0000000000 -0.2108135776 6.9559888669 0.4265186955 0.5915909481 0.6995901897 0.3468839382 -0.200662029636 +1403637215388318976.0000000000 -0.2666536526 6.9330324170 0.4298827944 0.5917350188 0.6972305623 0.3469803821 -0.208143760139 +1403637215438319104.0000000000 -0.3217756217 6.9054634643 0.4331987091 0.5917851410 0.6938545743 0.3465933370 -0.219611555674 +1403637215488318976.0000000000 -0.3751820070 6.8737544190 0.4372213942 0.5924227059 0.6889730642 0.3478178159 -0.231028615567 +1403637215538319104.0000000000 -0.4261059591 6.8376151717 0.4414253104 0.5919355107 0.6841194313 0.3513871039 -0.241081019706 +1403637215588318976.0000000000 -0.4742605812 6.7974724704 0.4458597917 0.5893583270 0.6802577775 0.3570635045 -0.249823482118 +1403637215638319104.0000000000 -0.5197806199 6.7528111829 0.4518914037 0.5848363830 0.6768833583 0.3645660267 -0.25862508884 +1403637215688318976.0000000000 -0.5622617229 6.7044301259 0.4591995384 0.5799965742 0.6729225012 0.3747850057 -0.265170663407 +1403637215738319104.0000000000 -0.6016904389 6.6522815265 0.4669777419 0.5711326043 0.6717791872 0.3863743405 -0.270619919924 +1403637215788318976.0000000000 -0.6391068483 6.5972993082 0.4762445603 0.5609372629 0.6711582805 0.3982784531 -0.276170641936 +1403637215838319104.0000000000 -0.6736019261 6.5389092966 0.4869539676 0.5507723745 0.6702165968 0.4100424550 -0.281646391713 +1403637215888318976.0000000000 -0.7064520765 6.4786052011 0.4997418621 0.5417085445 0.6685705516 0.4203784747 -0.287831909991 +1403637215938319104.0000000000 -0.7379082903 6.4167646783 0.5145683874 0.5332972717 0.6672473701 0.4285546306 -0.294475628427 +1403637215988318976.0000000000 -0.7668903538 6.3531859879 0.5310121151 0.5251947468 0.6662776947 0.4360337188 -0.300198446973 +1403637216038319104.0000000000 -0.7945977821 6.2884637136 0.5494021161 0.5184921413 0.6641291197 0.4418641275 -0.307984584905 +1403637216088318976.0000000000 -0.8207951280 6.2230215921 0.5686220277 0.5119243989 0.6616970601 0.4483611341 -0.314742281732 +1403637216138319104.0000000000 -0.8453762133 6.1571513239 0.5872355688 0.5061674005 0.6591040202 0.4539127411 -0.321464891862 +1403637216188318976.0000000000 -0.8687033539 6.0914319038 0.6049046861 0.5022479285 0.6559929188 0.4581523592 -0.327897430019 +1403637216238319104.0000000000 -0.8905316039 6.0263730819 0.6207152465 0.4981009942 0.6542863224 0.4612197383 -0.333288405075 +1403637216288318976.0000000000 -0.9107535876 5.9616523637 0.6353509604 0.4958009612 0.6521736608 0.4627076525 -0.338751459449 +1403637216338319104.0000000000 -0.9296413775 5.8975898158 0.6480611797 0.4949802425 0.6500303684 0.4638498903 -0.342488480113 +1403637216388318976.0000000000 -0.9473744525 5.8337385206 0.6596416518 0.4957398061 0.6474239201 0.4636717966 -0.346544048149 +1403637216438319104.0000000000 -0.9630905546 5.7698336944 0.6695857822 0.4981150988 0.6442781152 0.4628591353 -0.35006924959 +1403637216488318976.0000000000 -0.9767531608 5.7062250814 0.6777132538 0.5003709892 0.6417006936 0.4624242099 -0.352154714662 +1403637216538319104.0000000000 -0.9885624292 5.6429006259 0.6847094399 0.5029415337 0.6395173217 0.4607802663 -0.354610991266 +1403637216588318976.0000000000 -0.9979163259 5.5796830723 0.6903236413 0.5030964673 0.6391609819 0.4587872693 -0.357605124748 +1403637216638319104.0000000000 -1.0049703800 5.5167251147 0.6954105144 0.5038648616 0.6387160007 0.4562845085 -0.360508694748 +1403637216688318976.0000000000 -1.0091634503 5.4537127259 0.6997639046 0.5053976611 0.6380422537 0.4524682450 -0.364345679142 +1403637216738319104.0000000000 -1.0102415234 5.3906480768 0.7029561978 0.5083355086 0.6364275104 0.4490688214 -0.367276773427 +1403637216788318976.0000000000 -1.0083950186 5.3280088773 0.7056489046 0.5117508227 0.6347277750 0.4462222188 -0.368941023099 +1403637216838319104.0000000000 -1.0031532027 5.2657802593 0.7093283859 0.5156714255 0.6327060592 0.4443059994 -0.369267115267 +1403637216888318976.0000000000 -0.9944472715 5.2037020443 0.7144256766 0.5194746504 0.6308855841 0.4427696558 -0.368896325933 +1403637216938319104.0000000000 -0.9817098958 5.1416496332 0.7213432416 0.5225229958 0.6298865323 0.4419689153 -0.367254888512 +1403637216988318976.0000000000 -0.9648709177 5.0791020865 0.7300173677 0.5226633896 0.6311547985 0.4416199089 -0.365292290611 +1403637217038319104.0000000000 -0.9434199737 5.0154860822 0.7391255207 0.5187541599 0.6351822514 0.4410968454 -0.364515023088 +1403637217088318976.0000000000 -0.9185112530 4.9513849582 0.7487873758 0.5119809155 0.6411562455 0.4393647927 -0.365722285325 +1403637217138319104.0000000000 -0.8903906482 4.8869365748 0.7580431198 0.5060024239 0.6465173127 0.4373419244 -0.367027182325 +1403637217188318976.0000000000 -0.8594735011 4.8230861367 0.7664534141 0.5006011807 0.6512800220 0.4338737563 -0.370116676902 +1403637217238319104.0000000000 -0.8258102048 4.7601447796 0.7732635413 0.4964182480 0.6551070448 0.4299892380 -0.373514307897 +1403637217288318976.0000000000 -0.7894190595 4.6989305673 0.7775846172 0.4934745384 0.6581743691 0.4275394678 -0.374832473688 +1403637217338319104.0000000000 -0.7505490632 4.6396134205 0.7795788287 0.4906298000 0.6611246383 0.4252541074 -0.375972813012 +1403637217388318976.0000000000 -0.7091422034 4.5823712857 0.7795371271 0.4889040060 0.6632582652 0.4227913587 -0.377238404102 +1403637217438319104.0000000000 -0.6650802884 4.5273026690 0.7774846542 0.4875450766 0.6652261159 0.4207799849 -0.37778064705 +1403637217488318976.0000000000 -0.6181994317 4.4740934540 0.7736749612 0.4867575018 0.6662302044 0.4198385319 -0.378074141294 +1403637217538319104.0000000000 -0.5689827773 4.4246791520 0.7681588062 0.4880211322 0.6646918743 0.4204921457 -0.378426270439 +1403637217588318976.0000000000 -0.5170516485 4.3765293584 0.7619239794 0.4900756761 0.6612613109 0.4231347038 -0.378835495654 +1403637217638319104.0000000000 -0.4619808409 4.3307304339 0.7541308252 0.4936314074 0.6557090870 0.4284211339 -0.377927187246 +1403637217688318976.0000000000 -0.4045264943 4.2861132260 0.7457562198 0.5001993249 0.6464187556 0.4366909419 -0.37582502438 +1403637217738319104.0000000000 -0.3439411881 4.2428059274 0.7374172303 0.5059597254 0.6358829879 0.4475602788 -0.373292618179 +1403637217788318976.0000000000 -0.2798786847 4.1988103725 0.7310112613 0.5103151197 0.6245483911 0.4590783223 -0.37251158347 +1403637217838319104.0000000000 -0.2126712063 4.1535761667 0.7255447623 0.5082389076 0.6163767359 0.4713399716 -0.373646307877 +1403637217888318976.0000000000 -0.1425507650 4.1080085780 0.7217181024 0.5066585878 0.6073729374 0.4831993192 -0.375384613644 +1403637217938319104.0000000000 -0.0696783590 4.0615618627 0.7196138463 0.5022586062 0.6016102680 0.4929208111 -0.37792916256 +1403637217988318976.0000000000 0.0057903424 4.0143723189 0.7190373610 0.4971434175 0.5967410587 0.5018001783 -0.380716577354 +1403637218038319104.0000000000 0.0845824967 3.9681278202 0.7195551797 0.4918256224 0.5931122960 0.5086876995 -0.384138238023 +1403637218088318976.0000000000 0.1647550263 3.9205385666 0.7210182607 0.4850334106 0.5916497951 0.5149276128 -0.386707465933 +1403637218138319104.0000000000 0.2468887813 3.8728487752 0.7226004121 0.4807698478 0.5892726583 0.5199584721 -0.388923224938 +1403637218188318976.0000000000 0.3307478111 3.8250001670 0.7228731227 0.4768212808 0.5876843334 0.5242119226 -0.390474647923 +1403637218238319104.0000000000 0.4155799338 3.7769818333 0.7214452495 0.4739719801 0.5862729893 0.5278011327 -0.391229482992 +1403637218288318976.0000000000 0.5014068409 3.7285942358 0.7187037434 0.4718162220 0.5849478050 0.5301594691 -0.392627629435 +1403637218338319104.0000000000 0.5882147938 3.6804652021 0.7140889461 0.4719801597 0.5827961832 0.5326824067 -0.392215235875 +1403637218388318976.0000000000 0.6765860824 3.6317471108 0.7083508605 0.4709036866 0.5821698582 0.5332741840 -0.393632593699 +1403637218438319104.0000000000 0.7667574636 3.5828034090 0.7013618079 0.4701818653 0.5818066177 0.5336743666 -0.394489218561 +1403637218488318976.0000000000 0.8583581368 3.5336589474 0.6943754519 0.4709585391 0.5807467727 0.5338931414 -0.394828258812 +1403637218538319104.0000000000 0.9517660571 3.4840164658 0.6875668102 0.4708565106 0.5805503299 0.5344160846 -0.394531252749 +1403637218588318976.0000000000 1.0456618557 3.4341639214 0.6820680550 0.4713510020 0.5805334758 0.5344031569 -0.393982718237 +1403637218638319104.0000000000 1.1436107742 3.3702974566 0.6870842563 0.4695863260 0.5825314162 0.5350056315 -0.392319774952 +1403637218688318976.0000000000 1.2386098073 3.3160395496 0.6866553028 0.4693240950 0.5835072129 0.5362437830 -0.389482774397 +1403637218738319104.0000000000 1.3354945929 3.2602845487 0.6876896152 0.4660463163 0.5867289887 0.5364847935 -0.388244756919 +1403637218788318976.0000000000 1.4331381706 3.2037396676 0.6882309991 0.4650240761 0.5884880516 0.5359797987 -0.387504938213 +1403637218838319104.0000000000 1.5315955962 3.1470889505 0.6843626647 0.4662514059 0.5885696806 0.5380545897 -0.383004720617 +1403637218888318976.0000000000 1.6296692855 3.0900304260 0.6762923932 0.4678974002 0.5883726104 0.5403081355 -0.378096301191 +1403637218938319104.0000000000 1.7283521398 3.0323845276 0.6641762992 0.4705206443 0.5870115469 0.5417095787 -0.374937994289 +1403637218988318976.0000000000 1.8276287425 2.9743768240 0.6482508380 0.4728356607 0.5858845100 0.5437919651 -0.370750694771 +1403637219038319104.0000000000 1.9267471875 2.9157914607 0.6303172366 0.4746694631 0.5850160663 0.5451653461 -0.367749708963 +1403637219088318976.0000000000 2.0261127923 2.8561942842 0.6110316445 0.4755137416 0.5847026569 0.5457111402 -0.36634524149 +1403637219138319104.0000000000 2.1258612799 2.7954064093 0.5924123306 0.4762662612 0.5842518162 0.5457312197 -0.366056962104 +1403637219188318976.0000000000 2.2258934994 2.7336337885 0.5745351410 0.4758572075 0.5848551445 0.5457974308 -0.365526391015 +1403637219238319104.0000000000 2.3262860139 2.6705894511 0.5585686356 0.4751985558 0.5858057467 0.5450383186 -0.365993430181 +1403637219288318976.0000000000 2.4281936712 2.6062326636 0.5440856570 0.4737662193 0.5872158238 0.5448323147 -0.365897382523 +1403637219338319104.0000000000 2.5309092007 2.5408267685 0.5314970322 0.4725205459 0.5886356566 0.5436153787 -0.367035035699 +1403637219388318976.0000000000 2.6336698927 2.4745718598 0.5197172720 0.4708895981 0.5903505917 0.5440001910 -0.365804534396 +1403637219438319104.0000000000 2.7360572067 2.4069673158 0.5099392058 0.4690772490 0.5918687608 0.5438583486 -0.365890695533 +1403637219488318976.0000000000 2.8387036390 2.3381302356 0.5010796587 0.4623206050 0.5971368311 0.5457679842 -0.363076535312 +1403637219538319104.0000000000 2.9408349999 2.2683260904 0.4950594939 0.4575014010 0.6010260589 0.5474296901 -0.360251133116 +1403637219588318976.0000000000 3.0429439086 2.1979442819 0.4899172838 0.4512800244 0.6059196669 0.5494284323 -0.356841834078 +1403637219638319104.0000000000 3.1433591197 2.1272722723 0.4865101110 0.4464641382 0.6097813181 0.5505507259 -0.354584849627 +1403637219688318976.0000000000 3.2413623623 2.0555250169 0.4849269143 0.4428178658 0.6127977736 0.5518056342 -0.351996830102 +1403637219738319104.0000000000 3.3380113247 1.9836029865 0.4850096974 0.4409196193 0.6144841108 0.5520357463 -0.351077913966 +1403637219788318976.0000000000 3.4325999152 1.9116211837 0.4870777747 0.4387514831 0.6164812050 0.5521664199 -0.350086138844 +1403637219838319104.0000000000 3.5235420248 1.8387948183 0.4914099356 0.4374993122 0.6174952796 0.5532905881 -0.348085415727 +1403637219888318976.0000000000 3.6126947117 1.7663082193 0.4971069440 0.4349327263 0.6192309582 0.5539617183 -0.347149764009 +1403637219938319104.0000000000 3.6989351713 1.6940921647 0.5051883699 0.4347591750 0.6194957280 0.5535246287 -0.347591697452 +1403637219988318976.0000000000 3.7837560709 1.6219754242 0.5153147159 0.4347391103 0.6195455177 0.5534929280 -0.347578532416 +1403637220038319104.0000000000 3.8662028965 1.5499551834 0.5275762597 0.4338114057 0.6201111329 0.5536980002 -0.347402319509 +1403637220088318976.0000000000 3.9461498846 1.4782675477 0.5416901816 0.4329335617 0.6209499954 0.5534652043 -0.34736997841 +1403637220138319104.0000000000 4.0246824560 1.4070267743 0.5574973030 0.4341726619 0.6202065377 0.5543326158 -0.345764806406 +1403637220188318976.0000000000 4.1013867349 1.3354087609 0.5748047227 0.4324197083 0.6212269587 0.5536706544 -0.347187367545 +1403637220238319104.0000000000 4.1762412288 1.2639480850 0.5938796237 0.4316155219 0.6219726464 0.5523785607 -0.348906855844 +1403637220288318976.0000000000 4.2491674596 1.1927000243 0.6153246890 0.4307048665 0.6230178638 0.5494647864 -0.35274708777 +1403637220338319104.0000000000 4.3200928675 1.1219278923 0.6392744543 0.4295625367 0.6241141896 0.5463247409 -0.357052913375 +1403637220388318976.0000000000 4.3898480856 1.0517523642 0.6650620463 0.4280040049 0.6256709596 0.5422172331 -0.362420879898 +1403637220438319104.0000000000 4.4581112197 0.9828461987 0.6901326385 0.4277373389 0.6264264164 0.5388194439 -0.366475538731 +1403637220488318976.0000000000 4.5247259661 0.9150884962 0.7138064361 0.4272515980 0.6272344852 0.5363179379 -0.369318347972 +1403637220538319104.0000000000 4.5892452761 0.8486310846 0.7365875678 0.4275588494 0.6273638445 0.5333276172 -0.37305453975 +1403637220588318976.0000000000 4.6514759540 0.7834476344 0.7578680774 0.4276850671 0.6278066079 0.5306074392 -0.376032035799 +1403637220638319104.0000000000 4.7127517393 0.7197594858 0.7768497927 0.4284335930 0.6274619526 0.5309285976 -0.375301183876 +1403637220688318976.0000000000 4.7733324863 0.6571681318 0.7943278213 0.4276535697 0.6281613288 0.5310045195 -0.374913282736 +1403637220738319104.0000000000 4.8293637124 0.5953162321 0.8114223846 0.4283210811 0.6278984657 0.5315621068 -0.3737998058 +1403637220788318976.0000000000 4.8856889129 0.5349693961 0.8268390460 0.4278803832 0.6284081272 0.5319452441 -0.37290194515 +1403637220838319104.0000000000 4.9407261030 0.4760120832 0.8411589926 0.4272994831 0.6287929231 0.5323287343 -0.372371763489 +1403637220888318976.0000000000 4.9942337669 0.4189071534 0.8541010578 0.4274106709 0.6289770058 0.5327989284 -0.37125913662 +1403637220938319104.0000000000 5.0469935589 0.3631106892 0.8653818732 0.4266625966 0.6296911176 0.5330233174 -0.370586384313 +1403637220988318976.0000000000 5.0991930010 0.3089723445 0.8749416885 0.4264084088 0.6308742671 0.5326342471 -0.369424264012 +1403637221038319104.0000000000 5.1508763268 0.2563743597 0.8824588921 0.4259606913 0.6331170909 0.5327624146 -0.365902238671 +1403637221088318976.0000000000 5.2013550507 0.2051800379 0.8889824471 0.4265621801 0.6359369237 0.5307431569 -0.36323633761 +1403637221138319104.0000000000 5.2507974576 0.1556392131 0.8936471589 0.4268881307 0.6397641652 0.5288078154 -0.358929841634 +1403637221188318976.0000000000 5.2990623107 0.1079231149 0.8970442379 0.4287589405 0.6435723350 0.5258679799 -0.354179740197 +1403637221238319104.0000000000 5.3461326918 0.0618534290 0.8990303104 0.4312421161 0.6478372194 0.5218960521 -0.349230132229 +1403637221288318976.0000000000 5.3918475644 0.0172025045 0.8996817557 0.4344571156 0.6518268578 0.5174808213 -0.344357897926 +1403637221338319104.0000000000 5.4366096947 -0.0264275318 0.8990131951 0.4369079729 0.6559817029 0.5123717502 -0.340990642467 +1403637221388318976.0000000000 5.4803569259 -0.0692635546 0.8968275850 0.4387455833 0.6596218877 0.5082689993 -0.337733478715 +1403637221438319104.0000000000 5.5229688934 -0.1111540409 0.8937141965 0.4413815675 0.6622144449 0.5035893845 -0.336232170824 +1403637221488318976.0000000000 5.5647388258 -0.1519588031 0.8886969341 0.4425593760 0.6650756260 0.5007015261 -0.333337054878 +1403637221538319104.0000000000 5.6051309489 -0.1918233317 0.8828468075 0.4424354941 0.6682436423 0.4971731806 -0.332445629447 +1403637221588318976.0000000000 5.6442440201 -0.2302120318 0.8757795754 0.4432446047 0.6704848292 0.4948064044 -0.330379987805 +1403637221638319104.0000000000 5.6816458395 -0.2672032034 0.8675714615 0.4444240120 0.6721753481 0.4928092927 -0.328339154057 +1403637221688318976.0000000000 5.7174552034 -0.3032012713 0.8581893249 0.4441487160 0.6745238822 0.4909125248 -0.326732831978 +1403637221738319104.0000000000 5.7508374782 -0.3379489480 0.8483488750 0.4447326787 0.6760159071 0.4890139468 -0.325700318814 +1403637221788318976.0000000000 5.7816950038 -0.3714396913 0.8373511111 0.4449181400 0.6775174288 0.4871620096 -0.325101766704 +1403637221838319104.0000000000 5.8106614988 -0.4032037686 0.8252557064 0.4450712100 0.6796174349 0.4851095321 -0.323574569626 +1403637221888318976.0000000000 5.8375651247 -0.4332754405 0.8123390096 0.4453348816 0.6824072586 0.4819345284 -0.322081180563 +1403637221938319104.0000000000 5.8624791557 -0.4615535267 0.7984245511 0.4458543753 0.6863263827 0.4773616778 -0.319837147728 +1403637221988318976.0000000000 5.8856324295 -0.4877716521 0.7834133078 0.4484527471 0.6898808263 0.4725079679 -0.315738498337 +1403637222038319104.0000000000 5.9073872706 -0.5121499132 0.7675111513 0.4515279311 0.6944501907 0.4657872853 -0.311293535043 +1403637222088318976.0000000000 5.9276842433 -0.5346425967 0.7502857444 0.4545370840 0.6998709535 0.4586681180 -0.305287152211 +1403637222138319104.0000000000 5.9467367713 -0.5556565514 0.7325011641 0.4580291160 0.7053571308 0.4504988035 -0.299552123925 +1403637222188318976.0000000000 5.9646479346 -0.5749777688 0.7141269029 0.4620510057 0.7109046880 0.4417500628 -0.293223932776 +1403637222238319104.0000000000 5.9812959166 -0.5930103673 0.6954033129 0.4676843101 0.7147293855 0.4325721202 -0.288642776623 +1403637222288318976.0000000000 5.9967529041 -0.6097651262 0.6757774898 0.4737263873 0.7170708019 0.4251487592 -0.283974131671 +1403637222338319104.0000000000 6.0112392638 -0.6255979202 0.6554627065 0.4805712303 0.7179242527 0.4170564487 -0.28231184631 +1403637222388318976.0000000000 6.0249359611 -0.6404331942 0.6348811598 0.4873739492 0.7181490244 0.4094301713 -0.281239306001 +1403637222438319104.0000000000 6.0378256274 -0.6542912166 0.6151284641 0.4937810144 0.7177752484 0.4029581799 -0.280363527809 +1403637222488318976.0000000000 6.0505033538 -0.6675600350 0.5975056224 0.4995741836 0.7169679667 0.3981386367 -0.27904873366 +1403637222538319104.0000000000 6.0633402266 -0.6806835856 0.5811639303 0.5023002932 0.7176786397 0.3936690522 -0.278669092274 +1403637222588318976.0000000000 6.0763568692 -0.6934580976 0.5666161865 0.5042649926 0.7183911405 0.3906969785 -0.27746505642 +1403637222638319104.0000000000 6.0894291921 -0.7054570574 0.5537095352 0.5069535124 0.7181805620 0.3886892633 -0.27592657212 +1403637222688318976.0000000000 6.1028334966 -0.7172019954 0.5423735770 0.5075549378 0.7188158402 0.3882148795 -0.273826551345 +1403637222738319104.0000000000 6.1159613883 -0.7285729491 0.5330171687 0.5066130115 0.7202262977 0.3874920037 -0.272886943176 +1403637222788318976.0000000000 6.1290897081 -0.7394292214 0.5253816794 0.5045889270 0.7220954635 0.3883419788 -0.270478583102 +1403637222838319104.0000000000 6.1418756184 -0.7498759289 0.5196308811 0.5013641726 0.7243738292 0.3896870304 -0.268440943936 +1403637222888318976.0000000000 6.1542582039 -0.7597990159 0.5161326270 0.4972431573 0.7270739641 0.3912214102 -0.266568005132 +1403637222938319104.0000000000 6.1659319885 -0.7688719603 0.5148196779 0.4926257236 0.7298199186 0.3934718277 -0.264315538002 +1403637222988318976.0000000000 6.1767803310 -0.7767786560 0.5155631458 0.4892095402 0.7317627320 0.3953769180 -0.26243936912 +1403637223038319104.0000000000 6.1863481285 -0.7837806561 0.5182565803 0.4863230868 0.7331861501 0.3968169639 -0.261656686783 +1403637223088318976.0000000000 6.1947439422 -0.7895163786 0.5229940058 0.4842450779 0.7339483287 0.3984524622 -0.26088731412 +1403637223138319104.0000000000 6.2016088983 -0.7939608806 0.5297602787 0.4836644663 0.7337453259 0.3996551677 -0.260695661063 +1403637223188318976.0000000000 6.2070358836 -0.7972534169 0.5389884224 0.4836872811 0.7330123177 0.4005279541 -0.261375045183 +1403637223238319104.0000000000 6.2106179163 -0.7990125057 0.5503421646 0.4851346636 0.7313779921 0.4012337112 -0.262187146648 +1403637223288318976.0000000000 6.2128297571 -0.7996830683 0.5641233392 0.4881891155 0.7285441416 0.4016240346 -0.263804768797 +1403637223338319104.0000000000 6.2138016122 -0.7994853210 0.5798499323 0.4917308252 0.7252030554 0.4018051645 -0.26614645168 +1403637223388318976.0000000000 6.2138127351 -0.7985142512 0.5969074916 0.4951305811 0.7220448405 0.4023771063 -0.267562367039 +1403637223438319104.0000000000 6.2127961791 -0.7970462242 0.6158178085 0.4977928736 0.7193518477 0.4024079478 -0.269820343589 +1403637223488318976.0000000000 6.2110273684 -0.7950158614 0.6362243407 0.4999033847 0.7170841060 0.4028787481 -0.271248419783 +1403637223538319104.0000000000 6.2088022334 -0.7925493865 0.6569773712 0.5020773746 0.7149903005 0.4031515327 -0.272352752727 +1403637223588318976.0000000000 6.2062558909 -0.7899084158 0.6770090169 0.5037055214 0.7134076054 0.4032053666 -0.273415011538 +1403637223638319104.0000000000 6.2035194473 -0.7871542605 0.6954650916 0.5051440700 0.7120664311 0.4033479606 -0.274046143735 +1403637223688318976.0000000000 6.2006915558 -0.7843481583 0.7122696010 0.5058310707 0.7112900881 0.4034582972 -0.274632009804 +1403637223738319104.0000000000 6.1979189953 -0.7814457872 0.7269988688 0.5063739695 0.7106406278 0.4041171805 -0.274343954979 +1403637223788318976.0000000000 6.1947554203 -0.7785985182 0.7403356106 0.5070049429 0.7100424737 0.4038707652 -0.27508921894 +1403637223838319104.0000000000 6.1912655919 -0.7757580222 0.7518417087 0.5075715957 0.7095024438 0.4040053810 -0.275239912642 +1403637223888318976.0000000000 6.1877713954 -0.7728700810 0.7618358954 0.5085121426 0.7087721898 0.4040621483 -0.275301950834 +1403637223938319104.0000000000 6.1840989580 -0.7699726462 0.7697630278 0.5093560604 0.7080939497 0.4047405567 -0.274489423859 +1403637223988318976.0000000000 6.1805255853 -0.7673410097 0.7761522804 0.5094362298 0.7080922791 0.4043015199 -0.274991514638 +1403637224038319104.0000000000 6.1774003971 -0.7649434318 0.7808755963 0.5097722640 0.7079933109 0.4039455510 -0.275146692576 +1403637224088318976.0000000000 6.1742584598 -0.7627959981 0.7838201953 0.5095712081 0.7080979955 0.4040636214 -0.275076357472 +1403637224138319104.0000000000 6.1708860705 -0.7606317870 0.7852259226 0.5105952534 0.7074696855 0.4043207926 -0.274415429578 +1403637224188318976.0000000000 6.1674309976 -0.7588368484 0.7848598268 0.5107805018 0.7073781675 0.4041993024 -0.2744855751 +1403637224238319104.0000000000 6.1638321276 -0.7572144133 0.7827611461 0.5116770381 0.7068137955 0.4044534041 -0.273894707958 +1403637224288318976.0000000000 6.1604424401 -0.7559075345 0.7792427529 0.5125653725 0.7062403638 0.4042983278 -0.273941872568 +1403637224338319104.0000000000 6.1571300664 -0.7550909324 0.7744238938 0.5127818881 0.7060740976 0.4040325812 -0.274357025147 +1403637224388318976.0000000000 6.1537940104 -0.7545870490 0.7680680560 0.5130288332 0.7058852225 0.4044919243 -0.273703767136 +1403637224438319104.0000000000 6.1505510222 -0.7543081570 0.7602718038 0.5137756371 0.7055144685 0.4048838098 -0.272677520301 +1403637224488318976.0000000000 6.1471409246 -0.7545686223 0.7511692625 0.5141329713 0.7052034422 0.4051582392 -0.272400796714 +1403637224538319104.0000000000 6.1436158113 -0.7551272218 0.7408817225 0.5150460637 0.7046082800 0.4051670443 -0.27220284762 +1403637224588318976.0000000000 6.1396428833 -0.7562002296 0.7303600278 0.5148855778 0.7047953778 0.4045453149 -0.272945791999 +1403637224638319104.0000000000 6.1357414971 -0.7580410551 0.7211626055 0.5140327299 0.7053432830 0.4031869919 -0.275138974497 +1403637224688318976.0000000000 6.1318341091 -0.7604084641 0.7139986949 0.5124674234 0.7064611756 0.4006816664 -0.278826020075 +1403637224738319104.0000000000 6.1283851150 -0.7629998045 0.7074817541 0.5094714072 0.7085885990 0.3988398064 -0.281545540673 +1403637224788318976.0000000000 6.1255451076 -0.7653910708 0.7022938310 0.5084502208 0.7093173918 0.3982632742 -0.282371342413 +1403637224838319104.0000000000 6.1240069315 -0.7675981672 0.6985774465 0.5082399670 0.7095679902 0.3984477953 -0.281859464251 +1403637224888318976.0000000000 6.1229604085 -0.7693916389 0.6958832829 0.5102834673 0.7081299855 0.3993211564 -0.280544685629 +1403637224938319104.0000000000 6.1221135763 -0.7710157698 0.6921479630 0.5123732940 0.7067733801 0.4007227132 -0.278147989144 +1403637224988318976.0000000000 6.1213606633 -0.7730341086 0.6868526108 0.5136544392 0.7058601516 0.4017629933 -0.276599097435 +1403637225038319104.0000000000 6.1209067490 -0.7754730058 0.6801397011 0.5142660382 0.7053803975 0.4024557524 -0.275677899402 +1403637225088318976.0000000000 6.1205505545 -0.7782840472 0.6721653762 0.5150908159 0.7047914530 0.4033584010 -0.274321817291 +1403637225138319104.0000000000 6.1199621559 -0.7814348038 0.6633455933 0.5165536672 0.7036108171 0.4035955260 -0.27425312819 +1403637225188318976.0000000000 6.1197223852 -0.7851953575 0.6528720244 0.5169302817 0.7032293964 0.4037146388 -0.274346478615 +1403637225238319104.0000000000 6.1194115916 -0.7893032441 0.6409489053 0.5175545139 0.7024920971 0.4041174973 -0.274465347498 +1403637225288318976.0000000000 6.1190748594 -0.7941016402 0.6284745183 0.5169843184 0.7025802324 0.4040874458 -0.275357163854 +1403637225338319104.0000000000 6.1187883540 -0.7992727896 0.6163400706 0.5179477145 0.7017010683 0.4043302962 -0.275432001486 +1403637225388318976.0000000000 6.1183120342 -0.8049341134 0.6060376110 0.5185709472 0.7010105235 0.4044384771 -0.275858544968 +1403637225438319104.0000000000 6.1191453095 -0.8115135118 0.5977378881 0.5194363828 0.6999873782 0.4045744954 -0.276627894836 +1403637225488318976.0000000000 6.1212394692 -0.8191906012 0.5908938696 0.5198444851 0.6994879526 0.4047069843 -0.276930627274 +1403637225538319104.0000000000 6.1236893958 -0.8277224916 0.5861046096 0.5197916757 0.6991682572 0.4055696054 -0.276574867155 +1403637225588318976.0000000000 6.1265659548 -0.8369936895 0.5830626827 0.5186235914 0.6996377431 0.4063721424 -0.276402389154 +1403637225638319104.0000000000 6.1298643344 -0.8469329531 0.5820212166 0.5175985776 0.7001233145 0.4075868111 -0.275303556795 +1403637225688318976.0000000000 6.1328258357 -0.8574005518 0.5831964698 0.5143870810 0.7023124170 0.4086151065 -0.274220521771 +1403637225738319104.0000000000 6.1364363666 -0.8684573882 0.5853390020 0.5132326244 0.7029480470 0.4098522049 -0.272905636768 +1403637225788318976.0000000000 6.1391559926 -0.8796819746 0.5897213649 0.5105746823 0.7047660730 0.4111914146 -0.271182404877 +1403637225838319104.0000000000 6.1415629964 -0.8915125722 0.5963985823 0.5077462108 0.7067401598 0.4118577087 -0.270343040717 +1403637225888318976.0000000000 6.1431032695 -0.9034168547 0.6059404731 0.5058910095 0.7078538513 0.4128709781 -0.26935992117 +1403637225938319104.0000000000 6.1439191092 -0.9155890755 0.6181046132 0.5074206126 0.7065052655 0.4124331488 -0.27069083754 +1403637225988318976.0000000000 6.1446595850 -0.9282172395 0.6317579254 0.5100570892 0.7046270813 0.4112612675 -0.272408905732 +1403637226038319104.0000000000 6.1444620870 -0.9409069804 0.6474944651 0.5129356763 0.7024038228 0.4099720452 -0.274679420093 +1403637226088318976.0000000000 6.1444581748 -0.9538158364 0.6627298431 0.5149284152 0.7009058451 0.4092340620 -0.275875345193 +1403637226138319104.0000000000 6.1445015684 -0.9673389328 0.6763665930 0.5170196005 0.6993624492 0.4081621790 -0.277464471528 +1403637226188318976.0000000000 6.1448093486 -0.9813771462 0.6881503182 0.5181253496 0.6986300148 0.4076302794 -0.278028379457 +1403637226238319104.0000000000 6.1456264870 -0.9961206644 0.6985663295 0.5190360593 0.6979168949 0.4073347635 -0.278553347432 +1403637226288318976.0000000000 6.1471173970 -1.0113722871 0.7071749971 0.5186798622 0.6982385207 0.4080229409 -0.277401240836 +1403637226338319104.0000000000 6.1491196690 -1.0271924267 0.7141868600 0.5162528628 0.6999805518 0.4093913523 -0.275515751664 +1403637226388318976.0000000000 6.1513814947 -1.0435995130 0.7200685329 0.5131691738 0.7021456727 0.4113804942 -0.272791023109 +1403637226438319104.0000000000 6.1536067595 -1.0605833091 0.7245886721 0.5083713071 0.7055785581 0.4137394766 -0.269327232225 +1403637226488318976.0000000000 6.1554591790 -1.0779562278 0.7283509013 0.5041649027 0.7084915088 0.4152913667 -0.267190219777 +1403637226538319104.0000000000 6.1567860395 -1.0954402848 0.7314126306 0.5017692528 0.7100498417 0.4169272758 -0.265006577131 +1403637226588318976.0000000000 6.1571445745 -1.1129689095 0.7337103255 0.4997506126 0.7113510162 0.4186408208 -0.26261934458 +1403637226638319104.0000000000 6.1563491370 -1.1306331412 0.7353519399 0.4986385283 0.7120435681 0.4193041265 -0.261796914988 +1403637226688318976.0000000000 6.1547135910 -1.1484408022 0.7359081669 0.4977225671 0.7127163361 0.4193132496 -0.261694610475 +1403637226738319104.0000000000 6.1520510396 -1.1664372888 0.7351661828 0.4964853270 0.7135245257 0.4191171455 -0.262156231413 +1403637226788318976.0000000000 6.1484186221 -1.1841543725 0.7333895459 0.4957650563 0.7138039048 0.4191757581 -0.262664573764 +1403637226838319104.0000000000 6.1438904569 -1.2016272238 0.7304613566 0.4961029055 0.7136002577 0.4189909315 -0.262874834507 +1403637226888318976.0000000000 6.1380353538 -1.2191948560 0.7267489413 0.4953127897 0.7143229593 0.4175793021 -0.264642167403 +1403637226938319104.0000000000 6.1310015866 -1.2366520832 0.7227407045 0.4943348795 0.7153457657 0.4150472204 -0.267673807643 +1403637226988318976.0000000000 6.1226649898 -1.2536760200 0.7182894919 0.4934608725 0.7162709656 0.4117199998 -0.271917106707 +1403637227038319104.0000000000 6.1132702852 -1.2701377039 0.7138691758 0.4915689579 0.7178583772 0.4067870209 -0.27850247667 +1403637227088318976.0000000000 6.1037553485 -1.2857507985 0.7099119814 0.4899858908 0.7192914884 0.4017473060 -0.284837995541 +1403637227138319104.0000000000 6.0940247820 -1.3000274128 0.7073232655 0.4886863486 0.7205572378 0.3968468997 -0.290681024271 +1403637227188318976.0000000000 6.0847543666 -1.3126654611 0.7058889438 0.4885341490 0.7209528324 0.3949933700 -0.292475018293 +1403637227238319104.0000000000 6.0758478195 -1.3237093167 0.7064677439 0.4892276460 0.7207952295 0.3938904412 -0.293190838697 +1403637227288318976.0000000000 6.0679666087 -1.3332034915 0.7086237542 0.4919226646 0.7193362999 0.3957705742 -0.289711981695 +1403637227338319104.0000000000 6.0604927773 -1.3415051039 0.7129005445 0.4938000355 0.7184170954 0.3978186786 -0.285969755359 +1403637227388318976.0000000000 6.0528210381 -1.3485306683 0.7180512067 0.4960299649 0.7173569362 0.3994404316 -0.282490073472 +1403637227438319104.0000000000 6.0451051157 -1.3547420539 0.7223429874 0.4967670269 0.7171087516 0.4016749431 -0.278630220028 +1403637227488318976.0000000000 6.0370203141 -1.3602591742 0.7259330994 0.4972583058 0.7170745100 0.4023975670 -0.276793284711 +1403637227538319104.0000000000 6.0290881265 -1.3653348539 0.7279222239 0.4974190020 0.7175133886 0.4020965997 -0.275802824788 +1403637227588318976.0000000000 6.0211477748 -1.3700285522 0.7287081090 0.4962905653 0.7186894119 0.4013539219 -0.27585545755 +1403637227638319104.0000000000 6.0128782913 -1.3742257414 0.7283231299 0.4949678982 0.7199037432 0.3992383230 -0.278126125445 +1403637227688318976.0000000000 6.0043348333 -1.3774868723 0.7262757721 0.4933723843 0.7213454554 0.3980000109 -0.278998952957 +1403637227738319104.0000000000 5.9955340856 -1.3800050755 0.7233268614 0.4923026799 0.7222298053 0.3965431939 -0.280670046571 +1403637227788318976.0000000000 5.9866463846 -1.3816188280 0.7195231977 0.4910558931 0.7232778912 0.3950444794 -0.282264169349 +1403637227838319104.0000000000 5.9780835949 -1.3817252183 0.7145332972 0.4926977134 0.7224955784 0.3956225708 -0.280592023796 +1403637227888318976.0000000000 5.9693436501 -1.3809149001 0.7093081893 0.4964879350 0.7198676675 0.3951367170 -0.281348976433 +1403637227938319104.0000000000 5.9606590301 -1.3790314985 0.7030442292 0.5025979491 0.7157697694 0.3955410099 -0.280385891714 +1403637227988318976.0000000000 5.9521367693 -1.3768047533 0.6958068158 0.5075277946 0.7121888192 0.3960638749 -0.279885745619 +1403637228038319104.0000000000 5.9440494888 -1.3743762338 0.6879369304 0.5130090334 0.7081495712 0.3968791727 -0.278985373709 +1403637228088318976.0000000000 5.9364006701 -1.3725293374 0.6792050345 0.5154323242 0.7061451856 0.3973976728 -0.278861230101 +1403637228138319104.0000000000 5.9292143639 -1.3710275951 0.6706248701 0.5176998812 0.7040610016 0.3969297395 -0.280591733494 +1403637228188318976.0000000000 5.9227881030 -1.3699115587 0.6620530319 0.5188927340 0.7027692195 0.3974478388 -0.280893164906 +1403637228238319104.0000000000 5.9170634561 -1.3695061008 0.6550619875 0.5200808117 0.7013760614 0.3973038558 -0.282377789595 +1403637228288318976.0000000000 5.9121730535 -1.3695817157 0.6499237086 0.5208714393 0.7004603341 0.3981029948 -0.282067845722 +1403637228338319104.0000000000 5.9080040153 -1.3701564122 0.6468480064 0.5212655467 0.6998736689 0.3976452088 -0.283438468509 +1403637228388318976.0000000000 5.9048811744 -1.3710511517 0.6452089851 0.5219682156 0.6990185988 0.3995520834 -0.281567599519 +1403637228438319104.0000000000 5.9021363461 -1.3726535430 0.6452549776 0.5227663100 0.6981117041 0.4000626895 -0.281611928511 +1403637228488318976.0000000000 5.9003317281 -1.3750129247 0.6469607221 0.5242364024 0.6969173026 0.4009866520 -0.280521251774 +1403637228538319104.0000000000 5.8995019927 -1.3784263802 0.6502148371 0.5254844153 0.6955985717 0.4021417288 -0.279804907629 +1403637228588318976.0000000000 5.8995068234 -1.3826141469 0.6550863561 0.5269180386 0.6944173720 0.4032109438 -0.278501039193 +1403637228638319104.0000000000 5.8998451076 -1.3877886859 0.6617247124 0.5271791917 0.6939641296 0.4042283927 -0.277660391679 +1403637228688318976.0000000000 5.9010833102 -1.3941173864 0.6691351927 0.5247196148 0.6958162527 0.4050790629 -0.276441713748 +1403637228738319104.0000000000 5.9029190471 -1.4018175247 0.6760229599 0.5208554744 0.6987217755 0.4054762596 -0.275837738726 +1403637228788318976.0000000000 5.9049984755 -1.4104943289 0.6822335956 0.5159706507 0.7022450373 0.4052006728 -0.276475333344 +1403637228838319104.0000000000 5.9070810753 -1.4195536474 0.6871248353 0.5113549651 0.7057054743 0.4048844316 -0.276702873559 +1403637228888318976.0000000000 5.9092183460 -1.4287247332 0.6909779574 0.5077515622 0.7084165477 0.4041067130 -0.277546591637 +1403637228938319104.0000000000 5.9112373658 -1.4370535237 0.6937167253 0.5073761651 0.7089107877 0.4040800667 -0.277009425554 +1403637228988318976.0000000000 5.9134613830 -1.4454449545 0.6953953181 0.5094493690 0.7076566871 0.4051045016 -0.274906705098 +1403637229038319104.0000000000 5.9157020011 -1.4543036714 0.6962756013 0.5116541326 0.7061464553 0.4059431679 -0.273454524131 +1403637229088318976.0000000000 5.9178995700 -1.4632966651 0.6965217863 0.5149731101 0.7038187790 0.4058509332 -0.273362108402 +1403637229138319104.0000000000 5.9202426538 -1.4727572058 0.6960749886 0.5181768315 0.7015773166 0.4056976023 -0.273297449008 +1403637229188318976.0000000000 5.9229300046 -1.4828231319 0.6941686767 0.5203954462 0.6999340946 0.4062796232 -0.272429276189 +1403637229238319104.0000000000 5.9255295965 -1.4936117880 0.6911639271 0.5216551529 0.6992603759 0.4061551992 -0.271935254024 +1403637229288318976.0000000000 5.9282431155 -1.5049164359 0.6869637151 0.5224972302 0.6995312650 0.4055529812 -0.270516973885 +1403637229338319104.0000000000 5.9309625942 -1.5166861466 0.6813641222 0.5228356319 0.7011209963 0.4039055506 -0.268202454858 +1403637229388318976.0000000000 5.9335415240 -1.5288728265 0.6749903683 0.5203513984 0.7061101297 0.3996021324 -0.266385139849 +1403637229438319104.0000000000 5.9372911187 -1.5419531253 0.6668886948 0.5153132764 0.7138823245 0.3936354288 -0.26433956034 +1403637229488318976.0000000000 5.9412246360 -1.5552775708 0.6582442053 0.5093950926 0.7233959394 0.3847427345 -0.263036086211 +1403637229538319104.0000000000 5.9450514029 -1.5680474360 0.6497427141 0.5037688885 0.7334112643 0.3738000757 -0.261912824842 +1403637229588318976.0000000000 5.9486954529 -1.5794862324 0.6403981499 0.4993515466 0.7432401526 0.3619363557 -0.259314833487 +1403637229638319104.0000000000 5.9522489163 -1.5889539020 0.6306704914 0.4964355920 0.7526340731 0.3487450310 -0.255872152409 +1403637229688318976.0000000000 5.9558773404 -1.5962807669 0.6201299084 0.4951620370 0.7611946768 0.3352874665 -0.250957239225 +1403637229738319104.0000000000 5.9599204754 -1.6011271582 0.6090689147 0.4971392389 0.7676909797 0.3232133686 -0.242973774745 +1403637229788318976.0000000000 5.9640953302 -1.6028650834 0.5973170695 0.5048435583 0.7704883785 0.3136821943 -0.23039991578 +1403637229838319104.0000000000 5.9680712809 -1.6024192137 0.5853411420 0.5149414097 0.7714690742 0.3038496945 -0.217591762938 +1403637229888318976.0000000000 5.9722169678 -1.6005420306 0.5731481324 0.5257613505 0.7715195070 0.2944209826 -0.204080713388 +1403637229938319104.0000000000 5.9761584877 -1.5976038905 0.5608311889 0.5353879246 0.7720021746 0.2842785418 -0.191201786802 +1403637229988318976.0000000000 5.9794488114 -1.5938478558 0.5482813165 0.5444252494 0.7724189644 0.2732296036 -0.179765611386 +1403637230038319104.0000000000 5.9828079026 -1.5905265645 0.5351771204 0.5489813509 0.7755181524 0.2621698927 -0.168695047586 +1403637230088318976.0000000000 5.9862026824 -1.5883782891 0.5238877144 0.5497563260 0.7807812736 0.2497447460 -0.160549514539 +1403637230138319104.0000000000 5.9896298005 -1.5867952512 0.5131771042 0.5480308829 0.7872437126 0.2376937474 -0.153007094108 +1403637230188318976.0000000000 5.9927847493 -1.5848130674 0.5040537491 0.5469615255 0.7925670367 0.2269807267 -0.145431536244 +1403637230238319104.0000000000 5.9953474125 -1.5824827996 0.4971233113 0.5465469861 0.7965121703 0.2183846877 -0.138430064295 +1403637230288318976.0000000000 5.9971073629 -1.5796031353 0.4925027473 0.5466629860 0.7992845739 0.2121829376 -0.131461593782 +1403637230338319104.0000000000 5.9980459493 -1.5763554968 0.4898495849 0.5482046094 0.8003788961 0.2072281514 -0.126181702589 +1403637230388318976.0000000000 5.9976739399 -1.5722805792 0.4896453852 0.5509882191 0.8001849089 0.2020176165 -0.123713284064 +1403637230438319104.0000000000 5.9964869875 -1.5675843369 0.4917011761 0.5563993111 0.7978326049 0.1979836810 -0.12118334532 +1403637230488318976.0000000000 5.9945493481 -1.5627909659 0.4957075563 0.5625755363 0.7944526421 0.1949433405 -0.119795073154 +1403637230538319104.0000000000 5.9922150252 -1.5581798127 0.5013816696 0.5684905562 0.7911865944 0.1915078183 -0.119025273955 +1403637230588318976.0000000000 5.9897315613 -1.5534528974 0.5091833471 0.5750086774 0.7876992795 0.1874289474 -0.117325426456 +1403637230638319104.0000000000 5.9872033632 -1.5494851322 0.5188764309 0.5796049574 0.7860769464 0.1802442657 -0.116846619515 +1403637230688318976.0000000000 5.9851830531 -1.5465678549 0.5290704942 0.5824043985 0.7859792809 0.1728618399 -0.114719095497 +1403637230738319104.0000000000 5.9836317591 -1.5445473612 0.5401701554 0.5818862101 0.7886519781 0.1638003428 -0.112276193852 +1403637230788318976.0000000000 5.9827337566 -1.5434566993 0.5522722714 0.5787146881 0.7933970100 0.1543027784 -0.108633083598 +1403637230838319104.0000000000 5.9825013844 -1.5428323183 0.5644968777 0.5723938277 0.8005912120 0.1430515311 -0.104667458044 +1403637230888318976.0000000000 5.9831305320 -1.5417340724 0.5757413904 0.5665684144 0.8075222801 0.1313964969 -0.0981985717501 +1403637230938319104.0000000000 5.9846218816 -1.5403007847 0.5853718771 0.5610931096 0.8141335571 0.1183775336 -0.0913664768894 +1403637230988318976.0000000000 5.9871999720 -1.5380528136 0.5934450812 0.5571750137 0.8195421747 0.1051008654 -0.0828277492345 +1403637231038319104.0000000000 5.9908432224 -1.5347282562 0.6004629114 0.5543465022 0.8240755710 0.0910358672 -0.072882643016 +1403637231088318976.0000000000 5.9951620805 -1.5304367540 0.6057671030 0.5531297780 0.8272459482 0.0753566838 -0.0635055907244 +1403637231138319104.0000000000 6.0007204552 -1.5249289890 0.6074392476 0.5524748152 0.8297539875 0.0594451542 -0.052403935219 +1403637231188318976.0000000000 6.0070446056 -1.5177966666 0.6055897365 0.5523368374 0.8314842347 0.0411117129 -0.0432181970544 +1403637231238319104.0000000000 6.0146094991 -1.5091259101 0.5998739403 0.5529671596 0.8322647555 0.0224316816 -0.0325502200995 +1403637231288318976.0000000000 6.0231467731 -1.4994308916 0.5900420393 0.5532489361 0.8327241006 0.0032314780 -0.0218115710363 +1403637231338319104.0000000000 6.0328656235 -1.4887628030 0.5765287384 0.5545372016 0.8319262309 -0.0166299889 -0.0105205442123 +1403637231388318976.0000000000 6.0438317116 -1.4773102628 0.5594598541 0.5567672713 0.8298636024 -0.0365124942 0.00185599850966 +1403637231438319104.0000000000 6.0551268996 -1.4634701077 0.5388777409 0.5581399627 0.8276707452 -0.0570215325 0.0137646093063 +1403637231488318976.0000000000 6.0676956360 -1.4502204399 0.5137200731 0.5575197729 0.8260226522 -0.0792476289 0.0240435880478 +1403637231538319104.0000000000 6.0818229980 -1.4369739324 0.4845065054 0.5554654582 0.8245477643 -0.1018577154 0.0347003601286 +1403637231588318976.0000000000 6.0962619934 -1.4226083497 0.4517151622 0.5520983441 0.8232675932 -0.1238046246 0.0457198353601 +1403637231638319104.0000000000 6.1134559455 -1.4087957370 0.4167858363 0.5493013663 0.8210717557 -0.1434815135 0.059348430408 +1403637231688318976.0000000000 6.1328052001 -1.3945436871 0.3824810243 0.5467267111 0.8181702287 -0.1617684317 0.0742856289693 +1403637231738319104.0000000000 6.1537474834 -1.3796261257 0.3502331136 0.5453238289 0.8140493749 -0.1800642066 0.0867318761462 +1403637231788318976.0000000000 6.1749104865 -1.3626296023 0.3190921130 0.5441583399 0.8094177742 -0.1970879561 0.0994530312803 +1403637231838319104.0000000000 6.1985891283 -1.3461362472 0.2897962836 0.5414702228 0.8056806506 -0.2131162904 0.110770635867 +1403637231888318976.0000000000 6.2234951049 -1.3294222177 0.2624845485 0.5373704882 0.8028127505 -0.2281811722 0.12107022206 +1403637231938319104.0000000000 6.2499467703 -1.3121658233 0.2381885540 0.5342869365 0.7991653689 -0.2432724520 0.12919247928 +1403637231988318976.0000000000 6.2784405346 -1.2943807793 0.2157648861 0.5319805458 0.7949850350 -0.2569489635 0.137741508093 +1403637232038319104.0000000000 6.3098001830 -1.2750661380 0.1978858671 0.5354049911 0.7867374974 -0.2702237647 0.146166763417 +1403637232088318976.0000000000 6.3439385962 -1.2552071480 0.1829014989 0.5403420000 0.7771153094 -0.2832213001 0.154622165684 +1403637232138319104.0000000000 6.3798337530 -1.2366622573 0.1693000290 0.5445848107 0.7677424311 -0.2955689222 0.163211383127 +1403637232188318976.0000000000 6.4168218305 -1.2203486910 0.1571772758 0.5476772234 0.7590444744 -0.3078342428 0.170702149202 +1403637232238319104.0000000000 6.4555156885 -1.2058130911 0.1463991522 0.5475452127 0.7528092029 -0.3181548005 0.179583036495 +1403637232288318976.0000000000 6.4959091067 -1.1927883214 0.1374340880 0.5463230670 0.7473568987 -0.3273142787 0.189351882551 +1403637232338319104.0000000000 6.5375993057 -1.1819178347 0.1301361077 0.5453037853 0.7416163423 -0.3354486454 0.20030773528 +1403637232388318976.0000000000 6.5805340089 -1.1725840718 0.1246077895 0.5436433832 0.7361238469 -0.3426632949 0.212498047533 +1403637232438319104.0000000000 6.6245009968 -1.1645666330 0.1203813636 0.5416161061 0.7305481374 -0.3515205703 0.222226688747 +1403637232488318976.0000000000 6.6687808342 -1.1586885670 0.1173525619 0.5391710068 0.7248625478 -0.3621251504 0.229639473144 +1403637232538319104.0000000000 6.7129130864 -1.1544787748 0.1156123692 0.5342997280 0.7203988942 -0.3772038756 0.230795299514 +1403637232588318976.0000000000 6.7575365098 -1.1521576920 0.1150264060 0.5278410285 0.7166564716 -0.3921419660 0.232404881368 +1403637232638319104.0000000000 6.8036148343 -1.1518597713 0.1160255847 0.5208930751 0.7127237619 -0.4075743796 0.2336201377 +1403637232688318976.0000000000 6.8516626629 -1.1529157686 0.1194673917 0.5145490573 0.7080911104 -0.4223943837 0.235434134227 +1403637232738319104.0000000000 6.8999455516 -1.1566357276 0.1231239534 0.5067948513 0.7044538371 -0.4366019478 0.237239350138 +1403637232788318976.0000000000 6.9495959936 -1.1626374080 0.1286773439 0.4995619667 0.7005120500 -0.4502385336 0.238759234806 +1403637232838319104.0000000000 7.0009013641 -1.1706064994 0.1353327573 0.4908591262 0.6989828260 -0.4604008759 0.241891216478 +1403637232888318976.0000000000 7.0545596211 -1.1802664991 0.1434176834 0.4820017623 0.6986771433 -0.4680018852 0.24596500967 +1403637232938319104.0000000000 7.1106675008 -1.1911095077 0.1530911817 0.4731504266 0.6993403602 -0.4742130257 0.249346627353 +1403637232988318976.0000000000 7.1697321846 -1.2033381399 0.1642330164 0.4660365007 0.7001173376 -0.4777264367 0.253817149356 +1403637233038319104.0000000000 7.2319389927 -1.2163917134 0.1766033554 0.4590181770 0.7017278481 -0.4801298399 0.257595957287 +1403637233088318976.0000000000 7.2975236479 -1.2299445453 0.1902221216 0.4527736333 0.7036132200 -0.4814108725 0.261090109709 +1403637233138319104.0000000000 7.3664321901 -1.2435290416 0.2037362340 0.4470451576 0.7058990788 -0.4820912710 0.263524427754 +1403637233188318976.0000000000 7.4381607539 -1.2572892822 0.2158495563 0.4407472841 0.7091729947 -0.4827609002 0.264116278034 +1403637233238319104.0000000000 7.5129583523 -1.2707542311 0.2268144397 0.4364518562 0.7115016956 -0.4832633536 0.264067501634 +1403637233288318976.0000000000 7.5916349438 -1.2837854017 0.2360733549 0.4316827430 0.7146809478 -0.4829344080 0.263923302895 +1403637233338319104.0000000000 7.6737282699 -1.2961709498 0.2441372388 0.4280306750 0.7174371263 -0.4828710492 0.262505735229 +1403637233388318976.0000000000 7.7595554822 -1.3077341420 0.2499950928 0.4241919061 0.7205552343 -0.4825754727 0.260734144713 +1403637233438319104.0000000000 7.8501075693 -1.3184138309 0.2521574179 0.4205751953 0.7238200599 -0.4808401169 0.260756223372 +1403637233488318976.0000000000 7.9438102433 -1.3285455863 0.2506481025 0.4174656287 0.7274789793 -0.4751998475 0.26586065601 +1403637233538319104.0000000000 8.0409398341 -1.3375175887 0.2462759760 0.4154598704 0.7312284386 -0.4647342895 0.276983946965 +1403637233588318976.0000000000 8.1405903750 -1.3451915997 0.2388385852 0.4155288009 0.7337890139 -0.4498661261 0.29412576771 +1403637233638319104.0000000000 8.2426180221 -1.3503209930 0.2281494792 0.4175333510 0.7347732977 -0.4329917015 0.313516009572 +1403637233688318976.0000000000 8.3460168788 -1.3520378303 0.2145106290 0.4203178125 0.7343294579 -0.4172935390 0.33160109481 +1403637233738319104.0000000000 8.4496333466 -1.3497441423 0.1991757912 0.4228435982 0.7335147644 -0.4027132045 0.3478238877 +1403637233788318976.0000000000 8.5512968884 -1.3430583673 0.1828033096 0.4252143731 0.7319949913 -0.3902651206 0.362034812184 +1403637233838319104.0000000000 8.6508177108 -1.3315465697 0.1655193020 0.4268058775 0.7306752207 -0.3812464005 0.372292421054 +1403637233888318976.0000000000 8.7460866745 -1.3150878963 0.1475532927 0.4277441676 0.7296443158 -0.3743622559 0.380140764605 +1403637233938319104.0000000000 8.8385328979 -1.2931691130 0.1285854360 0.4274595461 0.7293580537 -0.3696328837 0.385599140635 +1403637233988318976.0000000000 8.9274160589 -1.2660223488 0.1087328260 0.4264001651 0.7295467908 -0.3658732423 0.389975832343 +1403637234038319104.0000000000 9.0131459376 -1.2336862811 0.0883300278 0.4257707579 0.7293053625 -0.3607560398 0.395838388323 +1403637234088318976.0000000000 9.0954985706 -1.1961496894 0.0673013605 0.4262402662 0.7284214432 -0.3556455878 0.401544085299 +1403637234138319104.0000000000 9.1741985324 -1.1534187234 0.0451529662 0.4256735761 0.7275238030 -0.3498502290 0.408798165247 +1403637234188318976.0000000000 9.2488121950 -1.1049770592 0.0222790405 0.4255208207 0.7263649026 -0.3453149223 0.414829680528 +1403637234238319104.0000000000 9.3188774213 -1.0503045871 -0.0009362012 0.4268235496 0.7247380560 -0.3438674362 0.417530351012 +1403637234288318976.0000000000 9.3843930841 -0.9897213199 -0.0250013624 0.4301354676 0.7221196487 -0.3443840424 0.418241943975 +1403637234338319104.0000000000 9.4461452132 -0.9228703597 -0.0495932069 0.4350491727 0.7191884519 -0.3466093832 0.416367774415 +1403637234388318976.0000000000 9.5024028174 -0.8502875720 -0.0745331067 0.4412878776 0.7161890543 -0.3506450712 0.411565646842 +1403637234438319104.0000000000 9.5536263985 -0.7720612667 -0.0996392542 0.4496125438 0.7133451568 -0.3548260750 0.403838710593 +1403637234488318976.0000000000 9.5999194060 -0.6894804468 -0.1251626516 0.4574645877 0.7113732799 -0.3567535508 0.396738089633 +1403637234538319104.0000000000 9.6415206528 -0.6027239051 -0.1510119367 0.4674652499 0.7089236648 -0.3578784381 0.388363877241 +1403637234588318976.0000000000 9.6784462195 -0.5129311413 -0.1781058036 0.4767281556 0.7074961767 -0.3588239002 0.378714713404 +1403637234638319104.0000000000 9.7112498085 -0.4205825176 -0.2063433557 0.4857222065 0.7065628503 -0.3579300611 0.369768776397 +1403637234688318976.0000000000 9.7398705374 -0.3266990641 -0.2357698939 0.4939368749 0.7065030599 -0.3556077911 0.36114109271 +1403637234738319104.0000000000 9.7643555073 -0.2312601001 -0.2663506185 0.5019449438 0.7070612645 -0.3540172673 0.350410353854 +1403637234788318976.0000000000 9.7847192773 -0.1348881892 -0.2979811327 0.5101008818 0.7079269660 -0.3521257471 0.338591138989 +1403637234838319104.0000000000 9.8014672251 -0.0380369580 -0.3299028091 0.5176091842 0.7091293357 -0.3494190106 0.327296001616 +1403637234888318976.0000000000 9.8144656302 0.0587211344 -0.3610790316 0.5248936757 0.7108444306 -0.3479584886 0.313227896142 +1403637234938319104.0000000000 9.8242553011 0.1547887843 -0.3908843868 0.5323052715 0.7125065571 -0.3442941510 0.300744146211 +1403637234988318976.0000000000 9.8313235633 0.2492897378 -0.4195909135 0.5374587979 0.7153233983 -0.3390689855 0.290659077988 +1403637235038319104.0000000000 9.8361217702 0.3420247651 -0.4466910179 0.5412752733 0.7187971095 -0.3310940621 0.284127640167 +1403637235088318976.0000000000 9.8386573118 0.4334223231 -0.4723069909 0.5443589509 0.7229156907 -0.3220881795 0.278074524815 +1403637235138319104.0000000000 9.8385350730 0.5235268345 -0.4961828666 0.5469148449 0.7274227773 -0.3125721323 0.272100932694 +1403637235188318976.0000000000 9.8363142724 0.6126499063 -0.5175768857 0.5499175891 0.7313380002 -0.3029825960 0.266339860142 +1403637235238319104.0000000000 9.8311542302 0.6997607938 -0.5370870576 0.5520566610 0.7352389547 -0.2945931390 0.260522561427 +1403637235288318976.0000000000 9.8231066894 0.7846331510 -0.5549715635 0.5516102928 0.7401580816 -0.2874111358 0.255513087943 +1403637235338319104.0000000000 9.8130515298 0.8680568603 -0.5722407005 0.5488735986 0.7459013491 -0.2815411615 0.251204149096 +1403637235388318976.0000000000 9.8013643883 0.9509740776 -0.5881328313 0.5432002854 0.7530353367 -0.2794025051 0.244551572835 +1403637235438319104.0000000000 9.7876280613 1.0328319461 -0.6024593671 0.5377141577 0.7598328094 -0.2777042220 0.237482528661 +1403637235488318976.0000000000 9.7722877565 1.1140013199 -0.6157059070 0.5319955329 0.7668414672 -0.2752332688 0.230611285255 +1403637235538319104.0000000000 9.7559585323 1.1953146787 -0.6269301843 0.5279522398 0.7726501723 -0.2727014039 0.223410134162 +1403637235588318976.0000000000 9.7392361692 1.2769268882 -0.6363375509 0.5250251178 0.7775650521 -0.2673725398 0.219665974559 +1403637235638319104.0000000000 9.7215607307 1.3586318138 -0.6435126470 0.5247139038 0.7808847366 -0.2620801614 0.214961243872 +1403637235688318976.0000000000 9.7031166750 1.4404847166 -0.6483467384 0.5267614019 0.7826216564 -0.2554293024 0.211616728688 +1403637235738319104.0000000000 9.6847084319 1.5235628507 -0.6508253917 0.5316287273 0.7825304913 -0.2466825987 0.210153805428 +1403637235788318976.0000000000 9.6658615246 1.6069877420 -0.6518029983 0.5368712447 0.7820106625 -0.2348393727 0.21231829733 +1403637235838319104.0000000000 9.6454272118 1.6902945782 -0.6504778198 0.5438406275 0.7801023142 -0.2201214194 0.217311555285 +1403637235888318976.0000000000 9.6226877418 1.7736372195 -0.6478272771 0.5488799898 0.7794756947 -0.2061283342 0.22058900259 +1403637235938319104.0000000000 9.5975696415 1.8573112204 -0.6440152358 0.5520175542 0.7798565045 -0.1905502970 0.225368667858 +1403637235988318976.0000000000 9.5687794612 1.9410880820 -0.6390347974 0.5533885461 0.7819333148 -0.1785939063 0.224601034959 +1403637236038319104.0000000000 9.5365974373 2.0255588181 -0.6322292574 0.5551685530 0.7835215551 -0.1651655529 0.224949306826 +1403637236088318976.0000000000 9.5004642773 2.1103136003 -0.6234088544 0.5562351195 0.7858354506 -0.1545465887 0.221766742939 +1403637236138319104.0000000000 9.4599838768 2.1947339033 -0.6129908937 0.5573583464 0.7879849944 -0.1432520427 0.218883929208 +1403637236188318976.0000000000 9.4155131233 2.2797044162 -0.6004609599 0.5573862117 0.7909962730 -0.1331035716 0.214310397394 +1403637236238319104.0000000000 9.3666156405 2.3648516693 -0.5859173380 0.5592206396 0.7924803100 -0.1225740911 0.210292241407 +1403637236288318976.0000000000 9.3128405131 2.4502074228 -0.5694263964 0.5610800717 0.7942985719 -0.1139255467 0.203223772386 +1403637236338319104.0000000000 9.2548410702 2.5355840344 -0.5503786363 0.5633802722 0.7957231549 -0.1052665064 0.195822093157 +1403637236388318976.0000000000 9.1917229681 2.6205232357 -0.5297636938 0.5659451302 0.7969778989 -0.0976224281 0.18708874837 +1403637236438319104.0000000000 9.1242913065 2.7053516045 -0.5075424998 0.5683602743 0.7981590187 -0.0915448858 0.177562139175 +1403637236488318976.0000000000 9.0532718568 2.7901177471 -0.4840748016 0.5716584733 0.7984411700 -0.0868637482 0.167788489783 +1403637236538319104.0000000000 8.9796360212 2.8754793391 -0.4599673265 0.5742797125 0.7985934915 -0.0829137157 0.159926742519 +1403637236588318976.0000000000 8.9034768161 2.9606874379 -0.4364590909 0.5772596507 0.7980300128 -0.0799753755 0.153373184142 +1403637236638319104.0000000000 8.8248847534 3.0449096406 -0.4144950034 0.5816318261 0.7958936249 -0.0766732515 0.149596020408 +1403637236688318976.0000000000 8.7432957514 3.1279655114 -0.3942471415 0.5850029279 0.7943876619 -0.0734557054 0.146027656025 +1403637236738319104.0000000000 8.6584775037 3.2098893077 -0.3742195676 0.5912494536 0.7908106108 -0.0694262490 0.142206389759 +1403637236788318976.0000000000 8.5702582097 3.2899659635 -0.3541846890 0.5970229777 0.7876676959 -0.0649277282 0.137577450741 +1403637236838319104.0000000000 8.4782831209 3.3676901711 -0.3331527866 0.6036635742 0.7840970461 -0.0605918548 0.130808022092 +1403637236888318976.0000000000 8.3831797649 3.4433783586 -0.3099613866 0.6121582241 0.7791574650 -0.0554922933 0.122868054598 +1403637236938319104.0000000000 8.2854277632 3.5159295775 -0.2850793956 0.6215182096 0.7732857663 -0.0504320566 0.114894936441 +1403637236988318976.0000000000 8.1856804427 3.5851575279 -0.2590683328 0.6311707922 0.7666331424 -0.0452659487 0.108848747787 +1403637237038319104.0000000000 8.0834738361 3.6504967085 -0.2316317877 0.6417223761 0.7589424870 -0.0414374548 0.102379835591 +1403637237088318976.0000000000 7.9787837344 3.7104032517 -0.2027955908 0.6512086372 0.7518836367 -0.0379565663 0.0956953856842 +1403637237138319104.0000000000 7.8717642378 3.7651591167 -0.1719333928 0.6603288091 0.7450864271 -0.0346138989 0.0872579973555 +1403637237188318976.0000000000 7.7628600395 3.8140412443 -0.1397042785 0.6661868901 0.7410723880 -0.0315497855 0.0775329237344 +1403637237238319104.0000000000 7.6523397251 3.8555977269 -0.1067268300 0.6689765398 0.7396888458 -0.0273567645 0.0676934853426 +1403637237288318976.0000000000 7.5405033731 3.8903226119 -0.0724168100 0.6691512785 0.7405172545 -0.0226438823 0.0579483984451 +1403637237338319104.0000000000 7.4278572132 3.9184297762 -0.0369466573 0.6680996761 0.7421028355 -0.0172669725 0.0512645684322 +1403637237388318976.0000000000 7.3142019060 3.9399458975 0.0006201904 0.6669919431 0.7436567426 -0.0133309648 0.0438027673924 +1403637237438319104.0000000000 7.2000844513 3.9548108961 0.0399722429 0.6664781888 0.7445441932 -0.0101045286 0.036860097022 +1403637237488318976.0000000000 7.0861939719 3.9632662818 0.0803051919 0.6654146670 0.7457463311 -0.0065323323 0.0322964274846 +1403637237538319104.0000000000 6.9723828553 3.9654764995 0.1224247908 0.6645553721 0.7467518038 -0.0045116539 0.0265997358588 +1403637237588318976.0000000000 6.8595458287 3.9616865103 0.1662157089 0.6636251040 0.7477494727 -0.0031933048 0.0215000061426 +1403637237638319104.0000000000 6.7476956844 3.9522089122 0.2123407737 0.6637280466 0.7478109122 -0.0033967578 0.0152440740157 +1403637237688318976.0000000000 6.6372249971 3.9373150480 0.2591889899 0.6640096186 0.7476602441 -0.0040469864 0.00888862863177 +1403637237738319104.0000000000 6.5294741212 3.9173895738 0.3059594051 0.6629526482 0.7486330262 -0.0059983049 0.00252957472329 +1403637237788318976.0000000000 6.4231065667 3.8924188098 0.3517075183 0.6615301232 0.7498659126 -0.0082692302 -0.00326022063118 +1403637237838319104.0000000000 6.3195613477 3.8632239750 0.3954215473 0.6582671689 0.7526461807 -0.0122495976 -0.00761632347067 +1403637237888318976.0000000000 6.2179841817 3.8291836749 0.4368525051 0.6537685261 0.7564153858 -0.0176838425 -0.0104766470343 +1403637237938319104.0000000000 6.1189503012 3.7902087551 0.4762081424 0.6490090716 0.7602780801 -0.0247449006 -0.0123351448917 +1403637237988318976.0000000000 6.0221545836 3.7465062324 0.5129619545 0.6429427162 0.7651013693 -0.0330215882 -0.0124150360464 +1403637238038319104.0000000000 5.9273856657 3.6990467658 0.5482991525 0.6362554381 0.7701433585 -0.0434249177 -0.013133979179 +1403637238088318976.0000000000 5.8353270948 3.6485863953 0.5820295102 0.6286506514 0.7754361584 -0.0571078600 -0.0153562730699 +1403637238138319104.0000000000 5.7471377847 3.5958941657 0.6144087862 0.6217447715 0.7797780713 -0.0715958623 -0.015925802132 +1403637238188318976.0000000000 5.6631085630 3.5410062445 0.6461845473 0.6156140785 0.7829256563 -0.0881507793 -0.0166181584913 +1403637238238319104.0000000000 5.5837243547 3.4841729902 0.6767706421 0.6099949382 0.7851237382 -0.1059232579 -0.0163448635293 +1403637238288318976.0000000000 5.5095133956 3.4254826927 0.7063447098 0.6052204871 0.7859578000 -0.1254075027 -0.01585739365 +1403637238338319104.0000000000 5.4401870179 3.3647306701 0.7342693151 0.6001001504 0.7865185878 -0.1451488009 -0.0141473001291 +1403637238388318976.0000000000 5.3771876605 3.3029908613 0.7612260657 0.5972915760 0.7846136094 -0.1658469521 -0.0109108072146 +1403637238438319104.0000000000 5.3187466861 3.2378260490 0.7865739243 0.5943247830 0.7823443349 -0.1862077296 -0.00648655565695 +1403637238488318976.0000000000 5.2657801361 3.1699078509 0.8108422735 0.5922291642 0.7789881528 -0.2060141871 -0.000479073363982 +1403637238538319104.0000000000 5.2184176199 3.0989642573 0.8335929467 0.5889949737 0.7762939085 -0.2245032178 0.00714099760965 +1403637238588318976.0000000000 5.1769517965 3.0247129449 0.8547634754 0.5847601022 0.7740724805 -0.2422062736 0.0142667039241 +1403637238638319104.0000000000 5.1395946584 2.9469968719 0.8745015436 0.5768239418 0.7741716938 -0.2600559485 0.0174135646801 +1403637238688318976.0000000000 5.1091119894 2.8669424922 0.8930026444 0.5651597875 0.7776002100 -0.2748014488 0.020408130694 +1403637238738319104.0000000000 5.0849766729 2.7846860409 0.9104081576 0.5512684081 0.7827478459 -0.2880213327 0.0212758996328 +1403637238788318976.0000000000 5.0680670550 2.7008287267 0.9270894180 0.5362821830 0.7887773100 -0.2996027917 0.0216781625616 +1403637238838319104.0000000000 5.0588157415 2.6160105449 0.9433630730 0.5206705229 0.7952714931 -0.3098333501 0.0211838139951 +1403637238888318976.0000000000 5.0578821101 2.5308334472 0.9594172744 0.5049319443 0.8020405090 -0.3183546922 0.0206165823406 +1403637238938319104.0000000000 5.0660576499 2.4463835138 0.9754223305 0.4893802746 0.8089092218 -0.3252208801 0.0201046471038 +1403637238988318976.0000000000 5.0839982255 2.3631497666 0.9918360694 0.4757653027 0.8150601762 -0.3299622736 0.0211939599945 +1403637239038319104.0000000000 5.1123526608 2.2817298255 1.0090853098 0.4663680105 0.8200745849 -0.3305120601 0.0272090465407 +1403637239088318976.0000000000 5.1513121913 2.2034411531 1.0270400321 0.4605295464 0.8238974360 -0.3283140502 0.0362689427783 +1403637239138319104.0000000000 5.2013255098 2.1294657744 1.0461546041 0.4610583619 0.8248610055 -0.3231836134 0.0508120127986 +1403637239188318976.0000000000 5.2605324462 2.0591262061 1.0665068992 0.4652474036 0.8235099487 -0.3176080666 0.0670919801851 +1403637239238319104.0000000000 5.3275450718 1.9922856840 1.0872767099 0.4723496778 0.8195765124 -0.3134655971 0.0831831815962 +1403637239288318976.0000000000 5.4004797968 1.9279907769 1.1076562520 0.4785109329 0.8151557172 -0.3118895432 0.0962982692358 +1403637239338319104.0000000000 5.4788006937 1.8660965795 1.1268282141 0.4827980700 0.8106919449 -0.3133280715 0.107285198036 +1403637239388318976.0000000000 5.5661449784 1.8015509301 1.1389157496 0.4858056811 0.8057800148 -0.3183701856 0.115550131051 +1403637239438319104.0000000000 5.6557660452 1.7433840852 1.1526169141 0.4873300366 0.8008270776 -0.3256006635 0.123165072745 +1403637239488318976.0000000000 5.7495003891 1.6865671566 1.1626048727 0.4881050326 0.7957053631 -0.3335717873 0.131667440738 +1403637239538319104.0000000000 5.8472174223 1.6308372845 1.1686176425 0.4895084927 0.7894598860 -0.3424033341 0.141047795792 +1403637239588318976.0000000000 5.9483850438 1.5760455276 1.1696027272 0.4898850929 0.7833292170 -0.3516430847 0.150847852116 +1403637239638319104.0000000000 6.0526153965 1.5219330438 1.1654686397 0.4894965320 0.7771455762 -0.3611624019 0.161243970553 +1403637239688318976.0000000000 6.1600498267 1.4686986469 1.1576140989 0.4903893042 0.7696565954 -0.3708072655 0.172188929079 +1403637239738319104.0000000000 6.2709064672 1.4161297356 1.1465492640 0.4932170697 0.7609049865 -0.3780118239 0.18672863924 +1403637239788318976.0000000000 6.3842176757 1.3642203855 1.1325098411 0.4977771499 0.7505842581 -0.3845277459 0.20243416988 +1403637239838319104.0000000000 6.4992254364 1.3123743352 1.1145732659 0.5018184985 0.7401728881 -0.3889918786 0.221376622036 +1403637239888318976.0000000000 6.6152205077 1.2608890029 1.0935989177 0.5050518899 0.7296697522 -0.3944864074 0.238506007421 +1403637239938319104.0000000000 6.7309767632 1.2088465449 1.0710186031 0.5069900916 0.7194192541 -0.4016252519 0.253168206627 +1403637239988318976.0000000000 6.8469890057 1.1566301431 1.0471442704 0.5072129737 0.7097186770 -0.4085049665 0.26862258125 +1403637240038319104.0000000000 6.9628618710 1.1044913809 1.0216339001 0.5059483280 0.7006018261 -0.4165655030 0.282217207912 +1403637240088318976.0000000000 7.0773127163 1.0518622920 0.9949441734 0.5037581534 0.6918143245 -0.4262180097 0.293187434096 +1403637240138319104.0000000000 7.1903887083 0.9984186390 0.9667445342 0.4993107416 0.6839644113 -0.4369153790 0.3032926293 +1403637240188318976.0000000000 7.3018037738 0.9440124852 0.9383441158 0.4946454902 0.6763536335 -0.4477486980 0.312078042985 +1403637240238319104.0000000000 7.4116502535 0.8890400938 0.9089575218 0.4878340363 0.6703966967 -0.4588085420 0.319501085835 +1403637240288318976.0000000000 7.5242659236 0.8334826165 0.8637812816 0.4786576923 0.6667097166 -0.4704314302 0.324159277052 +1403637240338319104.0000000000 7.6338547984 0.7787854530 0.8301345616 0.4681117147 0.6656602788 -0.4799390256 0.327759588068 +1403637240388318976.0000000000 7.7425528060 0.7240038819 0.7967918206 0.4567030456 0.6660481248 -0.4885092995 0.33039504809 +1403637240438319104.0000000000 7.8507386789 0.6697123015 0.7650122520 0.4443894295 0.6682068498 -0.4947201583 0.333570990684 +1403637240488318976.0000000000 7.9587777124 0.6164147024 0.7350495804 0.4341197306 0.6701548312 -0.4995045134 0.336047322341 +1403637240538319104.0000000000 8.0678043769 0.5646144801 0.7072161322 0.4263959910 0.6714816611 -0.5027559792 0.338430588185 +1403637240588318976.0000000000 8.1771730704 0.5148797684 0.6818065907 0.4228610020 0.6710116934 -0.5053715256 0.339899251833 +1403637240638319104.0000000000 8.2871713894 0.4666041339 0.6584776164 0.4201893822 0.6709456022 -0.5059684291 0.34244536894 +1403637240688318976.0000000000 8.3978557251 0.4199818458 0.6374905015 0.4187894057 0.6709174075 -0.5053217622 0.345159648006 +1403637240738319104.0000000000 8.5092580641 0.3752013609 0.6189461566 0.4193515732 0.6697888943 -0.5052811454 0.346724760081 +1403637240788318976.0000000000 8.6213163292 0.3322198685 0.6025086221 0.4211534714 0.6685933301 -0.5029008050 0.35029058328 +1403637240838319104.0000000000 8.7345586718 0.2912071406 0.5885642577 0.4251819025 0.6665159048 -0.4966026874 0.358277363582 +1403637240888318976.0000000000 8.8466884296 0.2520285991 0.5769532528 0.4325140262 0.6623376166 -0.4910451238 0.364849537688 +1403637240938319104.0000000000 8.9590275530 0.2147679352 0.5668732010 0.4378318956 0.6595573069 -0.4854737024 0.37094834459 +1403637240988318976.0000000000 9.0701476173 0.1791986215 0.5570748470 0.4416681689 0.6579463882 -0.4816258126 0.374262415177 +1403637241038319104.0000000000 9.1794098442 0.1450671720 0.5459534288 0.4433550973 0.6577660120 -0.4806688193 0.373814950696 +1403637241088318976.0000000000 9.2868533699 0.1127956322 0.5326661746 0.4441169641 0.6586389598 -0.4812389315 0.37062640716 +1403637241138319104.0000000000 9.3929082031 0.0816926026 0.5174461147 0.4438269435 0.6603067808 -0.4808349071 0.36852461459 +1403637241188318976.0000000000 9.4975033990 0.0519293734 0.5004740931 0.4435735254 0.6618781445 -0.4801852003 0.36685422561 +1403637241238319104.0000000000 9.6015679736 0.0233416044 0.4823361875 0.4424757070 0.6638973114 -0.4771237085 0.368522150545 +1403637241288318976.0000000000 9.7045470978 -0.0040754386 0.4629518177 0.4408281943 0.6662614317 -0.4739697720 0.370295642646 +1403637241338319104.0000000000 9.8072551627 -0.0293881720 0.4426603758 0.4405469024 0.6676841577 -0.4707129935 0.372217100764 +1403637241388318976.0000000000 9.9089465905 -0.0531311602 0.4211467268 0.4391152847 0.6695820098 -0.4665295926 0.375749701401 +1403637241438319104.0000000000 10.0090326700 -0.0749970570 0.3994068873 0.4375426965 0.6715709745 -0.4628636506 0.378557863229 +1403637241488318976.0000000000 10.1072829908 -0.0943874642 0.3788096065 0.4366213649 0.6729225642 -0.4586523036 0.382328485288 +1403637241538319104.0000000000 10.2040871026 -0.1108967804 0.3598972341 0.4368087598 0.6733656742 -0.4532238312 0.387769177409 +1403637241588318976.0000000000 10.2985716325 -0.1241729543 0.3424517099 0.4369460644 0.6740500522 -0.4491152771 0.391190659184 +1403637241638319104.0000000000 10.3911434566 -0.1338663574 0.3270877186 0.4390188208 0.6733054118 -0.4459414122 0.393774750805 +1403637241688318976.0000000000 10.4817415230 -0.1401195482 0.3134320945 0.4430329740 0.6712287499 -0.4425195701 0.396673895432 +1403637241738319104.0000000000 10.5632789211 -0.1452410453 0.3011603512 0.4468207045 0.6692097496 -0.4389917101 0.399744728038 +1403637241788318976.0000000000 10.6443496805 -0.1458720951 0.2904761827 0.4510652895 0.6665618082 -0.4362452504 0.402399729158 +1403637241838319104.0000000000 10.7217510925 -0.1435520988 0.2815830637 0.4563516322 0.6632534377 -0.4346542084 0.403625797339 +1403637241888318976.0000000000 10.7951321601 -0.1380083895 0.2753433398 0.4635213752 0.6589254074 -0.4360090364 0.401075257729 +1403637241938319104.0000000000 10.8639413663 -0.1302566656 0.2709471646 0.4736993240 0.6526936920 -0.4387020512 0.39640939081 +1403637241988318976.0000000000 10.9296626152 -0.1210133322 0.2672783379 0.4816920550 0.6475689337 -0.4403511100 0.393342268458 +1403637242038319104.0000000000 10.9915645378 -0.1114382851 0.2643657174 0.4869723897 0.6437455706 -0.4409721798 0.392419505952 +1403637242088318976.0000000000 11.0416839824 -0.1018858729 0.2644444222 0.4869460516 0.6430979475 -0.4411249193 0.39334130018 +1403637242138319104.0000000000 11.0944833212 -0.0917817932 0.2633408412 0.4838196664 0.6447327188 -0.4407124003 0.394982065336 +1403637242188318976.0000000000 11.1434873484 -0.0808122823 0.2635217855 0.4788373906 0.6475074297 -0.4399591459 0.397347243417 +1403637242238319104.0000000000 11.1889293672 -0.0683257950 0.2659128748 0.4747526965 0.6497295326 -0.4387222765 0.39998021908 +1403637242288318976.0000000000 11.2305210640 -0.0545445016 0.2685462126 0.4710953041 0.6514844541 -0.4375563372 0.402717856975 +1403637242338319104.0000000000 11.2721897840 -0.0390595544 0.2721452619 0.4673513947 0.6529991968 -0.4347554835 0.407630215439 +1403637242388318976.0000000000 11.3083282115 -0.0222176809 0.2733840888 0.4644198969 0.6539046615 -0.4312120295 0.413254205775 +1403637242438319104.0000000000 11.3410253436 -0.0034707791 0.2729162526 0.4625305281 0.6541449427 -0.4274453148 0.418868007091 +1403637242488318976.0000000000 11.3701302117 0.0173739021 0.2706844312 0.4612563938 0.6539097285 -0.4243320323 0.423776984391 +1403637242538319104.0000000000 11.3948654279 0.0409631924 0.2678767753 0.4618245200 0.6536503371 -0.4219277065 0.425953471662 +1403637242588318976.0000000000 11.4145726729 0.0676864617 0.2656602526 0.4645491597 0.6536303143 -0.4190777454 0.425834866698 +1403637242638319104.0000000000 11.4294595765 0.0977907948 0.2644503998 0.4678024805 0.6552293049 -0.4166754184 0.422157545224 +1403637242688318976.0000000000 11.4391510670 0.1306286892 0.2643595290 0.4719671376 0.6577521804 -0.4137153876 0.416471689669 +1403637242738319104.0000000000 11.4437059407 0.1661485453 0.2660297758 0.4776962423 0.6606025737 -0.4106043528 0.408429437309 +1403637242788318976.0000000000 11.4435997346 0.2037778492 0.2696865045 0.4848756882 0.6624849175 -0.4085781481 0.398839814998 +1403637242838319104.0000000000 11.4390432150 0.2427067220 0.2758360342 0.4926862057 0.6630669210 -0.4056578399 0.391208739551 +1403637242888318976.0000000000 11.4302359419 0.2825462617 0.2830702679 0.4994394960 0.6637550294 -0.4028485328 0.384320843134 +1403637242938319104.0000000000 11.4178501137 0.3225242416 0.2911512363 0.5048013630 0.6642641412 -0.3983440729 0.381117743114 +1403637242988318976.0000000000 11.4020356691 0.3629172344 0.3003121310 0.5089464892 0.6649227376 -0.3939996476 0.378966359701 +1403637243038319104.0000000000 11.3832706001 0.4036660198 0.3090602601 0.5090678062 0.6677890191 -0.3903038119 0.377585393139 +1403637243088318976.0000000000 11.3607370180 0.4444912110 0.3163554908 0.5073751233 0.6711092951 -0.3867269373 0.37765735037 +1403637243138319104.0000000000 11.3316695583 0.4862157948 0.3230298845 0.5046846275 0.6747510355 -0.3840787101 0.377475842055 +1403637243188318976.0000000000 11.3002380506 0.5284520200 0.3270660002 0.5015989820 0.6786400235 -0.3847337420 0.373933319559 +1403637243238319104.0000000000 11.2654066077 0.5714328816 0.3294927204 0.4988347170 0.6822407575 -0.3870900493 0.36860923427 +1403637243288318976.0000000000 11.2263637288 0.6150490759 0.3310747459 0.4974398283 0.6844433367 -0.3895720795 0.363764389463 +1403637243338319104.0000000000 11.1849296992 0.6591639072 0.3307068593 0.4959950092 0.6864588325 -0.3919367333 0.359372813786 +1403637243388318976.0000000000 11.1407496488 0.7038595553 0.3290268668 0.4956788930 0.6872758558 -0.3940305009 0.355941424008 +1403637243438319104.0000000000 11.0941865520 0.7489503325 0.3262300337 0.4958691066 0.6873234206 -0.3964870803 0.352843222536 +1403637243488318976.0000000000 11.0448356344 0.7941051452 0.3239195959 0.4960140201 0.6873615523 -0.3970294581 0.351954255213 +1403637243538319104.0000000000 10.9934555351 0.8401401576 0.3228262039 0.4958598099 0.6875237894 -0.3992964029 0.349279931467 +1403637243588318976.0000000000 10.9392854234 0.8863906764 0.3221000775 0.4944651494 0.6887489320 -0.4033233147 0.34417935515 +1403637243638319104.0000000000 10.8838366662 0.9331165812 0.3230435778 0.4930735535 0.6898546049 -0.4073734134 0.339154827417 +1403637243688318976.0000000000 10.8237915803 0.9802908630 0.3268218197 0.4902586372 0.6917760503 -0.4121350288 0.333522237533 +1403637243738319104.0000000000 10.7664474793 1.0279413223 0.3332920684 0.4899774998 0.6915985058 -0.4164612244 0.328897560198 +1403637243788318976.0000000000 10.7087326876 1.0758703929 0.3415113858 0.4887835799 0.6921795012 -0.4229396589 0.321092190821 +1403637243838319104.0000000000 10.6507051414 1.1236580118 0.3520277582 0.4888833374 0.6917819791 -0.4303049611 0.311878848786 +1403637243888318976.0000000000 10.5933357918 1.1703777684 0.3644450702 0.4877521079 0.6918602611 -0.4357643544 0.305837682143 +1403637243938319104.0000000000 10.5358063338 1.2159169548 0.3794829868 0.4879419361 0.6911410331 -0.4408430705 0.299823492294 +1403637243988318976.0000000000 10.4795481160 1.2600826001 0.3967310704 0.4874566665 0.6907246974 -0.4430559086 0.298306641668 +1403637244038319104.0000000000 10.4247367141 1.3030346084 0.4163870207 0.4870355823 0.6902671024 -0.4443046748 0.298196285732 +1403637244088318976.0000000000 10.3707437546 1.3444950279 0.4381110940 0.4867685532 0.6896272994 -0.4453505127 0.298552314316 +1403637244138319104.0000000000 10.3177211286 1.3845761691 0.4612968104 0.4856595761 0.6896343683 -0.4454694561 0.300160253788 +1403637244188318976.0000000000 10.2663582415 1.4238683442 0.4860471659 0.4859746117 0.6886177738 -0.4453273174 0.302188383064 +1403637244238319104.0000000000 10.2160938320 1.4621691695 0.5125923589 0.4861765829 0.6876717119 -0.4456606075 0.303523590187 +1403637244288318976.0000000000 10.1668038057 1.4996517389 0.5400759446 0.4853959394 0.6877420969 -0.4468099618 0.302923172112 +1403637244338319104.0000000000 10.1179396654 1.5356898212 0.5683658506 0.4838274393 0.6881656186 -0.4481237201 0.302529704129 +1403637244388318976.0000000000 10.0694264017 1.5706621927 0.5976231347 0.4823140528 0.6894948380 -0.4493315752 0.300118573869 +1403637244438319104.0000000000 10.0215509261 1.6045828095 0.6278708963 0.4806283656 0.6919833308 -0.4485308323 0.298287674053 +1403637244488318976.0000000000 9.9753507559 1.6378815223 0.6591726296 0.4788817783 0.6954133897 -0.4454449497 0.297743608915 +1403637244538319104.0000000000 9.9306699341 1.6707277027 0.6908649498 0.4769653789 0.7000487771 -0.4391780848 0.299263005949 +1403637244588318976.0000000000 9.8871130496 1.7033335212 0.7215022722 0.4747211828 0.7055315807 -0.4320812717 0.300284468268 +1403637244638319104.0000000000 9.8649239362 1.7389281906 0.7581849707 0.4724483708 0.7114752152 -0.4243000305 0.300940258573 +1403637244688318976.0000000000 9.8253346824 1.7720529485 0.7872469804 0.4713642973 0.7170205002 -0.4167414321 0.30003979795 +1403637244738319104.0000000000 9.7865264438 1.8057660451 0.8147381829 0.4710508138 0.7219952584 -0.4098185793 0.298132034032 +1403637244788318976.0000000000 9.7489452130 1.8403171141 0.8409827479 0.4711856999 0.7260055260 -0.4040326573 0.29607030281 +1403637244838319104.0000000000 9.7125035734 1.8756773567 0.8659563715 0.4716006291 0.7292697525 -0.3992453420 0.293873495936 +1403637244888318976.0000000000 9.6771245379 1.9119516656 0.8897302032 0.4724223563 0.7320339861 -0.3950254432 0.291373059288 +1403637244938319104.0000000000 9.6425941105 1.9495167211 0.9122249682 0.4730896743 0.7343311817 -0.3927973497 0.287496291626 +1403637244988318976.0000000000 9.6090275204 1.9878189875 0.9333238237 0.4733347457 0.7364490102 -0.3917758660 0.283034882506 +1403637245038319104.0000000000 9.5761289360 2.0269323305 0.9529234026 0.4734337851 0.7378320449 -0.3940364370 0.276042769967 +1403637245088318976.0000000000 9.5444144751 2.0669225126 0.9708583425 0.4731026749 0.7391104811 -0.3992921875 0.265434181442 +1403637245138319104.0000000000 9.5137779698 2.1068215932 0.9870358897 0.4718803607 0.7405835375 -0.4043012575 0.255744877404 +1403637245188318976.0000000000 9.4866650216 2.1475011892 1.0016274928 0.4695625020 0.7423146384 -0.4077404591 0.249454910558 +1403637245238319104.0000000000 9.4624393683 2.1880247800 1.0153695297 0.4686795428 0.7434451889 -0.4061069593 0.250411411471 +1403637245288318976.0000000000 9.4416183626 2.2291603719 1.0286284068 0.4694841770 0.7432920991 -0.4022557808 0.255522503376 +1403637245338319104.0000000000 9.4236560836 2.2709572435 1.0405022716 0.4693025226 0.7436081394 -0.3975302406 0.262243751431 +1403637245388318976.0000000000 9.4075221458 2.3138062647 1.0517940589 0.4704504191 0.7431591186 -0.3938451046 0.266977454452 +1403637245438319104.0000000000 9.3928370784 2.3573930724 1.0615634144 0.4711510650 0.7435443941 -0.3897581761 0.270641778284 +1403637245488318976.0000000000 9.3792951795 2.4025655491 1.0702159536 0.4718843401 0.7446056148 -0.3857186277 0.272229293354 +1403637245538319104.0000000000 9.3665916666 2.4493451637 1.0778810710 0.4732940944 0.7460780369 -0.3818874686 0.271149818956 +1403637245588318976.0000000000 9.3553190959 2.4967509242 1.0838852651 0.4740346095 0.7485221739 -0.3765975306 0.270518103249 +1403637245638319104.0000000000 9.3446416939 2.5456263146 1.0885783301 0.4752895059 0.7513916227 -0.3720198931 0.266667797126 +1403637245688318976.0000000000 9.3348217147 2.5954092855 1.0916691236 0.4765675322 0.7547819074 -0.3659272913 0.263220206474 +1403637245738319104.0000000000 9.3261379125 2.6469289587 1.0939842163 0.4807878775 0.7569751395 -0.3588985831 0.258888899155 +1403637245788318976.0000000000 9.3185703053 2.7001462748 1.0954510409 0.4884907200 0.7577448142 -0.3498223628 0.25460543511 +1403637245838319104.0000000000 9.3114401557 2.7544238690 1.0962048766 0.4984734221 0.7577587501 -0.3378877840 0.251312096067 +1403637245888318976.0000000000 9.3044012853 2.8091747934 1.0951590125 0.5078588847 0.7586280975 -0.3253615347 0.24637904664 +1403637245938319104.0000000000 9.2968146920 2.8642995247 1.0925914324 0.5167333209 0.7603927759 -0.3121659765 0.239461697408 +1403637245988318976.0000000000 9.2883797945 2.9190893568 1.0883642432 0.5243962487 0.7633142884 -0.2974349252 0.2321472308 +1403637246038319104.0000000000 9.2794708044 2.9740348206 1.0829601537 0.5313438656 0.7670412697 -0.2816307789 0.223619076636 +1403637246088318976.0000000000 9.2696154813 3.0290317159 1.0764573551 0.5383102138 0.7710134624 -0.2652282928 0.213106328308 +1403637246138319104.0000000000 9.2590123692 3.0842318030 1.0683481540 0.5446860674 0.7753882383 -0.2472950616 0.202324789357 +1403637246188318976.0000000000 9.2470811179 3.1383939488 1.0591240874 0.5504690817 0.7800313522 -0.2289008413 0.190103352278 +1403637246238319104.0000000000 9.2342786154 3.1921622926 1.0484215448 0.5563485325 0.7842606737 -0.2101160625 0.176812743997 +1403637246288318976.0000000000 9.2206431506 3.2454550606 1.0363420728 0.5606101019 0.7891341567 -0.1901920725 0.1637393414 +1403637246338319104.0000000000 9.2061025567 3.2982307159 1.0235050058 0.5656463212 0.7929364447 -0.1689740703 0.150810468665 +1403637246388318976.0000000000 9.1909894845 3.3500678981 1.0096597082 0.5696818553 0.7966165196 -0.1464414891 0.139354205829 +1403637246438319104.0000000000 9.1752106017 3.4013525126 0.9947046115 0.5731244656 0.7998124621 -0.1228120038 0.12940472997 +1403637246488318976.0000000000 9.1584867759 3.4520814315 0.9785337824 0.5778147570 0.8011754452 -0.0996362527 0.119668833332 +1403637246538319104.0000000000 9.1402364026 3.5018638880 0.9613973286 0.5831125193 0.8012900327 -0.0784824447 0.108418537389 +1403637246588318976.0000000000 9.1209501915 3.5504267971 0.9432856177 0.5887931755 0.8001600441 -0.0570087559 0.0990782619149 +1403637246638319104.0000000000 9.0997314746 3.5974253086 0.9243097542 0.5940640254 0.7987623413 -0.0378073504 0.0873914189858 +1403637246688318976.0000000000 9.0766762358 3.6428693861 0.9053189360 0.6007488933 0.7955903879 -0.0193956853 0.0758980185953 +1403637246738319104.0000000000 9.0514875417 3.6863589214 0.8862581995 0.6046164165 0.7938374016 -0.0010881277 0.0652685583331 +1403637246788318976.0000000000 9.0238337040 3.7273761791 0.8689726282 0.6078981895 0.7920689010 0.0157801985 0.0532694343067 +1403637246838319104.0000000000 8.9944818245 3.7653311880 0.8528386811 0.6099013397 0.7906985816 0.0325671480 0.041898565148 +1403637246888318976.0000000000 8.9628191193 3.8000381192 0.8383583664 0.6096345992 0.7906074365 0.0483532936 0.0307814197567 +1403637246938319104.0000000000 8.9291703380 3.8322904580 0.8254193409 0.6061682787 0.7926678069 0.0621722293 0.0192971424986 +1403637246988318976.0000000000 8.8939242014 3.8625091654 0.8141494881 0.6002724559 0.7962375123 0.0746685761 0.0101688910247 +1403637247038319104.0000000000 8.8570576833 3.8905858082 0.8047826985 0.5947327615 0.7995060563 0.0841506119 0.00129720362306 +1403637247088318976.0000000000 8.8190419200 3.9175168814 0.7959958408 0.5880923591 0.8036258317 0.0910755528 -0.00617604146141 +1403637247138319104.0000000000 8.7796496213 3.9431957396 0.7869704080 0.5819712807 0.8074834609 0.0953555964 -0.0136820711276 +1403637247188318976.0000000000 8.7394793056 3.9678216486 0.7766282859 0.5771395505 0.8104189248 0.0988917296 -0.0187491674272 +1403637247238319104.0000000000 8.6980376562 3.9923956489 0.7657941748 0.5734995097 0.8126993865 0.1001819878 -0.0241161540025 +1403637247288318976.0000000000 8.6559040106 4.0156242363 0.7532415161 0.5729910265 0.8128248950 0.1010546338 -0.0280166842943 +1403637247338319104.0000000000 8.6126950961 4.0386301476 0.7407708279 0.5773562705 0.8096336743 0.1008839635 -0.0312326146 +1403637247388318976.0000000000 8.5682668028 4.0621571044 0.7292691403 0.5883656804 0.8016208588 0.1006175696 -0.0332555190128 +1403637247438319104.0000000000 8.5229545585 4.0851621520 0.7174031661 0.6001012150 0.7929180751 0.0996525791 -0.035054550337 +1403637247488318976.0000000000 8.4772645151 4.1064485641 0.7035945218 0.6064274379 0.7882223264 0.0979691348 -0.03678825003 +1403637247538319104.0000000000 8.4312849756 4.1251551976 0.6876169162 0.6084676637 0.7865977478 0.0984217319 -0.0366639882006 +1403637247588318976.0000000000 8.3844019825 4.1413398685 0.6700641807 0.6088327090 0.7860452582 0.1004215989 -0.0370281904998 +1403637247638319104.0000000000 8.3369923409 4.1545984193 0.6515659678 0.6087997563 0.7855674035 0.1041693164 -0.037355922082 +1403637247688318976.0000000000 8.2891125046 4.1654698565 0.6325468296 0.6101585466 0.7836761025 0.1108464761 -0.0356563188359 +1403637247738319104.0000000000 8.2404399686 4.1735757695 0.6133513892 0.6110070955 0.7819386677 0.1186099498 -0.0342626482191 +1403637247788318976.0000000000 8.1906834299 4.1789240234 0.5950362434 0.6111293728 0.7805372353 0.1273374655 -0.0326754319481 +1403637247838319104.0000000000 8.1389375595 4.1815494880 0.5792656454 0.6121776118 0.7782662757 0.1358208268 -0.0330587170011 +1403637247888318976.0000000000 8.0851548008 4.1805566849 0.5661365626 0.6123697758 0.7768526127 0.1415976400 -0.0381232767218 +1403637247938319104.0000000000 8.0291497949 4.1762245587 0.5562616023 0.6140676378 0.7741943942 0.1460148657 -0.0471554367526 +1403637247988318976.0000000000 7.9722112716 4.1683544193 0.5478059797 0.6147727501 0.7722611298 0.1496829083 -0.0571160231722 +1403637248038319104.0000000000 7.9147094158 4.1568367596 0.5398508915 0.6112568797 0.7734105434 0.1542579019 -0.066375131818 +1403637248088318976.0000000000 7.8569529033 4.1423248227 0.5330284006 0.6051496148 0.7762493533 0.1610298097 -0.0728030610585 +1403637248138319104.0000000000 7.7987718578 4.1253092909 0.5275422714 0.5983373645 0.7794651753 0.1676429969 -0.0795126672451 +1403637248188318976.0000000000 7.7409713918 4.1068937890 0.5225971659 0.5917913150 0.7825027894 0.1738864638 -0.0850642216543 +1403637248238319104.0000000000 7.6828844507 4.0871496495 0.5160186705 0.5856853399 0.7853413936 0.1801343883 -0.0881089120374 +1403637248288318976.0000000000 7.6238488268 4.0661948778 0.5087929461 0.5813302045 0.7872032674 0.1831469514 -0.0939329724378 +1403637248338319104.0000000000 7.5649092020 4.0446266284 0.4993671809 0.5786442503 0.7878929253 0.1874383301 -0.0962415827437 +1403637248388318976.0000000000 7.5050727756 4.0224919928 0.4893195060 0.5775608834 0.7878395637 0.1893361749 -0.0994186134265 +1403637248438319104.0000000000 7.4449966926 3.9996455460 0.4780761752 0.5776208947 0.7871791621 0.1901067761 -0.102773938785 +1403637248488318976.0000000000 7.3848719228 3.9760884085 0.4661743353 0.5792321123 0.7855392781 0.1910788834 -0.104436884886 +1403637248538319104.0000000000 7.3240634733 3.9520144396 0.4547464889 0.5834084082 0.7821888742 0.1908404052 -0.106747993746 +1403637248588318976.0000000000 7.2631272875 3.9269002298 0.4443505426 0.5868899569 0.7794505611 0.1910692143 -0.107282601644 +1403637248638319104.0000000000 7.2024060954 3.9002075879 0.4351473652 0.5876172595 0.7789323833 0.1914240950 -0.106428917313 +1403637248688318976.0000000000 7.1417378110 3.8714463158 0.4270023955 0.5852214709 0.7808912589 0.1916897362 -0.104784143287 +1403637248738319104.0000000000 7.0807485614 3.8412110517 0.4208882466 0.5817912943 0.7837159518 0.1917506578 -0.102663927385 +1403637248788318976.0000000000 7.0198044880 3.8099841841 0.4170812850 0.5782207762 0.7867102198 0.1917726370 -0.099854993134 +1403637248838319104.0000000000 6.9576594281 3.7769814955 0.4159806025 0.5755214540 0.7891640189 0.1906502313 -0.0982226886895 +1403637248888318976.0000000000 6.8951333348 3.7435062512 0.4166566127 0.5733818865 0.7912548428 0.1889111220 -0.0972706228042 +1403637248938319104.0000000000 6.8320529750 3.7097792605 0.4196697929 0.5720118797 0.7927972698 0.1865471769 -0.0973398646087 +1403637248988318976.0000000000 6.7690419104 3.6751003952 0.4239320907 0.5709448774 0.7940955733 0.1845006218 -0.0969210400799 +1403637249038319104.0000000000 6.7054302744 3.6406238729 0.4304953444 0.5715023780 0.7941306037 0.1832068797 -0.0957959055899 +1403637249088318976.0000000000 6.6408972895 3.6059028939 0.4385436427 0.5713043865 0.7946981836 0.1821274469 -0.0943169547609 +1403637249138319104.0000000000 6.5752894611 3.5707128966 0.4487542022 0.5720469316 0.7945523482 0.1807127084 -0.0937645507854 +1403637249188318976.0000000000 6.5090584554 3.5344914404 0.4604005482 0.5717602755 0.7950341887 0.1800615550 -0.0926750373002 +1403637249238319104.0000000000 6.4422050106 3.4980423677 0.4740488861 0.5723792498 0.7948978064 0.1787709003 -0.0925226298365 +1403637249288318976.0000000000 6.3745970997 3.4619314824 0.4890567636 0.5730231838 0.7947394969 0.1772715082 -0.0927813302573 +1403637249338319104.0000000000 6.3089203661 3.4260113471 0.5046052738 0.5747725085 0.7937326616 0.1768176650 -0.0914359813883 +1403637249388318976.0000000000 6.2417773310 3.3895421097 0.5172153583 0.5746731274 0.7940340695 0.1757043033 -0.0915897966673 +1403637249438319104.0000000000 6.1740517753 3.3529280733 0.5261610176 0.5745351451 0.7942658816 0.1748262133 -0.0921242179085 +1403637249488318976.0000000000 6.1112771299 3.3174257097 0.5307058072 0.5750407448 0.7940257120 0.1742701387 -0.0920935899264 +1403637249538319104.0000000000 6.0447975134 3.2811098986 0.5303147942 0.5747438692 0.7942829747 0.1739614155 -0.0923117917005 +1403637249588318976.0000000000 5.9786613872 3.2438205177 0.5254323898 0.5747795668 0.7942352017 0.1736874786 -0.0930137289156 +1403637249638319104.0000000000 5.9124022154 3.2060077709 0.5163369375 0.5751336514 0.7939161616 0.1738242879 -0.0932927025907 +1403637249688318976.0000000000 5.8457306169 3.1684300019 0.5060266112 0.5769645497 0.7925413185 0.1737930653 -0.0937343976736 +1403637249738319104.0000000000 5.7823162651 3.1313463671 0.4952609296 0.5806561138 0.7897105675 0.1732727351 -0.0957718979197 +1403637249788318976.0000000000 5.7172357468 3.0937739139 0.4854456210 0.5843203784 0.7866967127 0.1741200918 -0.0967479777947 +1403637249838319104.0000000000 5.6518757371 3.0552910473 0.4771476936 0.5873318711 0.7838549077 0.1754839875 -0.099086462598 +1403637249888318976.0000000000 5.5863296297 3.0156601518 0.4703629800 0.5884805371 0.7819799306 0.1781223112 -0.102325401748 +1403637249938319104.0000000000 5.5322176021 2.9773560213 0.4618503346 0.5876352251 0.7811339620 0.1827840001 -0.105378294544 +1403637249988318976.0000000000 5.4687855801 2.9345094532 0.4574753652 0.5845285700 0.7817575821 0.1863924059 -0.111531631164 +1403637250038319104.0000000000 5.4049738947 2.8899207313 0.4550907748 0.5800144748 0.7834781531 0.1890806642 -0.118294949997 +1403637250088318976.0000000000 5.3406132818 2.8442770634 0.4552805102 0.5757103371 0.7849957310 0.1912133848 -0.125605539293 +1403637250138319104.0000000000 5.2775600372 2.7985056501 0.4565881222 0.5708486307 0.7867629735 0.1950214465 -0.130776525918 +1403637250188318976.0000000000 5.2118964222 2.7505744283 0.4590789847 0.5681221996 0.7867750075 0.1991952353 -0.136174565057 +1403637250238319104.0000000000 5.1478097482 2.7028537874 0.4604690900 0.5655086465 0.7865477052 0.2026823729 -0.143047313695 +1403637250288318976.0000000000 5.0841551377 2.6550681120 0.4604991999 0.5630304105 0.7864033907 0.2055506059 -0.149383440906 +1403637250338319104.0000000000 5.0216208932 2.6080839683 0.4593126899 0.5611093626 0.7860181128 0.2071657434 -0.156250325914 +1403637250388318976.0000000000 4.9593465281 2.5613378896 0.4564791599 0.5591248821 0.7859908738 0.2092312752 -0.160685985771 +1403637250438319104.0000000000 4.8988696950 2.5156055820 0.4522021302 0.5565077032 0.7866456062 0.2097417138 -0.165820022761 +1403637250488318976.0000000000 4.8409160324 2.4709923215 0.4464576552 0.5536169979 0.7875972701 0.2099861506 -0.170600634061 +1403637250538319104.0000000000 4.7852909246 2.4274258222 0.4397015939 0.5501899600 0.7892312749 0.2109169414 -0.172971230228 +1403637250588318976.0000000000 4.7319469369 2.3848012289 0.4337903374 0.5475812770 0.7903891646 0.2114675009 -0.175274669045 +1403637250638319104.0000000000 4.6804729618 2.3435061844 0.4293911903 0.5456132251 0.7907185903 0.2151969298 -0.175387003556 +1403637250688318976.0000000000 4.6306006657 2.3031995179 0.4267166826 0.5440743127 0.7907951738 0.2176858350 -0.176745615234 +1403637250738319104.0000000000 4.5819951980 2.2639767808 0.4259378348 0.5430861104 0.7906609335 0.2202034244 -0.177265949494 +1403637250788318976.0000000000 4.5342425089 2.2265986183 0.4269976760 0.5425657793 0.7903019927 0.2234230657 -0.176429218593 +1403637250838319104.0000000000 4.4879796381 2.1907147596 0.4307850309 0.5429846804 0.7894848644 0.2242882693 -0.177696533415 +1403637250888318976.0000000000 4.4424346739 2.1563526153 0.4361655260 0.5441260366 0.7882786354 0.2247621813 -0.17895700905 +1403637250938319104.0000000000 4.3983739598 2.1234483440 0.4422118604 0.5431233452 0.7886566819 0.2244958907 -0.180663402469 +1403637250988318976.0000000000 4.3557384445 2.0917074868 0.4502196708 0.5431063453 0.7884043669 0.2240318572 -0.182383603765 +1403637251038319104.0000000000 4.3143912632 2.0610476913 0.4600231255 0.5423135252 0.7882799680 0.2247521682 -0.184383283844 +1403637251088318976.0000000000 4.2742444319 2.0312112459 0.4715744421 0.5401155518 0.7887197479 0.2259216927 -0.187498636848 +1403637251138319104.0000000000 4.2350473726 2.0029760422 0.4848493124 0.5366886420 0.7896933355 0.2273851355 -0.191430764436 +1403637251188318976.0000000000 4.1977940784 1.9762817182 0.5002985588 0.5338909761 0.7902051328 0.2289304677 -0.19526165704 +1403637251238319104.0000000000 4.1622731949 1.9514129711 0.5174362565 0.5315145714 0.7904497550 0.2309268718 -0.198378993662 +1403637251288318976.0000000000 4.1289924878 1.9280455728 0.5362795300 0.5304722731 0.7898156562 0.2331542144 -0.201070905442 +1403637251338319104.0000000000 4.0979358304 1.9064253110 0.5575263972 0.5315732120 0.7874468314 0.2378010425 -0.202010079551 +1403637251388318976.0000000000 4.0691001119 1.8874583118 0.5806150584 0.5361126402 0.7827052050 0.2450720826 -0.199738512582 +1403637251438319104.0000000000 4.0412054936 1.8695086683 0.6047692290 0.5381387412 0.7791139238 0.2511981077 -0.200717960302 +1403637251488318976.0000000000 4.0145965590 1.8526875264 0.6279345088 0.5401298121 0.7751177576 0.2583508329 -0.201759993729 +1403637251538319104.0000000000 3.9890445638 1.8364580629 0.6496361503 0.5408269359 0.7716292861 0.2651057204 -0.204483317736 +1403637251588318976.0000000000 3.9647150092 1.8209098334 0.6694867303 0.5410485634 0.7683129053 0.2720278390 -0.207274181824 +1403637251638319104.0000000000 3.9412466746 1.8061079639 0.6878116840 0.5409988615 0.7654033086 0.2778569936 -0.210412685246 +1403637251688318976.0000000000 3.9187403485 1.7916724822 0.7044695418 0.5398368579 0.7634122275 0.2826124797 -0.214261812068 +1403637251738319104.0000000000 3.8972092334 1.7779060397 0.7197599133 0.5387672943 0.7617270077 0.2865128144 -0.217743370582 +1403637251788318976.0000000000 3.8766769633 1.7648704619 0.7339622686 0.5382608168 0.7600070996 0.2897467787 -0.220706379251 +1403637251838319104.0000000000 3.8575007022 1.7526081258 0.7468798442 0.5380919438 0.7584988043 0.2932881913 -0.221627301429 +1403637251888318976.0000000000 3.8393850531 1.7411010854 0.7592519954 0.5406388160 0.7553929335 0.2957366721 -0.222780177396 +1403637251938319104.0000000000 3.8223093592 1.7302502504 0.7701978535 0.5441057632 0.7517751727 0.2995953268 -0.22141736224 +1403637251988318976.0000000000 3.8061313069 1.7197668735 0.7803464906 0.5492108773 0.7472085618 0.3030780259 -0.219523319304 +1403637252038319104.0000000000 3.7904276152 1.7088871176 0.7896211025 0.5525214456 0.7442227800 0.3050902411 -0.21856909805 +1403637252088318976.0000000000 3.7760952304 1.6972476146 0.7980820527 0.5560696021 0.7409317640 0.3066048671 -0.218632509654 +1403637252138319104.0000000000 3.7624018461 1.6847365507 0.8055780001 0.5584628836 0.7387297654 0.3066250733 -0.219951371546 +1403637252188318976.0000000000 3.7494772922 1.6710667213 0.8122016484 0.5598178053 0.7373335509 0.3052706771 -0.223053969275 +1403637252238319104.0000000000 3.7379740682 1.6565593817 0.8170793994 0.5592045134 0.7375537963 0.3040881782 -0.225466382567 +1403637252288318976.0000000000 3.7279830294 1.6413369324 0.8201361356 0.5580023402 0.7382332887 0.3033819546 -0.227165995234 +1403637252338319104.0000000000 3.7193760986 1.6255186746 0.8212090806 0.5559747531 0.7396376142 0.3028654367 -0.228255998489 +1403637252388318976.0000000000 3.7126316998 1.6088703044 0.8202447674 0.5524849423 0.7421835612 0.3028482715 -0.228488236943 +1403637252438319104.0000000000 3.7068244074 1.5917912695 0.8174569235 0.5480234391 0.7455569450 0.3030065837 -0.228039825815 +1403637252488318976.0000000000 3.7019899479 1.5744470393 0.8132950625 0.5449327870 0.7479355709 0.3031184324 -0.227507923803 +1403637252538319104.0000000000 3.6981407096 1.5569757943 0.8075039141 0.5425559919 0.7497709820 0.3032848392 -0.226924605581 +1403637252588318976.0000000000 3.6951291716 1.5394788219 0.8005755850 0.5403580014 0.7515024620 0.3032056739 -0.226547123882 +1403637252638319104.0000000000 3.6924705393 1.5219803409 0.7924278306 0.5375694509 0.7536179461 0.3027017228 -0.22682756398 +1403637252688318976.0000000000 3.6907043737 1.5046795823 0.7829209579 0.5328816847 0.7570001773 0.3025105743 -0.226881453751 +1403637252738319104.0000000000 3.6897844404 1.4878368157 0.7732497318 0.5272792622 0.7609392371 0.3017258591 -0.227836702676 +1403637252788318976.0000000000 3.6896360980 1.4721057686 0.7649907706 0.5215916796 0.7649642399 0.3005306452 -0.229026554524 +1403637252838319104.0000000000 3.6908267190 1.4577271862 0.7580565571 0.5188012426 0.7669537194 0.3012568027 -0.227753379427 +1403637252888318976.0000000000 3.6923428856 1.4455021809 0.7534315305 0.5213117997 0.7654271525 0.3024194729 -0.225605283957 +1403637252938319104.0000000000 3.6939002724 1.4351475946 0.7517169452 0.5264691713 0.7621720064 0.3028718349 -0.224037264578 +1403637252988318976.0000000000 3.6958325675 1.4259766148 0.7519958079 0.5311308166 0.7590736267 0.3043048294 -0.221598411056 +1403637253038319104.0000000000 3.6988468071 1.4170390283 0.7535038936 0.5349737853 0.7565766408 0.3051224724 -0.21976149008 +1403637253088318976.0000000000 3.7024814636 1.4079033762 0.7566862635 0.5375872282 0.7548868260 0.3049466825 -0.219438767925 +1403637253138319104.0000000000 3.7066083361 1.3990550091 0.7611204546 0.5398903062 0.7534394332 0.3049992422 -0.218684567648 +1403637253188318976.0000000000 3.7110977181 1.3901547800 0.7647509680 0.5408529924 0.7529048557 0.3048689638 -0.218328270815 +1403637253238319104.0000000000 3.7154780582 1.3814759276 0.7679193450 0.5420663030 0.7521970944 0.3044081600 -0.218401754762 +1403637253288318976.0000000000 3.7201170025 1.3727705184 0.7693083712 0.5422973904 0.7522435166 0.3042976811 -0.217821379533 +1403637253338319104.0000000000 3.7250632832 1.3640017251 0.7693494862 0.5416658184 0.7528442008 0.3033518131 -0.21863537678 +1403637253388318976.0000000000 3.7306051533 1.3554584759 0.7677118226 0.5424413704 0.7523923200 0.3038334648 -0.217596833925 +1403637253438319104.0000000000 3.7366266855 1.3466753749 0.7647987806 0.5421048223 0.7527218862 0.3022786150 -0.21945332657 +1403637253488318976.0000000000 3.7434130918 1.3382183256 0.7597540068 0.5429386443 0.7522438225 0.3024056843 -0.218855345266 +1403637253538319104.0000000000 3.7507671239 1.3297070031 0.7529426291 0.5421452273 0.7529524648 0.3028481337 -0.217770857078 +1403637253588318976.0000000000 3.7586914449 1.3208104994 0.7462673174 0.5422027453 0.7529506622 0.3031762359 -0.217176548749 +1403637253638319104.0000000000 3.7670354713 1.3121118139 0.7404343835 0.5428694558 0.7524753745 0.3043870640 -0.215457838145 +1403637253688318976.0000000000 3.7756278717 1.3035167996 0.7363679417 0.5444348582 0.7513380347 0.3053938156 -0.214047799028 +1403637253738319104.0000000000 3.7850837723 1.2946705886 0.7342459247 0.5456219664 0.7504916624 0.3062013304 -0.212837214033 +1403637253788318976.0000000000 3.7946657563 1.2857558399 0.7342003422 0.5481892430 0.7485984278 0.3075587749 -0.210942048078 +1403637253838319104.0000000000 3.8043997894 1.2763017781 0.7356589994 0.5488915527 0.7482368271 0.3076950754 -0.210198607414 +1403637253888318976.0000000000 3.8140167279 1.2662911999 0.7385800594 0.5495610679 0.7476454021 0.3082352810 -0.209761762414 +1403637253938319104.0000000000 3.8239423536 1.2554373804 0.7427990582 0.5497661061 0.7475405740 0.3080798367 -0.209826435548 +1403637253988318976.0000000000 3.8339830916 1.2441421092 0.7482506249 0.5500243095 0.7474689384 0.3081666880 -0.209276700813 +1403637254038319104.0000000000 3.8439058960 1.2323149538 0.7558675350 0.5513549397 0.7464402498 0.3089045181 -0.208357103768 +1403637254088318976.0000000000 3.8541231604 1.2192333817 0.7646038009 0.5516551468 0.7460079530 0.3090226606 -0.208934746483 +1403637254138319104.0000000000 3.8643551634 1.2051177563 0.7747028008 0.5522242661 0.7445395109 0.3108576583 -0.20994473777 +1403637254188318976.0000000000 3.8747897278 1.1898328556 0.7860461543 0.5509703491 0.7438362855 0.3132480498 -0.212167184229 +1403637254238319104.0000000000 3.8856323435 1.1736007406 0.7984605379 0.5488514267 0.7432286860 0.3174990899 -0.213465593618 +1403637254288318976.0000000000 3.8967678871 1.1564438866 0.8121942522 0.5461101402 0.7427598526 0.3226338146 -0.21442699885 +1403637254338319104.0000000000 3.9081002439 1.1383939153 0.8266095322 0.5428626525 0.7427205489 0.3274257038 -0.215542884763 +1403637254388318976.0000000000 3.9191824442 1.1200480255 0.8409512510 0.5393805986 0.7428326921 0.3320568981 -0.216809542714 +1403637254438319104.0000000000 3.9299878158 1.1014641026 0.8545449400 0.5367105439 0.7426389982 0.3354904808 -0.218804130881 +1403637254488318976.0000000000 3.9407178118 1.0827739248 0.8665289708 0.5343086165 0.7426420367 0.3391894486 -0.218969462628 +1403637254538319104.0000000000 3.9507942751 1.0639096117 0.8774195191 0.5321978613 0.7424465402 0.3418333348 -0.220654804154 +1403637254588318976.0000000000 3.9602432760 1.0450820529 0.8870018834 0.5318161593 0.7412481704 0.3440775825 -0.222111097633 +1403637254638319104.0000000000 3.9691062526 1.0262315070 0.8951121385 0.5319305926 0.7401283695 0.3450715827 -0.224021079614 +1403637254688318976.0000000000 3.9776031746 1.0073640828 0.9013952342 0.5326887792 0.7385753045 0.3465533494 -0.225055460211 +1403637254738319104.0000000000 3.9855797177 0.9884837806 0.9067830257 0.5342936759 0.7366852148 0.3470703652 -0.226643605231 +1403637254788318976.0000000000 3.9931933146 0.9691349291 0.9109554045 0.5357031994 0.7351597014 0.3466773046 -0.228860529706 +1403637254838319104.0000000000 4.0007984937 0.9493043406 0.9138994200 0.5365055717 0.7341127456 0.3456770596 -0.231835326601 +1403637254888318976.0000000000 4.0085145452 0.9293313110 0.9149314859 0.5377581212 0.7328563687 0.3452325708 -0.23356416255 +1403637254938319104.0000000000 4.0160668702 0.9090713798 0.9146273601 0.5384207130 0.7321703702 0.3446027166 -0.235114126614 +1403637254988318976.0000000000 4.0236488277 0.8883394932 0.9133491046 0.5400808717 0.7308449483 0.3441360881 -0.236111555196 +1403637255038319104.0000000000 4.0316175363 0.8669461356 0.9106497092 0.5399907757 0.7305412610 0.3446829896 -0.236459436016 +1403637255088318976.0000000000 4.0398363895 0.8449530103 0.9081132113 0.5401600502 0.7292001978 0.3459272591 -0.238387338542 +1403637255138319104.0000000000 4.0485085067 0.8215520723 0.9057823667 0.5386148882 0.7283740209 0.3481771896 -0.24111808825 +1403637255188318976.0000000000 4.0572321985 0.7978742335 0.9042045927 0.5374579749 0.7267215543 0.3518198362 -0.243387573055 +1403637255238319104.0000000000 4.0660236578 0.7738592869 0.9046164983 0.5361507717 0.7249300392 0.3553127153 -0.246519091765 +1403637255288318976.0000000000 4.0755470292 0.7492531694 0.9072523983 0.5350636080 0.7231847865 0.3579400444 -0.250179184988 +1403637255338319104.0000000000 4.0854899856 0.7245138289 0.9115250232 0.5343077520 0.7212577548 0.3605424847 -0.253597306755 +1403637255388318976.0000000000 4.0960977579 0.6988280755 0.9160553925 0.5313879300 0.7204860093 0.3637980185 -0.257250422852 +1403637255438319104.0000000000 4.1073351359 0.6726324638 0.9197358508 0.5294663404 0.7186690137 0.3683549396 -0.259797770697 +1403637255488318976.0000000000 4.1188110757 0.6461566468 0.9221140744 0.5272302439 0.7166362220 0.3733377915 -0.262830151612 +1403637255538319104.0000000000 4.1308631135 0.6191123397 0.9229110139 0.5253528843 0.7138709770 0.3792808359 -0.265591081579 +1403637255588318976.0000000000 4.1429346369 0.5920540313 0.9219734695 0.5237873502 0.7103715569 0.3862253773 -0.268046676546 +1403637255638319104.0000000000 4.1555450468 0.5642515398 0.9197810218 0.5221673364 0.7065970058 0.3927872230 -0.271625001736 +1403637255688318976.0000000000 4.1685778741 0.5359227151 0.9163710149 0.5192210270 0.7031229613 0.4008515978 -0.274491571734 +1403637255738319104.0000000000 4.1819107080 0.5069239049 0.9131207669 0.5154759130 0.6996799088 0.4092656933 -0.277910418458 +1403637255788318976.0000000000 4.1953097454 0.4775576153 0.9111257095 0.5118244013 0.6958276682 0.4181895576 -0.281028703829 +1403637255838319104.0000000000 4.2085614706 0.4477862668 0.9110390803 0.5070649606 0.6924089008 0.4268500037 -0.285051072759 +1403637255888318976.0000000000 4.2217283286 0.4170275820 0.9128686858 0.5022846459 0.6887100538 0.4356582579 -0.289120180213 +1403637255938319104.0000000000 4.2342602984 0.3865359377 0.9174279294 0.4987910633 0.6843672533 0.4432787678 -0.293858591601 +1403637255988318976.0000000000 4.2463833260 0.3558320783 0.9241373850 0.4947833864 0.6810277843 0.4498647617 -0.298349214276 +1403637256038319104.0000000000 4.2586238084 0.3251817275 0.9331174618 0.4922523564 0.6773972806 0.4559418771 -0.301558529438 +1403637256088318976.0000000000 4.2714361276 0.2943919142 0.9439963167 0.4902191573 0.6744498995 0.4611316484 -0.30357884268 +1403637256138319104.0000000000 4.2835792036 0.2635482743 0.9556295855 0.4893847840 0.6715511052 0.4645817437 -0.306080789423 +1403637256188318976.0000000000 4.2950770526 0.2328251840 0.9671024216 0.4900296084 0.6684120895 0.4667673186 -0.308584723804 +1403637256238319104.0000000000 4.3061774493 0.2019639539 0.9773821654 0.4917543411 0.6650419854 0.4676362922 -0.31179019211 +1403637256288318976.0000000000 4.3169140706 0.1709883048 0.9860818940 0.4923474384 0.6631253149 0.4682396606 -0.314022987971 +1403637256338319104.0000000000 4.3276147241 0.1396392698 0.9926271779 0.4933291278 0.6614024005 0.4689994020 -0.314980629843 +1403637256388318976.0000000000 4.3382096923 0.1077571536 0.9975907867 0.4942925049 0.6601523702 0.4691503674 -0.315866586444 +1403637256438319104.0000000000 4.3490987667 0.0753638749 1.0007668392 0.4954272172 0.6591489345 0.4698136608 -0.315197840532 +1403637256488318976.0000000000 4.3600445826 0.0423698423 1.0027359347 0.4964574679 0.6587517653 0.4694819843 -0.314901191947 +1403637256538319104.0000000000 4.3710104261 0.0087536514 1.0035051664 0.4969566925 0.6587821722 0.4683565610 -0.3157249233 +1403637256588318976.0000000000 4.3823354335 -0.0252328848 1.0025636587 0.4971112380 0.6592596645 0.4676365284 -0.315552197068 +1403637256638319104.0000000000 4.3939228469 -0.0597102057 0.9997814163 0.4949773016 0.6617675774 0.4671261688 -0.31441101569 +1403637256688318976.0000000000 4.4057847488 -0.0952602340 0.9958396938 0.4894999095 0.6664779953 0.4655001804 -0.315446512679 +1403637256738319104.0000000000 4.4180850191 -0.1312816468 0.9906800665 0.4824564062 0.6722977826 0.4637102454 -0.31658224187 +1403637256788318976.0000000000 4.4302630977 -0.1670249579 0.9849432068 0.4765840642 0.6774881404 0.4610504624 -0.318292193659 +1403637256838319104.0000000000 4.4418732006 -0.2018508010 0.9787217305 0.4727080743 0.6810640040 0.4582091538 -0.320535911139 +1403637256888318976.0000000000 4.4530369888 -0.2357633074 0.9718204571 0.4717985175 0.6817038354 0.4570894936 -0.322110593642 +1403637256938319104.0000000000 4.4630940105 -0.2683451595 0.9647133348 0.4747305967 0.6787216670 0.4578919051 -0.322959382296 +1403637256988318976.0000000000 4.4737755722 -0.3006375386 0.9586134388 0.4759005490 0.6759205320 0.4600004358 -0.324113716233 +1403637257038319104.0000000000 4.4850743510 -0.3327221746 0.9540887898 0.4781219554 0.6712361465 0.4637507886 -0.325233204776 +1403637257088318976.0000000000 4.4939390669 -0.3638951658 0.9512850093 0.4795729392 0.6670682477 0.4674072218 -0.326435656653 +1403637257138319104.0000000000 4.5046626956 -0.3953300596 0.9501895065 0.4803142342 0.6636160290 0.4711165757 -0.327049192827 +1403637257188318976.0000000000 4.5147063813 -0.4266921759 0.9512093299 0.4803404577 0.6607578092 0.4742834823 -0.32821843455 +1403637257238319104.0000000000 4.5252095659 -0.4581416563 0.9536747497 0.4792744797 0.6589398465 0.4775309831 -0.328722393465 +1403637257288318976.0000000000 4.5355574097 -0.4896322164 0.9577565984 0.4778131097 0.6573689359 0.4808304621 -0.329185025466 +1403637257338319104.0000000000 4.5461365435 -0.5211028681 0.9639493499 0.4762759122 0.6560603883 0.4841231738 -0.329197167387 +1403637257388318976.0000000000 4.5563769694 -0.5523491485 0.9711012582 0.4756130386 0.6543266880 0.4874861641 -0.328642758497 +1403637257438319104.0000000000 4.5662871296 -0.5836061940 0.9784090898 0.4748223541 0.6530951550 0.4898954134 -0.328653213185 +1403637257488318976.0000000000 4.5759355968 -0.6148948709 0.9846749137 0.4741439676 0.6521417764 0.4915963730 -0.328985725445 +1403637257538319104.0000000000 4.5855338864 -0.6461111441 0.9894460243 0.4746359611 0.6504776838 0.4943715987 -0.32740832266 +1403637257588318976.0000000000 4.5948703309 -0.6779188552 0.9927586015 0.4723740727 0.6510897197 0.4956017671 -0.327603114581 +1403637257638319104.0000000000 4.6036791376 -0.7100693885 0.9946172356 0.4696735982 0.6523573282 0.4964000303 -0.327755453767 +1403637257688318976.0000000000 4.6119227589 -0.7426377899 0.9946535057 0.4657281005 0.6544229631 0.4978302676 -0.327097762812 +1403637257738319104.0000000000 4.6192534834 -0.7753453661 0.9938035920 0.4628094172 0.6552095131 0.4993975420 -0.327276690767 +1403637257788318976.0000000000 4.6262164317 -0.8081831637 0.9915257795 0.4590101602 0.6558843550 0.5015879928 -0.327925099999 +1403637257838319104.0000000000 4.6326008350 -0.8408705835 0.9877999384 0.4555906999 0.6557356508 0.5044093108 -0.328662619676 +1403637257888318976.0000000000 4.6379893638 -0.8736074013 0.9827606026 0.4517139601 0.6552074058 0.5076084235 -0.330138519495 +1403637257938319104.0000000000 4.6423246650 -0.9062211324 0.9767956610 0.4479129251 0.6538937294 0.5108452756 -0.332917567264 +1403637257988318976.0000000000 4.6454655055 -0.9385114115 0.9699759862 0.4448109357 0.6514186889 0.5147637755 -0.335879708629 +1403637258038319104.0000000000 4.6473627051 -0.9706730219 0.9629694345 0.4409173454 0.6483279429 0.5191003983 -0.340290389986 +1403637258088318976.0000000000 4.6479812305 -1.0026095000 0.9569220372 0.4371194865 0.6443435713 0.5240980917 -0.345063917118 +1403637258138319104.0000000000 4.6474486898 -1.0341455111 0.9527451728 0.4350115581 0.6382359956 0.5295714156 -0.350676309517 +1403637258188318976.0000000000 4.6455278613 -1.0650820981 0.9508641364 0.4348909313 0.6299097104 0.5355470007 -0.356753478835 +1403637258238319104.0000000000 4.6425300537 -1.0953350901 0.9504619673 0.4360023088 0.6214746303 0.5412683045 -0.361524401828 +1403637258288318976.0000000000 4.6383624861 -1.1251504313 0.9504147694 0.4371328454 0.6140223095 0.5453994472 -0.366648226402 +1403637258338319104.0000000000 4.6336212093 -1.1548820322 0.9493649374 0.4378720326 0.6073534812 0.5491849425 -0.371195003919 +1403637258388318976.0000000000 4.6288298698 -1.1845930721 0.9468616296 0.4365372675 0.6030743069 0.5520594611 -0.375455651016 +1403637258438319104.0000000000 4.6238254285 -1.2143825701 0.9429177217 0.4334589323 0.6008197357 0.5536021508 -0.380333613886 +1403637258488318976.0000000000 4.6189398679 -1.2440466923 0.9371878649 0.4284822651 0.6005783678 0.5550668162 -0.38419969048 +1403637258538319104.0000000000 4.6136188478 -1.2733790517 0.9301687739 0.4226745212 0.6017169751 0.5559438076 -0.387568592359 +1403637258588318976.0000000000 4.6078036138 -1.3017584120 0.9222317956 0.4196093333 0.6017270850 0.5565628026 -0.389987652768 +1403637258638319104.0000000000 4.6014973033 -1.3291026968 0.9137104883 0.4195813381 0.6002786677 0.5566178308 -0.392165287 +1403637258688318976.0000000000 4.5949738693 -1.3556759154 0.9044452517 0.4211037448 0.5983064804 0.5562961030 -0.393999539797 +1403637258738319104.0000000000 4.5885660568 -1.3816545356 0.8946211198 0.4216420747 0.5970952157 0.5559115412 -0.395799977982 +1403637258788318976.0000000000 4.5822468057 -1.4065712931 0.8841747763 0.4231328433 0.5958908516 0.5555976253 -0.396464334741 +1403637258838319104.0000000000 4.5765498056 -1.4309221988 0.8735434268 0.4239913770 0.5951277205 0.5548806555 -0.397695570391 +1403637258888318976.0000000000 4.5715227842 -1.4548290006 0.8633109685 0.4245736987 0.5947722207 0.5537385516 -0.399195185684 +1403637258938319104.0000000000 4.5667384005 -1.4781244255 0.8546669200 0.4238925915 0.5955973954 0.5526142169 -0.400245350752 +1403637258988318976.0000000000 4.5619338487 -1.5004877776 0.8486913846 0.4235353691 0.5962028997 0.5520504832 -0.400499884538 +1403637259038319104.0000000000 4.5573804563 -1.5221978208 0.8452504044 0.4223633933 0.5976146693 0.5507042740 -0.401485583295 +1403637259088318976.0000000000 4.5523319116 -1.5429103559 0.8434573409 0.4233575911 0.5977279960 0.5508350035 -0.400087980044 +1403637259138319104.0000000000 4.5473954258 -1.5629642617 0.8460540153 0.4239944396 0.5975083686 0.5504381957 -0.400287718236 +1403637259188318976.0000000000 4.5434811599 -1.5822296854 0.8512640829 0.4235568882 0.5983071741 0.5495507395 -0.400776836381 +1403637259238319104.0000000000 4.5396643485 -1.6005043605 0.8587326064 0.4243588430 0.5984560933 0.5486998530 -0.400871984568 +1403637259288318976.0000000000 4.5361426847 -1.6181726666 0.8670093702 0.4243654759 0.5988968674 0.5476988492 -0.401574968863 +1403637259338319104.0000000000 4.5329731492 -1.6350210160 0.8745011206 0.4240066978 0.5998748843 0.5470511762 -0.401376947554 +1403637259388318976.0000000000 4.5300248799 -1.6512242087 0.8811465207 0.4236304268 0.6006510929 0.5461941105 -0.401780437206 +1403637259438319104.0000000000 4.5285018165 -1.6669708171 0.8885012204 0.4223853585 0.6020970478 0.5436481579 -0.404371653658 +1403637259488318976.0000000000 4.5268264863 -1.6816743443 0.8942176241 0.4200595201 0.6040132339 0.5405778066 -0.408036331611 +1403637259538319104.0000000000 4.5257427940 -1.6948732023 0.8987434012 0.4186943192 0.6052384742 0.5386858815 -0.410120686435 +1403637259588318976.0000000000 4.5253043608 -1.7064134598 0.9021817687 0.4179708022 0.6059019599 0.5376810929 -0.411196140313 +1403637259638319104.0000000000 4.5252344190 -1.7162976529 0.9048478882 0.4189709520 0.6056062441 0.5374030935 -0.410977290713 +1403637259688318976.0000000000 4.5255185679 -1.7246900931 0.9062665254 0.4203003292 0.6050537104 0.5389118175 -0.408450356563 +1403637259738319104.0000000000 4.5263152751 -1.7317555011 0.9065050971 0.4204591552 0.6052011714 0.5414079699 -0.404750603584 +1403637259788318976.0000000000 4.5277372355 -1.7377276203 0.9058539203 0.4206917558 0.6052509806 0.5442279388 -0.400631561137 +1403637259838319104.0000000000 4.5292752860 -1.7427924514 0.9047294741 0.4214445813 0.6048666057 0.5462058147 -0.397718571564 +1403637259888318976.0000000000 4.5305683666 -1.7474266758 0.9036391712 0.4212388010 0.6051206337 0.5448663641 -0.399383946029 +1403637259938319104.0000000000 4.5320291676 -1.7513150711 0.9017956533 0.4208349826 0.6054467965 0.5423197862 -0.402767108416 +1403637259988318976.0000000000 4.5338848187 -1.7540110623 0.8983675678 0.4215098750 0.6048740896 0.5415333448 -0.403978214062 +1403637260038319104.0000000000 4.5360226446 -1.7554971308 0.8936425582 0.4238662007 0.6032042531 0.5419523165 -0.403447344248 +1403637260088318976.0000000000 4.5387088254 -1.7561470731 0.8877597071 0.4260998003 0.6015245868 0.5428768720 -0.402357842641 +1403637260138319104.0000000000 4.5419433808 -1.7558660301 0.8804578989 0.4276172422 0.6003578474 0.5448096682 -0.399870447452 +1403637260188318976.0000000000 4.5456325078 -1.7550486036 0.8721219606 0.4288613685 0.5993845404 0.5470002742 -0.396997228408 +1403637260238319104.0000000000 4.5497635654 -1.7539752063 0.8627086547 0.4302418900 0.5981079326 0.5500715992 -0.393166698404 +1403637260288318976.0000000000 4.5540801045 -1.7528175313 0.8531221395 0.4323268475 0.5964538271 0.5522205365 -0.390370091234 +1403637260338319104.0000000000 4.5588836443 -1.7514748222 0.8430985745 0.4348772448 0.5943379850 0.5546871865 -0.38725478274 +1403637260388318976.0000000000 4.5639110986 -1.7502247356 0.8327619675 0.4388398606 0.5912340695 0.5573328790 -0.383721140751 +1403637260438319104.0000000000 4.5689590973 -1.7494330202 0.8221229773 0.4421425786 0.5885123878 0.5594725930 -0.380990193171 +1403637260488318976.0000000000 4.5741427767 -1.7497504592 0.8111586209 0.4409107790 0.5890121102 0.5612379671 -0.379044012383 +1403637260538319104.0000000000 4.5793624959 -1.7508602039 0.7997314454 0.4377117667 0.5911588118 0.5634692255 -0.376087889162 +1403637260588318976.0000000000 4.5843941145 -1.7529016429 0.7882442179 0.4331063120 0.5942093120 0.5654065190 -0.373697316478 +1403637260638319104.0000000000 4.5886513623 -1.7558698837 0.7768478704 0.4286841152 0.5972538414 0.5665075588 -0.372272701319 +1403637260688318976.0000000000 4.5918621553 -1.7594268056 0.7655331541 0.4268386130 0.5986887418 0.5667645232 -0.371696871304 +1403637260738319104.0000000000 4.5942593653 -1.7637960661 0.7547572442 0.4261255028 0.5991209778 0.5650572493 -0.374408085901 +1403637260788318976.0000000000 4.5958986185 -1.7684015982 0.7438693133 0.4281990858 0.5975193313 0.5639465859 -0.376271763289 +1403637260838319104.0000000000 4.5970579850 -1.7736137912 0.7332267336 0.4304908858 0.5955459292 0.5617536067 -0.380046745573 +1403637260888318976.0000000000 4.5979403094 -1.7791745900 0.7222442083 0.4319510080 0.5941515959 0.5601625691 -0.382910046677 +1403637260938319104.0000000000 4.5987120038 -1.7850504810 0.7115285172 0.4340841611 0.5924418722 0.5581425194 -0.386083536567 +1403637260988318976.0000000000 4.5995081584 -1.7910570521 0.7002799300 0.4364755479 0.5904907655 0.5572580356 -0.387650917139 +1403637261038319104.0000000000 4.6006768043 -1.7974437409 0.6888969912 0.4364444607 0.5903778931 0.5568992942 -0.388372697493 +1403637261088318976.0000000000 4.6024678896 -1.8041265547 0.6772291802 0.4338978472 0.5920334996 0.5579484725 -0.387198263893 +1403637261138319104.0000000000 4.6042474584 -1.8110419454 0.6654426416 0.4300932672 0.5947550958 0.5599354547 -0.384393605778 +1403637261188318976.0000000000 4.6060966949 -1.8181517097 0.6539553300 0.4265716941 0.5971550992 0.5627642715 -0.380445465227 +1403637261238319104.0000000000 4.6076253975 -1.8256527123 0.6432642979 0.4226856249 0.5997455589 0.5651900565 -0.37709723817 +1403637261288318976.0000000000 4.6083638069 -1.8332201906 0.6339796979 0.4208352601 0.6010529775 0.5668674948 -0.374558734264 +1403637261338319104.0000000000 4.6078581633 -1.8408752015 0.6268863910 0.4220228475 0.6002978699 0.5663197311 -0.375261436466 +1403637261388318976.0000000000 4.6063516155 -1.8489734037 0.6217379650 0.4244296027 0.5987734873 0.5637856321 -0.378781710627 +1403637261438319104.0000000000 4.6043194393 -1.8573181024 0.6178435327 0.4256841132 0.5980931737 0.5602319807 -0.383689612919 +1403637261488318976.0000000000 4.6021872596 -1.8654619080 0.6147637826 0.4260631368 0.5977678218 0.5575583489 -0.387649999658 +1403637261538319104.0000000000 4.6003873806 -1.8731016976 0.6112353259 0.4238917713 0.5994872226 0.5578049293 -0.38702002144 +1403637261588318976.0000000000 4.5986588949 -1.8804212083 0.6076540409 0.4203394760 0.6020121457 0.5602293320 -0.383456903552 +1403637261638319104.0000000000 4.5964670093 -1.8873371554 0.6049856553 0.4171806692 0.6041747527 0.5633290714 -0.378937349322 +1403637261688318976.0000000000 4.5930277583 -1.8940984913 0.6042672015 0.4151866135 0.6056602843 0.5653018976 -0.375805083344 +1403637261738319104.0000000000 4.5881586506 -1.9004567026 0.6051784548 0.4158228471 0.6054344077 0.5661761912 -0.374145771547 +1403637261788318976.0000000000 4.5817342120 -1.9068127567 0.6083915825 0.4188511486 0.6033905062 0.5645836226 -0.376469049856 +1403637261838319104.0000000000 4.5739944783 -1.9130341752 0.6125142104 0.4237465046 0.6003351451 0.5620624099 -0.379634641048 +1403637261888318976.0000000000 4.5655986360 -1.9193668916 0.6161992641 0.4270698531 0.5982356301 0.5593059433 -0.383278401756 +1403637261938319104.0000000000 4.5574883368 -1.9256384350 0.6182516942 0.4301163747 0.5964401895 0.5570000268 -0.386018101521 +1403637261988318976.0000000000 4.5497907889 -1.9317143976 0.6177723467 0.4326187434 0.5952255710 0.5552498050 -0.387614752705 +1403637262038319104.0000000000 4.5419421446 -1.9380306282 0.6151638084 0.4333471016 0.5951931653 0.5527779048 -0.390374145621 +1403637262088318976.0000000000 4.5346057947 -1.9440446178 0.6103401900 0.4344841919 0.5948391422 0.5506695780 -0.392623098757 +1403637262138319104.0000000000 4.5278712155 -1.9501969470 0.6034598466 0.4332904988 0.5961870590 0.5490786408 -0.394123052613 +1403637262188318976.0000000000 4.5214424586 -1.9562265114 0.5948234677 0.4327496787 0.5969249777 0.5474156599 -0.395909562744 +1403637262238319104.0000000000 4.5156541842 -1.9618562360 0.5846148747 0.4322945066 0.5976887707 0.5460791108 -0.397098473565 +1403637262288318976.0000000000 4.5108240686 -1.9667176447 0.5726824782 0.4311171881 0.5991567262 0.5446093092 -0.398183234072 +1403637262338319104.0000000000 4.5127971884 -1.9672887373 0.5761294645 0.4283355784 0.5997133208 0.5194146259 -0.432528625142 +1403637262388318976.0000000000 4.5168987334 -1.9642046189 0.5725722445 0.4455642220 0.5884996087 0.5363933977 -0.409173383179 +1403637262438319104.0000000000 4.5183509225 -1.9604750192 0.5712207207 0.4446337208 0.6032209358 0.5306013653 -0.396090328148 +1403637262488318976.0000000000 4.5204113651 -1.9581259696 0.5669351403 0.4408841838 0.6179557945 0.5185598139 -0.393506660501 +1403637262538319104.0000000000 4.5238495082 -1.9590589364 0.5685795759 0.4456251779 0.6142812581 0.5047793112 -0.411429925678 +1403637262588318976.0000000000 4.5268725499 -1.9578512943 0.5710118457 0.4552182945 0.6086061983 0.5010941937 -0.41385916532 +1403637262638319104.0000000000 4.5267222813 -1.9561532050 0.5710752576 0.4572353954 0.6091241820 0.4989612224 -0.413450387239 +1403637262688318976.0000000000 4.5249731489 -1.9565211379 0.5654588691 0.4460361428 0.6164796051 0.5080285639 -0.403623133785 +1403637262738319104.0000000000 4.5234887370 -1.9565050092 0.5654304832 0.4452771449 0.6186268128 0.5086425114 -0.400389717977 +1403637262788318976.0000000000 4.5251733281 -1.9558522220 0.5663870807 0.4479397885 0.6160760031 0.5048981408 -0.406051932275 +1403637262838319104.0000000000 4.5251185135 -1.9558094221 0.5664790089 0.4483566465 0.6155124290 0.5055702860 -0.405609976741 +1403637262888318976.0000000000 4.5237962115 -1.9567194699 0.5663397171 0.4461348682 0.6165077980 0.5062457011 -0.405705687123 +1403637262938319104.0000000000 4.5244595522 -1.9555807923 0.5664653478 0.4482844985 0.6155272739 0.5060646191 -0.405050348486 +1403637262988318976.0000000000 4.5239742126 -1.9561096420 0.5665935745 0.4467191060 0.6162344645 0.5059323442 -0.405868929779 +1403637263038319104.0000000000 4.5240620515 -1.9557084824 0.5666220420 0.4474612420 0.6158989289 0.5062307586 -0.405188061685 +1403637263088318976.0000000000 4.5237404994 -1.9557909119 0.5666773108 0.4471147505 0.6160879021 0.5061513094 -0.405382472244 +1403637263138319104.0000000000 4.5237948681 -1.9558219024 0.5668495496 0.4469956473 0.6161613851 0.5060178205 -0.405568741632 +1403637263188318976.0000000000 4.5237149416 -1.9554945177 0.5668566597 0.4475081450 0.6159090577 0.5062141287 -0.40514164033 +1403637263238319104.0000000000 4.5236227186 -1.9558630116 0.5669063955 0.4467118390 0.6163193555 0.5060525420 -0.405598088929 +1403637263288318976.0000000000 4.5236430236 -1.9556039245 0.5669190861 0.4471395456 0.6161509412 0.5062210479 -0.40517217949 +1403637263338319104.0000000000 4.5236874611 -1.9556016460 0.5670194188 0.4470791337 0.6161538459 0.5061482203 -0.405325382162 +1403637263388318976.0000000000 4.5234876471 -1.9557595412 0.5670241295 0.4469537891 0.6162105629 0.5061523095 -0.405372288412 +1403637263438319104.0000000000 4.5235770445 -1.9558072913 0.5669772995 0.4467998427 0.6163191052 0.5061268120 -0.405408819951 +1403637263488318976.0000000000 4.5236033279 -1.9556869591 0.5669413568 0.4471118298 0.6161591887 0.5062600390 -0.405141504606 +1403637263538319104.0000000000 4.5237363454 -1.9559182865 0.5669337257 0.4467087913 0.6163589208 0.5060594881 -0.405532651008 +1403637263588318976.0000000000 4.5236729843 -1.9558193441 0.5668253872 0.4469449110 0.6162572218 0.5061740393 -0.405284005467 +1403637263638319104.0000000000 4.5237562545 -1.9559038515 0.5668505879 0.4467474108 0.6163678028 0.5060981433 -0.405428356112 +1403637263688318976.0000000000 4.5237412344 -1.9558308329 0.5668005261 0.4467878985 0.6163211566 0.5061841473 -0.405347276616 +1403637263738319104.0000000000 4.5236422264 -1.9558540654 0.5668400383 0.4468603596 0.6162907008 0.5061625048 -0.405340732997 +1403637263788318976.0000000000 4.5236156041 -1.9560019994 0.5669299967 0.4465866025 0.6164809507 0.5059366268 -0.405635025028 +1403637263838319104.0000000000 4.5237339180 -1.9557633463 0.5668818709 0.4469987480 0.6162443479 0.5062768870 -0.405115707673 +1403637263888318976.0000000000 4.5236265101 -1.9560614226 0.5669964853 0.4465263387 0.6165153579 0.5059146587 -0.405676472581 +1403637263938319104.0000000000 4.5236519531 -1.9559339938 0.5669204220 0.4467242522 0.6164334365 0.5061151927 -0.405332792397 +1403637263988318976.0000000000 4.5237056571 -1.9559393972 0.5669529855 0.4466170721 0.6164875201 0.5060497609 -0.405450327368 +1403637264038319104.0000000000 4.5237338087 -1.9560010819 0.5669490542 0.4465247209 0.6165228036 0.5060241278 -0.405530379085 +1403637264088318976.0000000000 4.5237625205 -1.9559304897 0.5668855010 0.4465511513 0.6165128988 0.5061096197 -0.405409629599 +1403637264138319104.0000000000 4.5238485948 -1.9560311731 0.5669615466 0.4463974278 0.6166042773 0.5059716496 -0.405612119469 +1403637264188318976.0000000000 4.5238589103 -1.9559051464 0.5669549575 0.4466009277 0.6165085070 0.5060616636 -0.405421342333 +1403637264238319104.0000000000 4.5238123500 -1.9559886095 0.5669541856 0.4462959299 0.6166730190 0.5059842153 -0.40560362966 +1403637264288318976.0000000000 4.5237410605 -1.9558664210 0.5669498817 0.4463918614 0.6166114942 0.5060199242 -0.405547047281 +1403637264338319104.0000000000 4.5237244845 -1.9556858436 0.5669014235 0.4464062094 0.6166010363 0.5060742828 -0.405479319619 +1403637264388318976.0000000000 4.5236701917 -1.9555772678 0.5667892589 0.4462904014 0.6166278820 0.5061063656 -0.405525929372 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_04_difficult.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_04_difficult.txt new file mode 100644 index 0000000000000000000000000000000000000000..b29e4c02430ec8d7436f073413d40677ac515df3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_04_difficult.txt @@ -0,0 +1,1977 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403638128945096960.0000000000 4.6265387629 -1.7083496317 0.5461395743 0.5103444218 0.7886542665 -0.2868608379 0.187840034894 +1403638128995097088.0000000000 4.6264667325 -1.7086660172 0.5459771241 0.5103545302 0.7886576935 -0.2868694803 0.187784975855 +1403638129045096960.0000000000 4.6265826468 -1.7086672982 0.5459224344 0.5105650855 0.7887041375 -0.2861953050 0.188046069704 +1403638129095097088.0000000000 4.6266594564 -1.7086902883 0.5461518903 0.5095481369 0.7896265709 -0.2838013806 0.190544879462 +1403638129145096960.0000000000 4.6265764041 -1.7085134380 0.5469755807 0.5093628176 0.7896618557 -0.2826272271 0.192627942413 +1403638129195097088.0000000000 4.6267783987 -1.7082456054 0.5488787730 0.5113749782 0.7883076370 -0.2827621014 0.192645516975 +1403638129245096960.0000000000 4.6272339803 -1.7077847482 0.5529592999 0.5180352556 0.7837527253 -0.2869508712 0.187163931189 +1403638129295097088.0000000000 4.6284473929 -1.7074542724 0.5599171069 0.5297565726 0.7745431633 -0.2957947689 0.178735325688 +1403638129345096960.0000000000 4.6302831126 -1.7077073301 0.5682943014 0.5432033052 0.7627725207 -0.3068792631 0.170098114669 +1403638129395097088.0000000000 4.6313335338 -1.7080333601 0.5758898882 0.5528686513 0.7537294017 -0.3167727016 0.160882872985 +1403638129445096960.0000000000 4.6320791899 -1.7088266421 0.5805192415 0.5528399619 0.7527759908 -0.3212247354 0.156559744282 +1403638129495097088.0000000000 4.6318611996 -1.7093173713 0.5825376902 0.5449275584 0.7596984092 -0.3184428401 0.156545331229 +1403638129545096960.0000000000 4.6309573253 -1.7095449163 0.5833191401 0.5337461913 0.7701087610 -0.3104013885 0.160307446978 +1403638129595097088.0000000000 4.6302519116 -1.7095513040 0.5849344727 0.5238058714 0.7795870088 -0.3001647552 0.166651206006 +1403638129645096960.0000000000 4.6300114780 -1.7093429283 0.5881647634 0.5178649796 0.7853048374 -0.2920117115 0.172746448889 +1403638129695097088.0000000000 4.6304285300 -1.7089230865 0.5934252807 0.5177596401 0.7857565457 -0.2884046889 0.177015087998 +1403638129745096960.0000000000 4.6306944381 -1.7081088690 0.6003197164 0.5214061138 0.7832112676 -0.2884830113 0.17746359357 +1403638129795097088.0000000000 4.6304825665 -1.7072738470 0.6079204169 0.5218352639 0.7830865853 -0.2890553360 0.175813452065 +1403638129845096960.0000000000 4.6297027466 -1.7064570789 0.6162028514 0.5172684881 0.7869778469 -0.2876369059 0.174253235359 +1403638129895097088.0000000000 4.6286399232 -1.7052582262 0.6264462279 0.5119891586 0.7915682497 -0.2851021437 0.173215401285 +1403638129945096960.0000000000 4.6279600712 -1.7038640313 0.6396164262 0.5094834911 0.7941344912 -0.2821404544 0.17370591852 +1403638129995097088.0000000000 4.6277633240 -1.7016933612 0.6561908476 0.5132090996 0.7920005591 -0.2817173545 0.173167163686 +1403638130045096960.0000000000 4.6281045230 -1.6994771070 0.6754077944 0.5213725722 0.7861464668 -0.2841499289 0.171473588627 +1403638130095097088.0000000000 4.6284529895 -1.6975694487 0.6956640076 0.5291457539 0.7806242435 -0.2865233267 0.168922896323 +1403638130145096960.0000000000 4.6282415200 -1.6959079523 0.7156849888 0.5334093264 0.7782817449 -0.2865478486 0.166259876663 +1403638130195097088.0000000000 4.6276764732 -1.6944425933 0.7352616017 0.5339174741 0.7792888961 -0.2836119682 0.164939985299 +1403638130245096960.0000000000 4.6271123313 -1.6930132430 0.7553323343 0.5343280568 0.7803863731 -0.2804693764 0.163791224804 +1403638130295097088.0000000000 4.6268829640 -1.6914049418 0.7769824585 0.5389111541 0.7777442633 -0.2804610415 0.161338876625 +1403638130345096960.0000000000 4.6270492809 -1.6897567594 0.7997074930 0.5457727377 0.7724039834 -0.2843000674 0.157154945355 +1403638130395097088.0000000000 4.6270277814 -1.6884224261 0.8221989396 0.5512874298 0.7682855539 -0.2871549260 0.15284477677 +1403638130445096960.0000000000 4.6262848221 -1.6871553033 0.8433924477 0.5535940737 0.7674663642 -0.2867644429 0.149315557294 +1403638130495097088.0000000000 4.6252078508 -1.6863522327 0.8631529546 0.5523071851 0.7700608784 -0.2820480095 0.149706169127 +1403638130545096960.0000000000 4.6241106227 -1.6857190502 0.8822442057 0.5489587499 0.7738667490 -0.2764449131 0.152816084847 +1403638130595097088.0000000000 4.6231970315 -1.6847369692 0.9018205256 0.5484397328 0.7746894934 -0.2737877688 0.155274936799 +1403638130645096960.0000000000 4.6228185538 -1.6839091400 0.9222932971 0.5523096620 0.7717372031 -0.2734342589 0.156873938856 +1403638130695097088.0000000000 4.6228592120 -1.6832799780 0.9435722070 0.5583280042 0.7666182068 -0.2766076355 0.155095392321 +1403638130745096960.0000000000 4.6226685485 -1.6824648947 0.9648519304 0.5661972694 0.7598849863 -0.2827591196 0.14846797625 +1403638130795097088.0000000000 4.6222318663 -1.6820673547 0.9843140109 0.5714577872 0.7555529981 -0.2874641521 0.141209156269 +1403638130845096960.0000000000 4.6219608266 -1.6825674650 1.0009325774 0.5732478263 0.7546098320 -0.2879027113 0.138068678372 +1403638130895097088.0000000000 4.6216363237 -1.6838736069 1.0140858267 0.5753420494 0.7534734684 -0.2877914510 0.135776799607 +1403638130945096960.0000000000 4.6224393857 -1.6857148998 1.0238896651 0.5800781962 0.7489702707 -0.2891081895 0.137728989894 +1403638130995097088.0000000000 4.6239067658 -1.6876855203 1.0296513732 0.5872912705 0.7417812693 -0.2911186248 0.141772558409 +1403638131045096960.0000000000 4.6250379999 -1.6889138555 1.0309189735 0.5934216524 0.7356904133 -0.2929760533 0.144136707762 +1403638131095097088.0000000000 4.6261631464 -1.6898518843 1.0267175475 0.5946903291 0.7341500336 -0.2927309603 0.147226782528 +1403638131145096960.0000000000 4.6263353024 -1.6902465238 1.0177860170 0.5907938818 0.7377397587 -0.2906631704 0.149055556781 +1403638131195097088.0000000000 4.6260877092 -1.6904104021 1.0052499983 0.5828187121 0.7452246769 -0.2859987011 0.152207991622 +1403638131245096960.0000000000 4.6258634630 -1.6907393971 0.9907177497 0.5730681062 0.7539968036 -0.2804380926 0.156320958685 +1403638131295097088.0000000000 4.6256303404 -1.6912456137 0.9757983129 0.5661029333 0.7603392537 -0.2764236526 0.158119108413 +1403638131345096960.0000000000 4.6258529103 -1.6922238522 0.9610684348 0.5626385386 0.7633223390 -0.2747855063 0.158964798466 +1403638131395097088.0000000000 4.6266504827 -1.6924519128 0.9437289418 0.5622804542 0.7630541384 -0.2760169853 0.159385371222 +1403638131445096960.0000000000 4.6269506490 -1.6939525026 0.9273699944 0.5629587519 0.7621149884 -0.2766885090 0.160317363547 +1403638131495097088.0000000000 4.6275920018 -1.6962274327 0.9090225914 0.5610188719 0.7631722782 -0.2747020949 0.165422665626 +1403638131545096960.0000000000 4.6272695152 -1.6982202325 0.8894975622 0.5584607715 0.7649807905 -0.2745011829 0.166057392319 +1403638131595097088.0000000000 4.6270446843 -1.7004386581 0.8688359884 0.5554514150 0.7672561878 -0.2741593543 0.166217677335 +1403638131645096960.0000000000 4.6270178675 -1.7026453032 0.8476821211 0.5533788535 0.7692642716 -0.2723517669 0.166819782796 +1403638131695097088.0000000000 4.6274675815 -1.7048614764 0.8254363502 0.5528120529 0.7697252283 -0.2709598326 0.168827356316 +1403638131745096960.0000000000 4.6276457809 -1.7070794275 0.8024277599 0.5522239519 0.7702022022 -0.2697380883 0.170524597746 +1403638131795097088.0000000000 4.6279815591 -1.7097851883 0.7787088536 0.5502246740 0.7715223488 -0.2668746583 0.175453669788 +1403638131845096960.0000000000 4.6282495263 -1.7126820576 0.7549320698 0.5470964149 0.7734009204 -0.2647347197 0.180144545321 +1403638131895097088.0000000000 4.6283044197 -1.7153954919 0.7324220877 0.5452953492 0.7741957028 -0.2638439878 0.183467561203 +1403638131945096960.0000000000 4.6282777896 -1.7177524606 0.7122689216 0.5441976417 0.7748712879 -0.2626418747 0.185587336954 +1403638131995097088.0000000000 4.6281892316 -1.7200748454 0.6952719558 0.5406572504 0.7780157531 -0.2583905435 0.188720832163 +1403638132045096960.0000000000 4.6275917333 -1.7217579045 0.6828220843 0.5357255419 0.7829294410 -0.2515579530 0.191672195455 +1403638132095097088.0000000000 4.6269947029 -1.7229936794 0.6761824548 0.5292850707 0.7887381769 -0.2451159018 0.194081418471 +1403638132145096960.0000000000 4.6262944218 -1.7231555251 0.6777960149 0.5262753314 0.7920382082 -0.2403833067 0.194745008057 +1403638132195097088.0000000000 4.6260844075 -1.7229057799 0.6881356840 0.5279155568 0.7915464824 -0.2391041173 0.193877673236 +1403638132245096960.0000000000 4.6259411212 -1.7221421351 0.7063153133 0.5350741592 0.7869203919 -0.2411009451 0.190584037212 +1403638132295097088.0000000000 4.6253899022 -1.7212390838 0.7295830399 0.5435152615 0.7813265684 -0.2438213185 0.186201822524 +1403638132345096960.0000000000 4.6249469043 -1.7205212828 0.7557942193 0.5491270062 0.7775776360 -0.2449090727 0.183989394191 +1403638132395097088.0000000000 4.6233217658 -1.7193359971 0.7835977071 0.5536942567 0.7753018415 -0.2474999889 0.176276714789 +1403638132445096960.0000000000 4.6224205262 -1.7184494731 0.8125742317 0.5602306109 0.7711851658 -0.2502111710 0.169733533833 +1403638132495097088.0000000000 4.6214893839 -1.7174250006 0.8423385441 0.5704548131 0.7637527803 -0.2552793090 0.161540927588 +1403638132545096960.0000000000 4.6210973439 -1.7165563482 0.8713397522 0.5825425352 0.7541972659 -0.2603079612 0.155146525057 +1403638132595097088.0000000000 4.6201792826 -1.7149820626 0.8980750145 0.5930339173 0.7456055039 -0.2644031228 0.149913955779 +1403638132645096960.0000000000 4.6199213138 -1.7127061589 0.9286692364 0.5975740938 0.7418814894 -0.2667080356 0.146232287559 +1403638132695097088.0000000000 4.6172603994 -1.7100562175 0.9478057892 0.5945963807 0.7444325000 -0.2678874872 0.143219032376 +1403638132745096960.0000000000 4.6136917601 -1.7064963560 0.9636961344 0.5901762297 0.7481711215 -0.2689187021 0.140052570101 +1403638132795097088.0000000000 4.6100469571 -1.7031121108 0.9763977642 0.5882991122 0.7491826898 -0.2709912186 0.138539565796 +1403638132845096960.0000000000 4.6063478065 -1.7006797564 0.9859776333 0.5922502896 0.7456132364 -0.2727543475 0.137497498537 +1403638132895097088.0000000000 4.6037842286 -1.6989095637 0.9917371694 0.5987520076 0.7392521202 -0.2765911882 0.136013421344 +1403638132945096960.0000000000 4.6022199728 -1.6982592159 0.9932430903 0.6049045087 0.7342216485 -0.2776671270 0.133828520141 +1403638132995097088.0000000000 4.6022668619 -1.6985964076 0.9901724288 0.6081623453 0.7327583425 -0.2751409474 0.132292222734 +1403638133045096960.0000000000 4.6044666201 -1.7005054613 0.9828690849 0.6057439350 0.7366033101 -0.2689989025 0.134645605593 +1403638133095097088.0000000000 4.6092834076 -1.7038210633 0.9728129140 0.6004652698 0.7421652719 -0.2630020660 0.139506566757 +1403638133145096960.0000000000 4.6158261408 -1.7073740388 0.9611870459 0.5958850250 0.7458801128 -0.2612102871 0.142664221631 +1403638133195097088.0000000000 4.6255609811 -1.7128249856 0.9497310312 0.5925462750 0.7468552717 -0.2626459939 0.148705066932 +1403638133245096960.0000000000 4.6371139319 -1.7197601498 0.9384764458 0.5904497298 0.7457426242 -0.2673588855 0.154130728345 +1403638133295097088.0000000000 4.6503831594 -1.7284801245 0.9256415764 0.5865820878 0.7450690115 -0.2724802329 0.162936015263 +1403638133345096960.0000000000 4.6647976028 -1.7396428312 0.9121574571 0.5803815956 0.7467351254 -0.2767875304 0.170095616848 +1403638133395097088.0000000000 4.6801298348 -1.7523343193 0.8989072282 0.5739165575 0.7484813193 -0.2811455313 0.177066907916 +1403638133445096960.0000000000 4.6963720143 -1.7671302728 0.8865358406 0.5673204152 0.7490185334 -0.2869625859 0.186470526808 +1403638133495097088.0000000000 4.7124818478 -1.7829605239 0.8759001653 0.5633160511 0.7469172476 -0.2952696078 0.193921403022 +1403638133545096960.0000000000 4.7288236116 -1.8001835225 0.8661200779 0.5603854688 0.7433394114 -0.3061344004 0.199239490835 +1403638133595097088.0000000000 4.7432917271 -1.8184161659 0.8567485606 0.5573105874 0.7410279049 -0.3167002359 0.199958780528 +1403638133645096960.0000000000 4.7562432703 -1.8366701772 0.8475578064 0.5543075331 0.7395596215 -0.3261571946 0.198535159058 +1403638133695097088.0000000000 4.7680474795 -1.8550558577 0.8382227977 0.5506144450 0.7385396531 -0.3343127289 0.199042490659 +1403638133745096960.0000000000 4.7794263974 -1.8732408968 0.8283982368 0.5458678316 0.7373892095 -0.3418357717 0.203552866377 +1403638133795097088.0000000000 4.7907204064 -1.8895299829 0.8184219055 0.5416451088 0.7357245956 -0.3478397462 0.210564494835 +1403638133845096960.0000000000 4.8016322438 -1.9036692032 0.8080932589 0.5360109939 0.7354689260 -0.3519343716 0.218906079031 +1403638133895097088.0000000000 4.8112889194 -1.9136637937 0.7987492405 0.5313512226 0.7354523542 -0.3558141644 0.223991056496 +1403638133945096960.0000000000 4.8193634801 -1.9184623688 0.7914168730 0.5291259435 0.7341708065 -0.3592767065 0.22790175752 +1403638133995097088.0000000000 4.8255064411 -1.9170026172 0.7864689290 0.5289902818 0.7326414346 -0.3608814217 0.230587097667 +1403638134045096960.0000000000 4.8293934309 -1.9101766575 0.7829605062 0.5279531968 0.7333659179 -0.3601126107 0.231859354145 +1403638134095097088.0000000000 4.8312268464 -1.8990061725 0.7801021534 0.5247906514 0.7371118465 -0.3568281995 0.232238097639 +1403638134145096960.0000000000 4.8322595155 -1.8840627143 0.7784661474 0.5219099832 0.7408501903 -0.3527350946 0.233085645224 +1403638134195097088.0000000000 4.8331102648 -1.8658486640 0.7790182594 0.5227607292 0.7404722676 -0.3512909408 0.234556423467 +1403638134245096960.0000000000 4.8336989478 -1.8444977933 0.7817889060 0.5296067202 0.7344425039 -0.3532515946 0.23521105684 +1403638134295097088.0000000000 4.8332406090 -1.8209756890 0.7847778222 0.5352581630 0.7291657057 -0.3558665662 0.234893719912 +1403638134345096960.0000000000 4.8307455475 -1.7958187967 0.7866835011 0.5364975653 0.7281008375 -0.3586980138 0.231030880501 +1403638134395097088.0000000000 4.8268157905 -1.7697186596 0.7878224099 0.5361035104 0.7289611508 -0.3608840878 0.225768336862 +1403638134445096960.0000000000 4.8216580003 -1.7438990613 0.7887996413 0.5352207203 0.7299572235 -0.3628377054 0.221472417999 +1403638134495097088.0000000000 4.8155888714 -1.7184814157 0.7904119529 0.5366427125 0.7288458574 -0.3648745725 0.218322837851 +1403638134545096960.0000000000 4.8081312527 -1.6942808607 0.7922865024 0.5387133276 0.7269852524 -0.3678096446 0.214467850338 +1403638134595097088.0000000000 4.7984142496 -1.6705922901 0.7943925979 0.5417189726 0.7254826249 -0.3692792917 0.209399905504 +1403638134645096960.0000000000 4.7869742887 -1.6485392019 0.7962969434 0.5412393307 0.7264213118 -0.3700161106 0.206058590159 +1403638134695097088.0000000000 4.7737865772 -1.6276258214 0.7982883372 0.5389709824 0.7291290340 -0.3694478163 0.203443955374 +1403638134745096960.0000000000 4.7592729175 -1.6074706669 0.8003974724 0.5357334761 0.7330332806 -0.3684046604 0.199824568955 +1403638134795097088.0000000000 4.7447896335 -1.5880392613 0.8033577355 0.5310748624 0.7377389956 -0.3665225096 0.198398373954 +1403638134845096960.0000000000 4.7306088675 -1.5695280801 0.8078785665 0.5279917178 0.7407419921 -0.3645915629 0.198995073571 +1403638134895097088.0000000000 4.7167151512 -1.5525650517 0.8132751344 0.5279047725 0.7409773354 -0.3634989506 0.200343835646 +1403638134945096960.0000000000 4.7036497478 -1.5369462696 0.8183990784 0.5309824186 0.7386530298 -0.3630686289 0.201570194771 +1403638134995097088.0000000000 4.6911125531 -1.5228223449 0.8217086385 0.5333031988 0.7368063129 -0.3630747606 0.202190191632 +1403638135045096960.0000000000 4.6790258405 -1.5105416337 0.8225212228 0.5316115172 0.7388381720 -0.3606110175 0.203634585552 +1403638135095097088.0000000000 4.6679670202 -1.5000214941 0.8214808543 0.5279189557 0.7429626905 -0.3572223345 0.204206318471 +1403638135145096960.0000000000 4.6579704581 -1.4918935358 0.8188538369 0.5250493275 0.7467330972 -0.3538046624 0.203801732192 +1403638135195097088.0000000000 4.6502179359 -1.4868548124 0.8151440900 0.5224296268 0.7494466051 -0.3517565430 0.204118606738 +1403638135245096960.0000000000 4.6447042341 -1.4854487124 0.8106206962 0.5195500906 0.7518597425 -0.3507315836 0.204357498645 +1403638135295097088.0000000000 4.6423921225 -1.4872189393 0.8057541917 0.5194804542 0.7518849510 -0.3498230933 0.205992430667 +1403638135345096960.0000000000 4.6420029251 -1.4917855504 0.8002272581 0.5211982118 0.7499399668 -0.3504173500 0.20772614433 +1403638135395097088.0000000000 4.6429693567 -1.4989186346 0.7944990579 0.5216107930 0.7485318447 -0.3511951619 0.210438153263 +1403638135445096960.0000000000 4.6456886739 -1.5087776615 0.7883335564 0.5186919358 0.7491771802 -0.3513587843 0.215033097684 +1403638135495097088.0000000000 4.6498477915 -1.5201713563 0.7824810008 0.5149997641 0.7507999178 -0.3513343356 0.218263398206 +1403638135545096960.0000000000 4.6555762074 -1.5327283945 0.7780485867 0.5102738860 0.7532136545 -0.3525543159 0.219078082442 +1403638135595097088.0000000000 4.6641199881 -1.5471863383 0.7760242000 0.5054122220 0.7550307592 -0.3529811420 0.223363721059 +1403638135645096960.0000000000 4.6747522840 -1.5628321079 0.7757214269 0.5052189058 0.7529231358 -0.3551616846 0.227422045193 +1403638135695097088.0000000000 4.6859571492 -1.5797192436 0.7754918289 0.5079801825 0.7475766373 -0.3608938824 0.229871509951 +1403638135745096960.0000000000 4.6959763848 -1.5970374537 0.7746977325 0.5114149801 0.7421008811 -0.3673735041 0.229733995892 +1403638135795097088.0000000000 4.7040060352 -1.6151182226 0.7724072723 0.5115340734 0.7400591438 -0.3721256820 0.228402785028 +1403638135845096960.0000000000 4.7107718952 -1.6335437983 0.7699010294 0.5083396883 0.7416583727 -0.3719776813 0.230578021498 +1403638135895097088.0000000000 4.7163911810 -1.6528555647 0.7678974681 0.5007895967 0.7463668112 -0.3696879471 0.235535952113 +1403638135945096960.0000000000 4.7211152808 -1.6720538080 0.7686894945 0.4933323299 0.7511693301 -0.3677004603 0.239090403928 +1403638135995097088.0000000000 4.7269690012 -1.6914970301 0.7732565549 0.4889410170 0.7527399431 -0.3673196398 0.243712006468 +1403638136045096960.0000000000 4.7350150743 -1.7112545980 0.7814821768 0.4892754135 0.7501874675 -0.3677907789 0.250116525436 +1403638136095097088.0000000000 4.7451708146 -1.7318407631 0.7914588141 0.4942756047 0.7437260667 -0.3705767860 0.255413409946 +1403638136145096960.0000000000 4.7557770310 -1.7537349066 0.8010496438 0.5008446956 0.7360528596 -0.3757355154 0.257300604811 +1403638136195097088.0000000000 4.7659528142 -1.7767003870 0.8079267910 0.5072944335 0.7291880866 -0.3801638950 0.257706237891 +1403638136245096960.0000000000 4.7757332551 -1.8004342790 0.8104964752 0.5084976749 0.7261451091 -0.3833017415 0.25927431442 +1403638136295097088.0000000000 4.7851921755 -1.8237411396 0.8094459400 0.5068880328 0.7249446663 -0.3842190927 0.264377460834 +1403638136345096960.0000000000 4.7935980015 -1.8458633241 0.8056147109 0.5031490749 0.7252635112 -0.3849394514 0.269546780057 +1403638136395097088.0000000000 4.8000707325 -1.8649556354 0.8005763326 0.4998163549 0.7262497606 -0.3857112416 0.271977452463 +1403638136445096960.0000000000 4.8050353899 -1.8811854619 0.7959202703 0.4957881627 0.7276677326 -0.3861940904 0.274859770186 +1403638136495097088.0000000000 4.8080051058 -1.8924920772 0.7936248089 0.4933026901 0.7276730456 -0.3885852509 0.275945460981 +1403638136545096960.0000000000 4.8085460239 -1.8982150862 0.7945601890 0.4918011391 0.7264577436 -0.3944444524 0.273503858063 +1403638136595097088.0000000000 4.8067412306 -1.8989390822 0.7984368387 0.4931810528 0.7244346122 -0.3988852269 0.269921317566 +1403638136645096960.0000000000 4.8023960092 -1.8950494681 0.8043211595 0.4969539190 0.7229113952 -0.4005838939 0.264515521251 +1403638136695097088.0000000000 4.7956631443 -1.8876727168 0.8112784211 0.5007143827 0.7225716079 -0.4003793750 0.258595697121 +1403638136745096960.0000000000 4.7869641793 -1.8774761100 0.8190805730 0.5038597466 0.7235178039 -0.3988286554 0.252156790193 +1403638136795097088.0000000000 4.7765344833 -1.8641871392 0.8276364015 0.5094302591 0.7236360993 -0.3966819178 0.243875097389 +1403638136845096960.0000000000 4.7650781550 -1.8482168715 0.8357196120 0.5178720790 0.7213371856 -0.3956519870 0.234394282631 +1403638136895097088.0000000000 4.7528246489 -1.8306377932 0.8413978496 0.5287457430 0.7162296561 -0.3960962098 0.224835076341 +1403638136945096960.0000000000 4.7404264125 -1.8121652918 0.8434918548 0.5399731066 0.7099479088 -0.3964258912 0.217369555878 +1403638136995097088.0000000000 4.7279936772 -1.7938656929 0.8406734805 0.5477797790 0.7057243911 -0.3960939909 0.212131911764 +1403638137045096960.0000000000 4.7151608502 -1.7762671209 0.8326184449 0.5517824606 0.7049644318 -0.3944045119 0.207379717227 +1403638137095097088.0000000000 4.7029796785 -1.7606023093 0.8199336670 0.5506672689 0.7080825954 -0.3910420719 0.20608419402 +1403638137145096960.0000000000 4.6913331677 -1.7467058891 0.8038860080 0.5469143312 0.7133704196 -0.3864161082 0.206567059525 +1403638137195097088.0000000000 4.6798889525 -1.7344219684 0.7856820806 0.5417117481 0.7202581409 -0.3812089797 0.206049281006 +1403638137245096960.0000000000 4.6678907751 -1.7214242431 0.7652443220 0.5354038318 0.7277911816 -0.3757022154 0.206180935483 +1403638137295097088.0000000000 4.6579512830 -1.7120455521 0.7453778344 0.5311097539 0.7333674686 -0.3709522628 0.206128610596 +1403638137345096960.0000000000 4.6487678900 -1.7040398703 0.7250403799 0.5281390893 0.7372453145 -0.3684044292 0.204491137123 +1403638137395097088.0000000000 4.6411350573 -1.6977074157 0.7047220045 0.5240470256 0.7409081920 -0.3659361632 0.206204971994 +1403638137445096960.0000000000 4.6344672403 -1.6924523266 0.6845639679 0.5178919055 0.7455805025 -0.3637531961 0.208761349206 +1403638137495097088.0000000000 4.6288463086 -1.6881143599 0.6651111126 0.5104869670 0.7512313424 -0.3605160997 0.212326796538 +1403638137545096960.0000000000 4.6240835586 -1.6845687730 0.6465479127 0.5018248703 0.7577475789 -0.3568438524 0.215992757428 +1403638137595097088.0000000000 4.6210427103 -1.6820432699 0.6298461919 0.4938758448 0.7630733883 -0.3528403165 0.222057121023 +1403638137645096960.0000000000 4.6183062798 -1.6792776522 0.6157631983 0.4905224798 0.7646852286 -0.3518994215 0.225412943484 +1403638137695097088.0000000000 4.6164551823 -1.6774320483 0.6037472911 0.4895451531 0.7636006914 -0.3531227580 0.229268063621 +1403638137745096960.0000000000 4.6148736982 -1.6762033134 0.5934907577 0.4901653155 0.7614096878 -0.3552200584 0.231974052073 +1403638137795097088.0000000000 4.6130439304 -1.6755546116 0.5841378734 0.4889413932 0.7609203927 -0.3580052594 0.231880797621 +1403638137845096960.0000000000 4.6113487001 -1.6755166203 0.5755994504 0.4851356912 0.7628708654 -0.3581157060 0.233290687743 +1403638137895097088.0000000000 4.6095737772 -1.6756082023 0.5677369316 0.4782572899 0.7674333318 -0.3566059088 0.234836691554 +1403638137945096960.0000000000 4.6079255779 -1.6759766594 0.5608743868 0.4697369449 0.7733027772 -0.3544230422 0.236081182022 +1403638137995097088.0000000000 4.6061883172 -1.6757315001 0.5555769801 0.4634921210 0.7782017782 -0.3522061620 0.235643513901 +1403638138045096960.0000000000 4.6053573660 -1.6754034781 0.5518336407 0.4611786045 0.7803065880 -0.3500134123 0.236487916654 +1403638138095097088.0000000000 4.6050197751 -1.6747687547 0.5492825084 0.4625988050 0.7796298652 -0.3491080658 0.237282905709 +1403638138145096960.0000000000 4.6056705633 -1.6745393517 0.5493813161 0.4700911217 0.7736147894 -0.3517817973 0.238294066381 +1403638138195097088.0000000000 4.6060761190 -1.6744248832 0.5484896104 0.4749450041 0.7693661049 -0.3542869507 0.238712790308 +1403638138245096960.0000000000 4.6062973748 -1.6744210628 0.5469850794 0.4781845262 0.7669694497 -0.3555357317 0.238100326818 +1403638138295097088.0000000000 4.6063730983 -1.6744387990 0.5465496232 0.4810345360 0.7647158483 -0.3559443986 0.238995882195 +1403638138345096960.0000000000 4.6059430229 -1.6746308408 0.5466604100 0.4834802103 0.7628860012 -0.3553943435 0.240721199911 +1403638138395097088.0000000000 4.6056136232 -1.6748900964 0.5465833447 0.4873754179 0.7600602905 -0.3552579407 0.242002794167 +1403638138445096960.0000000000 4.6052267438 -1.6754606781 0.5462141207 0.4874320337 0.7601416148 -0.3545211392 0.242712792827 +1403638138495097088.0000000000 4.6054494284 -1.6756819733 0.5460917338 0.4875047213 0.7601225992 -0.3542870683 0.242968010404 +1403638138545096960.0000000000 4.6053683746 -1.6756293713 0.5461135096 0.4878331226 0.7599034070 -0.3545425324 0.24262161767 +1403638138595097088.0000000000 4.6053035172 -1.6758637677 0.5459662600 0.4877193268 0.7599970310 -0.3544141389 0.242744699768 +1403638138645096960.0000000000 4.6051461213 -1.6757982787 0.5459240834 0.4879132958 0.7598253014 -0.3547866206 0.242348057501 +1403638138695097088.0000000000 4.6051217295 -1.6757195445 0.5458864985 0.4880198676 0.7597195893 -0.3550310641 0.242106790368 +1403638138745096960.0000000000 4.6051781284 -1.6757918424 0.5458674285 0.4879748203 0.7598222196 -0.3547875649 0.242232436245 +1403638138795097088.0000000000 4.6050346127 -1.6759404371 0.5457991445 0.4878923843 0.7599589717 -0.3546412481 0.242183748053 +1403638138845096960.0000000000 4.6050657191 -1.6759685581 0.5457643705 0.4878711943 0.7600694086 -0.3543221190 0.242346916301 +1403638138895097088.0000000000 4.6048235713 -1.6754075545 0.5460378961 0.4885331431 0.7594282880 -0.3556308864 0.241103123446 +1403638138945096960.0000000000 4.6050399900 -1.6758493422 0.5458948906 0.4878134567 0.7599883466 -0.3547741172 0.242055923701 +1403638138995097088.0000000000 4.6047581008 -1.6755406405 0.5459707361 0.4883158438 0.7596405044 -0.3553226268 0.241329176894 +1403638139045096960.0000000000 4.6049064468 -1.6755983848 0.5459766858 0.4881076841 0.7598114158 -0.3549493510 0.24176116167 +1403638139095097088.0000000000 4.6048611130 -1.6755393365 0.5460199616 0.4881072906 0.7598086687 -0.3550932861 0.241559139642 +1403638139145096960.0000000000 4.6047863232 -1.6754615731 0.5460403938 0.4882251260 0.7597224942 -0.3551594194 0.241494813537 +1403638139195097088.0000000000 4.6049225401 -1.6755444435 0.5460552180 0.4880743204 0.7598219321 -0.3549289573 0.241825400861 +1403638139245096960.0000000000 4.6047844919 -1.6753451992 0.5461084377 0.4882925523 0.7596244295 -0.3553890865 0.241329042337 +1403638139295097088.0000000000 4.6049452905 -1.6755410355 0.5460296713 0.4880714383 0.7597975320 -0.3549338407 0.241900703239 +1403638139345096960.0000000000 4.6047923315 -1.6753755064 0.5461292950 0.4882313896 0.7596554463 -0.3553800463 0.241368464837 +1403638139395097088.0000000000 4.6049287252 -1.6753967158 0.5461603426 0.4881017124 0.7597569344 -0.3551138999 0.24170278666 +1403638139445096960.0000000000 4.6049335202 -1.6754850316 0.5461260828 0.4882027746 0.7596820040 -0.3552766443 0.241494947554 +1403638139495097088.0000000000 4.6049208068 -1.6755173672 0.5461391008 0.4881539684 0.7597068766 -0.3552573861 0.241543690442 +1403638139545096960.0000000000 4.6049603434 -1.6755541695 0.5460994578 0.4881624410 0.7597048660 -0.3552375821 0.241562016992 +1403638139595097088.0000000000 4.6049242230 -1.6755123061 0.5460950368 0.4881825791 0.7596767487 -0.3553118517 0.241500507386 +1403638139645096960.0000000000 4.6049203523 -1.6755447490 0.5460656703 0.4881163361 0.7597232101 -0.3552439461 0.241588131611 +1403638139695097088.0000000000 4.6048785211 -1.6754878974 0.5460624875 0.4881677868 0.7596624221 -0.3553648416 0.241497506744 +1403638139745096960.0000000000 4.6049477275 -1.6754988418 0.5460599233 0.4880976622 0.7597121098 -0.3552914290 0.24159094133 +1403638139795097088.0000000000 4.6048611400 -1.6754501569 0.5460562759 0.4881546693 0.7596652186 -0.3554326078 0.241415483737 +1403638139845096960.0000000000 4.6048950374 -1.6755308447 0.5460000382 0.4880656098 0.7597151730 -0.3553252990 0.241596250764 +1403638139895097088.0000000000 4.6048877020 -1.6754748149 0.5460455825 0.4881063875 0.7596556881 -0.3554460572 0.241523271091 +1403638139945096960.0000000000 4.6048769526 -1.6755081082 0.5460458550 0.4880587876 0.7596717864 -0.3554765453 0.241523958667 +1403638139995097088.0000000000 4.6048515228 -1.6755454405 0.5460564652 0.4880525149 0.7596801041 -0.3554899050 0.241490806461 +1403638140045096960.0000000000 4.6048482421 -1.6755328503 0.5461039807 0.4880116607 0.7596934733 -0.3555649952 0.241420752589 +1403638140095097088.0000000000 4.6048679012 -1.6755215355 0.5461290410 0.4879868030 0.7596998602 -0.3555475974 0.241476517366 +1403638140145096960.0000000000 4.6048460289 -1.6755374202 0.5461382810 0.4879827431 0.7596943337 -0.3555799724 0.241454436728 +1403638140195097088.0000000000 4.6048863284 -1.6755443597 0.5461704381 0.4879837351 0.7596812912 -0.3556161503 0.241440186776 +1403638140245096960.0000000000 4.6049140491 -1.6755195211 0.5461928299 0.4880061663 0.7596503457 -0.3556572329 0.241431701828 +1403638140295097088.0000000000 4.6049121133 -1.6755249133 0.5461838871 0.4879877197 0.7596595800 -0.3556618684 0.241433103039 +1403638140345096960.0000000000 4.6049148536 -1.6755052071 0.5461877424 0.4879863942 0.7596412345 -0.3557207218 0.241406797752 +1403638140395097088.0000000000 4.6049358040 -1.6754750467 0.5461710690 0.4879729850 0.7596344347 -0.3557422992 0.241423503542 +1403638140445096960.0000000000 4.6049375151 -1.6754635432 0.5461156572 0.4879472966 0.7596337809 -0.3557569058 0.241455955958 +1403638140495097088.0000000000 4.6049029274 -1.6754757019 0.5460848213 0.4879563039 0.7596180987 -0.3558111101 0.241407215158 +1403638140545096960.0000000000 4.6048724192 -1.6754533516 0.5461113513 0.4879576516 0.7596206171 -0.3558039178 0.241407167299 +1403638140595097088.0000000000 4.6048475411 -1.6754516339 0.5461190055 0.4879625319 0.7595951395 -0.3558450789 0.241416799949 +1403638140645096960.0000000000 4.6048057671 -1.6754380949 0.5460888591 0.4879631864 0.7595892936 -0.3558657560 0.241403391529 +1403638140695097088.0000000000 4.6048290688 -1.6754607779 0.5460811023 0.4879645076 0.7595886068 -0.3558472443 0.241430168936 +1403638140745096960.0000000000 4.6048539527 -1.6754494159 0.5460736521 0.4879894699 0.7595600085 -0.3559115173 0.241374942056 +1403638140795097088.0000000000 4.6048567174 -1.6754727278 0.5460428564 0.4879782358 0.7595627048 -0.3559029327 0.241401825437 +1403638140845096960.0000000000 4.6048465390 -1.6754919407 0.5460258569 0.4879685541 0.7595490709 -0.3559468226 0.241399582909 +1403638140895097088.0000000000 4.6048484732 -1.6754994939 0.5460592589 0.4879474153 0.7595517282 -0.3559745949 0.241392998734 +1403638140945096960.0000000000 4.6048345322 -1.6755098232 0.5460917783 0.4879013268 0.7595831768 -0.3559790947 0.241380564793 +1403638140995097088.0000000000 4.6048370305 -1.6754991203 0.5461107389 0.4879024103 0.7595587022 -0.3560200239 0.241395026027 +1403638141045096960.0000000000 4.6048811570 -1.6754698682 0.5461411728 0.4878863220 0.7595505933 -0.3560374572 0.241427343343 +1403638141095097088.0000000000 4.6049179009 -1.6754506301 0.5461556117 0.4879094629 0.7595160931 -0.3560779059 0.241429462238 +1403638141145096960.0000000000 4.6049252935 -1.6754585176 0.5461531522 0.4879347032 0.7595039939 -0.3560625127 0.241439217398 +1403638141195097088.0000000000 4.6049334274 -1.6754503812 0.5461661092 0.4879421407 0.7594936867 -0.3561150686 0.241379090158 +1403638141245096960.0000000000 4.6049489761 -1.6754396090 0.5461533211 0.4879177823 0.7594985409 -0.3561046559 0.241428412015 +1403638141295097088.0000000000 4.6049302617 -1.6753771112 0.5461565393 0.4879133786 0.7594985995 -0.3561393124 0.241386002993 +1403638141345096960.0000000000 4.6049307378 -1.6753849548 0.5461068247 0.4879295419 0.7594764361 -0.3561610787 0.241390950894 +1403638141395097088.0000000000 4.6049398017 -1.6753958809 0.5460993274 0.4879398455 0.7594630454 -0.3561789391 0.241385900877 +1403638141445096960.0000000000 4.6049449230 -1.6754240435 0.5461034413 0.4879363231 0.7594652293 -0.3562044525 0.241348499293 +1403638141495097088.0000000000 4.6049245778 -1.6754002906 0.5461234281 0.4879349011 0.7594657997 -0.3562243134 0.241320264251 +1403638141545096960.0000000000 4.6049039099 -1.6754406789 0.5461125728 0.4879320616 0.7594607221 -0.3562208383 0.241347113475 +1403638141595097088.0000000000 4.6048916045 -1.6754788921 0.5461149169 0.4879162128 0.7594514870 -0.3562486088 0.241367224016 +1403638141645096960.0000000000 4.6048390710 -1.6755106989 0.5460989507 0.4879099736 0.7594548641 -0.3562848168 0.241315760584 +1403638141695097088.0000000000 4.6048049107 -1.6755473829 0.5460659133 0.4878856461 0.7594540027 -0.3562951356 0.24135241964 +1403638141745096960.0000000000 4.6047582657 -1.6755394171 0.5460640325 0.4879054941 0.7594262246 -0.3563478788 0.241321833884 +1403638141795097088.0000000000 4.6047616536 -1.6755759264 0.5460676799 0.4878556126 0.7594608454 -0.3563293803 0.241341041341 +1403638141845096960.0000000000 4.6047578845 -1.6755701308 0.5460756332 0.4878674347 0.7594529274 -0.3563592910 0.241297892395 +1403638141895097088.0000000000 4.6047711492 -1.6755554470 0.5460937136 0.4878433776 0.7594621466 -0.3563610864 0.241314862411 +1403638141945096960.0000000000 4.6048047701 -1.6755198826 0.5461202037 0.4878138271 0.7594356690 -0.3564428993 0.241337096489 +1403638141995097088.0000000000 4.6048071432 -1.6754979460 0.5461463388 0.4878474492 0.7594623819 -0.3563780184 0.241280883645 +1403638142045096960.0000000000 4.6047690212 -1.6755000707 0.5461358594 0.4878312794 0.7594737357 -0.3563983785 0.241247763645 +1403638142095097088.0000000000 4.6047717998 -1.6755326565 0.5461024217 0.4878305311 0.7594883252 -0.3563538192 0.241269170041 +1403638142145096960.0000000000 4.6047701127 -1.6755618198 0.5460941212 0.4878676351 0.7594660652 -0.3564103136 0.241180751264 +1403638142195097088.0000000000 4.6048994364 -1.6756467806 0.5460943215 0.4878011835 0.7593446643 -0.3566230210 0.241382905434 +1403638142245096960.0000000000 4.6049696827 -1.6756334662 0.5460806914 0.4875948454 0.7593107357 -0.3568583156 0.241558721467 +1403638142295097088.0000000000 4.6049264426 -1.6754630883 0.5461048246 0.4875861672 0.7592194835 -0.3569722126 0.241694734746 +1403638142345096960.0000000000 4.6049024782 -1.6753621700 0.5461379677 0.4875551269 0.7592992546 -0.3568974779 0.241617115461 +1403638142395097088.0000000000 4.6050115836 -1.6754082791 0.5461534930 0.4874762184 0.7592288035 -0.3570338215 0.241796217357 +1403638142445096960.0000000000 4.6050766978 -1.6754557277 0.5461838433 0.4874989811 0.7593273247 -0.3569532022 0.241559866035 +1403638142495097088.0000000000 4.6051478428 -1.6754713389 0.5462261857 0.4875220206 0.7592800087 -0.3570579317 0.241507311119 +1403638142545096960.0000000000 4.6051841930 -1.6754075830 0.5462680772 0.4875821137 0.7593466698 -0.3569361745 0.241356344091 +1403638142595097088.0000000000 4.6050242756 -1.6752229079 0.5463082648 0.4878289293 0.7594982183 -0.3565317405 0.24097823604 +1403638142645096960.0000000000 4.6049342105 -1.6751576493 0.5462589502 0.4877658763 0.7594880051 -0.3565794599 0.241067436194 +1403638142695097088.0000000000 4.6048021683 -1.6751537927 0.5462051313 0.4876902232 0.7595334144 -0.3565838038 0.24107100503 +1403638142745096960.0000000000 4.6047455476 -1.6752262984 0.5461399656 0.4876924235 0.7594519453 -0.3566897628 0.241166448608 +1403638142795097088.0000000000 4.6047895825 -1.6753555921 0.5460424927 0.4874726468 0.7594171248 -0.3568951644 0.241416426065 +1403638142845096960.0000000000 4.6046388878 -1.6754517476 0.5460307708 0.4875423002 0.7594326459 -0.3568468420 0.241298348839 +1403638142895097088.0000000000 4.6046238620 -1.6754983400 0.5460062889 0.4874920738 0.7594681189 -0.3568032165 0.241352686157 +1403638142945096960.0000000000 4.6046029848 -1.6754076991 0.5459771864 0.4875677689 0.7595149902 -0.3567039691 0.241198940261 +1403638142995097088.0000000000 4.6047002087 -1.6753685629 0.5459726665 0.4875972184 0.7595907177 -0.3564942866 0.241210940539 +1403638143045096960.0000000000 4.6048112864 -1.6753972923 0.5460057719 0.4875636895 0.7595777494 -0.3566605404 0.241073744525 +1403638143095097088.0000000000 4.6049128206 -1.6755077217 0.5461039512 0.4875335390 0.7596025986 -0.3565776615 0.241179003754 +1403638143145096960.0000000000 4.6049440772 -1.6755765028 0.5462111554 0.4876088809 0.7595506289 -0.3566556034 0.241075095944 +1403638143195097088.0000000000 4.6049453430 -1.6755991414 0.5462450797 0.4875171596 0.7596096119 -0.3566781916 0.241041333206 +1403638143245096960.0000000000 4.6048777863 -1.6755555764 0.5462076133 0.4875713888 0.7595799437 -0.3566668654 0.241041899033 +1403638143295097088.0000000000 4.6047430426 -1.6755147668 0.5461493444 0.4876026255 0.7595653030 -0.3566915759 0.240988277291 +1403638143345096960.0000000000 4.6046631969 -1.6754930351 0.5460590746 0.4875459524 0.7596104053 -0.3566055639 0.241088050948 +1403638143395097088.0000000000 4.6046532553 -1.6754218937 0.5460211607 0.4875836358 0.7595543726 -0.3567132567 0.241029055486 +1403638143445096960.0000000000 4.6046381464 -1.6754711363 0.5459717171 0.4875526745 0.7595508338 -0.3566949851 0.24112985734 +1403638143495097088.0000000000 4.6046481438 -1.6755384259 0.5459752889 0.4875542726 0.7595273130 -0.3567653925 0.241096550614 +1403638143545096960.0000000000 4.6046806021 -1.6755834817 0.5459797287 0.4875598117 0.7595034857 -0.3567929961 0.241119561986 +1403638143595097088.0000000000 4.6047651021 -1.6756285385 0.5459868891 0.4874388026 0.7594668372 -0.3569790821 0.24120421184 +1403638143645096960.0000000000 4.6047679479 -1.6755621790 0.5460043537 0.4874801181 0.7594870590 -0.3569867626 0.24104562414 +1403638143695097088.0000000000 4.6047951142 -1.6755470175 0.5460131829 0.4874813655 0.7594768082 -0.3569840104 0.241079473355 +1403638143745096960.0000000000 4.6047859415 -1.6755337159 0.5460185684 0.4874956735 0.7594769121 -0.3569785316 0.241058325425 +1403638143795097088.0000000000 4.6047925664 -1.6755217357 0.5460196907 0.4874931817 0.7595135715 -0.3569423308 0.241001462783 +1403638143845096960.0000000000 4.6047984395 -1.6754965681 0.5460365261 0.4874941867 0.7595060855 -0.3569741462 0.24097589708 +1403638143895097088.0000000000 4.6047627721 -1.6754954560 0.5460672426 0.4874815519 0.7594901330 -0.3570421202 0.240951030135 +1403638143945096960.0000000000 4.6047564130 -1.6755153474 0.5460681101 0.4874682350 0.7594748385 -0.3570348138 0.241036991495 +1403638143995097088.0000000000 4.6047281991 -1.6755059926 0.5460924100 0.4874663596 0.7594666062 -0.3570921579 0.24098176923 +1403638144045096960.0000000000 4.6047166595 -1.6755002957 0.5461068588 0.4874345599 0.7594897785 -0.3571334264 0.240911896463 +1403638144095097088.0000000000 4.6047589350 -1.6754506392 0.5461362029 0.4874090754 0.7595051803 -0.3571535478 0.240885071467 +1403638144145096960.0000000000 4.6047070214 -1.6755936125 0.5460667532 0.4873773590 0.7595025443 -0.3571444517 0.240971026985 +1403638144195097088.0000000000 4.6047205302 -1.6756084309 0.5460678343 0.4873894992 0.7594838035 -0.3571748095 0.240960543939 +1403638144245096960.0000000000 4.6047115410 -1.6755938117 0.5460744418 0.4873915457 0.7594912002 -0.3571653879 0.240947055705 +1403638144295097088.0000000000 4.6046747575 -1.6755765749 0.5460963066 0.4874105691 0.7594991445 -0.3571366892 0.240926071363 +1403638144345096960.0000000000 4.6046235304 -1.6755640334 0.5460924727 0.4874169946 0.7594937132 -0.3571894341 0.240851990114 +1403638144395097088.0000000000 4.6046394109 -1.6755362009 0.5460965452 0.4874338953 0.7594853110 -0.3571718938 0.24087029369 +1403638144445096960.0000000000 4.6045958955 -1.6755350369 0.5460540729 0.4874114612 0.7594887376 -0.3572196137 0.240834118262 +1403638144495097088.0000000000 4.6046558438 -1.6754653049 0.5460224093 0.4873833132 0.7594775434 -0.3572547664 0.240874239118 +1403638144545096960.0000000000 4.6046582358 -1.6753820547 0.5460050188 0.4873622864 0.7594542539 -0.3573465319 0.240854093097 +1403638144595097088.0000000000 4.6047088923 -1.6753008062 0.5460432525 0.4873354454 0.7594779443 -0.3573565812 0.240818789959 +1403638144645096960.0000000000 4.6047360113 -1.6752688264 0.5461356590 0.4873974374 0.7594667071 -0.3573203872 0.240782474008 +1403638144695097088.0000000000 4.6047196571 -1.6752862825 0.5462381044 0.4874415249 0.7594515370 -0.3572962691 0.240776865391 +1403638144745096960.0000000000 4.6046781485 -1.6753501100 0.5462579324 0.4873888450 0.7594570994 -0.3573256155 0.240822408562 +1403638144795097088.0000000000 4.6046841576 -1.6753756367 0.5462767262 0.4874452420 0.7594214342 -0.3573968373 0.240715022305 +1403638144845096960.0000000000 4.6046953138 -1.6754214522 0.5462221364 0.4874199285 0.7594312530 -0.3573866554 0.240750418202 +1403638144895097088.0000000000 4.6046624074 -1.6754706100 0.5461630305 0.4873814252 0.7594382617 -0.3574499758 0.24071225093 +1403638144945096960.0000000000 4.6046458908 -1.6755325150 0.5460848006 0.4872975081 0.7595026153 -0.3574128653 0.240734209572 +1403638144995097088.0000000000 4.6046360163 -1.6755373763 0.5460245634 0.4873903919 0.7594184111 -0.3574497442 0.240757062513 +1403638145045096960.0000000000 4.6046030539 -1.6755536896 0.5459310153 0.4873080035 0.7594796797 -0.3574703100 0.240700027726 +1403638145095097088.0000000000 4.6046332023 -1.6755849937 0.5459181538 0.4873753639 0.7594135017 -0.3575334240 0.240678704411 +1403638145145096960.0000000000 4.6046400432 -1.6755967496 0.5458582811 0.4872465954 0.7594751359 -0.3575301674 0.240749772 +1403638145195097088.0000000000 4.6046982386 -1.6755443862 0.5458887211 0.4873244172 0.7594176721 -0.3575708526 0.24071310122 +1403638145245096960.0000000000 4.6047279004 -1.6754991293 0.5459171248 0.4872572064 0.7594619582 -0.3575631631 0.240720861795 +1403638145295097088.0000000000 4.6046952378 -1.6754383379 0.5458810939 0.4872772405 0.7594312888 -0.3576281722 0.240680491339 +1403638145345096960.0000000000 4.6047079517 -1.6753866867 0.5458674218 0.4872855435 0.7594223508 -0.3576225836 0.240700186668 +1403638145395097088.0000000000 4.6047255956 -1.6753837899 0.5458742656 0.4872316704 0.7593997024 -0.3577053922 0.240757645153 +1403638145445096960.0000000000 4.6047754514 -1.6754201765 0.5459437845 0.4872029357 0.7593718752 -0.3577596167 0.240822987564 +1403638145495097088.0000000000 4.6047003752 -1.6754399001 0.5459898727 0.4872502656 0.7593666819 -0.3577640265 0.240737039865 +1403638145545096960.0000000000 4.6047175196 -1.6755022858 0.5460581911 0.4872887755 0.7593301722 -0.3577696762 0.240765856581 +1403638145595097088.0000000000 4.6046381349 -1.6755849468 0.5460620915 0.4872528621 0.7593908853 -0.3577674621 0.240650316265 +1403638145645096960.0000000000 4.6046070305 -1.6756248570 0.5461238324 0.4872258583 0.7594079946 -0.3578030868 0.240598029523 +1403638145695097088.0000000000 4.6045942286 -1.6756096239 0.5461256740 0.4872676615 0.7593782707 -0.3577983009 0.240614305495 +1403638145745096960.0000000000 4.6045342147 -1.6755679519 0.5460942877 0.4872281125 0.7594005289 -0.3578551892 0.240539532332 +1403638145795097088.0000000000 4.6045558387 -1.6755711790 0.5461273511 0.4871727810 0.7594358792 -0.3578156845 0.240598758861 +1403638145845096960.0000000000 4.6045206676 -1.6754372043 0.5461661230 0.4872299151 0.7593807964 -0.3578882217 0.240549031644 +1403638145895097088.0000000000 4.6045495909 -1.6753870541 0.5461394281 0.4871950958 0.7593882651 -0.3578870351 0.240597738017 +1403638145945096960.0000000000 4.6045547768 -1.6753108362 0.5461476505 0.4871599874 0.7593647734 -0.3580171196 0.240549432723 +1403638145995097088.0000000000 4.6045590344 -1.6752842315 0.5461385713 0.4872150566 0.7593505497 -0.3579812466 0.240536189217 +1403638146045096960.0000000000 4.6045574811 -1.6752706441 0.5461357658 0.4872556993 0.7593410230 -0.3579996757 0.240456496199 +1403638146095097088.0000000000 4.6045370170 -1.6753399997 0.5461557381 0.4871912404 0.7594023007 -0.3579828920 0.240418572408 +1403638146145096960.0000000000 4.6044748651 -1.6754577418 0.5462113804 0.4872439962 0.7593478331 -0.3580354068 0.24040549914 +1403638146195097088.0000000000 4.6044408242 -1.6753894374 0.5462448744 0.4872735344 0.7593251877 -0.3580195777 0.240440728441 +1403638146245096960.0000000000 4.6044572805 -1.6754189374 0.5462011474 0.4872137652 0.7593658147 -0.3580122748 0.240444416794 +1403638146295097088.0000000000 4.6045695890 -1.6754966076 0.5461375626 0.4872421996 0.7593278588 -0.3580745744 0.240413895197 +1403638146345096960.0000000000 4.6045685531 -1.6755533873 0.5461219799 0.4872226360 0.7593497339 -0.3580841401 0.24037020036 +1403638146395097088.0000000000 4.6045058855 -1.6755845822 0.5461125451 0.4872113585 0.7593648264 -0.3580418999 0.240408299394 +1403638146445096960.0000000000 4.6045040659 -1.6755452572 0.5461451438 0.4872910387 0.7592769993 -0.3581123186 0.240419319651 +1403638146495097088.0000000000 4.6045803994 -1.6755015671 0.5462635715 0.4871285963 0.7593811027 -0.3581541874 0.240357337152 +1403638146545096960.0000000000 4.6047022215 -1.6753938641 0.5463161464 0.4871662565 0.7593366647 -0.3581868609 0.240372712363 +1403638146595097088.0000000000 4.6047902129 -1.6752726498 0.5463868093 0.4871485266 0.7593311729 -0.3581848945 0.240428917118 +1403638146645096960.0000000000 4.6046954230 -1.6753246633 0.5463814043 0.4870591434 0.7593696822 -0.3582352417 0.240413369592 +1403638146695097088.0000000000 4.6047791847 -1.6753042113 0.5465367107 0.4871101693 0.7593341846 -0.3582249652 0.240437421026 +1403638146745096960.0000000000 4.6048803561 -1.6753081486 0.5465751342 0.4871199604 0.7593502166 -0.3581846603 0.240426998991 +1403638146795097088.0000000000 4.6048915746 -1.6752817306 0.5464202587 0.4872899820 0.7592453557 -0.3581753762 0.240427459205 +1403638146845096960.0000000000 4.6047499818 -1.6753125717 0.5461586350 0.4871078067 0.7593815301 -0.3581119474 0.240461035395 +1403638146895097088.0000000000 4.6044746428 -1.6754169499 0.5459852734 0.4872383380 0.7593129000 -0.3580646685 0.24048371039 +1403638146945096960.0000000000 4.6043231145 -1.6754606914 0.5457997419 0.4871469489 0.7593789978 -0.3581081482 0.240395387106 +1403638146995097088.0000000000 4.6043379386 -1.6754387975 0.5457201589 0.4869925010 0.7594309196 -0.3581963825 0.240412840512 +1403638147045096960.0000000000 4.6043229767 -1.6753794904 0.5458139280 0.4869599261 0.7594749039 -0.3581411160 0.240422215546 +1403638147095097088.0000000000 4.6042750929 -1.6751990436 0.5459534391 0.4869248146 0.7595534682 -0.3581497948 0.240232134142 +1403638147145096960.0000000000 4.6044718994 -1.6749174326 0.5459955052 0.4868204994 0.7596565947 -0.3581848276 0.240065176139 +1403638147195097088.0000000000 4.6047828925 -1.6748032830 0.5460316472 0.4867368223 0.7597243789 -0.3580831983 0.240171932019 +1403638147245096960.0000000000 4.6048537731 -1.6747876617 0.5461685785 0.4868579471 0.7596623871 -0.3581527572 0.240018748013 +1403638147295097088.0000000000 4.6048325683 -1.6749878579 0.5462343740 0.4868931855 0.7596080932 -0.3581790074 0.240079922642 +1403638147345096960.0000000000 4.6048283732 -1.6752429175 0.5462454153 0.4870136237 0.7595121281 -0.3580924963 0.240268228744 +1403638147395097088.0000000000 4.6046662345 -1.6755915023 0.5461496073 0.4871212490 0.7594855284 -0.3580559243 0.240188625763 +1403638147445096960.0000000000 4.6044732589 -1.6760118649 0.5460960410 0.4871500044 0.7594567917 -0.3580536502 0.240224558169 +1403638147495097088.0000000000 4.6042659015 -1.6761855812 0.5463894355 0.4878252105 0.7591592224 -0.3576832295 0.240346721101 +1403638147545096960.0000000000 4.6041186996 -1.6763077113 0.5464124065 0.4878880593 0.7590018557 -0.3579624707 0.240300424908 +1403638147595097088.0000000000 4.6039828750 -1.6762524572 0.5465378880 0.4885680002 0.7587612457 -0.3576841352 0.240093191681 +1403638147645096960.0000000000 4.6042064645 -1.6760815124 0.5462252140 0.4881096435 0.7592635762 -0.3572440353 0.240092684375 +1403638147695097088.0000000000 4.6042118541 -1.6756723479 0.5461428781 0.4885101436 0.7592766693 -0.3569704227 0.23964326891 +1403638147745096960.0000000000 4.6045303839 -1.6751803869 0.5460641487 0.4892944309 0.7588695259 -0.3567162357 0.239711346791 +1403638147795097088.0000000000 4.6055150553 -1.6743163945 0.5460364391 0.4913981670 0.7569923526 -0.3566991791 0.241363036356 +1403638147845096960.0000000000 4.6076712081 -1.6728744774 0.5465281457 0.4944048257 0.7538416639 -0.3574218300 0.244000511186 +1403638147895097088.0000000000 4.6108118176 -1.6706216286 0.5486287336 0.4998962315 0.7492139102 -0.3571335617 0.247462913418 +1403638147945096960.0000000000 4.6145335351 -1.6675992497 0.5524424054 0.5044459422 0.7453251426 -0.3568944775 0.250301928006 +1403638147995097088.0000000000 4.6185273094 -1.6639909968 0.5579577514 0.5084285312 0.7421952944 -0.3569389598 0.251477936494 +1403638148045096960.0000000000 4.6227661188 -1.6605658084 0.5650159039 0.5117099694 0.7397924105 -0.3553719425 0.254108006464 +1403638148095097088.0000000000 4.6271774494 -1.6568128933 0.5742466083 0.5150181184 0.7376032784 -0.3546564085 0.254787309947 +1403638148145096960.0000000000 4.6319242921 -1.6530333460 0.5854744645 0.5169513552 0.7367099696 -0.3524641630 0.256493140022 +1403638148195097088.0000000000 4.6366298358 -1.6492710243 0.6001796866 0.5188033101 0.7360489545 -0.3508267424 0.256896202551 +1403638148245096960.0000000000 4.6410431079 -1.6456394289 0.6190735263 0.5198389400 0.7361271975 -0.3497476821 0.256048402659 +1403638148295097088.0000000000 4.6449529103 -1.6425138403 0.6423922119 0.5201737225 0.7367974607 -0.3481715736 0.255588254081 +1403638148345096960.0000000000 4.6489064386 -1.6391567814 0.6690364483 0.5216287264 0.7366477660 -0.3466891601 0.255068945654 +1403638148395097088.0000000000 4.6523920732 -1.6360765537 0.6948042070 0.5215073433 0.7376314322 -0.3453388055 0.254305073694 +1403638148445096960.0000000000 4.6556559393 -1.6332180271 0.7171589864 0.5206340409 0.7389739488 -0.3443020283 0.253601679332 +1403638148495097088.0000000000 4.6584650311 -1.6305840926 0.7330078486 0.5167493936 0.7423732341 -0.3437784311 0.252326050653 +1403638148545096960.0000000000 4.6613773574 -1.6278187665 0.7430894491 0.5141376969 0.7446726431 -0.3430519880 0.251873811156 +1403638148595097088.0000000000 4.6640820511 -1.6248653444 0.7471781072 0.5115762848 0.7470601323 -0.3428544134 0.250283269037 +1403638148645096960.0000000000 4.6668087283 -1.6214830484 0.7465841303 0.5089863562 0.7494829022 -0.3422855820 0.249096063622 +1403638148695097088.0000000000 4.6699950951 -1.6171289091 0.7438950232 0.5070906008 0.7513232027 -0.3420845860 0.247690742035 +1403638148745096960.0000000000 4.6733671495 -1.6121858972 0.7411441978 0.5058040133 0.7528543651 -0.3419774050 0.245813058187 +1403638148795097088.0000000000 4.6772292671 -1.6064269190 0.7402414589 0.5046154340 0.7541365399 -0.3418109420 0.244553926233 +1403638148845096960.0000000000 4.6811292596 -1.6000172614 0.7419039629 0.5045175207 0.7548047893 -0.3414274134 0.243226484575 +1403638148895097088.0000000000 4.6856069680 -1.5929987186 0.7456700244 0.5043489211 0.7553876162 -0.3407054448 0.242778736798 +1403638148945096960.0000000000 4.6905664550 -1.5848194890 0.7524211165 0.5057134536 0.7548521794 -0.3400587399 0.242512151287 +1403638148995097088.0000000000 4.6956705961 -1.5762303546 0.7622164657 0.5075009356 0.7541656601 -0.3388857898 0.242555929494 +1403638149045096960.0000000000 4.7011799948 -1.5669493577 0.7762147560 0.5104486327 0.7525578537 -0.3375073651 0.24328511803 +1403638149095097088.0000000000 4.7070666422 -1.5569303275 0.7931892650 0.5128153101 0.7512577530 -0.3361491077 0.244204880445 +1403638149145096960.0000000000 4.7134150224 -1.5460800614 0.8120043615 0.5148522463 0.7501161262 -0.3351329610 0.244824141175 +1403638149195097088.0000000000 4.7198916853 -1.5345045844 0.8310458041 0.5160863059 0.7493431430 -0.3348071993 0.245038605408 +1403638149245096960.0000000000 4.7262062081 -1.5226766730 0.8493920262 0.5174545162 0.7485378587 -0.3346522828 0.244825953009 +1403638149295097088.0000000000 4.7322854050 -1.5106630362 0.8669810189 0.5184955567 0.7477588784 -0.3355857775 0.243723621018 +1403638149345096960.0000000000 4.7383184717 -1.4983299410 0.8842726603 0.5198277758 0.7469606386 -0.3356821842 0.243200244799 +1403638149395097088.0000000000 4.7441226658 -1.4861838828 0.9003806367 0.5205663665 0.7465162984 -0.3352138256 0.243630386896 +1403638149445096960.0000000000 4.7498117778 -1.4739786541 0.9152850512 0.5211214656 0.7461714413 -0.3351594486 0.243574921105 +1403638149495097088.0000000000 4.7554799069 -1.4618934146 0.9287165874 0.5214478678 0.7459836284 -0.3344285630 0.244454665509 +1403638149545096960.0000000000 4.7608438954 -1.4499087528 0.9407513663 0.5214712816 0.7460373372 -0.3339310282 0.244920522666 +1403638149595097088.0000000000 4.7659397648 -1.4378835204 0.9510641718 0.5214256908 0.7464314695 -0.3329191677 0.245194082293 +1403638149645096960.0000000000 4.7704488390 -1.4256907749 0.9597388358 0.5215875969 0.7473757068 -0.3311679238 0.244343483348 +1403638149695097088.0000000000 4.7745817849 -1.4134430252 0.9672791227 0.5226435133 0.7483364709 -0.3285728160 0.242644160967 +1403638149745096960.0000000000 4.7785980605 -1.4011957985 0.9733443786 0.5233355238 0.7494680060 -0.3256888460 0.241545882079 +1403638149795097088.0000000000 4.7824537778 -1.3887812829 0.9781037244 0.5239562271 0.7505242395 -0.3236700912 0.239626605633 +1403638149845096960.0000000000 4.7860844113 -1.3766043079 0.9817092489 0.5242421985 0.7517147855 -0.3215358778 0.23813793865 +1403638149895097088.0000000000 4.7897447816 -1.3642969454 0.9845777592 0.5253487432 0.7519611217 -0.3200437045 0.236928673983 +1403638149945096960.0000000000 4.7930432907 -1.3523224637 0.9858777204 0.5252642421 0.7529570413 -0.3184207608 0.236138495517 +1403638149995097088.0000000000 4.7961567902 -1.3404249189 0.9857941579 0.5251252143 0.7538791354 -0.3164354534 0.236174432013 +1403638150045096960.0000000000 4.7993161440 -1.3285169180 0.9839985771 0.5242989418 0.7549096245 -0.3133346539 0.238837754843 +1403638150095097088.0000000000 4.8020325558 -1.3165166400 0.9804459221 0.5229621491 0.7562834795 -0.3101806850 0.241523977921 +1403638150145096960.0000000000 4.8042050173 -1.3041687767 0.9751325950 0.5214165489 0.7576715575 -0.3067867344 0.24482747616 +1403638150195097088.0000000000 4.8056775476 -1.2912844390 0.9685787075 0.5201478237 0.7587020190 -0.3041116289 0.247656223294 +1403638150245096960.0000000000 4.8063287572 -1.2777120223 0.9609103543 0.5191775790 0.7593685010 -0.3015472143 0.250765624884 +1403638150295097088.0000000000 4.8055746789 -1.2632437307 0.9518880423 0.5175416178 0.7606658196 -0.3018548801 0.249843583174 +1403638150345096960.0000000000 4.8039139940 -1.2478425522 0.9418359090 0.5153301478 0.7622811648 -0.3024102721 0.24881778866 +1403638150395097088.0000000000 4.8006175952 -1.2315765433 0.9315985493 0.5132826453 0.7644846410 -0.3038001355 0.244560089478 +1403638150445096960.0000000000 4.7962657537 -1.2138876618 0.9225125373 0.5107973255 0.7676588360 -0.3055970317 0.23747938447 +1403638150495097088.0000000000 4.7910782278 -1.1951000986 0.9159483852 0.5102391118 0.7699952325 -0.3056851549 0.230911188218 +1403638150545096960.0000000000 4.7857216671 -1.1754733243 0.9106956719 0.5088281777 0.7730279828 -0.3042735359 0.225697227901 +1403638150595097088.0000000000 4.7808633665 -1.1544045216 0.9082698351 0.5085173787 0.7751197745 -0.3027272610 0.221259160808 +1403638150645096960.0000000000 4.7762564816 -1.1322130713 0.9086266452 0.5091477928 0.7764796895 -0.3008878591 0.217518535159 +1403638150695097088.0000000000 4.7722967754 -1.1091386772 0.9110112606 0.5107331587 0.7768538150 -0.2988285350 0.215293514391 +1403638150745096960.0000000000 4.7690188177 -1.0848453852 0.9148742797 0.5121147214 0.7775534625 -0.2958848231 0.213544600695 +1403638150795097088.0000000000 4.7666924772 -1.0589683208 0.9208478969 0.5138903179 0.7781590241 -0.2920363240 0.21236774682 +1403638150845096960.0000000000 4.7643406319 -1.0321959465 0.9283473701 0.5163582144 0.7787664410 -0.2871505507 0.210811731172 +1403638150895097088.0000000000 4.7622453826 -1.0046507513 0.9355334752 0.5191437407 0.7790131227 -0.2822407120 0.209686698737 +1403638150945096960.0000000000 4.7602879454 -0.9764174408 0.9417865688 0.5220899571 0.7787815876 -0.2778742999 0.20906264368 +1403638150995097088.0000000000 4.7580632268 -0.9472421546 0.9471883343 0.5265046369 0.7778063399 -0.2730347246 0.207995682966 +1403638151045096960.0000000000 4.7551701562 -0.9179417933 0.9504094224 0.5281929707 0.7791114300 -0.2677272785 0.205717451115 +1403638151095097088.0000000000 4.7516608524 -0.8879697122 0.9528632186 0.5313305348 0.7799545851 -0.2606930489 0.203464597297 +1403638151145096960.0000000000 4.7475186758 -0.8575342126 0.9539384689 0.5344994465 0.7813474803 -0.2521453369 0.200572145891 +1403638151195097088.0000000000 4.7425039282 -0.8266801780 0.9528607111 0.5368885637 0.7837535906 -0.2435152088 0.195400415835 +1403638151245096960.0000000000 4.7366019743 -0.7952866611 0.9502606939 0.5386269027 0.7869820663 -0.2347060127 0.188290665023 +1403638151295097088.0000000000 4.7301322394 -0.7635150767 0.9465474001 0.5404222096 0.7900327592 -0.2256102118 0.181361812325 +1403638151345096960.0000000000 4.7231494181 -0.7314192897 0.9422459986 0.5420181691 0.7932764900 -0.2158027579 0.174235141393 +1403638151395097088.0000000000 4.7152131674 -0.6989859750 0.9387111532 0.5445511153 0.7958425190 -0.2060856307 0.166215163559 +1403638151445096960.0000000000 4.7068632442 -0.6660050614 0.9366637921 0.5470501248 0.7981492786 -0.1970587183 0.157676096903 +1403638151495097088.0000000000 4.6979829695 -0.6332371622 0.9356913698 0.5491980290 0.8004318502 -0.1870470272 0.150677761118 +1403638151545096960.0000000000 4.6889230560 -0.6001393623 0.9362818747 0.5513338261 0.8021836449 -0.1784955354 0.143776757276 +1403638151595097088.0000000000 4.6799328301 -0.5667993778 0.9380065599 0.5524296468 0.8041199996 -0.1706657481 0.138151054698 +1403638151645096960.0000000000 4.6707149494 -0.5332735781 0.9411518325 0.5542537471 0.8050862659 -0.1639628137 0.133248204678 +1403638151695097088.0000000000 4.6614681670 -0.4993698382 0.9458145655 0.5553393314 0.8061316940 -0.1580870687 0.129454229735 +1403638151745096960.0000000000 4.6520260168 -0.4653407050 0.9527406661 0.5558040041 0.8071928967 -0.1533994136 0.126452190296 +1403638151795097088.0000000000 4.6421544979 -0.4312511223 0.9617205911 0.5556034866 0.8084373936 -0.1496143116 0.123892307961 +1403638151845096960.0000000000 4.6320327432 -0.3970796695 0.9729504026 0.5558290937 0.8091427041 -0.1467883341 0.121635882234 +1403638151895097088.0000000000 4.6218322162 -0.3626428841 0.9858438535 0.5557885160 0.8097308448 -0.1447791228 0.12030831285 +1403638151945096960.0000000000 4.6116086741 -0.3275406612 0.9998538315 0.5551821022 0.8105378923 -0.1424907194 0.1204057865 +1403638151995097088.0000000000 4.6008689238 -0.2920330714 1.0143768938 0.5548294613 0.8110644373 -0.1412165551 0.119985966182 +1403638152045096960.0000000000 4.5899282502 -0.2558938935 1.0281455656 0.5545123842 0.8114157827 -0.1409897251 0.119341278128 +1403638152095097088.0000000000 4.5784993792 -0.2198965383 1.0408769125 0.5541252217 0.8117279634 -0.1405131646 0.119578437389 +1403638152145096960.0000000000 4.5666939836 -0.1835953269 1.0524388344 0.5541646338 0.8117249740 -0.1398214903 0.120225105856 +1403638152195097088.0000000000 4.5545805462 -0.1469766966 1.0624741096 0.5539513709 0.8118287547 -0.1401441740 0.120131436776 +1403638152245096960.0000000000 4.5423250891 -0.1101391164 1.0706004242 0.5538559143 0.8118153475 -0.1393672661 0.1215575291 +1403638152295097088.0000000000 4.5296606616 -0.0729905244 1.0769485816 0.5535714345 0.8118901807 -0.1388773432 0.122906814025 +1403638152345096960.0000000000 4.5166439277 -0.0353265004 1.0815548657 0.5535178190 0.8116908661 -0.1383484199 0.125042699581 +1403638152395097088.0000000000 4.5028425897 0.0026091603 1.0840195127 0.5526380109 0.8120990048 -0.1379772695 0.126683496909 +1403638152445096960.0000000000 4.4883837964 0.0410472334 1.0844466507 0.5520245028 0.8122729363 -0.1380379370 0.12816845637 +1403638152495097088.0000000000 4.4732524488 0.0800492162 1.0832277103 0.5509342653 0.8127588992 -0.1376656107 0.130163691663 +1403638152545096960.0000000000 4.4571375902 0.1195591356 1.0814245261 0.5512805815 0.8124477893 -0.1376976582 0.130604996246 +1403638152595097088.0000000000 4.4402073826 0.1594112811 1.0783977548 0.5508976812 0.8125845470 -0.1385619007 0.130455734162 +1403638152645096960.0000000000 4.4220038274 0.1995405498 1.0745238784 0.5500935688 0.8132314423 -0.1402502284 0.127990469183 +1403638152695097088.0000000000 4.4028681600 0.2402788429 1.0714668121 0.5500061993 0.8136858919 -0.1409914012 0.124618918276 +1403638152745096960.0000000000 4.3832062921 0.2818425752 1.0700796454 0.5506320624 0.8139291468 -0.1393335813 0.12210581067 +1403638152795097088.0000000000 4.3628713990 0.3245662058 1.0714264902 0.5528613434 0.8133542715 -0.1376403037 0.117704336215 +1403638152845096960.0000000000 4.3420544618 0.3680076727 1.0747572903 0.5549336430 0.8130670318 -0.1347646418 0.113177492843 +1403638152895097088.0000000000 4.3210125080 0.4117887099 1.0804961928 0.5588304389 0.8116829583 -0.1309459790 0.108316510007 +1403638152945096960.0000000000 4.2997100130 0.4550728434 1.0874121294 0.5619669039 0.8109747354 -0.1253626527 0.103910455126 +1403638152995097088.0000000000 4.2781703576 0.4980227454 1.0956136630 0.5629401803 0.8118304482 -0.1193902629 0.0988718460262 +1403638153045096960.0000000000 4.2563526038 0.5407392888 1.1056258223 0.5620297305 0.8139038385 -0.1134793884 0.0938379038967 +1403638153095097088.0000000000 4.2344754630 0.5833840409 1.1169435617 0.5601481504 0.8164228161 -0.1084048769 0.0890854508971 +1403638153145096960.0000000000 4.2126507949 0.6262337134 1.1283626729 0.5581970228 0.8187684076 -0.1037576079 0.0852568894403 +1403638153195097088.0000000000 4.1911576622 0.6696558013 1.1392264468 0.5569585860 0.8203937643 -0.0997152712 0.0825110274666 +1403638153245096960.0000000000 4.1701434445 0.7135418037 1.1487754565 0.5560937749 0.8216156335 -0.0962050980 0.0803246127145 +1403638153295097088.0000000000 4.1492014980 0.7581202862 1.1572017722 0.5556207179 0.8226233400 -0.0915903655 0.0786617012959 +1403638153345096960.0000000000 4.1280195633 0.8027021214 1.1642561735 0.5551697115 0.8237275121 -0.0871460743 0.0752671177221 +1403638153395097088.0000000000 4.1067038404 0.8475835882 1.1703874011 0.5551898073 0.8245929288 -0.0813889780 0.0720181498922 +1403638153445096960.0000000000 4.0855062734 0.8928854187 1.1758748292 0.5548718729 0.8256942644 -0.0740215771 0.0697638333233 +1403638153495097088.0000000000 4.0644184448 0.9385648958 1.1818525221 0.5541516137 0.8269888026 -0.0648185199 0.0693113911604 +1403638153545096960.0000000000 4.0429591662 0.9852178231 1.1896601638 0.5531961027 0.8283947444 -0.0550168141 0.0686248462347 +1403638153595097088.0000000000 4.0205795084 1.0327998215 1.1994454549 0.5527160595 0.8294985120 -0.0459552990 0.0657669118825 +1403638153645096960.0000000000 3.9973165342 1.0812541580 1.2108450394 0.5529834764 0.8300273390 -0.0364795747 0.0627146865351 +1403638153695097088.0000000000 3.9728086538 1.1306830928 1.2231113163 0.5539440117 0.8301286400 -0.0282399621 0.0568768629647 +1403638153745096960.0000000000 3.9474172451 1.1811689762 1.2351230678 0.5563775005 0.8291822029 -0.0212606756 0.0494867156176 +1403638153795097088.0000000000 3.9217403788 1.2324430513 1.2454277487 0.5577534584 0.8287004359 -0.0140724277 0.0443692901382 +1403638153845096960.0000000000 3.8954087253 1.2843263818 1.2544638530 0.5595372408 0.8278481428 -0.0081246407 0.0389810069005 +1403638153895097088.0000000000 3.8685397506 1.3368409848 1.2623406936 0.5618969601 0.8264750083 -0.0033869117 0.0346322932061 +1403638153945096960.0000000000 3.8410949303 1.3902205078 1.2691412194 0.5653565629 0.8242957679 -0.0001419994 0.0301400666279 +1403638153995097088.0000000000 3.8133221846 1.4435019158 1.2737429739 0.5670238004 0.8232780280 0.0021749100 0.0263166885302 +1403638154045096960.0000000000 3.7852619395 1.4967913545 1.2767115295 0.5688481960 0.8221104711 0.0037133161 0.0230719421922 +1403638154095097088.0000000000 3.7569756203 1.5500762054 1.2782111995 0.5709306846 0.8206881965 0.0058380796 0.02179344689 +1403638154145096960.0000000000 3.7282624122 1.6033643088 1.2785339481 0.5738522135 0.8186482944 0.0075959547 0.0212346072042 +1403638154195097088.0000000000 3.6991683565 1.6565591529 1.2777510128 0.5768313888 0.8165298917 0.0090083648 0.0215251998462 +1403638154245096960.0000000000 3.6695058325 1.7093252528 1.2757983238 0.5795588737 0.8145520010 0.0106214829 0.0224440134866 +1403638154295097088.0000000000 3.6393334123 1.7614534382 1.2727581355 0.5816347834 0.8130456260 0.0112643067 0.0230413602304 +1403638154345096960.0000000000 3.6083311273 1.8130263221 1.2691932198 0.5850172990 0.8106357186 0.0107266134 0.0225705870607 +1403638154395097088.0000000000 3.5769968752 1.8638312816 1.2648181680 0.5896502588 0.8072575001 0.0106817120 0.023104154223 +1403638154445096960.0000000000 3.5450064133 1.9132402220 1.2589840894 0.5929979415 0.8048268866 0.0097765491 0.0226173181239 +1403638154495097088.0000000000 3.5124515369 1.9614155573 1.2522075674 0.5953283805 0.8031088927 0.0090819705 0.022753979208 +1403638154545096960.0000000000 3.4791401758 2.0080976291 1.2459009488 0.5951199436 0.8032918570 0.0082819600 0.0220421063584 +1403638154595097088.0000000000 3.4448295696 2.0521761459 1.2410478688 0.5940576176 0.8041254226 0.0083851781 0.0201876335573 +1403638154645096960.0000000000 3.4098400895 2.0943203403 1.2379420467 0.5918842136 0.8057673557 0.0095693727 0.017901769458 +1403638154695097088.0000000000 3.3742555885 2.1350310078 1.2365143342 0.5886237217 0.8081837890 0.0117323635 0.0149475408197 +1403638154745096960.0000000000 3.3383771553 2.1743997026 1.2361510751 0.5851454876 0.8106557428 0.0160776794 0.0135474403442 +1403638154795097088.0000000000 3.3022122878 2.2128179717 1.2377716335 0.5822514805 0.8126429941 0.0206517734 0.0129646353246 +1403638154845096960.0000000000 3.2656336620 2.2502075358 1.2406876780 0.5802908792 0.8139074618 0.0254586108 0.0129999371144 +1403638154895097088.0000000000 3.2284090276 2.2877580846 1.2456437419 0.5791292945 0.8145946311 0.0297888078 0.0125488706789 +1403638154945096960.0000000000 3.1903559633 2.3244082239 1.2528909495 0.5782544031 0.8150080342 0.0350636772 0.0124212717975 +1403638154995097088.0000000000 3.1511087625 2.3598349309 1.2623527894 0.5785470364 0.8146081046 0.0398196755 0.0105525325688 +1403638155045096960.0000000000 3.1105429877 2.3948680414 1.2737870812 0.5794379824 0.8137215585 0.0452778578 0.0076658545026 +1403638155095097088.0000000000 3.0689091702 2.4285482307 1.2864272089 0.5797872126 0.8131589380 0.0509965785 0.00432187447544 +1403638155145096960.0000000000 3.0264382023 2.4618263832 1.2990164511 0.5813398334 0.8117348176 0.0559495491 0.000481621016533 +1403638155195097088.0000000000 2.9832951106 2.4945294363 1.3106698792 0.5821964153 0.8108516118 0.0596074539 -0.00373483357918 +1403638155245096960.0000000000 2.9395131972 2.5267757684 1.3210247531 0.5847359567 0.8087392130 0.0630221998 -0.00727657800644 +1403638155295097088.0000000000 2.8951729123 2.5581288011 1.3296609702 0.5870096247 0.8068036711 0.0662989787 -0.00959073215819 +1403638155345096960.0000000000 2.8499861399 2.5885775052 1.3367500870 0.5893020635 0.8047599298 0.0704243115 -0.0111780880477 +1403638155395097088.0000000000 2.8039396359 2.6176369821 1.3422874820 0.5915382829 0.8026449616 0.0752003831 -0.0137269052789 +1403638155445096960.0000000000 2.7572338362 2.6456389660 1.3460210321 0.5932498345 0.8008002047 0.0808829809 -0.0152187181909 +1403638155495097088.0000000000 2.7095071121 2.6720766288 1.3480278300 0.5936310486 0.7998687874 0.0865080137 -0.0181235939031 +1403638155545096960.0000000000 2.6604118567 2.6969278752 1.3490629713 0.5944660693 0.7986110895 0.0904910884 -0.0253334398931 +1403638155595097088.0000000000 2.6107397162 2.7200872172 1.3485538100 0.5949771378 0.7974564364 0.0948189479 -0.0327842148326 +1403638155645096960.0000000000 2.5603113307 2.7415556999 1.3474013014 0.5967027319 0.7951790767 0.0992274913 -0.0423082799357 +1403638155695097088.0000000000 2.5096220724 2.7612628924 1.3449534315 0.5985100989 0.7925140897 0.1052505388 -0.0512777077104 +1403638155745096960.0000000000 2.4589054613 2.7792335038 1.3409451784 0.5987457127 0.7908167472 0.1118828874 -0.0599555112104 +1403638155795097088.0000000000 2.4083657666 2.7952902791 1.3354239677 0.5978408837 0.7896846102 0.1200027392 -0.067704037471 +1403638155845096960.0000000000 2.3577977555 2.8093585079 1.3290258338 0.5960812559 0.7889731417 0.1279006581 -0.0764848990288 +1403638155895097088.0000000000 2.3075555570 2.8212164367 1.3214951146 0.5919645188 0.7896729087 0.1373948328 -0.0843644809916 +1403638155945096960.0000000000 2.2577165246 2.8309669668 1.3145253059 0.5860072627 0.7913718243 0.1475447868 -0.0925022139879 +1403638155995097088.0000000000 2.2084066481 2.8389148319 1.3084656488 0.5791185645 0.7933104245 0.1587976877 -0.100317262326 +1403638156045096960.0000000000 2.1596261480 2.8461690875 1.3045551526 0.5720388168 0.7950638481 0.1704115138 -0.107726438532 +1403638156095097088.0000000000 2.1109898989 2.8527429204 1.3030215337 0.5651839240 0.7963488322 0.1817636138 -0.115575335987 +1403638156145096960.0000000000 2.0630665442 2.8587317908 1.3036913030 0.5609791116 0.7958771151 0.1915098941 -0.123312669623 +1403638156195097088.0000000000 2.0152033100 2.8650079804 1.3070604409 0.5573377608 0.7951418130 0.1995036919 -0.131614568236 +1403638156245096960.0000000000 1.9676688439 2.8717389761 1.3117841695 0.5537137719 0.7942760405 0.2085707326 -0.137930706402 +1403638156295097088.0000000000 1.9204822734 2.8788940220 1.3173750236 0.5486124130 0.7944950878 0.2171092141 -0.143755225751 +1403638156345096960.0000000000 1.8738853655 2.8865532541 1.3230675428 0.5443953146 0.7944398952 0.2245229813 -0.148621752179 +1403638156395097088.0000000000 1.8277049768 2.8947920683 1.3276866974 0.5410468764 0.7942746421 0.2298229947 -0.153549541281 +1403638156445096960.0000000000 1.7819372618 2.9037007297 1.3308802486 0.5378881675 0.7943414824 0.2346508406 -0.156961497196 +1403638156495097088.0000000000 1.7364066632 2.9137848439 1.3324709198 0.5354502545 0.7943904556 0.2380421620 -0.159914846147 +1403638156545096960.0000000000 1.6911208785 2.9249091066 1.3327768099 0.5344896665 0.7937483189 0.2408813861 -0.162051104713 +1403638156595097088.0000000000 1.6459420887 2.9370427827 1.3316188465 0.5338401409 0.7932156428 0.2428340944 -0.163875716746 +1403638156645096960.0000000000 1.6008354383 2.9504180027 1.3287161431 0.5333103392 0.7930122971 0.2442247005 -0.164517094512 +1403638156695097088.0000000000 1.5558854013 2.9646020111 1.3244675484 0.5324866152 0.7932173340 0.2449208858 -0.165160604783 +1403638156745096960.0000000000 1.5105629769 2.9803299601 1.3192023416 0.5328360816 0.7927345579 0.2457253196 -0.165156586868 +1403638156795097088.0000000000 1.4653199725 2.9971971558 1.3126717764 0.5325154800 0.7929784971 0.2457756281 -0.164944558279 +1403638156845096960.0000000000 1.4199846300 3.0154107838 1.3051931860 0.5322854558 0.7933383647 0.2455462656 -0.164296878035 +1403638156895097088.0000000000 1.3750088184 3.0341105390 1.2974326520 0.5323974895 0.7934939248 0.2452334456 -0.163648592076 +1403638156945096960.0000000000 1.3308234944 3.0531193671 1.2898861370 0.5320725090 0.7941458684 0.2446407496 -0.162425639768 +1403638156995097088.0000000000 1.2863309145 3.0733391769 1.2839547502 0.5322714025 0.7945241395 0.2435154339 -0.161613053957 +1403638157045096960.0000000000 1.2412531441 3.0955006611 1.2799175431 0.5311069126 0.7958140473 0.2424619560 -0.160678715089 +1403638157095097088.0000000000 1.1960864655 3.1193257025 1.2778515575 0.5298921971 0.7970557093 0.2416252803 -0.159792614552 +1403638157145096960.0000000000 1.1510413562 3.1443252809 1.2772357064 0.5281237756 0.7987506101 0.2408283025 -0.158380773181 +1403638157195097088.0000000000 1.1059105167 3.1707438740 1.2777797847 0.5265460505 0.8003080428 0.2404272308 -0.156368283661 +1403638157245096960.0000000000 1.0605550451 3.1980341061 1.2801109904 0.5261615494 0.8009126890 0.2389378079 -0.156849011469 +1403638157295097088.0000000000 1.0152026541 3.2262234915 1.2844338080 0.5271062913 0.8000970622 0.2393920085 -0.157146794255 +1403638157345096960.0000000000 0.9691177254 3.2557784552 1.2903519087 0.5284240610 0.7987964052 0.2412782427 -0.156451667866 +1403638157395097088.0000000000 0.9228802717 3.2870242163 1.2959969993 0.5299158105 0.7973741140 0.2435252401 -0.155174783484 +1403638157445096960.0000000000 0.8762341159 3.3190940656 1.3005242077 0.5323433788 0.7952765845 0.2458186322 -0.154009354657 +1403638157495097088.0000000000 0.8287792438 3.3515956832 1.3039582188 0.5344322598 0.7929760310 0.2480275218 -0.155091979988 +1403638157545096960.0000000000 0.7808747228 3.3844262540 1.3061765478 0.5366015822 0.7901313442 0.2511463541 -0.157088222655 +1403638157595097088.0000000000 0.7324193540 3.4174958242 1.3072189076 0.5389500576 0.7865712266 0.2554906023 -0.159884624187 +1403638157645096960.0000000000 0.6833552803 3.4506846273 1.3071087716 0.5419035961 0.7820836221 0.2611387185 -0.162764462386 +1403638157695097088.0000000000 0.6343930687 3.4832713930 1.3067650871 0.5444713015 0.7771434402 0.2685044723 -0.165844576313 +1403638157745096960.0000000000 0.5851668709 3.5154792254 1.3074438753 0.5457992032 0.7724961490 0.2770171784 -0.169157951426 +1403638157795097088.0000000000 0.5353446294 3.5471324012 1.3097632976 0.5454770327 0.7685247406 0.2854793539 -0.174143815291 +1403638157845096960.0000000000 0.4849841271 3.5780835697 1.3145074143 0.5441697386 0.7646737612 0.2938288816 -0.181157177004 +1403638157895097088.0000000000 0.4341690549 3.6084315890 1.3215168991 0.5425720152 0.7609138557 0.3015680662 -0.188897893022 +1403638157945096960.0000000000 0.3832262221 3.6380881470 1.3304653658 0.5401143790 0.7576882386 0.3093729991 -0.196146216172 +1403638157995097088.0000000000 0.3323665253 3.6676759966 1.3401909437 0.5384937737 0.7544422249 0.3165611190 -0.201569945339 +1403638158045096960.0000000000 0.2817219822 3.6965296473 1.3489454526 0.5334874658 0.7538381419 0.3221696923 -0.208148670566 +1403638158095097088.0000000000 0.2310101817 3.7252566684 1.3570789610 0.5299414572 0.7527161284 0.3260448432 -0.215116810636 +1403638158145096960.0000000000 0.1806232572 3.7542913474 1.3638320819 0.5272170772 0.7516029619 0.3290876364 -0.220989748106 +1403638158195097088.0000000000 0.1305006664 3.7835223576 1.3691331816 0.5243455963 0.7510372710 0.3309913704 -0.226824659062 +1403638158245096960.0000000000 0.0809980207 3.8134598640 1.3727362833 0.5232313929 0.7497786556 0.3336234627 -0.229687313946 +1403638158295097088.0000000000 0.0317608149 3.8439215091 1.3750305404 0.5231547686 0.7482068267 0.3362376049 -0.231170728205 +1403638158345096960.0000000000 -0.0170063790 3.8748823847 1.3759546321 0.5227836621 0.7472382284 0.3396137127 -0.230205992099 +1403638158395097088.0000000000 -0.0654189307 3.9059717394 1.3762756707 0.5229931425 0.7463285191 0.3413250111 -0.230150279702 +1403638158445096960.0000000000 -0.1132801346 3.9371460555 1.3753480499 0.5245923041 0.7446051946 0.3440707589 -0.227994148037 +1403638158495097088.0000000000 -0.1605715000 3.9679823279 1.3734086549 0.5260612805 0.7431880568 0.3458673940 -0.226510015539 +1403638158545096960.0000000000 -0.2078823364 3.9985929607 1.3704239675 0.5279585677 0.7416967484 0.3472573712 -0.224851067191 +1403638158595097088.0000000000 -0.2552208627 4.0288916270 1.3667357825 0.5289302719 0.7411151736 0.3479605962 -0.223393129939 +1403638158645096960.0000000000 -0.3028029139 4.0586808451 1.3630234790 0.5302676403 0.7404057252 0.3476992510 -0.222981664315 +1403638158695097088.0000000000 -0.3506429768 4.0875491284 1.3594206249 0.5300972534 0.7408999255 0.3461900157 -0.224090774926 +1403638158745096960.0000000000 -0.3986772613 4.1156306383 1.3560733911 0.5290398610 0.7419988619 0.3445372574 -0.225496325195 +1403638158795097088.0000000000 -0.4463557562 4.1429496988 1.3529033214 0.5260019745 0.7445146670 0.3428999183 -0.226802732461 +1403638158845096960.0000000000 -0.4938995664 4.1701126348 1.3514825386 0.5229223051 0.7472530529 0.3409123965 -0.227911991135 +1403638158895097088.0000000000 -0.5412575057 4.1972330380 1.3515848612 0.5196423408 0.7500182574 0.3397195291 -0.228112017903 +1403638158945096960.0000000000 -0.5890109808 4.2249002707 1.3543070514 0.5172463207 0.7520453510 0.3381297861 -0.22924284395 +1403638158995097088.0000000000 -0.6362240356 4.2527984587 1.3586861865 0.5142110380 0.7546010512 0.3378912394 -0.228021429409 +1403638159045096960.0000000000 -0.6830564069 4.2807258878 1.3649759861 0.5096456099 0.7579809600 0.3380749907 -0.226785178347 +1403638159095097088.0000000000 -0.7303882712 4.3095033289 1.3729524133 0.5050023854 0.7614644858 0.3389154892 -0.224233625628 +1403638159145096960.0000000000 -0.7779746794 4.3386397819 1.3807471457 0.4985297154 0.7660978083 0.3394271603 -0.222151916063 +1403638159195097088.0000000000 -0.8262123955 4.3688744370 1.3870920719 0.4931054310 0.7698839273 0.3410421500 -0.218668754897 +1403638159245096960.0000000000 -0.8757085588 4.4006639539 1.3926587048 0.4914969064 0.7712513931 0.3413585567 -0.21697100138 +1403638159295097088.0000000000 -0.9267031077 4.4344995018 1.3980008201 0.4950715197 0.7693996502 0.3392322783 -0.218746039933 +1403638159345096960.0000000000 -0.9788443065 4.4698562037 1.4027320163 0.5017113508 0.7654516789 0.3354541217 -0.223248695323 +1403638159395097088.0000000000 -1.0315972726 4.5065706452 1.4063619897 0.5103260826 0.7600125498 0.3317642920 -0.227773282172 +1403638159445096960.0000000000 -1.0842347111 4.5441886167 1.4101079141 0.5201832778 0.7536177077 0.3271860082 -0.233278855005 +1403638159495097088.0000000000 -1.1364817967 4.5821302149 1.4152444661 0.5287202069 0.7477950089 0.3219268085 -0.240043115911 +1403638159545096960.0000000000 -1.1877305730 4.6196756200 1.4215959048 0.5353779193 0.7429480021 0.3156707977 -0.248496875631 +1403638159595097088.0000000000 -1.2365507023 4.6567525064 1.4298551731 0.5387124385 0.7401988347 0.3090095274 -0.257696926076 +1403638159645096960.0000000000 -1.2831047768 4.6941240641 1.4398007294 0.5409136028 0.7381429775 0.3037416082 -0.265138557185 +1403638159695097088.0000000000 -1.3273645119 4.7324704380 1.4513944750 0.5424567761 0.7365781487 0.2994271879 -0.271176393057 +1403638159745096960.0000000000 -1.3685009212 4.7713061466 1.4641418320 0.5415237846 0.7367958649 0.2971004248 -0.274982148184 +1403638159795097088.0000000000 -1.4056218076 4.8105826589 1.4784389507 0.5444161371 0.7347257472 0.2981116187 -0.273712639204 +1403638159845096960.0000000000 -1.4391409901 4.8499770003 1.4942573679 0.5470025440 0.7329570769 0.3002637641 -0.270931379354 +1403638159895097088.0000000000 -1.4693116372 4.8897129538 1.5115303818 0.5497711253 0.7311856780 0.3057007462 -0.263943683174 +1403638159945096960.0000000000 -1.4959114882 4.9284679437 1.5305935859 0.5521683378 0.7298109048 0.3108216870 -0.256663298535 +1403638159995097088.0000000000 -1.5196855224 4.9660157189 1.5529405957 0.5534862763 0.7287163654 0.3150075754 -0.251784884838 +1403638160045096960.0000000000 -1.5403102535 5.0018260498 1.5771437170 0.5539736447 0.7282310927 0.3185155540 -0.247670180645 +1403638160095097088.0000000000 -1.5587655208 5.0363439054 1.6026904212 0.5520210331 0.7295051486 0.3211242425 -0.244896382312 +1403638160145096960.0000000000 -1.5754401005 5.0699184204 1.6301799922 0.5489297399 0.7315476634 0.3241593100 -0.241733114382 +1403638160195097088.0000000000 -1.5912346435 5.1028498691 1.6600491983 0.5421338050 0.7362210746 0.3277230975 -0.238048394485 +1403638160245096960.0000000000 -1.6057775037 5.1348615988 1.6924774779 0.5346665795 0.7413099433 0.3314280155 -0.233980100189 +1403638160295097088.0000000000 -1.6191039035 5.1662296792 1.7267279463 0.5278359140 0.7458215928 0.3341162777 -0.231313018564 +1403638160345096960.0000000000 -1.6321861203 5.1976252655 1.7628591362 0.5226762773 0.7491716002 0.3370410005 -0.227935926406 +1403638160395097088.0000000000 -1.6453065065 5.2290824777 1.8001046299 0.5188327166 0.7516430173 0.3390379194 -0.225607349051 +1403638160445096960.0000000000 -1.6585084563 5.2609257653 1.8369861395 0.5166543728 0.7530584278 0.3395426295 -0.225126778033 +1403638160495097088.0000000000 -1.6719029511 5.2930857274 1.8726665754 0.5153478750 0.7539780949 0.3398793992 -0.224534171575 +1403638160545096960.0000000000 -1.6858260932 5.3255602472 1.9071317802 0.5143746466 0.7546960287 0.3402232342 -0.223832031034 +1403638160595097088.0000000000 -1.7004722729 5.3583724399 1.9405719029 0.5139829201 0.7549508032 0.3402832310 -0.223781512612 +1403638160645096960.0000000000 -1.7159280372 5.3915253350 1.9727394216 0.5126907601 0.7559559417 0.3398680151 -0.223983327527 +1403638160695097088.0000000000 -1.7321922899 5.4254246306 2.0040938738 0.5140581132 0.7551104927 0.3397434484 -0.223890127974 +1403638160745096960.0000000000 -1.7491383560 5.4596218399 2.0350101151 0.5154281184 0.7542015668 0.3374735574 -0.227212344295 +1403638160795097088.0000000000 -1.7664759011 5.4947687108 2.0652808666 0.5182137675 0.7529326052 0.3332523026 -0.231278805956 +1403638160845096960.0000000000 -1.7837617266 5.5308382213 2.0952496842 0.5234489418 0.7507715557 0.3270372340 -0.235350640635 +1403638160895097088.0000000000 -1.8007498950 5.5674806495 2.1246435422 0.5290838097 0.7491743838 0.3190996889 -0.238712072281 +1403638160945096960.0000000000 -1.8161381444 5.6044090175 2.1526030257 0.5355145626 0.7477976204 0.3110934128 -0.239256683608 +1403638160995097088.0000000000 -1.8300860449 5.6417348053 2.1790528250 0.5406800338 0.7477799198 0.3037045346 -0.237178937269 +1403638161045096960.0000000000 -1.8429212682 5.6797374233 2.2050461986 0.5450590990 0.7487903318 0.2959527623 -0.233742550803 +1403638161095097088.0000000000 -1.8537941775 5.7171642521 2.2302172783 0.5480435455 0.7510624390 0.2880755885 -0.22927263293 +1403638161145096960.0000000000 -1.8624132606 5.7541049595 2.2540473555 0.5505533582 0.7540507193 0.2812013753 -0.22186549778 +1403638161195097088.0000000000 -1.8694752635 5.7907637027 2.2764685681 0.5520583149 0.7582511662 0.2732732849 -0.213561460835 +1403638161245096960.0000000000 -1.8755816028 5.8277904188 2.2986402890 0.5529011618 0.7631859854 0.2647468861 -0.204344178194 +1403638161295097088.0000000000 -1.8809056732 5.8651381816 2.3205872999 0.5543058017 0.7677883150 0.2548991864 -0.19563380641 +1403638161345096960.0000000000 -1.8848988095 5.9014965473 2.3426999316 0.5546993514 0.7728532739 0.2454847238 -0.186396611909 +1403638161395097088.0000000000 -1.8876711492 5.9364837266 2.3637919967 0.5528728821 0.7785401155 0.2377258546 -0.178026073374 +1403638161445096960.0000000000 -1.8895287091 5.9707197553 2.3842469044 0.5502783029 0.7841013396 0.2313286453 -0.169899783301 +1403638161495097088.0000000000 -1.8910030979 6.0048804541 2.4038298780 0.5475801311 0.7889405652 0.2266308272 -0.162379964111 +1403638161545096960.0000000000 -1.8922192571 6.0386315809 2.4223955855 0.5456975534 0.7926479465 0.2221288548 -0.156787068745 +1403638161595097088.0000000000 -1.8933414090 6.0727386317 2.4397009446 0.5446428457 0.7954492834 0.2174366774 -0.15279364983 +1403638161645096960.0000000000 -1.8943531240 6.1069844368 2.4554898785 0.5435011822 0.7979052803 0.2130584002 -0.150199023641 +1403638161695097088.0000000000 -1.8953183880 6.1416164787 2.4700674026 0.5428143046 0.7996850941 0.2084140730 -0.149732946358 +1403638161745096960.0000000000 -1.8961241452 6.1769467663 2.4834614304 0.5435937200 0.8001683024 0.2042657710 -0.150040162222 +1403638161795097088.0000000000 -1.8964842202 6.2131749216 2.4955770276 0.5452326061 0.8001618301 0.2001810016 -0.149632942246 +1403638161845096960.0000000000 -1.8963535143 6.2505562001 2.5065837849 0.5484736169 0.7991823992 0.1965892868 -0.147772922484 +1403638161895097088.0000000000 -1.8957402091 6.2885128456 2.5165732488 0.5519774525 0.7982212405 0.1918826923 -0.146098513414 +1403638161945096960.0000000000 -1.8943005315 6.3267890062 2.5247177863 0.5543696492 0.7981691567 0.1875050556 -0.142976024042 +1403638161995097088.0000000000 -1.8922232519 6.3650451290 2.5324893808 0.5556216362 0.7986992940 0.1835123589 -0.140311258121 +1403638162045096960.0000000000 -1.8896841209 6.4035986564 2.5413293296 0.5565918806 0.7991627814 0.1800187263 -0.138338661953 +1403638162095097088.0000000000 -1.8867908861 6.4431015450 2.5518529863 0.5568209603 0.7999147892 0.1773354836 -0.136524263364 +1403638162145096960.0000000000 -1.8830728692 6.4822931317 2.5642545191 0.5554195210 0.8016082401 0.1746854820 -0.135714286144 +1403638162195097088.0000000000 -1.8787513964 6.5215481554 2.5783831756 0.5533879037 0.8035719718 0.1718616177 -0.136005508922 +1403638162245096960.0000000000 -1.8735674782 6.5608861243 2.5929389068 0.5516580013 0.8052514597 0.1698476850 -0.135629274727 +1403638162295097088.0000000000 -1.8676930871 6.6009750236 2.6068590395 0.5501951995 0.8066490684 0.1679149809 -0.135672702342 +1403638162345096960.0000000000 -1.8610178915 6.6417764980 2.6196493374 0.5492975694 0.8074925169 0.1654758957 -0.137279799647 +1403638162395097088.0000000000 -1.8534045326 6.6837941977 2.6313322442 0.5498422985 0.8072836080 0.1634836912 -0.138707266437 +1403638162445096960.0000000000 -1.8448704411 6.7267206210 2.6419003114 0.5511696656 0.8064915679 0.1623270904 -0.139403251015 +1403638162495097088.0000000000 -1.8350247131 6.7702211562 2.6512616791 0.5527090494 0.8055771489 0.1622970372 -0.138628408426 +1403638162545096960.0000000000 -1.8241618067 6.8140589767 2.6605561191 0.5537495446 0.8048932425 0.1634313402 -0.137107648087 +1403638162595097088.0000000000 -1.8121743358 6.8586478898 2.6706753792 0.5539032552 0.8047968940 0.1655682908 -0.134462947755 +1403638162645096960.0000000000 -1.7993095782 6.9034630955 2.6825874420 0.5547912637 0.8041251104 0.1676423051 -0.132232817838 +1403638162695097088.0000000000 -1.7858244696 6.9488533771 2.6961985946 0.5546187537 0.8041194606 0.1702173601 -0.129676449282 +1403638162745096960.0000000000 -1.7717498730 6.9944184407 2.7119817348 0.5539579680 0.8044473351 0.1722198841 -0.12780988328 +1403638162795097088.0000000000 -1.7574020159 7.0405803628 2.7300377325 0.5523589316 0.8057443081 0.1706090982 -0.128717739079 +1403638162845096960.0000000000 -1.7422579224 7.0874044514 2.7499957068 0.5516870395 0.8067563364 0.1683328910 -0.128256235483 +1403638162895097088.0000000000 -1.7266705775 7.1350049887 2.7725018436 0.5528210384 0.8066842974 0.1637349138 -0.129769880248 +1403638162945096960.0000000000 -1.7100763438 7.1826271580 2.7967417666 0.5548941406 0.8058491094 0.1587162986 -0.132320981574 +1403638162995097088.0000000000 -1.6925727890 7.2315173686 2.8219709494 0.5601454814 0.8028751409 0.1551134739 -0.132545682823 +1403638163045096960.0000000000 -1.6741080791 7.2807851688 2.8462614408 0.5651655530 0.7999831125 0.1513368206 -0.133086754011 +1403638163095097088.0000000000 -1.6543106957 7.3299261858 2.8666912796 0.5691153409 0.7980034271 0.1467664128 -0.133258692317 +1403638163145096960.0000000000 -1.6331528951 7.3792607986 2.8822436360 0.5706020336 0.7980646664 0.1430002479 -0.130602589988 +1403638163195097088.0000000000 -1.6104473774 7.4280304387 2.8926735216 0.5709831219 0.7991453628 0.1396408424 -0.125878507972 +1403638163245096960.0000000000 -1.5863576066 7.4767678606 2.8990938986 0.5712790744 0.8005039015 0.1364156815 -0.119266444288 +1403638163295097088.0000000000 -1.5613260175 7.5257557752 2.9032348813 0.5715744130 0.8019741968 0.1324733333 -0.112209153301 +1403638163345096960.0000000000 -1.5351725187 7.5744020293 2.9058081115 0.5727552383 0.8029214979 0.1276984153 -0.104697755182 +1403638163395097088.0000000000 -1.5081586832 7.6228349695 2.9075754849 0.5740230820 0.8038124829 0.1223627283 -0.09700699101 +1403638163445096960.0000000000 -1.4804792982 7.6705603776 2.9081746109 0.5754453334 0.8045267870 0.1157834175 -0.0905180504676 +1403638163495097088.0000000000 -1.4523819501 7.7173697378 2.9087704336 0.5753107634 0.8060172568 0.1100131837 -0.085151668414 +1403638163545096960.0000000000 -1.4237594074 7.7628609714 2.9112081336 0.5766232337 0.8062486269 0.1045963677 -0.0807985016293 +1403638163595097088.0000000000 -1.3946877325 7.8069193273 2.9146671261 0.5756134976 0.8078193732 0.1002056329 -0.0778189753692 +1403638163645096960.0000000000 -1.3653398470 7.8507864222 2.9203555355 0.5759963798 0.8082137643 0.0973199716 -0.0744815738097 +1403638163695097088.0000000000 -1.3355191368 7.8937610140 2.9281127366 0.5765869447 0.8083549500 0.0948172050 -0.0715504553352 +1403638163745096960.0000000000 -1.3056777662 7.9362024203 2.9381427131 0.5764350977 0.8088481837 0.0927406111 -0.0699025956025 +1403638163795097088.0000000000 -1.2756266135 7.9781685111 2.9505183148 0.5776571072 0.8082572779 0.0916753846 -0.068029868318 +1403638163845096960.0000000000 -1.2453972532 8.0188045364 2.9648761678 0.5779926049 0.8082107245 0.0894630219 -0.0686756233573 +1403638163895097088.0000000000 -1.2148879493 8.0588734827 2.9810173532 0.5785058216 0.8079591325 0.0878924669 -0.0693395180432 +1403638163945096960.0000000000 -1.1840015087 8.0979648453 2.9984975998 0.5771109426 0.8089877892 0.0868271168 -0.0703048258021 +1403638163995097088.0000000000 -1.1528878308 8.1368370581 3.0179792303 0.5762260086 0.8095793007 0.0843489900 -0.0736898288209 +1403638164045096960.0000000000 -1.1211838661 8.1754704074 3.0387775538 0.5748083105 0.8104954132 0.0833601594 -0.0757870388174 +1403638164095097088.0000000000 -1.0888581149 8.2140616904 3.0617861524 0.5744824231 0.8105731935 0.0823886823 -0.0784420073712 +1403638164145096960.0000000000 -1.0556292285 8.2525422474 3.0863203669 0.5748075472 0.8102029733 0.0816355825 -0.0806415369794 +1403638164195097088.0000000000 -1.0214794562 8.2906704564 3.1111498434 0.5751605629 0.8097626797 0.0804846261 -0.0836478000214 +1403638164245096960.0000000000 -0.9861468915 8.3285278876 3.1349771382 0.5764929581 0.8086715826 0.0808980039 -0.0846265540432 +1403638164295097088.0000000000 -0.9500843573 8.3662945494 3.1576338588 0.5775457483 0.8077232410 0.0803614509 -0.0869833993959 +1403638164345096960.0000000000 -0.9127227724 8.4036144757 3.1787185576 0.5785737903 0.8068331480 0.0804357539 -0.0883330630012 +1403638164395097088.0000000000 -0.8742290958 8.4403782958 3.1982830169 0.5791285590 0.8062930103 0.0808045968 -0.0892877975491 +1403638164445096960.0000000000 -0.8345405214 8.4765922877 3.2162962520 0.5797125491 0.8057159647 0.0818611760 -0.0897434809932 +1403638164495097088.0000000000 -0.7937245810 8.5124473996 3.2331173813 0.5788336664 0.8061880215 0.0813773299 -0.0915979848102 +1403638164545096960.0000000000 -0.7516757563 8.5479648012 3.2492522610 0.5789956046 0.8059237658 0.0806877473 -0.0934904327646 +1403638164595097088.0000000000 -0.7082453517 8.5829048120 3.2639885219 0.5784216253 0.8062404418 0.0797453185 -0.0951076106005 +1403638164645096960.0000000000 -0.6631048086 8.6176174242 3.2775048269 0.5781670608 0.8065928911 0.0777353306 -0.0953308774039 +1403638164695097088.0000000000 -0.6158095810 8.6520073784 3.2893297704 0.5782948004 0.8070139593 0.0760290910 -0.092321019547 +1403638164745096960.0000000000 -0.5669326233 8.6861867643 3.2999378542 0.5801497163 0.8063027965 0.0746735915 -0.0878974501794 +1403638164795097088.0000000000 -0.5164179995 8.7198499932 3.3092301896 0.5831999425 0.8047794906 0.0764249323 -0.0797936605922 +1403638164845096960.0000000000 -0.4646858965 8.7527536236 3.3177674369 0.5868915860 0.8026997091 0.0790478831 -0.070589485776 +1403638164895097088.0000000000 -0.4124604231 8.7848567241 3.3255075958 0.5902897494 0.8006796919 0.0812070375 -0.0622531912083 +1403638164945096960.0000000000 -0.3603193229 8.8156039314 3.3323432745 0.5924239414 0.7994413791 0.0818564371 -0.0568056221116 +1403638164995097088.0000000000 -0.3086615418 8.8452044925 3.3390283517 0.5955487031 0.7974325124 0.0789583073 -0.0564687175574 +1403638165045096960.0000000000 -0.2572678166 8.8733563900 3.3447786740 0.5986837690 0.7954734161 0.0727167797 -0.0592626268147 +1403638165095097088.0000000000 -0.2055931947 8.9000118425 3.3488401958 0.5996082235 0.7952124760 0.0655528382 -0.0617245634604 +1403638165145096960.0000000000 -0.1533844307 8.9250688700 3.3511137042 0.5980125585 0.7967841088 0.0597678087 -0.0628002612265 +1403638165195097088.0000000000 -0.1002274111 8.9485453153 3.3515977852 0.5942344894 0.7999724333 0.0564461252 -0.0611826162073 +1403638165245096960.0000000000 -0.0463724703 8.9706876933 3.3504218019 0.5880150700 0.8048940232 0.0540655283 -0.0588286285508 +1403638165295097088.0000000000 0.0078551970 8.9917217447 3.3480793216 0.5809040455 0.8102798521 0.0510408298 -0.058239890521 +1403638165345096960.0000000000 0.0626742637 9.0124805364 3.3452409423 0.5769097754 0.8133440229 0.0470792641 -0.058567519253 +1403638165395097088.0000000000 0.1180524406 9.0332729833 3.3417073753 0.5751386538 0.8147306641 0.0432192358 -0.0596789034413 +1403638165445096960.0000000000 0.1744887609 9.0546774251 3.3368984307 0.5757183919 0.8145068830 0.0416713528 -0.0582268761393 +1403638165495097088.0000000000 0.2320743895 9.0761696811 3.3318857388 0.5806206190 0.8112284051 0.0404980777 -0.0561077290282 +1403638165545096960.0000000000 0.2906606884 9.0974607863 3.3256337024 0.5863059874 0.8073503079 0.0402713763 -0.0529998656594 +1403638165595097088.0000000000 0.3499182316 9.1180756608 3.3185549645 0.5931227920 0.8025193313 0.0398520567 -0.0507926180331 +1403638165645096960.0000000000 0.4100230767 9.1376115704 3.3099947995 0.6001231516 0.7974889888 0.0415721319 -0.0462090192852 +1403638165695097088.0000000000 0.4704114763 9.1554602525 3.3001580967 0.6057716059 0.7933119988 0.0418634907 -0.0440940148727 +1403638165745096960.0000000000 0.5314884971 9.1711605639 3.2885038845 0.6096199561 0.7904734761 0.0435329017 -0.0402502057874 +1403638165795097088.0000000000 0.5926751880 9.1844260286 3.2749207577 0.6091872484 0.7908443571 0.0446661757 -0.0382234480523 +1403638165845096960.0000000000 0.6540217527 9.1952622302 3.2608098727 0.6052598416 0.7938688444 0.0459253831 -0.0363818798824 +1403638165895097088.0000000000 0.7154053816 9.2039298203 3.2478702623 0.6002555976 0.7976441121 0.0466357955 -0.0358076893157 +1403638165945096960.0000000000 0.7769224236 9.2109209953 3.2363627824 0.5957051921 0.8010382333 0.0478858775 -0.0343513543545 +1403638165995097088.0000000000 0.8382671094 9.2164779445 3.2269543942 0.5902528673 0.8050237119 0.0487196082 -0.0341288120591 +1403638166045096960.0000000000 0.8994441784 9.2213454233 3.2197852637 0.5845362926 0.8091498435 0.0491077746 -0.0343842973778 +1403638166095097088.0000000000 0.9606630513 9.2260284216 3.2154022441 0.5806052748 0.8119224517 0.0518175240 -0.031533973522 +1403638166145096960.0000000000 1.0215050093 9.2299808623 3.2134354174 0.5777988928 0.8138366285 0.0544459337 -0.0292236512395 +1403638166195097088.0000000000 1.0814815754 9.2343475682 3.2162322522 0.5758953583 0.8150742646 0.0563867990 -0.0286183236859 +1403638166245096960.0000000000 1.1405976152 9.2391499230 3.2243586961 0.5748638187 0.8156836746 0.0583256356 -0.0281043280715 +1403638166295097088.0000000000 1.1989543589 9.2438102147 3.2377124175 0.5748921088 0.8155462166 0.0602370273 -0.0274760333875 +1403638166345096960.0000000000 1.2564949966 9.2483192455 3.2558938567 0.5741162152 0.8159594531 0.0624087887 -0.02656850457 +1403638166395097088.0000000000 1.3131911349 9.2523545681 3.2784238180 0.5741969284 0.8157996186 0.0640557894 -0.0258016564835 +1403638166445096960.0000000000 1.3688241553 9.2548002522 3.3036523203 0.5730038209 0.8165555097 0.0652145815 -0.0255103747422 +1403638166495097088.0000000000 1.4235315986 9.2573614449 3.3283111852 0.5731556370 0.8163580622 0.0663746375 -0.0254271022452 +1403638166545096960.0000000000 1.4771727448 9.2598029108 3.3516687076 0.5731192296 0.8163291679 0.0663615545 -0.0271511021671 +1403638166595097088.0000000000 1.5295640203 9.2609104744 3.3739804823 0.5738064095 0.8157770895 0.0671403455 -0.0273151724068 +1403638166645096960.0000000000 1.5814510754 9.2624291080 3.3940002295 0.5732689037 0.8161100813 0.0670661838 -0.0287962897654 +1403638166695097088.0000000000 1.6322272848 9.2639470160 3.4123144244 0.5730630422 0.8162589884 0.0659180823 -0.0312221075165 +1403638166745096960.0000000000 1.6821008693 9.2655804971 3.4286458376 0.5720051185 0.8169871002 0.0642298441 -0.034881938045 +1403638166795097088.0000000000 1.7311078941 9.2671485247 3.4430108370 0.5686925059 0.8192773316 0.0606337114 -0.0411951536465 +1403638166845096960.0000000000 1.7798344865 9.2690929267 3.4548909871 0.5632720115 0.8229576102 0.0570342546 -0.0470372897974 +1403638166895097088.0000000000 1.8287190021 9.2714028127 3.4642683588 0.5554469243 0.8281391419 0.0537205763 -0.0527102987553 +1403638166945096960.0000000000 1.8781672781 9.2748271239 3.4718631105 0.5487574259 0.8324988956 0.0519718907 -0.0557655708311 +1403638166995097088.0000000000 1.9282593699 9.2798044750 3.4778135451 0.5428862169 0.8363230903 0.0517994146 -0.0561699626399 +1403638167045096960.0000000000 1.9789985138 9.2868491758 3.4835154814 0.5391285389 0.8387815647 0.0530759176 -0.0544871756147 +1403638167095097088.0000000000 2.0302802000 9.2961208583 3.4904271856 0.5368042061 0.8402936387 0.0544699123 -0.0527339899919 +1403638167145096960.0000000000 2.0821218317 9.3079535317 3.4987993857 0.5364738706 0.8405451070 0.0572250946 -0.0490407769887 +1403638167195097088.0000000000 2.1337424073 9.3224911055 3.5097038104 0.5372799292 0.8400483505 0.0590093515 -0.046550434757 +1403638167245096960.0000000000 2.1851320903 9.3396662967 3.5223453072 0.5381033554 0.8395210539 0.0617743555 -0.0428148101704 +1403638167295097088.0000000000 2.2360811419 9.3589650180 3.5369791639 0.5399170079 0.8383634062 0.0630241856 -0.0407967615558 +1403638167345096960.0000000000 2.2863516598 9.3807698970 3.5532951935 0.5413289741 0.8374480356 0.0639474584 -0.0394265392408 +1403638167395097088.0000000000 2.3360198864 9.4043433282 3.5705592832 0.5421764810 0.8369382774 0.0637257304 -0.03896170573 +1403638167445096960.0000000000 2.3849435260 9.4297105053 3.5875796409 0.5442146034 0.8356503179 0.0629627233 -0.0394297753755 +1403638167495097088.0000000000 2.4335539960 9.4566721303 3.6034178470 0.5468208786 0.8339918909 0.0617621298 -0.0403719206037 +1403638167545096960.0000000000 2.4819449563 9.4851435087 3.6178483285 0.5504036369 0.8316718588 0.0605277201 -0.0414023054092 +1403638167595097088.0000000000 2.5298373602 9.5148428927 3.6309005581 0.5540401708 0.8293149970 0.0574269296 -0.0444777774644 +1403638167645096960.0000000000 2.5777194507 9.5451540310 3.6423455959 0.5569775402 0.8274484303 0.0523509559 -0.0486260454739 +1403638167695097088.0000000000 2.6260936499 9.5765927936 3.6518567626 0.5591929971 0.8261447725 0.0471398691 -0.0506541169148 +1403638167745096960.0000000000 2.6751803994 9.6089882746 3.6597835631 0.5613195485 0.8249792402 0.0407746317 -0.0516434618687 +1403638167795097088.0000000000 2.7250707460 9.6423051220 3.6664852413 0.5625735738 0.8243948641 0.0333173588 -0.0526691150961 +1403638167845096960.0000000000 2.7763177165 9.6766336836 3.6719475410 0.5628770483 0.8244949720 0.0254191869 -0.0522621713109 +1403638167895097088.0000000000 2.8289534554 9.7118517185 3.6764764033 0.5640458052 0.8240555524 0.0179643488 -0.0496191322975 +1403638167945096960.0000000000 2.8828723901 9.7475930873 3.6800883168 0.5652380004 0.8235396387 0.0103776928 -0.0466987151362 +1403638167995097088.0000000000 2.9383333676 9.7837974613 3.6824781787 0.5657158399 0.8235389310 0.0033088979 -0.0416925509231 +1403638168045096960.0000000000 2.9949660588 9.8206844493 3.6860886542 0.5667861705 0.8229953991 -0.0032338707 -0.0377034761393 +1403638168095097088.0000000000 3.0527839142 9.8584600920 3.6916973975 0.5676777558 0.8224547178 -0.0096691866 -0.0348813639501 +1403638168145096960.0000000000 3.1111648452 9.8972664852 3.6959805635 0.5679310145 0.8224200978 -0.0143291264 -0.0295672396408 +1403638168195097088.0000000000 3.1721744272 9.9346699855 3.7047217560 0.5689962824 0.8217039885 -0.0203067263 -0.0251678904321 +1403638168245096960.0000000000 3.2351640869 9.9719957271 3.7148789248 0.5685289997 0.8221169493 -0.0245314204 -0.0172252030797 +1403638168295097088.0000000000 3.2995406073 10.0089546078 3.7264884364 0.5683037239 0.8222061421 -0.0300000283 -0.0103892069286 +1403638168345096960.0000000000 3.3651526244 10.0461753911 3.7399035675 0.5688203003 0.8216824997 -0.0356738869 -0.00295118267311 +1403638168395097088.0000000000 3.4316732411 10.0839045104 3.7555344066 0.5699759277 0.8205691048 -0.0422081382 0.00350129764488 +1403638168445096960.0000000000 3.4991237254 10.1213980881 3.7719079422 0.5694812813 0.8206194457 -0.0461454135 0.0120580396306 +1403638168495097088.0000000000 3.5671695235 10.1589768557 3.7871538108 0.5664750197 0.8223965068 -0.0484940609 0.0204539427051 +1403638168545096960.0000000000 3.6353506193 10.1968285606 3.8006987804 0.5629217139 0.8245236207 -0.0491059982 0.0294710695755 +1403638168595097088.0000000000 3.7036904223 10.2352563750 3.8125064460 0.5578314536 0.8276453507 -0.0493385616 0.037322233585 +1403638168645096960.0000000000 3.7714596148 10.2742098718 3.8225648320 0.5542072921 0.8297241465 -0.0490990539 0.0447370203815 +1403638168695097088.0000000000 3.8384975820 10.3138688365 3.8307123282 0.5509078812 0.8315967788 -0.0488592271 0.0505972314209 +1403638168745096960.0000000000 3.9043441608 10.3542464934 3.8375464471 0.5488190936 0.8327364854 -0.0488247339 0.0544398169533 +1403638168795097088.0000000000 3.9688336018 10.3951246107 3.8430276540 0.5474554925 0.8334847117 -0.0492377632 0.0563148455149 +1403638168845096960.0000000000 4.0321850890 10.4368784282 3.8468700102 0.5455418647 0.8346193251 -0.0493243589 0.057980718427 +1403638168895097088.0000000000 4.0944982342 10.4801869954 3.8496006245 0.5446545801 0.8351200281 -0.0487296665 0.059593176002 +1403638168945096960.0000000000 4.1552661375 10.5248735813 3.8510329957 0.5436716291 0.8357749864 -0.0489200387 0.0592297359341 +1403638168995097088.0000000000 4.2147512260 10.5711781274 3.8513929014 0.5444281177 0.8353365393 -0.0478126000 0.0593704131678 +1403638169045096960.0000000000 4.2731336239 10.6191028672 3.8508516339 0.5478068856 0.8332182919 -0.0464005835 0.059176683896 +1403638169095097088.0000000000 4.3300380159 10.6683579461 3.8496790474 0.5535420750 0.8296062534 -0.0469933670 0.0560023114355 +1403638169145096960.0000000000 4.3851536106 10.7164430601 3.8467732043 0.5577797594 0.8269766030 -0.0475588756 0.0522454914146 +1403638169195097088.0000000000 4.4397831254 10.7666282947 3.8421045382 0.5610880959 0.8249501491 -0.0490649388 0.0472232132964 +1403638169245096960.0000000000 4.4937550901 10.8173865888 3.8364523121 0.5647664168 0.8225458912 -0.0526500820 0.0410502164715 +1403638169295097088.0000000000 4.5474404770 10.8685016892 3.8294399608 0.5688282361 0.8196357430 -0.0581694030 0.0353271449723 +1403638169345096960.0000000000 4.6011595444 10.9197883020 3.8215338127 0.5744668027 0.8153134801 -0.0668435493 0.0279957438225 +1403638169395097088.0000000000 4.6557833618 10.9708430071 3.8122840923 0.5794533483 0.8111427063 -0.0757603884 0.0232742521053 +1403638169445096960.0000000000 4.7115419140 11.0206547103 3.8019709764 0.5842933135 0.8068575386 -0.0844888776 0.0210681249754 +1403638169495097088.0000000000 4.7691369566 11.0693286356 3.7918590754 0.5874159295 0.8036245442 -0.0929499249 0.022145636969 +1403638169545096960.0000000000 4.8284662375 11.1168848515 3.7828705734 0.5902347676 0.8005820814 -0.1002509560 0.0253178982557 +1403638169595097088.0000000000 4.8901654932 11.1622585179 3.7754037025 0.5911463714 0.7987614066 -0.1074637470 0.0312686114554 +1403638169645096960.0000000000 4.9536006032 11.2054546393 3.7688826061 0.5907722642 0.7977867014 -0.1137994310 0.0396761956851 +1403638169695097088.0000000000 5.0188841200 11.2476852692 3.7627977146 0.5883612361 0.7981771675 -0.1191484176 0.0504769222763 +1403638169745096960.0000000000 5.0853492976 11.2882485418 3.7590418061 0.5865363257 0.7977941003 -0.1257813506 0.0606528155648 +1403638169795097088.0000000000 5.1531887621 11.3266785233 3.7569957666 0.5841593269 0.7975889611 -0.1304434705 0.0747945919112 +1403638169845096960.0000000000 5.2215521331 11.3637005791 3.7571570296 0.5810816988 0.7975201520 -0.1352584496 0.0895031746681 +1403638169895097088.0000000000 5.2898818503 11.3998189825 3.7598648509 0.5787936606 0.7965009594 -0.1409427446 0.103533873064 +1403638169945096960.0000000000 5.3576939397 11.4348781191 3.7644251537 0.5792151143 0.7931843646 -0.1459194094 0.118642071264 +1403638169995097088.0000000000 5.4241778162 11.4692024217 3.7716292237 0.5812890546 0.7884324281 -0.1526698444 0.131031522409 +1403638170045096960.0000000000 5.4890033984 11.5023117101 3.7799536393 0.5839697847 0.7830662271 -0.1616146826 0.140240040363 +1403638170095097088.0000000000 5.5522466332 11.5341569813 3.7881762825 0.5855182775 0.7783931238 -0.1716688321 0.147656031489 +1403638170145096960.0000000000 5.6137615702 11.5643149978 3.7947224201 0.5852288149 0.7748877328 -0.1836892186 0.152690885893 +1403638170195097088.0000000000 5.6737744820 11.5925514584 3.7995715696 0.5844433466 0.7715305712 -0.1961376636 0.157151421051 +1403638170245096960.0000000000 5.7322205547 11.6188283859 3.8024472257 0.5829061905 0.7685551223 -0.2086967959 0.161211179821 +1403638170295097088.0000000000 5.7893291632 11.6433718614 3.8040662072 0.5812838785 0.7654528002 -0.2219670247 0.164078344777 +1403638170345096960.0000000000 5.8456130971 11.6659536062 3.8034418921 0.5781139376 0.7633018393 -0.2344569087 0.167882504372 +1403638170395097088.0000000000 5.9011435817 11.6866564864 3.8012395205 0.5739834080 0.7616104224 -0.2468716688 0.171892382085 +1403638170445096960.0000000000 5.9558793810 11.7052859043 3.7977249532 0.5699369357 0.7597456767 -0.2582924536 0.176758039235 +1403638170495097088.0000000000 6.0099878752 11.7224606854 3.7941319917 0.5673208880 0.7567794306 -0.2707742632 0.179201567484 +1403638170545096960.0000000000 6.0638906487 11.7380686776 3.7921802376 0.5672685250 0.7519035278 -0.2830620881 0.180895991649 +1403638170595097088.0000000000 6.1183372900 11.7521339772 3.7918699522 0.5674491474 0.7466838011 -0.2942817553 0.184019061039 +1403638170645096960.0000000000 6.1734944318 11.7642445006 3.7940466188 0.5682994960 0.7407919980 -0.3040030671 0.189327847286 +1403638170695097088.0000000000 6.2281264921 11.7733514192 3.7980084065 0.5685645476 0.7352871511 -0.3133213497 0.194722603875 +1403638170745096960.0000000000 6.2822921311 11.7793627215 3.8033045916 0.5665310325 0.7316489273 -0.3219013218 0.200279742855 +1403638170795097088.0000000000 6.3364487243 11.7830529087 3.8103296819 0.5650588483 0.7273783533 -0.3301480478 0.206473958543 +1403638170845096960.0000000000 6.3904819416 11.7840752701 3.8177739009 0.5623101826 0.7240851824 -0.3382171261 0.212407821994 +1403638170895097088.0000000000 6.4442193978 11.7825387194 3.8240977740 0.5591446866 0.7209458214 -0.3455098770 0.219584305049 +1403638170945096960.0000000000 6.4976155075 11.7783177941 3.8286999520 0.5556296029 0.7178699630 -0.3533678994 0.225985814196 +1403638170995097088.0000000000 6.5508132576 11.7716682456 3.8319331294 0.5530344322 0.7139514140 -0.3608083204 0.23290266455 +1403638171045096960.0000000000 6.6036244972 11.7630373203 3.8340025259 0.5514217616 0.7094644550 -0.3680822399 0.238976343046 +1403638171095097088.0000000000 6.6548094081 11.7518498874 3.8354715121 0.5498328356 0.7055561663 -0.3747112011 0.243856238113 +1403638171145096960.0000000000 6.7059040252 11.7388260627 3.8358908995 0.5487105197 0.7019605951 -0.3801253162 0.248340154689 +1403638171195097088.0000000000 6.7560478509 11.7236236998 3.8356587436 0.5481512654 0.6985226202 -0.3854964219 0.250975791508 +1403638171245096960.0000000000 6.8055091100 11.7062031788 3.8349684355 0.5477855703 0.6955568980 -0.3898164824 0.253327220574 +1403638171295097088.0000000000 6.8542116313 11.6863444011 3.8336550117 0.5471889429 0.6933667157 -0.3928127017 0.255978592182 +1403638171345096960.0000000000 6.9018316581 11.6641953352 3.8319615378 0.5470677036 0.6913930747 -0.3955923775 0.257292080804 +1403638171395097088.0000000000 6.9488192329 11.6394543145 3.8298484440 0.5476263074 0.6889811905 -0.3978511881 0.259084501242 +1403638171445096960.0000000000 6.9952706915 11.6121090729 3.8270864998 0.5471854519 0.6867527143 -0.4009363939 0.261168142648 +1403638171495097088.0000000000 7.0408980479 11.5824178461 3.8241006191 0.5478147542 0.6841750875 -0.4036136415 0.262487091328 +1403638171545096960.0000000000 7.0856287756 11.5502958758 3.8207446711 0.5490748130 0.6812345808 -0.4067637820 0.262639527413 +1403638171595097088.0000000000 7.1300914957 11.5152078602 3.8166700574 0.5492560688 0.6787309280 -0.4091895953 0.264964098141 +1403638171645096960.0000000000 7.1736310601 11.4774316844 3.8123323235 0.5500936346 0.6754515560 -0.4129390230 0.265788547415 +1403638171695097088.0000000000 7.2163941083 11.4365961527 3.8075507456 0.5505756492 0.6718948385 -0.4174782080 0.266712816256 +1403638171745096960.0000000000 7.2585616433 11.3927845949 3.8021641041 0.5504641533 0.6683193240 -0.4220154800 0.268777662304 +1403638171795097088.0000000000 7.2995975885 11.3456923281 3.7969965499 0.5498485575 0.6654345148 -0.4263893304 0.270288011762 +1403638171845096960.0000000000 7.3396201967 11.2953517243 3.7935171172 0.5510999837 0.6612674581 -0.4303409775 0.271699834341 +1403638171895097088.0000000000 7.3787758203 11.2413747077 3.7912203910 0.5523663344 0.6571842120 -0.4340955496 0.273059330621 +1403638171945096960.0000000000 7.4169851883 11.1833827720 3.7905856891 0.5534690102 0.6536205504 -0.4351405761 0.277677708443 +1403638171995097088.0000000000 7.4540251082 11.1216222668 3.7910202405 0.5519446344 0.6524728761 -0.4359505204 0.282105317772 +1403638172045096960.0000000000 7.4897031174 11.0563990653 3.7931071824 0.5510688058 0.6510233862 -0.4368860487 0.285696171453 +1403638172095097088.0000000000 7.5235056582 10.9875846737 3.7959249445 0.5490228270 0.6509520968 -0.4371790789 0.289326383306 +1403638172145096960.0000000000 7.5557774060 10.9159295929 3.7986664716 0.5479371420 0.6505842367 -0.4376743824 0.291455269929 +1403638172195097088.0000000000 7.5864284413 10.8415986977 3.7995670169 0.5463895237 0.6508344608 -0.4387361420 0.292204706919 +1403638172245096960.0000000000 7.6154779449 10.7648204449 3.7978539378 0.5450088773 0.6512081076 -0.4387901658 0.293864789752 +1403638172295097088.0000000000 7.6448276521 10.6867945733 3.7989727252 0.5438039262 0.6517743481 -0.4386803649 0.295003434643 +1403638172345096960.0000000000 7.6712473765 10.6058445981 3.7939966118 0.5434723002 0.6517654695 -0.4383876396 0.29606740632 +1403638172395097088.0000000000 7.6963750736 10.5230034593 3.7866103309 0.5436499143 0.6517469328 -0.4381868982 0.296079294318 +1403638172445096960.0000000000 7.7210088250 10.4384839734 3.7768651537 0.5448125252 0.6510556365 -0.4375904679 0.296345158457 +1403638172495097088.0000000000 7.7444013650 10.3521657272 3.7646059038 0.5468462547 0.6498118089 -0.4373854850 0.295631061049 +1403638172545096960.0000000000 7.7668977321 10.2640150362 3.7502648096 0.5487241155 0.6487839067 -0.4370357045 0.294925550788 +1403638172595097088.0000000000 7.7881267048 10.1733005735 3.7338612882 0.5503615634 0.6481777676 -0.4361191240 0.294563814434 +1403638172645096960.0000000000 7.8072371189 10.0797623151 3.7154755929 0.5524840129 0.6473326015 -0.4363179108 0.292144825699 +1403638172695097088.0000000000 7.8248871077 9.9833801250 3.6951538767 0.5529171634 0.6478591339 -0.4358823177 0.290805361359 +1403638172745096960.0000000000 7.8411037210 9.8842216747 3.6738320937 0.5533930049 0.6483747242 -0.4354416455 0.289407968947 +1403638172795097088.0000000000 7.8560837921 9.7821429672 3.6513973438 0.5539318846 0.6488323653 -0.4346499728 0.288540170711 +1403638172845096960.0000000000 7.8696675219 9.6774364305 3.6283010790 0.5558726688 0.6483250290 -0.4350069434 0.285393048584 +1403638172895097088.0000000000 7.8820490705 9.5695485407 3.6037821845 0.5558461710 0.6492838805 -0.4339091887 0.284935593833 +1403638172945096960.0000000000 7.8927906288 9.4590386956 3.5784591140 0.5559595804 0.6505007566 -0.4348496861 0.280470071557 +1403638172995097088.0000000000 7.9025196751 9.3455512222 3.5521697472 0.5559440079 0.6516081733 -0.4356481880 0.276665329948 +1403638173045096960.0000000000 7.9112525354 9.2291754960 3.5239581740 0.5541447821 0.6542585389 -0.4360936126 0.273297796871 +1403638173095097088.0000000000 7.9193050347 9.1103319160 3.4942922713 0.5531163196 0.6562975466 -0.4377240213 0.267831194057 +1403638173145096960.0000000000 7.9276202011 8.9887301510 3.4626525233 0.5504897204 0.6592431026 -0.4378061225 0.265867257455 +1403638173195097088.0000000000 7.9358751729 8.8644388472 3.4289771268 0.5481315791 0.6618864508 -0.4374739501 0.264716152011 +1403638173245096960.0000000000 7.9440679127 8.7372474622 3.3936705765 0.5453126318 0.6649294430 -0.4351846620 0.26667823208 +1403638173295097088.0000000000 7.9524244080 8.6078627554 3.3572881452 0.5425348149 0.6675903316 -0.4332197316 0.268886198827 +1403638173345096960.0000000000 7.9608022954 8.4765891747 3.3188814349 0.5383504206 0.6713875239 -0.4310698463 0.271286573402 +1403638173395097088.0000000000 7.9697865101 8.3436613098 3.2791484976 0.5349647575 0.6740677051 -0.4263987114 0.278620846636 +1403638173445096960.0000000000 7.9783710749 8.2094931749 3.2359586623 0.5302886939 0.6776669671 -0.4222673774 0.285046741419 +1403638173495097088.0000000000 7.9869095182 8.0749739890 3.1897346630 0.5253289325 0.6814313927 -0.4194342597 0.289405721403 +1403638173545096960.0000000000 7.9958428509 7.9405724325 3.1428876101 0.5226916278 0.6831909668 -0.4166504812 0.294016906894 +1403638173595097088.0000000000 8.0049678319 7.8064608737 3.0955749778 0.5202180919 0.6847876715 -0.4145928152 0.29757651024 +1403638173645096960.0000000000 8.0135522858 7.6729676637 3.0482182699 0.5198894997 0.6848719862 -0.4148247022 0.297633561941 +1403638173695097088.0000000000 8.0209017239 7.5393183593 2.9993074038 0.5190533640 0.6851615297 -0.4143553521 0.299076789054 +1403638173745096960.0000000000 8.0274712426 7.4057721852 2.9495772887 0.5188360390 0.6852455753 -0.4150719756 0.29826652736 +1403638173795097088.0000000000 8.0340593124 7.2725764417 2.8998146028 0.5182477879 0.6852666863 -0.4159284836 0.298047471841 +1403638173845096960.0000000000 8.0394575009 7.1396164404 2.8506731004 0.5174810565 0.6854498692 -0.4171102503 0.297306024334 +1403638173895097088.0000000000 8.0438628637 7.0067239169 2.8032281787 0.5158665375 0.6864887942 -0.4166502339 0.298357895043 +1403638173945096960.0000000000 7.9504041005 6.7864928155 2.7562821639 0.5171691397 0.6852797768 -0.4168257363 0.298636926886 +1403638173995097088.0000000000 7.9480387683 6.6503889349 2.7124274319 0.5170432981 0.6852418750 -0.4173614590 0.298193247892 +1403638174045096960.0000000000 7.9437373150 6.5139344674 2.6695461635 0.5151043312 0.6865087999 -0.4178708681 0.297921354126 +1403638174095097088.0000000000 7.9382446351 6.3776141093 2.6290842465 0.5164431972 0.6855089637 -0.4183426927 0.297242790129 +1403638174145096960.0000000000 7.9319838052 6.2408428314 2.5885156879 0.5143544911 0.6869332976 -0.4175466260 0.298692010887 +1403638174195097088.0000000000 7.9254414878 6.1055623506 2.5482152680 0.5119137177 0.6886868795 -0.4189624914 0.296858819017 +1403638174245096960.0000000000 7.9179451572 5.9698350142 2.5066508053 0.5086032900 0.6912810946 -0.4187872434 0.296766552161 +1403638174295097088.0000000000 7.9095518292 5.8347699040 2.4632154746 0.5050942417 0.6940835979 -0.4210366813 0.293011738828 +1403638174345096960.0000000000 7.9020625260 5.7006344414 2.4187699199 0.5025450880 0.6960639603 -0.4206135738 0.293304652674 +1403638174395097088.0000000000 7.8948063352 5.5674500200 2.3731588767 0.5008054879 0.6974521813 -0.4222357471 0.290639453398 +1403638174445096960.0000000000 7.8874633799 5.4347962483 2.3265845406 0.4980578316 0.6997127337 -0.4216344733 0.290800374244 +1403638174495097088.0000000000 7.8803617887 5.3035099328 2.2817374458 0.4973444670 0.7005710595 -0.4227446955 0.288332436964 +1403638174545096960.0000000000 7.8740943770 5.1732448357 2.2375534191 0.4955578728 0.7019954289 -0.4235846904 0.286706858374 +1403638174595097088.0000000000 7.8690164303 5.0437826881 2.1944419832 0.4920258072 0.7047954454 -0.4219799582 0.288282673851 +1403638174645096960.0000000000 7.8641154465 4.9152170348 2.1530619033 0.4886350832 0.7071693392 -0.4225262531 0.287434943312 +1403638174695097088.0000000000 7.8596786467 4.7873258563 2.1126421051 0.4853971053 0.7096166239 -0.4218876585 0.287827553853 +1403638174745096960.0000000000 7.8560210503 4.6608552182 2.0741942492 0.4820170898 0.7119535286 -0.4224426355 0.286921449218 +1403638174795097088.0000000000 7.8526727023 4.5356226554 2.0382550164 0.4796153818 0.7136949100 -0.4227805865 0.286121017605 +1403638174845096960.0000000000 7.8501187781 4.4121020839 2.0038517011 0.4774794180 0.7152275895 -0.4227851057 0.28585950226 +1403638174895097088.0000000000 7.8485892225 4.2904766817 1.9707104419 0.4761842640 0.7161238768 -0.4219625260 0.286989139919 +1403638174945096960.0000000000 7.8473590509 4.1708607559 1.9389868322 0.4749246827 0.7167596857 -0.4226172206 0.286525362779 +1403638174995097088.0000000000 7.8465649161 4.0526874196 1.9089600470 0.4740809036 0.7171116405 -0.4229489177 0.286552621508 +1403638175045096960.0000000000 7.8474487284 3.9367973492 1.8807273015 0.4751493018 0.7162842246 -0.4217782354 0.28857091124 +1403638175095097088.0000000000 7.8492484926 3.8229486261 1.8536220533 0.4752278513 0.7158019465 -0.4227619452 0.288198543287 +1403638175145096960.0000000000 7.8522528965 3.7107169302 1.8283374101 0.4746212404 0.7156055121 -0.4221068834 0.290635868873 +1403638175195097088.0000000000 7.8561150305 3.6006107336 1.8045927851 0.4740240034 0.7156316166 -0.4224290457 0.29107788452 +1403638175245096960.0000000000 7.8611204017 3.4923243182 1.7821190221 0.4727430096 0.7160556436 -0.4221957353 0.29245362571 +1403638175295097088.0000000000 7.8669943594 3.3860706488 1.7615693534 0.4699716808 0.7174151120 -0.4233757912 0.291882023696 +1403638175345096960.0000000000 7.8729773132 3.2814018155 1.7429548081 0.4660997471 0.7195656627 -0.4247322718 0.290824311389 +1403638175395097088.0000000000 7.8799115932 3.1785838407 1.7257361604 0.4611977129 0.7224559611 -0.4251341191 0.290886635267 +1403638175445096960.0000000000 7.8882319828 3.0781954168 1.7100519818 0.4563475273 0.7253814376 -0.4253040482 0.291007166307 +1403638175495097088.0000000000 7.8989012003 2.9810995193 1.6966606026 0.4507061828 0.7288192079 -0.4256941746 0.290638897509 +1403638175545096960.0000000000 7.9113984570 2.8870616578 1.6861177378 0.4442253029 0.7329562123 -0.4256863518 0.290224397661 +1403638175595097088.0000000000 7.9249035068 2.7961078465 1.6778520762 0.4392569214 0.7360524766 -0.4278980618 0.286676398274 +1403638175645096960.0000000000 7.9405768348 2.7084019732 1.6712481040 0.4337406531 0.7393950361 -0.4297091167 0.283750068599 +1403638175695097088.0000000000 7.9582785326 2.6239578207 1.6661427915 0.4291031456 0.7425339009 -0.4310695579 0.280522606575 +1403638175745096960.0000000000 7.9785870699 2.5429493007 1.6626133729 0.4266838066 0.7441436779 -0.4322997572 0.278043226213 +1403638175795097088.0000000000 8.0017933026 2.4652336246 1.6579068254 0.4233062579 0.7463658370 -0.4326198374 0.276748849426 +1403638175845096960.0000000000 8.0277041315 2.3905671267 1.6503395587 0.4209798505 0.7480294311 -0.4323211586 0.276272241679 +1403638175895097088.0000000000 8.0565492087 2.3188761620 1.6393699659 0.4196814844 0.7491363809 -0.4308279824 0.277577708234 +1403638175945096960.0000000000 8.0884865992 2.2507959496 1.6263548680 0.4190056458 0.7500035761 -0.4284627782 0.279908114115 +1403638175995097088.0000000000 8.1233462140 2.1862590704 1.6119462725 0.4193052278 0.7504456831 -0.4238118227 0.285303245052 +1403638176045096960.0000000000 8.1610615384 2.1261226575 1.5976029624 0.4242381311 0.7479372575 -0.4201801162 0.289931952217 +1403638176095097088.0000000000 8.2014369533 2.0698452744 1.5829751565 0.4300490767 0.7449023698 -0.4140185075 0.29793778963 +1403638176145096960.0000000000 8.2437982517 2.0180989483 1.5700242533 0.4398837033 0.7391404369 -0.4090226314 0.304752734403 +1403638176195097088.0000000000 8.2872281141 1.9702788164 1.5590938484 0.4524928629 0.7312081311 -0.4062971448 0.309042890564 +1403638176245096960.0000000000 8.3306357441 1.9255789012 1.5495806730 0.4634631314 0.7240660326 -0.4058440741 0.310194928667 +1403638176295097088.0000000000 8.3741135950 1.8828603242 1.5410729388 0.4711100591 0.7188347740 -0.4034364307 0.313960071155 +1403638176345096960.0000000000 8.4163075447 1.8419790232 1.5332088737 0.4756957949 0.7156721418 -0.4026529395 0.315273700838 +1403638176395097088.0000000000 8.4579867764 1.8028394458 1.5262643443 0.4784068552 0.7134713408 -0.4019687314 0.317027862597 +1403638176445096960.0000000000 8.4988888379 1.7656261951 1.5201618874 0.4778830770 0.7136292136 -0.4015027833 0.318051293357 +1403638176495097088.0000000000 8.5389595527 1.7303167910 1.5160567096 0.4779765324 0.7133407727 -0.4012499491 0.318875923873 +1403638176545096960.0000000000 8.5778026290 1.6968178575 1.5129601933 0.4770316825 0.7136646741 -0.4016289523 0.319088845835 +1403638176595097088.0000000000 8.6154689723 1.6651901924 1.5105694015 0.4757367279 0.7144444788 -0.4021179444 0.318660965941 +1403638176645096960.0000000000 8.6526340248 1.6357000671 1.5098031255 0.4744967386 0.7150023532 -0.4021736252 0.319187805419 +1403638176695097088.0000000000 8.6893103332 1.6084271255 1.5116007193 0.4741426516 0.7151088446 -0.4023761402 0.319220187579 +1403638176745096960.0000000000 8.7252583112 1.5833158941 1.5154380133 0.4739867300 0.7152054807 -0.4024832227 0.319100228182 +1403638176795097088.0000000000 8.7599667821 1.5601910638 1.5212380804 0.4742010149 0.7150734243 -0.4035044361 0.317785407766 +1403638176845096960.0000000000 8.7924149629 1.5386171183 1.5288035035 0.4756638913 0.7141429383 -0.4051504638 0.315589650978 +1403638176895097088.0000000000 8.8234819803 1.5184998211 1.5368697271 0.4758109295 0.7140319547 -0.4069751923 0.313262701125 +1403638176945096960.0000000000 8.8542102758 1.4997916926 1.5443964531 0.4758568199 0.7139394800 -0.4071452921 0.313182721392 +1403638176995097088.0000000000 8.8815784714 1.4816203628 1.5511490917 0.4748413144 0.7145969339 -0.4066978896 0.313805313381 +1403638177045096960.0000000000 8.9095625609 1.4650534267 1.5561896363 0.4733519378 0.7155664736 -0.4064683264 0.314143382018 +1403638177095097088.0000000000 8.9367885130 1.4498650043 1.5597684448 0.4721082817 0.7162659652 -0.4055667702 0.315582686939 +1403638177145096960.0000000000 8.9638101243 1.4363521315 1.5614624009 0.4711478788 0.7166393790 -0.4049166096 0.31700191808 +1403638177195097088.0000000000 8.9904173385 1.4244949448 1.5609807062 0.4700624259 0.7173015052 -0.4040027616 0.318279177875 +1403638177245096960.0000000000 9.0164409490 1.4142668566 1.5589208366 0.4696549078 0.7174367691 -0.4035081989 0.319201947645 +1403638177295097088.0000000000 9.0421691727 1.4059001931 1.5553406482 0.4693365496 0.7175930917 -0.4032968446 0.319585689803 +1403638177345096960.0000000000 9.0673883737 1.3993966845 1.5505067658 0.4693457528 0.7175101500 -0.4029977146 0.320135269853 +1403638177395097088.0000000000 9.0918759771 1.3945990070 1.5443618014 0.4692202507 0.7174660959 -0.4032069322 0.320154536794 +1403638177445096960.0000000000 9.1160917054 1.3916832795 1.5366888501 0.4686128621 0.7175667570 -0.4043194715 0.319414620418 +1403638177495097088.0000000000 9.1392025512 1.3909819953 1.5287241047 0.4705473105 0.7160978948 -0.4069037498 0.316572854285 +1403638177545096960.0000000000 9.1616588381 1.3920346765 1.5200479903 0.4735531055 0.7138990861 -0.4107113355 0.312108555011 +1403638177595097088.0000000000 9.1834783151 1.3944912575 1.5103914868 0.4774214400 0.7112179367 -0.4159821224 0.305281327741 +1403638177645096960.0000000000 9.2053867995 1.3974031848 1.4993519623 0.4797482447 0.7093401384 -0.4189165224 0.30197207989 +1403638177695097088.0000000000 9.2273762133 1.4010062557 1.4871348109 0.4822529324 0.7070266495 -0.4232047538 0.297393951481 +1403638177745096960.0000000000 9.2498601884 1.4048135194 1.4739775401 0.4852113981 0.7039234890 -0.4271213014 0.294328073291 +1403638177795097088.0000000000 9.2728934515 1.4087760794 1.4602272940 0.4896123000 0.6996644362 -0.4303172880 0.292534620291 +1403638177845096960.0000000000 9.2964686294 1.4126141178 1.4460483246 0.4950790138 0.6948200056 -0.4321510843 0.292176950253 +1403638177895097088.0000000000 9.3203393323 1.4157350873 1.4320355498 0.5001100714 0.6902733330 -0.4330645076 0.29303203658 +1403638177945096960.0000000000 9.3438653641 1.4175974059 1.4188491311 0.5037871427 0.6867215255 -0.4334622446 0.294486916231 +1403638177995097088.0000000000 9.3673428980 1.4182382588 1.4073045188 0.5064959156 0.6839375350 -0.4333058870 0.296542313899 +1403638178045096960.0000000000 9.3908439088 1.4170984636 1.3972872590 0.5074100966 0.6819117594 -0.4324874287 0.300808859915 +1403638178095097088.0000000000 9.4144599536 1.4144801171 1.3888460099 0.5063570355 0.6801839135 -0.4329988789 0.305719425729 +1403638178145096960.0000000000 9.4383047879 1.4109584953 1.3831195614 0.5048208596 0.6778592266 -0.4351911775 0.310276340678 +1403638178195097088.0000000000 9.4610811577 1.4056681836 1.3786773280 0.5038566381 0.6741709780 -0.4390309105 0.314442109512 +1403638178245096960.0000000000 9.4833987467 1.3991027235 1.3768860941 0.5032308451 0.6692047251 -0.4441175456 0.318878281062 +1403638178295097088.0000000000 9.5051895287 1.3911089495 1.3778830666 0.5010830216 0.6644248522 -0.4502452709 0.323627281412 +1403638178345096960.0000000000 9.5261885694 1.3818278469 1.3815382066 0.4993068605 0.6586678794 -0.4572027043 0.32835190098 +1403638178395097088.0000000000 9.5455871848 1.3708105143 1.3856535211 0.4958605125 0.6531689318 -0.4646778976 0.334016691435 +1403638178445096960.0000000000 9.5635105933 1.3585365091 1.3892204790 0.4918251256 0.6473067387 -0.4744209828 0.337678490479 +1403638178495097088.0000000000 9.5804296240 1.3448669524 1.3911976998 0.4857619252 0.6423360506 -0.4843800214 0.34178318425 +1403638178545096960.0000000000 9.5962732651 1.3297220039 1.3920841670 0.4790020467 0.6374190476 -0.4953757520 0.344756234796 +1403638178595097088.0000000000 9.6111219321 1.3133433696 1.3915946669 0.4720211081 0.6325221555 -0.5065699091 0.347129260678 +1403638178645096960.0000000000 9.6256966235 1.2958410760 1.3904535089 0.4664426708 0.6266870707 -0.5170305054 0.349819963299 +1403638178695097088.0000000000 9.6400192615 1.2770147477 1.3885467443 0.4609819631 0.6205870379 -0.5266211647 0.353606429617 +1403638178745096960.0000000000 9.6542075086 1.2568249656 1.3859990349 0.4565961826 0.6137862700 -0.5353445402 0.358039891882 +1403638178795097088.0000000000 9.6679937746 1.2353394131 1.3822118977 0.4510984891 0.6078905018 -0.5433361511 0.362994652736 +1403638178845096960.0000000000 9.6815572823 1.2125424744 1.3771798832 0.4443701631 0.6034497991 -0.5511099961 0.36696221914 +1403638178895097088.0000000000 9.6947618832 1.1888886708 1.3713191260 0.4381528745 0.6000136681 -0.5578526635 0.369873035704 +1403638178945096960.0000000000 9.7076332652 1.1642927957 1.3644036403 0.4320025632 0.5975712395 -0.5638411933 0.37197514401 +1403638178995097088.0000000000 9.7202824922 1.1390481738 1.3563204525 0.4256768999 0.5964417797 -0.5693217812 0.372731927553 +1403638179045096960.0000000000 9.7332206030 1.1128272819 1.3470833088 0.4191975000 0.5962726559 -0.5734204730 0.374060605946 +1403638179095097088.0000000000 9.7468785811 1.0858454773 1.3369614514 0.4136283149 0.5963210616 -0.5763061659 0.3757446097 +1403638179145096960.0000000000 9.7611854158 1.0579808398 1.3256437632 0.4080794497 0.5960066347 -0.5792871187 0.377721707246 +1403638179195097088.0000000000 9.7764288587 1.0293618543 1.3134662473 0.4025572877 0.5954665365 -0.5817964824 0.380631169355 +1403638179245096960.0000000000 9.7927781765 1.0003368598 1.3003520209 0.3966786148 0.5951094737 -0.5842139263 0.383646815704 +1403638179295097088.0000000000 9.8104573871 0.9711536390 1.2862338098 0.3909390549 0.5939634222 -0.5877184518 0.385954828887 +1403638179345096960.0000000000 9.8296407768 0.9415859793 1.2717721094 0.3857498067 0.5915741763 -0.5911148659 0.389641240062 +1403638179395097088.0000000000 9.8505457574 0.9120268194 1.2576138806 0.3831983746 0.5863023851 -0.5948609634 0.394396948606 +1403638179445096960.0000000000 9.8729685643 0.8825795953 1.2436305952 0.3838659955 0.5778838867 -0.5990279845 0.399828194215 +1403638179495097088.0000000000 9.8964920205 0.8529075666 1.2290927992 0.3851650817 0.5681867565 -0.6030669964 0.406351901061 +1403638179545096960.0000000000 9.9208935745 0.8226938471 1.2136911685 0.3849599048 0.5584810022 -0.6079268434 0.41271030386 +1403638179595097088.0000000000 9.9456765558 0.7919764602 1.1975804273 0.3829647953 0.5494402189 -0.6131211646 0.418969985704 +1403638179645096960.0000000000 9.9701930526 0.7608387501 1.1817819702 0.3802211963 0.5405887154 -0.6193348224 0.423816069149 +1403638179695097088.0000000000 9.9945177334 0.7291421661 1.1674065507 0.3767334511 0.5317922394 -0.6246993528 0.430139093174 +1403638179745096960.0000000000 10.0184571737 0.6971038154 1.1546466488 0.3718541905 0.5233860608 -0.6310079885 0.435454257959 +1403638179795097088.0000000000 10.0419920925 0.6647511334 1.1437765055 0.3667899629 0.5152676004 -0.6371739404 0.440424559765 +1403638179845096960.0000000000 10.0650864769 0.6319377653 1.1350887735 0.3617059405 0.5068392375 -0.6427681528 0.446241976619 +1403638179895097088.0000000000 10.0882535070 0.5988813613 1.1274762387 0.3556344665 0.4995045142 -0.6495611304 0.44954388488 +1403638179945096960.0000000000 10.1111613127 0.5657081232 1.1207625570 0.3492296784 0.4938539852 -0.6561364885 0.451255782766 +1403638179995097088.0000000000 10.1339052648 0.5324805803 1.1151812599 0.3424842617 0.4896190919 -0.6627303392 0.451404666334 +1403638180045096960.0000000000 10.1568360602 0.4993027314 1.1107461312 0.3369732987 0.4859875797 -0.6689189589 0.450347082479 +1403638180095097088.0000000000 10.1803328320 0.4657297975 1.1075947161 0.3337295589 0.4816056970 -0.6735209580 0.450610755737 +1403638180145096960.0000000000 10.2040893800 0.4318939043 1.1051429483 0.3311204681 0.4780672392 -0.6770567084 0.451004616465 +1403638180195097088.0000000000 10.2281740940 0.3975186540 1.1030728410 0.3285417966 0.4757678669 -0.6785549977 0.453065491774 +1403638180245096960.0000000000 10.2522005358 0.3627181021 1.1001202340 0.3266266447 0.4738534955 -0.6802052910 0.453980904727 +1403638180295097088.0000000000 10.2763458631 0.3274523390 1.0958480059 0.3248494366 0.4727305698 -0.6820858593 0.453605040232 +1403638180345096960.0000000000 10.3011029460 0.2918168506 1.0904766509 0.3242982173 0.4715656155 -0.6835406497 0.453021761897 +1403638180395097088.0000000000 10.3261000133 0.2554108763 1.0833905505 0.3223873180 0.4717684576 -0.6837397521 0.453873210347 +1403638180445096960.0000000000 10.3514589327 0.2185876119 1.0746460807 0.3201222157 0.4729555463 -0.6838019278 0.454147268749 +1403638180495097088.0000000000 10.3774999170 0.1812470955 1.0651699320 0.3190580923 0.4735126253 -0.6826691107 0.456016022396 +1403638180545096960.0000000000 10.4039417012 0.1434453422 1.0547220525 0.3176778089 0.4748808926 -0.6813735905 0.457492052178 +1403638180595097088.0000000000 10.4307995744 0.1054743418 1.0439525373 0.3166226727 0.4760658122 -0.6807788644 0.457877236017 +1403638180645096960.0000000000 10.4581116434 0.0673169732 1.0337861513 0.3143039635 0.4784801344 -0.6802616557 0.457726839183 +1403638180695097088.0000000000 10.4863655446 0.0293251859 1.0254645961 0.3131129386 0.4803518714 -0.6803533839 0.456444564338 +1403638180745096960.0000000000 10.5152517095 -0.0087633649 1.0186621164 0.3106473312 0.4833800683 -0.6810889434 0.45382793694 +1403638180795097088.0000000000 10.5457839909 -0.0469060392 1.0141386483 0.3106947722 0.4847661383 -0.6816724138 0.451434679541 +1403638180845096960.0000000000 10.5777774492 -0.0852093848 1.0118478223 0.3108597660 0.4862482172 -0.6816691496 0.44972886016 +1403638180895097088.0000000000 10.6114217009 -0.1236135037 1.0112975044 0.3124670594 0.4868787674 -0.6813260513 0.44845090531 +1403638180945096960.0000000000 10.6462974596 -0.1623045738 1.0107328840 0.3141055325 0.4873533841 -0.6807451155 0.447672292155 +1403638180995097088.0000000000 10.6823056334 -0.2012771283 1.0094297488 0.3167277017 0.4869262815 -0.6801666912 0.447168459904 +1403638181045096960.0000000000 10.7195013414 -0.2404993816 1.0067934200 0.3195672649 0.4866118737 -0.6791902968 0.446974482788 +1403638181095097088.0000000000 10.7577964700 -0.2800210290 1.0026412219 0.3213301561 0.4868089182 -0.6786634094 0.446295848837 +1403638181145096960.0000000000 10.7972699299 -0.3199576273 0.9972665084 0.3241519623 0.4857638772 -0.6788157211 0.445160844828 +1403638181195097088.0000000000 10.8378731970 -0.3605740991 0.9909798819 0.3273879789 0.4846815049 -0.6773162165 0.446255188198 +1403638181245096960.0000000000 10.8794923128 -0.4018474515 0.9838968876 0.3316871587 0.4818324436 -0.6762845568 0.447727956709 +1403638181295097088.0000000000 10.9216670427 -0.4440828831 0.9760873364 0.3366232793 0.4765222081 -0.6760846010 0.450023294164 +1403638181345096960.0000000000 10.9644682461 -0.4875876308 0.9668770045 0.3391230499 0.4708299667 -0.6768275829 0.45301117268 +1403638181395097088.0000000000 11.0071376077 -0.5322234629 0.9564428276 0.3412887882 0.4635014850 -0.6790816527 0.455561681258 +1403638181445096960.0000000000 11.0491859203 -0.5780261758 0.9447155188 0.3425165334 0.4549288523 -0.6829948724 0.457427773453 +1403638181495097088.0000000000 11.0908930952 -0.6255211377 0.9322610293 0.3431221659 0.4448696736 -0.6862785353 0.461930649265 +1403638181545096960.0000000000 11.1320182838 -0.6745009097 0.9198972718 0.3455267268 0.4321102443 -0.6885461968 0.46882422361 +1403638181595097088.0000000000 11.1710542326 -0.7250587904 0.9070570998 0.3443271105 0.4208949443 -0.6900440735 0.477624814566 +1403638181645096960.0000000000 11.2077600402 -0.7770092213 0.8944601691 0.3393559932 0.4120217700 -0.6931246921 0.484410706097 +1403638181695097088.0000000000 11.2419118357 -0.8300191975 0.8825060467 0.3304264372 0.4058070403 -0.6969926971 0.490245036491 +1403638181745096960.0000000000 11.2739707388 -0.8838142058 0.8728362124 0.3212738837 0.3997817681 -0.7019136105 0.494241755553 +1403638181795097088.0000000000 11.3039740843 -0.9383810728 0.8656356447 0.3108066200 0.3940986386 -0.7064232174 0.499050844956 +1403638181845096960.0000000000 11.3320053283 -0.9933655506 0.8605364110 0.2994982776 0.3892777081 -0.7115286944 0.50248439248 +1403638181895097088.0000000000 11.3581354448 -1.0483811467 0.8579256160 0.2875480754 0.3850915631 -0.7163959912 0.505764150743 +1403638181945096960.0000000000 11.3830582756 -1.1030180883 0.8570062962 0.2786936566 0.3796245703 -0.7219829551 0.506907924565 +1403638181995097088.0000000000 11.4069343300 -1.1571429968 0.8579489980 0.2712224732 0.3752080304 -0.7270566181 0.506997019664 +1403638182045096960.0000000000 11.4300765853 -1.2109606950 0.8605170169 0.2649038340 0.3714627932 -0.7327436762 0.504904007652 +1403638182095097088.0000000000 11.4528326279 -1.2648620595 0.8652677350 0.2598534520 0.3678246146 -0.7371428761 0.503787273208 +1403638182145096960.0000000000 11.4753798146 -1.3188836566 0.8713047193 0.2552886808 0.3648980874 -0.7411217485 0.502409821931 +1403638182195097088.0000000000 11.4980353728 -1.3732019362 0.8772291375 0.2520492583 0.3620739380 -0.7443578859 0.501303273983 +1403638182245096960.0000000000 11.5209218671 -1.4275173769 0.8821844537 0.2512741564 0.3584886557 -0.7484394209 0.498182311316 +1403638182295097088.0000000000 11.5439496372 -1.4822410763 0.8859732006 0.2511933191 0.3556158418 -0.7517628152 0.49526958234 +1403638182345096960.0000000000 11.5655093236 -1.5383838440 0.8927419885 0.2519398637 0.3530230892 -0.7540469219 0.493268936013 +1403638182395097088.0000000000 11.5885669410 -1.5949929828 0.8959444995 0.2520274080 0.3518677481 -0.7565497769 0.490207821709 +1403638182445096960.0000000000 11.6117006810 -1.6534304638 0.9001377731 0.2484526839 0.3536810492 -0.7566751788 0.490534048943 +1403638182495097088.0000000000 11.6350233661 -1.7129410978 0.9058402466 0.2444097032 0.3567350265 -0.7566613160 0.490375030691 +1403638182545096960.0000000000 11.6590664815 -1.7737709283 0.9136664674 0.2391033433 0.3609422552 -0.7555036028 0.491695623113 +1403638182595097088.0000000000 11.6840255742 -1.8355626966 0.9236378283 0.2344844482 0.3650474623 -0.7541379014 0.492984198019 +1403638182645096960.0000000000 11.7102219657 -1.8978611698 0.9360973076 0.2324487611 0.3677042051 -0.7534794218 0.492980681076 +1403638182695097088.0000000000 11.7371463882 -1.9604827852 0.9504652889 0.2316272815 0.3699178986 -0.7526398662 0.492993694285 +1403638182745096960.0000000000 11.7652885183 -2.0234022942 0.9656567882 0.2329692032 0.3705632986 -0.7521721905 0.492590283945 +1403638182795097088.0000000000 11.7944526639 -2.0868956107 0.9805488097 0.2340197598 0.3712433223 -0.7512599823 0.492972196682 +1403638182845096960.0000000000 11.8249529640 -2.1506913098 0.9944691712 0.2355388512 0.3716488770 -0.7501957662 0.493563444936 +1403638182895097088.0000000000 11.8565359596 -2.2148091563 1.0071041825 0.2379143022 0.3714038765 -0.7485890048 0.495045904137 +1403638182945096960.0000000000 11.8889544615 -2.2793113419 1.0182641973 0.2406140384 0.3708288077 -0.7468402418 0.496810359256 +1403638182995097088.0000000000 11.9216927440 -2.3442163697 1.0284469896 0.2434956699 0.3700617791 -0.7439094276 0.500362770386 +1403638183045096960.0000000000 11.9547541822 -2.4093296526 1.0373532385 0.2462430586 0.3694173869 -0.7411952018 0.503512485657 +1403638183095097088.0000000000 11.9879032815 -2.4746477111 1.0448411337 0.2471905977 0.3699862890 -0.7380907599 0.507177468434 +1403638183145096960.0000000000 12.0213133561 -2.5399843941 1.0507581685 0.2463037440 0.3714058981 -0.7351621000 0.51081191373 +1403638183195097088.0000000000 12.0549129505 -2.6049273453 1.0554377926 0.2463987364 0.3721764459 -0.7336277709 0.512408674373 +1403638183245096960.0000000000 12.0884687353 -2.6693362701 1.0583359166 0.2434230145 0.3751507629 -0.7334325661 0.511941219392 +1403638183295097088.0000000000 12.1219767095 -2.7329948245 1.0599238180 0.2412197153 0.3770516085 -0.7345046458 0.510047114251 +1403638183345096960.0000000000 12.1557456071 -2.7957564894 1.0603664460 0.2395743750 0.3785716934 -0.7370419522 0.506020505956 +1403638183395097088.0000000000 12.1901185434 -2.8581093541 1.0598694470 0.2377819458 0.3800737626 -0.7395089899 0.502125616805 +1403638183445096960.0000000000 12.2253292713 -2.9204429050 1.0583081322 0.2348691062 0.3822394463 -0.7415646751 0.498809925065 +1403638183495097088.0000000000 12.2616857529 -2.9827395239 1.0560685633 0.2321923180 0.3840228958 -0.7428515529 0.496774308198 +1403638183545096960.0000000000 12.2992566808 -3.0448502134 1.0525803059 0.2295928912 0.3861235533 -0.7435548253 0.495299836103 +1403638183595097088.0000000000 12.3383602744 -3.1068070354 1.0487121370 0.2293830239 0.3861390780 -0.7442720568 0.494306732938 +1403638183645096960.0000000000 12.3792088291 -3.1686778424 1.0454527481 0.2310276466 0.3850593881 -0.7432015578 0.495990865497 +1403638183695097088.0000000000 12.4218635114 -3.2310257080 1.0437319978 0.2312445060 0.3850884113 -0.7395803014 0.501252303488 +1403638183745096960.0000000000 12.4676007308 -3.2932917149 1.0441089635 0.2351480943 0.3824166955 -0.7364455149 0.506073955473 +1403638183795097088.0000000000 12.5128765755 -3.3548094588 1.0453303266 0.2355223574 0.3821117432 -0.7328339975 0.511345447758 +1403638183845096960.0000000000 12.5587494467 -3.4152027787 1.0487338266 0.2372652054 0.3810416377 -0.7287119208 0.517195735863 +1403638183895097088.0000000000 12.6051215124 -3.4744580886 1.0539639678 0.2389017711 0.3795124963 -0.7265138371 0.520647532807 +1403638183945096960.0000000000 12.6507022556 -3.5319794178 1.0605465472 0.2395707917 0.3789131976 -0.7256681292 0.52195439521 +1403638183995097088.0000000000 12.6965532347 -3.5883595914 1.0691318509 0.2391840089 0.3787637334 -0.7260819823 0.521664642365 +1403638184045096960.0000000000 12.7423993142 -3.6430666936 1.0789529795 0.2393781679 0.3784326847 -0.7274314256 0.519932992742 +1403638184095097088.0000000000 12.7885263925 -3.6969460528 1.0898979876 0.2376562707 0.3793226419 -0.7299667022 0.516509868188 +1403638184145096960.0000000000 12.8347298765 -3.7498249835 1.1003217406 0.2349002194 0.3809018249 -0.7326716975 0.512764927041 +1403638184195097088.0000000000 12.8827484774 -3.8019103782 1.1117233382 0.2338756216 0.3810140886 -0.7361706207 0.508117383184 +1403638184245096960.0000000000 12.9306244884 -3.8534323508 1.1202410388 0.2322959564 0.3816932466 -0.7383344281 0.505184249938 +1403638184295097088.0000000000 12.9793677691 -3.9046970409 1.1277945661 0.2318920633 0.3813790556 -0.7393856144 0.504068447839 +1403638184345096960.0000000000 13.0289980482 -3.9557293506 1.1342369665 0.2314280357 0.3813800815 -0.7386095257 0.505416923158 +1403638184395097088.0000000000 13.0799268477 -4.0063059563 1.1402464375 0.2332942616 0.3798616117 -0.7372279534 0.507714376541 +1403638184445096960.0000000000 13.1315739991 -4.0565719780 1.1450260500 0.2339289742 0.3792315626 -0.7357721867 0.509999947234 +1403638184495097088.0000000000 13.1839599298 -4.1063394353 1.1491613823 0.2340022495 0.3789383606 -0.7340019001 0.512727877898 +1403638184545096960.0000000000 13.2368722022 -4.1551546592 1.1531507464 0.2349032783 0.3779932452 -0.7334106746 0.513858286627 +1403638184595097088.0000000000 13.2905433115 -4.2032738565 1.1572869979 0.2352641796 0.3773604375 -0.7327139285 0.515150623605 +1403638184645096960.0000000000 13.3443913716 -4.2503248701 1.1615933947 0.2365758107 0.3763649687 -0.7321459206 0.516084922373 +1403638184695097088.0000000000 13.3984966417 -4.2966147824 1.1653312376 0.2357007302 0.3767377650 -0.7321991063 0.516137860474 +1403638184745096960.0000000000 13.4532409663 -4.3420439342 1.1697182051 0.2371825542 0.3753997047 -0.7326618353 0.5157772124 +1403638184795097088.0000000000 13.5080357510 -4.3867801005 1.1741608497 0.2375572764 0.3752172023 -0.7323903126 0.516123068218 +1403638184845096960.0000000000 13.5628394408 -4.4307328721 1.1783812443 0.2369133837 0.3750178371 -0.7331117216 0.51553940119 +1403638184895097088.0000000000 13.6178476771 -4.4740592345 1.1828162127 0.2356085230 0.3757557623 -0.7323909211 0.516623431213 +1403638184945096960.0000000000 13.6732147734 -4.5167575747 1.1882826758 0.2362286243 0.3751497931 -0.7311153099 0.518583718734 +1403638184995097088.0000000000 13.7284791816 -4.5583049335 1.1940098605 0.2368099494 0.3745205492 -0.7314581597 0.518289848135 +1403638185045096960.0000000000 13.7838934289 -4.5989964559 1.2002675311 0.2376400875 0.3739544321 -0.7318268573 0.51779795525 +1403638185095097088.0000000000 13.8392956504 -4.6392126409 1.2063801670 0.2358749261 0.3750890401 -0.7318689331 0.517724923072 +1403638185145096960.0000000000 13.8951625684 -4.6784441524 1.2127438745 0.2351847323 0.3758606885 -0.7321073323 0.517141893899 +1403638185195097088.0000000000 13.9516497243 -4.7173591305 1.2194485559 0.2342353267 0.3764338520 -0.7315743705 0.517909555087 +1403638185245096960.0000000000 14.0083013496 -4.7556775698 1.2257289482 0.2312934200 0.3787371951 -0.7307291006 0.518745093871 +1403638185295097088.0000000000 14.0653492168 -4.7928446593 1.2321803072 0.2305756816 0.3795548796 -0.7298288800 0.519733349245 +1403638185345096960.0000000000 14.1232254875 -4.8291768101 1.2384579668 0.2288126663 0.3807354288 -0.7288131712 0.521072603897 +1403638185395097088.0000000000 14.1820217897 -4.8642280302 1.2451425605 0.2290002316 0.3823280215 -0.7263096682 0.523314861055 +1403638185445096960.0000000000 14.2413312952 -4.8976711677 1.2520088900 0.2301084588 0.3848572044 -0.7230274864 0.525515255053 +1403638185495097088.0000000000 14.3015081520 -4.9293540093 1.2591440816 0.2321061638 0.3889071835 -0.7186234791 0.527691412266 +1403638185545096960.0000000000 14.3619222518 -4.9592103965 1.2666053409 0.2347384322 0.3938622638 -0.7144280103 0.528548014502 +1403638185595097088.0000000000 14.4229254627 -4.9871777224 1.2743055484 0.2389727238 0.3987993158 -0.7102434028 0.528588168409 +1403638185645096960.0000000000 14.4844704499 -5.0135118410 1.2817447629 0.2419438089 0.4040956378 -0.7061396801 0.528712266847 +1403638185695097088.0000000000 14.5465837737 -5.0377370868 1.2899819967 0.2478442650 0.4068177914 -0.7032349328 0.527762384197 +1403638185745096960.0000000000 14.6086973805 -5.0601199302 1.2986680793 0.2545182882 0.4085038313 -0.7014561354 0.525646602609 +1403638185795097088.0000000000 14.6705826175 -5.0807058647 1.3073749349 0.2620129639 0.4087742768 -0.7025360137 0.520284486463 +1403638185845096960.0000000000 14.7316767295 -5.0993030646 1.3160834378 0.2719660330 0.4064128525 -0.7065394090 0.511532143377 +1403638185895097088.0000000000 14.7920235153 -5.1173281108 1.3236161769 0.2798798540 0.4048360393 -0.7101135146 0.503501583854 +1403638185945096960.0000000000 14.8513187028 -5.1351437060 1.3297429135 0.2868399168 0.4031239359 -0.7139248644 0.495505037825 +1403638185995097088.0000000000 14.9093386809 -5.1537887392 1.3342887774 0.2904031108 0.4030134470 -0.7151408554 0.491751717498 +1403638186045096960.0000000000 14.9662939973 -5.1732904697 1.3367286066 0.2892660181 0.4055455954 -0.7151064769 0.490388282424 +1403638186095097088.0000000000 15.0224684984 -5.1934534130 1.3377693618 0.2866508640 0.4086713617 -0.7146625740 0.489975923573 +1403638186145096960.0000000000 15.0779226350 -5.2142609498 1.3380237592 0.2837920140 0.4113179636 -0.7132861918 0.491428971663 +1403638186195097088.0000000000 15.1326925175 -5.2352060916 1.3375589862 0.2804562207 0.4142760620 -0.7119694515 0.492766834265 +1403638186245096960.0000000000 15.1873832838 -5.2562010635 1.3383729297 0.2790475258 0.4154275689 -0.7115753570 0.493166224167 +1403638186295097088.0000000000 15.2417980171 -5.2772001042 1.3406252142 0.2771439723 0.4170895339 -0.7105355184 0.494334721036 +1403638186345096960.0000000000 15.2970719212 -5.2986604571 1.3451466657 0.2751965345 0.4183759708 -0.7100078891 0.495093134504 +1403638186395097088.0000000000 15.3528208229 -5.3200128304 1.3512624112 0.2742252578 0.4188255134 -0.7100293429 0.495221192485 +1403638186445096960.0000000000 15.4080100791 -5.3408994978 1.3586553005 0.2740967854 0.4188216173 -0.7096608922 0.495823379159 +1403638186495097088.0000000000 15.4636797379 -5.3618918415 1.3675569723 0.2739322815 0.4183334699 -0.7090146995 0.497248799892 +1403638186545096960.0000000000 15.5191944574 -5.3826424860 1.3763427459 0.2717456004 0.4192989770 -0.7088646372 0.497848995847 +1403638186595097088.0000000000 15.5750193795 -5.4030896844 1.3844148056 0.2702274351 0.4197672587 -0.7084901477 0.498812883194 +1403638186645096960.0000000000 15.6310716771 -5.4232545056 1.3909158645 0.2680383632 0.4207847259 -0.7083537488 0.499330168213 +1403638186695097088.0000000000 15.6877280008 -5.4431253704 1.3960775109 0.2652704262 0.4220989179 -0.7071412607 0.501413344359 +1403638186745096960.0000000000 15.7448737134 -5.4621681838 1.3997881784 0.2628484636 0.4246730677 -0.7049835750 0.503549034093 +1403638186795097088.0000000000 15.8024942077 -5.4803446101 1.4022684156 0.2610543733 0.4283161500 -0.7022403083 0.505227116528 +1403638186845096960.0000000000 15.8607025911 -5.4973742737 1.4036338179 0.2603224997 0.4327460309 -0.6989835846 0.506344761252 +1403638186895097088.0000000000 15.9195101078 -5.5128470921 1.4036655680 0.2600862998 0.4384294599 -0.6963063999 0.505264408796 +1403638186945096960.0000000000 15.9790201051 -5.5264591505 1.4034346667 0.2630397137 0.4437379898 -0.6931325189 0.503462030994 +1403638186995097088.0000000000 16.0394032705 -5.5381070080 1.4039090157 0.2673093720 0.4503127506 -0.6895864683 0.500234574075 +1403638187045096960.0000000000 16.1008498700 -5.5474434200 1.4067054800 0.2770847960 0.4552106391 -0.6852623518 0.496409910366 +1403638187095097088.0000000000 16.1629986690 -5.5555297343 1.4115491285 0.2876975743 0.4610974806 -0.6795673580 0.492754934093 +1403638187145096960.0000000000 16.2254683895 -5.5620702275 1.4184121485 0.2996570990 0.4671656117 -0.6722905003 0.489885086045 +1403638187195097088.0000000000 16.2870996298 -5.5670566488 1.4268653250 0.3117424212 0.4736710983 -0.6650476772 0.48596701588 +1403638187245096960.0000000000 16.3481452433 -5.5712187410 1.4372498601 0.3241629282 0.4803476899 -0.6566866285 0.482646003561 +1403638187295097088.0000000000 16.4089026265 -5.5751427759 1.4495420388 0.3349358871 0.4876411730 -0.6473384631 0.48060061595 +1403638187345096960.0000000000 16.4684734452 -5.5783598587 1.4631220348 0.3442867888 0.4946459452 -0.6391264409 0.477817317092 +1403638187395097088.0000000000 16.5268107406 -5.5811625400 1.4784546789 0.3530794724 0.5003171383 -0.6309217188 0.476398396326 +1403638187445096960.0000000000 16.5839663637 -5.5835545969 1.4943669117 0.3596254083 0.5059337996 -0.6236916913 0.475088655235 +1403638187495097088.0000000000 16.6396172609 -5.5854707052 1.5107816451 0.3645150323 0.5109064227 -0.6190100375 0.472154627089 +1403638187545096960.0000000000 16.6911802345 -5.5852595826 1.5296077037 0.3669304155 0.5161651263 -0.6158766295 0.468648706126 +1403638187595097088.0000000000 16.7425062750 -5.5861823559 1.5460729274 0.3675969374 0.5211738920 -0.6148563456 0.46389863142 +1403638187645096960.0000000000 16.7925917474 -5.5868043107 1.5622414773 0.3671416929 0.5256159026 -0.6150409785 0.458976573529 +1403638187695097088.0000000000 16.8418395161 -5.5874110128 1.5777088293 0.3660730136 0.5293535438 -0.6145152188 0.45623066565 +1403638187745096960.0000000000 16.8905013223 -5.5876950185 1.5917430951 0.3644769134 0.5324690438 -0.6136371643 0.45506343249 +1403638187795097088.0000000000 16.9383700637 -5.5875435220 1.6044728306 0.3628445365 0.5350132648 -0.6127285513 0.454607931298 +1403638187845096960.0000000000 16.9857930393 -5.5869740566 1.6161525403 0.3616600694 0.5364052983 -0.6112092256 0.455954638842 +1403638187895097088.0000000000 17.0325625993 -5.5858039357 1.6265203015 0.3585247575 0.5387483276 -0.6089867661 0.458634229497 +1403638187945096960.0000000000 17.0791171806 -5.5833794091 1.6366714397 0.3578916963 0.5389089825 -0.6070136597 0.461546378134 +1403638187995097088.0000000000 17.1251042722 -5.5800561009 1.6460899484 0.3567311406 0.5388041167 -0.6043059407 0.466098001693 +1403638188045096960.0000000000 17.1700053725 -5.5751846918 1.6546019914 0.3557788985 0.5384905368 -0.6018500468 0.470346508727 +1403638188095097088.0000000000 17.2141780074 -5.5690482881 1.6617295168 0.3542151878 0.5384371348 -0.5995175389 0.474547967133 +1403638188145096960.0000000000 17.2573391807 -5.5612415935 1.6676102616 0.3524229450 0.5384270564 -0.5970789628 0.4789478938 +1403638188195097088.0000000000 17.2996736633 -5.5513661238 1.6724901648 0.3534930273 0.5365663349 -0.5954103436 0.482312938552 +1403638188245096960.0000000000 17.3408685789 -5.5393493096 1.6763681494 0.3575981120 0.5325309234 -0.5943300212 0.485083736897 +1403638188295097088.0000000000 17.3812039850 -5.5251029683 1.6795515838 0.3657660419 0.5261527142 -0.5930477947 0.487517012138 +1403638188345096960.0000000000 17.4197356360 -5.5091745057 1.6816566695 0.3743959674 0.5194306476 -0.5917555006 0.489739614014 +1403638188395097088.0000000000 17.4560352708 -5.4919910094 1.6824375779 0.3815479145 0.5132922187 -0.5898287557 0.493005401732 +1403638188445096960.0000000000 17.4893460929 -5.4734646130 1.6820021632 0.3876826872 0.5079392589 -0.5886573078 0.49515898183 +1403638188495097088.0000000000 17.5191727455 -5.4538417035 1.6804317069 0.3931483514 0.5034037523 -0.5879503232 0.496319910332 +1403638188545096960.0000000000 17.5456570659 -5.4333021843 1.6777260749 0.3974728322 0.4995051583 -0.5867505438 0.498230613107 +1403638188595097088.0000000000 17.5679719781 -5.4114148817 1.6747059962 0.4002555979 0.4982851454 -0.5863393236 0.4977083161 +1403638188645096960.0000000000 17.5856172227 -5.3883790590 1.6723269108 0.4006043997 0.4999707518 -0.5858601395 0.496299566016 +1403638188695097088.0000000000 17.5984698082 -5.3641520304 1.6718865915 0.4010160048 0.5029140193 -0.5856732641 0.493204299217 +1403638188745096960.0000000000 17.6065485559 -5.3387757527 1.6733440632 0.4008706178 0.5073014631 -0.5862046085 0.488172234317 +1403638188795097088.0000000000 17.6096777763 -5.3128846385 1.6749919963 0.3985349226 0.5128966309 -0.5868913815 0.483389561046 +1403638188845096960.0000000000 17.6109735724 -5.2864467422 1.6796947380 0.3975143934 0.5173634104 -0.5873631230 0.478875735778 +1403638188895097088.0000000000 17.6103620743 -5.2594303950 1.6880054728 0.3969564639 0.5210886255 -0.5874139118 0.47522321732 +1403638188945096960.0000000000 17.6075926080 -5.2321528539 1.6981836507 0.3963942045 0.5242984385 -0.5879041849 0.471541569106 +1403638188995097088.0000000000 17.6022591212 -5.2042836174 1.7110266973 0.3956371431 0.5276435345 -0.5875696986 0.468855415612 +1403638189045096960.0000000000 17.5935894219 -5.1754530850 1.7255032983 0.3970496145 0.5305221663 -0.5868129223 0.465347643064 +1403638189095097088.0000000000 17.5826067881 -5.1460167839 1.7411389605 0.3998896434 0.5334637917 -0.5846610607 0.462251122242 +1403638189145096960.0000000000 17.5692333533 -5.1162935124 1.7560322574 0.4029501738 0.5373460110 -0.5817556977 0.458749092644 +1403638189195097088.0000000000 17.5534531557 -5.0860615380 1.7695813204 0.4072920196 0.5415591675 -0.5786370046 0.45387894388 +1403638189245096960.0000000000 17.5350545159 -5.0557276680 1.7812476071 0.4110816740 0.5470900555 -0.5750882732 0.44830548346 +1403638189295097088.0000000000 17.5146426564 -5.0252639054 1.7915073861 0.4145669863 0.5535743555 -0.5710843790 0.442212933784 +1403638189345096960.0000000000 17.4919975769 -4.9950888670 1.7999393332 0.4160732560 0.5614177067 -0.5677978133 0.43508487376 +1403638189395097088.0000000000 17.4677465006 -4.9654286698 1.8066072552 0.4143725306 0.5706026549 -0.5661220573 0.426865121919 +1403638189445096960.0000000000 17.4422336158 -4.9360468556 1.8133170720 0.4121670776 0.5794753554 -0.5649581822 0.418507903108 +1403638189495097088.0000000000 17.4157380945 -4.9067859701 1.8212256634 0.4099297994 0.5872543863 -0.5638985717 0.411227730331 +1403638189545096960.0000000000 17.3890785590 -4.8779288540 1.8312396041 0.4089451538 0.5931166418 -0.5631126504 0.404821755126 +1403638189595097088.0000000000 17.3627615552 -4.8495551649 1.8438973970 0.4086927747 0.5974188023 -0.5618602154 0.400467338112 +1403638189645096960.0000000000 17.3372528838 -4.8211865829 1.8583825835 0.4084713882 0.6010549291 -0.5613137931 0.395993589469 +1403638189695097088.0000000000 17.3126018474 -4.7931136860 1.8725962393 0.4076444167 0.6043093196 -0.5622086824 0.390586319848 +1403638189745096960.0000000000 17.2886587930 -4.7654828201 1.8858399371 0.4066387236 0.6068296984 -0.5640234147 0.385071750732 +1403638189795097088.0000000000 17.2659966224 -4.7386076960 1.8976831671 0.4054756207 0.6089182231 -0.5652648631 0.381161059331 +1403638189845096960.0000000000 17.2442891174 -4.7123197032 1.9075436277 0.4031291421 0.6113215922 -0.5665890153 0.377822304003 +1403638189895097088.0000000000 17.2244688706 -4.6864568093 1.9160384683 0.4000679089 0.6139300779 -0.5672698005 0.375819772109 +1403638189945096960.0000000000 17.2065250041 -4.6609375412 1.9234563339 0.3981483727 0.6154325322 -0.5681012825 0.374141155764 +1403638189995097088.0000000000 17.1909243285 -4.6358765662 1.9298989207 0.3981123225 0.6152822768 -0.5676059135 0.375177058898 +1403638190045096960.0000000000 17.1773765081 -4.6112038443 1.9354700647 0.4002793904 0.6135448854 -0.5658496956 0.378355923997 +1403638190095097088.0000000000 17.1657725290 -4.5867311351 1.9399573141 0.4037233929 0.6110277431 -0.5638378397 0.38175831328 +1403638190145096960.0000000000 17.1558698650 -4.5627219099 1.9430502113 0.4072908347 0.6080434931 -0.5607790453 0.387200398736 +1403638190195097088.0000000000 17.1469069524 -4.5389575760 1.9441830671 0.4106806822 0.6051059751 -0.5579837908 0.392227262524 +1403638190245096960.0000000000 17.1385565388 -4.5154538721 1.9440449980 0.4136027288 0.6026480873 -0.5529489976 0.399994339519 +1403638190295097088.0000000000 17.1301158639 -4.4919420638 1.9420162038 0.4145013967 0.6029213569 -0.5455095073 0.40877109361 +1403638190345096960.0000000000 17.1212280703 -4.4679140147 1.9386415442 0.4151996414 0.6044303518 -0.5378392777 0.415935234146 +1403638190395097088.0000000000 17.1115140719 -4.4429020047 1.9342164947 0.4161243445 0.6067931204 -0.5292710059 0.422510167173 +1403638190445096960.0000000000 17.1004941045 -4.4168495356 1.9282861465 0.4155068884 0.6104726031 -0.5223151254 0.42645531566 +1403638190495097088.0000000000 17.0878848082 -4.3892272292 1.9213736030 0.4158240502 0.6133273999 -0.5179835452 0.427332314191 +1403638190545096960.0000000000 17.0752343826 -4.3601531566 1.9133776273 0.4174569213 0.6155691088 -0.5159774400 0.424937257163 +1403638190595097088.0000000000 17.0608113710 -4.3293120683 1.9048661313 0.4182316851 0.6181026798 -0.5147978440 0.421917663256 +1403638190645096960.0000000000 17.0456594416 -4.2970970466 1.8963827949 0.4198815378 0.6195933442 -0.5138567427 0.419231236882 +1403638190695097088.0000000000 17.0294302025 -4.2635343795 1.8884183815 0.4218202383 0.6204689014 -0.5138259397 0.416015543713 +1403638190745096960.0000000000 17.0124224182 -4.2287033920 1.8817252844 0.4236239927 0.6214609592 -0.5127155864 0.414067284979 +1403638190795097088.0000000000 16.9928752790 -4.1927193817 1.8758874522 0.4275725705 0.6205323465 -0.5144153472 0.409265383891 +1403638190845096960.0000000000 16.9728812788 -4.1558721012 1.8714691482 0.4306048831 0.6200408089 -0.5167048666 0.403912008568 +1403638190895097088.0000000000 16.9523569039 -4.1185699315 1.8693752126 0.4333702414 0.6194832065 -0.5185056229 0.39947804678 +1403638190945096960.0000000000 16.9315306244 -4.0806124705 1.8698506585 0.4338985840 0.6201623201 -0.5190500419 0.397136965749 +1403638190995097088.0000000000 16.9087643830 -4.0426958273 1.8718930226 0.4366274934 0.6190606953 -0.5196974963 0.395012404664 +1403638191045096960.0000000000 16.8854148327 -4.0048709079 1.8759046891 0.4397118858 0.6174393602 -0.5187006483 0.395438656941 +1403638191095097088.0000000000 16.8608631046 -3.9671910927 1.8814601062 0.4415536653 0.6164688436 -0.5180169507 0.395796619903 +1403638191145096960.0000000000 16.8354662489 -3.9299848633 1.8878146255 0.4406006324 0.6173747338 -0.5188392404 0.394367041537 +1403638191195097088.0000000000 16.8090595956 -3.8931184729 1.8954849327 0.4378636923 0.6196023559 -0.5205778598 0.39162098952 +1403638191245096960.0000000000 16.7823150341 -3.8563578296 1.9049748358 0.4337455886 0.6224747529 -0.5231737617 0.388174138067 +1403638191295097088.0000000000 16.7544954358 -3.8197457414 1.9156613600 0.4301052208 0.6250003097 -0.5265582222 0.383562968178 +1403638191345096960.0000000000 16.7268072091 -3.7832824548 1.9271144594 0.4263846917 0.6276122945 -0.5275267597 0.382118332778 +1403638191395097088.0000000000 16.6994739906 -3.7469296486 1.9380329708 0.4234298274 0.6292008462 -0.5286775865 0.381200060304 +1403638191445096960.0000000000 16.6724156743 -3.7104994694 1.9478151660 0.4218093528 0.6299611955 -0.5297297805 0.380279005016 +1403638191495097088.0000000000 16.6522736562 -3.6701511392 1.9633523559 0.4214143442 0.6297788424 -0.5308720205 0.379425167812 +1403638191545096960.0000000000 16.6283209923 -3.6328060574 1.9720478144 0.4207262857 0.6298032442 -0.5309294096 0.380067399397 +1403638191595097088.0000000000 16.6049809899 -3.5954398625 1.9791842788 0.4199623594 0.6299628518 -0.5304667466 0.381291820993 +1403638191645096960.0000000000 16.5821981572 -3.5578976275 1.9848102649 0.4192616846 0.6299890387 -0.5303237166 0.382217485882 +1403638191695097088.0000000000 16.5599619347 -3.5203553281 1.9886244172 0.4169378211 0.6313507554 -0.5291831878 0.384088831726 +1403638191745096960.0000000000 16.5385389766 -3.4824744727 1.9908870549 0.4146165400 0.6325637980 -0.5278522495 0.386430031151 +1403638191795097088.0000000000 16.5179529720 -3.4438300879 1.9917950548 0.4127071203 0.6336719191 -0.5263030920 0.388764436705 +1403638191845096960.0000000000 16.4976128372 -3.4043736357 1.9912011215 0.4107959874 0.6347060551 -0.5257623902 0.389831745054 +1403638191895097088.0000000000 16.4778567792 -3.3638206736 1.9899142896 0.4108578657 0.6344040910 -0.5255355104 0.390563299265 +1403638191945096960.0000000000 16.4585940515 -3.3225497383 1.9884403699 0.4109049113 0.6341940066 -0.5259759844 0.390261937437 +1403638191995097088.0000000000 16.4393307830 -3.2806868499 1.9874384969 0.4112468491 0.6341089749 -0.5260869923 0.389890130067 +1403638192045096960.0000000000 16.4209615284 -3.2378528078 1.9877636920 0.4109502409 0.6342565642 -0.5250962693 0.391295819404 +1403638192095097088.0000000000 16.4023044843 -3.1940193214 1.9899298648 0.4106500671 0.6344086607 -0.5251863213 0.391243532234 +1403638192145096960.0000000000 16.3848813366 -3.1488277028 1.9948090029 0.4122104373 0.6335456957 -0.5256055016 0.390437272225 +1403638192195097088.0000000000 16.3680349072 -3.1028425904 2.0018843008 0.4140421156 0.6323729822 -0.5258172321 0.390115080721 +1403638192245096960.0000000000 16.3516799848 -3.0560101388 2.0120278656 0.4166148859 0.6308127852 -0.5252298657 0.390692788469 +1403638192295097088.0000000000 16.3364548604 -3.0082986213 2.0249080297 0.4212823548 0.6276773429 -0.5248814007 0.391205631363 +1403638192345096960.0000000000 16.3219096215 -2.9601206194 2.0400033742 0.4251996412 0.6252665150 -0.5237597597 0.392329917895 +1403638192395097088.0000000000 16.3074950679 -2.9116677615 2.0562702703 0.4275092974 0.6237198623 -0.5232429281 0.392970955935 +1403638192445096960.0000000000 16.2925102402 -2.8629354469 2.0741184689 0.4289511172 0.6228624261 -0.5230295055 0.393043857181 +1403638192495097088.0000000000 16.2754884196 -2.8142993748 2.0911330782 0.4309655344 0.6215839255 -0.5225759797 0.393467250475 +1403638192545096960.0000000000 16.2592090008 -2.7656528814 2.1114638705 0.4324380023 0.6204387466 -0.5216519229 0.394882776656 +1403638192595097088.0000000000 16.2428323892 -2.7168849240 2.1326172310 0.4348960534 0.6186701862 -0.5203026498 0.396733885707 +1403638192645096960.0000000000 16.2265687149 -2.6679197399 2.1542842882 0.4389777373 0.6154317152 -0.5177060981 0.400652899725 +1403638192695097088.0000000000 16.2091854694 -2.6188411340 2.1748432871 0.4435027912 0.6119914570 -0.5172595419 0.401515002185 +1403638192745096960.0000000000 16.1907480975 -2.5702344255 2.1938215829 0.4471437140 0.6089771678 -0.5153959260 0.404445728824 +1403638192795097088.0000000000 16.1706696080 -2.5218735116 2.2113768568 0.4519776589 0.6053640347 -0.5144511339 0.405697685737 +1403638192845096960.0000000000 16.1491266711 -2.4738592037 2.2275434645 0.4561380465 0.6022866947 -0.5138104551 0.406432818789 +1403638192895097088.0000000000 16.1256848911 -2.4261106630 2.2435148998 0.4634322833 0.5968991201 -0.5130896045 0.407039331047 +1403638192945096960.0000000000 16.1003174215 -2.3789766362 2.2590178992 0.4733981332 0.5896406283 -0.5127186567 0.406617407373 +1403638192995097088.0000000000 16.0727194562 -2.3334360843 2.2731423705 0.4815186059 0.5839348658 -0.5122161259 0.405948943847 +1403638193045096960.0000000000 16.0419171162 -2.2896567575 2.2867112633 0.4881893341 0.5806556404 -0.5120564847 0.4028751145 +1403638193095097088.0000000000 16.0078705452 -2.2482008224 2.3002005067 0.4902294362 0.5820003040 -0.5110119377 0.399771866901 +1403638193145096960.0000000000 15.9704802381 -2.2089248862 2.3142576127 0.4883175184 0.5874164792 -0.5097193429 0.395820758102 +1403638193195097088.0000000000 15.9305314636 -2.1718783523 2.3300316539 0.4847078392 0.5939019895 -0.5083056772 0.392382563303 +1403638193245096960.0000000000 15.8876958603 -2.1369412201 2.3478915237 0.4812872987 0.6000261758 -0.5061501459 0.390055321992 +1403638193295097088.0000000000 15.8418154433 -2.1039639256 2.3683687014 0.4786132111 0.6052669547 -0.5041917972 0.387778209005 +1403638193345096960.0000000000 15.7936461502 -2.0728925349 2.3912423783 0.4746632796 0.6107400603 -0.5013073520 0.38779155309 +1403638193395097088.0000000000 15.7445131200 -2.0432932466 2.4167521250 0.4729661194 0.6143564331 -0.4976175207 0.388903620519 +1403638193445096960.0000000000 15.6938269581 -2.0149981601 2.4429838516 0.4717037520 0.6169177679 -0.4944983525 0.390358063096 +1403638193495097088.0000000000 15.6416786911 -1.9873749241 2.4691729324 0.4725542222 0.6179042456 -0.4920459689 0.390867771601 +1403638193545096960.0000000000 15.5877663317 -1.9606910029 2.4939639295 0.4729834176 0.6189465332 -0.4902581358 0.390946078104 +1403638193595097088.0000000000 15.5319068796 -1.9345475706 2.5167851601 0.4719831398 0.6207731601 -0.4901214412 0.389427236282 +1403638193645096960.0000000000 15.4742859201 -1.9091185853 2.5374638375 0.4689693702 0.6238969579 -0.4911034119 0.386830394988 +1403638193695097088.0000000000 15.4150989189 -1.8843198132 2.5563579064 0.4646841959 0.6277638469 -0.4933764595 0.382832626302 +1403638193745096960.0000000000 15.3547718344 -1.8601953989 2.5737153114 0.4615033189 0.6308591886 -0.4964357942 0.377601473832 +1403638193795097088.0000000000 15.2935038493 -1.8368357806 2.5892479956 0.4579151896 0.6337806211 -0.4985400614 0.374290810278 +1403638193845096960.0000000000 15.2319531528 -1.8141220690 2.6033602362 0.4551074195 0.6358379855 -0.4996690392 0.372717244248 +1403638193895097088.0000000000 15.1699587064 -1.7917097069 2.6164000830 0.4531112758 0.6372209054 -0.5012356117 0.370678500929 +1403638193945096960.0000000000 15.1080082261 -1.7696429752 2.6280845975 0.4507776484 0.6387714617 -0.5021779422 0.369577929249 +1403638193995097088.0000000000 15.0462692132 -1.7480053328 2.6384049518 0.4506244501 0.6388328126 -0.5035128772 0.367838313658 +1403638194045096960.0000000000 14.9847309151 -1.7265550260 2.6473972161 0.4503174523 0.6389220304 -0.5034964071 0.368081783545 +1403638194095097088.0000000000 14.9239394853 -1.7052384194 2.6555301684 0.4519753071 0.6371828346 -0.5019849091 0.371116569333 +1403638194145096960.0000000000 14.8634890512 -1.6839935128 2.6622521427 0.4548940856 0.6346915349 -0.5008181025 0.373388878488 +1403638194195097088.0000000000 14.8026441932 -1.6633352641 2.6672895916 0.4574017520 0.6323805105 -0.4991590550 0.376455528573 +1403638194245096960.0000000000 14.7409791810 -1.6431351359 2.6707693905 0.4600317232 0.6300307087 -0.4981654577 0.378501382421 +1403638194295097088.0000000000 14.6783626849 -1.6232281892 2.6724313477 0.4606538024 0.6294149661 -0.4978754709 0.379150221228 +1403638194345096960.0000000000 14.6146731248 -1.6038779786 2.6729001241 0.4589098450 0.6305794812 -0.4997694148 0.376831267379 +1403638194395097088.0000000000 14.5504942981 -1.5850984580 2.6747196649 0.4567389920 0.6319313010 -0.5015626625 0.374816247732 +1403638194445096960.0000000000 14.4854488457 -1.5668224986 2.6775884221 0.4548136940 0.6331488380 -0.5036749117 0.372261515584 +1403638194495097088.0000000000 14.4203394621 -1.5490503976 2.6819380925 0.4527044284 0.6343802319 -0.5058672483 0.369754985096 +1403638194545096960.0000000000 14.3549109980 -1.5319948649 2.6880385026 0.4498088588 0.6361540838 -0.5067459246 0.369037315288 +1403638194595097088.0000000000 14.2883847211 -1.5153570034 2.6955805636 0.4477322545 0.6373850690 -0.5083409840 0.367240447356 +1403638194645096960.0000000000 14.2224730924 -1.4989770322 2.7038598398 0.4444195840 0.6394773981 -0.5100055752 0.365313843135 +1403638194695097088.0000000000 14.1578887061 -1.4826754640 2.7126920567 0.4406186988 0.6418816730 -0.5121204475 0.362733686662 +1403638194745096960.0000000000 14.0947437163 -1.4666199709 2.7212820199 0.4377478929 0.6435038074 -0.5135444177 0.361319475073 +1403638194795097088.0000000000 14.0328398284 -1.4508993276 2.7286952166 0.4347520522 0.6452598723 -0.5145199849 0.360415781231 +1403638194845096960.0000000000 13.9724194574 -1.4350962425 2.7348906572 0.4322827306 0.6466001187 -0.5160074761 0.358854025987 +1403638194895097088.0000000000 13.9135927380 -1.4194870006 2.7397369850 0.4299735511 0.6477928418 -0.5163966682 0.358917345087 +1403638194945096960.0000000000 13.8564202726 -1.4037309878 2.7432675160 0.4283322974 0.6487859991 -0.5165198185 0.358908689617 +1403638194995097088.0000000000 13.8007516237 -1.3878294226 2.7453689775 0.4275890331 0.6491620875 -0.5173017107 0.357987629847 +1403638195045096960.0000000000 13.7466398954 -1.3719797167 2.7458688150 0.4263776019 0.6498141352 -0.5175462927 0.357896025561 +1403638195095097088.0000000000 13.6940515791 -1.3557361998 2.7450002024 0.4258803874 0.6502809190 -0.5175979362 0.35756537656 +1403638195145096960.0000000000 13.6428869612 -1.3392708196 2.7426816493 0.4241817640 0.6513257323 -0.5182092183 0.356796619446 +1403638195195097088.0000000000 13.5930011638 -1.3223479317 2.7388433480 0.4219648301 0.6526745929 -0.5206644847 0.353369568972 +1403638195245096960.0000000000 13.5444700235 -1.3053486876 2.7330567421 0.4170386605 0.6559054735 -0.5235004327 0.349018713502 +1403638195295097088.0000000000 13.4980906454 -1.2878771878 2.7263103865 0.4124314956 0.6588862857 -0.5266224619 0.344148088184 +1403638195345096960.0000000000 13.4544813244 -1.2701573213 2.7189433136 0.4092279225 0.6608514447 -0.5286162725 0.341134448565 +1403638195395097088.0000000000 13.4144898888 -1.2518988331 2.7115065796 0.4093302306 0.6608546627 -0.5282329782 0.341598884292 +1403638195445096960.0000000000 13.3777422057 -1.2332085074 2.7042929355 0.4135799695 0.6579355631 -0.5266825743 0.344496544954 +1403638195495097088.0000000000 13.3435422478 -1.2141944967 2.6969389825 0.4206430687 0.6533798614 -0.5231887114 0.34989675307 +1403638195545096960.0000000000 13.3107309652 -1.1948907402 2.6886434352 0.4272586125 0.6489664536 -0.5207531169 0.353707239687 +1403638195595097088.0000000000 13.2796928108 -1.1756160486 2.6790728847 0.4325266203 0.6454403115 -0.5172654118 0.358837039364 +1403638195645096960.0000000000 13.2495266144 -1.1562703341 2.6684313075 0.4357657381 0.6433796640 -0.5157245447 0.360831017902 +1403638195695097088.0000000000 13.2158545918 -1.1366342552 2.6555815328 0.4359331686 0.6434344223 -0.5151982142 0.361282737952 +1403638195745096960.0000000000 13.1861808656 -1.1173899055 2.6461357908 0.4357449973 0.6436382892 -0.5158867484 0.360162342327 +1403638195795097088.0000000000 13.1570803046 -1.0984042206 2.6377265539 0.4343877123 0.6448000744 -0.5166686608 0.358599601748 +1403638195845096960.0000000000 13.1292682547 -1.0793848663 2.6310801152 0.4320152066 0.6464700494 -0.5179333698 0.356629164361 +1403638195895097088.0000000000 13.1024384742 -1.0604672696 2.6259515266 0.4283126247 0.6493056373 -0.5188422357 0.354617003703 +1403638195945096960.0000000000 13.0773811186 -1.0415307124 2.6224434302 0.4256172092 0.6512523788 -0.5204097870 0.351985772413 +1403638195995097088.0000000000 13.0546337393 -1.0223987438 2.6207459034 0.4230871975 0.6530144649 -0.5215169751 0.350127657671 +1403638196045096960.0000000000 13.0340773080 -1.0029894282 2.6213682574 0.4224709518 0.6535303136 -0.5218428991 0.349422971102 +1403638196095097088.0000000000 13.0161157716 -0.9832526874 2.6246460191 0.4228894129 0.6532609199 -0.5213113969 0.350212995797 +1403638196145096960.0000000000 13.0011502596 -0.9630161840 2.6309350245 0.4246265731 0.6520741161 -0.5199411719 0.352353229316 +1403638196195097088.0000000000 12.9877179780 -0.9425496839 2.6396486408 0.4286113938 0.6496783891 -0.5177724065 0.355136591946 +1403638196245096960.0000000000 12.9749595634 -0.9222646018 2.6495549792 0.4321734014 0.6472524804 -0.5156742733 0.358288182272 +1403638196295097088.0000000000 12.9627294169 -0.9018360573 2.6594862063 0.4346545235 0.6455854739 -0.5144388676 0.36006595598 +1403638196345096960.0000000000 12.9511757062 -0.8814826558 2.6683085457 0.4362523113 0.6444194444 -0.5126577263 0.362752748084 +1403638196395097088.0000000000 12.9392018728 -0.8612639671 2.6774382421 0.4368453827 0.6440478501 -0.5138032381 0.361074384086 +1403638196445096960.0000000000 12.9283790320 -0.8408848189 2.6833449022 0.4366809857 0.6440259819 -0.5140283092 0.360991895676 +1403638196495097088.0000000000 12.9183517228 -0.8204564017 2.6874515872 0.4362194352 0.6441842178 -0.5147739282 0.360204248607 +1403638196545096960.0000000000 12.9087926316 -0.8000786757 2.6899103611 0.4354080722 0.6444226820 -0.5164882628 0.358300281945 +1403638196595097088.0000000000 12.8999271168 -0.7798128307 2.6902432146 0.4326941073 0.6461384758 -0.5183115716 0.355856704738 +1403638196645096960.0000000000 12.8920187081 -0.7599136042 2.6885669241 0.4282095567 0.6488653454 -0.5206943375 0.352828210286 +1403638196695097088.0000000000 12.8856204756 -0.7399757127 2.6858132448 0.4252147895 0.6506335575 -0.5235421913 0.348958350893 +1403638196745096960.0000000000 12.8811058488 -0.7201802663 2.6818955927 0.4229899415 0.6518722149 -0.5248337372 0.347407071099 +1403638196795097088.0000000000 12.8783524094 -0.7002008529 2.6769535011 0.4217866521 0.6524875433 -0.5249863643 0.34748430641 +1403638196845096960.0000000000 12.8772616906 -0.6799712449 2.6710638085 0.4220657732 0.6522809629 -0.5254537426 0.346826170981 +1403638196895097088.0000000000 12.8786201914 -0.6597660780 2.6651939277 0.4245624869 0.6503270005 -0.5237171468 0.350059762427 +1403638196945096960.0000000000 12.8813921739 -0.6395151769 2.6601479935 0.4274969950 0.6485266818 -0.5222080502 0.352077000801 +1403638196995097088.0000000000 12.8861581975 -0.6190885130 2.6564533807 0.4310206755 0.6462170564 -0.5201085661 0.355122194166 +1403638197045096960.0000000000 12.8914627834 -0.5990213111 2.6547042372 0.4336543625 0.6442895518 -0.5189852263 0.357056301308 +1403638197095097088.0000000000 12.8971496825 -0.5793129020 2.6539700945 0.4351199028 0.6431885936 -0.5179960922 0.358690886013 +1403638197145096960.0000000000 12.9033816073 -0.5599357960 2.6539811163 0.4361341198 0.6424299861 -0.5169554550 0.360316250116 +1403638197195097088.0000000000 12.9109226616 -0.5407661829 2.6551121383 0.4356167984 0.6427370185 -0.5156209552 0.362301201367 +1403638197245096960.0000000000 12.9198496734 -0.5211177494 2.6583083820 0.4359982876 0.6426114340 -0.5137957889 0.364650415336 +1403638197295097088.0000000000 12.9291536485 -0.5016560107 2.6635240859 0.4358966172 0.6425953635 -0.5096757066 0.370534765023 +1403638197345096960.0000000000 12.9383226754 -0.4818913549 2.6705318554 0.4356333753 0.6426162505 -0.5058553577 0.376003023878 +1403638197395097088.0000000000 12.9471729988 -0.4616092252 2.6788811338 0.4356031035 0.6425097309 -0.5030539289 0.379957795711 +1403638197445096960.0000000000 12.9556891627 -0.4407224050 2.6890675823 0.4359603014 0.6419915198 -0.5008818836 0.383279066441 +1403638197495097088.0000000000 12.9637639486 -0.4186916355 2.7014147961 0.4369088727 0.6414718381 -0.4998846379 0.384369440177 +1403638197545096960.0000000000 12.9706369216 -0.3961098548 2.7153209226 0.4388606355 0.6402214166 -0.5002210723 0.383792599077 +1403638197595097088.0000000000 12.9766095473 -0.3732219674 2.7304373189 0.4391764705 0.6401097342 -0.4997982282 0.384168305615 +1403638197645096960.0000000000 12.9821413787 -0.3497104947 2.7468275005 0.4395765911 0.6398182337 -0.4993481136 0.384781119419 +1403638197695097088.0000000000 12.9871787324 -0.3256699288 2.7641077671 0.4394347152 0.6400471499 -0.4994498493 0.384430260371 +1403638197745096960.0000000000 12.9946599936 -0.3002856066 2.7842146504 0.4389866819 0.6406198298 -0.4992510456 0.38424643167 +1403638197795097088.0000000000 12.9990892159 -0.2752127831 2.8006405328 0.4398472648 0.6400681099 -0.4995173688 0.383835377047 +1403638197845096960.0000000000 13.0030039530 -0.2495505824 2.8162033507 0.4426289405 0.6383559724 -0.5000310521 0.382818782734 +1403638197895097088.0000000000 13.0065489642 -0.2234498120 2.8304775462 0.4464751257 0.6359046170 -0.5003635113 0.381996906804 +1403638197945096960.0000000000 13.0098671627 -0.1970717795 2.8433325436 0.4525627511 0.6318148434 -0.4988490452 0.383596910959 +1403638197995097088.0000000000 13.0123840909 -0.1707457649 2.8526917161 0.4587834799 0.6273467973 -0.4970058687 0.385926004508 +1403638198045096960.0000000000 13.0138474294 -0.1446763817 2.8574365669 0.4627548635 0.6244569261 -0.4960643283 0.387080955187 +1403638198095097088.0000000000 13.0136919703 -0.1192647464 2.8564940429 0.4624404819 0.6248184159 -0.4965596313 0.386237336966 +1403638198145096960.0000000000 13.0120921068 -0.0942407767 2.8508524381 0.4617548110 0.6253520954 -0.4983595633 0.38386846308 +1403638198195097088.0000000000 13.0087336285 -0.0696801684 2.8403468663 0.4601468438 0.6266771930 -0.4997582246 0.381814477004 +1403638198245096960.0000000000 13.0038934743 -0.0454087742 2.8265674053 0.4578807103 0.6282833252 -0.5008780597 0.380429346614 +1403638198295097088.0000000000 12.9977166760 -0.0215198358 2.8109761952 0.4559704330 0.6297384432 -0.5012064195 0.379884959416 +1403638198345096960.0000000000 12.9905308684 0.0019976264 2.7940174043 0.4545752191 0.6308304672 -0.5012889377 0.379636263822 +1403638198395097088.0000000000 12.9824424933 0.0251507384 2.7751764676 0.4506551906 0.6337538145 -0.5015740279 0.37906397394 +1403638198445096960.0000000000 12.9737028111 0.0478676735 2.7554036517 0.4467434181 0.6365376845 -0.5006194866 0.380289658438 +1403638198495097088.0000000000 12.9642519443 0.0706599597 2.7350347701 0.4441979181 0.6382975566 -0.4990824332 0.382336453475 +1403638198545096960.0000000000 12.9539962498 0.0938066616 2.7133741912 0.4399970848 0.6414568793 -0.4962953766 0.385521123441 +1403638198595097088.0000000000 12.9434697438 0.1173580448 2.6911502940 0.4357151700 0.6440053509 -0.4909880619 0.392861453559 +1403638198645096960.0000000000 12.9321154176 0.1419046365 2.6684779935 0.4320704696 0.6460705311 -0.4848707138 0.401009188161 +1403638198695097088.0000000000 12.9195707572 0.1680682418 2.6465857352 0.4287247334 0.6480065472 -0.4789547370 0.408515578312 +1403638198745096960.0000000000 12.9052702286 0.1962729729 2.6262407367 0.4257932448 0.6496081362 -0.4732086261 0.415671719364 +1403638198795097088.0000000000 12.8888958052 0.2271746172 2.6081085780 0.4250998154 0.6497141306 -0.4691651584 0.420768047379 +1403638198845096960.0000000000 12.8830569422 0.2616150280 2.5953562426 0.4247499804 0.6501308447 -0.4669363810 0.422951244229 +1403638198895097088.0000000000 12.8628484031 0.2981755889 2.5819862012 0.4245772607 0.6502276135 -0.4665330271 0.42342075414 +1403638198945096960.0000000000 12.8404838753 0.3377232466 2.5706305028 0.4241378122 0.6506766649 -0.4671665014 0.422471838016 +1403638198995097088.0000000000 12.8165475398 0.3800994827 2.5612756053 0.4243840486 0.6506225323 -0.4687152158 0.420588333379 +1403638199045096960.0000000000 12.7904501274 0.4251147272 2.5544032491 0.4247089004 0.6505168089 -0.4698511365 0.419154077604 +1403638199095097088.0000000000 12.7628785843 0.4731693981 2.5506682858 0.4251513786 0.6502425922 -0.4715101343 0.417263789251 +1403638199145096960.0000000000 12.7338311199 0.5237261806 2.5499063847 0.4258852467 0.6494839109 -0.4722003918 0.416916293904 +1403638199195097088.0000000000 12.7027821847 0.5769283033 2.5515426226 0.4276369899 0.6482758040 -0.4733741438 0.415670550717 +1403638199245096960.0000000000 12.6701365306 0.6325075509 2.5562964963 0.4305591868 0.6463247139 -0.4739006346 0.415091965013 +1403638199295097088.0000000000 12.6362262848 0.6903511868 2.5637803724 0.4329967629 0.6445394954 -0.4730669030 0.416281572302 +1403638199345096960.0000000000 12.6004553145 0.7502350847 2.5721048683 0.4344763983 0.6433647926 -0.4731366926 0.416477698159 +1403638199395097088.0000000000 12.5621400346 0.8113918829 2.5811581009 0.4331334760 0.6438568868 -0.4715490139 0.418909571053 +1403638199445096960.0000000000 12.5214421456 0.8744394657 2.5921926683 0.4311046912 0.6449048175 -0.4708690762 0.420153346665 +1403638199495097088.0000000000 12.4786811730 0.9394237899 2.6048644420 0.4278326471 0.6465639493 -0.4707584052 0.421071026578 +1403638199545096960.0000000000 12.4344048085 1.0069831716 2.6191248616 0.4239427391 0.6496193652 -0.4699351980 0.42122220255 +1403638199595097088.0000000000 12.3884779791 1.0773724046 2.6348338128 0.4233207036 0.6518043635 -0.4688846773 0.419640099459 +1403638199645096960.0000000000 12.3407761679 1.1505113298 2.6519005123 0.4241742305 0.6543147857 -0.4671202580 0.41682975895 +1403638199695097088.0000000000 12.2911522816 1.2265034244 2.6711211172 0.4282028289 0.6556768822 -0.4660964438 0.41168467137 +1403638199745096960.0000000000 12.2400694001 1.3045239640 2.6910655300 0.4326358006 0.6567782024 -0.4667167608 0.404529507149 +1403638199795097088.0000000000 12.1875683459 1.3840505191 2.7101238212 0.4371805176 0.6573462976 -0.4700491885 0.394743968133 +1403638199845096960.0000000000 12.1343358319 1.4643895417 2.7278701484 0.4407194033 0.6580853387 -0.4718690114 0.387336714868 +1403638199895097088.0000000000 12.0805890416 1.5453674248 2.7438141186 0.4437935287 0.6588365333 -0.4732981241 0.380750064937 +1403638199945096960.0000000000 12.0266105716 1.6267465508 2.7580187621 0.4459946000 0.6596414747 -0.4740066040 0.375871894415 +1403638199995097088.0000000000 11.9723706135 1.7086126861 2.7710479756 0.4483178071 0.6607167205 -0.4729430066 0.372544590149 +1403638200045096960.0000000000 11.9177286148 1.7907117019 2.7827446823 0.4507896665 0.6624461114 -0.4709115238 0.36904764313 +1403638200095097088.0000000000 11.8628824373 1.8725376995 2.7927465668 0.4511743793 0.6662020339 -0.4660000557 0.36804955851 +1403638200145096960.0000000000 11.8077432405 1.9547226597 2.8024688392 0.4529235403 0.6698119211 -0.4590044562 0.368140144649 +1403638200195097088.0000000000 11.7517818507 2.0373053419 2.8130102076 0.4562440816 0.6726838101 -0.4504183407 0.369406480695 +1403638200245096960.0000000000 11.7088212469 2.1124357750 2.8202520045 0.4629683498 0.6739630625 -0.4425890217 0.368169872973 +1403638200295097088.0000000000 11.6500514490 2.1955803129 2.8335360690 0.4682325184 0.6764420581 -0.4341930726 0.366961614415 +1403638200345096960.0000000000 11.5897234382 2.2796336147 2.8486833554 0.4745085075 0.6784357334 -0.4267825802 0.363900070268 +1403638200395097088.0000000000 11.5287169953 2.3642107812 2.8654811982 0.4788059942 0.6812817311 -0.4185496524 0.362513739388 +1403638200445096960.0000000000 11.4660975703 2.4488135862 2.8828122069 0.4791735638 0.6863369844 -0.4107494614 0.361412672075 +1403638200495097088.0000000000 11.4027399598 2.5339866620 2.9024053893 0.4792953017 0.6904951930 -0.4034511081 0.361551663617 +1403638200545096960.0000000000 11.3378790554 2.6201950674 2.9236599201 0.4790128748 0.6949421609 -0.3966808687 0.360896588097 +1403638200595097088.0000000000 11.2709674765 2.7074772649 2.9465314895 0.4792697852 0.6993873417 -0.3905718098 0.358624428548 +1403638200645096960.0000000000 11.2026216607 2.7956324628 2.9707759932 0.4795942930 0.7038870432 -0.3824777088 0.358110523145 +1403638200695097088.0000000000 11.1328984336 2.8851227125 2.9965785620 0.4791150065 0.7087869116 -0.3742594262 0.357770605773 +1403638200745096960.0000000000 11.0457932132 2.9705405180 3.0243992259 0.4785472795 0.7132809036 -0.3690294740 0.355021268539 +1403638200795097088.0000000000 10.9695128361 3.0615591518 3.0502876928 0.4780009433 0.7172161218 -0.3651041900 0.351873646751 +1403638200845096960.0000000000 10.8906339855 3.1535515153 3.0754824565 0.4778237236 0.7202053621 -0.3627949635 0.348379878944 +1403638200895097088.0000000000 10.8108814861 3.2474367276 3.0991747477 0.4783441864 0.7223085252 -0.3624887134 0.343597389878 +1403638200945096960.0000000000 10.7299140798 3.3432136314 3.1217775173 0.4823408067 0.7219047180 -0.3651195746 0.335989018599 +1403638200995097088.0000000000 10.6480744061 3.4401142753 3.1427808135 0.4863033656 0.7209261800 -0.3677148601 0.329484842247 +1403638201045096960.0000000000 10.5652866677 3.5376505369 3.1619889451 0.4904075884 0.7194955524 -0.3708993227 0.322893542275 +1403638201095097088.0000000000 10.4820076591 3.6352606722 3.1786421271 0.4929889347 0.7184441689 -0.3725842012 0.319344483918 +1403638201145096960.0000000000 10.3982045426 3.7331089731 3.1929824973 0.4936936802 0.7183717719 -0.3743595448 0.31632811881 +1403638201195097088.0000000000 10.3142536865 3.8309689780 3.2061518934 0.4959191301 0.7167218720 -0.3760402561 0.314591322713 +1403638201245096960.0000000000 10.2299650557 3.9286985422 3.2172867600 0.4982588533 0.7148866504 -0.3779051935 0.312830396272 +1403638201295097088.0000000000 10.1455043334 4.0259251186 3.2263045870 0.4972095729 0.7151115436 -0.3788111924 0.312890078628 +1403638201345096960.0000000000 10.0607812380 4.1230792969 3.2336569970 0.4962702583 0.7153605728 -0.3793794089 0.313123531087 +1403638201395097088.0000000000 9.9759278767 4.2199473015 3.2395013811 0.4953126688 0.7154369939 -0.3789273399 0.315006887155 +1403638201445096960.0000000000 9.8907122739 4.3165600492 3.2435179738 0.4957417076 0.7144653520 -0.3796570810 0.315657917734 +1403638201495097088.0000000000 9.8055065163 4.4132955490 3.2457934069 0.4963419099 0.7134245271 -0.3803997384 0.31617430583 +1403638201545096960.0000000000 9.7058736926 4.5013004703 3.2495235187 0.4964158144 0.7127160379 -0.3802314758 0.317854075532 +1403638201595097088.0000000000 9.6185042843 4.5966306676 3.2485746668 0.4963576331 0.7119332853 -0.3799975923 0.319971760061 +1403638201645096960.0000000000 9.5304521907 4.6917543561 3.2459471797 0.4977422419 0.7105698864 -0.3804006404 0.320372361333 +1403638201695097088.0000000000 9.4417641758 4.7865124882 3.2407958357 0.4981399624 0.7097567556 -0.3813134714 0.320471468822 +1403638201745096960.0000000000 9.3525072777 4.8807816447 3.2334025707 0.4980516805 0.7093112951 -0.3821342316 0.320617278388 +1403638201795097088.0000000000 9.2626725826 4.9742995766 3.2239971599 0.4971971598 0.7093774569 -0.3818442327 0.32213908471 +1403638201845096960.0000000000 9.1720817824 5.0680204068 3.2135600592 0.4992767037 0.7078762341 -0.3833788748 0.320397641647 +1403638201895097088.0000000000 9.0805472714 5.1608890351 3.2015196437 0.4978635961 0.7088496844 -0.3832951879 0.320544479797 +1403638201945096960.0000000000 8.9874158099 5.2532612448 3.1900071573 0.4982824398 0.7097590803 -0.3822668886 0.319106070219 +1403638201995097088.0000000000 8.8927613531 5.3450462674 3.1795678512 0.4992089886 0.7115057379 -0.3796922923 0.316833921336 +1403638202045096960.0000000000 8.7963336977 5.4357722064 3.1705115446 0.5010353595 0.7128136842 -0.3778286930 0.313218292698 +1403638202095097088.0000000000 8.6987315869 5.5257162832 3.1622310250 0.5028965366 0.7140238514 -0.3781553726 0.307023659166 +1403638202145096960.0000000000 8.6121161776 5.6257786260 3.1489519915 0.5030066419 0.7163624270 -0.3787294145 0.30062139327 +1403638202195097088.0000000000 8.5164061121 5.7163994259 3.1429849922 0.5038387032 0.7177466030 -0.3797224084 0.29461376013 +1403638202245096960.0000000000 8.4206463947 5.8058174849 3.1383523301 0.5032845480 0.7198605144 -0.3807672841 0.289001347624 +1403638202295097088.0000000000 8.3259310983 5.8946044033 3.1350953614 0.5012782833 0.7228422268 -0.3806988212 0.28510981295 +1403638202345096960.0000000000 8.2329657344 5.9834257314 3.1341091025 0.5026766429 0.7230830953 -0.3811534898 0.281405485354 +1403638202395097088.0000000000 8.1413519374 6.0709339898 3.1328545304 0.5011711729 0.7249618179 -0.3798836853 0.280973670916 +1403638202445096960.0000000000 8.0508206697 6.1584889729 3.1307157170 0.5017180700 0.7254338374 -0.3796466949 0.279093376522 +1403638202495097088.0000000000 7.9612297220 6.2452861536 3.1263669266 0.5015311872 0.7261194811 -0.3790585925 0.278444879512 +1403638202545096960.0000000000 7.8724964221 6.3315727037 3.1203233625 0.5019955890 0.7261988608 -0.3801358141 0.275921014266 +1403638202595097088.0000000000 7.7852048297 6.4169965240 3.1125623383 0.5024541184 0.7260920755 -0.3810094609 0.274156793668 +1403638202645096960.0000000000 7.6987803711 6.5012178303 3.1025579227 0.5011416406 0.7270979695 -0.3815837615 0.273092350001 +1403638202695097088.0000000000 7.6138266420 6.5848836867 3.0915010645 0.5011594934 0.7270292639 -0.3819751457 0.272695067216 +1403638202745096960.0000000000 7.5304149885 6.6676367122 3.0792590614 0.5011210130 0.7269864005 -0.3818214958 0.273094945394 +1403638202795097088.0000000000 7.4481675196 6.7492031250 3.0656957696 0.5012785937 0.7266695785 -0.3813645453 0.274284849854 +1403638202845096960.0000000000 7.3670192534 6.8300356182 3.0518369575 0.5019047794 0.7260793337 -0.3809379697 0.275293764503 +1403638202895097088.0000000000 7.2870931368 6.9100871285 3.0375665808 0.5023032411 0.7256126269 -0.3802625065 0.276727656369 +1403638202945096960.0000000000 7.2074571099 6.9890963141 3.0237984081 0.5027160471 0.7250617478 -0.3811356006 0.276220368233 +1403638202995097088.0000000000 7.1285549301 7.0671500060 3.0112383609 0.5037530146 0.7242376382 -0.3813135314 0.276247596272 +1403638203045096960.0000000000 7.0506490740 7.1442352575 2.9995912204 0.5048827014 0.7233235565 -0.3816980301 0.276049097573 +1403638203095097088.0000000000 6.9725767003 7.2237955957 2.9821155197 0.5049076326 0.7232673350 -0.3816185416 0.276260625689 +1403638203145096960.0000000000 6.8965143524 7.2996790186 2.9732050441 0.5055048100 0.7226008114 -0.3806658913 0.278220117271 +1403638203195097088.0000000000 6.8211214753 7.3745433001 2.9661202093 0.5070614021 0.7214217760 -0.3787191416 0.281089251658 +1403638203245096960.0000000000 6.7458762865 7.4481134275 2.9606136369 0.5083041358 0.7204648856 -0.3770838807 0.283487214999 +1403638203295097088.0000000000 6.6710096567 7.5208662858 2.9571616391 0.5105916156 0.7188875661 -0.3770138991 0.283473789454 +1403638203345096960.0000000000 6.5968020975 7.5935458659 2.9537511130 0.5111622777 0.7184591679 -0.3774378065 0.282966874561 +1403638203395097088.0000000000 6.5225673275 7.6643022442 2.9498644200 0.5129472672 0.7173584610 -0.3772855430 0.282732309145 +1403638203445096960.0000000000 6.4486785972 7.7339790629 2.9443953612 0.5141534030 0.7165314852 -0.3777348951 0.282037688967 +1403638203495097088.0000000000 6.3751954882 7.8024456376 2.9370187110 0.5136185963 0.7168596752 -0.3784457735 0.281224003547 +1403638203545096960.0000000000 6.3021422823 7.8704418579 2.9287224991 0.5139198766 0.7167122065 -0.3791213297 0.280137449977 +1403638203595097088.0000000000 6.2296068365 7.9371190702 2.9204102389 0.5144241037 0.7163132254 -0.3804923022 0.27836812441 +1403638203645096960.0000000000 6.1575734349 8.0022842933 2.9125214983 0.5124291859 0.7177928306 -0.3806218837 0.278058920932 +1403638203695097088.0000000000 6.0859356568 8.0663376172 2.9066355968 0.5131478108 0.7173563739 -0.3810195616 0.277314353813 +1403638203745096960.0000000000 6.0147480238 8.1288193150 2.9027670767 0.5135418436 0.7170610393 -0.3808621649 0.27756486114 +1403638203795097088.0000000000 5.9441013604 8.1897760220 2.9003642344 0.5127837050 0.7176137570 -0.3798701193 0.278894353079 +1403638203845096960.0000000000 5.8741063782 8.2498549924 2.8996815771 0.5132640159 0.7174802897 -0.3796877247 0.278602432755 +1403638203895097088.0000000000 5.8043140353 8.3084023562 2.9005285915 0.5133241464 0.7175767252 -0.3787405976 0.27953089981 +1403638203945096960.0000000000 5.7347277107 8.3656652335 2.9025214152 0.5129344838 0.7181854273 -0.3788907800 0.278477439292 +1403638203995097088.0000000000 5.6656147536 8.4217594394 2.9063222620 0.5133374409 0.7182085602 -0.3788123007 0.277781167041 +1403638204045096960.0000000000 5.5963530115 8.4764996455 2.9115581571 0.5123519281 0.7193419683 -0.3794299703 0.275817932941 +1403638204095097088.0000000000 5.5272770189 8.5298506253 2.9188793810 0.5112376795 0.7204416059 -0.3795139810 0.274898282508 +1403638204145096960.0000000000 5.4588119631 8.5823694214 2.9281696274 0.5103773051 0.7215114063 -0.3809060659 0.271747798339 +1403638204195097088.0000000000 5.3912496405 8.6338085696 2.9396033385 0.5100379474 0.7218934738 -0.3830215913 0.26837579131 +1403638204245096960.0000000000 5.3247348352 8.6842952509 2.9525531198 0.5093168566 0.7225005576 -0.3857637100 0.264150797915 +1403638204295097088.0000000000 5.2595593772 8.7339703223 2.9669024936 0.5086714688 0.7228907979 -0.3900953462 0.257891163126 +1403638204345096960.0000000000 5.1958658065 8.7824070150 2.9817358962 0.5080570456 0.7229593747 -0.3953791864 0.250764989253 +1403638204395097088.0000000000 5.1344618485 8.8293383696 2.9968170993 0.5063375192 0.7237705624 -0.3995904819 0.245165120634 +1403638204445096960.0000000000 5.0754355256 8.8748287916 3.0114668250 0.5058753520 0.7235602727 -0.4026056545 0.241783678154 +1403638204495097088.0000000000 5.0188690202 8.9187955217 3.0248532606 0.5056148524 0.7233417229 -0.4042234125 0.240278600381 +1403638204545096960.0000000000 4.9645193776 8.9612736558 3.0369763178 0.5062586843 0.7225871460 -0.4050016034 0.239882600982 +1403638204595097088.0000000000 4.9125718774 9.0027182037 3.0478823710 0.5086911289 0.7214564536 -0.4040359865 0.239768310258 +1403638204645096960.0000000000 4.8624432380 9.0425484631 3.0563300774 0.5093371048 0.7223588480 -0.4017949015 0.239445746211 +1403638204695097088.0000000000 4.8140667491 9.0808551991 3.0627556556 0.5097418744 0.7244586134 -0.3971527895 0.239984584244 +1403638204745096960.0000000000 4.7674384284 9.1175499356 3.0672538484 0.5096448614 0.7278383330 -0.3902756185 0.24124348244 +1403638204795097088.0000000000 4.7224787994 9.1531841925 3.0700248131 0.5097306877 0.7318701391 -0.3817126283 0.242561734334 +1403638204845096960.0000000000 4.6786817922 9.1876790897 3.0709713931 0.5104485206 0.7364035842 -0.3699512822 0.245536387717 +1403638204895097088.0000000000 4.6357726443 9.2217068748 3.0701984255 0.5123720695 0.7410502114 -0.3563734950 0.247623461245 +1403638204945096960.0000000000 4.5929345525 9.2554767540 3.0676743281 0.5143368733 0.7465718315 -0.3430545230 0.245767523133 +1403638204995097088.0000000000 4.5500844431 9.2893209628 3.0639930728 0.5172170945 0.7521628190 -0.3288811938 0.242022170832 +1403638205045096960.0000000000 4.5076792194 9.3235122039 3.0591999578 0.5207085077 0.7580637969 -0.3129826636 0.237157715715 +1403638205095097088.0000000000 4.4649685455 9.3579134577 3.0535156180 0.5241427998 0.7646361981 -0.2964824080 0.229573499757 +1403638205145096960.0000000000 4.4213744831 9.3921688262 3.0483497961 0.5287511875 0.7709171675 -0.2798684790 0.218592170452 +1403638205195097088.0000000000 4.3774345358 9.4267742009 3.0448685863 0.5349317166 0.7762692095 -0.2616961344 0.206807413186 +1403638205245096960.0000000000 4.3333573615 9.4613136765 3.0429418699 0.5398561990 0.7823113542 -0.2421479085 0.194701360752 +1403638205295097088.0000000000 4.2892762636 9.4960861494 3.0434628399 0.5459767845 0.7870453201 -0.2225054798 0.181549790459 +1403638205345096960.0000000000 4.2403864628 9.5360678583 3.0375449460 0.5524972092 0.7908161198 -0.2029027692 0.1678903354 +1403638205395097088.0000000000 4.1962659385 9.5703605771 3.0411364556 0.5583982276 0.7941702375 -0.1819599240 0.156126997355 +1403638205445096960.0000000000 4.1527371989 9.6040623215 3.0466782693 0.5637438310 0.7966194147 -0.1625229388 0.145522147828 +1403638205495097088.0000000000 4.1095856757 9.6373072691 3.0533151073 0.5677741568 0.7986152273 -0.1423455752 0.139942712162 +1403638205545096960.0000000000 4.0661284181 9.6699550749 3.0613036825 0.5705927995 0.8002387588 -0.1250378385 0.135673597522 +1403638205595097088.0000000000 4.0221057275 9.7011548852 3.0716195333 0.5735680281 0.8006994543 -0.1089707763 0.134258969489 +1403638205645096960.0000000000 3.9769580589 9.7320153058 3.0829154118 0.5775136868 0.7995859309 -0.0952222840 0.13443584829 +1403638205695097088.0000000000 3.9299902130 9.7627432383 3.0963517938 0.5808965632 0.7984223207 -0.0834595711 0.134593761385 +1403638205745096960.0000000000 3.8807176961 9.7931486096 3.1113601147 0.5838963517 0.7973991776 -0.0734502568 0.133509032501 +1403638205795097088.0000000000 3.8283844366 9.8223144208 3.1269105485 0.5856082232 0.7975533340 -0.0649208221 0.129448736046 +1403638205845096960.0000000000 3.7728590856 9.8501282830 3.1439159756 0.5866040926 0.7983116731 -0.0564601292 0.124122379182 +1403638205895097088.0000000000 3.7144000197 9.8767457049 3.1616130450 0.5862921951 0.8000838898 -0.0480446684 0.117553991843 +1403638205945096960.0000000000 3.6529536423 9.9030449146 3.1807892120 0.5871487417 0.8011185361 -0.0396423237 0.109059306474 +1403638205995097088.0000000000 3.5886169296 9.9290504213 3.2015192424 0.5874495794 0.8026347525 -0.0321510532 0.0982178975665 +1403638206045096960.0000000000 3.5221861632 9.9534179568 3.2235946653 0.5875437978 0.8039230823 -0.0229879410 0.0892833575735 +1403638206095097088.0000000000 3.4536388028 9.9763643593 3.2472478829 0.5886862411 0.8042468013 -0.0140451490 0.0802391797594 +1403638206145096960.0000000000 3.3832742261 9.9980179777 3.2714471643 0.5903608248 0.8039527791 -0.0047676539 0.071493321446 +1403638206195097088.0000000000 3.3113663335 10.0187511233 3.2954830488 0.5914858465 0.8037907449 0.0043935877 0.0636052528053 +1403638206245096960.0000000000 3.2379853015 10.0384676276 3.3184507480 0.5929530855 0.8032078861 0.0130922788 0.055608653291 +1403638206295097088.0000000000 3.1631320105 10.0571375391 3.3401643266 0.5946885904 0.8023616231 0.0204124632 0.046310232395 +1403638206345096960.0000000000 3.0902351848 10.0684554135 3.3792560005 0.5962730693 0.8017018252 0.0240716700 0.0339582839178 +1403638206395097088.0000000000 3.0139609310 10.0839030822 3.4003899207 0.5971609440 0.8012490365 0.0274788193 0.0253713013268 +1403638206445096960.0000000000 2.9373791080 10.0981841755 3.4202034951 0.5984862356 0.8004079621 0.0294693896 0.0171135920499 +1403638206495097088.0000000000 2.8605960272 10.1110924412 3.4389733800 0.6002663280 0.7991036390 0.0313865603 0.0113399025747 +1403638206545096960.0000000000 2.7839742001 10.1225031193 3.4553897126 0.6015158329 0.7981703744 0.0326039402 0.00630391243597 +1403638206595097088.0000000000 2.7076977169 10.1322365507 3.4697661037 0.6025976580 0.7973079436 0.0341105539 0.00354623259336 +1403638206645096960.0000000000 2.6314102276 10.1405302152 3.4826948179 0.6038938916 0.7962762977 0.0354368916 0.000672357038177 +1403638206695097088.0000000000 2.5549944020 10.1467923469 3.4939089013 0.6046084169 0.7956348022 0.0374031965 -0.003863241074 +1403638206745096960.0000000000 2.4787177192 10.1511057245 3.5028025198 0.6037117651 0.7960776307 0.0418520990 -0.00639627579437 +1403638206795097088.0000000000 2.4027575358 10.1536309607 3.5103005501 0.6033809200 0.7961180590 0.0447509239 -0.0111739103662 +1403638206845096960.0000000000 2.3277136729 10.1547606736 3.5159399364 0.6029630863 0.7961780892 0.0486910827 -0.0128508890556 +1403638206895097088.0000000000 2.2530470917 10.1546493360 3.5205937478 0.6039798089 0.7951983212 0.0511511355 -0.0158613271909 +1403638206945096960.0000000000 2.1785175925 10.1530835695 3.5235533122 0.6053816648 0.7939689877 0.0527316871 -0.0185918188993 +1403638206995097088.0000000000 2.1046249161 10.1499772912 3.5249505247 0.6071228530 0.7924939389 0.0538064147 -0.0214491915354 +1403638207045096960.0000000000 2.0314641046 10.1449826330 3.5244811579 0.6083350095 0.7914397135 0.0548890666 -0.0232139303384 +1403638207095097088.0000000000 1.9592251166 10.1384261596 3.5222096593 0.6102311699 0.7898683240 0.0563523556 -0.0234597975829 +1403638207145096960.0000000000 1.8874683399 10.1297044712 3.5171936125 0.6104121803 0.7896553065 0.0567337861 -0.0249548507252 +1403638207195097088.0000000000 1.8162782546 10.1189996052 3.5105950504 0.6114492374 0.7887365934 0.0572143457 -0.0274031939955 +1403638207245096960.0000000000 1.7457200810 10.1061587180 3.5017113906 0.6117087769 0.7882750114 0.0599894576 -0.028916148139 +1403638207295097088.0000000000 1.6757022853 10.0911537498 3.4911011332 0.6128304044 0.7870001961 0.0637731307 -0.0316634567007 +1403638207345096960.0000000000 1.6061937928 10.0738071752 3.4790802090 0.6138995098 0.7856275068 0.0677784008 -0.0363717037289 +1403638207395097088.0000000000 1.5372650324 10.0543736315 3.4660226427 0.6156106790 0.7835278940 0.0738598048 -0.0406480060804 +1403638207445096960.0000000000 1.4690215733 10.0323465879 3.4535908751 0.6163058080 0.7819397946 0.0811828021 -0.0463320759062 +1403638207495097088.0000000000 1.4016207040 10.0071842953 3.4430788050 0.6167028348 0.7802936774 0.0899064926 -0.0523088243014 +1403638207545096960.0000000000 1.3347776535 9.9812908696 3.4307171621 0.6146120437 0.7804740759 0.0975971910 -0.0598919104802 +1403638207595097088.0000000000 1.2697964590 9.9518311040 3.4217552796 0.6109270645 0.7818782226 0.1065805560 -0.0638369167483 +1403638207645096960.0000000000 1.2059438679 9.9196302420 3.4144314987 0.6055453817 0.7846529199 0.1117140237 -0.071795284915 +1403638207695097088.0000000000 1.1439281359 9.8856743735 3.4084865002 0.5991452780 0.7882723241 0.1176709513 -0.0761920343431 +1403638207745096960.0000000000 1.0830940783 9.8506829847 3.4052488190 0.5948341532 0.7904215514 0.1210611359 -0.0821602256656 +1403638207795097088.0000000000 1.0239960449 9.8147252011 3.4038626157 0.5907916593 0.7924905517 0.1246621460 -0.0859260737032 +1403638207845096960.0000000000 0.9662941028 9.7780904257 3.4048016092 0.5860016012 0.7952886582 0.1269901910 -0.0893955533209 +1403638207895097088.0000000000 0.9100881325 9.7413223033 3.4076202388 0.5807543627 0.7985440236 0.1290717244 -0.0916095109208 +1403638207945096960.0000000000 0.8549270159 9.7040180707 3.4125262633 0.5772200855 0.8006856168 0.1306430224 -0.0930156796335 +1403638207995097088.0000000000 0.8012179794 9.6672102359 3.4183924432 0.5758508843 0.8014548896 0.1319796313 -0.0929903002499 +1403638208045096960.0000000000 0.7488269790 9.6298173312 3.4240477807 0.5744981588 0.8022784885 0.1324758918 -0.0935480118502 +1403638208095097088.0000000000 0.6977874368 9.5925863270 3.4290345216 0.5769956025 0.8004688047 0.1326149003 -0.0934829162368 +1403638208145096960.0000000000 0.6475092767 9.5539329434 3.4333008455 0.5790177686 0.7990500439 0.1307260702 -0.0957504340234 +1403638208195097088.0000000000 0.5986749150 9.5159998893 3.4356910908 0.5828714370 0.7963058155 0.1299871641 -0.0962355092528 +1403638208245096960.0000000000 0.5512336941 9.4775697631 3.4358289953 0.5849509425 0.7949801127 0.1294907887 -0.0952425900911 +1403638208295097088.0000000000 0.5048523256 9.4386809330 3.4341337390 0.5856388767 0.7946638814 0.1289275839 -0.0944145103541 +1403638208345096960.0000000000 0.4595973487 9.3993811129 3.4303259796 0.5835755463 0.7963290257 0.1289074965 -0.0931800506851 +1403638208395097088.0000000000 0.4154333251 9.3596230724 3.4249416055 0.5815338308 0.7979778704 0.1286851142 -0.0921404545355 +1403638208445096960.0000000000 0.3722990608 9.3193691383 3.4182090639 0.5795119768 0.7994096426 0.1296040919 -0.0911749497567 +1403638208495097088.0000000000 0.3299366855 9.2786528841 3.4120748107 0.5777334390 0.8003410293 0.1310710775 -0.0921883020494 +1403638208545096960.0000000000 0.2882847821 9.2373897241 3.4071437719 0.5758273520 0.8009614803 0.1338438966 -0.0947068058501 +1403638208595097088.0000000000 0.2476924286 9.1957040975 3.4035756399 0.5740494745 0.8010580359 0.1392753363 -0.0968277057854 +1403638208645096960.0000000000 0.2077316220 9.1542470194 3.4020587799 0.5738098763 0.7998485395 0.1444069376 -0.100653743486 +1403638208695097088.0000000000 0.1684923134 9.1133406220 3.4023932437 0.5731353527 0.7990459360 0.1485356543 -0.10477890554 +1403638208745096960.0000000000 0.1303915871 9.0724301220 3.4047471323 0.5723374919 0.7983347361 0.1520029136 -0.109483143931 +1403638208795097088.0000000000 0.0936769789 9.0321547010 3.4086296498 0.5721099346 0.7972720724 0.1559395755 -0.11282869379 +1403638208845096960.0000000000 0.0581619642 8.9923647063 3.4127904590 0.5726762684 0.7958062646 0.1591032837 -0.115846561901 +1403638208895097088.0000000000 0.0236738177 8.9530607776 3.4159992471 0.5730115323 0.7945897590 0.1632662224 -0.116743476756 +1403638208945096960.0000000000 -0.0099520555 8.9138582619 3.4181639111 0.5735532173 0.7933211650 0.1663413440 -0.118358748504 +1403638208995097088.0000000000 -0.0424269789 8.8746109098 3.4185145961 0.5736664525 0.7925656285 0.1687343294 -0.119479085291 +1403638209045096960.0000000000 -0.0738976468 8.8352130842 3.4172558734 0.5735545756 0.7920676520 0.1704038480 -0.120940117723 +1403638209095097088.0000000000 -0.1045382570 8.7957885373 3.4143632217 0.5730444795 0.7918839645 0.1715591578 -0.122911621119 +1403638209145096960.0000000000 -0.1340484574 8.7563103420 3.4097579827 0.5728761468 0.7916709027 0.1728993510 -0.123190570834 +1403638209195097088.0000000000 -0.1625013777 8.7164258493 3.4036909703 0.5723303001 0.7917818960 0.1737410864 -0.123828476943 +1403638209245096960.0000000000 -0.1899813473 8.6763300104 3.3962606920 0.5723323736 0.7916063301 0.1739481680 -0.124647932449 +1403638209295097088.0000000000 -0.2167470576 8.6362989068 3.3871993944 0.5718173609 0.7918023996 0.1735874159 -0.126258761062 +1403638209345096960.0000000000 -0.2424612746 8.5960422679 3.3765070381 0.5708752032 0.7924089426 0.1736507170 -0.126629374487 +1403638209395097088.0000000000 -0.2674585812 8.5553920184 3.3646230863 0.5710758810 0.7921685215 0.1731516316 -0.12790576248 +1403638209445096960.0000000000 -0.2914207686 8.5146745733 3.3508570180 0.5705476189 0.7924618923 0.1732291104 -0.128340325926 +1403638209495097088.0000000000 -0.3144846220 8.4748532390 3.3359538764 0.5723904631 0.7911687679 0.1723061381 -0.129351201068 +1403638209545096960.0000000000 -0.3366772747 8.4354230523 3.3177395446 0.5741819692 0.7898868523 0.1721934016 -0.129395746708 +1403638209595097088.0000000000 -0.3578321043 8.3962115159 3.2951830592 0.5751913992 0.7892513103 0.1713309604 -0.129934311798 +1403638209645096960.0000000000 -0.3781889096 8.3568833238 3.2675469722 0.5748430141 0.7896310153 0.1703853539 -0.130411655778 +1403638209695097088.0000000000 -0.3974411465 8.3178187135 3.2352820747 0.5738876379 0.7905083077 0.1699052592 -0.129929970974 +1403638209745096960.0000000000 -0.4156757088 8.2789430177 3.1982252645 0.5737283737 0.7907418429 0.1700317700 -0.129043745628 +1403638209795097088.0000000000 -0.4328445295 8.2403291313 3.1566849116 0.5749223347 0.7899811784 0.1716276898 -0.126245724136 +1403638209845096960.0000000000 -0.4494942064 8.2017825676 3.1112563488 0.5756167521 0.7895609907 0.1723477575 -0.124719874603 +1403638209895097088.0000000000 -0.4651090058 8.1629009359 3.0635448712 0.5775460107 0.7882671068 0.1728591805 -0.123269126388 +1403638209945096960.0000000000 -0.4800406900 8.1238242377 3.0146477854 0.5803275146 0.7863049045 0.1727918135 -0.122831438302 +1403638209995097088.0000000000 -0.4942393881 8.0843647069 2.9647284241 0.5834011073 0.7840701845 0.1728294006 -0.122503437267 +1403638210045096960.0000000000 -0.5076696351 8.0444048268 2.9150355127 0.5869275138 0.7814920811 0.1725338521 -0.122549135652 +1403638210095097088.0000000000 -0.5203436861 8.0038689125 2.8667326425 0.5901845937 0.7790968823 0.1716491223 -0.123396807821 +1403638210145096960.0000000000 -0.5318217367 7.9621286917 2.8203667357 0.5926093776 0.7772701012 0.1706179163 -0.124719052163 +1403638210195097088.0000000000 -0.5428365785 7.9157098894 2.7776007037 0.5959259268 0.7747389283 0.1702346506 -0.125188044512 +1403638210245096960.0000000000 -0.5520694961 7.8733778941 2.7340042634 0.5958354114 0.7748059284 0.1693273055 -0.126428633674 +1403638210295097088.0000000000 -0.5595395450 7.8290587547 2.6915049626 0.5957958999 0.7748564148 0.1695051118 -0.126066645521 +1403638210345096960.0000000000 -0.5654711927 7.7833777647 2.6501568538 0.5959987940 0.7747372664 0.1702543276 -0.124824154495 +1403638210395097088.0000000000 -0.5704252714 7.7361709405 2.6085195838 0.5948884593 0.7756167055 0.1695820417 -0.125572203114 +1403638210445096960.0000000000 -0.5740797490 7.6880211059 2.5659541156 0.5946895237 0.7757853835 0.1698520201 -0.125106756179 +1403638210495097088.0000000000 -0.5767869506 7.6388259389 2.5225712262 0.5951491679 0.7754690360 0.1686529148 -0.126496784803 +1403638210545096960.0000000000 -0.5782221349 7.5889339470 2.4776382007 0.5955711851 0.7752087127 0.1686363116 -0.126127751581 +1403638210595097088.0000000000 -0.5785067289 7.5379051309 2.4312107176 0.5961737841 0.7748493701 0.1683208299 -0.125910170631 +1403638210645096960.0000000000 -0.5780192363 7.4859137048 2.3838158591 0.5972248245 0.7740799972 0.1675639101 -0.126668871058 +1403638210695097088.0000000000 -0.5762077202 7.4322447095 2.3358942497 0.5970385802 0.7742918217 0.1660648915 -0.128216849457 +1403638210745096960.0000000000 -0.5727221830 7.3769718348 2.2887656399 0.5973258504 0.7741160488 0.1660454705 -0.127965124631 +1403638210795097088.0000000000 -0.5677056109 7.3196470211 2.2428890236 0.5972866548 0.7741943997 0.1657450617 -0.128063492387 +1403638210845096960.0000000000 -0.5611235729 7.2598765601 2.1987492979 0.5957837130 0.7753680159 0.1655756875 -0.128183068063 +1403638210895097088.0000000000 -0.5535232477 7.1995295436 2.1561928850 0.5931656143 0.7772888605 0.1649918295 -0.129438315861 +1403638210945096960.0000000000 -0.5442236510 7.1383318679 2.1152765209 0.5903148930 0.7794666688 0.1658623901 -0.128256410216 +1403638210995097088.0000000000 -0.5335700598 7.0755092598 2.0761848623 0.5877758728 0.7813007331 0.1656087966 -0.129082974431 +1403638211045096960.0000000000 -0.5215592611 7.0115064168 2.0389460529 0.5855233378 0.7829240679 0.1656852966 -0.129385884883 +1403638211095097088.0000000000 -0.5083926711 6.9468658765 2.0043159180 0.5832403591 0.7845841802 0.1659705903 -0.12927532956 +1403638211145096960.0000000000 -0.4942998684 6.8822979517 1.9723479885 0.5810618410 0.7861255514 0.1661590681 -0.129479412795 +1403638211195097088.0000000000 -0.4792659453 6.8178938934 1.9417130502 0.5789484472 0.7875991118 0.1656489247 -0.130639841622 +1403638211245096960.0000000000 -0.4633344499 6.7543973589 1.9129635098 0.5779675808 0.7883058726 0.1660411079 -0.130221646757 +1403638211295097088.0000000000 -0.4467497520 6.6918674962 1.8863591907 0.5774049499 0.7889003212 0.1657600238 -0.129473632207 +1403638211345096960.0000000000 -0.4284767998 6.6290752010 1.8612680345 0.5770015990 0.7897593081 0.1640272878 -0.128235872104 +1403638211395097088.0000000000 -0.4090598634 6.5663285331 1.8355621286 0.5778723072 0.7901922657 0.1608739811 -0.12561585087 +1403638211445096960.0000000000 -0.3886365517 6.5036460580 1.8083432112 0.5773381838 0.7919671702 0.1561554689 -0.122817312718 +1403638211495097088.0000000000 -0.3668368528 6.4402233139 1.7803512334 0.5781723578 0.7929998343 0.1506453364 -0.119054483743 +1403638211545096960.0000000000 -0.3441541889 6.3771012726 1.7510018991 0.5785130409 0.7945722896 0.1439857077 -0.115089765457 +1403638211595097088.0000000000 -0.3204227611 6.3145364266 1.7204240843 0.5794405328 0.7959268069 0.1351428662 -0.11173894927 +1403638211645096960.0000000000 -0.2955080607 6.2522712485 1.6885355380 0.5808504673 0.7970239919 0.1256393274 -0.107611572105 +1403638211695097088.0000000000 -0.2691532690 6.1902859107 1.6546861466 0.5825451463 0.7981175694 0.1147042081 -0.102432624742 +1403638211745096960.0000000000 -0.2418108014 6.1290799448 1.6199531288 0.5823837855 0.8005341241 0.1032085189 -0.0965517691295 +1403638211795097088.0000000000 -0.2129269529 6.0680657007 1.5851160609 0.5828504796 0.8024649972 0.0901937948 -0.0905556519765 +1403638211845096960.0000000000 -0.1831173762 6.0073286202 1.5506142525 0.5822673728 0.8048615876 0.0762104681 -0.0857583575618 +1403638211895097088.0000000000 -0.1516560839 5.9474478632 1.5175572674 0.5828319201 0.8062407766 0.0632501431 -0.0792602203978 +1403638211945096960.0000000000 -0.1183449818 5.8876432591 1.4860826100 0.5833892605 0.8074428405 0.0507925703 -0.0715062575011 +1403638211995097088.0000000000 -0.0834360636 5.8276700891 1.4566035623 0.5834266715 0.8087217829 0.0386977239 -0.0639130892821 +1403638212045096960.0000000000 -0.0469660627 5.7673943725 1.4285290007 0.5839188927 0.8093992813 0.0269879923 -0.0564196629391 +1403638212095097088.0000000000 -0.0086197889 5.7077874542 1.4021326072 0.5845012924 0.8098580264 0.0165570354 -0.0470540212019 +1403638212145096960.0000000000 0.0310558036 5.6483550571 1.3777362345 0.5848922366 0.8102075692 0.0065855961 -0.0377014106545 +1403638212195097088.0000000000 0.0722741787 5.5891174476 1.3554876738 0.5860570980 0.8098050640 -0.0029057244 -0.0272835653798 +1403638212245096960.0000000000 0.1144206897 5.5296540308 1.3350806261 0.5860773132 0.8099287148 -0.0137231494 -0.0184535886422 +1403638212295097088.0000000000 0.1576316313 5.4694529983 1.3176587590 0.5864718430 0.8095534330 -0.0240457016 -0.00978880468594 +1403638212345096960.0000000000 0.2018244096 5.4090074114 1.3013248795 0.5855738089 0.8098942993 -0.0342480836 -0.00126770033256 +1403638212395097088.0000000000 0.2468750481 5.3498798842 1.2859431114 0.5864292582 0.8087733537 -0.0436669387 0.0089210897748 +1403638212445096960.0000000000 0.2928063436 5.2902483668 1.2729991300 0.5854027407 0.8087519604 -0.0540995839 0.01723753735 +1403638212495097088.0000000000 0.3396694459 5.2299230729 1.2633518985 0.5865415048 0.8069128311 -0.0651999758 0.024692291014 +1403638212545096960.0000000000 0.3871066132 5.1689188738 1.2546225831 0.5857194951 0.8062613515 -0.0769345198 0.0309254873429 +1403638212595097088.0000000000 0.4355130491 5.1084190581 1.2470537817 0.5845898349 0.8056597506 -0.0871998331 0.0395383392242 +1403638212645096960.0000000000 0.4843719708 5.0470638000 1.2412812653 0.5835549201 0.8046782438 -0.0994061346 0.0455521631083 +1403638212695097088.0000000000 0.5341644474 4.9852404202 1.2370806571 0.5821915311 0.8037729475 -0.1100110745 0.0538482446174 +1403638212745096960.0000000000 0.5845545210 4.9234910111 1.2348734477 0.5795176299 0.8035653668 -0.1200637373 0.0634564175285 +1403638212795097088.0000000000 0.6355571706 4.8616746572 1.2355752990 0.5796288522 0.8010001092 -0.1316501306 0.0713965121943 +1403638212845096960.0000000000 0.6873104997 4.7993269325 1.2368527285 0.5779408009 0.7994315425 -0.1433466093 0.0796579502574 +1403638212895097088.0000000000 0.7395180822 4.7371163391 1.2394385440 0.5760485582 0.7976479826 -0.1563544991 0.0864813572052 +1403638212945096960.0000000000 0.7926397500 4.6749002829 1.2434684842 0.5744296024 0.7953482918 -0.1682820847 0.0955660322651 +1403638212995097088.0000000000 0.8465731228 4.6129892561 1.2490785971 0.5712533305 0.7937983302 -0.1808207744 0.104200244242 +1403638213045096960.0000000000 0.9013495501 4.5513461230 1.2573989920 0.5695984912 0.7907429115 -0.1937213958 0.112939043235 +1403638213095097088.0000000000 0.9565914240 4.4894349487 1.2661540217 0.5668793783 0.7881518818 -0.2070542069 0.120801229356 +1403638213145096960.0000000000 1.0121937266 4.4274485878 1.2752538154 0.5637279523 0.7854808122 -0.2214096817 0.127312380753 +1403638213195097088.0000000000 1.0684827033 4.3650191215 1.2827083659 0.5588247344 0.7837488831 -0.2360325637 0.133196220739 +1403638213245096960.0000000000 1.1252664688 4.3019299061 1.2894219094 0.5528178113 0.7824403330 -0.2516208888 0.137355455449 +1403638213295097088.0000000000 1.1832101628 4.2388137140 1.2944444936 0.5470746567 0.7805267883 -0.2676606561 0.140872374411 +1403638213345096960.0000000000 1.2421699483 4.1754771657 1.2976726893 0.5404874829 0.7788612308 -0.2838533822 0.143790546963 +1403638213395097088.0000000000 1.3028159250 4.1121905659 1.2997636385 0.5352630969 0.7758727346 -0.2998729845 0.146939137197 +1403638213445096960.0000000000 1.3654109485 4.0488058731 1.3005518792 0.5302914319 0.7725111404 -0.3157788905 0.149335955636 +1403638213495097088.0000000000 1.4307284273 3.9854686913 1.3000945105 0.5273042241 0.7676197098 -0.3303714177 0.15350883625 +1403638213545096960.0000000000 1.4988278647 3.9219715524 1.2977751374 0.5245948922 0.7629930408 -0.3421829008 0.159852060258 +1403638213595097088.0000000000 1.5698811636 3.8583843217 1.2944499431 0.5248847328 0.7574076623 -0.3484513638 0.17149722258 +1403638213645096960.0000000000 1.6430050369 3.7943919814 1.2909633195 0.5266280194 0.7518243234 -0.3506148819 0.18572108244 +1403638213695097088.0000000000 1.7172679494 3.7301262697 1.2887890436 0.5290731402 0.7464998745 -0.3511522918 0.198775294455 +1403638213745096960.0000000000 1.7922227181 3.6650436789 1.2874106826 0.5306919457 0.7424242099 -0.3501574298 0.211097431661 +1403638213795097088.0000000000 1.8675817990 3.5998447407 1.2876040012 0.5313174282 0.7394855583 -0.3492815063 0.221055035761 +1403638213845096960.0000000000 1.9429890158 3.5343790191 1.2895427172 0.5310912186 0.7377273791 -0.3484433582 0.228664946639 +1403638213895097088.0000000000 2.0181970826 3.4691845520 1.2932610351 0.5311121021 0.7363891835 -0.3485966963 0.232661231849 +1403638213945096960.0000000000 2.0930307144 3.4033180896 1.2977208381 0.5289369362 0.7370021813 -0.3477295801 0.236933833306 +1403638213995097088.0000000000 2.1667098206 3.3372224502 1.3040464350 0.5285200386 0.7370078869 -0.3486091230 0.236553636238 +1403638214045096960.0000000000 2.2398193820 3.2707683463 1.3110773976 0.5248024602 0.7396012180 -0.3485709882 0.236792487761 +1403638214095097088.0000000000 2.3125060588 3.2046417107 1.3188598065 0.5198815931 0.7432866475 -0.3487848884 0.23579056477 +1403638214145096960.0000000000 2.3849693052 3.1386492507 1.3288648852 0.5160798499 0.7464329137 -0.3491153677 0.233704843485 +1403638214195097088.0000000000 2.4573761434 3.0739350841 1.3394403765 0.5110246529 0.7507298567 -0.3490082033 0.231196367633 +1403638214245096960.0000000000 2.5302103365 3.0101375335 1.3502439703 0.5077348789 0.7538339499 -0.3485093930 0.229087039706 +1403638214295097088.0000000000 2.6028464556 2.9472027773 1.3593206194 0.5046573998 0.7568333189 -0.3481941993 0.226461996489 +1403638214345096960.0000000000 2.6764572756 2.8858073318 1.3671702615 0.5022822890 0.7594061233 -0.3473651232 0.224393211234 +1403638214395097088.0000000000 2.7509174228 2.8256263140 1.3731657338 0.5005825583 0.7615714073 -0.3458479789 0.223193345431 +1403638214445096960.0000000000 2.8263678673 2.7671188631 1.3781487728 0.5007919739 0.7625523848 -0.3438031049 0.222532434617 +1403638214495097088.0000000000 2.9028611734 2.7100429702 1.3824416907 0.5041189441 0.7614093969 -0.3409963150 0.223251727087 +1403638214545096960.0000000000 2.9799928816 2.6543775673 1.3852576396 0.5087521785 0.7592332242 -0.3381666102 0.224453727614 +1403638214595097088.0000000000 3.0577535076 2.5999326714 1.3865882329 0.5131959017 0.7570902625 -0.3351577388 0.226083150505 +1403638214645096960.0000000000 3.1355646541 2.5467205391 1.3866320540 0.5181120020 0.7546045575 -0.3325113909 0.227086085144 +1403638214695097088.0000000000 3.2131719362 2.4940703241 1.3854392619 0.5227229293 0.7522734792 -0.3296171448 0.228468574395 +1403638214745096960.0000000000 3.2901950650 2.4418818996 1.3831280614 0.5271227069 0.7500430497 -0.3269303897 0.229550856691 +1403638214795097088.0000000000 3.3664165812 2.3899581422 1.3794184367 0.5303158188 0.7486057603 -0.3248773725 0.229802612726 +1403638214845096960.0000000000 3.4418376043 2.3382210958 1.3744647189 0.5330219904 0.7474331098 -0.3227109050 0.230410451259 +1403638214895097088.0000000000 3.5165371172 2.2864887057 1.3679079906 0.5347378472 0.7468432467 -0.3211402065 0.230541899682 +1403638214945096960.0000000000 3.5906195375 2.2350967690 1.3599080394 0.5366119682 0.7460072519 -0.3196456382 0.230970651135 +1403638214995097088.0000000000 3.6638994069 2.1840041852 1.3505289761 0.5374381991 0.7458541109 -0.3188018031 0.230710289815 +1403638215045096960.0000000000 3.7365319303 2.1332345291 1.3399491506 0.5380755453 0.7457476069 -0.3182448696 0.23033761595 +1403638215095097088.0000000000 3.8082025523 2.0823462317 1.3280725622 0.5375858126 0.7464374804 -0.3169507478 0.231029879849 +1403638215145096960.0000000000 3.8789163249 2.0314789967 1.3152919019 0.5375581122 0.7466614415 -0.3166529607 0.230778834193 +1403638215195097088.0000000000 3.9486867448 1.9804998999 1.3011906652 0.5359526375 0.7479350746 -0.3165119723 0.230582015738 +1403638215245096960.0000000000 4.0177970874 1.9296565506 1.2863249385 0.5343144266 0.7490900454 -0.3160467146 0.231271856487 +1403638215295097088.0000000000 4.0863770432 1.8790862675 1.2708474625 0.5321239568 0.7506446229 -0.3149481477 0.232775447558 +1403638215345096960.0000000000 4.1542046405 1.8289863339 1.2550344129 0.5306425720 0.7515559460 -0.3142316055 0.234180739715 +1403638215395097088.0000000000 4.2213339606 1.7795343818 1.2392844760 0.5296991309 0.7521211922 -0.3128645493 0.236322484585 +1403638215445096960.0000000000 4.2875435161 1.7308734127 1.2254708024 0.5292144200 0.7524450653 -0.3105375855 0.239426250136 +1403638215495097088.0000000000 4.3522074485 1.6827195555 1.2137608472 0.5286857537 0.7527878349 -0.3101049368 0.24007660781 +1403638215545096960.0000000000 4.4153227179 1.6353838462 1.2042263703 0.5284592084 0.7528670024 -0.3101229656 0.240303741045 +1403638215595097088.0000000000 4.4772166600 1.5886488637 1.1967082755 0.5297178755 0.7519050705 -0.3089021071 0.24210994524 +1403638215645096960.0000000000 4.5372097240 1.5427190060 1.1910763949 0.5312454232 0.7509253068 -0.3094878444 0.241053434178 +1403638215695097088.0000000000 4.5955232727 1.4973264215 1.1869375399 0.5319166895 0.7504394965 -0.3106153607 0.239631582399 +1403638215745096960.0000000000 4.6522515864 1.4526977065 1.1836309321 0.5334340739 0.7493620028 -0.3122403639 0.237509226503 +1403638215795097088.0000000000 4.7081250750 1.4083324526 1.1794052206 0.5335924188 0.7485246298 -0.3140806469 0.237367555695 +1403638215845096960.0000000000 4.7629532249 1.3639186439 1.1738876027 0.5335724165 0.7472283654 -0.3176085536 0.236801716331 +1403638215895097088.0000000000 4.8166218891 1.3197263065 1.1669327666 0.5329202220 0.7464155945 -0.3194943278 0.238292198251 +1403638215945096960.0000000000 4.8694112415 1.2755566790 1.1586317695 0.5327392607 0.7452833424 -0.3218064199 0.239128099106 +1403638215995097088.0000000000 4.9213418675 1.2314599176 1.1491014511 0.5325141250 0.7443739937 -0.3238197771 0.239743229589 +1403638216045096960.0000000000 4.9728395213 1.1875137287 1.1382622100 0.5320981051 0.7436778327 -0.3255173446 0.24052722524 +1403638216095097088.0000000000 5.0237127775 1.1440530327 1.1272827489 0.5313277815 0.7432910244 -0.3257507047 0.243096112758 +1403638216145096960.0000000000 5.0733562202 1.1008971258 1.1175547762 0.5307163121 0.7429728341 -0.3270778983 0.243621863291 +1403638216195097088.0000000000 5.1218721218 1.0578725684 1.1093601361 0.5302923744 0.7426536513 -0.3271709338 0.245386902455 +1403638216245096960.0000000000 5.1693138276 1.0151268718 1.1030577402 0.5310799565 0.7414357958 -0.3274060566 0.247047191094 +1403638216295097088.0000000000 5.2156769765 0.9726889801 1.0983790413 0.5306998896 0.7411559304 -0.3277261896 0.248276174337 +1403638216345096960.0000000000 5.2613759562 0.9309034353 1.0954476205 0.5312850329 0.7403398423 -0.3276158499 0.249601655943 +1403638216395097088.0000000000 5.3056631776 0.8892274038 1.0942139889 0.5317218834 0.7396217343 -0.3276022060 0.250815317381 +1403638216445096960.0000000000 5.3485442649 0.8478983055 1.0949153860 0.5320876572 0.7390359027 -0.3277031597 0.251633262145 +1403638216495097088.0000000000 5.3898384254 0.8068565839 1.0960979462 0.5320361970 0.7389597023 -0.3279157779 0.251688867546 +1403638216545096960.0000000000 5.4298568698 0.7657924296 1.0963309797 0.5312503394 0.7393050919 -0.3280031536 0.252220120529 +1403638216595097088.0000000000 5.4687607000 0.7250083313 1.0946088438 0.5301891455 0.7398474017 -0.3276630072 0.253302676449 +1403638216645096960.0000000000 5.5060257849 0.6839286197 1.0915103819 0.5280566763 0.7411637603 -0.3271507967 0.254567836179 +1403638216695097088.0000000000 5.5424183701 0.6436310684 1.0859458150 0.5266710048 0.7420969662 -0.3269205192 0.255015136032 +1403638216745096960.0000000000 5.5778305927 0.6036721948 1.0788235659 0.5253818165 0.7430508173 -0.3259038342 0.256195473648 +1403638216795097088.0000000000 5.6123488273 0.5645043128 1.0712173049 0.5263512242 0.7418207051 -0.3252236098 0.258623343564 +1403638216845096960.0000000000 5.6457872386 0.5261999427 1.0627181000 0.5282507993 0.7391278989 -0.3260113975 0.261452884528 +1403638216895097088.0000000000 5.6779323827 0.4883912629 1.0532059747 0.5292110110 0.7365219473 -0.3280037080 0.264357134465 +1403638216945096960.0000000000 5.7084438549 0.4506477243 1.0431107175 0.5290335922 0.7341233951 -0.3318074776 0.266627262228 +1403638216995097088.0000000000 5.7376956821 0.4130722572 1.0323804346 0.5284501380 0.7315469487 -0.3373739392 0.267877469505 +1403638217045096960.0000000000 5.7653147363 0.3752367234 1.0201988596 0.5265001987 0.7293313932 -0.3444502076 0.268751398254 +1403638217095097088.0000000000 5.7917140771 0.3373747412 1.0070268113 0.5233683637 0.7275070371 -0.3517869520 0.270305396253 +1403638217145096960.0000000000 5.8171133835 0.2995542717 0.9930976859 0.5200318015 0.7254428349 -0.3594797855 0.272165211767 +1403638217195097088.0000000000 5.8416304749 0.2620304145 0.9783602107 0.5169802890 0.7235791033 -0.3659099406 0.274362128211 +1403638217245096960.0000000000 5.8652810736 0.2249564042 0.9633807933 0.5135289167 0.7224893905 -0.3706548737 0.277330302916 +1403638217295097088.0000000000 5.8880875625 0.1885537196 0.9500648202 0.5111286123 0.7211895520 -0.3750142642 0.279280277487 +1403638217345096960.0000000000 5.9102111809 0.1526151601 0.9380355324 0.5087386951 0.7202635551 -0.3780564808 0.28191957814 +1403638217395097088.0000000000 5.9311309399 0.1172152090 0.9284452264 0.5062780167 0.7197406500 -0.3813078691 0.283302445195 +1403638217445096960.0000000000 5.9510812765 0.0821208650 0.9212568382 0.5049105829 0.7189458671 -0.3834514873 0.284863301135 +1403638217495097088.0000000000 5.9704318506 0.0473490711 0.9158352128 0.5028408050 0.7189329436 -0.3842979759 0.28740496367 +1403638217545096960.0000000000 5.9896016610 0.0131875038 0.9124189803 0.5003400398 0.7193711133 -0.3843730354 0.290555357214 +1403638217595097088.0000000000 6.0078006867 -0.0203708765 0.9109224041 0.4982786194 0.7199911309 -0.3840627626 0.292962426203 +1403638217645096960.0000000000 6.0254336673 -0.0530020401 0.9111937526 0.4960480678 0.7209870401 -0.3822220445 0.296682172053 +1403638217695097088.0000000000 6.0421835823 -0.0845660950 0.9135888898 0.4940559296 0.7217535083 -0.3804337375 0.30041768112 +1403638217745096960.0000000000 6.0578711231 -0.1149611670 0.9179405253 0.4916732941 0.7232663929 -0.3785477716 0.303058874611 +1403638217795097088.0000000000 6.0716994137 -0.1441680507 0.9239195776 0.4894755961 0.7247751497 -0.3767227688 0.30527787134 +1403638217845096960.0000000000 6.0843264688 -0.1716157294 0.9315019791 0.4874776894 0.7261145170 -0.3753677447 0.306956457324 +1403638217895097088.0000000000 6.0958330604 -0.1970013182 0.9400199975 0.4878663487 0.7261388265 -0.3745971249 0.307222760325 +1403638217945096960.0000000000 6.1067450735 -0.2206650641 0.9476662593 0.4884724827 0.7258925791 -0.3721026482 0.309861608454 +1403638217995097088.0000000000 6.1163100026 -0.2424039280 0.9541123199 0.4905466354 0.7250568355 -0.3712916292 0.309514312853 +1403638218045096960.0000000000 6.1248949543 -0.2627413770 0.9588069152 0.4914786574 0.7248486049 -0.3698170860 0.31028785362 +1403638218095097088.0000000000 6.1322342978 -0.2813981797 0.9620550948 0.4925041737 0.7244716153 -0.3688641548 0.310676282918 +1403638218145096960.0000000000 6.1384818407 -0.2984317026 0.9640534058 0.4944390156 0.7236294300 -0.3689593603 0.309450316571 +1403638218195097088.0000000000 6.1433519459 -0.3143344195 0.9643926781 0.4960291094 0.7229793199 -0.3679581363 0.309617240339 +1403638218245096960.0000000000 6.1468663921 -0.3288293670 0.9635688487 0.4988839172 0.7215892187 -0.3666677149 0.309804169517 +1403638218295097088.0000000000 6.1490080269 -0.3421335507 0.9617741260 0.5020133449 0.7200443605 -0.3654738844 0.309754031831 +1403638218345096960.0000000000 6.1493825223 -0.3540561356 0.9603301999 0.5060282332 0.7179062873 -0.3658103937 0.307780353088 +1403638218395097088.0000000000 6.1480387335 -0.3650469539 0.9594853732 0.5079845559 0.7172994280 -0.3665233069 0.305112908668 +1403638218445096960.0000000000 6.1443549477 -0.3755579815 0.9605605590 0.5094175746 0.7169681737 -0.3673398492 0.302509186359 +1403638218495097088.0000000000 6.1399363751 -0.3849395919 0.9634231414 0.5101832452 0.7168899950 -0.3682855590 0.300245796772 +1403638218545096960.0000000000 6.1337289902 -0.3938223272 0.9683856092 0.5096900273 0.7175874138 -0.3681743812 0.29955300827 +1403638218595097088.0000000000 6.1257114054 -0.4022939490 0.9754906880 0.5098604017 0.7177979842 -0.3690047090 0.297731337538 +1403638218645096960.0000000000 6.1162006965 -0.4106376877 0.9833338062 0.5085031510 0.7190709412 -0.3698516384 0.295924470982 +1403638218695097088.0000000000 6.1055102114 -0.4189642230 0.9907856660 0.5059310855 0.7206695139 -0.3721950822 0.293496182892 +1403638218745096960.0000000000 6.0943128383 -0.4272370494 0.9972167486 0.5018504863 0.7221524750 -0.3748384656 0.293492788631 +1403638218795097088.0000000000 6.0827627175 -0.4348722369 1.0028548606 0.4980793127 0.7226113077 -0.3788779161 0.293600784987 +1403638218845096960.0000000000 6.0708682873 -0.4417502577 1.0072654299 0.4945085443 0.7225556991 -0.3825852253 0.294962890311 +1403638218895097088.0000000000 6.0587123016 -0.4477322805 1.0102254966 0.4927245625 0.7213521548 -0.3867753546 0.295429178181 +1403638218945096960.0000000000 6.0457688582 -0.4520673863 1.0128044414 0.4940316960 0.7184439371 -0.3937069072 0.291145777606 +1403638218995097088.0000000000 6.0328526740 -0.4558347508 1.0141690046 0.4961759487 0.7150489336 -0.4004070359 0.286685639756 +1403638219045096960.0000000000 6.0199938429 -0.4592789553 1.0144508018 0.4987159436 0.7114599591 -0.4062630901 0.282944227353 +1403638219095097088.0000000000 6.0076695945 -0.4629571944 1.0137885243 0.5012188516 0.7080807042 -0.4105740080 0.280767453785 +1403638219145096960.0000000000 5.9959116203 -0.4670944060 1.0120165917 0.5017541499 0.7062464470 -0.4125327384 0.281558997126 +1403638219195097088.0000000000 5.9845705465 -0.4718690500 1.0093815741 0.5023278244 0.7048205079 -0.4116965795 0.285308140316 +1403638219245096960.0000000000 5.9734847701 -0.4774322801 1.0061697271 0.5035401154 0.7030109136 -0.4090776667 0.291339098436 +1403638219295097088.0000000000 5.9622104582 -0.4831650722 1.0020981419 0.5057154026 0.7005654678 -0.4068521256 0.296532131193 +1403638219345096960.0000000000 5.9506204186 -0.4890971302 0.9975961905 0.5078844695 0.6983741258 -0.4035795576 0.302407815258 +1403638219395097088.0000000000 5.9380043904 -0.4952229986 0.9941524032 0.5124990722 0.6945058625 -0.4014716786 0.306311604816 +1403638219445096960.0000000000 5.9255774174 -0.5017261588 0.9919905465 0.5154653207 0.6919224070 -0.3989206121 0.310485476476 +1403638219495097088.0000000000 5.9113176553 -0.5086940882 0.9906851510 0.5172296447 0.6904650135 -0.3974118482 0.312722533063 +1403638219545096960.0000000000 5.8957578268 -0.5159600109 0.9905748364 0.5175712130 0.6901465557 -0.3977195751 0.312469055643 +1403638219595097088.0000000000 5.8786223564 -0.5244809605 0.9923815169 0.5172849692 0.6904794472 -0.3991765794 0.310342475633 +1403638219645096960.0000000000 5.8600796378 -0.5331005071 0.9946802282 0.5161743347 0.6915181969 -0.4008692578 0.307685680097 +1403638219695097088.0000000000 5.8398786206 -0.5423962893 0.9977506730 0.5164972197 0.6915254867 -0.4034055033 0.303787957744 +1403638219745096960.0000000000 5.8183072355 -0.5526125447 0.9997861872 0.5152873900 0.6926127183 -0.4058328911 0.300110300755 +1403638219795097088.0000000000 5.7958119897 -0.5636009520 1.0011121754 0.5150810574 0.6929624142 -0.4090518541 0.295247654555 +1403638219845096960.0000000000 5.7726612220 -0.5756179282 1.0009274362 0.5143987990 0.6936054547 -0.4124589024 0.290143072685 +1403638219895097088.0000000000 5.7492259959 -0.5887561663 0.9993895376 0.5144854563 0.6936161004 -0.4154718392 0.285630130375 +1403638219945096960.0000000000 5.7260585079 -0.6029974550 0.9962776545 0.5142134359 0.6937511354 -0.4185081618 0.281326896954 +1403638219995097088.0000000000 5.7030410088 -0.6186236092 0.9918102699 0.5138673252 0.6940597070 -0.4209410989 0.27754294506 +1403638220045096960.0000000000 5.6806519016 -0.6357726611 0.9856594487 0.5127742791 0.6947764628 -0.4226414561 0.275177042864 +1403638220095097088.0000000000 5.6590389415 -0.6544072819 0.9787122187 0.5116148823 0.6956588581 -0.4231778024 0.274279990061 +1403638220145096960.0000000000 5.6387032848 -0.6746392811 0.9715734056 0.5091264523 0.6975166148 -0.4218972950 0.276158469205 +1403638220195097088.0000000000 5.6200779773 -0.6959081751 0.9662857504 0.5058414173 0.6998305221 -0.4189652382 0.280766504472 +1403638220245096960.0000000000 5.6022584204 -0.7182395081 0.9622982315 0.5017087715 0.7027707113 -0.4140312809 0.288062032169 +1403638220295097088.0000000000 5.5844815624 -0.7410905345 0.9598357581 0.4971145642 0.7059574104 -0.4102431388 0.29360145042 +1403638220345096960.0000000000 5.5666413147 -0.7637911030 0.9601119355 0.4947761154 0.7075856646 -0.4069956378 0.298116879254 +1403638220395097088.0000000000 5.5479278018 -0.7864839326 0.9623028969 0.4928622266 0.7086098465 -0.4051312325 0.301376169441 +1403638220445096960.0000000000 5.5286490871 -0.8087801121 0.9659187903 0.4918887186 0.7093013664 -0.4042878879 0.302470434582 +1403638220495097088.0000000000 5.5094367590 -0.8306881235 0.9713172203 0.4910604056 0.7096957306 -0.4031633830 0.304386160268 +1403638220545096960.0000000000 5.4897672360 -0.8518980471 0.9781097760 0.4917663440 0.7090230269 -0.4035682587 0.304277621257 +1403638220595097088.0000000000 5.4706271284 -0.8726843194 0.9848304833 0.4913098301 0.7089519463 -0.4033705781 0.305440608553 +1403638220645096960.0000000000 5.4511499000 -0.8927790358 0.9904923875 0.4912385345 0.7085746877 -0.4038539345 0.305791781566 +1403638220695097088.0000000000 5.4315285530 -0.9122793702 0.9945667101 0.4912316245 0.7081977300 -0.4040160362 0.306461268066 +1403638220745096960.0000000000 5.4116562638 -0.9313021733 0.9971170404 0.4910157719 0.7078907226 -0.4051945952 0.305960089823 +1403638220795097088.0000000000 5.3914318657 -0.9499380777 0.9980058880 0.4910253274 0.7075864654 -0.4059350179 0.305666948051 +1403638220845096960.0000000000 5.3711614237 -0.9681278890 0.9973317310 0.4917447613 0.7067489109 -0.4066793488 0.305458628811 +1403638220895097088.0000000000 5.3510865065 -0.9863090904 0.9948742042 0.4908397004 0.7069762834 -0.4070782219 0.305856574984 +1403638220945096960.0000000000 5.3306940709 -1.0038485707 0.9906717834 0.4906666965 0.7067027259 -0.4086298460 0.304695092106 +1403638220995097088.0000000000 5.3102843772 -1.0210826885 0.9847490212 0.4899383548 0.7070103466 -0.4090972507 0.304526218491 +1403638221045096960.0000000000 5.2898371768 -1.0377195438 0.9777728574 0.4896349624 0.7070559232 -0.4093708913 0.304540635204 +1403638221095097088.0000000000 5.2691178397 -1.0539225313 0.9699957100 0.4890979742 0.7070260632 -0.4101343091 0.304445670141 +1403638221145096960.0000000000 5.2482842047 -1.0697256557 0.9626557794 0.4881040575 0.7074775379 -0.4104270119 0.304597489059 +1403638221195097088.0000000000 5.2272465303 -1.0850543831 0.9568815443 0.4871598367 0.7079976722 -0.4112675443 0.30376569359 +1403638221245096960.0000000000 5.2063388483 -1.0998369459 0.9532554156 0.4863280493 0.7084118283 -0.4119423056 0.303218150536 +1403638221295097088.0000000000 5.1854939177 -1.1140797870 0.9516907146 0.4857669879 0.7087150716 -0.4132682679 0.301600264483 +1403638221345096960.0000000000 5.1643152460 -1.1282190676 0.9513469324 0.4849900076 0.7090670670 -0.4143033207 0.300601639261 +1403638221395097088.0000000000 5.1438160778 -1.1417883630 0.9524212075 0.4849751668 0.7088643617 -0.4158626070 0.298945975764 +1403638221445096960.0000000000 5.1236577642 -1.1549129153 0.9532034451 0.4850270474 0.7086845427 -0.4169163999 0.297818229201 +1403638221495097088.0000000000 5.1037881850 -1.1677273013 0.9527612407 0.4853400638 0.7083547250 -0.4178831016 0.296736110756 +1403638221545096960.0000000000 5.0844330065 -1.1803343080 0.9508561134 0.4858684095 0.7078508231 -0.4188157485 0.295757450877 +1403638221595097088.0000000000 5.0655618205 -1.1929338542 0.9476972150 0.4867656175 0.7068573616 -0.4194741453 0.29572511814 +1403638221645096960.0000000000 5.0473620136 -1.2053031730 0.9432437572 0.4872544808 0.7065123288 -0.4192104305 0.296118245177 +1403638221695097088.0000000000 5.0298477537 -1.2173860435 0.9383706579 0.4892727317 0.7050536581 -0.4193648678 0.296048375959 +1403638221745096960.0000000000 5.0129336269 -1.2292749431 0.9336754002 0.4913360185 0.7034654473 -0.4197836223 0.295815807417 +1403638221795097088.0000000000 4.9959628181 -1.2413036115 0.9296041665 0.4929168829 0.7026158503 -0.4197692311 0.295224839818 +1403638221845096960.0000000000 4.9796313625 -1.2535066709 0.9272109372 0.4931220705 0.7025783223 -0.4191994947 0.295780506978 +1403638221895097088.0000000000 4.9637864710 -1.2658183489 0.9269027595 0.4937305608 0.7022878089 -0.4175566116 0.297772468375 +1403638221945096960.0000000000 4.9478151684 -1.2785974003 0.9285207143 0.4935077860 0.7026058034 -0.4155141221 0.30023851264 +1403638221995097088.0000000000 4.9319274107 -1.2915120443 0.9318801513 0.4931559880 0.7029691511 -0.4142123633 0.301760935468 +1403638222045096960.0000000000 4.9162690250 -1.3043625897 0.9371095362 0.4918934401 0.7038138028 -0.4132540691 0.303163403017 +1403638222095097088.0000000000 4.9003807160 -1.3169555259 0.9424376001 0.4896374359 0.7054509453 -0.4125691838 0.303942122224 +1403638222145096960.0000000000 4.8843003919 -1.3294865897 0.9471712986 0.4870712675 0.7072461756 -0.4133557845 0.302822428078 +1403638222195097088.0000000000 4.8681765952 -1.3418185854 0.9506618661 0.4843471291 0.7090474096 -0.4139875295 0.302115797163 +1403638222245096960.0000000000 4.8521819092 -1.3535974363 0.9530212494 0.4821563975 0.7104783329 -0.4151871562 0.300608336878 +1403638222295097088.0000000000 4.8365948494 -1.3648454087 0.9541769721 0.4799925626 0.7118171489 -0.4163312645 0.299318834302 +1403638222345096960.0000000000 4.8215429045 -1.3755705499 0.9540530827 0.4778998732 0.7133117602 -0.4172086688 0.297884156499 +1403638222395097088.0000000000 4.8072747928 -1.3859159538 0.9529414301 0.4762663279 0.7142297703 -0.4182110877 0.296893425837 +1403638222445096960.0000000000 4.7936582428 -1.3954083714 0.9504407342 0.4743365399 0.7156098315 -0.4188187294 0.29580109512 +1403638222495097088.0000000000 4.7808480353 -1.4041909889 0.9470796048 0.4732535314 0.7163689613 -0.4190738387 0.295336628294 +1403638222545096960.0000000000 4.7690480308 -1.4122176971 0.9432344506 0.4749692244 0.7152011622 -0.4187963496 0.295805934748 +1403638222595097088.0000000000 4.7583308684 -1.4194413827 0.9388329826 0.4783177856 0.7130218377 -0.4173938657 0.297647973044 +1403638222645096960.0000000000 4.7482086919 -1.4259534446 0.9337794485 0.4827551878 0.7099549532 -0.4167417075 0.298726869026 +1403638222695097088.0000000000 4.7385649318 -1.4322478437 0.9278024765 0.4858894375 0.7077861267 -0.4160482882 0.299756693574 +1403638222745096960.0000000000 4.7291352538 -1.4384552393 0.9206733338 0.4873952901 0.7066492576 -0.4150740756 0.301340620658 +1403638222795097088.0000000000 4.7196967578 -1.4443295319 0.9128715317 0.4886660606 0.7057729135 -0.4146913888 0.301862763245 +1403638222845096960.0000000000 4.7104967434 -1.4498722009 0.9046861588 0.4905339159 0.7044608439 -0.4135751270 0.303425462291 +1403638222895097088.0000000000 4.7015314395 -1.4548444694 0.8968315002 0.4954321089 0.7010486587 -0.4114395238 0.306260219307 +1403638222945096960.0000000000 4.6920658519 -1.4596975718 0.8885682996 0.5003470005 0.6976128763 -0.4102116425 0.307758935275 +1403638222995097088.0000000000 4.6818024993 -1.4649761776 0.8798301471 0.5018514822 0.6966731136 -0.4098124463 0.307969838461 +1403638223045096960.0000000000 4.6709364584 -1.4705515892 0.8722757692 0.5011840317 0.6972852598 -0.4099913269 0.307432829573 +1403638223095097088.0000000000 4.6590618952 -1.4765787058 0.8666986788 0.4982949315 0.6993627064 -0.4105440148 0.30667177591 +1403638223145096960.0000000000 4.6456488684 -1.4833546001 0.8622950513 0.4934135474 0.7027314535 -0.4120871504 0.304788050897 +1403638223195097088.0000000000 4.6318246206 -1.4900167916 0.8589110107 0.4873856997 0.7069705033 -0.4158744384 0.299493470032 +1403638223245096960.0000000000 4.6183349213 -1.4962713965 0.8563990973 0.4824947181 0.7102189891 -0.4203121007 0.293471587159 +1403638223295097088.0000000000 4.6056011414 -1.5021888928 0.8542700955 0.4792427033 0.7124723090 -0.4226874989 0.289905016312 +1403638223345096960.0000000000 4.5942735165 -1.5075658990 0.8529159403 0.4805041633 0.7114366503 -0.4233447876 0.289400816212 +1403638223395097088.0000000000 4.5836990949 -1.5126483563 0.8509426218 0.4827980846 0.7097772148 -0.4243102778 0.288241397275 +1403638223445096960.0000000000 4.5739750239 -1.5175327642 0.8486498183 0.4875719673 0.7064294602 -0.4264226219 0.285297637447 +1403638223495097088.0000000000 4.5652726202 -1.5225103643 0.8464274786 0.4931645392 0.7024545815 -0.4290624487 0.281516808243 +1403638223545096960.0000000000 4.5575991500 -1.5285369612 0.8429072602 0.4964982915 0.6999707297 -0.4304073028 0.279785592588 +1403638223595097088.0000000000 4.5509886666 -1.5357751838 0.8383436503 0.4967893410 0.6998177488 -0.4289417518 0.281894382271 +1403638223645096960.0000000000 4.5455272919 -1.5440285204 0.8330142510 0.4953534122 0.7007722840 -0.4254731380 0.287255655819 +1403638223695097088.0000000000 4.5406302594 -1.5528258298 0.8271578795 0.4932443286 0.7022597145 -0.4221405127 0.29212790569 +1403638223745096960.0000000000 4.5362764970 -1.5619697085 0.8209259546 0.4903884910 0.7042155828 -0.4182756526 0.297733134092 +1403638223795097088.0000000000 4.5319469464 -1.5711910590 0.8142412211 0.4877778799 0.7058693393 -0.4158823881 0.301434992991 +1403638223845096960.0000000000 4.5274128242 -1.5802073665 0.8076953012 0.4862172849 0.7070359777 -0.4137525910 0.304140874413 +1403638223895097088.0000000000 4.5226845657 -1.5888924438 0.8008907221 0.4848860424 0.7079277517 -0.4123857705 0.306042154765 +1403638223945096960.0000000000 4.5181811788 -1.5970109178 0.7940853267 0.4839494328 0.7085470468 -0.4104101072 0.308735441745 +1403638223995097088.0000000000 4.5133495641 -1.6046370997 0.7867258021 0.4829275824 0.7092597180 -0.4100015537 0.309241537476 +1403638224045096960.0000000000 4.5081417854 -1.6117481956 0.7787679272 0.4805134938 0.7109515054 -0.4102660516 0.308766102576 +1403638224095097088.0000000000 4.5025629089 -1.6180841758 0.7703056921 0.4779343660 0.7128780983 -0.4117672740 0.306318903801 +1403638224145096960.0000000000 4.4968881430 -1.6239295904 0.7612974728 0.4739391371 0.7157512626 -0.4135743774 0.303377749228 +1403638224195097088.0000000000 4.4917856142 -1.6286044651 0.7523798429 0.4702602924 0.7181946283 -0.4155566714 0.300606696614 +1403638224245096960.0000000000 4.4874346062 -1.6319915834 0.7447555172 0.4700091745 0.7184155936 -0.4160424254 0.299798450583 +1403638224295097088.0000000000 4.4839397281 -1.6342438085 0.7379924854 0.4714139987 0.7175186856 -0.4155445170 0.300430577708 +1403638224345096960.0000000000 4.4811515476 -1.6352970567 0.7323212347 0.4758221074 0.7144575188 -0.4144553222 0.302275638929 +1403638224395097088.0000000000 4.4787453397 -1.6351151071 0.7266999786 0.4807260653 0.7108473820 -0.4154684764 0.301636196199 +1403638224445096960.0000000000 4.4764730420 -1.6342396210 0.7210261980 0.4865447698 0.7068700807 -0.4166358786 0.300039031776 +1403638224495097088.0000000000 4.4746627654 -1.6332051341 0.7153222911 0.4927426747 0.7025464445 -0.4157448888 0.301312690287 +1403638224545096960.0000000000 4.4726667858 -1.6325160766 0.7092460878 0.4960829594 0.7001342887 -0.4137730125 0.304147282264 +1403638224595097088.0000000000 4.4700102293 -1.6319317072 0.7026489801 0.4964381738 0.7000188073 -0.4130555110 0.304808060639 +1403638224645096960.0000000000 4.4669007986 -1.6317160129 0.6951902597 0.4925434727 0.7027673352 -0.4134158812 0.30431284771 +1403638224695097088.0000000000 4.4629173385 -1.6317174852 0.6876682875 0.4864237505 0.7071215147 -0.4154801940 0.301242936395 +1403638224745096960.0000000000 4.4588723040 -1.6315673281 0.6805735315 0.4792778424 0.7120274264 -0.4178410914 0.297856536306 +1403638224795097088.0000000000 4.4555318516 -1.6306246947 0.6750852979 0.4747653780 0.7150164405 -0.4192865278 0.295885337953 +1403638224845096960.0000000000 4.4532255676 -1.6282839746 0.6718739210 0.4758031548 0.7144427871 -0.4193580814 0.295502388108 +1403638224895097088.0000000000 4.4518040088 -1.6247418537 0.6706099489 0.4815499606 0.7105796561 -0.4201873410 0.294327685091 +1403638224945096960.0000000000 4.4510652154 -1.6207612179 0.6704511871 0.4883220514 0.7060634253 -0.4208179067 0.29313529804 +1403638224995097088.0000000000 4.4506701075 -1.6167186296 0.6713259181 0.4953085576 0.7013963825 -0.4215426207 0.291572231515 +1403638225045096960.0000000000 4.4506265394 -1.6134190853 0.6720966701 0.4993233902 0.6988313500 -0.4214625951 0.290998586214 +1403638225095097088.0000000000 4.4512956846 -1.6110222152 0.6730439753 0.5007194953 0.6979889811 -0.4197923894 0.293028529361 +1403638225145096960.0000000000 4.4519425629 -1.6097493363 0.6741538957 0.4988670011 0.6995788418 -0.4176469149 0.295452557628 +1403638225195097088.0000000000 4.4524271448 -1.6092092006 0.6754583218 0.4944650884 0.7029246820 -0.4166171277 0.296363521183 +1403638225245096960.0000000000 4.4525894387 -1.6089655018 0.6769067570 0.4888637613 0.7072446143 -0.4162393313 0.295908934384 +1403638225295097088.0000000000 4.4531664784 -1.6087863354 0.6791009226 0.4836315507 0.7109545531 -0.4164165082 0.295366616822 +1403638225345096960.0000000000 4.4544415585 -1.6079153505 0.6821003841 0.4828246874 0.7115788861 -0.4154750356 0.296506837875 +1403638225395097088.0000000000 4.4563684942 -1.6065305913 0.6846809980 0.4838487955 0.7110413406 -0.4141007947 0.298045444259 +1403638225445096960.0000000000 4.4589593783 -1.6044619313 0.6858501731 0.4875642777 0.7083296316 -0.4126447103 0.30045723691 +1403638225495097088.0000000000 4.4617891649 -1.6021598921 0.6855049370 0.4936414675 0.7041019506 -0.4095629555 0.30465838276 +1403638225545096960.0000000000 4.4645074314 -1.5999705031 0.6836297160 0.4999328872 0.6994027365 -0.4069968543 0.308636487097 +1403638225595097088.0000000000 4.4666528408 -1.5979686720 0.6802864769 0.5061686562 0.6946893150 -0.4040130374 0.313007208744 +1403638225645096960.0000000000 4.4675740653 -1.5961939647 0.6752992579 0.5121365032 0.6903268542 -0.4015281441 0.316133177697 +1403638225695097088.0000000000 4.4668021229 -1.5954053380 0.6664829770 0.5120862865 0.6903177772 -0.4011642322 0.316695848435 +1403638225745096960.0000000000 4.4642443282 -1.5952926260 0.6544316940 0.5090519420 0.6926941619 -0.4017326087 0.315676780148 +1403638225795097088.0000000000 4.4600929538 -1.5955715022 0.6399784607 0.5035022182 0.6968341020 -0.4043307860 0.312128765272 +1403638225845096960.0000000000 4.4549818871 -1.5961390519 0.6233016701 0.4951951864 0.7029056134 -0.4069392555 0.308392393461 +1403638225895097088.0000000000 4.4495211920 -1.5965127420 0.6050260318 0.4875819554 0.7083222669 -0.4094675926 0.304761699606 +1403638225945096960.0000000000 4.4438755814 -1.5963942932 0.5859733822 0.4823376031 0.7120861348 -0.4116156187 0.301423880526 +1403638225995097088.0000000000 4.4382028726 -1.5954832839 0.5659919275 0.4780964316 0.7150414413 -0.4151449850 0.29630082822 +1403638226045096960.0000000000 4.4331451797 -1.5909218941 0.5571146728 0.4706342666 0.7216426671 -0.4155134365 0.291691330267 +1403638226095097088.0000000000 4.4314535531 -1.5833953872 0.5660597734 0.4813292011 0.7145618769 -0.4257597718 0.276499802814 +1403638226145096960.0000000000 4.4308802886 -1.5767858953 0.5690192966 0.4820747212 0.7146871785 -0.4279840915 0.271396052765 +1403638226195097088.0000000000 4.4315517529 -1.5714071069 0.5640751862 0.4744146884 0.7204677903 -0.4251910233 0.273988065939 +1403638226245096960.0000000000 4.4331221163 -1.5663193536 0.5523825207 0.4652904640 0.7249336392 -0.4149829640 0.292856863568 +1403638226295097088.0000000000 4.4294022085 -1.5639826349 0.5554742141 0.4797551747 0.7131214473 -0.4209344085 0.290012064434 +1403638226345096960.0000000000 4.4263733436 -1.5624041737 0.5516408827 0.4718675813 0.7210420484 -0.4142518555 0.29297568228 +1403638226395097088.0000000000 4.4262216730 -1.5617447422 0.5511205349 0.4724204159 0.7216256331 -0.4123699871 0.293302557287 +1403638226445096960.0000000000 4.4270108288 -1.5613997764 0.5524373921 0.4722295672 0.7207154015 -0.4143439798 0.293065883846 +1403638226495097088.0000000000 4.4267213182 -1.5613056180 0.5528097378 0.4725117656 0.7207113331 -0.4142080557 0.292813067165 +1403638226545096960.0000000000 4.4266603155 -1.5607791130 0.5524503953 0.4732196501 0.7203418859 -0.4136003477 0.293437357055 +1403638226595097088.0000000000 4.4262663217 -1.5608618008 0.5527538978 0.4728210607 0.7203777086 -0.4137331712 0.293804466474 +1403638226645096960.0000000000 4.4264229969 -1.5605841087 0.5526822590 0.4733073932 0.7201454421 -0.4140701813 0.293115231298 +1403638226695097088.0000000000 4.4265433249 -1.5609685688 0.5527218552 0.4724628026 0.7207563792 -0.4136508431 0.293567917027 +1403638226745096960.0000000000 4.4262615215 -1.5607811898 0.5528513358 0.4727885231 0.7204156527 -0.4146584160 0.29245631772 +1403638226795097088.0000000000 4.4265273406 -1.5608496515 0.5523350353 0.4726154797 0.7205675536 -0.4135853124 0.293877863164 +1403638226845096960.0000000000 4.4260324935 -1.5607491856 0.5525739872 0.4730960791 0.7202843915 -0.4142929644 0.292799991373 +1403638226895097088.0000000000 4.4263561962 -1.5609992572 0.5522689531 0.4725367925 0.7206612555 -0.4137873636 0.293489952646 +1403638226945096960.0000000000 4.4264694369 -1.5608105147 0.5524651386 0.4726399450 0.7205123796 -0.4141956038 0.293113280136 +1403638226995097088.0000000000 4.4261466669 -1.5608290438 0.5523692612 0.4727104665 0.7204697990 -0.4145520903 0.292599808571 +1403638227045096960.0000000000 4.4261711870 -1.5610119609 0.5520443096 0.4725330562 0.7206265319 -0.4137602555 0.293619419165 +1403638227095097088.0000000000 4.4259835904 -1.5607489522 0.5522113142 0.4728530228 0.7203372687 -0.4146684112 0.292530933348 +1403638227145096960.0000000000 4.4263902015 -1.5609570109 0.5520966923 0.4724269764 0.7206350166 -0.4140780224 0.293321182737 +1403638227195097088.0000000000 4.4261546980 -1.5608495782 0.5520568190 0.4727668091 0.7204116818 -0.4145121733 0.292708406105 +1403638227245096960.0000000000 4.4262302677 -1.5610229470 0.5518861831 0.4725262179 0.7206318324 -0.4141604796 0.293052610807 +1403638227295097088.0000000000 4.4263113836 -1.5608694525 0.5518940261 0.4726099151 0.7205507356 -0.4143022858 0.292916577913 +1403638227345096960.0000000000 4.4260396796 -1.5608294064 0.5519564607 0.4726660221 0.7204989569 -0.4145037319 0.292668312098 +1403638227395097088.0000000000 4.4262890217 -1.5608467929 0.5518435628 0.4725151241 0.7206273719 -0.4141785602 0.293055913936 +1403638227445096960.0000000000 4.4261333672 -1.5607166926 0.5518662051 0.4726173366 0.7205204543 -0.4145322500 0.292653620811 +1403638227495097088.0000000000 4.4261888313 -1.5607683033 0.5519387301 0.4725070405 0.7206223075 -0.4143119451 0.292892811052 +1403638227545096960.0000000000 4.4260096415 -1.5607697351 0.5519794193 0.4726031266 0.7205775876 -0.4143829574 0.292747313651 +1403638227595097088.0000000000 4.4258321182 -1.5608420822 0.5521122602 0.4726344526 0.7205626985 -0.4143949888 0.292716355884 +1403638227645096960.0000000000 4.4256827638 -1.5609091842 0.5523300395 0.4725487375 0.7206066936 -0.4143110540 0.292865215373 +1403638227695097088.0000000000 4.4252461608 -1.5609127549 0.5525184891 0.4726017927 0.7205648505 -0.4145368621 0.292562867899 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_05_difficult.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_05_difficult.txt new file mode 100644 index 0000000000000000000000000000000000000000..e90d414ba7c557020f8068f83d077639d816dc85 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/MH_05_difficult.txt @@ -0,0 +1,2222 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403638519527829504.0000000000 4.4114848107 -1.6382993190 0.5566335472 0.5168054265 0.7809012394 -0.2896911447 0.197950615321 +1403638519577829376.0000000000 4.4117223430 -1.6383497358 0.5565030977 0.5168002679 0.7809096436 -0.2896862709 0.197938061343 +1403638519627829504.0000000000 4.4119381051 -1.6384016691 0.5564142755 0.5167891427 0.7809082410 -0.2897143265 0.197931579507 +1403638519677829376.0000000000 4.4120858172 -1.6384694491 0.5563356162 0.5167515536 0.7809305733 -0.2897342002 0.197912518047 +1403638519727829504.0000000000 4.4121811145 -1.6385157618 0.5562781838 0.5167334657 0.7809494262 -0.2897339123 0.197885772982 +1403638519777829376.0000000000 4.4122267628 -1.6385318947 0.5562435635 0.5167254954 0.7809495921 -0.2897742156 0.197846913171 +1403638519827829504.0000000000 4.4121863893 -1.6385343752 0.5562542470 0.5167106432 0.7809406892 -0.2898228566 0.197849596824 +1403638519877829376.0000000000 4.4122001584 -1.6385562898 0.5562100697 0.5166669416 0.7809634586 -0.2898573343 0.197823339358 +1403638519927829504.0000000000 4.4121636677 -1.6385266727 0.5562220406 0.5166864443 0.7809345942 -0.2899032465 0.197819072632 +1403638519977829376.0000000000 4.4121296012 -1.6384938939 0.5562095640 0.5166655216 0.7809550159 -0.2899085875 0.197785269463 +1403638520027829504.0000000000 4.4120761491 -1.6384616660 0.5561955235 0.5166655796 0.7809462002 -0.2899559476 0.197750498644 +1403638520077829376.0000000000 4.4120325809 -1.6384421205 0.5561908291 0.5166615517 0.7809350071 -0.2899870764 0.197759579238 +1403638520127829504.0000000000 4.4120039665 -1.6384345784 0.5561990170 0.5166657332 0.7809292265 -0.2900106023 0.197736981784 +1403638520177829376.0000000000 4.4119689471 -1.6384299928 0.5562079993 0.5166398689 0.7809374057 -0.2900462577 0.197719959922 +1403638520227829504.0000000000 4.4119255241 -1.6384288292 0.5562099064 0.5166215626 0.7809423638 -0.2900673862 0.197717214283 +1403638520277829376.0000000000 4.4119022414 -1.6384292971 0.5562381933 0.5166083002 0.7809436023 -0.2900896915 0.197714251338 +1403638520327829504.0000000000 4.4118440464 -1.6384462865 0.5563290931 0.5166186210 0.7809457101 -0.2900665342 0.197712933419 +1403638520377829376.0000000000 4.4119220659 -1.6384779560 0.5562922494 0.5166337326 0.7809269140 -0.2901249375 0.197661989116 +1403638520427829504.0000000000 4.4119466369 -1.6384952992 0.5563160635 0.5166374180 0.7809213102 -0.2901194647 0.197682527485 +1403638520477829376.0000000000 4.4119496605 -1.6384785402 0.5563516989 0.5166455531 0.7809006033 -0.2901931292 0.19763493624 +1403638520527829504.0000000000 4.4119552063 -1.6384793724 0.5563777482 0.5166240299 0.7808948820 -0.2902333710 0.197654712704 +1403638520577829376.0000000000 4.4118906473 -1.6384580420 0.5564528330 0.5166168047 0.7808853695 -0.2902926414 0.197624136184 +1403638520627829504.0000000000 4.4119498586 -1.6384631461 0.5564164153 0.5166037641 0.7808807509 -0.2903215640 0.197633987979 +1403638520677829376.0000000000 4.4119355563 -1.6384475924 0.5564024116 0.5165691967 0.7809006312 -0.2903444493 0.197612170439 +1403638520727829504.0000000000 4.4119154220 -1.6384401204 0.5563646056 0.5165462028 0.7809090498 -0.2903858255 0.197578208919 +1403638520777829376.0000000000 4.4119245016 -1.6384307470 0.5563398154 0.5165201483 0.7809166064 -0.2904100243 0.197580890098 +1403638520827829504.0000000000 4.4119132726 -1.6384314631 0.5563145851 0.5165217261 0.7809077820 -0.2904635297 0.197532985565 +1403638520877829376.0000000000 4.4119186588 -1.6384527633 0.5562584721 0.5165403830 0.7809048008 -0.2904191366 0.197561256037 +1403638520927829504.0000000000 4.4119210107 -1.6385060751 0.5561678938 0.5165583117 0.7809075444 -0.2903774671 0.197564785253 +1403638520977829376.0000000000 4.4119492191 -1.6385378578 0.5561556668 0.5165662851 0.7809104270 -0.2903924935 0.197510450008 +1403638521027829504.0000000000 4.4119648328 -1.6385572268 0.5561848558 0.5165775533 0.7808958222 -0.2903800204 0.197557055205 +1403638521077829376.0000000000 4.4119841951 -1.6385849392 0.5560895965 0.5165817088 0.7809013933 -0.2904047549 0.197487798127 +1403638521127829504.0000000000 4.4120361333 -1.6385874015 0.5561659150 0.5165546238 0.7808577793 -0.2905520837 0.19751439382 +1403638521177829376.0000000000 4.4120487612 -1.6386022810 0.5562408357 0.5165952769 0.7808235060 -0.2906695181 0.197370726304 +1403638521227829504.0000000000 4.4121243729 -1.6387431713 0.5561870151 0.5165048264 0.7808922555 -0.2904884853 0.197601845641 +1403638521277829376.0000000000 4.4122231177 -1.6387722593 0.5562380210 0.5165106519 0.7809184305 -0.2903796205 0.197643181939 +1403638521327829504.0000000000 4.4122827133 -1.6387973784 0.5563526704 0.5164545182 0.7809963408 -0.2902471638 0.197676579922 +1403638521377829376.0000000000 4.4122712318 -1.6387123106 0.5563281573 0.5165502852 0.7809016964 -0.2905058808 0.19742005142 +1403638521427829504.0000000000 4.4122928654 -1.6386702748 0.5563792876 0.5165153694 0.7809064242 -0.2905745862 0.197391589568 +1403638521477829376.0000000000 4.4122981495 -1.6385643661 0.5564629161 0.5164948573 0.7809154184 -0.2906410214 0.197311855524 +1403638521527829504.0000000000 4.4122982768 -1.6384396580 0.5565210533 0.5165158645 0.7807360392 -0.2911766385 0.197176986545 +1403638521577829376.0000000000 4.4122031404 -1.6382238054 0.5566523116 0.5168511200 0.7804114087 -0.2918507178 0.196586142785 +1403638521627829504.0000000000 4.4124217884 -1.6384619647 0.5564786216 0.5165175164 0.7807761251 -0.2909099244 0.197407481166 +1403638521677829376.0000000000 4.4123578211 -1.6385505629 0.5563708623 0.5165006959 0.7808675468 -0.2908261127 0.197213279799 +1403638521727829504.0000000000 4.4122979711 -1.6384838278 0.5564812975 0.5166906273 0.7806866992 -0.2911572629 0.196942940069 +1403638521777829376.0000000000 4.4124744782 -1.6385359849 0.5562855534 0.5165303681 0.7807662656 -0.2909777055 0.197312929691 +1403638521827829504.0000000000 4.4125095068 -1.6385423928 0.5562095060 0.5165942312 0.7808384010 -0.2907951293 0.197129359969 +1403638521877829376.0000000000 4.4126089522 -1.6385516579 0.5561137704 0.5167285978 0.7807610099 -0.2909039320 0.196923091304 +1403638521927829504.0000000000 4.4125002672 -1.6383614170 0.5559204944 0.5168979081 0.7808192676 -0.2909127497 0.1962335243 +1403638521977829376.0000000000 4.4126181916 -1.6379730424 0.5557556452 0.5177264588 0.7809053765 -0.2893055505 0.196082648818 +1403638522027829504.0000000000 4.4123155095 -1.6373367037 0.5550988442 0.5169677580 0.7821224562 -0.2883135374 0.19468976577 +1403638522077829376.0000000000 4.4122334669 -1.6371607265 0.5556865979 0.5148497997 0.7836617788 -0.2877034820 0.195014375318 +1403638522127829504.0000000000 4.4113510653 -1.6368383711 0.5584266493 0.5130823856 0.7853494935 -0.2874097430 0.193308764015 +1403638522177829376.0000000000 4.4104003678 -1.6359806251 0.5643406503 0.5143343233 0.7852013618 -0.2872134160 0.190859841356 +1403638522227829504.0000000000 4.4100471869 -1.6350787119 0.5732505875 0.5177547854 0.7836373780 -0.2861796710 0.189588074057 +1403638522277829376.0000000000 4.4100693646 -1.6336252584 0.5855414445 0.5228860975 0.7812507885 -0.2844066560 0.188016458053 +1403638522327829504.0000000000 4.4107475442 -1.6321904682 0.6011339311 0.5282202893 0.7787144960 -0.2825743949 0.186383397831 +1403638522377829376.0000000000 4.4115581435 -1.6311673144 0.6192995612 0.5317213031 0.7773917892 -0.2810022884 0.184315424664 +1403638522427829504.0000000000 4.4122268304 -1.6301735237 0.6395899303 0.5333967130 0.7776291389 -0.2798598332 0.180164765566 +1403638522477829376.0000000000 4.4128553969 -1.6291238659 0.6611511714 0.5334150041 0.7788685804 -0.2799540894 0.174521848804 +1403638522527829504.0000000000 4.4135401656 -1.6281934251 0.6836360211 0.5321156740 0.7805349930 -0.2812440166 0.168878172753 +1403638522577829376.0000000000 4.4141913508 -1.6268362432 0.7066318335 0.5320090085 0.7814749183 -0.2826570779 0.162383322101 +1403638522627829504.0000000000 4.4156628168 -1.6250651745 0.7297998191 0.5335469938 0.7813486688 -0.2820364235 0.158988424065 +1403638522677829376.0000000000 4.4177507543 -1.6223421458 0.7530075072 0.5366564179 0.7804862269 -0.2784414060 0.159095952783 +1403638522727829504.0000000000 4.4193351523 -1.6189134383 0.7769180400 0.5406337550 0.7793387063 -0.2733612000 0.160062419669 +1403638522777829376.0000000000 4.4206862887 -1.6156458940 0.8021182617 0.5456155065 0.7774910477 -0.2694318029 0.158801427457 +1403638522827829504.0000000000 4.4218491848 -1.6127178649 0.8281605437 0.5511093056 0.7750111559 -0.2678271616 0.154611943287 +1403638522877829376.0000000000 4.4231648074 -1.6098010449 0.8554633908 0.5567199958 0.7716706466 -0.2689573945 0.149161588073 +1403638522927829504.0000000000 4.4250142709 -1.6083101449 0.8823569592 0.5618346643 0.7680957067 -0.2709192073 0.144822575726 +1403638522977829376.0000000000 4.4276505510 -1.6077644692 0.9073487158 0.5657447672 0.7651843857 -0.2717545142 0.143440574061 +1403638523027829504.0000000000 4.4302081302 -1.6079944134 0.9288833349 0.5682443095 0.7632037497 -0.2724962214 0.142703365186 +1403638523077829376.0000000000 4.4327877165 -1.6086080541 0.9460457288 0.5693206014 0.7623118867 -0.2722680871 0.143613122576 +1403638523127829504.0000000000 4.4346766732 -1.6092878653 0.9590825176 0.5700618049 0.7619883774 -0.2716245680 0.143608305387 +1403638523177829376.0000000000 4.4365511902 -1.6112169633 0.9665658510 0.5704627628 0.7614973928 -0.2715590577 0.144739887969 +1403638523227829504.0000000000 4.4389086215 -1.6139853045 0.9677394823 0.5710190017 0.7604628677 -0.2713247468 0.148379271767 +1403638523277829376.0000000000 4.4420546067 -1.6165587633 0.9618095177 0.5712573011 0.7591404150 -0.2708783533 0.154905919784 +1403638523327829504.0000000000 4.4444836490 -1.6181048048 0.9503027068 0.5716323645 0.7580272569 -0.2711322628 0.158487897637 +1403638523377829376.0000000000 4.4462434630 -1.6195327006 0.9343074815 0.5714341894 0.7578226724 -0.2713876575 0.159738861178 +1403638523427829504.0000000000 4.4483535512 -1.6217610767 0.9148699282 0.5695465731 0.7591469032 -0.2708294121 0.161133826096 +1403638523477829376.0000000000 4.4501813627 -1.6250143254 0.8932691745 0.5654338518 0.7622159159 -0.2700996283 0.162350385336 +1403638523527829504.0000000000 4.4514141603 -1.6290419307 0.8702124732 0.5590577952 0.7668647600 -0.2694672034 0.163585597782 +1403638523577829376.0000000000 4.4523963446 -1.6335822568 0.8463260538 0.5513674277 0.7724327625 -0.2689047031 0.164413648309 +1403638523627829504.0000000000 4.4533246434 -1.6384947993 0.8223830969 0.5431514722 0.7779162943 -0.2690638236 0.165642314188 +1403638523677829376.0000000000 4.4540028220 -1.6434748778 0.7989339721 0.5366251635 0.7823357611 -0.2690135388 0.166180343865 +1403638523727829504.0000000000 4.4545485940 -1.6482298719 0.7763366488 0.5320039152 0.7855429317 -0.2685149439 0.166714911014 +1403638523777829376.0000000000 4.4546568558 -1.6509195051 0.7447254121 0.5291589357 0.7876534673 -0.2676293709 0.167234434214 +1403638523827829504.0000000000 4.4541807074 -1.6552472002 0.7222559068 0.5278828960 0.7887306889 -0.2667362110 0.16761665253 +1403638523877829376.0000000000 4.4537387219 -1.6602149497 0.6998797933 0.5272624497 0.7891910935 -0.2650241991 0.170099679559 +1403638523927829504.0000000000 4.4532650560 -1.6650573972 0.6796844234 0.5261259610 0.7897544967 -0.2625320969 0.174803335664 +1403638523977829376.0000000000 4.4522047435 -1.6693242414 0.6628441633 0.5241278380 0.7912341558 -0.2592934758 0.178900568917 +1403638524027829504.0000000000 4.4509858524 -1.6727589128 0.6505451722 0.5209138097 0.7936843159 -0.2557962633 0.182434320307 +1403638524077829376.0000000000 4.4496527442 -1.6753217476 0.6445400966 0.5170558047 0.7969501856 -0.2523955685 0.183902619523 +1403638524127829504.0000000000 4.4485867749 -1.6772846611 0.6458254090 0.5130816548 0.8003005432 -0.2500561502 0.183679551829 +1403638524177829376.0000000000 4.4477079250 -1.6784816077 0.6547398554 0.5104488874 0.8028703722 -0.2492486195 0.180876268624 +1403638524227829504.0000000000 4.4476684084 -1.6788540343 0.6707557233 0.5096541848 0.8042641479 -0.2487896712 0.177526031614 +1403638524277829376.0000000000 4.4486283960 -1.6786588000 0.6919347487 0.5108137213 0.8041686840 -0.2488009115 0.17458572718 +1403638524327829504.0000000000 4.4497147711 -1.6778256900 0.7168703222 0.5136877676 0.8030863217 -0.2491300753 0.17062075779 +1403638524377829376.0000000000 4.4513666137 -1.6761654182 0.7439288730 0.5176317476 0.8010674765 -0.2496961518 0.167332315038 +1403638524427829504.0000000000 4.4534754569 -1.6740486465 0.7723768907 0.5229365156 0.7979995209 -0.2500207734 0.164996297213 +1403638524477829376.0000000000 4.4557836556 -1.6717547136 0.8013973042 0.5290135653 0.7942743418 -0.2495234437 0.16435014053 +1403638524527829504.0000000000 4.4581887717 -1.6687766746 0.8303069053 0.5358231502 0.7899976577 -0.2484438718 0.164538430593 +1403638524577829376.0000000000 4.4607012010 -1.6652940977 0.8582414977 0.5420450308 0.7854937160 -0.2481881224 0.166100760449 +1403638524627829504.0000000000 4.4632515935 -1.6612820616 0.8849540243 0.5468440951 0.7812151320 -0.2495004579 0.168564452688 +1403638524677829376.0000000000 4.4660277982 -1.6570847791 0.9200214587 0.5496703744 0.7775066450 -0.2514398796 0.173562332758 +1403638524727829504.0000000000 4.4678013100 -1.6526131792 0.9425007602 0.5508391339 0.7746914251 -0.2529354322 0.180147471783 +1403638524777829376.0000000000 4.4696178000 -1.6482908911 0.9622916484 0.5508739461 0.7721216466 -0.2550807643 0.187882574999 +1403638524827829504.0000000000 4.4708918641 -1.6443852124 0.9785281457 0.5503962533 0.7704652936 -0.2568881614 0.193534669275 +1403638524877829376.0000000000 4.4711376355 -1.6408373786 0.9920688817 0.5515643077 0.7697753511 -0.2572861095 0.192422922741 +1403638524927829504.0000000000 4.4711963011 -1.6380979334 1.0017688481 0.5530660475 0.7694327363 -0.2566629163 0.190303333714 +1403638524977829376.0000000000 4.4707823571 -1.6365717236 1.0066900917 0.5553894800 0.7691769838 -0.2548080335 0.187035181645 +1403638525027829504.0000000000 4.4707200637 -1.6356535139 1.0058352750 0.5571367431 0.7685435698 -0.2527834883 0.18718957988 +1403638525077829376.0000000000 4.4710647901 -1.6348336231 0.9985693214 0.5578867554 0.7678533787 -0.2507662495 0.190472688402 +1403638525127829504.0000000000 4.4711067443 -1.6336575660 0.9858051090 0.5585978236 0.7676446503 -0.2483543870 0.192380510122 +1403638525177829376.0000000000 4.4711498581 -1.6329306272 0.9687220768 0.5586781488 0.7680938066 -0.2460590641 0.193301752188 +1403638525227829504.0000000000 4.4710097870 -1.6328298292 0.9484123639 0.5575668628 0.7695928997 -0.2437828335 0.193431880108 +1403638525277829376.0000000000 4.4712713793 -1.6326159828 0.9242771912 0.5549237891 0.7723548211 -0.2423124420 0.191865314719 +1403638525327829504.0000000000 4.4703678722 -1.6332830930 0.8989564573 0.5500075381 0.7768141955 -0.2410798084 0.189557219951 +1403638525377829376.0000000000 4.4685540309 -1.6342532465 0.8731932059 0.5436736872 0.7825107517 -0.2405796226 0.184979162303 +1403638525427829504.0000000000 4.4660577759 -1.6356133451 0.8477235630 0.5363563769 0.7886719380 -0.2414816435 0.178899488831 +1403638525477829376.0000000000 4.4630585930 -1.6372014423 0.8233509296 0.5293674034 0.7947891000 -0.2428385463 0.170616174853 +1403638525527829504.0000000000 4.4605113151 -1.6388589825 0.8004020584 0.5230407195 0.7997921831 -0.2445322035 0.164209838514 +1403638525577829376.0000000000 4.4585775747 -1.6405805404 0.7789471757 0.5182595215 0.8032370734 -0.2462852601 0.159877587434 +1403638525627829504.0000000000 4.4574007429 -1.6418951935 0.7594437194 0.5155911927 0.8047806935 -0.2481815141 0.157796366967 +1403638525677829376.0000000000 4.4575376014 -1.6423351404 0.7331848297 0.5144003846 0.8049903124 -0.2501205505 0.157551742283 +1403638525727829504.0000000000 4.4574848603 -1.6427397163 0.7159195914 0.5145471888 0.8038394248 -0.2524522161 0.159220753299 +1403638525777829376.0000000000 4.4573208113 -1.6425571395 0.7007038921 0.5161271792 0.8015135787 -0.2552313365 0.161386749363 +1403638525827829504.0000000000 4.4573279676 -1.6422985288 0.6875943163 0.5178835665 0.7989933530 -0.2570784118 0.165278321598 +1403638525877829376.0000000000 4.4577492169 -1.6425376780 0.6765874407 0.5194046532 0.7965811801 -0.2582338624 0.170271847366 +1403638525927829504.0000000000 4.4592201258 -1.6447523296 0.6679688015 0.5195913525 0.7951244603 -0.2587581580 0.175630676739 +1403638525977829376.0000000000 4.4619836793 -1.6492839012 0.6621169520 0.5187108436 0.7948584436 -0.2589476745 0.179123469305 +1403638526027829504.0000000000 4.4670307346 -1.6556969067 0.6589096253 0.5171869421 0.7952435281 -0.2591921636 0.181451977807 +1403638526077829376.0000000000 4.4743631390 -1.6637172557 0.6579462829 0.5149807623 0.7956401417 -0.2615705430 0.182571713168 +1403638526127829504.0000000000 4.4834129314 -1.6732493618 0.6596977322 0.5127630620 0.7955087284 -0.2660881061 0.182857936789 +1403638526177829376.0000000000 4.4941147590 -1.6842091763 0.6635076047 0.5112035563 0.7947723683 -0.2709660115 0.183262727521 +1403638526227829504.0000000000 4.5059542733 -1.6964161921 0.6687690080 0.5107133786 0.7932569275 -0.2753604941 0.184639893253 +1403638526277829376.0000000000 4.5175458366 -1.7095457804 0.6759946186 0.5114915329 0.7907962304 -0.2792258920 0.187218147813 +1403638526327829504.0000000000 4.5301773856 -1.7237908220 0.6829061116 0.5137683058 0.7876438851 -0.2825604149 0.189258686037 +1403638526377829376.0000000000 4.5426749922 -1.7392215699 0.6903947374 0.5165733978 0.7839310078 -0.2860750528 0.191742441286 +1403638526427829504.0000000000 4.5560818837 -1.7558712304 0.6972476139 0.5197497161 0.7797546459 -0.2900609207 0.194184415451 +1403638526477829376.0000000000 4.5698884181 -1.7733845859 0.7037418923 0.5230958963 0.7753322733 -0.2948520934 0.195685442436 +1403638526527829504.0000000000 4.5850751230 -1.7924403814 0.7091226785 0.5262494436 0.7709286500 -0.2994263258 0.197672494772 +1403638526577829376.0000000000 4.6016346225 -1.8130470588 0.7136265134 0.5296176187 0.7665037511 -0.3035022680 0.199658585577 +1403638526627829504.0000000000 4.6195789735 -1.8352410235 0.7174836077 0.5325858219 0.7623408388 -0.3067223614 0.202756457136 +1403638526677829376.0000000000 4.6383514623 -1.8591264777 0.7207163723 0.5346307486 0.7587481519 -0.3096785626 0.206325937406 +1403638526727829504.0000000000 4.6575996255 -1.8844487383 0.7234077695 0.5357171413 0.7559689305 -0.3121921521 0.209890878164 +1403638526777829376.0000000000 4.6778746035 -1.9111288295 0.7252675211 0.5353672335 0.7539423831 -0.3137326189 0.215695739605 +1403638526827829504.0000000000 4.6980707969 -1.9381631310 0.7264578388 0.5345196323 0.7525953665 -0.3148626096 0.220795185865 +1403638526877829376.0000000000 4.7175619198 -1.9653160165 0.7274472113 0.5331395045 0.7521406411 -0.3164090501 0.223454778141 +1403638526927829504.0000000000 4.7364452994 -1.9920825154 0.7283129761 0.5308753882 0.7523193972 -0.3190382924 0.22450259393 +1403638526977829376.0000000000 4.7553230490 -2.0182537878 0.7289338032 0.5269494165 0.7528362028 -0.3233316385 0.225873007927 +1403638527027829504.0000000000 4.7740567518 -2.0431302877 0.7298041305 0.5220508343 0.7529778358 -0.3295757849 0.227743512185 +1403638527077829376.0000000000 4.7924115322 -2.0666647928 0.7309944131 0.5167774324 0.7524876069 -0.3370045465 0.230502543525 +1403638527127829504.0000000000 4.8106469138 -2.0890991225 0.7327416071 0.5125133764 0.7511347197 -0.3446913110 0.233054869074 +1403638527177829376.0000000000 4.8279276530 -2.1093579612 0.7350386442 0.5095710198 0.7488291833 -0.3517172101 0.236404809878 +1403638527227829504.0000000000 4.8442194896 -2.1270106372 0.7375693535 0.5079902041 0.7453956478 -0.3581819618 0.240908619563 +1403638527277829376.0000000000 4.8593504168 -2.1416102735 0.7401407567 0.5068919492 0.7412136745 -0.3635485467 0.247982448533 +1403638527327829504.0000000000 4.8723837558 -2.1524610600 0.7423750038 0.5062146226 0.7370121408 -0.3674238280 0.256046071722 +1403638527377829376.0000000000 4.8823822373 -2.1593614254 0.7442781768 0.5056524256 0.7332385805 -0.3699302914 0.264250616028 +1403638527427829504.0000000000 4.8897896653 -2.1623577958 0.7454741596 0.5053101234 0.7301877186 -0.3716663403 0.270835201386 +1403638527477829376.0000000000 4.8934722356 -2.1612355485 0.7463935608 0.5049947872 0.7282008385 -0.3727746930 0.275214156603 +1403638527527829504.0000000000 4.8940773539 -2.1555455284 0.7466480317 0.5046092443 0.7272160654 -0.3734452151 0.277605792624 +1403638527577829376.0000000000 4.8912471832 -2.1457013740 0.7465038893 0.5042748956 0.7270650245 -0.3736627328 0.278315364006 +1403638527627829504.0000000000 4.8852442277 -2.1320096195 0.7458702881 0.5043064001 0.7275512360 -0.3729240934 0.277978190337 +1403638527677829376.0000000000 4.8764892685 -2.1149474080 0.7446778096 0.5049621977 0.7286938066 -0.3705793419 0.276928630703 +1403638527727829504.0000000000 4.8659369362 -2.0949397106 0.7434322008 0.5058327046 0.7303912703 -0.3672404968 0.275311250653 +1403638527777829376.0000000000 4.8540661905 -2.0727054970 0.7426587145 0.5066490819 0.7324242346 -0.3645072782 0.272021860236 +1403638527827829504.0000000000 4.8405026203 -2.0492341333 0.7430622647 0.5076861880 0.7347412833 -0.3628866070 0.265938510955 +1403638527877829376.0000000000 4.8251279821 -2.0240101349 0.7444432807 0.5093130934 0.7370241172 -0.3613583014 0.25848752696 +1403638527927829504.0000000000 4.8090360378 -1.9984331553 0.7463778580 0.5111556694 0.7385648817 -0.3598231264 0.252525473748 +1403638527977829376.0000000000 4.7924981258 -1.9726097511 0.7484060429 0.5130397518 0.7394069994 -0.3574669286 0.249569423756 +1403638528027829504.0000000000 4.7755208807 -1.9463523921 0.7499383644 0.5152978031 0.7399728498 -0.3541514328 0.247961929147 +1403638528077829376.0000000000 4.7580410076 -1.9202215396 0.7505979872 0.5182429441 0.7406170659 -0.3505663926 0.24497717655 +1403638528127829504.0000000000 4.7400282491 -1.8941144487 0.7503353966 0.5207624843 0.7419146516 -0.3467628620 0.241090444067 +1403638528177829376.0000000000 4.7235523636 -1.8685936914 0.7489899694 0.5224309402 0.7439008638 -0.3428576649 0.236909348009 +1403638528227829504.0000000000 4.7091701355 -1.8428088601 0.7470074142 0.5242100447 0.7463634255 -0.3385773225 0.231324151172 +1403638528277829376.0000000000 4.6980220517 -1.8168138843 0.7443646972 0.5261946924 0.7488404755 -0.3338711396 0.225581803394 +1403638528327829504.0000000000 4.6903719121 -1.7913462032 0.7411526907 0.5279308800 0.7506828221 -0.3296370726 0.221593517429 +1403638528377829376.0000000000 4.6861277113 -1.7669008439 0.7376605524 0.5298628744 0.7511943082 -0.3265268474 0.219846909265 +1403638528427829504.0000000000 4.6852027833 -1.7433515555 0.7339962477 0.5307407579 0.7511833636 -0.3243397428 0.221001206705 +1403638528477829376.0000000000 4.6866964058 -1.7204991960 0.7305421114 0.5304537776 0.7514403754 -0.3233833395 0.222214688671 +1403638528527829504.0000000000 4.6900558157 -1.6986303810 0.7275332289 0.5289672278 0.7516139251 -0.3248981053 0.22296053623 +1403638528577829376.0000000000 4.6946828624 -1.6775724463 0.7251070774 0.5269986062 0.7515023119 -0.3283753510 0.222904403638 +1403638528627829504.0000000000 4.7013351707 -1.6571157046 0.7228707367 0.5256402170 0.7508558495 -0.3327948688 0.221732791693 +1403638528677829376.0000000000 4.7086570028 -1.6381941869 0.7216835213 0.5250757021 0.7498724555 -0.3361181114 0.221385236026 +1403638528727829504.0000000000 4.7166146838 -1.6214550448 0.7210808211 0.5243224848 0.7486859677 -0.3383501257 0.223773202576 +1403638528777829376.0000000000 4.7241891681 -1.6074840490 0.7215754333 0.5238557032 0.7470446306 -0.3407394317 0.226707215966 +1403638528827829504.0000000000 4.7296084899 -1.5969372702 0.7235102660 0.5244976768 0.7453090781 -0.3438215967 0.226281406397 +1403638528877829376.0000000000 4.7326625483 -1.5896101265 0.7268987946 0.5258922829 0.7433283786 -0.3475770621 0.223808878905 +1403638528927829504.0000000000 4.7330137091 -1.5857008951 0.7320626608 0.5271307025 0.7416159066 -0.3510898869 0.221076821193 +1403638528977829376.0000000000 4.7300688034 -1.5849655674 0.7392560479 0.5279990225 0.7406800931 -0.3538849834 0.217659023405 +1403638529027829504.0000000000 4.7235962357 -1.5871980123 0.7470924413 0.5277561341 0.7405657020 -0.3555635484 0.215894573879 +1403638529077829376.0000000000 4.7140884554 -1.5912819937 0.7542943800 0.5261843248 0.7409000357 -0.3555201190 0.218638144882 +1403638529127829504.0000000000 4.7018960796 -1.5963446084 0.7595067834 0.5230891048 0.7422264976 -0.3527464854 0.225937008232 +1403638529177829376.0000000000 4.6869249455 -1.6021346798 0.7623220178 0.5192410979 0.7439290683 -0.3493259702 0.234370625575 +1403638529227829504.0000000000 4.6696115920 -1.6085044372 0.7628723846 0.5160262228 0.7456991627 -0.3463880408 0.24013542293 +1403638529277829376.0000000000 4.6509150907 -1.6153550636 0.7614800202 0.5125434818 0.7476351250 -0.3443167852 0.244513497764 +1403638529327829504.0000000000 4.6313947982 -1.6225909870 0.7580364310 0.5088403311 0.7503852496 -0.3427886180 0.245966375694 +1403638529377829376.0000000000 4.6116298008 -1.6305610331 0.7521989976 0.5040377731 0.7540088721 -0.3420156373 0.245849238314 +1403638529427829504.0000000000 4.5928594565 -1.6376820790 0.7438496905 0.4977892033 0.7588021984 -0.3419793836 0.243875447647 +1403638529477829376.0000000000 4.5754936342 -1.6439599083 0.7338064454 0.4906726772 0.7642891451 -0.3431614492 0.239463246228 +1403638529527829504.0000000000 4.5598294271 -1.6498451067 0.7225884843 0.4834735757 0.7699189922 -0.3441700871 0.234574078146 +1403638529577829376.0000000000 4.5464444875 -1.6551414975 0.7105767780 0.4769426124 0.7748393007 -0.3440002571 0.231977640385 +1403638529627829504.0000000000 4.5349409777 -1.6591707280 0.6982229866 0.4723245342 0.7780395731 -0.3435276410 0.231414599616 +1403638529677829376.0000000000 4.5248994155 -1.6618715735 0.6862140105 0.4706987428 0.7794546923 -0.3426303404 0.231295322006 +1403638529727829504.0000000000 4.5162025004 -1.6631695907 0.6746514986 0.4724210490 0.7788030415 -0.3416599253 0.231414499193 +1403638529777829376.0000000000 4.5091794638 -1.6634421940 0.6635521963 0.4763032570 0.7763059144 -0.3408614002 0.233018970112 +1403638529827829504.0000000000 4.5030556309 -1.6627890505 0.6530576099 0.4818371582 0.7728542117 -0.3403774034 0.233821606397 +1403638529877829376.0000000000 4.4982423854 -1.6619478843 0.6434374016 0.4861350785 0.7698810794 -0.3397642977 0.235618401325 +1403638529927829504.0000000000 4.4951164349 -1.6604906728 0.6351529367 0.4889701711 0.7680668169 -0.3390990615 0.236629167631 +1403638529977829376.0000000000 4.4941033533 -1.6583925452 0.6280298913 0.4900248301 0.7673370963 -0.3390732187 0.236851850083 +1403638530027829504.0000000000 4.4951398628 -1.6552429565 0.6216521227 0.4892134140 0.7676083963 -0.3392668629 0.237372242034 +1403638530077829376.0000000000 4.4971729113 -1.6515066886 0.6159169442 0.4876826314 0.7683978701 -0.3400846485 0.236796951236 +1403638530127829504.0000000000 4.5007265841 -1.6471405270 0.6104479234 0.4858229019 0.7687651290 -0.3421200671 0.236495547878 +1403638530177829376.0000000000 4.5052412463 -1.6423684827 0.6052799118 0.4844261798 0.7683084354 -0.3448627911 0.236860886938 +1403638530227829504.0000000000 4.5106517284 -1.6371485156 0.6000218152 0.4836478897 0.7670516156 -0.3477934764 0.238235672419 +1403638530277829376.0000000000 4.5164114434 -1.6321806795 0.5948185468 0.4835857137 0.7656261433 -0.3504238539 0.239091172428 +1403638530327829504.0000000000 4.5218447348 -1.6280199099 0.5896162179 0.4835532204 0.7641850359 -0.3532434866 0.239617514199 +1403638530377829376.0000000000 4.5280110765 -1.6241800358 0.5845631955 0.4828790106 0.7630508758 -0.3551520408 0.241760728934 +1403638530427829504.0000000000 4.5338452844 -1.6205245237 0.5802426660 0.4824818601 0.7621212193 -0.3568727506 0.242949257428 +1403638530477829376.0000000000 4.5390730795 -1.6173792443 0.5767125776 0.4826301573 0.7613630548 -0.3588081785 0.24217993532 +1403638530527829504.0000000000 4.5437985574 -1.6151243928 0.5737373531 0.4832823395 0.7605382871 -0.3605667333 0.240855402631 +1403638530577829376.0000000000 4.5482338866 -1.6138409976 0.5707810660 0.4825224932 0.7601142818 -0.3620294091 0.241522315824 +1403638530627829504.0000000000 4.5517283118 -1.6129539185 0.5678866228 0.4804297210 0.7607487261 -0.3633942420 0.241647023224 +1403638530677829376.0000000000 4.5546650321 -1.6124500974 0.5649033247 0.4773864796 0.7620445365 -0.3651783003 0.240904716462 +1403638530727829504.0000000000 4.5570364745 -1.6117970647 0.5618075708 0.4743930782 0.7635140885 -0.3668185471 0.23966976783 +1403638530777829376.0000000000 4.5592310358 -1.6113757042 0.5586694317 0.4720824002 0.7646336068 -0.3678736102 0.239045313111 +1403638530827829504.0000000000 4.5611565323 -1.6108976958 0.5557766476 0.4712454199 0.7652050204 -0.3681478716 0.238445330263 +1403638530877829376.0000000000 4.5624395313 -1.6103730450 0.5536226377 0.4719866716 0.7654457783 -0.3676045579 0.237040568733 +1403638530927829504.0000000000 4.5635831668 -1.6098588948 0.5519151048 0.4736450853 0.7646432559 -0.3672823497 0.236822084917 +1403638530977829376.0000000000 4.5644368742 -1.6092848802 0.5504745698 0.4757899331 0.7633694422 -0.3669112564 0.237207007159 +1403638531027829504.0000000000 4.5648900297 -1.6086853459 0.5490347179 0.4782679213 0.7622462624 -0.3661451288 0.23701935691 +1403638531077829376.0000000000 4.5650823491 -1.6085086251 0.5481117827 0.4807093241 0.7606171858 -0.3644628966 0.23988922334 +1403638531127829504.0000000000 4.5644230719 -1.6079115246 0.5483304261 0.4828060327 0.7593201136 -0.3635290030 0.241201086206 +1403638531177829376.0000000000 4.5641527255 -1.6071115810 0.5483411568 0.4838445218 0.7593071734 -0.3617789436 0.241791420643 +1403638531227829504.0000000000 4.5640315603 -1.6066117269 0.5471954733 0.4827405317 0.7599933618 -0.3607735599 0.243339490323 +1403638531277829376.0000000000 4.5637275124 -1.6059483243 0.5465113948 0.4845946337 0.7586367125 -0.3600424047 0.244964989923 +1403638531327829504.0000000000 4.5632288376 -1.6053129591 0.5461085194 0.4876636878 0.7564730290 -0.3597200648 0.246036905809 +1403638531377829376.0000000000 4.5628408361 -1.6053391564 0.5457392790 0.4865218142 0.7573323437 -0.3597817679 0.245563281116 +1403638531427829504.0000000000 4.5629492258 -1.6056559291 0.5454695643 0.4863938997 0.7573855249 -0.3594090588 0.246197622675 +1403638531477829376.0000000000 4.5627800946 -1.6058348387 0.5455391019 0.4879959488 0.7562082937 -0.3597330568 0.246172903192 +1403638531527829504.0000000000 4.5625034321 -1.6060313642 0.5452535559 0.4877705450 0.7564613802 -0.3595540222 0.246103597737 +1403638531577829376.0000000000 4.5624321086 -1.6062360876 0.5450512675 0.4874447620 0.7568911515 -0.3587925339 0.246538650785 +1403638531627829504.0000000000 4.5622956473 -1.6062534871 0.5449884121 0.4874892182 0.7569653946 -0.3586200381 0.246473775082 +1403638531677829376.0000000000 4.5619910722 -1.6060916738 0.5450307776 0.4875899044 0.7567751167 -0.3593766694 0.24575580825 +1403638531727829504.0000000000 4.5621459640 -1.6062263723 0.5450229185 0.4873327954 0.7568931049 -0.3591061632 0.246297255101 +1403638531777829376.0000000000 4.5621527473 -1.6060601834 0.5451192299 0.4875512425 0.7567097126 -0.3594084971 0.245987253839 +1403638531827829504.0000000000 4.5621709687 -1.6062310046 0.5450678585 0.4873831897 0.7568364348 -0.3592279425 0.246194075127 +1403638531877829376.0000000000 4.5620913201 -1.6062230089 0.5450827799 0.4874634128 0.7567745352 -0.3593218750 0.246088427678 +1403638531927829504.0000000000 4.5621609757 -1.6062501499 0.5451163804 0.4874918375 0.7567269072 -0.3593928844 0.246074888888 +1403638531977829376.0000000000 4.5622587993 -1.6062851141 0.5451359603 0.4873814325 0.7567694389 -0.3593425051 0.246236308469 +1403638532027829504.0000000000 4.5621395163 -1.6062261840 0.5450891114 0.4875577495 0.7566550980 -0.3595201881 0.245979141125 +1403638532077829376.0000000000 4.5623063235 -1.6062782471 0.5450500264 0.4873292271 0.7568074030 -0.3592426157 0.246368671523 +1403638532127829504.0000000000 4.5622597111 -1.6061376678 0.5451141488 0.4875543328 0.7566304723 -0.3596047414 0.245938063059 +1403638532177829376.0000000000 4.5623191989 -1.6062845244 0.5449933588 0.4873667662 0.7567721457 -0.3593048544 0.246311949171 +1403638532227829504.0000000000 4.5622201534 -1.6062358945 0.5449855041 0.4874517336 0.7566904533 -0.3595070172 0.246099715334 +1403638532277829376.0000000000 4.5623034947 -1.6062130785 0.5450100062 0.4874062951 0.7567020770 -0.3594793939 0.246194304411 +1403638532327829504.0000000000 4.5623056959 -1.6061889446 0.5450223313 0.4874068463 0.7566957358 -0.3594886409 0.246199201153 +1403638532377829376.0000000000 4.5622771989 -1.6061179649 0.5450532753 0.4874518294 0.7566905604 -0.3595056662 0.246101169684 +1403638532427829504.0000000000 4.5623206849 -1.6062121150 0.5450602371 0.4873861059 0.7567206838 -0.3594457582 0.246226191502 +1403638532477829376.0000000000 4.5622883729 -1.6060692610 0.5451605976 0.4874884929 0.7566464883 -0.3595899641 0.24604088817 +1403638532527829504.0000000000 4.5622724204 -1.6061990445 0.5451184020 0.4873734131 0.7567053891 -0.3594909474 0.246232347815 +1403638532577829376.0000000000 4.5621914740 -1.6061467776 0.5451318862 0.4874474891 0.7566447619 -0.3596410907 0.24605270896 +1403638532627829504.0000000000 4.5622840739 -1.6061647002 0.5451317061 0.4873495389 0.7567104398 -0.3595471313 0.246182041651 +1403638532677829376.0000000000 4.5623070600 -1.6060928964 0.5451565417 0.4874233312 0.7566454571 -0.3596472406 0.246089436425 +1403638532727829504.0000000000 4.5622866563 -1.6061426706 0.5451002482 0.4873825565 0.7566814478 -0.3595832519 0.246153031792 +1403638532777829376.0000000000 4.5622784246 -1.6061408194 0.5450846996 0.4873594525 0.7567044133 -0.3595579730 0.246165104959 +1403638532827829504.0000000000 4.5622905466 -1.6060038476 0.5451314307 0.4873802173 0.7566731771 -0.3596265667 0.246119806784 +1403638532877829376.0000000000 4.5622400827 -1.6060973338 0.5450604441 0.4873164404 0.7567020286 -0.3595807730 0.246224276858 +1403638532927829504.0000000000 4.5622126339 -1.6060991040 0.5450530250 0.4873711668 0.7566807167 -0.3595866941 0.246172801289 +1403638532977829376.0000000000 4.5622703281 -1.6061226157 0.5450720049 0.4873426156 0.7566915999 -0.3595861147 0.24619671775 +1403638533027829504.0000000000 4.5622652137 -1.6061547081 0.5450617640 0.4873720953 0.7566639750 -0.3596207651 0.246172652744 +1403638533077829376.0000000000 4.5622483220 -1.6061553745 0.5450730404 0.4873181148 0.7566928009 -0.3596275133 0.246181054939 +1403638533127829504.0000000000 4.5622467420 -1.6062119437 0.5450678617 0.4873497144 0.7566648416 -0.3596508185 0.246170392448 +1403638533177829376.0000000000 4.5622694258 -1.6062254429 0.5450495224 0.4873434647 0.7566540251 -0.3596754181 0.246180070742 +1403638533227829504.0000000000 4.5622572179 -1.6062617503 0.5450283523 0.4873408051 0.7566532463 -0.3596883262 0.246168870013 +1403638533277829376.0000000000 4.5622708482 -1.6062563593 0.5450509961 0.4873481497 0.7566336355 -0.3597182684 0.246170855179 +1403638533327829504.0000000000 4.5622988750 -1.6062505810 0.5450492826 0.4873111786 0.7566446560 -0.3597191047 0.246208946728 +1403638533377829376.0000000000 4.5622511902 -1.6062620630 0.5450249832 0.4873094729 0.7566445094 -0.3597053881 0.246232812197 +1403638533427829504.0000000000 4.5621982609 -1.6062222492 0.5450422975 0.4873172751 0.7566353357 -0.3597532204 0.246175674086 +1403638533477829376.0000000000 4.5622401589 -1.6061928420 0.5450806282 0.4872914164 0.7566482975 -0.3597340496 0.246215034067 +1403638533527829504.0000000000 4.5622099730 -1.6060968084 0.5451011238 0.4872971880 0.7566378472 -0.3597819610 0.246165715047 +1403638533577829376.0000000000 4.5621753404 -1.6061799351 0.5450664848 0.4872843989 0.7566412159 -0.3597796436 0.246184063071 +1403638533627829504.0000000000 4.5622225799 -1.6061891881 0.5450795338 0.4872852326 0.7566412493 -0.3597740582 0.246190473018 +1403638533677829376.0000000000 4.5621851694 -1.6061869256 0.5450974743 0.4872999081 0.7566055019 -0.3598565918 0.246150659898 +1403638533727829504.0000000000 4.5621420166 -1.6062429306 0.5450844274 0.4872289596 0.7566390639 -0.3598318975 0.246224030899 +1403638533777829376.0000000000 4.5621462931 -1.6061998631 0.5451157472 0.4872916278 0.7565770101 -0.3599144572 0.246170023897 +1403638533827829504.0000000000 4.5622191654 -1.6061410376 0.5451768650 0.4872705228 0.7565850928 -0.3599192242 0.246179989141 +1403638533877829376.0000000000 4.5621273688 -1.6061606121 0.5451201398 0.4873412884 0.7567263734 -0.3596918322 0.245937899049 +1403638533927829504.0000000000 4.5621952816 -1.6061164350 0.5450684560 0.4872473727 0.7566667012 -0.3598177978 0.246123248621 +1403638533977829376.0000000000 4.5622019725 -1.6060833245 0.5449883676 0.4872437679 0.7566430103 -0.3599199498 0.246053846314 +1403638534027829504.0000000000 4.5622825580 -1.6060899046 0.5449417711 0.4872650089 0.7565671001 -0.3599631674 0.246181949384 +1403638534077829376.0000000000 4.5624361227 -1.6061373951 0.5449329572 0.4871136745 0.7564050530 -0.3603416607 0.246425549684 +1403638534127829504.0000000000 4.5624725602 -1.6061930637 0.5449731227 0.4871455375 0.7565297756 -0.3601807984 0.246214776744 +1403638534177829376.0000000000 4.5625076021 -1.6062065420 0.5450539964 0.4872475858 0.7564725361 -0.3602189178 0.246132938812 +1403638534227829504.0000000000 4.5624966485 -1.6062192829 0.5451430738 0.4872169014 0.7564901618 -0.3602316798 0.246120829908 +1403638534277829376.0000000000 4.5623979742 -1.6061247521 0.5452557092 0.4872338535 0.7566053735 -0.3601362105 0.245872712439 +1403638534327829504.0000000000 4.5624099552 -1.6061068689 0.5453010388 0.4872361458 0.7565621823 -0.3601773563 0.245940794916 +1403638534377829376.0000000000 4.5622870289 -1.6061051041 0.5452200155 0.4872349949 0.7565686131 -0.3601653418 0.245940887169 +1403638534427829504.0000000000 4.5622028764 -1.6060615657 0.5451743717 0.4871958049 0.7565916930 -0.3602205454 0.245866663966 +1403638534477829376.0000000000 4.5622551093 -1.6060717180 0.5451822885 0.4871062363 0.7564762839 -0.3604461043 0.246068592856 +1403638534527829504.0000000000 4.5621216504 -1.6060869553 0.5451424880 0.4870216043 0.7564791646 -0.3605362918 0.246095129626 +1403638534577829376.0000000000 4.5619568325 -1.6061521862 0.5450986077 0.4870819558 0.7566567405 -0.3602200057 0.245892848286 +1403638534627829504.0000000000 4.5620098390 -1.6061867012 0.5451061595 0.4870378626 0.7566704047 -0.3602413085 0.245906931048 +1403638534677829376.0000000000 4.5619775061 -1.6061414052 0.5451491886 0.4871431861 0.7567684456 -0.3600534547 0.245671621519 +1403638534727829504.0000000000 4.5619721602 -1.6061859211 0.5451277044 0.4870952935 0.7568012974 -0.3600057860 0.245735234399 +1403638534777829376.0000000000 4.5619871716 -1.6061630906 0.5451576792 0.4871042928 0.7568099527 -0.3599598799 0.245757987436 +1403638534827829504.0000000000 4.5621076497 -1.6060817251 0.5451836631 0.4870701676 0.7567665352 -0.3600850741 0.24577591937 +1403638534877829376.0000000000 4.5622139036 -1.6061175986 0.5451295560 0.4870071214 0.7566958717 -0.3601492666 0.246024240998 +1403638534927829504.0000000000 4.5623056321 -1.6061261425 0.5450888512 0.4869276732 0.7566626149 -0.3603245686 0.246027099173 +1403638534977829376.0000000000 4.5623768491 -1.6061780051 0.5450885244 0.4869165065 0.7566781523 -0.3602674839 0.246085005026 +1403638535027829504.0000000000 4.5623465147 -1.6061905693 0.5450619548 0.4869338400 0.7566725953 -0.3603240730 0.245984920982 +1403638535077829376.0000000000 4.5623054406 -1.6062501638 0.5450258478 0.4868839988 0.7567227183 -0.3603010358 0.245963133147 +1403638535127829504.0000000000 4.5622970209 -1.6062357228 0.5450079957 0.4868927880 0.7567268656 -0.3602813458 0.24596181767 +1403638535177829376.0000000000 4.5622600294 -1.6061712228 0.5449792919 0.4869314560 0.7566968271 -0.3603302991 0.245905966914 +1403638535227829504.0000000000 4.5621510278 -1.6061502157 0.5449415318 0.4869286306 0.7567134188 -0.3602793403 0.245935169296 +1403638535277829376.0000000000 4.5620521749 -1.6061237664 0.5449281668 0.4869720785 0.7566955645 -0.3603180142 0.245847404128 +1403638535327829504.0000000000 4.5620269448 -1.6061302815 0.5449906559 0.4869118140 0.7567128762 -0.3603385060 0.245883446901 +1403638535377829376.0000000000 4.5619708512 -1.6062038140 0.5449616273 0.4869525337 0.7567048132 -0.3603306869 0.24583907688 +1403638535427829504.0000000000 4.5620267522 -1.6062430189 0.5450040270 0.4868893896 0.7567307217 -0.3603331990 0.245880708624 +1403638535477829376.0000000000 4.5620618978 -1.6062845203 0.5450398037 0.4868618839 0.7567143053 -0.3603998465 0.24588801669 +1403638535527829504.0000000000 4.5621183111 -1.6062989352 0.5450978031 0.4868641825 0.7567143560 -0.3604163253 0.24585915428 +1403638535577829376.0000000000 4.5621354584 -1.6062881231 0.5450834439 0.4868131611 0.7567612872 -0.3603928103 0.245850203694 +1403638535627829504.0000000000 4.5621798440 -1.6062368224 0.5450768083 0.4868039812 0.7567582422 -0.3604091601 0.245853786066 +1403638535677829376.0000000000 4.5622219222 -1.6061817644 0.5451113138 0.4868032637 0.7567447164 -0.3604685553 0.245809758316 +1403638535727829504.0000000000 4.5622405482 -1.6061713410 0.5451127091 0.4867762398 0.7567375445 -0.3604870811 0.245858181804 +1403638535777829376.0000000000 4.5622327944 -1.6061433937 0.5451136934 0.4867969008 0.7567196543 -0.3604961932 0.245858977435 +1403638535827829504.0000000000 4.5621870689 -1.6060969141 0.5451504763 0.4868006356 0.7567479844 -0.3604728849 0.245798552754 +1403638535877829376.0000000000 4.5621321082 -1.6060650093 0.5451462856 0.4868051029 0.7567553750 -0.3604715110 0.245768964617 +1403638535927829504.0000000000 4.5620368505 -1.6060947364 0.5451143620 0.4867958151 0.7567416679 -0.3605293758 0.245744688034 +1403638535977829376.0000000000 4.5620119778 -1.6061525674 0.5450707442 0.4867467901 0.7567941724 -0.3605333692 0.245674240627 +1403638536027829504.0000000000 4.5620865831 -1.6061475899 0.5450618282 0.4867887169 0.7567494070 -0.3606016064 0.245628910396 +1403638536077829376.0000000000 4.5620224046 -1.6062204702 0.5449736267 0.4867792408 0.7567251647 -0.3606481748 0.245654004415 +1403638536127829504.0000000000 4.5620057970 -1.6062712230 0.5449259489 0.4867386829 0.7567449510 -0.3606850032 0.245619344198 +1403638536177829376.0000000000 4.5619874410 -1.6062946235 0.5449176871 0.4867532415 0.7567142893 -0.3607167310 0.245638364793 +1403638536227829504.0000000000 4.5619254469 -1.6063337437 0.5448961081 0.4867079024 0.7567486726 -0.3607356098 0.24559455224 +1403638536277829376.0000000000 4.5619489720 -1.6063433437 0.5448983054 0.4866925599 0.7567559249 -0.3607064135 0.24564548761 +1403638536327829504.0000000000 4.5620591750 -1.6062440923 0.5449853988 0.4867566472 0.7567421259 -0.3607180472 0.245543910134 +1403638536377829376.0000000000 4.5620599540 -1.6062708912 0.5449594856 0.4866837650 0.7567424056 -0.3607447523 0.245648261096 +1403638536427829504.0000000000 4.5620628155 -1.6062319030 0.5449809238 0.4867125226 0.7567310963 -0.3607811973 0.245572587747 +1403638536477829376.0000000000 4.5620900967 -1.6062453541 0.5449979890 0.4866707000 0.7567512565 -0.3607506461 0.245638223499 +1403638536527829504.0000000000 4.5620929619 -1.6062202641 0.5450505370 0.4866719795 0.7567764007 -0.3607811188 0.245513437501 +1403638536577829376.0000000000 4.5621072860 -1.6062175512 0.5450654099 0.4866580300 0.7567703429 -0.3607949806 0.245539389646 +1403638536627829504.0000000000 4.5621374445 -1.6062013218 0.5450851399 0.4866896990 0.7567156431 -0.3608815577 0.245517970135 +1403638536677829376.0000000000 4.5621581307 -1.6061957246 0.5450710496 0.4866284097 0.7567859456 -0.3608165733 0.245518275986 +1403638536727829504.0000000000 4.5621703417 -1.6061955181 0.5450468067 0.4866573904 0.7567262792 -0.3608602000 0.245580615707 +1403638536777829376.0000000000 4.5621420121 -1.6062393570 0.5450025152 0.4866337002 0.7567260604 -0.3608960252 0.245575590075 +1403638536827829504.0000000000 4.5622145147 -1.6061601983 0.5450441777 0.4866603269 0.7566923397 -0.3609414148 0.245560021925 +1403638536877829376.0000000000 4.5621128064 -1.6061178284 0.5450921945 0.4866947784 0.7566462472 -0.3610100466 0.245532880698 +1403638536927829504.0000000000 4.5620812413 -1.6061381957 0.5451508478 0.4866585570 0.7566777765 -0.3609705502 0.245565578508 +1403638536977829376.0000000000 4.5620132066 -1.6061342890 0.5451788213 0.4866650992 0.7566433872 -0.3611180881 0.245441626888 +1403638537027829504.0000000000 4.5619426166 -1.6062014341 0.5451359045 0.4866150786 0.7567023890 -0.3610079066 0.245520978935 +1403638537077829376.0000000000 4.5618952446 -1.6061779467 0.5450941027 0.4866453429 0.7566823977 -0.3610815244 0.245414327374 +1403638537127829504.0000000000 4.5618265133 -1.6062642195 0.5450067098 0.4865864017 0.7567081624 -0.3609846064 0.245594268134 +1403638537177829376.0000000000 4.5618199367 -1.6062817310 0.5449877625 0.4866052436 0.7566633135 -0.3610985345 0.245527626369 +1403638537227829504.0000000000 4.5618382468 -1.6063119833 0.5449904668 0.4865106806 0.7566988122 -0.3611309891 0.245557883217 +1403638537277829376.0000000000 4.5618881020 -1.6063147380 0.5450217532 0.4864709925 0.7567164976 -0.3611118731 0.245610119704 +1403638537327829504.0000000000 4.5619269367 -1.6062676486 0.5450397904 0.4865031338 0.7566842040 -0.3611891229 0.245532347609 +1403638537377829376.0000000000 4.5619913835 -1.6062091582 0.5450502394 0.4864439121 0.7567276163 -0.3611404558 0.245587471887 +1403638537427829504.0000000000 4.5621323026 -1.6060584256 0.5451003985 0.4865000372 0.7567075322 -0.3611889666 0.24546681025 +1403638537477829376.0000000000 4.5621634028 -1.6059729087 0.5450686970 0.4864355560 0.7567379502 -0.3611722612 0.245525400684 +1403638537527829504.0000000000 4.5622740044 -1.6059635855 0.5451080410 0.4864528928 0.7567377047 -0.3611925248 0.245461991958 +1403638537577829376.0000000000 4.5623107845 -1.6060939099 0.5450738573 0.4863900043 0.7567991837 -0.3611261495 0.245494732053 +1403638537627829504.0000000000 4.5622318732 -1.6062016846 0.5450032369 0.4864586593 0.7567560903 -0.3611004659 0.24552931827 +1403638537677829376.0000000000 4.5621460315 -1.6063549103 0.5449412067 0.4863448255 0.7568125619 -0.3611336774 0.245531920405 +1403638537727829504.0000000000 4.5620078213 -1.6064507052 0.5448780114 0.4863634271 0.7568042200 -0.3611270092 0.245530594017 +1403638537777829376.0000000000 4.5617946777 -1.6065797912 0.5449390888 0.4863942542 0.7567865849 -0.3611436642 0.245499385216 +1403638537827829504.0000000000 4.5619188860 -1.6065397354 0.5449568456 0.4863577697 0.7568017820 -0.3611646667 0.245493922911 +1403638537877829376.0000000000 4.5620482570 -1.6064154488 0.5448804155 0.4862562823 0.7568853944 -0.3611030039 0.245527896981 +1403638537927829504.0000000000 4.5622176494 -1.6062381879 0.5449306872 0.4863076439 0.7568201599 -0.3611976363 0.24548806217 +1403638537977829376.0000000000 4.5621173973 -1.6063099748 0.5449925985 0.4862350843 0.7568221502 -0.3612304195 0.245577400731 +1403638538027829504.0000000000 4.5619452116 -1.6063520888 0.5450849750 0.4862255144 0.7568418074 -0.3612557860 0.245498441558 +1403638538077829376.0000000000 4.5618716042 -1.6064105587 0.5452291355 0.4863015191 0.7567867658 -0.3612314843 0.245553331133 +1403638538127829504.0000000000 4.5615745174 -1.6066443191 0.5453744486 0.4863229188 0.7567745438 -0.3611907973 0.245608461668 +1403638538177829376.0000000000 4.5615401136 -1.6066590038 0.5454974354 0.4862993988 0.7567848297 -0.3612379008 0.245554057829 +1403638538227829504.0000000000 4.5618353466 -1.6064653076 0.5454143829 0.4862320479 0.7568145405 -0.3612715930 0.245546294919 +1403638538277829376.0000000000 4.5620461080 -1.6062683086 0.5452449634 0.4862321818 0.7568643701 -0.3611993049 0.245498783686 +1403638538327829504.0000000000 4.5620739639 -1.6062349198 0.5451513594 0.4862272955 0.7568510804 -0.3612146896 0.245526795074 +1403638538377829376.0000000000 4.5621339626 -1.6061079308 0.5451901507 0.4862306950 0.7568147959 -0.3611807130 0.245681843917 +1403638538427829504.0000000000 4.5621656867 -1.6059886084 0.5453427956 0.4863817224 0.7567165936 -0.3612245234 0.245620969888 +1403638538477829376.0000000000 4.5620695038 -1.6060666809 0.5455788978 0.4862348381 0.7568293004 -0.3611844510 0.245623460936 +1403638538527829504.0000000000 4.5619507813 -1.6061996353 0.5457661922 0.4864433630 0.7566589729 -0.3612930678 0.245575594371 +1403638538577829376.0000000000 4.5619453630 -1.6063733766 0.5459610544 0.4862170622 0.7567571892 -0.3612331418 0.245809158295 +1403638538627829504.0000000000 4.5617615010 -1.6063578079 0.5461411910 0.4866295738 0.7564480263 -0.3613305196 0.245801336359 +1403638538677829376.0000000000 4.5617415690 -1.6063145518 0.5460504192 0.4865307149 0.7565585347 -0.3612770446 0.245735516433 +1403638538727829504.0000000000 4.5618601328 -1.6063841912 0.5459862052 0.4870901862 0.7561650347 -0.3611451371 0.246032072704 +1403638538777829376.0000000000 4.5619694762 -1.6061549875 0.5457285130 0.4877520212 0.7558996121 -0.3608535906 0.245964282723 +1403638538827829504.0000000000 4.5624326242 -1.6054490687 0.5450435841 0.4881801737 0.7558395553 -0.3604611385 0.245874871153 +1403638538877829376.0000000000 4.5632383067 -1.6044417125 0.5448827518 0.4895793223 0.7551706876 -0.3600215454 0.24579220202 +1403638538927829504.0000000000 4.5647109925 -1.6032390511 0.5453280966 0.4923800169 0.7534036398 -0.3587598348 0.247459603538 +1403638538977829376.0000000000 4.5661847087 -1.6017119869 0.5465480800 0.4960544235 0.7509384343 -0.3577342835 0.24909367546 +1403638539027829504.0000000000 4.5679422059 -1.6001249506 0.5467459439 0.4983358174 0.7487691400 -0.3577694601 0.251012353319 +1403638539077829376.0000000000 4.5702029231 -1.5981019393 0.5482791926 0.5029355007 0.7451295403 -0.3572126259 0.253450173301 +1403638539127829504.0000000000 4.5729209455 -1.5953341584 0.5508909436 0.5073722378 0.7420331198 -0.3567360835 0.254361215954 +1403638539177829376.0000000000 4.5759841732 -1.5921742356 0.5546357115 0.5103338269 0.7400275217 -0.3558217281 0.255557332269 +1403638539227829504.0000000000 4.5793067928 -1.5887730764 0.5605620882 0.5139540644 0.7377715242 -0.3544500327 0.256728596265 +1403638539277829376.0000000000 4.5827577405 -1.5853504819 0.5683585217 0.5154082932 0.7368531777 -0.3538419358 0.257288884881 +1403638539327829504.0000000000 4.5858391113 -1.5820899355 0.5783410874 0.5154789977 0.7369905522 -0.3538364639 0.256760755841 +1403638539377829376.0000000000 4.5891061618 -1.5788957029 0.5901031067 0.5144099646 0.7379364652 -0.3536472124 0.256448456426 +1403638539427829504.0000000000 4.5925243078 -1.5756408388 0.6036762964 0.5135500459 0.7388630438 -0.3533762313 0.255876907998 +1403638539477829376.0000000000 4.5960890905 -1.5722952902 0.6189608275 0.5119463245 0.7402463176 -0.3533786977 0.255087918501 +1403638539527829504.0000000000 4.5997037784 -1.5689806020 0.6352359187 0.5111943228 0.7411349648 -0.3529959396 0.254545074318 +1403638539577829376.0000000000 4.6035432938 -1.5655689013 0.6520476317 0.5109410702 0.7416246356 -0.3524674613 0.254359610161 +1403638539627829504.0000000000 4.6074485153 -1.5620424271 0.6678077065 0.5107420977 0.7421238241 -0.3523680992 0.253439266783 +1403638539677829376.0000000000 4.6113775407 -1.5585348196 0.6812039463 0.5108743311 0.7423537927 -0.3523147503 0.25257193232 +1403638539727829504.0000000000 4.6153683757 -1.5548135230 0.6916303710 0.5102268878 0.7430949619 -0.3516849158 0.252578939195 +1403638539777829376.0000000000 4.6193017796 -1.5509759695 0.6990164416 0.5091557139 0.7441923629 -0.3510869748 0.252341281212 +1403638539827829504.0000000000 4.6234272661 -1.5468451028 0.7049840940 0.5082439986 0.7450984188 -0.3510091715 0.251612689987 +1403638539877829376.0000000000 4.6276624278 -1.5423473779 0.7101145929 0.5061072543 0.7468243139 -0.3514359832 0.250203199376 +1403638539927829504.0000000000 4.6321050162 -1.5374359874 0.7149591658 0.5036020874 0.7489735611 -0.3517392389 0.248400986643 +1403638539977829376.0000000000 4.6370900622 -1.5320783299 0.7198425609 0.5005940559 0.7512455402 -0.3527508949 0.246175822592 +1403638540027829504.0000000000 4.6429681497 -1.5262458489 0.7246166329 0.4966235391 0.7538952414 -0.3540585139 0.24423266391 +1403638540077829376.0000000000 4.6491700265 -1.5198831120 0.7288235181 0.4924043268 0.7568705759 -0.3546212181 0.242752346993 +1403638540127829504.0000000000 4.6564932782 -1.5122593823 0.7328031084 0.4884765795 0.7594523413 -0.3559223737 0.240711521192 +1403638540177829376.0000000000 4.6652887647 -1.5032943648 0.7369134359 0.4868615485 0.7606850723 -0.3557634555 0.240325648134 +1403638540227829504.0000000000 4.6757768289 -1.4928578195 0.7417277784 0.4884989832 0.7598490802 -0.3547041099 0.241211760149 +1403638540277829376.0000000000 4.6875821278 -1.4811105037 0.7472218811 0.4926924323 0.7572420846 -0.3531304533 0.243181979998 +1403638540327829504.0000000000 4.7004646365 -1.4683673877 0.7526775886 0.4970381597 0.7544200249 -0.3516157171 0.245295497989 +1403638540377829376.0000000000 4.7138069400 -1.4550308923 0.7572388195 0.5010333580 0.7522488550 -0.3492341597 0.247230127701 +1403638540427829504.0000000000 4.7273173780 -1.4409005639 0.7613789538 0.5039904626 0.7515482381 -0.3464344964 0.247289302649 +1403638540477829376.0000000000 4.7406610577 -1.4261515947 0.7651757755 0.5060461806 0.7522716963 -0.3429297362 0.245771751882 +1403638540527829504.0000000000 4.7540171748 -1.4107999243 0.7684601491 0.5075733773 0.7542340013 -0.3383769098 0.242902047754 +1403638540577829376.0000000000 4.7675357974 -1.3947165548 0.7717913115 0.5095601728 0.7566732679 -0.3324171606 0.239359201257 +1403638540627829504.0000000000 4.7810837142 -1.3780167785 0.7750103051 0.5117254108 0.7595022794 -0.3255781351 0.235143082921 +1403638540677829376.0000000000 4.7949194962 -1.3608029268 0.7779626670 0.5135555992 0.7630393218 -0.3165701299 0.23198058709 +1403638540727829504.0000000000 4.8088773423 -1.3429134972 0.7812118744 0.5163495741 0.7664850860 -0.3054153453 0.229358228875 +1403638540777829376.0000000000 4.8223479549 -1.3243127654 0.7840946883 0.5182291467 0.7708765474 -0.2940126132 0.225265362466 +1403638540827829504.0000000000 4.8354717853 -1.3049737585 0.7868491769 0.5204892756 0.7754195194 -0.2807328736 0.221369683259 +1403638540877829376.0000000000 4.8477942240 -1.2847475179 0.7890439727 0.5223258764 0.7803306215 -0.2677858833 0.215755696926 +1403638540927829504.0000000000 4.8596939631 -1.2634924444 0.7910036346 0.5247307597 0.7846817335 -0.2542864220 0.210405851784 +1403638540977829376.0000000000 4.8707245132 -1.2412592473 0.7927603250 0.5275062825 0.7883806874 -0.2428749468 0.202989590443 +1403638541027829504.0000000000 4.8813429275 -1.2182021023 0.7939954563 0.5301972694 0.7912641207 -0.2327873951 0.19647385456 +1403638541077829376.0000000000 4.8913620286 -1.1943096696 0.7946744323 0.5330069501 0.7933909543 -0.2240810976 0.19032090392 +1403638541127829504.0000000000 4.9010587942 -1.1696185838 0.7943435359 0.5353328238 0.7950079398 -0.2169096034 0.185287256426 +1403638541177829376.0000000000 4.9103649901 -1.1441208957 0.7926713472 0.5367034963 0.7965521801 -0.2111795677 0.181265472598 +1403638541227829504.0000000000 4.9192246679 -1.1179882613 0.7901833807 0.5373322838 0.7981310631 -0.2064318352 0.177895251042 +1403638541277829376.0000000000 4.9276151058 -1.0909652002 0.7884390694 0.5380612441 0.7989566460 -0.2027524620 0.176209575723 +1403638541327829504.0000000000 4.9352342573 -1.0629657402 0.7887121222 0.5384129880 0.7996895050 -0.2007758262 0.174060959288 +1403638541377829376.0000000000 4.9421067883 -1.0341821760 0.7903793222 0.5386415601 0.8000929238 -0.1993441942 0.173142933205 +1403638541427829504.0000000000 4.9481778724 -1.0048856710 0.7931127072 0.5388389731 0.8002032006 -0.1997257423 0.171572219873 +1403638541477829376.0000000000 4.9532052902 -0.9750998664 0.7970465146 0.5392561034 0.7999957548 -0.1990460050 0.1720184152 +1403638541527829504.0000000000 4.9576496296 -0.9443597975 0.8026478406 0.5398994374 0.7993830161 -0.1986318784 0.173322727906 +1403638541577829376.0000000000 4.9610300692 -0.9123095011 0.8101887885 0.5408838802 0.7988721004 -0.1979998850 0.173332169063 +1403638541627829504.0000000000 4.9634810534 -0.8785399173 0.8195993191 0.5419145607 0.7987627116 -0.1959935877 0.172896654478 +1403638541677829376.0000000000 4.9642829357 -0.8440039809 0.8311256127 0.5439179300 0.7983907840 -0.1946201213 0.169848314216 +1403638541727829504.0000000000 4.9637049684 -0.8089430641 0.8445459914 0.5456222260 0.7986803226 -0.1914306961 0.166614577112 +1403638541777829376.0000000000 4.9617685483 -0.7735031925 0.8598532873 0.5474669879 0.7992358176 -0.1890159048 0.160545920951 +1403638541827829504.0000000000 4.9588374143 -0.7379377041 0.8766033071 0.5491611142 0.8001227149 -0.1851893735 0.15469520881 +1403638541877829376.0000000000 4.9544288904 -0.7023943317 0.8940663947 0.5508018249 0.8012145433 -0.1802832273 0.148897828246 +1403638541927829504.0000000000 4.9494022484 -0.6666204767 0.9104743111 0.5513064563 0.8033490255 -0.1741049557 0.142755031097 +1403638541977829376.0000000000 4.9436887113 -0.6307196835 0.9253490916 0.5521343224 0.8054165987 -0.1666341614 0.136692533653 +1403638542027829504.0000000000 4.9372405285 -0.5948615549 0.9388372868 0.5532339069 0.8074238638 -0.1590102541 0.129285294855 +1403638542077829376.0000000000 4.9305074513 -0.5589175542 0.9508206254 0.5540612027 0.8096204148 -0.1501465048 0.122421381687 +1403638542127829504.0000000000 4.9232607077 -0.5229841847 0.9613118328 0.5551643856 0.8116708008 -0.1402246329 0.115412600673 +1403638542177829376.0000000000 4.9155839003 -0.4867196424 0.9707370639 0.5569540192 0.8132297225 -0.1303971872 0.107033697925 +1403638542227829504.0000000000 4.9076987363 -0.4506078212 0.9782785590 0.5573574297 0.8156679348 -0.1194346867 0.0988628915567 +1403638542277829376.0000000000 4.8997691495 -0.4142953618 0.9844945693 0.5577568575 0.8179354695 -0.1074283332 0.0913674386487 +1403638542327829504.0000000000 4.8916115228 -0.3776027934 0.9898045221 0.5589177963 0.8194121013 -0.0957470779 0.0837090332263 +1403638542377829376.0000000000 4.8838832085 -0.3402571438 0.9944833067 0.5626961198 0.8185667703 -0.0845774386 0.0785377376574 +1403638542427829504.0000000000 4.8763193501 -0.3026085514 0.9982069426 0.5678830311 0.8163508806 -0.0727452294 0.0760804468378 +1403638542477829376.0000000000 4.8686672076 -0.2650032134 1.0008668109 0.5739525764 0.8130505890 -0.0610541646 0.0761548997272 +1403638542527829504.0000000000 4.8609287839 -0.2276343648 1.0022282594 0.5780685542 0.8106136255 -0.0500828708 0.0789557011917 +1403638542577829376.0000000000 4.8519256586 -0.1904597914 1.0038319522 0.5816680323 0.8082004715 -0.0395848100 0.0831104133283 +1403638542627829504.0000000000 4.8408379444 -0.1540750887 1.0059583892 0.5823089951 0.8080092824 -0.0334117825 0.0831918662899 +1403638542677829376.0000000000 4.8276059797 -0.1181874790 1.0099234942 0.5823200508 0.8082259508 -0.0295462672 0.0824693212749 +1403638542727829504.0000000000 4.8118151833 -0.0833629798 1.0159808297 0.5805885058 0.8099143933 -0.0294770052 0.0780177452101 +1403638542777829376.0000000000 4.7937024952 -0.0487536521 1.0244593763 0.5789140123 0.8116486799 -0.0318263962 0.0712184473439 +1403638542827829504.0000000000 4.7739636199 -0.0150784805 1.0348597625 0.5772054436 0.8131888504 -0.0337371423 0.0664798815332 +1403638542877829376.0000000000 4.7529231326 0.0176230357 1.0463251731 0.5742778653 0.8155105283 -0.0363693662 0.0618448122581 +1403638542927829504.0000000000 4.7309151007 0.0504016915 1.0600692487 0.5721846304 0.8171632272 -0.0387084184 0.0578849482161 +1403638542977829376.0000000000 4.7082399584 0.0822858458 1.0756311608 0.5701906345 0.8186265644 -0.0406779444 0.0554841713297 +1403638543027829504.0000000000 4.6848602661 0.1137468553 1.0918183197 0.5683998195 0.8199377320 -0.0426209732 0.0529831423035 +1403638543077829376.0000000000 4.6611073257 0.1457642297 1.1076662345 0.5671470954 0.8208199320 -0.0446090204 0.051076869564 +1403638543127829504.0000000000 4.6371384361 0.1782156127 1.1222090447 0.5669164280 0.8209370115 -0.0463416283 0.0502059782575 +1403638543177829376.0000000000 4.6128883151 0.2109743743 1.1352328874 0.5666615071 0.8210502615 -0.0471792704 0.0504511728379 +1403638543227829504.0000000000 4.5883553994 0.2436496306 1.1466180509 0.5664301363 0.8211492556 -0.0480734258 0.0505939366009 +1403638543277829376.0000000000 4.5636759343 0.2765627451 1.1567130136 0.5673288060 0.8204668349 -0.0494159338 0.0503017312184 +1403638543327829504.0000000000 4.5391636469 0.3094385439 1.1649115481 0.5666034611 0.8208991412 -0.0504044424 0.0504431364436 +1403638543377829376.0000000000 4.5141131581 0.3425174524 1.1722124607 0.5662172200 0.8211658834 -0.0505654332 0.0502771192798 +1403638543427829504.0000000000 4.4887845525 0.3757444571 1.1784051382 0.5661203479 0.8214083291 -0.0490028278 0.0489370152261 +1403638543477829376.0000000000 4.4633160945 0.4090124124 1.1832765096 0.5659417543 0.8217922271 -0.0459475560 0.0475004031781 +1403638543527829504.0000000000 4.4373192295 0.4422036612 1.1869741110 0.5656843014 0.8223770874 -0.0415976083 0.0443490273594 +1403638543577829376.0000000000 4.4110493314 0.4752149274 1.1895809074 0.5655026377 0.8229837224 -0.0344063795 0.0414820489743 +1403638543627829504.0000000000 4.3840127530 0.5080423594 1.1906658886 0.5650456271 0.8237744478 -0.0254669135 0.0383475522557 +1403638543677829376.0000000000 4.3564145436 0.5408870090 1.1914973919 0.5653529762 0.8240115822 -0.0158119606 0.0336289557552 +1403638543727829504.0000000000 4.3282011819 0.5740182319 1.1926990199 0.5653618307 0.8243455983 -0.0048906837 0.0282208447783 +1403638543777829376.0000000000 4.2994558461 0.6073382357 1.1951725161 0.5659091531 0.8241284266 0.0069645456 0.0225978327841 +1403638543827829504.0000000000 4.2703058675 0.6408636625 1.1994203543 0.5666661829 0.8235072344 0.0201142683 0.0179077721503 +1403638543877829376.0000000000 4.2401652373 0.6748780021 1.2061949590 0.5673931984 0.8227797887 0.0314456028 0.0104666936362 +1403638543927829504.0000000000 4.2093741578 0.7094369473 1.2152420096 0.5676468886 0.8221623080 0.0426434694 0.00277192975862 +1403638543977829376.0000000000 4.1783449159 0.7446288020 1.2262376450 0.5679442243 0.8214422853 0.0514900698 -0.00455002785917 +1403638544027829504.0000000000 4.1469101381 0.7793828633 1.2388303656 0.5672374282 0.8213785255 0.0583413060 -0.0132404642499 +1403638544077829376.0000000000 4.1153278195 0.8144173258 1.2516737940 0.5657761520 0.8218350291 0.0634251674 -0.0214890405575 +1403638544127829504.0000000000 4.0840068658 0.8502655586 1.2653306771 0.5654146693 0.8215523437 0.0682085915 -0.0265628741983 +1403638544177829376.0000000000 4.0523858450 0.8865237629 1.2781253264 0.5651064812 0.8213268517 0.0706203223 -0.0330096604211 +1403638544227829504.0000000000 4.0211320371 0.9233137922 1.2890911271 0.5656661320 0.8205573334 0.0732366112 -0.0366590834848 +1403638544277829376.0000000000 3.9901501977 0.9603985196 1.2985221695 0.5657891819 0.8201746374 0.0747223836 -0.0401588247248 +1403638544327829504.0000000000 3.9596089763 0.9975449973 1.3060732158 0.5654736200 0.8201383388 0.0767964520 -0.0414125029155 +1403638544377829376.0000000000 3.9293547954 1.0350467654 1.3128864685 0.5647620484 0.8205218498 0.0774169504 -0.0423596324582 +1403638544427829504.0000000000 3.8992476050 1.0729024378 1.3184842067 0.5636944776 0.8211805273 0.0777096761 -0.0432698932724 +1403638544477829376.0000000000 3.8695861568 1.1115873556 1.3231777452 0.5632770782 0.8214707181 0.0783163551 -0.0420873016429 +1403638544527829504.0000000000 3.8398939294 1.1505182584 1.3274504532 0.5647026483 0.8205250291 0.0780543758 -0.0419178962032 +1403638544577829376.0000000000 3.8100769202 1.1894072598 1.3324035460 0.5672367783 0.8187110972 0.0783774884 -0.0425622607334 +1403638544627829504.0000000000 3.7801154611 1.2287504201 1.3387448740 0.5718212485 0.8153736848 0.0791914030 -0.0437599774324 +1403638544677829376.0000000000 3.7502498367 1.2685771908 1.3469495636 0.5757706723 0.8124635194 0.0799372510 -0.0447347571593 +1403638544727829504.0000000000 3.7207324439 1.3073571059 1.3561891477 0.5772854433 0.8112670696 0.0807737606 -0.0454187015185 +1403638544777829376.0000000000 3.6917710797 1.3455796704 1.3657174989 0.5760432291 0.8120881979 0.0810614203 -0.0460000358203 +1403638544827829504.0000000000 3.6630927405 1.3832910393 1.3743474972 0.5737036304 0.8136603742 0.0820436273 -0.045714146792 +1403638544877829376.0000000000 3.6346034258 1.4208698861 1.3816613826 0.5702869146 0.8160217238 0.0821495775 -0.0461825536604 +1403638544927829504.0000000000 3.6062716172 1.4587417030 1.3878258760 0.5688953460 0.8169547522 0.0824137815 -0.046378732719 +1403638544977829376.0000000000 3.5778733068 1.4966842961 1.3928187396 0.5686039649 0.8171162923 0.0824812901 -0.046982260341 +1403638545027829504.0000000000 3.5495433662 1.5346985472 1.3964239422 0.5693554425 0.8165302373 0.0827453490 -0.0476020891395 +1403638545077829376.0000000000 3.5214626236 1.5727827295 1.3986036906 0.5700963915 0.8159879799 0.0827727038 -0.0479833375754 +1403638545127829504.0000000000 3.4936935690 1.6108793083 1.3992502010 0.5704628699 0.8156735595 0.0832618754 -0.0481271064582 +1403638545177829376.0000000000 3.4663216262 1.6486633630 1.3978981559 0.5698152066 0.8160895815 0.0838340974 -0.0477521668167 +1403638545227829504.0000000000 3.4390516192 1.6863379558 1.3949084904 0.5690231306 0.8165780183 0.0847024302 -0.0473129498186 +1403638545277829376.0000000000 3.4117303103 1.7242007478 1.3907423000 0.5695620897 0.8161301758 0.0855291185 -0.0470673139401 +1403638545327829504.0000000000 3.3844469302 1.7621800614 1.3853359663 0.5714061758 0.8148177059 0.0857687015 -0.0470193387786 +1403638545377829376.0000000000 3.3570987077 1.7998309436 1.3785842682 0.5734854446 0.8133548021 0.0855385127 -0.04745074895 +1403638545427829504.0000000000 3.3297598026 1.8368326986 1.3703563026 0.5730738250 0.8136057512 0.0853421460 -0.0484643245641 +1403638545477829376.0000000000 3.3022971367 1.8734010046 1.3616240405 0.5727464665 0.8136415879 0.0863153248 -0.049985160204 +1403638545527829504.0000000000 3.2744983853 1.9094512718 1.3541891246 0.5720761593 0.8136744626 0.0890968523 -0.0521966253195 +1403638545577829376.0000000000 3.2465027463 1.9453122722 1.3476015309 0.5706666017 0.8139828592 0.0933053204 -0.0553683281166 +1403638545627829504.0000000000 3.2181340621 1.9807181671 1.3427089443 0.5697412517 0.8136235988 0.0985702120 -0.0607902867084 +1403638545677829376.0000000000 3.1900346491 2.0162457740 1.3394350342 0.5688490071 0.8129490953 0.1059085784 -0.0656349652308 +1403638545727829504.0000000000 3.1620826852 2.0514162830 1.3377934131 0.5666530608 0.8129374596 0.1139925916 -0.0710118622859 +1403638545777829376.0000000000 3.1343833810 2.0864846033 1.3379714467 0.5656715857 0.8116462693 0.1240286559 -0.0765694667416 +1403638545827829504.0000000000 3.1065765383 2.1213257996 1.3400229062 0.5648579769 0.8098505067 0.1349324271 -0.0828906681917 +1403638545877829376.0000000000 3.0787224751 2.1556840077 1.3439956635 0.5626591384 0.8087205198 0.1460252789 -0.0897910504554 +1403638545927829504.0000000000 3.0510266174 2.1901307107 1.3497133988 0.5611347748 0.8066777847 0.1588668168 -0.0957081532768 +1403638545977829376.0000000000 3.0233281927 2.2243237304 1.3573928385 0.5588796733 0.8049677276 0.1709970280 -0.102178690387 +1403638546027829504.0000000000 2.9960056884 2.2585792792 1.3664555451 0.5576454351 0.8027361132 0.1824938242 -0.106500259646 +1403638546077829376.0000000000 2.9685649706 2.2929151875 1.3754212704 0.5565055708 0.8005560855 0.1929397469 -0.110389119351 +1403638546127829504.0000000000 2.9407393086 2.3275146051 1.3833373258 0.5555395717 0.7985919248 0.2013731429 -0.114348499485 +1403638546177829376.0000000000 2.9122319900 2.3622214884 1.3900123145 0.5546471706 0.7968638233 0.2075401263 -0.119589544543 +1403638546227829504.0000000000 2.8833313028 2.3972366617 1.3947103731 0.5532622354 0.7960101746 0.2123870046 -0.12312782424 +1403638546277829376.0000000000 2.8543103945 2.4322197022 1.3980665088 0.5522782092 0.7951805330 0.2162977515 -0.12606340549 +1403638546327829504.0000000000 2.8246889533 2.4673765418 1.4002044673 0.5511275773 0.7947945419 0.2179818049 -0.130552527919 +1403638546377829376.0000000000 2.7948219061 2.5028083631 1.4007396865 0.5503292486 0.7945790668 0.2188789340 -0.133693070196 +1403638546427829504.0000000000 2.7646419491 2.5384322270 1.3997305963 0.5490304288 0.7949086374 0.2191618242 -0.13657943213 +1403638546477829376.0000000000 2.7348087310 2.5740270686 1.3970996744 0.5486764052 0.7947337854 0.2202133145 -0.137326285797 +1403638546527829504.0000000000 2.7045976395 2.6098092188 1.3938850203 0.5482069051 0.7946101932 0.2212667971 -0.138220239361 +1403638546577829376.0000000000 2.6738958834 2.6459281345 1.3920527308 0.5478719856 0.7939995557 0.2239315156 -0.138764798239 +1403638546627829504.0000000000 2.6434646617 2.6812481145 1.3909441642 0.5474636806 0.7929766246 0.2272770782 -0.14077187573 +1403638546677829376.0000000000 2.6126316462 2.7167327379 1.3915884410 0.5471950527 0.7916619867 0.2311113585 -0.142955982816 +1403638546727829504.0000000000 2.5814063945 2.7524424072 1.3946950762 0.5468070131 0.7905562685 0.2344601793 -0.145090665085 +1403638546777829376.0000000000 2.5494628639 2.7889742616 1.4008024695 0.5465758492 0.7895201160 0.2380021193 -0.145834902187 +1403638546827829504.0000000000 2.5172691275 2.8254021147 1.4086438459 0.5462852824 0.7886277028 0.2413831697 -0.146194740227 +1403638546877829376.0000000000 2.4844665863 2.8624221992 1.4181889063 0.5460086930 0.7879679625 0.2438281910 -0.14672699352 +1403638546927829504.0000000000 2.4516112750 2.8990205601 1.4269767911 0.5458344145 0.7873650123 0.2463071993 -0.146471474709 +1403638546977829376.0000000000 2.4184280121 2.9354112607 1.4341804370 0.5461342898 0.7865302868 0.2490306875 -0.145227965843 +1403638547027829504.0000000000 2.3846010188 2.9717130069 1.4398066924 0.5463183078 0.7858970960 0.2509333692 -0.14468761272 +1403638547077829376.0000000000 2.3503273853 3.0078630619 1.4438863376 0.5465687139 0.7853942491 0.2529644738 -0.142924768266 +1403638547127829504.0000000000 2.3151140151 3.0440479763 1.4463518735 0.5467718159 0.7848908408 0.2554196813 -0.140526636917 +1403638547177829376.0000000000 2.2789901278 3.0798045524 1.4476924056 0.5467344627 0.7846999110 0.2566172780 -0.139553035217 +1403638547227829504.0000000000 2.2419989534 3.1152902506 1.4480881119 0.5468872730 0.7844385678 0.2577508425 -0.138329125922 +1403638547277829376.0000000000 2.2039879115 3.1504205941 1.4477998529 0.5475420551 0.7839583648 0.2584568328 -0.137138782875 +1403638547327829504.0000000000 2.1648171368 3.1850909401 1.4468670858 0.5475927884 0.7839818779 0.2586300647 -0.136473597662 +1403638547377829376.0000000000 2.1241992460 3.2187652145 1.4456397150 0.5469675375 0.7846660619 0.2557060186 -0.140499523841 +1403638547427829504.0000000000 2.0828673114 3.2523085584 1.4431966467 0.5456239205 0.7858373729 0.2537603760 -0.142687884197 +1403638547477829376.0000000000 2.0406228841 3.2856951604 1.4404863241 0.5452038117 0.7863791630 0.2510582596 -0.146049190234 +1403638547527829504.0000000000 1.9978849011 3.3189416444 1.4363820534 0.5439030725 0.7875874937 0.2487317473 -0.148350616259 +1403638547577829376.0000000000 1.9546948419 3.3523906235 1.4311183337 0.5431038010 0.7884835299 0.2465975985 -0.150072012303 +1403638547627829504.0000000000 1.9111888196 3.3859919797 1.4242079283 0.5428367413 0.7889079690 0.2453366544 -0.150872180157 +1403638547677829376.0000000000 1.8674990672 3.4199008813 1.4160279126 0.5429100734 0.7891724612 0.2445173441 -0.150554797891 +1403638547727829504.0000000000 1.8234510787 3.4538372260 1.4065848789 0.5432282731 0.7891219897 0.2448282438 -0.149159846137 +1403638547777829376.0000000000 1.7789405338 3.4877466018 1.3961051545 0.5438409974 0.7888250787 0.2451975777 -0.147885471696 +1403638547827829504.0000000000 1.7341135758 3.5218677734 1.3842700006 0.5450821354 0.7879792731 0.2476215901 -0.143727794738 +1403638547877829376.0000000000 1.6885235928 3.5556700574 1.3721722648 0.5466130276 0.7869549709 0.2480404417 -0.142800599048 +1403638547927829504.0000000000 1.6421338599 3.5890655052 1.3603963258 0.5454816569 0.7878096695 0.2476434887 -0.14310272265 +1403638547977829376.0000000000 1.5948690492 3.6227380277 1.3505392278 0.5462913371 0.7870203360 0.2483959712 -0.143053162379 +1403638548027829504.0000000000 1.5470051886 3.6558023654 1.3423970657 0.5445506869 0.7877498807 0.2488445630 -0.144882912297 +1403638548077829376.0000000000 1.4978440178 3.6892626034 1.3363681821 0.5434044489 0.7875766314 0.2506697588 -0.146967093401 +1403638548127829504.0000000000 1.4481493169 3.7225678912 1.3323383376 0.5426996916 0.7867284576 0.2534840871 -0.149268872697 +1403638548177829376.0000000000 1.3973197649 3.7558841234 1.3304068566 0.5409077085 0.7861211358 0.2570950197 -0.152756543469 +1403638548227829504.0000000000 1.3460604888 3.7887958139 1.3308541491 0.5400845610 0.7843834088 0.2616403770 -0.156829997593 +1403638548277829376.0000000000 1.2946323470 3.8209689521 1.3327033581 0.5374421970 0.7833690028 0.2673464199 -0.161290985643 +1403638548327829504.0000000000 1.2425501156 3.8532399927 1.3373513215 0.5364979995 0.7807066664 0.2737331625 -0.166544748992 +1403638548377829376.0000000000 1.1898410510 3.8853311364 1.3438716044 0.5337712364 0.7788277669 0.2814763964 -0.171133325181 +1403638548427829504.0000000000 1.1362995394 3.9173220587 1.3526553016 0.5317633420 0.7763783977 0.2888083728 -0.176221609128 +1403638548477829376.0000000000 1.0825495275 3.9495367503 1.3618863929 0.5303846411 0.7738441103 0.2948983185 -0.181362640288 +1403638548527829504.0000000000 1.0281796520 3.9817192993 1.3705202855 0.5290222809 0.7717370093 0.3000382592 -0.1858344905 +1403638548577829376.0000000000 0.9734650256 4.0143334868 1.3776986958 0.5282442317 0.7694220438 0.3051444589 -0.189300315516 +1403638548627829504.0000000000 0.9184173705 4.0474109360 1.3834735600 0.5273818365 0.7676507106 0.3092708983 -0.192177773259 +1403638548677829376.0000000000 0.8629863540 4.0807835677 1.3883110625 0.5263957623 0.7663514761 0.3122216573 -0.195270461443 +1403638548727829504.0000000000 0.8074083507 4.1146203623 1.3920233476 0.5256516121 0.7652012080 0.3152570156 -0.196902280702 +1403638548777829376.0000000000 0.7516110926 4.1486219138 1.3960666196 0.5250937254 0.7642331704 0.3173592571 -0.198764541229 +1403638548827829504.0000000000 0.6954563096 4.1828489837 1.4015876051 0.5242370525 0.7636909292 0.3192716279 -0.200043258196 +1403638548877829376.0000000000 0.6383930530 4.2181567174 1.4091548370 0.5238192534 0.7632353333 0.3206361122 -0.200693047747 +1403638548927829504.0000000000 0.5807934747 4.2534042443 1.4184157179 0.5236992812 0.7626792158 0.3211244822 -0.202332754435 +1403638548977829376.0000000000 0.5231146355 4.2886997652 1.4291046147 0.5232580451 0.7626496457 0.3218751307 -0.202393024602 +1403638549027829504.0000000000 0.4654450758 4.3237911462 1.4411625898 0.5226475752 0.7627191210 0.3230741824 -0.201797242896 +1403638549077829376.0000000000 0.4075487348 4.3587589585 1.4549714625 0.5227547610 0.7625843262 0.3223727795 -0.203146243623 +1403638549127829504.0000000000 0.3498153850 4.3936316711 1.4701432979 0.5227308268 0.7626678818 0.3215604378 -0.204179013851 +1403638549177829376.0000000000 0.2916311066 4.4289622079 1.4874909665 0.5234543663 0.7622066441 0.3215010422 -0.204141220758 +1403638549227829504.0000000000 0.2327449145 4.4648445005 1.5058649702 0.5230519158 0.7625676831 0.3210845996 -0.204479588117 +1403638549277829376.0000000000 0.1728748838 4.5016032998 1.5258110461 0.5231524820 0.7627034707 0.3202701486 -0.204992507665 +1403638549327829504.0000000000 0.1128968577 4.5383379635 1.5472599655 0.5229690783 0.7630553193 0.3189467184 -0.206210847573 +1403638549377829376.0000000000 0.0528330765 4.5750576194 1.5695796080 0.5229856154 0.7632885727 0.3175398963 -0.207472926342 +1403638549427829504.0000000000 -0.0074367564 4.6122686521 1.5912555687 0.5232568909 0.7633541294 0.3161286450 -0.208699255289 +1403638549477829376.0000000000 -0.0678917337 4.6497974273 1.6113797610 0.5227895698 0.7639167811 0.3150190200 -0.20948802919 +1403638549527829504.0000000000 -0.1282467374 4.6878396057 1.6299007581 0.5229725003 0.7640025786 0.3143670258 -0.209697870511 +1403638549577829376.0000000000 -0.1885747538 4.7260514925 1.6473218651 0.5242051941 0.7633545258 0.3134042681 -0.210419930664 +1403638549627829504.0000000000 -0.2486065405 4.7648345487 1.6634280650 0.5255013169 0.7625949059 0.3128297290 -0.210795958349 +1403638549677829376.0000000000 -0.3080857608 4.8036633992 1.6785783913 0.5261607507 0.7623498067 0.3121335891 -0.211069323401 +1403638549727829504.0000000000 -0.3665963833 4.8425317928 1.6929436430 0.5269462244 0.7620017749 0.3130335921 -0.209023782988 +1403638549777829376.0000000000 -0.4250366797 4.8812506265 1.7080422056 0.5260498473 0.7626882521 0.3125997757 -0.209426761448 +1403638549827829504.0000000000 -0.4838163111 4.9206805054 1.7247202551 0.5251398063 0.7633804630 0.3121284466 -0.209891127647 +1403638549877829376.0000000000 -0.5423622978 4.9605540770 1.7433175530 0.5242624262 0.7641792919 0.3122204045 -0.209039080628 +1403638549927829504.0000000000 -0.6010584967 5.0008690489 1.7634566388 0.5239664646 0.7644484120 0.3125903281 -0.208242781968 +1403638549977829376.0000000000 -0.6600984641 5.0413613035 1.7851440214 0.5230944773 0.7650378887 0.3120089167 -0.209140222369 +1403638550027829504.0000000000 -0.7191357555 5.0823517288 1.8090253945 0.5230728347 0.7651323714 0.3117182282 -0.209282130259 +1403638550077829376.0000000000 -0.7786634903 5.1243436729 1.8348989522 0.5227487361 0.7653089230 0.3116565835 -0.209538028344 +1403638550127829504.0000000000 -0.8370309719 5.1649292031 1.8617094388 0.5218299308 0.7658586817 0.3109245110 -0.210902705988 +1403638550177829376.0000000000 -0.8950485528 5.2062213231 1.8903249469 0.5217608278 0.7657689649 0.3114088811 -0.210684692599 +1403638550227829504.0000000000 -0.9524911130 5.2470438320 1.9206379188 0.5211905408 0.7659600704 0.3117626214 -0.210878303017 +1403638550277829376.0000000000 -1.0097278260 5.2881336505 1.9528616501 0.5214623395 0.7657038013 0.3123743391 -0.210230800293 +1403638550327829504.0000000000 -1.0668669345 5.3296433923 1.9862689808 0.5216664793 0.7654744662 0.3128082641 -0.209914067962 +1403638550377829376.0000000000 -1.1233334283 5.3704310084 2.0183682509 0.5222162082 0.7649656833 0.3131395922 -0.209907911129 +1403638550427829504.0000000000 -1.1799309014 5.4117932203 2.0489307828 0.5222271801 0.7647991139 0.3121938841 -0.211886919209 +1403638550477829376.0000000000 -1.2363447256 5.4537951743 2.0772715221 0.5219071475 0.7650174282 0.3114917181 -0.212918231735 +1403638550527829504.0000000000 -1.2927366677 5.4965106982 2.1042474020 0.5210366556 0.7654942777 0.3103119774 -0.215048345863 +1403638550577829376.0000000000 -1.3490586473 5.5406472453 2.1301610067 0.5218688089 0.7648835742 0.3090824757 -0.216965636577 +1403638550627829504.0000000000 -1.4047567722 5.5853062633 2.1545713045 0.5234559907 0.7638125747 0.3076858453 -0.218891747721 +1403638550677829376.0000000000 -1.4597605872 5.6303879140 2.1779926757 0.5257445669 0.7622444063 0.3064815815 -0.220556468085 +1403638550727829504.0000000000 -1.5148023076 5.6781788550 2.2004502536 0.5264734260 0.7617105673 0.3053582310 -0.222214072795 +1403638550777829376.0000000000 -1.5685275139 5.7253032227 2.2215551980 0.5278527787 0.7608525372 0.3047134014 -0.222765804337 +1403638550827829504.0000000000 -1.6215070766 5.7730429028 2.2420252003 0.5310907929 0.7586981020 0.3035761319 -0.223967166739 +1403638550877829376.0000000000 -1.6736704835 5.8210532919 2.2618087922 0.5350420884 0.7558866197 0.3020231187 -0.226157948153 +1403638550927829504.0000000000 -1.7247645541 5.8692697592 2.2804896857 0.5396582169 0.7528494867 0.3006238658 -0.227182637177 +1403638550977829376.0000000000 -1.7746939243 5.9168148553 2.2978657940 0.5429808295 0.7504303253 0.2992680593 -0.229051902986 +1403638551027829504.0000000000 -1.8232406552 5.9639034191 2.3140768017 0.5455047612 0.7486658986 0.2981140090 -0.230330122766 +1403638551077829376.0000000000 -1.8699092617 6.0104791065 2.3298412293 0.5476658811 0.7471122870 0.2974221390 -0.231139318392 +1403638551127829504.0000000000 -1.9149421393 6.0564647709 2.3461789368 0.5477147153 0.7470306868 0.2961737430 -0.232883785419 +1403638551177829376.0000000000 -1.9579923878 6.1019068440 2.3639968897 0.5478689926 0.7465943298 0.2946592054 -0.235822870485 +1403638551227829504.0000000000 -1.9987810901 6.1471327450 2.3829275656 0.5473973574 0.7467594080 0.2941366259 -0.237044647832 +1403638551277829376.0000000000 -2.0373943491 6.1922801646 2.4030824976 0.5464841958 0.7478385139 0.2930248135 -0.237126631802 +1403638551327829504.0000000000 -2.0733491971 6.2369690446 2.4239940068 0.5442347428 0.7505302032 0.2917412571 -0.235372041165 +1403638551377829376.0000000000 -2.1074182657 6.2814159997 2.4449774983 0.5426208930 0.7538884980 0.2875318798 -0.233538256206 +1403638551427829504.0000000000 -2.1390061957 6.3262659047 2.4645626001 0.5415858732 0.7578096803 0.2818775075 -0.230118015722 +1403638551477829376.0000000000 -2.1686773712 6.3708745917 2.4830886474 0.5410127362 0.7621695357 0.2743996427 -0.226070020683 +1403638551527829504.0000000000 -2.1966551632 6.4159206799 2.5005190059 0.5409515740 0.7667016722 0.2647070150 -0.222418831726 +1403638551577829376.0000000000 -2.2224568334 6.4610233576 2.5163823135 0.5426192263 0.7703135025 0.2537968213 -0.21856041873 +1403638551627829504.0000000000 -2.2462909585 6.5063897327 2.5307417919 0.5421762572 0.7753412864 0.2420427654 -0.215188511288 +1403638551677829376.0000000000 -2.2679811719 6.5524508873 2.5437938565 0.5430298587 0.7794381008 0.2305263009 -0.210837482749 +1403638551727829504.0000000000 -2.2872968654 6.5993750588 2.5558109610 0.5451903707 0.7826515512 0.2193331670 -0.205224197092 +1403638551777829376.0000000000 -2.3042888858 6.6469801041 2.5658057913 0.5472304568 0.7858520709 0.2082053859 -0.199062470111 +1403638551827829504.0000000000 -2.3191311833 6.6955891575 2.5748282987 0.5495746879 0.7884370862 0.1978032063 -0.192895088162 +1403638551877829376.0000000000 -2.3311260620 6.7440594762 2.5832107279 0.5525588483 0.7899849723 0.1898774715 -0.185873636147 +1403638551927829504.0000000000 -2.3405082269 6.7928872503 2.5922084846 0.5561510815 0.7905784260 0.1852130337 -0.177137966185 +1403638551977829376.0000000000 -2.3477977140 6.8420291265 2.6029280086 0.5601570529 0.7902004423 0.1814667361 -0.169932812577 +1403638552027829504.0000000000 -2.3527175799 6.8912128875 2.6159822832 0.5638555197 0.7897713911 0.1786967357 -0.162467163853 +1403638552077829376.0000000000 -2.3557050518 6.9395752699 2.6307277731 0.5662605275 0.7896912266 0.1761986265 -0.157133146167 +1403638552127829504.0000000000 -2.3569557380 6.9873834982 2.6467753361 0.5660872391 0.7910747861 0.1740374404 -0.153156423128 +1403638552177829376.0000000000 -2.3565637111 7.0346032489 2.6644664448 0.5644399520 0.7931184987 0.1715896426 -0.15141856584 +1403638552227829504.0000000000 -2.3545567173 7.0817454313 2.6835834781 0.5628123274 0.7949210248 0.1704117282 -0.149340856527 +1403638552277829376.0000000000 -2.3510950383 7.1288065374 2.7032889870 0.5612732558 0.7964754281 0.1692991213 -0.148111553311 +1403638552327829504.0000000000 -2.3460676836 7.1754582094 2.7232099069 0.5609161645 0.7969795618 0.1683825355 -0.147797010312 +1403638552377829376.0000000000 -2.3401303116 7.2222321672 2.7424730530 0.5616123256 0.7965172272 0.1662752494 -0.150014812328 +1403638552427829504.0000000000 -2.3328016476 7.2694532301 2.7607075514 0.5654748045 0.7938104152 0.1641854130 -0.152139476618 +1403638552477829376.0000000000 -2.3238218678 7.3167666059 2.7778906951 0.5688598147 0.7912453570 0.1623283615 -0.154850893773 +1403638552527829504.0000000000 -2.3130730403 7.3638762993 2.7935481769 0.5719162411 0.7889362803 0.1609391111 -0.156811866193 +1403638552577829376.0000000000 -2.3004952713 7.4103459782 2.8077461928 0.5747897501 0.7866625143 0.1603297281 -0.158345224529 +1403638552627829504.0000000000 -2.2859385080 7.4566154341 2.8205735611 0.5765083858 0.7852466599 0.1607851850 -0.158662813911 +1403638552677829376.0000000000 -2.2691282601 7.5016921988 2.8312434903 0.5764763465 0.7850576749 0.1622532137 -0.158219353032 +1403638552727829504.0000000000 -2.2502135545 7.5460930010 2.8407430543 0.5759243797 0.7852621163 0.1628282510 -0.158623700282 +1403638552777829376.0000000000 -2.2290972557 7.5897604744 2.8487639658 0.5755424225 0.7853390061 0.1645599955 -0.157840340871 +1403638552827829504.0000000000 -2.2061898867 7.6328252788 2.8556543512 0.5752005046 0.7853175228 0.1661533882 -0.157524028208 +1403638552877829376.0000000000 -2.1812095822 7.6750845158 2.8611305664 0.5746263946 0.7855060498 0.1687598999 -0.15590012343 +1403638552927829504.0000000000 -2.1544382562 7.7164377757 2.8650394876 0.5734845476 0.7860031537 0.1720528812 -0.153988058544 +1403638552977829376.0000000000 -2.1259836763 7.7570106584 2.8676501325 0.5738539002 0.7855076378 0.1752570149 -0.151507197487 +1403638553027829504.0000000000 -2.0961430903 7.7966900538 2.8688902279 0.5728247318 0.7859699182 0.1785638562 -0.14912432274 +1403638553077829376.0000000000 -2.0653821154 7.8355487185 2.8689521524 0.5732162748 0.7853348086 0.1811394284 -0.147854144935 +1403638553127829504.0000000000 -2.0339946803 7.8738132462 2.8687128782 0.5743597152 0.7840994927 0.1818783303 -0.149060981044 +1403638553177829376.0000000000 -2.0016628767 7.9115256690 2.8680372917 0.5774896994 0.7813830498 0.1812291385 -0.15199399976 +1403638553227829504.0000000000 -1.9680831206 7.9483712779 2.8671637310 0.5814230659 0.7780816581 0.1802269203 -0.155094838421 +1403638553277829376.0000000000 -1.9328390032 7.9839549392 2.8668631331 0.5851321060 0.7749642799 0.1801752527 -0.156804533524 +1403638553327829504.0000000000 -1.8961401133 8.0184608839 2.8679364698 0.5884645796 0.7721183216 0.1808959064 -0.157541763 +1403638553377829376.0000000000 -1.8573554059 8.0509915836 2.8695770795 0.5903323757 0.7704507178 0.1827851801 -0.156534199272 +1403638553427829504.0000000000 -1.8168565281 8.0819463940 2.8727046779 0.5932618170 0.7681951567 0.1854254469 -0.153408022426 +1403638553477829376.0000000000 -1.7750952162 8.1110951774 2.8771906503 0.5951516125 0.7665955183 0.1880368493 -0.150890731527 +1403638553527829504.0000000000 -1.7321270503 8.1384099500 2.8837053895 0.5968615080 0.7651749031 0.1902110129 -0.148605109347 +1403638553577829376.0000000000 -1.6873860077 8.1626663978 2.8917442701 0.5987828319 0.7636097068 0.1923236104 -0.146188114362 +1403638553627829504.0000000000 -1.6409588960 8.1835701363 2.9002360141 0.5991023092 0.7633284527 0.1936749342 -0.14455489037 +1403638553677829376.0000000000 -1.5935118920 8.2015303029 2.9107223466 0.5986936523 0.7635153376 0.1947466112 -0.143819321796 +1403638553727829504.0000000000 -1.5451665872 8.2173152534 2.9241264779 0.5983688158 0.7636982653 0.1955463257 -0.14311308214 +1403638553777829376.0000000000 -1.4955100938 8.2296869717 2.9381083988 0.5971038869 0.7646367490 0.1962669307 -0.142396917963 +1403638553827829504.0000000000 -1.4458924504 8.2409323852 2.9544332085 0.5958110607 0.7656497403 0.1967719249 -0.141670267771 +1403638553877829376.0000000000 -1.3952881105 8.2494174504 2.9722640391 0.5943033659 0.7668677798 0.1970407843 -0.141039877008 +1403638553927829504.0000000000 -1.3440962760 8.2558091723 2.9904140699 0.5931381262 0.7678296287 0.1973019971 -0.140345097391 +1403638553977829376.0000000000 -1.2926666850 8.2601973573 3.0076498111 0.5904861804 0.7698810412 0.1962942116 -0.14169627926 +1403638554027829504.0000000000 -1.2405656979 8.2629303439 3.0236552631 0.5876890980 0.7720455834 0.1953660340 -0.142825956967 +1403638554077829376.0000000000 -1.1877384958 8.2641746075 3.0385982920 0.5860859273 0.7732978629 0.1960058683 -0.141758247122 +1403638554127829504.0000000000 -1.1344328015 8.2637617503 3.0522492383 0.5846717876 0.7743383540 0.1963399554 -0.141455421625 +1403638554177829376.0000000000 -1.0806426283 8.2620700871 3.0634246825 0.5807323337 0.7772921100 0.1983918550 -0.138591501086 +1403638554227829504.0000000000 -1.0268107758 8.2592900083 3.0729613360 0.5753473211 0.7812215576 0.2003169828 -0.136166972916 +1403638554277829376.0000000000 -0.9729440040 8.2556483648 3.0813312871 0.5703848168 0.7848092482 0.2018458771 -0.134141144634 +1403638554327829504.0000000000 -0.9191690248 8.2513871657 3.0885774304 0.5667447024 0.7873303963 0.2037323386 -0.131925826392 +1403638554377829376.0000000000 -0.8656078738 8.2462483391 3.0946379044 0.5637087179 0.7894294081 0.2050040932 -0.130410938141 +1403638554427829504.0000000000 -0.8128058939 8.2412503492 3.1003594792 0.5619426856 0.7906184876 0.2056450590 -0.12981885454 +1403638554477829376.0000000000 -0.7606800653 8.2359817724 3.1051343295 0.5606020867 0.7915044028 0.2065501198 -0.128775497287 +1403638554527829504.0000000000 -0.7094359797 8.2307621901 3.1093305977 0.5601604195 0.7917930395 0.2065960116 -0.128849427679 +1403638554577829376.0000000000 -0.6588247828 8.2252390877 3.1126762768 0.5594546753 0.7921989493 0.2059401486 -0.130460516328 +1403638554627829504.0000000000 -0.6088583772 8.2193565597 3.1165922108 0.5583906857 0.7929522896 0.2045627995 -0.132591739931 +1403638554677829376.0000000000 -0.5595240254 8.2134913576 3.1225687518 0.5582697185 0.7930178777 0.2015606547 -0.137225615388 +1403638554727829504.0000000000 -0.5097077233 8.2072634378 3.1294306051 0.5590132008 0.7925038491 0.2007191180 -0.138396987452 +1403638554777829376.0000000000 -0.4602038397 8.2006769132 3.1376363718 0.5589224543 0.7924951869 0.1982725555 -0.142285145561 +1403638554827829504.0000000000 -0.4108472170 8.1951824592 3.1466986012 0.5590554337 0.7923218463 0.1978959760 -0.143249072067 +1403638554877829376.0000000000 -0.3616241819 8.1902637907 3.1573278050 0.5595677935 0.7919710227 0.1963471562 -0.145305120041 +1403638554927829504.0000000000 -0.3122512544 8.1856266956 3.1683575868 0.5600190304 0.7916849977 0.1953732546 -0.146433744208 +1403638554977829376.0000000000 -0.2625904710 8.1814536660 3.1787725697 0.5607664865 0.7915164303 0.1930759275 -0.147527537798 +1403638555027829504.0000000000 -0.2124369235 8.1774682589 3.1875554215 0.5615925078 0.7917728531 0.1906909803 -0.146104600192 +1403638555077829376.0000000000 -0.1615748394 8.1736495112 3.1941828941 0.5617102016 0.7928811606 0.1879198421 -0.143203518154 +1403638555127829504.0000000000 -0.1101312878 8.1702211914 3.2001393448 0.5620240225 0.7941942772 0.1844535421 -0.13914502842 +1403638555177829376.0000000000 -0.0583286173 8.1669610483 3.2043894778 0.5617440613 0.7960811377 0.1795322697 -0.13589185351 +1403638555227829504.0000000000 -0.0062426761 8.1640435373 3.2070931841 0.5622401092 0.7974930450 0.1742487309 -0.132394420347 +1403638555277829376.0000000000 0.0461566859 8.1608394313 3.2084550553 0.5624448132 0.7988858824 0.1697602763 -0.128913256093 +1403638555327829504.0000000000 0.0987340388 8.1578424310 3.2089050671 0.5630297873 0.7998201357 0.1659028093 -0.125544681145 +1403638555377829376.0000000000 0.1515971911 8.1552901570 3.2085225260 0.5642841552 0.8000803793 0.1641695489 -0.120428975042 +1403638555427829504.0000000000 0.2044227604 8.1530418011 3.2069692986 0.5647301581 0.8007325570 0.1623514559 -0.116401140252 +1403638555477829376.0000000000 0.2571737403 8.1508734093 3.2042781112 0.5656421639 0.8008689046 0.1605090419 -0.113555218115 +1403638555527829504.0000000000 0.3095493250 8.1487549111 3.2008094335 0.5658182425 0.8013324011 0.1581599131 -0.112701115085 +1403638555577829376.0000000000 0.3619961859 8.1466551720 3.1970590628 0.5667022846 0.8011432136 0.1574937209 -0.110516061681 +1403638555627829504.0000000000 0.4141071842 8.1444812235 3.1941478000 0.5662635079 0.8017588944 0.1563438918 -0.10993135298 +1403638555677829376.0000000000 0.4662690947 8.1421680805 3.1940275052 0.5659140779 0.8021868713 0.1552933194 -0.110097524593 +1403638555727829504.0000000000 0.5186968560 8.1392884085 3.1954810368 0.5653280041 0.8026786884 0.1545314044 -0.110594827927 +1403638555777829376.0000000000 0.5713714163 8.1362877865 3.1996362277 0.5643849648 0.8033746876 0.1550349021 -0.109648994153 +1403638555827829504.0000000000 0.6239376366 8.1331015641 3.2067484886 0.5642517295 0.8034124229 0.1554879740 -0.10941642713 +1403638555877829376.0000000000 0.6766628077 8.1295652614 3.2145737944 0.5636999689 0.8037342537 0.1559595057 -0.109225578401 +1403638555927829504.0000000000 0.7290888246 8.1269676114 3.2230836513 0.5637040552 0.8036644588 0.1570325010 -0.108175641614 +1403638555977829376.0000000000 0.7808092911 8.1255698559 3.2337701228 0.5643044794 0.8031301574 0.1579793872 -0.10763325733 +1403638556027829504.0000000000 0.8322057992 8.1245218235 3.2460224152 0.5643409325 0.8030548472 0.1587024582 -0.106938085516 +1403638556077829376.0000000000 0.8835263725 8.1236572035 3.2579859121 0.5633837103 0.8036959194 0.1592135046 -0.106408289069 +1403638556127829504.0000000000 0.9345043868 8.1224340108 3.2695687115 0.5610404110 0.8052967507 0.1590337979 -0.10695350189 +1403638556177829376.0000000000 0.9855010063 8.1213331813 3.2791358441 0.5572459439 0.8079612501 0.1582279814 -0.107886432379 +1403638556227829504.0000000000 1.0363785023 8.1205977686 3.2869094766 0.5542461121 0.8100065044 0.1586179873 -0.107429251745 +1403638556277829376.0000000000 1.0868501092 8.1204762617 3.2936381909 0.5522255705 0.8113678105 0.1580873369 -0.108340155623 +1403638556327829504.0000000000 1.1368607417 8.1208699004 3.2995609493 0.5503437150 0.8126522037 0.1582923410 -0.107989471799 +1403638556377829376.0000000000 1.1863827915 8.1222130912 3.3048169428 0.5489178044 0.8135991350 0.1580942264 -0.108406212999 +1403638556427829504.0000000000 1.2355191877 8.1248535257 3.3096409701 0.5472540271 0.8147096306 0.1582969117 -0.108181954447 +1403638556477829376.0000000000 1.2840097622 8.1288475026 3.3140818003 0.5440297841 0.8169302134 0.1582397638 -0.107781248735 +1403638556527829504.0000000000 1.3320644928 8.1342890125 3.3185306629 0.5417600231 0.8184751038 0.1583067311 -0.107394416927 +1403638556577829376.0000000000 1.3794862134 8.1412263788 3.3235266351 0.5402975698 0.8195292709 0.1568894481 -0.108793434023 +1403638556627829504.0000000000 1.4259087928 8.1498404795 3.3287809023 0.5396298719 0.8200228418 0.1537020673 -0.112861927877 +1403638556677829376.0000000000 1.4724066765 8.1599899628 3.3350042403 0.5401483073 0.8197485618 0.1502778494 -0.116913085589 +1403638556727829504.0000000000 1.5192089387 8.1719055080 3.3433478004 0.5436445389 0.8174623712 0.1481596383 -0.11939266516 +1403638556777829376.0000000000 1.5669764922 8.1841289578 3.3532989736 0.5471214458 0.8150963880 0.1468559059 -0.121282087082 +1403638556827829504.0000000000 1.6153579958 8.1974658760 3.3648780052 0.5498537261 0.8132324979 0.1449907777 -0.123658637337 +1403638556877829376.0000000000 1.6638842475 8.2129459091 3.3781530277 0.5513605390 0.8121625166 0.1433319982 -0.125894959904 +1403638556927829504.0000000000 1.7132461288 8.2296696597 3.3927355588 0.5533899983 0.8107567647 0.1422106021 -0.127315053589 +1403638556977829376.0000000000 1.7632489181 8.2472211146 3.4067113089 0.5546678632 0.8098597436 0.1413940783 -0.128368500207 +1403638557027829504.0000000000 1.8142055379 8.2656361491 3.4190242703 0.5554172630 0.8093167040 0.1420745079 -0.127800511559 +1403638557077829376.0000000000 1.8660032581 8.2848133003 3.4295046243 0.5559594867 0.8089441580 0.1432823776 -0.126445872442 +1403638557127829504.0000000000 1.9184739976 8.3047068971 3.4381607945 0.5567360433 0.8084152225 0.1447739127 -0.12470092346 +1403638557177829376.0000000000 1.9714221902 8.3252469990 3.4452829648 0.5573451505 0.8079606556 0.1453398626 -0.124266997256 +1403638557227829504.0000000000 2.0248140308 8.3468403663 3.4505859093 0.5580130636 0.8075117054 0.1462212671 -0.123148721103 +1403638557277829376.0000000000 2.0790166758 8.3685631414 3.4545219521 0.5582189642 0.8073143766 0.1467466288 -0.122884141937 +1403638557327829504.0000000000 2.1339913858 8.3910812670 3.4573663134 0.5585206312 0.8071222358 0.1476489250 -0.12168893118 +1403638557377829376.0000000000 2.1895955203 8.4140992430 3.4600696013 0.5588123247 0.8068759890 0.1491895419 -0.120093316952 +1403638557427829504.0000000000 2.2456949743 8.4375698224 3.4636674668 0.5597338437 0.8062395415 0.1511387727 -0.11761333808 +1403638557477829376.0000000000 2.3023640479 8.4619720830 3.4682301553 0.5606836341 0.8055409997 0.1543772352 -0.113601186174 +1403638557527829504.0000000000 2.3589007448 8.4865214809 3.4749301283 0.5613140429 0.8051376901 0.1561686295 -0.110865704152 +1403638557577829376.0000000000 2.4157858534 8.5102410504 3.4832661256 0.5624245635 0.8043405893 0.1581259168 -0.108217471608 +1403638557627829504.0000000000 2.4721402136 8.5345568919 3.4926185839 0.5630428705 0.8038985636 0.1592329749 -0.106652169015 +1403638557677829376.0000000000 2.5279487209 8.5590427262 3.5034400779 0.5630130430 0.8038836669 0.1602599073 -0.105376115538 +1403638557727829504.0000000000 2.5830731096 8.5834548853 3.5155362195 0.5636592670 0.8034894172 0.1600657892 -0.105223240255 +1403638557777829376.0000000000 2.6376953221 8.6076738578 3.5271349181 0.5637263310 0.8034641012 0.1600196158 -0.105127467385 +1403638557827829504.0000000000 2.6919651443 8.6317373255 3.5370296786 0.5638342483 0.8034979980 0.1608266486 -0.103037356019 +1403638557877829376.0000000000 2.7454594739 8.6554219664 3.5454146140 0.5632562228 0.8039107534 0.1613197537 -0.102205015101 +1403638557927829504.0000000000 2.7985916900 8.6788370870 3.5519722643 0.5626503524 0.8043521928 0.1623087728 -0.100488771125 +1403638557977829376.0000000000 2.8510133918 8.7020188329 3.5567535072 0.5608182214 0.8056550094 0.1624013732 -0.100143508708 +1403638558027829504.0000000000 2.9028031063 8.7251238353 3.5598332878 0.5584957118 0.8072477841 0.1623457627 -0.100386295548 +1403638558077829376.0000000000 2.9538900627 8.7480446111 3.5612357502 0.5552715732 0.8094792192 0.1618027073 -0.101176862732 +1403638558127829504.0000000000 3.0046685393 8.7711292698 3.5611894230 0.5511533132 0.8123729090 0.1614268022 -0.101102272701 +1403638558177829376.0000000000 3.0545914569 8.7946191652 3.5613129667 0.5465647356 0.8154797123 0.1611995400 -0.101363390902 +1403638558227829504.0000000000 3.1037491261 8.8191819800 3.5625013232 0.5419016394 0.8187014188 0.1604763046 -0.101577338525 +1403638558277829376.0000000000 3.1522222832 8.8452909567 3.5650996472 0.5400277245 0.8199652448 0.1613427074 -0.099977922312 +1403638558327829504.0000000000 3.1995072240 8.8729473055 3.5698108721 0.5382913950 0.8211498826 0.1620486116 -0.0984656885207 +1403638558377829376.0000000000 3.2455986382 8.9023686009 3.5775639975 0.5367219280 0.8221898894 0.1634136832 -0.0960693805214 +1403638558427829504.0000000000 3.2908853790 8.9320421033 3.5870604009 0.5328986412 0.8246876504 0.1645554483 -0.0939724533303 +1403638558477829376.0000000000 3.3345215699 8.9634832560 3.5978392945 0.5294886682 0.8269061732 0.1655485307 -0.0919870368332 +1403638558527829504.0000000000 3.3763655205 8.9967428442 3.6111999654 0.5275305511 0.8282434409 0.1648892039 -0.0923897759237 +1403638558577829376.0000000000 3.4164477526 9.0319836244 3.6264796680 0.5266606191 0.8288723658 0.1634085698 -0.0943230234016 +1403638558627829504.0000000000 3.4551077171 9.0696004954 3.6441575578 0.5282466962 0.8280579217 0.1606923048 -0.0972290565448 +1403638558677829376.0000000000 3.4921032417 9.1088567705 3.6630849569 0.5296486013 0.8273069397 0.1569790289 -0.101946903671 +1403638558727829504.0000000000 3.5283761998 9.1501957145 3.6819950174 0.5321334514 0.8258414560 0.1530401038 -0.106764254683 +1403638558777829376.0000000000 3.5646045220 9.1931197826 3.6988875256 0.5337259291 0.8248890856 0.1512724775 -0.108679651332 +1403638558827829504.0000000000 3.6006686245 9.2372083190 3.7142253093 0.5353768054 0.8238696911 0.1491289601 -0.111224824524 +1403638558877829376.0000000000 3.6363547404 9.2832061049 3.7286459815 0.5368388580 0.8229615991 0.1496387445 -0.110211130078 +1403638558927829504.0000000000 3.6721648721 9.3303585966 3.7408528341 0.5402933421 0.8207328691 0.1495858006 -0.11002159044 +1403638558977829376.0000000000 3.7079462624 9.3788936942 3.7515015397 0.5443830126 0.8180402073 0.1501136119 -0.109193673603 +1403638559027829504.0000000000 3.7437177667 9.4284741397 3.7601925034 0.5476043570 0.8158806487 0.1512224326 -0.107703347533 +1403638559077829376.0000000000 3.7791491218 9.4790580500 3.7676202433 0.5506783386 0.8138006597 0.1514698901 -0.107418462316 +1403638559127829504.0000000000 3.8143016976 9.5302819507 3.7731747670 0.5529245711 0.8122275033 0.1522615082 -0.106664589522 +1403638559177829376.0000000000 3.8493328877 9.5817787835 3.7773019770 0.5549998880 0.8107477016 0.1530133101 -0.106067033543 +1403638559227829504.0000000000 3.8843247239 9.6334802624 3.7797491377 0.5563721293 0.8096966086 0.1548514114 -0.104223299511 +1403638559277829376.0000000000 3.9188931408 9.6852947029 3.7808827771 0.5573655716 0.8089207917 0.1561774182 -0.102953321196 +1403638559327829504.0000000000 3.9532427980 9.7371469753 3.7803747593 0.5582367534 0.8082205744 0.1575957158 -0.101561905969 +1403638559377829376.0000000000 3.9874266641 9.7886801753 3.7780102767 0.5585323123 0.8079044364 0.1600117199 -0.0986322826071 +1403638559427829504.0000000000 4.0207525113 9.8398166873 3.7746317170 0.5595864685 0.8070361706 0.1619545267 -0.0965729511179 +1403638559477829376.0000000000 4.0531927850 9.8904996208 3.7698541788 0.5602442911 0.8064945158 0.1628707429 -0.0957394968454 +1403638559527829504.0000000000 4.0848540603 9.9410824074 3.7636502292 0.5611570684 0.8057797555 0.1639882052 -0.0944965539717 +1403638559577829376.0000000000 4.1156052370 9.9913604247 3.7563607556 0.5620589502 0.8050011570 0.1650532568 -0.0939164317389 +1403638559627829504.0000000000 4.1454937140 10.0414728983 3.7480820605 0.5628725884 0.8043873151 0.1651379870 -0.0941538196983 +1403638559677829376.0000000000 4.1746167634 10.0909526135 3.7397852102 0.5631770980 0.8040810957 0.1655829800 -0.0941670030961 +1403638559727829504.0000000000 4.2075051034 10.1579088471 3.7396862178 0.5634842227 0.8037642445 0.1659583095 -0.0943737760763 +1403638559777829376.0000000000 4.2353355096 10.2080793629 3.7345196691 0.5636165477 0.8035600201 0.1664626933 -0.0944343847596 +1403638559827829504.0000000000 4.2620400501 10.2581148630 3.7308276111 0.5624482602 0.8043223142 0.1657664887 -0.0961199285375 +1403638559877829376.0000000000 4.2878963035 10.3085934320 3.7285525506 0.5629624441 0.8040274417 0.1654700533 -0.096087569582 +1403638559927829504.0000000000 4.3131691579 10.3592240465 3.7267085604 0.5631691873 0.8044028777 0.1629689517 -0.0960083201951 +1403638559977829376.0000000000 4.3384693560 10.4101244094 3.7235674641 0.5635554865 0.8051717369 0.1586346108 -0.0945449521046 +1403638560027829504.0000000000 4.3632622101 10.4608378171 3.7188397451 0.5640404416 0.8063993270 0.1519649555 -0.0921149169558 +1403638560077829376.0000000000 4.3877476248 10.5116466567 3.7124217720 0.5648732298 0.8077725289 0.1437860321 -0.0880190480101 +1403638560127829504.0000000000 4.4119569975 10.5621201224 3.7041067940 0.5663032559 0.8090008144 0.1339262193 -0.0829582572538 +1403638560177829376.0000000000 4.4360253937 10.6126850523 3.6939745670 0.5680492264 0.8101352087 0.1233902289 -0.0759991536885 +1403638560227829504.0000000000 4.4599319699 10.6628907391 3.6822444169 0.5692523560 0.8116161806 0.1117361102 -0.0688910170223 +1403638560277829376.0000000000 4.4837484170 10.7122983457 3.6700589716 0.5713372575 0.8123419076 0.0996844974 -0.0611339874392 +1403638560327829504.0000000000 4.5071382139 10.7614829634 3.6572136184 0.5752805548 0.8115639359 0.0870292879 -0.0533119520497 +1403638560377829376.0000000000 4.5301941345 10.8096932636 3.6435760890 0.5790454854 0.8106345795 0.0741162811 -0.0456583095754 +1403638560427829504.0000000000 4.5530853820 10.8567937653 3.6288591182 0.5821269053 0.8099433487 0.0610013216 -0.0374015605483 +1403638560477829376.0000000000 4.5758003002 10.9032350267 3.6130038465 0.5854424744 0.8087861806 0.0476854595 -0.0291225040017 +1403638560527829504.0000000000 4.5985950600 10.9484230738 3.5960405503 0.5877915265 0.8080124542 0.0341600581 -0.0212152212997 +1403638560577829376.0000000000 4.6213249457 10.9924100055 3.5782254992 0.5894157457 0.8074598951 0.0192622475 -0.0150519915217 +1403638560627829504.0000000000 4.6442653443 11.0359121059 3.5590634076 0.5900822121 0.8072817551 0.0043168589 -0.00897304633847 +1403638560677829376.0000000000 4.6675197307 11.0775276474 3.5398128472 0.5905050049 0.8069546977 -0.0106305320 -0.00386612312405 +1403638560727829504.0000000000 4.6912262728 11.1187661512 3.5213998687 0.5904828764 0.8066604207 -0.0250691347 -0.000690615117877 +1403638560777829376.0000000000 4.7159558904 11.1579034897 3.5045311870 0.5910309146 0.8057576320 -0.0376544094 0.00438656554615 +1403638560827829504.0000000000 4.7419477626 11.1951367634 3.4894775567 0.5911900729 0.8049493134 -0.0492639154 0.0111340572479 +1403638560877829376.0000000000 4.7687867932 11.2306366075 3.4764056300 0.5921480408 0.8033223268 -0.0612904853 0.016655730811 +1403638560927829504.0000000000 4.7969536426 11.2654979918 3.4648064964 0.5927242596 0.8017950033 -0.0725574942 0.0231977339979 +1403638560977829376.0000000000 4.8263544928 11.2984859590 3.4556281131 0.5941758977 0.7995014256 -0.0824361032 0.0309315696372 +1403638561027829504.0000000000 4.8570617757 11.3299434036 3.4484612778 0.5961949502 0.7966013770 -0.0920122069 0.0388790587285 +1403638561077829376.0000000000 4.8886507564 11.3589215703 3.4433123955 0.5970174956 0.7944167073 -0.1019980676 0.0454818580675 +1403638561127829504.0000000000 4.9210204586 11.3848994125 3.4394447695 0.5986074944 0.7915685265 -0.1109649912 0.0526792768211 +1403638561177829376.0000000000 4.9540766774 11.4088937173 3.4374436750 0.5998348727 0.7890410242 -0.1190826724 0.0585807534781 +1403638561227829504.0000000000 4.9877678311 11.4304997229 3.4373677501 0.6010168608 0.7866649255 -0.1259872373 0.06375142379 +1403638561277829376.0000000000 5.0216867756 11.4492941281 3.4390928532 0.6025524282 0.7842494111 -0.1317635726 0.0672442809801 +1403638561327829504.0000000000 5.0563985656 11.4653850802 3.4417706289 0.6011691687 0.7842942199 -0.1359163788 0.0707456379614 +1403638561377829376.0000000000 5.0915973120 11.4790103328 3.4435275687 0.5971245241 0.7866477241 -0.1378879167 0.0749305237827 +1403638561427829504.0000000000 5.1273316924 11.4906059600 3.4438799295 0.5921023973 0.7899453268 -0.1377520940 0.0801591687393 +1403638561477829376.0000000000 5.1634506133 11.5004810972 3.4430311037 0.5871760966 0.7932488872 -0.1365655416 0.0856170979272 +1403638561527829504.0000000000 5.1996465351 11.5089842271 3.4410462026 0.5834346992 0.7958000108 -0.1347504040 0.0902697251307 +1403638561577829376.0000000000 5.2357522855 11.5165803962 3.4375879417 0.5802119061 0.7980352775 -0.1333964959 0.0932695811524 +1403638561627829504.0000000000 5.2717412408 11.5232637796 3.4331055677 0.5778890904 0.7996549322 -0.1322604673 0.0954115159713 +1403638561677829376.0000000000 5.3073449020 11.5290990934 3.4277742189 0.5767847340 0.8005301528 -0.1313284286 0.0960400377126 +1403638561727829504.0000000000 5.3425939785 11.5341795359 3.4212123567 0.5759095325 0.8012964367 -0.1303067907 0.0962931520957 +1403638561777829376.0000000000 5.3776600040 11.5385659268 3.4133339756 0.5758720386 0.8014569668 -0.1292081524 0.0966611552858 +1403638561827829504.0000000000 5.4127414073 11.5424225073 3.4040706318 0.5758210069 0.8014950520 -0.1283322603 0.0978094096228 +1403638561877829376.0000000000 5.4478279635 11.5456524094 3.3933253319 0.5761448314 0.8010503459 -0.1283811088 0.0994674191773 +1403638561927829504.0000000000 5.4828970200 11.5484337587 3.3808767711 0.5755592459 0.8009326034 -0.1294342908 0.102397674081 +1403638561977829376.0000000000 5.5175174157 11.5508148660 3.3677708691 0.5753198632 0.8002530480 -0.1327489618 0.104784671142 +1403638562027829504.0000000000 5.5520886142 11.5529663969 3.3552561363 0.5749113303 0.7993942942 -0.1368958343 0.108190828166 +1403638562077829376.0000000000 5.5864592366 11.5539811778 3.3442423468 0.5740839466 0.7986287704 -0.1414838896 0.112258711404 +1403638562127829504.0000000000 5.6199269367 11.5533477440 3.3352475613 0.5736033601 0.7975107392 -0.1467276850 0.115874038096 +1403638562177829376.0000000000 5.6524303086 11.5516068683 3.3271567005 0.5727669671 0.7966831832 -0.1511207113 0.119985155355 +1403638562227829504.0000000000 5.6842311357 11.5502907653 3.3199736727 0.5726061771 0.7955935268 -0.1548303620 0.123209841662 +1403638562277829376.0000000000 5.7154929081 11.5489107042 3.3143825872 0.5721401740 0.7945368007 -0.1590647240 0.126748992718 +1403638562327829504.0000000000 5.7458590896 11.5465098130 3.3108916664 0.5721937442 0.7929370452 -0.1643683245 0.129723611829 +1403638562377829376.0000000000 5.7754880857 11.5429851385 3.3083465854 0.5723621228 0.7909296681 -0.1704046814 0.133394546566 +1403638562427829504.0000000000 5.8046594091 11.5385282604 3.3064983469 0.5718719611 0.7890101342 -0.1777356523 0.13724250894 +1403638562477829376.0000000000 5.8338706495 11.5342065781 3.3064382911 0.5707677891 0.7871631593 -0.1860534179 0.141359178194 +1403638562527829504.0000000000 5.8626950659 11.5294166655 3.3085065546 0.5693659065 0.7850685888 -0.1953118601 0.146092616653 +1403638562577829376.0000000000 5.8915535759 11.5244463295 3.3125068055 0.5688746880 0.7819180531 -0.2054483476 0.150919594542 +1403638562627829504.0000000000 5.9200587404 11.5186252660 3.3175367874 0.5681555631 0.7785317965 -0.2168642992 0.155104396033 +1403638562677829376.0000000000 5.9488218925 11.5120363637 3.3233431291 0.5662191571 0.7756965059 -0.2287805314 0.159217666405 +1403638562727829504.0000000000 5.9779419281 11.5049245189 3.3297563686 0.5656123186 0.7715324479 -0.2408002004 0.163815904055 +1403638562777829376.0000000000 6.0071392039 11.4966913465 3.3357772958 0.5642094708 0.7675896720 -0.2535904070 0.167826320631 +1403638562827829504.0000000000 6.0367615185 11.4869673486 3.3402852544 0.5623451015 0.7635586269 -0.2649995574 0.17470387715 +1403638562877829376.0000000000 6.0664548806 11.4759970305 3.3433305903 0.5601071408 0.7596717103 -0.2767107774 0.180582471687 +1403638562927829504.0000000000 6.0922827862 11.4604319532 3.3469605216 0.5574351472 0.7559334782 -0.2875609432 0.187454893687 +1403638562977829376.0000000000 6.1213564772 11.4463413390 3.3477412010 0.5550559899 0.7520894207 -0.2977687378 0.193928157001 +1403638563027829504.0000000000 6.1502992025 11.4312044398 3.3475003528 0.5534408970 0.7476168148 -0.3086300622 0.198795765844 +1403638563077829376.0000000000 6.1792627478 11.4148956316 3.3459431148 0.5517312823 0.7432838789 -0.3198434603 0.202044125018 +1403638563127829504.0000000000 6.2085221819 11.3970680319 3.3430743413 0.5497939792 0.7390986170 -0.3309248432 0.204813483503 +1403638563177829376.0000000000 6.2385594245 11.3775245229 3.3385838831 0.5467589084 0.7360767206 -0.3377525807 0.212529884356 +1403638563227829504.0000000000 6.2686589126 11.3568920056 3.3335204220 0.5463675846 0.7316482663 -0.3447142555 0.217589886963 +1403638563277829376.0000000000 6.2989059702 11.3347308778 3.3267855922 0.5454680499 0.7282721869 -0.3491186486 0.224054452112 +1403638563327829504.0000000000 6.3289179199 11.3112684711 3.3193760303 0.5476311498 0.7234121037 -0.3529194764 0.228523292258 +1403638563377829376.0000000000 6.3589467727 11.2861385807 3.3111334313 0.5517739164 0.7176789095 -0.3550438891 0.23329458817 +1403638563427829504.0000000000 6.3883169618 11.2592246932 3.3016211439 0.5560018338 0.7124236593 -0.3573087675 0.235891787117 +1403638563477829376.0000000000 6.4166029552 11.2303538592 3.2900165274 0.5579272888 0.7096824106 -0.3591356564 0.236832423337 +1403638563527829504.0000000000 6.4443168337 11.1987969035 3.2780531022 0.5570100050 0.7094741053 -0.3588517787 0.240024476103 +1403638563577829376.0000000000 6.4710856811 11.1649091097 3.2669091958 0.5551099046 0.7104378604 -0.3588509034 0.241572079289 +1403638563627829504.0000000000 6.4969949425 11.1289237792 3.2573748146 0.5524297684 0.7123252314 -0.3589472624 0.242014417948 +1403638563677829376.0000000000 6.5217173909 11.0906354913 3.2501443378 0.5506920006 0.7138047537 -0.3600579293 0.239957041216 +1403638563727829504.0000000000 6.5461454172 11.0502049368 3.2443762728 0.5497476899 0.7148601990 -0.3604977297 0.238314414717 +1403638563777829376.0000000000 6.5704664825 11.0083472822 3.2404363395 0.5489664688 0.7158930328 -0.3611379232 0.236034705334 +1403638563827829504.0000000000 6.5945160957 10.9643506802 3.2388407677 0.5494273309 0.7162044663 -0.3610215228 0.234188450873 +1403638563877829376.0000000000 6.6184594771 10.9187091596 3.2396163673 0.5506824069 0.7159254907 -0.3601947887 0.233365148954 +1403638563927829504.0000000000 6.6424646071 10.8721556179 3.2424423706 0.5515037338 0.7161128794 -0.3597992206 0.231453011151 +1403638563977829376.0000000000 6.6664867674 10.8231307476 3.2458596996 0.5534519677 0.7156094929 -0.3582892425 0.230700654133 +1403638564027829504.0000000000 6.6899804522 10.7719030341 3.2479723881 0.5536140961 0.7166015030 -0.3576294826 0.228243010154 +1403638564077829376.0000000000 6.7134064446 10.7187082507 3.2489791816 0.5544645177 0.7171206279 -0.3564822539 0.226334942757 +1403638564127829504.0000000000 6.7369289462 10.6635336386 3.2486234594 0.5553208706 0.7177328127 -0.3544907390 0.22542106405 +1403638564177829376.0000000000 6.7611785908 10.6084920998 3.2489570361 0.5556243837 0.7188155236 -0.3521415923 0.224904615838 +1403638564227829504.0000000000 6.7850820743 10.5501281507 3.2473281313 0.5568787780 0.7190581572 -0.3492126699 0.225592341221 +1403638564277829376.0000000000 6.8087443556 10.4896825076 3.2457302304 0.5578338515 0.7193176992 -0.3464394221 0.226678557567 +1403638564327829504.0000000000 6.8324252826 10.4277242106 3.2458092059 0.5580106083 0.7204081800 -0.3428677367 0.228205894785 +1403638564377829376.0000000000 6.8555366604 10.3638583624 3.2479797617 0.5599918455 0.7198934589 -0.3412495608 0.227401139274 +1403638564427829504.0000000000 6.8787899367 10.2979485465 3.2519274994 0.5608321332 0.7200241160 -0.3385435462 0.228956017955 +1403638564477829376.0000000000 6.9012859641 10.2301000819 3.2574345680 0.5616313281 0.7202960809 -0.3367686537 0.228759001992 +1403638564527829504.0000000000 6.9228531556 10.1599305872 3.2641350104 0.5614038682 0.7209130220 -0.3363815504 0.227942019038 +1403638564577829376.0000000000 6.9433496537 10.0877335184 3.2712069244 0.5604549863 0.7222161488 -0.3369286737 0.225328896571 +1403638564627829504.0000000000 6.9638294713 10.0139058039 3.2779132274 0.5601834430 0.7226704441 -0.3379687816 0.222977671567 +1403638564677829376.0000000000 6.9837887635 9.9381570046 3.2831656663 0.5599015168 0.7228888461 -0.3401791315 0.219590906542 +1403638564727829504.0000000000 7.0034984223 9.8601383679 3.2865663468 0.5599680016 0.7228456364 -0.3414334213 0.217608000831 +1403638564777829376.0000000000 7.0208295053 9.7785708425 3.2933202705 0.5601755140 0.7224144343 -0.3432754509 0.21559857024 +1403638564827829504.0000000000 7.0402568213 9.6969361085 3.2947861083 0.5604227929 0.7219531123 -0.3444054613 0.214697170555 +1403638564877829376.0000000000 7.0598037901 9.6137121423 3.2929253524 0.5612785098 0.7211004544 -0.3454036394 0.213721536031 +1403638564927829504.0000000000 7.0794302654 9.5288428800 3.2865906404 0.5619794464 0.7203220125 -0.3463504614 0.212971026471 +1403638564977829376.0000000000 7.0986380643 9.4415473496 3.2751525119 0.5623484179 0.7200274615 -0.3468364064 0.212200892513 +1403638565027829504.0000000000 7.1180612906 9.3526603197 3.2595558647 0.5623610361 0.7199760696 -0.3472119142 0.211727208771 +1403638565077829376.0000000000 7.1380428839 9.2626537620 3.2403379074 0.5621790970 0.7201498571 -0.3476478598 0.210902375263 +1403638565127829504.0000000000 7.1587116071 9.1713325142 3.2168791862 0.5617909186 0.7203991066 -0.3479739035 0.210547509077 +1403638565177829376.0000000000 7.1798523337 9.0786849909 3.1904415068 0.5613433884 0.7208078624 -0.3480988336 0.210135260823 +1403638565227829504.0000000000 7.2017822981 8.9844536040 3.1626538962 0.5606418365 0.7213630671 -0.3478451110 0.21052276683 +1403638565277829376.0000000000 7.2240494578 8.8883176062 3.1339707320 0.5596392739 0.7220109810 -0.3476583046 0.211276429478 +1403638565327829504.0000000000 7.2467883612 8.7907483334 3.1044976679 0.5588076917 0.7225069864 -0.3473263051 0.21232535438 +1403638565377829376.0000000000 7.2695720152 8.6920215032 3.0746473537 0.5575315629 0.7234078485 -0.3468092180 0.213454930686 +1403638565427829504.0000000000 7.2923793354 8.5918422984 3.0446003386 0.5570370358 0.7237806818 -0.3464088448 0.214131215869 +1403638565477829376.0000000000 7.3159003139 8.4899632457 3.0154695600 0.5574192976 0.7230898507 -0.3456549005 0.216673681529 +1403638565527829504.0000000000 7.3398756486 8.3867247015 2.9877047480 0.5578011495 0.7224081924 -0.3440977225 0.220411067294 +1403638565577829376.0000000000 7.3642615640 8.2823963843 2.9623661954 0.5579533532 0.7218234926 -0.3427324210 0.224038810755 +1403638565627829504.0000000000 7.3880566238 8.1763783908 2.9391624627 0.5569727806 0.7221188504 -0.3402526774 0.229246162744 +1403638565677829376.0000000000 7.4113331559 8.0693515466 2.9175531247 0.5545300757 0.7235676984 -0.3369498661 0.235395345612 +1403638565727829504.0000000000 7.4343041549 7.9621364642 2.8979923521 0.5515528476 0.7253379844 -0.3346581587 0.24016282286 +1403638565777829376.0000000000 7.4557033593 7.8540197586 2.8803519608 0.5481107611 0.7275503151 -0.3337309532 0.242628900574 +1403638565827829504.0000000000 7.4754728402 7.7454117721 2.8650848594 0.5456400111 0.7289620999 -0.3333106062 0.244530724206 +1403638565877829376.0000000000 7.4940912216 7.6361977684 2.8513000417 0.5428178613 0.7306612093 -0.3313659366 0.248353745357 +1403638565927829504.0000000000 7.5112747429 7.5269192463 2.8391746015 0.5404450573 0.7318165038 -0.3322689544 0.248919840019 +1403638565977829376.0000000000 7.5273796930 7.4180594316 2.8269044007 0.5395520400 0.7320835399 -0.3325153299 0.24974155043 +1403638566027829504.0000000000 7.5423614905 7.3097481881 2.8129485541 0.5386095136 0.7325212802 -0.3336269737 0.249008852026 +1403638566077829376.0000000000 7.5563546153 7.2016842827 2.7971301827 0.5376623534 0.7328282723 -0.3332259583 0.250683820375 +1403638566127829504.0000000000 7.5731166150 7.0813910765 2.7680549357 0.5382012418 0.7325010744 -0.3342205747 0.249154985538 +1403638566177829376.0000000000 7.5857597325 6.9732306295 2.7468246019 0.5381660576 0.7324762331 -0.3347731278 0.248561491997 +1403638566227829504.0000000000 7.5970843997 6.8648346523 2.7235365895 0.5385047243 0.7322127191 -0.3339802202 0.249668597234 +1403638566277829376.0000000000 7.6081319543 6.7574563485 2.6987171002 0.5385332055 0.7323440283 -0.3338655031 0.249375292889 +1403638566327829504.0000000000 7.6184355485 6.6507417153 2.6715993793 0.5375146704 0.7331371951 -0.3343316872 0.248616482247 +1403638566377829376.0000000000 7.6266327219 6.5430286657 2.6411777299 0.5372989139 0.7336026683 -0.3332511466 0.249159939492 +1403638566427829504.0000000000 7.6350785408 6.4367517363 2.6106894520 0.5379589191 0.7334140447 -0.3331958892 0.248363725038 +1403638566477829376.0000000000 7.6421125448 6.3303932928 2.5781380412 0.5383443211 0.7335656768 -0.3340142640 0.245970041186 +1403638566527829504.0000000000 7.6488007928 6.2242564381 2.5446605539 0.5384774641 0.7339191148 -0.3327496419 0.24633803903 +1403638566577829376.0000000000 7.6546165574 6.1185275795 2.5087518902 0.5348209592 0.7371337249 -0.3334100259 0.243799441947 +1403638566627829504.0000000000 7.6587996198 6.0125462313 2.4709905956 0.5309423594 0.7405141371 -0.3340056823 0.241203706419 +1403638566677829376.0000000000 7.6626328663 5.9070035393 2.4311758485 0.5232151736 0.7465172664 -0.3348903514 0.238340734326 +1403638566727829504.0000000000 7.6664192859 5.8026500326 2.3903548468 0.5152923475 0.7524000473 -0.3373139194 0.233639220255 +1403638566777829376.0000000000 7.6710714930 5.6997062623 2.3486849949 0.5079020949 0.7581344516 -0.3371658031 0.231488307771 +1403638566827829504.0000000000 7.6762628865 5.5983868211 2.3061490316 0.5020631127 0.7625818987 -0.3377791617 0.228706616877 +1403638566877829376.0000000000 7.6822934596 5.4986536209 2.2629285586 0.4974362593 0.7661208399 -0.3387343063 0.225555084885 +1403638566927829504.0000000000 7.6898708375 5.4009305969 2.2191167097 0.4935841541 0.7693198974 -0.3375166297 0.224953557573 +1403638566977829376.0000000000 7.6987476869 5.3055844802 2.1746957978 0.4920650158 0.7708199273 -0.3373490114 0.223392713431 +1403638567027829504.0000000000 7.7095202761 5.2129535531 2.1309330079 0.4944371352 0.7696197446 -0.3362251702 0.223986613482 +1403638567077829376.0000000000 7.7220927734 5.1230938313 2.0889543539 0.5039185904 0.7637071481 -0.3331038447 0.227726315756 +1403638567127829504.0000000000 7.7356147777 5.0348233341 2.0453979795 0.5115797928 0.7586727682 -0.3294534170 0.232727721613 +1403638567177829376.0000000000 7.7499597835 4.9486871045 2.0007767538 0.5202746065 0.7527981935 -0.3267969648 0.236247661417 +1403638567227829504.0000000000 7.7649698755 4.8639526489 1.9550807745 0.5261761814 0.7485975507 -0.3239905309 0.240354881506 +1403638567277829376.0000000000 7.7796440168 4.7799953305 1.9077166522 0.5306344303 0.7452479708 -0.3220418790 0.243560242278 +1403638567327829504.0000000000 7.7935870896 4.6965233364 1.8584758186 0.5323079038 0.7437130346 -0.3208042652 0.246219091723 +1403638567377829376.0000000000 7.8066048146 4.6136354275 1.8092653330 0.5320378115 0.7436349969 -0.3207177254 0.247149547914 +1403638567427829504.0000000000 7.8189139166 4.5315214507 1.7613513565 0.5320045386 0.7431328441 -0.3208652567 0.24853618248 +1403638567477829376.0000000000 7.8301486886 4.4498301806 1.7143660162 0.5302377422 0.7440479140 -0.3217410877 0.248441765732 +1403638567527829504.0000000000 7.8408264538 4.3689200819 1.6687832701 0.5280232934 0.7450691504 -0.3227948812 0.248730431186 +1403638567577829376.0000000000 7.8500465077 4.2883372655 1.6256010948 0.5250460523 0.7467361516 -0.3244917950 0.247824207503 +1403638567627829504.0000000000 7.8587898337 4.2085223700 1.5840562070 0.5221067519 0.7482335455 -0.3251740114 0.24862212968 +1403638567677829376.0000000000 7.8670176501 4.1300702242 1.5452073970 0.5193511009 0.7495793756 -0.3260543002 0.249186249532 +1403638567727829504.0000000000 7.8743655407 4.0530179870 1.5085334949 0.5168356561 0.7509070459 -0.3268914901 0.249322014118 +1403638567777829376.0000000000 7.8809679244 3.9772155053 1.4741683380 0.5141218748 0.7524113330 -0.3276989726 0.249337657039 +1403638567827829504.0000000000 7.8872927535 3.9031356485 1.4421274263 0.5106607464 0.7544497147 -0.3287075665 0.248962980822 +1403638567877829376.0000000000 7.8936192251 3.8312575170 1.4119536221 0.5097168074 0.7547797179 -0.3310173413 0.246827619044 +1403638567927829504.0000000000 7.9004380782 3.7616390226 1.3836008530 0.5094584379 0.7548879064 -0.3317535428 0.246040516196 +1403638567977829376.0000000000 7.9071413102 3.6930400808 1.3567239539 0.5083966662 0.7552433184 -0.3323348770 0.246361298311 +1403638568027829504.0000000000 7.9138835309 3.6262585826 1.3317823391 0.5080552055 0.7553933895 -0.3321698714 0.246827696395 +1403638568077829376.0000000000 7.9209405179 3.5611911388 1.3090308032 0.5074464546 0.7556322433 -0.3306715181 0.249347860843 +1403638568127829504.0000000000 7.9272683609 3.4976475090 1.2893132288 0.5080877008 0.7550504783 -0.3305775067 0.249928340759 +1403638568177829376.0000000000 7.9333480589 3.4353251089 1.2712171236 0.5076142573 0.7553242949 -0.3293108730 0.251728671828 +1403638568227829504.0000000000 7.9386476215 3.3743622514 1.2556757596 0.5081443907 0.7547044425 -0.3294279442 0.25236424527 +1403638568277829376.0000000000 7.9437627679 3.3148711694 1.2410307779 0.5073474815 0.7550037345 -0.3296166107 0.252825599834 +1403638568327829504.0000000000 7.9486696129 3.2569880552 1.2267066651 0.5075405334 0.7547741947 -0.3295853188 0.253164056452 +1403638568377829376.0000000000 7.9531102892 3.2005550537 1.2118087749 0.5066311978 0.7552439078 -0.3302059386 0.252775606724 +1403638568427829504.0000000000 7.9574194680 3.1455197655 1.1953435915 0.5057298056 0.7557835952 -0.3304685636 0.25262432484 +1403638568477829376.0000000000 7.9615173402 3.0919716629 1.1777599118 0.5052560850 0.7560431187 -0.3304552771 0.252812976675 +1403638568527829504.0000000000 7.9653603847 3.0399710153 1.1593069543 0.5043176424 0.7566373410 -0.3303789745 0.253008661869 +1403638568577829376.0000000000 7.9691783147 2.9899617078 1.1402640227 0.5029895902 0.7574840127 -0.3304219508 0.2530627927 +1403638568627829504.0000000000 7.9730430152 2.9416954286 1.1204415602 0.5018011662 0.7582807979 -0.3306509904 0.252736510439 +1403638568677829376.0000000000 7.9769536556 2.8950677163 1.1001738199 0.5000041090 0.7596360950 -0.3297876515 0.253355479624 +1403638568727829504.0000000000 7.9808518639 2.8503942622 1.0805956638 0.4992136575 0.7601380522 -0.3296636236 0.25357003182 +1403638568777829376.0000000000 7.9845309434 2.8075255211 1.0623791993 0.4983024316 0.7608330530 -0.3303401596 0.252394792048 +1403638568827829504.0000000000 7.9877822669 2.7666820380 1.0469861771 0.5000372073 0.7597204238 -0.3306838815 0.251864724445 +1403638568877829376.0000000000 7.9908646496 2.7272554799 1.0323895559 0.4999262657 0.7596302578 -0.3316915257 0.251030540235 +1403638568927829504.0000000000 7.9946719745 2.6900762461 1.0197048498 0.4996310537 0.7598968466 -0.3301154986 0.252882087677 +1403638568977829376.0000000000 7.9982543462 2.6546912259 1.0092961178 0.4999293274 0.7596985899 -0.3299324911 0.253126986714 +1403638569027829504.0000000000 8.0021381536 2.6214419015 1.0011952396 0.5007442207 0.7590756814 -0.3298959245 0.253432465209 +1403638569077829376.0000000000 8.0063167785 2.5897301377 0.9944321018 0.4995888129 0.7598251843 -0.3289324120 0.254715872258 +1403638569127829504.0000000000 8.0101566726 2.5597942379 0.9900444501 0.4998903421 0.7596065844 -0.3288564096 0.254874370322 +1403638569177829376.0000000000 8.0137431799 2.5314039693 0.9867702280 0.4981943203 0.7605831706 -0.3292035412 0.254834629321 +1403638569227829504.0000000000 8.0169323789 2.5046272122 0.9835429953 0.4968916797 0.7613528972 -0.3285826063 0.255878673144 +1403638569277829376.0000000000 8.0200485070 2.4796464287 0.9796368706 0.4955637505 0.7620782604 -0.3287088985 0.256132298424 +1403638569327829504.0000000000 8.0230292107 2.4561699779 0.9744666540 0.4953654591 0.7620827227 -0.3286780866 0.256541811476 +1403638569377829376.0000000000 8.0261124515 2.4345272645 0.9679766976 0.4952988844 0.7620646149 -0.3284649438 0.256996728536 +1403638569427829504.0000000000 8.0294868147 2.4148533694 0.9604669230 0.4962320409 0.7613479203 -0.3278933611 0.258048541146 +1403638569477829376.0000000000 8.0327528075 2.3970656494 0.9516644588 0.4970366212 0.7608423502 -0.3276000036 0.258363606261 +1403638569527829504.0000000000 8.0359550470 2.3810275131 0.9417434679 0.4978814953 0.7602923138 -0.3272262235 0.258829312219 +1403638569577829376.0000000000 8.0390706528 2.3665998294 0.9319365306 0.4985028126 0.7597487995 -0.3268343026 0.259723018231 +1403638569627829504.0000000000 8.0418217998 2.3539759684 0.9238421880 0.4999648324 0.7587406071 -0.3273354829 0.259228353085 +1403638569677829376.0000000000 8.0443642699 2.3429644831 0.9174522073 0.5004201170 0.7583370772 -0.3273353207 0.259530675773 +1403638569727829504.0000000000 8.0459714079 2.3331467213 0.9123942946 0.5008459991 0.7579689907 -0.3266971128 0.260586436484 +1403638569777829376.0000000000 8.0473822937 2.3253525666 0.9090688287 0.5011928090 0.7577398485 -0.3264614943 0.260881166145 +1403638569827829504.0000000000 8.0481951975 2.3191120563 0.9075620439 0.5017504502 0.7575071598 -0.3260770831 0.260965753245 +1403638569877829376.0000000000 8.0487481925 2.3142544297 0.9072831917 0.5025239228 0.7568861884 -0.3250016124 0.262615606546 +1403638569927829504.0000000000 8.0487249562 2.3108750647 0.9083814419 0.5037912895 0.7559746492 -0.3248315027 0.263023119322 +1403638569977829376.0000000000 8.0480373453 2.3088442548 0.9098551551 0.5051345952 0.7551217119 -0.3252729455 0.262350437067 +1403638570027829504.0000000000 8.0468355989 2.3081488187 0.9106545153 0.5063465581 0.7543855467 -0.3255823996 0.261747418604 +1403638570077829376.0000000000 8.0449919445 2.3087578313 0.9100714895 0.5069249583 0.7539922661 -0.3265136012 0.2605985755 +1403638570127829504.0000000000 8.0424633440 2.3105488083 0.9081298641 0.5076288060 0.7536664496 -0.3278340545 0.258504759664 +1403638570177829376.0000000000 8.0394465915 2.3133417550 0.9049158381 0.5087702094 0.7531378952 -0.3292116179 0.256038855497 +1403638570227829504.0000000000 8.0359327892 2.3170091579 0.9005924440 0.5107194709 0.7520454876 -0.3308477952 0.253244828106 +1403638570277829376.0000000000 8.0318974007 2.3214068731 0.8950294116 0.5124828008 0.7510061883 -0.3333992681 0.24939128303 +1403638570327829504.0000000000 8.0279092106 2.3264552753 0.8887561428 0.5144677986 0.7495234884 -0.3366913030 0.245308766753 +1403638570377829376.0000000000 8.0243607384 2.3315284065 0.8810248628 0.5150152688 0.7481278961 -0.3401647810 0.243622342622 +1403638570427829504.0000000000 8.0215350000 2.3369663002 0.8719724706 0.5156776746 0.7455428004 -0.3460359361 0.24187103922 +1403638570477829376.0000000000 8.0190462498 2.3425979176 0.8618952376 0.5161556018 0.7420037458 -0.3544671071 0.239513895014 +1403638570527829504.0000000000 8.0176515331 2.3480152635 0.8506230991 0.5176981447 0.7364454811 -0.3660032378 0.235962527066 +1403638570577829376.0000000000 8.0176715565 2.3524188780 0.8378181815 0.5192842738 0.7297510745 -0.3787143046 0.233200960099 +1403638570627829504.0000000000 8.0185742039 2.3556052433 0.8238472711 0.5201516845 0.7224186121 -0.3918005308 0.232477779704 +1403638570677829376.0000000000 8.0217408017 2.3572354331 0.8085181991 0.5210863571 0.7142616821 -0.4039722858 0.234745926938 +1403638570727829504.0000000000 8.0265625848 2.3569956658 0.7924608722 0.5233165985 0.7049224003 -0.4144947266 0.239621094515 +1403638570777829376.0000000000 8.0329773562 2.3545335556 0.7763777967 0.5269443136 0.6937393549 -0.4256028326 0.244780772671 +1403638570827829504.0000000000 8.0402181966 2.3489566631 0.7594030419 0.5294024450 0.6832828369 -0.4350772981 0.252121717988 +1403638570877829376.0000000000 8.0482441842 2.3406290116 0.7415526763 0.5305305029 0.6737452928 -0.4440759136 0.259617504819 +1403638570927829504.0000000000 8.0568715259 2.3288087924 0.7226822966 0.5296701058 0.6656725033 -0.4526560478 0.267268029761 +1403638570977829376.0000000000 8.0661258660 2.3135028923 0.7028631510 0.5279675992 0.6581471916 -0.4609029069 0.275065444679 +1403638571027829504.0000000000 8.0757384055 2.2948365431 0.6821027745 0.5249957107 0.6515488949 -0.4696914427 0.281519963549 +1403638571077829376.0000000000 8.0852351135 2.2726396721 0.6595787293 0.5176604196 0.6484625651 -0.4775148637 0.288969802178 +1403638571127829504.0000000000 8.0949486668 2.2472041400 0.6369148302 0.5088487177 0.6466371037 -0.4847200483 0.29661408164 +1403638571177829376.0000000000 8.1042140950 2.2185226879 0.6164313400 0.4996481722 0.6461962158 -0.4897768468 0.304796317095 +1403638571227829504.0000000000 8.1135938242 2.1871589539 0.5978650823 0.4918309223 0.6455599932 -0.4934800169 0.312781252676 +1403638571277829376.0000000000 8.1232376122 2.1536525398 0.5821492207 0.4851257669 0.6447615453 -0.4960964670 0.320661559001 +1403638571327829504.0000000000 8.1329183508 2.1182519027 0.5689113083 0.4795615019 0.6440066113 -0.4980318078 0.327476058702 +1403638571377829376.0000000000 8.1423895355 2.0817406599 0.5585957123 0.4769679438 0.6420287773 -0.5007768179 0.330942908167 +1403638571427829504.0000000000 8.1515196069 2.0438117002 0.5509338894 0.4756057006 0.6397372153 -0.5028057714 0.334248214984 +1403638571477829376.0000000000 8.1603269157 2.0042199208 0.5457652766 0.4753675508 0.6375806547 -0.5041515667 0.336671647403 +1403638571527829504.0000000000 8.1689447176 1.9632085166 0.5414616893 0.4747783330 0.6355933214 -0.5047917566 0.340282157445 +1403638571577829376.0000000000 8.1772600983 1.9208675945 0.5365296294 0.4727736279 0.6336932614 -0.5071770718 0.34305883626 +1403638571627829504.0000000000 8.1855149788 1.8770308109 0.5311986500 0.4698592676 0.6317828018 -0.5106792156 0.345383118956 +1403638571677829376.0000000000 8.1935134264 1.8322088459 0.5240574151 0.4657361735 0.6298891287 -0.5157190078 0.346934298121 +1403638571727829504.0000000000 8.2016963227 1.7861133342 0.5157950365 0.4609980761 0.6273755607 -0.5214085548 0.349304736135 +1403638571777829376.0000000000 8.2098913249 1.7387350320 0.5062502950 0.4558896661 0.6243558938 -0.5278593974 0.351722599205 +1403638571827829504.0000000000 8.2181708344 1.6905794383 0.4956196141 0.4510671582 0.6203768966 -0.5350208290 0.354151997607 +1403638571877829376.0000000000 8.2273994500 1.6414955126 0.4848780378 0.4471919419 0.6150003923 -0.5430841871 0.356164919957 +1403638571927829504.0000000000 8.2369567952 1.5910799273 0.4747532371 0.4436600839 0.6087495864 -0.5510786733 0.359029200575 +1403638571977829376.0000000000 8.2469789470 1.5393785707 0.4662683390 0.4404136905 0.6019504626 -0.5592939257 0.361775795843 +1403638572027829504.0000000000 8.2572072634 1.4861573737 0.4595559274 0.4365490032 0.5954638190 -0.5667053203 0.365640380662 +1403638572077829376.0000000000 8.2678395487 1.4315977603 0.4553636152 0.4334289071 0.5883646964 -0.5744275121 0.368780964619 +1403638572127829504.0000000000 8.2787190365 1.3751732256 0.4528138864 0.4291484813 0.5818766872 -0.5805855029 0.374394946244 +1403638572177829376.0000000000 8.2891092169 1.3170185392 0.4520864019 0.4232576290 0.5762541161 -0.5857912910 0.381618574754 +1403638572227829504.0000000000 8.2994572115 1.2577224231 0.4524347350 0.4164372802 0.5711106638 -0.5921253494 0.387040271764 +1403638572277829376.0000000000 8.3097324005 1.1973262651 0.4528076816 0.4091351954 0.5660053135 -0.5993753866 0.391146421393 +1403638572327829504.0000000000 8.3204374126 1.1358901968 0.4523765182 0.4016568571 0.5604560714 -0.6068905730 0.395277868879 +1403638572377829376.0000000000 8.3317583553 1.0735674943 0.4509516617 0.3943112583 0.5546258636 -0.6143699569 0.39932234974 +1403638572427829504.0000000000 8.3434489747 1.0104428529 0.4485739269 0.3869509048 0.5497041178 -0.6204491875 0.403902446055 +1403638572477829376.0000000000 8.3554411966 0.9468650189 0.4454171407 0.3801292543 0.5459502016 -0.6248279591 0.408693220969 +1403638572527829504.0000000000 8.3679514801 0.8830456225 0.4418521987 0.3744836639 0.5424398310 -0.6288279038 0.412427548346 +1403638572577829376.0000000000 8.3813290230 0.8191644090 0.4385002482 0.3705402128 0.5390755952 -0.6312831282 0.416628210038 +1403638572627829504.0000000000 8.3952181877 0.7549610951 0.4348915853 0.3673226657 0.5368927772 -0.6336482399 0.418700505299 +1403638572677829376.0000000000 8.4098083748 0.6904843138 0.4326131482 0.3643155767 0.5353252841 -0.6355144971 0.420502467108 +1403638572727829504.0000000000 8.4255944381 0.6256648580 0.4320850769 0.3600260036 0.5355658144 -0.6358208581 0.423417490889 +1403638572777829376.0000000000 8.4422191973 0.5607947618 0.4339460091 0.3560803198 0.5366070081 -0.6356532560 0.425681410087 +1403638572827829504.0000000000 8.4595685274 0.4963742591 0.4378926523 0.3528359106 0.5378051233 -0.6357056822 0.426791231473 +1403638572877829376.0000000000 8.4784041761 0.4322504480 0.4440144346 0.3501868153 0.5390881033 -0.6357663805 0.427263760054 +1403638572927829504.0000000000 8.4985227887 0.3688288947 0.4519962222 0.3494586461 0.5397636915 -0.6358139800 0.426936054723 +1403638572977829376.0000000000 8.5196760887 0.3058109073 0.4598957542 0.3473893762 0.5414717447 -0.6355392874 0.426870923273 +1403638573027829504.0000000000 8.5410831320 0.2435127349 0.4671616984 0.3464926204 0.5424791493 -0.6356240617 0.426193956841 +1403638573077829376.0000000000 8.5639746579 0.1817709740 0.4729435245 0.3459527947 0.5438494623 -0.6351375355 0.42561101638 +1403638573127829504.0000000000 8.5871545345 0.1206873871 0.4770920069 0.3455732238 0.5451297437 -0.6349706669 0.424529105848 +1403638573177829376.0000000000 8.6119226037 0.0600566893 0.4804034197 0.3460839132 0.5457943592 -0.6346031374 0.423808094049 +1403638573227829504.0000000000 8.6379029762 -0.0000652704 0.4833537159 0.3468293858 0.5466298084 -0.6337273673 0.423432230377 +1403638573277829376.0000000000 8.6651116137 -0.0596048549 0.4862161799 0.3469340950 0.5478325986 -0.6332957083 0.422436650331 +1403638573327829504.0000000000 8.6942568373 -0.1186948240 0.4895562932 0.3480609655 0.5483469154 -0.6322601753 0.422393531387 +1403638573377829376.0000000000 8.7246942631 -0.1776467799 0.4927821810 0.3471134059 0.5488820066 -0.6327632832 0.42172438129 +1403638573427829504.0000000000 8.7564162622 -0.2362358392 0.4968298636 0.3453374969 0.5491732038 -0.6330147128 0.422425352941 +1403638573477829376.0000000000 8.7911219980 -0.2941968747 0.5019385594 0.3441923990 0.5488926223 -0.6329015226 0.423891665861 +1403638573527829504.0000000000 8.8275978148 -0.3516095248 0.5098481572 0.3429364920 0.5489346252 -0.6330034177 0.424702263809 +1403638573577829376.0000000000 8.8661721210 -0.4084809344 0.5202264725 0.3426135613 0.5486663924 -0.6331388712 0.425107406752 +1403638573627829504.0000000000 8.9060648341 -0.4646025289 0.5325988189 0.3419827945 0.5484019166 -0.6333092819 0.425702313343 +1403638573677829376.0000000000 8.9467728891 -0.5201601537 0.5458238624 0.3391682475 0.5487278532 -0.6337849007 0.426824721263 +1403638573727829504.0000000000 8.9891784014 -0.5749213006 0.5599255181 0.3376302878 0.5470173377 -0.6348608851 0.428636766548 +1403638573777829376.0000000000 9.0346838863 -0.6293715455 0.5755589325 0.3357424853 0.5439942548 -0.6356244875 0.432814908729 +1403638573827829504.0000000000 9.0810343979 -0.6830591209 0.5906903692 0.3350662667 0.5387057361 -0.6360599429 0.439265837305 +1403638573877829376.0000000000 9.1294875955 -0.7362639202 0.6050386464 0.3339348184 0.5321251586 -0.6370719734 0.446620256328 +1403638573927829504.0000000000 9.1791051007 -0.7884093537 0.6182916697 0.3330241233 0.5236266743 -0.6395960914 0.453681473241 +1403638573977829376.0000000000 9.2293404162 -0.8394479409 0.6302746662 0.3341308829 0.5125833315 -0.6440550173 0.459138340908 +1403638574027829504.0000000000 9.2804987895 -0.8896688391 0.6409873420 0.3364467143 0.4997080154 -0.6499551066 0.463307529777 +1403638574077829376.0000000000 9.3309953371 -0.9392494214 0.6502595032 0.3387642592 0.4856407503 -0.6568004475 0.466910066825 +1403638574127829504.0000000000 9.3809361952 -0.9887290624 0.6583289049 0.3406809839 0.4710566858 -0.6634996967 0.470967322116 +1403638574177829376.0000000000 9.4298195240 -1.0382196203 0.6647343564 0.3417302939 0.4560684511 -0.6710969225 0.474184452244 +1403638574227829504.0000000000 9.4770897400 -1.0881620510 0.6698457872 0.3403047921 0.4425541143 -0.6777916652 0.47847357604 +1403638574277829376.0000000000 9.5219942742 -1.1384640163 0.6736458372 0.3366302069 0.4304719782 -0.6849376427 0.481907050517 +1403638574327829504.0000000000 9.5649204664 -1.1892448877 0.6756969735 0.3303019667 0.4200361913 -0.6917338526 0.485772051369 +1403638574377829376.0000000000 9.6059243154 -1.2404906230 0.6765546947 0.3225148895 0.4107496304 -0.6984247180 0.489358560172 +1403638574427829504.0000000000 9.6454102691 -1.2923360910 0.6761341960 0.3137356359 0.4021438628 -0.7042900548 0.493787183987 +1403638574477829376.0000000000 9.6831949388 -1.3444906727 0.6748918581 0.3054805691 0.3933038393 -0.7107385137 0.49683445629 +1403638574527829504.0000000000 9.7194049069 -1.3969432649 0.6746705668 0.2984653074 0.3853569973 -0.7158471557 0.49998129431 +1403638574577829376.0000000000 9.7545992849 -1.4492190401 0.6754610987 0.2930828112 0.3781903603 -0.7198474225 0.502885877188 +1403638574627829504.0000000000 9.7887273825 -1.5022172979 0.6785513324 0.2878224116 0.3724801054 -0.7220618561 0.50699458213 +1403638574677829376.0000000000 9.8212593151 -1.5555525696 0.6830195932 0.2805474003 0.3696394592 -0.7239207150 0.510488613715 +1403638574727829504.0000000000 9.8530285764 -1.6086324507 0.6891213772 0.2736079274 0.3681503689 -0.7246554865 0.514274667733 +1403638574777829376.0000000000 9.8837147535 -1.6611900004 0.6967125967 0.2659187966 0.3685413530 -0.7259726338 0.516166833223 +1403638574827829504.0000000000 9.9136271814 -1.7128412248 0.7057053787 0.2603192342 0.3690861743 -0.7278698932 0.515959989558 +1403638574877829376.0000000000 9.9431327335 -1.7640824106 0.7145621049 0.2566875649 0.3689752317 -0.7306626068 0.513907508721 +1403638574927829504.0000000000 9.9724469282 -1.8149889342 0.7225346062 0.2535688435 0.3695287244 -0.7329665888 0.511772745589 +1403638574977829376.0000000000 10.0014579984 -1.8656462258 0.7292319380 0.2513777573 0.3701460216 -0.7344654928 0.510256392149 +1403638575027829504.0000000000 10.0305098270 -1.9158566005 0.7348622582 0.2526881868 0.3690198923 -0.7367137723 0.507174345838 +1403638575077829376.0000000000 10.0594308405 -1.9659215531 0.7392631981 0.2556251993 0.3670716560 -0.7389961728 0.503784491132 +1403638575127829504.0000000000 10.0882617766 -2.0162257237 0.7424138032 0.2588837855 0.3650311309 -0.7402410378 0.501771526743 +1403638575177829376.0000000000 10.1167781346 -2.0669019845 0.7443616815 0.2618806502 0.3634760462 -0.7411888353 0.499942796019 +1403638575227829504.0000000000 10.1448492015 -2.1183360481 0.7454454400 0.2643809228 0.3623868993 -0.7412454782 0.499333159263 +1403638575277829376.0000000000 10.1724624202 -2.1703273593 0.7453102716 0.2664211706 0.3619751551 -0.7415538375 0.49808799722 +1403638575327829504.0000000000 10.1996049778 -2.2232236876 0.7437541112 0.2668433267 0.3627758192 -0.7420350592 0.496560484606 +1403638575377829376.0000000000 10.2263559272 -2.2769940458 0.7406350377 0.2655649948 0.3651850211 -0.7427629399 0.494386841418 +1403638575427829504.0000000000 10.2531456243 -2.3314236970 0.7363359538 0.2643627731 0.3677017812 -0.7435849267 0.491923958679 +1403638575477829376.0000000000 10.2802788228 -2.3869230909 0.7309998885 0.2622617204 0.3709461311 -0.7431825391 0.49122038993 +1403638575527829504.0000000000 10.3076627859 -2.4431263701 0.7256564455 0.2621222258 0.3728794285 -0.7433407208 0.489589055612 +1403638575577829376.0000000000 10.3348935329 -2.5003305839 0.7208669108 0.2594038587 0.3765858435 -0.7426313437 0.489276433008 +1403638575627829504.0000000000 10.3625853458 -2.5585686540 0.7173845814 0.2558022081 0.3808243636 -0.7415628573 0.489512577014 +1403638575677829376.0000000000 10.3912241495 -2.6184776137 0.7152560936 0.2530106692 0.3843947716 -0.7399211354 0.490655657551 +1403638575727829504.0000000000 10.4198996591 -2.6785665841 0.7153026058 0.2497519655 0.3882536238 -0.7395677401 0.489818984046 +1403638575777829376.0000000000 10.4491512178 -2.7388285748 0.7172951829 0.2462393412 0.3916295675 -0.7393630715 0.489218475964 +1403638575827829504.0000000000 10.4798207478 -2.7997938104 0.7212523008 0.2435222841 0.3946796081 -0.7392689911 0.488268638056 +1403638575877829376.0000000000 10.5123016681 -2.8606132197 0.7285325274 0.2427652026 0.3963398325 -0.7388842892 0.48788297853 +1403638575927829504.0000000000 10.5463279948 -2.9213884424 0.7380105649 0.2431954332 0.3968021855 -0.7389193321 0.487239394423 +1403638575977829376.0000000000 10.5822720545 -2.9826200495 0.7504529078 0.2437157318 0.3969401216 -0.7383066498 0.487795523518 +1403638576027829504.0000000000 10.6187334126 -3.0433905392 0.7642571626 0.2438642718 0.3975940064 -0.7379153443 0.487780860269 +1403638576077829376.0000000000 10.6564149010 -3.1043052358 0.7798239177 0.2437216387 0.3979946028 -0.7372199979 0.488576231075 +1403638576127829504.0000000000 10.6953294699 -3.1652939924 0.7969469696 0.2440808330 0.3975403049 -0.7371903235 0.488811497259 +1403638576177829376.0000000000 10.7358532895 -3.2262852373 0.8150928826 0.2455101540 0.3966208748 -0.7362591813 0.490243881989 +1403638576227829504.0000000000 10.7772072359 -3.2874208736 0.8317358395 0.2444701753 0.3972402777 -0.7353054190 0.491691403228 +1403638576277829376.0000000000 10.8196923818 -3.3484877041 0.8469474994 0.2430962342 0.3979666183 -0.7340080248 0.493719567377 +1403638576327829504.0000000000 10.8572008434 -3.4136029394 0.8585166246 0.2411886828 0.3992172493 -0.7326603017 0.495643510513 +1403638576377829376.0000000000 10.8995777622 -3.4747612149 0.8709989357 0.2391427816 0.4003575140 -0.7316739575 0.497169800934 +1403638576427829504.0000000000 10.9427358566 -3.5353290243 0.8819918379 0.2366472976 0.4018631764 -0.7313952227 0.497559114235 +1403638576477829376.0000000000 10.9873086843 -3.5956870974 0.8917556155 0.2338325228 0.4036687403 -0.7301603858 0.499239131503 +1403638576527829504.0000000000 11.0333149186 -3.6557070927 0.9001084175 0.2290441609 0.4066768270 -0.7292381820 0.500364271944 +1403638576577829376.0000000000 11.0815112429 -3.7149958660 0.9077566470 0.2258017865 0.4085256417 -0.7287852821 0.500991383008 +1403638576627829504.0000000000 11.1313397145 -3.7732776469 0.9145278205 0.2232797728 0.4100715369 -0.7280226331 0.501966655605 +1403638576677829376.0000000000 11.1831292709 -3.8302117761 0.9205167415 0.2223844714 0.4106698577 -0.7272081540 0.503054386298 +1403638576727829504.0000000000 11.2370895586 -3.8858356374 0.9258917904 0.2233035031 0.4102587041 -0.7254530327 0.50551086882 +1403638576777829376.0000000000 11.2927936060 -3.9404633198 0.9301831480 0.2243332104 0.4096946923 -0.7229310515 0.50911252646 +1403638576827829504.0000000000 11.3499268478 -3.9935545221 0.9335470063 0.2273555477 0.4076336330 -0.7207844829 0.512458784155 +1403638576877829376.0000000000 11.4079520226 -4.0450211090 0.9354716732 0.2304177540 0.4055664395 -0.7195638586 0.5144427812 +1403638576927829504.0000000000 11.4672639042 -4.0949220897 0.9364874541 0.2349948010 0.4022404836 -0.7190255632 0.515734695713 +1403638576977829376.0000000000 11.5273457594 -4.1431388056 0.9365804340 0.2398461610 0.3989069198 -0.7190599878 0.516042461837 +1403638577027829504.0000000000 11.5876372314 -4.1899594663 0.9360096296 0.2431122694 0.3966913404 -0.7201546085 0.514693836012 +1403638577077829376.0000000000 11.6481054972 -4.2357278476 0.9367005318 0.2462997652 0.3941506384 -0.7209674449 0.51399187086 +1403638577127829504.0000000000 11.7089072352 -4.2805982645 0.9393100585 0.2489434223 0.3922561963 -0.7213581467 0.513619190784 +1403638577177829376.0000000000 11.7913500860 -4.3337550154 0.9404070294 0.2510972418 0.3907245651 -0.7219670724 0.512882087607 +1403638577227829504.0000000000 11.8550076201 -4.3778839125 0.9452256420 0.2517936032 0.3900263329 -0.7224551730 0.512384586045 +1403638577277829376.0000000000 11.9191418827 -4.4216910022 0.9511638702 0.2502060964 0.3913053201 -0.7219272014 0.512930961854 +1403638577327829504.0000000000 11.9835402252 -4.4648927577 0.9592407217 0.2471777369 0.3932404760 -0.7206758048 0.514676091178 +1403638577377829376.0000000000 12.0477059517 -4.5072512301 0.9689385373 0.2421231579 0.3969660887 -0.7187667860 0.516883553744 +1403638577427829504.0000000000 12.1119135748 -4.5480292123 0.9804475688 0.2389827395 0.3993342620 -0.7177352647 0.5179531709 +1403638577477829376.0000000000 12.1771016346 -4.5875875689 0.9929581011 0.2371498324 0.4004102784 -0.7165497685 0.519603690573 +1403638577527829504.0000000000 12.2430492241 -4.6252993160 1.0048700770 0.2382204494 0.4001210888 -0.7174687603 0.51806631787 +1403638577577829376.0000000000 12.3092232531 -4.6616027476 1.0154949223 0.2386735760 0.3997874909 -0.7182363991 0.517050636941 +1403638577627829504.0000000000 12.3755743770 -4.6965021684 1.0246807353 0.2406517823 0.3986008067 -0.7189917946 0.515998949429 +1403638577677829376.0000000000 12.4417866164 -4.7301940281 1.0322138886 0.2417524764 0.3980886210 -0.7198838720 0.51463423991 +1403638577727829504.0000000000 12.5079833039 -4.7629297040 1.0378120119 0.2421482785 0.3979016024 -0.7202900506 0.514024093728 +1403638577777829376.0000000000 12.5750040939 -4.7948326062 1.0414668291 0.2439041920 0.3971401412 -0.7211874776 0.512522268351 +1403638577827829504.0000000000 12.6412690542 -4.8255122405 1.0432391021 0.2440462300 0.3972589832 -0.7213033556 0.512199382188 +1403638577877829376.0000000000 12.7084951669 -4.8556091821 1.0437630673 0.2443448692 0.3974296508 -0.7210070789 0.512341731403 +1403638577927829504.0000000000 12.7762040092 -4.8847491192 1.0434333745 0.2446456185 0.3977578154 -0.7207131901 0.512357042729 +1403638577977829376.0000000000 12.8443319099 -4.9129318768 1.0439156852 0.2442699706 0.3984879262 -0.7198950367 0.513118592796 +1403638578027829504.0000000000 12.9133529353 -4.9400333688 1.0453498258 0.2448905973 0.3984875717 -0.7194732708 0.513414514039 +1403638578077829376.0000000000 12.9831320305 -4.9660524363 1.0492587805 0.2466904715 0.3977963321 -0.7195995856 0.512911616053 +1403638578127829504.0000000000 13.0534309798 -4.9911389972 1.0549037303 0.2490899729 0.3968190300 -0.7197007672 0.512366712843 +1403638578177829376.0000000000 13.1244373642 -5.0154864242 1.0625323805 0.2534788830 0.3942141278 -0.7208705118 0.510577499015 +1403638578227829504.0000000000 13.1960335374 -5.0394887202 1.0719558243 0.2596010403 0.3902459561 -0.7226807769 0.507984141834 +1403638578277829376.0000000000 13.2677066042 -5.0637846191 1.0822658512 0.2635262250 0.3877954093 -0.7244116019 0.505367668351 +1403638578327829504.0000000000 13.3387260894 -5.0878336205 1.0923866210 0.2664902444 0.3856819265 -0.7252276253 0.504259152361 +1403638578377829376.0000000000 13.4090197034 -5.1122393385 1.1008226496 0.2671503988 0.3850629339 -0.7251317562 0.504520700776 +1403638578427829504.0000000000 13.4783933555 -5.1367233317 1.1075428556 0.2669521630 0.3849577837 -0.7254642477 0.504227798519 +1403638578477829376.0000000000 13.5468715515 -5.1612543278 1.1127534719 0.2670680709 0.3845873785 -0.7253716009 0.504582237562 +1403638578527829504.0000000000 13.6144291481 -5.1856611743 1.1164925825 0.2670858903 0.3842589589 -0.7257842665 0.504229489659 +1403638578577829376.0000000000 13.6813757307 -5.2101361186 1.1194749297 0.2670514928 0.3838541929 -0.7258231596 0.504499950192 +1403638578627829504.0000000000 13.7478003860 -5.2348745242 1.1214890394 0.2670702142 0.3834905055 -0.7253544646 0.505439841735 +1403638578677829376.0000000000 13.8135883806 -5.2599171992 1.1222965150 0.2657766884 0.3841379490 -0.7246829066 0.506592018242 +1403638578727829504.0000000000 13.8786612847 -5.2852595038 1.1218880125 0.2632207349 0.3857860497 -0.7237211251 0.508046948255 +1403638578777829376.0000000000 13.9432252047 -5.3104723346 1.1204334510 0.2601969761 0.3877535632 -0.7223694921 0.510026494206 +1403638578827829504.0000000000 14.0075354414 -5.3351783957 1.1176741012 0.2564101413 0.3905255847 -0.7216185958 0.510891582679 +1403638578877829376.0000000000 14.0722959588 -5.3597825094 1.1145897249 0.2546639332 0.3916542548 -0.7199132544 0.513301209846 +1403638578927829504.0000000000 14.1368519379 -5.3836344947 1.1107270572 0.2530982126 0.3926895183 -0.7194127040 0.513985990356 +1403638578977829376.0000000000 14.2010253950 -5.4066999715 1.1078494769 0.2523598765 0.3937312659 -0.7184155208 0.514945941224 +1403638579027829504.0000000000 14.2657797085 -5.4291998581 1.1071365328 0.2517912939 0.3944853343 -0.7178730916 0.515403424207 +1403638579077829376.0000000000 14.3295184661 -5.4505169965 1.1088488478 0.2520556814 0.3947460287 -0.7177130009 0.51529753996 +1403638579127829504.0000000000 14.3938709992 -5.4713749843 1.1135617103 0.2520562305 0.3951415137 -0.7170814135 0.515873130914 +1403638579177829376.0000000000 14.4574713132 -5.4909496333 1.1198411582 0.2522949987 0.3951453798 -0.7169697639 0.515908635486 +1403638579227829504.0000000000 14.5200430422 -5.5090703150 1.1272340178 0.2526154528 0.3951874698 -0.7168469384 0.515890263136 +1403638579277829376.0000000000 14.5825769817 -5.5260982495 1.1361425717 0.2549783630 0.3938874736 -0.7176618953 0.514587307107 +1403638579327829504.0000000000 14.6445440550 -5.5424521165 1.1461578251 0.2565791915 0.3931287703 -0.7178913454 0.514051461013 +1403638579377829376.0000000000 14.7069903107 -5.5582517904 1.1561307736 0.2617155713 0.3896516144 -0.7201049165 0.511004391811 +1403638579427829504.0000000000 14.7690022992 -5.5740132195 1.1647991143 0.2656309043 0.3869842058 -0.7211913096 0.509476733639 +1403638579477829376.0000000000 14.8304449650 -5.5896044930 1.1718897377 0.2695069765 0.3843398888 -0.7223051128 0.507862347126 +1403638579527829504.0000000000 14.8915316623 -5.6050752348 1.1780610468 0.2728033414 0.3832143107 -0.7222790279 0.506989284814 +1403638579577829376.0000000000 14.9520026026 -5.6207092334 1.1831525455 0.2770988325 0.3829995556 -0.7190052601 0.50946934493 +1403638579627829504.0000000000 15.0120065572 -5.6363430848 1.1875832549 0.2822801543 0.3839454130 -0.7140400462 0.512884632969 +1403638579677829376.0000000000 15.0705872546 -5.6513821596 1.1902881738 0.2868013451 0.3879374542 -0.7080892518 0.515615294206 +1403638579727829504.0000000000 15.1280185266 -5.6657805889 1.1916860857 0.2901781691 0.3952064787 -0.7012948751 0.517488132726 +1403638579777829376.0000000000 15.1840186752 -5.6790160308 1.1916718330 0.2945025519 0.4046203536 -0.6943840607 0.517089346781 +1403638579827829504.0000000000 15.2382479967 -5.6911498181 1.1896519890 0.2972575154 0.4169396338 -0.6885168848 0.513559938705 +1403638579877829376.0000000000 15.2917428751 -5.7021371876 1.1866302971 0.3007042214 0.4311216720 -0.6821149361 0.508360392871 +1403638579927829504.0000000000 15.3442209445 -5.7117771960 1.1825709038 0.3069295450 0.4449020333 -0.6749768081 0.502257646709 +1403638579977829376.0000000000 15.3959825321 -5.7203907974 1.1776131241 0.3149320571 0.4590823775 -0.6664161529 0.495934150116 +1403638580027829504.0000000000 15.4469634237 -5.7279935116 1.1724157217 0.3259734212 0.4722779202 -0.6541326782 0.492752812263 +1403638580077829376.0000000000 15.4964766506 -5.7343829824 1.1671410187 0.3386445727 0.4852154347 -0.6400296723 0.49015084805 +1403638580127829504.0000000000 15.5434718778 -5.7388902875 1.1614097519 0.3529366210 0.4978879223 -0.6255785993 0.485998739295 +1403638580177829376.0000000000 15.5885450306 -5.7420648091 1.1543126882 0.3657892430 0.5120380065 -0.6113530040 0.479857076664 +1403638580227829504.0000000000 15.6313757391 -5.7438476532 1.1461292971 0.3785764016 0.5262776665 -0.5978124235 0.471520977505 +1403638580277829376.0000000000 15.6716554941 -5.7447320232 1.1364100502 0.3897388442 0.5407190259 -0.5855780302 0.461329533951 +1403638580327829504.0000000000 15.7098995070 -5.7448645617 1.1254146621 0.3996189269 0.5544364006 -0.5754096012 0.449231323333 +1403638580377829376.0000000000 15.7462237136 -5.7448787628 1.1135954867 0.4091152078 0.5656686722 -0.5673818606 0.43671675524 +1403638580427829504.0000000000 15.7808740324 -5.7451997692 1.1007164758 0.4170405525 0.5750075008 -0.5618141123 0.424038270578 +1403638580477829376.0000000000 15.8143333328 -5.7460509293 1.0870135100 0.4230858028 0.5827357934 -0.5565467789 0.414334504311 +1403638580527829504.0000000000 15.8469505550 -5.7473201048 1.0729467531 0.4290249532 0.5884866219 -0.5518899980 0.406249326886 +1403638580577829376.0000000000 15.8783375137 -5.7488738693 1.0578266759 0.4331687242 0.5945716275 -0.5469639970 0.399599577227 +1403638580627829504.0000000000 15.9082034311 -5.7506706985 1.0424406093 0.4364665310 0.6014127106 -0.5423282596 0.392020124124 +1403638580677829376.0000000000 15.9369454129 -5.7529933999 1.0274287283 0.4378887269 0.6095104173 -0.5371168427 0.385040272451 +1403638580727829504.0000000000 15.9651593283 -5.7556357958 1.0140759877 0.4388420711 0.6175441968 -0.5318639988 0.378388013053 +1403638580777829376.0000000000 15.9925046499 -5.7591830716 1.0029464464 0.4385332264 0.6245864181 -0.5268459549 0.374184119777 +1403638580827829504.0000000000 16.0194170001 -5.7631039707 0.9937583816 0.4385760962 0.6299774606 -0.5228727325 0.370652819481 +1403638580877829376.0000000000 16.0454904300 -5.7674789185 0.9865577416 0.4373509537 0.6351272391 -0.5191575288 0.36852814516 +1403638580927829504.0000000000 16.0721936922 -5.7715892558 0.9826813356 0.4390531369 0.6370385432 -0.5168466898 0.366447454302 +1403638580977829376.0000000000 16.0991569788 -5.7757060499 0.9812960730 0.4408371191 0.6379012023 -0.5163556988 0.363485189318 +1403638581027829504.0000000000 16.1257267901 -5.7803082352 0.9815884154 0.4411584324 0.6389451562 -0.5153890054 0.362632731484 +1403638581077829376.0000000000 16.1533623191 -5.7847500979 0.9845943707 0.4411439253 0.6396066999 -0.5149095558 0.362164956878 +1403638581127829504.0000000000 16.1812717016 -5.7893576355 0.9894545438 0.4406938338 0.6400635877 -0.5138129524 0.363460862281 +1403638581177829376.0000000000 16.2093669858 -5.7937524223 0.9957995754 0.4402468547 0.6401207814 -0.5133882101 0.364500532198 +1403638581227829504.0000000000 16.2364315004 -5.7981941139 1.0019549763 0.4389959702 0.6404411767 -0.5132761989 0.365602490406 +1403638581277829376.0000000000 16.2628906405 -5.8027461909 1.0075091942 0.4376081106 0.6403089101 -0.5130897125 0.367753433974 +1403638581327829504.0000000000 16.2893576068 -5.8068540924 1.0129070074 0.4367274800 0.6398387032 -0.5136722171 0.368804006995 +1403638581377829376.0000000000 16.3216292599 -5.8113966237 1.0236244930 0.4366818417 0.6387661360 -0.5136009841 0.370811032443 +1403638581427829504.0000000000 16.3493482379 -5.8151261748 1.0317546564 0.4365935254 0.6377142456 -0.5139005768 0.372307442521 +1403638581477829376.0000000000 16.3768372082 -5.8184651314 1.0415765953 0.4369861430 0.6361297390 -0.5144102762 0.373850416368 +1403638581527829504.0000000000 16.4040979388 -5.8215397276 1.0533076447 0.4356609659 0.6356353288 -0.5155550012 0.374660235864 +1403638581577829376.0000000000 16.4312571340 -5.8241554824 1.0663167222 0.4348418394 0.6349481694 -0.5160066831 0.37615222955 +1403638581627829504.0000000000 16.4586640555 -5.8261193729 1.0792938065 0.4357123803 0.6330041128 -0.5156833962 0.378855051162 +1403638581677829376.0000000000 16.4855806906 -5.8276650837 1.0909686375 0.4368443183 0.6310478031 -0.5144990958 0.382408671683 +1403638581727829504.0000000000 16.5117849948 -5.8286416923 1.1014221382 0.4387661753 0.6286551383 -0.5138341731 0.385034288034 +1403638581777829376.0000000000 16.5368103923 -5.8292350647 1.1097243481 0.4394543434 0.6271581310 -0.5146651170 0.38558057013 +1403638581827829504.0000000000 16.5608430173 -5.8295703506 1.1160311606 0.4392418625 0.6265736486 -0.5144821359 0.387014445383 +1403638581877829376.0000000000 16.5841790503 -5.8292996909 1.1213086873 0.4414568183 0.6242959632 -0.5135047822 0.389465360023 +1403638581927829504.0000000000 16.6066569730 -5.8285647769 1.1256821108 0.4458935178 0.6204373949 -0.5115286016 0.393160144852 +1403638581977829376.0000000000 16.6274371517 -5.8276046010 1.1284589204 0.4490908672 0.6177212164 -0.5093041138 0.396670154472 +1403638582027829504.0000000000 16.6459845861 -5.8265122300 1.1300201831 0.4490532300 0.6174168065 -0.5095461785 0.396875768453 +1403638582077829376.0000000000 16.6628154225 -5.8251320783 1.1321140483 0.4470191147 0.6187776111 -0.5115276392 0.394496709109 +1403638582127829504.0000000000 16.6780073997 -5.8237233198 1.1350599369 0.4416019944 0.6225035876 -0.5139042291 0.39163682833 +1403638582177829376.0000000000 16.6920239103 -5.8215442455 1.1411685970 0.4390219145 0.6245589234 -0.5171239862 0.386999602979 +1403638582227829504.0000000000 16.7057117821 -5.8194020301 1.1485976375 0.4347704769 0.6272923708 -0.5182897935 0.385816800926 +1403638582277829376.0000000000 16.7188498109 -5.8165307158 1.1591637807 0.4348059674 0.6273501408 -0.5181788969 0.385831831795 +1403638582327829504.0000000000 16.7312621297 -5.8135097893 1.1721389459 0.4360042118 0.6264891646 -0.5160902942 0.388667547177 +1403638582377829376.0000000000 16.7432927265 -5.8098215620 1.1864774405 0.4382710854 0.6250452915 -0.5149398528 0.389966392523 +1403638582427829504.0000000000 16.7545746311 -5.8059244263 1.2018009696 0.4387022736 0.6246660935 -0.5137845466 0.391609533171 +1403638582477829376.0000000000 16.7642252433 -5.8016641885 1.2191462238 0.4390069594 0.6244666855 -0.5130454700 0.392553937627 +1403638582527829504.0000000000 16.7730160224 -5.7968557323 1.2391882122 0.4398438565 0.6239459442 -0.5124578166 0.393212190627 +1403638582577829376.0000000000 16.7808741392 -5.7916426504 1.2615678951 0.4395014305 0.6242634421 -0.5118435474 0.393890632554 +1403638582627829504.0000000000 16.7871322149 -5.7859485826 1.2846514799 0.4398073956 0.6239750183 -0.5119317226 0.393891536658 +1403638582677829376.0000000000 16.7923569861 -5.7798649573 1.3099815432 0.4381555852 0.6251540784 -0.5124603539 0.393174830237 +1403638582727829504.0000000000 16.7964162971 -5.7730691381 1.3359350958 0.4367368640 0.6260323930 -0.5137254381 0.391702092007 +1403638582777829376.0000000000 16.8000979840 -5.7657597842 1.3644068517 0.4366226929 0.6259752040 -0.5146713253 0.390677737884 +1403638582827829504.0000000000 16.8028815668 -5.7581614362 1.3927946442 0.4349910168 0.6269078286 -0.5150945963 0.390444550041 +1403638582877829376.0000000000 16.8049171000 -5.7499123555 1.4207314907 0.4343700702 0.6269967966 -0.5156512273 0.390258210524 +1403638582927829504.0000000000 16.8061887153 -5.7411808873 1.4468076668 0.4330866809 0.6276690128 -0.5166088962 0.389336339886 +1403638582977829376.0000000000 16.8067295107 -5.7319728822 1.4709943900 0.4315989028 0.6284885036 -0.5179264648 0.387913347323 +1403638583027829504.0000000000 16.8067634552 -5.7225940166 1.4932756284 0.4294890797 0.6296434750 -0.5190681088 0.386854653791 +1403638583077829376.0000000000 16.8063813123 -5.7128067823 1.5138487833 0.4282034410 0.6302281323 -0.5203874883 0.385553078597 +1403638583127829504.0000000000 16.8056698363 -5.7025915494 1.5324235063 0.4266511369 0.6311330895 -0.5208919973 0.385112136716 +1403638583177829376.0000000000 16.8049246767 -5.6917652471 1.5493572291 0.4257859620 0.6314524827 -0.5216272081 0.384550558878 +1403638583227829504.0000000000 16.8042690718 -5.6802527048 1.5647621804 0.4253341971 0.6315487149 -0.5226073091 0.383560480084 +1403638583277829376.0000000000 16.8038038782 -5.6682348608 1.5789828179 0.4253041940 0.6315432746 -0.5230434254 0.383007845887 +1403638583327829504.0000000000 16.8034681673 -5.6559124320 1.5917601743 0.4252422985 0.6314863231 -0.5224286507 0.384008224228 +1403638583377829376.0000000000 16.8029319129 -5.6429135994 1.6030393592 0.4256132160 0.6313928759 -0.5225300327 0.383612814708 +1403638583427829504.0000000000 16.8026482725 -5.6296070691 1.6135900995 0.4249426555 0.6316927479 -0.5227685266 0.383537585407 +1403638583477829376.0000000000 16.8026959598 -5.6156321404 1.6245094941 0.4245488949 0.6319963250 -0.5228534837 0.383357686276 +1403638583527829504.0000000000 16.8030682297 -5.6010190863 1.6372555556 0.4243583063 0.6321994310 -0.5230478989 0.382968409655 +1403638583577829376.0000000000 16.8035087862 -5.5859309409 1.6523264790 0.4245469844 0.6319972203 -0.5227519706 0.383496738957 +1403638583627829504.0000000000 16.8037006720 -5.5704262718 1.6689138772 0.4241915730 0.6322997838 -0.5224776565 0.383765020862 +1403638583677829376.0000000000 16.8032949172 -5.5544667771 1.6868826868 0.4235159737 0.6326960906 -0.5217081023 0.384903277411 +1403638583727829504.0000000000 16.8026485071 -5.5377404366 1.7052237512 0.4237974956 0.6324754043 -0.5217156556 0.384945866843 +1403638583777829376.0000000000 16.8033200176 -5.5204101407 1.7222375202 0.4241353348 0.6323861920 -0.5216135156 0.384858756306 +1403638583827829504.0000000000 16.8034272627 -5.5027460949 1.7376687531 0.4238992338 0.6325061880 -0.5211254678 0.385582168312 +1403638583877829376.0000000000 16.8041369637 -5.4842312304 1.7519193596 0.4249695130 0.6318021319 -0.5208639087 0.385911606172 +1403638583927829504.0000000000 16.8045210892 -5.4651176723 1.7642310255 0.4252332496 0.6317282032 -0.5208051903 0.385821350408 +1403638583977829376.0000000000 16.8048761253 -5.4455632627 1.7748629595 0.4248323891 0.6319129749 -0.5205623596 0.386287798171 +1403638584027829504.0000000000 16.8051025470 -5.4254209997 1.7845089479 0.4257516726 0.6313496500 -0.5198202422 0.387195103988 +1403638584077829376.0000000000 16.8054327586 -5.4048093247 1.7936993160 0.4283477760 0.6294390416 -0.5172854830 0.390820169325 +1403638584127829504.0000000000 16.8056323096 -5.3833547986 1.8023719384 0.4332004349 0.6260121128 -0.5142073857 0.395015167178 +1403638584177829376.0000000000 16.8053302962 -5.3614874023 1.8100631478 0.4385553941 0.6222307555 -0.5109401068 0.399297208336 +1403638584227829504.0000000000 16.8044286314 -5.3391640799 1.8165513222 0.4440235818 0.6182524408 -0.5072571637 0.40410041847 +1403638584277829376.0000000000 16.8018790139 -5.3163839334 1.8211760215 0.4493210998 0.6145236462 -0.5056442371 0.405949680384 +1403638584327829504.0000000000 16.7975430413 -5.2937185567 1.8232124151 0.4507844906 0.6132171661 -0.5039211099 0.408437957558 +1403638584377829376.0000000000 16.7910160416 -5.2706999021 1.8236756118 0.4520976202 0.6123440312 -0.5035136503 0.408798890966 +1403638584427829504.0000000000 16.7822984762 -5.2476376456 1.8225270292 0.4520731742 0.6123364960 -0.5035174782 0.40883249629 +1403638584477829376.0000000000 16.7714699250 -5.2243918510 1.8206131104 0.4519222529 0.6125017264 -0.5028507518 0.409571768804 +1403638584527829504.0000000000 16.7584169357 -5.2006743231 1.8191912010 0.4529639607 0.6117526021 -0.5035934076 0.408627071956 +1403638584577829376.0000000000 16.7431754663 -5.1770844524 1.8186826219 0.4518978235 0.6126420042 -0.5030042492 0.409200265367 +1403638584627829504.0000000000 16.7258170191 -5.1530833371 1.8206137628 0.4518225709 0.6129398481 -0.5038498754 0.407794568392 +1403638584677829376.0000000000 16.7064714246 -5.1287609335 1.8247866848 0.4507582722 0.6138611334 -0.5048927262 0.40629401182 +1403638584727829504.0000000000 16.6848348720 -5.1043581089 1.8300876382 0.4483929231 0.6159434225 -0.5062603668 0.404051887458 +1403638584777829376.0000000000 16.6610373748 -5.0798962588 1.8370222485 0.4438941161 0.6194940581 -0.5093973004 0.399624218517 +1403638584827829504.0000000000 16.6362065793 -5.0551431680 1.8454522402 0.4401966790 0.6223281746 -0.5121466465 0.395778144085 +1403638584877829376.0000000000 16.6100986392 -5.0300509450 1.8544392881 0.4365590687 0.6250922696 -0.5163909063 0.389892633741 +1403638584927829504.0000000000 16.5841282670 -5.0049633969 1.8633793753 0.4342250236 0.6265331586 -0.5181939149 0.387788468857 +1403638584977829376.0000000000 16.5578464649 -4.9797283057 1.8712147915 0.4323363984 0.6277793073 -0.5194661795 0.386177767813 +1403638585027829504.0000000000 16.5316550045 -4.9541685639 1.8777118342 0.4312414352 0.6286014722 -0.5204452589 0.384743740907 +1403638585077829376.0000000000 16.5057492181 -4.9286459161 1.8828201748 0.4306046048 0.6287368766 -0.5205241850 0.385128792946 +1403638585127829504.0000000000 16.4794710601 -4.9027492954 1.8865677502 0.4313290764 0.6283264774 -0.5216789019 0.383421685599 +1403638585177829376.0000000000 16.4531868716 -4.8769929948 1.8887215626 0.4317580732 0.6280045187 -0.5220010895 0.383027614091 +1403638585227829504.0000000000 16.4270485426 -4.8512073281 1.8899336650 0.4326885670 0.6272019847 -0.5215122144 0.383957399425 +1403638585277829376.0000000000 16.4009475064 -4.8251725861 1.8900484182 0.4337514244 0.6265134021 -0.5206673757 0.385027457068 +1403638585327829504.0000000000 16.3742057359 -4.7991633614 1.8888612396 0.4353558316 0.6253649006 -0.5197462871 0.386326077442 +1403638585377829376.0000000000 16.3472531578 -4.7730555590 1.8862307042 0.4363576656 0.6247978732 -0.5193116959 0.386697514651 +1403638585427829504.0000000000 16.3191889383 -4.7471717876 1.8822711418 0.4362638378 0.6248791829 -0.5194221828 0.386523565373 +1403638585477829376.0000000000 16.2911283484 -4.7212019788 1.8792051910 0.4359385222 0.6249752430 -0.5196251200 0.386462527576 +1403638585527829504.0000000000 16.2628914094 -4.6948698924 1.8771457693 0.4348238114 0.6258388908 -0.5197181713 0.386195492149 +1403638585577829376.0000000000 16.2350144023 -4.6681482975 1.8775082690 0.4340375981 0.6266453952 -0.5204411809 0.384795906161 +1403638585627829504.0000000000 16.2065678427 -4.6417514191 1.8794036319 0.4326105618 0.6277225973 -0.5206179712 0.384407818277 +1403638585677829376.0000000000 16.1779732169 -4.6154052190 1.8829157579 0.4306744518 0.6290893107 -0.5213711101 0.383325346568 +1403638585727829504.0000000000 16.1480581284 -4.5890288806 1.8877287654 0.4278787589 0.6311536277 -0.5228822036 0.380997463327 +1403638585777829376.0000000000 16.1188870095 -4.5621487989 1.8954404289 0.4251465096 0.6330801926 -0.5251593162 0.377713658359 +1403638585827829504.0000000000 16.0916253495 -4.5348643441 1.9052963923 0.4225434568 0.6347981475 -0.5265818541 0.375765738064 +1403638585877829376.0000000000 16.0648044253 -4.5071677896 1.9165629306 0.4206919110 0.6360532629 -0.5283434347 0.373239571533 +1403638585927829504.0000000000 16.0394893102 -4.4791461534 1.9299888204 0.4202357358 0.6360745303 -0.5298972947 0.371510397463 +1403638585977829376.0000000000 16.0143781301 -4.4511064078 1.9456759817 0.4210414294 0.6352731041 -0.5302436740 0.371475226721 +1403638586027829504.0000000000 15.9906511324 -4.4227997510 1.9620516109 0.4235707155 0.6333878555 -0.5293177198 0.373135933695 +1403638586077829376.0000000000 15.9678552699 -4.3946275364 1.9771358820 0.4255509887 0.6315997676 -0.5282280939 0.375450623135 +1403638586127829504.0000000000 15.9449604872 -4.3664528137 1.9909760878 0.4270935061 0.6299832565 -0.5277236166 0.377120694251 +1403638586177829376.0000000000 15.9222935198 -4.3381569911 2.0028130588 0.4282595001 0.6291364113 -0.5267951881 0.378507604034 +1403638586227829504.0000000000 15.9001230677 -4.3100030606 2.0138171116 0.4293377669 0.6281639854 -0.5259388549 0.380088687308 +1403638586277829376.0000000000 15.8783470141 -4.2820294605 2.0234805041 0.4305650763 0.6271230735 -0.5248626413 0.381902570806 +1403638586327829504.0000000000 15.8569037731 -4.2540890411 2.0320144045 0.4319771628 0.6258107538 -0.5231336419 0.384821808015 +1403638586377829376.0000000000 15.8355243713 -4.2262574266 2.0391084038 0.4321437017 0.6255171253 -0.5204049638 0.388791487403 +1403638586427829504.0000000000 15.8141465059 -4.1984190589 2.0452270472 0.4319899335 0.6251319035 -0.5176577629 0.393224161306 +1403638586477829376.0000000000 15.7922806594 -4.1703007946 2.0501343656 0.4307359407 0.6257122389 -0.5151916754 0.396898325802 +1403638586527829504.0000000000 15.7697827006 -4.1415876731 2.0540596036 0.4303200076 0.6256806919 -0.5134088376 0.399699547512 +1403638586577829376.0000000000 15.7465017642 -4.1120192517 2.0566219364 0.4305709450 0.6254524940 -0.5138492972 0.399220163288 +1403638586627829504.0000000000 15.7228902109 -4.0818088313 2.0577149785 0.4305818529 0.6255320201 -0.5153846115 0.397099058105 +1403638586677829376.0000000000 15.6988037587 -4.0513590782 2.0574380303 0.4304790585 0.6255162682 -0.5162566617 0.396101297319 +1403638586727829504.0000000000 15.6748649134 -4.0204768893 2.0557607551 0.4319664422 0.6245969674 -0.5178087578 0.393900636631 +1403638586777829376.0000000000 15.6505174045 -3.9893588956 2.0522046980 0.4326235211 0.6242338956 -0.5187083625 0.39256918792 +1403638586827829504.0000000000 15.6260152122 -3.9579971561 2.0475036741 0.4343503608 0.6231139756 -0.5193883549 0.391541152661 +1403638586877829376.0000000000 15.6009564976 -3.9265106843 2.0409948781 0.4351502028 0.6228837298 -0.5192288330 0.391230851466 +1403638586927829504.0000000000 15.5753464513 -3.8949800121 2.0331474093 0.4353291753 0.6227086284 -0.5187702670 0.391918209923 +1403638586977829376.0000000000 15.5491182941 -3.8632923895 2.0241323669 0.4354178696 0.6227328692 -0.5188973695 0.391612783817 +1403638587027829504.0000000000 15.5225509938 -3.8315401223 2.0144779123 0.4359746198 0.6224384416 -0.5189998876 0.391325483336 +1403638587077829376.0000000000 15.4953812814 -3.7997782372 2.0048578428 0.4359576896 0.6223685116 -0.5193289383 0.391018902935 +1403638587127829504.0000000000 15.4669349391 -3.7681185127 1.9941373398 0.4360295831 0.6223785209 -0.5196376370 0.390512362821 +1403638587177829376.0000000000 15.4384050255 -3.7363402785 1.9871946951 0.4347265940 0.6235082323 -0.5197350633 0.390032994422 +1403638587227829504.0000000000 15.4092295732 -3.7044759147 1.9821989297 0.4334667364 0.6246985881 -0.5199845040 0.389197094083 +1403638587277829376.0000000000 15.3799750914 -3.6722650299 1.9797673696 0.4329867016 0.6250450031 -0.5204742378 0.388520048598 +1403638587327829504.0000000000 15.3502918939 -3.6399034338 1.9785437954 0.4314200151 0.6259778790 -0.5210541511 0.387983295149 +1403638587377829376.0000000000 15.3195932940 -3.6074262210 1.9785384036 0.4311406149 0.6264149054 -0.5213761932 0.387155009821 +1403638587427829504.0000000000 15.2888008658 -3.5749785204 1.9797994010 0.4311876975 0.6262033066 -0.5221886791 0.386349028444 +1403638587477829376.0000000000 15.2584905976 -3.5421965884 1.9811052412 0.4315479754 0.6258331289 -0.5230721632 0.385350167787 +1403638587527829504.0000000000 15.2284026402 -3.5094625907 1.9815892714 0.4319485392 0.6255774340 -0.5230784383 0.385308033902 +1403638587577829376.0000000000 15.1983569956 -3.4768795493 1.9808014451 0.4315901295 0.6255295940 -0.5240155901 0.384513131823 +1403638587627829504.0000000000 15.1686723512 -3.4444202011 1.9788004231 0.4321449729 0.6250599024 -0.5242318057 0.384359017953 +1403638587677829376.0000000000 15.1389672389 -3.4121594678 1.9755357584 0.4320644495 0.6249054767 -0.5243984312 0.38447333063 +1403638587727829504.0000000000 15.1093498310 -3.3798993230 1.9712301583 0.4321354107 0.6248945223 -0.5241917244 0.384693200943 +1403638587777829376.0000000000 15.0797532035 -3.3477360669 1.9657114349 0.4324059072 0.6243983209 -0.5246531235 0.384565947919 +1403638587827829504.0000000000 15.0503288326 -3.3155326373 1.9589947649 0.4327377990 0.6239923945 -0.5251508723 0.384171901854 +1403638587877829376.0000000000 15.0207677393 -3.2833913542 1.9511155273 0.4331306342 0.6236842359 -0.5253436555 0.3839659767 +1403638587927829504.0000000000 14.9911209625 -3.2515207915 1.9420540305 0.4332563443 0.6234084478 -0.5255222495 0.384027619573 +1403638587977829376.0000000000 14.9613788131 -3.2198734532 1.9320426108 0.4335701240 0.6231322771 -0.5256650395 0.383926267786 +1403638588027829504.0000000000 14.9315512768 -3.1884133137 1.9212936710 0.4342043868 0.6227645331 -0.5253381860 0.384253402126 +1403638588077829376.0000000000 14.9018388958 -3.1572404466 1.9095189652 0.4339302002 0.6230600913 -0.5244530349 0.385291731269 +1403638588127829504.0000000000 14.8721227354 -3.1265693971 1.8964475638 0.4324699843 0.6238497993 -0.5233941434 0.387091347468 +1403638588177829376.0000000000 14.8422526216 -3.0960333945 1.8823900505 0.4301878213 0.6253676929 -0.5206113608 0.390918787077 +1403638588227829504.0000000000 14.8119757117 -3.0649789351 1.8685966804 0.4288193026 0.6263752430 -0.5193709243 0.392456244317 +1403638588277829376.0000000000 14.7812656430 -3.0333385954 1.8558225414 0.4282489605 0.6269338782 -0.5186096358 0.393193064359 +1403638588327829504.0000000000 14.7506252648 -3.0011810555 1.8443663967 0.4278804158 0.6272657494 -0.5187453009 0.392885914897 +1403638588377829376.0000000000 14.7199221725 -2.9684265255 1.8352167288 0.4276110686 0.6275236028 -0.5180866796 0.393635738148 +1403638588427829504.0000000000 14.6891058949 -2.9349313797 1.8281351150 0.4281659962 0.6271947215 -0.5186325950 0.392836979439 +1403638588477829376.0000000000 14.6582255716 -2.9008821251 1.8234448990 0.4284938582 0.6270753201 -0.5190165278 0.392162466706 +1403638588527829504.0000000000 14.6259314368 -2.8664947702 1.8206714862 0.4294301091 0.6264063089 -0.5198949790 0.391042361389 +1403638588577829376.0000000000 14.5930908688 -2.8319542045 1.8203618953 0.4304177049 0.6258208194 -0.5203161380 0.390333213803 +1403638588627829504.0000000000 14.5594616374 -2.7971487156 1.8219701045 0.4313727017 0.6253471312 -0.5208038041 0.389386639959 +1403638588677829376.0000000000 14.5248233746 -2.7623100525 1.8252879588 0.4325531709 0.6245840402 -0.5212662664 0.388682403238 +1403638588727829504.0000000000 14.4902789804 -2.7271185895 1.8307806974 0.4346227074 0.6230147090 -0.5220303614 0.38786605469 +1403638588777829376.0000000000 14.4556132737 -2.6920873588 1.8358791009 0.4349798118 0.6226803304 -0.5220346642 0.38799687986 +1403638588827829504.0000000000 14.4205834127 -2.6570144187 1.8400235783 0.4357033094 0.6221059317 -0.5225222653 0.387449762257 +1403638588877829376.0000000000 14.3854196454 -2.6221207615 1.8424452958 0.4364714100 0.6212876225 -0.5239561146 0.385959050063 +1403638588927829504.0000000000 14.3530418419 -2.5875329562 1.8451501344 0.4363009997 0.6212922843 -0.5238369388 0.386305833092 +1403638588977829376.0000000000 14.3190738047 -2.5533440434 1.8446231371 0.4362623176 0.6210952775 -0.5241995982 0.386174348968 +1403638589027829504.0000000000 14.2851265414 -2.5194377052 1.8423028057 0.4361165960 0.6209851996 -0.5244885688 0.386123604409 +1403638589077829376.0000000000 14.2510703750 -2.4857345276 1.8382060463 0.4356037835 0.6211515423 -0.5245117872 0.386403274286 +1403638589127829504.0000000000 14.2170180048 -2.4521539102 1.8327622898 0.4351041270 0.6212695710 -0.5241276725 0.387296658598 +1403638589177829376.0000000000 14.1830695057 -2.4187653821 1.8264276718 0.4351227736 0.6211621450 -0.5237623760 0.387941664518 +1403638589227829504.0000000000 14.1486927536 -2.3854239095 1.8188353907 0.4354958329 0.6209500888 -0.5239526223 0.387605490438 +1403638589277829376.0000000000 14.1144665867 -2.3523972218 1.8107253267 0.4366667374 0.6201135872 -0.5234856376 0.388257758011 +1403638589327829504.0000000000 14.0798509151 -2.3197542965 1.8013583933 0.4362570371 0.6202195124 -0.5237986339 0.38812697034 +1403638589377829376.0000000000 14.0452492326 -2.2871714481 1.7933951547 0.4368803077 0.6199965592 -0.5232318924 0.388546329497 +1403638589427829504.0000000000 14.0098916066 -2.2547732921 1.7861884847 0.4365330904 0.6201732714 -0.5240319695 0.387575114459 +1403638589477829376.0000000000 13.9747950363 -2.2227521441 1.7798709307 0.4358239320 0.6205165679 -0.5240850604 0.387751903484 +1403638589527829504.0000000000 13.9396252472 -2.1908131662 1.7752833823 0.4362568917 0.6204466898 -0.5241910882 0.387233176037 +1403638589577829376.0000000000 13.9038294015 -2.1592996557 1.7722268405 0.4361712344 0.6203357085 -0.5244392043 0.387171517674 +1403638589627829504.0000000000 13.8676813758 -2.1277513671 1.7714817660 0.4363375633 0.6203480783 -0.5239090572 0.387681689524 +1403638589677829376.0000000000 13.8318128410 -2.0960860109 1.7730365762 0.4357428670 0.6208107030 -0.5246809100 0.386564571165 +1403638589727829504.0000000000 13.7952060643 -2.0649273441 1.7766040788 0.4342670922 0.6216314874 -0.5252760454 0.386097737147 +1403638589777829376.0000000000 13.7585053151 -2.0340604139 1.7810567815 0.4333231627 0.6221038813 -0.5255733355 0.385992832261 +1403638589827829504.0000000000 13.7216486453 -2.0034162332 1.7851900041 0.4330626200 0.6220385653 -0.5264428055 0.385204832395 +1403638589877829376.0000000000 13.6849137251 -1.9730050034 1.7878988087 0.4322591839 0.6221812230 -0.5266806315 0.385551599794 +1403638589927829504.0000000000 13.6482050610 -1.9426423190 1.7889863793 0.4316544525 0.6224202116 -0.5266358033 0.385904450019 +1403638589977829376.0000000000 13.6115224479 -1.9124385940 1.7895885104 0.4318182367 0.6219953097 -0.5270887944 0.385787827645 +1403638590027829504.0000000000 13.5747959049 -1.8822066566 1.7886434560 0.4322986316 0.6214549100 -0.5278004007 0.385147277041 +1403638590077829376.0000000000 13.5379709426 -1.8522044295 1.7862515934 0.4318315133 0.6216183287 -0.5278457574 0.385345369621 +1403638590127829504.0000000000 13.5011291607 -1.8223753201 1.7831692332 0.4324526473 0.6207996446 -0.5278745030 0.38592877343 +1403638590177829376.0000000000 13.4642926231 -1.7926880609 1.7786763710 0.4326664352 0.6205016197 -0.5277415980 0.38634997285 +1403638590227829504.0000000000 13.4273173704 -1.7631332589 1.7731037445 0.4331535851 0.6198768256 -0.5278401127 0.386672352581 +1403638590277829376.0000000000 13.3901623502 -1.7337496813 1.7666542198 0.4336241819 0.6195504430 -0.5280529630 0.386377258238 +1403638590327829504.0000000000 13.3523410113 -1.7047735253 1.7591477283 0.4334624031 0.6194840893 -0.5279380714 0.386821924107 +1403638590377829376.0000000000 13.3142657552 -1.6758166881 1.7505384457 0.4328654277 0.6196679044 -0.5285739661 0.386327286368 +1403638590427829504.0000000000 13.2760721152 -1.6470292332 1.7411945408 0.4317393858 0.6203304666 -0.5285347695 0.38657756322 +1403638590477829376.0000000000 13.2370288436 -1.6182999540 1.7312302861 0.4319449334 0.6201081500 -0.5290121603 0.386051280491 +1403638590527829504.0000000000 13.1978137442 -1.5898169885 1.7217854199 0.4320917184 0.6200431251 -0.5293461199 0.38553333871 +1403638590577829376.0000000000 13.1586210586 -1.5616464139 1.7130848295 0.4309244864 0.6208711421 -0.5300456134 0.384544873437 +1403638590627829504.0000000000 13.1198964050 -1.5335790280 1.7062858912 0.4297850481 0.6217708438 -0.5305615556 0.383653836027 +1403638590677829376.0000000000 13.0820059123 -1.5055271691 1.7016426359 0.4295173882 0.6220992413 -0.5316097706 0.381966489402 +1403638590727829504.0000000000 13.0445200628 -1.4778106902 1.6992571814 0.4292944229 0.6221896975 -0.5322860044 0.381127128881 +1403638590777829376.0000000000 13.0071034977 -1.4502902870 1.6986914185 0.4287126435 0.6227041678 -0.5323488988 0.380853828545 +1403638590827829504.0000000000 12.9706300984 -1.4230326435 1.6993077338 0.4278671216 0.6232598322 -0.5324753238 0.380718974384 +1403638590877829376.0000000000 12.9356892491 -1.3958898049 1.7018064274 0.4274214975 0.6234875144 -0.5326621043 0.380585424713 +1403638590927829504.0000000000 12.9011978636 -1.3687889674 1.7065812166 0.4274204204 0.6234977483 -0.5333716542 0.379574789102 +1403638590977829376.0000000000 12.8664160070 -1.3420308970 1.7134138099 0.4270501845 0.6237300578 -0.5337441401 0.379085937287 +1403638591027829504.0000000000 12.8313775668 -1.3156687731 1.7207925325 0.4266303287 0.6237666306 -0.5347928947 0.378018932127 +1403638591077829376.0000000000 12.7972227212 -1.2895965598 1.7278907906 0.4261382985 0.6240514876 -0.5353977723 0.377246758293 +1403638591127829504.0000000000 12.7633792323 -1.2640168256 1.7333481999 0.4231956727 0.6259598511 -0.5364810454 0.375856056563 +1403638591177829376.0000000000 12.7302084599 -1.2386132686 1.7373115832 0.4205157943 0.6275903392 -0.5379814857 0.373995660239 +1403638591227829504.0000000000 12.7014589745 -1.2142640632 1.7408966092 0.4168109151 0.6299765277 -0.5398456510 0.371436278123 +1403638591277829376.0000000000 12.6716879934 -1.1890020808 1.7420587073 0.4130914991 0.6323193971 -0.5420947680 0.368321674506 +1403638591327829504.0000000000 12.6435494119 -1.1637018846 1.7423899976 0.4100150236 0.6343102041 -0.5443744420 0.364958507634 +1403638591377829376.0000000000 12.6172598463 -1.1384615362 1.7417662979 0.4080438202 0.6354577238 -0.5460063721 0.362726844522 +1403638591427829504.0000000000 12.5927764193 -1.1131813940 1.7403420522 0.4061504184 0.6364933209 -0.5475785489 0.360660259626 +1403638591477829376.0000000000 12.5700585580 -1.0878947155 1.7373819734 0.4049099267 0.6372687354 -0.5489766903 0.358554185124 +1403638591527829504.0000000000 12.5495138752 -1.0625383357 1.7328379151 0.4033534935 0.6380125946 -0.5507221555 0.356301832432 +1403638591577829376.0000000000 12.5303506745 -1.0373517347 1.7269405928 0.4016408666 0.6390218212 -0.5520934732 0.354300046856 +1403638591627829504.0000000000 12.5138828544 -1.0121373726 1.7199345719 0.4010783693 0.6393732245 -0.5528482543 0.353124381997 +1403638591677829376.0000000000 12.4997879496 -0.9868532445 1.7125520783 0.4015708954 0.6388693357 -0.5532530807 0.352842481238 +1403638591727829504.0000000000 12.4882155486 -0.9617422999 1.7049217965 0.4025360684 0.6380145189 -0.5530912166 0.353542491632 +1403638591777829376.0000000000 12.4790520081 -0.9369236426 1.6972589619 0.4036098774 0.6374643556 -0.5516490388 0.355558152997 +1403638591827829504.0000000000 12.4720367159 -0.9121718967 1.6900701278 0.4056032078 0.6361336440 -0.5511450855 0.35645353073 +1403638591877829376.0000000000 12.4657580977 -0.8880465613 1.6829711547 0.4067158482 0.6355564522 -0.5500594123 0.357889449148 +1403638591927829504.0000000000 12.4628438236 -0.8636433847 1.6782934679 0.4092012897 0.6341091651 -0.5489122963 0.359381638684 +1403638591977829376.0000000000 12.4615559602 -0.8395980401 1.6752267275 0.4103199327 0.6333063414 -0.5484696246 0.360196754013 +1403638592027829504.0000000000 12.4627824814 -0.8155049441 1.6752411068 0.4128504182 0.6317864907 -0.5474244806 0.361561613534 +1403638592077829376.0000000000 12.4662681444 -0.7915366585 1.6768410973 0.4141352382 0.6312257190 -0.5466138687 0.36229735675 +1403638592127829504.0000000000 12.4712109506 -0.7676807327 1.6802118705 0.4155929932 0.6307690053 -0.5456428350 0.362886790384 +1403638592177829376.0000000000 12.4783225053 -0.7434662482 1.6866636973 0.4202748974 0.6292209504 -0.5439492174 0.362724764794 +1403638592227829504.0000000000 12.4862097899 -0.7197427162 1.6963572802 0.4261334520 0.6276713297 -0.5409141305 0.363112773683 +1403638592277829376.0000000000 12.4949468437 -0.6963539653 1.7085470764 0.4335242905 0.6260115918 -0.5371928065 0.362753449473 +1403638592327829504.0000000000 12.5039410623 -0.6738119468 1.7223525977 0.4399436461 0.6257990948 -0.5331008984 0.361425667918 +1403638592377829376.0000000000 12.5131783161 -0.6519073474 1.7378578114 0.4466494308 0.6268828072 -0.5282313170 0.358460468967 +1403638592427829504.0000000000 12.5224227910 -0.6309419718 1.7553982505 0.4523064641 0.6299098144 -0.5223028964 0.354728308232 +1403638592477829376.0000000000 12.5313245868 -0.6113140113 1.7744549453 0.4565165353 0.6343702713 -0.5164747038 0.34988697078 +1403638592527829504.0000000000 12.5407613014 -0.5933236193 1.7946730532 0.4575711194 0.6403536399 -0.5109589830 0.345683098022 +1403638592577829376.0000000000 12.5503911398 -0.5768272116 1.8164584551 0.4571943478 0.6465324330 -0.5060610917 0.341864465698 +1403638592627829504.0000000000 12.5605953493 -0.5613315729 1.8398777078 0.4566910120 0.6522892699 -0.5016458286 0.338087992433 +1403638592677829376.0000000000 12.5715483012 -0.5467683523 1.8642714111 0.4554046905 0.6576977726 -0.4983888921 0.334138773702 +1403638592727829504.0000000000 12.5832861654 -0.5329262932 1.8880554883 0.4536986478 0.6626365604 -0.4956779744 0.330716905408 +1403638592777829376.0000000000 12.5960868653 -0.5196213567 1.9105227174 0.4515765277 0.6671285285 -0.4939925453 0.327092542333 +1403638592827829504.0000000000 12.6103644674 -0.5063623405 1.9336750153 0.4499061332 0.6706927621 -0.4930285615 0.323540612058 +1403638592877829376.0000000000 12.6251340526 -0.4940063834 1.9540462359 0.4486350219 0.6735738542 -0.4915738565 0.321527640489 +1403638592927829504.0000000000 12.6410829698 -0.4821449344 1.9733399034 0.4476077500 0.6755911283 -0.4903768651 0.320553364707 +1403638592977829376.0000000000 12.6584290347 -0.4704451867 1.9912965269 0.4467856659 0.6773120114 -0.4890785130 0.320051895822 +1403638593027829504.0000000000 12.6769958670 -0.4590713134 2.0083450139 0.4470359438 0.6778970117 -0.4885658783 0.319245812787 +1403638593077829376.0000000000 12.6970119712 -0.4478876148 2.0238447889 0.4467761205 0.6785155003 -0.4881391216 0.318948290409 +1403638593127829504.0000000000 12.7185031199 -0.4366628781 2.0396175177 0.4475368808 0.6783706815 -0.4876039627 0.319008360847 +1403638593177829376.0000000000 12.7420704137 -0.4254462803 2.0570950093 0.4493982371 0.6772996064 -0.4866694978 0.320092591987 +1403638593227829504.0000000000 12.7674136501 -0.4144747301 2.0758860945 0.4512069719 0.6758934322 -0.4845179779 0.323763286916 +1403638593277829376.0000000000 12.7938230666 -0.4037180684 2.0958671857 0.4513064551 0.6755640725 -0.4819316182 0.328142625833 +1403638593327829504.0000000000 12.8216220874 -0.3926378829 2.1176823523 0.4515432070 0.6751681168 -0.4791388000 0.332690181052 +1403638593377829376.0000000000 12.8495319920 -0.3818172033 2.1403126764 0.4522861260 0.6742417395 -0.4758778048 0.338194695278 +1403638593427829504.0000000000 12.8776259890 -0.3709144578 2.1625405440 0.4534091322 0.6728792330 -0.4722498710 0.344432512869 +1403638593477829376.0000000000 12.9054214426 -0.3593410747 2.1835726038 0.4548068264 0.6713448333 -0.4704589554 0.348016144295 +1403638593527829504.0000000000 12.9330727662 -0.3472732689 2.2029845913 0.4556662991 0.6700789852 -0.4690886910 0.351166879737 +1403638593577829376.0000000000 12.9604065226 -0.3346523909 2.2206727578 0.4561816568 0.6691641434 -0.4681596769 0.353474414945 +1403638593627829504.0000000000 12.9873033208 -0.3215247349 2.2367620649 0.4563868943 0.6683498283 -0.4681338551 0.354781909527 +1403638593677829376.0000000000 13.0135894183 -0.3078983541 2.2512023459 0.4562241457 0.6681609787 -0.4673713002 0.356348850379 +1403638593727829504.0000000000 13.0391738426 -0.2935824415 2.2644471877 0.4577966932 0.6666820949 -0.4671215448 0.357427803003 +1403638593777829376.0000000000 13.0643120990 -0.2784820062 2.2764497918 0.4596851069 0.6649522971 -0.4664351484 0.359118779076 +1403638593827829504.0000000000 13.0883858850 -0.2623620663 2.2894382408 0.4662830951 0.6604240552 -0.4657468601 0.359861090936 +1403638593877829376.0000000000 13.1112149730 -0.2457234178 2.3038984615 0.4756138883 0.6551963477 -0.4628364998 0.360959207675 +1403638593927829504.0000000000 13.1318265722 -0.2294006125 2.3187864691 0.4818689023 0.6527154395 -0.4604145034 0.360254633634 +1403638593977829376.0000000000 13.1503024833 -0.2134196747 2.3340126690 0.4846759771 0.6532352014 -0.4588202619 0.357570882653 +1403638594027829504.0000000000 13.1666746446 -0.1980220984 2.3495010894 0.4842688823 0.6561337787 -0.4588232589 0.352779437064 +1403638594077829376.0000000000 13.1812788734 -0.1833142184 2.3667826641 0.4831777998 0.6592788227 -0.4590274881 0.348115516599 +1403638594127829504.0000000000 13.1943059463 -0.1694770856 2.3849102049 0.4808772129 0.6628499217 -0.4583286400 0.345430087155 +1403638594177829376.0000000000 13.2061171502 -0.1563177368 2.4028840408 0.4780113448 0.6667119083 -0.4569837705 0.343753136817 +1403638594227829504.0000000000 13.2174917981 -0.1435674828 2.4202295065 0.4761850896 0.6692271195 -0.4555220001 0.343340254402 +1403638594277829376.0000000000 13.2279897831 -0.1306994426 2.4371183136 0.4759877046 0.6707317195 -0.4534556840 0.343413174037 +1403638594327829504.0000000000 13.2377759924 -0.1179201692 2.4533045722 0.4768414243 0.6710768872 -0.4516547291 0.343927424309 +1403638594377829376.0000000000 13.2465560553 -0.1053950728 2.4699023936 0.4771206486 0.6716109536 -0.4485549426 0.346544480709 +1403638594427829504.0000000000 13.2543255829 -0.0925320214 2.4871203287 0.4776595502 0.6721146568 -0.4452720551 0.349050195749 +1403638594477829376.0000000000 13.2606359693 -0.0793932784 2.5059247073 0.4780108883 0.6723581220 -0.4430450338 0.350929115958 +1403638594527829504.0000000000 13.2646973853 -0.0660129753 2.5266803479 0.4792251083 0.6723070940 -0.4440421774 0.348099140439 +1403638594577829376.0000000000 13.2667728222 -0.0529436877 2.5497004451 0.4804202477 0.6719853421 -0.4449612540 0.345892422662 +1403638594627829504.0000000000 13.2680617170 -0.0394748355 2.5744109199 0.4812637512 0.6719333302 -0.4465826277 0.342716731824 +1403638594677829376.0000000000 13.2685119715 -0.0262604913 2.5991750983 0.4820593399 0.6714172360 -0.4482167350 0.34046944997 +1403638594727829504.0000000000 13.2682114385 -0.0133407384 2.6234378137 0.4819726125 0.6713641036 -0.4495446903 0.338942786691 +1403638594777829376.0000000000 13.2675617488 -0.0006597405 2.6459869422 0.4818017783 0.6713798496 -0.4503666106 0.33806221325 +1403638594827829504.0000000000 13.2662595324 0.0118132783 2.6667176367 0.4819350795 0.6710511505 -0.4513066492 0.337270278786 +1403638594877829376.0000000000 13.2637284952 0.0240559180 2.6863694771 0.4819615758 0.6708528123 -0.4519860437 0.336716735647 +1403638594927829504.0000000000 13.2604978637 0.0355200876 2.7036340402 0.4806389844 0.6714831858 -0.4525621889 0.336576830745 +1403638594977829376.0000000000 13.2561777342 0.0466392849 2.7191993937 0.4788337394 0.6723887604 -0.4530900164 0.336631908489 +1403638595027829504.0000000000 13.2512942676 0.0575372393 2.7332031034 0.4786616436 0.6723227352 -0.4546062560 0.33496018068 +1403638595077829376.0000000000 13.2458003490 0.0682095177 2.7454731335 0.4775890188 0.6728656596 -0.4551721369 0.33463242375 +1403638595127829504.0000000000 13.2400078322 0.0786027860 2.7559590184 0.4772647396 0.6727669564 -0.4560111606 0.334150882343 +1403638595177829376.0000000000 13.2339237254 0.0886698104 2.7646683953 0.4767044898 0.6728857041 -0.4564742648 0.334079188489 +1403638595227829504.0000000000 13.2274991371 0.0983066842 2.7714739548 0.4761294507 0.6730793484 -0.4564800643 0.334500953366 +1403638595277829376.0000000000 13.2205958107 0.1077518023 2.7765212873 0.4757531353 0.6732085102 -0.4568685901 0.334245938606 +1403638595327829504.0000000000 13.2134299185 0.1169226328 2.7801989654 0.4757349837 0.6730857991 -0.4567119943 0.334732559769 +1403638595377829376.0000000000 13.2058374477 0.1260365816 2.7823529665 0.4760761419 0.6726671879 -0.4574293896 0.334108837028 +1403638595427829504.0000000000 13.1980100199 0.1346790599 2.7832267526 0.4759383244 0.6726359634 -0.4574358124 0.334359162624 +1403638595477829376.0000000000 13.1899795754 0.1429946163 2.7825715417 0.4755357421 0.6729132005 -0.4577406901 0.333956648595 +1403638595527829504.0000000000 13.1817320533 0.1509333321 2.7810449085 0.4751884588 0.6732016586 -0.4576440552 0.334002057129 +1403638595577829376.0000000000 13.1732188777 0.1585983778 2.7795749383 0.4745753612 0.6737855314 -0.4577299069 0.333578501396 +1403638595627829504.0000000000 13.1648884549 0.1662673726 2.7798190977 0.4742759215 0.6740612532 -0.4571962371 0.334178661778 +1403638595677829376.0000000000 13.1562215120 0.1736161799 2.7825615452 0.4736223487 0.6744552999 -0.4561664379 0.335714313344 +1403638595727829504.0000000000 13.1471302345 0.1806392035 2.7860590640 0.4720215405 0.6756632249 -0.4545635316 0.337708257972 +1403638595777829376.0000000000 13.1370949246 0.1874941278 2.7901963360 0.4707263085 0.6764347653 -0.4537234658 0.339098462646 +1403638595827829504.0000000000 13.1267625538 0.1943652093 2.7939722174 0.4698104737 0.6770036755 -0.4533506394 0.339731275915 +1403638595877829376.0000000000 13.1161306281 0.2014513165 2.7950037300 0.4696597156 0.6770550986 -0.4532305944 0.339997313574 +1403638595927829504.0000000000 13.1053395430 0.2086398407 2.7920238935 0.4695988557 0.6769669345 -0.4527178767 0.340938716442 +1403638595977829376.0000000000 13.0943403477 0.2161449232 2.7852192632 0.4690408063 0.6773102923 -0.4517612175 0.342291239135 +1403638596027829504.0000000000 13.0834700111 0.2238976914 2.7765593090 0.4682626040 0.6777193920 -0.4501331802 0.344683448296 +1403638596077829376.0000000000 13.0722576280 0.2317959295 2.7656331641 0.4649765595 0.6797359657 -0.4474326325 0.348654349519 +1403638596127829504.0000000000 13.0604663062 0.2403853923 2.7549895184 0.4624284948 0.6812667474 -0.4440921250 0.353295472187 +1403638596177829376.0000000000 13.0472942607 0.2496119457 2.7444548081 0.4582807496 0.6838965260 -0.4405182022 0.35806146096 +1403638596227829504.0000000000 13.0327204653 0.2600736936 2.7357494699 0.4546582059 0.6862663606 -0.4366732275 0.362823497767 +1403638596277829376.0000000000 13.0173414928 0.2722876892 2.7289351242 0.4508030758 0.6886106490 -0.4329518271 0.367620288293 +1403638596327829504.0000000000 13.0021807749 0.2854473628 2.7248805456 0.4481827037 0.6902885776 -0.4293711981 0.371852548761 +1403638596377829376.0000000000 12.9851503495 0.3019870718 2.7230696374 0.4463406252 0.6914966360 -0.4258561492 0.375844367872 +1403638596427829504.0000000000 12.9660672599 0.3211053871 2.7239225015 0.4451764745 0.6922264870 -0.4241461555 0.377810052944 +1403638596477829376.0000000000 12.9455538358 0.3428149149 2.7263514885 0.4442386659 0.6929126529 -0.4212044806 0.380934178896 +1403638596527829504.0000000000 12.9236196700 0.3676463998 2.7310669180 0.4423687318 0.6940643818 -0.4187272667 0.383734302791 +1403638596577829376.0000000000 12.9002760056 0.3955333898 2.7384114367 0.4398920704 0.6955926614 -0.4162654377 0.386482730591 +1403638596627829504.0000000000 12.8752686702 0.4270845911 2.7475888763 0.4380575537 0.6966125229 -0.4134337053 0.389755235869 +1403638596677829376.0000000000 12.8478454341 0.4619954192 2.7584566824 0.4355854333 0.6979793716 -0.4106976925 0.392959962939 +1403638596727829504.0000000000 12.8185094645 0.5009170881 2.7712437662 0.4339255501 0.6989487926 -0.4090441800 0.394793694331 +1403638596777829376.0000000000 12.7873320248 0.5439724882 2.7861364482 0.4334229017 0.6992791645 -0.4075493087 0.396303922866 +1403638596827829504.0000000000 12.7536411325 0.5905806279 2.8026064906 0.4322914684 0.6998404668 -0.4056109211 0.39853128862 +1403638596877829376.0000000000 12.7176841380 0.6411900242 2.8208122907 0.4323823677 0.6997152138 -0.4045208278 0.399758686602 +1403638596927829504.0000000000 12.6796880985 0.6956092138 2.8393881993 0.4323725876 0.6995849156 -0.4034284067 0.4010990053 +1403638596977829376.0000000000 12.6396606881 0.7534497765 2.8572515860 0.4330027902 0.6988273708 -0.4032230379 0.401945358348 +1403638597027829504.0000000000 12.5975408683 0.8146365182 2.8734196721 0.4325687661 0.6986127575 -0.4029998537 0.40300818291 +1403638597077829376.0000000000 12.5535184346 0.8792988830 2.8880223748 0.4323792658 0.6983991314 -0.4018520138 0.404724329285 +1403638597127829504.0000000000 12.5077830410 0.9475836614 2.9013447170 0.4329743352 0.6974859496 -0.4014321896 0.406077298534 +1403638597177829376.0000000000 12.4598506887 1.0192633743 2.9132082559 0.4331427529 0.6967976694 -0.4009342861 0.407568474959 +1403638597227829504.0000000000 12.4094628579 1.0947887546 2.9235308519 0.4352300241 0.6950174113 -0.4018203642 0.407511986349 +1403638597277829376.0000000000 12.3568594698 1.1738668981 2.9324510539 0.4377463347 0.6932258669 -0.4028583185 0.406842990692 +1403638597327829504.0000000000 12.3015998171 1.2557783498 2.9398011269 0.4397640745 0.6917560459 -0.4045490872 0.405488801003 +1403638597377829376.0000000000 12.2440504625 1.3406752399 2.9457965940 0.4423375027 0.6898553639 -0.4068735113 0.403597641622 +1403638597427829504.0000000000 12.1842132181 1.4283748715 2.9505394513 0.4455561788 0.6877569950 -0.4091577523 0.40132273927 +1403638597477829376.0000000000 12.1221695120 1.5187181550 2.9546486391 0.4510040941 0.6843445848 -0.4123167359 0.397822454859 +1403638597527829504.0000000000 12.0579822412 1.6112130073 2.9576487715 0.4575267282 0.6803538859 -0.4159984869 0.393361337586 +1403638597577829376.0000000000 11.9917854050 1.7050623571 2.9592126939 0.4632706441 0.6766948511 -0.4196318538 0.389067469956 +1403638597627829504.0000000000 11.9239528803 1.7996036900 2.9594393269 0.4661970436 0.6745588452 -0.4217209371 0.387016966172 +1403638597677829376.0000000000 11.8544519543 1.8948223338 2.9581234528 0.4680952151 0.6731152885 -0.4226016225 0.386277810084 +1403638597727829504.0000000000 11.7833297257 1.9903582311 2.9549305534 0.4673174410 0.6735974593 -0.4220008906 0.387035037721 +1403638597777829376.0000000000 11.7102143044 2.0863717180 2.9501119590 0.4642564774 0.6766629490 -0.4184483336 0.389222518267 +1403638597827829504.0000000000 11.6353799420 2.1837389276 2.9444405016 0.4627068807 0.6796644307 -0.4138551442 0.390746111557 +1403638597877829376.0000000000 11.5582096673 2.2820856805 2.9374199851 0.4606105409 0.6832764068 -0.4087895729 0.392252937034 +1403638597927829504.0000000000 11.4789842382 2.3816665407 2.9296466121 0.4588759325 0.6863736912 -0.4042816860 0.393548412514 +1403638597977829376.0000000000 11.3975530089 2.4830031712 2.9224898710 0.4595936162 0.6882063324 -0.4008391173 0.393031492454 +1403638598027829504.0000000000 11.3143813207 2.5866043820 2.9165412109 0.4603786467 0.6897669372 -0.3986096379 0.391641967373 +1403638598077829376.0000000000 11.2289902725 2.6927252692 2.9134160499 0.4643411756 0.6894062960 -0.3986381833 0.387548487915 +1403638598127829504.0000000000 11.1406042122 2.8005900711 2.9123270762 0.4691092900 0.6889114820 -0.4026086089 0.378475563258 +1403638598177829376.0000000000 11.0494866249 2.9089574213 2.9126630527 0.4743905217 0.6876694812 -0.4079348834 0.368311618711 +1403638598227829504.0000000000 10.9569768058 3.0177652303 2.9142487309 0.4789433747 0.6864268442 -0.4121012908 0.36000549651 +1403638598277829376.0000000000 10.8632420485 3.1264592055 2.9156183674 0.4807691697 0.6865337720 -0.4166241707 0.352074829663 +1403638598327829504.0000000000 10.7693000317 3.2347206531 2.9167415784 0.4828007347 0.6861751831 -0.4199280268 0.346016648353 +1403638598377829376.0000000000 10.6751667359 3.3423651734 2.9158916167 0.4836988342 0.6863620786 -0.4222948115 0.341481517805 +1403638598427829504.0000000000 10.5811601501 3.4493626909 2.9136585567 0.4836614170 0.6867521629 -0.4239912752 0.338636233923 +1403638598477829376.0000000000 10.4865136269 3.5554627643 2.9100413627 0.4828162678 0.6878653298 -0.4248032981 0.336558906531 +1403638598527829504.0000000000 10.3915142293 3.6609351904 2.9048932590 0.4838360597 0.6883366571 -0.4244679573 0.334547854793 +1403638598577829376.0000000000 10.2963633832 3.7655704881 2.8970893288 0.4835358590 0.6904838022 -0.4237035234 0.331512467738 +1403638598627829504.0000000000 10.2010099589 3.8692040665 2.8875025953 0.4834766706 0.6932406322 -0.4209987530 0.329283745232 +1403638598677829376.0000000000 10.1059493766 3.9723168119 2.8776009038 0.4848610953 0.6958180253 -0.4166438310 0.327345249072 +1403638598727829504.0000000000 10.0111662359 4.0749586978 2.8684060411 0.4866394730 0.6987924366 -0.4122100331 0.323966113081 +1403638598777829376.0000000000 9.9159432450 4.1766434738 2.8596422015 0.4888046533 0.7019337971 -0.4074771190 0.319877090267 +1403638598827829504.0000000000 9.8208705369 4.2779199257 2.8534640024 0.4923071804 0.7046322651 -0.4009877978 0.316758262974 +1403638598877829376.0000000000 9.6794081824 4.3921590895 2.8711122130 0.4948147306 0.7084163906 -0.3945274095 0.312494356892 +1403638598927829504.0000000000 9.5834580923 4.4932454367 2.8659140119 0.4962736226 0.7129691801 -0.3875636636 0.308515553009 +1403638598977829376.0000000000 9.4875726057 4.5940403247 2.8617805286 0.4992178876 0.7168998296 -0.3803347767 0.303614216724 +1403638599027829504.0000000000 9.3916213364 4.6942370531 2.8591753877 0.5024526658 0.7206161716 -0.3738626733 0.29745647302 +1403638599077829376.0000000000 9.2967363045 4.7950683809 2.8573227262 0.5055029899 0.7245152322 -0.3655008213 0.293178367471 +1403638599127829504.0000000000 9.2011159881 4.8945843589 2.8579974456 0.5081411278 0.7286202057 -0.3575907650 0.288156268145 +1403638599177829376.0000000000 9.1045529168 4.9931315261 2.8599875597 0.5112780734 0.7323962921 -0.3497190500 0.28264286499 +1403638599227829504.0000000000 9.0079489417 5.0906627154 2.8620161499 0.5129877325 0.7370771330 -0.3411438531 0.277816050323 +1403638599277829376.0000000000 8.9112206396 5.1878993958 2.8659187055 0.5150997189 0.7413692073 -0.3328916685 0.272446536153 +1403638599327829504.0000000000 8.8140205875 5.2845252791 2.8722191292 0.5171670065 0.7458500693 -0.3253100722 0.265366385317 +1403638599377829376.0000000000 8.7167185277 5.3798388112 2.8796670336 0.5171283226 0.7508972141 -0.3180999896 0.259892416989 +1403638599427829504.0000000000 8.6198719571 5.4746916544 2.8887865727 0.5178238631 0.7547382735 -0.3112561276 0.255632956171 +1403638599477829376.0000000000 8.5235917633 5.5695237998 2.8983381585 0.5183808204 0.7579344778 -0.3065456032 0.250691933373 +1403638599527829504.0000000000 8.4279927128 5.6639263837 2.9075352480 0.5178650218 0.7609914592 -0.3018487869 0.248183658104 +1403638599577829376.0000000000 8.3329737012 5.7582047325 2.9155821830 0.5175862439 0.7633120014 -0.2994803284 0.244480677212 +1403638599627829504.0000000000 8.2385362356 5.8519268458 2.9216808867 0.5180118728 0.7645862692 -0.2976015937 0.241877712987 +1403638599677829376.0000000000 8.1442691984 5.9448572974 2.9255104986 0.5170632289 0.7664518645 -0.2956925926 0.240339441961 +1403638599727829504.0000000000 8.0504346544 6.0376627213 2.9275738912 0.5172411970 0.7669332471 -0.2950836415 0.239166433959 +1403638599777829376.0000000000 7.9576973002 6.1308949592 2.9279095975 0.5174207376 0.7669908141 -0.2946902322 0.239078519234 +1403638599827829504.0000000000 7.8659711758 6.2241699673 2.9264786007 0.5168678241 0.7672288022 -0.2960941544 0.237772726098 +1403638599877829376.0000000000 7.7748370826 6.3172032646 2.9242598513 0.5164960176 0.7673685808 -0.2973601298 0.23654656679 +1403638599927829504.0000000000 7.6842853143 6.4101550727 2.9212062614 0.5164440703 0.7670007597 -0.3000257280 0.234477972079 +1403638599977829376.0000000000 7.5946206583 6.5033807318 2.9171226534 0.5177885692 0.7655644659 -0.3025808910 0.232918119562 +1403638600027829504.0000000000 7.5061746814 6.5967988434 2.9124185411 0.5193426275 0.7640260284 -0.3058732367 0.230193454009 +1403638600077829376.0000000000 7.4190067347 6.6902448619 2.9068345737 0.5187085188 0.7638668777 -0.3101992055 0.226330109753 +1403638600127829504.0000000000 7.3333293251 6.7832785890 2.9010042308 0.5196877465 0.7625427572 -0.3153953605 0.2213118979 +1403638600177829376.0000000000 7.2487693834 6.8756225149 2.8943074529 0.5206368065 0.7613172974 -0.3217375068 0.214052014808 +1403638600227829504.0000000000 7.1659293987 6.9664536655 2.8861757391 0.5200239956 0.7609238940 -0.3272421003 0.208524529309 +1403638600277829376.0000000000 7.0849615164 7.0560142898 2.8768589753 0.5208808452 0.7595047621 -0.3323751630 0.203377512295 +1403638600327829504.0000000000 7.0068721293 7.1445306959 2.8669686545 0.5204375281 0.7590283379 -0.3367348625 0.199073840449 +1403638600377829376.0000000000 6.9317121242 7.2318049946 2.8577429310 0.5210386152 0.7577784550 -0.3408371781 0.195244955506 +1403638600427829504.0000000000 6.8593997654 7.3174164901 2.8492853145 0.5209355724 0.7571609179 -0.3448950377 0.190737743332 +1403638600477829376.0000000000 6.7906840323 7.4010999828 2.8431386194 0.5210341450 0.7565684205 -0.3472484822 0.18853683059 +1403638600527829504.0000000000 6.7257627838 7.4827306631 2.8391004848 0.5201658840 0.7568072583 -0.3477323405 0.189083172989 +1403638600577829376.0000000000 6.6645488270 7.5627640975 2.8375081681 0.5195555295 0.7568437373 -0.3479885405 0.190140960332 +1403638600627829504.0000000000 6.6061448182 7.6407868920 2.8376933010 0.5180903410 0.7575622140 -0.3494308580 0.18862652489 +1403638600677829376.0000000000 6.5511077700 7.7171327670 2.8401619799 0.5181804635 0.7571706080 -0.3512712767 0.186521226069 +1403638600727829504.0000000000 6.5000464812 7.7920628777 2.8440139336 0.5151476162 0.7591693662 -0.3512838201 0.186773886715 +1403638600777829376.0000000000 6.4520933240 7.8654864704 2.8494355654 0.5128347892 0.7607298960 -0.3523846922 0.184703906016 +1403638600827829504.0000000000 6.4082286873 7.9373253602 2.8555674386 0.5085644231 0.7640396989 -0.3497507069 0.187829734457 +1403638600877829376.0000000000 6.3676802813 8.0078662121 2.8624896390 0.5044072691 0.7674279971 -0.3454355546 0.193136878568 +1403638600927829504.0000000000 6.3300822999 8.0774786848 2.8680283106 0.4993217389 0.7715055351 -0.3392727215 0.200875659908 +1403638600977829376.0000000000 6.2951544694 8.1471323966 2.8723358730 0.4961468812 0.7741906143 -0.3335333801 0.207900575635 +1403638601027829504.0000000000 6.2625267685 8.2170987653 2.8755595055 0.4935046132 0.7763388047 -0.3291533508 0.213094647267 +1403638601077829376.0000000000 6.2318380496 8.2879273204 2.8777695681 0.4923954684 0.7774040678 -0.3261870477 0.216313725923 +1403638601127829504.0000000000 6.2031818281 8.3593494885 2.8790218838 0.4928085614 0.7772678936 -0.3234043203 0.220009065698 +1403638601177829376.0000000000 6.1760706775 8.4311363083 2.8785099406 0.4914640074 0.7783562879 -0.3197149878 0.224514910502 +1403638601227829504.0000000000 6.1506357126 8.5041076538 2.8776680622 0.4937232438 0.7770717119 -0.3155281221 0.229867173021 +1403638601277829376.0000000000 6.1268729558 8.5782950876 2.8757901535 0.4969255583 0.7749642281 -0.3104437632 0.236896822565 +1403638601327829504.0000000000 6.1034338601 8.6537960260 2.8740636379 0.5015740217 0.7724859696 -0.3067964169 0.239926834918 +1403638601377829376.0000000000 6.0796778737 8.7303421217 2.8729270040 0.5051609458 0.7716148856 -0.3051475876 0.237292724173 +1403638601427829504.0000000000 6.0561648733 8.8084160995 2.8735645453 0.5118780385 0.7693690384 -0.3030329191 0.232858769145 +1403638601477829376.0000000000 6.0325156317 8.8865579018 2.8751439062 0.5163960443 0.7692983478 -0.2993994726 0.227761132033 +1403638601527829504.0000000000 6.0089562737 8.9648116615 2.8782809170 0.5219834217 0.7691080416 -0.2927601535 0.224271309797 +1403638601577829376.0000000000 5.9851268814 9.0426804319 2.8826121484 0.5266589316 0.7701721692 -0.2845240714 0.220252701075 +1403638601627829504.0000000000 5.9614462685 9.1205354051 2.8876933889 0.5298659584 0.7724550820 -0.2759242730 0.215455350433 +1403638601677829376.0000000000 5.9374339302 9.1982274354 2.8941747150 0.5331621018 0.7752749908 -0.2650409299 0.210808366223 +1403638601727829504.0000000000 5.9127759266 9.2754682542 2.9020523946 0.5358380070 0.7788328112 -0.2537397534 0.204727184221 +1403638601777829376.0000000000 5.8875814623 9.3522655730 2.9117899121 0.5390962561 0.7821272414 -0.2404283767 0.199615632195 +1403638601827829504.0000000000 5.8613141658 9.4288867277 2.9234312108 0.5428797680 0.7853077556 -0.2265957654 0.192944669762 +1403638601877829376.0000000000 5.8344025657 9.5050898708 2.9364546103 0.5463571252 0.7883345575 -0.2117364086 0.187590539603 +1403638601927829504.0000000000 5.8065738385 9.5808983346 2.9499323934 0.5488173832 0.7915806342 -0.1994453506 0.18005868938 +1403638601977829376.0000000000 5.7785311919 9.6566533859 2.9626716020 0.5508448594 0.7942270769 -0.1889526562 0.173407568905 +1403638602027829504.0000000000 5.7501589502 9.7321525987 2.9740100938 0.5516697641 0.7970843356 -0.1799975188 0.167086583865 +1403638602077829376.0000000000 5.7215028123 9.8073082602 2.9835244911 0.5526765519 0.7991072542 -0.1726942222 0.161718678207 +1403638602127829504.0000000000 5.6925635486 9.8823209516 2.9914040041 0.5544113002 0.8000834456 -0.1647136405 0.159260814305 +1403638602177829376.0000000000 5.6627471200 9.9568584138 2.9975760780 0.5567190541 0.8005847348 -0.1565247692 0.156933023583 +1403638602227829504.0000000000 5.6320031909 10.0567701300 3.0251152972 0.5598444847 0.8005325078 -0.1469347944 0.155344852286 +1403638602277829376.0000000000 5.6014029259 10.1337283131 3.0299945190 0.5632343552 0.8005503222 -0.1378671084 0.151257737436 +1403638602327829504.0000000000 5.5691657587 10.2104966707 3.0353714051 0.5696112993 0.7987200576 -0.1289624602 0.144768508973 +1403638602377829376.0000000000 5.5348301649 10.2865376573 3.0427647162 0.5788377625 0.7951194995 -0.1223990065 0.13323028726 +1403638602427829504.0000000000 5.4987029874 10.3619050226 3.0540137622 0.5935971165 0.7872674668 -0.1162340236 0.119758301373 +1403638602477829376.0000000000 5.4616925175 10.4350547147 3.0676325652 0.6101575757 0.7772922440 -0.1087791936 0.108127643151 +1403638602527829504.0000000000 5.4235709799 10.5047736583 3.0831725905 0.6255320996 0.7676104163 -0.1029951324 0.0942116971702 +1403638602577829376.0000000000 5.3851949920 10.5699455162 3.1004391692 0.6383315025 0.7593184956 -0.0966456697 0.0814120976493 +1403638602627829504.0000000000 5.3463197941 10.6295158982 3.1187998235 0.6455600575 0.7551576757 -0.0894465962 0.0706286298765 +1403638602677829376.0000000000 5.3079926653 10.6832043529 3.1370311291 0.6477555660 0.7549649936 -0.0806019835 0.0628005200185 +1403638602727829504.0000000000 5.2698960867 10.7305015389 3.1566871645 0.6483808874 0.7559302759 -0.0715448094 0.055253805777 +1403638602777829376.0000000000 5.2323007116 10.7722441965 3.1775282568 0.6469770593 0.7584004028 -0.0608255838 0.0504951699894 +1403638602827829504.0000000000 5.1948019410 10.8081149378 3.1994328469 0.6457440539 0.7605458690 -0.0504956447 0.0451086230148 +1403638602877829376.0000000000 5.1572807890 10.8382992868 3.2222765291 0.6442931543 0.7627440077 -0.0414127376 0.037321509965 +1403638602927829504.0000000000 5.1198438693 10.8631868335 3.2461951198 0.6412976459 0.7660716592 -0.0331258415 0.0278248249582 +1403638602977829376.0000000000 5.0822435365 10.8835931465 3.2704338274 0.6385959271 0.7689365879 -0.0272483323 0.0137584173644 +1403638603027829504.0000000000 5.0458455156 10.9001031382 3.2935031450 0.6374357265 0.7702402838 -0.0199963448 0.00239709024903 +1403638603077829376.0000000000 5.0108281261 10.9128177566 3.3152033461 0.6378341348 0.7700506046 -0.0118885738 -0.00695303006821 +1403638603127829504.0000000000 4.9774154581 10.9218431015 3.3352701226 0.6396976207 0.7684664516 -0.0041656125 -0.0151299235171 +1403638603177829376.0000000000 4.9458718437 10.9270589901 3.3524342756 0.6392330319 0.7687508743 0.0040155655 -0.0196748417844 +1403638603227829504.0000000000 4.9161086600 10.9279915966 3.3659826919 0.6327005908 0.7739749972 0.0109159386 -0.0230977992558 +1403638603277829376.0000000000 4.8880728802 10.9252222967 3.3767283324 0.6224609915 0.7820690312 0.0173578416 -0.024678935039 +1403638603327829504.0000000000 4.8614075156 10.9192394139 3.3851346342 0.6103955437 0.7913608298 0.0222587477 -0.0258817605118 +1403638603377829376.0000000000 4.8358711231 10.9115843384 3.3917019921 0.5997237811 0.7993306559 0.0262926123 -0.026656845328 +1403638603427829504.0000000000 4.8113241941 10.9026856886 3.3969927664 0.5909628590 0.8057020362 0.0288340004 -0.0278519037884 +1403638603477829376.0000000000 4.7880064304 10.8931506397 3.4012663716 0.5851879418 0.8098215417 0.0301219803 -0.0289276632812 +1403638603527829504.0000000000 4.7654643213 10.8834424442 3.4047550513 0.5833878807 0.8110166927 0.0326348802 -0.029076956315 +1403638603577829376.0000000000 4.7434670720 10.8736574683 3.4073752309 0.5854350618 0.8093871102 0.0350783074 -0.030459916716 +1403638603627829504.0000000000 4.7223215179 10.8633339069 3.4085823229 0.5895429907 0.8062675855 0.0371382626 -0.031502257345 +1403638603677829376.0000000000 4.7021997818 10.8524365515 3.4074947031 0.5938076841 0.8030455349 0.0403613141 -0.0296861499399 +1403638603727829504.0000000000 4.6831998343 10.8403448812 3.4040421471 0.5974641766 0.8002336405 0.0449841250 -0.0252805625361 +1403638603777829376.0000000000 4.6401570405 10.8179847465 3.4241628640 0.6015287658 0.7970595390 0.0495531714 -0.0200927471381 +1403638603827829504.0000000000 4.6206735631 10.8021461629 3.4189177237 0.6045811459 0.7946059246 0.0531894753 -0.0159355713838 +1403638603877829376.0000000000 4.6012119461 10.7844681516 3.4120931763 0.6082878520 0.7915861501 0.0571575559 -0.0105009502637 +1403638603927829504.0000000000 4.5809382741 10.7650221548 3.4037111397 0.6108619410 0.7894201621 0.0602113141 -0.00617206889389 +1403638603977829376.0000000000 4.5598217156 10.7436789182 3.3945517079 0.6148499656 0.7861654654 0.0624180598 -0.00271414305135 +1403638604027829504.0000000000 4.5378754242 10.7197520853 3.3833715981 0.6154317498 0.7855380636 0.0645898571 0.00136464960591 +1403638604077829376.0000000000 4.5144153846 10.6942114572 3.3727677137 0.6174329549 0.7838118478 0.0662880557 0.00462894438913 +1403638604127829504.0000000000 4.4891129601 10.6663506173 3.3633617833 0.6180473035 0.7832254291 0.0673600338 0.00617119716962 +1403638604177829376.0000000000 4.4656160354 10.6366178443 3.3558341607 0.6176702890 0.7835206308 0.0674151934 0.00583326404093 +1403638604227829504.0000000000 4.4381212747 10.6043767357 3.3515098887 0.6173175427 0.7839856256 0.0654153127 0.00253517526424 +1403638604277829376.0000000000 4.4092749699 10.5693738951 3.3488222590 0.6151250488 0.7859529798 0.0624119418 -0.00195892649048 +1403638604327829504.0000000000 4.3792608229 10.5315230160 3.3473940563 0.6119108563 0.7886690105 0.0593252471 -0.00684185357544 +1403638604377829376.0000000000 4.3492631234 10.4912825811 3.3470862376 0.6076436239 0.7921101185 0.0567211197 -0.0106536850295 +1403638604427829504.0000000000 4.3187527523 10.4490745182 3.3480864604 0.6028127944 0.7958743911 0.0550947984 -0.0128550214308 +1403638604477829376.0000000000 4.2880146887 10.4060346139 3.3506222704 0.5971855792 0.8000951600 0.0553579657 -0.0123537238759 +1403638604527829504.0000000000 4.2567378020 10.3623846879 3.3550999609 0.5927117489 0.8034685020 0.0542748406 -0.0136158225951 +1403638604577829376.0000000000 4.2255159215 10.3179316581 3.3591688125 0.5906494412 0.8049644140 0.0548186277 -0.0126668003117 +1403638604627829504.0000000000 4.1938308512 10.2728996814 3.3619867684 0.5882616661 0.8067521441 0.0538328465 -0.0141850198153 +1403638604677829376.0000000000 4.1619557905 10.2275937655 3.3637261123 0.5873313493 0.8074989615 0.0520520701 -0.0166701930825 +1403638604727829504.0000000000 4.1300752213 10.1819199947 3.3640746381 0.5862849909 0.8083156524 0.0502419328 -0.0192733947802 +1403638604777829376.0000000000 4.0968792844 10.1252495694 3.3609997592 0.5861428075 0.8084610338 0.0486989248 -0.0213490231398 +1403638604827829504.0000000000 4.0647089382 10.0758725156 3.3598996744 0.5845140397 0.8096757527 0.0471359229 -0.0233819928407 +1403638604877829376.0000000000 4.0330152000 10.0259514982 3.3592360128 0.5822984483 0.8112795581 0.0467817163 -0.0237795457409 +1403638604927829504.0000000000 4.0018018459 9.9757628532 3.3593449355 0.5785624172 0.8139571177 0.0465098504 -0.0240036208119 +1403638604977829376.0000000000 3.9704744079 9.9249698575 3.3604269599 0.5734276337 0.8175876067 0.0461728467 -0.0244810642929 +1403638605027829504.0000000000 3.9397311572 9.8748361938 3.3635384159 0.5678449390 0.8214758609 0.0457744700 -0.0251839839765 +1403638605077829376.0000000000 3.9095228115 9.8249843705 3.3691023545 0.5636275413 0.8243746466 0.0456341611 -0.0254550610016 +1403638605127829504.0000000000 3.8799209726 9.7761649433 3.3764663830 0.5593536925 0.8272760914 0.0456632153 -0.0255457659516 +1403638605177829376.0000000000 3.8511211328 9.7302185485 3.3860968265 0.5570028503 0.8288467463 0.0460700617 -0.0252674741235 +1403638605227829504.0000000000 3.8229899913 9.6867896519 3.3965959990 0.5555618214 0.8298054882 0.0470011374 -0.0237656784081 +1403638605277829376.0000000000 3.7950080757 9.6449751749 3.4059343429 0.5543225100 0.8306032059 0.0483225131 -0.0221315154512 +1403638605327829504.0000000000 3.7679236734 9.6057971265 3.4145558859 0.5550760215 0.8300490920 0.0505449337 -0.0188235206458 +1403638605377829376.0000000000 3.7407842898 9.5679697068 3.4218389944 0.5583477525 0.8277282116 0.0540317544 -0.0139414689375 +1403638605427829504.0000000000 3.7133630365 9.5313092387 3.4279137991 0.5625075216 0.8247036813 0.0581139904 -0.00847881735035 +1403638605477829376.0000000000 3.6855709485 9.4960151518 3.4328365730 0.5685725900 0.8202298768 0.0628010862 -0.00204515186961 +1403638605527829504.0000000000 3.6566178127 9.4603925510 3.4362106493 0.5731949091 0.8167460228 0.0660875468 0.00244264159133 +1403638605577829376.0000000000 3.6267355989 9.4249792734 3.4380379295 0.5767867002 0.8138799060 0.0697483296 0.00719524566796 +1403638605627829504.0000000000 3.5954966011 9.3892822527 3.4383917251 0.5798439355 0.8113669019 0.0729729458 0.011819905291 +1403638605677829376.0000000000 3.5623051858 9.3530139894 3.4382408593 0.5819818908 0.8096229593 0.0748889086 0.0141206897608 +1403638605727829504.0000000000 3.5273056401 9.3158758897 3.4388074108 0.5825754722 0.8090436590 0.0761612198 0.0159262580378 +1403638605777829376.0000000000 3.4900624478 9.2782164344 3.4414328290 0.5824050070 0.8091551108 0.0762739197 0.0159594364959 +1403638605827829504.0000000000 3.4505231988 9.2396913377 3.4467926682 0.5813197698 0.8098666334 0.0767782375 0.0169842189998 +1403638605877829376.0000000000 3.4088774628 9.2013397091 3.4538036382 0.5813832090 0.8096859980 0.0778293480 0.0185672177708 +1403638605927829504.0000000000 3.3650137827 9.1636485606 3.4627813395 0.5810040221 0.8098673751 0.0784316087 0.019941008852 +1403638605977829376.0000000000 3.3191641326 9.1264363088 3.4729821554 0.5809814495 0.8096658615 0.0798886097 0.0227938163189 +1403638606027829504.0000000000 3.2713055193 9.0889797381 3.4828185963 0.5806627644 0.8098142476 0.0802870154 0.0241998692234 +1403638606077829376.0000000000 3.2214109247 9.0516414493 3.4915441585 0.5802622337 0.8100421773 0.0805259810 0.0253570009792 +1403638606127829504.0000000000 3.1694231334 9.0144491543 3.4989594195 0.5799097789 0.8101835935 0.0810893300 0.0270502085551 +1403638606177829376.0000000000 3.1154238883 8.9769607723 3.5047082350 0.5794118153 0.8103844475 0.0820454251 0.0287670604633 +1403638606227829504.0000000000 3.0589894499 8.9388984719 3.5087146522 0.5786470413 0.8108565110 0.0823687297 0.0299117459991 +1403638606277829376.0000000000 3.0003385200 8.9010571196 3.5114447461 0.5775854349 0.8116388163 0.0819499550 0.0303595462099 +1403638606327829504.0000000000 2.9387607820 8.8625004232 3.5122345827 0.5750381259 0.8138408201 0.0791073474 0.0271348641416 +1403638606377829376.0000000000 2.8749546178 8.8237822966 3.5111695254 0.5700443390 0.8179583662 0.0744002391 0.0214048386044 +1403638606427829504.0000000000 2.8095196800 8.7854859163 3.5087510390 0.5658717865 0.8213647777 0.0699754346 0.015889043718 +1403638606477829376.0000000000 2.7418321076 8.7459854508 3.5045349854 0.5610211290 0.8252348453 0.0644981687 0.00909555334708 +1403638606527829504.0000000000 2.6735281220 8.7081132489 3.4986185540 0.5563387193 0.8288031621 0.0597078919 0.00274145708416 +1403638606577829376.0000000000 2.6046566984 8.6713841408 3.4910913397 0.5522804899 0.8317005422 0.0570706253 -0.00184724250792 +1403638606627829504.0000000000 2.5350875708 8.6362167919 3.4819996873 0.5487534571 0.8340683873 0.0562076046 -0.00634616386883 +1403638606677829376.0000000000 2.4650824823 8.6027148470 3.4717860963 0.5462374973 0.8355650659 0.0578947536 -0.0101889498873 +1403638606727829504.0000000000 2.3944354459 8.5702612645 3.4590915885 0.5420349552 0.8379769953 0.0617161194 -0.0135566689054 +1403638606777829376.0000000000 2.3234002803 8.5394436504 3.4458378494 0.5397159563 0.8390194265 0.0665261150 -0.0180932195913 +1403638606827829504.0000000000 2.2520525164 8.5105153461 3.4315921144 0.5372287339 0.8399633051 0.0729888761 -0.0227938032276 +1403638606877829376.0000000000 2.1799251667 8.4834283506 3.4173226455 0.5351583104 0.8404752108 0.0796796061 -0.0292944221731 +1403638606927829504.0000000000 2.1077584632 8.4596265738 3.4048053422 0.5342372142 0.8399713212 0.0885164254 -0.034693240101 +1403638606977829376.0000000000 2.0347577176 8.4388799501 3.3933429923 0.5327947258 0.8396377060 0.0967362785 -0.0421947286828 +1403638607027829504.0000000000 1.9619341175 8.4212279179 3.3849505349 0.5327092174 0.8382201163 0.1054437996 -0.0498952054363 +1403638607077829376.0000000000 1.8892494103 8.4059781667 3.3790410082 0.5321654366 0.8370364651 0.1133031764 -0.0577260286331 +1403638607127829504.0000000000 1.8165109275 8.3937383298 3.3756902379 0.5331585953 0.8350999228 0.1171216977 -0.0680627581409 +1403638607177829376.0000000000 1.7443538936 8.3850975967 3.3738600242 0.5377659233 0.8308008258 0.1232998153 -0.0733140856065 +1403638607227829504.0000000000 1.6724473978 8.3784002676 3.3723965242 0.5434836828 0.8258499226 0.1275111670 -0.0796134044291 +1403638607277829376.0000000000 1.6015713788 8.3736831079 3.3699191116 0.5507614181 0.8199325168 0.1321737678 -0.0830820279138 +1403638607327829504.0000000000 1.5311539855 8.3701199665 3.3656310764 0.5556137368 0.8158069678 0.1337343647 -0.0886988525782 +1403638607377829376.0000000000 1.4614189481 8.3675761242 3.3595430423 0.5597715695 0.8122004182 0.1352121581 -0.0932949249224 +1403638607427829504.0000000000 1.3926261981 8.3658520497 3.3512727180 0.5620592299 0.8100257575 0.1367421977 -0.096173102743 +1403638607477829376.0000000000 1.3248263917 8.3646378300 3.3410269276 0.5617450360 0.8098065023 0.1373990301 -0.098880988342 +1403638607527829504.0000000000 1.2582393549 8.3637400002 3.3291682646 0.5618221014 0.8094462569 0.1376454991 -0.101026729927 +1403638607577829376.0000000000 1.1932204665 8.3631819155 3.3156414525 0.5616040642 0.8093508128 0.1390129481 -0.101131287007 +1403638607627829504.0000000000 1.1292354539 8.3629507541 3.3014561126 0.5622047493 0.8087531771 0.1392786746 -0.102203567131 +1403638607677829376.0000000000 1.0663922153 8.3632952047 3.2865019852 0.5635616528 0.8077600055 0.1395898478 -0.102160224006 +1403638607727829504.0000000000 1.0046514231 8.3642700420 3.2713435223 0.5651849373 0.8066611064 0.1404847361 -0.100637393623 +1403638607777829376.0000000000 0.9442629259 8.3655011397 3.2545099569 0.5655171630 0.8065412862 0.1405084154 -0.0996939178987 +1403638607827829504.0000000000 0.8848901176 8.3667879881 3.2367608349 0.5648139080 0.8070915657 0.1399324997 -0.100036740528 +1403638607877829376.0000000000 0.8263308983 8.3684007944 3.2182340134 0.5639550943 0.8078737196 0.1377575856 -0.101575352844 +1403638607927829504.0000000000 0.7688401551 8.3704476210 3.1981818733 0.5613694650 0.8097961841 0.1352247950 -0.1039649885 +1403638607977829376.0000000000 0.7126598524 8.3733395405 3.1771029271 0.5601404860 0.8108188482 0.1330390350 -0.105432663281 +1403638608027829504.0000000000 0.6578676981 8.3773895705 3.1550646823 0.5615139557 0.8100582455 0.1312064377 -0.106266585109 +1403638608077829376.0000000000 0.6047150116 8.3821486141 3.1318608693 0.5637538485 0.8087208369 0.1310729494 -0.104747735389 +1403638608127829504.0000000000 0.5530386400 8.3875145320 3.1071603446 0.5662864380 0.8072045462 0.1312180043 -0.102578390084 +1403638608177829376.0000000000 0.5026828055 8.3932000096 3.0808776636 0.5684205633 0.8059834758 0.1324675679 -0.0986967247039 +1403638608227829504.0000000000 0.4533079760 8.3989749219 3.0538718272 0.5719550231 0.8036426570 0.1331636968 -0.0964020807845 +1403638608277829376.0000000000 0.4050623871 8.4045267362 3.0257611616 0.5753122353 0.8014291954 0.1334196407 -0.0944789722176 +1403638608327829504.0000000000 0.3577108767 8.4098770186 2.9968685168 0.5796755829 0.7984185331 0.1335019385 -0.0931734781803 +1403638608377829376.0000000000 0.3112234713 8.4145685938 2.9666223798 0.5836821186 0.7955693320 0.1342861911 -0.0913884088431 +1403638608427829504.0000000000 0.2655331929 8.4183105413 2.9347616170 0.5847437836 0.7948022468 0.1340281655 -0.0916544976469 +1403638608477829376.0000000000 0.2209527535 8.4210359826 2.9011421103 0.5840710231 0.7953446015 0.1339494945 -0.0913539154715 +1403638608527829504.0000000000 0.1772516289 8.4231503533 2.8658835219 0.5821315285 0.7968061307 0.1339840605 -0.0909458365442 +1403638608577829376.0000000000 0.1345603459 8.4247113035 2.8298559805 0.5819274702 0.7970229424 0.1340412779 -0.0902650792011 +1403638608627829504.0000000000 0.0924345022 8.4257166119 2.7948959849 0.5845418464 0.7952063995 0.1320515803 -0.0923038036385 +1403638608677829376.0000000000 0.0513491076 8.4254878709 2.7616477987 0.5873348423 0.7930661251 0.1313157414 -0.0940217013496 +1403638608727829504.0000000000 0.0115091667 8.4238954928 2.7288021123 0.5890102481 0.7917955441 0.1309574933 -0.0947463923787 +1403638608777829376.0000000000 -0.0269929950 8.4207639720 2.6963314656 0.5872910407 0.7930904936 0.1309769155 -0.0945608273836 +1403638608827829504.0000000000 -0.0645336383 8.4166381053 2.6652578679 0.5848752961 0.7948107017 0.1312659239 -0.0946894594108 +1403638608877829376.0000000000 -0.1010937973 8.4118633053 2.6364021400 0.5821669168 0.7967772192 0.1309791614 -0.0952481137037 +1403638608927829504.0000000000 -0.1364019617 8.4060825028 2.6095183208 0.5791483016 0.7989448096 0.1311034239 -0.0953222333743 +1403638608977829376.0000000000 -0.1704649206 8.3991804569 2.5845982083 0.5763639376 0.8009188846 0.1303747443 -0.0966228633781 +1403638609027829504.0000000000 -0.2036970001 8.3926702030 2.5612751810 0.5741574624 0.8024567889 0.1298936433 -0.097641957543 +1403638609077829376.0000000000 -0.2358594750 8.3865052381 2.5400422320 0.5724971476 0.8036573201 0.1298690473 -0.0975497741235 +1403638609127829504.0000000000 -0.2667818821 8.3800994945 2.5203309005 0.5718530113 0.8041138146 0.1299821768 -0.0974152987534 +1403638609177829376.0000000000 -0.2967772109 8.3740037345 2.5023860299 0.5725828693 0.8035850899 0.1283995455 -0.0995661480612 +1403638609227829504.0000000000 -0.3257589211 8.3677010856 2.4849891733 0.5741913903 0.8023700275 0.1254080578 -0.103823914406 +1403638609277829376.0000000000 -0.3532878687 8.3611198582 2.4661837469 0.5750952607 0.8016615416 0.1229745226 -0.107151671136 +1403638609327829504.0000000000 -0.3789746406 8.3545204234 2.4451944306 0.5751442967 0.8016487847 0.1224454328 -0.107588939804 +1403638609377829376.0000000000 -0.4029447512 8.3480448466 2.4222858268 0.5746959431 0.8020287945 0.1233628900 -0.10609421846 +1403638609427829504.0000000000 -0.4255423147 8.3414679910 2.3978616308 0.5744291537 0.8022806845 0.1242970812 -0.10453270445 +1403638609477829376.0000000000 -0.4466563885 8.3345454407 2.3717060162 0.5738266316 0.8028055484 0.1253557163 -0.102528984689 +1403638609527829504.0000000000 -0.4665881576 8.3276837749 2.3442470014 0.5735126509 0.8030892234 0.1262851780 -0.100910813672 +1403638609577829376.0000000000 -0.4854037769 8.3206062604 2.3149334653 0.5730965138 0.8034632342 0.1272182602 -0.0991096938643 +1403638609627829504.0000000000 -0.5033676139 8.3135383145 2.2845087590 0.5731983287 0.8034162686 0.1271873112 -0.0989412105745 +1403638609677829376.0000000000 -0.5203543421 8.3065727632 2.2523907335 0.5736909238 0.8030459247 0.1290090956 -0.0967089449194 +1403638609727829504.0000000000 -0.5364524836 8.2994596922 2.2202189438 0.5736803121 0.8030934482 0.1296606053 -0.0954983787281 +1403638609777829376.0000000000 -0.5518812954 8.2919635701 2.1889272705 0.5732362557 0.8034004157 0.1296649726 -0.0955769953693 +1403638609827829504.0000000000 -0.5667860047 8.2847993374 2.1593345617 0.5724711617 0.8039318198 0.1290793845 -0.096482696018 +1403638609877829376.0000000000 -0.5805144698 8.2777441228 2.1318559463 0.5730851048 0.8034881313 0.1293452410 -0.096177409798 +1403638609927829504.0000000000 -0.5931022040 8.2701924465 2.1064137900 0.5731657014 0.8034585332 0.1289936085 -0.096416352887 +1403638609977829376.0000000000 -0.6047596546 8.2625944345 2.0822012249 0.5741662008 0.8027510748 0.1287279728 -0.0967108823253 +1403638610027829504.0000000000 -0.6157314537 8.2553954782 2.0604717041 0.5754758309 0.8018005720 0.1278975975 -0.0979061560909 +1403638610077829376.0000000000 -0.6256425241 8.2478302678 2.0410108926 0.5783448089 0.7997639014 0.1271608493 -0.0986159344004 +1403638610127829504.0000000000 -0.6343300170 8.2397216351 2.0225727961 0.5803379717 0.7983026933 0.1267751031 -0.0992407256174 +1403638610177829376.0000000000 -0.6418937424 8.2312598153 2.0038132545 0.5827924850 0.7965649775 0.1274197160 -0.0979865908966 +1403638610227829504.0000000000 -0.6486415570 8.2220596631 1.9842162021 0.5844199964 0.7953448266 0.1268326257 -0.0989614046358 +1403638610277829376.0000000000 -0.6542887959 8.2124287303 1.9630320283 0.5854590106 0.7946507030 0.1259892092 -0.0994722388232 +1403638610327829504.0000000000 -0.6589438565 8.2022607490 1.9402457261 0.5862501819 0.7940618081 0.1259950553 -0.0995078646579 +1403638610377829376.0000000000 -0.6626918337 8.1915999060 1.9159573714 0.5862421798 0.7940767673 0.1254977103 -0.100062574933 +1403638610427829504.0000000000 -0.6652681232 8.1803331662 1.8906541304 0.5873372635 0.7933021448 0.1249991023 -0.100408517363 +1403638610477829376.0000000000 -0.6666772181 8.1684349823 1.8638015087 0.5886192493 0.7923941156 0.1256606636 -0.0992388156633 +1403638610527829504.0000000000 -0.6670568526 8.1557057756 1.8361674551 0.5912320661 0.7905007777 0.1260041082 -0.0983673177114 +1403638610577829376.0000000000 -0.6665526307 8.1419609272 1.8081718382 0.5962419559 0.7867127032 0.1254378556 -0.0992169186797 +1403638610627829504.0000000000 -0.6648837313 8.1267704385 1.7799918759 0.6019439555 0.7823580960 0.1248588065 -0.0999477988263 +1403638610677829376.0000000000 -0.6619053599 8.1092422603 1.7517883217 0.6038748948 0.7808409681 0.1242247445 -0.100949030562 +1403638610727829504.0000000000 -0.6575034738 8.0891694803 1.7238775272 0.6008386822 0.7831076652 0.1248673265 -0.100714514368 +1403638610777829376.0000000000 -0.6516378023 8.0666923475 1.6969288003 0.5958562033 0.7867889443 0.1248779126 -0.101607327879 +1403638610827829504.0000000000 -0.6447146616 8.0435019544 1.6714770250 0.5898489675 0.7911810873 0.1254329262 -0.10186885503 +1403638610877829376.0000000000 -0.6367006488 8.0197629635 1.6491641303 0.5856602775 0.7941627910 0.1263491164 -0.101702514857 +1403638610927829504.0000000000 -0.6278650441 7.9967132208 1.6292577268 0.5844789015 0.7948804892 0.1267657778 -0.102371183601 +1403638610977829376.0000000000 -0.6179108323 7.9730333148 1.6103474125 0.5847632948 0.7946518943 0.1265687278 -0.102764843216 +1403638611027829504.0000000000 -0.6068966585 7.9486464159 1.5912525667 0.5865254586 0.7932904847 0.1255304054 -0.104499811396 +1403638611077829376.0000000000 -0.5944135333 7.9235202397 1.5710245659 0.5890503484 0.7913579644 0.1259198274 -0.104481846978 +1403638611127829504.0000000000 -0.5808049404 7.8975701374 1.5491024652 0.5901049599 0.7904527516 0.1255971381 -0.105763617018 +1403638611177829376.0000000000 -0.5660502982 7.8711773029 1.5253698091 0.5898410036 0.7905318931 0.1264145054 -0.105670663816 +1403638611227829504.0000000000 -0.5500376887 7.8443633290 1.5017956441 0.5901065882 0.7902976729 0.1267045183 -0.105592460845 +1403638611277829376.0000000000 -0.5328822898 7.8170256991 1.4790839682 0.5897133565 0.7905219831 0.1274701028 -0.105188042254 +1403638611327829504.0000000000 -0.5139437938 7.7885023944 1.4576131489 0.5897306813 0.7905432666 0.1291484649 -0.102857868671 +1403638611377829376.0000000000 -0.4935813777 7.7589298017 1.4366705698 0.5907589094 0.7898425507 0.1325228052 -0.097930394418 +1403638611427829504.0000000000 -0.4724240930 7.7291039519 1.4173647519 0.5922791628 0.7887672035 0.1374872067 -0.0902715905277 +1403638611477829376.0000000000 -0.4511738290 7.6984639948 1.4003680879 0.5924129796 0.7886292858 0.1415213991 -0.0841570242713 +1403638611527829504.0000000000 -0.4299234234 7.6663123273 1.3852512726 0.5924002063 0.7885645201 0.1450536810 -0.0786601738102 +1403638611577829376.0000000000 -0.4092001092 7.6324195961 1.3720769554 0.5904500642 0.7900523912 0.1466012415 -0.0754587097193 +1403638611627829504.0000000000 -0.3893080652 7.5971646627 1.3607880435 0.5889426496 0.7912351037 0.1467898517 -0.074473522189 +1403638611677829376.0000000000 -0.3703492118 7.5609965752 1.3504231751 0.5874394756 0.7924337085 0.1461405144 -0.0748774346857 +1403638611727829504.0000000000 -0.3520390906 7.5227298485 1.3398762543 0.5848600629 0.7944728226 0.1436222552 -0.0782578353626 +1403638611777829376.0000000000 -0.3342991835 7.4843554508 1.3280413100 0.5825200067 0.7963357804 0.1401160165 -0.082989569157 +1403638611827829504.0000000000 -0.3165638901 7.4450446260 1.3145673449 0.5802635436 0.7981228981 0.1367968184 -0.0870671574845 +1403638611877829376.0000000000 -0.2987079228 7.4055463000 1.2996813139 0.5777277785 0.8000479720 0.1340123763 -0.090523695446 +1403638611927829504.0000000000 -0.2804656751 7.3651389460 1.2833893343 0.5761189381 0.8013244276 0.1317755138 -0.0927434358285 +1403638611977829376.0000000000 -0.2621287076 7.3251200538 1.2661543807 0.5747943561 0.8022863698 0.1303831461 -0.0945952660837 +1403638612027829504.0000000000 -0.2434372982 7.2853196497 1.2490729386 0.5735352654 0.8032522966 0.1292433879 -0.0955991317477 +1403638612077829376.0000000000 -0.2242928839 7.2457072162 1.2333392669 0.5725481319 0.8040079432 0.1294668324 -0.0948588595402 +1403638612127829504.0000000000 -0.2049667277 7.2059411006 1.2197584045 0.5720033958 0.8044339633 0.1270590962 -0.097745076836 +1403638612177829376.0000000000 -0.1846444119 7.1664784673 1.2073902576 0.5718291465 0.8046123669 0.1275529089 -0.0966468914436 +1403638612227829504.0000000000 -0.1642968263 7.1285439522 1.1975351911 0.5713423023 0.8049915564 0.1269988809 -0.0970971263156 +1403638612277829376.0000000000 -0.1435231628 7.0917389088 1.1897405903 0.5722282471 0.8043768160 0.1269561422 -0.0970304541446 +1403638612327829504.0000000000 -0.1218695895 7.0549169263 1.1833374894 0.5716994521 0.8047701692 0.1273745776 -0.0963349791111 +1403638612377829376.0000000000 -0.0998518325 7.0185745875 1.1775049835 0.5726939186 0.8041692976 0.1276575575 -0.0950629498248 +1403638612427829504.0000000000 -0.0774538858 6.9822151883 1.1710091158 0.5734135394 0.8037222726 0.1275234016 -0.0946847575375 +1403638612477829376.0000000000 -0.0545119934 6.9462275415 1.1629870752 0.5749713412 0.8027729346 0.1274372126 -0.0933987637678 +1403638612527829504.0000000000 -0.0310600063 6.9102025221 1.1531196767 0.5765439655 0.8017832669 0.1281543021 -0.0911982657069 +1403638612577829376.0000000000 -0.0071850103 6.8740974633 1.1415458566 0.5779466283 0.8009197069 0.1287336605 -0.0890671803653 +1403638612627829504.0000000000 0.0167422696 6.8379802283 1.1282121591 0.5781995948 0.8008601091 0.1305004512 -0.0853108814387 +1403638612677829376.0000000000 0.0402673814 6.8021384160 1.1137121330 0.5796352963 0.7999594262 0.1317035067 -0.0821098417805 +1403638612727829504.0000000000 0.0636235684 6.7661086099 1.0977224397 0.5803877216 0.7995746398 0.1321644958 -0.0797686285887 +1403638612777829376.0000000000 0.0867374654 6.7295865766 1.0806555016 0.5814324772 0.7990111607 0.1318903061 -0.0782456810542 +1403638612827829504.0000000000 0.1095340773 6.6923632322 1.0637044788 0.5830040192 0.7980753294 0.1309852821 -0.0776204741071 +1403638612877829376.0000000000 0.1320141872 6.6544337384 1.0474549767 0.5845721210 0.7971087830 0.1301504943 -0.0771613391374 +1403638612927829504.0000000000 0.1538413197 6.6159471789 1.0322931031 0.5852373592 0.7967757142 0.1288647397 -0.0777146930123 +1403638612977829376.0000000000 0.1753153035 6.5769611522 1.0179759789 0.5851875676 0.7969380004 0.1279972390 -0.0778591098827 +1403638613027829504.0000000000 0.1961591184 6.5378992233 1.0057005376 0.5828763553 0.7987165703 0.1270418246 -0.0785326020175 +1403638613077829376.0000000000 0.2168101744 6.4980570796 0.9959675114 0.5823840874 0.7991453925 0.1259233286 -0.0796161517081 +1403638613127829504.0000000000 0.2374233485 6.4580495123 0.9878613481 0.5815658370 0.7998109054 0.1256763492 -0.079304149886 +1403638613177829376.0000000000 0.2577434736 6.4175939230 0.9810763813 0.5795254721 0.8013300609 0.1248210632 -0.0802500024756 +1403638613227829504.0000000000 0.2777431053 6.3778350231 0.9764150817 0.5795647981 0.8013301525 0.1247494277 -0.0800762879046 +1403638613277829376.0000000000 0.2978376861 6.3380097472 0.9736107840 0.5788855162 0.8018543135 0.1248543489 -0.0795777015093 +1403638613327829504.0000000000 0.3175647831 6.2978747500 0.9726255081 0.5785803317 0.8020688565 0.1250201006 -0.0793745781052 +1403638613377829376.0000000000 0.3371477207 6.2576069790 0.9729302153 0.5791875489 0.8016299522 0.1254821515 -0.0786475210333 +1403638613427829504.0000000000 0.3565705772 6.2168572754 0.9725436738 0.5791984260 0.8016189502 0.1257038860 -0.0783248051873 +1403638613477829376.0000000000 0.3757580932 6.1760491952 0.9713958133 0.5805582394 0.8007640421 0.1246318326 -0.0787145850024 +1403638613527829504.0000000000 0.3947865422 6.1354390276 0.9686411454 0.5817712975 0.8002433625 0.1224885210 -0.0784173475731 +1403638613577829376.0000000000 0.4139435154 6.0946028975 0.9644725739 0.5822639154 0.8003719385 0.1201003894 -0.0771322849166 +1403638613627829504.0000000000 0.4324365350 6.0535236455 0.9594338243 0.5840520880 0.7994351300 0.1161091494 -0.079405898893 +1403638613677829376.0000000000 0.4511231953 6.0118619855 0.9523129469 0.5856575606 0.7985804893 0.1135494811 -0.0798807810786 +1403638613727829504.0000000000 0.4697057800 5.9695168114 0.9438115905 0.5894657741 0.7960954189 0.1101832549 -0.0813746613583 +1403638613777829376.0000000000 0.4889706064 5.9262944915 0.9332849252 0.5921058866 0.7946074134 0.1067758303 -0.0812932943632 +1403638613827829504.0000000000 0.5090342355 5.8825141877 0.9206779961 0.5941474984 0.7937850256 0.1031076211 -0.0791384970388 +1403638613877829376.0000000000 0.5298388057 5.8371967746 0.9063389705 0.5955029527 0.7936272396 0.0983944041 -0.0764890787757 +1403638613927829504.0000000000 0.5513339669 5.7915077078 0.8906775778 0.5959040640 0.7943152870 0.0932883136 -0.0725180104929 +1403638613977829376.0000000000 0.5736466160 5.7447334880 0.8741074721 0.5958453401 0.7954942460 0.0869036193 -0.0678601223861 +1403638614027829504.0000000000 0.5967789264 5.6972459076 0.8559323025 0.5957744899 0.7967581434 0.0807120494 -0.0609490213204 +1403638614077829376.0000000000 0.6201444331 5.6492894540 0.8370650627 0.5950641206 0.7984714444 0.0728760702 -0.0550556373398 +1403638614127829504.0000000000 0.6442596448 5.6008172590 0.8177661895 0.5938462315 0.8005351031 0.0650680290 -0.0475010918279 +1403638614177829376.0000000000 0.6686420184 5.5518657843 0.7992642406 0.5917721466 0.8030716113 0.0570645443 -0.0403156477915 +1403638614227829504.0000000000 0.6932332665 5.5025293327 0.7827150572 0.5907562511 0.8046502031 0.0489510707 -0.0338953544465 +1403638614277829376.0000000000 0.7176981215 5.4523313365 0.7671734286 0.5894185359 0.8062494810 0.0411827291 -0.0291812748857 +1403638614327829504.0000000000 0.7419995632 5.4019942967 0.7528719606 0.5880589117 0.8076779638 0.0354992707 -0.0241417654726 +1403638614377829376.0000000000 0.7661465619 5.3508544873 0.7408469342 0.5868078718 0.8089069195 0.0298956650 -0.0207934213961 +1403638614427829504.0000000000 0.7899560908 5.2995345746 0.7313920639 0.5863968909 0.8094365195 0.0242969164 -0.0189965020513 +1403638614477829376.0000000000 0.8138688900 5.2474336040 0.7242219763 0.5858585105 0.8099859217 0.0198149819 -0.0173198969499 +1403638614527829504.0000000000 0.8379868350 5.1948980091 0.7193848687 0.5852733699 0.8105358089 0.0150441159 -0.0161387590737 +1403638614577829376.0000000000 0.8625986058 5.1420861217 0.7158150597 0.5847361982 0.8110460699 0.0103715616 -0.0134269026556 +1403638614627829504.0000000000 0.8873763628 5.0895307945 0.7140581271 0.5849719077 0.8109506370 0.0040266215 -0.0122767192868 +1403638614677829376.0000000000 0.9128093365 5.0375505184 0.7148880529 0.5843217734 0.8114541096 -0.0027304161 -0.0101409050454 +1403638614727829504.0000000000 0.9388810419 4.9855211687 0.7187195647 0.5825643030 0.8126287193 -0.0119659954 -0.0104982138286 +1403638614777829376.0000000000 0.9659918174 4.9326017611 0.7245583912 0.5795712087 0.8145706679 -0.0217628964 -0.00991046921981 +1403638614827829504.0000000000 0.9943824771 4.8793263021 0.7321304226 0.5769376134 0.8161428241 -0.0316857364 -0.00706364436979 +1403638614877829376.0000000000 1.0239882373 4.8260802039 0.7415496207 0.5730862152 0.8184013185 -0.0421205638 -0.00416292503401 +1403638614927829504.0000000000 1.0555153953 4.7744936418 0.7523722451 0.5713958789 0.8190340178 -0.0518094725 0.00240951251843 +1403638614977829376.0000000000 1.0896173977 4.7269306281 0.7648138296 0.5691158585 0.8197788358 -0.0632172255 0.0085663490117 +1403638615027829504.0000000000 1.1251218254 4.6781221775 0.7776736481 0.5680050884 0.8194953705 -0.0742311172 0.0169498843068 +1403638615077829376.0000000000 1.1624039627 4.6298847729 0.7911388027 0.5671721364 0.8187211386 -0.0851910641 0.0274581038022 +1403638615127829504.0000000000 1.2022889870 4.5852787590 0.8065091815 0.5669523637 0.8171738937 -0.0963189879 0.038916542427 +1403638615177829376.0000000000 1.2431989382 4.5388735493 0.8232476965 0.5693993718 0.8134282772 -0.1069918257 0.0516869663707 +1403638615227829504.0000000000 1.2852781392 4.4922214265 0.8411817916 0.5697640138 0.8107900352 -0.1164892552 0.0664736092483 +1403638615277829376.0000000000 1.3277268444 4.4457991252 0.8596837348 0.5706273280 0.8073271345 -0.1277075094 0.0793608373057 +1403638615327829504.0000000000 1.3702359859 4.3988429987 0.8772414237 0.5704716327 0.8041990911 -0.1398951971 0.0908585271627 +1403638615377829376.0000000000 1.4128227217 4.3514312016 0.8934915856 0.5697651256 0.8010251602 -0.1525798441 0.102204626327 +1403638615427829504.0000000000 1.4554128303 4.3041842067 0.9085882785 0.5693721260 0.7973552632 -0.1651248285 0.113021048266 +1403638615477829376.0000000000 1.4979789771 4.2571045334 0.9221267254 0.5680571168 0.7940278733 -0.1776743393 0.123542210134 +1403638615527829504.0000000000 1.5401369856 4.2098200223 0.9340839509 0.5659289018 0.7911686954 -0.1900720851 0.132850201042 +1403638615577829376.0000000000 1.5818751831 4.1625265882 0.9447291458 0.5646449016 0.7879043399 -0.2014108076 0.140771349248 +1403638615627829504.0000000000 1.6230459578 4.1151021522 0.9541519221 0.5630304198 0.7853476720 -0.2103889287 0.148196758359 +1403638615677829376.0000000000 1.6634976837 4.0678355393 0.9634683416 0.5613994862 0.7832905528 -0.2181914795 0.153879839944 +1403638615727829504.0000000000 1.7033577350 4.0207987676 0.9741361472 0.5603311334 0.7813793797 -0.2247072055 0.158056817805 +1403638615777829376.0000000000 1.7427003008 3.9738761448 0.9867814116 0.5593382701 0.7797967639 -0.2301951152 0.161455614926 +1403638615827829504.0000000000 1.7816597763 3.9265862972 1.0015190460 0.5583398512 0.7783517748 -0.2351952919 0.164645983528 +1403638615877829376.0000000000 1.8201846438 3.8790076425 1.0174330412 0.5576322538 0.7765280594 -0.2415507299 0.166444247266 +1403638615927829504.0000000000 1.8587241485 3.8314023130 1.0328135623 0.5570038491 0.7744767582 -0.2472310440 0.169732948658 +1403638615977829376.0000000000 1.8970567399 3.7836050743 1.0468138461 0.5546922077 0.7734946200 -0.2531073882 0.173087485489 +1403638616027829504.0000000000 1.9353795110 3.7355879473 1.0597600561 0.5536874648 0.7714138406 -0.2587494798 0.177199279274 +1403638616077829376.0000000000 1.9735545877 3.6872181682 1.0707019987 0.5522011398 0.7694143723 -0.2646480955 0.181760310578 +1403638616127829504.0000000000 2.0116262081 3.6387120502 1.0794261482 0.5504650370 0.7674178340 -0.2707112529 0.186476616998 +1403638616177829376.0000000000 2.0494784415 3.5899769865 1.0841422123 0.5483741101 0.7651969981 -0.2780897319 0.190854631885 +1403638616227829504.0000000000 2.0873458221 3.5409018004 1.0845611578 0.5463134615 0.7624790811 -0.2863599179 0.195359284654 +1403638616277829376.0000000000 2.1255478116 3.4917174229 1.0807557907 0.5441239567 0.7592598731 -0.2952610746 0.200684983565 +1403638616327829504.0000000000 2.1634750945 3.4418743010 1.0726378605 0.5413160127 0.7560958000 -0.3042065377 0.206771608459 +1403638616377829376.0000000000 2.2015905496 3.3919252356 1.0618302793 0.5386296429 0.7525975636 -0.3133317747 0.212833770909 +1403638616427829504.0000000000 2.2394446046 3.3417598456 1.0489039640 0.5357356421 0.7494458671 -0.3218717075 0.218441795431 +1403638616477829376.0000000000 2.2769122614 3.2922731696 1.0344205501 0.5335668873 0.7463002906 -0.3300657558 0.222258520163 +1403638616527829504.0000000000 2.3140696813 3.2424951844 1.0192499380 0.5305935117 0.7442338686 -0.3365194788 0.226585777629 +1403638616577829376.0000000000 2.3509857178 3.1926782893 1.0032734403 0.5271430119 0.7430956803 -0.3422120475 0.229825954623 +1403638616627829504.0000000000 2.3884833687 3.1442549256 0.9850436924 0.5230759929 0.7427717457 -0.3476390014 0.23201026725 +1403638616677829376.0000000000 2.4252720141 3.0948627498 0.9667722997 0.5179999986 0.7437623224 -0.3527719831 0.232476960636 +1403638616727829504.0000000000 2.4618928671 3.0460363427 0.9464702940 0.5120141831 0.7458462139 -0.3591173236 0.229324332271 +1403638616777829376.0000000000 2.4988897265 2.9976068651 0.9254146925 0.5066860022 0.7478808622 -0.3653061670 0.224710737401 +1403638616827829504.0000000000 2.5369816783 2.9497650109 0.9038822961 0.5024707473 0.7495335995 -0.3703707652 0.220336169504 +1403638616877829376.0000000000 2.5767380027 2.9024399285 0.8827474487 0.4993812116 0.7507804179 -0.3736167630 0.217618206982 +1403638616927829504.0000000000 2.6185431022 2.8553405991 0.8632542319 0.4993578823 0.7504320142 -0.3736827018 0.218757253176 +1403638616977829376.0000000000 2.6626930335 2.8085478729 0.8459637698 0.5001729569 0.7499369977 -0.3706967158 0.223619001022 +1403638617027829504.0000000000 2.7088119671 2.7627808531 0.8310547648 0.5017179100 0.7491482612 -0.3679022330 0.227385066464 +1403638617077829376.0000000000 2.7561806609 2.7175584026 0.8187008262 0.5035952293 0.7483453766 -0.3646374137 0.231107331877 +1403638617127829504.0000000000 2.8045969872 2.6725007529 0.8081297109 0.5049284054 0.7480174462 -0.3601025717 0.236311962123 +1403638617177829376.0000000000 2.8535218860 2.6284655783 0.7998945315 0.5057706830 0.7481850906 -0.3571135584 0.238505750006 +1403638617227829504.0000000000 2.9031922503 2.5853102940 0.7930761500 0.5042038008 0.7499566674 -0.3547296032 0.239813329213 +1403638617277829376.0000000000 2.9531081477 2.5431261691 0.7879963841 0.5021613675 0.7521605073 -0.3535770198 0.238897097756 +1403638617327829504.0000000000 3.0038540356 2.5020349229 0.7845690467 0.5002918492 0.7540592193 -0.3531442444 0.237469791769 +1403638617377829376.0000000000 3.0551846969 2.4619645902 0.7825396714 0.4968219328 0.7570390390 -0.3523522749 0.236448165132 +1403638617427829504.0000000000 3.1069629000 2.4234191949 0.7827493700 0.4944022456 0.7593254703 -0.3512385327 0.235844743171 +1403638617477829376.0000000000 3.1590648101 2.3862869278 0.7850472259 0.4931964909 0.7608406320 -0.3503785037 0.23476298299 +1403638617527829504.0000000000 3.2120800609 2.3507722461 0.7889931511 0.4921459003 0.7622224796 -0.3488411103 0.234774751876 +1403638617577829376.0000000000 3.2648822052 2.3150335306 0.7972971738 0.4923316202 0.7626486987 -0.3479302875 0.234352412335 +1403638617627829504.0000000000 3.3188134666 2.2821071941 0.8059640266 0.4928963418 0.7628717534 -0.3460949029 0.23515569791 +1403638617677829376.0000000000 3.3733967708 2.2508944669 0.8168435251 0.4940208099 0.7628232032 -0.3438324226 0.236269899148 +1403638617727829504.0000000000 3.4273139561 2.2200073287 0.8312090284 0.4948229447 0.7628245227 -0.3415744197 0.23785692517 +1403638617777829376.0000000000 3.4822424374 2.1916550672 0.8469541046 0.4962995994 0.7623570702 -0.3407576895 0.237450209848 +1403638617827829504.0000000000 3.5378275286 2.1645391332 0.8637956385 0.4949677756 0.7637419122 -0.3390433951 0.238232594133 +1403638617877829376.0000000000 3.5940249894 2.1392604900 0.8832571436 0.4959590602 0.7636435395 -0.3376853997 0.238415028787 +1403638617927829504.0000000000 3.6505791051 2.1159594304 0.9043070293 0.4972504148 0.7630836912 -0.3376463397 0.237571577506 +1403638617977829376.0000000000 3.7075873020 2.0942880928 0.9249261446 0.4982007400 0.7629033825 -0.3369515357 0.237145765651 +1403638618027829504.0000000000 3.7650446024 2.0741030633 0.9441659395 0.4983711020 0.7631090896 -0.3364045114 0.236902441629 +1403638618077829376.0000000000 3.8230824903 2.0554931970 0.9620683110 0.4990319082 0.7630690334 -0.3356746845 0.23667553984 +1403638618127829504.0000000000 3.8816043596 2.0383981454 0.9781624373 0.4990339059 0.7634187535 -0.3360516583 0.235002660513 +1403638618177829376.0000000000 3.9409546549 2.0226067841 0.9929471262 0.4997672508 0.7632964747 -0.3356728288 0.234382035595 +1403638618227829504.0000000000 4.0006841334 2.0079102797 1.0058272663 0.4996571997 0.7636405542 -0.3348850868 0.234622601848 +1403638618277829376.0000000000 4.0604339951 1.9945392473 1.0173740428 0.4996400580 0.7638924951 -0.3342127772 0.234797546524 +1403638618327829504.0000000000 4.1200671074 1.9821884921 1.0278471446 0.5005303964 0.7635708874 -0.3332396700 0.235329863093 +1403638618377829376.0000000000 4.1798109377 1.9712617472 1.0374935081 0.5008067988 0.7636097870 -0.3329721932 0.234993961694 +1403638618427829504.0000000000 4.2397862401 1.9614191155 1.0463966083 0.5008122924 0.7638755346 -0.3321877732 0.235228609641 +1403638618477829376.0000000000 4.2997008148 1.9528234952 1.0545763173 0.5008012285 0.7642164541 -0.3317963227 0.234696700052 +1403638618527829504.0000000000 4.3596596377 1.9456150974 1.0624455995 0.5018797117 0.7638074005 -0.3309110429 0.234974236124 +1403638618577829376.0000000000 4.4197425413 1.9392539263 1.0697272460 0.5017933817 0.7635604594 -0.3306680783 0.236299489966 +1403638618627829504.0000000000 4.4797771206 1.9339209556 1.0766646926 0.5012541243 0.7627380541 -0.3324638024 0.237576900858 +1403638618677829376.0000000000 4.5399140372 1.9295782191 1.0833629355 0.5002790108 0.7622489063 -0.3334213282 0.239849398908 +1403638618727829504.0000000000 4.5997529041 1.9264674892 1.0914131018 0.4998209910 0.7616135644 -0.3344105842 0.241440089214 +1403638618777829376.0000000000 4.6599338640 1.9250118018 1.1011475776 0.5000725966 0.7603707830 -0.3360878411 0.242504914506 +1403638618827829504.0000000000 4.7200819923 1.9248929276 1.1124980521 0.5007654608 0.7590064589 -0.3376338157 0.243200648064 +1403638618877829376.0000000000 4.7806171076 1.9257233433 1.1256104350 0.5010866498 0.7574471328 -0.3385099098 0.246164683463 +1403638618927829504.0000000000 4.8414313997 1.9278762041 1.1398544567 0.5021520026 0.7544569659 -0.3415763253 0.248925022694 +1403638618977829376.0000000000 4.9024350102 1.9308347349 1.1531956998 0.5036437513 0.7501988172 -0.3452660011 0.253645609172 +1403638619027829504.0000000000 4.9634308923 1.9344565097 1.1646465460 0.5037238089 0.7459453369 -0.3503917214 0.258946944998 +1403638619077829376.0000000000 5.0242725019 1.9384618419 1.1737926718 0.5021670648 0.7416169575 -0.3565798724 0.265863352246 +1403638619127829504.0000000000 5.0850191441 1.9430545119 1.1821001921 0.5009113881 0.7364334302 -0.3636928035 0.272912309736 +1403638619177829376.0000000000 5.1456313454 1.9484221878 1.1882446866 0.4986672251 0.7311199891 -0.3727048594 0.279080002784 +1403638619227829504.0000000000 5.2061117920 1.9547233586 1.1928413869 0.4967226101 0.7247205424 -0.3824067183 0.286027770971 +1403638619277829376.0000000000 5.2660461842 1.9614092534 1.1952704244 0.4937114163 0.7183615503 -0.3935270885 0.29213378978 +1403638619327829504.0000000000 5.3254393908 1.9680317851 1.1947331774 0.4900353592 0.7118089909 -0.4040113377 0.299946905709 +1403638619377829376.0000000000 5.3830550205 1.9745289881 1.1918802117 0.4869978940 0.7049143713 -0.4144788792 0.306815969388 +1403638619427829504.0000000000 5.4393878658 1.9815410891 1.1879721260 0.4846780395 0.6986002882 -0.4238774081 0.312046115687 +1403638619477829376.0000000000 5.4943290117 1.9890160563 1.1833701158 0.4824046028 0.6929574863 -0.4324915103 0.316301778219 +1403638619527829504.0000000000 5.5480241503 1.9972594718 1.1783796980 0.4812798910 0.6879072084 -0.4393537574 0.319564727517 +1403638619577829376.0000000000 5.6009747133 2.0057931658 1.1723823464 0.4797340461 0.6836535279 -0.4456907656 0.322231035666 +1403638619627829504.0000000000 5.6515442749 2.0141470136 1.1652662003 0.4797126646 0.6792983206 -0.4525701813 0.321884734076 +1403638619677829376.0000000000 5.7019832213 2.0228757064 1.1578621062 0.4818153295 0.6743515470 -0.4596724524 0.319069296198 +1403638619727829504.0000000000 5.7516521753 2.0307896982 1.1492044328 0.4819980045 0.6713098139 -0.4653954066 0.316904043848 +1403638619777829376.0000000000 5.8009181215 2.0379912392 1.1402979360 0.4834939239 0.6678441901 -0.4695195624 0.315862539371 +1403638619827829504.0000000000 5.8498948042 2.0442708310 1.1305196829 0.4841984294 0.6653389780 -0.4726885397 0.315343415746 +1403638619877829376.0000000000 5.8984316923 2.0493239569 1.1199059448 0.4843859485 0.6634869727 -0.4747235570 0.315900038616 +1403638619927829504.0000000000 5.9468741383 2.0531749949 1.1085851986 0.4843337345 0.6619985488 -0.4767689387 0.31602236324 +1403638619977829376.0000000000 5.9954742786 2.0557096134 1.0964133804 0.4835825720 0.6613104446 -0.4778064708 0.317044741993 +1403638620027829504.0000000000 6.0439704053 2.0567907297 1.0844129389 0.4838639615 0.6600759679 -0.4781368996 0.31868556383 +1403638620077829376.0000000000 6.0926344917 2.0566970220 1.0734091398 0.4851498273 0.6583710177 -0.4783263381 0.319970564857 +1403638620127829504.0000000000 6.1405563606 2.0548239229 1.0639601839 0.4855193743 0.6574115759 -0.4771759415 0.32308524863 +1403638620177829376.0000000000 6.1881636867 2.0517180256 1.0566326763 0.4868499411 0.6558726508 -0.4761860319 0.325660964408 +1403638620227829504.0000000000 6.2350685960 2.0471732020 1.0508669832 0.4869936620 0.6554985930 -0.4758434986 0.326698228712 +1403638620277829376.0000000000 6.2810533836 2.0409715425 1.0466427487 0.4849434217 0.6568577557 -0.4752833983 0.327831447363 +1403638620327829504.0000000000 6.3264156243 2.0335048840 1.0446999617 0.4834008256 0.6579530954 -0.4741168568 0.329597591281 +1403638620377829376.0000000000 6.3709016473 2.0249462461 1.0450540796 0.4822906009 0.6589426054 -0.4737877348 0.329720489765 +1403638620427829504.0000000000 6.4147047762 2.0153121246 1.0472937425 0.4817534402 0.6596359229 -0.4729311149 0.330348653018 +1403638620477829376.0000000000 6.4577642751 2.0047245154 1.0503767376 0.4808733542 0.6608118081 -0.4722257033 0.330289958418 +1403638620527829504.0000000000 6.5004816880 1.9934018691 1.0531617545 0.4804213479 0.6616415957 -0.4713889474 0.330481750786 +1403638620577829376.0000000000 6.5424952817 1.9812712958 1.0552465365 0.4798146382 0.6626933475 -0.4712649061 0.329431067764 +1403638620627829504.0000000000 6.5842068254 1.9685940193 1.0559182204 0.4789007501 0.6640027664 -0.4714905299 0.327797312408 +1403638620677829376.0000000000 6.6255393510 1.9551659268 1.0553459093 0.4781823530 0.6651551787 -0.4720865718 0.32564473616 +1403638620727829504.0000000000 6.6661595594 1.9409254430 1.0531126418 0.4766857472 0.6668097645 -0.4732713298 0.322722302887 +1403638620777829376.0000000000 6.7064955349 1.9260568116 1.0496930223 0.4756343523 0.6682423903 -0.4736614639 0.32073180114 +1403638620827829504.0000000000 6.7469076795 1.9104544411 1.0450972470 0.4738528185 0.6702294713 -0.4730412418 0.320137385674 +1403638620877829376.0000000000 6.7870351487 1.8936621464 1.0393459770 0.4710257471 0.6728721708 -0.4706067230 0.322346241857 +1403638620927829504.0000000000 6.8273402424 1.8769518831 1.0331429136 0.4703853374 0.6742115269 -0.4681296474 0.324084995806 +1403638620977829376.0000000000 6.8676774549 1.8599773062 1.0257077851 0.4694528381 0.6756091790 -0.4652914456 0.326603950918 +1403638621027829504.0000000000 6.9079845240 1.8427851100 1.0179404855 0.4704713570 0.6756500020 -0.4623843847 0.329172383025 +1403638621077829376.0000000000 6.9477546049 1.8254148455 1.0104244708 0.4709363247 0.6759777627 -0.4600229842 0.331137277231 +1403638621127829504.0000000000 6.9864786270 1.8083257576 1.0043761782 0.4724522723 0.6757090536 -0.4592191172 0.330641690826 +1403638621177829376.0000000000 7.0248494567 1.7914070029 1.0000686420 0.4737903768 0.6755243811 -0.4579295361 0.330892776249 +1403638621227829504.0000000000 7.0629887398 1.7748377036 0.9974910728 0.4752989005 0.6751588852 -0.4564901940 0.331463629447 +1403638621277829376.0000000000 7.1011229939 1.7585797178 0.9968571149 0.4758792502 0.6753744771 -0.4551617215 0.332018165497 +1403638621327829504.0000000000 7.1383032882 1.7421136024 0.9975823523 0.4745979845 0.6766790605 -0.4539672962 0.332830131116 +1403638621377829376.0000000000 7.1750941482 1.7261516152 0.9980991491 0.4745824732 0.6773150818 -0.4526742584 0.333319324232 +1403638621427829504.0000000000 7.2109867738 1.7102796396 0.9975445982 0.4767247111 0.6763616765 -0.4516348786 0.333608106742 +1403638621477829376.0000000000 7.2460055444 1.6942887805 0.9952821591 0.4771811779 0.6763598654 -0.4501357802 0.334982440259 +1403638621527829504.0000000000 7.2802663365 1.6787698917 0.9919191405 0.4794455464 0.6753954322 -0.4486510141 0.335686230999 +1403638621577829376.0000000000 7.3132606789 1.6633981204 0.9872528638 0.4805378261 0.6751072664 -0.4474617538 0.336290879219 +1403638621627829504.0000000000 7.3456107702 1.6484676723 0.9817268058 0.4819930834 0.6743854791 -0.4467598316 0.336589581032 +1403638621677829376.0000000000 7.3767615879 1.6334229518 0.9746882679 0.4822491948 0.6745989025 -0.4461929121 0.336547054841 +1403638621727829504.0000000000 7.4069169867 1.6185164039 0.9668646798 0.4832092479 0.6739960326 -0.4454850951 0.337314690996 +1403638621777829376.0000000000 7.4360828387 1.6035364117 0.9580291913 0.4841569556 0.6735178407 -0.4444557258 0.338267450922 +1403638621827829504.0000000000 7.4642339188 1.5883456436 0.9484785288 0.4857078783 0.6724384663 -0.4431784647 0.339863523257 +1403638621877829376.0000000000 7.4908451476 1.5731079196 0.9381644419 0.4879108957 0.6709803646 -0.4415237893 0.341738279608 +1403638621927829504.0000000000 7.5157836389 1.5578377476 0.9269410188 0.4895846420 0.6698350247 -0.4404584517 0.342963949024 +1403638621977829376.0000000000 7.5392116737 1.5427020533 0.9150618726 0.4910178728 0.6688567607 -0.4400243498 0.343381207832 +1403638622027829504.0000000000 7.5611149607 1.5275248249 0.9022227095 0.4919245467 0.6683946255 -0.4399885481 0.343029069435 +1403638622077829376.0000000000 7.5815246375 1.5123523836 0.8883376196 0.4921156729 0.6680788540 -0.4409328872 0.342156394625 +1403638622127829504.0000000000 7.6003768784 1.4971547192 0.8735908586 0.4920689086 0.6682049067 -0.4422601658 0.340259221233 +1403638622177829376.0000000000 7.6172104811 1.4817020008 0.8586438156 0.4922035892 0.6683264927 -0.4430815791 0.338753657024 +1403638622227829504.0000000000 7.6328663785 1.4658663015 0.8449435287 0.4925603740 0.6678969031 -0.4440156153 0.337858162838 +1403638622277829376.0000000000 7.6470519904 1.4499410738 0.8328459818 0.4939794085 0.6668733850 -0.4450957438 0.336383726139 +1403638622327829504.0000000000 7.6595287884 1.4331145781 0.8217505864 0.4933401750 0.6671528328 -0.4458949103 0.335708651039 +1403638622377829376.0000000000 7.6704312484 1.4157532440 0.8128419899 0.4922770675 0.6676074573 -0.4459292692 0.33631928091 +1403638622427829504.0000000000 7.6792943291 1.3975015818 0.8063782256 0.4910422702 0.6681784161 -0.4456369888 0.337376299266 +1403638622477829376.0000000000 7.6868791403 1.3786716703 0.8018286907 0.4897183610 0.6689110590 -0.4447122145 0.339064843687 +1403638622527829504.0000000000 7.6930669618 1.3595044047 0.7985582038 0.4896535838 0.6686400047 -0.4445363292 0.339922585344 +1403638622577829376.0000000000 7.6979937145 1.3400940496 0.7962899613 0.4883871089 0.6691749196 -0.4433804940 0.342193945681 +1403638622627829504.0000000000 7.7014817076 1.3207504401 0.7962803739 0.4894016757 0.6681050009 -0.4415967240 0.34512902074 +1403638622677829376.0000000000 7.7031517669 1.3012319849 0.7989060769 0.4917204909 0.6659694196 -0.4403035661 0.347603884826 +1403638622727829504.0000000000 7.7029518024 1.2814660245 0.8052531885 0.4977498480 0.6612161626 -0.4371895094 0.351999443168 +1403638622777829376.0000000000 7.7012039118 1.2619092462 0.8143333762 0.5040611030 0.6559948165 -0.4349980843 0.355485403141 +1403638622827829504.0000000000 7.6976643234 1.2423182120 0.8245476396 0.5082505881 0.6523661131 -0.4332448103 0.358327683164 +1403638622877829376.0000000000 7.6913409124 1.2222736504 0.8345133511 0.5089212427 0.6516335514 -0.4328869999 0.359140263341 +1403638622927829504.0000000000 7.6816998245 1.2015801240 0.8445579455 0.5081899755 0.6519495121 -0.4344162646 0.357753115317 +1403638622977829376.0000000000 7.6691306979 1.1800600903 0.8531991846 0.5047452869 0.6543134379 -0.4364935336 0.355780150484 +1403638623027829504.0000000000 7.6538407889 1.1581647433 0.8604858134 0.5017255172 0.6565730845 -0.4394773437 0.35219732323 +1403638623077829376.0000000000 7.6363470264 1.1355584963 0.8662845490 0.4981297501 0.6591672471 -0.4421127337 0.349144129443 +1403638623127829504.0000000000 7.6168804454 1.1124640543 0.8709222606 0.4961648294 0.6606391542 -0.4449064435 0.345593151837 +1403638623177829376.0000000000 7.5954111722 1.0887873447 0.8746542131 0.4952189405 0.6615121742 -0.4470595598 0.342487363686 +1403638623227829504.0000000000 7.5724343100 1.0644787724 0.8769735855 0.4939356688 0.6624356326 -0.4487595726 0.340325482165 +1403638623277829376.0000000000 7.5482186925 1.0394980076 0.8778626825 0.4921889718 0.6638007816 -0.4505198039 0.337861576254 +1403638623327829504.0000000000 7.5230574373 1.0141569495 0.8777993453 0.4905602176 0.6649711863 -0.4517493179 0.336283434101 +1403638623377829376.0000000000 7.4970930376 0.9883341689 0.8764818025 0.4897384181 0.6656299807 -0.4530956808 0.334361054302 +1403638623427829504.0000000000 7.4704714725 0.9618323476 0.8737544871 0.4869923289 0.6675165651 -0.4528465527 0.334947916255 +1403638623477829376.0000000000 7.4430467286 0.9354306278 0.8709876997 0.4872933905 0.6672459664 -0.4535715205 0.334067130502 +1403638623527829504.0000000000 7.4149407458 0.9087206307 0.8684607191 0.4868311251 0.6676893102 -0.4538505054 0.333475875242 +1403638623577829376.0000000000 7.3862877167 0.8814705988 0.8675683989 0.4865497487 0.6676196636 -0.4529753440 0.335211372955 +1403638623627829504.0000000000 7.3574015106 0.8539288182 0.8685698795 0.4863096233 0.6675749806 -0.4524598478 0.336343101118 +1403638623677829376.0000000000 7.3279143545 0.8259959218 0.8717093267 0.4852487003 0.6682214948 -0.4526986419 0.336270237319 +1403638623727829504.0000000000 7.2981771025 0.7977722493 0.8770352358 0.4845077042 0.6683275479 -0.4523984668 0.337529555062 +1403638623777829376.0000000000 7.2675008664 0.7692053219 0.8833606773 0.4827481838 0.6692431648 -0.4528338140 0.337652653434 +1403638623827829504.0000000000 7.2361053476 0.7403920348 0.8917342360 0.4825286419 0.6692101336 -0.4524469167 0.338549397172 +1403638623877829376.0000000000 7.2032575638 0.7110716649 0.9005379544 0.4804681706 0.6702585436 -0.4533155505 0.338243748587 +1403638623927829504.0000000000 7.1700448210 0.6819020604 0.9092654692 0.4792291663 0.6705524961 -0.4536744031 0.338937003024 +1403638623977829376.0000000000 7.1365164549 0.6528881117 0.9168652921 0.4779463668 0.6710738194 -0.4542118572 0.33899673762 +1403638624027829504.0000000000 7.1027385494 0.6241378720 0.9234157579 0.4778959480 0.6706654759 -0.4550943967 0.338692149975 +1403638624077829376.0000000000 7.0682969385 0.5955860667 0.9283453119 0.4777105578 0.6703356349 -0.4569218578 0.337142663287 +1403638624127829504.0000000000 7.0339681027 0.5671365233 0.9325981027 0.4777541162 0.6700169278 -0.4579721091 0.336288370707 +1403638624177829376.0000000000 6.9991054696 0.5386055939 0.9355113680 0.4784806764 0.6692541825 -0.4593170411 0.334937214037 +1403638624227829504.0000000000 6.9640234794 0.5098489655 0.9370242634 0.4784190747 0.6688525177 -0.4607034645 0.333921871728 +1403638624277829376.0000000000 6.9285837034 0.4810335045 0.9377260920 0.4792770469 0.6679662574 -0.4616859129 0.333107653984 +1403638624327829504.0000000000 6.8933681060 0.4521162355 0.9373313050 0.4793750370 0.6674040561 -0.4623154465 0.333220389016 +1403638624377829376.0000000000 6.8581696463 0.4231041338 0.9354861412 0.4795913702 0.6668411667 -0.4631626439 0.332859341595 +1403638624427829504.0000000000 6.8227568874 0.3936565621 0.9323166384 0.4793439999 0.6666462621 -0.4634620083 0.333189222191 +1403638624477829376.0000000000 6.7878411284 0.3636595097 0.9275239843 0.4789351941 0.6664565170 -0.4634189858 0.334214952281 +1403638624527829504.0000000000 6.7526209497 0.3339442067 0.9233094331 0.4832838840 0.6627960456 -0.4645353449 0.333683986304 +1403638624577829376.0000000000 6.7183969030 0.3039849027 0.9184265949 0.4906238992 0.6568991074 -0.4649576068 0.334045170765 +1403638624627829504.0000000000 6.6830125255 0.2732018413 0.9124408626 0.4960342012 0.6527869446 -0.4633462804 0.336347291734 +1403638624677829376.0000000000 6.6477507618 0.2411460919 0.9048226244 0.4956265538 0.6537003828 -0.4613416785 0.337926004191 +1403638624727829504.0000000000 6.6108507550 0.2079771525 0.8977671636 0.4924646082 0.6575517446 -0.4579861717 0.339636540029 +1403638624777829376.0000000000 6.5726810287 0.1742079994 0.8918394901 0.4883360070 0.6628057712 -0.4543550751 0.340261545965 +1403638624827829504.0000000000 6.5340900184 0.1405767735 0.8882718248 0.4845497815 0.6676505003 -0.4516434492 0.339812468134 +1403638624877829376.0000000000 6.4939196251 0.1066035846 0.8873808265 0.4820996449 0.6715266288 -0.4489145522 0.339275174566 +1403638624927829504.0000000000 6.4530017243 0.0730304162 0.8881840389 0.4817745462 0.6738763261 -0.4483166999 0.33585133673 +1403638624977829376.0000000000 6.4111971315 0.0397799699 0.8908259057 0.4826441255 0.6753181407 -0.4482540202 0.331765565228 +1403638625027829504.0000000000 6.3694642481 0.0066290665 0.8938505812 0.4842834362 0.6760056966 -0.4473923520 0.329129055197 +1403638625077829376.0000000000 6.3276060817 -0.0264306082 0.8958871679 0.4858203834 0.6766295899 -0.4478526825 0.324929112136 +1403638625127829504.0000000000 6.2855733371 -0.0597018248 0.8972061190 0.4873068300 0.6768072105 -0.4484017174 0.321558630964 +1403638625177829376.0000000000 6.2434696171 -0.0932267142 0.8970908479 0.4880401412 0.6774365326 -0.4484478356 0.319047180919 +1403638625227829504.0000000000 6.2013055977 -0.1270300134 0.8956914871 0.4882454895 0.6782253435 -0.4480832556 0.31756593252 +1403638625277829376.0000000000 6.1591812238 -0.1612035216 0.8936194894 0.4884372131 0.6788093221 -0.4473282501 0.317087416606 +1403638625327829504.0000000000 6.1173722004 -0.1955953524 0.8913547577 0.4888752295 0.6790677223 -0.4468849369 0.316483635637 +1403638625377829376.0000000000 6.0758386613 -0.2303020861 0.8896667208 0.4891013473 0.6793221421 -0.4464659095 0.316179523331 +1403638625427829504.0000000000 6.0347709930 -0.2653664703 0.8895590725 0.4896164917 0.6793720656 -0.4457252834 0.316319868659 +1403638625477829376.0000000000 5.9936372184 -0.3007281969 0.8913583364 0.4904226618 0.6789387280 -0.4459534611 0.31567915196 +1403638625527829504.0000000000 5.9528492098 -0.3364431623 0.8941452940 0.4899865692 0.6793709486 -0.4452175095 0.316464287653 +1403638625577829376.0000000000 5.9119251906 -0.3726114314 0.8983637816 0.4895119751 0.6797102214 -0.4455095001 0.316059055408 +1403638625627829504.0000000000 5.8716405501 -0.4089232579 0.9044520681 0.4878301812 0.6808241062 -0.4455642014 0.316184745332 +1403638625677829376.0000000000 5.8319123382 -0.4450910074 0.9127552224 0.4873313354 0.6812563971 -0.4460478951 0.31533976301 +1403638625727829504.0000000000 5.7921684183 -0.4817668505 0.9210455906 0.4844098772 0.6832911543 -0.4473560454 0.313580672161 +1403638625777829376.0000000000 5.7527364477 -0.5186472651 0.9286939875 0.4817412183 0.6850979332 -0.4487220841 0.311792738455 +1403638625827829504.0000000000 5.7140025955 -0.5555010224 0.9351261969 0.4788051770 0.6869897312 -0.4498772965 0.310485313476 +1403638625877829376.0000000000 5.6763171067 -0.5921313458 0.9407951281 0.4780112088 0.6874104131 -0.4500403511 0.310541286548 +1403638625927829504.0000000000 5.6393887250 -0.6287462633 0.9453224179 0.4768354596 0.6880322295 -0.4500283056 0.310988938436 +1403638625977829376.0000000000 5.6031932428 -0.6651193889 0.9488987865 0.4768150453 0.6877401113 -0.4503324210 0.311226063241 +1403638626027829504.0000000000 5.5674388704 -0.7014665541 0.9508292231 0.4755888928 0.6883468888 -0.4512683185 0.310404043944 +1403638626077829376.0000000000 5.5323992521 -0.7376703476 0.9518001534 0.4754370638 0.6882785217 -0.4524795733 0.309021861232 +1403638626127829504.0000000000 5.4986787955 -0.7734507394 0.9515844703 0.4754304688 0.6880360747 -0.4532037346 0.308510298194 +1403638626177829376.0000000000 5.4657693992 -0.8091368959 0.9499479058 0.4746583660 0.6884908567 -0.4530093238 0.308969785571 +1403638626227829504.0000000000 5.4336195614 -0.8447432234 0.9471513767 0.4749140741 0.6881345921 -0.4525737902 0.310007048017 +1403638626277829376.0000000000 5.4021462914 -0.8803363109 0.9431701092 0.4753862324 0.6876033475 -0.4511814774 0.312481745108 +1403638626327829504.0000000000 5.3714019344 -0.9159167076 0.9380193167 0.4750251826 0.6877395597 -0.4482502923 0.316918048245 +1403638626377829376.0000000000 5.3409494469 -0.9508349778 0.9321839492 0.4749311964 0.6877232460 -0.4455894849 0.320822546729 +1403638626427829504.0000000000 5.3106506889 -0.9849658964 0.9257766371 0.4757974853 0.6872298635 -0.4436140993 0.323323984055 +1403638626477829376.0000000000 5.2802660552 -1.0186409605 0.9181543246 0.4757623607 0.6873534070 -0.4431060360 0.32380937429 +1403638626527829504.0000000000 5.2500607306 -1.0519317655 0.9099786870 0.4736375680 0.6889568979 -0.4427861589 0.323954108748 +1403638626577829376.0000000000 5.2198952357 -1.0844963903 0.9015622609 0.4725073250 0.6898642209 -0.4431230785 0.323212193266 +1403638626627829504.0000000000 5.1898768725 -1.1164475233 0.8932737840 0.4713437144 0.6906439062 -0.4442466170 0.32170023467 +1403638626677829376.0000000000 5.1602707420 -1.1477417136 0.8853058149 0.4705219135 0.6915069791 -0.4442063527 0.321104255599 +1403638626727829504.0000000000 5.1311470351 -1.1782542613 0.8780800112 0.4682975450 0.6930361061 -0.4459761214 0.318596396847 +1403638626777829376.0000000000 5.1031194298 -1.2078605893 0.8723098642 0.4662528000 0.6945243096 -0.4472482988 0.316564794374 +1403638626827829504.0000000000 5.0767073569 -1.2363414143 0.8690658653 0.4646468970 0.6956726283 -0.4480844721 0.315219227174 +1403638626877829376.0000000000 5.0514005270 -1.2642188104 0.8675025382 0.4628745347 0.6971230453 -0.4480727470 0.314638583557 +1403638626927829504.0000000000 5.0273647233 -1.2908913818 0.8681856427 0.4616532718 0.6979816839 -0.4484598004 0.313977121685 +1403638626977829376.0000000000 5.0042136966 -1.3165295734 0.8696622929 0.4619755179 0.6979027531 -0.4485381815 0.313566369096 +1403638627027829504.0000000000 4.9819310777 -1.3414351107 0.8705478923 0.4619515244 0.6981114813 -0.4483402382 0.31342013277 +1403638627077829376.0000000000 4.9604438799 -1.3654629268 0.8703275290 0.4622798312 0.6981506577 -0.4482373691 0.312995651333 +1403638627127829504.0000000000 4.9399642716 -1.3886530589 0.8693449336 0.4626854289 0.6979874236 -0.4481224204 0.312924985707 +1403638627177829376.0000000000 4.9202220721 -1.4112035152 0.8673111628 0.4628299141 0.6980960422 -0.4481323291 0.312454480125 +1403638627227829504.0000000000 4.9015738007 -1.4331021000 0.8646154973 0.4632055177 0.6979706109 -0.4479095084 0.312497595158 +1403638627277829376.0000000000 4.8837732610 -1.4543214910 0.8609132269 0.4624070159 0.6986019471 -0.4468989188 0.313713926225 +1403638627327829504.0000000000 4.8669500010 -1.4746354977 0.8568238240 0.4622702418 0.6988334530 -0.4458032744 0.314956297094 +1403638627377829376.0000000000 4.8508297912 -1.4942099866 0.8520735647 0.4625467065 0.6987336943 -0.4449409272 0.315989461946 +1403638627427829504.0000000000 4.8356282634 -1.5128510207 0.8462946517 0.4620239846 0.6991138348 -0.4447885851 0.316127819349 +1403638627477829376.0000000000 4.8213021487 -1.5304594759 0.8402370944 0.4619572575 0.6992157742 -0.4448035654 0.315978767619 +1403638627527829504.0000000000 4.8078496048 -1.5472346472 0.8339208032 0.4625800249 0.6987034117 -0.4449290546 0.316024365282 +1403638627577829376.0000000000 4.7950789060 -1.5630712920 0.8271356505 0.4629369484 0.6982779214 -0.4440057205 0.317736127106 +1403638627627829504.0000000000 4.7829217355 -1.5781716089 0.8203993440 0.4639259074 0.6973320931 -0.4427601487 0.320100226487 +1403638627677829376.0000000000 4.7714306637 -1.5923304888 0.8136063436 0.4661032770 0.6957215135 -0.4421712825 0.321253587806 +1403638627727829504.0000000000 4.7603882644 -1.6057099315 0.8064807326 0.4676127817 0.6945592294 -0.4414140400 0.322613404246 +1403638627777829376.0000000000 4.7494286240 -1.6184118704 0.7987281008 0.4678546996 0.6942875486 -0.4406667330 0.323866655209 +1403638627827829504.0000000000 4.7387019941 -1.6302971582 0.7911118280 0.4688242752 0.6934196275 -0.4406260617 0.324378934271 +1403638627877829376.0000000000 4.7282453840 -1.6413484097 0.7829304674 0.4682144753 0.6936552271 -0.4404265081 0.325026340424 +1403638627927829504.0000000000 4.7178031057 -1.6516907142 0.7746544112 0.4668269923 0.6945106513 -0.4410022444 0.324414141094 +1403638627977829376.0000000000 4.7076117105 -1.6613330870 0.7662675423 0.4653407225 0.6954303414 -0.4412235626 0.324278306555 +1403638628027829504.0000000000 4.6977656750 -1.6700986955 0.7583402413 0.4640509131 0.6959803318 -0.4414983917 0.324572484832 +1403638628077829376.0000000000 4.6879704119 -1.6779067345 0.7508854015 0.4632577609 0.6963445762 -0.4418288952 0.324474506884 +1403638628127829504.0000000000 4.6784848298 -1.6847623559 0.7438271728 0.4623024907 0.6966595001 -0.4423344208 0.324472199571 +1403638628177829376.0000000000 4.6695621401 -1.6905720763 0.7371984835 0.4617243233 0.6966777906 -0.4425055848 0.325022326602 +1403638628227829504.0000000000 4.6608811609 -1.6952298817 0.7311067121 0.4617705449 0.6964768467 -0.4430400799 0.324658980255 +1403638628277829376.0000000000 4.6527985306 -1.6991032846 0.7255802339 0.4611650172 0.6966169329 -0.4432272213 0.324963545592 +1403638628327829504.0000000000 4.6453895482 -1.7015085340 0.7207714404 0.4608119628 0.6966602914 -0.4443420186 0.323847099465 +1403638628377829376.0000000000 4.6383598257 -1.7030186007 0.7168032547 0.4607987912 0.6965590412 -0.4448491761 0.323387054092 +1403638628427829504.0000000000 4.6318242200 -1.7031516498 0.7134928592 0.4623034856 0.6955035581 -0.4461247568 0.321749886154 +1403638628477829376.0000000000 4.6258587011 -1.7021851920 0.7115053626 0.4667422718 0.6922621257 -0.4482029467 0.319435313522 +1403638628527829504.0000000000 4.6204008863 -1.7005504830 0.7109936518 0.4731971929 0.6877495236 -0.4499177186 0.317268113486 +1403638628577829376.0000000000 4.6151244295 -1.6989390083 0.7109245299 0.4792466665 0.6834973576 -0.4509669990 0.315884093623 +1403638628627829504.0000000000 4.6100226572 -1.6974710387 0.7115373743 0.4843438099 0.6796908720 -0.4518322326 0.315085743686 +1403638628677829376.0000000000 4.6046470547 -1.6966738320 0.7115044178 0.4864479213 0.6782550766 -0.4532662016 0.312870934179 +1403638628727829504.0000000000 4.5993646222 -1.6969353083 0.7105950563 0.4858685188 0.6785946657 -0.4532888330 0.313002070342 +1403638628777829376.0000000000 4.5942001412 -1.6980975945 0.7081360592 0.4842025664 0.6795685845 -0.4530298414 0.313844509948 +1403638628827829504.0000000000 4.5894138552 -1.7000053216 0.7042317415 0.4825893180 0.6806528780 -0.4519502370 0.315531604058 +1403638628877829376.0000000000 4.5851047152 -1.7024744080 0.6989439343 0.4817624261 0.6811110380 -0.4506670421 0.317634909652 +1403638628927829504.0000000000 4.5810675304 -1.7053399448 0.6929306150 0.4807068218 0.6815918680 -0.4497416041 0.319508945727 +1403638628977829376.0000000000 4.5769822838 -1.7083880732 0.6870002527 0.4789851146 0.6827786692 -0.4481710531 0.321759624688 +1403638629027829504.0000000000 4.5729666000 -1.7113407396 0.6817583214 0.4775233597 0.6837804378 -0.4469150924 0.323546988863 +1403638629077829376.0000000000 4.5688227257 -1.7142863864 0.6772334335 0.4757156387 0.6850896052 -0.4453904399 0.325536818137 +1403638629127829504.0000000000 4.5646312817 -1.7168629123 0.6734774896 0.4745498295 0.6860186041 -0.4448421601 0.326031266499 +1403638629177829376.0000000000 4.5603424049 -1.7192129622 0.6703102957 0.4733177884 0.6869291661 -0.4439763283 0.327083493603 +1403638629227829504.0000000000 4.5556874992 -1.7212091936 0.6679307426 0.4726172759 0.6875363391 -0.4438152950 0.327039258832 +1403638629277829376.0000000000 4.5509620737 -1.7228292791 0.6665793438 0.4727482811 0.6875192825 -0.4433756318 0.32748182844 +1403638629327829504.0000000000 4.5460053927 -1.7242423113 0.6654800376 0.4709546945 0.6885262684 -0.4435479548 0.327717050596 +1403638629377829376.0000000000 4.5405762763 -1.7249798102 0.6645785401 0.4681153322 0.6903606783 -0.4446133842 0.32647987415 +1403638629427829504.0000000000 4.5354076625 -1.7250381110 0.6639629076 0.4655081326 0.6920140723 -0.4459078119 0.324938341184 +1403638629477829376.0000000000 4.5302927629 -1.7243620796 0.6633523352 0.4624175808 0.6938926067 -0.4478733429 0.322633693267 +1403638629527829504.0000000000 4.5255941813 -1.7228575841 0.6630796078 0.4601182975 0.6953820602 -0.4500497860 0.319671914387 +1403638629577829376.0000000000 4.5219810882 -1.7201609188 0.6634980956 0.4595626329 0.6956729898 -0.4516033116 0.317640876934 +1403638629627829504.0000000000 4.5190855272 -1.7165092737 0.6648174432 0.4622484905 0.6936474486 -0.4552764083 0.312894458528 +1403638629677829376.0000000000 4.5171083973 -1.7124477180 0.6668648460 0.4662399825 0.6906787223 -0.4586713361 0.308551108709 +1403638629727829504.0000000000 4.5164538783 -1.7083001937 0.6695085341 0.4711566360 0.6870357304 -0.4610519972 0.305654028715 +1403638629777829376.0000000000 4.5170755594 -1.7044597771 0.6720410711 0.4759271549 0.6834836542 -0.4616746765 0.305286636895 +1403638629827829504.0000000000 4.5186561449 -1.7010068535 0.6735766733 0.4803764301 0.6802108775 -0.4619118538 0.305268876376 +1403638629877829376.0000000000 4.5212582235 -1.6982690621 0.6734969345 0.4847777541 0.6768629129 -0.4609607569 0.307184483473 +1403638629927829504.0000000000 4.5247079503 -1.6967177687 0.6705542341 0.4864547366 0.6754065273 -0.4571773993 0.313331514185 +1403638629977829376.0000000000 4.5284807513 -1.6961776275 0.6652038831 0.4880110010 0.6740791875 -0.4526088139 0.32032448155 +1403638630027829504.0000000000 4.5317561179 -1.6966340586 0.6577126853 0.4900208802 0.6725137400 -0.4483223992 0.326514674875 +1403638630077829376.0000000000 4.5345378966 -1.6974455620 0.6471226386 0.4892580039 0.6728982008 -0.4456116636 0.330552359323 +1403638630127829504.0000000000 4.5363045111 -1.6984371302 0.6338697769 0.4871095135 0.6745466954 -0.4441057710 0.332387035973 +1403638630177829376.0000000000 4.5371237466 -1.6994803052 0.6191479730 0.4841927384 0.6767155670 -0.4433934364 0.333190176982 +1403638630227829504.0000000000 4.5367147051 -1.7008236311 0.6027432501 0.4809526121 0.6791118544 -0.4436622141 0.332649235487 +1403638630277829376.0000000000 4.5363082295 -1.7020266518 0.5847651651 0.4780085033 0.6812212501 -0.4443801458 0.331619910832 +1403638630327829504.0000000000 4.5355028558 -1.7033476467 0.5652803058 0.4710317062 0.6854731339 -0.4456598927 0.331123805544 +1403638630377829376.0000000000 4.5357493620 -1.7000535388 0.5588233861 0.4538180723 0.6991028232 -0.4522099169 0.317506835931 +1403638630427829504.0000000000 4.5405138938 -1.6943831239 0.5650889335 0.4693237918 0.6889837948 -0.4539886423 0.314532703448 +1403638630477829376.0000000000 4.5464684943 -1.6902271408 0.5709906549 0.4788344185 0.6828182091 -0.4442994108 0.327223053173 +1403638630527829504.0000000000 4.5508949603 -1.6863154345 0.5725110996 0.4788095743 0.6826836728 -0.4437154655 0.328330595755 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_01_easy.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_01_easy.txt new file mode 100644 index 0000000000000000000000000000000000000000..981336f1d8e3cc4f25d2e675cf7a90a7737618ba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_01_easy.txt @@ -0,0 +1,2872 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403715274312143104.0000000000 0.8687393558 2.2070275302 0.9257726725 0.4259596512 0.6262011737 -0.5441421096 0.361026079545 +1403715274362142976.0000000000 0.8691033299 2.2061947719 0.9256472293 0.4259403229 0.6261063148 -0.5441748130 0.361164085649 +1403715274412143104.0000000000 0.8693648353 2.2055550838 0.9255692117 0.4258371731 0.6261730257 -0.5442021227 0.361128915443 +1403715274462142976.0000000000 0.8695852871 2.2051432993 0.9255480440 0.4258848709 0.6260224315 -0.5443200517 0.361156023422 +1403715274512143104.0000000000 0.8697087755 2.2048731526 0.9255085442 0.4258841322 0.6262328711 -0.5440339412 0.361223155228 +1403715274562142976.0000000000 0.8697613444 2.2047771590 0.9255325015 0.4260009065 0.6261932119 -0.5441235745 0.361019147279 +1403715274612143104.0000000000 0.8697750289 2.2047088262 0.9255397116 0.4260703795 0.6262367730 -0.5440090116 0.361034252072 +1403715274662142976.0000000000 0.8698110062 2.2046846689 0.9255249065 0.4259791602 0.6262786477 -0.5439174156 0.361207219538 +1403715274712143104.0000000000 0.8697598745 2.2047787792 0.9256188575 0.4262045754 0.6260968063 -0.5439590617 0.361193837466 +1403715274762142976.0000000000 0.8697574351 2.2048802415 0.9256004091 0.4261057224 0.6260827089 -0.5440007454 0.36127211891 +1403715274812143104.0000000000 0.8697769664 2.2050028696 0.9256114190 0.4261366092 0.6260066783 -0.5440845900 0.361241176903 +1403715274862142976.0000000000 0.8697276497 2.2050993607 0.9256334050 0.4262027941 0.6259287580 -0.5441196857 0.361245257209 +1403715274912143104.0000000000 0.8697095377 2.2052939037 0.9256165910 0.4262176857 0.6259154849 -0.5441583043 0.361192511166 +1403715274962142976.0000000000 0.8697107648 2.2054559648 0.9256241203 0.4262906082 0.6258756256 -0.5442420710 0.361049285853 +1403715275012143104.0000000000 0.8696795453 2.2056134407 0.9256739613 0.4263311253 0.6258142510 -0.5442970316 0.361024980119 +1403715275062142976.0000000000 0.8696018254 2.2057909216 0.9256932636 0.4263806245 0.6257926611 -0.5443083865 0.360986826351 +1403715275112143104.0000000000 0.8695932276 2.2059105888 0.9257035883 0.4264222451 0.6257659882 -0.5443687426 0.360892877331 +1403715275162142976.0000000000 0.8695763962 2.2059719462 0.9257185918 0.4263973458 0.6257714731 -0.5443946246 0.360873744808 +1403715275212143104.0000000000 0.8695388514 2.2060079611 0.9257791408 0.4264729238 0.6257110989 -0.5444146844 0.360858860729 +1403715275262142976.0000000000 0.8695416609 2.2060576064 0.9257923326 0.4265148449 0.6256688055 -0.5444933648 0.360763923578 +1403715275312143104.0000000000 0.8695360814 2.2060870695 0.9257901711 0.4265528851 0.6256322257 -0.5445318421 0.360724309405 +1403715275362142976.0000000000 0.8695145347 2.2061060944 0.9257694308 0.4265449402 0.6256456426 -0.5445391123 0.360699458178 +1403715275412143104.0000000000 0.8695089389 2.2060930407 0.9257456809 0.4265647547 0.6256229782 -0.5445617620 0.360681142644 +1403715275462142976.0000000000 0.8695065127 2.2060654764 0.9257443406 0.4265787637 0.6256007579 -0.5445586045 0.360707882363 +1403715275512143104.0000000000 0.8695298564 2.2060556327 0.9257574333 0.4265935056 0.6255564328 -0.5446076917 0.360693211038 +1403715275562142976.0000000000 0.8695373885 2.2060053972 0.9257347863 0.4266184513 0.6255057215 -0.5446410018 0.360701356383 +1403715275612143104.0000000000 0.8695048653 2.2059316201 0.9256947421 0.4265920184 0.6255101547 -0.5446852307 0.360658142315 +1403715275662142976.0000000000 0.8694744558 2.2058992746 0.9256694586 0.4266266395 0.6254910751 -0.5447113585 0.360610817058 +1403715275712143104.0000000000 0.8694759165 2.2058916596 0.9256164932 0.4266480698 0.6255327276 -0.5446860695 0.360551406694 +1403715275762142976.0000000000 0.8694808821 2.2058715527 0.9255846602 0.4266735127 0.6255276031 -0.5447047535 0.360501959534 +1403715275812143104.0000000000 0.8694877466 2.2058210611 0.9255684159 0.4266882435 0.6255016377 -0.5447422146 0.360472972222 +1403715275862142976.0000000000 0.8695027622 2.2057557850 0.9256134978 0.4268293774 0.6254026573 -0.5446856908 0.360563027816 +1403715275912143104.0000000000 0.8695064686 2.2057207266 0.9257204888 0.4268859737 0.6253193424 -0.5446770151 0.360653621476 +1403715275962142976.0000000000 0.8694398023 2.2057069178 0.9259780034 0.4272643800 0.6250607147 -0.5444635308 0.360976060251 +1403715276012143104.0000000000 0.8694776160 2.2057300484 0.9261698742 0.4273674425 0.6249205800 -0.5445404896 0.360980599248 +1403715276062142976.0000000000 0.8695250432 2.2057683284 0.9262217182 0.4271350910 0.6250900705 -0.5445893461 0.360888434122 +1403715276112143104.0000000000 0.8696242879 2.2057870386 0.9260768560 0.4269471029 0.6252570114 -0.5446938304 0.360663932317 +1403715276162142976.0000000000 0.8695811705 2.2058031721 0.9259404822 0.4271041616 0.6251249153 -0.5447315157 0.360650039833 +1403715276212143104.0000000000 0.8695265774 2.2057747985 0.9258470059 0.4269827609 0.6252435380 -0.5447017713 0.360633082811 +1403715276262142976.0000000000 0.8695283598 2.2057591606 0.9257715003 0.4270209839 0.6251952603 -0.5447775231 0.360557091571 +1403715276312143104.0000000000 0.8695430596 2.2057213412 0.9256510523 0.4269855439 0.6252243658 -0.5448093035 0.360500569372 +1403715276362142976.0000000000 0.8695333796 2.2057117866 0.9256466572 0.4269538262 0.6252438880 -0.5448429736 0.360453388018 +1403715276412143104.0000000000 0.8694896517 2.2057320055 0.9256815744 0.4269470383 0.6252600498 -0.5448734950 0.360387251448 +1403715276462142976.0000000000 0.8694401617 2.2057653814 0.9257195709 0.4269843874 0.6252317556 -0.5448314869 0.360455594376 +1403715276512143104.0000000000 0.8693011260 2.2057910128 0.9259869399 0.4273665883 0.6250553137 -0.5446699567 0.36055275936 +1403715276562142976.0000000000 0.8692265926 2.2057178136 0.9261961984 0.4272349525 0.6250852986 -0.5447451779 0.360543140191 +1403715276612143104.0000000000 0.8692164666 2.2056779864 0.9260778135 0.4270969890 0.6251877557 -0.5448175248 0.360419612027 +1403715276662142976.0000000000 0.8691783149 2.2056672740 0.9259607426 0.4271156000 0.6251841877 -0.5448293374 0.360385888603 +1403715276712143104.0000000000 0.8690416108 2.2056514115 0.9260283652 0.4271783326 0.6251784833 -0.5447052692 0.360508953962 +1403715276762142976.0000000000 0.8689167877 2.2055540390 0.9261616224 0.4274341457 0.6250422675 -0.5446397333 0.36054094879 +1403715276812143104.0000000000 0.8689940549 2.2054434173 0.9261529341 0.4273088431 0.6251067683 -0.5447242848 0.360449905505 +1403715276862142976.0000000000 0.8691205060 2.2053500143 0.9262460948 0.4272821177 0.6251027409 -0.5447356444 0.36047140381 +1403715276912143104.0000000000 0.8692363327 2.2055429308 0.9263479943 0.4275282703 0.6249552426 -0.5446221181 0.360606809869 +1403715276962142976.0000000000 0.8694342770 2.2058115131 0.9264091286 0.4276747627 0.6248600992 -0.5444587167 0.360844647275 +1403715277012143104.0000000000 0.8696236618 2.2059679894 0.9266123305 0.4278201851 0.6247605820 -0.5444541580 0.360851457355 +1403715277062142976.0000000000 0.8700057771 2.2058457682 0.9266714458 0.4276043036 0.6249087981 -0.5445393736 0.360722087254 +1403715277112143104.0000000000 0.8703669939 2.2057725790 0.9266868077 0.4276819006 0.6248768272 -0.5444358817 0.360841673683 +1403715277162142976.0000000000 0.8708201437 2.2058063051 0.9267478303 0.4276508198 0.6249561900 -0.5443787291 0.360827294292 +1403715277212143104.0000000000 0.8707574619 2.2057769775 0.9269343520 0.4277425298 0.6248548071 -0.5445380364 0.360653746852 +1403715277262142976.0000000000 0.8704606850 2.2056331885 0.9269381999 0.4274933472 0.6249479574 -0.5445322445 0.36079651228 +1403715277312143104.0000000000 0.8700810716 2.2055384952 0.9268643184 0.4274180502 0.6249290498 -0.5447129990 0.360645590254 +1403715277362142976.0000000000 0.8695702168 2.2054742001 0.9268844824 0.4272308457 0.6250904561 -0.5445760593 0.360794459297 +1403715277412143104.0000000000 0.8690493994 2.2054078348 0.9269312782 0.4274097506 0.6249749524 -0.5445687619 0.360793677151 +1403715277462142976.0000000000 0.8686596319 2.2052969095 0.9268473407 0.4275812325 0.6248678714 -0.5445764362 0.360764380222 +1403715277512143104.0000000000 0.8689049516 2.2053364727 0.9269776227 0.4274512925 0.6249389467 -0.5446285191 0.360716622336 +1403715277562142976.0000000000 0.8691105926 2.2052854385 0.9272863617 0.4275358251 0.6249484413 -0.5443656228 0.360996721006 +1403715277612143104.0000000000 0.8692889589 2.2052908540 0.9272069603 0.4275344642 0.6250068947 -0.5444391591 0.360786177041 +1403715277662142976.0000000000 0.8695771154 2.2053433415 0.9272475714 0.4276894120 0.6248722331 -0.5444854338 0.36076595123 +1403715277712143104.0000000000 0.8696279707 2.2052900224 0.9275500772 0.4276621982 0.6249528012 -0.5444045249 0.360780755856 +1403715277762142976.0000000000 0.8696146365 2.2053551197 0.9277772099 0.4277756264 0.6248965944 -0.5443789052 0.360782299163 +1403715277812143104.0000000000 0.8695206061 2.2053280588 0.9276435347 0.4275392141 0.6250922543 -0.5441653002 0.361045731216 +1403715277862142976.0000000000 0.8694615808 2.2051066438 0.9275550658 0.4275035146 0.6250197349 -0.5446391968 0.360498573118 +1403715277912143104.0000000000 0.8694153604 2.2048905278 0.9276950177 0.4272524146 0.6252564547 -0.5442380523 0.360991249805 +1403715277962142976.0000000000 0.8694332881 2.2047352274 0.9280033510 0.4276461052 0.6250383284 -0.5442261010 0.360920833044 +1403715278012143104.0000000000 0.8696323881 2.2045281633 0.9280984562 0.4275012831 0.6251696946 -0.5443811909 0.360630870647 +1403715278062142976.0000000000 0.8698018156 2.2045599054 0.9280399783 0.4274771816 0.6252367274 -0.5441381913 0.360909853953 +1403715278112143104.0000000000 0.8699207684 2.2047514760 0.9282154357 0.4276618210 0.6250244547 -0.5440582327 0.361179231599 +1403715278162142976.0000000000 0.8700876099 2.2050201539 0.9284372775 0.4276586668 0.6251226843 -0.5442414351 0.360736683285 +1403715278212143104.0000000000 0.8704029906 2.2051637918 0.9284757707 0.4277864293 0.6251089578 -0.5440987749 0.360824174507 +1403715278262142976.0000000000 0.8702995514 2.2052097048 0.9282723685 0.4277372038 0.6249898355 -0.5438445054 0.361471636518 +1403715278312143104.0000000000 0.8702653439 2.2052672696 0.9286694653 0.4278103604 0.6243019262 -0.5442555047 0.3619548951 +1403715278362142976.0000000000 0.8703622862 2.2051476091 0.9294179822 0.4277321150 0.6235252885 -0.5444532984 0.363086846772 +1403715278412143104.0000000000 0.8708207527 2.2051795622 0.9301646980 0.4274049186 0.6232228945 -0.5444620668 0.363977083356 +1403715278462142976.0000000000 0.8723348895 2.2057901098 0.9310349993 0.4285647408 0.6218091732 -0.5447677004 0.364573405115 +1403715278512143104.0000000000 0.8750917799 2.2069771447 0.9321762497 0.4299106730 0.6201374095 -0.5447561997 0.365851184906 +1403715278562142976.0000000000 0.8791483777 2.2089433096 0.9350705015 0.4334191202 0.6169573477 -0.5439682182 0.368252732415 +1403715278612143104.0000000000 0.8842869498 2.2114391537 0.9399381553 0.4369311037 0.6138478918 -0.5431969317 0.370430924339 +1403715278662142976.0000000000 0.8904270234 2.2144524940 0.9468184971 0.4376532235 0.6130779324 -0.5420946855 0.372462691805 +1403715278712143104.0000000000 0.8975052812 2.2183291242 0.9570613639 0.4402331184 0.6108676600 -0.5424756345 0.372499247504 +1403715278762142976.0000000000 0.9054323518 2.2224753777 0.9704680994 0.4437171718 0.6081986604 -0.5419550854 0.373489151686 +1403715278812143104.0000000000 0.9137361710 2.2267330647 0.9861705274 0.4462479370 0.6064455185 -0.5412847631 0.37429589512 +1403715278862142976.0000000000 0.9223647718 2.2309425869 1.0043522497 0.4493335573 0.6043917886 -0.5404198563 0.375175024577 +1403715278912143104.0000000000 0.9304926779 2.2347412430 1.0233080973 0.4500145011 0.6039743920 -0.5401339195 0.375442714142 +1403715278962142976.0000000000 0.9381452083 2.2383112521 1.0417256202 0.4504961830 0.6035863653 -0.5395755839 0.376290948641 +1403715279012143104.0000000000 0.9452606290 2.2414589946 1.0563603072 0.4502177335 0.6037684473 -0.5389260291 0.377261699049 +1403715279062142976.0000000000 0.9517637487 2.2446141162 1.0659779441 0.4498372849 0.6040446502 -0.5388332847 0.377405841165 +1403715279112143104.0000000000 0.9579898541 2.2476501666 1.0702966254 0.4497441747 0.6040807919 -0.5386062526 0.377782846165 +1403715279162142976.0000000000 0.9635460385 2.2505729261 1.0695497651 0.4490408947 0.6047993103 -0.5381824012 0.378073765554 +1403715279212143104.0000000000 0.9685106852 2.2531736505 1.0655800760 0.4480662640 0.6055611156 -0.5380675126 0.378174179829 +1403715279262142976.0000000000 0.9733639770 2.2557828286 1.0608579498 0.4475912828 0.6061932276 -0.5379252421 0.377926247283 +1403715279312143104.0000000000 0.9776649525 2.2582108796 1.0562781501 0.4469019076 0.6068035706 -0.5383134847 0.377209098406 +1403715279362142976.0000000000 0.9814980792 2.2604337758 1.0528127023 0.4464426389 0.6070973591 -0.5391179553 0.376129760864 +1403715279412143104.0000000000 0.9850130008 2.2625135496 1.0506811982 0.4469494337 0.6068961385 -0.5395382258 0.375248962253 +1403715279462142976.0000000000 0.9881015011 2.2640573769 1.0494038901 0.4463986818 0.6074651083 -0.5400226409 0.374285861793 +1403715279512143104.0000000000 0.9909593802 2.2653990657 1.0496097885 0.4464624301 0.6075731911 -0.5402307970 0.373733597645 +1403715279562142976.0000000000 0.9937423396 2.2665889201 1.0508705038 0.4462181629 0.6078337163 -0.5397252203 0.374331685875 +1403715279612143104.0000000000 0.9960904129 2.2675749799 1.0531890722 0.4456674870 0.6081751603 -0.5399430791 0.374118880472 +1403715279662142976.0000000000 0.9980832392 2.2682131358 1.0563464177 0.4454704183 0.6084848206 -0.5398838169 0.373935547619 +1403715279712143104.0000000000 1.0001309899 2.2686834569 1.0603323773 0.4456695102 0.6083210574 -0.5397889806 0.374101637482 +1403715279762142976.0000000000 1.0019071609 2.2690208739 1.0652577464 0.4456524925 0.6083661623 -0.5398568628 0.373950579869 +1403715279812143104.0000000000 1.0032807992 2.2690157306 1.0708731000 0.4457004072 0.6082225735 -0.5402150055 0.373609683945 +1403715279862142976.0000000000 1.0041970775 2.2686431121 1.0771213728 0.4454773414 0.6084890067 -0.5402638257 0.373371217106 +1403715279912143104.0000000000 1.0049799906 2.2681493868 1.0840319328 0.4449135981 0.6088281667 -0.5405167987 0.373124301097 +1403715279962142976.0000000000 1.0056276004 2.2675433915 1.0911307888 0.4430736263 0.6101592045 -0.5412630088 0.372056262111 +1403715280012143104.0000000000 1.0060496693 2.2669088815 1.0978069639 0.4394439201 0.6127371562 -0.5434279348 0.368955686016 +1403715280062142976.0000000000 1.0066403386 2.2662603840 1.1041541790 0.4347930788 0.6161331576 -0.5459498545 0.365066661165 +1403715280112143104.0000000000 1.0079466628 2.2653417519 1.1104562908 0.4288245689 0.6203322788 -0.5468501370 0.363665066589 +1403715280162142976.0000000000 1.0102629583 2.2646022192 1.1174763003 0.4250037440 0.6232497845 -0.5466006057 0.363537207985 +1403715280212143104.0000000000 1.0136805950 2.2640153334 1.1249514539 0.4216127389 0.6257770777 -0.5446442008 0.366071634972 +1403715280262142976.0000000000 1.0181737901 2.2640899672 1.1331698725 0.4197504886 0.6271074942 -0.5422246865 0.369510632415 +1403715280312143104.0000000000 1.0234806882 2.2652496516 1.1417453712 0.4190842233 0.6276834682 -0.5398826719 0.372704411073 +1403715280362142976.0000000000 1.0295451181 2.2673944857 1.1506758163 0.4192324066 0.6273258467 -0.5378104267 0.376120215265 +1403715280412143104.0000000000 1.0363942698 2.2704072206 1.1596057704 0.4193354600 0.6261070209 -0.5365293411 0.379847385971 +1403715280462142976.0000000000 1.0438759782 2.2744925438 1.1686750103 0.4203134639 0.6233257031 -0.5384463641 0.380627341237 +1403715280512143104.0000000000 1.0520847976 2.2794976583 1.1778038809 0.4223143801 0.6180385903 -0.5426983317 0.380995257148 +1403715280562142976.0000000000 1.0606022314 2.2851656948 1.1867093888 0.4234403275 0.6122121490 -0.5477138959 0.381973902097 +1403715280612143104.0000000000 1.0695720745 2.2909072633 1.1953391299 0.4238613664 0.6053115632 -0.5536233940 0.38397993588 +1403715280662142976.0000000000 1.0790896993 2.2964354433 1.2034048116 0.4220669345 0.5983793603 -0.5599433243 0.387640448764 +1403715280712143104.0000000000 1.0887783656 2.3019574779 1.2109588665 0.4197762136 0.5906958360 -0.5670530196 0.391557445157 +1403715280762142976.0000000000 1.0986707268 2.3073762180 1.2176745183 0.4160495603 0.5831509778 -0.5746018071 0.395816199343 +1403715280812143104.0000000000 1.1085764915 2.3125919352 1.2235505761 0.4114723888 0.5756497800 -0.5825903960 0.399882775931 +1403715280862142976.0000000000 1.1187246264 2.3177123705 1.2293765546 0.4071301987 0.5676334920 -0.5898875882 0.405055370732 +1403715280912143104.0000000000 1.1286714270 2.3229133051 1.2346804286 0.4026059660 0.5604684597 -0.5965612142 0.409753901246 +1403715280962142976.0000000000 1.1384374185 2.3283325077 1.2398540176 0.3988260657 0.5542113164 -0.6020482478 0.413914838279 +1403715281012143104.0000000000 1.1477283817 2.3338254505 1.2447417028 0.3956510223 0.5485038474 -0.6070767409 0.417206937369 +1403715281062142976.0000000000 1.1567646692 2.3394909785 1.2493028184 0.3918678309 0.5442245775 -0.6112076128 0.420338514105 +1403715281112143104.0000000000 1.1659344006 2.3452901801 1.2538171306 0.3892119207 0.5401537431 -0.6146528952 0.423024624631 +1403715281162142976.0000000000 1.1751796395 2.3513276011 1.2581670708 0.3870686489 0.5367542174 -0.6171384096 0.42569114931 +1403715281212143104.0000000000 1.1846252095 2.3573533032 1.2623565464 0.3848214693 0.5337022911 -0.6196995540 0.427839647621 +1403715281262142976.0000000000 1.1942286931 2.3631928565 1.2663131273 0.3825691815 0.5302182111 -0.6229273849 0.429500806912 +1403715281312143104.0000000000 1.2036594306 2.3686978608 1.2696333390 0.3793508248 0.5266719258 -0.6266801466 0.43125587317 +1403715281362142976.0000000000 1.2130391286 2.3739485631 1.2721672927 0.3757881618 0.5226527560 -0.6308565336 0.433171314854 +1403715281412143104.0000000000 1.2227034358 2.3790138764 1.2741129589 0.3716477942 0.5183437590 -0.6352860592 0.43544148582 +1403715281462142976.0000000000 1.2327240584 2.3836275211 1.2756336118 0.3671536235 0.5129460323 -0.6398321583 0.438975390893 +1403715281512143104.0000000000 1.2429058535 2.3879447646 1.2768707555 0.3620989656 0.5067071117 -0.6450476701 0.442770533415 +1403715281562142976.0000000000 1.2532160413 2.3918615024 1.2773565041 0.3560129342 0.4998900024 -0.6507866692 0.447036337957 +1403715281612143104.0000000000 1.2636971413 2.3955916614 1.2772060224 0.3498913758 0.4918783198 -0.6570113578 0.451627965598 +1403715281662142976.0000000000 1.2743649790 2.3992653359 1.2764059227 0.3435391481 0.4828317365 -0.6638918090 0.456182018464 +1403715281712143104.0000000000 1.2851673320 2.4028305961 1.2751154330 0.3362651949 0.4735043923 -0.6709554471 0.461018543175 +1403715281762142976.0000000000 1.2961629045 2.4062529023 1.2737477443 0.3289058189 0.4635441960 -0.6784648628 0.465438686255 +1403715281812143104.0000000000 1.3072944251 2.4097563164 1.2719386640 0.3212401234 0.4532957498 -0.6860390134 0.469764002935 +1403715281862142976.0000000000 1.3186641547 2.4133651917 1.2696985514 0.3138731231 0.4423470325 -0.6931642657 0.474695761761 +1403715281912143104.0000000000 1.3301832428 2.4169544752 1.2668158262 0.3057486126 0.4318349144 -0.7001997585 0.479329417909 +1403715281962142976.0000000000 1.3419914861 2.4206552083 1.2634459314 0.2983805046 0.4209472673 -0.7070687554 0.483555837293 +1403715282012143104.0000000000 1.3541023219 2.4244372665 1.2596608235 0.2911543623 0.4100264967 -0.7138037090 0.487433764069 +1403715282062142976.0000000000 1.3666639960 2.4280806678 1.2551661151 0.2841122946 0.3992524277 -0.7201040217 0.491251362304 +1403715282112143104.0000000000 1.3795328490 2.4316297899 1.2501218721 0.2761441689 0.3895244516 -0.7253880900 0.495809659524 +1403715282162142976.0000000000 1.3926957873 2.4352169031 1.2449379226 0.2693485034 0.3792523283 -0.7311110862 0.499094815425 +1403715282212143104.0000000000 1.4062292973 2.4387685778 1.2396141909 0.2620545023 0.3695046763 -0.7358955206 0.50324101061 +1403715282262142976.0000000000 1.4201562290 2.4422798670 1.2340902928 0.2546541208 0.3595252700 -0.7412202515 0.506443874176 +1403715282312143104.0000000000 1.4346381405 2.4457097282 1.2285439112 0.2473968263 0.3496228334 -0.7463001978 0.509504366468 +1403715282362142976.0000000000 1.4494088530 2.4491105609 1.2228692191 0.2399738810 0.3396583185 -0.7511072309 0.512720870239 +1403715282412143104.0000000000 1.4643806005 2.4522632418 1.2168253977 0.2310597889 0.3309275300 -0.7556551574 0.515832944737 +1403715282462142976.0000000000 1.4800177217 2.4556591801 1.2108176847 0.2242590571 0.3204453869 -0.7605181312 0.518299914583 +1403715282512143104.0000000000 1.4964881251 2.4587243285 1.2045525699 0.2170781022 0.3104158724 -0.7644424444 0.521676942963 +1403715282562142976.0000000000 1.5134891888 2.4618130433 1.1980111688 0.2100504190 0.3002991574 -0.7684246472 0.524616811723 +1403715282612143104.0000000000 1.5310667748 2.4649849056 1.1916261263 0.2035956204 0.2902344911 -0.7713024281 0.528588051274 +1403715282662142976.0000000000 1.5491467535 2.4682383007 1.1851732429 0.1980495037 0.2797040310 -0.7742183471 0.532097735457 +1403715282712143104.0000000000 1.5675592503 2.4716432372 1.1784604427 0.1927822368 0.2687237295 -0.7772295439 0.535291324929 +1403715282762142976.0000000000 1.5862038165 2.4753446563 1.1714425534 0.1884823014 0.2576334979 -0.7802769400 0.537835755327 +1403715282812143104.0000000000 1.6049366276 2.4787508121 1.1639016180 0.1836320329 0.2468033451 -0.7837876410 0.539485235344 +1403715282862142976.0000000000 1.6237114441 2.4819400302 1.1561850484 0.1776016793 0.2367091999 -0.7863330085 0.542316142045 +1403715282912143104.0000000000 1.6423910495 2.4852501949 1.1484561096 0.1713571887 0.2266880993 -0.7883725478 0.545635359291 +1403715282962142976.0000000000 1.6611945248 2.4885665248 1.1405783757 0.1653833345 0.2163542301 -0.7910179366 0.547841057066 +1403715283012143104.0000000000 1.6800243300 2.4919430031 1.1330098525 0.1597245807 0.2056618072 -0.7933233440 0.550299328737 +1403715283062142976.0000000000 1.6988533762 2.4953392350 1.1255458111 0.1546115579 0.1944798637 -0.7955582292 0.552593840622 +1403715283112143104.0000000000 1.7175503785 2.4989693515 1.1181717487 0.1498703029 0.1833067502 -0.7979648891 0.554246843434 +1403715283162142976.0000000000 1.7358917431 2.5026036332 1.1111447731 0.1458554232 0.1718355565 -0.8000613755 0.555968103783 +1403715283212143104.0000000000 1.7536446146 2.5063658299 1.1042716299 0.1414597686 0.1605499307 -0.8018953151 0.557832194536 +1403715283262142976.0000000000 1.7708216842 2.5101435701 1.0975323511 0.1362444064 0.1502005543 -0.8035471631 0.55963310474 +1403715283312143104.0000000000 1.7876068954 2.5139203937 1.0908797814 0.1315737598 0.1396779149 -0.8053817605 0.560837450279 +1403715283362142976.0000000000 1.8034714372 2.5176098181 1.0845862215 0.1258764138 0.1301922613 -0.8064178366 0.562934611079 +1403715283412143104.0000000000 1.8184142919 2.5214923676 1.0780305224 0.1199794610 0.1213441342 -0.8088258260 0.562744447548 +1403715283462142976.0000000000 1.8325415714 2.5254029204 1.0714364986 0.1140663576 0.1129941369 -0.8114402914 0.561948257861 +1403715283512143104.0000000000 1.8458449374 2.5292351027 1.0650315988 0.1066806030 0.1059478995 -0.8139108512 0.561198198433 +1403715283562142976.0000000000 1.8583869395 2.5330428032 1.0589935852 0.0990981335 0.0994270618 -0.8162334953 0.560407619907 +1403715283612143104.0000000000 1.8705354583 2.5368707724 1.0532778692 0.0921708478 0.0934924179 -0.8186532019 0.559080170988 +1403715283662142976.0000000000 1.8826688919 2.5404408694 1.0478042252 0.0865023528 0.0888213387 -0.8204614470 0.55809598349 +1403715283712143104.0000000000 1.8947768853 2.5435224857 1.0424893130 0.0820070335 0.0847863427 -0.8214392356 0.557963891947 +1403715283762142976.0000000000 1.9070053559 2.5463321482 1.0373676324 0.0791213019 0.0811983349 -0.8220169373 0.558063441481 +1403715283812143104.0000000000 1.9194374174 2.5487493707 1.0327142413 0.0777389399 0.0775707885 -0.8216828367 0.559264468584 +1403715283862142976.0000000000 1.9318113247 2.5507896911 1.0277879320 0.0756820814 0.0753732332 -0.8210483199 0.560776920579 +1403715283912143104.0000000000 1.9441846470 2.5525379647 1.0230540793 0.0756029743 0.0729734892 -0.8201988446 0.562345903738 +1403715283962142976.0000000000 1.9564231597 2.5540053560 1.0180098362 0.0751407224 0.0713762804 -0.8196580491 0.563400373569 +1403715284012143104.0000000000 1.9688633763 2.5554264901 1.0121222369 0.0751339956 0.0705249085 -0.8206863000 0.562009890536 +1403715284062142976.0000000000 1.9814122753 2.5565240998 1.0061648998 0.0751181226 0.0704489966 -0.8218360699 0.56033889806 +1403715284112143104.0000000000 1.9939642442 2.5573326100 1.0004844795 0.0761920523 0.0700512893 -0.8230653027 0.558436294915 +1403715284162142976.0000000000 2.0062860667 2.5579987120 0.9950542642 0.0781365643 0.0696795300 -0.8240470445 0.556763781887 +1403715284212143104.0000000000 2.0183900077 2.5580900323 0.9900254416 0.0820056185 0.0682727099 -0.8248853406 0.555137902166 +1403715284262142976.0000000000 2.0299092665 2.5574300586 0.9854626276 0.0859324878 0.0670287624 -0.8254141454 0.553908152187 +1403715284312143104.0000000000 2.0409280337 2.5558423908 0.9813028953 0.0904479175 0.0656502878 -0.8257672305 0.552827002793 +1403715284362142976.0000000000 2.0510502013 2.5531849932 0.9775121318 0.0938132143 0.0651139316 -0.8254183820 0.552850568812 +1403715284412143104.0000000000 2.0599828335 2.5493760766 0.9737592563 0.0930013172 0.0675704176 -0.8244234795 0.554175892781 +1403715284462142976.0000000000 2.0680845964 2.5446298849 0.9700985307 0.0914767787 0.0707650935 -0.8233721360 0.555592140052 +1403715284512143104.0000000000 2.0754516732 2.5389813351 0.9665626951 0.0885649057 0.0751079386 -0.8220676303 0.557422520401 +1403715284562142976.0000000000 2.0826007762 2.5324148475 0.9633907142 0.0867080073 0.0788243037 -0.8204050512 0.559646319109 +1403715284612143104.0000000000 2.0895379598 2.5254675117 0.9604127040 0.0850632863 0.0824821256 -0.8185678155 0.562056641028 +1403715284662142976.0000000000 2.0963551829 2.5184132418 0.9572831909 0.0833502947 0.0860972542 -0.8172985500 0.563616067397 +1403715284712143104.0000000000 2.1032581256 2.5110992982 0.9545658795 0.0828064501 0.0886715109 -0.8161281543 0.564991407675 +1403715284762142976.0000000000 2.1100949566 2.5036689057 0.9520166261 0.0816803417 0.0904622562 -0.8150111481 0.566481888911 +1403715284812143104.0000000000 2.1167809337 2.4961610721 0.9495195834 0.0798835299 0.0903990293 -0.8139853980 0.568220387694 +1403715284862142976.0000000000 2.1233678795 2.4887261827 0.9475452396 0.0779840921 0.0880876128 -0.8126620171 0.570735928218 +1403715284912143104.0000000000 2.1300314950 2.4813989307 0.9460435789 0.0771267971 0.0827625135 -0.8116526674 0.573080946296 +1403715284962142976.0000000000 2.1363857576 2.4741037932 0.9449289793 0.0748428708 0.0755496010 -0.8100736874 0.576603350176 +1403715285012143104.0000000000 2.1425896793 2.4672010952 0.9443044635 0.0734301496 0.0654623372 -0.8081841500 0.580655728645 +1403715285062142976.0000000000 2.1484273128 2.4606808111 0.9440901083 0.0702853535 0.0551831940 -0.8067675263 0.584072720348 +1403715285112143104.0000000000 2.1534185382 2.4546956548 0.9440974519 0.0639992318 0.0453848708 -0.8062489467 0.586350533174 +1403715285162142976.0000000000 2.1578437839 2.4503249381 0.9447263379 0.0575687484 0.0356071610 -0.8072117294 0.586367796924 +1403715285212143104.0000000000 2.1618305831 2.4472319868 0.9454085818 0.0518579120 0.0251842458 -0.8094001351 0.584421022947 +1403715285262142976.0000000000 2.1656050240 2.4450466823 0.9472434218 0.0474623713 0.0157096919 -0.8118530025 0.581717484037 +1403715285312143104.0000000000 2.1690896783 2.4442017753 0.9512065970 0.0450151494 0.0068512667 -0.8150810676 0.577554802272 +1403715285362142976.0000000000 2.1719829661 2.4437383835 0.9583532069 0.0428567766 -0.0007160538 -0.8184083213 0.573036302188 +1403715285412143104.0000000000 2.1742604861 2.4432287751 0.9692200739 0.0407784165 -0.0062308324 -0.8217901871 0.568294981389 +1403715285462142976.0000000000 2.1757003736 2.4424801376 0.9839258254 0.0388076014 -0.0102449580 -0.8241355292 0.564968707427 +1403715285512143104.0000000000 2.1761750072 2.4415943593 1.0013329694 0.0377421555 -0.0137817939 -0.8258759170 0.562418493287 +1403715285562142976.0000000000 2.1757542225 2.4398152927 1.0211573186 0.0377477312 -0.0173699963 -0.8266593268 0.561166418694 +1403715285612143104.0000000000 2.1745417291 2.4374275593 1.0415998248 0.0379005499 -0.0203628034 -0.8269380499 0.560644598846 +1403715285662142976.0000000000 2.1722312500 2.4344286345 1.0616918024 0.0370954878 -0.0219957068 -0.8272742192 0.560140589379 +1403715285712143104.0000000000 2.1687670511 2.4304161501 1.0813498038 0.0369398075 -0.0238711684 -0.8275246799 0.559703959353 +1403715285762142976.0000000000 2.1639436054 2.4256349858 1.1007246668 0.0348515057 -0.0241924771 -0.8266962335 0.561046730831 +1403715285812143104.0000000000 2.1579421940 2.4201596445 1.1195588939 0.0330042422 -0.0243896951 -0.8261295094 0.561983893357 +1403715285862142976.0000000000 2.1508565809 2.4141310335 1.1369878727 0.0287854975 -0.0224722165 -0.8259769122 0.56251980867 +1403715285912143104.0000000000 2.1428861121 2.4073311102 1.1540510719 0.0236232905 -0.0194230087 -0.8257558167 0.563198027357 +1403715285962142976.0000000000 2.1343896230 2.4001115780 1.1704172150 0.0188706975 -0.0164364306 -0.8264513955 0.562451625814 +1403715286012143104.0000000000 2.1257535709 2.3922239659 1.1861517920 0.0143056460 -0.0133451032 -0.8266518156 0.562373570173 +1403715286062142976.0000000000 2.1172832454 2.3836820662 1.2010075917 0.0103149516 -0.0109743596 -0.8267529488 0.562363518442 +1403715286112143104.0000000000 2.1092812259 2.3746407085 1.2152200376 0.0089102997 -0.0103857181 -0.8269427448 0.562119595974 +1403715286162142976.0000000000 2.1017373571 2.3649600111 1.2291038262 0.0098095606 -0.0115207293 -0.8271804006 0.561732703558 +1403715286212143104.0000000000 2.0943487774 2.3547264590 1.2423409659 0.0117415265 -0.0135282239 -0.8276942198 0.560893396514 +1403715286262142976.0000000000 2.0869896603 2.3438044960 1.2549271543 0.0129810626 -0.0145673727 -0.8280160798 0.56036475204 +1403715286312143104.0000000000 2.0794665087 2.3320017981 1.2670326585 0.0121200508 -0.0140347533 -0.8278920345 0.560580867735 +1403715286362142976.0000000000 2.0720109266 2.3196442656 1.2786506702 0.0110006933 -0.0133046843 -0.8273032653 0.561490229024 +1403715286412143104.0000000000 2.0648527835 2.3066572772 1.2893579769 0.0097988198 -0.0125105384 -0.8270449535 0.561911126845 +1403715286462142976.0000000000 2.0578333211 2.2929207483 1.2993207082 0.0080374107 -0.0114298517 -0.8263790724 0.562940838069 +1403715286512143104.0000000000 2.0509821302 2.2785814128 1.3090035968 0.0061696563 -0.0106648967 -0.8259543898 0.563602289971 +1403715286562142976.0000000000 2.0445240344 2.2636113126 1.3184979642 0.0046975014 -0.0104055741 -0.8249572973 0.565079742273 +1403715286612143104.0000000000 2.0382653033 2.2480561043 1.3278389157 0.0037781732 -0.0120647682 -0.8237638522 0.566792098265 +1403715286662142976.0000000000 2.0320669754 2.2318761718 1.3372989985 0.0016167915 -0.0154071962 -0.8216317444 0.569808108855 +1403715286712143104.0000000000 2.0260179789 2.2153531904 1.3462627239 0.0011889674 0.0199767513 0.8184400428 -0.574243338799 +1403715286762142976.0000000000 2.0200850595 2.1988448118 1.3542182576 0.0051693105 0.0252745522 0.8163051782 -0.577044479407 +1403715286812143104.0000000000 2.0143310482 2.1830100750 1.3608227447 0.0098285691 0.0303176008 0.8164791060 -0.576494676309 +1403715286862142976.0000000000 2.0090840223 2.1677928063 1.3663235639 0.0135762837 0.0352610244 0.8181734480 -0.573728641117 +1403715286912143104.0000000000 2.0042703249 2.1526428172 1.3716306343 0.0177587342 0.0388053507 0.8204179397 -0.570169427757 +1403715286962142976.0000000000 1.9999563352 2.1373565705 1.3771090948 0.0215290195 0.0420573260 0.8221398316 -0.567321584226 +1403715287012143104.0000000000 1.9962028345 2.1216300281 1.3828437556 0.0254818618 0.0447215307 0.8231652396 -0.565464099437 +1403715287062142976.0000000000 1.9930928316 2.1058047800 1.3889895818 0.0280700806 0.0478606894 0.8235678701 -0.564497465325 +1403715287112143104.0000000000 1.9906493752 2.0894641114 1.3951650241 0.0315108876 0.0495686432 0.8232788546 -0.564590064617 +1403715287162142976.0000000000 1.9889658060 2.0723714761 1.4016732408 0.0338050261 0.0516762641 0.8217242741 -0.566529788494 +1403715287212143104.0000000000 1.9879449279 2.0547210917 1.4085404957 0.0357575101 0.0533931566 0.8190557580 -0.57010370683 +1403715287262142976.0000000000 1.9876167064 2.0370265399 1.4152389166 0.0374935785 0.0549873937 0.8168717354 -0.572967002572 +1403715287312143104.0000000000 1.9880175673 2.0191696037 1.4221440895 0.0377386587 0.0567746916 0.8145769518 -0.576035430811 +1403715287362142976.0000000000 1.9890288092 2.0014468504 1.4286341546 0.0379712204 0.0582656301 0.8131997381 -0.577814406814 +1403715287412143104.0000000000 1.9909589133 1.9840900106 1.4351953622 0.0362344210 0.0602599638 0.8124543977 -0.57876908621 +1403715287462142976.0000000000 1.9933898224 1.9670775572 1.4420825293 0.0331448840 0.0637610814 0.8119958758 -0.5792224433 +1403715287512143104.0000000000 1.9958427790 1.9504593925 1.4491583795 0.0308226292 0.0679893962 0.8117456447 -0.579220524378 +1403715287562142976.0000000000 1.9980218961 1.9344220180 1.4563454745 0.0296757656 0.0738814113 0.8113968605 -0.579047511656 +1403715287612143104.0000000000 1.9996771605 1.9189767069 1.4638101800 0.0291101896 0.0815959067 0.8114945221 -0.577902539785 +1403715287662142976.0000000000 2.0004157661 1.9039062707 1.4716883173 0.0300162528 0.0902058815 0.8112540623 -0.576913139001 +1403715287712143104.0000000000 1.9999392049 1.8892391343 1.4799003860 0.0328281767 0.0991289799 0.8107584950 -0.575991683039 +1403715287762142976.0000000000 1.9982794382 1.8749746642 1.4885089390 0.0374847286 0.1079988326 0.8097922836 -0.575471636773 +1403715287812143104.0000000000 1.9952213165 1.8611467594 1.4973735855 0.0447526731 0.1164202842 0.8081856449 -0.575568830809 +1403715287862142976.0000000000 1.9909705660 1.8478054527 1.5066990394 0.0526895530 0.1254524984 0.8061615974 -0.57583761651 +1403715287912143104.0000000000 1.9853241333 1.8344850535 1.5162930183 0.0624415387 0.1347453724 0.8036646298 -0.576253331145 +1403715287962142976.0000000000 1.9788472573 1.8219416677 1.5259540315 0.0727871649 0.1445366988 0.8010541225 -0.576301539286 +1403715288012143104.0000000000 1.9718383656 1.8100222487 1.5354252502 0.0828535463 0.1552182472 0.7983226749 -0.575954418622 +1403715288062142976.0000000000 1.9647056299 1.7988771010 1.5450722794 0.0920075732 0.1662128807 0.7951712862 -0.575856327834 +1403715288112143104.0000000000 1.9576654787 1.7884201851 1.5543218135 0.0993051691 0.1765702504 0.7926053185 -0.575098460443 +1403715288162142976.0000000000 1.9506233401 1.7788564379 1.5619388565 0.1058784929 0.1851668980 0.7906698544 -0.573885133081 +1403715288212143104.0000000000 1.9437796608 1.7702083569 1.5666037956 0.1114861922 0.1922711171 0.7894578755 -0.572152872262 +1403715288262142976.0000000000 1.9371502687 1.7623853277 1.5682383350 0.1159186868 0.1985001141 0.7886902642 -0.570200166503 +1403715288312143104.0000000000 1.9304481809 1.7550612176 1.5665700633 0.1209569882 0.2024741687 0.7879023879 -0.568843955044 +1403715288362142976.0000000000 1.9241982586 1.7482621232 1.5615787640 0.1239306820 0.2062565068 0.7874564722 -0.56746078617 +1403715288412143104.0000000000 1.9182177710 1.7415959701 1.5543832297 0.1252547658 0.2096984208 0.7869249786 -0.566645298149 +1403715288462142976.0000000000 1.9121929473 1.7355180048 1.5478850758 0.1258102255 0.2124098865 0.7863037582 -0.566374634985 +1403715288512143104.0000000000 1.9058247631 1.7303110704 1.5437388088 0.1266209977 0.2139891406 0.7855580212 -0.566634243573 +1403715288562142976.0000000000 1.8995180774 1.7259731342 1.5424826837 0.1260703703 0.2155376050 0.7855436471 -0.566189880725 +1403715288612143104.0000000000 1.8928766325 1.7223611924 1.5448359514 0.1249390691 0.2167954032 0.7850258396 -0.566678403856 +1403715288662142976.0000000000 1.8854868746 1.7188383632 1.5506320477 0.1240126290 0.2175994886 0.7852657905 -0.566241087009 +1403715288712143104.0000000000 1.8777157432 1.7159116886 1.5589713706 0.1241491050 0.2171064945 0.7851714006 -0.566531236108 +1403715288762142976.0000000000 1.8695895151 1.7134980871 1.5674716062 0.1261083820 0.2150774380 0.7862000141 -0.565444877416 +1403715288812143104.0000000000 1.8612485244 1.7116608834 1.5750220647 0.1273300030 0.2136246405 0.7869246043 -0.564713423318 +1403715288862142976.0000000000 1.8526681448 1.7102457658 1.5791680928 0.1299319078 0.2121700017 0.7877023742 -0.563583675601 +1403715288912143104.0000000000 1.8436825579 1.7091106106 1.5801363830 0.1338120914 0.2114420350 0.7881696140 -0.56229462878 +1403715288962142976.0000000000 1.8344136599 1.7079540179 1.5779129573 0.1376388664 0.2122791980 0.7881449897 -0.561088727135 +1403715289012143104.0000000000 1.8253301821 1.7073517581 1.5722660397 0.1405294765 0.2150142187 0.7882907708 -0.559122538141 +1403715289062142976.0000000000 1.8163236594 1.7068512777 1.5632558861 0.1434608390 0.2188913145 0.7880223744 -0.557248882933 +1403715289112143104.0000000000 1.8074579963 1.7063900737 1.5510699101 0.1474739099 0.2230900075 0.7875647254 -0.555179338373 +1403715289162142976.0000000000 1.7989207756 1.7058427054 1.5372140973 0.1519260475 0.2266191219 0.7871278701 -0.553165405537 +1403715289212143104.0000000000 1.7906146135 1.7049333556 1.5231072988 0.1563563426 0.2297298060 0.7863620637 -0.551735095137 +1403715289262142976.0000000000 1.7829376675 1.7039396054 1.5090403226 0.1596198825 0.2336605531 0.7857738300 -0.549985206271 +1403715289312143104.0000000000 1.7753567285 1.7028217632 1.4945444091 0.1642640063 0.2377396698 0.7850100197 -0.54795661749 +1403715289362142976.0000000000 1.7682289340 1.7017717599 1.4797502348 0.1692556357 0.2427388925 0.7836228707 -0.546228483712 +1403715289412143104.0000000000 1.7615374290 1.7001529968 1.4640949246 0.1734538389 0.2492848568 0.7823768746 -0.543743737473 +1403715289462142976.0000000000 1.7551333958 1.6980315838 1.4472901708 0.1774388988 0.2566996237 0.7808936081 -0.541133914351 +1403715289512143104.0000000000 1.7490854711 1.6954318376 1.4295750943 0.1817343567 0.2644429253 0.7795456069 -0.53791375672 +1403715289562142976.0000000000 1.7432751451 1.6921367814 1.4112371684 0.1861372703 0.2724863800 0.7774850700 -0.53537001715 +1403715289612143104.0000000000 1.7378542354 1.6880556601 1.3922760162 0.1899894535 0.2802918034 0.7758562136 -0.532341665084 +1403715289662142976.0000000000 1.7329123160 1.6833740161 1.3725482355 0.1932226253 0.2869171278 0.7751247313 -0.528701456127 +1403715289712143104.0000000000 1.7282864264 1.6776761498 1.3526988308 0.1948755760 0.2930342552 0.7739860650 -0.526402893628 +1403715289762142976.0000000000 1.7239715924 1.6712061317 1.3340048477 0.1975068562 0.2965058664 0.7728921416 -0.525083850859 +1403715289812143104.0000000000 1.7200589981 1.6638971561 1.3178194304 0.1986375326 0.2991752647 0.7720372584 -0.524400384509 +1403715289862142976.0000000000 1.7163952539 1.6556361795 1.3043737616 0.1990871036 0.3008410262 0.7709294819 -0.524906407029 +1403715289912143104.0000000000 1.7129596382 1.6462576459 1.2939202380 0.1978443208 0.3022275775 0.7699062035 -0.526080368378 +1403715289962142976.0000000000 1.7098653100 1.6364195484 1.2858651477 0.1967482164 0.3020579351 0.7703638716 -0.525918861108 +1403715290012143104.0000000000 1.7066954364 1.6256808994 1.2804295257 0.1952558211 0.3014136862 0.7709351098 -0.526007614569 +1403715290062142976.0000000000 1.7036011315 1.6143167124 1.2781227311 0.1941453711 0.2994147581 0.7713071394 -0.527013922268 +1403715290112143104.0000000000 1.7009052486 1.6023488342 1.2786677301 0.1938665221 0.2961994789 0.7711478583 -0.529162187697 +1403715290162142976.0000000000 1.6981277971 1.5895677431 1.2816420190 0.1925950716 0.2927868677 0.7720733674 -0.530175163417 +1403715290212143104.0000000000 1.6952146290 1.5762448100 1.2872983810 0.1913337880 0.2894186512 0.7744004144 -0.529086216064 +1403715290262142976.0000000000 1.6925910731 1.5623865758 1.2951692610 0.1886595523 0.2871608791 0.7768181929 -0.527730705954 +1403715290312143104.0000000000 1.6898561912 1.5470804028 1.3030530794 0.1858832378 0.2852582509 0.7788156368 -0.526802957535 +1403715290362142976.0000000000 1.6870910253 1.5306723466 1.3100544172 0.1828641601 0.2838320961 0.7809829297 -0.525419550152 +1403715290412143104.0000000000 1.6845627302 1.5133091783 1.3163757878 0.1784324410 0.2842073980 0.7826790474 -0.524215153999 +1403715290462142976.0000000000 1.6822581085 1.4952892534 1.3219407095 0.1750138265 0.2843279983 0.7843435259 -0.522812569987 +1403715290512143104.0000000000 1.6794317878 1.4762484468 1.3275023575 0.1731454934 0.2838883962 0.7840377043 -0.52413060864 +1403715290562142976.0000000000 1.6756990419 1.4560561861 1.3323093405 0.1732726357 0.2827923016 0.7832092798 -0.525916658685 +1403715290612143104.0000000000 1.6717776475 1.4349927461 1.3371168633 0.1727493127 0.2828707253 0.7810950893 -0.529180771764 +1403715290662142976.0000000000 1.6679601726 1.4134980474 1.3407444022 0.1717959297 0.2837656554 0.7800510106 -0.530550310732 +1403715290712143104.0000000000 1.6633397126 1.3913594183 1.3437962670 0.1738148449 0.2830478805 0.7781033489 -0.533129886136 +1403715290762142976.0000000000 1.6584884146 1.3688620816 1.3466266105 0.1761682211 0.2823616837 0.7760078165 -0.535769079147 +1403715290812143104.0000000000 1.6537571383 1.3461297908 1.3495233740 0.1768188491 0.2829038064 0.7739531084 -0.538235187321 +1403715290862142976.0000000000 1.6492972224 1.3232301041 1.3520677542 0.1758489795 0.2845175031 0.7728428387 -0.539296646954 +1403715290912143104.0000000000 1.6449540657 1.3002682799 1.3536729396 0.1755319792 0.2860568983 0.7725171616 -0.539052140632 +1403715290962142976.0000000000 1.6410693232 1.2772834447 1.3551010922 0.1745291645 0.2888682717 0.7707184356 -0.540451464343 +1403715291012143104.0000000000 1.6371140348 1.2542002216 1.3566496730 0.1728395916 0.2927963470 0.7680720601 -0.542643607964 +1403715291062142976.0000000000 1.6330249103 1.2311893254 1.3582517639 0.1701437920 0.2974230239 0.7652982798 -0.544893730829 +1403715291112143104.0000000000 1.6282170332 1.2086345705 1.3593251085 0.1676561380 0.3026740155 0.7629256784 -0.546099138431 +1403715291162142976.0000000000 1.6227236485 1.1866628030 1.3603361343 0.1655267641 0.3076783550 0.7602399862 -0.54769524696 +1403715291212143104.0000000000 1.6163945489 1.1657031863 1.3609666266 0.1647625080 0.3124461604 0.7577572101 -0.548666313342 +1403715291262142976.0000000000 1.6090166327 1.1458579113 1.3603750749 0.1652330452 0.3168490599 0.7556062334 -0.548966241311 +1403715291312143104.0000000000 1.6006954770 1.1273948292 1.3584400337 0.1667183193 0.3208210385 0.7540606397 -0.548335130113 +1403715291362142976.0000000000 1.5911849724 1.1099588079 1.3559216385 0.1689240267 0.3244669442 0.7523417176 -0.547875729847 +1403715291412143104.0000000000 1.5809177731 1.0936531249 1.3522772023 0.1709311061 0.3284015594 0.7513762898 -0.546231309826 +1403715291462142976.0000000000 1.5699136016 1.0784812035 1.3480414288 0.1735972400 0.3321412826 0.7506690135 -0.544097600496 +1403715291512143104.0000000000 1.5578822912 1.0645651259 1.3428986607 0.1768401490 0.3355122323 0.7512915983 -0.5401111349 +1403715291562142976.0000000000 1.5451225413 1.0517557284 1.3375842602 0.1791556302 0.3399423794 0.7510819540 -0.536859699798 +1403715291612143104.0000000000 1.5313026956 1.0397915578 1.3324113196 0.1808260888 0.3447006022 0.7504766578 -0.534105051879 +1403715291662142976.0000000000 1.5162515054 1.0283532707 1.3271929484 0.1822512057 0.3492489085 0.7494841746 -0.532055607943 +1403715291712143104.0000000000 1.4998683714 1.0176338931 1.3218215812 0.1834562000 0.3535672225 0.7487255741 -0.529852863146 +1403715291762142976.0000000000 1.4820672270 1.0074002802 1.3165763459 0.1879398292 0.3549034113 0.7488409552 -0.527218562983 +1403715291812143104.0000000000 1.4631854476 0.9975702855 1.3112678768 0.1932164735 0.3551172557 0.7490406447 -0.524878311221 +1403715291862142976.0000000000 1.4430003685 0.9881817322 1.3051281784 0.2016247889 0.3524170476 0.7505679760 -0.521341905482 +1403715291912143104.0000000000 1.4219174952 0.9786943764 1.2984352157 0.2092405646 0.3497737140 0.7520193192 -0.518018994485 +1403715291962142976.0000000000 1.4004531233 0.9687946320 1.2915717914 0.2130433775 0.3492258611 0.7527740837 -0.515737332452 +1403715292012143104.0000000000 1.3788005615 0.9586056628 1.2844653531 0.2163746104 0.3484119218 0.7537970847 -0.513401515177 +1403715292062142976.0000000000 1.3570540407 0.9475417854 1.2778207950 0.2182105530 0.3478182335 0.7543829323 -0.512165034448 +1403715292112143104.0000000000 1.3353298710 0.9354226388 1.2712907912 0.2177962408 0.3464082645 0.7552699795 -0.51198961893 +1403715292162142976.0000000000 1.3140035312 0.9227212078 1.2640676760 0.2161709270 0.3436425364 0.7569541838 -0.512054978582 +1403715292212143104.0000000000 1.2927571032 0.9091872278 1.2569925052 0.2141129083 0.3387042675 0.7592023893 -0.512880896324 +1403715292262142976.0000000000 1.2715375872 0.8946970231 1.2503071847 0.2108031555 0.3326475571 0.7621522921 -0.513839971239 +1403715292312143104.0000000000 1.2505350542 0.8795567170 1.2434281274 0.2065749384 0.3249281119 0.7659633284 -0.514828803102 +1403715292362142976.0000000000 1.2292904788 0.8635453950 1.2365950545 0.2030997020 0.3151834771 0.7701998915 -0.515947685311 +1403715292412143104.0000000000 1.2085311272 0.8463619974 1.2304088970 0.1976928242 0.3056726551 0.7737708006 -0.51842118337 +1403715292462142976.0000000000 1.1877315662 0.8280419658 1.2241829895 0.1918524959 0.2947767161 0.7788600588 -0.519303683948 +1403715292512143104.0000000000 1.1671101865 0.8084407733 1.2189486745 0.1851166171 0.2837958267 0.7817048643 -0.523573559247 +1403715292562142976.0000000000 1.1468849101 0.7879485760 1.2142572369 0.1785126709 0.2713211534 0.7833864059 -0.529928105516 +1403715292612143104.0000000000 1.1269183288 0.7666928240 1.2100113049 0.1729340414 0.2570960436 0.7846847873 -0.536903367672 +1403715292662142976.0000000000 1.1073167678 0.7447095540 1.2070625715 0.1685661011 0.2411350578 0.7840988508 -0.546468979607 +1403715292712143104.0000000000 1.0889602772 0.7227109690 1.2041499920 0.1628563795 0.2256630668 0.7852849721 -0.553065540939 +1403715292762142976.0000000000 1.0715990651 0.7004715905 1.2024424377 0.1573621819 0.2097249766 0.7861460591 -0.559666821967 +1403715292812143104.0000000000 1.0559552588 0.6785953910 1.2025008498 0.1505606732 0.1946258992 0.7877236349 -0.564751023101 +1403715292862142976.0000000000 1.0422170195 0.6571763618 1.2048833406 0.1424935048 0.1806686330 0.7907882975 -0.567193366192 +1403715292912143104.0000000000 1.0303537348 0.6360700737 1.2099210313 0.1324582419 0.1682180483 0.7952012246 -0.567285214597 +1403715292962142976.0000000000 1.0199755953 0.6151424188 1.2184110231 0.1201406880 0.1580593534 0.7990067417 -0.567601693631 +1403715293012143104.0000000000 1.0107296662 0.5945917079 1.2300511378 0.1078729633 0.1488279496 0.8011688627 -0.569510420119 +1403715293062142976.0000000000 1.0025560260 0.5744802673 1.2444716717 0.0958414624 0.1394690299 0.8030414463 -0.571390618811 +1403715293112143104.0000000000 0.9950738243 0.5544764210 1.2604086013 0.0841892051 0.1306176970 0.8040197921 -0.573936729031 +1403715293162142976.0000000000 0.9879464192 0.5348925495 1.2763377666 0.0736060275 0.1216615119 0.8056695104 -0.575045449768 +1403715293212143104.0000000000 0.9810819580 0.5158190454 1.2922273699 0.0643072609 0.1118245972 0.8073465985 -0.575804919649 +1403715293262142976.0000000000 0.9742774020 0.4968068283 1.3084566887 0.0550901637 0.1026408599 0.8076397642 -0.578055307886 +1403715293312143104.0000000000 0.9674180222 0.4780662184 1.3243704030 0.0479579745 0.0922009538 0.8075299098 -0.580598365149 +1403715293362142976.0000000000 0.9605690027 0.4599002688 1.3401932107 0.0410886907 0.0821307811 0.8067204539 -0.583753684034 +1403715293412143104.0000000000 0.9537529262 0.4423678129 1.3562430509 0.0334113563 0.0729939744 0.8046762886 -0.588261533327 +1403715293462142976.0000000000 0.9466186837 0.4259505582 1.3718814370 0.0268559018 0.0638599726 0.8033686509 -0.591438479677 +1403715293512143104.0000000000 0.9394401672 0.4109666754 1.3870681255 0.0204193679 0.0550588911 0.8041318242 -0.591543385715 +1403715293562142976.0000000000 0.9322773496 0.3970634867 1.4024011481 0.0137098770 0.0468336881 0.8053803117 -0.590746306352 +1403715293612143104.0000000000 0.9248842884 0.3840700880 1.4177503231 0.0076368863 0.0387618360 0.8074020803 -0.588677397802 +1403715293662142976.0000000000 0.9172762838 0.3718042163 1.4331866953 0.0021060169 0.0308339255 0.8100506613 -0.585544840153 +1403715293712143104.0000000000 0.9093522037 0.3601837617 1.4490278902 0.0031077465 -0.0227156179 -0.8118081146 0.583474016353 +1403715293762142976.0000000000 0.9010693822 0.3491434680 1.4648736616 0.0084393339 -0.0148206949 -0.8137400558 0.580978696893 +1403715293812143104.0000000000 0.8927153319 0.3385518173 1.4805119850 0.0133635337 -0.0065648366 -0.8150162519 0.57924677647 +1403715293862142976.0000000000 0.8844444839 0.3282250250 1.4960418873 0.0194155691 0.0010113281 -0.8161083885 0.577571736715 +1403715293912143104.0000000000 0.8761198468 0.3178718701 1.5111778407 0.0249159330 0.0092823368 -0.8171220947 0.575851123929 +1403715293962142976.0000000000 0.8676170960 0.3074055496 1.5257800740 0.0305020810 0.0179703806 -0.8171589453 0.575324209946 +1403715294012143104.0000000000 0.8590376471 0.2971437257 1.5380381397 0.0364947504 0.0269653540 -0.8167275294 0.575236599683 +1403715294062142976.0000000000 0.8504984983 0.2869224835 1.5468583878 0.0427536536 0.0362328732 -0.8161848840 0.575066551899 +1403715294112143104.0000000000 0.8419252163 0.2768348729 1.5527490669 0.0499184644 0.0450321587 -0.8145851658 0.576134757901 +1403715294162142976.0000000000 0.8331733958 0.2668897570 1.5556562238 0.0573054433 0.0536641612 -0.8123437939 0.577870058455 +1403715294212143104.0000000000 0.8243306306 0.2572888516 1.5554281952 0.0648014273 0.0622952851 -0.8099761345 0.579533203582 +1403715294262142976.0000000000 0.8154397225 0.2485167121 1.5519017366 0.0728822715 0.0707239416 -0.8079774645 0.580395309644 +1403715294312143104.0000000000 0.8061604045 0.2402570412 1.5448516255 0.0803807381 0.0794272673 -0.8060935103 0.580898871438 +1403715294362142976.0000000000 0.7963737963 0.2326635107 1.5342352178 0.0875466400 0.0884863445 -0.8047067216 0.58047639484 +1403715294412143104.0000000000 0.7862843866 0.2253141964 1.5214075061 0.0944442616 0.0978932849 -0.8027758604 0.580558441709 +1403715294462142976.0000000000 0.7755702528 0.2186475083 1.5074831480 0.1002746659 0.1079541588 -0.8010302716 0.580208061771 +1403715294512143104.0000000000 0.7644140228 0.2127556461 1.4933426014 0.1059413226 0.1183171162 -0.7993609594 0.579482141939 +1403715294562142976.0000000000 0.7529131959 0.2080066073 1.4787831373 0.1120588125 0.1286916613 -0.7993604410 0.576111242865 +1403715294612143104.0000000000 0.7409428968 0.2041064943 1.4641531291 0.1173699652 0.1398576592 -0.8000948023 0.571412665077 +1403715294662142976.0000000000 0.7284629853 0.2005328359 1.4495882941 0.1210384443 0.1521275004 -0.8004822803 0.566952412011 +1403715294712143104.0000000000 0.7160078133 0.1972090202 1.4350770707 0.1247717953 0.1644307147 -0.8008196096 0.562212141505 +1403715294762142976.0000000000 0.7036822478 0.1939203785 1.4207832329 0.1289854525 0.1760839369 -0.8003638131 0.558368128489 +1403715294812143104.0000000000 0.6918356340 0.1906252647 1.4068160459 0.1343464174 0.1867686824 -0.7994719264 0.554899214583 +1403715294862142976.0000000000 0.6804392643 0.1871086992 1.3927626344 0.1394411962 0.1973247227 -0.7978273804 0.552350049914 +1403715294912143104.0000000000 0.6699881224 0.1832288771 1.3791639043 0.1444868638 0.2076355547 -0.7953205147 0.550886831819 +1403715294962142976.0000000000 0.6603028052 0.1791353958 1.3664852736 0.1502429734 0.2172503880 -0.7912776008 0.551460856615 +1403715295012143104.0000000000 0.6515426804 0.1751014853 1.3542513407 0.1572063479 0.2257069988 -0.7871913427 0.551971289895 +1403715295062142976.0000000000 0.6435018451 0.1713982248 1.3420401787 0.1643393670 0.2339627490 -0.7836197284 0.551537964092 +1403715295112143104.0000000000 0.6361916437 0.1677906991 1.3308188380 0.1737106204 0.2407215108 -0.7794424182 0.551676799705 +1403715295162142976.0000000000 0.6290910149 0.1646064672 1.3204940131 0.1830827608 0.2469251618 -0.7751885414 0.551897991049 +1403715295212143104.0000000000 0.6220291087 0.1620539432 1.3113448331 0.1919226889 0.2535467647 -0.7709691039 0.551802827473 +1403715295262142976.0000000000 0.6146072386 0.1603023107 1.3045282967 0.2002635172 0.2605165853 -0.7677592211 0.5500649152 +1403715295312143104.0000000000 0.6069394630 0.1589444689 1.3012034524 0.2075144499 0.2690280980 -0.7643494794 0.548025098764 +1403715295362142976.0000000000 0.5988918549 0.1585188395 1.3006596405 0.2140470172 0.2794271782 -0.7620803793 0.543449926 +1403715295412143104.0000000000 0.5904224233 0.1583980966 1.3027798091 0.2202037819 0.2902781689 -0.7589623205 0.539652735782 +1403715295462142976.0000000000 0.5819593693 0.1584745031 1.3078508225 0.2266021040 0.3015110876 -0.7553943842 0.535837545249 +1403715295512143104.0000000000 0.5733557248 0.1586156230 1.3130842619 0.2324967636 0.3127301465 -0.7514239019 0.532453969904 +1403715295562142976.0000000000 0.5644558413 0.1584082944 1.3154944566 0.2364913773 0.3237805615 -0.7468262601 0.530554911086 +1403715295612143104.0000000000 0.5555309843 0.1583219988 1.3144502304 0.2407175885 0.3328138942 -0.7429032752 0.528568517828 +1403715295662142976.0000000000 0.5466425239 0.1581895458 1.3099359392 0.2444147556 0.3399880011 -0.7388013770 0.528055027221 +1403715295712143104.0000000000 0.5379628097 0.1583779957 1.3024750706 0.2483296983 0.3455142702 -0.7352615035 0.52758200451 +1403715295762142976.0000000000 0.5294595694 0.1592838585 1.2931555829 0.2525296758 0.3512423136 -0.7317929143 0.5266276964 +1403715295812143104.0000000000 0.5209238968 0.1610833775 1.2828379755 0.2587389336 0.3557705565 -0.7285304125 0.525095147063 +1403715295862142976.0000000000 0.5123641481 0.1634016900 1.2724062827 0.2654230246 0.3596426516 -0.7248022310 0.524279989182 +1403715295912143104.0000000000 0.5031285338 0.1664657634 1.2612145940 0.2718665926 0.3641645033 -0.7219057582 0.521847532047 +1403715295962142976.0000000000 0.4934920542 0.1697587125 1.2497416732 0.2793534595 0.3674019079 -0.7186810144 0.520072189411 +1403715296012143104.0000000000 0.4828842916 0.1733408193 1.2367567991 0.2858897200 0.3702728433 -0.7160738966 0.518076504195 +1403715296062142976.0000000000 0.4712440911 0.1770606852 1.2229633643 0.2921605335 0.3723861957 -0.7153879231 0.5139950033 +1403715296112143104.0000000000 0.4587285732 0.1808043204 1.2083672092 0.2969999210 0.3745448803 -0.7165385469 0.508015443015 +1403715296162142976.0000000000 0.4452240870 0.1844645874 1.1928690689 0.2996025088 0.3788712007 -0.7181597870 0.500940585731 +1403715296212143104.0000000000 0.4309568079 0.1875079905 1.1767820505 0.3008877923 0.3843295030 -0.7191821289 0.494504231475 +1403715296262142976.0000000000 0.4161012048 0.1897805322 1.1604214237 0.3021609526 0.3902483746 -0.7200760797 0.487745224811 +1403715296312143104.0000000000 0.4009049661 0.1911483086 1.1445888217 0.3017442217 0.3974890773 -0.7217166748 0.47966436112 +1403715296362142976.0000000000 0.3854514440 0.1913701791 1.1310547370 0.3006015869 0.4053985577 -0.7224483313 0.47260882763 +1403715296412143104.0000000000 0.3706630110 0.1903121173 1.1207857530 0.3019875692 0.4122344847 -0.7217096231 0.46690626201 +1403715296462142976.0000000000 0.3568817967 0.1875835991 1.1135825654 0.3055913386 0.4174623629 -0.7199732461 0.462577165788 +1403715296512143104.0000000000 0.3436776844 0.1832020541 1.1085918323 0.3091939076 0.4214817795 -0.7187039616 0.45849411408 +1403715296562142976.0000000000 0.3312487408 0.1768387623 1.1060328115 0.3117281299 0.4257760914 -0.7161105281 0.456865411893 +1403715296612143104.0000000000 0.3192263927 0.1686184122 1.1059275048 0.3123943656 0.4304513669 -0.7125965050 0.457523334996 +1403715296662142976.0000000000 0.3081422641 0.1589181199 1.1071910386 0.3136471859 0.4339496442 -0.7077624590 0.460852959895 +1403715296712143104.0000000000 0.2979003621 0.1479737428 1.1083519237 0.3149675390 0.4366907016 -0.7037707221 0.463468932322 +1403715296762142976.0000000000 0.2886220141 0.1359665154 1.1098569259 0.3166421032 0.4384630725 -0.7008819641 0.465029445232 +1403715296812143104.0000000000 0.2799771319 0.1232140070 1.1105766873 0.3168649938 0.4414531876 -0.6973090586 0.467413880475 +1403715296862142976.0000000000 0.2720340086 0.1098436684 1.1114537864 0.3167805268 0.4447571639 -0.6929953109 0.47074267067 +1403715296912143104.0000000000 0.2647443205 0.0967429117 1.1120061336 0.3173686109 0.4491278696 -0.6881629985 0.473278996929 +1403715296962142976.0000000000 0.2579840778 0.0840674257 1.1123286530 0.3192621506 0.4539095812 -0.6828655740 0.475113017197 +1403715297012143104.0000000000 0.2513080972 0.0724592726 1.1122165870 0.3231799076 0.4591630916 -0.6795079310 0.472221319245 +1403715297062142976.0000000000 0.2440054746 0.0621232897 1.1115481199 0.3286716519 0.4647738445 -0.6785497422 0.464252588631 +1403715297112143104.0000000000 0.2370142466 0.0520487838 1.1107203406 0.3347706864 0.4707435505 -0.6765442086 0.456746134157 +1403715297162142976.0000000000 0.2307707127 0.0418631553 1.1078363296 0.3394056100 0.4787890522 -0.6762162932 0.445304839621 +1403715297212143104.0000000000 0.2254327730 0.0312372274 1.1041970526 0.3436323658 0.4881857170 -0.6746219869 0.434139007238 +1403715297262142976.0000000000 0.2214239392 0.0199980099 1.1005249476 0.3495740817 0.4971587261 -0.6713198071 0.424217961837 +1403715297312143104.0000000000 0.2190768001 0.0074349746 1.0963477093 0.3561150799 0.5061160000 -0.6661895944 0.416197151139 +1403715297362142976.0000000000 0.2179893221 -0.0063064194 1.0910092255 0.3621653766 0.5152889283 -0.6600498181 0.409448162715 +1403715297412143104.0000000000 0.2183059658 -0.0216874407 1.0854357490 0.3673297746 0.5246355280 -0.6518143892 0.406158099079 +1403715297462142976.0000000000 0.2204396202 -0.0386013836 1.0800756367 0.3721429122 0.5331585893 -0.6441152991 0.402947953197 +1403715297512143104.0000000000 0.2244454958 -0.0567344726 1.0752149667 0.3765968349 0.5414844855 -0.6356891695 0.40108434988 +1403715297562142976.0000000000 0.2298919295 -0.0756278919 1.0702204882 0.3811949221 0.5484695637 -0.6293083939 0.397293989965 +1403715297612143104.0000000000 0.2366910930 -0.0949965484 1.0648197069 0.3852960526 0.5552310562 -0.6247943193 0.391021079709 +1403715297662142976.0000000000 0.2452858712 -0.1149093226 1.0595264453 0.3893908130 0.5611089787 -0.6212922221 0.384093066219 +1403715297712143104.0000000000 0.2554227491 -0.1353542988 1.0547363875 0.3947062439 0.5655789539 -0.6180479939 0.377285177589 +1403715297762142976.0000000000 0.2677489906 -0.1565208448 1.0502019653 0.4004708217 0.5695579752 -0.6143060764 0.371288133898 +1403715297812143104.0000000000 0.2824594688 -0.1787119445 1.0470329201 0.4083935297 0.5719206104 -0.6077937212 0.36974089943 +1403715297862142976.0000000000 0.2990178685 -0.2019954242 1.0450893022 0.4174226572 0.5736584347 -0.5999840985 0.369720714819 +1403715297912143104.0000000000 0.3172355516 -0.2263071084 1.0439018347 0.4263837382 0.5754552642 -0.5910987756 0.371012646928 +1403715297962142976.0000000000 0.3366012437 -0.2514992771 1.0437101380 0.4384113067 0.5752719512 -0.5811119407 0.373050426471 +1403715298012143104.0000000000 0.3556481189 -0.2776642377 1.0432872756 0.4496677893 0.5764017268 -0.5691994550 0.376260427079 +1403715298062142976.0000000000 0.3735453547 -0.3046425446 1.0425802554 0.4582684018 0.5801295096 -0.5568806025 0.378581323511 +1403715298112143104.0000000000 0.3904660449 -0.3327304358 1.0415640932 0.4633806958 0.5865444235 -0.5433078779 0.382178649222 +1403715298162142976.0000000000 0.4060114880 -0.3616055129 1.0393162676 0.4638019266 0.5966534644 -0.5297097651 0.385097365841 +1403715298212143104.0000000000 0.4197796549 -0.3910748950 1.0364641736 0.4615643600 0.6084900066 -0.5162471768 0.387539812025 +1403715298262142976.0000000000 0.4317068927 -0.4200169914 1.0339699510 0.4593285447 0.6201020047 -0.5035832060 0.388451729896 +1403715298312143104.0000000000 0.4418903855 -0.4481521510 1.0321879332 0.4577712864 0.6298483640 -0.4933579249 0.38772986161 +1403715298362142976.0000000000 0.4501885874 -0.4749309685 1.0304949117 0.4553013160 0.6389791997 -0.4860090851 0.384969431405 +1403715298412143104.0000000000 0.4566963632 -0.5000477568 1.0301370881 0.4528111592 0.6464992077 -0.4810072176 0.381618769393 +1403715298462142976.0000000000 0.4617309327 -0.5235749901 1.0305521834 0.4504114275 0.6526196371 -0.4771031225 0.37893240272 +1403715298512143104.0000000000 0.4659041211 -0.5452714958 1.0313094590 0.4478930433 0.6576692376 -0.4730998339 0.378205688636 +1403715298562142976.0000000000 0.4695096862 -0.5645691186 1.0326058637 0.4444261965 0.6621579545 -0.4689729534 0.379600537629 +1403715298612143104.0000000000 0.4722715903 -0.5810104761 1.0343697177 0.4412840226 0.6654887309 -0.4649088388 0.382430297 +1403715298662142976.0000000000 0.4737533527 -0.5945728488 1.0363800242 0.4386486067 0.6680872369 -0.4611607274 0.385457685449 +1403715298712143104.0000000000 0.4739461647 -0.6048261895 1.0391597228 0.4363834785 0.6697507029 -0.4587061403 0.388062021525 +1403715298762142976.0000000000 0.4726386300 -0.6113072600 1.0429077525 0.4354378215 0.6699881110 -0.4577213989 0.389872999438 +1403715298812143104.0000000000 0.4694269548 -0.6140627798 1.0474234203 0.4354179571 0.6695862564 -0.4596113960 0.38835912845 +1403715298862142976.0000000000 0.4639028827 -0.6130750703 1.0518562246 0.4367461413 0.6687951113 -0.4682183025 0.377806204821 +1403715298912143104.0000000000 0.4572695082 -0.6084197795 1.0569524362 0.4404051848 0.6672176368 -0.4782856285 0.363464930865 +1403715298962142976.0000000000 0.4500108468 -0.6013422121 1.0617524168 0.4445537357 0.6663068566 -0.4870515990 0.348120509104 +1403715299012143104.0000000000 0.4430472772 -0.5925285869 1.0661880247 0.4471874836 0.6672372924 -0.4919111518 0.335918396241 +1403715299062142976.0000000000 0.4367105728 -0.5823773151 1.0704204836 0.4502438480 0.6688009554 -0.4940235596 0.325463487856 +1403715299112143104.0000000000 0.4315734186 -0.5712672261 1.0747142184 0.4531949050 0.6712804808 -0.4931124374 0.31754845018 +1403715299162142976.0000000000 0.4279022998 -0.5592475043 1.0791800576 0.4562245898 0.6740739243 -0.4907037907 0.310955395691 +1403715299212143104.0000000000 0.4255673134 -0.5464115796 1.0834188532 0.4591826814 0.6775186295 -0.4868946046 0.305046579668 +1403715299262142976.0000000000 0.4246228688 -0.5329086247 1.0873058392 0.4618225848 0.6816537398 -0.4823767232 0.298966178822 +1403715299312143104.0000000000 0.4252003146 -0.5188547815 1.0913890235 0.4656884789 0.6854558307 -0.4766803897 0.293360445216 +1403715299362142976.0000000000 0.4273429226 -0.5044268357 1.0953360713 0.4691146593 0.6899298367 -0.4705046949 0.287321403614 +1403715299412143104.0000000000 0.4314105599 -0.4894025322 1.0997356046 0.4734272553 0.6941679155 -0.4635067519 0.281352145877 +1403715299462142976.0000000000 0.4374473879 -0.4741425832 1.1044092247 0.4779926046 0.6985957047 -0.4554418211 0.275789519413 +1403715299512143104.0000000000 0.4453824554 -0.4585202579 1.1094628715 0.4838450325 0.7024873184 -0.4463678163 0.270483501602 +1403715299562142976.0000000000 0.4545072716 -0.4426073701 1.1141928201 0.4895785246 0.7067648774 -0.4365610340 0.264973092868 +1403715299612143104.0000000000 0.4649886616 -0.4264408397 1.1185495916 0.4959116495 0.7106113528 -0.4257591901 0.260446257989 +1403715299662142976.0000000000 0.4760132738 -0.4100405229 1.1221165990 0.5013695063 0.7152337141 -0.4153547215 0.254066541951 +1403715299712143104.0000000000 0.4880470956 -0.3935771736 1.1255153344 0.5078049296 0.7190782329 -0.4047878316 0.247401414284 +1403715299762142976.0000000000 0.5010382226 -0.3772499532 1.1282538074 0.5120765081 0.7246600198 -0.3935367518 0.240362914336 +1403715299812143104.0000000000 0.5148332218 -0.3610349596 1.1308632535 0.5180235461 0.7290417313 -0.3821119258 0.232680544625 +1403715299862142976.0000000000 0.5292678915 -0.3453404030 1.1322061541 0.5227785278 0.7341799384 -0.3705951826 0.224369426374 +1403715299912143104.0000000000 0.5445277709 -0.3298755634 1.1335963481 0.5276822246 0.7390631130 -0.3578259339 0.217480541352 +1403715299962142976.0000000000 0.5604343924 -0.3145165552 1.1349070574 0.5325363525 0.7435931443 -0.3452045826 0.210494810402 +1403715300012143104.0000000000 0.5771176828 -0.2994723706 1.1358597856 0.5360198330 0.7481182730 -0.3338438314 0.203838378221 +1403715300062142976.0000000000 0.5948805589 -0.2845191726 1.1373680676 0.5417860836 0.7501092644 -0.3219652154 0.200355511967 +1403715300112143104.0000000000 0.6131748003 -0.2702616788 1.1387444903 0.5473920009 0.7510535435 -0.3120915422 0.197178704153 +1403715300162142976.0000000000 0.6319931373 -0.2568482190 1.1394472931 0.5510953551 0.7524614353 -0.3018940262 0.197371971015 +1403715300212143104.0000000000 0.6510831099 -0.2440709369 1.1397180953 0.5531666147 0.7542448993 -0.2916205591 0.200196847879 +1403715300262142976.0000000000 0.6697352396 -0.2315736004 1.1404935470 0.5567497056 0.7541522349 -0.2833778187 0.202438098761 +1403715300312143104.0000000000 0.6872230049 -0.2194970091 1.1418478169 0.5608014604 0.7531194567 -0.2792977124 0.200762530719 +1403715300362142976.0000000000 0.7038047689 -0.2079327387 1.1434948880 0.5649333761 0.7514647942 -0.2772652264 0.198179055153 +1403715300412143104.0000000000 0.7194615743 -0.1969947285 1.1456824827 0.5683244355 0.7499963636 -0.2770298508 0.194337985123 +1403715300462142976.0000000000 0.7342882534 -0.1872534022 1.1477421001 0.5709611796 0.7485601084 -0.2778121820 0.191001275007 +1403715300512143104.0000000000 0.7482412903 -0.1788766302 1.1496433283 0.5720139050 0.7480692628 -0.2779213584 0.189610624915 +1403715300562142976.0000000000 0.7613670289 -0.1718386574 1.1513588514 0.5722708013 0.7478077419 -0.2794431109 0.187619985127 +1403715300612143104.0000000000 0.7737781721 -0.1662096659 1.1528116572 0.5713782790 0.7481922024 -0.2810670335 0.186377608947 +1403715300662142976.0000000000 0.7857047141 -0.1619551659 1.1540864215 0.5705489564 0.7483627609 -0.2827331823 0.185712180758 +1403715300712143104.0000000000 0.7971048730 -0.1589839515 1.1557124673 0.5697213703 0.7483709452 -0.2850980154 0.184601219558 +1403715300762142976.0000000000 0.8080484004 -0.1575134829 1.1575024253 0.5694053134 0.7478134815 -0.2869740491 0.184928313503 +1403715300812143104.0000000000 0.8186188489 -0.1575058344 1.1589401247 0.5691133372 0.7472851082 -0.2876714949 0.186869172403 +1403715300862142976.0000000000 0.8289377036 -0.1587952619 1.1601525535 0.5684234641 0.7470382191 -0.2873568296 0.190406714947 +1403715300912143104.0000000000 0.8385764546 -0.1614978985 1.1607590918 0.5671067918 0.7472718915 -0.2865129021 0.194640601862 +1403715300962142976.0000000000 0.8474533322 -0.1654583492 1.1612236718 0.5657690531 0.7475397670 -0.2856390764 0.198746052308 +1403715301012143104.0000000000 0.8554099166 -0.1703138451 1.1614982089 0.5647320256 0.7476048062 -0.2851390993 0.202139771416 +1403715301062142976.0000000000 0.8623517125 -0.1758769691 1.1614812625 0.5642952498 0.7471462919 -0.2845276926 0.205881717697 +1403715301112143104.0000000000 0.8682535223 -0.1822934073 1.1614811545 0.5647474607 0.7459519809 -0.2835654372 0.210253634045 +1403715301162142976.0000000000 0.8728616401 -0.1893167543 1.1611331782 0.5651339734 0.7449247354 -0.2819609442 0.214962221579 +1403715301212143104.0000000000 0.8759189032 -0.1973204775 1.1604720289 0.5655365956 0.7438228631 -0.2802458758 0.219904880741 +1403715301262142976.0000000000 0.8769824969 -0.2061239323 1.1593166529 0.5652803937 0.7434920066 -0.2784778827 0.2238923434 +1403715301312143104.0000000000 0.8757565311 -0.2154081870 1.1577725099 0.5655457663 0.7430239279 -0.2768850215 0.226733574163 +1403715301362142976.0000000000 0.8719825161 -0.2253519579 1.1557351959 0.5656048061 0.7428050064 -0.2763035779 0.228009339031 +1403715301412143104.0000000000 0.8657228819 -0.2357759883 1.1530098528 0.5650364703 0.7432750279 -0.2768518104 0.227220367328 +1403715301462142976.0000000000 0.8570390027 -0.2466123159 1.1500373331 0.5649014041 0.7436535400 -0.2797589173 0.222712290481 +1403715301512143104.0000000000 0.8463008815 -0.2582119651 1.1460559512 0.5625368327 0.7457421260 -0.2841790788 0.216016769266 +1403715301562142976.0000000000 0.8340447944 -0.2704715854 1.1409667420 0.5583239732 0.7490204278 -0.2887604669 0.209428108079 +1403715301612143104.0000000000 0.8207356077 -0.2831553962 1.1354868838 0.5536211163 0.7523739078 -0.2932639487 0.20355200503 +1403715301662142976.0000000000 0.8069254136 -0.2961330760 1.1297523543 0.5501977562 0.7545549334 -0.2974800255 0.198582265001 +1403715301712143104.0000000000 0.7930824073 -0.3096503990 1.1234771540 0.5475547925 0.7559904783 -0.3000822190 0.196501419405 +1403715301762142976.0000000000 0.7793323208 -0.3237184960 1.1164893334 0.5453416588 0.7569843079 -0.3011717387 0.197161904376 +1403715301812143104.0000000000 0.7658145417 -0.3380669525 1.1094719042 0.5443556749 0.7572013021 -0.2998158611 0.20108092088 +1403715301862142976.0000000000 0.7520351923 -0.3522179299 1.1024510646 0.5434113042 0.7573148615 -0.2982334306 0.205511984895 +1403715301912143104.0000000000 0.7376578151 -0.3662577297 1.0957041858 0.5421935754 0.7575535986 -0.2974963057 0.208889014043 +1403715301962142976.0000000000 0.7225287806 -0.3801955630 1.0897859302 0.5412888658 0.7576432375 -0.2986090776 0.209322018144 +1403715302012143104.0000000000 0.7069947055 -0.3938921328 1.0847249175 0.5405891601 0.7575317714 -0.2983633091 0.211868617287 +1403715302062142976.0000000000 0.6906410499 -0.4074144599 1.0801097527 0.5395307334 0.7576734426 -0.2983427998 0.214077359735 +1403715302112143104.0000000000 0.6734506858 -0.4206971116 1.0757295824 0.5374291043 0.7586102612 -0.2988082249 0.215392837061 +1403715302162142976.0000000000 0.6552373086 -0.4337461054 1.0716332188 0.5339987718 0.7604339259 -0.2996184702 0.216366190297 +1403715302212143104.0000000000 0.6362702221 -0.4463900664 1.0681207981 0.5309548659 0.7618305373 -0.3008000679 0.217302742461 +1403715302262142976.0000000000 0.6166098670 -0.4581317537 1.0648647150 0.5273444574 0.7635242270 -0.3023869470 0.217946581076 +1403715302312143104.0000000000 0.5967465322 -0.4686524692 1.0624435141 0.5243159902 0.7647875727 -0.3032543485 0.219612183337 +1403715302362142976.0000000000 0.5763807697 -0.4778133893 1.0609596562 0.5223682152 0.7651114185 -0.3044353083 0.221483877753 +1403715302412143104.0000000000 0.5554391808 -0.4857043898 1.0601189096 0.5213496960 0.7648376638 -0.3053522502 0.223557253809 +1403715302462142976.0000000000 0.5338229689 -0.4922908570 1.0602338768 0.5218203827 0.7635152642 -0.3082120703 0.223054363988 +1403715302512143104.0000000000 0.5112363057 -0.4976375964 1.0613887620 0.5231339641 0.7616685002 -0.3133704786 0.219068241985 +1403715302562142976.0000000000 0.4884266894 -0.5021172262 1.0627012428 0.5231812051 0.7606788999 -0.3183776354 0.21513883708 +1403715302612143104.0000000000 0.4653280970 -0.5059656866 1.0639434385 0.5237535790 0.7594662640 -0.3228582964 0.211318960116 +1403715302662142976.0000000000 0.4422051487 -0.5095982239 1.0646574486 0.5228292667 0.7593161758 -0.3258048314 0.209618021321 +1403715302712143104.0000000000 0.4193765211 -0.5125102317 1.0653120237 0.5225761341 0.7588039258 -0.3294977083 0.206305711334 +1403715302762142976.0000000000 0.3969883159 -0.5150468979 1.0648532717 0.5213227005 0.7591418521 -0.3321122351 0.204028805956 +1403715302812143104.0000000000 0.3752239808 -0.5170603636 1.0629913427 0.5189462958 0.7603810406 -0.3348128919 0.201036669629 +1403715302862142976.0000000000 0.3547203815 -0.5183793847 1.0600633267 0.5156875296 0.7624383680 -0.3360967233 0.199482077637 +1403715302912143104.0000000000 0.3351095060 -0.5185837339 1.0567873808 0.5134327420 0.7645721199 -0.3364862096 0.19645183551 +1403715302962142976.0000000000 0.3164157153 -0.5179438740 1.0537254827 0.5118850939 0.7671880344 -0.3348080040 0.193131486179 +1403715303012143104.0000000000 0.2989442032 -0.5164349376 1.0504085433 0.5105990563 0.7705269674 -0.3308751661 0.189995843796 +1403715303062142976.0000000000 0.2827229118 -0.5138085066 1.0470653571 0.5104456865 0.7738011081 -0.3259104396 0.185632517486 +1403715303112143104.0000000000 0.2678011914 -0.5101230997 1.0433377722 0.5108048868 0.7776777865 -0.3186735893 0.180949638035 +1403715303162142976.0000000000 0.2541439527 -0.5049708176 1.0395678074 0.5124268012 0.7814058230 -0.3093923413 0.176352182751 +1403715303212143104.0000000000 0.2416588721 -0.4983226677 1.0363543102 0.5161249713 0.7843373316 -0.2984176870 0.171396757132 +1403715303262142976.0000000000 0.2303401929 -0.4902713539 1.0342498096 0.5226332273 0.7857859193 -0.2855131961 0.166964707915 +1403715303312143104.0000000000 0.2199331639 -0.4810998620 1.0323775594 0.5295430019 0.7871182710 -0.2709233394 0.163185724775 +1403715303362142976.0000000000 0.2101016968 -0.4710584388 1.0305043930 0.5359606365 0.7886952649 -0.2554313621 0.159564390091 +1403715303412143104.0000000000 0.2007669599 -0.4604046914 1.0288920340 0.5416591065 0.7903623271 -0.2402277198 0.155638834861 +1403715303462142976.0000000000 0.1912635942 -0.4490004311 1.0271903373 0.5460608227 0.7926000400 -0.2256110679 0.150673158054 +1403715303512143104.0000000000 0.1810716091 -0.4370632605 1.0254960481 0.5497446733 0.7950268813 -0.2122567068 0.143736364844 +1403715303562142976.0000000000 0.1706710627 -0.4246314078 1.0239379943 0.5534558317 0.7970619179 -0.1980236695 0.138439761717 +1403715303612143104.0000000000 0.1592834604 -0.4117619739 1.0229261118 0.5572758252 0.7987950073 -0.1867506007 0.128430541552 +1403715303662142976.0000000000 0.1474851464 -0.3983560823 1.0224023616 0.5625664481 0.7991901167 -0.1758441883 0.117868444975 +1403715303712143104.0000000000 0.1351757335 -0.3849235306 1.0217327896 0.5666474775 0.8001047825 -0.1652854168 0.10688173021 +1403715303762142976.0000000000 0.1224595561 -0.3717279359 1.0212045095 0.5711164823 0.8003876877 -0.1550961077 0.0956593457116 +1403715303812143104.0000000000 0.1095504583 -0.3588903245 1.0203460027 0.5751497161 0.8006464151 -0.1440813058 0.0860738013221 +1403715303862142976.0000000000 0.0965250712 -0.3464838194 1.0198577864 0.5799004975 0.7999460968 -0.1343814043 0.0757845194885 +1403715303912143104.0000000000 0.0835667775 -0.3347680701 1.0191928179 0.5836010064 0.7994234073 -0.1257828191 0.0671622181696 +1403715303962142976.0000000000 0.0711036971 -0.3235086883 1.0183876622 0.5863808779 0.7990565237 -0.1183411820 0.0605103510314 +1403715304012143104.0000000000 0.0590008035 -0.3131597475 1.0171664340 0.5881046650 0.7990792964 -0.1122949722 0.0547267777588 +1403715304062142976.0000000000 0.0473255125 -0.3035785788 1.0155952664 0.5894628270 0.7990392043 -0.1074590773 0.050224220271 +1403715304112143104.0000000000 0.0361084633 -0.2950426600 1.0139805173 0.5909046614 0.7986152201 -0.1047128352 0.0456139622996 +1403715304162142976.0000000000 0.0256072137 -0.2875791185 1.0123526147 0.5924764103 0.7979246219 -0.1024150536 0.0424164796747 +1403715304212143104.0000000000 0.0157703032 -0.2814947785 1.0099798730 0.5922857531 0.7983806252 -0.1008727426 0.0401329514859 +1403715304262142976.0000000000 0.0065173170 -0.2764139389 1.0070252938 0.5911665623 0.7993799495 -0.1002086907 0.0383667859803 +1403715304312143104.0000000000 -0.0021557085 -0.2721351191 1.0037605633 0.5894357053 0.8007491387 -0.0998955450 0.0372457545273 +1403715304362142976.0000000000 -0.0101600462 -0.2685031368 0.9999470873 0.5877716392 0.8019384687 -0.1003002052 0.0368654495442 +1403715304412143104.0000000000 -0.0174863747 -0.2658398766 0.9955298642 0.5858792525 0.8032274798 -0.1009800787 0.0370694050948 +1403715304462142976.0000000000 -0.0239578971 -0.2637681024 0.9907398872 0.5844905428 0.8040617431 -0.1018462994 0.0385077900249 +1403715304512143104.0000000000 -0.0295573369 -0.2622121842 0.9846625931 0.5844801162 0.8039126858 -0.1014367096 0.0426377918265 +1403715304562142976.0000000000 -0.0348464706 -0.2610491813 0.9755503027 0.5838784301 0.8041216818 -0.1016053150 0.046375204838 +1403715304612143104.0000000000 -0.0399136325 -0.2601516002 0.9639054880 0.5836097684 0.8040587452 -0.1019815336 0.0498892707311 +1403715304662142976.0000000000 -0.0450742052 -0.2598008805 0.9510757932 0.5844644438 0.8031249753 -0.1033757338 0.0520100536194 +1403715304712143104.0000000000 -0.0502984690 -0.2601078375 0.9374495035 0.5845704286 0.8027314251 -0.1046165607 0.0543603568058 +1403715304762142976.0000000000 -0.0554447895 -0.2609016988 0.9236224064 0.5834436923 0.8032378737 -0.1054360250 0.0573203340484 +1403715304812143104.0000000000 -0.0608310122 -0.2625544659 0.9116133418 0.5827890244 0.8034391518 -0.1065570448 0.0590599578316 +1403715304862142976.0000000000 -0.0662962563 -0.2646535225 0.9024618920 0.5814576648 0.8041431979 -0.1076013605 0.0606848293541 +1403715304912143104.0000000000 -0.0717120227 -0.2666691550 0.8965306693 0.5803857756 0.8046938955 -0.1082220093 0.0625146601186 +1403715304962142976.0000000000 -0.0772483031 -0.2689096789 0.8942213114 0.5790308498 0.8055048088 -0.1091564868 0.0630090418062 +1403715305012143104.0000000000 -0.0830298070 -0.2714103321 0.8949320852 0.5785898622 0.8057230500 -0.1095646389 0.0635588537754 +1403715305062142976.0000000000 -0.0892376971 -0.2741601641 0.8979712571 0.5776289391 0.8063390404 -0.1106095102 0.0626713408457 +1403715305112143104.0000000000 -0.0956596721 -0.2769429803 0.9030141444 0.5772534209 0.8065744203 -0.1111505663 0.0621429335597 +1403715305162142976.0000000000 -0.1023414737 -0.2797277246 0.9085421107 0.5762481808 0.8073069820 -0.1113390368 0.0616205301172 +1403715305212143104.0000000000 -0.1089567228 -0.2824567753 0.9135216624 0.5748322428 0.8083647955 -0.1118825446 0.0599712126936 +1403715305262142976.0000000000 -0.1153120056 -0.2847993816 0.9179818845 0.5740494117 0.8089701148 -0.1122306145 0.0586422665759 +1403715305312143104.0000000000 -0.1213932625 -0.2872480586 0.9217958377 0.5734668270 0.8095150828 -0.1113615708 0.0584784533337 +1403715305362142976.0000000000 -0.1276232156 -0.2895700617 0.9253218316 0.5724811812 0.8103544065 -0.1112904226 0.0566169137054 +1403715305412143104.0000000000 -0.1336286976 -0.2916579816 0.9288774165 0.5719828109 0.8109225340 -0.1097268413 0.0565714431039 +1403715305462142976.0000000000 -0.1396285235 -0.2935225701 0.9338726590 0.5726697165 0.8107331668 -0.1080006136 0.0556506563907 +1403715305512143104.0000000000 -0.1454120031 -0.2955412319 0.9418285024 0.5738945510 0.8101710979 -0.1066857060 0.053721471353 +1403715305562142976.0000000000 -0.1509416329 -0.2975573445 0.9529061788 0.5745445088 0.8100816680 -0.1044752396 0.0524521017202 +1403715305612143104.0000000000 -0.1562248044 -0.2997084530 0.9670251386 0.5743775367 0.8105907037 -0.1022244002 0.0508264527206 +1403715305662142976.0000000000 -0.1614047200 -0.3015038378 0.9849225540 0.5754528258 0.8102064939 -0.0999677730 0.0492536995934 +1403715305712143104.0000000000 -0.1665816209 -0.3031136155 1.0053670792 0.5757576124 0.8102423980 -0.0997811765 0.0453226772017 +1403715305762142976.0000000000 -0.1711883750 -0.3048261676 1.0270124372 0.5763815388 0.8100850939 -0.0981784458 0.0436744221184 +1403715305812143104.0000000000 -0.1752741856 -0.3065721400 1.0484597892 0.5764244196 0.8102707045 -0.0971883139 0.0418414340017 +1403715305862142976.0000000000 -0.1786570794 -0.3082030436 1.0690596384 0.5760205063 0.8107596884 -0.0956142959 0.0415573140956 +1403715305912143104.0000000000 -0.1816835772 -0.3098798555 1.0888872063 0.5750803250 0.8115634478 -0.0945791780 0.0412573529669 +1403715305962142976.0000000000 -0.1841371668 -0.3109189557 1.1082452089 0.5748014928 0.8118545245 -0.0937501906 0.0413083124718 +1403715306012143104.0000000000 -0.1863141656 -0.3116741579 1.1265225783 0.5743444106 0.8122324646 -0.0933258440 0.0411971881994 +1403715306062142976.0000000000 -0.1880069537 -0.3124145154 1.1434532556 0.5731750783 0.8130984276 -0.0926956494 0.0418185761116 +1403715306112143104.0000000000 -0.1894430906 -0.3129779536 1.1593862844 0.5714783357 0.8142894652 -0.0929033297 0.0414022948915 +1403715306162142976.0000000000 -0.1907309274 -0.3130606449 1.1751154188 0.5710620474 0.8144789441 -0.0952491271 0.0379445850454 +1403715306212143104.0000000000 -0.1912513779 -0.3124447884 1.1907506415 0.5728361892 0.8129220922 -0.0992364228 0.0341833980464 +1403715306262142976.0000000000 -0.1905859933 -0.3116183976 1.2059189506 0.5756699871 0.8104120107 -0.1043390275 0.0308189258103 +1403715306312143104.0000000000 -0.1886459423 -0.3108074938 1.2205105170 0.5794408626 0.8069265995 -0.1111821840 0.0275003970024 +1403715306362142976.0000000000 -0.1851983727 -0.3101366562 1.2349753502 0.5831950156 0.8032426291 -0.1184118129 0.0257583988874 +1403715306412143104.0000000000 -0.1797537034 -0.3098923523 1.2494962596 0.5881945224 0.7984211533 -0.1260557541 0.0257062741129 +1403715306462142976.0000000000 -0.1721258602 -0.3103854066 1.2636422937 0.5916955533 0.7945047763 -0.1336795843 0.0280767055996 +1403715306512143104.0000000000 -0.1623330804 -0.3122097886 1.2769023659 0.5942008767 0.7911835212 -0.1409010156 0.0331791758588 +1403715306562142976.0000000000 -0.1503928290 -0.3154262844 1.2897858799 0.5961854075 0.7880341326 -0.1481443281 0.0402296381946 +1403715306612143104.0000000000 -0.1363198617 -0.3200137191 1.3029922627 0.5988639490 0.7839924546 -0.1561743688 0.048242805657 +1403715306662142976.0000000000 -0.1203960620 -0.3263309992 1.3162405672 0.6011747709 0.7799534026 -0.1639371053 0.0581911511122 +1403715306712143104.0000000000 -0.1030017024 -0.3349051541 1.3289685141 0.6023080967 0.7765873604 -0.1707824239 0.0705010072505 +1403715306762142976.0000000000 -0.0845377580 -0.3460055320 1.3409339813 0.6022202402 0.7737816304 -0.1773513383 0.0844942222474 +1403715306812143104.0000000000 -0.0654871329 -0.3594817908 1.3534287066 0.6040390404 0.7690132590 -0.1845556591 0.0984614337695 +1403715306862142976.0000000000 -0.0462693960 -0.3752786174 1.3656277958 0.6055226001 0.7640536211 -0.1917629690 0.113099109161 +1403715306912143104.0000000000 -0.0272681477 -0.3934976390 1.3763955344 0.6048714651 0.7603006797 -0.1983944386 0.12927889916 +1403715306962142976.0000000000 -0.0089753776 -0.4138135471 1.3863779301 0.6014316720 0.7583411134 -0.2044781417 0.146244279073 +1403715307012143104.0000000000 0.0082565999 -0.4360875808 1.3947907887 0.5963438120 0.7571429895 -0.2100184834 0.164319164995 +1403715307062142976.0000000000 0.0234745990 -0.4605661498 1.4003616960 0.5900089157 0.7565315545 -0.2166384142 0.180602557845 +1403715307112143104.0000000000 0.0362378842 -0.4867911555 1.4020992244 0.5817139186 0.7572862150 -0.2249019396 0.193766929722 +1403715307162142976.0000000000 0.0465421070 -0.5140306426 1.3997017520 0.5715307670 0.7592279659 -0.2340877016 0.205252103772 +1403715307212143104.0000000000 0.0543000466 -0.5417547679 1.3944469740 0.5618628387 0.7605607156 -0.2435340635 0.215751496389 +1403715307262142976.0000000000 0.0594535690 -0.5695402527 1.3863168262 0.5520851338 0.7618311320 -0.2526691969 0.225773355931 +1403715307312143104.0000000000 0.0620099115 -0.5968420391 1.3759122545 0.5436877263 0.7620034334 -0.2630298658 0.233601612693 +1403715307362142976.0000000000 0.0618571057 -0.6231999343 1.3640296871 0.5359459396 0.7618147402 -0.2753993756 0.237813867112 +1403715307412143104.0000000000 0.0591606709 -0.6480268434 1.3520000987 0.5295387223 0.7607525019 -0.2908584564 0.237161824061 +1403715307462142976.0000000000 0.0545947103 -0.6716309732 1.3400569885 0.5245053941 0.7586352134 -0.3061694246 0.235853742777 +1403715307512143104.0000000000 0.0488044876 -0.6942981680 1.3281716520 0.5199875761 0.7561323356 -0.3203652936 0.235038061686 +1403715307562142976.0000000000 0.0423444109 -0.7157313751 1.3164582454 0.5162523216 0.7529069147 -0.3340567436 0.234565151332 +1403715307612143104.0000000000 0.0357724605 -0.7359011525 1.3047657187 0.5129030662 0.7492786555 -0.3466333606 0.235281224169 +1403715307662142976.0000000000 0.0294697476 -0.7553081486 1.2931177568 0.5094378858 0.7453815187 -0.3585115084 0.237379296441 +1403715307712143104.0000000000 0.0235195972 -0.7741617331 1.2805988092 0.5046934769 0.7419190944 -0.3695536193 0.241393194126 +1403715307762142976.0000000000 0.0180066918 -0.7926982807 1.2675711456 0.4999626500 0.7380780273 -0.3796258290 0.247310339824 +1403715307812143104.0000000000 0.0132377213 -0.8104807570 1.2540930800 0.4948095443 0.7340862467 -0.3894719856 0.254150486391 +1403715307862142976.0000000000 0.0088629645 -0.8274737125 1.2405143061 0.4899273451 0.7297056687 -0.3990390422 0.261282751887 +1403715307912143104.0000000000 0.0049304458 -0.8435334781 1.2268254184 0.4845220495 0.7255728920 -0.4081849713 0.268639891252 +1403715307962142976.0000000000 0.0015657124 -0.8585712201 1.2131699306 0.4795502231 0.7209922512 -0.4168605617 0.276458006518 +1403715308012143104.0000000000 -0.0011504484 -0.8725474485 1.1995587286 0.4750704189 0.7158323748 -0.4255783828 0.28420969071 +1403715308062142976.0000000000 -0.0032909902 -0.8853344399 1.1862331494 0.4706136702 0.7105707383 -0.4343772081 0.291424845257 +1403715308112143104.0000000000 -0.0048990995 -0.8968882863 1.1731662543 0.4662887287 0.7052163961 -0.4429810640 0.298349514973 +1403715308162142976.0000000000 -0.0060472788 -0.9072184403 1.1603766153 0.4620166655 0.7004597144 -0.4507714293 0.304469879965 +1403715308212143104.0000000000 -0.0067436714 -0.9162464139 1.1477994556 0.4587009954 0.6957990856 -0.4574103272 0.310214154976 +1403715308262142976.0000000000 -0.0071188496 -0.9240006284 1.1350635457 0.4551635824 0.6913050916 -0.4644507058 0.314974483785 +1403715308312143104.0000000000 -0.0071358746 -0.9305248579 1.1222485858 0.4514218591 0.6870254042 -0.4707909430 0.320265962938 +1403715308362142976.0000000000 -0.0067897878 -0.9354738294 1.1098820053 0.4490006638 0.6822942286 -0.4769763980 0.32460207219 +1403715308412143104.0000000000 -0.0063913091 -0.9389593459 1.0975246586 0.4467948865 0.6782012712 -0.4831586527 0.327070453497 +1403715308462142976.0000000000 -0.0056747870 -0.9409618162 1.0853819736 0.4459634150 0.6741957699 -0.4885442916 0.328483137372 +1403715308512143104.0000000000 -0.0045091218 -0.9414694569 1.0742301049 0.4464839236 0.6702397813 -0.4933967902 0.32861885054 +1403715308562142976.0000000000 -0.0027801408 -0.9406367334 1.0652831943 0.4473478755 0.6670230452 -0.4977163274 0.327473041536 +1403715308612143104.0000000000 -0.0003152682 -0.9391406321 1.0589446685 0.4482149983 0.6645511696 -0.5012133436 0.325975831222 +1403715308662142976.0000000000 0.0031284590 -0.9373630595 1.0552543784 0.4490718902 0.6627185401 -0.5034001047 0.325156744703 +1403715308712143104.0000000000 0.0075078605 -0.9352144644 1.0540578189 0.4494459717 0.6615527149 -0.5056522125 0.323515322504 +1403715308762142976.0000000000 0.0130057297 -0.9328774652 1.0556327868 0.4499356650 0.6608076913 -0.5066996993 0.322717379675 +1403715308812143104.0000000000 0.0194924541 -0.9304131447 1.0593660684 0.4495831365 0.6610039101 -0.5073908417 0.321719393136 +1403715308862142976.0000000000 0.0270330588 -0.9278280638 1.0646372224 0.4497782836 0.6609910274 -0.5085020738 0.319712367973 +1403715308912143104.0000000000 0.0354503664 -0.9252252378 1.0699558225 0.4505273961 0.6609963925 -0.5093595752 0.317272213623 +1403715308962142976.0000000000 0.0452969135 -0.9224921493 1.0753468077 0.4524502112 0.6604863314 -0.5093118026 0.31567087322 +1403715309012143104.0000000000 0.0564099459 -0.9196379939 1.0807003560 0.4555624435 0.6596632423 -0.5085443169 0.31414955764 +1403715309062142976.0000000000 0.0687716427 -0.9168412364 1.0860756431 0.4600762029 0.6580250971 -0.5076634196 0.312427130053 +1403715309112143104.0000000000 0.0818673396 -0.9144801118 1.0909634680 0.4643267244 0.6567258263 -0.5070155603 0.30991467142 +1403715309162142976.0000000000 0.0958034730 -0.9127066092 1.0954149779 0.4686863826 0.6556708273 -0.5053738776 0.308263012455 +1403715309212143104.0000000000 0.1105174813 -0.9114517980 1.1003089585 0.4753175028 0.6530291318 -0.5036134349 0.306593758525 +1403715309262142976.0000000000 0.1261179723 -0.9110947539 1.1056632198 0.4838618278 0.6489633365 -0.5007028690 0.306628368579 +1403715309312143104.0000000000 0.1419069203 -0.9122173631 1.1104694810 0.4910482151 0.6460670721 -0.4969145256 0.307481614109 +1403715309362142976.0000000000 0.1575916281 -0.9149795190 1.1137730465 0.4932520820 0.6468567910 -0.4926993960 0.309072775784 +1403715309412143104.0000000000 0.1730292240 -0.9192162391 1.1161818875 0.4925110551 0.6499016475 -0.4880547377 0.311228665369 +1403715309462142976.0000000000 0.1881501587 -0.9246816563 1.1185269647 0.4903257813 0.6537084714 -0.4837315931 0.313447935777 +1403715309512143104.0000000000 0.2029524422 -0.9311418946 1.1213246558 0.4885989622 0.6570902432 -0.4795559260 0.315483090407 +1403715309562142976.0000000000 0.2174360401 -0.9379231501 1.1242509069 0.4869326177 0.6602707360 -0.4761539469 0.316570055122 +1403715309612143104.0000000000 0.2315863029 -0.9447551394 1.1279343123 0.4861772113 0.6624527950 -0.4733855807 0.317323345485 +1403715309662142976.0000000000 0.2450756510 -0.9519414589 1.1313712948 0.4859175710 0.6643098969 -0.4710431747 0.317324443825 +1403715309712143104.0000000000 0.2579559774 -0.9590924060 1.1346354990 0.4861363842 0.6656525411 -0.4699588944 0.315779587848 +1403715309762142976.0000000000 0.2699625967 -0.9663955030 1.1382630759 0.4865690747 0.6667023418 -0.4694503762 0.313647680296 +1403715309812143104.0000000000 0.2812235159 -0.9738894019 1.1423456034 0.4877886838 0.6673132599 -0.4697457504 0.309990553198 +1403715309862142976.0000000000 0.2922343371 -0.9815674768 1.1463372693 0.4895916426 0.6669160815 -0.4718101260 0.304824816527 +1403715309912143104.0000000000 0.3032571658 -0.9893683251 1.1500832083 0.4915953498 0.6664534933 -0.4743517592 0.298603686843 +1403715309962142976.0000000000 0.3143830639 -0.9982726671 1.1530263675 0.4947408093 0.6648745357 -0.4758806329 0.294467326963 +1403715310012143104.0000000000 0.3259966935 -1.0080298847 1.1552462698 0.4989751485 0.6624237018 -0.4761609024 0.292385764979 +1403715310062142976.0000000000 0.3386750475 -1.0185908521 1.1571749852 0.5040001380 0.6585255865 -0.4758141263 0.293136197095 +1403715310112143104.0000000000 0.3518915609 -1.0309053906 1.1586006869 0.5079878875 0.6542945985 -0.4756053507 0.296051405719 +1403715310162142976.0000000000 0.3649976710 -1.0450557363 1.1597008949 0.5107450956 0.6499589335 -0.4755406228 0.300921830718 +1403715310212143104.0000000000 0.3779911057 -1.0612150078 1.1608027774 0.5108532434 0.6466823567 -0.4757617707 0.307378643943 +1403715310262142976.0000000000 0.3904697071 -1.0794149626 1.1617791921 0.5084152030 0.6444516689 -0.4757913445 0.315940855818 +1403715310312143104.0000000000 0.4017941162 -1.0993764843 1.1628266294 0.5042061002 0.6427804070 -0.4759379445 0.325718636193 +1403715310362142976.0000000000 0.4115196331 -1.1203295519 1.1646306645 0.4997015204 0.6404893499 -0.4780626124 0.333957964127 +1403715310412143104.0000000000 0.4194562509 -1.1419923936 1.1667016811 0.4943487514 0.6380417886 -0.4818519825 0.341087459292 +1403715310462142976.0000000000 0.4258053245 -1.1640228907 1.1689240633 0.4887096321 0.6352588737 -0.4871754292 0.346798442897 +1403715310512143104.0000000000 0.4304721797 -1.1862117339 1.1708437413 0.4819280263 0.6338836258 -0.4931075564 0.350402431792 +1403715310562142976.0000000000 0.4337494822 -1.2081738326 1.1727741441 0.4749005104 0.6332761053 -0.4992622916 0.352374862543 +1403715310612143104.0000000000 0.4356262069 -1.2300149575 1.1750777392 0.4676814413 0.6334961498 -0.5051562753 0.353233400507 +1403715310662142976.0000000000 0.4367547260 -1.2513525912 1.1775360674 0.4609014761 0.6340331190 -0.5106401197 0.353296619718 +1403715310712143104.0000000000 0.4372337260 -1.2721009380 1.1797365326 0.4554121347 0.6342166589 -0.5153967933 0.353178655311 +1403715310762142976.0000000000 0.4374294545 -1.2921393143 1.1820414879 0.4511813754 0.6341408400 -0.5192971185 0.353031534305 +1403715310812143104.0000000000 0.4378311092 -1.3113572015 1.1843780063 0.4486798098 0.6334803763 -0.5224697672 0.352724231487 +1403715310862142976.0000000000 0.4382189653 -1.3299414585 1.1866075235 0.4473662274 0.6322123944 -0.5249247791 0.353022553487 +1403715310912143104.0000000000 0.4389470904 -1.3478531648 1.1888952780 0.4467122682 0.6308472705 -0.5268332500 0.353449568512 +1403715310962142976.0000000000 0.4397807637 -1.3652399959 1.1915988367 0.4460153750 0.6295225782 -0.5294817981 0.352733092083 +1403715311012143104.0000000000 0.4404159231 -1.3821737001 1.1937159676 0.4456562009 0.6281188089 -0.5328715777 0.350578371005 +1403715311062142976.0000000000 0.4414479341 -1.3985231711 1.1953806201 0.4459377718 0.6262052415 -0.5370488951 0.347253485894 +1403715311112143104.0000000000 0.4431256786 -1.4146650727 1.1966363036 0.4458154743 0.6249167512 -0.5401921195 0.344847924461 +1403715311162142976.0000000000 0.4457043010 -1.4306594539 1.1976436744 0.4463120403 0.6233552874 -0.5430236994 0.342577013577 +1403715311212143104.0000000000 0.4490966026 -1.4467220213 1.1987621282 0.4477891542 0.6211142123 -0.5458742002 0.340181372521 +1403715311262142976.0000000000 0.4533039999 -1.4630220821 1.1991479149 0.4480475761 0.6199773723 -0.5477429189 0.338908722556 +1403715311312143104.0000000000 0.4584479490 -1.4796086307 1.1998849748 0.4488034330 0.6186633826 -0.5498423454 0.336904278267 +1403715311362142976.0000000000 0.4646389200 -1.4967283194 1.2007289165 0.4485930904 0.6181094996 -0.5516067731 0.335313068013 +1403715311412143104.0000000000 0.4723486765 -1.5144464472 1.2022033624 0.4470163312 0.6185835638 -0.5519262060 0.336018209876 +1403715311462142976.0000000000 0.4812196121 -1.5328093143 1.2039034136 0.4443510452 0.6200644230 -0.5509542656 0.338410486315 +1403715311512143104.0000000000 0.4912091156 -1.5519458904 1.2055342620 0.4409797366 0.6218180214 -0.5494121840 0.342089859826 +1403715311562142976.0000000000 0.5021308238 -1.5710919415 1.2075473581 0.4388538325 0.6227785792 -0.5479607522 0.345388432094 +1403715311612143104.0000000000 0.5141307330 -1.5901255349 1.2101377966 0.4377723427 0.6230346092 -0.5467630862 0.348185840016 +1403715311662142976.0000000000 0.5269488114 -1.6088292568 1.2127062977 0.4365874426 0.6232113761 -0.5459921995 0.350558844964 +1403715311712143104.0000000000 0.5404463360 -1.6270435424 1.2153629076 0.4372677908 0.6220726592 -0.5464906864 0.350956429512 +1403715311762142976.0000000000 0.5546414633 -1.6448721387 1.2180089862 0.4381448536 0.6208560532 -0.5471445815 0.350998084711 +1403715311812143104.0000000000 0.5698805024 -1.6625667462 1.2206423385 0.4390534267 0.6192319627 -0.5483501333 0.350850390158 +1403715311862142976.0000000000 0.5859389792 -1.6802395884 1.2235007641 0.4408543666 0.6166365019 -0.5504076095 0.349940445453 +1403715311912143104.0000000000 0.6027178791 -1.6976863204 1.2264818071 0.4417614797 0.6146919646 -0.5512640612 0.350868235242 +1403715311962142976.0000000000 0.6200673127 -1.7152486297 1.2290672383 0.4406191471 0.6140332832 -0.5518227504 0.352575589817 +1403715312012143104.0000000000 0.6384733164 -1.7327398429 1.2312866211 0.4382338111 0.6143083762 -0.5516517360 0.355326199318 +1403715312062142976.0000000000 0.6575970837 -1.7501178922 1.2333216972 0.4354247797 0.6149400426 -0.5512387302 0.358315318598 +1403715312112143104.0000000000 0.6773558558 -1.7672501637 1.2356302297 0.4342903627 0.6143574287 -0.5509342059 0.361148627959 +1403715312162142976.0000000000 0.6972361668 -1.7839726718 1.2380375860 0.4328131640 0.6140631891 -0.5505177240 0.364045876776 +1403715312212143104.0000000000 0.7175080537 -1.8000077469 1.2407108454 0.4315241173 0.6136993695 -0.5506912535 0.36592234614 +1403715312262142976.0000000000 0.7380578953 -1.8155110308 1.2436304083 0.4307323599 0.6129233795 -0.5515592163 0.366847374259 +1403715312312143104.0000000000 0.7587232397 -1.8303960237 1.2468037037 0.4314444918 0.6112114871 -0.5531736886 0.366435586137 +1403715312362142976.0000000000 0.7795360146 -1.8448087277 1.2494826394 0.4319821204 0.6096974305 -0.5551471602 0.365338365622 +1403715312412143104.0000000000 0.8007606053 -1.8590768396 1.2520055963 0.4329647438 0.6079717210 -0.5566920005 0.364699785732 +1403715312462142976.0000000000 0.8224837592 -1.8731904572 1.2542718505 0.4343755824 0.6059854020 -0.5580971145 0.364180115964 +1403715312512143104.0000000000 0.8443655686 -1.8871853833 1.2560292607 0.4364117730 0.6039898796 -0.5583426880 0.364684017254 +1403715312562142976.0000000000 0.8665998848 -1.9013509817 1.2566375931 0.4367722439 0.6034213878 -0.5575924166 0.36633773035 +1403715312612143104.0000000000 0.8889626748 -1.9157073854 1.2565891138 0.4376430660 0.6027595848 -0.5554059788 0.369693965818 +1403715312662142976.0000000000 0.9114214095 -1.9300925097 1.2559098282 0.4388052472 0.6021910587 -0.5521408559 0.374107416437 +1403715312712143104.0000000000 0.9336137059 -1.9442034621 1.2546360394 0.4406289628 0.6013196802 -0.5490395907 0.377910422308 +1403715312762142976.0000000000 0.9552427857 -1.9580849378 1.2523260370 0.4414967475 0.6014995281 -0.5456298835 0.381532396877 +1403715312812143104.0000000000 0.9763587637 -1.9715030953 1.2494204955 0.4417250784 0.6025727639 -0.5416249434 0.385262819397 +1403715312862142976.0000000000 0.9965918475 -1.9840465296 1.2472101157 0.4439049919 0.6027038286 -0.5368714762 0.389185651377 +1403715312912143104.0000000000 1.0155816973 -1.9958612898 1.2463836371 0.4467049618 0.6026537341 -0.5324545773 0.392116407418 +1403715312962142976.0000000000 1.0330296867 -2.0068954223 1.2481461576 0.4492218534 0.6030064637 -0.5281231492 0.394548945611 +1403715313012143104.0000000000 1.0482211944 -2.0173219213 1.2526056370 0.4513009737 0.6036494797 -0.5245348737 0.395977149655 +1403715313062142976.0000000000 1.0616411469 -2.0268436198 1.2593336098 0.4520549043 0.6052788192 -0.5214946618 0.396644970033 +1403715313112143104.0000000000 1.0727417528 -2.0355491673 1.2682800471 0.4516519401 0.6077224916 -0.5192997159 0.396247023069 +1403715313162142976.0000000000 1.0822772710 -2.0432562093 1.2793110363 0.4521692933 0.6093804323 -0.5175177278 0.395441298243 +1403715313212143104.0000000000 1.0902048013 -2.0497559480 1.2909675437 0.4533332947 0.6104885918 -0.5173631761 0.392591323305 +1403715313262142976.0000000000 1.0960781566 -2.0553583871 1.3022263125 0.4541654055 0.6118065710 -0.5182853475 0.388338515493 +1403715313312143104.0000000000 1.0998708619 -2.0603886451 1.3123324623 0.4545634259 0.6132906509 -0.5195748424 0.38378203772 +1403715313362142976.0000000000 1.1026729886 -2.0648097610 1.3218286030 0.4540054479 0.6150360669 -0.5209797578 0.379723296246 +1403715313412143104.0000000000 1.1044921806 -2.0688700487 1.3309508840 0.4525765701 0.6171210719 -0.5221667935 0.376401209574 +1403715313462142976.0000000000 1.1056970909 -2.0729279049 1.3395384886 0.4512325129 0.6178150255 -0.5242158673 0.374020772252 +1403715313512143104.0000000000 1.1062342419 -2.0772503357 1.3481357959 0.4491755837 0.6175318408 -0.5259159578 0.374577263004 +1403715313562142976.0000000000 1.1063121415 -2.0815418440 1.3567669743 0.4464323931 0.6167775093 -0.5283258213 0.375706599544 +1403715313612143104.0000000000 1.1060734925 -2.0854532983 1.3653980146 0.4425518510 0.6164464573 -0.5303121325 0.37803527146 +1403715313662142976.0000000000 1.1054014027 -2.0889063461 1.3740326585 0.4393220307 0.6157263380 -0.5316974691 0.381018413471 +1403715313712143104.0000000000 1.1039732724 -2.0917767441 1.3832552533 0.4369992528 0.6147884835 -0.5329402686 0.383459833199 +1403715313762142976.0000000000 1.1020310571 -2.0939300612 1.3931051715 0.4356147515 0.6134957097 -0.5350775957 0.384128583968 +1403715313812143104.0000000000 1.0996496845 -2.0950323774 1.4034572392 0.4348493584 0.6119573071 -0.5367994184 0.385046327314 +1403715313862142976.0000000000 1.0968894305 -2.0953909831 1.4137102514 0.4339167520 0.6106300053 -0.5384412042 0.385912319801 +1403715313912143104.0000000000 1.0938658406 -2.0948028573 1.4242639937 0.4345692075 0.6086639941 -0.5404388823 0.385491323824 +1403715313962142976.0000000000 1.0902437957 -2.0934600435 1.4345253851 0.4363239646 0.6062845050 -0.5427070703 0.384069697811 +1403715314012143104.0000000000 1.0863248196 -2.0918667655 1.4431177555 0.4362270925 0.6045623056 -0.5455667792 0.382841000749 +1403715314062142976.0000000000 1.0821516153 -2.0905924084 1.4504541212 0.4337255233 0.6031468286 -0.5483325552 0.383962866058 +1403715314112143104.0000000000 1.0778878073 -2.0896017706 1.4566156770 0.4288640464 0.6012726933 -0.5514215262 0.387918907022 +1403715314162142976.0000000000 1.0736711053 -2.0885938136 1.4620340339 0.4233093834 0.5976880707 -0.5560415200 0.39293251854 +1403715314212143104.0000000000 1.0693057923 -2.0874613866 1.4663905524 0.4159484202 0.5939835395 -0.5615991890 0.39846808825 +1403715314262142976.0000000000 1.0650808106 -2.0857743150 1.4708931156 0.4092037414 0.5889205919 -0.5673755278 0.404734289185 +1403715314312143104.0000000000 1.0606049594 -2.0832890283 1.4745332678 0.4018834493 0.5837172803 -0.5745883300 0.409404544343 +1403715314362142976.0000000000 1.0562892526 -2.0797675570 1.4776673670 0.3951947888 0.5779515361 -0.5814477678 0.414380977076 +1403715314412143104.0000000000 1.0519021534 -2.0747852094 1.4800461005 0.3905562499 0.5715910391 -0.5883859714 0.41779354751 +1403715314462142976.0000000000 1.0475737924 -2.0684922052 1.4816356620 0.3853023770 0.5668041618 -0.5945327581 0.420482960385 +1403715314512143104.0000000000 1.0440407892 -2.0608271749 1.4836983743 0.3818782259 0.5617604203 -0.5999801592 0.422632297965 +1403715314562142976.0000000000 1.0411925226 -2.0520341025 1.4857041399 0.3796567780 0.5569017668 -0.6057966170 0.42276661644 +1403715314612143104.0000000000 1.0386629706 -2.0423249768 1.4873028906 0.3787670364 0.5520928564 -0.6105074815 0.423095290777 +1403715314662142976.0000000000 1.0362797795 -2.0319115122 1.4883887063 0.3780556195 0.5480422414 -0.6137467932 0.424309467411 +1403715314712143104.0000000000 1.0341560289 -2.0206545298 1.4888138545 0.3771254266 0.5449807968 -0.6163227546 0.425345278364 +1403715314762142976.0000000000 1.0322953883 -2.0088035706 1.4889808214 0.3761082984 0.5426292400 -0.6177936266 0.427114844941 +1403715314812143104.0000000000 1.0309063365 -1.9963708377 1.4895103966 0.3763111788 0.5401404262 -0.6182200874 0.429467274956 +1403715314862142976.0000000000 1.0296837766 -1.9835153237 1.4898669614 0.3751403650 0.5390784129 -0.6183410841 0.431646238194 +1403715314912143104.0000000000 1.0285473600 -1.9699023798 1.4902158154 0.3749936768 0.5377851040 -0.6185875845 0.433031551395 +1403715314962142976.0000000000 1.0273464457 -1.9555032875 1.4907516786 0.3758418410 0.5363794264 -0.6188450151 0.433671383406 +1403715315012143104.0000000000 1.0265822351 -1.9401690208 1.4911089838 0.3773238514 0.5351270911 -0.6189967972 0.433714966866 +1403715315062142976.0000000000 1.0263056648 -1.9240671670 1.4914129558 0.3803453669 0.5327708969 -0.6189349048 0.434064692055 +1403715315112143104.0000000000 1.0262044350 -1.9076397197 1.4907242084 0.3815958614 0.5320136424 -0.6187585272 0.434147403332 +1403715315162142976.0000000000 1.0259726938 -1.8909268258 1.4899166503 0.3821679705 0.5318177217 -0.6192348379 0.433204072884 +1403715315212143104.0000000000 1.0255373768 -1.8740181270 1.4891365311 0.3825695487 0.5319930793 -0.6194696998 0.432297577007 +1403715315262142976.0000000000 1.0249828150 -1.8571254428 1.4886712063 0.3826034532 0.5318429949 -0.6196178574 0.432239906903 +1403715315312143104.0000000000 1.0241273213 -1.8405726388 1.4879981197 0.3815984304 0.5308379228 -0.6207107407 0.432795464409 +1403715315362142976.0000000000 1.0234778421 -1.8242797984 1.4879436970 0.3800101455 0.5285293063 -0.6223416690 0.434672185324 +1403715315412143104.0000000000 1.0227199289 -1.8079044976 1.4880607972 0.3782479529 0.5252116855 -0.6252090441 0.436113314206 +1403715315462142976.0000000000 1.0220686493 -1.7914830090 1.4880867423 0.3761338374 0.5208775213 -0.6289185842 0.437802876476 +1403715315512143104.0000000000 1.0212054329 -1.7752094132 1.4884897146 0.3740031826 0.5158576713 -0.6328164833 0.439949748137 +1403715315562142976.0000000000 1.0203492419 -1.7590501133 1.4891747765 0.3720614602 0.5105773493 -0.6367010872 0.442145638656 +1403715315612143104.0000000000 1.0185899995 -1.7430493053 1.4898529680 0.3696382155 0.5050785246 -0.6408867509 0.444440599141 +1403715315662142976.0000000000 1.0167031047 -1.7274250049 1.4909654214 0.3670350026 0.4990234300 -0.6451161630 0.447309802557 +1403715315712143104.0000000000 1.0147270824 -1.7118991602 1.4923007736 0.3667056601 0.4906011997 -0.6507972159 0.448665137384 +1403715315762142976.0000000000 1.0123299695 -1.6967321453 1.4937861473 0.3665315989 0.4814523791 -0.6572395965 0.44932650316 +1403715315812143104.0000000000 1.0093901480 -1.6824057352 1.4948472115 0.3653676936 0.4723932247 -0.6640606731 0.449860547329 +1403715315862142976.0000000000 1.0061892073 -1.6694094746 1.4955640629 0.3621539328 0.4641354874 -0.6704229569 0.451614699965 +1403715315912143104.0000000000 1.0024167664 -1.6576066474 1.4958634055 0.3569851566 0.4569105773 -0.6762685312 0.454373410349 +1403715315962142976.0000000000 0.9980457081 -1.6466919170 1.4959200129 0.3509909298 0.4498467999 -0.6812120601 0.458686552015 +1403715316012143104.0000000000 0.9928816322 -1.6367166168 1.4948482780 0.3440667674 0.4431419912 -0.6865682818 0.462457813903 +1403715316062142976.0000000000 0.9872359624 -1.6276836540 1.4929094764 0.3361534442 0.4369622872 -0.6908862531 0.467697559057 +1403715316112143104.0000000000 0.9814722047 -1.6195276679 1.4899139833 0.3270800088 0.4313440238 -0.6951207030 0.473041445564 +1403715316162142976.0000000000 0.9755335928 -1.6122581513 1.4855742792 0.3172784970 0.4258217417 -0.6994785209 0.478267705795 +1403715316212143104.0000000000 0.9693734447 -1.6055837533 1.4803598999 0.3068703474 0.4204357773 -0.7042006781 0.482872397292 +1403715316262142976.0000000000 0.9629854511 -1.5994187839 1.4742947316 0.2941267079 0.4160736354 -0.7098019679 0.486367531823 +1403715316312143104.0000000000 0.9570031326 -1.5934792213 1.4680459728 0.2815343294 0.4110668121 -0.7163033218 0.488540733762 +1403715316362142976.0000000000 0.9515336070 -1.5872419303 1.4603401467 0.2683816268 0.4074760672 -0.7226743295 0.48956753421 +1403715316412143104.0000000000 0.9471301650 -1.5804246353 1.4524565713 0.2568357242 0.4040207947 -0.7283103098 0.490272068237 +1403715316462142976.0000000000 0.9445176174 -1.5729388930 1.4447743578 0.2480402504 0.3999039927 -0.7326469380 0.491712614334 +1403715316512143104.0000000000 0.9441389984 -1.5647310767 1.4370981986 0.2430340378 0.3948406388 -0.7361896049 0.493011350805 +1403715316562142976.0000000000 0.9457882219 -1.5561835447 1.4294106763 0.2400840856 0.3892989502 -0.7383823820 0.495577861814 +1403715316612143104.0000000000 0.9494278501 -1.5472191854 1.4215733052 0.2394948936 0.3833564369 -0.7398640348 0.498278283927 +1403715316662142976.0000000000 0.9548151457 -1.5380067151 1.4135376946 0.2399833334 0.3776998885 -0.7400255111 0.502108590719 +1403715316712143104.0000000000 0.9617034550 -1.5285110606 1.4048945726 0.2407854427 0.3715398790 -0.7405590718 0.505522254729 +1403715316762142976.0000000000 0.9695771527 -1.5189536073 1.3955387280 0.2405536653 0.3652424146 -0.7412424675 0.50920675275 +1403715316812143104.0000000000 0.9783362339 -1.5093412200 1.3854687884 0.2392258761 0.3590222094 -0.7423286101 0.512661943199 +1403715316862142976.0000000000 0.9879433958 -1.4997506997 1.3749387167 0.2368833267 0.3520641014 -0.7438278348 0.516388720118 +1403715316912143104.0000000000 0.9985248807 -1.4901355609 1.3641788973 0.2342205994 0.3440130906 -0.7458730026 0.520066503768 +1403715316962142976.0000000000 1.0096192624 -1.4805450969 1.3535986225 0.2299414313 0.3355302840 -0.7473870086 0.525318023695 +1403715317012143104.0000000000 1.0206899576 -1.4706425394 1.3434043691 0.2264136971 0.3251700330 -0.7491570606 0.530815397303 +1403715317062142976.0000000000 1.0317869400 -1.4599488374 1.3327597747 0.2220579009 0.3145187772 -0.7527443879 0.53398887058 +1403715317112143104.0000000000 1.0426186934 -1.4488802293 1.3220462216 0.2157568637 0.3041497730 -0.7574158431 0.535969338607 +1403715317162142976.0000000000 1.0533243407 -1.4375720765 1.3116635049 0.2084296825 0.2936265152 -0.7627377588 0.537188652397 +1403715317212143104.0000000000 1.0639114060 -1.4260438856 1.3015924832 0.2004022856 0.2828963975 -0.7681168504 0.538335449664 +1403715317262142976.0000000000 1.0746272461 -1.4145275566 1.2920056580 0.1912634411 0.2726272877 -0.7726886216 0.5404118357 +1403715317312143104.0000000000 1.0855554959 -1.4029494756 1.2828268679 0.1824680800 0.2615606546 -0.7771406781 0.542534598179 +1403715317362142976.0000000000 1.0966341372 -1.3909181456 1.2742812954 0.1746936601 0.2493050169 -0.7817991375 0.544168395227 +1403715317412143104.0000000000 1.1078985056 -1.3785506130 1.2663975091 0.1682579331 0.2358252560 -0.7861533316 0.54592916742 +1403715317462142976.0000000000 1.1192559543 -1.3661770612 1.2587545054 0.1613584138 0.2229897808 -0.7904315090 0.547226689287 +1403715317512143104.0000000000 1.1306698430 -1.3538621726 1.2515065339 0.1543018144 0.2104860109 -0.7941280809 0.548859891424 +1403715317562142976.0000000000 1.1420674111 -1.3419096169 1.2444367580 0.1467760395 0.1984203265 -0.7969317872 0.551349158661 +1403715317612143104.0000000000 1.1536227803 -1.3301816614 1.2376263481 0.1397542156 0.1863285255 -0.7995833882 0.553549315911 +1403715317662142976.0000000000 1.1652100625 -1.3186746901 1.2312054324 0.1338991314 0.1736616914 -0.8020858134 0.555491662839 +1403715317712143104.0000000000 1.1765060172 -1.3074417055 1.2249340150 0.1275490014 0.1614758021 -0.8044396842 0.557255428009 +1403715317762142976.0000000000 1.1875346623 -1.2964105894 1.2189633582 0.1225640196 0.1485999136 -0.8069482045 0.558328507209 +1403715317812143104.0000000000 1.1983105727 -1.2855981593 1.2135433140 0.1206202464 0.1338955945 -0.8096112883 0.55861640488 +1403715317862142976.0000000000 1.2083399589 -1.2753601004 1.2081311569 0.1182824755 0.1192536272 -0.8125952709 0.558101025059 +1403715317912143104.0000000000 1.2173194293 -1.2657072471 1.2027310249 0.1139496724 0.1067741112 -0.8146593198 0.558520325576 +1403715317962142976.0000000000 1.2249123275 -1.2566548284 1.1972489226 0.1082282407 0.0956234000 -0.8164565137 0.55905417854 +1403715318012143104.0000000000 1.2312693618 -1.2480648857 1.1915580251 0.1021993870 0.0852181683 -0.8180413939 0.559554668433 +1403715318062142976.0000000000 1.2366457958 -1.2398994175 1.1860846159 0.0978969730 0.0756862726 -0.8186651109 0.560780890427 +1403715318112143104.0000000000 1.2408408705 -1.2324283430 1.1807326060 0.0948353588 0.0672803320 -0.8193927494 0.561315538612 +1403715318162142976.0000000000 1.2436367404 -1.2257294116 1.1754924715 0.0911792839 0.0608508188 -0.8197011951 0.562204114825 +1403715318212143104.0000000000 1.2450802780 -1.2198307310 1.1699147003 0.0870138767 0.0563669617 -0.8203072912 0.562447596545 +1403715318262142976.0000000000 1.2452806937 -1.2144841319 1.1644445247 0.0840253457 0.0523243362 -0.8205643794 0.562917404614 +1403715318312143104.0000000000 1.2438146847 -1.2099687645 1.1586407142 0.0800536398 0.0492059594 -0.8210766705 0.563030451611 +1403715318362142976.0000000000 1.2408491341 -1.2063167515 1.1531087249 0.0757725429 0.0460193947 -0.8213134125 0.563546817426 +1403715318412143104.0000000000 1.2364446620 -1.2031475078 1.1474327142 0.0698458696 0.0437974606 -0.8218438796 0.563716218104 +1403715318462142976.0000000000 1.2305122392 -1.2004805282 1.1412739849 0.0612470903 0.0424692631 -0.8224880963 0.56387807826 +1403715318512143104.0000000000 1.2237077002 -1.1982288682 1.1348107672 0.0518015998 0.0414217771 -0.8234075932 0.563560791829 +1403715318562142976.0000000000 1.2164519581 -1.1964644338 1.1282675394 0.0431138807 0.0390462048 -0.8251792502 0.561868127015 +1403715318612143104.0000000000 1.2090725201 -1.1952932370 1.1214997207 0.0349849251 0.0357325870 -0.8283054626 0.558040587957 +1403715318662142976.0000000000 1.2018167386 -1.1949144511 1.1146246663 0.0276086632 0.0311393699 -0.8321178819 0.553035199575 +1403715318712143104.0000000000 1.1949129452 -1.1954296539 1.1074488875 0.0211805403 0.0256050990 -0.8367474461 0.546579797521 +1403715318762142976.0000000000 1.1885201585 -1.1977164846 1.1008058437 0.0165023687 0.0179997885 -0.8398581852 0.542256312216 +1403715318812143104.0000000000 1.1821734877 -1.2021627216 1.0940366486 0.0097526752 0.0110985403 -0.8423724819 0.538693149622 +1403715318862142976.0000000000 1.1763153764 -1.2090263882 1.0880068145 0.0040177728 0.0033544006 -0.8429505483 0.537965592375 +1403715318912143104.0000000000 1.1709174227 -1.2180613198 1.0822196676 0.0017787199 0.0035641600 0.8424327443 -0.538786789282 +1403715318962142976.0000000000 1.1660832446 -1.2295363533 1.0768562036 0.0072905112 0.0098329205 0.8411740816 -0.540625865629 +1403715319012143104.0000000000 1.1616399771 -1.2430052531 1.0717660902 0.0125822187 0.0169720710 0.8393723522 -0.543146104645 +1403715319062142976.0000000000 1.1574692940 -1.2583168371 1.0668097897 0.0189950808 0.0238696829 0.8371516412 -0.546119542574 +1403715319112143104.0000000000 1.1537637939 -1.2748455865 1.0621012730 0.0263251139 0.0302467702 0.8342213390 -0.549969889077 +1403715319162142976.0000000000 1.1505722813 -1.2927071091 1.0578089915 0.0341390744 0.0366392854 0.8312217362 -0.553680875199 +1403715319212143104.0000000000 1.1481753706 -1.3119148917 1.0540210771 0.0414423094 0.0440366044 0.8285100292 -0.556699599356 +1403715319262142976.0000000000 1.1466522824 -1.3321905944 1.0503866508 0.0486858694 0.0518674130 0.8266622482 -0.558183648019 +1403715319312143104.0000000000 1.1460494223 -1.3534673611 1.0471084198 0.0563607684 0.0594064703 0.8248242497 -0.559427646888 +1403715319362142976.0000000000 1.1464007418 -1.3754997262 1.0439059438 0.0641597170 0.0673406253 0.8230895389 -0.56024314523 +1403715319412143104.0000000000 1.1482132578 -1.3984197822 1.0409403557 0.0708610219 0.0757390369 0.8210301480 -0.561383834706 +1403715319462142976.0000000000 1.1513054876 -1.4218311214 1.0381157309 0.0754216307 0.0853706883 0.8188640801 -0.562570032504 +1403715319512143104.0000000000 1.1551297937 -1.4455031900 1.0351258286 0.0799422782 0.0955891639 0.8167189261 -0.563420038339 +1403715319562142976.0000000000 1.1598129016 -1.4697565787 1.0320481230 0.0852823309 0.1049334895 0.8149619624 -0.56351831082 +1403715319612143104.0000000000 1.1657226584 -1.4943817556 1.0303071714 0.0892345066 0.1140554079 0.8130266966 -0.563929213103 +1403715319662142976.0000000000 1.1729227544 -1.5191204922 1.0304126468 0.0939247334 0.1204081024 0.8118553660 -0.563534291828 +1403715319712143104.0000000000 1.1813732868 -1.5439241989 1.0334818029 0.0961675631 0.1260690447 0.8107302594 -0.563537791322 +1403715319762142976.0000000000 1.1908192565 -1.5690575690 1.0393092052 0.0983207959 0.1294301681 0.8105498998 -0.562663054223 +1403715319812143104.0000000000 1.2011705198 -1.5946977129 1.0485591179 0.0987774271 0.1321929564 0.8100596063 -0.562646848806 +1403715319862142976.0000000000 1.2120312068 -1.6207658775 1.0605994504 0.0995601468 0.1344255707 0.8096126581 -0.562623219282 +1403715319912143104.0000000000 1.2234568483 -1.6473682929 1.0751280372 0.0998541064 0.1373118396 0.8094546333 -0.562101247778 +1403715319962142976.0000000000 1.2354159486 -1.6739997327 1.0907021874 0.1012338905 0.1394587517 0.8088876777 -0.562142046886 +1403715320012143104.0000000000 1.2479106173 -1.7013046436 1.1059858013 0.1032697459 0.1425424212 0.8079658537 -0.562323925257 +1403715320062142976.0000000000 1.2609348192 -1.7291749447 1.1206573432 0.1060164122 0.1465137587 0.8070026167 -0.562175253333 +1403715320112143104.0000000000 1.2743360231 -1.7574259327 1.1345052983 0.1108624683 0.1507781671 0.8052210425 -0.562667335266 +1403715320162142976.0000000000 1.2883476191 -1.7857473197 1.1474427505 0.1163251204 0.1566810549 0.8035072990 -0.562401576973 +1403715320212143104.0000000000 1.3028669348 -1.8142524914 1.1602458991 0.1225882796 0.1643547224 0.8003964416 -0.563316230172 +1403715320262142976.0000000000 1.3180009675 -1.8428365460 1.1728463087 0.1301465616 0.1732432367 0.7955868182 -0.565765205776 +1403715320312143104.0000000000 1.3339649742 -1.8712931204 1.1852136151 0.1364344008 0.1848859303 0.7893351920 -0.569344185658 +1403715320362142976.0000000000 1.3507429704 -1.8992948152 1.1969758333 0.1416393818 0.1991738622 0.7831832769 -0.571744709546 +1403715320412143104.0000000000 1.3680492002 -1.9265175094 1.2084088090 0.1466151648 0.2148243581 0.7780006615 -0.571899868238 +1403715320462142976.0000000000 1.3857762247 -1.9526644890 1.2198467938 0.1525185450 0.2308722330 0.7729665652 -0.570928011726 +1403715320512143104.0000000000 1.4040001104 -1.9769846801 1.2307148945 0.1581013582 0.2472898851 0.7687016986 -0.568286346711 +1403715320562142976.0000000000 1.4224175579 -2.0004143460 1.2411459413 0.1634690363 0.2637328524 0.7640112417 -0.565693980254 +1403715320612143104.0000000000 1.4410182818 -2.0227193834 1.2520646221 0.1680094579 0.2801869804 0.7590409222 -0.563138487896 +1403715320662142976.0000000000 1.4594514956 -2.0436466278 1.2628786693 0.1720246050 0.2968006913 0.7533231909 -0.561089168452 +1403715320712143104.0000000000 1.4776960240 -2.0629241474 1.2729903363 0.1750497924 0.3124380623 0.7475914820 -0.55932727752 +1403715320762142976.0000000000 1.4958312736 -2.0807955948 1.2826467965 0.1760334987 0.3272347954 0.7413866444 -0.558816105302 +1403715320812143104.0000000000 1.5137510814 -2.0968254467 1.2917512733 0.1763458254 0.3400009839 0.7355765059 -0.558774269987 +1403715320862142976.0000000000 1.5311074501 -2.1106749689 1.2996608362 0.1756412292 0.3512096227 0.7316954566 -0.557156816621 +1403715320912143104.0000000000 1.5473006401 -2.1221365302 1.3067563721 0.1751649172 0.3603410515 0.7296195490 -0.554190303165 +1403715320962142976.0000000000 1.5617034330 -2.1313237469 1.3133268562 0.1764607679 0.3668000493 0.7285364503 -0.550957313983 +1403715321012143104.0000000000 1.5743505325 -2.1382513147 1.3192475447 0.1792446008 0.3710212348 0.7285922836 -0.547145228161 +1403715321062142976.0000000000 1.5850594928 -2.1431684872 1.3247822430 0.1828422964 0.3735403951 0.7288196989 -0.543928409197 +1403715321112143104.0000000000 1.5939564741 -2.1465360282 1.3301537040 0.1864265315 0.3750643867 0.7290897070 -0.541294793311 +1403715321162142976.0000000000 1.6009714594 -2.1484654080 1.3350862099 0.1895831284 0.3759895556 0.7294155711 -0.539113175751 +1403715321212143104.0000000000 1.6062925062 -2.1489944465 1.3394020436 0.1923169699 0.3763575528 0.7303465220 -0.536621965084 +1403715321262142976.0000000000 1.6103725203 -2.1481837101 1.3436454670 0.1940369101 0.3766871255 0.7309275068 -0.534978005905 +1403715321312143104.0000000000 1.6129501293 -2.1461478724 1.3478473219 0.1940506176 0.3772481925 0.7312151223 -0.534184054324 +1403715321362142976.0000000000 1.6139597250 -2.1428399190 1.3519311460 0.1936397337 0.3776950666 0.7313362630 -0.533851440586 +1403715321412143104.0000000000 1.6133599316 -2.1382083944 1.3561288456 0.1930333132 0.3779520468 0.7306558158 -0.534820034291 +1403715321462142976.0000000000 1.6110633295 -2.1323540050 1.3602203344 0.1929532230 0.3774603885 0.7299030166 -0.536222244162 +1403715321512143104.0000000000 1.6072730727 -2.1252440689 1.3639632208 0.1930029344 0.3760281911 0.7304092519 -0.536521193969 +1403715321562142976.0000000000 1.6020363434 -2.1170504930 1.3676023196 0.1922193942 0.3745188045 0.7314826132 -0.536395894998 +1403715321612143104.0000000000 1.5951612502 -2.1075802652 1.3710177843 0.1931508465 0.3713848035 0.7331441958 -0.535971702935 +1403715321662142976.0000000000 1.5863611068 -2.0972001651 1.3748786789 0.1951255398 0.3690198036 0.7334911335 -0.536415105453 +1403715321712143104.0000000000 1.5756136962 -2.0861566409 1.3796348946 0.1975532873 0.3679972663 0.7310575457 -0.539542005307 +1403715321762142976.0000000000 1.5635138925 -2.0740122307 1.3845612446 0.1998711911 0.3683492581 0.7286260673 -0.541732761642 +1403715321812143104.0000000000 1.5504080028 -2.0606489694 1.3899911735 0.2002726987 0.3711905234 0.7242136774 -0.545548339681 +1403715321862142976.0000000000 1.5362844541 -2.0459274880 1.3961996188 0.2005104409 0.3743861036 0.7182279131 -0.551161748875 +1403715321912143104.0000000000 1.5210849847 -2.0292302551 1.4019496712 0.2020992767 0.3771086563 0.7133215108 -0.555083206254 +1403715321962142976.0000000000 1.5050862919 -2.0098314282 1.4068283350 0.2039982637 0.3807856307 0.7105132132 -0.555479959739 +1403715322012143104.0000000000 1.4885414511 -1.9878258566 1.4109463275 0.2062104826 0.3851047735 0.7101578125 -0.552129904682 +1403715322062142976.0000000000 1.4713593483 -1.9636974410 1.4153422866 0.2063748493 0.3904551148 0.7107799626 -0.547490702786 +1403715322112143104.0000000000 1.4531378166 -1.9373159627 1.4199189143 0.2090858664 0.3938352392 0.7125618777 -0.541694079032 +1403715322162142976.0000000000 1.4339893871 -1.9090036814 1.4239150364 0.2157543661 0.3936087664 0.7159771807 -0.534695118002 +1403715322212143104.0000000000 1.4135216196 -1.8793989306 1.4280100729 0.2239774391 0.3922123949 0.7189235776 -0.528348780245 +1403715322262142976.0000000000 1.3920227084 -1.8487742967 1.4320000256 0.2320766354 0.3923970706 0.7207456917 -0.522197876492 +1403715322312143104.0000000000 1.3700610540 -1.8176554627 1.4357745443 0.2390075330 0.3941281100 0.7223618327 -0.515491818337 +1403715322362142976.0000000000 1.3473155030 -1.7865005891 1.4384515399 0.2457280343 0.3973302986 0.7229679687 -0.508982989102 +1403715322412143104.0000000000 1.3237712804 -1.7556210404 1.4381949348 0.2528162694 0.4018127803 0.7226505713 -0.502400811481 +1403715322462142976.0000000000 1.3001146686 -1.7252349379 1.4349549021 0.2586935741 0.4074245711 0.7218154060 -0.496049768848 +1403715322512143104.0000000000 1.2765401654 -1.6957787993 1.4287228412 0.2636342354 0.4130589011 0.7205580933 -0.490586759204 +1403715322562142976.0000000000 1.2530910873 -1.6675162820 1.4196585314 0.2664288705 0.4185766129 0.7194956701 -0.48593750295 +1403715322612143104.0000000000 1.2295010943 -1.6404630609 1.4088809758 0.2696523946 0.4225189818 0.7187161619 -0.481884192153 +1403715322662142976.0000000000 1.2054371334 -1.6151036787 1.3975062216 0.2715951776 0.4260174229 0.7180951660 -0.4786277755 +1403715322712143104.0000000000 1.1807020356 -1.5914036709 1.3860683267 0.2734760741 0.4285250721 0.7170798907 -0.476837005511 +1403715322762142976.0000000000 1.1549069659 -1.5694573389 1.3747652153 0.2754745778 0.4300975581 0.7156115039 -0.47647667629 +1403715322812143104.0000000000 1.1282508219 -1.5489024451 1.3640920846 0.2770251683 0.4311708504 0.7150182849 -0.475497219913 +1403715322862142976.0000000000 1.1007844092 -1.5300713011 1.3555422822 0.2783655373 0.4315438754 0.7150564774 -0.474317135916 +1403715322912143104.0000000000 1.0726708943 -1.5127484882 1.3501236496 0.2808553581 0.4307950943 0.7146522864 -0.474139182177 +1403715322962142976.0000000000 1.0440614288 -1.4971430617 1.3476798945 0.2827832493 0.4302657068 0.7140982966 -0.474308631888 +1403715323012143104.0000000000 1.0151867117 -1.4833668619 1.3481808268 0.2841331024 0.4294839284 0.7139757081 -0.47439500798 +1403715323062142976.0000000000 0.9859762810 -1.4714062839 1.3513910946 0.2845412856 0.4289129316 0.7140502609 -0.474554716397 +1403715323112143104.0000000000 0.9560603668 -1.4612861081 1.3560583887 0.2853284967 0.4282042112 0.7141849405 -0.474519412903 +1403715323162142976.0000000000 0.9257870937 -1.4531836463 1.3591831511 0.2859507777 0.4272436550 0.7147315331 -0.474187565817 +1403715323212143104.0000000000 0.8953586337 -1.4468499428 1.3596753616 0.2874206228 0.4254812266 0.7152678487 -0.474074905452 +1403715323262142976.0000000000 0.8648641603 -1.4421678733 1.3571203848 0.2888789045 0.4240547926 0.7151726261 -0.474609972919 +1403715323312143104.0000000000 0.8344395435 -1.4393297441 1.3516335166 0.2894249218 0.4231030750 0.7154165571 -0.474759046584 +1403715323362142976.0000000000 0.8039640270 -1.4384218741 1.3451415672 0.2890355481 0.4230859947 0.7148862061 -0.475809211006 +1403715323412143104.0000000000 0.7732347319 -1.4396503339 1.3403826527 0.2892412574 0.4228539191 0.7147073478 -0.476159075462 +1403715323462142976.0000000000 0.7423114885 -1.4429866912 1.3375154556 0.2886652072 0.4231683070 0.7149620960 -0.475846806746 +1403715323512143104.0000000000 0.7109617815 -1.4486060313 1.3373173321 0.2886329719 0.4232318976 0.7149122422 -0.475884706992 +1403715323562142976.0000000000 0.6796537689 -1.4559643602 1.3397918285 0.2883946603 0.4236355619 0.7149889279 -0.475554690448 +1403715323612143104.0000000000 0.6478814799 -1.4652288128 1.3468178017 0.2906108888 0.4225205900 0.7111753933 -0.480885872356 +1403715323662142976.0000000000 0.6155848563 -1.4762186678 1.3560078307 0.2941194944 0.4207460455 0.7050941050 -0.489191977847 +1403715323712143104.0000000000 0.5838334858 -1.4881639312 1.3654768754 0.2989062095 0.4183968362 0.6987123453 -0.497393429738 +1403715323762142976.0000000000 0.5532958028 -1.5008589113 1.3747048493 0.3041534258 0.4153949810 0.6918370198 -0.506260053084 +1403715323812143104.0000000000 0.5248343628 -1.5140331334 1.3831673196 0.3081373903 0.4128867436 0.6857658089 -0.514102267021 +1403715323862142976.0000000000 0.4984917193 -1.5273773630 1.3912071185 0.3116791110 0.4107774939 0.6803215949 -0.520845955927 +1403715323912143104.0000000000 0.4744686136 -1.5407477637 1.3993006715 0.3155275115 0.4081146155 0.6750493756 -0.527440224715 +1403715323962142976.0000000000 0.4535664131 -1.5542251460 1.4081163471 0.3194574929 0.4047784321 0.6683785233 -0.536070406573 +1403715324012143104.0000000000 0.4361815041 -1.5670281167 1.4169014709 0.3216384831 0.4026101512 0.6630307466 -0.542995378806 +1403715324062142976.0000000000 0.4227068889 -1.5788867548 1.4245471155 0.3214430644 0.4019845931 0.6606908768 -0.546415875075 +1403715324112143104.0000000000 0.4132802506 -1.5894505904 1.4308380965 0.3179706936 0.4036778115 0.6615987894 -0.546100635757 +1403715324162142976.0000000000 0.4075228816 -1.5988470318 1.4366543372 0.3132090987 0.4063249683 0.6641896591 -0.543739070983 +1403715324212143104.0000000000 0.4047111641 -1.6075399455 1.4423245909 0.3080633869 0.4093220590 0.6664704743 -0.541635955746 +1403715324262142976.0000000000 0.4046910378 -1.6154314901 1.4484710357 0.3025280978 0.4123972147 0.6682021383 -0.540288061826 +1403715324312143104.0000000000 0.4070653838 -1.6223142390 1.4546161976 0.2959671410 0.4158971430 0.6693295513 -0.539843467689 +1403715324362142976.0000000000 0.4115721118 -1.6279158669 1.4617845061 0.2871774148 0.4212567229 0.6702242436 -0.539324919831 +1403715324412143104.0000000000 0.4180982915 -1.6317428427 1.4682849651 0.2772991477 0.4269708810 0.6737980359 -0.535534551862 +1403715324462142976.0000000000 0.4259718907 -1.6336053837 1.4746369744 0.2681145613 0.4324820862 0.6788064526 -0.529429529816 +1403715324512143104.0000000000 0.4338069036 -1.6340706753 1.4808784707 0.2610229505 0.4368353153 0.6832512340 -0.523650339316 +1403715324562142976.0000000000 0.4408033538 -1.6333422764 1.4875750694 0.2562687319 0.4398846413 0.6873126303 -0.518101522491 +1403715324612143104.0000000000 0.4464719871 -1.6317110220 1.4951033216 0.2541011116 0.4415360676 0.6898712682 -0.514350230306 +1403715324662142976.0000000000 0.4508195756 -1.6290666753 1.5025584257 0.2542964467 0.4416402395 0.6916491970 -0.511770069853 +1403715324712143104.0000000000 0.4540262433 -1.6252744948 1.5102633209 0.2556498903 0.4410976694 0.6925252493 -0.510377075054 +1403715324762142976.0000000000 0.4561455554 -1.6205365259 1.5174112914 0.2586006579 0.4394004805 0.6934395768 -0.509111452265 +1403715324812143104.0000000000 0.4574302084 -1.6152191741 1.5239234161 0.2642774310 0.4356945568 0.6949738001 -0.507286023677 +1403715324862142976.0000000000 0.4580768898 -1.6096516502 1.5296983239 0.2712777879 0.4309214145 0.6961682289 -0.506028549972 +1403715324912143104.0000000000 0.4582738824 -1.6043593156 1.5353397070 0.2780239265 0.4260381701 0.6961213993 -0.506566058212 +1403715324962142976.0000000000 0.4585616632 -1.5994980228 1.5407910348 0.2826697899 0.4224193084 0.6946822328 -0.508995396161 +1403715325012143104.0000000000 0.4592042049 -1.5949160158 1.5457731016 0.2860254131 0.4194222326 0.6929336731 -0.511974001751 +1403715325062142976.0000000000 0.4605755157 -1.5905394725 1.5503589457 0.2879834705 0.4175175973 0.6911834785 -0.514791196233 +1403715325112143104.0000000000 0.4630134698 -1.5861170559 1.5545207487 0.2885994803 0.4161823387 0.6890479861 -0.518377732731 +1403715325162142976.0000000000 0.4663692491 -1.5814759663 1.5576163596 0.2888830104 0.4150862416 0.6881909627 -0.520233810122 +1403715325212143104.0000000000 0.4706958271 -1.5765279694 1.5605065845 0.2889314022 0.4141753951 0.6873979720 -0.521978366347 +1403715325262142976.0000000000 0.4762824643 -1.5714191189 1.5622491918 0.2875477802 0.4141436432 0.6874586764 -0.522687177165 +1403715325312143104.0000000000 0.4831134198 -1.5660702565 1.5636271843 0.2855014032 0.4144819730 0.6882607125 -0.522485248088 +1403715325362142976.0000000000 0.4909653784 -1.5600099039 1.5646660418 0.2829845252 0.4153533632 0.6899993202 -0.52086685458 +1403715325412143104.0000000000 0.4996479578 -1.5535263105 1.5654626296 0.2787026868 0.4172234932 0.6919731731 -0.519059242111 +1403715325462142976.0000000000 0.5089338188 -1.5466011037 1.5657565153 0.2741605197 0.4196499596 0.6943396304 -0.51635491522 +1403715325512143104.0000000000 0.5180434673 -1.5396021288 1.5655354494 0.2699182563 0.4219796150 0.6963607053 -0.513964111148 +1403715325562142976.0000000000 0.5269848994 -1.5327132958 1.5655810107 0.2657207323 0.4246319296 0.6969257379 -0.513200479957 +1403715325612143104.0000000000 0.5351056660 -1.5258839957 1.5668750565 0.2601898449 0.4284283808 0.6955734639 -0.514711495318 +1403715325662142976.0000000000 0.5423296019 -1.5183387802 1.5674798108 0.2548435622 0.4321751368 0.6939327033 -0.516465694115 +1403715325712143104.0000000000 0.5486312120 -1.5098383810 1.5677599676 0.2507212500 0.4351236200 0.6930453511 -0.517198638258 +1403715325762142976.0000000000 0.5535752029 -1.5001016365 1.5679372498 0.2475254293 0.4375967956 0.6929350693 -0.516798989944 +1403715325812143104.0000000000 0.5574413807 -1.4888727599 1.5680112686 0.2464081633 0.4387007436 0.6937787020 -0.515262833191 +1403715325862142976.0000000000 0.5600904936 -1.4767155275 1.5676686765 0.2464703675 0.4390903117 0.6947251707 -0.513623396375 +1403715325912143104.0000000000 0.5616576259 -1.4634842101 1.5668992742 0.2470623301 0.4392669161 0.6957475698 -0.511800840704 +1403715325962142976.0000000000 0.5619848869 -1.4493951683 1.5658162890 0.2480492892 0.4390123588 0.6971101907 -0.509683314406 +1403715326012143104.0000000000 0.5605543321 -1.4345638253 1.5643443942 0.2506445065 0.4381793624 0.6979109815 -0.508031927719 +1403715326062142976.0000000000 0.5574685004 -1.4190653829 1.5624629041 0.2547951855 0.4364965046 0.6985350082 -0.506556075074 +1403715326112143104.0000000000 0.5530903845 -1.4030785109 1.5595670189 0.2603279918 0.4340337355 0.6994491764 -0.504593799749 +1403715326162142976.0000000000 0.5477061833 -1.3869780377 1.5564555746 0.2662959720 0.4312333961 0.7000762610 -0.503008391821 +1403715326212143104.0000000000 0.5416793220 -1.3708329651 1.5524493080 0.2713599809 0.4289893870 0.7004558934 -0.501690550046 +1403715326262142976.0000000000 0.5350459799 -1.3550139144 1.5478696575 0.2765868170 0.4265757655 0.7002068490 -0.501241675727 +1403715326312143104.0000000000 0.5284556252 -1.3393595761 1.5433246348 0.2809504273 0.4247134487 0.6986186780 -0.502610472105 +1403715326362142976.0000000000 0.5217192356 -1.3241774383 1.5389932097 0.2859855496 0.4225103563 0.6955571031 -0.505863203371 +1403715326412143104.0000000000 0.5150919009 -1.3097610710 1.5350108181 0.2901522754 0.4208584202 0.6915882072 -0.510289720636 +1403715326462142976.0000000000 0.5086061261 -1.2960186703 1.5311190602 0.2930322463 0.4199704818 0.6881734382 -0.513978808972 +1403715326512143104.0000000000 0.5031326108 -1.2821618916 1.5272267316 0.2961598271 0.4187816065 0.6849132190 -0.517498990629 +1403715326562142976.0000000000 0.4995978506 -1.2678524722 1.5223332026 0.2985681403 0.4181362999 0.6824794190 -0.519847038061 +1403715326612143104.0000000000 0.4975844400 -1.2531602030 1.5169926466 0.3012773733 0.4171259415 0.6808098856 -0.521282833943 +1403715326662142976.0000000000 0.4971649839 -1.2380114598 1.5120721978 0.3022818026 0.4174815932 0.6797529288 -0.521795732932 +1403715326712143104.0000000000 0.4979625879 -1.2223551764 1.5069671397 0.3027110712 0.4183984687 0.6795494430 -0.521077041575 +1403715326762142976.0000000000 0.5002068478 -1.2065818430 1.5013397487 0.3002463134 0.4212349355 0.6803801468 -0.519130172714 +1403715326812143104.0000000000 0.5038379767 -1.1903705113 1.4956865737 0.2961158123 0.4250247339 0.6818885948 -0.516427483319 +1403715326862142976.0000000000 0.5087229069 -1.1739865472 1.4899345669 0.2917515818 0.4292769747 0.6832079313 -0.513643082394 +1403715326912143104.0000000000 0.5145000788 -1.1570995769 1.4839740837 0.2880454896 0.4326726601 0.6854054329 -0.509944661355 +1403715326962142976.0000000000 0.5208906639 -1.1398508086 1.4785672297 0.2846241354 0.4362401361 0.6861082874 -0.507877015832 +1403715327012143104.0000000000 0.5272960362 -1.1223609634 1.4735275932 0.2808173429 0.4398294565 0.6861770593 -0.506806385602 +1403715327062142976.0000000000 0.5334970427 -1.1043756363 1.4691172248 0.2774675515 0.4429292570 0.6858189386 -0.506436387526 +1403715327112143104.0000000000 0.5390919259 -1.0857505526 1.4647288372 0.2745203458 0.4457589209 0.6857876441 -0.505601494645 +1403715327162142976.0000000000 0.5441398023 -1.0663782967 1.4601942825 0.2720390061 0.4479411989 0.6863459587 -0.504254584987 +1403715327212143104.0000000000 0.5484487433 -1.0463376228 1.4554838088 0.2695170919 0.4501850648 0.6867945457 -0.502998207331 +1403715327262142976.0000000000 0.5518551095 -1.0253571666 1.4513878118 0.2673389977 0.4524039149 0.6871554741 -0.501675106564 +1403715327312143104.0000000000 0.5539943586 -1.0038778688 1.4481961594 0.2653522198 0.4545052897 0.6870855719 -0.500925701029 +1403715327362142976.0000000000 0.5546965454 -0.9817550404 1.4451526083 0.2636078757 0.4564746928 0.6870934572 -0.500044321853 +1403715327412143104.0000000000 0.5540812959 -0.9588594093 1.4418549894 0.2621244748 0.4584674515 0.6867426783 -0.499482581711 +1403715327462142976.0000000000 0.5521475236 -0.9353347746 1.4384136300 0.2616135890 0.4584584258 0.6875015311 -0.498714193347 +1403715327512143104.0000000000 0.5489309683 -0.9109501382 1.4352641340 0.2605012157 0.4577275256 0.6882492195 -0.498936509802 +1403715327562142976.0000000000 0.5441406628 -0.8853870430 1.4317697174 0.2614400851 0.4542133434 0.6906850079 -0.498290618394 +1403715327612143104.0000000000 0.5377113576 -0.8593885033 1.4281093006 0.2629288297 0.4491693877 0.6939183433 -0.497586800957 +1403715327662142976.0000000000 0.5303067658 -0.8332508087 1.4243842343 0.2632908332 0.4434382612 0.6975903790 -0.497401355928 +1403715327712143104.0000000000 0.5219197013 -0.8069933676 1.4206525426 0.2631652940 0.4364818825 0.7018055142 -0.497691284394 +1403715327762142976.0000000000 0.5128617353 -0.7810820164 1.4172077873 0.2610381714 0.4293093188 0.7059444433 -0.499194375745 +1403715327812143104.0000000000 0.5030649324 -0.7552542589 1.4132681359 0.2580844875 0.4214866210 0.7108122739 -0.500487099611 +1403715327862142976.0000000000 0.4926957850 -0.7298457404 1.4091575806 0.2538577618 0.4132333432 0.7155208291 -0.50281645153 +1403715327912143104.0000000000 0.4816735842 -0.7051123277 1.4048467752 0.2502178255 0.4040172152 0.7198332729 -0.505965600522 +1403715327962142976.0000000000 0.4698021936 -0.6808534237 1.4002449275 0.2471475886 0.3943788050 0.7237873866 -0.509426389813 +1403715328012143104.0000000000 0.4571595528 -0.6568169538 1.3957807471 0.2456563901 0.3852811543 0.7268214754 -0.512778619965 +1403715328062142976.0000000000 0.4439343452 -0.6329719133 1.3914541175 0.2441589913 0.3780840266 0.7288792388 -0.515920450303 +1403715328112143104.0000000000 0.4299820801 -0.6095998332 1.3876082140 0.2442656857 0.3715469386 0.7296764902 -0.519479900354 +1403715328162142976.0000000000 0.4158234023 -0.5866813335 1.3845392838 0.2453408024 0.3661480765 0.7297787855 -0.522653232069 +1403715328212143104.0000000000 0.4017768421 -0.5642291526 1.3821023931 0.2478764863 0.3613725930 0.7290405620 -0.525801250953 +1403715328262142976.0000000000 0.3885263142 -0.5419999466 1.3801608318 0.2502645969 0.3579931897 0.7276771572 -0.528861477636 +1403715328312143104.0000000000 0.3761007070 -0.5197589126 1.3783287493 0.2534740400 0.3555104958 0.7262533322 -0.530960729205 +1403715328362142976.0000000000 0.3647408171 -0.4977851454 1.3765009671 0.2567900316 0.3543763128 0.7249835970 -0.531860031037 +1403715328412143104.0000000000 0.3548894516 -0.4759063983 1.3750118671 0.2599552232 0.3541390912 0.7236195520 -0.532337796866 +1403715328462142976.0000000000 0.3467840511 -0.4541440529 1.3735205286 0.2625146420 0.3547609906 0.7228556039 -0.531705255026 +1403715328512143104.0000000000 0.3403007120 -0.4327329533 1.3720446887 0.2641420049 0.3562597767 0.7223755546 -0.530548330355 +1403715328562142976.0000000000 0.3355722764 -0.4115210762 1.3700440521 0.2642519494 0.3585924301 0.7234881646 -0.527396674317 +1403715328612143104.0000000000 0.3325317495 -0.3908059953 1.3675394047 0.2631137011 0.3598998024 0.7262809963 -0.523220055922 +1403715328662142976.0000000000 0.3309774461 -0.3709390398 1.3650756493 0.2607390492 0.3604134212 0.7299435120 -0.518941020962 +1403715328712143104.0000000000 0.3307758098 -0.3522100488 1.3630253517 0.2576570263 0.3594966353 0.7327777278 -0.517118775111 +1403715328762142976.0000000000 0.3320212774 -0.3348947789 1.3607553184 0.2518821536 0.3578812108 0.7364903822 -0.515808430095 +1403715328812143104.0000000000 0.3344257460 -0.3189590854 1.3585795606 0.2456222555 0.3537689575 0.7400122330 -0.516622809492 +1403715328862142976.0000000000 0.3376698789 -0.3044253009 1.3566505452 0.2385812506 0.3477250650 0.7431598550 -0.519499466754 +1403715328912143104.0000000000 0.3414692607 -0.2911061320 1.3546293616 0.2306918794 0.3397723101 0.7468171689 -0.52306801694 +1403715328962142976.0000000000 0.3462205628 -0.2787490620 1.3524973513 0.2223877770 0.3295629984 0.7508965928 -0.527338803442 +1403715329012143104.0000000000 0.3516202973 -0.2673239778 1.3504623964 0.2132236989 0.3178964921 0.7550359648 -0.532351543947 +1403715329062142976.0000000000 0.3578013421 -0.2564373503 1.3479561175 0.2031883862 0.3055084022 0.7598044230 -0.536727430449 +1403715329112143104.0000000000 0.3643914143 -0.2462934523 1.3455950766 0.1916784885 0.2929004835 0.7641459834 -0.541802159358 +1403715329162142976.0000000000 0.3710248766 -0.2368102134 1.3427026633 0.1803085018 0.2795203191 0.7690804836 -0.545776918875 +1403715329212143104.0000000000 0.3775608972 -0.2277216725 1.3390784318 0.1696962294 0.2661252192 0.7740938362 -0.548779819476 +1403715329262142976.0000000000 0.3839444575 -0.2189259885 1.3349562297 0.1598025508 0.2534782407 0.7790945092 -0.550657490647 +1403715329312143104.0000000000 0.3897761008 -0.2106242177 1.3310345423 0.1510698387 0.2427164077 0.7828279598 -0.552672628828 +1403715329362142976.0000000000 0.3952682594 -0.2027265371 1.3266651432 0.1435392674 0.2339285511 0.7858512247 -0.554176654443 +1403715329412143104.0000000000 0.4005018748 -0.1951206289 1.3212084680 0.1372451795 0.2266476974 0.7877880040 -0.556043741769 +1403715329462142976.0000000000 0.4053577992 -0.1877049146 1.3144412372 0.1320176588 0.2208634910 0.7900206260 -0.556469286253 +1403715329512143104.0000000000 0.4097748214 -0.1808818691 1.3077986913 0.1286740924 0.2158855998 0.7915906714 -0.556974500971 +1403715329562142976.0000000000 0.4140099678 -0.1745785771 1.3009207536 0.1248763387 0.2126449217 0.7933084922 -0.556641422732 +1403715329612143104.0000000000 0.4178206130 -0.1684468041 1.2946588552 0.1232577770 0.2095695971 0.7948138853 -0.556020676028 +1403715329662142976.0000000000 0.4208884674 -0.1630799341 1.2893529953 0.1222863122 0.2077027722 0.7950677240 -0.556572484482 +1403715329712143104.0000000000 0.4235918274 -0.1583750543 1.2837057685 0.1223245079 0.2063219101 0.7946188082 -0.557717611194 +1403715329762142976.0000000000 0.4265148464 -0.1539925127 1.2772478400 0.1221163356 0.2059578241 0.7936203906 -0.559317129037 +1403715329812143104.0000000000 0.4292804957 -0.1500171232 1.2699152815 0.1220481355 0.2058647583 0.7927873173 -0.560546361535 +1403715329862142976.0000000000 0.4320532409 -0.1464344133 1.2620398561 0.1217577453 0.2064680002 0.7922888728 -0.561092112173 +1403715329912143104.0000000000 0.4344218885 -0.1434683443 1.2536122091 0.1221681987 0.2069672613 0.7916517721 -0.561717861256 +1403715329962142976.0000000000 0.4366259788 -0.1409841186 1.2450173365 0.1217738037 0.2076664289 0.7913868690 -0.561918693983 +1403715330012143104.0000000000 0.4391119646 -0.1384545527 1.2357590687 0.1202511333 0.2074810913 0.7911533495 -0.562643438835 +1403715330062142976.0000000000 0.4418105491 -0.1361314652 1.2257672460 0.1181309849 0.2064060108 0.7909123124 -0.563825631981 +1403715330112143104.0000000000 0.4443422401 -0.1334962791 1.2143420273 0.1164711479 0.2049755535 0.7916968579 -0.563591677842 +1403715330162142976.0000000000 0.4463368567 -0.1308628550 1.2021923399 0.1166857183 0.2022922833 0.7929517492 -0.562751986909 +1403715330212143104.0000000000 0.4479565154 -0.1285746381 1.1905027523 0.1171275901 0.1999570764 0.7946407290 -0.561109977704 +1403715330262142976.0000000000 0.4493641738 -0.1269892216 1.1792428376 0.1174645570 0.1984058863 0.7966890908 -0.558680297373 +1403715330312143104.0000000000 0.4505610058 -0.1257689856 1.1687030589 0.1182666347 0.1970638365 0.7981942300 -0.556834642186 +1403715330362142976.0000000000 0.4517260916 -0.1251041080 1.1586351108 0.1186400322 0.1965604798 0.7993218847 -0.555313465655 +1403715330412143104.0000000000 0.4528917805 -0.1252555663 1.1497200685 0.1180938070 0.1966819491 0.7994403754 -0.555216309034 +1403715330462142976.0000000000 0.4540344347 -0.1256600576 1.1433305505 0.1173648777 0.1970365037 0.7984857279 -0.55661714318 +1403715330512143104.0000000000 0.4549160872 -0.1264295357 1.1394499038 0.1158843341 0.1980657057 0.7978801293 -0.557429902787 +1403715330562142976.0000000000 0.4552739654 -0.1278798157 1.1383940102 0.1161759473 0.1977206335 0.7977771236 -0.557639095993 +1403715330612143104.0000000000 0.4552724030 -0.1300509040 1.1410998292 0.1155301682 0.1984201945 0.7962054552 -0.559766987053 +1403715330662142976.0000000000 0.4552239227 -0.1322546531 1.1475744103 0.1142456884 0.1998501653 0.7932571950 -0.563693938867 +1403715330712143104.0000000000 0.4553557204 -0.1340534385 1.1566505170 0.1116762699 0.2017502790 0.7906620871 -0.567167259033 +1403715330762142976.0000000000 0.4556796077 -0.1355990746 1.1669653560 0.1065203174 0.2036816005 0.7888938602 -0.569924297476 +1403715330812143104.0000000000 0.4562927952 -0.1367561542 1.1774196412 0.0997806133 0.2039713444 0.7880717988 -0.572173365228 +1403715330862142976.0000000000 0.4569582896 -0.1372045370 1.1873629551 0.0941932297 0.2008628597 0.7889754761 -0.572974209806 +1403715330912143104.0000000000 0.4576192343 -0.1372679068 1.1966337978 0.0867398797 0.1962577634 0.7903826658 -0.573806871001 +1403715330962142976.0000000000 0.4576892032 -0.1371128753 1.2057027050 0.0790439618 0.1896543557 0.7917177013 -0.575296757252 +1403715331012143104.0000000000 0.4571274329 -0.1361121188 1.2147495864 0.0706355562 0.1816393714 0.7935408310 -0.576463968015 +1403715331062142976.0000000000 0.4557655857 -0.1340760009 1.2241467195 0.0609982884 0.1730257337 0.7956797562 -0.577265129612 +1403715331112143104.0000000000 0.4531348710 -0.1310465095 1.2343662115 0.0523802244 0.1628376187 0.7980931092 -0.577743551347 +1403715331162142976.0000000000 0.4488756290 -0.1273548612 1.2452545514 0.0462882374 0.1504852592 0.8017895887 -0.576493747805 +1403715331212143104.0000000000 0.4426959790 -0.1234299773 1.2574974856 0.0414311107 0.1388021610 0.8045016450 -0.576016081635 +1403715331262142976.0000000000 0.4347705026 -0.1192176501 1.2709320334 0.0386285701 0.1276250190 0.8067951390 -0.57558777933 +1403715331312143104.0000000000 0.4253643271 -0.1146707745 1.2854098899 0.0382511628 0.1168220131 0.8091583642 -0.574588728984 +1403715331362142976.0000000000 0.4148562963 -0.1101823101 1.3015675914 0.0393364763 0.1068009919 0.8109129924 -0.57399155783 +1403715331412143104.0000000000 0.4034500470 -0.1057079568 1.3193802861 0.0395344402 0.0993181083 0.8120665766 -0.573690523282 +1403715331462142976.0000000000 0.3915254676 -0.1014441727 1.3381367716 0.0385130453 0.0945489802 0.8123033732 -0.57423032455 +1403715331512143104.0000000000 0.3792777612 -0.0973975009 1.3570230982 0.0378141248 0.0904197058 0.8128241239 -0.574204939412 +1403715331562142976.0000000000 0.3668272183 -0.0935410111 1.3759370338 0.0365193707 0.0875130116 0.8127051648 -0.574907056376 +1403715331612143104.0000000000 0.3542489824 -0.0897030864 1.3940141525 0.0344310292 0.0860875388 0.8131111526 -0.574677033999 +1403715331662142976.0000000000 0.3412197835 -0.0860051870 1.4116260991 0.0344724021 0.0842196274 0.8127575997 -0.57545094662 +1403715331712143104.0000000000 0.3277662850 -0.0824253139 1.4284215861 0.0372066450 0.0816585736 0.8122740085 -0.576331916507 +1403715331762142976.0000000000 0.3142415883 -0.0790274334 1.4443543832 0.0403052962 0.0795230677 0.8124862824 -0.576122908546 +1403715331812143104.0000000000 0.3007186616 -0.0757400925 1.4593574448 0.0425079637 0.0788966906 0.8122456496 -0.576389963365 +1403715331862142976.0000000000 0.2875728368 -0.0727371178 1.4738974156 0.0432208563 0.0797612946 0.8117847091 -0.576867124699 +1403715331912143104.0000000000 0.2747037122 -0.0698061980 1.4870123791 0.0442815977 0.0809539558 0.8118432515 -0.576538057821 +1403715331962142976.0000000000 0.2623964578 -0.0668408571 1.4980183245 0.0430049949 0.0836010616 0.8131740475 -0.574377403325 +1403715332012143104.0000000000 0.2506193791 -0.0642226769 1.5063708486 0.0409892382 0.0874492780 0.8135948316 -0.573355000142 +1403715332062142976.0000000000 0.2386856591 -0.0618737467 1.5113165033 0.0410965408 0.0906601917 0.8148842143 -0.571012715429 +1403715332112143104.0000000000 0.2267063700 -0.0599097137 1.5133571306 0.0417891713 0.0935987563 0.8160918025 -0.568759270621 +1403715332162142976.0000000000 0.2148845057 -0.0585066576 1.5138732362 0.0395594887 0.0987370892 0.8171648020 -0.566504828281 +1403715332212143104.0000000000 0.2030614689 -0.0583160186 1.5143030732 0.0349731979 0.1044155975 0.8173287498 -0.565551034978 +1403715332262142976.0000000000 0.1911257743 -0.0589206123 1.5156042057 0.0297948862 0.1088747407 0.8162695376 -0.566535610115 +1403715332312143104.0000000000 0.1786460329 -0.0598658358 1.5174450611 0.0254184755 0.1115959702 0.8150325265 -0.567998434218 +1403715332362142976.0000000000 0.1654798678 -0.0609758161 1.5192858207 0.0216300246 0.1119735865 0.8153602236 -0.567610573974 +1403715332412143104.0000000000 0.1512703153 -0.0624648992 1.5210994278 0.0195151323 0.1101364790 0.8163322299 -0.566648750202 +1403715332462142976.0000000000 0.1357046056 -0.0647056417 1.5231829616 0.0189126275 0.1074741907 0.8179618160 -0.564827476698 +1403715332512143104.0000000000 0.1190948582 -0.0677827937 1.5254890602 0.0173090196 0.1053065239 0.8199085961 -0.562459623396 +1403715332562142976.0000000000 0.1013875154 -0.0721299159 1.5272123136 0.0174924104 0.1026495038 0.8215631712 -0.560527475372 +1403715332612143104.0000000000 0.0825582622 -0.0779640397 1.5295586922 0.0171461973 0.1009062058 0.8215098216 -0.560932757673 +1403715332662142976.0000000000 0.0626831797 -0.0849679399 1.5325708628 0.0167391868 0.0993584875 0.8207007083 -0.562403803346 +1403715332712143104.0000000000 0.0414944322 -0.0927440295 1.5359033056 0.0167761049 0.0972175587 0.8197337985 -0.564184197038 +1403715332762142976.0000000000 0.0193422802 -0.1012723039 1.5391714965 0.0168650228 0.0945887579 0.8198706143 -0.564429547101 +1403715332812143104.0000000000 -0.0036019846 -0.1109367102 1.5423639397 0.0175274082 0.0907045711 0.8198657051 -0.565053711069 +1403715332862142976.0000000000 -0.0272387090 -0.1218956561 1.5453427123 0.0179343394 0.0860775009 0.8201563982 -0.565342821468 +1403715332912143104.0000000000 -0.0511131061 -0.1341395104 1.5495226504 0.0174833030 0.0811866053 0.8165525286 -0.571266170262 +1403715332962142976.0000000000 -0.0754220338 -0.1472670203 1.5546245674 0.0167001981 0.0756640911 0.8104705777 -0.580631975805 +1403715333012143104.0000000000 -0.0998152538 -0.1601747174 1.5603263079 0.0149831710 0.0697908999 0.8039838400 -0.590351352884 +1403715333062142976.0000000000 -0.1246568709 -0.1722551720 1.5654469664 0.0126990411 0.0644975197 0.7984722449 -0.598432016498 +1403715333112143104.0000000000 -0.1499146787 -0.1828224764 1.5694143062 0.0111591008 0.0599216381 0.7944358623 -0.604281831979 +1403715333162142976.0000000000 -0.1753056316 -0.1921135225 1.5722555544 0.0103957285 0.0557625162 0.7918995009 -0.608011226096 +1403715333212143104.0000000000 -0.2008366737 -0.1996086118 1.5736467917 0.0099143177 0.0525966391 0.7907991409 -0.609731103519 +1403715333262142976.0000000000 -0.2262659469 -0.2051175863 1.5736515221 0.0092612833 0.0502137153 0.7916850220 -0.608791949202 +1403715333312143104.0000000000 -0.2515954430 -0.2090639200 1.5725881185 0.0084352303 0.0484843114 0.7937412445 -0.606261457749 +1403715333362142976.0000000000 -0.2768624679 -0.2116066000 1.5706028364 0.0086675701 0.0469292778 0.7961895032 -0.603162325701 +1403715333412143104.0000000000 -0.3017422325 -0.2126089918 1.5679727800 0.0086366476 0.0458935794 0.7988729473 -0.599684251679 +1403715333462142976.0000000000 -0.3263046425 -0.2121488064 1.5649381265 0.0084608958 0.0453753258 0.8009384754 -0.596964866316 +1403715333512143104.0000000000 -0.3506274056 -0.2105073151 1.5620860786 0.0081114479 0.0454966856 0.8015761133 -0.596104009911 +1403715333562142976.0000000000 -0.3748115720 -0.2081141241 1.5592671311 0.0072960806 0.0460375324 0.8012875890 -0.596460822346 +1403715333612143104.0000000000 -0.3988750118 -0.2048999112 1.5558873708 0.0075172451 0.0458238655 0.8005957267 -0.597402834612 +1403715333662142976.0000000000 -0.4226517971 -0.2004593300 1.5515451968 0.0069130313 0.0458453748 0.8022052805 -0.595245411183 +1403715333712143104.0000000000 -0.4462397841 -0.1948080354 1.5465356429 0.0061969017 0.0458587162 0.8053349193 -0.591011204854 +1403715333762142976.0000000000 -0.4697415725 -0.1882810487 1.5410969411 0.0052985253 0.0460782441 0.8099446484 -0.584669468678 +1403715333812143104.0000000000 -0.4930510568 -0.1811687895 1.5358102425 0.0038219249 0.0456489259 0.8141706592 -0.578815779146 +1403715333862142976.0000000000 -0.5161460451 -0.1738347796 1.5311525626 0.0013949439 0.0436853646 0.8174846563 -0.57428954355 +1403715333912143104.0000000000 -0.5392223849 -0.1667833111 1.5273393216 0.0015967074 -0.0408299912 -0.8198603500 0.57110364111 +1403715333962142976.0000000000 -0.5621820436 -0.1604664220 1.5245931075 0.0039763960 -0.0362646986 -0.8210478191 0.569692494794 +1403715334012143104.0000000000 -0.5848937246 -0.1548004240 1.5230011618 0.0081404307 -0.0317596851 -0.8214010703 0.569407883245 +1403715334062142976.0000000000 -0.6073884721 -0.1501081152 1.5220931415 0.0129188106 -0.0270838013 -0.8219212502 0.568810188408 +1403715334112143104.0000000000 -0.6300838822 -0.1460593313 1.5219467073 0.0172054850 -0.0227031466 -0.8221885443 0.568502010537 +1403715334162142976.0000000000 -0.6531866402 -0.1426286866 1.5222299148 0.0206272985 -0.0180570626 -0.8227934270 0.567678988085 +1403715334212143104.0000000000 -0.6766458446 -0.1399135647 1.5229553365 0.0240793755 -0.0145851164 -0.8233746327 0.566799499241 +1403715334262142976.0000000000 -0.7002660707 -0.1379649954 1.5238588117 0.0267928330 -0.0115841745 -0.8240534886 0.565759488582 +1403715334312143104.0000000000 -0.7242668401 -0.1368320485 1.5248976701 0.0287779733 -0.0089322095 -0.8239904646 0.565801871788 +1403715334362142976.0000000000 -0.7486070364 -0.1363811224 1.5257286066 0.0301593750 -0.0065396623 -0.8242422161 0.565395803029 +1403715334412143104.0000000000 -0.7732853507 -0.1370240513 1.5265657020 0.0310042504 -0.0047286069 -0.8241286650 0.56553365974 +1403715334462142976.0000000000 -0.7979651150 -0.1385286018 1.5276857812 0.0320951005 -0.0033978488 -0.8240173565 0.565644548642 +1403715334512143104.0000000000 -0.8228524775 -0.1407494176 1.5287692143 0.0325603302 -0.0023794778 -0.8237457881 0.566018585829 +1403715334562142976.0000000000 -0.8480444461 -0.1436073133 1.5299374320 0.0325912667 -0.0011534065 -0.8229313435 0.567204092827 +1403715334612143104.0000000000 -0.8732672836 -0.1468257446 1.5305418397 0.0319112409 0.0007679979 -0.8227902469 0.567448052637 +1403715334662142976.0000000000 -0.8986272471 -0.1504574333 1.5307207226 0.0303055957 0.0027759274 -0.8228532447 0.567438457258 +1403715334712143104.0000000000 -0.9238865573 -0.1546261538 1.5309062736 0.0296521127 0.0035851761 -0.8225022596 0.567977052135 +1403715334762142976.0000000000 -0.9489624523 -0.1594249888 1.5308633371 0.0288574984 0.0042542407 -0.8222187295 0.56842370381 +1403715334812143104.0000000000 -0.9737265721 -0.1648006189 1.5308008221 0.0278260972 0.0047419581 -0.8223176331 0.568328190826 +1403715334862142976.0000000000 -0.9983114288 -0.1706840193 1.5305675272 0.0267584541 0.0051462505 -0.8220893243 0.568706114026 +1403715334912143104.0000000000 -1.0228118190 -0.1769925213 1.5302099215 0.0260415213 0.0053003753 -0.8220491340 0.568796067511 +1403715334962142976.0000000000 -1.0470713522 -0.1837397670 1.5294070646 0.0249788866 0.0054091961 -0.8225307353 0.568146094978 +1403715335012143104.0000000000 -1.0709105841 -0.1906786806 1.5286826741 0.0247594677 0.0055849288 -0.8224230414 0.568309878791 +1403715335062142976.0000000000 -1.0941693002 -0.1978666954 1.5276973632 0.0249295353 0.0064682595 -0.8228091046 0.567733967006 +1403715335112143104.0000000000 -1.1169395028 -0.2056140368 1.5268261813 0.0250314547 0.0073639581 -0.8230137340 0.567421881904 +1403715335162142976.0000000000 -1.1394193275 -0.2138567332 1.5258458501 0.0246176844 0.0084822047 -0.8230720639 0.567339756608 +1403715335212143104.0000000000 -1.1611944747 -0.2226002784 1.5248765823 0.0247741299 0.0088234335 -0.8233621795 0.566906615659 +1403715335262142976.0000000000 -1.1823884837 -0.2315254935 1.5237320415 0.0248153108 0.0104583282 -0.8235895849 0.566546573027 +1403715335312143104.0000000000 -1.2028560921 -0.2407271549 1.5226567048 0.0258866740 0.0126270133 -0.8236152132 0.566417177733 +1403715335362142976.0000000000 -1.2226503281 -0.2503554129 1.5217601903 0.0278678520 0.0155998150 -0.8234581778 0.566477411687 +1403715335412143104.0000000000 -1.2418289658 -0.2602790635 1.5208205102 0.0303120585 0.0194341271 -0.8231416293 0.566693349166 +1403715335462142976.0000000000 -1.2603603422 -0.2705538185 1.5196458864 0.0332037282 0.0231848638 -0.8230153441 0.56657366499 +1403715335512143104.0000000000 -1.2784922303 -0.2814904706 1.5186639738 0.0373993698 0.0254021300 -0.8230571830 0.566156243886 +1403715335562142976.0000000000 -1.2964436928 -0.2929417535 1.5180509802 0.0419124810 0.0267550079 -0.8226992519 0.566298026153 +1403715335612143104.0000000000 -1.3140110335 -0.3046535439 1.5171941459 0.0459122751 0.0286206137 -0.8225349995 0.566135229459 +1403715335662142976.0000000000 -1.3311287971 -0.3165752709 1.5163455150 0.0503415462 0.0314446523 -0.8222418517 0.566034716127 +1403715335712143104.0000000000 -1.3479600303 -0.3289252867 1.5151129490 0.0533718630 0.0365374437 -0.8223579563 0.565282098689 +1403715335762142976.0000000000 -1.3644674649 -0.3417610100 1.5139475116 0.0570757425 0.0419534968 -0.8218052081 0.565348090672 +1403715335812143104.0000000000 -1.3809162964 -0.3549824548 1.5123288861 0.0602267312 0.0471370990 -0.8213260884 0.565309022809 +1403715335862142976.0000000000 -1.3973538778 -0.3686963883 1.5106530776 0.0631688809 0.0517717605 -0.8207217028 0.565460223056 +1403715335912143104.0000000000 -1.4137661262 -0.3827003602 1.5088020176 0.0655890546 0.0562335718 -0.8202408439 0.565456292976 +1403715335962142976.0000000000 -1.4301108564 -0.3971300442 1.5074895591 0.0689169443 0.0595536337 -0.8186057433 0.567087697369 +1403715336012143104.0000000000 -1.4465623496 -0.4117941197 1.5059642687 0.0703018703 0.0637704136 -0.8169773645 0.568804858686 +1403715336062142976.0000000000 -1.4627954915 -0.4267277089 1.5048939858 0.0723399617 0.0663923898 -0.8147721672 0.571406419358 +1403715336112143104.0000000000 -1.4788670756 -0.4417430070 1.5038671652 0.0745241602 0.0681470020 -0.8124207713 0.574260068302 +1403715336162142976.0000000000 -1.4948892523 -0.4567213402 1.5024880932 0.0752205466 0.0702773637 -0.8099920218 0.57733515923 +1403715336212143104.0000000000 -1.5105287081 -0.4714611259 1.5012428267 0.0769967757 0.0711908560 -0.8078360542 0.580003679371 +1403715336262142976.0000000000 -1.5260595738 -0.4851792156 1.4993952184 0.0790108715 0.0718899048 -0.8074627351 0.580166403024 +1403715336312143104.0000000000 -1.5417875233 -0.4983085097 1.4971088732 0.0794926693 0.0733058519 -0.8086894934 0.578211441279 +1403715336362142976.0000000000 -1.5575980838 -0.5109314708 1.4946115729 0.0802312153 0.0749199532 -0.8108730022 0.574834695345 +1403715336412143104.0000000000 -1.5733873618 -0.5232913645 1.4924582263 0.0799944453 0.0765159714 -0.8127186376 0.572044238569 +1403715336462142976.0000000000 -1.5890960512 -0.5356099449 1.4908010760 0.0785435158 0.0788432992 -0.8141111314 0.569945362285 +1403715336512143104.0000000000 -1.6042441051 -0.5479309628 1.4895854643 0.0788396968 0.0794653113 -0.8151768025 0.568292483758 +1403715336562142976.0000000000 -1.6191931789 -0.5605280368 1.4888843299 0.0788453289 0.0796726104 -0.8154925858 0.567809414974 +1403715336612143104.0000000000 -1.6337561803 -0.5732075496 1.4884304335 0.0794095124 0.0794436157 -0.8155173404 0.567727319058 +1403715336662142976.0000000000 -1.6480582127 -0.5860634622 1.4878536546 0.0791325443 0.0793651794 -0.8157968933 0.567375217654 +1403715336712143104.0000000000 -1.6620124769 -0.5989206624 1.4873666433 0.0787239055 0.0791658464 -0.8159205368 0.567282110689 +1403715336762142976.0000000000 -1.6757201753 -0.6121079024 1.4872938737 0.0784287571 0.0787961239 -0.8160565625 0.567178796925 +1403715336812143104.0000000000 -1.6891308782 -0.6256181277 1.4876494621 0.0774775993 0.0790896045 -0.8159767277 0.567383499834 +1403715336862142976.0000000000 -1.7021256944 -0.6393112802 1.4886568545 0.0768616573 0.0790749323 -0.8157036407 0.567861788826 +1403715336912143104.0000000000 -1.7145436039 -0.6532590108 1.4903891753 0.0768062589 0.0789656173 -0.8155893326 0.568048651534 +1403715336962142976.0000000000 -1.7266151931 -0.6673918025 1.4929794974 0.0758434071 0.0792904229 -0.8151284578 0.568793814797 +1403715337012143104.0000000000 -1.7380697478 -0.6814149004 1.4962230274 0.0756273319 0.0798342751 -0.8150057828 0.568922287531 +1403715337062142976.0000000000 -1.7487494092 -0.6949864453 1.5002374351 0.0756803373 0.0816978283 -0.8150434080 0.568596688701 +1403715337112143104.0000000000 -1.7585717080 -0.7079393141 1.5046042920 0.0774795071 0.0840253931 -0.8158543476 0.566849488642 +1403715337162142976.0000000000 -1.7674853666 -0.7205300975 1.5090815794 0.0788965781 0.0887197302 -0.8164903179 0.565020088262 +1403715337212143104.0000000000 -1.7753963080 -0.7331477724 1.5137824164 0.0825468211 0.0931517260 -0.8170813550 0.562927026856 +1403715337262142976.0000000000 -1.7822873568 -0.7460533181 1.5186870642 0.0882141894 0.0975491040 -0.8175561002 0.560628622287 +1403715337312143104.0000000000 -1.7884372102 -0.7591845927 1.5235929993 0.0947390193 0.1026034018 -0.8180270085 0.557968523814 +1403715337362142976.0000000000 -1.7942585454 -0.7729565715 1.5282515761 0.1014033269 0.1069311134 -0.8185364769 0.555230707191 +1403715337412143104.0000000000 -1.8000241637 -0.7875337780 1.5328024378 0.1079592360 0.1104402973 -0.8188388245 0.552856874436 +1403715337462142976.0000000000 -1.8058173779 -0.8030583851 1.5374443434 0.1144551299 0.1130324998 -0.8180233956 0.552233104254 +1403715337512143104.0000000000 -1.8116651963 -0.8193003628 1.5420883410 0.1221863892 0.1136849160 -0.8173965178 0.551370255652 +1403715337562142976.0000000000 -1.8179797661 -0.8365689679 1.5462123678 0.1275513410 0.1148788259 -0.8159743658 0.552013899317 +1403715337612143104.0000000000 -1.8248471019 -0.8548779909 1.5499219421 0.1291918251 0.1181018720 -0.8146839778 0.552857519161 +1403715337662142976.0000000000 -1.8321810666 -0.8739861754 1.5535107812 0.1294585034 0.1213478848 -0.8128569076 0.554778184944 +1403715337712143104.0000000000 -1.8397768922 -0.8935533093 1.5563707080 0.1290274967 0.1243862648 -0.8117751849 0.555788639069 +1403715337762142976.0000000000 -1.8475703857 -0.9136290111 1.5594281574 0.1287582395 0.1265013049 -0.8110873354 0.556377632522 +1403715337812143104.0000000000 -1.8555511308 -0.9342813276 1.5624960340 0.1282738645 0.1276848182 -0.8103663105 0.557269096235 +1403715337862142976.0000000000 -1.8637192964 -0.9553462894 1.5655625673 0.1271946164 0.1281992484 -0.8097383332 0.558310230983 +1403715337912143104.0000000000 -1.8717713908 -0.9768082996 1.5685975876 0.1249688639 0.1289688064 -0.8094109594 0.559109764512 +1403715337962142976.0000000000 -1.8797254735 -0.9985854645 1.5717930895 0.1228295029 0.1290409176 -0.8092570529 0.559789582983 +1403715338012143104.0000000000 -1.8875678751 -1.0202118566 1.5752594846 0.1218512484 0.1276148257 -0.8090853869 0.560577885933 +1403715338062142976.0000000000 -1.8954704881 -1.0418152198 1.5787458083 0.1215330120 0.1252706760 -0.8091703804 0.561052831958 +1403715338112143104.0000000000 -1.9033367739 -1.0632577088 1.5823424911 0.1215128790 0.1226756235 -0.8092218204 0.561556192151 +1403715338162142976.0000000000 -1.9111490262 -1.0845169942 1.5854869840 0.1217803894 0.1216126211 -0.8091887875 0.561777013879 +1403715338212143104.0000000000 -1.9187217395 -1.1056176895 1.5880533065 0.1228590073 0.1209541150 -0.8091660005 0.561717144127 +1403715338262142976.0000000000 -1.9258711260 -1.1265270862 1.5904526586 0.1250471908 0.1208632762 -0.8089301040 0.561593585568 +1403715338312143104.0000000000 -1.9328944241 -1.1473599475 1.5926709684 0.1278527504 0.1216012804 -0.8090359128 0.560649350894 +1403715338362142976.0000000000 -1.9397926823 -1.1679687045 1.5953009154 0.1320813234 0.1228834663 -0.8091453168 0.559229857917 +1403715338412143104.0000000000 -1.9468901066 -1.1886490451 1.5982833632 0.1364893438 0.1261339675 -0.8083400477 0.558611894413 +1403715338462142976.0000000000 -1.9545706776 -1.2093649122 1.6014325943 0.1410694675 0.1305454083 -0.8074889662 0.557690659028 +1403715338512143104.0000000000 -1.9624853665 -1.2301888099 1.6046451803 0.1460484588 0.1361482135 -0.8067242578 0.556173968808 +1403715338562142976.0000000000 -1.9708372049 -1.2515095828 1.6082748721 0.1500657925 0.1436909683 -0.8048601784 0.555907597305 +1403715338612143104.0000000000 -1.9797146798 -1.2729220771 1.6125253483 0.1540294714 0.1522608081 -0.8027159810 0.555642530918 +1403715338662142976.0000000000 -1.9889544613 -1.2945897434 1.6170865987 0.1585621274 0.1615524793 -0.8001843875 0.555395169442 +1403715338712143104.0000000000 -1.9987727752 -1.3163105754 1.6217535112 0.1630104851 0.1711158558 -0.7976753131 0.554852269093 +1403715338762142976.0000000000 -2.0090140447 -1.3378421730 1.6263619033 0.1681070992 0.1798897402 -0.7957313074 0.55334561624 +1403715338812143104.0000000000 -2.0199056895 -1.3592873162 1.6303381036 0.1711010928 0.1885409466 -0.7942479816 0.551676418893 +1403715338862142976.0000000000 -2.0308595560 -1.3810348364 1.6343848886 0.1745374929 0.1950909942 -0.7927909336 0.550416844826 +1403715338912143104.0000000000 -2.0420453959 -1.4030204964 1.6377891861 0.1773796677 0.2006430646 -0.7921153231 0.548481657854 +1403715338962142976.0000000000 -2.0537652420 -1.4248528159 1.6402514355 0.1784239439 0.2066223947 -0.7915480763 0.546739174646 +1403715339012143104.0000000000 -2.0654828042 -1.4466350266 1.6420600359 0.1796694562 0.2111726035 -0.7916416886 0.544452435892 +1403715339062142976.0000000000 -2.0771779053 -1.4685933380 1.6432665288 0.1805073488 0.2150678365 -0.7919833763 0.542148738227 +1403715339112143104.0000000000 -2.0888440393 -1.4909820003 1.6436114945 0.1798491045 0.2191851443 -0.7917975225 0.540988775747 +1403715339162142976.0000000000 -2.0999531294 -1.5136771567 1.6433708515 0.1787218590 0.2231249429 -0.7910585109 0.540832866285 +1403715339212143104.0000000000 -2.1105967942 -1.5366508457 1.6424905141 0.1768078061 0.2267449839 -0.7903949313 0.540926579598 +1403715339262142976.0000000000 -2.1204115216 -1.5595712287 1.6414948757 0.1767091613 0.2285501474 -0.7897024161 0.54121049178 +1403715339312143104.0000000000 -2.1294132285 -1.5827347941 1.6409022290 0.1789204168 0.2281910620 -0.7887541908 0.542017665885 +1403715339362142976.0000000000 -2.1377597510 -1.6062393651 1.6400565872 0.1809689161 0.2272631727 -0.7876292203 0.543361678009 +1403715339412143104.0000000000 -2.1457933020 -1.6294853138 1.6387641413 0.1831060073 0.2257266644 -0.7871380183 0.543997613302 +1403715339462142976.0000000000 -2.1538011750 -1.6525665915 1.6368953006 0.1842580886 0.2242673171 -0.7869646123 0.544462878704 +1403715339512143104.0000000000 -2.1616743216 -1.6758248871 1.6346975201 0.1847881125 0.2225817027 -0.7864040816 0.545783253225 +1403715339562142976.0000000000 -2.1695458734 -1.6985711097 1.6318187756 0.1854839196 0.2206456539 -0.7870607453 0.545386646505 +1403715339612143104.0000000000 -2.1773667205 -1.7211121473 1.6276026013 0.1840212669 0.2198757097 -0.7890051837 0.543379853916 +1403715339662142976.0000000000 -2.1852953542 -1.7434094802 1.6227459028 0.1804255193 0.2199762858 -0.7901585110 0.542868854425 +1403715339712143104.0000000000 -2.1930262670 -1.7657682841 1.6172847839 0.1748204257 0.2215937713 -0.7908833155 0.542989503154 +1403715339762142976.0000000000 -2.2002597511 -1.7883156666 1.6115982190 0.1684476478 0.2232672025 -0.7902038796 0.545302645189 +1403715339812143104.0000000000 -2.2066830663 -1.8103435113 1.6051887753 0.1614777932 0.2253635315 -0.7894240250 0.547673177771 +1403715339862142976.0000000000 -2.2120063660 -1.8317521708 1.5986388868 0.1555051893 0.2274526130 -0.7881781460 0.550325953482 +1403715339912143104.0000000000 -2.2158652215 -1.8520378020 1.5920983504 0.1512782146 0.2306389976 -0.7865104522 0.552559375251 +1403715339962142976.0000000000 -2.2178412017 -1.8711902091 1.5852691325 0.1484340736 0.2352914590 -0.7850362348 0.553464872587 +1403715340012143104.0000000000 -2.2180057914 -1.8890611594 1.5792618605 0.1462850290 0.2414776308 -0.7829321815 0.554352273645 +1403715340062142976.0000000000 -2.2155063927 -1.9052625463 1.5741976748 0.1475525193 0.2477240356 -0.7810570218 0.553905212909 +1403715340112143104.0000000000 -2.2107605620 -1.9194852104 1.5706327378 0.1517777684 0.2538653982 -0.7792441862 0.552534493855 +1403715340162142976.0000000000 -2.2040716088 -1.9318417193 1.5690588873 0.1579760528 0.2600742788 -0.7765975469 0.551635011956 +1403715340212143104.0000000000 -2.1953280989 -1.9420190320 1.5690504881 0.1676447784 0.2658047810 -0.7744576568 0.549052260207 +1403715340262142976.0000000000 -2.1847109348 -1.9507085971 1.5707562076 0.1788994020 0.2716553894 -0.7718764936 0.546264617233 +1403715340312143104.0000000000 -2.1723484516 -1.9581817393 1.5744205482 0.1907835661 0.2790510458 -0.7687275541 0.542945754555 +1403715340362142976.0000000000 -2.1586983064 -1.9645515427 1.5802047497 0.2045119410 0.2866648714 -0.7654557296 0.5385867094 +1403715340412143104.0000000000 -2.1446635565 -1.9699776689 1.5872957285 0.2165767505 0.2961649016 -0.7615888130 0.534194105309 +1403715340462142976.0000000000 -2.1301277633 -1.9746060542 1.5952901771 0.2266425738 0.3058627614 -0.7582563000 0.529271667928 +1403715340512143104.0000000000 -2.1149770153 -1.9789522380 1.6032481892 0.2351456047 0.3144539998 -0.7553916416 0.524603368661 +1403715340562142976.0000000000 -2.0994798082 -1.9830860488 1.6105446631 0.2435019110 0.3211865406 -0.7540925830 0.518546431646 +1403715340612143104.0000000000 -2.0840036377 -1.9873581307 1.6171896365 0.2502994966 0.3270998447 -0.7520301425 0.514593546824 +1403715340662142976.0000000000 -2.0683530635 -1.9921789002 1.6229925083 0.2559070432 0.3319139455 -0.7504613757 0.511030763942 +1403715340712143104.0000000000 -2.0525004377 -1.9975387346 1.6281810320 0.2599430904 0.3357421766 -0.7493158811 0.50816581051 +1403715340762142976.0000000000 -2.0363466594 -2.0033616372 1.6327788490 0.2626895500 0.3386762993 -0.7489523385 0.505334502335 +1403715340812143104.0000000000 -2.0199434148 -2.0098902754 1.6373247667 0.2646932940 0.3407626816 -0.7486902006 0.503270541944 +1403715340862142976.0000000000 -2.0035282801 -2.0170131516 1.6421538750 0.2683688155 0.3397874516 -0.7496672559 0.500521400111 +1403715340912143104.0000000000 -1.9868185696 -2.0248801805 1.6467426139 0.2720825816 0.3378142209 -0.7509589701 0.497908873352 +1403715340962142976.0000000000 -1.9700802816 -2.0336403662 1.6508429119 0.2737655210 0.3362857521 -0.7521785320 0.496177174431 +1403715341012143104.0000000000 -1.9533333099 -2.0436252946 1.6549600035 0.2750194800 0.3342011116 -0.7538662477 0.494327404848 +1403715341062142976.0000000000 -1.9366481455 -2.0552919215 1.6591992232 0.2745488217 0.3324349495 -0.7543851172 0.494987922855 +1403715341112143104.0000000000 -1.9201611170 -2.0685539999 1.6631020013 0.2717132260 0.3318494803 -0.7536965003 0.497985371961 +1403715341162142976.0000000000 -1.9037627002 -2.0830714201 1.6670238401 0.2669827546 0.3324762442 -0.7520905752 0.502533105896 +1403715341212143104.0000000000 -1.8870375805 -2.0984529190 1.6720218045 0.2665836109 0.3291393378 -0.7504168233 0.507420009553 +1403715341262142976.0000000000 -1.8704297430 -2.1147625679 1.6771858111 0.2658412751 0.3257813373 -0.7495497027 0.511243757773 +1403715341312143104.0000000000 -1.8541851207 -2.1317286499 1.6821501772 0.2636959522 0.3232300337 -0.7483637781 0.515692200547 +1403715341362142976.0000000000 -1.8390043718 -2.1485868466 1.6872956329 0.2608030743 0.3211812897 -0.7467756889 0.520721044341 +1403715341412143104.0000000000 -1.8240733673 -2.1651221471 1.6926084613 0.2585595399 0.3185975571 -0.7460235053 0.524491649598 +1403715341462142976.0000000000 -1.8098911471 -2.1811128639 1.6972830766 0.2541573083 0.3179766735 -0.7459801913 0.527075376007 +1403715341512143104.0000000000 -1.7962184306 -2.1967860650 1.7024358712 0.2508327329 0.3167801540 -0.7469967890 0.527947981649 +1403715341562142976.0000000000 -1.7831501304 -2.2121828313 1.7071950353 0.2453960388 0.3174806449 -0.7470337910 0.53002579118 +1403715341612143104.0000000000 -1.7702914279 -2.2271780305 1.7118078538 0.2412657667 0.3179765331 -0.7455580663 0.53368991377 +1403715341662142976.0000000000 -1.7577418868 -2.2415492794 1.7161481822 0.2369998687 0.3184299131 -0.7436590534 0.53796344202 +1403715341712143104.0000000000 -1.7453188656 -2.2549367709 1.7201767357 0.2322047556 0.3196769367 -0.7414014358 0.54241268297 +1403715341762142976.0000000000 -1.7328324189 -2.2670518759 1.7234265509 0.2277129169 0.3212381598 -0.7411624940 0.543719624112 +1403715341812143104.0000000000 -1.7204865134 -2.2772535089 1.7258619997 0.2239361447 0.3228297465 -0.7412607835 0.54421136408 +1403715341862142976.0000000000 -1.7074921689 -2.2859219261 1.7279154960 0.2198445720 0.3250779589 -0.7408821148 0.54505630602 +1403715341912143104.0000000000 -1.6933998527 -2.2920659306 1.7303790907 0.2220723810 0.3240708734 -0.7430185917 0.541835121612 +1403715341962142976.0000000000 -1.6787714730 -2.2966388681 1.7331323703 0.2263074700 0.3221381373 -0.7455172981 0.537787976609 +1403715342012143104.0000000000 -1.6643165846 -2.2998417346 1.7356546377 0.2309279082 0.3200209408 -0.7486432723 0.532721455902 +1403715342062142976.0000000000 -1.6497889080 -2.3022653642 1.7379423886 0.2343441134 0.3191734300 -0.7518104424 0.527249672194 +1403715342112143104.0000000000 -1.6355880451 -2.3037543585 1.7400631550 0.2364749742 0.3194576671 -0.7546489156 0.522045400093 +1403715342162142976.0000000000 -1.6215887956 -2.3044848376 1.7423095381 0.2403806500 0.3182977240 -0.7582403313 0.515727934023 +1403715342212143104.0000000000 -1.6073333478 -2.3054601159 1.7442099147 0.2427936598 0.3185099704 -0.7602506664 0.511489551939 +1403715342262142976.0000000000 -1.5926341638 -2.3073384657 1.7460072515 0.2453233340 0.3186586948 -0.7613886573 0.508488358328 +1403715342312143104.0000000000 -1.5774109622 -2.3103033407 1.7469865451 0.2480438184 0.3193251483 -0.7615279700 0.506538117816 +1403715342362142976.0000000000 -1.5622001675 -2.3135544275 1.7471535431 0.2496962301 0.3225531473 -0.7608751806 0.504658517631 +1403715342412143104.0000000000 -1.5468367309 -2.3170417398 1.7469227144 0.2510321006 0.3280012313 -0.7588363188 0.503552894879 +1403715342462142976.0000000000 -1.5309358175 -2.3208692977 1.7464245419 0.2536979575 0.3342256276 -0.7575737368 0.50001260939 +1403715342512143104.0000000000 -1.5145076208 -2.3254519721 1.7457643563 0.2554331274 0.3424905161 -0.7547877492 0.497744530357 +1403715342562142976.0000000000 -1.4975054007 -2.3308831643 1.7449865527 0.2560818801 0.3521931449 -0.7506050113 0.496964964929 +1403715342612143104.0000000000 -1.4798499587 -2.3372400500 1.7446624538 0.2557718466 0.3630975874 -0.7445622145 0.498365341124 +1403715342662142976.0000000000 -1.4610953234 -2.3438850667 1.7445952721 0.2556732599 0.3741967033 -0.7367260835 0.501839306202 +1403715342712143104.0000000000 -1.4409145541 -2.3500813688 1.7446113972 0.2573787221 0.3842824206 -0.7294597439 0.503956046297 +1403715342762142976.0000000000 -1.4198172158 -2.3554036772 1.7445720887 0.2612241737 0.3919958716 -0.7243611355 0.503390616743 +1403715342812143104.0000000000 -1.3978790105 -2.3595391045 1.7450947240 0.2683855244 0.3962310520 -0.7216908826 0.500132416178 +1403715342862142976.0000000000 -1.3751971242 -2.3631208716 1.7463446613 0.2754098158 0.3991129057 -0.7187272827 0.498286478776 +1403715342912143104.0000000000 -1.3518230523 -2.3661674616 1.7472540595 0.2818901128 0.4008478640 -0.7172009736 0.495461116202 +1403715342962142976.0000000000 -1.3277924221 -2.3692307815 1.7480860173 0.2878678634 0.4016354513 -0.7149534554 0.494633818164 +1403715343012143104.0000000000 -1.3032860397 -2.3724229444 1.7483388309 0.2926843572 0.4020828253 -0.7129475341 0.494339035762 +1403715343062142976.0000000000 -1.2784775256 -2.3756379197 1.7479922041 0.2971854113 0.4020552338 -0.7117482614 0.493403316542 +1403715343112143104.0000000000 -1.2535653952 -2.3789185043 1.7466186016 0.2986799395 0.4036218292 -0.7101326981 0.493549656806 +1403715343162142976.0000000000 -1.2286742280 -2.3820733998 1.7446936616 0.3004451506 0.4047589060 -0.7095673995 0.492358654976 +1403715343212143104.0000000000 -1.2036125651 -2.3852990508 1.7427290669 0.3026188191 0.4052845440 -0.7083274551 0.492380447547 +1403715343262142976.0000000000 -1.1787259084 -2.3884965879 1.7395712332 0.3026845448 0.4069029793 -0.7086491981 0.490538832193 +1403715343312143104.0000000000 -1.1540738778 -2.3916739437 1.7359792928 0.3025587511 0.4080891496 -0.7093544192 0.488607977974 +1403715343362142976.0000000000 -1.1295076892 -2.3949011465 1.7319299387 0.3017568369 0.4092255750 -0.7107414534 0.486131491072 +1403715343412143104.0000000000 -1.1049546935 -2.3981981152 1.7274945869 0.2990312734 0.4114820618 -0.7117145811 0.484484432471 +1403715343462142976.0000000000 -1.0803699108 -2.4016003862 1.7231549615 0.2967513728 0.4128312113 -0.7121386458 0.48411523715 +1403715343512143104.0000000000 -1.0551200482 -2.4050818432 1.7190062926 0.2960444534 0.4126099535 -0.7130605230 0.483379145615 +1403715343562142976.0000000000 -1.0293375762 -2.4085792266 1.7147665120 0.2943742809 0.4128346229 -0.7134823414 0.483584848096 +1403715343612143104.0000000000 -1.0027342232 -2.4119639035 1.7109323313 0.2934233577 0.4123699367 -0.7139570194 0.483858598116 +1403715343662142976.0000000000 -0.9755262113 -2.4153922300 1.7071145585 0.2918337211 0.4122372275 -0.7137685669 0.485209213027 +1403715343712143104.0000000000 -0.9476528211 -2.4190558900 1.7039536466 0.2902791819 0.4120712817 -0.7131431093 0.487198276823 +1403715343762142976.0000000000 -0.9190646118 -2.4227930949 1.7014311454 0.2881241408 0.4121052446 -0.7114649045 0.490888415535 +1403715343812143104.0000000000 -0.8898012897 -2.4261652965 1.6996915097 0.2879572657 0.4108177591 -0.7095114525 0.494876631808 +1403715343862142976.0000000000 -0.8600109882 -2.4288418104 1.6978451932 0.2875522917 0.4100185520 -0.7091115162 0.496345972276 +1403715343912143104.0000000000 -0.8300227181 -2.4306205847 1.6964930493 0.2883199012 0.4091128928 -0.7085003476 0.497519379435 +1403715343962142976.0000000000 -0.7994852713 -2.4314169003 1.6958626141 0.2909477797 0.4086965493 -0.7076046060 0.497606512889 +1403715344012143104.0000000000 -0.7687161314 -2.4313343379 1.6952147140 0.2930499494 0.4100371003 -0.7063614221 0.497036059965 +1403715344062142976.0000000000 -0.7379281704 -2.4301403128 1.6946974316 0.2971417432 0.4120076321 -0.7036173997 0.496869248838 +1403715344112143104.0000000000 -0.7072264461 -2.4280032005 1.6944934853 0.3018994962 0.4152633240 -0.7003244902 0.49594220873 +1403715344162142976.0000000000 -0.6764767594 -2.4249202988 1.6937873913 0.3071415371 0.4197565498 -0.6964459863 0.494400144813 +1403715344212143104.0000000000 -0.6461357094 -2.4213132958 1.6924061663 0.3103402055 0.4264287455 -0.6913157603 0.493892702358 +1403715344262142976.0000000000 -0.6160113151 -2.4171663504 1.6910003049 0.3127371765 0.4329326938 -0.6851392131 0.495327164454 +1403715344312143104.0000000000 -0.5866205436 -2.4120857383 1.6894046151 0.3140292002 0.4395681998 -0.6783204423 0.498043006891 +1403715344362142976.0000000000 -0.5578652266 -2.4058610056 1.6877694215 0.3158062100 0.4449126091 -0.6718932277 0.50087792782 +1403715344412143104.0000000000 -0.5294792931 -2.3984362682 1.6860892261 0.3177418898 0.4496568287 -0.6652208838 0.504311415312 +1403715344462142976.0000000000 -0.5018357347 -2.3893961551 1.6840714544 0.3198103925 0.4534783193 -0.6602764022 0.50607687109 +1403715344512143104.0000000000 -0.4753626540 -2.3786243729 1.6816783594 0.3206022627 0.4574853668 -0.6553264069 0.508398100659 +1403715344562142976.0000000000 -0.4498562187 -2.3656306626 1.6789052358 0.3223372144 0.4605330838 -0.6522987329 0.508443076485 +1403715344612143104.0000000000 -0.4253694392 -2.3504429550 1.6753323644 0.3234483932 0.4636073725 -0.6515150650 0.505942151987 +1403715344662142976.0000000000 -0.4019902347 -2.3331455648 1.6706315986 0.3214255998 0.4683156331 -0.6516746150 0.502679070405 +1403715344712143104.0000000000 -0.3793162769 -2.3135615034 1.6656823368 0.3199852722 0.4720565514 -0.6527089653 0.498741460478 +1403715344762142976.0000000000 -0.3570012055 -2.2916378062 1.6605816762 0.3184704724 0.4754187654 -0.6540853155 0.494697842917 +1403715344812143104.0000000000 -0.3349252638 -2.2676829152 1.6558328335 0.3179896090 0.4777171916 -0.6546404622 0.49205158131 +1403715344862142976.0000000000 -0.3131348563 -2.2419142741 1.6511474612 0.3177267365 0.4792906572 -0.6549974042 0.49021279804 +1403715344912143104.0000000000 -0.2914028188 -2.2141444436 1.6465007825 0.3180324145 0.4803477887 -0.6554313012 0.488396554751 +1403715344962142976.0000000000 -0.2694750113 -2.1843970429 1.6421229718 0.3205892821 0.4794640943 -0.6557502103 0.487163582619 +1403715345012143104.0000000000 -0.2472078124 -2.1526401814 1.6388090467 0.3269520517 0.4756326513 -0.6567567492 0.485331339625 +1403715345062142976.0000000000 -0.2248815145 -2.1194471940 1.6358026987 0.3328222195 0.4718317462 -0.6572178062 0.48442639137 +1403715345112143104.0000000000 -0.2030739573 -2.0851981636 1.6330856614 0.3380015941 0.4683032354 -0.6573726223 0.484053961332 +1403715345162142976.0000000000 -0.1820187908 -2.0500345081 1.6297850742 0.3412268082 0.4659443159 -0.6582162357 0.482919814139 +1403715345212143104.0000000000 -0.1618184385 -2.0144574633 1.6262956024 0.3431508069 0.4644292698 -0.6597458617 0.480924500352 +1403715345262142976.0000000000 -0.1425743282 -1.9785376885 1.6224215774 0.3426715402 0.4646943016 -0.6607011942 0.479697147852 +1403715345312143104.0000000000 -0.1243734593 -1.9422964934 1.6185243041 0.3435143733 0.4638351410 -0.6619457452 0.478207766316 +1403715345362142976.0000000000 -0.1070088968 -1.9055247156 1.6144143302 0.3433907828 0.4638561272 -0.6627519797 0.47715833541 +1403715345412143104.0000000000 -0.0902339610 -1.8682691985 1.6102969477 0.3432747775 0.4639207866 -0.6636016235 0.475996655666 +1403715345462142976.0000000000 -0.0740854815 -1.8305181809 1.6062376484 0.3438687380 0.4637319737 -0.6643428573 0.474716247335 +1403715345512143104.0000000000 -0.0586587682 -1.7925199708 1.6018091096 0.3429991709 0.4644525816 -0.6641311708 0.474937002305 +1403715345562142976.0000000000 -0.0437862314 -1.7540530116 1.5978642055 0.3438592948 0.4641618564 -0.6640197681 0.474754993689 +1403715345612143104.0000000000 -0.0294709339 -1.7152366929 1.5937468990 0.3447651869 0.4638602035 -0.6642340690 0.474092585006 +1403715345662142976.0000000000 -0.0158831735 -1.6760992068 1.5893990303 0.3454450188 0.4637706203 -0.6642205101 0.473704195368 +1403715345712143104.0000000000 -0.0031509876 -1.6368100676 1.5848642931 0.3462031286 0.4635436552 -0.6644737672 0.473017215493 +1403715345762142976.0000000000 0.0089567928 -1.5973863950 1.5800978122 0.3469362657 0.4631814692 -0.6647240938 0.472482839057 +1403715345812143104.0000000000 0.0204777236 -1.5580764523 1.5751681459 0.3473105560 0.4631317936 -0.6651423160 0.47166727566 +1403715345862142976.0000000000 0.0311933758 -1.5186534978 1.5699537483 0.3470980792 0.4635363428 -0.6662868101 0.469807267889 +1403715345912143104.0000000000 0.0409716125 -1.4793383174 1.5639411677 0.3438467466 0.4659451953 -0.6692224367 0.465624118902 +1403715345962142976.0000000000 0.0506830162 -1.4398052713 1.5578601721 0.3394219943 0.4693100525 -0.6731613784 0.459776623039 +1403715346012143104.0000000000 0.0604062838 -1.4003543865 1.5528603445 0.3362248058 0.4715188104 -0.6766852623 0.454664653527 +1403715346062142976.0000000000 0.0705104209 -1.3612549237 1.5484526192 0.3335431546 0.4731872977 -0.6805942316 0.449037010968 +1403715346112143104.0000000000 0.0816398114 -1.3229997052 1.5449969882 0.3313173298 0.4741817608 -0.6829631300 0.446028976485 +1403715346162142976.0000000000 0.0938164192 -1.2852733933 1.5425195589 0.3304197162 0.4744587108 -0.6840731896 0.444697216257 +1403715346212143104.0000000000 0.1073751738 -1.2483640952 1.5414359995 0.3316710236 0.4730145968 -0.6835005007 0.446182237313 +1403715346262142976.0000000000 0.1220920323 -1.2121308888 1.5407651700 0.3333135170 0.4711529845 -0.6821435801 0.448995657823 +1403715346312143104.0000000000 0.1373120671 -1.1763556802 1.5400906107 0.3350305875 0.4686596322 -0.6814027381 0.451445415468 +1403715346362142976.0000000000 0.1531140943 -1.1408641655 1.5396188811 0.3363203886 0.4667832966 -0.6803547736 0.454003669864 +1403715346412143104.0000000000 0.1693594153 -1.1059308250 1.5397109504 0.3380766941 0.4641081706 -0.6794141197 0.456841557685 +1403715346462142976.0000000000 0.1855966406 -1.0716764658 1.5401545948 0.3394745732 0.4614537286 -0.6785127331 0.45982381577 +1403715346512143104.0000000000 0.2017633931 -1.0377745468 1.5410100166 0.3414202993 0.4583253889 -0.6782282375 0.461926915179 +1403715346562142976.0000000000 0.2176900032 -1.0043437012 1.5417281774 0.3425487423 0.4555570929 -0.6788209018 0.462958181151 +1403715346612143104.0000000000 0.2331842963 -0.9715843950 1.5427387059 0.3441839784 0.4518737932 -0.6798958015 0.463777061863 +1403715346662142976.0000000000 0.2478404577 -0.9395903235 1.5436119222 0.3441428096 0.4490834095 -0.6812827526 0.464482108358 +1403715346712143104.0000000000 0.2617007412 -0.9082765001 1.5449412900 0.3443968773 0.4460419537 -0.6820391706 0.466111506251 +1403715346762142976.0000000000 0.2746388901 -0.8774793041 1.5461627245 0.3442117386 0.4434881888 -0.6833559337 0.466756010446 +1403715346812143104.0000000000 0.2867046696 -0.8474152984 1.5471827583 0.3430389812 0.4415216298 -0.6851243061 0.46689141449 +1403715346862142976.0000000000 0.2981022866 -0.8181325102 1.5478357158 0.3401559196 0.4410234447 -0.6868132228 0.466990223143 +1403715346912143104.0000000000 0.3089506895 -0.7892450729 1.5485744183 0.3391338556 0.4392278990 -0.6899858440 0.464743602247 +1403715346962142976.0000000000 0.3193296798 -0.7611831633 1.5491987170 0.3376932780 0.4377602807 -0.6936286309 0.461745069308 +1403715347012143104.0000000000 0.3294709244 -0.7341653974 1.5500987462 0.3362646049 0.4366655520 -0.6968553096 0.458957502106 +1403715347062142976.0000000000 0.3390661400 -0.7084647343 1.5512690924 0.3342617488 0.4362997891 -0.6996800398 0.456464039291 +1403715347112143104.0000000000 0.3485473873 -0.6840108843 1.5530028444 0.3314109722 0.4382523251 -0.6995598938 0.456856237784 +1403715347162142976.0000000000 0.3577669554 -0.6601505621 1.5544951792 0.3289271525 0.4419440376 -0.6980890041 0.457344660302 +1403715347212143104.0000000000 0.3672501175 -0.6372032546 1.5568235366 0.3274948665 0.4470872506 -0.6946009843 0.45868243411 +1403715347262142976.0000000000 0.3772037239 -0.6146536562 1.5596227044 0.3283356497 0.4525416244 -0.6900390175 0.459617159875 +1403715347312143104.0000000000 0.3878093819 -0.5925224121 1.5632731663 0.3302204482 0.4591534664 -0.6842043925 0.460431210065 +1403715347362142976.0000000000 0.3978974610 -0.5705698013 1.5667588996 0.3330679555 0.4665907289 -0.6772645106 0.46116332406 +1403715347412143104.0000000000 0.4080990089 -0.5486199696 1.5704752584 0.3356280295 0.4753200192 -0.6688954146 0.462605263223 +1403715347462142976.0000000000 0.4181208925 -0.5258376876 1.5744016811 0.3390399748 0.4840176453 -0.6613735018 0.461913309639 +1403715347512143104.0000000000 0.4281891897 -0.5026484520 1.5785805550 0.3417029368 0.4922670763 -0.6539388505 0.461818371656 +1403715347562142976.0000000000 0.4385911124 -0.4790505154 1.5830681359 0.3444637360 0.4990217260 -0.6471319066 0.462106423824 +1403715347612143104.0000000000 0.4488657943 -0.4545727392 1.5877712688 0.3472574530 0.5046479813 -0.6412779562 0.462066293126 +1403715347662142976.0000000000 0.4592401143 -0.4291244009 1.5926167945 0.3513125643 0.5082147179 -0.6368072670 0.461274091293 +1403715347712143104.0000000000 0.4692552872 -0.4028193762 1.5975911553 0.3572666918 0.5092696444 -0.6348976466 0.45815927207 +1403715347762142976.0000000000 0.4790508031 -0.3756201605 1.6023327282 0.3632455785 0.5096504697 -0.6345509260 0.453491092276 +1403715347812143104.0000000000 0.4887204363 -0.3477584418 1.6068474739 0.3686540092 0.5109684328 -0.6333760568 0.449266349521 +1403715347862142976.0000000000 0.4979148957 -0.3193425606 1.6107381967 0.3753427264 0.5123351631 -0.6323490837 0.443582184847 +1403715347912143104.0000000000 0.5062838510 -0.2906870359 1.6144822889 0.3823656331 0.5145521028 -0.6304841574 0.437632703843 +1403715347962142976.0000000000 0.5138785552 -0.2622303991 1.6185219060 0.3912370020 0.5162167244 -0.6290812644 0.429779786015 +1403715348012143104.0000000000 0.5209032731 -0.2342976810 1.6227306627 0.4008601563 0.5185156334 -0.6266958373 0.421550709349 +1403715348062142976.0000000000 0.5273406205 -0.2073825356 1.6260484038 0.4087879533 0.5232083874 -0.6231647095 0.413293040691 +1403715348112143104.0000000000 0.5331485730 -0.1816761895 1.6299306387 0.4163576232 0.5294479476 -0.6171653422 0.406740876705 +1403715348162142976.0000000000 0.5380855941 -0.1573994379 1.6329799549 0.4223906785 0.5377146337 -0.6108214738 0.399181931669 +1403715348212143104.0000000000 0.5423923954 -0.1347616807 1.6360744832 0.4285676599 0.5465375532 -0.6031666534 0.392194405899 +1403715348262142976.0000000000 0.5464000480 -0.1139234535 1.6385638161 0.4325100045 0.5572342426 -0.5951095495 0.385058072022 +1403715348312143104.0000000000 0.5503202425 -0.0951240174 1.6407113367 0.4360740905 0.5674354087 -0.5866994269 0.378998980183 +1403715348362142976.0000000000 0.5543965798 -0.0779188110 1.6414899576 0.4391968195 0.5765933533 -0.5797073980 0.372270857485 +1403715348412143104.0000000000 0.5590037700 -0.0625152571 1.6406799978 0.4409020586 0.5848153965 -0.5732525063 0.367393373257 +1403715348462142976.0000000000 0.5638636587 -0.0487972437 1.6373520653 0.4421590419 0.5914513472 -0.5688939358 0.361994993534 +1403715348512143104.0000000000 0.5693334039 -0.0365581623 1.6307693758 0.4429481246 0.5968966083 -0.5647593708 0.358550207162 +1403715348562142976.0000000000 0.5758766091 -0.0253058343 1.6213138499 0.4442793440 0.6004674654 -0.5617984919 0.355580007796 +1403715348612143104.0000000000 0.5838319612 -0.0151848515 1.6096924736 0.4473850343 0.6018602272 -0.5590153646 0.353712764959 +1403715348662142976.0000000000 0.5921357612 -0.0061050916 1.5957183722 0.4521749968 0.6010575189 -0.5575405368 0.351306392012 +1403715348712143104.0000000000 0.6010045598 0.0012900192 1.5795973799 0.4560770751 0.6004069579 -0.5563715852 0.349221771448 +1403715348762142976.0000000000 0.6108433806 0.0071093367 1.5625071086 0.4589872429 0.6004066290 -0.5557903505 0.346323081815 +1403715348812143104.0000000000 0.6209884984 0.0114437051 1.5453612586 0.4617195631 0.6012740099 -0.5538745433 0.344249328814 +1403715348862142976.0000000000 0.6314221239 0.0141762140 1.5287229973 0.4649885370 0.6026455201 -0.5507260053 0.34249803607 +1403715348912143104.0000000000 0.6418888669 0.0148357002 1.5125203221 0.4674579392 0.6044073747 -0.5478687260 0.340609247674 +1403715348962142976.0000000000 0.6524312420 0.0135205336 1.4969765656 0.4688273652 0.6068121737 -0.5452999452 0.3385673598 +1403715349012143104.0000000000 0.6636388075 0.0102396019 1.4821236793 0.4699901421 0.6091603767 -0.5414831842 0.338864077498 +1403715349062142976.0000000000 0.6754129056 0.0052525811 1.4675399860 0.4705746442 0.6116751924 -0.5377068667 0.339535401152 +1403715349112143104.0000000000 0.6873676999 -0.0012726434 1.4534672642 0.4707747023 0.6150365134 -0.5324751930 0.341425593079 +1403715349162142976.0000000000 0.6990136745 -0.0091878104 1.4400519502 0.4721063138 0.6175666349 -0.5278624539 0.342181691087 +1403715349212143104.0000000000 0.7108803039 -0.0184052553 1.4272078641 0.4737757372 0.6196002792 -0.5230366637 0.343605432625 +1403715349262142976.0000000000 0.7225641849 -0.0286850497 1.4149123134 0.4759782834 0.6209912462 -0.5190192367 0.344141798931 +1403715349312143104.0000000000 0.7340330738 -0.0402444028 1.4035923254 0.4793781783 0.6209221750 -0.5158610482 0.344295793865 +1403715349362142976.0000000000 0.7452092227 -0.0531546244 1.3918433718 0.4804848111 0.6222686095 -0.5125395334 0.345281552623 +1403715349412143104.0000000000 0.7558362176 -0.0672869978 1.3798719533 0.4811728194 0.6232240395 -0.5090519079 0.347750872753 +1403715349462142976.0000000000 0.7657752120 -0.0825271066 1.3674357169 0.4804993726 0.6244560792 -0.5068248015 0.349719285638 +1403715349512143104.0000000000 0.7750367342 -0.0983251015 1.3549598985 0.4792974846 0.6257646114 -0.5045858833 0.352257943455 +1403715349562142976.0000000000 0.7831761516 -0.1144821396 1.3415901926 0.4769985143 0.6286058452 -0.5029819259 0.352613514985 +1403715349612143104.0000000000 0.7900782591 -0.1307858475 1.3281789491 0.4757079979 0.6318139287 -0.5007641848 0.351778753582 +1403715349662142976.0000000000 0.7958169468 -0.1471472956 1.3150879336 0.4756289202 0.6350556471 -0.4984092892 0.349384652972 +1403715349712143104.0000000000 0.8003276063 -0.1633351304 1.3022008775 0.4761660236 0.6389603712 -0.4959179935 0.345052033218 +1403715349762142976.0000000000 0.8041611210 -0.1794978263 1.2904222670 0.4779195426 0.6429275931 -0.4923950621 0.340270662394 +1403715349812143104.0000000000 0.8071239841 -0.1955951114 1.2796938062 0.4807902454 0.6468828959 -0.4891732318 0.333305877854 +1403715349862142976.0000000000 0.8096109243 -0.2116946671 1.2695926518 0.4844666538 0.6508505493 -0.4845583019 0.326938642288 +1403715349912143104.0000000000 0.8119350905 -0.2279837008 1.2599181158 0.4877732730 0.6556296075 -0.4782813759 0.321673712719 +1403715349962142976.0000000000 0.8136569522 -0.2444639949 1.2507210430 0.4911413193 0.6607420397 -0.4716810980 0.3157801502 +1403715350012143104.0000000000 0.8151256857 -0.2617595893 1.2414920402 0.4933312831 0.6663143972 -0.4645866445 0.311140834554 +1403715350062142976.0000000000 0.8165917062 -0.2797536816 1.2325418025 0.4950872331 0.6711592239 -0.4579314803 0.307786755907 +1403715350112143104.0000000000 0.8175967444 -0.2983775217 1.2225806553 0.4931009883 0.6777622142 -0.4529443106 0.30386057294 +1403715350162142976.0000000000 0.8186848702 -0.3172707080 1.2126836186 0.4915445452 0.6830070143 -0.4497908555 0.299288430663 +1403715350212143104.0000000000 0.8204937985 -0.3364676562 1.2028818552 0.4886411339 0.6882726747 -0.4466579464 0.296660153143 +1403715350262142976.0000000000 0.8225527092 -0.3559606628 1.1925569229 0.4829566638 0.6947460155 -0.4441457631 0.29464449092 +1403715350312143104.0000000000 0.8253174475 -0.3749547904 1.1822439377 0.4776132434 0.7002265952 -0.4417462156 0.293987391255 +1403715350362142976.0000000000 0.8286613631 -0.3931769021 1.1719009911 0.4726509863 0.7046690609 -0.4403901421 0.29342645155 +1403715350412143104.0000000000 0.8328343072 -0.4102551552 1.1616490103 0.4675815825 0.7086075306 -0.4385777830 0.294775099992 +1403715350462142976.0000000000 0.8377548543 -0.4255913643 1.1514984900 0.4633457761 0.7115507710 -0.4371266993 0.296523929617 +1403715350512143104.0000000000 0.8434655937 -0.4388185932 1.1415498621 0.4601546379 0.7134254052 -0.4357481058 0.299007506204 +1403715350562142976.0000000000 0.8499538569 -0.4498167411 1.1318625509 0.4577471153 0.7145222634 -0.4354947345 0.300449412943 +1403715350612143104.0000000000 0.8573382364 -0.4581154858 1.1227264017 0.4573358548 0.7139868170 -0.4364341521 0.300985002805 +1403715350662142976.0000000000 0.8653845438 -0.4639214398 1.1141691538 0.4579065548 0.7128527796 -0.4380336211 0.300481361337 +1403715350712143104.0000000000 0.8740654869 -0.4673280734 1.1060614292 0.4596782376 0.7109855961 -0.4402485036 0.298959286545 +1403715350762142976.0000000000 0.8835861894 -0.4687468887 1.0983088483 0.4613753627 0.7092563398 -0.4424479805 0.297200275613 +1403715350812143104.0000000000 0.8940849158 -0.4683342869 1.0911383051 0.4635035493 0.7075753470 -0.4434497772 0.296401557289 +1403715350862142976.0000000000 0.9055521528 -0.4666117650 1.0843243334 0.4647985222 0.7066379361 -0.4423241897 0.298285890058 +1403715350912143104.0000000000 0.9175504338 -0.4634059226 1.0778498830 0.4648811146 0.7067696002 -0.4400937289 0.30113085396 +1403715350962142976.0000000000 0.9299877015 -0.4584997304 1.0720634824 0.4655021209 0.7064991745 -0.4378604448 0.304047566546 +1403715351012143104.0000000000 0.9424915661 -0.4518394109 1.0667194901 0.4656795834 0.7066857651 -0.4363346146 0.30553209166 +1403715351062142976.0000000000 0.9548667945 -0.4431180726 1.0620451360 0.4657140537 0.7071530306 -0.4352679770 0.305919596923 +1403715351112143104.0000000000 0.9673446984 -0.4323086489 1.0584310058 0.4659558885 0.7071939791 -0.4345211183 0.306517835832 +1403715351162142976.0000000000 0.9796673113 -0.4193939591 1.0555654671 0.4667973982 0.7069857724 -0.4351329785 0.304845202887 +1403715351212143104.0000000000 0.9920605998 -0.4048278892 1.0529408244 0.4674819289 0.7070069738 -0.4357972261 0.302791285845 +1403715351262142976.0000000000 1.0046991285 -0.3886696485 1.0507543843 0.4679585130 0.7070576271 -0.4361179678 0.301472154881 +1403715351312143104.0000000000 1.0178728247 -0.3704651798 1.0500615346 0.4722168883 0.7044896858 -0.4357928055 0.30131399502 +1403715351362142976.0000000000 1.0311222172 -0.3510541415 1.0493769424 0.4750826386 0.7026435538 -0.4348792928 0.302437635665 +1403715351412143104.0000000000 1.0441790147 -0.3304059530 1.0491522940 0.4785246910 0.7002867337 -0.4342081004 0.303440169086 +1403715351462142976.0000000000 1.0570419327 -0.3088452362 1.0490051548 0.4802444813 0.6989782132 -0.4330786331 0.305348314464 +1403715351512143104.0000000000 1.0694159365 -0.2862279910 1.0490774147 0.4814188103 0.6979042013 -0.4324402924 0.306856722928 +1403715351562142976.0000000000 1.0814965556 -0.2624976216 1.0502481247 0.4848092381 0.6951889145 -0.4308035636 0.309968813637 +1403715351612143104.0000000000 1.0929160732 -0.2378539151 1.0523033843 0.4895887465 0.6913497296 -0.4281715500 0.31465462739 +1403715351662142976.0000000000 1.1027788872 -0.2123293278 1.0539741018 0.4919483154 0.6899189109 -0.4262917608 0.316660837567 +1403715351712143104.0000000000 1.1111314324 -0.1857787876 1.0556456505 0.4923119890 0.6908520750 -0.4244246162 0.316569204346 +1403715351762142976.0000000000 1.1178057730 -0.1582039508 1.0576386750 0.4920164403 0.6932399914 -0.4227775094 0.314002092948 +1403715351812143104.0000000000 1.1229179201 -0.1293985128 1.0603515546 0.4939288763 0.6951815072 -0.4211322533 0.308876289746 +1403715351862142976.0000000000 1.1267681089 -0.0996197809 1.0635436607 0.4962852998 0.6976838001 -0.4192736077 0.301907035592 +1403715351912143104.0000000000 1.1295868791 -0.0691985244 1.0666267835 0.4991982065 0.7004111326 -0.4163678513 0.294725649289 +1403715351962142976.0000000000 1.1318245404 -0.0381203246 1.0702399652 0.5028315244 0.7031057262 -0.4137555874 0.285673082 +1403715352012143104.0000000000 1.1334641485 -0.0068733487 1.0747171296 0.5065220535 0.7061853403 -0.4098588348 0.277044058008 +1403715352062142976.0000000000 1.1346483642 0.0241825524 1.0798123805 0.5097928034 0.7096023473 -0.4055275603 0.2685576367 +1403715352112143104.0000000000 1.1361599884 0.0548939167 1.0859265772 0.5119773465 0.7131634570 -0.4004102375 0.262580886765 +1403715352162142976.0000000000 1.1376003247 0.0853752385 1.0923580444 0.5150405256 0.7154197872 -0.3965338518 0.256259028111 +1403715352212143104.0000000000 1.1391383650 0.1153905999 1.0988549922 0.5181727263 0.7168314651 -0.3934916142 0.250627264925 +1403715352262142976.0000000000 1.1410549513 0.1447179436 1.1048467006 0.5192423400 0.7189225058 -0.3908645495 0.246500967671 +1403715352312143104.0000000000 1.1435337392 0.1736481995 1.1101983095 0.5192220624 0.7213479918 -0.3888347250 0.242637757292 +1403715352362142976.0000000000 1.1467014169 0.2020498885 1.1152195413 0.5197840359 0.7228270149 -0.3870414412 0.23988452505 +1403715352412143104.0000000000 1.1502840366 0.2300269529 1.1199207163 0.5220567535 0.7224456302 -0.3878135159 0.234797219897 +1403715352462142976.0000000000 1.1542034036 0.2574090263 1.1245153230 0.5258792678 0.7204995316 -0.3907993446 0.227172385744 +1403715352512143104.0000000000 1.1593500464 0.2839079116 1.1288066779 0.5299759588 0.7181608533 -0.3927796189 0.221573109458 +1403715352562142976.0000000000 1.1657000447 0.3089916021 1.1320342926 0.5319393188 0.7175069040 -0.3920876813 0.220208206061 +1403715352612143104.0000000000 1.1734133180 0.3325715066 1.1342483979 0.5318144202 0.7184080521 -0.3885870804 0.223748461619 +1403715352662142976.0000000000 1.1817853660 0.3549030127 1.1357217381 0.5310950466 0.7196313820 -0.3853255855 0.227140746414 +1403715352712143104.0000000000 1.1910513805 0.3764090718 1.1374409187 0.5317559793 0.7195043356 -0.3823860629 0.23093286548 +1403715352762142976.0000000000 1.2006318793 0.3969517995 1.1387844399 0.5321209742 0.7195433657 -0.3785272158 0.236266291836 +1403715352812143104.0000000000 1.2100979316 0.4165913963 1.1401788229 0.5337202852 0.7185730633 -0.3755002046 0.240405919692 +1403715352862142976.0000000000 1.2192792501 0.4353700616 1.1411755084 0.5343383298 0.7183522782 -0.3728036290 0.243864732724 +1403715352912143104.0000000000 1.2279977089 0.4532791098 1.1420924809 0.5335951803 0.7189751792 -0.3706869326 0.246864483468 +1403715352962142976.0000000000 1.2357672387 0.4705254051 1.1435975730 0.5347489193 0.7182358908 -0.3705581787 0.246713264044 +1403715353012143104.0000000000 1.2428217366 0.4872180712 1.1455291619 0.5364491083 0.7171143738 -0.3715810250 0.244738372507 +1403715353062142976.0000000000 1.2494617224 0.5029480175 1.1475424859 0.5366080905 0.7171948466 -0.3715334200 0.24422577088 +1403715353112143104.0000000000 1.2555704896 0.5177799875 1.1502042856 0.5356058639 0.7183585259 -0.3707857450 0.244142003862 +1403715353162142976.0000000000 1.2612257448 0.5316313726 1.1546484404 0.5342296305 0.7199118140 -0.3701208999 0.243590232568 +1403715353212143104.0000000000 1.2663874842 0.5446163028 1.1617591417 0.5334653630 0.7210229826 -0.3692179343 0.243348889651 +1403715353262142976.0000000000 1.2709711614 0.5567122420 1.1719845554 0.5332663632 0.7219355744 -0.3682384172 0.242562322761 +1403715353312143104.0000000000 1.2750358278 0.5678774485 1.1849890885 0.5327674741 0.7230651267 -0.3675960304 0.241264998492 +1403715353362142976.0000000000 1.2786726169 0.5782798840 1.1990201145 0.5319234726 0.7246265390 -0.3666223041 0.239920579276 +1403715353412143104.0000000000 1.2821169127 0.5881771276 1.2114683876 0.5307204939 0.7266236846 -0.3644812684 0.239806553886 +1403715353462142976.0000000000 1.2853941211 0.5981254654 1.2211907537 0.5304268025 0.7279262661 -0.3623730864 0.239700864747 +1403715353512143104.0000000000 1.2883987280 0.6078559645 1.2273439668 0.5297327448 0.7293689542 -0.3609255433 0.239033261152 +1403715353562142976.0000000000 1.2910562518 0.6171047404 1.2295694263 0.5289755195 0.7307235934 -0.3593421779 0.238958425375 +1403715353612143104.0000000000 1.2931783580 0.6261939887 1.2281858971 0.5289470714 0.7316661317 -0.3581681685 0.237897521047 +1403715353662142976.0000000000 1.2951306794 0.6349183753 1.2238878157 0.5287439464 0.7326883203 -0.3560443283 0.238390647192 +1403715353712143104.0000000000 1.2967051528 0.6433794318 1.2179152975 0.5286074169 0.7335539093 -0.3542506230 0.238703492007 +1403715353762142976.0000000000 1.2977824791 0.6516604245 1.2110928994 0.5287410535 0.7343169070 -0.3524663724 0.23870281703 +1403715353812143104.0000000000 1.2984175095 0.6601576127 1.2036274707 0.5290095746 0.7349451795 -0.3503092992 0.239348799843 +1403715353862142976.0000000000 1.2985129455 0.6687711341 1.1956927396 0.5292999455 0.7353947213 -0.3492242987 0.23891119832 +1403715353912143104.0000000000 1.2981158392 0.6774275155 1.1875416837 0.5302055967 0.7354660936 -0.3478938414 0.238624234916 +1403715353962142976.0000000000 1.2969467008 0.6859641841 1.1786270258 0.5299928543 0.7362428790 -0.3472457601 0.237643387496 +1403715354012143104.0000000000 1.2953041950 0.6944618912 1.1690592974 0.5298950025 0.7369195226 -0.3469048298 0.236258211745 +1403715354062142976.0000000000 1.2930338694 0.7032215902 1.1591086875 0.5294172748 0.7377840303 -0.3486360393 0.232045223735 +1403715354112143104.0000000000 1.2902345001 0.7120577957 1.1499548955 0.5309844326 0.7370896643 -0.3523860501 0.224896489228 +1403715354162142976.0000000000 1.2874455713 0.7204403270 1.1407860703 0.5325481664 0.7362367650 -0.3561353445 0.217980486963 +1403715354212143104.0000000000 1.2849317932 0.7280539867 1.1313494657 0.5333291812 0.7359289736 -0.3590513688 0.212251371845 +1403715354262142976.0000000000 1.2833675628 0.7347437381 1.1220107462 0.5326656450 0.7366542697 -0.3603311605 0.209211023457 +1403715354312143104.0000000000 1.2826502920 0.7405914651 1.1130031238 0.5317309019 0.7376778410 -0.3596363643 0.209177762631 +1403715354362142976.0000000000 1.2827469536 0.7455678893 1.1036022744 0.5291380358 0.7398666108 -0.3579049168 0.21098437809 +1403715354412143104.0000000000 1.2837473866 0.7500806331 1.0942934645 0.5260938219 0.7423594069 -0.3553658471 0.214109589301 +1403715354462142976.0000000000 1.2855860777 0.7545352851 1.0852934175 0.5234616466 0.7445701018 -0.3528904521 0.216959896896 +1403715354512143104.0000000000 1.2879759471 0.7590683077 1.0765837857 0.5217206293 0.7460716665 -0.3507268367 0.219488813931 +1403715354562142976.0000000000 1.2906378884 0.7638931073 1.0685484265 0.5210678899 0.7466457990 -0.3498145963 0.220540366236 +1403715354612143104.0000000000 1.2935230363 0.7690560474 1.0629989763 0.5217210764 0.7461756888 -0.3496286137 0.220881851404 +1403715354662142976.0000000000 1.2969510281 0.7745140383 1.0597891294 0.5216963553 0.7460695745 -0.3497452728 0.221113877809 +1403715354712143104.0000000000 1.3011947518 0.7803482384 1.0597478990 0.5219886709 0.7457003201 -0.3501997282 0.220950244276 +1403715354762142976.0000000000 1.3061528581 0.7862126965 1.0632434403 0.5220864227 0.7453935025 -0.3506494408 0.221041315826 +1403715354812143104.0000000000 1.3113751824 0.7922728440 1.0699308187 0.5219486047 0.7453920940 -0.3515550173 0.219930330048 +1403715354862142976.0000000000 1.3170447557 0.7982606700 1.0793007703 0.5219188869 0.7453240509 -0.3513069578 0.220626734693 +1403715354912143104.0000000000 1.3229267837 0.8046297242 1.0919243177 0.5239380036 0.7440350288 -0.3527879619 0.217810693611 +1403715354962142976.0000000000 1.3291611451 0.8110374962 1.1061981177 0.5259434169 0.7428876160 -0.3536373800 0.215504328767 +1403715355012143104.0000000000 1.3358155791 0.8171882768 1.1217543116 0.5284629874 0.7415104997 -0.3538127722 0.213788615296 +1403715355062142976.0000000000 1.3430576622 0.8229707159 1.1363890651 0.5290434742 0.7415830141 -0.3529078860 0.2135969557 +1403715355112143104.0000000000 1.3505674729 0.8284242762 1.1500644006 0.5284284097 0.7429475719 -0.3508008511 0.213848273428 +1403715355162142976.0000000000 1.3580464817 0.8338218586 1.1631190780 0.5286815627 0.7447154015 -0.3472512926 0.212864547965 +1403715355212143104.0000000000 1.3654513895 0.8391303914 1.1755906317 0.5289226489 0.7473533317 -0.3432372385 0.209504241476 +1403715355262142976.0000000000 1.3731443606 0.8442607225 1.1874214723 0.5300044147 0.7501818323 -0.3369893121 0.206786707386 +1403715355312143104.0000000000 1.3809314094 0.8494091150 1.1982231562 0.5303698019 0.7542806442 -0.3290824747 0.203649963944 +1403715355362142976.0000000000 1.3887603971 0.8547496868 1.2086288591 0.5314669473 0.7582879584 -0.3204979427 0.199557823111 +1403715355412143104.0000000000 1.3965706690 0.8603651797 1.2193989524 0.5344188839 0.7613024153 -0.3114760025 0.194416534378 +1403715355462142976.0000000000 1.4044363298 0.8660303389 1.2300072190 0.5380117600 0.7641163710 -0.3024987709 0.187520695584 +1403715355512143104.0000000000 1.4125727520 0.8717349147 1.2407882087 0.5424686905 0.7662825929 -0.2928275513 0.181082116358 +1403715355562142976.0000000000 1.4206528409 0.8770541108 1.2511600519 0.5461116827 0.7689308013 -0.2829152934 0.174546239238 +1403715355612143104.0000000000 1.4286267006 0.8822282733 1.2609588533 0.5492017867 0.7718552917 -0.2731599637 0.16733332096 +1403715355662142976.0000000000 1.4371324007 0.8870563115 1.2697010065 0.5512639278 0.7749773247 -0.2629720226 0.162369773586 +1403715355712143104.0000000000 1.4458897776 0.8916154872 1.2780874488 0.5530335428 0.7775895090 -0.2541602178 0.15783231509 +1403715355762142976.0000000000 1.4548958772 0.8957505177 1.2858822695 0.5540954534 0.7799721165 -0.2465643120 0.154362450316 +1403715355812143104.0000000000 1.4639184304 0.8995371343 1.2931767985 0.5540010790 0.7824154306 -0.2405317763 0.151833339562 +1403715355862142976.0000000000 1.4728815248 0.9034298463 1.3003592399 0.5534683885 0.7846128536 -0.2360465942 0.149457078392 +1403715355912143104.0000000000 1.4821019259 0.9076701676 1.3077249526 0.5532419253 0.7861918877 -0.2322571982 0.147926609266 +1403715355962142976.0000000000 1.4916200446 0.9119942131 1.3146106059 0.5521382146 0.7879590773 -0.2288940029 0.147889891142 +1403715356012143104.0000000000 1.5008685108 0.9164590708 1.3214501320 0.5514547443 0.7890083724 -0.2262006613 0.148985617126 +1403715356062142976.0000000000 1.5099805340 0.9211889268 1.3280350390 0.5496620218 0.7905129039 -0.2235488971 0.151614317471 +1403715356112143104.0000000000 1.5186689165 0.9262893072 1.3344308889 0.5472779076 0.7919768921 -0.2214023018 0.155693657434 +1403715356162142976.0000000000 1.5266895311 0.9320397682 1.3406524944 0.5449896117 0.7930161146 -0.2202753312 0.159970446122 +1403715356212143104.0000000000 1.5337527848 0.9384541891 1.3470377054 0.5437881853 0.7929277552 -0.2204658525 0.164179147067 +1403715356262142976.0000000000 1.5399744755 0.9458501231 1.3529788082 0.5426769458 0.7926309528 -0.2217583450 0.167514601297 +1403715356312143104.0000000000 1.5449905638 0.9539116062 1.3581821158 0.5405560811 0.7929094029 -0.2238586296 0.17023840915 +1403715356362142976.0000000000 1.5488182815 0.9632606263 1.3626316030 0.5375858140 0.7937153639 -0.2275126795 0.171042083568 +1403715356412143104.0000000000 1.5514845150 0.9738558662 1.3663215157 0.5345837431 0.7946076412 -0.2315382866 0.170906231426 +1403715356462142976.0000000000 1.5531612718 0.9857128502 1.3693912831 0.5326136908 0.7947381972 -0.2367297814 0.169330637886 +1403715356512143104.0000000000 1.5538832324 0.9988824645 1.3720328935 0.5323908915 0.7937016077 -0.2440259784 0.164465857875 +1403715356562142976.0000000000 1.5543065885 1.0131349002 1.3739005250 0.5330005100 0.7925093483 -0.2490615972 0.16064778265 +1403715356612143104.0000000000 1.5544226067 1.0285445554 1.3751798006 0.5339678310 0.7916747510 -0.2521834437 0.156629993197 +1403715356662142976.0000000000 1.5544642706 1.0450587772 1.3760723666 0.5359658339 0.7907824596 -0.2531790763 0.152656744914 +1403715356712143104.0000000000 1.5547729207 1.0626429253 1.3765458733 0.5373579994 0.7909933298 -0.2518438718 0.148830765856 +1403715356762142976.0000000000 1.5553222471 1.0811900064 1.3768474745 0.5393478108 0.7913332016 -0.2490112951 0.144530543258 +1403715356812143104.0000000000 1.5560979188 1.1001181567 1.3767891640 0.5420812217 0.7917518478 -0.2444800546 0.139665541746 +1403715356862142976.0000000000 1.5571930685 1.1191886465 1.3761632809 0.5429316936 0.7940255390 -0.2380298666 0.134500565519 +1403715356912143104.0000000000 1.5587838193 1.1391204294 1.3760719353 0.5448322316 0.7958502835 -0.2314625102 0.127299929797 +1403715356962142976.0000000000 1.5614338218 1.1596195670 1.3779195030 0.5481001386 0.7971105199 -0.2236409911 0.119104006016 +1403715357012143104.0000000000 1.5650584592 1.1804550312 1.3812403732 0.5518838043 0.7982893142 -0.2131987052 0.112715346826 +1403715357062142976.0000000000 1.5694056069 1.2011983176 1.3859904277 0.5549820104 0.7999923340 -0.2025056335 0.104874696758 +1403715357112143104.0000000000 1.5743457200 1.2220027181 1.3919427408 0.5588919649 0.8009445301 -0.1910883634 0.0980452372442 +1403715357162142976.0000000000 1.5798227089 1.2426170099 1.3981745203 0.5616057531 0.8025029147 -0.1793154204 0.091836975309 +1403715357212143104.0000000000 1.5862573785 1.2632687378 1.4051222573 0.5636019871 0.8041034398 -0.1681753818 0.0865303362815 +1403715357262142976.0000000000 1.5939066888 1.2841151367 1.4125547252 0.5661280957 0.8047495482 -0.1576793067 0.0837518961984 +1403715357312143104.0000000000 1.6027920440 1.3052421238 1.4202707648 0.5675438422 0.8055690196 -0.1485866965 0.0829128184357 +1403715357362142976.0000000000 1.6124859091 1.3267492890 1.4289127100 0.5683844104 0.8063391788 -0.1409753549 0.0829592674517 +1403715357412143104.0000000000 1.6219747646 1.3481255420 1.4376451317 0.5689429060 0.8069321557 -0.1357787151 0.082028083162 +1403715357462142976.0000000000 1.6313497380 1.3692757297 1.4458210266 0.5692427475 0.8074717874 -0.1307821235 0.0827529048061 +1403715357512143104.0000000000 1.6403075461 1.3902509329 1.4531451828 0.5678307018 0.8090315075 -0.1272461627 0.0827328716583 +1403715357562142976.0000000000 1.6489226342 1.4113565882 1.4592472996 0.5662984185 0.8105338747 -0.1244507012 0.082782619792 +1403715357612143104.0000000000 1.6571082410 1.4326265621 1.4648225696 0.5647637743 0.8119773858 -0.1217059259 0.0832001912306 +1403715357662142976.0000000000 1.6649212949 1.4544224570 1.4698601031 0.5644990419 0.8124212180 -0.1191198490 0.084398209917 +1403715357712143104.0000000000 1.6723808659 1.4766022475 1.4754502306 0.5664725260 0.8112300563 -0.1164729382 0.0863060121486 +1403715357762142976.0000000000 1.6791589599 1.4987520053 1.4801073573 0.5668657019 0.8110733750 -0.1139189086 0.0885761742176 +1403715357812143104.0000000000 1.6850198061 1.5210383784 1.4839827956 0.5673911102 0.8107747920 -0.1104058396 0.0923153037111 +1403715357862142976.0000000000 1.6896556732 1.5434863887 1.4864203726 0.5667805744 0.8111788615 -0.1069405282 0.096500562063 +1403715357912143104.0000000000 1.6928135666 1.5664078048 1.4880287853 0.5658337517 0.8118017833 -0.1048856168 0.0990405848347 +1403715357962142976.0000000000 1.6945402649 1.5899000251 1.4890464591 0.5639586255 0.8130611187 -0.1041156157 0.100210900594 +1403715358012143104.0000000000 1.6948131935 1.6139305286 1.4893028561 0.5620406922 0.8143864691 -0.1035558747 0.100802381132 +1403715358062142976.0000000000 1.6935787046 1.6385768450 1.4889862600 0.5601254996 0.8156702573 -0.1033042236 0.101339495622 +1403715358112143104.0000000000 1.6905550009 1.6640267323 1.4885662666 0.5591652884 0.8163663706 -0.1048915364 0.0993875988815 +1403715358162142976.0000000000 1.6860538441 1.6905202080 1.4880838666 0.5592788532 0.8163061169 -0.1076761238 0.0962150723684 +1403715358212143104.0000000000 1.6801409455 1.7180828443 1.4871385428 0.5581231196 0.8171044953 -0.1118041374 0.0913162740622 +1403715358262142976.0000000000 1.6731942777 1.7465098135 1.4863801818 0.5580116122 0.8171827644 -0.1147932879 0.0875092638184 +1403715358312143104.0000000000 1.6658310196 1.7757247440 1.4848834803 0.5566800778 0.8180975419 -0.1164810288 0.0851814113331 +1403715358362142976.0000000000 1.6582905805 1.8062323119 1.4829944323 0.5553736630 0.8191660048 -0.1156186334 0.0846137262189 +1403715358412143104.0000000000 1.6501810352 1.8375477834 1.4809594766 0.5550519507 0.8197935616 -0.1115149757 0.0861409224612 +1403715358462142976.0000000000 1.6409883647 1.8695849534 1.4787385600 0.5562680422 0.8196264894 -0.1063675116 0.0863958073992 +1403715358512143104.0000000000 1.6307055106 1.9030041921 1.4765792838 0.5594227651 0.8182768450 -0.0999734476 0.0864551013738 +1403715358562142976.0000000000 1.6194671622 1.9371953914 1.4741582005 0.5626214541 0.8169056371 -0.0938162048 0.0855616689577 +1403715358612143104.0000000000 1.6069795844 1.9717948679 1.4712673219 0.5659354836 0.8154356694 -0.0883549206 0.0835170974965 +1403715358662142976.0000000000 1.5930028857 2.0069495646 1.4688854530 0.5703067202 0.8132514790 -0.0846675808 0.078763428121 +1403715358712143104.0000000000 1.5775633558 2.0422931541 1.4673188679 0.5759057851 0.8102378452 -0.0837549477 0.0695145278214 +1403715358762142976.0000000000 1.5614014329 2.0774525874 1.4657193851 0.5804343246 0.8078350757 -0.0826728654 0.0605283631921 +1403715358812143104.0000000000 1.5450074852 2.1121515380 1.4637316430 0.5842476441 0.8057655507 -0.0810547810 0.0531666263756 +1403715358862142976.0000000000 1.5284446528 2.1461468096 1.4613519411 0.5872975186 0.8041375341 -0.0793708842 0.0463110537724 +1403715358912143104.0000000000 1.5122499355 2.1793587025 1.4584566592 0.5906497116 0.8021468040 -0.0771594197 0.0417114716539 +1403715358962142976.0000000000 1.4960446440 2.2114523038 1.4546878381 0.5922679509 0.8013662103 -0.0746400230 0.0382065210806 +1403715359012143104.0000000000 1.4800237276 2.2425406515 1.4504500310 0.5921263523 0.8018085007 -0.0730820001 0.0338900040946 +1403715359062142976.0000000000 1.4645317435 2.2727006578 1.4453530205 0.5906624151 0.8031772401 -0.0710817342 0.0311708114368 +1403715359112143104.0000000000 1.4496270706 2.3016256942 1.4405835554 0.5904199205 0.8035725373 -0.0692391823 0.0296888948454 +1403715359162142976.0000000000 1.4351302645 2.3295691132 1.4358282997 0.5913409806 0.8030727185 -0.0674528240 0.028985686733 +1403715359212143104.0000000000 1.4209438773 2.3567252752 1.4309919797 0.5929822043 0.8019687368 -0.0663728551 0.0285113078911 +1403715359262142976.0000000000 1.4072946605 2.3825116115 1.4261800503 0.5941961313 0.8011460562 -0.0650272140 0.0294519199471 +1403715359312143104.0000000000 1.3941373146 2.4068255440 1.4213733839 0.5943106384 0.8010982910 -0.0635190880 0.0316499417546 +1403715359362142976.0000000000 1.3809101882 2.4295847618 1.4163679663 0.5936434295 0.8016018830 -0.0621271177 0.0340898965587 +1403715359412143104.0000000000 1.3677349187 2.4511148793 1.4116731399 0.5931198640 0.8019413729 -0.0601346618 0.0385056335502 +1403715359462142976.0000000000 1.3542278847 2.4716969460 1.4073642491 0.5927409856 0.8021315592 -0.0581149687 0.0431941681708 +1403715359512143104.0000000000 1.3399736289 2.4912362585 1.4043790986 0.5926422957 0.8020899864 -0.0566587239 0.0470802729282 +1403715359562142976.0000000000 1.3249468814 2.5098101307 1.4025154121 0.5932458571 0.8015007883 -0.0563011990 0.0498599484727 +1403715359612143104.0000000000 1.3087528299 2.5272611571 1.4015342575 0.5940540289 0.8008174830 -0.0569342325 0.0504941867389 +1403715359662142976.0000000000 1.2914352676 2.5435662931 1.4009896852 0.5939249024 0.8008514088 -0.0584485953 0.049739250661 +1403715359712143104.0000000000 1.2732776152 2.5587588485 1.4011429420 0.5933343293 0.8012306519 -0.0605757083 0.0481082087887 +1403715359762142976.0000000000 1.2543665518 2.5728787585 1.4017175374 0.5921437979 0.8020590262 -0.0626574323 0.0462718848523 +1403715359812143104.0000000000 1.2348764623 2.5858387470 1.4030002316 0.5920944316 0.8020247283 -0.0647777524 0.0445461800699 +1403715359862142976.0000000000 1.2150397322 2.5976658686 1.4044523153 0.5908121776 0.8029357149 -0.0658709964 0.0435456127828 +1403715359912143104.0000000000 1.1947872681 2.6083052108 1.4061873646 0.5885158943 0.8045886228 -0.0677643999 0.0411603720583 +1403715359962142976.0000000000 1.1743179867 2.6181139848 1.4083947075 0.5867192321 0.8058465169 -0.0706754302 0.037106839065 +1403715360012143104.0000000000 1.1540836200 2.6271706122 1.4105416393 0.5847482896 0.8072754077 -0.0712795063 0.0359873024007 +1403715360062142976.0000000000 1.1340251190 2.6357262438 1.4123770650 0.5830670607 0.8085076049 -0.0711605140 0.0358390417676 +1403715360112143104.0000000000 1.1140309456 2.6439643318 1.4141452236 0.5819095935 0.8093832346 -0.0705843027 0.0360258343197 +1403715360162142976.0000000000 1.0941370065 2.6521180478 1.4159819915 0.5811567046 0.8099773833 -0.0696460882 0.0366462223736 +1403715360212143104.0000000000 1.0744444039 2.6599873354 1.4178699753 0.5806117446 0.8104054333 -0.0689836869 0.0370713717059 +1403715360262142976.0000000000 1.0550982957 2.6674151117 1.4199956525 0.5802117056 0.8106453086 -0.0693388242 0.0374257641081 +1403715360312143104.0000000000 1.0360395160 2.6746919599 1.4221879585 0.5800638018 0.8105406496 -0.0718471369 0.037253591092 +1403715360362142976.0000000000 1.0174403725 2.6819098703 1.4247470549 0.5799475905 0.8101779617 -0.0777385698 0.0350596266331 +1403715360412143104.0000000000 0.9994375664 2.6888444508 1.4278188188 0.5801046508 0.8093502385 -0.0861184187 0.0318497010743 +1403715360462142976.0000000000 0.9824747373 2.6953397822 1.4311416182 0.5799089032 0.8084909488 -0.0957947568 0.0295197267529 +1403715360512143104.0000000000 0.9669622270 2.7017329155 1.4343463171 0.5797234213 0.8073437070 -0.1063317195 0.0284685606132 +1403715360562142976.0000000000 0.9532156920 2.7078492301 1.4369253040 0.5795416493 0.8059993692 -0.1166602058 0.0297806990111 +1403715360612143104.0000000000 0.9414623966 2.7136306838 1.4395624293 0.5788403784 0.8048729728 -0.1262597057 0.0343773276358 +1403715360662142976.0000000000 0.9318729285 2.7190608900 1.4428011532 0.5785892858 0.8032735265 -0.1350156020 0.0419150003185 +1403715360712143104.0000000000 0.9243430502 2.7233424665 1.4465182154 0.5778226992 0.8018009668 -0.1438089974 0.0505480978695 +1403715360762142976.0000000000 0.9189346006 2.7269499357 1.4503751298 0.5759914911 0.8009300817 -0.1510987330 0.0625618036359 +1403715360812143104.0000000000 0.9150700607 2.7300766331 1.4538971714 0.5736223330 0.8000079368 -0.1590669541 0.0751160713673 +1403715360862142976.0000000000 0.9121811229 2.7328980459 1.4578319853 0.5711475160 0.7987956779 -0.1672050611 0.0880820497952 +1403715360912143104.0000000000 0.9102326763 2.7353323595 1.4618454431 0.5692046096 0.7968091438 -0.1758012384 0.100971408557 +1403715360962142976.0000000000 0.9088001953 2.7376931818 1.4661066652 0.5663404815 0.7950770028 -0.1855417282 0.112628974171 +1403715361012143104.0000000000 0.9077415583 2.7399340639 1.4708574205 0.5636756834 0.7928904806 -0.1959527839 0.123275773496 +1403715361062142976.0000000000 0.9068070414 2.7419918252 1.4755948137 0.5607712647 0.7905455814 -0.2068091548 0.13342880449 +1403715361112143104.0000000000 0.9056654936 2.7440412885 1.4802787254 0.5576011560 0.7880748620 -0.2184486453 0.142475092585 +1403715361162142976.0000000000 0.9043562391 2.7461442293 1.4849533720 0.5543104903 0.7854685149 -0.2300552148 0.151174371253 +1403715361212143104.0000000000 0.9033376888 2.7482975607 1.4895952531 0.5505588203 0.7828696485 -0.2412731378 0.1605844691 +1403715361262142976.0000000000 0.9022973436 2.7507573064 1.4943005713 0.5471555107 0.7798566972 -0.2523333546 0.169623869597 +1403715361312143104.0000000000 0.9010945921 2.7533615206 1.4986775231 0.5434122287 0.7768830855 -0.2629439346 0.178931015798 +1403715361362142976.0000000000 0.8998734805 2.7562025864 1.5028901508 0.5400629984 0.7733209070 -0.2733206273 0.188686425653 +1403715361412143104.0000000000 0.8983376137 2.7592923768 1.5062340775 0.5365237190 0.7697215867 -0.2838864684 0.197685231942 +1403715361462142976.0000000000 0.8963467409 2.7629751270 1.5088856094 0.5334096574 0.7659047610 -0.2941627434 0.205748183391 +1403715361512143104.0000000000 0.8937926606 2.7672631679 1.5109641435 0.5308777272 0.7622453567 -0.3029279183 0.213038802254 +1403715361562142976.0000000000 0.8906442491 2.7721556091 1.5122610305 0.5280424221 0.7594667192 -0.3103379742 0.219252924016 +1403715361612143104.0000000000 0.8867937058 2.7775953324 1.5129023552 0.5248235990 0.7575580751 -0.3158866397 0.225569465255 +1403715361662142976.0000000000 0.8823439532 2.7839093916 1.5131345781 0.5224565804 0.7556926096 -0.3210228748 0.230026335973 +1403715361712143104.0000000000 0.8774990030 2.7911728862 1.5126570295 0.5197724359 0.7539953860 -0.3271477821 0.233027683759 +1403715361762142976.0000000000 0.8724864306 2.7992482255 1.5113998572 0.5163380689 0.7525112782 -0.3343199156 0.235269991355 +1403715361812143104.0000000000 0.8675062297 2.8082006283 1.5095018889 0.5127306679 0.7509382184 -0.3419449948 0.237218622431 +1403715361862142976.0000000000 0.8628004493 2.8180016338 1.5070714982 0.5087992590 0.7490743053 -0.3500636449 0.239721596318 +1403715361912143104.0000000000 0.8586967891 2.8285067477 1.5040904136 0.5047347012 0.7466056502 -0.3579294823 0.244355008337 +1403715361962142976.0000000000 0.8549375590 2.8400575498 1.5014330055 0.5026894253 0.7423222212 -0.3662908563 0.249182804929 +1403715362012143104.0000000000 0.8516697532 2.8522448145 1.4984507260 0.5004924266 0.7375430511 -0.3750602567 0.254690758685 +1403715362062142976.0000000000 0.8488371800 2.8651420583 1.4948794718 0.4974502163 0.7328693625 -0.3834518619 0.261553913246 +1403715362112143104.0000000000 0.8465215402 2.8787449749 1.4909035513 0.4943601869 0.7275282802 -0.3925930329 0.268665810371 +1403715362162142976.0000000000 0.8446001385 2.8929611489 1.4859829773 0.4898620227 0.7226037652 -0.4017709567 0.276512378789 +1403715362212143104.0000000000 0.8433413432 2.9078076905 1.4809529489 0.4854927544 0.7168642545 -0.4113572620 0.284934429474 +1403715362262142976.0000000000 0.8425530082 2.9233769630 1.4756357165 0.4812664630 0.7104445101 -0.4210409362 0.293897464661 +1403715362312143104.0000000000 0.8420916076 2.9398351957 1.4697267611 0.4759062698 0.7043909494 -0.4310802580 0.302516815856 +1403715362362142976.0000000000 0.8419824265 2.9572867385 1.4638635754 0.4706041164 0.6977905879 -0.4415299120 0.31092024357 +1403715362412143104.0000000000 0.8417425015 2.9756758971 1.4580194405 0.4654221215 0.6907477357 -0.4521351784 0.319098096049 +1403715362462142976.0000000000 0.8413624680 2.9952104827 1.4521747183 0.4606383554 0.6830094648 -0.4631140021 0.326857457472 +1403715362512143104.0000000000 0.8409751675 3.0156214089 1.4461752746 0.4556259980 0.6750260559 -0.4739251617 0.334872684439 +1403715362562142976.0000000000 0.8406514161 3.0369940302 1.4400073824 0.4492399631 0.6678996609 -0.4844525559 0.342635695122 +1403715362612143104.0000000000 0.8405885537 3.0596120240 1.4343434340 0.4440153955 0.6599986373 -0.4950944593 0.34947618478 +1403715362662142976.0000000000 0.8407878307 3.0833495355 1.4292354686 0.4389220467 0.6519696616 -0.5053502430 0.35623605825 +1403715362712143104.0000000000 0.8413873018 3.1081776259 1.4246840093 0.4345027036 0.6433786516 -0.5158855209 0.362123515649 +1403715362762142976.0000000000 0.8423802714 3.1341556740 1.4207525118 0.4315623625 0.6337551547 -0.5275531766 0.365781324095 +1403715362812143104.0000000000 0.8435661774 3.1610178369 1.4177627866 0.4300151542 0.6230881239 -0.5400103853 0.367745755536 +1403715362862142976.0000000000 0.8449551136 3.1883962266 1.4156605438 0.4312855920 0.6104171965 -0.5535573544 0.367366084206 +1403715362912143104.0000000000 0.8469862953 3.2156585851 1.4149319876 0.4358418069 0.5953241754 -0.5665393604 0.366966209105 +1403715362962142976.0000000000 0.8497851920 3.2417032025 1.4149235831 0.4395668636 0.5810469515 -0.5770169654 0.369075648461 +1403715363012143104.0000000000 0.8530180801 3.2661506951 1.4153350053 0.4425794422 0.5679050188 -0.5866492930 0.370742409154 +1403715363062142976.0000000000 0.8563012445 3.2885111397 1.4159975804 0.4432262575 0.5568632479 -0.5954573071 0.37267197801 +1403715363112143104.0000000000 0.8593730695 3.3083847304 1.4169977754 0.4418789626 0.5477821353 -0.6031986968 0.375271963875 +1403715363162142976.0000000000 0.8619803850 3.3255349824 1.4178130793 0.4377905758 0.5411891114 -0.6107901247 0.377344909909 +1403715363212143104.0000000000 0.8644658878 3.3397629309 1.4192927212 0.4332012098 0.5349855059 -0.6175948045 0.380399628968 +1403715363262142976.0000000000 0.8670688985 3.3511479752 1.4214415842 0.4282338035 0.5291624359 -0.6236115733 0.384332579589 +1403715363312143104.0000000000 0.8696937494 3.3599658880 1.4243063375 0.4234104240 0.5233461776 -0.6296033093 0.387855725878 +1403715363362142976.0000000000 0.8720835360 3.3661315890 1.4277468484 0.4186279829 0.5172514585 -0.6351375501 0.392175768002 +1403715363412143104.0000000000 0.8743420542 3.3699345712 1.4318716006 0.4142277560 0.5110757220 -0.6399486093 0.397092873205 +1403715363462142976.0000000000 0.8765073783 3.3709848441 1.4362835745 0.4091597544 0.5048788031 -0.6447575871 0.402459120118 +1403715363512143104.0000000000 0.8784975049 3.3695041452 1.4410999990 0.4037139943 0.4988005487 -0.6493441615 0.408123980428 +1403715363562142976.0000000000 0.8801760361 3.3656657862 1.4459639607 0.3960880624 0.4941781865 -0.6529040640 0.415473765758 +1403715363612143104.0000000000 0.8818202671 3.3595634584 1.4506106415 0.3863768043 0.4908484655 -0.6553770624 0.424572320099 +1403715363662142976.0000000000 0.8834035482 3.3518171462 1.4556475814 0.3778137514 0.4864885360 -0.6586095481 0.432225793676 +1403715363712143104.0000000000 0.8849825922 3.3425826444 1.4609812147 0.3695283815 0.4811989036 -0.6618941391 0.440218739959 +1403715363762142976.0000000000 0.8863726514 3.3324737508 1.4664255714 0.3623672258 0.4743011647 -0.6662045383 0.447101679671 +1403715363812143104.0000000000 0.8875036432 3.3217088221 1.4718114404 0.3553160127 0.4664277684 -0.6710602842 0.453733140682 +1403715363862142976.0000000000 0.8884535693 3.3104064632 1.4769573022 0.3485703884 0.4573022352 -0.6771230512 0.459214245692 +1403715363912143104.0000000000 0.8891166907 3.2985577163 1.4821115303 0.3413443602 0.4477654504 -0.6827061227 0.465727902492 +1403715363962142976.0000000000 0.8894493551 3.2858428521 1.4873039607 0.3335060848 0.4373532720 -0.6878831645 0.473616468164 +1403715364012143104.0000000000 0.8892763347 3.2728975365 1.4922708271 0.3260385123 0.4259965729 -0.6944628452 0.47952806479 +1403715364062142976.0000000000 0.8886255145 3.2596509484 1.4971508139 0.3181001895 0.4148249392 -0.7003549759 0.48604058161 +1403715364112143104.0000000000 0.8871733400 3.2466845216 1.5023809069 0.3115814052 0.4040313669 -0.7058643668 0.491356467555 +1403715364162142976.0000000000 0.8848384241 3.2340964546 1.5077478984 0.3055202773 0.3944796772 -0.7103603715 0.496418459567 +1403715364212143104.0000000000 0.8819176495 3.2221120775 1.5126730006 0.2996689070 0.3870404776 -0.7148830856 0.499339953096 +1403715364262142976.0000000000 0.8788345619 3.2105850440 1.5180576633 0.2955983406 0.3802282157 -0.7193662165 0.500560058 +1403715364312143104.0000000000 0.8749806849 3.1992997625 1.5238387041 0.2928894559 0.3744076081 -0.7237842501 0.500171039712 +1403715364362142976.0000000000 0.8703371259 3.1884949508 1.5299090361 0.2909437738 0.3699745645 -0.7278958402 0.498636328242 +1403715364412143104.0000000000 0.8654054407 3.1777118061 1.5368056456 0.2905520059 0.3659508208 -0.7312804512 0.496878687708 +1403715364462142976.0000000000 0.8603239695 3.1662907639 1.5440786663 0.2900364622 0.3631106232 -0.7330474734 0.496659770421 +1403715364512143104.0000000000 0.8548519558 3.1542651031 1.5513679727 0.2908522486 0.3609199430 -0.7348050043 0.495180138815 +1403715364562142976.0000000000 0.8484841710 3.1416701943 1.5591684787 0.2918414541 0.3595624681 -0.7353203821 0.494820505707 +1403715364612143104.0000000000 0.8415549921 3.1280725812 1.5672770148 0.2920365231 0.3590685793 -0.7354397477 0.49488665579 +1403715364662142976.0000000000 0.8341606637 3.1132790268 1.5756558221 0.2921258268 0.3577284848 -0.7351725127 0.496199767272 +1403715364712143104.0000000000 0.8259349127 3.0973087110 1.5845424547 0.2896295868 0.3571033443 -0.7339172817 0.499957325691 +1403715364762142976.0000000000 0.8166052286 3.0804941115 1.5931781962 0.2839238033 0.3575697252 -0.7330075486 0.504213346986 +1403715364812143104.0000000000 0.8066722279 3.0632961072 1.6011273516 0.2761101945 0.3585351012 -0.7330759719 0.507755217628 +1403715364862142976.0000000000 0.7964048660 3.0461302899 1.6089900520 0.2682915481 0.3586484018 -0.7341086592 0.510367951143 +1403715364912143104.0000000000 0.7860839991 3.0293741088 1.6170169539 0.2617956617 0.3572260716 -0.7359587993 0.512071490076 +1403715364962142976.0000000000 0.7758451762 3.0128932117 1.6249633947 0.2543432730 0.3555403136 -0.7380595603 0.513973413983 +1403715365012143104.0000000000 0.7660266366 2.9967754505 1.6333910567 0.2497530716 0.3514306253 -0.7409764355 0.514853222678 +1403715365062142976.0000000000 0.7563135999 2.9806871772 1.6415669375 0.2437173696 0.3478292554 -0.7437484400 0.516192707078 +1403715365112143104.0000000000 0.7470594556 2.9649876191 1.6501913089 0.2392933067 0.3425404800 -0.7458322086 0.518786130823 +1403715365162142976.0000000000 0.7383951685 2.9498685944 1.6591916689 0.2361433399 0.3357676502 -0.7470185978 0.522933669383 +1403715365212143104.0000000000 0.7302266931 2.9354316266 1.6680867705 0.2327932852 0.3292159774 -0.7483884548 0.526629706047 +1403715365262142976.0000000000 0.7223532851 2.9218983978 1.6764331866 0.2291499213 0.3237905238 -0.7494883521 0.530016245272 +1403715365312143104.0000000000 0.7146832243 2.9092981644 1.6842497060 0.2257252078 0.3191441287 -0.7505187654 0.532838379272 +1403715365362142976.0000000000 0.7073942155 2.8978109891 1.6916443239 0.2231944348 0.3143125834 -0.7519378897 0.534772151711 +1403715365412143104.0000000000 0.7004242703 2.8871616192 1.6989237487 0.2216396376 0.3077645471 -0.7538530915 0.536528071027 +1403715365462142976.0000000000 0.6931972050 2.8772102580 1.7054574184 0.2181557387 0.3015688282 -0.7562102958 0.538154535403 +1403715365512143104.0000000000 0.6860613788 2.8680543911 1.7117390664 0.2151571165 0.2939949205 -0.7585915170 0.540197475282 +1403715365562142976.0000000000 0.6788734110 2.8595601505 1.7174705338 0.2103553674 0.2863717380 -0.7614361086 0.542177922491 +1403715365612143104.0000000000 0.6716104214 2.8518109232 1.7233623479 0.2074215243 0.2760295248 -0.7650736611 0.543549727051 +1403715365662142976.0000000000 0.6641613411 2.8445049977 1.7292638820 0.2050546196 0.2640620424 -0.7690832141 0.544733742851 +1403715365712143104.0000000000 0.6564301427 2.8373897877 1.7347849402 0.2021379194 0.2515832754 -0.7732593897 0.545816849623 +1403715365762142976.0000000000 0.6480343862 2.8301896433 1.7398193481 0.1983827430 0.2390077202 -0.7775396715 0.546764717368 +1403715365812143104.0000000000 0.6387729908 2.8232800844 1.7444475629 0.1936133931 0.2272011915 -0.7816578011 0.547635421264 +1403715365862142976.0000000000 0.6287394162 2.8167064760 1.7489421242 0.1885207068 0.2168685894 -0.7847819588 0.549131346082 +1403715365912143104.0000000000 0.6179461126 2.8105201168 1.7529796222 0.1833461952 0.2076759267 -0.7878687539 0.550016098721 +1403715365962142976.0000000000 0.6065921233 2.8044440906 1.7567673258 0.1794150097 0.1992876356 -0.7907800184 0.550237816847 +1403715366012143104.0000000000 0.5946861861 2.7984307881 1.7604321056 0.1785979953 0.1903528432 -0.7928939704 0.550624829571 +1403715366062142976.0000000000 0.5818670177 2.7923882590 1.7633415051 0.1777512765 0.1827813501 -0.7952304767 0.550094492558 +1403715366112143104.0000000000 0.5679958958 2.7860434979 1.7661504481 0.1784991721 0.1752867125 -0.7971029689 0.549581177789 +1403715366162142976.0000000000 0.5525848093 2.7794273376 1.7686333279 0.1773327895 0.1703991920 -0.7979775554 0.550226333634 +1403715366212143104.0000000000 0.5354266502 2.7728419007 1.7705089040 0.1764963452 0.1668397554 -0.7985221423 0.550795719328 +1403715366262142976.0000000000 0.5167548309 2.7659148175 1.7721642224 0.1753839902 0.1643588916 -0.7986531949 0.551706158237 +1403715366312143104.0000000000 0.4966822370 2.7585554152 1.7737839962 0.1728671398 0.1639748013 -0.7987457642 0.552480244645 +1403715366362142976.0000000000 0.4753820786 2.7507085853 1.7756036451 0.1707398088 0.1640184483 -0.7985706881 0.553381172833 +1403715366412143104.0000000000 0.4525808278 2.7429292285 1.7768691313 0.1672420229 0.1661722754 -0.7993789036 0.55263934819 +1403715366462142976.0000000000 0.4282568263 2.7350237089 1.7779131744 0.1618111341 0.1697814264 -0.7995047921 0.552976953932 +1403715366512143104.0000000000 0.4033987073 2.7269876392 1.7791215626 0.1568001581 0.1737232328 -0.7996139975 0.553038338421 +1403715366562142976.0000000000 0.3782241411 2.7191497947 1.7801598093 0.1539204228 0.1768797515 -0.7999894739 0.552303266814 +1403715366612143104.0000000000 0.3527196326 2.7112282069 1.7808195996 0.1512226024 0.1800588714 -0.8009049356 0.550692120343 +1403715366662142976.0000000000 0.3275639912 2.7031251715 1.7814402647 0.1493321897 0.1829220224 -0.8015119624 0.549379654593 +1403715366712143104.0000000000 0.3027899767 2.6949066662 1.7819652402 0.1482867308 0.1857939390 -0.8024187296 0.547371756738 +1403715366762142976.0000000000 0.2781779052 2.6865003591 1.7826477069 0.1480000167 0.1878872956 -0.8035368312 0.545089827625 +1403715366812143104.0000000000 0.2536587043 2.6779892163 1.7829720500 0.1471984384 0.1904686289 -0.8050428303 0.54218111596 +1403715366862142976.0000000000 0.2296360795 2.6689884169 1.7836863385 0.1472525870 0.1926790249 -0.8061955413 0.539666765824 +1403715366912143104.0000000000 0.2063620748 2.6592948718 1.7849287157 0.1477895162 0.1943195648 -0.8067171113 0.538150228098 +1403715366962142976.0000000000 0.1838055993 2.6492332950 1.7866148530 0.1496590063 0.1948458860 -0.8077095658 0.535950109425 +1403715367012143104.0000000000 0.1618789762 2.6384362293 1.7887254147 0.1513745707 0.1955836137 -0.8081415242 0.534546598757 +1403715367062142976.0000000000 0.1407392243 2.6268166175 1.7914004929 0.1534850987 0.1957953493 -0.8083705519 0.533519968269 +1403715367112143104.0000000000 0.1201660700 2.6143412347 1.7943835995 0.1550425648 0.1965194250 -0.8084309746 0.532711252093 +1403715367162142976.0000000000 0.1002704037 2.6010702419 1.7975342841 0.1567437143 0.1972928505 -0.8088530106 0.53128499551 +1403715367212143104.0000000000 0.0809227997 2.5866997734 1.8010538098 0.1576258408 0.1985305526 -0.8082886557 0.531421831596 +1403715367262142976.0000000000 0.0621788769 2.5715890275 1.8046054443 0.1605075349 0.1982638571 -0.8084975539 0.530339966043 +1403715367312143104.0000000000 0.0434646062 2.5555373053 1.8075750873 0.1615413136 0.1992464229 -0.8090654680 0.528789500154 +1403715367362142976.0000000000 0.0253822793 2.5381011058 1.8106284780 0.1629671306 0.1997473213 -0.8099223246 0.526847748451 +1403715367412143104.0000000000 0.0075534135 2.5195052434 1.8133891578 0.1641433478 0.2003673369 -0.8102904971 0.525679752254 +1403715367462142976.0000000000 -0.0099019647 2.4997131988 1.8160910605 0.1650532796 0.2011992813 -0.8102651704 0.525115813693 +1403715367512143104.0000000000 -0.0272488036 2.4787332686 1.8190220937 0.1654694099 0.2022189107 -0.8108161654 0.52374090213 +1403715367562142976.0000000000 -0.0441469707 2.4563293043 1.8222403254 0.1660267374 0.2033973787 -0.8107748241 0.523171877435 +1403715367612143104.0000000000 -0.0606269600 2.4325656646 1.8258334288 0.1669468034 0.2041139590 -0.8102198122 0.523459752555 +1403715367662142976.0000000000 -0.0765781184 2.4076781428 1.8295345900 0.1682814050 0.2045485831 -0.8098933013 0.523368021956 +1403715367712143104.0000000000 -0.0920933354 2.3813231310 1.8333681205 0.1683245468 0.2056979825 -0.8088609130 0.524499008948 +1403715367762142976.0000000000 -0.1070794159 2.3537903835 1.8374443230 0.1688863706 0.2064673706 -0.8082327376 0.524984247866 +1403715367812143104.0000000000 -0.1216539180 2.3250660818 1.8415072446 0.1684673235 0.2077635125 -0.8072690733 0.526089086671 +1403715367862142976.0000000000 -0.1360137541 2.2954309729 1.8456458868 0.1675808547 0.2092192265 -0.8057198105 0.528166223291 +1403715367912143104.0000000000 -0.1500616427 2.2645973417 1.8496891669 0.1660957611 0.2106311204 -0.8033820401 0.531623952582 +1403715367962142976.0000000000 -0.1633697658 2.2329378073 1.8541478412 0.1665409277 0.2102635734 -0.8005273579 0.535919115513 +1403715368012143104.0000000000 -0.1763398153 2.2007495999 1.8581278032 0.1673450254 0.2093356039 -0.7982673154 0.539391824662 +1403715368062142976.0000000000 -0.1890588367 2.1681577609 1.8618070481 0.1690537137 0.2076427438 -0.7963188003 0.542385196333 +1403715368112143104.0000000000 -0.2019379791 2.1355056777 1.8646519497 0.1699944705 0.2063907764 -0.7949653658 0.544550084513 +1403715368162142976.0000000000 -0.2149652879 2.1028515416 1.8668345773 0.1711066333 0.2048096339 -0.7940409100 0.54614518876 +1403715368212143104.0000000000 -0.2282767729 2.0704798140 1.8682808405 0.1723768413 0.2032025779 -0.7937909363 0.546709142339 +1403715368262142976.0000000000 -0.2419685883 2.0384013638 1.8693060198 0.1750599519 0.2006433193 -0.7940672624 0.546400452483 +1403715368312143104.0000000000 -0.2562588328 2.0062490319 1.8700626791 0.1776094345 0.1981137562 -0.7946383609 0.545669958658 +1403715368362142976.0000000000 -0.2712156000 1.9739334783 1.8707435031 0.1816431264 0.1944728226 -0.7950546493 0.54504513626 +1403715368412143104.0000000000 -0.2872718168 1.9414035119 1.8709563980 0.1846858679 0.1916287088 -0.7953077204 0.544660626453 +1403715368462142976.0000000000 -0.3041215919 1.9082913598 1.8711864810 0.1873835903 0.1888572322 -0.7945913642 0.545751683299 +1403715368512143104.0000000000 -0.3221899269 1.8747381776 1.8709902501 0.1883004588 0.1871924755 -0.7939728671 0.546908585273 +1403715368562142976.0000000000 -0.3418603998 1.8410363615 1.8701258335 0.1861804223 0.1876593670 -0.7929881744 0.548899414861 +1403715368612143104.0000000000 -0.3629122827 1.8071884964 1.8686538834 0.1813133462 0.1900181079 -0.7920569010 0.551057578417 +1403715368662142976.0000000000 -0.3851799688 1.7734892615 1.8668856267 0.1758378721 0.1929114115 -0.7915684359 0.552526597857 +1403715368712143104.0000000000 -0.4081801108 1.7402821759 1.8649758631 0.1722793389 0.1945545569 -0.7915743707 0.553062717494 +1403715368762142976.0000000000 -0.4319472587 1.7070535096 1.8630734740 0.1683064258 0.1962126158 -0.7914977896 0.553809358521 +1403715368812143104.0000000000 -0.4561369140 1.6742841285 1.8613543704 0.1651412411 0.1974073066 -0.7913376802 0.55456595793 +1403715368862142976.0000000000 -0.4803729231 1.6421491069 1.8596119844 0.1633200155 0.1976487290 -0.7920620073 0.553984953882 +1403715368912143104.0000000000 -0.5046295140 1.6104557581 1.8578637061 0.1622287976 0.1988442811 -0.7925426576 0.553189755005 +1403715368962142976.0000000000 -0.5288990025 1.5798686918 1.8559723120 0.1623443685 0.2011569481 -0.7932453295 0.551309382704 +1403715369012143104.0000000000 -0.5529321360 1.5500840168 1.8538360573 0.1637509754 0.2045072854 -0.7941785375 0.548309072323 +1403715369062142976.0000000000 -0.5768959160 1.5206824923 1.8519324423 0.1661151834 0.2092038837 -0.7949503602 0.544695700083 +1403715369112143104.0000000000 -0.6005313664 1.4915852519 1.8505217974 0.1694352645 0.2152479535 -0.7948773028 0.541414890037 +1403715369162142976.0000000000 -0.6236094799 1.4624824437 1.8489280982 0.1730477506 0.2227351097 -0.7940270955 0.538483536011 +1403715369212143104.0000000000 -0.6460746830 1.4331858342 1.8477489071 0.1776800607 0.2309686995 -0.7926316023 0.535554291359 +1403715369262142976.0000000000 -0.6680699261 1.4037708173 1.8467440315 0.1820596498 0.2406248731 -0.7900309467 0.533671301136 +1403715369312143104.0000000000 -0.6895980780 1.3747656105 1.8456943958 0.1875187500 0.2506240555 -0.7876693452 0.530661194927 +1403715369362142976.0000000000 -0.7103282099 1.3454862367 1.8452916499 0.1938226822 0.2608280802 -0.7843265350 0.528425365499 +1403715369412143104.0000000000 -0.7303396771 1.3161793480 1.8448659540 0.1999974527 0.2718525743 -0.7809491007 0.525562269267 +1403715369462142976.0000000000 -0.7493495410 1.2867891007 1.8447306322 0.2070252820 0.2825931501 -0.7773431196 0.522512505677 +1403715369512143104.0000000000 -0.7677283195 1.2573942599 1.8447507045 0.2144347756 0.2934600965 -0.7733353381 0.519472187596 +1403715369562142976.0000000000 -0.7855475240 1.2280555906 1.8447396588 0.2219895581 0.3042398285 -0.7690641487 0.516429180091 +1403715369612143104.0000000000 -0.8027239285 1.1988621000 1.8446470286 0.2294748097 0.3152320417 -0.7644053444 0.513473018831 +1403715369662142976.0000000000 -0.8191767356 1.1694471925 1.8446871293 0.2360919816 0.3256546741 -0.7599389678 0.510590221918 +1403715369712143104.0000000000 -0.8350471415 1.1393420695 1.8446955191 0.2418323029 0.3346769650 -0.7556708955 0.508399413884 +1403715369762142976.0000000000 -0.8503066430 1.1089549883 1.8444556913 0.2459707022 0.3432909293 -0.7516594740 0.506614041051 +1403715369812143104.0000000000 -0.8647128614 1.0782928152 1.8440723647 0.2495085252 0.3501947462 -0.7486229922 0.504651118249 +1403715369862142976.0000000000 -0.8782997330 1.0474087404 1.8431484153 0.2509474613 0.3567555712 -0.7456647357 0.503721089479 +1403715369912143104.0000000000 -0.8908476173 1.0165441384 1.8415614372 0.2511412267 0.3625063946 -0.7440003008 0.501976842695 +1403715369962142976.0000000000 -0.9023816943 0.9857447197 1.8395343107 0.2505703789 0.3675592597 -0.7432467768 0.499698813958 +1403715370012143104.0000000000 -0.9126492082 0.9549811383 1.8371522379 0.2486274668 0.3722105912 -0.7422542315 0.498700625938 +1403715370062142976.0000000000 -0.9213946891 0.9244805744 1.8342889011 0.2459017588 0.3764625801 -0.7409348960 0.498822343904 +1403715370112143104.0000000000 -0.9283358940 0.8942109381 1.8316544112 0.2442806409 0.3789750286 -0.7394158604 0.499969080666 +1403715370162142976.0000000000 -0.9332925123 0.8643232091 1.8293985137 0.2440421177 0.3801240428 -0.7365884657 0.503375197056 +1403715370212143104.0000000000 -0.9361229321 0.8354945573 1.8279711177 0.2486386339 0.3769081117 -0.7353123644 0.505405611118 +1403715370262142976.0000000000 -0.9377455601 0.8074719284 1.8270218710 0.2537494061 0.3726832439 -0.7345580536 0.507092599526 +1403715370312143104.0000000000 -0.9383141734 0.7801148545 1.8259248281 0.2582140799 0.3687617361 -0.7343240072 0.508043820383 +1403715370362142976.0000000000 -0.9382662210 0.7536081434 1.8251044656 0.2631112754 0.3640617783 -0.7349350034 0.50803741909 +1403715370412143104.0000000000 -0.9376658757 0.7275623344 1.8245632068 0.2680182132 0.3591719144 -0.7360092717 0.507397403741 +1403715370462142976.0000000000 -0.9369549008 0.7019383958 1.8239168707 0.2712483050 0.3552825886 -0.7372827220 0.506569666538 +1403715370512143104.0000000000 -0.9361957929 0.6762648492 1.8233965294 0.2734118098 0.3517421722 -0.7383487726 0.50632451715 +1403715370562142976.0000000000 -0.9357494488 0.6506021324 1.8226448418 0.2747529207 0.3491637096 -0.7394789661 0.505733521947 +1403715370612143104.0000000000 -0.9356446346 0.6247164426 1.8221605953 0.2751459583 0.3471965470 -0.7398003997 0.506403621619 +1403715370662142976.0000000000 -0.9360810407 0.5986631810 1.8214272948 0.2751720509 0.3455885690 -0.7409326032 0.505833728475 +1403715370712143104.0000000000 -0.9368197948 0.5722259056 1.8206864242 0.2744912633 0.3448365703 -0.7413594890 0.506091290464 +1403715370762142976.0000000000 -0.9376360471 0.5454823859 1.8199849022 0.2720917615 0.3454424760 -0.7410992390 0.507353414353 +1403715370812143104.0000000000 -0.9387886374 0.5187309909 1.8193729899 0.2690018009 0.3467146458 -0.7410528380 0.508200429723 +1403715370862142976.0000000000 -0.9401441757 0.4920709945 1.8187668140 0.2657486103 0.3480099647 -0.7414705963 0.508417245338 +1403715370912143104.0000000000 -0.9414093178 0.4656660066 1.8181354782 0.2636593601 0.3485933316 -0.7421033350 0.508182123989 +1403715370962142976.0000000000 -0.9425355893 0.4395841237 1.8168348034 0.2611534136 0.3493597874 -0.7440163705 0.506148470305 +1403715371012143104.0000000000 -0.9433047698 0.4135652706 1.8150409880 0.2581777566 0.3505708611 -0.7470010032 0.502427923695 +1403715371062142976.0000000000 -0.9438932324 0.3875577680 1.8127284199 0.2542807377 0.3523641337 -0.7511554967 0.496936860639 +1403715371112143104.0000000000 -0.9434279588 0.3614146835 1.8102652355 0.2501062439 0.3544374330 -0.7548377256 0.491976605934 +1403715371162142976.0000000000 -0.9416456755 0.3350889353 1.8078299943 0.2469455413 0.3560275219 -0.7580151753 0.487519535242 +1403715371212143104.0000000000 -0.9381627776 0.3080805241 1.8050636234 0.2438669645 0.3577251293 -0.7603518684 0.484176281704 +1403715371262142976.0000000000 -0.9327350431 0.2801787441 1.8022568740 0.2419189057 0.3586593893 -0.7616317593 0.482447664197 +1403715371312143104.0000000000 -0.9252790427 0.2513388518 1.7992676815 0.2408783675 0.3593500735 -0.7618538530 0.482103560944 +1403715371362142976.0000000000 -0.9160639943 0.2218729399 1.7962033606 0.2406433719 0.3595464290 -0.7618704195 0.482048334588 +1403715371412143104.0000000000 -0.9051582356 0.1917809893 1.7931325692 0.2412086382 0.3594314910 -0.7609606010 0.483287036771 +1403715371462142976.0000000000 -0.8924258925 0.1610368898 1.7907878417 0.2449884133 0.3570443295 -0.7589634288 0.486286477126 +1403715371512143104.0000000000 -0.8779815300 0.1297092122 1.7890127944 0.2511844186 0.3527483511 -0.7566259825 0.489889897057 +1403715371562142976.0000000000 -0.8625650451 0.0980499238 1.7873183835 0.2582271169 0.3482598621 -0.7543761395 0.492900055576 +1403715371612143104.0000000000 -0.8464655436 0.0656996074 1.7852821849 0.2642793321 0.3444165933 -0.7522860887 0.495579746979 +1403715371662142976.0000000000 -0.8301846480 0.0327614536 1.7831982391 0.2702874131 0.3404623316 -0.7507629334 0.497378259421 +1403715371712143104.0000000000 -0.8141004018 -0.0007555177 1.7807750458 0.2759192181 0.3369335688 -0.7501709039 0.497582124141 +1403715371762142976.0000000000 -0.7984505754 -0.0351616216 1.7780077752 0.2796114649 0.3350346997 -0.7497196114 0.497483349438 +1403715371812143104.0000000000 -0.7833491839 -0.0707514879 1.7748556465 0.2810616609 0.3345758815 -0.7490598061 0.497968602673 +1403715371862142976.0000000000 -0.7693278095 -0.1067781038 1.7702995762 0.2782370124 0.3377464954 -0.7489450597 0.49758694451 +1403715371912143104.0000000000 -0.7561782165 -0.1434860418 1.7655331448 0.2739628127 0.3417920240 -0.7482724630 0.498207698296 +1403715371962142976.0000000000 -0.7432358962 -0.1808059627 1.7606830935 0.2694597832 0.3459634744 -0.7473771886 0.499127275919 +1403715372012143104.0000000000 -0.7302542266 -0.2182870720 1.7561717904 0.2664774260 0.3489423778 -0.7471263209 0.499030318698 +1403715372062142976.0000000000 -0.7168778960 -0.2561563760 1.7523877687 0.2652978280 0.3504390288 -0.7457594987 0.500651894718 +1403715372112143104.0000000000 -0.7032507591 -0.2940099504 1.7491584475 0.2654532833 0.3508715264 -0.7447982237 0.501696454356 +1403715372162142976.0000000000 -0.6893042474 -0.3319031694 1.7465129579 0.2663480352 0.3513145298 -0.7437983206 0.502395146832 +1403715372212143104.0000000000 -0.6751726539 -0.3695516880 1.7451660952 0.2694104639 0.3518319643 -0.7425764193 0.502207658533 +1403715372262142976.0000000000 -0.6606812601 -0.4072440206 1.7445775588 0.2709186885 0.3545262190 -0.7408072729 0.50211433826 +1403715372312143104.0000000000 -0.6461757603 -0.4447041742 1.7448892353 0.2734430597 0.3580787923 -0.7386134390 0.501456537849 +1403715372362142976.0000000000 -0.6317095524 -0.4818581959 1.7461450599 0.2764029942 0.3627405319 -0.7360544153 0.50024452926 +1403715372412143104.0000000000 -0.6171733797 -0.5188140091 1.7486791886 0.2796165753 0.3686936453 -0.7320896405 0.499924319225 +1403715372462142976.0000000000 -0.6026562997 -0.5556506961 1.7523087623 0.2830426396 0.3736642295 -0.7289975752 0.498823057982 +1403715372512143104.0000000000 -0.5881979582 -0.5922511755 1.7568420392 0.2855147804 0.3787092462 -0.7260458106 0.497913745467 +1403715372562142976.0000000000 -0.5736358751 -0.6288201979 1.7628269976 0.2882725631 0.3829170414 -0.7227890842 0.497844763494 +1403715372612143104.0000000000 -0.5590850466 -0.6651680866 1.7693718431 0.2908250323 0.3864031078 -0.7202790494 0.497304262775 +1403715372662142976.0000000000 -0.5444914486 -0.7014057630 1.7758915595 0.2926017715 0.3896967702 -0.7180603781 0.496900315973 +1403715372712143104.0000000000 -0.5300267636 -0.7372562190 1.7823349271 0.2947473039 0.3918644681 -0.7166420145 0.495974282128 +1403715372762142976.0000000000 -0.5157718628 -0.7726742053 1.7878357368 0.2954145580 0.3942608347 -0.7154615726 0.495382045707 +1403715372812143104.0000000000 -0.5016061410 -0.8077186716 1.7931635460 0.2968938662 0.3954889867 -0.7144620242 0.494961119315 +1403715372862142976.0000000000 -0.4875026867 -0.8425185886 1.7980613360 0.2980796448 0.3963814036 -0.7141840336 0.493934686421 +1403715372912143104.0000000000 -0.4732471821 -0.8770564871 1.8027457273 0.2999959286 0.3962890245 -0.7142957634 0.492685512483 +1403715372962142976.0000000000 -0.4590169019 -0.9113795676 1.8073104324 0.3022317731 0.3954879786 -0.7145995751 0.491520763916 +1403715373012143104.0000000000 -0.4449146071 -0.9455206043 1.8116487259 0.3038734178 0.3948567145 -0.7152521769 0.490064734842 +1403715373062142976.0000000000 -0.4308736678 -0.9796074351 1.8155740301 0.3054188780 0.3939925143 -0.7157371288 0.489090554086 +1403715373112143104.0000000000 -0.4170866398 -1.0137349871 1.8189845895 0.3065729844 0.3929905171 -0.7162673572 0.488397923555 +1403715373162142976.0000000000 -0.4036743318 -1.0479792555 1.8220608014 0.3072183764 0.3922873609 -0.7167238428 0.487887721602 +1403715373212143104.0000000000 -0.3905594597 -1.0825301166 1.8248110447 0.3074066760 0.3915807757 -0.7170880830 0.487801509688 +1403715373262142976.0000000000 -0.3780223898 -1.1171189850 1.8273316593 0.3062960819 0.3916094546 -0.7174140947 0.487997707039 +1403715373312143104.0000000000 -0.3657174927 -1.1519791140 1.8300142545 0.3035981799 0.3926570194 -0.7166183495 0.490006889122 +1403715373362142976.0000000000 -0.3536070543 -1.1866064368 1.8327315752 0.3021028321 0.3926686507 -0.7165637336 0.491000636677 +1403715373412143104.0000000000 -0.3416548320 -1.2211281067 1.8353897418 0.3009556904 0.3926037525 -0.7165820907 0.491729674974 +1403715373462142976.0000000000 -0.3297287653 -1.2553415516 1.8377718765 0.2996717477 0.3928456391 -0.7162612289 0.492786971671 +1403715373512143104.0000000000 -0.3179673471 -1.2889186927 1.8395301167 0.2989903519 0.3939342469 -0.7156976655 0.493150514761 +1403715373562142976.0000000000 -0.3061837441 -1.3221785711 1.8410114932 0.2978335637 0.3969501099 -0.7136517605 0.494395533225 +1403715373612143104.0000000000 -0.2944548894 -1.3547718914 1.8417936414 0.2954764247 0.4025980285 -0.7107757511 0.495385043623 +1403715373662142976.0000000000 -0.2827433708 -1.3863200827 1.8425878400 0.2948816385 0.4089061775 -0.7069812235 0.496002123873 +1403715373712143104.0000000000 -0.2710979470 -1.4164521392 1.8431754822 0.2950086772 0.4166518542 -0.7019145146 0.496676078512 +1403715373762142976.0000000000 -0.2591322870 -1.4449233996 1.8440290348 0.2972451287 0.4243364636 -0.6970023507 0.49575359015 +1403715373812143104.0000000000 -0.2465239897 -1.4716562736 1.8446486898 0.3019858407 0.4316827469 -0.6920542653 0.49347284823 +1403715373862142976.0000000000 -0.2333362466 -1.4967887751 1.8454243398 0.3083714479 0.4392267455 -0.6873040214 0.489489630488 +1403715373912143104.0000000000 -0.2198082185 -1.5205137158 1.8466070075 0.3157614512 0.4469727095 -0.6822296081 0.484843134135 +1403715373962142976.0000000000 -0.2061846932 -1.5429640076 1.8481540375 0.3240612410 0.4547337351 -0.6767758851 0.479766551201 +1403715374012143104.0000000000 -0.1928431099 -1.5640814618 1.8491708708 0.3317313832 0.4634813008 -0.6706745649 0.474694640043 +1403715374062142976.0000000000 -0.1796382521 -1.5837310939 1.8496065983 0.3398931653 0.4722391528 -0.6642876083 0.469238523771 +1403715374112143104.0000000000 -0.1662018416 -1.6021798424 1.8499323015 0.3482328197 0.4810649084 -0.6574502986 0.463755929363 +1403715374162142976.0000000000 -0.1529614400 -1.6196702926 1.8500441183 0.3549060193 0.4908705051 -0.6500105549 0.458883583548 +1403715374212143104.0000000000 -0.1396939901 -1.6361229081 1.8503760787 0.3623500048 0.5001416832 -0.6428764776 0.453067992005 +1403715374262142976.0000000000 -0.1269193375 -1.6518506142 1.8507129416 0.3695659541 0.5093035519 -0.6354278727 0.447506777732 +1403715374312143104.0000000000 -0.1142738184 -1.6667554691 1.8509244674 0.3763769423 0.5183631429 -0.6288442376 0.440675588439 +1403715374362142976.0000000000 -0.1020935205 -1.6815219262 1.8512965856 0.3815953531 0.5275148975 -0.6220104540 0.434989671748 +1403715374412143104.0000000000 -0.0900253197 -1.6959129832 1.8518135736 0.3854399100 0.5359604510 -0.6163572157 0.429285747922 +1403715374462142976.0000000000 -0.0776034839 -1.7098472688 1.8525453264 0.3882335026 0.5433172797 -0.6117411576 0.42409177913 +1403715374512143104.0000000000 -0.0648971839 -1.7233906686 1.8528444406 0.3886511438 0.5504299859 -0.6090162438 0.418421239728 +1403715374562142976.0000000000 -0.0516609679 -1.7365528404 1.8534472409 0.3890459978 0.5559228182 -0.6068031158 0.413984311861 +1403715374612143104.0000000000 -0.0381687314 -1.7493201845 1.8540172703 0.3883262031 0.5608528641 -0.6053270573 0.410153603584 +1403715374662142976.0000000000 -0.0236067374 -1.7613228883 1.8549342103 0.3882862661 0.5638609473 -0.6046996078 0.406980333696 +1403715374712143104.0000000000 -0.0078229451 -1.7727415612 1.8558911526 0.3878093704 0.5663120064 -0.6039828560 0.405091734498 +1403715374762142976.0000000000 0.0090312522 -1.7836776399 1.8569905454 0.3870344284 0.5679504710 -0.6035389443 0.404199649211 +1403715374812143104.0000000000 0.0271987763 -1.7939279207 1.8582180950 0.3862759159 0.5689251268 -0.6031770130 0.404094800577 +1403715374862142976.0000000000 0.0468418031 -1.8034899225 1.8594132329 0.3857810483 0.5690209397 -0.6033450721 0.404181737498 +1403715374912143104.0000000000 0.0678095709 -1.8123478269 1.8605954846 0.3849122205 0.5689962990 -0.6027664807 0.405904377926 +1403715374962142976.0000000000 0.0898917998 -1.8201871908 1.8622263213 0.3862115328 0.5672042643 -0.6012960138 0.409344693734 +1403715375012143104.0000000000 0.1129116604 -1.8270222893 1.8634938550 0.3873790774 0.5651059147 -0.6003680553 0.412493580339 +1403715375062142976.0000000000 0.1369150729 -1.8329602054 1.8646241054 0.3876230665 0.5634217857 -0.5990737311 0.416431164106 +1403715375112143104.0000000000 0.1613941170 -1.8375780002 1.8652783094 0.3877040651 0.5616225536 -0.5990078396 0.418873815432 +1403715375162142976.0000000000 0.1863330376 -1.8410783319 1.8657039999 0.3880559625 0.5593802400 -0.5993544596 0.421046967477 +1403715375212143104.0000000000 0.2116103601 -1.8433328538 1.8658714960 0.3882587235 0.5569989531 -0.6001507403 0.422878728201 +1403715375262142976.0000000000 0.2368329373 -1.8441976471 1.8653943905 0.3882470191 0.5548101747 -0.6019552652 0.423201820645 +1403715375312143104.0000000000 0.2620405464 -1.8440734006 1.8644291567 0.3875208654 0.5528985756 -0.6035830138 0.424049866712 +1403715375362142976.0000000000 0.2870878151 -1.8429617522 1.8634703998 0.3887721954 0.5496384256 -0.6060676958 0.423598547465 +1403715375412143104.0000000000 0.3125176083 -1.8414286003 1.8615227348 0.3860992385 0.5489963482 -0.6078436421 0.424330642836 +1403715375462142976.0000000000 0.3383761620 -1.8387624865 1.8601520767 0.3865986916 0.5463282914 -0.6099794316 0.424254572948 +1403715375512143104.0000000000 0.3642372527 -1.8354780292 1.8582179936 0.3859282899 0.5447049615 -0.6119597878 0.424100316084 +1403715375562142976.0000000000 0.3904802252 -1.8314261853 1.8560500436 0.3861451085 0.5423409912 -0.6145558811 0.423177590893 +1403715375612143104.0000000000 0.4165264268 -1.8269085332 1.8532930813 0.3860208698 0.5403510821 -0.6164892369 0.42302436912 +1403715375662142976.0000000000 0.4426287231 -1.8221917674 1.8500923644 0.3860840190 0.5383570228 -0.6178581459 0.423511697292 +1403715375712143104.0000000000 0.4689777773 -1.8172145155 1.8466810982 0.3857875947 0.5367920567 -0.6182645490 0.425171926569 +1403715375762142976.0000000000 0.4957009373 -1.8116715096 1.8432199430 0.3860540712 0.5352864819 -0.6187040443 0.426187683983 +1403715375812143104.0000000000 0.5224075387 -1.8058891264 1.8397290121 0.3859265633 0.5340790657 -0.6189720590 0.427426987323 +1403715375862142976.0000000000 0.5492559598 -1.7998318322 1.8364605820 0.3852695211 0.5335187292 -0.6182253352 0.429793667393 +1403715375912143104.0000000000 0.5760854312 -1.7933602497 1.8328174566 0.3836600744 0.5339839894 -0.6173215433 0.431949254587 +1403715375962142976.0000000000 0.6026670448 -1.7862080463 1.8298351156 0.3837003151 0.5334404688 -0.6163134765 0.434019623022 +1403715376012143104.0000000000 0.6288827735 -1.7785625570 1.8267545752 0.3832392068 0.5336632452 -0.6151623881 0.435782614906 +1403715376062142976.0000000000 0.6547920154 -1.7700247423 1.8234624809 0.3844335422 0.5327736490 -0.6152710108 0.435665782176 +1403715376112143104.0000000000 0.6801770711 -1.7608113045 1.8197009468 0.3864130492 0.5317993806 -0.6156412726 0.434580484744 +1403715376162142976.0000000000 0.7050382572 -1.7511914438 1.8156456529 0.3892231086 0.5304750891 -0.6161532207 0.432962770074 +1403715376212143104.0000000000 0.7296936336 -1.7413187192 1.8114003295 0.3920675927 0.5288333499 -0.6168908092 0.431351388491 +1403715376262142976.0000000000 0.7537583722 -1.7311449894 1.8067020806 0.3946358932 0.5275798812 -0.6173983510 0.429815375418 +1403715376312143104.0000000000 0.7775936433 -1.7211100398 1.8024271451 0.3983750306 0.5253339459 -0.6146453855 0.433050378534 +1403715376362142976.0000000000 0.8008252923 -1.7111939727 1.7983206128 0.4034347154 0.5218894170 -0.6110830979 0.43754921355 +1403715376412143104.0000000000 0.8228108927 -1.7013543925 1.7935549480 0.4054411149 0.5208245482 -0.6069214908 0.442725192856 +1403715376462142976.0000000000 0.8428057017 -1.6914242122 1.7875967457 0.4031930294 0.5229452394 -0.6049807302 0.444929178362 +1403715376512143104.0000000000 0.8611123062 -1.6811037378 1.7808871610 0.3994795865 0.5265057198 -0.6046431540 0.444538461024 +1403715376562142976.0000000000 0.8781721662 -1.6701977339 1.7740530224 0.3958058961 0.5303562802 -0.6050826294 0.442645366266 +1403715376612143104.0000000000 0.8941043849 -1.6585930636 1.7672032030 0.3929406985 0.5335635932 -0.6053850331 0.4409268206 +1403715376662142976.0000000000 0.9091860975 -1.6463300354 1.7603141701 0.3905401857 0.5366286856 -0.6061810728 0.438237976595 +1403715376712143104.0000000000 0.9237370152 -1.6334222918 1.7541907602 0.3902150244 0.5380849603 -0.6060731510 0.436889168768 +1403715376762142976.0000000000 0.9376914596 -1.6198910580 1.7482189016 0.3898004864 0.5396131068 -0.6048661756 0.437047120328 +1403715376812143104.0000000000 0.9511123910 -1.6057172126 1.7426805064 0.3910140400 0.5399549067 -0.6030914583 0.437992479576 +1403715376862142976.0000000000 0.9638592612 -1.5908396912 1.7379639546 0.3940108074 0.5391741934 -0.6010154882 0.439120775873 +1403715376912143104.0000000000 0.9757264024 -1.5752799118 1.7340532028 0.3986426374 0.5372253104 -0.5975278916 0.442078536347 +1403715376962142976.0000000000 0.9865029445 -1.5590117692 1.7305474691 0.4031309545 0.5353238844 -0.5927180034 0.44676519649 +1403715377012143104.0000000000 0.9955014389 -1.5417083978 1.7266984905 0.4081238097 0.5333771465 -0.5903668931 0.447672544477 +1403715377062142976.0000000000 1.0026091971 -1.5237295812 1.7217484896 0.4089221962 0.5347533292 -0.5889742340 0.447136294697 +1403715377112143104.0000000000 1.0079103049 -1.5050670420 1.7159357801 0.4064842915 0.5383457055 -0.5897800700 0.443975101908 +1403715377162142976.0000000000 1.0116532899 -1.4859661519 1.7102566820 0.4034207222 0.5424008998 -0.5899780011 0.441564200269 +1403715377212143104.0000000000 1.0143308253 -1.4659475306 1.7047462275 0.4007698641 0.5459495840 -0.5903313352 0.439125816214 +1403715377262142976.0000000000 1.0161526534 -1.4449681035 1.6996742729 0.3997360368 0.5484438985 -0.5904486724 0.436796012353 +1403715377312143104.0000000000 1.0170152641 -1.4229534189 1.6953402760 0.4003014347 0.5495803817 -0.5907398112 0.434449813932 +1403715377362142976.0000000000 1.0170000321 -1.4002894707 1.6913615554 0.4013960625 0.5500248099 -0.5902739079 0.433509657537 +1403715377412143104.0000000000 1.0162318819 -1.3768589590 1.6877401176 0.4044371468 0.5492368003 -0.5894505039 0.432802073684 +1403715377462142976.0000000000 1.0145625142 -1.3530845305 1.6839108460 0.4061065178 0.5490024782 -0.5882334681 0.43319183062 +1403715377512143104.0000000000 1.0117932758 -1.3287063751 1.6799675133 0.4076032772 0.5489642323 -0.5874426382 0.432907596227 +1403715377562142976.0000000000 1.0081111451 -1.3037071755 1.6759398956 0.4089269028 0.5488201025 -0.5873852458 0.431918807457 +1403715377612143104.0000000000 1.0033429761 -1.2783323198 1.6715784777 0.4089667304 0.5493297404 -0.5874527144 0.431140763558 +1403715377662142976.0000000000 0.9976243237 -1.2523043326 1.6670893234 0.4081011068 0.5505573214 -0.5881439199 0.429449475404 +1403715377712143104.0000000000 0.9911972726 -1.2259332842 1.6624762286 0.4071926421 0.5514341142 -0.5891464624 0.427809555428 +1403715377762142976.0000000000 0.9842215530 -1.1990866079 1.6580940178 0.4068514325 0.5518419820 -0.5893720573 0.427297223032 +1403715377812143104.0000000000 0.9764275214 -1.1716354074 1.6541079996 0.4065140907 0.5522030088 -0.5898654524 0.426470255856 +1403715377862142976.0000000000 0.9678816674 -1.1437074747 1.6501678739 0.4062433678 0.5524503659 -0.5903775664 0.425698541679 +1403715377912143104.0000000000 0.9587320150 -1.1154133450 1.6457313814 0.4062205065 0.5525802225 -0.5905058734 0.42537373126 +1403715377962142976.0000000000 0.9491093546 -1.0866906361 1.6410915340 0.4067672408 0.5523798022 -0.5905668395 0.425026792142 +1403715378012143104.0000000000 0.9389553133 -1.0574183256 1.6366930297 0.4081974587 0.5514491739 -0.5915041053 0.423558185716 +1403715378062142976.0000000000 0.9283849048 -1.0276854002 1.6325028236 0.4108508584 0.5499195644 -0.5923559924 0.421787177503 +1403715378112143104.0000000000 0.9170467143 -0.9978475380 1.6279449450 0.4131479710 0.5486788280 -0.5932265863 0.419931559916 +1403715378162142976.0000000000 0.9051005545 -0.9679653706 1.6233683905 0.4158952438 0.5472608021 -0.5939374134 0.418061131528 +1403715378212143104.0000000000 0.8927206392 -0.9385480864 1.6189482978 0.4188410623 0.5453980262 -0.5948566025 0.416243654561 +1403715378262142976.0000000000 0.8796838500 -0.9096091251 1.6141185177 0.4199685282 0.5450559808 -0.5967179429 0.41287783872 +1403715378312143104.0000000000 0.8662726973 -0.8812743583 1.6091610010 0.4211436503 0.5445608924 -0.5990478103 0.408941537535 +1403715378362142976.0000000000 0.8524851115 -0.8539911010 1.6038717677 0.4211510709 0.5448145893 -0.6016766652 0.404714750496 +1403715378412143104.0000000000 0.8382619396 -0.8278765992 1.5985261227 0.4194686930 0.5462784061 -0.6040015548 0.401008778427 +1403715378462142976.0000000000 0.8241344084 -0.8031910987 1.5933864944 0.4168970315 0.5480271720 -0.6050492867 0.399722959776 +1403715378512143104.0000000000 0.8101162081 -0.7796541642 1.5885690848 0.4133882220 0.5506473865 -0.6051158708 0.399665380765 +1403715378562142976.0000000000 0.7963261582 -0.7572518862 1.5844921538 0.4097584032 0.5532218464 -0.6042400201 0.40117033508 +1403715378612143104.0000000000 0.7828831088 -0.7353787154 1.5814771199 0.4076291314 0.5546725131 -0.6040534666 0.401617111108 +1403715378662142976.0000000000 0.7697210434 -0.7137755117 1.5785470578 0.4050153981 0.5565239076 -0.6039932326 0.401790794499 +1403715378712143104.0000000000 0.7574784170 -0.6925380347 1.5762132126 0.4027439147 0.5582172434 -0.6041506305 0.401488311201 +1403715378762142976.0000000000 0.7456542723 -0.6718413425 1.5745023321 0.4007014444 0.5596568109 -0.6049063545 0.400388447312 +1403715378812143104.0000000000 0.7346327320 -0.6515240949 1.5731986399 0.3985603155 0.5612252165 -0.6062278065 0.398326220467 +1403715378862142976.0000000000 0.7245849108 -0.6315263435 1.5727084991 0.3972105278 0.5622101810 -0.6074938457 0.396351783741 +1403715378912143104.0000000000 0.7160874299 -0.6119055662 1.5728605332 0.3963760808 0.5629081288 -0.6084119501 0.39478518229 +1403715378962142976.0000000000 0.7088939779 -0.5926252381 1.5738584553 0.3959825280 0.5630844163 -0.6091102077 0.393850901229 +1403715379012143104.0000000000 0.7030912045 -0.5736636945 1.5757684047 0.3961432196 0.5629149370 -0.6093496041 0.393561155696 +1403715379062142976.0000000000 0.6986633880 -0.5551797858 1.5780727291 0.3954931042 0.5631143666 -0.6088041262 0.394772023462 +1403715379112143104.0000000000 0.6953713965 -0.5370124921 1.5809828226 0.3954659068 0.5632855687 -0.6073806305 0.396742806265 +1403715379162142976.0000000000 0.6933565500 -0.5192951449 1.5842802899 0.3947228828 0.5635501684 -0.6044893088 0.401494369987 +1403715379212143104.0000000000 0.6920941900 -0.5015602736 1.5875331042 0.3933137183 0.5643148461 -0.6022376481 0.405170197148 +1403715379262142976.0000000000 0.6911773698 -0.4835367965 1.5908270789 0.3918277872 0.5651896517 -0.6000958482 0.408554299489 +1403715379312143104.0000000000 0.6909105258 -0.4653825748 1.5943501365 0.3902932982 0.5659439090 -0.5985292526 0.41126799905 +1403715379362142976.0000000000 0.6913422327 -0.4465591863 1.5979878147 0.3891621767 0.5666970841 -0.5967446731 0.413887678268 +1403715379412143104.0000000000 0.6922551158 -0.4270005881 1.6015897782 0.3876710764 0.5674613415 -0.5957595436 0.415655300312 +1403715379462142976.0000000000 0.6936219822 -0.4065588040 1.6049064390 0.3858525033 0.5686171371 -0.5953777895 0.416314406288 +1403715379512143104.0000000000 0.6955691149 -0.3852822186 1.6082393238 0.3841578351 0.5696192089 -0.5950735445 0.41694626894 +1403715379562142976.0000000000 0.6981814022 -0.3629112307 1.6115917260 0.3833325391 0.5700853501 -0.5957791783 0.416060126405 +1403715379612143104.0000000000 0.7017343991 -0.3396710797 1.6151696329 0.3819765332 0.5710846992 -0.5958014266 0.41590486231 +1403715379662142976.0000000000 0.7057807306 -0.3154713351 1.6186144224 0.3800782683 0.5722178682 -0.5967493377 0.414725751794 +1403715379712143104.0000000000 0.7108962285 -0.2902677852 1.6224737102 0.3796501612 0.5725875437 -0.5959945599 0.415691886501 +1403715379762142976.0000000000 0.7168612671 -0.2639572236 1.6266413162 0.3795593275 0.5725557176 -0.5956941387 0.416248916344 +1403715379812143104.0000000000 0.7237694623 -0.2365670952 1.6315077421 0.3808441294 0.5717491385 -0.5942479242 0.418246430179 +1403715379862142976.0000000000 0.7315424040 -0.2082041509 1.6363928229 0.3820752653 0.5708892653 -0.5921183389 0.421307264499 +1403715379912143104.0000000000 0.7399603731 -0.1786658589 1.6414066718 0.3841226459 0.5695058197 -0.5898734034 0.424455277064 +1403715379962142976.0000000000 0.7488040559 -0.1480210725 1.6461299436 0.3855051700 0.5682820373 -0.5883722246 0.426918511422 +1403715380012143104.0000000000 0.7578065810 -0.1160391979 1.6504228307 0.3856205852 0.5678342052 -0.5870119971 0.429276128888 +1403715380062142976.0000000000 0.7669886941 -0.0826110901 1.6548453071 0.3879241247 0.5658125937 -0.5865306757 0.430526130087 +1403715380112143104.0000000000 0.7757893743 -0.0477531446 1.6589374500 0.3916977586 0.5627527435 -0.5877743149 0.429422368164 +1403715380162142976.0000000000 0.7840138062 -0.0117111821 1.6629462511 0.3966425429 0.5589889030 -0.5897034140 0.427148666133 +1403715380212143104.0000000000 0.7918281009 0.0246016517 1.6665468774 0.3996107397 0.5567248408 -0.5907862406 0.425840728795 +1403715380262142976.0000000000 0.7990761741 0.0613901626 1.6698928143 0.4022414593 0.5547452786 -0.5926219201 0.423389589138 +1403715380312143104.0000000000 0.8057962261 0.0981708254 1.6728411766 0.4035501188 0.5535168309 -0.5944050853 0.42124697515 +1403715380362142976.0000000000 0.8122608158 0.1346268120 1.6753853057 0.4034408243 0.5527242634 -0.5963014921 0.419709328546 +1403715380412143104.0000000000 0.8187803474 0.1707513696 1.6777789977 0.4020404418 0.5530915114 -0.5975937339 0.418730214284 +1403715380462142976.0000000000 0.8255445282 0.2065247097 1.6803142713 0.4007251922 0.5536982361 -0.5972958066 0.419613277995 +1403715380512143104.0000000000 0.8318998405 0.2419741625 1.6827736659 0.3999277626 0.5542662879 -0.5965454860 0.420690087802 +1403715380562142976.0000000000 0.8376291073 0.2773610491 1.6851296250 0.3989204648 0.5551344533 -0.5957175447 0.421673817633 +1403715380612143104.0000000000 0.8427918028 0.3129875361 1.6879047713 0.3983530468 0.5560571339 -0.5950597409 0.42192323795 +1403715380662142976.0000000000 0.8478043192 0.3488908157 1.6911267672 0.3983211330 0.5564632498 -0.5946196779 0.422038345764 +1403715380712143104.0000000000 0.8525874243 0.3850411526 1.6945744786 0.3988743567 0.5564981914 -0.5940706395 0.42224292277 +1403715380762142976.0000000000 0.8573076394 0.4214710344 1.6982323997 0.3991069273 0.5566303348 -0.5933130053 0.422913713036 +1403715380812143104.0000000000 0.8616997548 0.4581849537 1.7023746415 0.3997428909 0.5565535273 -0.5926753801 0.42330802761 +1403715380862142976.0000000000 0.8658131481 0.4949138057 1.7061364994 0.4002025649 0.5564892169 -0.5919036709 0.42403738389 +1403715380912143104.0000000000 0.8693607375 0.5315362812 1.7090432682 0.3999500383 0.5567988590 -0.5913136032 0.424691911963 +1403715380962142976.0000000000 0.8724451605 0.5685393676 1.7119425570 0.3999786868 0.5569054838 -0.5906370529 0.425465867065 +1403715381012143104.0000000000 0.8749981704 0.6058314394 1.7146486206 0.3992558098 0.5574357069 -0.5900594279 0.42625122007 +1403715381062142976.0000000000 0.8771409564 0.6432645059 1.7174784781 0.3993624549 0.5567520934 -0.5899356064 0.427215070412 +1403715381112143104.0000000000 0.8786826669 0.6811562872 1.7200083105 0.4000053626 0.5557173879 -0.5911132561 0.426332045726 +1403715381162142976.0000000000 0.8799925659 0.7190963210 1.7229011755 0.4015035328 0.5537395751 -0.5924421252 0.425652116699 +1403715381212143104.0000000000 0.8808069750 0.7571210771 1.7254537126 0.4028316323 0.5518506127 -0.5935729151 0.425274936745 +1403715381262142976.0000000000 0.8811407422 0.7949727586 1.7273727462 0.4040929085 0.5497849147 -0.5947277273 0.425140446493 +1403715381312143104.0000000000 0.8808109486 0.8325299086 1.7288968866 0.4048768370 0.5481424081 -0.5955356689 0.425384431319 +1403715381362142976.0000000000 0.8801194871 0.8695352772 1.7300089618 0.4056627689 0.5461278040 -0.5973509869 0.424680983875 +1403715381412143104.0000000000 0.8790743274 0.9060000637 1.7311318436 0.4068267710 0.5436502164 -0.5987331303 0.424800022803 +1403715381462142976.0000000000 0.8776433449 0.9417424854 1.7318806457 0.4070075985 0.5417810655 -0.5997830385 0.425533075687 +1403715381512143104.0000000000 0.8755656866 0.9767538089 1.7325318967 0.4082128619 0.5391835092 -0.5997848566 0.427669882721 +1403715381562142976.0000000000 0.8722762894 1.0110890604 1.7318828445 0.4062088570 0.5394160647 -0.5990000717 0.430376100309 +1403715381612143104.0000000000 0.8681582782 1.0449915543 1.7307380659 0.4041868905 0.5397404938 -0.5989364311 0.431958688252 +1403715381662142976.0000000000 0.8630959612 1.0785816440 1.7285580210 0.4006062867 0.5414020381 -0.5992186434 0.432822658433 +1403715381712143104.0000000000 0.8573708729 1.1121136145 1.7260153210 0.3958687483 0.5441243304 -0.6002641919 0.432318802617 +1403715381762142976.0000000000 0.8514204774 1.1457156085 1.7238515667 0.3915985846 0.5469412997 -0.6012096009 0.431338357862 +1403715381812143104.0000000000 0.8451288615 1.1793727482 1.7219318786 0.3876019170 0.5497345894 -0.6023100455 0.429859563401 +1403715381862142976.0000000000 0.8388652096 1.2132874097 1.7195964561 0.3831232561 0.5524427740 -0.6041736782 0.427782326197 +1403715381912143104.0000000000 0.8332871858 1.2472437801 1.7171823764 0.3783587813 0.5539422803 -0.6066030919 0.426644197814 +1403715381962142976.0000000000 0.8282979162 1.2813991752 1.7148324063 0.3731048720 0.5539026509 -0.6096144300 0.427030273537 +1403715382012143104.0000000000 0.8241572425 1.3160163522 1.7130564697 0.3693991012 0.5512536578 -0.6138260790 0.427646177952 +1403715382062142976.0000000000 0.8213085714 1.3508079794 1.7113812644 0.3651032817 0.5475381060 -0.6187522834 0.429007258674 +1403715382112143104.0000000000 0.8195697345 1.3862149836 1.7099336552 0.3620605423 0.5419316386 -0.6243964805 0.430524445172 +1403715382162142976.0000000000 0.8185655725 1.4218988421 1.7088215545 0.3592044712 0.5352305707 -0.6304549545 0.432466107808 +1403715382212143104.0000000000 0.8187610895 1.4576557534 1.7085089258 0.3564984393 0.5274891038 -0.6369455198 0.434700486399 +1403715382262142976.0000000000 0.8198661180 1.4933831971 1.7082455029 0.3527025844 0.5198289430 -0.6430388498 0.43804085961 +1403715382312143104.0000000000 0.8220150900 1.5289834209 1.7081029761 0.3490832330 0.5114519671 -0.6494708437 0.441299677056 +1403715382362142976.0000000000 0.8251326909 1.5644032497 1.7077534858 0.3446021763 0.5032198561 -0.6555230944 0.445318525613 +1403715382412143104.0000000000 0.8292483942 1.5994853392 1.7071617617 0.3401871589 0.4943084164 -0.6613347100 0.450075868809 +1403715382462142976.0000000000 0.8341221597 1.6346004288 1.7063282847 0.3353043406 0.4865807014 -0.6673828513 0.453222186114 +1403715382512143104.0000000000 0.8400132848 1.6699313184 1.7055558425 0.3314913687 0.4790692725 -0.6726309250 0.456260609098 +1403715382562142976.0000000000 0.8468257704 1.7053865272 1.7048045422 0.3278231706 0.4723577178 -0.6776011565 0.458548610208 +1403715382612143104.0000000000 0.8543408886 1.7404447056 1.7039779624 0.3249466372 0.4654803933 -0.6825111984 0.460343513552 +1403715382662142976.0000000000 0.8626864668 1.7750010876 1.7025289232 0.3205062102 0.4593181846 -0.6872153454 0.462642025219 +1403715382712143104.0000000000 0.8719077356 1.8091894068 1.7009999472 0.3171326588 0.4522406193 -0.6920818904 0.464680488017 +1403715382762142976.0000000000 0.8821071461 1.8427744076 1.6988398843 0.3114655223 0.4466127085 -0.6967786587 0.466932348182 +1403715382812143104.0000000000 0.8932729265 1.8758183004 1.6969067385 0.3067439703 0.4403152612 -0.7005686474 0.470355373966 +1403715382862142976.0000000000 0.9051267552 1.9084728006 1.6947805925 0.3019587388 0.4338092947 -0.7050041462 0.47286316173 +1403715382912143104.0000000000 0.9179151031 1.9406996600 1.6926156526 0.2970718579 0.4275078597 -0.7089853363 0.475736412326 +1403715382962142976.0000000000 0.9318071892 1.9725240248 1.6904146376 0.2927589929 0.4209261095 -0.7136021994 0.477373316543 +1403715383012143104.0000000000 0.9467350037 2.0037897029 1.6883743649 0.2890559002 0.4140204469 -0.7180090978 0.479058129675 +1403715383062142976.0000000000 0.9623770243 2.0347707200 1.6860044789 0.2863848038 0.4076380418 -0.7225506759 0.47930730422 +1403715383112143104.0000000000 0.9788536724 2.0653122557 1.6835620718 0.2850442947 0.4018768678 -0.7264787603 0.479033760756 +1403715383162142976.0000000000 0.9959646901 2.0952523923 1.6807981901 0.2837508394 0.3976569599 -0.7293797153 0.478915059523 +1403715383212143104.0000000000 1.0141761931 2.1245547524 1.6780403996 0.2831520765 0.3937736232 -0.7327245754 0.477369806129 +1403715383262142976.0000000000 1.0337365722 2.1527458584 1.6751382043 0.2816117912 0.3919411443 -0.7340774454 0.477710417039 +1403715383312143104.0000000000 1.0542451803 2.1800345992 1.6721512312 0.2818029560 0.3895365430 -0.7356941272 0.477077066035 +1403715383362142976.0000000000 1.0755656464 2.2062621354 1.6693091780 0.2829051969 0.3872287489 -0.7367304861 0.476704034423 +1403715383412143104.0000000000 1.0973065464 2.2311566015 1.6660306610 0.2834145439 0.3859848457 -0.7367332110 0.477405562411 +1403715383462142976.0000000000 1.1196440421 2.2546034996 1.6627272368 0.2845004973 0.3841927504 -0.7365976237 0.478413355104 +1403715383512143104.0000000000 1.1426484696 2.2765081053 1.6598545766 0.2857730187 0.3810328866 -0.7361204314 0.480910003694 +1403715383562142976.0000000000 1.1661324703 2.2969001711 1.6567250564 0.2854771723 0.3778969183 -0.7355882179 0.484362134136 +1403715383612143104.0000000000 1.1899711993 2.3157882653 1.6532662135 0.2842697346 0.3737789556 -0.7350251681 0.489099184761 +1403715383662142976.0000000000 1.2136206867 2.3334829518 1.6491605848 0.2816864423 0.3687543824 -0.7362236201 0.492592869282 +1403715383712143104.0000000000 1.2368183391 2.3498520189 1.6450182630 0.2780929799 0.3628749231 -0.7381865798 0.496051064024 +1403715383762142976.0000000000 1.2598265261 2.3649093846 1.6407121906 0.2738776455 0.3555366703 -0.7406855073 0.499969689697 +1403715383812143104.0000000000 1.2825851157 2.3789686020 1.6364042066 0.2690359487 0.3470928959 -0.7440465205 0.503528504936 +1403715383862142976.0000000000 1.3050465987 2.3921732750 1.6321832160 0.2628069705 0.3382746986 -0.7482041981 0.506648993395 +1403715383912143104.0000000000 1.3270684184 2.4044353821 1.6281797544 0.2563376563 0.3280375473 -0.7526748033 0.510061774643 +1403715383962142976.0000000000 1.3486068053 2.4158273250 1.6238180627 0.2478818592 0.3179137307 -0.7573012182 0.513790140581 +1403715384012143104.0000000000 1.3700312683 2.4265853720 1.6201131107 0.2404924550 0.3064257842 -0.7619680382 0.517369622803 +1403715384062142976.0000000000 1.3906430779 2.4367807087 1.6162303667 0.2321657550 0.2952131029 -0.7669968073 0.520253960736 +1403715384112143104.0000000000 1.4105066833 2.4466162972 1.6129791558 0.2240327188 0.2833310922 -0.7716792293 0.523492120482 +1403715384162142976.0000000000 1.4298341026 2.4558206103 1.6100538721 0.2162083983 0.2714818450 -0.7760395718 0.526606228032 +1403715384212143104.0000000000 1.4487843513 2.4643818576 1.6074386775 0.2085483881 0.2596679856 -0.7806848516 0.528782818941 +1403715384262142976.0000000000 1.4674043029 2.4722247625 1.6053624488 0.2016179491 0.2473895779 -0.7847651833 0.531311778948 +1403715384312143104.0000000000 1.4855769291 2.4795928729 1.6037563189 0.1951605023 0.2348253891 -0.7888728424 0.533337654357 +1403715384362142976.0000000000 1.5030534980 2.4863389671 1.6024171987 0.1883800853 0.2224272857 -0.7925148457 0.53568578981 +1403715384412143104.0000000000 1.5198556046 2.4925603377 1.6011597269 0.1812878657 0.2107134176 -0.7958598982 0.537904812982 +1403715384462142976.0000000000 1.5358895816 2.4984121942 1.5998447884 0.1745812858 0.1988751719 -0.7995557842 0.539148020972 +1403715384512143104.0000000000 1.5511016385 2.5037204000 1.5985119303 0.1681282028 0.1871355919 -0.8035598422 0.539448568141 +1403715384562142976.0000000000 1.5655446126 2.5079551335 1.5967941127 0.1602254456 0.1767031521 -0.8078146454 0.539016976875 +1403715384612143104.0000000000 1.5795384929 2.5110316957 1.5957636169 0.1533632416 0.1655962426 -0.8117854000 0.538574103515 +1403715384662142976.0000000000 1.5925434611 2.5133090292 1.5946705601 0.1457067774 0.1550755417 -0.8156865231 0.537937363828 +1403715384712143104.0000000000 1.6046549603 2.5142214186 1.5935772633 0.1369323318 0.1457142078 -0.8191320856 0.537623969386 +1403715384762142976.0000000000 1.6162299123 2.5139736730 1.5935166651 0.1302782800 0.1352191767 -0.8217880098 0.537966365926 +1403715384812143104.0000000000 1.6269785447 2.5125513332 1.5935168413 0.1230750689 0.1254113709 -0.8243982497 0.53804464627 +1403715384862142976.0000000000 1.6372799587 2.5099210909 1.5938381139 0.1165529300 0.1157701500 -0.8266441852 0.538211926561 +1403715384912143104.0000000000 1.6472810047 2.5058863985 1.5947524091 0.1110838213 0.1065287999 -0.8279579371 0.539256575195 +1403715384962142976.0000000000 1.6567150176 2.5007014727 1.5962858399 0.1069202409 0.0989014192 -0.8280723391 0.541371196659 +1403715385012143104.0000000000 1.6656034812 2.4943071911 1.5979392018 0.1021463079 0.0936490703 -0.8277926009 0.543650065149 +1403715385062142976.0000000000 1.6736560238 2.4868362164 1.5995226563 0.0967894423 0.0899608665 -0.8276582148 0.545454604775 +1403715385112143104.0000000000 1.6809702305 2.4781886178 1.6015514555 0.0906112186 0.0869160033 -0.8274322957 0.547349076448 +1403715385162142976.0000000000 1.6879136399 2.4686030495 1.6039018554 0.0842367491 0.0834360660 -0.8273192349 0.549076931304 +1403715385212143104.0000000000 1.6945238998 2.4583685991 1.6064953635 0.0778333228 0.0798007800 -0.8272847119 0.550612218185 +1403715385262142976.0000000000 1.7011684834 2.4474991812 1.6094032618 0.0723581383 0.0767404437 -0.8274078854 0.55160800871 +1403715385312143104.0000000000 1.7081436047 2.4360091058 1.6123606364 0.0682067986 0.0738166095 -0.8279323823 0.551748956538 +1403715385362142976.0000000000 1.7155302647 2.4236875829 1.6156140461 0.0659266878 0.0709028423 -0.8279700665 0.552351362665 +1403715385412143104.0000000000 1.7228846599 2.4108266126 1.6187198066 0.0636925024 0.0689712812 -0.8285956314 0.551919837643 +1403715385462142976.0000000000 1.7303069301 2.3976357595 1.6225479866 0.0639921141 0.0662100691 -0.8284041322 0.552510479329 +1403715385512143104.0000000000 1.7378871728 2.3839073938 1.6268111053 0.0658159725 0.0633951647 -0.8275009982 0.553977805431 +1403715385562142976.0000000000 1.7454405192 2.3695756177 1.6314382176 0.0694278509 0.0596196407 -0.8268078506 0.554990135244 +1403715385612143104.0000000000 1.7528467897 2.3548197367 1.6365284301 0.0746225821 0.0557167563 -0.8261106671 0.555759191584 +1403715385662142976.0000000000 1.7596653584 2.3397406474 1.6412967174 0.0792655709 0.0525584035 -0.8266608256 0.554604780766 +1403715385712143104.0000000000 1.7655442747 2.3241399588 1.6463187351 0.0832370872 0.0505166650 -0.8264448035 0.55453461629 +1403715385762142976.0000000000 1.7701795889 2.3079488240 1.6512487739 0.0856952402 0.0497520099 -0.8257015231 0.555335986586 +1403715385812143104.0000000000 1.7733602688 2.2911228543 1.6570108627 0.0884261419 0.0487902545 -0.8242480901 0.557149364628 +1403715385862142976.0000000000 1.7747561901 2.2736311730 1.6632350742 0.0896755949 0.0489024022 -0.8226245967 0.559334976188 +1403715385912143104.0000000000 1.7744081567 2.2555566628 1.6699245631 0.0894916428 0.0498887733 -0.8202652883 0.562731919332 +1403715385962142976.0000000000 1.7723658010 2.2370887124 1.6764044240 0.0863330595 0.0528442554 -0.8172466203 0.567328872149 +1403715386012143104.0000000000 1.7688247420 2.2187896720 1.6824028051 0.0819067421 0.0564611376 -0.8146438744 0.571365717736 +1403715386062142976.0000000000 1.7641309444 2.2012303735 1.6881623157 0.0779109087 0.0596498073 -0.8130523285 0.573862093088 +1403715386112143104.0000000000 1.7584614253 2.1844804831 1.6937193236 0.0746584890 0.0621947298 -0.8119918490 0.575523381577 +1403715386162142976.0000000000 1.7519275821 2.1687224467 1.6988568968 0.0718586045 0.0640202670 -0.8118669168 0.575855759561 +1403715386212143104.0000000000 1.7449245959 2.1537990929 1.7032137564 0.0693304328 0.0655455128 -0.8123977323 0.57524516639 +1403715386262142976.0000000000 1.7376026416 2.1394046089 1.7066106497 0.0680687795 0.0659275205 -0.8133225916 0.574044044722 +1403715386312143104.0000000000 1.7300876258 2.1257379729 1.7098610486 0.0681866079 0.0650831356 -0.8139782385 0.573196475303 +1403715386362142976.0000000000 1.7220834848 2.1123261018 1.7131191211 0.0683051306 0.0643682733 -0.8135844448 0.573821823987 +1403715386412143104.0000000000 1.7136225137 2.0996346886 1.7161020202 0.0685463503 0.0633900147 -0.8124512169 0.575505103435 +1403715386462142976.0000000000 1.7048327904 2.0874577345 1.7185042654 0.0688653477 0.0622731747 -0.8112389557 0.577296260506 +1403715386512143104.0000000000 1.6955813996 2.0759779533 1.7204799251 0.0697796104 0.0609679089 -0.8098362612 0.579291765925 +1403715386562142976.0000000000 1.6858984107 2.0655016204 1.7220170970 0.0723596064 0.0586385941 -0.8089756983 0.580417024317 +1403715386612143104.0000000000 1.6756046850 2.0561304048 1.7225794037 0.0740611342 0.0571536889 -0.8085784176 0.58090390494 +1403715386662142976.0000000000 1.6646265257 2.0477146620 1.7229844559 0.0780049280 0.0540958544 -0.8077425818 0.581842582928 +1403715386712143104.0000000000 1.6526597964 2.0403289495 1.7226245767 0.0812126907 0.0519747263 -0.8076625849 0.581708067325 +1403715386762142976.0000000000 1.6397163951 2.0341656256 1.7217290079 0.0841857612 0.0500122829 -0.8085455142 0.580228989881 +1403715386812143104.0000000000 1.6253757132 2.0290968937 1.7195619793 0.0883635013 0.0475048099 -0.8116647753 0.575443721989 +1403715386862142976.0000000000 1.6094514913 2.0244689580 1.7174162365 0.0930188076 0.0450461420 -0.8144279269 0.570986425807 +1403715386912143104.0000000000 1.5914222161 2.0202109806 1.7149735330 0.0969334090 0.0427070022 -0.8170367364 0.566772438906 +1403715386962142976.0000000000 1.5714529237 2.0158660527 1.7121007864 0.0997395060 0.0412663584 -0.8191153686 0.56338187008 +1403715387012143104.0000000000 1.5492200653 2.0111285816 1.7087218325 0.1013360886 0.0405121274 -0.8207790403 0.560724113655 +1403715387062142976.0000000000 1.5245870572 2.0059773080 1.7045946303 0.1007114500 0.0412894235 -0.8218103238 0.559267537922 +1403715387112143104.0000000000 1.4979845055 1.9999742398 1.6999734445 0.0978541809 0.0439372613 -0.8219919584 0.559306084923 +1403715387162142976.0000000000 1.4693927719 1.9933356530 1.6950507818 0.0935632850 0.0473922263 -0.8221465854 0.559530947067 +1403715387212143104.0000000000 1.4392677156 1.9863163197 1.6899128137 0.0886593377 0.0518951373 -0.8216882721 0.560602176247 +1403715387262142976.0000000000 1.4079002017 1.9790078883 1.6846849829 0.0853022167 0.0552082750 -0.8214542187 0.561149307061 +1403715387312143104.0000000000 1.3755632446 1.9712817107 1.6794243431 0.0823038992 0.0582627108 -0.8206817078 0.562417157642 +1403715387362142976.0000000000 1.3427032979 1.9630803311 1.6739789668 0.0803546226 0.0607618633 -0.8200298501 0.563384571606 +1403715387412143104.0000000000 1.3093015184 1.9547365922 1.6683007569 0.0783836854 0.0632342734 -0.8196435655 0.563951992687 +1403715387462142976.0000000000 1.2755511806 1.9463511077 1.6627079320 0.0773124356 0.0651887759 -0.8196808676 0.563823098159 +1403715387512143104.0000000000 1.2412909820 1.9378645601 1.6574295049 0.0761983653 0.0674170733 -0.8209967867 0.561794467466 +1403715387562142976.0000000000 1.2067955700 1.9291369193 1.6535867277 0.0759160323 0.0689006374 -0.8223811502 0.559623714696 +1403715387612143104.0000000000 1.1719545650 1.9203559403 1.6518135279 0.0771257965 0.0694671450 -0.8244422952 0.556345961757 +1403715387662142976.0000000000 1.1369472718 1.9109119866 1.6527678618 0.0777544983 0.0704337200 -0.8263502146 0.553297977439 +1403715387712143104.0000000000 1.1019682817 1.9004637943 1.6568632068 0.0779147496 0.0722720582 -0.8277301782 0.550970773729 +1403715387762142976.0000000000 1.0670758850 1.8890823083 1.6643021754 0.0787930278 0.0737904835 -0.8289563716 0.548796826953 +1403715387812143104.0000000000 1.0319218223 1.8764680373 1.6746106227 0.0796863510 0.0752812290 -0.8295733699 0.547531593577 +1403715387862142976.0000000000 0.9968725096 1.8623926183 1.6865709709 0.0808886053 0.0764269300 -0.8303665375 0.54599209825 +1403715387912143104.0000000000 0.9618810734 1.8472491714 1.6978216419 0.0822151568 0.0774826850 -0.8307145103 0.545115129079 +1403715387962142976.0000000000 0.9268113215 1.8313990768 1.7062257136 0.0830681607 0.0786545721 -0.8307958322 0.544693881161 +1403715388012143104.0000000000 0.8919249311 1.8143055672 1.7113682641 0.0842797468 0.0792732139 -0.8305123461 0.544850369253 +1403715388062142976.0000000000 0.8569290871 1.7962535466 1.7132613133 0.0843306697 0.0808456770 -0.8300239847 0.545355388252 +1403715388112143104.0000000000 0.8219186901 1.7775796934 1.7118109598 0.0847416019 0.0816334053 -0.8291021493 0.546575222681 +1403715388162142976.0000000000 0.7870588842 1.7580659904 1.7068707807 0.0852353366 0.0825232423 -0.8280208764 0.548002080435 +1403715388212143104.0000000000 0.7524176025 1.7375521821 1.6988704835 0.0851438351 0.0835640729 -0.8262270619 0.550560092305 +1403715388262142976.0000000000 0.7179888261 1.7162705864 1.6885160580 0.0850950851 0.0844703651 -0.8240845759 0.55363182326 +1403715388312143104.0000000000 0.6833606155 1.6943012979 1.6766166539 0.0847543842 0.0856276374 -0.8222783764 0.556186006419 +1403715388362142976.0000000000 0.6487076867 1.6716345345 1.6642127681 0.0838315014 0.0867862972 -0.8206241098 0.558584361052 +1403715388412143104.0000000000 0.6141942607 1.6486403975 1.6515600890 0.0838812538 0.0874017603 -0.8196991319 0.559837655678 +1403715388462142976.0000000000 0.5796008668 1.6251914386 1.6386858960 0.0826153941 0.0885424192 -0.8186644459 0.561358585724 +1403715388512143104.0000000000 0.5453027360 1.6016364502 1.6252905039 0.0822674959 0.0888500237 -0.8185593392 0.561514328141 +1403715388562142976.0000000000 0.5114254455 1.5779210536 1.6123626381 0.0832040272 0.0885219237 -0.8181032153 0.562092597324 +1403715388612143104.0000000000 0.4773979932 1.5541629832 1.5997057612 0.0835203466 0.0882496488 -0.8177973744 0.562533381794 +1403715388662142976.0000000000 0.4435341530 1.5304969027 1.5872281202 0.0836598676 0.0884092883 -0.8172687336 0.563255396244 +1403715388712143104.0000000000 0.4098971430 1.5068040283 1.5752272189 0.0840617274 0.0885464400 -0.8166054387 0.564135366314 +1403715388762142976.0000000000 0.3762744950 1.4829590658 1.5636870045 0.0836428760 0.0890983280 -0.8163010392 0.564551123099 +1403715388812143104.0000000000 0.3429218088 1.4591821669 1.5528843898 0.0838640608 0.0892784127 -0.8160884236 0.564797193054 +1403715388862142976.0000000000 0.3097705994 1.4353887968 1.5428101117 0.0838317318 0.0901138233 -0.8158696874 0.564985303164 +1403715388912143104.0000000000 0.2765004337 1.4116542657 1.5345115740 0.0824795890 0.0916570858 -0.8151515424 0.565971782886 +1403715388962142976.0000000000 0.2435146922 1.3880860181 1.5287313089 0.0826236687 0.0924955535 -0.8145591677 0.566666801776 +1403715389012143104.0000000000 0.2106190988 1.3642149703 1.5254353791 0.0822726530 0.0935841031 -0.8141742121 0.567092213507 +1403715389062142976.0000000000 0.1781367808 1.3401294730 1.5254421322 0.0824358559 0.0945585552 -0.8134675638 0.567920357001 +1403715389112143104.0000000000 0.1458930396 1.3161378199 1.5286386092 0.0819205055 0.0959270485 -0.8132171523 0.56812401408 +1403715389162142976.0000000000 0.1139764099 1.2922101402 1.5343830979 0.0811625590 0.0975670603 -0.8129653177 0.568313909667 +1403715389212143104.0000000000 0.0825631140 1.2683333714 1.5407826826 0.0805009095 0.0990765035 -0.8124894291 0.568827194879 +1403715389262142976.0000000000 0.0515532562 1.2447443357 1.5470109223 0.0787579608 0.1013735133 -0.8121129298 0.569203991198 +1403715389312143104.0000000000 0.0211038779 1.2219414398 1.5530982303 0.0777085163 0.1030544787 -0.8118738456 0.569387407439 +1403715389362142976.0000000000 -0.0086625859 1.1995269757 1.5587417869 0.0768949302 0.1049571152 -0.8116497234 0.569469841346 +1403715389412143104.0000000000 -0.0377632324 1.1772305822 1.5638157860 0.0758695012 0.1065750352 -0.8114039609 0.569657083615 +1403715389462142976.0000000000 -0.0660233213 1.1552255328 1.5682798456 0.0758094996 0.1075308964 -0.8115214956 0.569317914882 +1403715389512143104.0000000000 -0.0934661321 1.1334996807 1.5725235061 0.0765027037 0.1078937663 -0.8116631899 0.568954424919 +1403715389562142976.0000000000 -0.1201474919 1.1120046297 1.5764868284 0.0781525228 0.1072481087 -0.8117660792 0.56870542377 +1403715389612143104.0000000000 -0.1459548231 1.0908272804 1.5803879168 0.0813828920 0.1063718886 -0.8116508436 0.56858135238 +1403715389662142976.0000000000 -0.1708045671 1.0699579736 1.5834968336 0.0850474622 0.1069812231 -0.8115669485 0.568050204853 +1403715389712143104.0000000000 -0.1950082181 1.0492988534 1.5861389993 0.0891535447 0.1088350288 -0.8113475968 0.567381405386 +1403715389762142976.0000000000 -0.2187694436 1.0288415673 1.5881731497 0.0936408795 0.1119138456 -0.8110772031 0.56644544965 +1403715389812143104.0000000000 -0.2421401541 1.0086384050 1.5897631898 0.0985576346 0.1165058469 -0.8103433263 0.565735339033 +1403715389862142976.0000000000 -0.2653026684 0.9887763073 1.5903894037 0.1034406405 0.1222290050 -0.8104106962 0.563555328065 +1403715389912143104.0000000000 -0.2883474917 0.9690618981 1.5903688269 0.1079188795 0.1293672541 -0.8108165085 0.560530301246 +1403715389962142976.0000000000 -0.3112900400 0.9491882301 1.5898484887 0.1122381593 0.1370047600 -0.8113957331 0.557018182461 +1403715390012143104.0000000000 -0.3341108603 0.9291827837 1.5884715214 0.1158463231 0.1457476564 -0.8123345292 0.552675187413 +1403715390062142976.0000000000 -0.3567121399 0.9088021938 1.5862043756 0.1196066085 0.1548172153 -0.8129672724 0.548461578479 +1403715390112143104.0000000000 -0.3787972681 0.8879135986 1.5837895302 0.1234992430 0.1642570974 -0.8130077895 0.54478057706 +1403715390162142976.0000000000 -0.4001095035 0.8660712827 1.5810240240 0.1267586525 0.1744352093 -0.8125082703 0.541604018211 +1403715390212143104.0000000000 -0.4203752594 0.8433206194 1.5778847350 0.1303781219 0.1846773967 -0.8114621074 0.538910987697 +1403715390262142976.0000000000 -0.4393862911 0.8198549647 1.5739732725 0.1337980832 0.1951201633 -0.8105855762 0.535702546635 +1403715390312143104.0000000000 -0.4566934213 0.7951819184 1.5700528881 0.1380701477 0.2051242365 -0.8078657658 0.53498933293 +1403715390362142976.0000000000 -0.4728428608 0.7698558298 1.5660610760 0.1428423502 0.2148934811 -0.8051547058 0.533987597746 +1403715390412143104.0000000000 -0.4877395196 0.7437536162 1.5620058962 0.1465827531 0.2253545863 -0.8018356569 0.533655681318 +1403715390462142976.0000000000 -0.5012911095 0.7170271585 1.5577508907 0.1495872210 0.2365485426 -0.7979470516 0.533806100631 +1403715390512143104.0000000000 -0.5131596727 0.6901109034 1.5535251891 0.1532475286 0.2471863092 -0.7941521337 0.533607076478 +1403715390562142976.0000000000 -0.5233721019 0.6629330505 1.5493447221 0.1567653702 0.2578912752 -0.7897187130 0.5340983648 +1403715390612143104.0000000000 -0.5319594762 0.6359628546 1.5452891408 0.1607300677 0.2681610614 -0.7848438590 0.535047294585 +1403715390662142976.0000000000 -0.5387666641 0.6092529136 1.5411899439 0.1661107221 0.2771055309 -0.7808618321 0.534672378131 +1403715390712143104.0000000000 -0.5436334246 0.5831659907 1.5373576290 0.1736932145 0.2841985870 -0.7778791349 0.532884492088 +1403715390762142976.0000000000 -0.5464649435 0.5578230319 1.5338387258 0.1839185178 0.2889706806 -0.7762437850 0.529259398464 +1403715390812143104.0000000000 -0.5479572142 0.5323506472 1.5300974527 0.1919134160 0.2943303254 -0.7748515553 0.525494022373 +1403715390862142976.0000000000 -0.5481811845 0.5064768054 1.5262140206 0.1988927819 0.2981736154 -0.7740785237 0.521858788874 +1403715390912143104.0000000000 -0.5472402339 0.4802724592 1.5220561347 0.2031699154 0.3021014163 -0.7733545916 0.519017721712 +1403715390962142976.0000000000 -0.5450170034 0.4536767793 1.5181572207 0.2072866475 0.3047415853 -0.7732434530 0.516003269681 +1403715391012143104.0000000000 -0.5418545360 0.4266930684 1.5140971875 0.2108798501 0.3071480974 -0.7733570243 0.512941174109 +1403715391062142976.0000000000 -0.5375941561 0.3994097098 1.5099718196 0.2152916718 0.3097293816 -0.7730856616 0.509956631584 +1403715391112143104.0000000000 -0.5324167929 0.3716607137 1.5058065877 0.2201915664 0.3126143759 -0.7726397419 0.506769923381 +1403715391162142976.0000000000 -0.5258999828 0.3433355062 1.5023016405 0.2268138335 0.3149454499 -0.7714890560 0.50415224388 +1403715391212143104.0000000000 -0.5184723985 0.3141568801 1.4988724315 0.2326685647 0.3178695392 -0.7699556170 0.50198868805 +1403715391262142976.0000000000 -0.5101598625 0.2837384010 1.4961371597 0.2387379072 0.3194707995 -0.7678973356 0.501274677088 +1403715391312143104.0000000000 -0.5014022592 0.2520713837 1.4936658238 0.2433849030 0.3207931896 -0.7660414061 0.501035011392 +1403715391362142976.0000000000 -0.4922566686 0.2191112659 1.4908833890 0.2461031722 0.3225603262 -0.7643024168 0.501228371324 +1403715391412143104.0000000000 -0.4829084648 0.1850927207 1.4878252468 0.2475612986 0.3243972478 -0.7629496104 0.501385800563 +1403715391462142976.0000000000 -0.4733561011 0.1502211729 1.4846168642 0.2485350551 0.3254850264 -0.7627249478 0.500540186131 +1403715391512143104.0000000000 -0.4632236024 0.1140570350 1.4813638397 0.2486565866 0.3265945608 -0.7625148685 0.500076964265 +1403715391562142976.0000000000 -0.4525553283 0.0771752764 1.4784687975 0.2501127203 0.3268729509 -0.7622299763 0.499603006724 +1403715391612143104.0000000000 -0.4414759090 0.0397755946 1.4761171491 0.2536182882 0.3267410700 -0.7624265503 0.497618119155 +1403715391662142976.0000000000 -0.4302104456 0.0011565074 1.4746769390 0.2571237883 0.3274175449 -0.7617127953 0.496466238818 +1403715391712143104.0000000000 -0.4188522598 -0.0386096259 1.4754226603 0.2598594190 0.3297472845 -0.7599225036 0.496243487824 +1403715391762142976.0000000000 -0.4075195603 -0.0793133654 1.4791133875 0.2628406933 0.3330907282 -0.7574910775 0.496157841996 +1403715391812143104.0000000000 -0.3958703147 -0.1214407833 1.4857776555 0.2640701379 0.3386870409 -0.7540792491 0.496913007109 +1403715391862142976.0000000000 -0.3839783789 -0.1647168252 1.4948940883 0.2639916659 0.3461571790 -0.7502805664 0.497556709777 +1403715391912143104.0000000000 -0.3721430300 -0.2086230678 1.5067567074 0.2643135502 0.3531412827 -0.7469577078 0.497477400787 +1403715391962142976.0000000000 -0.3602166317 -0.2531367826 1.5200754087 0.2640005573 0.3596876019 -0.7446764497 0.496372360259 +1403715392012143104.0000000000 -0.3477885663 -0.2977817375 1.5332593014 0.2630457666 0.3654494650 -0.7444440583 0.493007765984 +1403715392062142976.0000000000 -0.3346126701 -0.3428469207 1.5463424201 0.2629199882 0.3700691018 -0.7437484583 0.49067318088 +1403715392112143104.0000000000 -0.3205280827 -0.3883615835 1.5591227983 0.2631702721 0.3730978243 -0.7438081595 0.488148382465 +1403715392162142976.0000000000 -0.3054524042 -0.4342590890 1.5715667627 0.2635761862 0.3758182624 -0.7434085464 0.486448312655 +1403715392212143104.0000000000 -0.2893610382 -0.4805167260 1.5841930202 0.2655872294 0.3782003652 -0.7420816632 0.485533430881 +1403715392262142976.0000000000 -0.2721124067 -0.5269433664 1.5970243303 0.2684598165 0.3814489403 -0.7392722289 0.485698058861 +1403715392312143104.0000000000 -0.2537440080 -0.5732061925 1.6093398692 0.2727887750 0.3850642851 -0.7357985645 0.485707991551 +1403715392362142976.0000000000 -0.2340918950 -0.6197826911 1.6219263050 0.2780826025 0.3896963990 -0.7299144879 0.487884846191 +1403715392412143104.0000000000 -0.2138294379 -0.6662335953 1.6350822751 0.2863334116 0.3931197166 -0.7221851186 0.491852335814 +1403715392462142976.0000000000 -0.1932651675 -0.7126696924 1.6482618338 0.2952997157 0.3966477163 -0.7129763315 0.497125152996 +1403715392512143104.0000000000 -0.1733012422 -0.7584360603 1.6602002344 0.3025073743 0.4021623229 -0.7042079895 0.500845147823 +1403715392562142976.0000000000 -0.1540773063 -0.8031518229 1.6705081343 0.3084061790 0.4091129821 -0.6974323384 0.501099121899 +1403715392612143104.0000000000 -0.1355571491 -0.8467373740 1.6792810845 0.3125701310 0.4175210415 -0.6923183798 0.49866958402 +1403715392662142976.0000000000 -0.1180000768 -0.8893014150 1.6875639191 0.3180504997 0.4254807950 -0.6866095481 0.496364081243 +1403715392712143104.0000000000 -0.1014984349 -0.9311521686 1.6952465546 0.3240684964 0.4330787011 -0.6806273263 0.494134486743 +1403715392762142976.0000000000 -0.0860286977 -0.9719799669 1.7016775923 0.3292512859 0.4413138316 -0.6752941336 0.490727547502 +1403715392812143104.0000000000 -0.0712587251 -1.0117777778 1.7069677133 0.3324374498 0.4513758935 -0.6712991686 0.484873768056 +1403715392862142976.0000000000 -0.0573361192 -1.0503396110 1.7117426441 0.3350311961 0.4619380244 -0.6683534309 0.477148876857 +1403715392912143104.0000000000 -0.0439356655 -1.0879133441 1.7163046858 0.3379822556 0.4724401048 -0.6644993587 0.470115884207 +1403715392962142976.0000000000 -0.0310781259 -1.1243069413 1.7203208283 0.3404618426 0.4835615888 -0.6599887587 0.463323604004 +1403715393012143104.0000000000 -0.0178858092 -1.1599313901 1.7247203260 0.3440660647 0.4939343119 -0.6545752814 0.457360513827 +1403715393062142976.0000000000 -0.0045038429 -1.1946805414 1.7296491310 0.3492920649 0.5031878957 -0.6491723079 0.450968191397 +1403715393112143104.0000000000 0.0092563027 -1.2286073268 1.7339967053 0.3537925574 0.5132526168 -0.6420463438 0.446294824255 +1403715393162142976.0000000000 0.0231799833 -1.2615681404 1.7374403973 0.3580276239 0.5236470712 -0.6332350069 0.443422362199 +1403715393212143104.0000000000 0.0372014250 -1.2931816850 1.7399171497 0.3625740500 0.5341858165 -0.6235366247 0.440894147689 +1403715393262142976.0000000000 0.0514836697 -1.3232217034 1.7422692877 0.3689320288 0.5434956814 -0.6135224919 0.438282733394 +1403715393312143104.0000000000 0.0657432487 -1.3514389858 1.7445396943 0.3757135086 0.5527058534 -0.6030262712 0.435562757131 +1403715393362142976.0000000000 0.0797921928 -1.3781922675 1.7466134592 0.3824496423 0.5619099390 -0.5927655153 0.431993675168 +1403715393412143104.0000000000 0.0935399467 -1.4034913140 1.7484618711 0.3883393775 0.5715839243 -0.5821470923 0.428472995973 +1403715393462142976.0000000000 0.1069401158 -1.4270741995 1.7495027625 0.3939463236 0.5812985620 -0.5713647683 0.424782976953 +1403715393512143104.0000000000 0.1198386777 -1.4488301608 1.7501114409 0.4005204300 0.5901245031 -0.5604043215 0.421050415588 +1403715393562142976.0000000000 0.1319561023 -1.4684730113 1.7503182571 0.4066270771 0.5991808968 -0.5490634865 0.417331955347 +1403715393612143104.0000000000 0.1431611639 -1.4858578632 1.7503937137 0.4135907171 0.6076706131 -0.5385133809 0.411925336978 +1403715393662142976.0000000000 0.1529789098 -1.5008835722 1.7502915716 0.4220236176 0.6150053687 -0.5297971783 0.403707087409 +1403715393712143104.0000000000 0.1621062675 -1.5137903127 1.7498798194 0.4300265224 0.6225202073 -0.5224982368 0.393117506678 +1403715393762142976.0000000000 0.1700786122 -1.5246411002 1.7492187515 0.4377764065 0.6298525955 -0.5158748303 0.381458628603 +1403715393812143104.0000000000 0.1774425124 -1.5339226881 1.7480257134 0.4442618986 0.6377686340 -0.5089969493 0.369871113397 +1403715393862142976.0000000000 0.1841457321 -1.5421864886 1.7471663633 0.4508890730 0.6450790872 -0.5022220225 0.358252781165 +1403715393912143104.0000000000 0.1905192608 -1.5497126467 1.7459393956 0.4561098294 0.6529729195 -0.4934231212 0.34946217735 +1403715393962142976.0000000000 0.1963820866 -1.5561969340 1.7448928097 0.4619376420 0.6600503817 -0.4855643124 0.339373550829 +1403715394012143104.0000000000 0.2018460693 -1.5620674108 1.7438248980 0.4683806975 0.6664458378 -0.4768578655 0.330266624964 +1403715394062142976.0000000000 0.2071474629 -1.5672541156 1.7427408841 0.4743964378 0.6730110993 -0.4673833618 0.321802537504 +1403715394112143104.0000000000 0.2122957588 -1.5719373213 1.7414015920 0.4798336755 0.6799598449 -0.4574061837 0.313358957612 +1403715394162142976.0000000000 0.2173346198 -1.5761162550 1.7398554877 0.4848894201 0.6870900884 -0.4458559706 0.306597316022 +1403715394212143104.0000000000 0.2218185534 -1.5796872553 1.7381181136 0.4899757573 0.6942455645 -0.4344570293 0.298653550274 +1403715394262142976.0000000000 0.2257774606 -1.5827930009 1.7361040147 0.4949547084 0.7013456205 -0.4225943823 0.290771637686 +1403715394312143104.0000000000 0.2294105391 -1.5852525815 1.7345698969 0.5011672178 0.7073056731 -0.4106352888 0.28271675599 +1403715394362142976.0000000000 0.2330222633 -1.5872347059 1.7330857677 0.5070169133 0.7133379424 -0.3968512629 0.276752424936 +1403715394412143104.0000000000 0.2360986487 -1.5888329942 1.7319908264 0.5129914459 0.7190702839 -0.3829910293 0.270361932806 +1403715394462142976.0000000000 0.2389371723 -1.5898277231 1.7313519488 0.5193168585 0.7240774729 -0.3683825076 0.265171909989 +1403715394512143104.0000000000 0.2408833618 -1.5903689033 1.7306252006 0.5248514314 0.7292812574 -0.3539889731 0.259560454415 +1403715394562142976.0000000000 0.2416356867 -1.5905050899 1.7299424670 0.5299248771 0.7346398480 -0.3402943427 0.252356253517 +1403715394612143104.0000000000 0.2411041111 -1.5902624142 1.7292179533 0.5349829909 0.7398056995 -0.3274465775 0.243432670931 +1403715394662142976.0000000000 0.2387956280 -1.5898565006 1.7282995265 0.5396676466 0.7450917988 -0.3152249097 0.232873997938 +1403715394712143104.0000000000 0.2351375569 -1.5890667699 1.7271059123 0.5432380917 0.7508748928 -0.3029979553 0.221971867936 +1403715394762142976.0000000000 0.2299403048 -1.5881892888 1.7255742073 0.5455325126 0.7573737143 -0.2908017838 0.210270438183 +1403715394812143104.0000000000 0.2237998063 -1.5872945218 1.7240868310 0.5474296457 0.7638526977 -0.2781876021 0.198649181252 +1403715394862142976.0000000000 0.2169357035 -1.5864473974 1.7227359735 0.5495605673 0.7700206017 -0.2647744999 0.186938278585 +1403715394912143104.0000000000 0.2094170641 -1.5855211475 1.7211825560 0.5512827885 0.7763454353 -0.2502446808 0.175364340745 +1403715394962142976.0000000000 0.2014128818 -1.5841356696 1.7199969151 0.5536451912 0.7819571706 -0.2350319199 0.163645904641 +1403715395012143104.0000000000 0.1930751564 -1.5826416647 1.7185986230 0.5555004973 0.7875204257 -0.2189407023 0.152629438354 +1403715395062142976.0000000000 0.1839904470 -1.5808159374 1.7171326846 0.5578727454 0.7923377328 -0.2025958201 0.141187289694 +1403715395112143104.0000000000 0.1745442844 -1.5784266996 1.7156853176 0.5604196276 0.7964184325 -0.1864833763 0.129890229463 +1403715395162142976.0000000000 0.1648727676 -1.5755175015 1.7140889523 0.5622799956 0.8002729315 -0.1707949558 0.119304336518 +1403715395212143104.0000000000 0.1548370401 -1.5721764342 1.7125385128 0.5635749586 0.8038745991 -0.1569318587 0.107430380577 +1403715395262142976.0000000000 0.1444559287 -1.5684328601 1.7106808959 0.5650837014 0.8067132608 -0.1427217746 0.0975941610001 +1403715395312143104.0000000000 0.1336733411 -1.5639984311 1.7083514320 0.5665483473 0.8090425405 -0.1288737505 0.0886831114404 +1403715395362142976.0000000000 0.1226385571 -1.5592284925 1.7054779610 0.5675086940 0.8111988038 -0.1159763463 0.0802488011342 +1403715395412143104.0000000000 0.1112174533 -1.5542468115 1.7020189265 0.5681985589 0.8131358429 -0.1040476728 0.0716559859462 +1403715395462142976.0000000000 0.0994715692 -1.5488624406 1.6979762635 0.5682235241 0.8151653780 -0.0931525648 0.0628492867129 +1403715395512143104.0000000000 0.0875619332 -1.5430290888 1.6932231419 0.5685291976 0.8166836872 -0.0827237611 0.0543974799147 +1403715395562142976.0000000000 0.0753620082 -1.5366888741 1.6879295839 0.5689469757 0.8178463078 -0.0729165099 0.0459340637123 +1403715395612143104.0000000000 0.0629270273 -1.5299643814 1.6820033932 0.5695982060 0.8185355132 -0.0643984915 0.0375543823157 +1403715395662142976.0000000000 0.0504107954 -1.5226597701 1.6756130190 0.5702796301 0.8190034792 -0.0554509663 0.0306534635699 +1403715395712143104.0000000000 0.0377609002 -1.5149742094 1.6682483756 0.5697251863 0.8201607122 -0.0460115006 0.0251507470302 +1403715395762142976.0000000000 0.0250200772 -1.5063896251 1.6606522828 0.5705244388 0.8202168844 -0.0368138709 0.0197703390423 +1403715395812143104.0000000000 0.0121907282 -1.4970556316 1.6524970133 0.5708735815 0.8204089728 -0.0278572518 0.0160138909735 +1403715395862142976.0000000000 -0.0010686387 -1.4871922490 1.6446239028 0.5710589251 0.8205491535 -0.0221954872 0.00990712470367 +1403715395912143104.0000000000 -0.0144741988 -1.4767012031 1.6366382078 0.5710687724 0.8206851332 -0.0184539749 0.00397746325661 +1403715395962142976.0000000000 -0.0280527655 -1.4654788431 1.6289393951 0.5710522989 0.8207314165 -0.0170819776 -0.00272394542328 +1403715396012143104.0000000000 -0.0416573473 -1.4535385253 1.6214076288 0.5712142714 0.8205638313 -0.0171620982 -0.00973228180265 +1403715396062142976.0000000000 -0.0548164332 -1.4409464236 1.6146419852 0.5719761290 0.8198588071 -0.0193871927 -0.0172910670803 +1403715396112143104.0000000000 -0.0669741905 -1.4283988096 1.6082271354 0.5726361568 0.8191916356 -0.0217927053 -0.0231942669916 +1403715396162142976.0000000000 -0.0777480708 -1.4153908802 1.6022485525 0.5740769515 0.8179887721 -0.0241352748 -0.0273406446487 +1403715396212143104.0000000000 -0.0869093329 -1.4021564218 1.5965221475 0.5752177615 0.8170905331 -0.0255429947 -0.0288988403983 +1403715396262142976.0000000000 -0.0944971363 -1.3887236985 1.5909184489 0.5764701511 0.8162899844 -0.0252066272 -0.0267852971737 +1403715396312143104.0000000000 -0.1005289292 -1.3748086630 1.5851632425 0.5769800091 0.8161440106 -0.0230819295 -0.0216851938928 +1403715396362142976.0000000000 -0.1053898683 -1.3605484405 1.5795923596 0.5781628608 0.8155322177 -0.0200721155 -0.0152321507745 +1403715396412143104.0000000000 -0.1098207599 -1.3464020248 1.5742273519 0.5789118052 0.8151204572 -0.0180201498 -0.0107254974653 +1403715396462142976.0000000000 -0.1138343957 -1.3324514440 1.5684287785 0.5786994439 0.8153775494 -0.0152822610 -0.0057321953667 +1403715396512143104.0000000000 -0.1181181327 -1.3185452089 1.5630037179 0.5792653193 0.8150507893 -0.0117144635 -0.00258305074622 +1403715396562142976.0000000000 -0.1229919894 -1.3045543029 1.5578559342 0.5802462132 0.8143945883 -0.0085338211 -0.00172063615937 +1403715396612143104.0000000000 -0.1284914759 -1.2908801241 1.5524537053 0.5806698858 0.8141260546 -0.0043022741 -0.00165573089376 +1403715396662142976.0000000000 -0.1346749209 -1.2775710947 1.5470240236 0.5821047241 0.8131059750 0.0003890733 -0.00355137634284 +1403715396712143104.0000000000 -0.1413824658 -1.2649087816 1.5408751422 0.5829064235 0.8124988941 0.0047316107 -0.00657725911405 +1403715396762142976.0000000000 -0.1486225402 -1.2527115134 1.5342047940 0.5821301554 0.8129835425 0.0079578848 -0.0109047636507 +1403715396812143104.0000000000 -0.1563299068 -1.2408142277 1.5274131993 0.5809968610 0.8136801847 0.0106097434 -0.0159573774164 +1403715396862142976.0000000000 -0.1642719759 -1.2290558901 1.5201087895 0.5788257243 0.8150926183 0.0135651400 -0.0200197775575 +1403715396912143104.0000000000 -0.1724203025 -1.2174164963 1.5122983855 0.5765512371 0.8165612752 0.0162058331 -0.0235313792839 +1403715396962142976.0000000000 -0.1807280809 -1.2057883215 1.5033568520 0.5719560342 0.8196551325 0.0194168597 -0.0255879711799 +1403715397012143104.0000000000 -0.1890307992 -1.1937266378 1.4939866401 0.5671759212 0.8228312778 0.0212814731 -0.0284123498915 +1403715397062142976.0000000000 -0.1972417759 -1.1811365698 1.4841426906 0.5627006172 0.8257734333 0.0236659565 -0.0301027367848 +1403715397112143104.0000000000 -0.2055621599 -1.1676605388 1.4742947727 0.5594052187 0.8278802207 0.0249151167 -0.0325480943671 +1403715397162142976.0000000000 -0.2141672340 -1.1526553659 1.4644395210 0.5567513527 0.8295155765 0.0249337712 -0.0361959477189 +1403715397212143104.0000000000 -0.2230141183 -1.1362876792 1.4549400206 0.5548521999 0.8305929290 0.0233592684 -0.0413372379976 +1403715397262142976.0000000000 -0.2319091115 -1.1185643785 1.4456181253 0.5531457214 0.8314637735 0.0207453175 -0.0476176017927 +1403715397312143104.0000000000 -0.2403746729 -1.0989588198 1.4369303629 0.5530913596 0.8312183278 0.0175460763 -0.0534619002511 +1403715397362142976.0000000000 -0.2478237505 -1.0777872994 1.4280817151 0.5531757663 0.8309018492 0.0150661599 -0.0580663364615 +1403715397412143104.0000000000 -0.2543356493 -1.0550316637 1.4192919503 0.5532333011 0.8306667976 0.0132774317 -0.0612314930076 +1403715397462142976.0000000000 -0.2596671522 -1.0307747956 1.4107046937 0.5527378457 0.8308201466 0.0122757206 -0.0637813820735 +1403715397512143104.0000000000 -0.2636768842 -1.0049347509 1.4025702190 0.5525244976 0.8308846708 0.0118171341 -0.0648667760611 +1403715397562142976.0000000000 -0.2663218147 -0.9773771319 1.3947851699 0.5534428178 0.8301726625 0.0114020188 -0.0662147405417 +1403715397612143104.0000000000 -0.2673004451 -0.9481405183 1.3880181418 0.5550302628 0.8290249087 0.0109195261 -0.0673785726923 +1403715397662142976.0000000000 -0.2665879220 -0.9174274124 1.3824618766 0.5580511027 0.8270198779 0.0112171627 -0.0670168910902 +1403715397712143104.0000000000 -0.2644039082 -0.8855358096 1.3782025280 0.5627795632 0.8238630280 0.0118647769 -0.0662427467568 +1403715397762142976.0000000000 -0.2608673935 -0.8528581886 1.3746840308 0.5666101545 0.8213813411 0.0128582433 -0.0641894915826 +1403715397812143104.0000000000 -0.2562863687 -0.8197521707 1.3720807241 0.5703091861 0.8189205602 0.0132738213 -0.0627722387786 +1403715397862142976.0000000000 -0.2504249145 -0.7860875837 1.3701193373 0.5730560628 0.8171326916 0.0139806147 -0.06087245451 +1403715397912143104.0000000000 -0.2433719891 -0.7521189656 1.3685116168 0.5758298209 0.8153999364 0.0155135884 -0.0574655521936 +1403715397962142976.0000000000 -0.2354467492 -0.7179576233 1.3677468195 0.5808699739 0.8120229148 0.0167398334 -0.0541168848236 +1403715398012143104.0000000000 -0.2268853775 -0.6838641256 1.3668128436 0.5863362806 0.8083003685 0.0179863782 -0.050366362584 +1403715398062142976.0000000000 -0.2178969865 -0.6504510123 1.3655906046 0.5915212634 0.8046881650 0.0187864644 -0.0471870817109 +1403715398112143104.0000000000 -0.2085946871 -0.6179440384 1.3634873526 0.5957716461 0.8016846302 0.0192477172 -0.0445805435921 +1403715398162142976.0000000000 -0.1991678292 -0.5863816489 1.3608996001 0.5993706920 0.7991236493 0.0195803450 -0.0421043566979 +1403715398212143104.0000000000 -0.1896613600 -0.5564988717 1.3573908831 0.6008191604 0.7981423735 0.0196575649 -0.0399833500707 +1403715398262142976.0000000000 -0.1801316147 -0.5285192164 1.3528633112 0.6002836720 0.7986298570 0.0192128193 -0.0384802819156 +1403715398312143104.0000000000 -0.1704414879 -0.5022682717 1.3474654404 0.5985140997 0.8000581952 0.0190743135 -0.036385811442 +1403715398362142976.0000000000 -0.1606946109 -0.4775530659 1.3417058997 0.5971065462 0.8012121545 0.0187248057 -0.0342379553159 +1403715398412143104.0000000000 -0.1511985618 -0.4539813520 1.3362431428 0.5957754837 0.8022322051 0.0168594189 -0.034508288997 +1403715398462142976.0000000000 -0.1414602789 -0.4316160464 1.3301666266 0.5941924800 0.8035099964 0.0167074605 -0.0320599929484 +1403715398512143104.0000000000 -0.1317499671 -0.4104328523 1.3242135867 0.5931220018 0.8044021707 0.0162800862 -0.0296377712235 +1403715398562142976.0000000000 -0.1223169152 -0.3903501317 1.3186801614 0.5928342355 0.8047095958 0.0162128747 -0.0269662447355 +1403715398612143104.0000000000 -0.1132246579 -0.3713092953 1.3142385161 0.5948542914 0.8032918136 0.0153714796 -0.0251863424419 +1403715398662142976.0000000000 -0.1043678688 -0.3535287375 1.3100304557 0.5975698704 0.8013731552 0.0159768364 -0.021355485992 +1403715398712143104.0000000000 -0.0958520547 -0.3370824626 1.3060868671 0.6011636149 0.7987679172 0.0176171886 -0.0161789156854 +1403715398762142976.0000000000 -0.0879217958 -0.3222201461 1.3024163975 0.6044410943 0.7963441399 0.0194735239 -0.0103805669853 +1403715398812143104.0000000000 -0.0809709864 -0.3094293989 1.2989487634 0.6065930799 0.7947122156 0.0210713933 -0.00577287684191 +1403715398862142976.0000000000 -0.0754917487 -0.2986623024 1.2955779462 0.6078409689 0.7937340707 0.0226132882 -0.00205444468727 +1403715398912143104.0000000000 -0.0716859482 -0.2897882099 1.2924499997 0.6087579321 0.7930045060 0.0236120313 0.000324944482243 +1403715398962142976.0000000000 -0.0696918660 -0.2827940746 1.2897035208 0.6091302466 0.7927086288 0.0239279444 0.000908843727516 +1403715399012143104.0000000000 -0.0691467801 -0.2779383779 1.2875410008 0.6098645132 0.7921252238 0.0245127203 0.00142543584157 +1403715399062142976.0000000000 -0.0702416985 -0.2754247348 1.2858034152 0.6094860896 0.7924238907 0.0243120938 7.82475475027e-05 +1403715399112143104.0000000000 -0.0730253823 -0.2750954883 1.2838908926 0.6078016542 0.7937272982 0.0238263321 -0.00253599060034 +1403715399162142976.0000000000 -0.0774754482 -0.2765555062 1.2822374248 0.6068424384 0.7944746157 0.0225569323 -0.0065973336658 +1403715399212143104.0000000000 -0.0830658739 -0.2798787566 1.2809004897 0.6061642349 0.7949726516 0.0222590762 -0.00937747541908 +1403715399262142976.0000000000 -0.0896927457 -0.2854197889 1.2801370589 0.6063774246 0.7947859803 0.0218140105 -0.0120753216206 +1403715399312143104.0000000000 -0.0970486723 -0.2927902685 1.2788180352 0.6048781136 0.7958907656 0.0228433169 -0.0125912553983 +1403715399362142976.0000000000 -0.1051363336 -0.3018796955 1.2774107572 0.6024033975 0.7977361639 0.0238486150 -0.0125858266716 +1403715399412143104.0000000000 -0.1141178256 -0.3125026317 1.2757938316 0.5987999865 0.8004055074 0.0254593774 -0.011892016547 +1403715399462142976.0000000000 -0.1240307955 -0.3243346997 1.2745922937 0.5963013998 0.8022348058 0.0268689055 -0.0110462131035 +1403715399512143104.0000000000 -0.1347892558 -0.3370575557 1.2735826632 0.5949515819 0.8032047783 0.0286806629 -0.00849228566275 +1403715399562142976.0000000000 -0.1468316046 -0.3513580323 1.2718820011 0.5899099073 0.8068975273 0.0294455864 -0.0074591687532 +1403715399612143104.0000000000 -0.1605368665 -0.3665592966 1.2701965171 0.5828864754 0.8120319496 0.0271781266 -0.0104316402941 +1403715399662142976.0000000000 -0.1753970945 -0.3822070526 1.2688140562 0.5762678238 0.8167776425 0.0248785269 -0.0130666329317 +1403715399712143104.0000000000 -0.1914027133 -0.3975961043 1.2677895054 0.5703635467 0.8209407904 0.0224697905 -0.0153867419425 +1403715399762142976.0000000000 -0.2081068615 -0.4121307096 1.2677736820 0.5660098749 0.8239777934 0.0206379104 -0.0163552489655 +1403715399812143104.0000000000 -0.2253814239 -0.4258340982 1.2686552187 0.5631124501 0.8259908014 0.0189644420 -0.0168497634362 +1403715399862142976.0000000000 -0.2432617753 -0.4390278246 1.2699245411 0.5610326942 0.8274282197 0.0180290812 -0.0167275077258 +1403715399912143104.0000000000 -0.2617357534 -0.4513412854 1.2716839989 0.5592789546 0.8286442795 0.0173692510 -0.0159379489018 +1403715399962142976.0000000000 -0.2806901738 -0.4622528087 1.2738684031 0.5579726524 0.8295872891 0.0161016399 -0.013863120581 +1403715400012143104.0000000000 -0.3001407837 -0.4717947683 1.2768595771 0.5579008998 0.8297258009 0.0140869206 -0.0101607062021 +1403715400062142976.0000000000 -0.3203730056 -0.4798670005 1.2805803731 0.5589877903 0.8290805480 0.0110864970 -0.0059316785701 +1403715400112143104.0000000000 -0.3415410885 -0.4864065122 1.2844100924 0.5603135366 0.8282472269 0.0073967842 -0.00074791952283 +1403715400162142976.0000000000 -0.3635128282 -0.4919060512 1.2883774306 0.5612436706 0.8276374147 0.0019080552 0.00426747121119 +1403715400212143104.0000000000 -0.3864017306 -0.4962175739 1.2925270208 0.5622329206 0.8268999729 -0.0038913921 0.0107440665594 +1403715400262142976.0000000000 -0.4102678881 -0.4994499114 1.2966603467 0.5621642833 0.8267342800 -0.0084109172 0.0202732668127 +1403715400312143104.0000000000 -0.4354300164 -0.5016409296 1.3010004215 0.5617470746 0.8266694266 -0.0145213032 0.0291035225262 +1403715400362142976.0000000000 -0.4620926036 -0.5028671528 1.3049121446 0.5614220572 0.8263628458 -0.0212298075 0.0384579784928 +1403715400412143104.0000000000 -0.4903601130 -0.5033340145 1.3084475768 0.5601329870 0.8265552533 -0.0296449861 0.0466757414785 +1403715400462142976.0000000000 -0.5203840778 -0.5026987908 1.3121900753 0.5596152254 0.8260884935 -0.0406008154 0.0525373606333 +1403715400512143104.0000000000 -0.5520427275 -0.5009633030 1.3157997983 0.5585383778 0.8257850007 -0.0533745409 0.0571416793933 +1403715400562142976.0000000000 -0.5851451106 -0.4980935995 1.3187803861 0.5567578242 0.8256599029 -0.0668778490 0.0619177138256 +1403715400612143104.0000000000 -0.6193473147 -0.4942213787 1.3214205797 0.5550775908 0.8251157544 -0.0818796793 0.0660952206003 +1403715400662142976.0000000000 -0.6542601202 -0.4894379049 1.3232968841 0.5523412504 0.8248847299 -0.0970987648 0.0711066479158 +1403715400712143104.0000000000 -0.6896669235 -0.4833458562 1.3245670912 0.5498192206 0.8240958479 -0.1123234863 0.077125174551 +1403715400762142976.0000000000 -0.7254634491 -0.4759467442 1.3253723892 0.5470232728 0.8231212143 -0.1281539791 0.0825443106875 +1403715400812143104.0000000000 -0.7616228007 -0.4671316741 1.3260296632 0.5456794860 0.8208087573 -0.1446668865 0.0870538593184 +1403715400862142976.0000000000 -0.7977203739 -0.4569918338 1.3262271503 0.5447443171 0.8178546603 -0.1613695120 0.0912538449837 +1403715400912143104.0000000000 -0.8338401839 -0.4457287586 1.3253693988 0.5420104338 0.8161789930 -0.1763464534 0.0947547854313 +1403715400962142976.0000000000 -0.8697184218 -0.4331691070 1.3240041217 0.5392451295 0.8147770772 -0.1894588744 0.0972539955875 +1403715401012143104.0000000000 -0.9047834843 -0.4194755523 1.3227565650 0.5364815831 0.8135611193 -0.2010215165 0.0994794750248 +1403715401062142976.0000000000 -0.9386755555 -0.4046706284 1.3215470496 0.5328967294 0.8133926901 -0.2093672428 0.102853124573 +1403715401112143104.0000000000 -0.9711344291 -0.3887696422 1.3211129290 0.5309575329 0.8125338481 -0.2159391673 0.106033578984 +1403715401162142976.0000000000 -1.0021979386 -0.3714470826 1.3210167480 0.5284952823 0.8123274286 -0.2204379314 0.110562216794 +1403715401212143104.0000000000 -1.0317435523 -0.3527107728 1.3213492534 0.5261653423 0.8124934853 -0.2226600236 0.115874426938 +1403715401262142976.0000000000 -1.0597156663 -0.3320627271 1.3220693576 0.5240370346 0.8128784168 -0.2234515451 0.121174555084 +1403715401312143104.0000000000 -1.0867231033 -0.3094643519 1.3231477038 0.5225639412 0.8128873272 -0.2242407662 0.125925372118 +1403715401362142976.0000000000 -1.1129485365 -0.2843954577 1.3254130886 0.5235855537 0.8115019665 -0.2252798914 0.128731102881 +1403715401412143104.0000000000 -1.1383974208 -0.2568732773 1.3286863625 0.5252874444 0.8098730344 -0.2261263810 0.130558908783 +1403715401462142976.0000000000 -1.1626109650 -0.2275895532 1.3321971702 0.5272364320 0.8082423771 -0.2262963218 0.132498978559 +1403715401512143104.0000000000 -1.1856195836 -0.1966578808 1.3364527231 0.5304979294 0.8058478884 -0.2269522424 0.132942872484 +1403715401562142976.0000000000 -1.2076651251 -0.1649054109 1.3412688564 0.5335463285 0.8035428519 -0.2283982373 0.132217418271 +1403715401612143104.0000000000 -1.2284822349 -0.1322535715 1.3472500819 0.5388740411 0.7998082719 -0.2296552986 0.131072269399 +1403715401662142976.0000000000 -1.2480931783 -0.0990348194 1.3532768730 0.5429451642 0.7966771138 -0.2311141989 0.130775961383 +1403715401712143104.0000000000 -1.2664279556 -0.0646493101 1.3600232513 0.5489202100 0.7915514823 -0.2357565864 0.128653355197 +1403715401762142976.0000000000 -1.2834996144 -0.0297205251 1.3664790370 0.5540604033 0.7863433809 -0.2426416718 0.125722614817 +1403715401812143104.0000000000 -1.2987781592 0.0049544262 1.3724802006 0.5571220791 0.7824921611 -0.2475367016 0.126675128765 +1403715401862142976.0000000000 -1.3125665481 0.0385885465 1.3784591505 0.5588225257 0.7795069795 -0.2522173215 0.128345924853 +1403715401912143104.0000000000 -1.3252326333 0.0712554165 1.3835991245 0.5587402361 0.7785301651 -0.2531882789 0.132649259483 +1403715401962142976.0000000000 -1.3365495221 0.1030969820 1.3878796414 0.5578401676 0.7785714900 -0.2518746726 0.138563818024 +1403715402012143104.0000000000 -1.3472188297 0.1339432913 1.3916747253 0.5569865657 0.7788504019 -0.2497493421 0.144164084176 +1403715402062142976.0000000000 -1.3572355382 0.1646738110 1.3956974936 0.5558853920 0.7795593658 -0.2473421966 0.14866224761 +1403715402112143104.0000000000 -1.3666305542 0.1955612125 1.4000021303 0.5583556715 0.7778948722 -0.2449306515 0.152077243061 +1403715402162142976.0000000000 -1.3755059559 0.2257943449 1.4047177951 0.5647661100 0.7732440497 -0.2421175788 0.156562954589 +1403715402212143104.0000000000 -1.3843962042 0.2552597328 1.4089804468 0.5698321908 0.7690778438 -0.2412999302 0.159952768488 +1403715402262142976.0000000000 -1.3933677761 0.2833192226 1.4124188414 0.5725899125 0.7661746503 -0.2420124623 0.162933008939 +1403715402312143104.0000000000 -1.4024989128 0.3096007579 1.4141889492 0.5707530930 0.7663637328 -0.2427899900 0.167273897053 +1403715402362142976.0000000000 -1.4117066287 0.3344799616 1.4151057126 0.5660379031 0.7680522025 -0.2446831048 0.172705195846 +1403715402412143104.0000000000 -1.4208875050 0.3584468865 1.4160421647 0.5623341232 0.7682526276 -0.2475506968 0.179685521507 +1403715402462142976.0000000000 -1.4303121652 0.3815063602 1.4165012434 0.5587449092 0.7676658860 -0.2509140923 0.188508175499 +1403715402512143104.0000000000 -1.4404324103 0.4044048514 1.4171030626 0.5571532143 0.7654426224 -0.2532816354 0.198812224903 +1403715402562142976.0000000000 -1.4518660991 0.4271998376 1.4179251698 0.5556097285 0.7636278257 -0.2562728060 0.206142238191 +1403715402612143104.0000000000 -1.4645621380 0.4498953580 1.4191240990 0.5561254331 0.7606012404 -0.2587288263 0.212766656718 +1403715402662142976.0000000000 -1.4789129581 0.4724768324 1.4198158075 0.5559423391 0.7583710512 -0.2611891828 0.218132242138 +1403715402712143104.0000000000 -1.4953274049 0.4950629260 1.4204086362 0.5561259501 0.7562708684 -0.2642760794 0.221215856344 +1403715402762142976.0000000000 -1.5141702532 0.5174349353 1.4207977691 0.5544448950 0.7559478639 -0.2714412907 0.217837809241 +1403715402812143104.0000000000 -1.5348551404 0.5392063075 1.4212606897 0.5533154640 0.7554484179 -0.2785997156 0.213358580194 +1403715402862142976.0000000000 -1.5568761311 0.5604735338 1.4216040664 0.5521821590 0.7551920381 -0.2853188070 0.208261919923 +1403715402912143104.0000000000 -1.5796788210 0.5814200018 1.4216921475 0.5507508950 0.7551420010 -0.2919439460 0.202984586558 +1403715402962142976.0000000000 -1.6028973577 0.6021214269 1.4216648124 0.5477849511 0.7561809612 -0.2983428364 0.197771467185 +1403715403012143104.0000000000 -1.6260222780 0.6225927607 1.4217793901 0.5440875062 0.7578678976 -0.3048961944 0.191424517948 +1403715403062142976.0000000000 -1.6483442512 0.6423938654 1.4218123403 0.5385863395 0.7608507090 -0.3099629776 0.186959637263 +1403715403112143104.0000000000 -1.6694391888 0.6619503795 1.4223888973 0.5338917954 0.7633363471 -0.3145870775 0.182516143733 +1403715403162142976.0000000000 -1.6891095982 0.6811571997 1.4232647579 0.5296354060 0.7657663278 -0.3178810605 0.178996925062 +1403715403212143104.0000000000 -1.7068999669 0.7006425658 1.4254067369 0.5268831444 0.7671160817 -0.3205738543 0.176520461076 +1403715403262142976.0000000000 -1.7225988272 0.7203611532 1.4276097128 0.5238335634 0.7691965864 -0.3202921599 0.177053499508 +1403715403312143104.0000000000 -1.7364523114 0.7405250716 1.4299600291 0.5223469284 0.7703823092 -0.3187846871 0.179000299629 +1403715403362142976.0000000000 -1.7484817909 0.7609121229 1.4326374890 0.5218741146 0.7705130750 -0.3174042757 0.182240323698 +1403715403412143104.0000000000 -1.7584497756 0.7818532514 1.4355131754 0.5216806238 0.7698842145 -0.3170601456 0.186012061796 +1403715403462142976.0000000000 -1.7664627074 0.8034230147 1.4387499755 0.5216266732 0.7685094334 -0.3180572815 0.190101105339 +1403715403512143104.0000000000 -1.7725571329 0.8256628604 1.4421149330 0.5217741330 0.7660812008 -0.3208183389 0.194799746517 +1403715403562142976.0000000000 -1.7772349084 0.8485619059 1.4452075555 0.5214317447 0.7631791998 -0.3257508395 0.198878946097 +1403715403612143104.0000000000 -1.7807014569 0.8718802350 1.4475371445 0.5190277942 0.7609657853 -0.3320593536 0.203169407482 +1403715403662142976.0000000000 -1.7831079490 0.8954979930 1.4494385868 0.5161794277 0.7584526547 -0.3392609908 0.207870991797 +1403715403712143104.0000000000 -1.7844566224 0.9195177529 1.4506018159 0.5118622912 0.7564242184 -0.3480194473 0.211428146202 +1403715403762142976.0000000000 -1.7844189529 0.9440640796 1.4519313539 0.5078255465 0.7535825283 -0.3583242278 0.214080207194 +1403715403812143104.0000000000 -1.7825106652 0.9693785734 1.4536508844 0.5045121973 0.7497920338 -0.3688866803 0.217260134326 +1403715403862142976.0000000000 -1.7786233875 0.9951915870 1.4559628252 0.5017396238 0.7453490806 -0.3790167573 0.221491299395 +1403715403912143104.0000000000 -1.7727550169 1.0212410246 1.4582507478 0.4984575069 0.7410157700 -0.3887448425 0.226524148607 +1403715403962142976.0000000000 -1.7648005572 1.0477876388 1.4608487211 0.4956734755 0.7361806852 -0.3982460610 0.23183157516 +1403715404012143104.0000000000 -1.7550341297 1.0744276239 1.4637361808 0.4929398051 0.7312833916 -0.4065392407 0.238664609035 +1403715404062142976.0000000000 -1.7433779913 1.1009834020 1.4675653104 0.4918386013 0.7250499790 -0.4138689355 0.247204009785 +1403715404112143104.0000000000 -1.7301309033 1.1276184158 1.4714719959 0.4901107238 0.7193315222 -0.4200660639 0.256706333183 +1403715404162142976.0000000000 -1.7153382195 1.1543299456 1.4751887913 0.4876216015 0.7140143793 -0.4242705245 0.269078356555 +1403715404212143104.0000000000 -1.6995568392 1.1812968647 1.4786912486 0.4847202166 0.7090038652 -0.4288197143 0.280131189634 +1403715404262142976.0000000000 -1.6833992433 1.2088540313 1.4816462161 0.4818339684 0.7047513553 -0.4317761921 0.291085681468 +1403715404312143104.0000000000 -1.6669407952 1.2372472038 1.4836337823 0.4781173338 0.7016753361 -0.4343801675 0.300615049316 +1403715404362142976.0000000000 -1.6508278295 1.2666937639 1.4854041030 0.4753106931 0.6989988604 -0.4375926454 0.306582802599 +1403715404412143104.0000000000 -1.6348505304 1.2969820844 1.4867601278 0.4728552983 0.6967348976 -0.4396427394 0.312542174824 +1403715404462142976.0000000000 -1.6190960735 1.3284934519 1.4881332406 0.4721778778 0.6939655204 -0.4416168954 0.316913909277 +1403715404512143104.0000000000 -1.6036235794 1.3610374242 1.4888963759 0.4712876560 0.6920914010 -0.4423859530 0.321235282267 +1403715404562142976.0000000000 -1.5887147454 1.3945949995 1.4890442172 0.4711443021 0.6902955009 -0.4431709559 0.324213929234 +1403715404612143104.0000000000 -1.5747663417 1.4290850499 1.4881744143 0.4718407555 0.6882486203 -0.4443061933 0.325994086933 +1403715404662142976.0000000000 -1.5614207194 1.4649719417 1.4869461616 0.4745744928 0.6853980112 -0.4468752483 0.324516763182 +1403715404712143104.0000000000 -1.5487731246 1.5013671443 1.4852094983 0.4772399333 0.6828351549 -0.4488242368 0.323318730983 +1403715404762142976.0000000000 -1.5366534871 1.5384203432 1.4834545626 0.4810339004 0.6796019499 -0.4513275281 0.321015636261 +1403715404812143104.0000000000 -1.5248912746 1.5754373843 1.4809590028 0.4824737982 0.6774473157 -0.4542210611 0.319323340953 +1403715404862142976.0000000000 -1.5130174871 1.6123061284 1.4780547985 0.4827250200 0.6749149170 -0.4578610742 0.319107578317 +1403715404912143104.0000000000 -1.5013888366 1.6491095359 1.4749020571 0.4833228649 0.6712801560 -0.4618376974 0.320137316974 +1403715404962142976.0000000000 -1.4899304804 1.6855784541 1.4715884959 0.4840063889 0.6664078292 -0.4669609478 0.32184762526 +1403715405012143104.0000000000 -1.4783727419 1.7213708286 1.4681911678 0.4846593535 0.6604110775 -0.4730230594 0.32436353848 +1403715405062142976.0000000000 -1.4671631933 1.7563095688 1.4647384960 0.4844395507 0.6537105340 -0.4805940307 0.327124192206 +1403715405112143104.0000000000 -1.4566662939 1.7903112725 1.4612900173 0.4839111115 0.6459907656 -0.4901048315 0.329124932229 +1403715405162142976.0000000000 -1.4466324078 1.8227712242 1.4573746890 0.4809246381 0.6384941967 -0.5007944479 0.332026466156 +1403715405212143104.0000000000 -1.4370409146 1.8535401046 1.4533314953 0.4766428073 0.6305779417 -0.5123887202 0.335620161843 +1403715405262142976.0000000000 -1.4276803344 1.8828076387 1.4489426849 0.4714336039 0.6222508108 -0.5243229836 0.340058369272 +1403715405312143104.0000000000 -1.4183197879 1.9103049735 1.4443193529 0.4647103194 0.6143238561 -0.5355027047 0.346247559056 +1403715405362142976.0000000000 -1.4089206380 1.9362637939 1.4396490943 0.4572952307 0.6065393519 -0.5463162080 0.352887641443 +1403715405412143104.0000000000 -1.3996806097 1.9605902664 1.4348358745 0.4487831391 0.5992573101 -0.5566758954 0.359994885875 +1403715405462142976.0000000000 -1.3904624305 1.9837400597 1.4301092706 0.4406370502 0.5914448238 -0.5674992403 0.36602817191 +1403715405512143104.0000000000 -1.3811526836 2.0054742742 1.4256828598 0.4328564140 0.5829816487 -0.5779858012 0.372424671249 +1403715405562142976.0000000000 -1.3717846735 2.0259916559 1.4213863915 0.4247804793 0.5744501459 -0.5880877008 0.379106093811 +1403715405612143104.0000000000 -1.3624268757 2.0450505860 1.4168449992 0.4150096619 0.5671053511 -0.5968212609 0.387250414733 +1403715405662142976.0000000000 -1.3527880711 2.0631942053 1.4119358515 0.4037271346 0.5610041159 -0.6050637730 0.395191869017 +1403715405712143104.0000000000 -1.3426648026 2.0809374737 1.4072110167 0.3932656328 0.5545699636 -0.6132852649 0.402088897333 +1403715405762142976.0000000000 -1.3318886837 2.0982476123 1.4027098649 0.3831915780 0.5479133095 -0.6210265178 0.409000347343 +1403715405812143104.0000000000 -1.3207887061 2.1154053063 1.3979856566 0.3735872389 0.5408570733 -0.6295876847 0.414156429975 +1403715405862142976.0000000000 -1.3087653470 2.1322781831 1.3933602976 0.3643219755 0.5334590901 -0.6377999395 0.419406884183 +1403715405912143104.0000000000 -1.2959767564 2.1491866563 1.3887289232 0.3575761177 0.5235893770 -0.6461943265 0.424766261333 +1403715405962142976.0000000000 -1.2819291337 2.1657831640 1.3840779730 0.3523154837 0.5124058929 -0.6535432758 0.4315034037 +1403715406012143104.0000000000 -1.2667106050 2.1819302566 1.3795073876 0.3473474016 0.5004894801 -0.6598036034 0.439908249261 +1403715406062142976.0000000000 -1.2509337401 2.1980837936 1.3744601562 0.3427340528 0.4878316317 -0.6665898827 0.447450104972 +1403715406112143104.0000000000 -1.2348652874 2.2137265987 1.3685048780 0.3369727575 0.4760961897 -0.6730068878 0.454800514236 +1403715406162142976.0000000000 -1.2187167764 2.2293123929 1.3616273984 0.3313302594 0.4641268770 -0.6799458487 0.460955685579 +1403715406212143104.0000000000 -1.2023972513 2.2445752701 1.3542688444 0.3256350452 0.4521651153 -0.6870338000 0.466361537364 +1403715406262142976.0000000000 -1.1862514055 2.2595833777 1.3461741299 0.3188258633 0.4411246210 -0.6939332920 0.471397628119 +1403715406312143104.0000000000 -1.1699784742 2.2744329862 1.3378204111 0.3121802852 0.4301955695 -0.7010213998 0.475441098974 +1403715406362142976.0000000000 -1.1539754676 2.2892645005 1.3290453586 0.3062501373 0.4190075183 -0.7090039982 0.477448304592 +1403715406412143104.0000000000 -1.1377697849 2.3033745865 1.3198896307 0.2998892333 0.4081702432 -0.7168932627 0.479090336184 +1403715406462142976.0000000000 -1.1212924746 2.3167867650 1.3105729106 0.2950195427 0.3962970787 -0.7250698916 0.479776767973 +1403715406512143104.0000000000 -1.1049315483 2.3294810042 1.3008096067 0.2886158743 0.3856416700 -0.7324337496 0.48116751961 +1403715406562142976.0000000000 -1.0885453566 2.3414005425 1.2906834127 0.2826396688 0.3746469678 -0.7394986889 0.482593158136 +1403715406612143104.0000000000 -1.0723899957 2.3521726852 1.2805699312 0.2766596556 0.3638185109 -0.7455675477 0.484999544136 +1403715406662142976.0000000000 -1.0563496953 2.3616284210 1.2707544641 0.2704656756 0.3532623294 -0.7509215032 0.488027602724 +1403715406712143104.0000000000 -1.0403226519 2.3695651495 1.2606537365 0.2641921695 0.3430336407 -0.7557333171 0.49132226933 +1403715406762142976.0000000000 -1.0242705791 2.3759042218 1.2500575571 0.2566627749 0.3333937173 -0.7595249304 0.49607935794 +1403715406812143104.0000000000 -1.0085133378 2.3811250245 1.2396474207 0.2492798840 0.3234802351 -0.7631111820 0.500880625419 +1403715406862142976.0000000000 -0.9928785486 2.3851705190 1.2295563891 0.2413356467 0.3138602095 -0.7665923715 0.505554161755 +1403715406912143104.0000000000 -0.9773135251 2.3883649928 1.2198448284 0.2331979812 0.3045184027 -0.7701895287 0.509603114101 +1403715406962142976.0000000000 -0.9618405784 2.3906730049 1.2108253615 0.2250823842 0.2950147888 -0.7733783933 0.513994217319 +1403715407012143104.0000000000 -0.9463219125 2.3923154165 1.2023559817 0.2175953230 0.2854681984 -0.7771514883 0.516909805835 +1403715407062142976.0000000000 -0.9305398356 2.3929280321 1.1944075220 0.2107409192 0.2755154249 -0.7814407267 0.518680929156 +1403715407112143104.0000000000 -0.9150855398 2.3927588108 1.1864099211 0.2036744771 0.2658250947 -0.7859345830 0.519769715909 +1403715407162142976.0000000000 -0.8998023799 2.3920750092 1.1783119987 0.1967276525 0.2569916155 -0.7906320197 0.519763936503 +1403715407212143104.0000000000 -0.8847427589 2.3911004712 1.1703862373 0.1895180876 0.2503653855 -0.7959330885 0.51758147854 +1403715407262142976.0000000000 -0.8692874016 2.3890434187 1.1631482926 0.1831747050 0.2448806915 -0.8010783923 0.514542402252 +1403715407312143104.0000000000 -0.8534088133 2.3860340077 1.1559163161 0.1765868309 0.2416016923 -0.8056182022 0.511297394589 +1403715407362142976.0000000000 -0.8365478393 2.3814234006 1.1500643207 0.1717240217 0.2385273510 -0.8088389203 0.509308515738 +1403715407412143104.0000000000 -0.8186419355 2.3748080440 1.1450461432 0.1680043462 0.2361396177 -0.8105581638 0.508928367954 +1403715407462142976.0000000000 -0.7994624749 2.3662582101 1.1411835370 0.1661907587 0.2336098670 -0.8105006266 0.510779596333 +1403715407512143104.0000000000 -0.7795729841 2.3557440792 1.1379961474 0.1637497159 0.2322772286 -0.8101447184 0.512736633087 +1403715407562142976.0000000000 -0.7584754720 2.3438300643 1.1356086187 0.1635709383 0.2301025063 -0.8094574886 0.514855279514 +1403715407612143104.0000000000 -0.7366839928 2.3306276958 1.1340843510 0.1626712467 0.2292095819 -0.8079071062 0.517964420471 +1403715407662142976.0000000000 -0.7142272660 2.3161673618 1.1335062565 0.1605134502 0.2299617666 -0.8055344356 0.521983995141 +1403715407712143104.0000000000 -0.6909824492 2.3007873584 1.1337042782 0.1572702609 0.2324489760 -0.8017317869 0.527692789928 +1403715407762142976.0000000000 -0.6666819203 2.2848030550 1.1348279959 0.1546384458 0.2350371913 -0.7985686495 0.532102040801 +1403715407812143104.0000000000 -0.6415585724 2.2685890336 1.1362060514 0.1529512686 0.2373387871 -0.7964776831 0.534695717033 +1403715407862142976.0000000000 -0.6155146785 2.2523334604 1.1374478245 0.1521148347 0.2389944266 -0.7946952177 0.536844718835 +1403715407912143104.0000000000 -0.5880858288 2.2361996962 1.1390549811 0.1542449156 0.2386215548 -0.7938254661 0.537688933223 +1403715407962142976.0000000000 -0.5599619700 2.2201038021 1.1418760488 0.1553035966 0.2389282444 -0.7935791305 0.537611616782 +1403715408012143104.0000000000 -0.5308233455 2.2039311703 1.1473008981 0.1588218836 0.2369586167 -0.7931801494 0.538044118857 +1403715408062142976.0000000000 -0.5014536586 2.1880287049 1.1548441390 0.1605376709 0.2364259396 -0.7933452827 0.537525528452 +1403715408112143104.0000000000 -0.4715837403 2.1721598049 1.1659074442 0.1627954845 0.2354709610 -0.7930860545 0.537648181324 +1403715408162142976.0000000000 -0.4414604509 2.1559125190 1.1804478555 0.1651796153 0.2347683492 -0.7927289060 0.537754961445 +1403715408212143104.0000000000 -0.4110669100 2.1393369667 1.1977878112 0.1675997868 0.2339732883 -0.7919767506 0.538460433364 +1403715408262142976.0000000000 -0.3806408945 2.1224350714 1.2155810381 0.1687011233 0.2339344825 -0.7915339016 0.538784438787 +1403715408312143104.0000000000 -0.3501048496 2.1055400269 1.2326685533 0.1704019743 0.2335222160 -0.7914276362 0.53858410535 +1403715408362142976.0000000000 -0.3192449210 2.0883561452 1.2477770775 0.1717680617 0.2331952013 -0.7908410610 0.539153176141 +1403715408412143104.0000000000 -0.2879986915 2.0709969437 1.2603137701 0.1742583945 0.2332101581 -0.7890769123 0.540929441429 +1403715408462142976.0000000000 -0.2567970035 2.0540324797 1.2691729477 0.1767623812 0.2346137046 -0.7863184642 0.543520692325 +1403715408512143104.0000000000 -0.2255866784 2.0374866038 1.2747073893 0.1814456514 0.2366441625 -0.7825739322 0.54649341861 +1403715408562142976.0000000000 -0.1947341740 2.0216174326 1.2763811889 0.1857446969 0.2407451882 -0.7785839817 0.548951405231 +1403715408612143104.0000000000 -0.1640507901 2.0062929124 1.2753004154 0.1918131054 0.2451267607 -0.7735827897 0.551987564391 +1403715408662142976.0000000000 -0.1340263023 1.9916397897 1.2719840877 0.1965326904 0.2521528006 -0.7680629906 0.55486314459 +1403715408712143104.0000000000 -0.1049708063 1.9783331871 1.2683009959 0.2028141240 0.2595073944 -0.7628808012 0.55635890083 +1403715408762142976.0000000000 -0.0769997058 1.9664747200 1.2647013474 0.2101673350 0.2676409715 -0.7581481892 0.556245741406 +1403715408812143104.0000000000 -0.0500440980 1.9556827049 1.2617259023 0.2173937971 0.2770742859 -0.7531808386 0.555597337555 +1403715408862142976.0000000000 -0.0239577494 1.9463472445 1.2593717845 0.2254826943 0.2868899183 -0.7490347993 0.552990595549 +1403715408912143104.0000000000 0.0008748077 1.9382513103 1.2578263019 0.2338488966 0.2974314735 -0.7446243997 0.549894276628 +1403715408962142976.0000000000 0.0247051509 1.9316273974 1.2568228420 0.2417313030 0.3088840821 -0.7399664987 0.54644869999 +1403715409012143104.0000000000 0.0473521824 1.9260319852 1.2567905255 0.2507677505 0.3200376646 -0.7346627441 0.543104116183 +1403715409062142976.0000000000 0.0686369147 1.9216600040 1.2575809061 0.2590929988 0.3318039168 -0.7295125093 0.539062591567 +1403715409112143104.0000000000 0.0885127788 1.9183908244 1.2600715544 0.2690210208 0.3421588206 -0.7246850380 0.534215899675 +1403715409162142976.0000000000 0.1067315320 1.9156255121 1.2630962188 0.2790177623 0.3507853325 -0.7205450959 0.529068524435 +1403715409212143104.0000000000 0.1232636967 1.9132291628 1.2667494125 0.2868950927 0.3591542481 -0.7173015639 0.523619994124 +1403715409262142976.0000000000 0.1382895893 1.9110474668 1.2710677215 0.2925401038 0.3665455568 -0.7154486966 0.517878175825 +1403715409312143104.0000000000 0.1520842033 1.9089848585 1.2767326871 0.2980294303 0.3723000939 -0.7135644648 0.513222031178 +1403715409362142976.0000000000 0.1646129924 1.9067292220 1.2832822037 0.3021227593 0.3772696764 -0.7114857158 0.510075980472 +1403715409412143104.0000000000 0.1756161137 1.9041394931 1.2905551588 0.3046418559 0.3814997883 -0.7093738766 0.508369899165 +1403715409462142976.0000000000 0.1851823529 1.9013747986 1.2985342481 0.3055660373 0.3854828077 -0.7068061591 0.508387111632 +1403715409512143104.0000000000 0.1936027573 1.8985124227 1.3072877913 0.3047291470 0.3891143995 -0.7038867205 0.510170183139 +1403715409562142976.0000000000 0.2006736727 1.8954973395 1.3159924859 0.3007756979 0.3922533296 -0.7029803391 0.511360878161 +1403715409612143104.0000000000 0.2069576729 1.8929866389 1.3251183722 0.2979796575 0.3926633218 -0.7054710842 0.509248651306 +1403715409662142976.0000000000 0.2126145014 1.8911226404 1.3346489850 0.2955473496 0.3924918820 -0.7084060017 0.506717696105 +1403715409712143104.0000000000 0.2176219723 1.8894841811 1.3442605115 0.2927823527 0.3922199229 -0.7124980110 0.50278087715 +1403715409762142976.0000000000 0.2221825243 1.8878792138 1.3541150746 0.2893347568 0.3919870051 -0.7167620926 0.498882440074 +1403715409812143104.0000000000 0.2268216498 1.8862052919 1.3642298356 0.2856621125 0.3917924255 -0.7210268613 0.494991028195 +1403715409862142976.0000000000 0.2316667301 1.8844315010 1.3749921666 0.2819920317 0.3910814945 -0.7248455783 0.492071789918 +1403715409912143104.0000000000 0.2369696182 1.8825517360 1.3856466855 0.2783161676 0.3901900415 -0.7295318466 0.487929428495 +1403715409962142976.0000000000 0.2430024606 1.8801793818 1.3963186049 0.2744888783 0.3897016384 -0.7331329471 0.485082024572 +1403715410012143104.0000000000 0.2500526230 1.8772102515 1.4072446616 0.2718894697 0.3881933639 -0.7363772349 0.482835993292 +1403715410062142976.0000000000 0.2583681939 1.8735165205 1.4185095738 0.2701421250 0.3865025252 -0.7381356684 0.482488098593 +1403715410112143104.0000000000 0.2681548504 1.8687647272 1.4302637096 0.2694150879 0.3841501836 -0.7379509637 0.485048989383 +1403715410162142976.0000000000 0.2789932577 1.8631461229 1.4416215175 0.2693496602 0.3819413385 -0.7359519370 0.489843159555 +1403715410212143104.0000000000 0.2904734989 1.8571594291 1.4508234962 0.2703482089 0.3793615424 -0.7341286749 0.494015945844 +1403715410262142976.0000000000 0.3024472036 1.8510996312 1.4567017874 0.2712612532 0.3770375956 -0.7322198154 0.498110556009 +1403715410312143104.0000000000 0.3149752715 1.8450592266 1.4591599209 0.2717817890 0.3753148230 -0.7305742820 0.501532313307 +1403715410362142976.0000000000 0.3277874629 1.8394953214 1.4586513644 0.2722690828 0.3742166184 -0.7292332657 0.504034039761 +1403715410412143104.0000000000 0.3410026686 1.8340039462 1.4565680908 0.2715578802 0.3741617254 -0.7282328160 0.505901459393 +1403715410462142976.0000000000 0.3539894092 1.8288038652 1.4534691318 0.2698727050 0.3752074508 -0.7273744055 0.507261832004 +1403715410512143104.0000000000 0.3668917180 1.8238851120 1.4501434808 0.2669178740 0.3773645670 -0.7262924807 0.508773097394 +1403715410562142976.0000000000 0.3802281358 1.8194815358 1.4473569864 0.2647798336 0.3792008701 -0.7247845572 0.510671798258 +1403715410612143104.0000000000 0.3941972600 1.8159213830 1.4444127834 0.2636979331 0.3808942215 -0.7241464865 0.5108765587 +1403715410662142976.0000000000 0.4087628765 1.8129765191 1.4417701310 0.2635922470 0.3819270320 -0.7231870644 0.511518659884 +1403715410712143104.0000000000 0.4238131132 1.8107619882 1.4393482083 0.2652909681 0.3818588613 -0.7227260845 0.511342858543 +1403715410762142976.0000000000 0.4393151544 1.8089101185 1.4377227486 0.2686960982 0.3808994778 -0.7205002735 0.513417325885 +1403715410812143104.0000000000 0.4550400192 1.8077021839 1.4368872491 0.2743134055 0.3783604483 -0.7170477549 0.517144122937 +1403715410862142976.0000000000 0.4702235594 1.8071388428 1.4356040490 0.2781559925 0.3773971491 -0.7131800343 0.521128462441 +1403715410912143104.0000000000 0.4846270504 1.8077679373 1.4337934258 0.2827600053 0.3762447926 -0.7110926073 0.522335083347 +1403715410962142976.0000000000 0.4979211664 1.8094172435 1.4308289349 0.2837862584 0.3777119042 -0.7103010416 0.521796423155 +1403715411012143104.0000000000 0.5103510538 1.8124163199 1.4272149669 0.2851969150 0.3794367144 -0.7114846863 0.518150596386 +1403715411062142976.0000000000 0.5217910335 1.8163293706 1.4232359228 0.2861647040 0.3814746167 -0.7127816241 0.5143240568 +1403715411112143104.0000000000 0.5325733954 1.8207879149 1.4192129227 0.2865939438 0.3838776686 -0.7142631108 0.510225494819 +1403715411162142976.0000000000 0.5433079953 1.8255895591 1.4156986961 0.2885387248 0.3849725781 -0.7158310521 0.506090331114 +1403715411212143104.0000000000 0.5536737901 1.8303923436 1.4130723729 0.2917890030 0.3846806369 -0.7172629324 0.502408072281 +1403715411262142976.0000000000 0.5636522992 1.8351748865 1.4108979341 0.2948347278 0.3845318169 -0.7180186943 0.499656801945 +1403715411312143104.0000000000 0.5730153287 1.8396911857 1.4090697965 0.2982124125 0.3836907738 -0.7176202902 0.498870590642 +1403715411362142976.0000000000 0.5817954390 1.8440075112 1.4074446206 0.3019281687 0.3824799529 -0.7160489060 0.499822399223 +1403715411412143104.0000000000 0.5898022661 1.8479658426 1.4057223952 0.3063702192 0.3806304542 -0.7141046370 0.501310595795 +1403715411462142976.0000000000 0.5969898417 1.8515234550 1.4038470386 0.3104871750 0.3788747018 -0.7117083468 0.503510579395 +1403715411512143104.0000000000 0.6027178975 1.8548269590 1.4012888654 0.3118771225 0.3790688170 -0.7098306269 0.505153415784 +1403715411562142976.0000000000 0.6069430029 1.8581565362 1.3979568889 0.3110058371 0.3811668781 -0.7094836879 0.504598926787 +1403715411612143104.0000000000 0.6098651269 1.8613026031 1.3946503606 0.3089429712 0.3838422107 -0.7096093214 0.503660608792 +1403715411662142976.0000000000 0.6117879488 1.8643856705 1.3914059374 0.3065409345 0.3868552704 -0.7101537254 0.502053126199 +1403715411712143104.0000000000 0.6129774648 1.8672795483 1.3885485978 0.3048999954 0.3891795771 -0.7103000280 0.501048021471 +1403715411762142976.0000000000 0.6135868542 1.8700332361 1.3858119590 0.3034449517 0.3913365380 -0.7102615857 0.500305261919 +1403715411812143104.0000000000 0.6135216088 1.8727297855 1.3829614326 0.3027819365 0.3925772611 -0.7096120915 0.500656441631 +1403715411862142976.0000000000 0.6127982714 1.8758128705 1.3795283090 0.3023676115 0.3937071375 -0.7095784937 0.500066874163 +1403715411912143104.0000000000 0.6115027473 1.8790041994 1.3763526997 0.3024717264 0.3941527887 -0.7094093525 0.499892793016 +1403715411962142976.0000000000 0.6095972744 1.8823942057 1.3734970027 0.3034086189 0.3940014736 -0.7095353793 0.499265054249 +1403715412012143104.0000000000 0.6073088199 1.8856997092 1.3705784841 0.3036727713 0.3941358457 -0.7097511095 0.498691433391 +1403715412062142976.0000000000 0.6046000115 1.8889965710 1.3675732937 0.3038725196 0.3940898103 -0.7102589024 0.497882521082 +1403715412112143104.0000000000 0.6013911384 1.8923550799 1.3649368681 0.3040073534 0.3940221617 -0.7105803463 0.497394849787 +1403715412162142976.0000000000 0.5976983525 1.8955989976 1.3621155160 0.3026398421 0.3947703589 -0.7114302070 0.496419731947 +1403715412212143104.0000000000 0.5937722942 1.8990286271 1.3592942791 0.3018765094 0.3952718119 -0.7120416321 0.495608193949 +1403715412262142976.0000000000 0.5895470618 1.9024464303 1.3562297787 0.3009732310 0.3957556233 -0.7123558640 0.495319819821 +1403715412312143104.0000000000 0.5849795262 1.9058551037 1.3530869529 0.3002867207 0.3961017409 -0.7127660899 0.494869474955 +1403715412362142976.0000000000 0.5803041485 1.9091474506 1.3500624270 0.2997072574 0.3962030053 -0.7133771740 0.494258784497 +1403715412412143104.0000000000 0.5754436270 1.9125235978 1.3471927430 0.2993291097 0.3962304043 -0.7139312950 0.493665531338 +1403715412462142976.0000000000 0.5703798507 1.9160200565 1.3444620161 0.2988967445 0.3962379831 -0.7151832039 0.492106880351 +1403715412512143104.0000000000 0.5651857155 1.9195025475 1.3418273908 0.2981737878 0.3965087847 -0.7161758495 0.49088219419 +1403715412562142976.0000000000 0.5601269323 1.9228373894 1.3390790118 0.2975888992 0.3968034025 -0.7170969238 0.489652845152 +1403715412612143104.0000000000 0.5552888997 1.9259584547 1.3365925119 0.2962848574 0.3975068799 -0.7173895819 0.489444329291 +1403715412662142976.0000000000 0.5508612002 1.9289113173 1.3344441562 0.2957638362 0.3978877424 -0.7177128389 0.488975846615 +1403715412712143104.0000000000 0.5464020062 1.9316358144 1.3323347088 0.2942986687 0.3989975128 -0.7184371769 0.48789066521 +1403715412762142976.0000000000 0.5423947332 1.9340286078 1.3308765663 0.2933781159 0.3995489677 -0.7188200027 0.487429694641 +1403715412812143104.0000000000 0.5385619216 1.9364200639 1.3295420457 0.2925182125 0.4000365361 -0.7192747478 0.486875448526 +1403715412862142976.0000000000 0.5351625107 1.9386432657 1.3285760771 0.2919977576 0.4004976380 -0.7196071549 0.486317277233 +1403715412912143104.0000000000 0.5323573316 1.9406089576 1.3279597499 0.2915174204 0.4006636735 -0.7196148971 0.486457207009 +1403715412962142976.0000000000 0.5301462769 1.9423243859 1.3278172035 0.2917112567 0.4001537278 -0.7192977154 0.487229241212 +1403715413012143104.0000000000 0.5283720926 1.9438800365 1.3272051291 0.2921639685 0.3994643555 -0.7181871746 0.489158079209 +1403715413062142976.0000000000 0.5268164848 1.9455574423 1.3240154850 0.2919195685 0.3991577733 -0.7173253191 0.490816079748 +1403715413112143104.0000000000 0.5256603842 1.9473680938 1.3183467607 0.2919806970 0.3988963605 -0.7165672356 0.492097920159 +1403715413162142976.0000000000 0.5249157317 1.9492780884 1.3106204215 0.2924351484 0.3982737663 -0.7158991290 0.493303282156 +1403715413212143104.0000000000 0.5242662174 1.9513056885 1.3001728178 0.2923810607 0.3982189900 -0.7151274147 0.494497454097 +1403715413262142976.0000000000 0.5236180498 1.9536794313 1.2875640631 0.2932957215 0.3974924573 -0.7148289479 0.494971657103 +1403715413312143104.0000000000 0.5229380678 1.9564228005 1.2728812736 0.2956233151 0.3956016373 -0.7152085453 0.494553269956 +1403715413362142976.0000000000 0.5222392452 1.9594329619 1.2571152563 0.2990344018 0.3931718946 -0.7158275015 0.493543590702 +1403715413412143104.0000000000 0.5214231668 1.9621888714 1.2417790820 0.3020550154 0.3908604603 -0.7165594305 0.492476853049 +1403715413462142976.0000000000 0.5203573451 1.9646352150 1.2273892787 0.3044912712 0.3889976103 -0.7172671952 0.491420080613 +1403715413512143104.0000000000 0.5188069052 1.9665284064 1.2141114188 0.3059270323 0.3879964756 -0.7174039316 0.491120132647 +1403715413562142976.0000000000 0.5166493930 1.9677551096 1.2020003500 0.3054709093 0.3881750446 -0.7172511009 0.491486028824 +1403715413612143104.0000000000 0.5138469757 1.9684447045 1.1912935273 0.3043283370 0.3886790616 -0.7166212775 0.492713704846 +1403715413662142976.0000000000 0.5105668705 1.9684626401 1.1819123863 0.3028368965 0.3896057887 -0.7154243870 0.494636321047 +1403715413712143104.0000000000 0.5068645014 1.9682938624 1.1734368315 0.3008119591 0.3909187936 -0.7140069166 0.496879044766 +1403715413762142976.0000000000 0.5028913930 1.9681958908 1.1644660691 0.2985719047 0.3922028428 -0.7135592944 0.497860302932 +1403715413812143104.0000000000 0.4986465741 1.9682967814 1.1540245512 0.2969266788 0.3932082763 -0.7136557853 0.497912862924 +1403715413862142976.0000000000 0.4945103119 1.9685922349 1.1422642390 0.2952808914 0.3941554484 -0.7138164195 0.497912439083 +1403715413912143104.0000000000 0.4904572063 1.9690755556 1.1297759752 0.2946861491 0.3945389617 -0.7132913063 0.498712937095 +1403715413962142976.0000000000 0.4862172150 1.9698391189 1.1169518476 0.2937964666 0.3953350973 -0.7121514497 0.500234054966 +1403715414012143104.0000000000 0.4816715164 1.9711347427 1.1058128472 0.2930746968 0.3956933466 -0.7119052611 0.500724372144 +1403715414062142976.0000000000 0.4768775980 1.9732854358 1.0976007126 0.2929297689 0.3959033085 -0.7123438300 0.500018988318 +1403715414112143104.0000000000 0.4718420377 1.9760094124 1.0922042405 0.2915780395 0.3967031475 -0.7135815352 0.498407716821 +1403715414162142976.0000000000 0.4667447630 1.9793666780 1.0897786403 0.2899221470 0.3977857416 -0.7159855327 0.495051885563 +1403715414212143104.0000000000 0.4618644489 1.9831176544 1.0895448348 0.2872064297 0.3993134268 -0.7194122345 0.490415426777 +1403715414262142976.0000000000 0.4577329017 1.9872479875 1.0920365238 0.2848895095 0.4007610454 -0.7223112205 0.486307569928 +1403715414312143104.0000000000 0.4547168625 1.9912206973 1.0960830101 0.2825222777 0.4021663147 -0.7251849010 0.482234670325 +1403715414362142976.0000000000 0.4530158661 1.9946819071 1.1002761176 0.2798088097 0.4037495940 -0.7269347321 0.479853301038 +1403715414412143104.0000000000 0.4528224828 1.9977631512 1.1042218586 0.2786297388 0.4044900508 -0.7271247623 0.479627821837 +1403715414462142976.0000000000 0.4540385377 2.0005958406 1.1067948901 0.2783062729 0.4046157518 -0.7266101339 0.480488735661 +1403715414512143104.0000000000 0.4566343987 2.0033857863 1.1079384010 0.2784365015 0.4044051455 -0.7254088711 0.482401868387 +1403715414562142976.0000000000 0.4605147716 2.0061880928 1.1072730966 0.2796810135 0.4034112126 -0.7233536102 0.485589825776 +1403715414612143104.0000000000 0.4654727621 2.0092009159 1.1049850222 0.2810276902 0.4023279786 -0.7208982870 0.489347826024 +1403715414662142976.0000000000 0.4713002591 2.0126897160 1.1017079021 0.2834560119 0.4003132106 -0.7197077081 0.491347980136 +1403715414712143104.0000000000 0.4778226687 2.0168425987 1.0975400454 0.2865275150 0.3975529045 -0.7186554913 0.493343649078 +1403715414762142976.0000000000 0.4846578142 2.0215200985 1.0924724664 0.2902182714 0.3943796428 -0.7184593546 0.494018428903 +1403715414812143104.0000000000 0.4914310779 2.0264212360 1.0864482031 0.2938757651 0.3909299704 -0.7195414189 0.493022250371 +1403715414862142976.0000000000 0.4985117387 2.0311758170 1.0796874398 0.2985075580 0.3865880746 -0.7211786336 0.491268029638 +1403715414912143104.0000000000 0.5054069582 2.0355755776 1.0715734541 0.3036304668 0.3817309888 -0.7228651592 0.489444535532 +1403715414962142976.0000000000 0.5118002783 2.0393627583 1.0625976460 0.3075354102 0.3777605928 -0.7245505330 0.487591459311 +1403715415012143104.0000000000 0.5173447284 2.0424472619 1.0532879668 0.3110871797 0.3737588323 -0.7260212357 0.486232729448 +1403715415062142976.0000000000 0.5223178240 2.0446657005 1.0434179602 0.3133619281 0.3706469832 -0.7272331578 0.48534219893 +1403715415112143104.0000000000 0.5267189811 2.0458184271 1.0332878925 0.3143779984 0.3682399100 -0.7282412567 0.485005685365 +1403715415162142976.0000000000 0.5300422295 2.0458656774 1.0231125468 0.3148042214 0.3661539662 -0.7291867471 0.484887887104 +1403715415212143104.0000000000 0.5321707063 2.0447983411 1.0134836070 0.3141966956 0.3647270465 -0.7292321519 0.486287041486 +1403715415262142976.0000000000 0.5333768485 2.0427586481 1.0042834820 0.3127875902 0.3642148340 -0.7293268479 0.487435972231 +1403715415312143104.0000000000 0.5333763291 2.0392948014 0.9954380471 0.3065814297 0.3672060986 -0.7273757181 0.49202852851 +1403715415362142976.0000000000 0.5327483903 2.0350060818 0.9873067336 0.2996426286 0.3705015027 -0.7259836644 0.495873623732 +1403715415412143104.0000000000 0.5316831480 2.0302876634 0.9807543456 0.2926171692 0.3735435336 -0.7237397808 0.501040068802 +1403715415462142976.0000000000 0.5300439912 2.0257452794 0.9749540136 0.2846665301 0.3775014301 -0.7227202819 0.504116088888 +1403715415512143104.0000000000 0.5285682186 2.0214784833 0.9712587319 0.2794841610 0.3796833854 -0.7208476242 0.508043141168 +1403715415562142976.0000000000 0.5274023497 2.0182751631 0.9681011542 0.2764138096 0.3808849741 -0.7202047293 0.509732469395 +1403715415612143104.0000000000 0.5265256981 2.0160780580 0.9641677479 0.2743778309 0.3812588302 -0.7190502537 0.512176964535 +1403715415662142976.0000000000 0.5254865550 2.0148589499 0.9577913822 0.2724128440 0.3812541016 -0.7186800233 0.513746607411 +1403715415712143104.0000000000 0.5245165887 2.0148289702 0.9487288218 0.2713550881 0.3809930379 -0.7191811044 0.513798852016 +1403715415762142976.0000000000 0.5242727909 2.0146151333 0.9453703764 0.2715901522 0.3807285870 -0.7204971350 0.512023838069 +1403715415812143104.0000000000 0.5246510620 2.0150587346 0.9487191653 0.2707007597 0.3813133584 -0.7198641601 0.512949132424 +1403715415862142976.0000000000 0.5252955389 2.0163279523 0.9509710448 0.2712250828 0.3807810469 -0.7186913284 0.514709163777 +1403715415912143104.0000000000 0.5264462951 2.0186095118 0.9510148843 0.2727038113 0.3791030233 -0.7181647913 0.515900049924 +1403715415962142976.0000000000 0.5273645500 2.0215402148 0.9487328066 0.2724802277 0.3795221778 -0.7180104446 0.515924842856 +1403715416012143104.0000000000 0.5272233726 2.0222267477 0.9474736977 0.2705304774 0.3817616860 -0.7188184419 0.514170519814 +1403715416062142976.0000000000 0.5267286198 2.0212520233 0.9483548397 0.2692738791 0.3819410032 -0.7185748524 0.51503672639 +1403715416112143104.0000000000 0.5269698869 2.0211138873 0.9488795886 0.2692745280 0.3812863858 -0.7185835564 0.515509062029 +1403715416162142976.0000000000 0.5272818628 2.0212567508 0.9483904664 0.2697309223 0.3808080050 -0.7186333827 0.515554608395 +1403715416212143104.0000000000 0.5273077693 2.0211815680 0.9482115313 0.2697424837 0.3806398585 -0.7197577915 0.514102141846 +1403715416262142976.0000000000 0.5273668694 2.0217480293 0.9476142200 0.2697842053 0.3807907052 -0.7205643156 0.512837194936 +1403715416312143104.0000000000 0.5273099856 2.0220219192 0.9472206386 0.2699363336 0.3806263596 -0.7208375086 0.512495108657 +1403715416362142976.0000000000 0.5273626687 2.0216077792 0.9470429243 0.2696028408 0.3808568745 -0.7211739108 0.51202591706 +1403715416412143104.0000000000 0.5275022179 2.0211325008 0.9471109196 0.2696372532 0.3807659062 -0.7213979522 0.51175977847 +1403715416462142976.0000000000 0.5275374594 2.0210804288 0.9468618258 0.2694459854 0.3809336884 -0.7217388328 0.511254773273 +1403715416512143104.0000000000 0.5275770624 2.0214474180 0.9465042863 0.2695695698 0.3805866893 -0.7218249848 0.511326422341 +1403715416562142976.0000000000 0.5274688140 2.0214393837 0.9463934198 0.2697013609 0.3805305185 -0.7214512795 0.511825899817 +1403715416612143104.0000000000 0.5274573042 2.0211044519 0.9462235447 0.2695432980 0.3806511240 -0.7217513149 0.511396296176 +1403715416662142976.0000000000 0.5275025711 2.0210106552 0.9460909176 0.2698111899 0.3804066858 -0.7220285551 0.511045439096 +1403715416712143104.0000000000 0.5273614946 2.0211768309 0.9458537990 0.2697685887 0.3804137361 -0.7220598731 0.511018431703 +1403715416762142976.0000000000 0.5271586706 2.0214257873 0.9456811878 0.2698069875 0.3803811413 -0.7221544604 0.510888747325 +1403715416812143104.0000000000 0.5270655692 2.0215036215 0.9455757041 0.2699785692 0.3801735262 -0.7219549726 0.511234466528 +1403715416862142976.0000000000 0.5271435976 2.0214481397 0.9454783133 0.2698758882 0.3802942091 -0.7222236764 0.510819225108 +1403715416912143104.0000000000 0.5271555661 2.0213197982 0.9454149938 0.2697849385 0.3803010413 -0.7225127167 0.510453307528 +1403715416962142976.0000000000 0.5270604563 2.0214778241 0.9453871143 0.2698271877 0.3802714500 -0.7223202277 0.510725368213 +1403715417012143104.0000000000 0.5270185473 2.0217299911 0.9452934415 0.2700842411 0.3800413693 -0.7222548041 0.510853264923 +1403715417062142976.0000000000 0.5270373219 2.0216813812 0.9452118491 0.2699562374 0.3801242302 -0.7222586118 0.5108538902 +1403715417112143104.0000000000 0.5271682508 2.0215084103 0.9451720228 0.2699660895 0.3800864368 -0.7225280482 0.510495671548 +1403715417162142976.0000000000 0.5272086715 2.0214253048 0.9451771189 0.2699822821 0.3800261958 -0.7226082471 0.510418435279 +1403715417212143104.0000000000 0.5271885330 2.0215744685 0.9451798559 0.2700997492 0.3799307614 -0.7225078788 0.51056939501 +1403715417262142976.0000000000 0.5271891524 2.0217650296 0.9451628655 0.2701314232 0.3799292995 -0.7225383284 0.510510632233 +1403715417312143104.0000000000 0.5272027578 2.0218203766 0.9452016001 0.2701862748 0.3798215169 -0.7225169448 0.510592064763 +1403715417362142976.0000000000 0.5272653967 2.0217665499 0.9451859700 0.2701770297 0.3798915423 -0.7226683748 0.510330489782 +1403715417412143104.0000000000 0.5272837587 2.0217508456 0.9451710902 0.2701594561 0.3798261654 -0.7227575959 0.510262099192 +1403715417462142976.0000000000 0.5272102105 2.0219064128 0.9451294787 0.2702562423 0.3797645936 -0.7227364538 0.510286620771 +1403715417512143104.0000000000 0.5270933448 2.0220061532 0.9450763465 0.2703463492 0.3797277474 -0.7226964077 0.510323026792 +1403715417562142976.0000000000 0.5270295697 2.0218879889 0.9450605417 0.2703151867 0.3796735169 -0.7227378147 0.510321243536 +1403715417612143104.0000000000 0.5269915325 2.0217135259 0.9450268009 0.2702935601 0.3796591926 -0.7228483250 0.510186816734 +1403715417662142976.0000000000 0.5269400037 2.0216377121 0.9449850977 0.2702581815 0.3796865625 -0.7228909590 0.510124779799 +1403715417712143104.0000000000 0.5269172696 2.0216197157 0.9450235034 0.2703605118 0.3796028279 -0.7228665374 0.510167478151 +1403715417762142976.0000000000 0.5269290501 2.0215745393 0.9450942475 0.2703804029 0.3795952194 -0.7228192478 0.510229597566 +1403715417812143104.0000000000 0.5270096472 2.0214076633 0.9451792752 0.2703311448 0.3795785990 -0.7229010420 0.510152176171 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_02_medium.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_02_medium.txt new file mode 100644 index 0000000000000000000000000000000000000000..aa815c0910bb007c580f03ea86ff7f4839492eaa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_02_medium.txt @@ -0,0 +1,1672 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403715524912143104.0000000000 0.5493701398 2.0509640750 0.9455930356 0.2656202293 0.4116597639 -0.7031751512 0.515292964635 +1403715524962142976.0000000000 0.5491333966 2.0503565652 0.9453359435 0.2656659227 0.4115273888 -0.7032155778 0.51531997529 +1403715525012143104.0000000000 0.5489640733 2.0499457879 0.9451654031 0.2657705007 0.4114530940 -0.7032184722 0.515321426672 +1403715525062142976.0000000000 0.5487788913 2.0496252245 0.9449970840 0.2658001352 0.4115288947 -0.7032196597 0.515243987942 +1403715525112143104.0000000000 0.5486024796 2.0493540096 0.9449108527 0.2659336063 0.4113830342 -0.7033295670 0.515141569248 +1403715525162142976.0000000000 0.5484760499 2.0491368486 0.9448253278 0.2658876242 0.4114090569 -0.7033250842 0.515150643146 +1403715525212143104.0000000000 0.5484385574 2.0490520775 0.9447950415 0.2659377858 0.4111871746 -0.7034812052 0.515088725857 +1403715525262142976.0000000000 0.5484558007 2.0490109208 0.9448013375 0.2657586109 0.4109784677 -0.7036069355 0.515176028408 +1403715525312143104.0000000000 0.5485237270 2.0490429932 0.9447799416 0.2657458561 0.4110124459 -0.7036837488 0.51505057124 +1403715525362142976.0000000000 0.5486226253 2.0490741364 0.9448130070 0.2657471031 0.4110361881 -0.7037562415 0.514931919596 +1403715525412143104.0000000000 0.5486710351 2.0491532762 0.9448393193 0.2657915784 0.4110925767 -0.7037708387 0.514843992637 +1403715525462142976.0000000000 0.5487357476 2.0492992642 0.9448284950 0.2658490354 0.4112574482 -0.7037765305 0.514674845762 +1403715525512143104.0000000000 0.5487966247 2.0493318730 0.9448296062 0.2657775967 0.4112923625 -0.7037610199 0.514705050001 +1403715525562142976.0000000000 0.5488244767 2.0493206712 0.9448401577 0.2657767769 0.4112312682 -0.7038390413 0.514647600605 +1403715525612143104.0000000000 0.5488198967 2.0492442710 0.9448492958 0.2655669557 0.4112071292 -0.7039371064 0.514641077944 +1403715525662142976.0000000000 0.5487810853 2.0491391023 0.9448933764 0.2653793865 0.4109748282 -0.7040839723 0.514722480335 +1403715525712143104.0000000000 0.5487316211 2.0491806774 0.9449440279 0.2653945771 0.4111415874 -0.7039499269 0.514764814159 +1403715525762142976.0000000000 0.5487214463 2.0492576861 0.9450276754 0.2655249469 0.4111870740 -0.7039160238 0.514707610374 +1403715525812143104.0000000000 0.5487738394 2.0493633243 0.9450779536 0.2655641428 0.4113583724 -0.7038196968 0.514682241736 +1403715525862142976.0000000000 0.5488467381 2.0495252173 0.9451635965 0.2656682543 0.4115403227 -0.7037233696 0.514614769009 +1403715525912143104.0000000000 0.5488505835 2.0495642270 0.9453095493 0.2656633338 0.4114362199 -0.7036743715 0.514767528946 +1403715525962142976.0000000000 0.5488248091 2.0496136763 0.9454040823 0.2656505507 0.4113506291 -0.7036346353 0.514896829347 +1403715526012143104.0000000000 0.5488482442 2.0496963296 0.9454228536 0.2656661919 0.4113474414 -0.7036428510 0.514880078462 +1403715526062142976.0000000000 0.5488689410 2.0497397200 0.9454688727 0.2656891910 0.4112803044 -0.7036102870 0.514966337702 +1403715526112143104.0000000000 0.5488643892 2.0497385706 0.9454662604 0.2657061120 0.4112949590 -0.7036562490 0.514883095484 +1403715526162142976.0000000000 0.5488512919 2.0497563596 0.9454354305 0.2657160954 0.4112774415 -0.7036326877 0.514924133808 +1403715526212143104.0000000000 0.5488248660 2.0497630369 0.9453831708 0.2656881961 0.4112839633 -0.7036537193 0.514904580743 +1403715526262142976.0000000000 0.5488269194 2.0497619200 0.9453534887 0.2657112912 0.4112393578 -0.7036872062 0.514882526524 +1403715526312143104.0000000000 0.5488240058 2.0497301040 0.9453308199 0.2656756919 0.4112195505 -0.7036969588 0.514903387212 +1403715526362142976.0000000000 0.5488345696 2.0497014455 0.9452973208 0.2657277742 0.4112586887 -0.7037101717 0.514827189698 +1403715526412143104.0000000000 0.5488283078 2.0497133907 0.9452810556 0.2658150982 0.4112488682 -0.7036738241 0.514839636522 +1403715526462142976.0000000000 0.5488261959 2.0497059167 0.9452665746 0.2658000936 0.4112332211 -0.7037016232 0.514821885381 +1403715526512143104.0000000000 0.5488029175 2.0496570240 0.9452776596 0.2658237662 0.4112007227 -0.7036966264 0.51484245073 +1403715526562142976.0000000000 0.5488030247 2.0496244113 0.9452984753 0.2658702840 0.4111426391 -0.7037243599 0.514826910328 +1403715526612143104.0000000000 0.5488121997 2.0496170182 0.9453054212 0.2659181180 0.4111215271 -0.7037415966 0.514795502749 +1403715526662142976.0000000000 0.5488183691 2.0495980223 0.9452732493 0.2659274830 0.4111290896 -0.7037504437 0.514772530855 +1403715526712143104.0000000000 0.5488042596 2.0495858912 0.9452565810 0.2659706337 0.4111048092 -0.7037662870 0.514747968612 +1403715526762142976.0000000000 0.5487852087 2.0495617738 0.9452710580 0.2659734831 0.4111105646 -0.7037690547 0.514738115602 +1403715526812143104.0000000000 0.5487783535 2.0495536903 0.9452780391 0.2660086417 0.4110790267 -0.7037887918 0.514718149013 +1403715526862142976.0000000000 0.5487694547 2.0495559992 0.9452931796 0.2660114088 0.4110666413 -0.7038032496 0.514706841395 +1403715526912143104.0000000000 0.5487241155 2.0495867779 0.9456181758 0.2661083313 0.4109558934 -0.7038205532 0.514721515542 +1403715526962142976.0000000000 0.5486979636 2.0495512639 0.9456150251 0.2660204891 0.4110106836 -0.7039126051 0.514597281069 +1403715527012143104.0000000000 0.5486109761 2.0495907556 0.9454099812 0.2660146756 0.4110428694 -0.7038496080 0.51466074375 +1403715527062142976.0000000000 0.5486056474 2.0497446702 0.9454128357 0.2660915143 0.4109944090 -0.7039226792 0.51455977635 +1403715527112143104.0000000000 0.5484781821 2.0496812817 0.9453290283 0.2660125210 0.4110717643 -0.7038980161 0.514572566577 +1403715527162142976.0000000000 0.5485065533 2.0496724305 0.9451883980 0.2661006918 0.4109915349 -0.7038977638 0.514591408946 +1403715527212143104.0000000000 0.5485901196 2.0496591854 0.9451879106 0.2660800008 0.4110014682 -0.7040054698 0.51444681434 +1403715527262142976.0000000000 0.5485327619 2.0496012587 0.9451411568 0.2660474613 0.4110205809 -0.7039819640 0.514480538788 +1403715527312143104.0000000000 0.5485116793 2.0497292677 0.9453118254 0.2663243506 0.4110598804 -0.7038674434 0.514462571215 +1403715527362142976.0000000000 0.5486095809 2.0496636010 0.9454802652 0.2662002934 0.4110439769 -0.7039504438 0.514425918429 +1403715527412143104.0000000000 0.5485941481 2.0495772231 0.9455072021 0.2661548917 0.4111479104 -0.7039975219 0.514301913858 +1403715527462142976.0000000000 0.5487631048 2.0497092586 0.9456547274 0.2662408965 0.4110957274 -0.7040656624 0.514205825463 +1403715527512143104.0000000000 0.5488556604 2.0498124924 0.9457503209 0.2663083236 0.4110774556 -0.7040099338 0.514261815988 +1403715527562142976.0000000000 0.5489060220 2.0498235313 0.9457693254 0.2663200477 0.4110109088 -0.7039709842 0.514362244363 +1403715527612143104.0000000000 0.5490372638 2.0498760092 0.9458543333 0.2662631389 0.4110412077 -0.7040811867 0.514216636222 +1403715527662142976.0000000000 0.5490603372 2.0498360759 0.9459497131 0.2662118638 0.4111428575 -0.7041577323 0.514057080855 +1403715527712143104.0000000000 0.5491577646 2.0497907291 0.9461083083 0.2661831428 0.4111752854 -0.7041653076 0.514035639587 +1403715527762142976.0000000000 0.5492068441 2.0499661072 0.9461077733 0.2663628536 0.4110348624 -0.7041824342 0.514031391548 +1403715527812143104.0000000000 0.5492457272 2.0500404346 0.9461174902 0.2663111573 0.4110840800 -0.7042499949 0.513926250891 +1403715527862142976.0000000000 0.5492194850 2.0499429034 0.9461883069 0.2661198195 0.4111670456 -0.7044459020 0.513690445059 +1403715527912143104.0000000000 0.5491222448 2.0498387727 0.9462853664 0.2661645666 0.4111726160 -0.7044835611 0.513611151959 +1403715527962142976.0000000000 0.5490316168 2.0496809376 0.9463281989 0.2661664490 0.4111914525 -0.7045609914 0.513488870599 +1403715528012143104.0000000000 0.5487628905 2.0495317454 0.9465011435 0.2662408970 0.4111935745 -0.7043715112 0.5137084809 +1403715528062142976.0000000000 0.5484369021 2.0493170029 0.9465994142 0.2660596829 0.4113254571 -0.7043322472 0.513750619517 +1403715528112143104.0000000000 0.5483808629 2.0493351648 0.9466172454 0.2661930271 0.4111886808 -0.7043966037 0.513702799113 +1403715528162142976.0000000000 0.5484098540 2.0495139937 0.9466187239 0.2659872069 0.4113126057 -0.7045002208 0.513568091968 +1403715528212143104.0000000000 0.5484356230 2.0497899666 0.9468505441 0.2659296843 0.4113588990 -0.7046701952 0.513327551615 +1403715528262142976.0000000000 0.5484931285 2.0500579644 0.9470306878 0.2657726096 0.4114553486 -0.7048045907 0.513147059916 +1403715528312143104.0000000000 0.5489454671 2.0500726482 0.9471553573 0.2654702647 0.4117022751 -0.7052192024 0.512535512718 +1403715528362142976.0000000000 0.5493487036 2.0498414835 0.9469395562 0.2651775783 0.4119027465 -0.7058824591 0.511612092615 +1403715528412143104.0000000000 0.5497105161 2.0496189545 0.9470994677 0.2641189230 0.4126599437 -0.7072377538 0.509674136008 +1403715528462142976.0000000000 0.5503024087 2.0497577828 0.9482435730 0.2626557623 0.4131031457 -0.7100766273 0.506111573542 +1403715528512143104.0000000000 0.5514830208 2.0501762576 0.9505834535 0.2614821669 0.4129932783 -0.7130330001 0.502640596475 +1403715528562142976.0000000000 0.5534389094 2.0511540200 0.9550125286 0.2619182867 0.4120083223 -0.7144306966 0.501235207475 +1403715528612143104.0000000000 0.5564416361 2.0521688642 0.9616067009 0.2629919360 0.4104578671 -0.7144178198 0.501962906786 +1403715528662142976.0000000000 0.5604883613 2.0531766066 0.9697234951 0.2645692431 0.4083299436 -0.7141402715 0.503262799574 +1403715528712143104.0000000000 0.5652792042 2.0542541534 0.9794676753 0.2655277377 0.4065979372 -0.7137375069 0.504729540673 +1403715528762142976.0000000000 0.5700731709 2.0554772282 0.9899771553 0.2664712585 0.4050219263 -0.7134217885 0.505944324257 +1403715528812143104.0000000000 0.5750433210 2.0566348325 1.0010641460 0.2663326534 0.4041546459 -0.7130317390 0.507258986295 +1403715528862142976.0000000000 0.5802433833 2.0582029681 1.0129696830 0.2666309337 0.4033529216 -0.7118122376 0.509448431402 +1403715528912143104.0000000000 0.5857467133 2.0602038208 1.0252694159 0.2666411841 0.4025862546 -0.7115061357 0.510476057683 +1403715528962142976.0000000000 0.5913969048 2.0626917850 1.0377778650 0.2659139098 0.4025310347 -0.7112336825 0.511278013972 +1403715529012143104.0000000000 0.5971820175 2.0656334750 1.0501389196 0.2644657793 0.4043967430 -0.7110239130 0.510848432424 +1403715529062142976.0000000000 0.6031496551 2.0698815071 1.0627774882 0.2658535009 0.4059677602 -0.7113100964 0.508478161287 +1403715529112143104.0000000000 0.6095016493 2.0748699252 1.0777072281 0.2692052945 0.4083022640 -0.7101847909 0.506414191586 +1403715529162142976.0000000000 0.6160185946 2.0806631587 1.0949865458 0.2729113738 0.4125091215 -0.7081316626 0.503890022858 +1403715529212143104.0000000000 0.6227176365 2.0867478385 1.1142648543 0.2764365858 0.4181413143 -0.7061467415 0.500097425297 +1403715529262142976.0000000000 0.6297900423 2.0928843480 1.1346700514 0.2796820640 0.4250464252 -0.7040615311 0.495389583994 +1403715529312143104.0000000000 0.6370751383 2.0992844167 1.1547512362 0.2828281125 0.4329520338 -0.7014108845 0.490493186893 +1403715529362142976.0000000000 0.6447388558 2.1057928713 1.1731499246 0.2855583137 0.4416858001 -0.6981718538 0.485722313692 +1403715529412143104.0000000000 0.6532160604 2.1121048778 1.1897386793 0.2892694645 0.4499056187 -0.6937177721 0.482352323401 +1403715529462142976.0000000000 0.6626256163 2.1181696047 1.2044526976 0.2933498018 0.4567118915 -0.6890655356 0.480155005814 +1403715529512143104.0000000000 0.6729971605 2.1239480744 1.2171793094 0.2967811696 0.4624012958 -0.6847720041 0.478741351235 +1403715529562142976.0000000000 0.6839520727 2.1296745689 1.2277533196 0.3000154234 0.4670197350 -0.6813057842 0.477185227481 +1403715529612143104.0000000000 0.6955168026 2.1351685026 1.2364999393 0.3026735033 0.4708344863 -0.6778811579 0.476634842047 +1403715529662142976.0000000000 0.7077756618 2.1406557755 1.2437267672 0.3054973827 0.4736874088 -0.6746636730 0.476571627657 +1403715529712143104.0000000000 0.7207669725 2.1463189401 1.2504905229 0.3069039140 0.4772225559 -0.6710165442 0.477289657431 +1403715529762142976.0000000000 0.7344393164 2.1524193745 1.2576597455 0.3078964899 0.4804745538 -0.6685846861 0.476800243468 +1403715529812143104.0000000000 0.7488114232 2.1588509197 1.2663006735 0.3102728465 0.4819290997 -0.6667378136 0.47637778239 +1403715529862142976.0000000000 0.7634742693 2.1656782990 1.2758121730 0.3117596993 0.4833896048 -0.6653279323 0.475898226922 +1403715529912143104.0000000000 0.7785769217 2.1730447082 1.2868706171 0.3145425403 0.4834052464 -0.6640998863 0.475766433272 +1403715529962142976.0000000000 0.7940483554 2.1805378612 1.2989778466 0.3172514554 0.4829907533 -0.6626088853 0.476467114754 +1403715530012143104.0000000000 0.8098550629 2.1879746072 1.3119000459 0.3186914063 0.4831736957 -0.6599000867 0.479072899402 +1403715530062142976.0000000000 0.8257644848 2.1957224876 1.3259374605 0.3197733667 0.4832866393 -0.6559423400 0.483651387721 +1403715530112143104.0000000000 0.8414851885 2.2041039279 1.3407976076 0.3195714293 0.4838541970 -0.6517092672 0.488911289128 +1403715530162142976.0000000000 0.8567357815 2.2136318546 1.3565313190 0.3175718596 0.4851608770 -0.6496097790 0.491705371636 +1403715530212143104.0000000000 0.8713510640 2.2246186349 1.3744866085 0.3141281439 0.4874525115 -0.6492118649 0.492176302533 +1403715530262142976.0000000000 0.8856459055 2.2370796770 1.3951209052 0.3095744809 0.4901796685 -0.6498517564 0.491508115915 +1403715530312143104.0000000000 0.9001787729 2.2513807423 1.4198912605 0.3061649261 0.4921247573 -0.6505461672 0.490780954887 +1403715530362142976.0000000000 0.9150638154 2.2676338955 1.4484239548 0.3062113963 0.4915613519 -0.6527345977 0.488405121854 +1403715530412143104.0000000000 0.9302360675 2.2858096976 1.4803820388 0.3080329481 0.4902940876 -0.6550106316 0.485477582408 +1403715530462142976.0000000000 0.9457808063 2.3054803695 1.5147048549 0.3112480608 0.4897229520 -0.6564932891 0.481988211792 +1403715530512143104.0000000000 0.9614829154 2.3263055132 1.5493312902 0.3143013023 0.4909041280 -0.6560426715 0.479411974994 +1403715530562142976.0000000000 0.9772263691 2.3481008492 1.5823766667 0.3174415217 0.4927755580 -0.6552810826 0.476455488521 +1403715530612143104.0000000000 0.9929349445 2.3703124237 1.6123714567 0.3201872060 0.4946182155 -0.6539863063 0.474483809216 +1403715530662142976.0000000000 1.0086175016 2.3931122969 1.6389201401 0.3235146978 0.4957962853 -0.6525736168 0.472939698575 +1403715530712143104.0000000000 1.0241175330 2.4163661062 1.6622344500 0.3266540973 0.4973934602 -0.6511006617 0.471131377493 +1403715530762142976.0000000000 1.0396856882 2.4402559002 1.6838295262 0.3301678169 0.5002150049 -0.6490727574 0.468485556974 +1403715530812143104.0000000000 1.0551969059 2.4649606239 1.7049138383 0.3343285097 0.5044893128 -0.6460587801 0.465105400338 +1403715530862142976.0000000000 1.0706543151 2.4899780283 1.7257290303 0.3392491040 0.5091720347 -0.6423489629 0.461564398968 +1403715530912143104.0000000000 1.0862900949 2.5151029779 1.7461750642 0.3434266455 0.5138642029 -0.6388657568 0.458096348907 +1403715530962142976.0000000000 1.1021372645 2.5397489433 1.7661309689 0.3450075223 0.5192456866 -0.6354454522 0.455590609816 +1403715531012143104.0000000000 1.1179620359 2.5643815871 1.7849342903 0.3456606687 0.5245199966 -0.6350809374 0.449521610411 +1403715531062142976.0000000000 1.1338117021 2.5890551733 1.8022321504 0.3436249790 0.5308512656 -0.6363142101 0.441840506979 +1403715531112143104.0000000000 1.1498787107 2.6137876445 1.8179402505 0.3401796167 0.5370610910 -0.6396806645 0.432032244617 +1403715531162142976.0000000000 1.1671918767 2.6382236589 1.8329222635 0.3373611964 0.5421504661 -0.6425702523 0.423513596133 +1403715531212143104.0000000000 1.1864029459 2.6628109838 1.8478018272 0.3395540740 0.5431735053 -0.6471079266 0.413420978342 +1403715531262142976.0000000000 1.2084938995 2.6865759466 1.8641117477 0.3474129452 0.5399865305 -0.6485376956 0.408800256611 +1403715531312143104.0000000000 1.2330349144 2.7088286454 1.8813139371 0.3572549890 0.5350108899 -0.6473585476 0.408728676902 +1403715531362142976.0000000000 1.2593127952 2.7292013353 1.8986361047 0.3663136428 0.5302660992 -0.6445471875 0.411328460342 +1403715531412143104.0000000000 1.2863586925 2.7476801049 1.9152579367 0.3730710012 0.5268124012 -0.6414418276 0.414534804048 +1403715531462142976.0000000000 1.3132799516 2.7640308978 1.9286015412 0.3766798131 0.5252995553 -0.6379189496 0.418607345066 +1403715531512143104.0000000000 1.3402217327 2.7786770569 1.9380697930 0.3795195991 0.5241528673 -0.6351224803 0.42172038201 +1403715531562142976.0000000000 1.3667946604 2.7920095068 1.9443898355 0.3813262128 0.5235466117 -0.6334492724 0.423357159083 +1403715531612143104.0000000000 1.3930053979 2.8043406535 1.9473984304 0.3829151182 0.5229948400 -0.6334240181 0.422642192485 +1403715531662142976.0000000000 1.4189756949 2.8154793876 1.9475294898 0.3837804860 0.5226623395 -0.6343631842 0.420856232012 +1403715531712143104.0000000000 1.4450711955 2.8247289246 1.9461823084 0.3823174650 0.5238359558 -0.6331367310 0.422572037905 +1403715531762142976.0000000000 1.4709717393 2.8322770072 1.9443786473 0.3789272304 0.5260180787 -0.6305438644 0.426771097841 +1403715531812143104.0000000000 1.4969179226 2.8384085816 1.9434066236 0.3770624161 0.5268849924 -0.6263247696 0.433512885805 +1403715531862142976.0000000000 1.5224360304 2.8436778094 1.9432241496 0.3762333272 0.5268417279 -0.6218824332 0.440622873285 +1403715531912143104.0000000000 1.5474164531 2.8485374436 1.9435866667 0.3767486563 0.5256887050 -0.6183108717 0.446546191782 +1403715531962142976.0000000000 1.5711633313 2.8530666871 1.9437631003 0.3765926291 0.5247772105 -0.6151774687 0.45204375135 +1403715532012143104.0000000000 1.5934915638 2.8578482565 1.9435546201 0.3766310979 0.5239249016 -0.6137297328 0.454958820911 +1403715532062142976.0000000000 1.6146607033 2.8627270622 1.9431232917 0.3757900115 0.5238117938 -0.6120665957 0.458014797068 +1403715532112143104.0000000000 1.6343357303 2.8675823305 1.9424077816 0.3743552418 0.5242120876 -0.6107675716 0.460459350664 +1403715532162142976.0000000000 1.6526651425 2.8728220663 1.9418213686 0.3741190055 0.5239964587 -0.6099780177 0.461941012358 +1403715532212143104.0000000000 1.6695382859 2.8784822409 1.9410444632 0.3747011463 0.5235846838 -0.6096694954 0.462343201747 +1403715532262142976.0000000000 1.6848216779 2.8847553511 1.9402209683 0.3765134692 0.5238511126 -0.6086470233 0.461916031764 +1403715532312143104.0000000000 1.6984671053 2.8917684135 1.9390949109 0.3788210152 0.5245904001 -0.6086206621 0.459217203787 +1403715532362142976.0000000000 1.7107403411 2.8991192395 1.9373888869 0.3808435653 0.5254219314 -0.6103303921 0.454298123816 +1403715532412143104.0000000000 1.7218951740 2.9065549201 1.9360016979 0.3841741268 0.5249181775 -0.6122443063 0.449475312462 +1403715532462142976.0000000000 1.7316861275 2.9135408910 1.9341085418 0.3864173988 0.5252352289 -0.6135879740 0.445330603358 +1403715532512143104.0000000000 1.7406440111 2.9199757030 1.9323291800 0.3892316004 0.5247799332 -0.6151540386 0.441237228455 +1403715532562142976.0000000000 1.7486045922 2.9256869231 1.9303458770 0.3938842831 0.5227425041 -0.6173027867 0.436500533163 +1403715532612143104.0000000000 1.7554898072 2.9302474126 1.9285807057 0.3998869314 0.5195140840 -0.6192219433 0.432157082086 +1403715532662142976.0000000000 1.7613986618 2.9332221739 1.9268355858 0.4067706304 0.5154713645 -0.6208089424 0.428279329069 +1403715532712143104.0000000000 1.7658947758 2.9341444493 1.9249141388 0.4132545728 0.5115267038 -0.6216692107 0.425544923507 +1403715532762142976.0000000000 1.7685030363 2.9326566142 1.9220739525 0.4184356263 0.5086083576 -0.6220994857 0.423345479665 +1403715532812143104.0000000000 1.7693706212 2.9283768982 1.9183914048 0.4217575196 0.5061328366 -0.6226967060 0.422136185047 +1403715532862142976.0000000000 1.7687001175 2.9211660779 1.9140519774 0.4231839376 0.5035373493 -0.6239037632 0.422030315245 +1403715532912143104.0000000000 1.7665959403 2.9109989938 1.9083343386 0.4227133752 0.5004408457 -0.6266619098 0.422098582299 +1403715532962142976.0000000000 1.7630053567 2.8977489762 1.9003040822 0.4210390453 0.4957808907 -0.6312302253 0.422464002479 +1403715533012143104.0000000000 1.7580137922 2.8814091503 1.8893055091 0.4182526783 0.4898519082 -0.6368455072 0.423718780785 +1403715533062142976.0000000000 1.7516127380 2.8619207548 1.8752810113 0.4137342031 0.4833571860 -0.6434848245 0.425578571443 +1403715533112143104.0000000000 1.7433975538 2.8393963132 1.8586040046 0.4082510887 0.4757580829 -0.6501798368 0.429245238772 +1403715533162142976.0000000000 1.7337915821 2.8135814336 1.8408436450 0.4020477834 0.4672590144 -0.6551897186 0.436752820255 +1403715533212143104.0000000000 1.7222892143 2.7842503167 1.8249903266 0.3956513147 0.4581024734 -0.6571382351 0.449189827411 +1403715533262142976.0000000000 1.7081793468 2.7522475716 1.8124632530 0.3895012521 0.4487015995 -0.6595247945 0.460415784561 +1403715533312143104.0000000000 1.6906116114 2.7180509780 1.8028951375 0.3819609672 0.4410654377 -0.6620433781 0.470388844145 +1403715533362142976.0000000000 1.6701485106 2.6823582301 1.7971464835 0.3738683116 0.4360140471 -0.6656655204 0.476449001741 +1403715533412143104.0000000000 1.6476046766 2.6449228936 1.7956420789 0.3659493501 0.4322666253 -0.6695495418 0.480551817077 +1403715533462142976.0000000000 1.6221087070 2.6066137268 1.7974118944 0.3586217500 0.4294512653 -0.6748401265 0.481199391964 +1403715533512143104.0000000000 1.5946244942 2.5673537902 1.8037947154 0.3543984246 0.4255245062 -0.6811692925 0.478893564621 +1403715533562142976.0000000000 1.5650118474 2.5269945558 1.8140878249 0.3536602185 0.4199065280 -0.6882213621 0.474293489688 +1403715533612143104.0000000000 1.5330648440 2.4852676793 1.8278072109 0.3535625327 0.4150291855 -0.6945746322 0.469372337136 +1403715533662142976.0000000000 1.4989677175 2.4416729152 1.8450025209 0.3543288638 0.4102317907 -0.7012731361 0.46300855591 +1403715533712143104.0000000000 1.4628769842 2.3949920170 1.8659668527 0.3545914754 0.4064167275 -0.7064731495 0.45824231385 +1403715533762142976.0000000000 1.4252816955 2.3452004790 1.8900901190 0.3550865093 0.4029060098 -0.7104613312 0.454780183214 +1403715533812143104.0000000000 1.3864667177 2.2918595901 1.9153818529 0.3518508370 0.4029709700 -0.7125051557 0.454039413424 +1403715533862142976.0000000000 1.3464812154 2.2352434723 1.9404430799 0.3473322595 0.4044448784 -0.7129172589 0.455558584361 +1403715533912143104.0000000000 1.3056612588 2.1760217272 1.9631649331 0.3403845119 0.4083815050 -0.7120543547 0.458630053859 +1403715533962142976.0000000000 1.2645036499 2.1148015649 1.9836844796 0.3349246098 0.4114960660 -0.7105433686 0.46219542914 +1403715534012143104.0000000000 1.2226114566 2.0521395009 2.0005835111 0.3294696693 0.4151149801 -0.7090086525 0.465226849062 +1403715534062142976.0000000000 1.1800983928 1.9881193681 2.0139033519 0.3247369335 0.4184566405 -0.7072349756 0.468250630912 +1403715534112143104.0000000000 1.1377009765 1.9224759793 2.0239709534 0.3192775759 0.4224594645 -0.7043585021 0.472725005481 +1403715534162142976.0000000000 1.0949834614 1.8563545835 2.0305329917 0.3141122151 0.4268792199 -0.7016855946 0.476177460814 +1403715534212143104.0000000000 1.0522238086 1.7898362803 2.0338594900 0.3082665432 0.4315817004 -0.6989649217 0.479746821207 +1403715534262142976.0000000000 1.0097482625 1.7232359656 2.0343482926 0.3034994186 0.4356537326 -0.6965398717 0.482624217496 +1403715534312143104.0000000000 0.9681701863 1.6568130456 2.0322443242 0.3006075163 0.4385928151 -0.6947768743 0.484310394949 +1403715534362142976.0000000000 0.9270779428 1.5907691093 2.0273772634 0.2980241223 0.4405401545 -0.6935839346 0.485847013522 +1403715534412143104.0000000000 0.8866758903 1.5249819310 2.0193034911 0.2954668891 0.4407058382 -0.6937972578 0.486952817749 +1403715534462142976.0000000000 0.8470335045 1.4593717077 2.0086348311 0.2928591719 0.4394438578 -0.6948534874 0.488161072106 +1403715534512143104.0000000000 0.8080469765 1.3939085639 1.9954934944 0.2894612479 0.4369538956 -0.6964183304 0.490188727132 +1403715534562142976.0000000000 0.7702702334 1.3285784026 1.9816059910 0.2859345408 0.4328646799 -0.6989429930 0.492288837821 +1403715534612143104.0000000000 0.7337747585 1.2635363882 1.9676970520 0.2825412146 0.4271353627 -0.7027874717 0.493776886426 +1403715534662142976.0000000000 0.6977642060 1.1988860122 1.9534024409 0.2773661879 0.4210744240 -0.7071548584 0.495677650817 +1403715534712143104.0000000000 0.6623664634 1.1346564266 1.9388704317 0.2715365541 0.4139371081 -0.7122773931 0.497579024428 +1403715534762142976.0000000000 0.6278080201 1.0708315702 1.9237131739 0.2636122199 0.4063928079 -0.7192257886 0.498064000101 +1403715534812143104.0000000000 0.5939246864 1.0074096868 1.9080198614 0.2537535473 0.3984553416 -0.7268074717 0.498591392886 +1403715534862142976.0000000000 0.5612405468 0.9442389134 1.8921097489 0.2432713385 0.3895607655 -0.7348096162 0.499115511411 +1403715534912143104.0000000000 0.5299843778 0.8813588675 1.8758547719 0.2326153673 0.3801542276 -0.7428697019 0.499517227045 +1403715534962142976.0000000000 0.5005626705 0.8184041920 1.8598941205 0.2220761529 0.3707107408 -0.7498547212 0.500972679979 +1403715535012143104.0000000000 0.4731565970 0.7557347176 1.8441631256 0.2127975085 0.3616200642 -0.7556450385 0.502940081282 +1403715535062142976.0000000000 0.4477220432 0.6934634351 1.8282765366 0.2045229510 0.3535642602 -0.7612460471 0.503653782031 +1403715535112143104.0000000000 0.4242055488 0.6315476111 1.8122728595 0.1963760688 0.3466549889 -0.7671796802 0.502694834349 +1403715535162142976.0000000000 0.4030142195 0.5699007019 1.7964828107 0.1899912976 0.3404955944 -0.7730253293 0.500397739095 +1403715535212143104.0000000000 0.3844868586 0.5083493018 1.7805355613 0.1844517957 0.3354024003 -0.7788007834 0.496942757998 +1403715535262142976.0000000000 0.3688920541 0.4462619047 1.7655179569 0.1801316343 0.3309617075 -0.7835295222 0.494063184614 +1403715535312143104.0000000000 0.3561562158 0.3832603204 1.7514427392 0.1769692409 0.3269508183 -0.7874667594 0.491610773964 +1403715535362142976.0000000000 0.3470819001 0.3189847209 1.7385159849 0.1757986942 0.3224780298 -0.7906720751 0.489837125089 +1403715535412143104.0000000000 0.3409291945 0.2536897914 1.7266899466 0.1808508633 0.3146650760 -0.7940788097 0.487563020769 +1403715535462142976.0000000000 0.3373663623 0.1865203846 1.7157597726 0.1877598295 0.3062797265 -0.7951410900 0.488558719701 +1403715535512143104.0000000000 0.3358203921 0.1174008357 1.7055388814 0.1952672055 0.2989097735 -0.7938889012 0.492203289629 +1403715535562142976.0000000000 0.3352529424 0.0465467205 1.6953937722 0.2004705502 0.2944444827 -0.7905117678 0.498201917071 +1403715535612143104.0000000000 0.3355188630 -0.0259385475 1.6856501227 0.2049891592 0.2917178628 -0.7852400516 0.506239266109 +1403715535662142976.0000000000 0.3364203914 -0.0993302545 1.6751286280 0.2076364687 0.2919627865 -0.7806930252 0.51201877759 +1403715535712143104.0000000000 0.3379891460 -0.1732894100 1.6642166189 0.2091556357 0.2954386818 -0.7762053957 0.516212252 +1403715535762142976.0000000000 0.3395079961 -0.2472888862 1.6530710982 0.2112033601 0.3009517001 -0.7721402423 0.518286273339 +1403715535812143104.0000000000 0.3408306911 -0.3212698091 1.6417194872 0.2116515496 0.3095065270 -0.7666916593 0.521146074359 +1403715535862142976.0000000000 0.3421260194 -0.3948310052 1.6295425078 0.2104234609 0.3208869890 -0.7610808022 0.522981376338 +1403715535912143104.0000000000 0.3440338118 -0.4678072320 1.6169287256 0.2101717064 0.3326154898 -0.7573521460 0.521164577386 +1403715535962142976.0000000000 0.3467773825 -0.5402780653 1.6043504241 0.2105003514 0.3445815958 -0.7539832725 0.518133525952 +1403715536012143104.0000000000 0.3504652067 -0.6121240236 1.5917751616 0.2122396564 0.3544359130 -0.7525507684 0.51283218781 +1403715536062142976.0000000000 0.3553785133 -0.6835265216 1.5800272371 0.2129347459 0.3639265237 -0.7515362050 0.507355508443 +1403715536112143104.0000000000 0.3624334669 -0.7547181289 1.5688894872 0.2144633589 0.3716801652 -0.7509443410 0.501938162662 +1403715536162142976.0000000000 0.3714094730 -0.8259251851 1.5583398521 0.2154096327 0.3790226627 -0.7500836421 0.497307793188 +1403715536212143104.0000000000 0.3826719397 -0.8976203607 1.5483481447 0.2145079125 0.3866954004 -0.7485807682 0.494044386928 +1403715536262142976.0000000000 0.3966313039 -0.9690334529 1.5391270911 0.2132082558 0.3939400071 -0.7466491871 0.491801282869 +1403715536312143104.0000000000 0.4134176592 -1.0399346909 1.5310439300 0.2125129756 0.4002891110 -0.7438729152 0.491182195192 +1403715536362142976.0000000000 0.4330216846 -1.1102465468 1.5242202973 0.2121029179 0.4062089833 -0.7393930308 0.493259120627 +1403715536412143104.0000000000 0.4554720995 -1.1799474033 1.5183172997 0.2101698862 0.4123973393 -0.7334648083 0.497781506727 +1403715536462142976.0000000000 0.4808237747 -1.2484816337 1.5133393180 0.2079654800 0.4179800802 -0.7270159029 0.503478786662 +1403715536512143104.0000000000 0.5091346858 -1.3151373224 1.5091773218 0.2062065331 0.4223104327 -0.7211169625 0.509041344689 +1403715536562142976.0000000000 0.5404329108 -1.3795139888 1.5058910010 0.2054554753 0.4253554543 -0.7155299295 0.5146627101 +1403715536612143104.0000000000 0.5745967809 -1.4411838601 1.5032685145 0.2058983854 0.4270760100 -0.7107089678 0.519715979773 +1403715536662142976.0000000000 0.6115755457 -1.5000790967 1.5013590545 0.2070082538 0.4278710963 -0.7054391155 0.525765691215 +1403715536712143104.0000000000 0.6509904322 -1.5555319587 1.5002992456 0.2102186198 0.4269090677 -0.7003705830 0.532012994475 +1403715536762142976.0000000000 0.6926373354 -1.6070026840 1.5007891334 0.2162579525 0.4246313122 -0.6936816911 0.540117078163 +1403715536812143104.0000000000 0.7355904247 -1.6542304703 1.5017788009 0.2220703875 0.4233942898 -0.6867713717 0.547509909816 +1403715536862142976.0000000000 0.7792462818 -1.6973403561 1.5032043109 0.2259735574 0.4236300744 -0.6792142869 0.555104912506 +1403715536912143104.0000000000 0.8230044303 -1.7361454625 1.5048110408 0.2276489652 0.4245405681 -0.6711391654 0.563483340856 +1403715536962142976.0000000000 0.8662148814 -1.7701434422 1.5067182925 0.2267884039 0.4260636142 -0.6624826567 0.572846878373 +1403715537012143104.0000000000 0.9088292634 -1.7987906286 1.5091961596 0.2258536519 0.4270706291 -0.6541381252 0.581982919732 +1403715537062142976.0000000000 0.9512223450 -1.8212039050 1.5131122108 0.2271285686 0.4259843041 -0.6455903720 0.59174577103 +1403715537112143104.0000000000 0.9929216443 -1.8370620920 1.5184212529 0.2294944840 0.4238305275 -0.6361079309 0.602550135665 +1403715537162142976.0000000000 1.0330283112 -1.8454416675 1.5250928826 0.2332683929 0.4203058667 -0.6264591880 0.613577803566 +1403715537212143104.0000000000 1.0709560679 -1.8458389900 1.5328172554 0.2382165642 0.4157811196 -0.6181510900 0.623111674652 +1403715537262142976.0000000000 1.1061662360 -1.8379673804 1.5417299487 0.2447234247 0.4102746269 -0.6118843676 0.630382976126 +1403715537312143104.0000000000 1.1382034825 -1.8209857575 1.5520471027 0.2571567602 0.4020028962 -0.6119005134 0.630747044239 +1403715537362142976.0000000000 1.1660463493 -1.7956311988 1.5629870306 0.2702405810 0.3941300019 -0.6181764291 0.624090916897 +1403715537412143104.0000000000 1.1892154027 -1.7635787829 1.5731879542 0.2789338108 0.3889565190 -0.6298596795 0.611707070153 +1403715537462142976.0000000000 1.2077205833 -1.7257609785 1.5833131921 0.2859635996 0.3850772581 -0.6454530274 0.594416280464 +1403715537512143104.0000000000 1.2218154890 -1.6837680226 1.5932120287 0.2888333272 0.3834303319 -0.6627388494 0.574746646004 +1403715537562142976.0000000000 1.2320762935 -1.6388198298 1.6028086210 0.2887505478 0.3834404880 -0.6793381448 0.555064138912 +1403715537612143104.0000000000 1.2396067941 -1.5920900885 1.6130895641 0.2880462792 0.3832650757 -0.6935676145 0.53768130609 +1403715537662142976.0000000000 1.2450168024 -1.5448176495 1.6242346904 0.2865232875 0.3827939299 -0.7038337789 0.525348669633 +1403715537712143104.0000000000 1.2494684840 -1.4980938151 1.6373970106 0.2885680242 0.3794126916 -0.7079241608 0.521169729958 +1403715537762142976.0000000000 1.2526514862 -1.4518888194 1.6514153107 0.2912016843 0.3754655483 -0.7074474008 0.523206819744 +1403715537812143104.0000000000 1.2542041302 -1.4059090889 1.6661021741 0.2959907853 0.3702974595 -0.7042080545 0.528545421403 +1403715537862142976.0000000000 1.2532506430 -1.3602962865 1.6801242145 0.2979221634 0.3671591833 -0.7004066448 0.534665363161 +1403715537912143104.0000000000 1.2495379496 -1.3142654225 1.6933764352 0.3000622860 0.3645407401 -0.6984277662 0.5378395009 +1403715537962142976.0000000000 1.2427320010 -1.2678480754 1.7045111068 0.2980805003 0.3653226880 -0.6990236615 0.537636745036 +1403715538012143104.0000000000 1.2332296172 -1.2208414943 1.7148561974 0.2977162469 0.3657382853 -0.7026159643 0.532852089898 +1403715538062142976.0000000000 1.2214821437 -1.1741930324 1.7250413414 0.2963057601 0.3654929660 -0.7063756111 0.528820654291 +1403715538112143104.0000000000 1.2074875062 -1.1279187493 1.7351028404 0.2957022887 0.3637468220 -0.7116353701 0.523281478659 +1403715538162142976.0000000000 1.1913029766 -1.0827163807 1.7439518504 0.2940434021 0.3608962313 -0.7172306280 0.518529279937 +1403715538212143104.0000000000 1.1731817483 -1.0388610579 1.7502808589 0.2907603577 0.3573378547 -0.7225759243 0.515414498798 +1403715538262142976.0000000000 1.1534654934 -0.9962888984 1.7535414720 0.2865280232 0.3529674351 -0.7270261908 0.514537267366 +1403715538312143104.0000000000 1.1325421359 -0.9550020054 1.7544086373 0.2826922837 0.3469465895 -0.7302637770 0.516166594014 +1403715538362142976.0000000000 1.1102607621 -0.9153024181 1.7523243943 0.2782535665 0.3403983169 -0.7323614665 0.519952518013 +1403715538412143104.0000000000 1.0864369904 -0.8770908195 1.7484529808 0.2734969349 0.3328387685 -0.7312336719 0.528880986446 +1403715538462142976.0000000000 1.0606165822 -0.8398928239 1.7434943981 0.2657564059 0.3263815719 -0.7281832256 0.540923092706 +1403715538512143104.0000000000 1.0325132305 -0.8026770581 1.7393803282 0.2581252411 0.3190184265 -0.7248775832 0.553309219886 +1403715538562142976.0000000000 1.0022620914 -0.7651735508 1.7355380199 0.2487929800 0.3120026070 -0.7227492751 0.564260499887 +1403715538612143104.0000000000 0.9695522821 -0.7264082571 1.7318865255 0.2401249584 0.3038084407 -0.7227626853 0.572411160386 +1403715538662142976.0000000000 0.9347136674 -0.6861877174 1.7284218433 0.2311239726 0.2950876266 -0.7253848711 0.577340272877 +1403715538712143104.0000000000 0.8977862750 -0.6446777347 1.7246094920 0.2214297928 0.2855268773 -0.7303530242 0.579678970856 +1403715538762142976.0000000000 0.8588074124 -0.6016222748 1.7196936238 0.2098744853 0.2760466743 -0.7383026791 0.578498131346 +1403715538812143104.0000000000 0.8183128930 -0.5573811068 1.7142551427 0.1971808907 0.2660309301 -0.7483891509 0.574683320935 +1403715538862142976.0000000000 0.7764240077 -0.5122931175 1.7089331394 0.1834881844 0.2550178888 -0.7577260138 0.571969623786 +1403715538912143104.0000000000 0.7334988755 -0.4665044076 1.7025432205 0.1697328142 0.2423967083 -0.7666993961 0.569742611638 +1403715538962142976.0000000000 0.6902538842 -0.4206584299 1.6938849032 0.1560531584 0.2281090221 -0.7743776250 0.569168674141 +1403715539012143104.0000000000 0.6465505642 -0.3746486689 1.6825717991 0.1419812248 0.2125524282 -0.7806049063 0.570367230231 +1403715539062142976.0000000000 0.6027314139 -0.3282205342 1.6681938989 0.1285038733 0.1953937403 -0.7866221333 0.571431238343 +1403715539112143104.0000000000 0.5587440675 -0.2813327624 1.6507559604 0.1146504150 0.1777537758 -0.7920208047 0.572679598404 +1403715539162142976.0000000000 0.5149157320 -0.2342925904 1.6306188778 0.1014489986 0.1591876655 -0.7964450376 0.574493420279 +1403715539212143104.0000000000 0.4713359901 -0.1867137947 1.6075383757 0.0888442805 0.1401523407 -0.8007688147 0.575528731362 +1403715539262142976.0000000000 0.4281586001 -0.1388623486 1.5814118854 0.0754142035 0.1225484262 -0.8054268009 0.574962824426 +1403715539312143104.0000000000 0.3851676418 -0.0903987848 1.5520082999 0.0621064509 0.1057771308 -0.8105140275 0.572731174814 +1403715539362142976.0000000000 0.3426703454 -0.0414405366 1.5202041325 0.0495782656 0.0898447448 -0.8153569169 0.569792080918 +1403715539412143104.0000000000 0.3006366969 0.0069441455 1.4876522689 0.0375512235 0.0753900598 -0.8191892493 0.567305224941 +1403715539462142976.0000000000 0.2597730888 0.0544357159 1.4579027645 0.0272996939 0.0625982155 -0.8205421406 0.567491661215 +1403715539512143104.0000000000 0.2201696668 0.1015114873 1.4316421298 0.0197536642 0.0506812796 -0.8227130488 0.565848424908 +1403715539562142976.0000000000 0.1820877557 0.1478471955 1.4102926008 0.0174130959 0.0379520838 -0.8251426045 0.563379184599 +1403715539612143104.0000000000 0.1450233102 0.1923519416 1.3937708847 0.0172236585 0.0261923918 -0.8262136698 0.562484022977 +1403715539662142976.0000000000 0.1087477348 0.2355681841 1.3823137392 0.0175941332 0.0163851330 -0.8262020532 0.562860676499 +1403715539712143104.0000000000 0.0728184664 0.2774327011 1.3755610713 0.0177236555 0.0083670819 -0.8246308070 0.565331669127 +1403715539762142976.0000000000 0.0368385194 0.3180021116 1.3729125022 0.0164379276 0.0035115542 -0.8234435735 0.567149138048 +1403715539812143104.0000000000 0.0004083798 0.3581006099 1.3740463142 0.0151312969 0.0009872572 -0.8221081869 0.569129333445 +1403715539862142976.0000000000 -0.0362907173 0.3977780091 1.3779204361 0.0134629876 0.0013658514 -0.8226896765 0.568329639064 +1403715539912143104.0000000000 -0.0730637708 0.4367005209 1.3854651377 0.0135303925 0.0027661889 -0.8260942036 0.563362799143 +1403715539962142976.0000000000 -0.1102664004 0.4744169854 1.3978689545 0.0170362977 0.0027150873 -0.8296418826 0.558029335673 +1403715540012143104.0000000000 -0.1483197790 0.5106083488 1.4119692228 0.0192587370 0.0041139454 -0.8347560303 0.550267704306 +1403715540062142976.0000000000 -0.1866440645 0.5445306125 1.4271968484 0.0240738321 0.0034375308 -0.8403062958 0.541566213212 +1403715540112143104.0000000000 -0.2255374095 0.5757890484 1.4427580976 0.0294976331 0.0026914875 -0.8465949746 0.531412828685 +1403715540162142976.0000000000 -0.2649902978 0.6030638954 1.4605657307 0.0361503031 0.0010816031 -0.8502314741 0.525165141837 +1403715540212143104.0000000000 -0.3056477522 0.6264901870 1.4786601922 0.0405223965 0.0002758624 -0.8529187263 0.520468544367 +1403715540262142976.0000000000 -0.3480499189 0.6455159515 1.4976719607 0.0428086388 0.0004300383 -0.8523501474 0.521216329193 +1403715540312143104.0000000000 -0.3920659395 0.6608822481 1.5164022313 0.0412293188 0.0036141385 -0.8512612212 0.523107459895 +1403715540362142976.0000000000 -0.4375649206 0.6727096662 1.5347139631 0.0361905093 0.0092345550 -0.8500147052 0.525433126993 +1403715540412143104.0000000000 -0.4837750854 0.6817067024 1.5519975792 0.0309519130 0.0150271355 -0.8497908139 0.525995947545 +1403715540462142976.0000000000 -0.5303800395 0.6874618642 1.5685348803 0.0251833550 0.0207627985 -0.8496779291 0.526290909675 +1403715540512143104.0000000000 -0.5774575644 0.6909229637 1.5832568790 0.0180123418 0.0268134740 -0.8522794922 0.52208836442 +1403715540562142976.0000000000 -0.6242603319 0.6908764730 1.5971327637 0.0132511814 0.0296451381 -0.8552857158 0.517138198449 +1403715540612143104.0000000000 -0.6706630883 0.6874226056 1.6099901551 0.0087162353 0.0317838744 -0.8583460129 0.512011654857 +1403715540662142976.0000000000 -0.7159117709 0.6800871841 1.6228400415 0.0087758315 0.0301745779 -0.8613573595 0.507026605729 +1403715540712143104.0000000000 -0.7601335250 0.6685391182 1.6356075471 0.0134893737 0.0240808863 -0.8635071682 0.503580696803 +1403715540762142976.0000000000 -0.8038559880 0.6528479255 1.6478446950 0.0181275303 0.0179531378 -0.8648197966 0.501433741276 +1403715540812143104.0000000000 -0.8476253142 0.6323756892 1.6599007099 0.0216131780 0.0125819126 -0.8631697476 0.504294113372 +1403715540862142976.0000000000 -0.8918271688 0.6079604947 1.6711258386 0.0228878095 0.0093227878 -0.8605992387 0.508682793208 +1403715540912143104.0000000000 -0.9364934918 0.5797327144 1.6820651588 0.0242939905 0.0063741493 -0.8575619853 0.513767081122 +1403715540962142976.0000000000 -0.9818960377 0.5480025838 1.6923735177 0.0231352927 0.0058493744 -0.8539940633 0.519735204587 +1403715541012143104.0000000000 -1.0277315251 0.5130041758 1.7020430085 0.0205943050 0.0068281916 -0.8508074499 0.525029459819 +1403715541062142976.0000000000 -1.0737820696 0.4754330203 1.7115114529 0.0184643707 0.0081498849 -0.8482529860 0.529206498497 +1403715541112143104.0000000000 -1.1201699909 0.4357601054 1.7199372194 0.0156778664 0.0102476758 -0.8471585137 0.531010020924 +1403715541162142976.0000000000 -1.1661523139 0.3940236454 1.7282401968 0.0171568242 0.0094239185 -0.8462412914 0.532440146808 +1403715541212143104.0000000000 -1.2118424382 0.3496642469 1.7374124240 0.0243090216 0.0045471528 -0.8436766458 0.536281746975 +1403715541262142976.0000000000 -1.2580902151 0.3029211083 1.7468133050 0.0320356954 -0.0012391198 -0.8396061086 0.54224880003 +1403715541312143104.0000000000 -1.3058660240 0.2546055437 1.7553341654 0.0353600373 -0.0054583603 -0.8350812138 0.54896196621 +1403715541362142976.0000000000 -1.3554645801 0.2052913386 1.7620693673 0.0319953673 -0.0052320262 -0.8316764096 0.554313333821 +1403715541412143104.0000000000 -1.4062553030 0.1553110572 1.7674984427 0.0269410266 -0.0035010132 -0.8296303133 0.557651743623 +1403715541462142976.0000000000 -1.4579906656 0.1053620705 1.7706435460 0.0204236921 -0.0001918806 -0.8316800500 0.55487938364 +1403715541512143104.0000000000 -1.5100166002 0.0546541871 1.7731965536 0.0150307881 0.0024944056 -0.8354272693 0.549389780603 +1403715541562142976.0000000000 -1.5621936912 0.0028628306 1.7751982385 0.0096196604 0.0054546634 -0.8398123101 0.542764214574 +1403715541612143104.0000000000 -1.6139322223 -0.0504125815 1.7775061860 0.0069107581 0.0068171747 -0.8438576328 0.536479322153 +1403715541662142976.0000000000 -1.6655859039 -0.1052086891 1.7797297597 0.0016937868 0.0102776123 -0.8464107069 0.5324287906 +1403715541712143104.0000000000 -1.7165847051 -0.1619968518 1.7821378494 0.0052417419 -0.0152746333 0.8475748255 -0.530430131921 +1403715541762142976.0000000000 -1.7666101238 -0.2217827647 1.7850630064 0.0152507615 -0.0230149066 0.8454169073 -0.533392895719 +1403715541812143104.0000000000 -1.8151139406 -0.2836718908 1.7875439690 0.0264866572 -0.0315540268 0.8423979584 -0.537278773103 +1403715541862142976.0000000000 -1.8611105346 -0.3474275977 1.7910615362 0.0367327949 -0.0398127195 0.8373208783 -0.544021503202 +1403715541912143104.0000000000 -1.9037898136 -0.4122955160 1.7944881758 0.0457312362 -0.0482427621 0.8330625627 -0.549170334767 +1403715541962142976.0000000000 -1.9425400780 -0.4778546023 1.7978333715 0.0522445644 -0.0565768086 0.8295544807 -0.553090348712 +1403715542012143104.0000000000 -1.9771914593 -0.5437031408 1.8007686941 0.0572652138 -0.0657225524 0.8270410058 -0.55534171106 +1403715542062142976.0000000000 -2.0067587479 -0.6096567771 1.8041418439 0.0596792696 -0.0755201793 0.8227332241 -0.560218822724 +1403715542112143104.0000000000 -2.0308740441 -0.6752161073 1.8083327933 0.0570536367 -0.0834837876 0.8176268831 -0.566799452901 +1403715542162142976.0000000000 -2.0498145537 -0.7398207502 1.8129056997 0.0536422977 -0.0923506899 0.8115519927 -0.574436434387 +1403715542212143104.0000000000 -2.0633009097 -0.8033909901 1.8180905199 0.0459627289 -0.0999115545 0.8049658644 -0.583039506416 +1403715542262142976.0000000000 -2.0716694407 -0.8649167921 1.8241082056 0.0361549084 -0.1071843435 0.7985722589 -0.591173989965 +1403715542312143104.0000000000 -2.0753521262 -0.9237145324 1.8310161698 0.0216698683 -0.1120748338 0.7936900681 -0.597516296267 +1403715542362142976.0000000000 -2.0748687789 -0.9795356629 1.8386007812 0.0068962223 -0.1181114112 0.7882628994 -0.60385738222 +1403715542412143104.0000000000 -2.0707100134 -1.0322075275 1.8466961905 0.0126635023 0.1218970544 -0.7833867915 0.609332322075 +1403715542462142976.0000000000 -2.0639725305 -1.0819855155 1.8558342262 0.0334379006 0.1247686658 -0.7771298082 0.615941513452 +1403715542512143104.0000000000 -2.0560793370 -1.1282823280 1.8648657550 0.0516510596 0.1277488517 -0.7718760504 0.620660746095 +1403715542562142976.0000000000 -2.0477273826 -1.1713111844 1.8731446529 0.0653748413 0.1318995768 -0.7683839976 0.622827956982 +1403715542612143104.0000000000 -2.0396966577 -1.2105130357 1.8786018078 0.0749116691 0.1371181166 -0.7692200225 0.619586491822 +1403715542662142976.0000000000 -2.0321828373 -1.2461292147 1.8828103412 0.0814979654 0.1427667848 -0.7717534450 0.614306395043 +1403715542712143104.0000000000 -2.0249920127 -1.2786553442 1.8866772349 0.0882684903 0.1466678758 -0.7733161576 0.610474674469 +1403715542762142976.0000000000 -2.0182078568 -1.3086618803 1.8891587952 0.0916638656 0.1513931707 -0.7750704981 0.606583519919 +1403715542812143104.0000000000 -2.0116193174 -1.3362017715 1.8901777591 0.0934565864 0.1559085651 -0.7777837782 0.601673316777 +1403715542862142976.0000000000 -2.0051810450 -1.3616564587 1.8898901447 0.0958159495 0.1588841137 -0.7809695010 0.596373859838 +1403715542912143104.0000000000 -1.9989116474 -1.3847376166 1.8886743238 0.0991884046 0.1602759243 -0.7834790396 0.592143464833 +1403715542962142976.0000000000 -1.9925827630 -1.4062757143 1.8862676865 0.1042755507 0.1595086608 -0.7854701538 0.588829545927 +1403715543012143104.0000000000 -1.9867060510 -1.4262980698 1.8818859367 0.1099445410 0.1576762968 -0.7865295494 0.586874476516 +1403715543062142976.0000000000 -1.9814846700 -1.4452778968 1.8759144341 0.1145406663 0.1556745208 -0.7864976099 0.58657257777 +1403715543112143104.0000000000 -1.9771636709 -1.4631493376 1.8685721552 0.1182320426 0.1536121954 -0.7866267089 0.586210626242 +1403715543162142976.0000000000 -1.9739836353 -1.4799570910 1.8603323789 0.1196522776 0.1522374737 -0.7858953314 0.587261110783 +1403715543212143104.0000000000 -1.9720589433 -1.4957513602 1.8520611844 0.1212011521 0.1501510320 -0.7846290931 0.589170717739 +1403715543262142976.0000000000 -1.9713948766 -1.5103031837 1.8440363184 0.1232389481 0.1474557205 -0.7829914522 0.591602364668 +1403715543312143104.0000000000 -1.9722265983 -1.5232456460 1.8357720510 0.1249728260 0.1446838828 -0.7823028287 0.5928327344 +1403715543362142976.0000000000 -1.9749468248 -1.5347614942 1.8271085030 0.1239003656 0.1440671754 -0.7820355251 0.593560263015 +1403715543412143104.0000000000 -1.9794107012 -1.5446196880 1.8190664786 0.1227046681 0.1433693707 -0.7812357363 0.595029001278 +1403715543462142976.0000000000 -1.9853114395 -1.5529710537 1.8106603098 0.1187185602 0.1448777491 -0.7807969298 0.596047393868 +1403715543512143104.0000000000 -1.9925220199 -1.5597179805 1.8023000165 0.1143839814 0.1464421137 -0.7802872424 0.597179061449 +1403715543562142976.0000000000 -2.0005855443 -1.5650298058 1.7946706585 0.1114661943 0.1471056079 -0.7781909500 0.600294988305 +1403715543612143104.0000000000 -2.0094126348 -1.5685587973 1.7871515610 0.1091430825 0.1476076491 -0.7749845868 0.604730237082 +1403715543662142976.0000000000 -2.0194193857 -1.5696976113 1.7792780517 0.1052817637 0.1493157219 -0.7704231831 0.610793487427 +1403715543712143104.0000000000 -2.0305812141 -1.5682434770 1.7705673744 0.0995045316 0.1504625447 -0.7666489239 0.616205564964 +1403715543762142976.0000000000 -2.0428411100 -1.5642674034 1.7610350867 0.0900710835 0.1514177533 -0.7630336819 0.621883802749 +1403715543812143104.0000000000 -2.0555958276 -1.5572257706 1.7506351087 0.0783883786 0.1516865675 -0.7603695381 0.626645524083 +1403715543862142976.0000000000 -2.0683017846 -1.5467063800 1.7392058855 0.0660006414 0.1499763726 -0.7594377438 0.629607271493 +1403715543912143104.0000000000 -2.0804999812 -1.5325543052 1.7271920509 0.0531488101 0.1462385768 -0.7597399560 0.631335633285 +1403715543962142976.0000000000 -2.0918717836 -1.5144297129 1.7141535638 0.0397762881 0.1405651571 -0.7622212825 0.630617158103 +1403715544012143104.0000000000 -2.1019195438 -1.4924951116 1.7006521548 0.0257493077 0.1333455749 -0.7654361938 0.629017777217 +1403715544062142976.0000000000 -2.1102097654 -1.4667056285 1.6860041938 0.0120791762 0.1234073989 -0.7693727652 0.626650026386 +1403715544112143104.0000000000 -2.1161398910 -1.4377832697 1.6695663627 0.0043675630 0.1068540103 -0.7754093906 0.622337064456 +1403715544162142976.0000000000 -2.1202897484 -1.4062679019 1.6501294059 0.0024168874 -0.0869839600 0.7819149016 -0.617281974471 +1403715544212143104.0000000000 -2.1231059425 -1.3724155429 1.6275725744 0.0095871928 -0.0650082959 0.7875834719 -0.612694281001 +1403715544262142976.0000000000 -2.1247400075 -1.3368867173 1.6016928152 0.0184058822 -0.0418694913 0.7922692570 -0.608455087532 +1403715544312143104.0000000000 -2.1251799134 -1.2998238359 1.5721244614 0.0273143953 -0.0171429131 0.7963705265 -0.60394869715 +1403715544362142976.0000000000 -2.1246218205 -1.2614283435 1.5392135929 0.0361642610 0.0080955437 0.7996147387 -0.599368733022 +1403715544412143104.0000000000 -2.1229527117 -1.2217743632 1.5034777290 0.0442172338 0.0335473073 0.8016799838 -0.595171082995 +1403715544462142976.0000000000 -2.1207192357 -1.1809176772 1.4658866198 0.0538481568 0.0569795779 0.8018075720 -0.592417353832 +1403715544512143104.0000000000 -2.1177878071 -1.1386798069 1.4279394532 0.0641314306 0.0780955631 0.8013734042 -0.58956671352 +1403715544562142976.0000000000 -2.1141252932 -1.0954973774 1.3921800674 0.0736096675 0.0969393289 0.8002117889 -0.587235452207 +1403715544612143104.0000000000 -2.1096384451 -1.0512755171 1.3598527315 0.0821594098 0.1122897437 0.7985815526 -0.585583767412 +1403715544662142976.0000000000 -2.1040645377 -1.0062524710 1.3323759543 0.0897509506 0.1241404908 0.7972068258 -0.583947927717 +1403715544712143104.0000000000 -2.0979453653 -0.9607129370 1.3119758329 0.0978056333 0.1316182200 0.7934822077 -0.586085905211 +1403715544762142976.0000000000 -2.0908527273 -0.9143620880 1.2983057581 0.1041698051 0.1366349295 0.7892196032 -0.58958626655 +1403715544812143104.0000000000 -2.0826122542 -0.8664261948 1.2915787947 0.1092987921 0.1396479039 0.7857265447 -0.592609512158 +1403715544862142976.0000000000 -2.0731766490 -0.8167746761 1.2920009726 0.1131903124 0.1409910817 0.7831763279 -0.594932187331 +1403715544912143104.0000000000 -2.0624079571 -0.7651235974 1.2982338151 0.1149097135 0.1417851131 0.7828303900 -0.594869162009 +1403715544962142976.0000000000 -2.0505259525 -0.7118207841 1.3074937334 0.1157175440 0.1424528241 0.7846714751 -0.592121034211 +1403715545012143104.0000000000 -2.0378472879 -0.6572951958 1.3176770774 0.1167212281 0.1433274001 0.7878333858 -0.587496355367 +1403715545062142976.0000000000 -2.0246974769 -0.6020009435 1.3284097946 0.1180608443 0.1454094298 0.7900005170 -0.583795270492 +1403715545112143104.0000000000 -2.0112301342 -0.5461274397 1.3383947490 0.1205617078 0.1483501310 0.7919212101 -0.579929228684 +1403715545162142976.0000000000 -1.9974227522 -0.4898296669 1.3463333542 0.1243163141 0.1522008857 0.7933742580 -0.576140287702 +1403715545212143104.0000000000 -1.9832062809 -0.4334435089 1.3517249822 0.1278694218 0.1581189287 0.7938876828 -0.573053367898 +1403715545262142976.0000000000 -1.9688131575 -0.3771690862 1.3537181989 0.1323760783 0.1644077899 0.7946305331 -0.569217856753 +1403715545312143104.0000000000 -1.9541015072 -0.3209163184 1.3529060828 0.1365448866 0.1720385284 0.7946249119 -0.56597657906 +1403715545362142976.0000000000 -1.9387934577 -0.2648801339 1.3500163599 0.1389208904 0.1802933621 0.7937193763 -0.564096482391 +1403715545412143104.0000000000 -1.9227844895 -0.2091939583 1.3467612909 0.1372200833 0.1901384376 0.7917239974 -0.564084333482 +1403715545462142976.0000000000 -1.9063169279 -0.1533732403 1.3443134863 0.1334325463 0.2003970615 0.7897914976 -0.56415083414 +1403715545512143104.0000000000 -1.8899818914 -0.0976320336 1.3429974245 0.1281759659 0.2103941430 0.7876329256 -0.564747377846 +1403715545562142976.0000000000 -1.8749345775 -0.0419136838 1.3436909255 0.1235904329 0.2192588987 0.7856146822 -0.565208378683 +1403715545612143104.0000000000 -1.8612298598 0.0141478105 1.3466169111 0.1190084553 0.2268371318 0.7835869556 -0.566015358634 +1403715545662142976.0000000000 -1.8491698397 0.0711006466 1.3502567460 0.1155386406 0.2320066791 0.7820917539 -0.56670646013 +1403715545712143104.0000000000 -1.8389146993 0.1289269581 1.3537299922 0.1129793687 0.2340318328 0.7814685083 -0.567249269767 +1403715545762142976.0000000000 -1.8307992296 0.1875952476 1.3563316025 0.1119508804 0.2332967764 0.7821245422 -0.566851669228 +1403715545812143104.0000000000 -1.8245873188 0.2472409309 1.3579876871 0.1123700010 0.2294008759 0.7836511265 -0.566250062258 +1403715545862142976.0000000000 -1.8199751877 0.3074827082 1.3597108323 0.1124830533 0.2230987844 0.7850914746 -0.566750272723 +1403715545912143104.0000000000 -1.8167352974 0.3686357347 1.3613343678 0.1134993410 0.2132954291 0.7878671121 -0.566470099031 +1403715545962142976.0000000000 -1.8144842320 0.4305000771 1.3631528261 0.1143030253 0.2005143005 0.7906210351 -0.5671395001 +1403715546012143104.0000000000 -1.8128611272 0.4925409023 1.3650573135 0.1136732889 0.1855701308 0.7941626772 -0.567404399075 +1403715546062142976.0000000000 -1.8114423866 0.5547192558 1.3675376278 0.1108464270 0.1692436596 0.7972537579 -0.568732009672 +1403715546112143104.0000000000 -1.8096158794 0.6168966619 1.3707787352 0.1054601043 0.1518077020 0.8006226044 -0.569943886125 +1403715546162142976.0000000000 -1.8073912560 0.6789100973 1.3749745473 0.0959301880 0.1343540904 0.8035898194 -0.571830201723 +1403715546212143104.0000000000 -1.8051248397 0.7406944307 1.3794880472 0.0857508485 0.1151423019 0.8063927525 -0.573689612019 +1403715546262142976.0000000000 -1.8024374977 0.8026141405 1.3843827494 0.0729612859 0.0960043234 0.8091930698 -0.575035995829 +1403715546312143104.0000000000 -1.7996290067 0.8645364634 1.3900543551 0.0591227284 0.0767271156 0.8115797046 -0.576156086382 +1403715546362142976.0000000000 -1.7963901900 0.9264496495 1.3962775711 0.0452005018 0.0566868878 0.8131840497 -0.577473127218 +1403715546412143104.0000000000 -1.7929756427 0.9883453433 1.4027926439 0.0304269424 0.0368423533 0.8154600519 -0.576837711961 +1403715546462142976.0000000000 -1.7898046153 1.0504860007 1.4103765345 0.0155924632 0.0165803114 0.8165613963 -0.576809721174 +1403715546512143104.0000000000 -1.7867699788 1.1126166874 1.4183607226 0.0009803834 -0.0040406734 0.8177119775 -0.5756125725 +1403715546562142976.0000000000 -1.7839173605 1.1743471115 1.4264575038 0.0138501789 0.0248363518 -0.8176941406 0.574950102642 +1403715546612143104.0000000000 -1.7815719392 1.2359049674 1.4340008332 0.0266164016 0.0472356127 -0.8179879104 0.572674551944 +1403715546662142976.0000000000 -1.7794251023 1.2971031925 1.4409847895 0.0391424924 0.0700705986 -0.8188085022 0.568428195251 +1403715546712143104.0000000000 -1.7773475761 1.3576515698 1.4472858450 0.0512084198 0.0934084296 -0.8201812147 0.562099046438 +1403715546762142976.0000000000 -1.7751994139 1.4175006749 1.4523067930 0.0628002375 0.1168743884 -0.8232457034 0.551962878554 +1403715546812143104.0000000000 -1.7724622730 1.4758832229 1.4572033364 0.0758031294 0.1386236897 -0.8263536530 0.540533993716 +1403715546862142976.0000000000 -1.7690295398 1.5322924496 1.4626835981 0.0897666198 0.1588688553 -0.8275766003 0.530866849014 +1403715546912143104.0000000000 -1.7651146854 1.5861933656 1.4688966632 0.1044804542 0.1778362597 -0.8265143458 0.523767253345 +1403715546962142976.0000000000 -1.7612456091 1.6372281907 1.4745007258 0.1137152432 0.2006816852 -0.8232012313 0.518782649494 +1403715547012143104.0000000000 -1.7565259464 1.6853257696 1.4803147520 0.1213097812 0.2239874220 -0.8180214629 0.515707725383 +1403715547062142976.0000000000 -1.7502982355 1.7311206743 1.4859147800 0.1297897736 0.2461337658 -0.8126982602 0.511951483871 +1403715547112143104.0000000000 -1.7418994595 1.7746840392 1.4917080514 0.1395565897 0.2669794520 -0.8066273546 0.508525556274 +1403715547162142976.0000000000 -1.7314390068 1.8163187501 1.4975219332 0.1493484443 0.2873654359 -0.7997599936 0.505470178173 +1403715547212143104.0000000000 -1.7187736814 1.8559241100 1.5035103007 0.1595143347 0.3072837698 -0.7922828557 0.502413911443 +1403715547262142976.0000000000 -1.7037969608 1.8935267623 1.5094491956 0.1685973024 0.3269776812 -0.7842100705 0.49967500535 +1403715547312143104.0000000000 -1.6863643421 1.9293442396 1.5152218464 0.1769244229 0.3456105690 -0.7765730486 0.496170720057 +1403715547362142976.0000000000 -1.6664555637 1.9637012948 1.5208044211 0.1855991231 0.3624235386 -0.7696600026 0.491757688833 +1403715547412143104.0000000000 -1.6438286160 1.9968077764 1.5258165981 0.1943232427 0.3777748875 -0.7641059493 0.485455157557 +1403715547462142976.0000000000 -1.6183112621 2.0289166568 1.5298937775 0.2023340699 0.3924816945 -0.7596181218 0.477492777732 +1403715547512143104.0000000000 -1.5899314667 2.0599593768 1.5333749335 0.2106945586 0.4066819446 -0.7547859439 0.469591074993 +1403715547562142976.0000000000 -1.5583634136 2.0898370516 1.5360498762 0.2185437776 0.4219604724 -0.7486189857 0.462339259848 +1403715547612143104.0000000000 -1.5231748204 2.1187787064 1.5385230085 0.2270840142 0.4374015116 -0.7412282953 0.455733894249 +1403715547662142976.0000000000 -1.4844487639 2.1467689311 1.5407582572 0.2350631817 0.4531031730 -0.7330969869 0.449457031374 +1403715547712143104.0000000000 -1.4421278692 2.1736110404 1.5429533224 0.2423801694 0.4688561311 -0.7242913687 0.443652786548 +1403715547762142976.0000000000 -1.3959629333 2.1997005948 1.5455224416 0.2502091240 0.4839540643 -0.7150870618 0.43798898614 +1403715547812143104.0000000000 -1.3459545994 2.2249482866 1.5481475763 0.2586411310 0.4979528445 -0.7059247407 0.432224467697 +1403715547862142976.0000000000 -1.2919479749 2.2496346319 1.5507953242 0.2678144390 0.5109939856 -0.6966151984 0.426483104448 +1403715547912143104.0000000000 -1.2339197639 2.2735718530 1.5538503569 0.2778904597 0.5225866490 -0.6856811137 0.423699772383 +1403715547962142976.0000000000 -1.1720865555 2.2969943818 1.5571283990 0.2895405498 0.5315613365 -0.6749165438 0.42201477994 +1403715548012143104.0000000000 -1.1066256032 2.3200047229 1.5609057859 0.3028493592 0.5365426332 -0.6651555527 0.421867703338 +1403715548062142976.0000000000 -1.0381793819 2.3426242168 1.5644706996 0.3142576063 0.5402974469 -0.6546792930 0.425106867781 +1403715548112143104.0000000000 -0.9678111501 2.3648479684 1.5678742211 0.3243674750 0.5425788603 -0.6440960983 0.430736738181 +1403715548162142976.0000000000 -0.8961399863 2.3870570283 1.5704884225 0.3322347381 0.5440371343 -0.6355522082 0.435565225886 +1403715548212143104.0000000000 -0.8234992028 2.4093633969 1.5724657694 0.3376650516 0.5452186682 -0.6281274540 0.440652718587 +1403715548262142976.0000000000 -0.7502102943 2.4320985061 1.5739509000 0.3413599975 0.5458606495 -0.6219123917 0.445796456399 +1403715548312143104.0000000000 -0.6764813275 2.4556501352 1.5740966600 0.3442525518 0.5458622926 -0.6175698312 0.449590971653 +1403715548362142976.0000000000 -0.6027595509 2.4798993006 1.5707571747 0.3451853264 0.5457395902 -0.6158977622 0.451315118989 +1403715548412143104.0000000000 -0.5292708118 2.5047926970 1.5641821232 0.3444677306 0.5459753811 -0.6144407956 0.453558567849 +1403715548462142976.0000000000 -0.4556721059 2.5306847104 1.5548565052 0.3439792704 0.5452393257 -0.6153360326 0.453601042939 +1403715548512143104.0000000000 -0.3822141479 2.5575270514 1.5441082141 0.3439209152 0.5440134409 -0.6166903229 0.453277868266 +1403715548562142976.0000000000 -0.3089326989 2.5854861915 1.5333387679 0.3452373757 0.5412304355 -0.6195703967 0.451678307666 +1403715548612143104.0000000000 -0.2359574819 2.6141733034 1.5223941749 0.3461270152 0.5386258826 -0.6225214243 0.450050357387 +1403715548662142976.0000000000 -0.1632217103 2.6433902058 1.5113474648 0.3465991285 0.5359161372 -0.6252469757 0.449142691613 +1403715548712143104.0000000000 -0.0908737576 2.6733392229 1.5004028360 0.3472602558 0.5330359178 -0.6275942813 0.448785520219 +1403715548762142976.0000000000 -0.0189529235 2.7037125878 1.4897217789 0.3478727266 0.5304098535 -0.6293657351 0.448941783407 +1403715548812143104.0000000000 0.0528996218 2.7341592663 1.4793143486 0.3473891700 0.5283193965 -0.6316056894 0.448635300562 +1403715548862142976.0000000000 0.1247660865 2.7647745537 1.4692776296 0.3469999961 0.5261914313 -0.6328574778 0.449672095123 +1403715548912143104.0000000000 0.1966874939 2.7953173876 1.4595473249 0.3474917587 0.5236382981 -0.6343627195 0.450151475122 +1403715548962142976.0000000000 0.2683848690 2.8260469550 1.4496457996 0.3483151375 0.5228681679 -0.6343076802 0.450487747669 +1403715549012143104.0000000000 0.3395265424 2.8573378739 1.4396771999 0.3500770780 0.5233387355 -0.6331073057 0.450264085702 +1403715549062142976.0000000000 0.4100183586 2.8892442145 1.4299759708 0.3531131957 0.5249555351 -0.6301335940 0.450182641651 +1403715549112143104.0000000000 0.4801898333 2.9216427212 1.4212821575 0.3587985465 0.5259194492 -0.6257007056 0.45074489792 +1403715549162142976.0000000000 0.5497521721 2.9538847640 1.4136707481 0.3648699667 0.5266403764 -0.6194257570 0.453686624222 +1403715549212143104.0000000000 0.6181532673 2.9861829208 1.4068944206 0.3711634007 0.5267510466 -0.6131171216 0.457010350158 +1403715549262142976.0000000000 0.6850701861 3.0185365129 1.4003684412 0.3778959751 0.5261122826 -0.6071351704 0.460203632097 +1403715549312143104.0000000000 0.7497783753 3.0507302207 1.3937251083 0.3829535036 0.5262308448 -0.6017574436 0.462942427508 +1403715549362142976.0000000000 0.8117952251 3.0836914502 1.3877866942 0.3909473221 0.5241307667 -0.5996960143 0.461315316359 +1403715549412143104.0000000000 0.8711209208 3.1166818681 1.3814723851 0.3975635291 0.5226136866 -0.6002668465 0.456615689485 +1403715549462142976.0000000000 0.9277872865 3.1491186003 1.3749970680 0.4033324691 0.5214958778 -0.6027231450 0.449543968141 +1403715549512143104.0000000000 0.9822090718 3.1803091467 1.3682567723 0.4068958192 0.5214252115 -0.6057083722 0.442344785229 +1403715549562142976.0000000000 1.0341138686 3.2102525231 1.3610798588 0.4081080961 0.5227683255 -0.6102840076 0.433260302584 +1403715549612143104.0000000000 1.0841196174 3.2382311194 1.3541661626 0.4089160590 0.5226642065 -0.6158865459 0.42460987564 +1403715549662142976.0000000000 1.1326439198 3.2636892818 1.3471753792 0.4079683495 0.5215739648 -0.6229058961 0.416546119452 +1403715549712143104.0000000000 1.1805280677 3.2860877844 1.3410412103 0.4079112304 0.5170790977 -0.6295693355 0.41216512071 +1403715549762142976.0000000000 1.2277473425 3.3049020246 1.3355755085 0.4075018061 0.5107839800 -0.6357334916 0.410956118658 +1403715549812143104.0000000000 1.2744860444 3.3201105339 1.3311663582 0.4067626165 0.5023868228 -0.6415293575 0.413027526489 +1403715549862142976.0000000000 1.3199455253 3.3317902924 1.3269257040 0.4052870767 0.4927688280 -0.6478654006 0.416163057343 +1403715549912143104.0000000000 1.3642363338 3.3398191633 1.3233072527 0.4037738321 0.4812789386 -0.6565597623 0.417452457624 +1403715549962142976.0000000000 1.4072732519 3.3438304012 1.3210396411 0.4024427363 0.4675316223 -0.6664945843 0.418615569831 +1403715550012143104.0000000000 1.4489186531 3.3431913585 1.3191729007 0.3993342768 0.4531894233 -0.6776449172 0.419462570588 +1403715550062142976.0000000000 1.4884233853 3.3379208888 1.3168110248 0.3926465714 0.4397869596 -0.6893201449 0.421015246727 +1403715550112143104.0000000000 1.5257118247 3.3273745776 1.3147994518 0.3818734670 0.4280702440 -0.6995899755 0.426030970121 +1403715550162142976.0000000000 1.5610563572 3.3115350723 1.3145214534 0.3678745616 0.4182002472 -0.7085683765 0.433252485224 +1403715550212143104.0000000000 1.5942913988 3.2909001626 1.3177021827 0.3538114589 0.4081958276 -0.7165038854 0.441379428718 +1403715550262142976.0000000000 1.6254828184 3.2662013088 1.3242316072 0.3390849923 0.3987543963 -0.7243576073 0.448689598882 +1403715550312143104.0000000000 1.6551875317 3.2375664278 1.3346232592 0.3250637473 0.3889370126 -0.7318867702 0.455415542144 +1403715550362142976.0000000000 1.6833378803 3.2051387355 1.3489132504 0.3120742307 0.3782549980 -0.7380343269 0.463506378965 +1403715550412143104.0000000000 1.7102919281 3.1691491847 1.3659434050 0.2983658667 0.3676099580 -0.7431026065 0.472905111525 +1403715550462142976.0000000000 1.7361284778 3.1302741804 1.3835279789 0.2840332005 0.3566644785 -0.7477093228 0.482748753861 +1403715550512143104.0000000000 1.7608926759 3.0890349539 1.4014374702 0.2704267086 0.3446023703 -0.7523947037 0.491956107298 +1403715550562142976.0000000000 1.7846514797 3.0461290511 1.4180517925 0.2574931716 0.3316407737 -0.7579227664 0.499264202563 +1403715550612143104.0000000000 1.8076686132 3.0022678001 1.4320399091 0.2470261718 0.3167452112 -0.7640137978 0.50490935655 +1403715550662142976.0000000000 1.8297875193 2.9573441879 1.4429238676 0.2385213181 0.3000164875 -0.7703994694 0.509492242882 +1403715550712143104.0000000000 1.8509214538 2.9110349835 1.4507855679 0.2307184698 0.2824438693 -0.7767274292 0.513506522964 +1403715550762142976.0000000000 1.8710398263 2.8636315072 1.4559460164 0.2250587920 0.2633511498 -0.7832541837 0.516243736747 +1403715550812143104.0000000000 1.8895900759 2.8150406659 1.4578309201 0.2203754931 0.2435991176 -0.7897707100 0.518031212996 +1403715550862142976.0000000000 1.9062291008 2.7648878308 1.4564985515 0.2151507540 0.2242489765 -0.7958723049 0.519624695256 +1403715550912143104.0000000000 1.9206924417 2.7130640902 1.4526550745 0.2099979766 0.2046886117 -0.8015669639 0.521050692792 +1403715550962142976.0000000000 1.9325984987 2.6589317318 1.4468587581 0.2033762174 0.1860156113 -0.8062978587 0.52337373797 +1403715551012143104.0000000000 1.9414055712 2.6025676206 1.4406089689 0.1946720845 0.1690268216 -0.8104798428 0.525980168361 +1403715551062142976.0000000000 1.9467265155 2.5433749307 1.4362659309 0.1818903169 0.1549111731 -0.8130892699 0.530852409039 +1403715551112143104.0000000000 1.9482767769 2.4819934366 1.4353598767 0.1688930264 0.1408307635 -0.8151270796 0.535919476877 +1403715551162142976.0000000000 1.9462372461 2.4186481336 1.4379778773 0.1559353620 0.1266707271 -0.8169092591 0.540645865751 +1403715551212143104.0000000000 1.9410969496 2.3534702070 1.4442649640 0.1457362366 0.1104990594 -0.8189363567 0.543961534349 +1403715551262142976.0000000000 1.9328441742 2.2863290918 1.4540891630 0.1368469844 0.0929958199 -0.8199593194 0.547988498803 +1403715551312143104.0000000000 1.9212109711 2.2179940861 1.4655676037 0.1294510412 0.0738749526 -0.8217309987 0.550039166857 +1403715551362142976.0000000000 1.9058413386 2.1486773420 1.4774653565 0.1215240962 0.0549390756 -0.8232856062 0.551737621234 +1403715551412143104.0000000000 1.8867308174 2.0782304511 1.4893410126 0.1133774048 0.0358983860 -0.8240716634 0.553861682711 +1403715551462142976.0000000000 1.8638423127 2.0070023221 1.5008592013 0.1036999171 0.0176137974 -0.8237780490 0.55706894298 +1403715551512143104.0000000000 1.8370475681 1.9351948589 1.5119124442 0.0926558597 0.0004181246 -0.8231628596 0.560194272984 +1403715551562142976.0000000000 1.8058842560 1.8628540454 1.5226763270 0.0788353484 -0.0152088628 -0.8211830027 0.564988632157 +1403715551612143104.0000000000 1.7706266711 1.7906095060 1.5329063271 0.0622777802 -0.0285969224 -0.8190499274 0.569614703649 +1403715551662142976.0000000000 1.7314847323 1.7187107466 1.5435746852 0.0441132009 -0.0408475862 -0.8148113582 0.576600338783 +1403715551712143104.0000000000 1.6893119652 1.6475464406 1.5546355202 0.0262743390 -0.0534702507 -0.8093738733 0.584264088142 +1403715551762142976.0000000000 1.6444437833 1.5781024745 1.5656311001 0.0097360179 -0.0666921272 -0.8043366083 0.590338877859 +1403715551812143104.0000000000 1.5971958340 1.5107294124 1.5768301751 0.0044823324 0.0815638554 0.7977896555 -0.597376691696 +1403715551862142976.0000000000 1.5479589178 1.4456489699 1.5881376560 0.0172332818 0.0972106558 0.7907210817 -0.604163283656 +1403715551912143104.0000000000 1.4969484873 1.3833367833 1.5995213376 0.0290254410 0.1132934545 0.7819591327 -0.612259774757 +1403715551962142976.0000000000 1.4441566876 1.3245659054 1.6101404977 0.0433076338 0.1274403481 0.7746323179 -0.617922469705 +1403715552012143104.0000000000 1.3897316735 1.2697946937 1.6200523306 0.0604735343 0.1394509102 0.7689807803 -0.620938769034 +1403715552062142976.0000000000 1.3344760053 1.2193629411 1.6284775414 0.0799549672 0.1494594725 0.7666311806 -0.619310666975 +1403715552112143104.0000000000 1.2790802533 1.1730505839 1.6366200821 0.0949379957 0.1617858318 0.7643947407 -0.616857197461 +1403715552162142976.0000000000 1.2236494759 1.1307878113 1.6439520583 0.1101216357 0.1738794304 0.7628953807 -0.612886455347 +1403715552212143104.0000000000 1.1689145774 1.0924443341 1.6518042596 0.1249632283 0.1860500079 0.7584874989 -0.611936516386 +1403715552262142976.0000000000 1.1143608002 1.0574298256 1.6597323295 0.1419769038 0.1972971195 0.7523886304 -0.612231781421 +1403715552312143104.0000000000 1.0608455973 1.0261018776 1.6676371410 0.1574071149 0.2097571281 0.7446382967 -0.613790480953 +1403715552362142976.0000000000 1.0086658387 0.9987526958 1.6746181022 0.1726902859 0.2230474123 0.7378729380 -0.613165103658 +1403715552412143104.0000000000 0.9581408967 0.9756175365 1.6809807381 0.1878399628 0.2373626912 0.7320268298 -0.610337465417 +1403715552462142976.0000000000 0.9097651066 0.9566838917 1.6873985885 0.2022166356 0.2527735228 0.7256381137 -0.607176503468 +1403715552512143104.0000000000 0.8635356643 0.9415135795 1.6939827125 0.2153272005 0.2695137037 0.7179925215 -0.604552147661 +1403715552562142976.0000000000 0.8199425336 0.9301526995 1.7004388482 0.2270216331 0.2876168808 0.7094108744 -0.602058069661 +1403715552612143104.0000000000 0.7786692736 0.9228781127 1.7068735851 0.2383954510 0.3064176834 0.6993319837 -0.600175465023 +1403715552662142976.0000000000 0.7400998957 0.9199383749 1.7128120258 0.2480894516 0.3268011828 0.6890140518 -0.597421331464 +1403715552712143104.0000000000 0.7041394367 0.9213077173 1.7177272543 0.2576493533 0.3477696996 0.6791421806 -0.592822861595 +1403715552762142976.0000000000 0.6705201538 0.9268948041 1.7217454602 0.2669176543 0.3694415057 0.6696985323 -0.586320574048 +1403715552812143104.0000000000 0.6391698952 0.9367558180 1.7252616624 0.2766308208 0.3908686841 0.6597475757 -0.579163359692 +1403715552862142976.0000000000 0.6100633389 0.9513081379 1.7274740739 0.2860836388 0.4124811107 0.6501373886 -0.570383082501 +1403715552912143104.0000000000 0.5834492867 0.9702629501 1.7288876853 0.2929068547 0.4350754561 0.6398744807 -0.561672120451 +1403715552962142976.0000000000 0.5592439979 0.9934856308 1.7291970074 0.2974804259 0.4582225882 0.6297030637 -0.552278469097 +1403715553012143104.0000000000 0.5367280934 1.0212520937 1.7287306336 0.3013398596 0.4811663127 0.6182847138 -0.543504628567 +1403715553062142976.0000000000 0.5154732459 1.0535176721 1.7272099020 0.3056968639 0.5028694565 0.6060912092 -0.535093620992 +1403715553112143104.0000000000 0.4954940121 1.0905882445 1.7246486739 0.3122189732 0.5223264998 0.5940591567 -0.526106508971 +1403715553162142976.0000000000 0.4765566960 1.1325282556 1.7214699329 0.3229919452 0.5383581439 0.5817510269 -0.517119381759 +1403715553212143104.0000000000 0.4586051910 1.1791208118 1.7182394279 0.3355545579 0.5521833234 0.5684923703 -0.50922798528 +1403715553262142976.0000000000 0.4416885290 1.2301224175 1.7149074222 0.3467767656 0.5656262774 0.5532491095 -0.503714415093 +1403715553312143104.0000000000 0.4260675001 1.2859366609 1.7111061925 0.3612909110 0.5764445977 0.5379435564 -0.497792359853 +1403715553362142976.0000000000 0.4125287996 1.3467579977 1.7069974378 0.3796616707 0.5842388404 0.5216595526 -0.492334545125 +1403715553412143104.0000000000 0.4019621507 1.4119356213 1.7020030806 0.3993973465 0.5906372151 0.5064294883 -0.484931555062 +1403715553462142976.0000000000 0.3948504093 1.4810540192 1.6963494955 0.4235495267 0.5935552716 0.4920404330 -0.475598728162 +1403715553512143104.0000000000 0.3917769919 1.5529833876 1.6897518172 0.4449469881 0.5972680172 0.4774445316 -0.466197182179 +1403715553562142976.0000000000 0.3932173474 1.6270384309 1.6817306308 0.4645520183 0.6008855077 0.4646913101 -0.45518129926 +1403715553612143104.0000000000 0.3998155114 1.7024546047 1.6725252085 0.4801049950 0.6056669882 0.4542604669 -0.443073494338 +1403715553662142976.0000000000 0.4118206497 1.7784213453 1.6627285166 0.4933042754 0.6096087288 0.4467152696 -0.430666411038 +1403715553712143104.0000000000 0.4294512438 1.8541558272 1.6518108975 0.5001190107 0.6156524314 0.4425729118 -0.418308829225 +1403715553762142976.0000000000 0.4523751185 1.9293066312 1.6393920544 0.5016129967 0.6239185664 0.4444571338 -0.401955072474 +1403715553812143104.0000000000 0.4797469963 2.0035986780 1.6262520980 0.4988900958 0.6335121904 0.4494907443 -0.384355366547 +1403715553862142976.0000000000 0.5108545064 2.0766566617 1.6140806870 0.4951555243 0.6418236066 0.4556421628 -0.367795710026 +1403715553912143104.0000000000 0.5446991506 2.1485505000 1.6030254043 0.4915278179 0.6484049195 0.4619605393 -0.352936148369 +1403715553962142976.0000000000 0.5802117284 2.2189833133 1.5928012230 0.4849871888 0.6555587526 0.4681607401 -0.340375777604 +1403715554012143104.0000000000 0.6162877473 2.2880571265 1.5832682421 0.4753429227 0.6639929960 0.4737855889 -0.329681092609 +1403715554062142976.0000000000 0.6524567565 2.3556952849 1.5734898702 0.4628408675 0.6732074705 0.4794991183 -0.320391367854 +1403715554112143104.0000000000 0.6878002674 2.4226316497 1.5639461359 0.4496177533 0.6821424240 0.4853776152 -0.311342512311 +1403715554162142976.0000000000 0.7215649489 2.4891711712 1.5545762997 0.4371782169 0.6897069678 0.4920415208 -0.301785763586 +1403715554212143104.0000000000 0.7520882532 2.5556470639 1.5464181168 0.4264949480 0.6958318514 0.4968444703 -0.295068917914 +1403715554262142976.0000000000 0.7786605943 2.6225248615 1.5388063466 0.4191529778 0.6991689622 0.5023034430 -0.288383069377 +1403715554312143104.0000000000 0.8010213527 2.6899675408 1.5309604434 0.4152012704 0.7001047916 0.5083660104 -0.281114185326 +1403715554362142976.0000000000 0.8186068198 2.7582222056 1.5212623905 0.4176119337 0.6959140225 0.5170960420 -0.271874289843 +1403715554412143104.0000000000 0.8311650449 2.8263733400 1.5094214690 0.4277161263 0.6847650019 0.5284190202 -0.262543608931 +1403715554462142976.0000000000 0.8389480218 2.8937628144 1.4958304631 0.4505827395 0.6618045133 0.5438326377 -0.251467777886 +1403715554512143104.0000000000 0.8425277278 2.9583455977 1.4791040521 0.4762135211 0.6341112024 0.5597430820 -0.240439904054 +1403715554562142976.0000000000 0.8426564551 3.0180149181 1.4595591314 0.5028481110 0.6042620611 0.5747311991 -0.227365757163 +1403715554612143104.0000000000 0.8394289780 3.0702138603 1.4385611656 0.5280223196 0.5750384509 0.5864851924 -0.215773791528 +1403715554662142976.0000000000 0.8336302382 3.1133971737 1.4154263954 0.5479058623 0.5505659450 0.5954419268 -0.205244289098 +1403715554712143104.0000000000 0.8257871143 3.1455206024 1.3911021913 0.5632268125 0.5313503991 0.6011484373 -0.197643283232 +1403715554762142976.0000000000 0.8163230531 3.1647669005 1.3661996363 0.5757725660 0.5159395376 0.6045002095 -0.192020422297 +1403715554812143104.0000000000 0.8048530335 3.1692082099 1.3427091095 0.5874109827 0.5023792856 0.6055951246 -0.189256270495 +1403715554862142976.0000000000 0.7923230629 3.1557985839 1.3234942857 0.5948283129 0.4950467880 0.6030747617 -0.193413514759 +1403715554912143104.0000000000 0.7790062678 3.1232003457 1.3102850259 0.5985562820 0.4937665519 0.5979925046 -0.200823140893 +1403715554962142976.0000000000 0.7655279369 3.0714052450 1.3052379812 0.6021960390 0.4943342721 0.5895196422 -0.213213858545 +1403715555012143104.0000000000 0.7532906149 3.0009156457 1.3071888690 0.5953726594 0.5081624850 0.5773244129 -0.232376435001 +1403715555062142976.0000000000 0.7431369371 2.9145345366 1.3156966968 0.5784252733 0.5321960524 0.5625764209 -0.256318816536 +1403715555112143104.0000000000 0.7344793478 2.8158750902 1.3299800124 0.5541028430 0.5613434812 0.5456483511 -0.283074923795 +1403715555162142976.0000000000 0.7272308120 2.7095612331 1.3472104025 0.5239044378 0.5924886115 0.5285232533 -0.308455111892 +1403715555212143104.0000000000 0.7210148859 2.5995522128 1.3648960389 0.4920892565 0.6210453265 0.5113978390 -0.332600535729 +1403715555262142976.0000000000 0.7154086566 2.4880781087 1.3802089201 0.4536162703 0.6510560707 0.4918501933 -0.35838758278 +1403715555312143104.0000000000 0.7099018300 2.3788128675 1.3913731471 0.4182933667 0.6755124723 0.4724875645 -0.38140406471 +1403715555362142976.0000000000 0.7040116865 2.2745338641 1.3968377397 0.3971045650 0.6889963335 0.4598520387 -0.39513050936 +1403715555412143104.0000000000 0.6980085327 2.1765108115 1.4000123523 0.3858105108 0.6959286575 0.4510746504 -0.404184627573 +1403715555462142976.0000000000 0.6923189910 2.0866976980 1.4040534624 0.3891352704 0.6943788864 0.4482878762 -0.406755065653 +1403715555512143104.0000000000 0.6873835251 2.0046310523 1.4106304414 0.3968525540 0.6900699996 0.4488150014 -0.406049923636 +1403715555562142976.0000000000 0.6833370127 1.9299816791 1.4201358543 0.4081847430 0.6831999286 0.4528221411 -0.401964154734 +1403715555612143104.0000000000 0.6802779124 1.8615451423 1.4331454756 0.4176289956 0.6768647061 0.4570752316 -0.398148746527 +1403715555662142976.0000000000 0.6787643710 1.7986136819 1.4494062105 0.4248358251 0.6715029736 0.4632009586 -0.392483311871 +1403715555712143104.0000000000 0.6787925808 1.7399445501 1.4683813184 0.4278663350 0.6684178807 0.4693837963 -0.387074654302 +1403715555762142976.0000000000 0.6799140028 1.6846913962 1.4907578192 0.4233711448 0.6693895273 0.4722815681 -0.386813462723 +1403715555812143104.0000000000 0.6818196863 1.6335181443 1.5166487131 0.4156650025 0.6722793871 0.4735833094 -0.388563869354 +1403715555862142976.0000000000 0.6836755092 1.5870521062 1.5459383871 0.4067338807 0.6760285011 0.4730484058 -0.392145663851 +1403715555912143104.0000000000 0.6854146535 1.5460611454 1.5779263700 0.4014078996 0.6776283471 0.4734274330 -0.394408401444 +1403715555962142976.0000000000 0.6872104290 1.5101353265 1.6113952590 0.3956187533 0.6796001811 0.4742188263 -0.395911480881 +1403715556012143104.0000000000 0.6888691913 1.4789716235 1.6440997626 0.3874837515 0.6832032441 0.4731811741 -0.398985270469 +1403715556062142976.0000000000 0.6899657402 1.4527951139 1.6751482302 0.3758426469 0.6889686648 0.4699608561 -0.403981778519 +1403715556112143104.0000000000 0.6906903042 1.4322560636 1.7034991223 0.3688599824 0.6920549093 0.4675766974 -0.40789011754 +1403715556162142976.0000000000 0.6909904578 1.4180005579 1.7295166594 0.3689985031 0.6913600923 0.4653036537 -0.411526229304 +1403715556212143104.0000000000 0.6908613532 1.4101713413 1.7547817621 0.3718555909 0.6890853463 0.4628756419 -0.415488802789 +1403715556262142976.0000000000 0.6907063440 1.4089335027 1.7796638804 0.3774820251 0.6851173853 0.4620376026 -0.417902791138 +1403715556312143104.0000000000 0.6908212855 1.4137229313 1.8039133425 0.3830489742 0.6807647522 0.4630115725 -0.418871244229 +1403715556362142976.0000000000 0.6915690089 1.4241629105 1.8272079503 0.3869013279 0.6770830019 0.4652030158 -0.418870057639 +1403715556412143104.0000000000 0.6928884136 1.4401323735 1.8490704544 0.3909942973 0.6732139090 0.4682809578 -0.417874905699 +1403715556462142976.0000000000 0.6949183162 1.4606391780 1.8674085180 0.3967433597 0.6683768063 0.4745787704 -0.413088540093 +1403715556512143104.0000000000 0.6975708656 1.4854729766 1.8811304102 0.4053744007 0.6619303652 0.4852584879 -0.402546875258 +1403715556562142976.0000000000 0.7003036612 1.5133200836 1.8905831176 0.4137470213 0.6552724187 0.4961685665 -0.391469300618 +1403715556612143104.0000000000 0.7029546520 1.5434218538 1.8968050644 0.4200331572 0.6497713986 0.5053915354 -0.38203229229 +1403715556662142976.0000000000 0.7061243918 1.5750118336 1.8993436193 0.4223120122 0.6468038358 0.5137697519 -0.37328006155 +1403715556712143104.0000000000 0.7090551066 1.6077368597 1.8979842632 0.4217752372 0.6456673780 0.5212807291 -0.365356931969 +1403715556762142976.0000000000 0.7108612606 1.6414638386 1.8934623453 0.4219415753 0.6439264447 0.5282478046 -0.358159598212 +1403715556812143104.0000000000 0.7108534923 1.6761603778 1.8868730611 0.4268236091 0.6390926238 0.5338607862 -0.352668237504 +1403715556862142976.0000000000 0.7093828334 1.7108290887 1.8795452240 0.4311554233 0.6349569063 0.5378193724 -0.34883384408 +1403715556912143104.0000000000 0.7066969663 1.7453299309 1.8720035163 0.4362606495 0.6300955725 0.5418926001 -0.344976267629 +1403715556962142976.0000000000 0.7028564405 1.7790828818 1.8644906956 0.4396286735 0.6269055542 0.5447717091 -0.341964677212 +1403715557012143104.0000000000 0.6976597849 1.8113212127 1.8568085407 0.4365388994 0.6285768144 0.5468096326 -0.33959417441 +1403715557062142976.0000000000 0.6909532938 1.8422730673 1.8489831902 0.4296608817 0.6330320828 0.5483989724 -0.337521074806 +1403715557112143104.0000000000 0.6824656715 1.8721157986 1.8414316638 0.4207386005 0.6389192983 0.5497131010 -0.335524465379 +1403715557162142976.0000000000 0.6718339266 1.9013291503 1.8345658263 0.4107464773 0.6458447162 0.5504249564 -0.333473089316 +1403715557212143104.0000000000 0.6581932154 1.9304615967 1.8281340668 0.4019950399 0.6517706067 0.5510262937 -0.33160984282 +1403715557262142976.0000000000 0.6411642041 1.9599360015 1.8218641955 0.3943572039 0.6570746564 0.5516293097 -0.329302894472 +1403715557312143104.0000000000 0.6201976300 1.9901271203 1.8162643305 0.3902623341 0.6602909767 0.5518952476 -0.327296153958 +1403715557362142976.0000000000 0.5954894810 2.0206763800 1.8106036314 0.3867590306 0.6630832132 0.5520949082 -0.325467843322 +1403715557412143104.0000000000 0.5665026413 2.0522316252 1.8054263706 0.3872238672 0.6637442128 0.5505834352 -0.326127547918 +1403715557462142976.0000000000 0.5335081833 2.0846788404 1.8002794019 0.3916926631 0.6617599723 0.5487632462 -0.327886407607 +1403715557512143104.0000000000 0.4966986894 2.1179231654 1.7952921788 0.4008168034 0.6567755664 0.5461677950 -0.3311985585 +1403715557562142976.0000000000 0.4570601106 2.1515831406 1.7899213611 0.4112949953 0.6508761069 0.5435362198 -0.334312874392 +1403715557612143104.0000000000 0.4149662862 2.1852797325 1.7838702234 0.4212383203 0.6450955697 0.5419958565 -0.335634436527 +1403715557662142976.0000000000 0.3707142880 2.2187176563 1.7776709965 0.4310216473 0.6392343120 0.5402994812 -0.337159167915 +1403715557712143104.0000000000 0.3247739459 2.2515457175 1.7712281116 0.4402283281 0.6340417517 0.5388151546 -0.337443781062 +1403715557762142976.0000000000 0.2778119099 2.2828618434 1.7648943873 0.4452950426 0.6316932625 0.5366848501 -0.338593146306 +1403715557812143104.0000000000 0.2299675829 2.3127661124 1.7601306648 0.4466636219 0.6324297790 0.5336190319 -0.340257126674 +1403715557862142976.0000000000 0.1815340304 2.3416598826 1.7579772076 0.4463267400 0.6347865492 0.5305663621 -0.341083294068 +1403715557912143104.0000000000 0.1323449382 2.3695440760 1.7586885556 0.4455295905 0.6375677251 0.5277413995 -0.341320663237 +1403715557962142976.0000000000 0.0822922445 2.3965906127 1.7628703193 0.4454092711 0.6400348111 0.5246491578 -0.341627403785 +1403715558012143104.0000000000 0.0318899072 2.4227782610 1.7699339233 0.4455021976 0.6421557379 0.5215792942 -0.342226299603 +1403715558062142976.0000000000 -0.0189793457 2.4485756315 1.7796958827 0.4464075276 0.6434436416 0.5197744590 -0.341372393727 +1403715558112143104.0000000000 -0.0705544688 2.4738307539 1.7921240578 0.4456031423 0.6457799893 0.5183652964 -0.340152119556 +1403715558162142976.0000000000 -0.1230695730 2.4985866609 1.8069462048 0.4451122887 0.6474485854 0.5177920577 -0.338491897541 +1403715558212143104.0000000000 -0.1759550119 2.5231441610 1.8217692983 0.4461760897 0.6477755186 0.5193544489 -0.334043007528 +1403715558262142976.0000000000 -0.2297444260 2.5473005092 1.8365619491 0.4483640922 0.6471086748 0.5206566606 -0.330358359306 +1403715558312143104.0000000000 -0.2845027878 2.5712282712 1.8506006681 0.4541288869 0.6435402648 0.5231826196 -0.325427147211 +1403715558362142976.0000000000 -0.3401805411 2.5939562971 1.8644369084 0.4611521681 0.6391269891 0.5234377574 -0.323833728706 +1403715558412143104.0000000000 -0.3967337118 2.6150448390 1.8781615435 0.4685692115 0.6339841039 0.5227312745 -0.324436534199 +1403715558462142976.0000000000 -0.4541790744 2.6336687700 1.8913558214 0.4737120685 0.6306043261 0.5175892281 -0.331717426531 +1403715558512143104.0000000000 -0.5113566508 2.6507025531 1.9025375511 0.4799666184 0.6261719913 0.5108207833 -0.341471536027 +1403715558562142976.0000000000 -0.5671287653 2.6661872662 1.9109755809 0.4851021046 0.6223280019 0.5038970472 -0.351385218796 +1403715558612143104.0000000000 -0.6212436127 2.6807251734 1.9165612783 0.4899435532 0.6186446790 0.4978503654 -0.359693048999 +1403715558662142976.0000000000 -0.6732083595 2.6944528529 1.9180137510 0.4911578952 0.6177797459 0.4937687533 -0.365108923271 +1403715558712143104.0000000000 -0.7228144606 2.7071400004 1.9160307917 0.4921305553 0.6164028699 0.4914931677 -0.369174057249 +1403715558762142976.0000000000 -0.7698479038 2.7182780361 1.9117201959 0.4916080125 0.6146018737 0.4929215140 -0.370964256972 +1403715558812143104.0000000000 -0.8144280290 2.7282193053 1.9071469726 0.4915140951 0.6110580735 0.4964717445 -0.372206571644 +1403715558862142976.0000000000 -0.8564030594 2.7367804429 1.9028438907 0.4909633002 0.6063491964 0.5020800652 -0.373110302776 +1403715558912143104.0000000000 -0.8953840085 2.7441135459 1.8989083601 0.4910679352 0.6000123923 0.5096237235 -0.372989373331 +1403715558962142976.0000000000 -0.9316163305 2.7497230003 1.8958758615 0.4908986641 0.5927980465 0.5168709999 -0.374771059582 +1403715559012143104.0000000000 -0.9646172633 2.7535961065 1.8935696740 0.4908840844 0.5847202706 0.5254438926 -0.375557900362 +1403715559062142976.0000000000 -0.9943851800 2.7548338488 1.8922833788 0.4883018724 0.5775356582 0.5337127962 -0.378370844599 +1403715559112143104.0000000000 -1.0212824893 2.7535615368 1.8923518466 0.4845961679 0.5702617050 0.5408044881 -0.384055526603 +1403715559162142976.0000000000 -1.0452577592 2.7499303885 1.8931228264 0.4801532977 0.5629020442 0.5482263412 -0.389925605851 +1403715559212143104.0000000000 -1.0663492780 2.7442809966 1.8944146964 0.4762416255 0.5543962731 0.5560175606 -0.395832235718 +1403715559262142976.0000000000 -1.0847400000 2.7366367839 1.8956391818 0.4724849951 0.5454652621 0.5640903241 -0.401282548084 +1403715559312143104.0000000000 -1.1001809731 2.7270321584 1.8963583124 0.4686181604 0.5359889119 0.5728187863 -0.406191511634 +1403715559362142976.0000000000 -1.1123938477 2.7156225186 1.8966456138 0.4641146786 0.5268081831 0.5822419297 -0.40995736185 +1403715559412143104.0000000000 -1.1216195323 2.7023223882 1.8963350996 0.4573736914 0.5192984913 0.5923126844 -0.412679133658 +1403715559462142976.0000000000 -1.1283504226 2.6875503810 1.8945541054 0.4494532248 0.5136390276 0.6039961338 -0.411528150329 +1403715559512143104.0000000000 -1.1332497323 2.6704697013 1.8906392061 0.4371366553 0.5128327479 0.6138949695 -0.411153357817 +1403715559562142976.0000000000 -1.1365250141 2.6514591073 1.8838901387 0.4231510599 0.5144327116 0.6210318831 -0.413063634195 +1403715559612143104.0000000000 -1.1387971473 2.6312174971 1.8741643085 0.4104170409 0.5161182888 0.6261698840 -0.416042114293 +1403715559662142976.0000000000 -1.1405639564 2.6103823390 1.8611702548 0.4018932685 0.5155971637 0.6309000794 -0.417859372583 +1403715559712143104.0000000000 -1.1424012632 2.5886315473 1.8453313846 0.3969379743 0.5123579976 0.6363728444 -0.418281161135 +1403715559762142976.0000000000 -1.1443093228 2.5657416406 1.8284193632 0.3944053276 0.5067999836 0.6419294782 -0.41895675099 +1403715559812143104.0000000000 -1.1458145064 2.5415363588 1.8111608227 0.3914410439 0.5009244972 0.6474711659 -0.420273299809 +1403715559862142976.0000000000 -1.1465206943 2.5157362457 1.7940080888 0.3878326260 0.4946077994 0.6532651345 -0.422129888812 +1403715559912143104.0000000000 -1.1468002271 2.4884315137 1.7767742249 0.3854231539 0.4861412340 0.6602876834 -0.423244454377 +1403715559962142976.0000000000 -1.1467041587 2.4591960092 1.7596876328 0.3828679902 0.4768878059 0.6677686207 -0.424352674001 +1403715560012143104.0000000000 -1.1461974234 2.4277200005 1.7429532335 0.3801799691 0.4669782479 0.6756387916 -0.425331318336 +1403715560062142976.0000000000 -1.1452254989 2.3936264324 1.7272463839 0.3756234834 0.4579885744 0.6823595987 -0.428414335115 +1403715560112143104.0000000000 -1.1437233524 2.3570216607 1.7134674000 0.3709697411 0.4488258859 0.6899353194 -0.430030266843 +1403715560162142976.0000000000 -1.1416436952 2.3171022851 1.7031993332 0.3635844105 0.4411313468 0.6957608267 -0.434886632811 +1403715560212143104.0000000000 -1.1388775448 2.2742467120 1.6966277690 0.3527681370 0.4361462025 0.7004119378 -0.441309697342 +1403715560262142976.0000000000 -1.1358843516 2.2289093155 1.6936520965 0.3414957838 0.4313464427 0.7038980059 -0.449275498273 +1403715560312143104.0000000000 -1.1329434289 2.1818419964 1.6934266691 0.3303059575 0.4264317301 0.7083676653 -0.455268277709 +1403715560362142976.0000000000 -1.1303110449 2.1333919592 1.6950647720 0.3200214042 0.4205690023 0.7123965341 -0.461734981786 +1403715560412143104.0000000000 -1.1279366088 2.0841031169 1.6973078235 0.3112973782 0.4133972591 0.7164224369 -0.467905482285 +1403715560462142976.0000000000 -1.1259025745 2.0341548604 1.6989060576 0.3035968855 0.4054627339 0.7218360912 -0.471573493791 +1403715560512143104.0000000000 -1.1244017097 1.9832691736 1.7002697933 0.2964827893 0.3973093514 0.7261735085 -0.476356243178 +1403715560562142976.0000000000 -1.1230212214 1.9318783742 1.7010513232 0.2888902042 0.3893784383 0.7302888379 -0.481253670114 +1403715560612143104.0000000000 -1.1218935741 1.8800595931 1.7017445756 0.2823318895 0.3799361993 0.7354157810 -0.484871960056 +1403715560662142976.0000000000 -1.1210386127 1.8272010772 1.7033800088 0.2755745597 0.3700236184 0.7399584213 -0.489492307016 +1403715560712143104.0000000000 -1.1205196332 1.7732718170 1.7052166870 0.2684597230 0.3598326247 0.7449490818 -0.493457926157 +1403715560762142976.0000000000 -1.1203351426 1.7187292585 1.7071000637 0.2629435686 0.3480361389 0.7499939046 -0.4972330125 +1403715560812143104.0000000000 -1.1201586946 1.6636679606 1.7087149467 0.2573160138 0.3359043004 0.7551308524 -0.500733627535 +1403715560862142976.0000000000 -1.1200738944 1.6080681044 1.7099271220 0.2539056903 0.3216195364 0.7610686442 -0.502859118459 +1403715560912143104.0000000000 -1.1193744006 1.5514267679 1.7112427276 0.2484398288 0.3082564687 0.7671012674 -0.50478831857 +1403715560962142976.0000000000 -1.1182397573 1.4934256353 1.7129908114 0.2424692749 0.2944170623 0.7725097542 -0.507696684913 +1403715561012143104.0000000000 -1.1163428896 1.4343445954 1.7149686292 0.2347048404 0.2810269491 0.7775545153 -0.511220566416 +1403715561062142976.0000000000 -1.1138264741 1.3742973484 1.7172097889 0.2256738244 0.2682779209 0.7823478119 -0.514810822909 +1403715561112143104.0000000000 -1.1105645419 1.3133446902 1.7192035970 0.2148145644 0.2565413210 0.7866515781 -0.518864672423 +1403715561162142976.0000000000 -1.1068133185 1.2513652297 1.7209895017 0.2027912910 0.2459494025 0.7902994714 -0.523269843608 +1403715561212143104.0000000000 -1.1027605774 1.1886459151 1.7227004373 0.1915796781 0.2361496046 0.7936738965 -0.526889302555 +1403715561262142976.0000000000 -1.0985804944 1.1249187598 1.7252745962 0.1775064398 0.2311077308 0.7947917995 -0.53234075181 +1403715561312143104.0000000000 -1.0946797165 1.0609061524 1.7274020744 0.1624791064 0.2284985987 0.7954233891 -0.537299322974 +1403715561362142976.0000000000 -1.0914692833 0.9966290715 1.7292288897 0.1484847293 0.2261655737 0.7960059462 -0.541457248567 +1403715561412143104.0000000000 -1.0891512969 0.9326152937 1.7306649657 0.1365433097 0.2222421624 0.7963753397 -0.545665340748 +1403715561462142976.0000000000 -1.0882784013 0.8691353866 1.7315900294 0.1289880500 0.2153050878 0.7974936332 -0.54864351554 +1403715561512143104.0000000000 -1.0890835950 0.8061580959 1.7327212173 0.1265592232 0.2045722769 0.7986628192 -0.551607331213 +1403715561562142976.0000000000 -1.0908640713 0.7437468064 1.7339723163 0.1250193390 0.1933123493 0.7995208574 -0.554767427866 +1403715561612143104.0000000000 -1.0935428027 0.6818781982 1.7352929139 0.1254839762 0.1807454374 0.8006959639 -0.557199095468 +1403715561662142976.0000000000 -1.0968508495 0.6201739921 1.7363256210 0.1269979994 0.1673205276 0.8019820871 -0.559195923818 +1403715561712143104.0000000000 -1.0995922865 0.5582867703 1.7382395028 0.1257467585 0.1553508121 0.8006668698 -0.564788846858 +1403715561762142976.0000000000 -1.1017351705 0.4972656390 1.7398407923 0.1250226887 0.1421269594 0.7999901143 -0.569372524602 +1403715561812143104.0000000000 -1.1025643273 0.4371304564 1.7424369090 0.1207833391 0.1304606956 0.7982841366 -0.575442290051 +1403715561862142976.0000000000 -1.1022666837 0.3781605839 1.7450974781 0.1165125582 0.1179963641 0.7972438842 -0.580434208973 +1403715561912143104.0000000000 -1.1001423773 0.3204426836 1.7486465953 0.1098059309 0.1058512761 0.7954006785 -0.586579854414 +1403715561962142976.0000000000 -1.0968253109 0.2638308157 1.7528551436 0.1046206655 0.0930916800 0.7921307468 -0.594068460291 +1403715562012143104.0000000000 -1.0919668104 0.2093524245 1.7575907394 0.0985721653 0.0812083978 0.7881914854 -0.602032313715 +1403715562062142976.0000000000 -1.0856562621 0.1573207140 1.7628911759 0.0924037333 0.0710915079 0.7837720435 -0.610007320805 +1403715562112143104.0000000000 -1.0781971094 0.1083169423 1.7683961946 0.0893957614 0.0612834272 0.7791760766 -0.617363248911 +1403715562162142976.0000000000 -1.0692896879 0.0622779716 1.7741196170 0.0874249444 0.0530830499 0.7749842204 -0.623649362262 +1403715562212143104.0000000000 -1.0587191964 0.0196622480 1.7796300477 0.0873082001 0.0453768911 0.7720644948 -0.627881065032 +1403715562262142976.0000000000 -1.0464592717 -0.0189650005 1.7841081379 0.0897747511 0.0378454397 0.7723024541 -0.627739704146 +1403715562312143104.0000000000 -1.0319012165 -0.0534956528 1.7880537380 0.0929062764 0.0315836367 0.7743853591 -0.6250585679 +1403715562362142976.0000000000 -1.0148602810 -0.0844373691 1.7913715722 0.0966975976 0.0263359863 0.7792157945 -0.618691147521 +1403715562412143104.0000000000 -0.9947827018 -0.1123985746 1.7939588887 0.1005285325 0.0217084508 0.7862944574 -0.609232126208 +1403715562462142976.0000000000 -0.9714495054 -0.1378413123 1.7961290744 0.1044545934 0.0166555491 0.7933387347 -0.599521044383 +1403715562512143104.0000000000 -0.9445685149 -0.1613999615 1.7982913585 0.1070219354 0.0107846360 0.7994619705 -0.591008083495 +1403715562562142976.0000000000 -0.9139028861 -0.1841580006 1.8013922840 0.1101916360 0.0021356697 0.8019099781 -0.587191305558 +1403715562612143104.0000000000 -0.8785529192 -0.2063946794 1.8051944434 0.1093789298 -0.0059149660 0.8026888845 -0.586252349763 +1403715562662142976.0000000000 -0.8385133434 -0.2273464258 1.8091929378 0.1000948153 -0.0083697390 0.8057757453 -0.583640663139 +1403715562712143104.0000000000 -0.7944837296 -0.2474383907 1.8136372098 0.0839939755 -0.0051642349 0.8095533272 -0.580983436236 +1403715562762142976.0000000000 -0.7476707106 -0.2670395146 1.8182494472 0.0683083371 -0.0011552235 0.8125440206 -0.578882415607 +1403715562812143104.0000000000 -0.6988944344 -0.2863007294 1.8227240010 0.0539879764 0.0018418253 0.8145771638 -0.577534371506 +1403715562862142976.0000000000 -0.6486246917 -0.3049658977 1.8267723834 0.0398127487 0.0034509744 0.8166710225 -0.575718226991 +1403715562912143104.0000000000 -0.5974581108 -0.3228489549 1.8305316304 0.0264299122 0.0027417538 0.8178338191 -0.574840662195 +1403715562962142976.0000000000 -0.5462278335 -0.3402588717 1.8336559442 0.0151220791 -0.0008397999 0.8183723723 -0.574488709817 +1403715563012143104.0000000000 -0.4950464017 -0.3573648851 1.8363976949 0.0046914006 -0.0062933338 0.8184365508 -0.574543294286 +1403715563062142976.0000000000 -0.4441719755 -0.3742167735 1.8386619988 0.0042752602 0.0142808480 -0.8166871540 0.576888093212 +1403715563112143104.0000000000 -0.3937002728 -0.3907639771 1.8405803230 0.0099002486 0.0264669389 -0.8134669414 0.580924282032 +1403715563162142976.0000000000 -0.3432325450 -0.4068148356 1.8426517940 0.0168304238 0.0395451398 -0.8093213211 0.585791701917 +1403715563212143104.0000000000 -0.2926951732 -0.4220326534 1.8447853380 0.0244150727 0.0548662577 -0.8038504354 0.591792257005 +1403715563262142976.0000000000 -0.2418525001 -0.4360880990 1.8469790159 0.0351972300 0.0707346504 -0.7975977441 0.597992978922 +1403715563312143104.0000000000 -0.1908549921 -0.4477719604 1.8486561733 0.0462104917 0.0887531386 -0.7917298013 0.602620438209 +1403715563362142976.0000000000 -0.1399865070 -0.4566639283 1.8499695499 0.0592054704 0.1078269596 -0.7863621813 0.605394564585 +1403715563412143104.0000000000 -0.0896533232 -0.4628035257 1.8510695306 0.0727947121 0.1277132938 -0.7812929428 0.606606612275 +1403715563462142976.0000000000 -0.0399155098 -0.4671135446 1.8511489682 0.0840134617 0.1491749983 -0.7765698042 0.606323261429 +1403715563512143104.0000000000 0.0094033224 -0.4692749462 1.8490054752 0.0953158436 0.1700250922 -0.7718197022 0.605227812726 +1403715563562142976.0000000000 0.0582383825 -0.4688861549 1.8439794329 0.1061785562 0.1904400942 -0.7659565076 0.60478865162 +1403715563612143104.0000000000 0.1063936938 -0.4659147132 1.8356504206 0.1157101885 0.2104351308 -0.7598170436 0.604157486307 +1403715563662142976.0000000000 0.1540563083 -0.4602868907 1.8245776032 0.1256492635 0.2286166163 -0.7531932460 0.603859784609 +1403715563712143104.0000000000 0.2009923337 -0.4519107228 1.8109555985 0.1344630574 0.2466584430 -0.7457958895 0.604042870891 +1403715563762142976.0000000000 0.2476618776 -0.4406829223 1.7954814050 0.1445271167 0.2630067859 -0.7381066406 0.604266439733 +1403715563812143104.0000000000 0.2942317967 -0.4260015991 1.7777888748 0.1574492185 0.2775039430 -0.7309432536 0.603260528453 +1403715563862142976.0000000000 0.3404403481 -0.4078688080 1.7579252903 0.1762563078 0.2885906496 -0.7248282497 0.600227589645 +1403715563912143104.0000000000 0.3854713822 -0.3866466443 1.7353744907 0.1935937010 0.3006560755 -0.7196630051 0.595157594466 +1403715563962142976.0000000000 0.4290643948 -0.3619704371 1.7107146854 0.2130679655 0.3118004176 -0.7149623695 0.588397273913 +1403715564012143104.0000000000 0.4706432695 -0.3342899271 1.6844322586 0.2332464534 0.3226881914 -0.7119632359 0.578426117818 +1403715564062142976.0000000000 0.5098065430 -0.3041839664 1.6580669156 0.2534862596 0.3340655904 -0.7089445261 0.567047225899 +1403715564112143104.0000000000 0.5457922413 -0.2721991173 1.6317967563 0.2722858008 0.3460759948 -0.7046372467 0.556397518915 +1403715564162142976.0000000000 0.5786275610 -0.2389375956 1.6064455674 0.2902987295 0.3582645549 -0.6987250457 0.546951978598 +1403715564212143104.0000000000 0.6083573953 -0.2049842443 1.5812781161 0.3062364926 0.3719292893 -0.6930961360 0.536195450045 +1403715564262142976.0000000000 0.6347380188 -0.1710048088 1.5578201603 0.3203830059 0.3871199414 -0.6857916191 0.52648146746 +1403715564312143104.0000000000 0.6573641532 -0.1372161223 1.5371433441 0.3314405631 0.4051055159 -0.6762535570 0.518379977134 +1403715564362142976.0000000000 0.6766859470 -0.1034256194 1.5199250005 0.3431926508 0.4234361295 -0.6659120422 0.50939356171 +1403715564412143104.0000000000 0.6923631676 -0.0697024688 1.5052670179 0.3513012080 0.4451552732 -0.6574142607 0.496216418369 +1403715564462142976.0000000000 0.7051346982 -0.0363918745 1.4940966544 0.3572966849 0.4683832084 -0.6488681848 0.481587300211 +1403715564512143104.0000000000 0.7160070178 -0.0036585046 1.4876137271 0.3643649501 0.4901950734 -0.6391353844 0.467389488162 +1403715564562142976.0000000000 0.7249023910 0.0285039437 1.4851137363 0.3703910663 0.5117822545 -0.6278578233 0.454625049534 +1403715564612143104.0000000000 0.7320887570 0.0601270165 1.4864920615 0.3775813510 0.5321006481 -0.6146951736 0.443228008248 +1403715564662142976.0000000000 0.7383866430 0.0910970158 1.4917064014 0.3847052243 0.5511449028 -0.6003783477 0.433344004418 +1403715564712143104.0000000000 0.7440997713 0.1215371218 1.5003871614 0.3913001418 0.5696332193 -0.5845505292 0.425091605735 +1403715564762142976.0000000000 0.7493318360 0.1521030613 1.5127155776 0.3988232540 0.5867861485 -0.5685366855 0.416398925578 +1403715564812143104.0000000000 0.7543294819 0.1826424418 1.5286885873 0.4064083302 0.6028664289 -0.5513074748 0.40919971434 +1403715564862142976.0000000000 0.7593350295 0.2135478753 1.5479291237 0.4145461862 0.6174024932 -0.5348537166 0.401119835925 +1403715564912143104.0000000000 0.7643214753 0.2448183834 1.5708913738 0.4238358624 0.6300213654 -0.5172217650 0.394864390316 +1403715564962142976.0000000000 0.7689037962 0.2767367918 1.5971692710 0.4335312262 0.6413823027 -0.4989863265 0.389476653461 +1403715565012143104.0000000000 0.7723684789 0.3097073882 1.6264834409 0.4428725864 0.6523429757 -0.4817716051 0.382372377128 +1403715565062142976.0000000000 0.7742608603 0.3436546839 1.6585755859 0.4514548248 0.6635317470 -0.4647451105 0.374067031574 +1403715565112143104.0000000000 0.7744831218 0.3786701952 1.6923216629 0.4613268728 0.6737006738 -0.4491373506 0.362740346339 +1403715565162142976.0000000000 0.7730794187 0.4144647078 1.7251512524 0.4716846326 0.6831725768 -0.4347759843 0.348939365929 +1403715565212143104.0000000000 0.7702694344 0.4505028496 1.7551903131 0.4810947885 0.6923672412 -0.4208695717 0.334730057735 +1403715565262142976.0000000000 0.7664671766 0.4866278634 1.7820414644 0.4909254767 0.7001247028 -0.4070972874 0.321075342329 +1403715565312143104.0000000000 0.7622532971 0.5228877601 1.8059245521 0.5022136360 0.7055333357 -0.3932414228 0.308812822735 +1403715565362142976.0000000000 0.7572470407 0.5588360481 1.8268323753 0.5135492706 0.7099563861 -0.3781498410 0.298716879751 +1403715565412143104.0000000000 0.7513054146 0.5941521999 1.8447064361 0.5254382100 0.7133161563 -0.3630085987 0.288651183822 +1403715565462142976.0000000000 0.7437535130 0.6284813924 1.8594266177 0.5372994149 0.7161872946 -0.3484845840 0.277387080517 +1403715565512143104.0000000000 0.7346973587 0.6613145072 1.8711031308 0.5473868500 0.7200657762 -0.3326815619 0.266825584918 +1403715565562142976.0000000000 0.7236580204 0.6924311282 1.8815109096 0.5559185460 0.7250310721 -0.3158897545 0.255926117814 +1403715565612143104.0000000000 0.7104071991 0.7215160800 1.8924425239 0.5637462449 0.7305098400 -0.2986045689 0.24368187538 +1403715565662142976.0000000000 0.6950507463 0.7486533409 1.9046388262 0.5709689592 0.7363558269 -0.2808835600 0.229954276825 +1403715565712143104.0000000000 0.6775803055 0.7735737672 1.9181378242 0.5767969812 0.7431099848 -0.2620107360 0.215506768313 +1403715565762142976.0000000000 0.6579771730 0.7959950970 1.9323779518 0.5810925258 0.7508397100 -0.2419129424 0.200123298622 +1403715565812143104.0000000000 0.6363352312 0.8156078322 1.9471284195 0.5830883641 0.7598297593 -0.2203974319 0.184639292924 +1403715565862142976.0000000000 0.6126031281 0.8325147948 1.9627865449 0.5855174014 0.7682227317 -0.1991462535 0.16536014273 +1403715565912143104.0000000000 0.5875657211 0.8468818111 1.9789493566 0.5882477133 0.7755801701 -0.1748025471 0.147932745313 +1403715565962142976.0000000000 0.5613437609 0.8591432780 1.9950617564 0.5916143628 0.7814907754 -0.1500537694 0.129415918695 +1403715566012143104.0000000000 0.5342697175 0.8694140037 2.0111629696 0.5956487065 0.7857653402 -0.1246103816 0.110669333664 +1403715566062142976.0000000000 0.5066043118 0.8775097610 2.0271560630 0.5981707127 0.7898266414 -0.1000733074 0.0913838511866 +1403715566112143104.0000000000 0.4786864617 0.8833029176 2.0428951031 0.5997563067 0.7932570858 -0.0746724336 0.0738890798675 +1403715566162142976.0000000000 0.4508389314 0.8868796203 2.0584680146 0.6019174644 0.7950025263 -0.0496510692 0.056578446691 +1403715566212143104.0000000000 0.4227749290 0.8882828659 2.0731867171 0.6028954427 0.7964638690 -0.0249439404 0.0392452590449 +1403715566262142976.0000000000 0.3945285615 0.8871191105 2.0881199152 0.6040826597 0.7966350381 -0.0007129628 0.0213599611663 +1403715566312143104.0000000000 0.3663176756 0.8838086336 2.1027478340 0.6045362861 0.7962325297 0.0232124839 0.00328906854818 +1403715566362142976.0000000000 0.3385020223 0.8780520527 2.1164395609 0.6041740295 0.7953423073 0.0471146312 -0.0135855724247 +1403715566412143104.0000000000 0.3110598562 0.8700288674 2.1278713004 0.6031057983 0.7939769560 0.0706834983 -0.0294589966021 +1403715566462142976.0000000000 0.2838635498 0.8602081940 2.1365369052 0.6026902669 0.7911985088 0.0929652368 -0.0461175304583 +1403715566512143104.0000000000 0.2570209708 0.8489508039 2.1423279437 0.6029808626 0.7870677998 0.1145978911 -0.0616902032518 +1403715566562142976.0000000000 0.2304165280 0.8359324461 2.1451515213 0.6025231264 0.7828190355 0.1347109982 -0.0775447396579 +1403715566612143104.0000000000 0.2041122596 0.8206357239 2.1449765613 0.6019933934 0.7779267409 0.1545932057 -0.0923844187525 +1403715566662142976.0000000000 0.1782768592 0.8030209768 2.1418651239 0.6008778099 0.7726489596 0.1750843913 -0.106324497532 +1403715566712143104.0000000000 0.1528518772 0.7830690088 2.1369429146 0.5986020430 0.7671658777 0.1964675063 -0.120551354961 +1403715566762142976.0000000000 0.1280535426 0.7603238918 2.1315962790 0.5954578595 0.7612235458 0.2179924787 -0.135823157075 +1403715566812143104.0000000000 0.1038991474 0.7344293574 2.1263228513 0.5901200844 0.7556741179 0.2397014485 -0.152506160695 +1403715566862142976.0000000000 0.0805541370 0.7060246797 2.1219940732 0.5852472457 0.7484729442 0.2610599682 -0.17065053835 +1403715566912143104.0000000000 0.0580942885 0.6751662764 2.1185399045 0.5803197306 0.7397517500 0.2830930084 -0.189353392581 +1403715566962142976.0000000000 0.0367348731 0.6419241346 2.1152154238 0.5744108783 0.7302133840 0.3057416336 -0.208236908917 +1403715567012143104.0000000000 0.0170280140 0.6062650504 2.1112547634 0.5655156975 0.7213721341 0.3291696236 -0.226851490803 +1403715567062142976.0000000000 -0.0008943716 0.5680615682 2.1072663062 0.5544747353 0.7122032632 0.3525322348 -0.247073477393 +1403715567112143104.0000000000 -0.0173317111 0.5280317745 2.1037504757 0.5417735483 0.7023923304 0.3750665151 -0.269168248106 +1403715567162142976.0000000000 -0.0317824860 0.4865461226 2.1003226678 0.5295842225 0.6904371411 0.3988305275 -0.289432748187 +1403715567212143104.0000000000 -0.0438434158 0.4439241953 2.0969091680 0.5158026028 0.6777538003 0.4228998388 -0.309440119159 +1403715567262142976.0000000000 -0.0539359995 0.4006347809 2.0925856174 0.4995146877 0.6653470077 0.4489568945 -0.325938863812 +1403715567312143104.0000000000 -0.0628018659 0.3571314753 2.0883268426 0.4834661401 0.6508056583 0.4746818774 -0.342621659813 +1403715567362142976.0000000000 -0.0703458285 0.3137065130 2.0828915972 0.4684459938 0.6338678602 0.5015766669 -0.356638099404 +1403715567412143104.0000000000 -0.0762833754 0.2702725004 2.0760514605 0.4531834109 0.6157978911 0.5283669388 -0.369115335962 +1403715567462142976.0000000000 -0.0812081637 0.2270172435 2.0665923730 0.4378538925 0.5967126465 0.5539368309 -0.381276767854 +1403715567512143104.0000000000 -0.0854197174 0.1840837090 2.0536201216 0.4230572654 0.5768659030 0.5784232117 -0.392013862456 +1403715567562142976.0000000000 -0.0890565308 0.1411241399 2.0375564849 0.4089039411 0.5562896624 0.6002247658 -0.403818782357 +1403715567612143104.0000000000 -0.0924748387 0.0981003462 2.0187917380 0.3945310278 0.5358081176 0.6198322711 -0.416008275095 +1403715567662142976.0000000000 -0.0953177268 0.0548197142 1.9977954043 0.3811652051 0.5141392663 0.6374623409 -0.428970471288 +1403715567712143104.0000000000 -0.0978762901 0.0111985963 1.9756931910 0.3676430855 0.4917030220 0.6539677802 -0.442032625772 +1403715567762142976.0000000000 -0.0999885959 -0.0327263168 1.9537809392 0.3547897886 0.4681960361 0.6678837364 -0.456998897554 +1403715567812143104.0000000000 -0.1011586716 -0.0768476327 1.9319000868 0.3411221698 0.4448769644 0.6811271582 -0.470941552862 +1403715567862142976.0000000000 -0.1013644717 -0.1208607748 1.9102578740 0.3274927179 0.4209248764 0.6941275752 -0.483484930005 +1403715567912143104.0000000000 -0.1005876327 -0.1649903925 1.8887978785 0.3130927986 0.3969078434 0.7071295816 -0.494373156797 +1403715567962142976.0000000000 -0.0987501449 -0.2088006740 1.8676723697 0.2992943058 0.3720788213 0.7196493321 -0.504068554999 +1403715568012143104.0000000000 -0.0958964325 -0.2523795627 1.8473125763 0.2868016536 0.3468475588 0.7304144298 -0.513747353475 +1403715568062142976.0000000000 -0.0914527162 -0.2959855433 1.8281007906 0.2733839718 0.3225294800 0.7388694684 -0.524697862824 +1403715568112143104.0000000000 -0.0851197007 -0.3394366963 1.8098626460 0.2598523753 0.2983858367 0.7461059769 -0.535507709357 +1403715568162142976.0000000000 -0.0765652861 -0.3822555239 1.7922262694 0.2453774700 0.2745978835 0.7527196187 -0.545709698688 +1403715568212143104.0000000000 -0.0659231954 -0.4242320446 1.7746044437 0.2311642546 0.2505622759 0.7593962056 -0.554165170515 +1403715568262142976.0000000000 -0.0528014491 -0.4653263782 1.7573395907 0.2136453180 0.2289690701 0.7656694590 -0.561853292684 +1403715568312143104.0000000000 -0.0376528430 -0.5055651532 1.7401071386 0.1965415613 0.2071558192 0.7715964168 -0.568416089528 +1403715568362142976.0000000000 -0.0206294039 -0.5445036525 1.7236344281 0.1796227295 0.1855251773 0.7764260183 -0.574872787516 +1403715568412143104.0000000000 -0.0018545676 -0.5819115860 1.7075270496 0.1628484307 0.1639702679 0.7812394348 -0.579878509102 +1403715568462142976.0000000000 0.0185476396 -0.6177361728 1.6926677524 0.1468217957 0.1415884690 0.7849630649 -0.585003463737 +1403715568512143104.0000000000 0.0406107997 -0.6518577272 1.6788923880 0.1310138496 0.1189985587 0.7887643014 -0.588664243116 +1403715568562142976.0000000000 0.0646161576 -0.6840639607 1.6667517045 0.1141552627 0.0971733300 0.7918559282 -0.592022051087 +1403715568612143104.0000000000 0.0902821665 -0.7144449795 1.6557806613 0.0991298527 0.0740764612 0.7945535129 -0.594449884658 +1403715568662142976.0000000000 0.1176320907 -0.7427034690 1.6460283118 0.0838171552 0.0511601588 0.7968915348 -0.596088252138 +1403715568712143104.0000000000 0.1468489011 -0.7690166406 1.6377844728 0.0669079058 0.0291888016 0.7985158198 -0.597531448107 +1403715568762142976.0000000000 0.1775564961 -0.7934223900 1.6305037997 0.0504749119 0.0069964917 0.7996024499 -0.598363814531 +1403715568812143104.0000000000 0.2095238533 -0.8159762589 1.6240683113 0.0339696324 -0.0148542663 0.8007757626 -0.597815684703 +1403715568862142976.0000000000 0.2425228075 -0.8368152495 1.6183853719 0.0189126129 -0.0367017287 0.8013658617 -0.596747896392 +1403715568912143104.0000000000 0.2764604270 -0.8559341899 1.6129540849 0.0036853200 -0.0574120065 0.8015507897 -0.595152595136 +1403715568962142976.0000000000 0.3113067514 -0.8730295330 1.6071942252 0.0119245096 0.0762470815 -0.8033095082 0.590540449597 +1403715569012143104.0000000000 0.3466640842 -0.8887836130 1.6013123919 0.0254732727 0.0948658527 -0.8042270034 0.586148879926 +1403715569062142976.0000000000 0.3826009832 -0.9032509060 1.5955588029 0.0387170944 0.1130026869 -0.8038802285 0.582673113845 +1403715569112143104.0000000000 0.4191540956 -0.9165596549 1.5893994661 0.0520412613 0.1307241255 -0.8032000899 0.578854494402 +1403715569162142976.0000000000 0.4565999831 -0.9288586979 1.5834034315 0.0664121148 0.1468691247 -0.8018795234 0.57533305241 +1403715569212143104.0000000000 0.4945571253 -0.9403459334 1.5776526173 0.0807589469 0.1613285736 -0.8000731543 0.572131131403 +1403715569262142976.0000000000 0.5327515964 -0.9516088741 1.5730305052 0.0944373487 0.1741049272 -0.7961074123 0.571823442596 +1403715569312143104.0000000000 0.5711149824 -0.9625877861 1.5691112290 0.1067949891 0.1857213430 -0.7893268992 0.575382880551 +1403715569362142976.0000000000 0.6092770879 -0.9729522940 1.5655131561 0.1179543652 0.1964660089 -0.7819448835 0.579698261414 +1403715569412143104.0000000000 0.6473677619 -0.9817814321 1.5624292536 0.1285903350 0.2063061754 -0.7746771767 0.583761560593 +1403715569462142976.0000000000 0.6850644701 -0.9889133554 1.5595406885 0.1377299315 0.2165740475 -0.7681215181 0.586613570682 +1403715569512143104.0000000000 0.7222718461 -0.9941494041 1.5566528584 0.1444751582 0.2284888526 -0.7620575794 0.588377445723 +1403715569562142976.0000000000 0.7588303801 -0.9969354443 1.5540193679 0.1514513841 0.2406657974 -0.7570367416 0.58824979734 +1403715569612143104.0000000000 0.7947706791 -0.9973067910 1.5513717645 0.1576976821 0.2534762661 -0.7523846235 0.587195539802 +1403715569662142976.0000000000 0.8301201660 -0.9948405151 1.5485754916 0.1645288937 0.2667731542 -0.7488448950 0.583946616123 +1403715569712143104.0000000000 0.8649791255 -0.9898018305 1.5459785688 0.1719326547 0.2801896659 -0.7459103713 0.57926732293 +1403715569762142976.0000000000 0.8994249225 -0.9819038083 1.5440477119 0.1817006760 0.2935868847 -0.7425633314 0.573926218544 +1403715569812143104.0000000000 0.9332900089 -0.9712176241 1.5425875792 0.1923420674 0.3077329093 -0.7386166551 0.568111276405 +1403715569862142976.0000000000 0.9666105524 -0.9579289407 1.5416518056 0.2056569647 0.3214243969 -0.7341659025 0.561597718554 +1403715569912143104.0000000000 0.9993104453 -0.9427771544 1.5411539819 0.2177356957 0.3362451343 -0.7263427859 0.558530691904 +1403715569962142976.0000000000 1.0312766712 -0.9253648878 1.5409370142 0.2304264142 0.3506993206 -0.7179175539 0.555435000741 +1403715570012143104.0000000000 1.0623951331 -0.9060814631 1.5408303433 0.2432744661 0.3652644546 -0.7093541978 0.551557825122 +1403715570062142976.0000000000 1.0923306023 -0.8849723614 1.5402178269 0.2557007363 0.3801136786 -0.7002093414 0.547574289908 +1403715570112143104.0000000000 1.1212577577 -0.8618456289 1.5392786037 0.2682145644 0.3952014252 -0.6908514380 0.542771656978 +1403715570162142976.0000000000 1.1490689314 -0.8369392375 1.5381773047 0.2806321281 0.4103564744 -0.6812650781 0.53733701333 +1403715570212143104.0000000000 1.1749032983 -0.8100247642 1.5368935424 0.2932359366 0.4256014532 -0.6712595448 0.531306608387 +1403715570262142976.0000000000 1.1990754464 -0.7811307884 1.5353934753 0.3058487963 0.4411610196 -0.6608719309 0.524482372933 +1403715570312143104.0000000000 1.2216836686 -0.7504262022 1.5335637769 0.3190211404 0.4563651760 -0.6490076563 0.518406597346 +1403715570362142976.0000000000 1.2423217082 -0.7178287014 1.5312840981 0.3324192165 0.4718376890 -0.6363051734 0.511842149552 +1403715570412143104.0000000000 1.2607197319 -0.6833712681 1.5283959743 0.3456120401 0.4873970310 -0.6230176647 0.504822187798 +1403715570462142976.0000000000 1.2770839093 -0.6471774043 1.5255561271 0.3604007675 0.5019301954 -0.6095496796 0.496615096295 +1403715570512143104.0000000000 1.2911390569 -0.6095819898 1.5225549437 0.3742397868 0.5170711723 -0.5950943689 0.488307973313 +1403715570562142976.0000000000 1.3022029217 -0.5706312532 1.5186123313 0.3870679989 0.5326256213 -0.5792980250 0.480522746595 +1403715570612143104.0000000000 1.3099999844 -0.5302408541 1.5138334952 0.3990969654 0.5484174199 -0.5638848594 0.471162191918 +1403715570662142976.0000000000 1.3145051756 -0.4887266120 1.5079099750 0.4097762660 0.5650596369 -0.5506626192 0.457779093425 +1403715570712143104.0000000000 1.3162025973 -0.4463745064 1.5015212766 0.4195839469 0.5817442898 -0.5378415874 0.44300036087 +1403715570762142976.0000000000 1.3152862312 -0.4033835356 1.4949154118 0.4291986795 0.5981722854 -0.5230318251 0.429436980838 +1403715570812143104.0000000000 1.3119029664 -0.3595433298 1.4884239635 0.4392250637 0.6140467190 -0.5071393057 0.41573753122 +1403715570862142976.0000000000 1.3066235599 -0.3152230008 1.4818748718 0.4486074445 0.6292813499 -0.4914120583 0.401585025084 +1403715570912143104.0000000000 1.2994401790 -0.2705169166 1.4755487083 0.4583090305 0.6433485022 -0.4754781096 0.387267484505 +1403715570962142976.0000000000 1.2901144214 -0.2259535219 1.4683978880 0.4647354339 0.6577896382 -0.4609558983 0.372630417718 +1403715571012143104.0000000000 1.2792506437 -0.1811150719 1.4615310673 0.4716921327 0.6700754586 -0.4476057779 0.35798670268 +1403715571062142976.0000000000 1.2676575393 -0.1364374788 1.4548108483 0.4783417582 0.6796496951 -0.4362505838 0.344892566532 +1403715571112143104.0000000000 1.2553017755 -0.0920274341 1.4480530787 0.4852757982 0.6863851469 -0.4273844930 0.332754150956 +1403715571162142976.0000000000 1.2425294387 -0.0481461491 1.4416954980 0.4930742811 0.6900494138 -0.4197228044 0.323330059229 +1403715571212143104.0000000000 1.2297132805 -0.0047463234 1.4361340681 0.5025189191 0.6906125930 -0.4115418825 0.318060153485 +1403715571262142976.0000000000 1.2162310397 0.0375346648 1.4313312203 0.5111566936 0.6897375255 -0.4029319094 0.317217365404 +1403715571312143104.0000000000 1.2013639290 0.0783002847 1.4265528646 0.5180174941 0.6885640145 -0.3952245505 0.318331632736 +1403715571362142976.0000000000 1.1847630243 0.1176043643 1.4220012725 0.5237389728 0.6869562309 -0.3894756388 0.319526762528 +1403715571412143104.0000000000 1.1659437060 0.1554802303 1.4171171256 0.5246975983 0.6881744716 -0.3867936565 0.318589067997 +1403715571462142976.0000000000 1.1452076158 0.1921004436 1.4119065510 0.5209884552 0.6922618487 -0.3867022117 0.315920815827 +1403715571512143104.0000000000 1.1225918853 0.2274031895 1.4067726384 0.5165511292 0.6964304041 -0.3886627428 0.311610165947 +1403715571562142976.0000000000 1.0980698007 0.2619102647 1.4009394317 0.5126384406 0.7001416960 -0.3948153430 0.301867983788 +1403715571612143104.0000000000 1.0723726201 0.2957480182 1.3934179824 0.5089339925 0.7032365264 -0.4036872296 0.288931133423 +1403715571662142976.0000000000 1.0465815659 0.3290932349 1.3839059766 0.5074286998 0.7041765375 -0.4162052632 0.270969920019 +1403715571712143104.0000000000 1.0217758390 0.3612205500 1.3712990648 0.5049343851 0.7049249927 -0.4304376562 0.250689938974 +1403715571762142976.0000000000 0.9987419721 0.3914134487 1.3556030056 0.5009980328 0.7057154225 -0.4453641788 0.229384964309 +1403715571812143104.0000000000 0.9786209609 0.4190566517 1.3376727465 0.4946658071 0.7078096244 -0.4583182832 0.21037021193 +1403715571862142976.0000000000 0.9631453409 0.4441252527 1.3194960934 0.4881971349 0.7095540368 -0.4693165600 0.194778317253 +1403715571912143104.0000000000 0.9532498527 0.4662707736 1.3012019332 0.4807581084 0.7118440326 -0.4786966595 0.181656881723 +1403715571962142976.0000000000 0.9496677841 0.4853145721 1.2827285680 0.4711034506 0.7156655705 -0.4862115142 0.171705251841 +1403715572012143104.0000000000 0.9535389735 0.5014815485 1.2647502403 0.4607758331 0.7207473740 -0.4905441083 0.166058219482 +1403715572062142976.0000000000 0.9655983731 0.5149952879 1.2474234960 0.4496956485 0.7274079611 -0.4911168957 0.165697545613 +1403715572112143104.0000000000 0.9858536581 0.5259041742 1.2304519812 0.4379103148 0.7364369029 -0.4856901010 0.173206148904 +1403715572162142976.0000000000 1.0142556854 0.5357466062 1.2144301625 0.4291504477 0.7456211237 -0.4743048515 0.186852725444 +1403715572212143104.0000000000 1.0501234956 0.5461754523 1.1999274783 0.4259149645 0.7525188178 -0.4592534910 0.203465237337 +1403715572262142976.0000000000 1.0927080473 0.5582432912 1.1865995337 0.4293061438 0.7573555058 -0.4371298431 0.225890179375 +1403715572312143104.0000000000 1.1398829113 0.5727670666 1.1735410243 0.4371712774 0.7599152320 -0.4111847173 0.249674273081 +1403715572362142976.0000000000 1.1898853756 0.5907880495 1.1614090198 0.4493222666 0.7594269381 -0.3863762690 0.268502523544 +1403715572412143104.0000000000 1.2405880765 0.6119369020 1.1493643129 0.4634475867 0.7572499580 -0.3618024771 0.28440781109 +1403715572462142976.0000000000 1.2901343414 0.6361375947 1.1372119544 0.4770907317 0.7549493253 -0.3411357381 0.293363866249 +1403715572512143104.0000000000 1.3376098811 0.6628521314 1.1248513279 0.4895810732 0.7534724715 -0.3249237688 0.294981612836 +1403715572562142976.0000000000 1.3824598476 0.6917398011 1.1123186067 0.5002945067 0.7533795151 -0.3114564644 0.291752606703 +1403715572612143104.0000000000 1.4243259496 0.7224291268 1.0998210134 0.5087323278 0.7548365895 -0.2986649201 0.286727060793 +1403715572662142976.0000000000 1.4628793338 0.7547702221 1.0877632489 0.5166979629 0.7569579029 -0.2853607936 0.280369695099 +1403715572712143104.0000000000 1.4979159609 0.7882291726 1.0754548309 0.5216072706 0.7612428760 -0.2726641749 0.27219365674 +1403715572762142976.0000000000 1.5296012296 0.8230210011 1.0641313442 0.5243583479 0.7668055267 -0.2601356723 0.263414196946 +1403715572812143104.0000000000 1.5575821359 0.8591586445 1.0556133370 0.5272107163 0.7723980605 -0.2502191331 0.250680039548 +1403715572862142976.0000000000 1.5819505419 0.8963127845 1.0503303605 0.5309107070 0.7771753036 -0.2404651286 0.237294944197 +1403715572912143104.0000000000 1.6037538941 0.9348108604 1.0491041330 0.5363004919 0.7804409235 -0.2314256105 0.22301554687 +1403715572962142976.0000000000 1.6233667455 0.9742628983 1.0510348576 0.5422753756 0.7828818761 -0.2208144161 0.210414777518 +1403715573012143104.0000000000 1.6406943310 1.0141179051 1.0558346870 0.5485419159 0.7847157408 -0.2095049828 0.198571485357 +1403715573062142976.0000000000 1.6555718936 1.0541931932 1.0638427592 0.5544496878 0.7865865478 -0.1984160002 0.185737011239 +1403715573112143104.0000000000 1.6684878533 1.0942209762 1.0747922225 0.5597492655 0.7885612289 -0.1869274037 0.172945349012 +1403715573162142976.0000000000 1.6793446197 1.1337307272 1.0880699843 0.5643113910 0.7907431946 -0.1766227475 0.158373795856 +1403715573212143104.0000000000 1.6889920365 1.1721868293 1.1017520040 0.5672981637 0.7935668328 -0.1640583948 0.14666055537 +1403715573262142976.0000000000 1.6972102838 1.2099652062 1.1154060593 0.5698945747 0.7964193885 -0.1528974482 0.132509251287 +1403715573312143104.0000000000 1.7044849623 1.2466437531 1.1282216321 0.5709930611 0.7999465383 -0.1408965880 0.119166318996 +1403715573362142976.0000000000 1.7111863380 1.2825202307 1.1404971308 0.5716116639 0.8033828752 -0.1292011074 0.105561050098 +1403715573412143104.0000000000 1.7175378699 1.3175610614 1.1522554247 0.5718883751 0.8066925455 -0.1174243061 0.0916643652718 +1403715573462142976.0000000000 1.7238959153 1.3523254714 1.1637474616 0.5719088016 0.8097367453 -0.1080722969 0.0746130325981 +1403715573512143104.0000000000 1.7307736221 1.3862805287 1.1749607369 0.5717684764 0.8124000907 -0.0982793410 0.0585497485673 +1403715573562142976.0000000000 1.7383069179 1.4196132564 1.1860459995 0.5713432138 0.8148105585 -0.0881101283 0.0434429628669 +1403715573612143104.0000000000 1.7469874276 1.4524447161 1.1968860939 0.5706366952 0.8171086152 -0.0751156459 0.0326330003885 +1403715573662142976.0000000000 1.7569347495 1.4849410834 1.2071751832 0.5690360649 0.8197352853 -0.0600173684 0.0250984935492 +1403715573712143104.0000000000 1.7679206173 1.5174159805 1.2166939930 0.5659155304 0.8231037333 -0.0424858154 0.020852150035 +1403715573762142976.0000000000 1.7793491844 1.5500435254 1.2259383570 0.5612633541 0.8270916864 -0.0256292016 0.0156822710454 +1403715573812143104.0000000000 1.7912762792 1.5831661130 1.2348657842 0.5563738281 0.8308166526 -0.0070444956 0.0119259524872 +1403715573862142976.0000000000 1.8028333202 1.6168808548 1.2439799676 0.5510338382 0.8343920293 0.0107351807 0.00603377449204 +1403715573912143104.0000000000 1.8136486810 1.6512453471 1.2533630658 0.5458459966 0.8374132115 0.0280604817 -0.00196737731 +1403715573962142976.0000000000 1.8235637744 1.6870273412 1.2632182088 0.5417728791 0.8392325853 0.0449335056 -0.0123205235099 +1403715574012143104.0000000000 1.8325068977 1.7241919600 1.2728872467 0.5370868780 0.8409026555 0.0618616757 -0.0243627274761 +1403715574062142976.0000000000 1.8406664830 1.7630792572 1.2827876318 0.5320273304 0.8421467298 0.0797972170 -0.0369893142441 +1403715574112143104.0000000000 1.8477120738 1.8042642385 1.2934249474 0.5288601193 0.8415622971 0.0975073311 -0.0507168081897 +1403715574162142976.0000000000 1.8538067117 1.8478671535 1.3048640938 0.5279183712 0.8389463511 0.1151621745 -0.0648759343755 +1403715574212143104.0000000000 1.8592845517 1.8936200424 1.3162666061 0.5291469854 0.8342615299 0.1343543980 -0.0772014459617 +1403715574262142976.0000000000 1.8641671497 1.9413178225 1.3279831841 0.5347954858 0.8260899650 0.1543341904 -0.0880347416474 +1403715574312143104.0000000000 1.8685764944 1.9904668292 1.3391112845 0.5416342355 0.8165523477 0.1758335803 -0.094642328778 +1403715574362142976.0000000000 1.8719050950 2.0404537103 1.3496047132 0.5484303437 0.8066158133 0.1970000289 -0.0989245995415 +1403715574412143104.0000000000 1.8739811957 2.0908265595 1.3591110954 0.5541022613 0.7973591475 0.2169557532 -0.100594607319 +1403715574462142976.0000000000 1.8744774596 2.1408929944 1.3673149298 0.5572367040 0.7903445716 0.2338119465 -0.100869656368 +1403715574512143104.0000000000 1.8727941295 2.1901732574 1.3749650351 0.5598518193 0.7842304386 0.2475694726 -0.101281370043 +1403715574562142976.0000000000 1.8684032377 2.2379235214 1.3820065310 0.5599544478 0.7803073803 0.2586525225 -0.103297053419 +1403715574612143104.0000000000 1.8614392052 2.2840734801 1.3878419109 0.5578311225 0.7780116527 0.2694875933 -0.104397050544 +1403715574662142976.0000000000 1.8516361904 2.3285219050 1.3933648813 0.5554788329 0.7760667138 0.2790167657 -0.106364309716 +1403715574712143104.0000000000 1.8383592954 2.3710687488 1.3987430730 0.5527804555 0.7745011687 0.2870914255 -0.110273392258 +1403715574762142976.0000000000 1.8214707863 2.4117706736 1.4039707141 0.5491635177 0.7738994933 0.2931940670 -0.11634536593 +1403715574812143104.0000000000 1.8011582736 2.4511045670 1.4097504225 0.5451357615 0.7744868771 0.2953926531 -0.125460190133 +1403715574862142976.0000000000 1.7773350446 2.4892559541 1.4163715119 0.5408515502 0.7759999915 0.2940681169 -0.137213543396 +1403715574912143104.0000000000 1.7510075608 2.5266968422 1.4236736261 0.5386975892 0.7764566686 0.2917676320 -0.147619775103 +1403715574962142976.0000000000 1.7227642905 2.5636658810 1.4320857193 0.5400743462 0.7747785806 0.2890454556 -0.156494652408 +1403715575012143104.0000000000 1.6932860496 2.6001844283 1.4409565496 0.5416559721 0.7732255643 0.2864356638 -0.163357415069 +1403715575062142976.0000000000 1.6628067903 2.6367135384 1.4505837436 0.5464423326 0.7697285127 0.2844816779 -0.167299040074 +1403715575112143104.0000000000 1.6315651106 2.6725127942 1.4601223833 0.5518808873 0.7659786166 0.2830528640 -0.169071941203 +1403715575162142976.0000000000 1.5996041283 2.7074287531 1.4707978845 0.5615980210 0.7594282291 0.2799688042 -0.171737871204 +1403715575212143104.0000000000 1.5673930027 2.7411281251 1.4819774717 0.5734226203 0.7513618424 0.2767379430 -0.173372406176 +1403715575262142976.0000000000 1.5354032744 2.7725484496 1.4925673044 0.5835144253 0.7446036562 0.2747101253 -0.172077475757 +1403715575312143104.0000000000 1.5039514703 2.8010981513 1.5019102809 0.5886155074 0.7418898290 0.2735762070 -0.168188361661 +1403715575362142976.0000000000 1.4729538836 2.8260653443 1.5096679611 0.5850411974 0.7461347674 0.2717943657 -0.164734723305 +1403715575412143104.0000000000 1.4421079217 2.8478857815 1.5172898107 0.5791394371 0.7521349983 0.2696209924 -0.161848624296 +1403715575462142976.0000000000 1.4113638256 2.8675407137 1.5249688010 0.5739074124 0.7575210631 0.2687742493 -0.156692449791 +1403715575512143104.0000000000 1.3802560866 2.8854031276 1.5334525488 0.5715280364 0.7607666575 0.2685511754 -0.149900175122 +1403715575562142976.0000000000 1.3485477329 2.9017536406 1.5432431788 0.5746606044 0.7595731818 0.2705451045 -0.140068260566 +1403715575612143104.0000000000 1.3157615086 2.9160487668 1.5540633678 0.5812422242 0.7555590951 0.2729304606 -0.129602833088 +1403715575662142976.0000000000 1.2816104749 2.9273256048 1.5650266546 0.5865687599 0.7522515010 0.2749454906 -0.120248685078 +1403715575712143104.0000000000 1.2454747541 2.9355344827 1.5764270286 0.5918434590 0.7488075111 0.2769194723 -0.111014580619 +1403715575762142976.0000000000 1.2069058676 2.9398879767 1.5876906377 0.5943844364 0.7474725859 0.2776914762 -0.104303974907 +1403715575812143104.0000000000 1.1658045440 2.9403027226 1.5985917398 0.5935760210 0.7489703799 0.2768432284 -0.100342933407 +1403715575862142976.0000000000 1.1219973987 2.9367951961 1.6095807612 0.5922448511 0.7509111815 0.2748688576 -0.0991238871544 +1403715575912143104.0000000000 1.0756959481 2.9291742685 1.6204747442 0.5905419393 0.7532465025 0.2712352780 -0.101544809491 +1403715575962142976.0000000000 1.0268980851 2.9178335984 1.6311944365 0.5861456912 0.7579837798 0.2645875906 -0.109028552309 +1403715576012143104.0000000000 0.9760653727 2.9037701012 1.6417730104 0.5818153943 0.7624404106 0.2575289703 -0.1177042765 +1403715576062142976.0000000000 0.9238058780 2.8874346668 1.6520700706 0.5780615278 0.7660379179 0.2517957471 -0.125018719365 +1403715576112143104.0000000000 0.8709213214 2.8688062379 1.6616436073 0.5759571573 0.7681005215 0.2474469880 -0.130632806144 +1403715576162142976.0000000000 0.8172771235 2.8484971977 1.6707253679 0.5744474957 0.7696331271 0.2428514714 -0.136740948793 +1403715576212143104.0000000000 0.7632033553 2.8269788335 1.6792978544 0.5726127109 0.7711261261 0.2392267732 -0.142301552881 +1403715576262142976.0000000000 0.7092938331 2.8044663326 1.6875881871 0.5720649522 0.7714694718 0.2375407849 -0.145433558723 +1403715576312143104.0000000000 0.6552981188 2.7813761636 1.6968619519 0.5745474898 0.7695098606 0.2364584836 -0.147773955835 +1403715576362142976.0000000000 0.6017993121 2.7572613296 1.7066358093 0.5793700554 0.7656851598 0.2363833331 -0.148927817177 +1403715576412143104.0000000000 0.5485936013 2.7314752355 1.7176039782 0.5868509323 0.7596711930 0.2350979731 -0.152429015676 +1403715576462142976.0000000000 0.4959550313 2.7039755962 1.7293130872 0.5942770517 0.7536762498 0.2339493936 -0.155159844992 +1403715576512143104.0000000000 0.4442569194 2.6742696927 1.7412790725 0.6013257563 0.7480448127 0.2328541375 -0.15689245888 +1403715576562142976.0000000000 0.3939929755 2.6420550765 1.7532560973 0.6082686529 0.7429157474 0.2309627438 -0.157294784016 +1403715576612143104.0000000000 0.3452806009 2.6067837184 1.7656311530 0.6155001750 0.7376601790 0.2292091280 -0.156461402689 +1403715576662142976.0000000000 0.2984281237 2.5678652052 1.7770639638 0.6180073511 0.7365480101 0.2277685961 -0.153900648027 +1403715576712143104.0000000000 0.2532872589 2.5256932669 1.7884230712 0.6191906847 0.7369348172 0.2261182411 -0.149668006935 +1403715576762142976.0000000000 0.2096852267 2.4798492887 1.7997567717 0.6171116881 0.7403192175 0.2232167288 -0.145859221823 +1403715576812143104.0000000000 0.1675512868 2.4305890642 1.8106279053 0.6118792227 0.7465175437 0.2202386639 -0.140749084482 +1403715576862142976.0000000000 0.1266861615 2.3780238870 1.8212629311 0.6045756197 0.7541871928 0.2176992789 -0.135266486236 +1403715576912143104.0000000000 0.0865389373 2.3228373402 1.8321144347 0.5971203358 0.7617781691 0.2150972843 -0.12990182423 +1403715576962142976.0000000000 0.0466779077 2.2655584110 1.8432210675 0.5906949779 0.7683967049 0.2119216490 -0.125439873045 +1403715577012143104.0000000000 0.0068724964 2.2066500740 1.8550018424 0.5862858751 0.7735522946 0.2058902269 -0.124478651493 +1403715577062142976.0000000000 -0.0327902974 2.1464242911 1.8669769362 0.5825924228 0.7782396207 0.1975384206 -0.126125865825 +1403715577112143104.0000000000 -0.0720210455 2.0855555199 1.8782513183 0.5790743836 0.7829331311 0.1878408887 -0.128079549325 +1403715577162142976.0000000000 -0.1105154705 2.0243974413 1.8885147524 0.5766116818 0.7868023117 0.1779603782 -0.129580841216 +1403715577212143104.0000000000 -0.1481237521 1.9630811566 1.8961981826 0.5749890093 0.7897904973 0.1689722022 -0.130640746182 +1403715577262142976.0000000000 -0.1846695976 1.9019573307 1.8986402852 0.5748315107 0.7914333789 0.1618486024 -0.130410777758 +1403715577312143104.0000000000 -0.2202210956 1.8411544055 1.8945906798 0.5751539870 0.7924668814 0.1576168754 -0.127871238708 +1403715577362142976.0000000000 -0.2547148340 1.7805319751 1.8845951682 0.5764599145 0.7925927864 0.1558073067 -0.123347983843 +1403715577412143104.0000000000 -0.2880545531 1.7197350875 1.8708561636 0.5776838982 0.7925396212 0.1551248903 -0.118737235194 +1403715577462142976.0000000000 -0.3204440948 1.6582289903 1.8557561534 0.5782963468 0.7927607585 0.1546221270 -0.114872594132 +1403715577512143104.0000000000 -0.3519101513 1.5965099340 1.8404225698 0.5790300160 0.7927206237 0.1541306316 -0.112080336013 +1403715577562142976.0000000000 -0.3826140008 1.5346043661 1.8262853471 0.5792842068 0.7928906596 0.1539314589 -0.109814914989 +1403715577612143104.0000000000 -0.4124973236 1.4723357506 1.8152590165 0.5790108327 0.7933990985 0.1530923421 -0.108752291037 +1403715577662142976.0000000000 -0.4414703248 1.4099878010 1.8081031915 0.5788049154 0.7937409949 0.1523904690 -0.108338579744 +1403715577712143104.0000000000 -0.4695917684 1.3472821016 1.8045927774 0.5772483580 0.7949707629 0.1508831016 -0.109727430481 +1403715577762142976.0000000000 -0.4970711557 1.2846667519 1.8044204849 0.5757776849 0.7960672782 0.1480360474 -0.113323760595 +1403715577812143104.0000000000 -0.5232878350 1.2228300521 1.8049983776 0.5751387374 0.7968577797 0.1432757148 -0.117069130124 +1403715577862142976.0000000000 -0.5479008680 1.1614268694 1.8032492039 0.5738552633 0.7983622697 0.1370358838 -0.12053625873 +1403715577912143104.0000000000 -0.5707098280 1.1009459972 1.7982064736 0.5729512098 0.7999603266 0.1298760824 -0.122158054423 +1403715577962142976.0000000000 -0.5915181797 1.0408946643 1.7889692137 0.5710440457 0.8025194631 0.1212632783 -0.123152046498 +1403715578012143104.0000000000 -0.6101063270 0.9815484420 1.7756607417 0.5679992547 0.8060877553 0.1108813367 -0.123712192831 +1403715578062142976.0000000000 -0.6264736360 0.9231994678 1.7589147925 0.5637108198 0.8105646410 0.0993611895 -0.123864557053 +1403715578112143104.0000000000 -0.6406367280 0.8657072061 1.7390322918 0.5556765487 0.8174240230 0.0850635964 -0.125720819132 +1403715578162142976.0000000000 -0.6519444440 0.8096406092 1.7163739398 0.5448238368 0.8258083143 0.0677970373 -0.128884353849 +1403715578212143104.0000000000 -0.6595243994 0.7567926953 1.6921286181 0.5387453925 0.8312437188 0.0513975093 -0.127065251159 +1403715578262142976.0000000000 -0.6627475081 0.7080102969 1.6673976929 0.5380450180 0.8337123122 0.0384396407 -0.11812592084 +1403715578312143104.0000000000 -0.6614815691 0.6627883917 1.6430727690 0.5394419286 0.8348312882 0.0259028109 -0.106715370187 +1403715578362142976.0000000000 -0.6558388891 0.6197404974 1.6186505360 0.5422040738 0.8350252523 0.0146831816 -0.0923686887333 +1403715578412143104.0000000000 -0.6464869137 0.5790118160 1.5940453790 0.5443716655 0.8353214804 0.0039745769 -0.0766923523726 +1403715578462142976.0000000000 -0.6340744405 0.5405025701 1.5691949125 0.5443640799 0.8367332602 -0.0056758973 -0.0592704307181 +1403715578512143104.0000000000 -0.6191519723 0.5042803033 1.5435735977 0.5406537189 0.8401440795 -0.0139879001 -0.0406917759208 +1403715578562142976.0000000000 -0.6020367757 0.4697136557 1.5168665222 0.5325861341 0.8459143028 -0.0194266064 -0.0200900245021 +1403715578612143104.0000000000 -0.5839228006 0.4370708036 1.4892813160 0.5187152493 0.8545970808 -0.0243356674 -0.00246880292612 +1403715578662142976.0000000000 -0.5653668472 0.4075862515 1.4618950765 0.5037697004 0.8632881202 -0.0279181765 0.0130493659877 +1403715578712143104.0000000000 -0.5469772569 0.3824008364 1.4355562026 0.4893903719 0.8711089210 -0.0324285689 0.0247931358167 +1403715578762142976.0000000000 -0.5288114656 0.3628438856 1.4104383107 0.4781706999 0.8768468781 -0.0366687390 0.0338782762904 +1403715578812143104.0000000000 -0.5111933556 0.3494470099 1.3867890511 0.4707398488 0.8804121820 -0.0418897348 0.0390337620055 +1403715578862142976.0000000000 -0.4939576183 0.3426804515 1.3640811371 0.4676486405 0.8816406099 -0.0457370719 0.0438486514994 +1403715578912143104.0000000000 -0.4771978000 0.3428793828 1.3427083796 0.4698362831 0.8801022042 -0.0470035491 0.0496451769429 +1403715578962142976.0000000000 -0.4608167589 0.3502418496 1.3231887936 0.4779834255 0.8753066765 -0.0440644714 0.05855244939 +1403715579012143104.0000000000 -0.4456118997 0.3640924116 1.3055955119 0.4896570444 0.8683250009 -0.0393582721 0.0685463213261 +1403715579062142976.0000000000 -0.4318529832 0.3833325246 1.2902725780 0.5006900150 0.8612236102 -0.0311455873 0.0814454083666 +1403715579112143104.0000000000 -0.4206195557 0.4072711573 1.2783595720 0.5124809129 0.8529866302 -0.0209120060 0.0966426954679 +1403715579162142976.0000000000 -0.4132203175 0.4351160387 1.2702117239 0.5248257708 0.8438705504 -0.0104652585 0.111044508317 +1403715579212143104.0000000000 -0.4103424293 0.4665138241 1.2649785697 0.5381777348 0.8333278121 0.0016128037 0.126201751801 +1403715579262142976.0000000000 -0.4136885028 0.4999016925 1.2622479272 0.5488741109 0.8250614423 0.0071718502 0.134012653504 +1403715579312143104.0000000000 -0.4231497543 0.5342006693 1.2601293277 0.5562299992 0.8193944728 0.0100394917 0.138203091389 +1403715579362142976.0000000000 -0.4386730406 0.5692656078 1.2575439507 0.5592057014 0.8170112910 0.0108982483 0.140223970893 +1403715579412143104.0000000000 -0.4598514745 0.6046866438 1.2544712019 0.5595984240 0.8169975103 0.0089216116 0.138870719982 +1403715579462142976.0000000000 -0.4869036414 0.6405101337 1.2514735105 0.5590284303 0.8180010674 0.0057019551 0.135384473186 +1403715579512143104.0000000000 -0.5196313024 0.6766131376 1.2478415745 0.5555371833 0.8214831347 0.0000970435 0.128623045735 +1403715579562142976.0000000000 -0.5574831032 0.7132683658 1.2446358125 0.5521585209 0.8253324585 -0.0080412333 0.117824612214 +1403715579612143104.0000000000 -0.5989129253 0.7513702681 1.2420892553 0.5515823272 0.8264825672 -0.0114587413 0.112036599949 +1403715579662142976.0000000000 -0.6437576883 0.7909001034 1.2405572321 0.5539574029 0.8255866882 -0.0137882580 0.10652558382 +1403715579712143104.0000000000 -0.6920580038 0.8314234266 1.2403506308 0.5575565833 0.8238917326 -0.0164110438 0.100318228983 +1403715579762142976.0000000000 -0.7432059812 0.8725291173 1.2418270433 0.5621525694 0.8213612836 -0.0179789939 0.0950099277504 +1403715579812143104.0000000000 -0.7966614545 0.9139395174 1.2450615253 0.5651561994 0.8194537409 -0.0165397877 0.0939173692123 +1403715579862142976.0000000000 -0.8527071184 0.9554079928 1.2514080810 0.5683896838 0.8170592829 -0.0146257924 0.0955687281105 +1403715579912143104.0000000000 -0.9115913881 0.9967324121 1.2601899809 0.5697836817 0.8160134991 -0.0152254150 0.0961078147951 +1403715579962142976.0000000000 -0.9734061231 1.0381534720 1.2708277540 0.5720322033 0.8146143910 -0.0208142186 0.0935378029207 +1403715580012143104.0000000000 -1.0370140381 1.0797548109 1.2807343379 0.5736733580 0.8134262615 -0.0291179311 0.0915900733322 +1403715580062142976.0000000000 -1.1017751213 1.1212420368 1.2883229012 0.5751654974 0.8119607892 -0.0394146676 0.0913827740083 +1403715580112143104.0000000000 -1.1674971126 1.1621361069 1.2925801550 0.5762513375 0.8103973720 -0.0512557915 0.0925383126315 +1403715580162142976.0000000000 -1.2340785791 1.2024291621 1.2930761329 0.5766298542 0.8089063379 -0.0640764902 0.0951984825321 +1403715580212143104.0000000000 -1.3011971463 1.2422640932 1.2904974500 0.5767010405 0.8071901395 -0.0777942987 0.0990355279483 +1403715580262142976.0000000000 -1.3689941129 1.2815674371 1.2858534291 0.5760383928 0.8055558232 -0.0917533808 0.104119656938 +1403715580312143104.0000000000 -1.4374552974 1.3199887824 1.2809100354 0.5758985390 0.8032059162 -0.1074227920 0.107988298914 +1403715580362142976.0000000000 -1.5061000066 1.3576190762 1.2762967891 0.5762810635 0.8000476461 -0.1252424619 0.110173615325 +1403715580412143104.0000000000 -1.5744468824 1.3940124980 1.2720395747 0.5755847512 0.7971429012 -0.1428116205 0.113447037314 +1403715580462142976.0000000000 -1.6424968198 1.4292463580 1.2683930238 0.5750892686 0.7937564996 -0.1609348980 0.115424915437 +1403715580512143104.0000000000 -1.7100795253 1.4629250360 1.2650902960 0.5736105816 0.7909999615 -0.1775481330 0.117331249553 +1403715580562142976.0000000000 -1.7769062251 1.4951617303 1.2621873987 0.5716103778 0.7888701254 -0.1925261099 0.117810009482 +1403715580612143104.0000000000 -1.8426126295 1.5260269139 1.2592884526 0.5686347426 0.7877758553 -0.2067164325 0.115464487326 +1403715580662142976.0000000000 -1.9065921707 1.5552938972 1.2563140686 0.5655191151 0.7868065487 -0.2207597665 0.111304586271 +1403715580712143104.0000000000 -1.9680305981 1.5831660783 1.2533572220 0.5621267727 0.7862184140 -0.2336649721 0.106182756076 +1403715580762142976.0000000000 -2.0261774392 1.6099364954 1.2507135653 0.5587864079 0.7858240053 -0.2448105164 0.101519427098 +1403715580812143104.0000000000 -2.0806474188 1.6353670458 1.2491324513 0.5569267807 0.7844006651 -0.2560072756 0.0949127614168 +1403715580862142976.0000000000 -2.1310287747 1.6592937573 1.2478227089 0.5543221658 0.7834227807 -0.2673302794 0.086661438812 +1403715580912143104.0000000000 -2.1767986400 1.6816736285 1.2475204235 0.5516743743 0.7823167524 -0.2791989734 0.0753910929432 +1403715580962142976.0000000000 -2.2167371128 1.7021496743 1.2475735218 0.5479114122 0.7822466703 -0.2891332446 0.0654614239698 +1403715581012143104.0000000000 -2.2497250762 1.7206124528 1.2474756239 0.5431304326 0.7843623559 -0.2928076722 0.0636293555453 +1403715581062142976.0000000000 -2.2760194015 1.7371853499 1.2475181816 0.5362587662 0.7886269738 -0.2940109107 0.0636523073642 +1403715581112143104.0000000000 -2.2952270364 1.7527040762 1.2479640373 0.5292610785 0.7933994572 -0.2931043871 0.0670061966358 +1403715581162142976.0000000000 -2.3074045206 1.7679543248 1.2494858129 0.5248709028 0.7968010058 -0.2901435164 0.0737253853777 +1403715581212143104.0000000000 -2.3127408336 1.7829084885 1.2515769890 0.5230522172 0.7989811143 -0.2844186717 0.0845669927816 +1403715581262142976.0000000000 -2.3127967866 1.7981777193 1.2549832404 0.5252757756 0.7982832687 -0.2798378689 0.0923035733129 +1403715581312143104.0000000000 -2.3085132797 1.8138096135 1.2589508383 0.5293822392 0.7965861745 -0.2757140301 0.0958471963335 +1403715581362142976.0000000000 -2.3000578548 1.8294168007 1.2630037044 0.5335132592 0.7956430906 -0.2698297254 0.0975068910704 +1403715581412143104.0000000000 -2.2880301745 1.8442519412 1.2665150333 0.5370819704 0.7959025734 -0.2615030797 0.0984793884747 +1403715581462142976.0000000000 -2.2725881815 1.8583247737 1.2691325316 0.5396119011 0.7977483117 -0.2492731163 0.101388070581 +1403715581512143104.0000000000 -2.2538158769 1.8721665640 1.2705338866 0.5426256483 0.7999903143 -0.2321124648 0.108151312996 +1403715581562142976.0000000000 -2.2328911782 1.8863037317 1.2692041743 0.5458093697 0.8024258190 -0.2120163147 0.115126101277 +1403715581612143104.0000000000 -2.2107956525 1.9010629710 1.2646758620 0.5481851793 0.8052069727 -0.1914197891 0.120387726255 +1403715581662142976.0000000000 -2.1882541371 1.9161469794 1.2574730521 0.5505917686 0.8077767299 -0.1707016727 0.123314223967 +1403715581712143104.0000000000 -2.1658515966 1.9314220708 1.2475884300 0.5516919686 0.8109962040 -0.1493556187 0.124956104569 +1403715581762142976.0000000000 -2.1440184125 1.9473388529 1.2368355505 0.5526001697 0.8140954097 -0.1267459475 0.125766374934 +1403715581812143104.0000000000 -2.1233637144 1.9640856812 1.2275273860 0.5537066828 0.8165974639 -0.1036284110 0.125851673894 +1403715581862142976.0000000000 -2.1048766860 1.9817071915 1.2208302245 0.5544487396 0.8189781475 -0.0821424864 0.122939013374 +1403715581912143104.0000000000 -2.0894173954 2.0002612019 1.2179467748 0.5562740263 0.8205368530 -0.0651384675 0.114172941854 +1403715581962142976.0000000000 -2.0768746765 2.0197905865 1.2182988199 0.5585520133 0.8217259922 -0.0526299343 0.100080628095 +1403715582012143104.0000000000 -2.0666879245 2.0404926555 1.2228332821 0.5655132677 0.8191800868 -0.0407828639 0.0864609017219 +1403715582062142976.0000000000 -2.0586628256 2.0615569081 1.2309472539 0.5751892355 0.8143013386 -0.0309023502 0.071524247591 +1403715582112143104.0000000000 -2.0517581311 2.0824187570 1.2397379205 0.5852822940 0.8083317507 -0.0200328566 0.0603581125147 +1403715582162142976.0000000000 -2.0461534486 2.1018690044 1.2481609684 0.5939937415 0.8028221037 -0.0105980602 0.0503565886764 +1403715582212143104.0000000000 -2.0414741429 2.1200057958 1.2546173874 0.6011481258 0.7980586268 -0.0029635942 0.0414074404064 +1403715582262142976.0000000000 -2.0372113030 2.1363176969 1.2565081719 0.6025871530 0.7972353837 0.0039715500 0.0358983694091 +1403715582312143104.0000000000 -2.0336205255 2.1509137087 1.2537254177 0.5985178534 0.8004131777 0.0095270277 0.0320056220181 +1403715582362142976.0000000000 -2.0305201590 2.1642179537 1.2484232680 0.5924896703 0.8049080216 0.0139171516 0.0297553393534 +1403715582412143104.0000000000 -2.0281612637 2.1766307971 1.2423673438 0.5859632700 0.8096361090 0.0174093952 0.0288674602779 +1403715582462142976.0000000000 -2.0268708731 2.1880978169 1.2362815920 0.5779088647 0.8153763334 0.0197093541 0.0281836911895 +1403715582512143104.0000000000 -2.0266041569 2.1992654326 1.2314711433 0.5697033020 0.8210869226 0.0211430284 0.028414532923 +1403715582562142976.0000000000 -2.0277090708 2.2109983681 1.2295356651 0.5634828629 0.8253810520 0.0211003059 0.0280706130578 +1403715582612143104.0000000000 -2.0300507868 2.2236336084 1.2307433765 0.5579439818 0.8291154275 0.0207379332 0.0289146883433 +1403715582662142976.0000000000 -2.0337836340 2.2373794505 1.2352951969 0.5534944005 0.8321027535 0.0192595833 0.029631480971 +1403715582712143104.0000000000 -2.0386917678 2.2525833622 1.2418478851 0.5495365298 0.8347380320 0.0169460105 0.0305753661137 +1403715582762142976.0000000000 -2.0445753377 2.2693422822 1.2478304183 0.5464634904 0.8367455765 0.0141982517 0.0321388180502 +1403715582812143104.0000000000 -2.0513109831 2.2869113199 1.2511654014 0.5421508336 0.8395289187 0.0111123774 0.0337666006588 +1403715582862142976.0000000000 -2.0588799563 2.3059273653 1.2513642120 0.5366064988 0.8430584190 0.0077090302 0.0353063501379 +1403715582912143104.0000000000 -2.0674148078 2.3263651049 1.2481015663 0.5302490448 0.8469869215 0.0049920004 0.0377383783771 +1403715582962142976.0000000000 -2.0768991120 2.3489871153 1.2416370358 0.5239831456 0.8508108577 0.0019053412 0.0394831257678 +1403715583012143104.0000000000 -2.0875165331 2.3740361113 1.2321940390 0.5184981684 0.8540911917 -0.0012049580 0.0410662117442 +1403715583062142976.0000000000 -2.0990219548 2.4023218718 1.2197814138 0.5150768923 0.8560710184 -0.0037842262 0.0427069793661 +1403715583112143104.0000000000 -2.1117523849 2.4341487742 1.2066502572 0.5161055129 0.8554043201 -0.0072108079 0.0432036224841 +1403715583162142976.0000000000 -2.1252966808 2.4702763867 1.1946246431 0.5260953061 0.8492368847 -0.0098755734 0.0438510615554 +1403715583212143104.0000000000 -2.1397374374 2.5091381174 1.1832803604 0.5391848825 0.8409737644 -0.0132992755 0.0431962886781 +1403715583262142976.0000000000 -2.1549633436 2.5495607904 1.1730872975 0.5548791333 0.8307700906 -0.0174733632 0.040309869158 +1403715583312143104.0000000000 -2.1704241712 2.5906449611 1.1627497486 0.5699117193 0.8205909420 -0.0215689853 0.036958312998 +1403715583362142976.0000000000 -2.1860759804 2.6311182498 1.1521660415 0.5852416701 0.8097937090 -0.0255091651 0.0327966311311 +1403715583412143104.0000000000 -2.2017615958 2.6706262983 1.1410620704 0.5991937964 0.7995697218 -0.0291088014 0.0284206272705 +1403715583462142976.0000000000 -2.2173272898 2.7081863935 1.1290023176 0.6113866433 0.7903141161 -0.0315193573 0.0248294266076 +1403715583512143104.0000000000 -2.2325065147 2.7432698270 1.1168632021 0.6227277992 0.7814390205 -0.0322502998 0.0228705823511 +1403715583562142976.0000000000 -2.2468238193 2.7746639053 1.1050568606 0.6346275918 0.7718458593 -0.0328806919 0.020509737076 +1403715583612143104.0000000000 -2.2603594439 2.8017150508 1.0943535164 0.6508327213 0.7582853207 -0.0326485549 0.0188205513762 +1403715583662142976.0000000000 -2.2728226140 2.8232526936 1.0835937603 0.6682297644 0.7430534655 -0.0308870016 0.0196601745504 +1403715583712143104.0000000000 -2.2844323062 2.8383245618 1.0728130321 0.6849735260 0.7277169715 -0.0288057708 0.0202362457378 +1403715583762142976.0000000000 -2.2955040415 2.8455965702 1.0616768898 0.6993460787 0.7139840338 -0.0262306251 0.0213029571351 +1403715583812143104.0000000000 -2.3061224944 2.8438098309 1.0513674461 0.7113124826 0.7021230657 -0.0238146368 0.0221498468373 +1403715583862142976.0000000000 -2.3166397300 2.8314992081 1.0438151869 0.7196170062 0.6936893482 -0.0226540735 0.0208145497675 +1403715583912143104.0000000000 -2.3267913321 2.8075399112 1.0405590964 0.7222046599 0.6910529458 -0.0230798361 0.0182640735966 +1403715583962142976.0000000000 -2.3365058889 2.7715419948 1.0418338413 0.7211832346 0.6921638050 -0.0251108060 0.0131702958266 +1403715584012143104.0000000000 -2.3449925089 2.7237311451 1.0479445704 0.7165519989 0.6969279016 -0.0284413071 0.005985382192 +1403715584062142976.0000000000 -2.3517919190 2.6649334194 1.0586404015 0.7079763078 0.7055007518 -0.0322128611 -0.000753948030746 +1403715584112143104.0000000000 -2.3568914177 2.5962921436 1.0728517170 0.6950930538 0.7179462456 -0.0364863746 -0.00822067226558 +1403715584162142976.0000000000 -2.3595719388 2.5187231891 1.0906396328 0.6788961115 0.7330113454 -0.0400560052 -0.0137823715399 +1403715584212143104.0000000000 -2.3596892041 2.4335662327 1.1122951577 0.6597264338 0.7499669587 -0.0436546944 -0.0201211601796 +1403715584262142976.0000000000 -2.3564396329 2.3426433400 1.1353404692 0.6364263094 0.7696520715 -0.0453701181 -0.023211934803 +1403715584312143104.0000000000 -2.3503930508 2.2485727540 1.1574188056 0.6140646128 0.7875281895 -0.0456306036 -0.0253347587309 +1403715584362142976.0000000000 -2.3418575058 2.1533163509 1.1762958461 0.5947713398 0.8020841765 -0.0462119575 -0.0277935637329 +1403715584412143104.0000000000 -2.3307563859 2.0579705060 1.1900130525 0.5785169320 0.8140023254 -0.0447026236 -0.0268337293795 +1403715584462142976.0000000000 -2.3170744946 1.9628875574 1.1982856941 0.5658102960 0.8230566641 -0.0427868363 -0.0246114466688 +1403715584512143104.0000000000 -2.3009902277 1.8689295397 1.2034194189 0.5572335047 0.8290260846 -0.0410386966 -0.0228560212056 +1403715584562142976.0000000000 -2.2825466212 1.7770052806 1.2075000264 0.5500024808 0.8339640878 -0.0394252283 -0.02113818105 +1403715584612143104.0000000000 -2.2618993282 1.6878819351 1.2117231683 0.5450602887 0.8373712571 -0.0373582798 -0.0179727134396 +1403715584662142976.0000000000 -2.2388350960 1.6012568563 1.2161359281 0.5407537448 0.8404727102 -0.0325225110 -0.0115454434612 +1403715584712143104.0000000000 -2.2135524856 1.5175760355 1.2204447865 0.5363152122 0.8436449879 -0.0250346116 -0.00154784326209 +1403715584762142976.0000000000 -2.1870969476 1.4377968695 1.2256977180 0.5319612392 0.8465267042 -0.0186068862 0.00797263025304 +1403715584812143104.0000000000 -2.1604598230 1.3618219979 1.2322989787 0.5295304021 0.8480271779 -0.0139725884 0.0158816104953 +1403715584862142976.0000000000 -2.1340987928 1.2893267845 1.2397724075 0.5272120379 0.8493714202 -0.0109909766 0.0222453608729 +1403715584912143104.0000000000 -2.1081765226 1.2200096262 1.2472795529 0.5228291596 0.8519217398 -0.0075429906 0.028672677366 +1403715584962142976.0000000000 -2.0827872088 1.1542705098 1.2544031150 0.5168208288 0.8552581370 -0.0022066141 0.0377475942507 +1403715585012143104.0000000000 -2.0590913886 1.0919855475 1.2611150849 0.5082201074 0.8601436682 0.0005035435 0.0431849374356 +1403715585062142976.0000000000 -2.0372291753 1.0338858652 1.2677765079 0.4989985681 0.8654211384 0.0002222902 0.0452397270627 +1403715585112143104.0000000000 -2.0174169576 0.9808617359 1.2747946596 0.4902109257 0.8704373007 -0.0019181179 0.0450385911029 +1403715585162142976.0000000000 -1.9994379361 0.9332191206 1.2822050726 0.4826667055 0.8746219546 -0.0032091313 0.0453760876823 +1403715585212143104.0000000000 -1.9832045623 0.8918182340 1.2905577748 0.4790316642 0.8766962501 -0.0053383389 0.0436331517693 +1403715585262142976.0000000000 -1.9684320250 0.8571240941 1.2997015301 0.4806106015 0.8758126334 -0.0050688347 0.0440452935931 +1403715585312143104.0000000000 -1.9552593422 0.8291572287 1.3102781385 0.4874460868 0.8720794258 -0.0054492320 0.0429429087533 +1403715585362142976.0000000000 -1.9433178294 0.8067720026 1.3211449588 0.4959888445 0.8672007703 -0.0031004268 0.0441392957715 +1403715585412143104.0000000000 -1.9329211790 0.7893001310 1.3321138822 0.5045816252 0.8622072680 -0.0013782000 0.0446554718969 +1403715585462142976.0000000000 -1.9241109076 0.7755905171 1.3426032461 0.5115927436 0.8580600998 0.0004597493 0.0447830157993 +1403715585512143104.0000000000 -1.9170143147 0.7658512405 1.3530735496 0.5196660498 0.8531368401 0.0029906840 0.0457797406126 +1403715585562142976.0000000000 -1.9117481779 0.7590868186 1.3632130672 0.5285251316 0.8476044112 0.0057545924 0.0468490346828 +1403715585612143104.0000000000 -1.9083008143 0.7549581962 1.3719991504 0.5347522178 0.8436379687 0.0079521537 0.0474532044787 +1403715585662142976.0000000000 -1.9065907290 0.7529445447 1.3795889765 0.5395570878 0.8405449390 0.0097323990 0.0476196909817 +1403715585712143104.0000000000 -1.9065745418 0.7526040933 1.3851323437 0.5407147076 0.8397813260 0.0109057039 0.0477073909924 +1403715585762142976.0000000000 -1.9083247987 0.7540146263 1.3877695146 0.5412695754 0.8394581097 0.0112745362 0.0470129090015 +1403715585812143104.0000000000 -1.9118237516 0.7570656869 1.3855801609 0.5414586886 0.8395599356 0.0092133117 0.0433211036188 +1403715585862142976.0000000000 -1.9165615948 0.7613656042 1.3771695852 0.5408117460 0.8402447020 0.0061669063 0.0383857445909 +1403715585912143104.0000000000 -1.9226041799 0.7671333554 1.3643614799 0.5400821751 0.8411090227 -0.0004138379 0.0290978503572 +1403715585962142976.0000000000 -1.9290477246 0.7746551353 1.3498690075 0.5395871879 0.8416794574 -0.0084113643 0.0187244924562 +1403715586012143104.0000000000 -1.9357667436 0.7843704609 1.3357834039 0.5395463369 0.8417327230 -0.0185533502 0.00561664081036 +1403715586062142976.0000000000 -1.9413006985 0.7967381531 1.3244510858 0.5428706931 0.8393165868 -0.0282885061 -0.00623201908175 +1403715586112143104.0000000000 -1.9445362137 0.8116172404 1.3169762916 0.5534662944 0.8320365921 -0.0348338020 -0.0132957352719 +1403715586162142976.0000000000 -1.9451129253 0.8277712245 1.3125355094 0.5648018178 0.8242716875 -0.0368424642 -0.0147554968191 +1403715586212143104.0000000000 -1.9429998564 0.8436660282 1.3104983609 0.5750885925 0.8172756482 -0.0348428385 -0.0109362846264 +1403715586262142976.0000000000 -1.9386402215 0.8585691340 1.3100234538 0.5838691233 0.8113263033 -0.0290273632 -0.00197196791666 +1403715586312143104.0000000000 -1.9327963911 0.8724749889 1.3096146764 0.5901693269 0.8069455847 -0.0213025099 0.00922994747792 +1403715586362142976.0000000000 -1.9263042304 0.8853268929 1.3093646765 0.5964597120 0.8022540531 -0.0126866634 0.0215242859784 +1403715586412143104.0000000000 -1.9202184060 0.8968980615 1.3089838338 0.6024295344 0.7975146250 -0.0054151057 0.0319336121538 +1403715586462142976.0000000000 -1.9151495711 0.9066436486 1.3085516317 0.6079119793 0.7930487801 -0.0000202346 0.038944286698 +1403715586512143104.0000000000 -1.9114344880 0.9142845200 1.3084573228 0.6119862722 0.7896553554 0.0037024813 0.0436292794651 +1403715586562142976.0000000000 -1.9095102621 0.9194638270 1.3089242069 0.6149775327 0.7872296464 0.0050973483 0.0452342263704 +1403715586612143104.0000000000 -1.9092344488 0.9219006609 1.3096867508 0.6166780705 0.7858627599 0.0055592677 0.0457927338392 +1403715586662142976.0000000000 -1.9105617979 0.9214367758 1.3099370672 0.6153930433 0.7868748461 0.0051009839 0.0457532381704 +1403715586712143104.0000000000 -1.9135430533 0.9182583596 1.3103226082 0.6123300545 0.7894313717 0.0026242978 0.0429316531098 +1403715586762142976.0000000000 -1.9180137686 0.9122803702 1.3104980359 0.6061929017 0.7943991264 -0.0015333202 0.0381817072799 +1403715586812143104.0000000000 -1.9236204825 0.9039114072 1.3105627915 0.5972337912 0.8013866173 -0.0066586062 0.0323566262384 +1403715586862142976.0000000000 -1.9296886264 0.8940418995 1.3108171421 0.5870299016 0.8090330892 -0.0114968279 0.0270032990417 +1403715586912143104.0000000000 -1.9358947112 0.8835902272 1.3117178195 0.5776756220 0.8157835178 -0.0152902773 0.0235443272215 +1403715586962142976.0000000000 -1.9419359759 0.8731475839 1.3132085346 0.5706871122 0.8206787798 -0.0177939375 0.0220439584287 +1403715587012143104.0000000000 -1.9478683174 0.8629447265 1.3152443527 0.5667116368 0.8234065422 -0.0198436940 0.0211143264396 +1403715587062142976.0000000000 -1.9535430806 0.8532341689 1.3175074563 0.5646937409 0.8247604766 -0.0216750267 0.020526288269 +1403715587112143104.0000000000 -1.9587821945 0.8445072841 1.3206469292 0.5656863173 0.8240463943 -0.0225629071 0.0209152029663 +1403715587162142976.0000000000 -1.9636077659 0.8363115274 1.3250230666 0.5701622773 0.8209215665 -0.0204656648 0.0241643476172 +1403715587212143104.0000000000 -1.9683396309 0.8286449879 1.3311813191 0.5768242379 0.8162226341 -0.0175074716 0.0273477324872 +1403715587262142976.0000000000 -1.9734309231 0.8208126565 1.3380027964 0.5821516328 0.8124094565 -0.0146610318 0.0295872538451 +1403715587312143104.0000000000 -1.9793450796 0.8126227330 1.3457816264 0.5864222669 0.8093582977 -0.0122876610 0.0299513651085 +1403715587362142976.0000000000 -1.9863375058 0.8034639046 1.3538518260 0.5888976577 0.8077024255 -0.0125574520 0.0256641981329 +1403715587412143104.0000000000 -1.9937754621 0.7934776912 1.3622105670 0.5914096311 0.8060152510 -0.0147351875 0.0188927947571 +1403715587462142976.0000000000 -2.0010328550 0.7825885584 1.3703880844 0.5918746136 0.8057387217 -0.0182892873 0.0116213624068 +1403715587512143104.0000000000 -2.0076560033 0.7707690145 1.3784689760 0.5907225196 0.8065168710 -0.0234700672 0.00515728053336 +1403715587562142976.0000000000 -2.0128859091 0.7581738730 1.3870275058 0.5894020136 0.8072345197 -0.0312442687 -0.0012216134725 +1403715587612143104.0000000000 -2.0162329194 0.7448185578 1.3958144932 0.5871228986 0.8084337145 -0.0410196120 -0.00624681203727 +1403715587662142976.0000000000 -2.0170010446 0.7307123332 1.4044756460 0.5841380518 0.8099579125 -0.0516980007 -0.00884495682139 +1403715587712143104.0000000000 -2.0150407213 0.7158157084 1.4123181453 0.5797731053 0.8123501491 -0.0623432466 -0.00798130855074 +1403715587762142976.0000000000 -2.0096790902 0.7007636953 1.4201457266 0.5763645688 0.8138048398 -0.0742161532 -0.00418679052782 +1403715587812143104.0000000000 -2.0011897043 0.6858949655 1.4279543789 0.5742918513 0.8139656036 -0.0874304086 0.0021884712371 +1403715587862142976.0000000000 -1.9893853678 0.6709456559 1.4357709266 0.5736859850 0.8127484531 -0.1009443915 0.011600532809 +1403715587912143104.0000000000 -1.9741150520 0.6559610924 1.4435805973 0.5737356102 0.8106877928 -0.1138987972 0.0252945895734 +1403715587962142976.0000000000 -1.9557492108 0.6406892004 1.4513917458 0.5758868572 0.8065828660 -0.1265387014 0.0420281448782 +1403715588012143104.0000000000 -1.9349404699 0.6247149167 1.4591250843 0.5788030373 0.8013114320 -0.1389526943 0.0598262626903 +1403715588062142976.0000000000 -1.9124098005 0.6078714051 1.4661722829 0.5823393294 0.7949098023 -0.1514454572 0.0778690255628 +1403715588112143104.0000000000 -1.8885643896 0.5896090248 1.4710845882 0.5851754275 0.7883597419 -0.1640370352 0.0956581805359 +1403715588162142976.0000000000 -1.8640804217 0.5696514841 1.4718073955 0.5878744038 0.7811820354 -0.1772328347 0.112901882797 +1403715588212143104.0000000000 -1.8393180549 0.5484491427 1.4672513573 0.5900060903 0.7738033333 -0.1909129571 0.129125742984 +1403715588262142976.0000000000 -1.8149629647 0.5255889506 1.4567900218 0.5908829146 0.7667962657 -0.2059199810 0.143100766785 +1403715588312143104.0000000000 -1.7912003876 0.5008852941 1.4411217881 0.5901784446 0.7604955120 -0.2218817063 0.155256201955 +1403715588362142976.0000000000 -1.7680284278 0.4739132114 1.4223212872 0.5886371351 0.7545105766 -0.2374636436 0.166826649389 +1403715588412143104.0000000000 -1.7455759692 0.4441614757 1.4028514854 0.5860970838 0.7489824876 -0.2520951303 0.17878335209 +1403715588462142976.0000000000 -1.7239212722 0.4119168644 1.3835590253 0.5831557864 0.7436791368 -0.2658047212 0.190311640381 +1403715588512143104.0000000000 -1.7031918437 0.3771047474 1.3645015939 0.5785926194 0.7394368318 -0.2799301671 0.200256969916 +1403715588562142976.0000000000 -1.6831470989 0.3398798834 1.3461420921 0.5743872345 0.7346306113 -0.2937130210 0.210071014414 +1403715588612143104.0000000000 -1.6639058390 0.3004207035 1.3277848986 0.5679939389 0.7313440737 -0.3077806159 0.21860883722 +1403715588662142976.0000000000 -1.6457658737 0.2587636541 1.3092183886 0.5596534503 0.7294773517 -0.3222156096 0.225450460032 +1403715588712143104.0000000000 -1.6282102929 0.2151951805 1.2904051521 0.5492270603 0.7289444359 -0.3358382568 0.232813897474 +1403715588762142976.0000000000 -1.6113481141 0.1701777077 1.2713808954 0.5376314162 0.7289264750 -0.3495809794 0.239607581826 +1403715588812143104.0000000000 -1.5946874004 0.1237932322 1.2518137684 0.5233062015 0.7304231662 -0.3627710180 0.247042114375 +1403715588862142976.0000000000 -1.5779091079 0.0768816118 1.2315301940 0.5068230804 0.7328786588 -0.3760813775 0.254129955481 +1403715588912143104.0000000000 -1.5607337575 0.0300546262 1.2107650761 0.4888114098 0.7360061334 -0.3892048499 0.260533993926 +1403715588962142976.0000000000 -1.5426225778 -0.0158937919 1.1901084642 0.4713247167 0.7382523646 -0.4024211126 0.266258719298 +1403715589012143104.0000000000 -1.5230287769 -0.0601954772 1.1701988807 0.4546620626 0.7396164993 -0.4151572692 0.271835032006 +1403715589062142976.0000000000 -1.5014706873 -0.1021567460 1.1524154872 0.4410913547 0.7386604401 -0.4282805466 0.276396354084 +1403715589112143104.0000000000 -1.4770939396 -0.1414010123 1.1382183201 0.4308746473 0.7359069961 -0.4394992374 0.282184960039 +1403715589162142976.0000000000 -1.4495694015 -0.1774647640 1.1271546797 0.4224416125 0.7324918293 -0.4502633971 0.286812965822 +1403715589212143104.0000000000 -1.4184995387 -0.2102154718 1.1206280624 0.4163012719 0.7282690257 -0.4594112697 0.291991031528 +1403715589262142976.0000000000 -1.3843275860 -0.2400482971 1.1171315831 0.4101887381 0.7239052065 -0.4682988436 0.297325821791 +1403715589312143104.0000000000 -1.3467898185 -0.2668662949 1.1169499486 0.4033207139 0.7201665122 -0.4778211426 0.300631921303 +1403715589362142976.0000000000 -1.3057508812 -0.2909892671 1.1197376401 0.3945992065 0.7172540276 -0.4875293312 0.303567582904 +1403715589412143104.0000000000 -1.2610887342 -0.3121435041 1.1253877376 0.3875283670 0.7132638398 -0.4978261767 0.305361355628 +1403715589462142976.0000000000 -1.2125182262 -0.3305082449 1.1317897016 0.3805772294 0.7089653146 -0.5082206617 0.306986830842 +1403715589512143104.0000000000 -1.1597718756 -0.3462673949 1.1382132660 0.3732540437 0.7053451712 -0.5171885239 0.309330953934 +1403715589562142976.0000000000 -1.1027369056 -0.3594319561 1.1452609033 0.3667611954 0.7025523784 -0.5238861338 0.312169344948 +1403715589612143104.0000000000 -1.0411231300 -0.3696139368 1.1549940307 0.3612457785 0.7002938372 -0.5295469536 0.314117896806 +1403715589662142976.0000000000 -0.9737816460 -0.3765315295 1.1689524568 0.3593497343 0.6971260382 -0.5336401796 0.316403561915 +1403715589712143104.0000000000 -0.9007869557 -0.3801769538 1.1871214097 0.3604772660 0.6935841333 -0.5346978946 0.321084649596 +1403715589762142976.0000000000 -0.8215629498 -0.3803755056 1.2107142110 0.3678071899 0.6875293479 -0.5321030141 0.329981286199 +1403715589812143104.0000000000 -0.7372887976 -0.3777031790 1.2395187736 0.3809574326 0.6788516393 -0.5254612496 0.34339825491 +1403715589862142976.0000000000 -0.6497741471 -0.3723845159 1.2717990744 0.3971065752 0.6686952939 -0.5177568817 0.356483917353 +1403715589912143104.0000000000 -0.5612859648 -0.3649942437 1.3039673391 0.4111572348 0.6596083679 -0.5122628837 0.365312561 +1403715589962142976.0000000000 -0.4727973128 -0.3560048304 1.3349895502 0.4231054883 0.6519579735 -0.5074802765 0.372016552868 +1403715590012143104.0000000000 -0.3851338032 -0.3459741100 1.3640714610 0.4323284791 0.6463508795 -0.5039861955 0.375926244669 +1403715590062142976.0000000000 -0.2984174474 -0.3350212291 1.3913901737 0.4378897172 0.6434207049 -0.5006483954 0.378963819047 +1403715590112143104.0000000000 -0.2131583469 -0.3235476520 1.4170583741 0.4400711144 0.6428019472 -0.4979800396 0.380997311212 +1403715590162142976.0000000000 -0.1295268341 -0.3114400552 1.4414977785 0.4398649874 0.6440323802 -0.4959978186 0.381742387097 +1403715590212143104.0000000000 -0.0477781022 -0.2985261606 1.4641999963 0.4373615387 0.6478899064 -0.4946709537 0.379808110979 +1403715590262142976.0000000000 0.0324578409 -0.2846673332 1.4863683789 0.4351752695 0.6527632387 -0.4910657757 0.378651611599 +1403715590312143104.0000000000 0.1110712294 -0.2693531694 1.5082728029 0.4329481473 0.6590957679 -0.4851336924 0.377880895233 +1403715590362142976.0000000000 0.1882695632 -0.2525899573 1.5295247888 0.4305827292 0.6667900164 -0.4762006691 0.378447499728 +1403715590412143104.0000000000 0.2643231608 -0.2330576289 1.5505253669 0.4288288117 0.6754861512 -0.4656071094 0.37819879627 +1403715590462142976.0000000000 0.3391823824 -0.2105987708 1.5711937824 0.4295477558 0.6840112312 -0.4529403216 0.377441950607 +1403715590512143104.0000000000 0.4123888109 -0.1851039356 1.5911112783 0.4305763008 0.6932205156 -0.4400542205 0.374702080352 +1403715590562142976.0000000000 0.4840201421 -0.1564178011 1.6108732695 0.4321583918 0.7029524537 -0.4253763245 0.371687980273 +1403715590612143104.0000000000 0.5538601987 -0.1244212819 1.6300217533 0.4337769346 0.7132374132 -0.4119758919 0.365247625455 +1403715590662142976.0000000000 0.6213182408 -0.0887884332 1.6490548291 0.4379724332 0.7223448479 -0.4020359439 0.353221132216 +1403715590712143104.0000000000 0.6868353543 -0.0494881602 1.6680512769 0.4444817576 0.7304654112 -0.3946287774 0.336339676977 +1403715590762142976.0000000000 0.7511550973 -0.0070020417 1.6873929641 0.4536907804 0.7366404967 -0.3864651401 0.319640657572 +1403715590812143104.0000000000 0.8146366951 0.0381262473 1.7074837293 0.4652043769 0.7412168728 -0.3764732253 0.304056484612 +1403715590862142976.0000000000 0.8772808530 0.0851321083 1.7276788321 0.4770874520 0.7451999286 -0.3640673299 0.290722563243 +1403715590912143104.0000000000 0.9387531788 0.1334424143 1.7473693334 0.4889292154 0.7491227557 -0.3496286430 0.278429759986 +1403715590962142976.0000000000 0.9990626515 0.1829378314 1.7665193341 0.4976732949 0.7549389154 -0.3336843349 0.266539472189 +1403715591012143104.0000000000 1.0579039311 0.2331537501 1.7847559763 0.5038741460 0.7619200274 -0.3172983366 0.254775356914 +1403715591062142976.0000000000 1.1151284771 0.2841851590 1.8022442352 0.5086644131 0.7697715501 -0.3002175305 0.242036587634 +1403715591112143104.0000000000 1.1713133233 0.3360802888 1.8190637645 0.5128214860 0.7775931472 -0.2819197729 0.22996578578 +1403715591162142976.0000000000 1.2266937077 0.3885865360 1.8349464306 0.5155167314 0.7860390408 -0.2608413534 0.219879317707 +1403715591212143104.0000000000 1.2804606080 0.4418125308 1.8502798026 0.5174201261 0.7943432891 -0.2390057519 0.210169938037 +1403715591262142976.0000000000 1.3326434984 0.4961529463 1.8646551165 0.5191081924 0.8020202606 -0.2153701838 0.2022519966 +1403715591312143104.0000000000 1.3830823260 0.5519968770 1.8783665487 0.5209894513 0.8087813913 -0.1914808178 0.194364989558 +1403715591362142976.0000000000 1.4311751308 0.6097295325 1.8924835884 0.5238373014 0.8141899222 -0.1696284220 0.184161479852 +1403715591412143104.0000000000 1.4769439797 0.6694087827 1.9062393614 0.5264708282 0.8190078429 -0.1476658238 0.1739236177 +1403715591462142976.0000000000 1.5199474880 0.7306730653 1.9194783091 0.5297562490 0.8226937584 -0.1270421818 0.162461012729 +1403715591512143104.0000000000 1.5600725881 0.7933583895 1.9314352718 0.5313633851 0.8268206279 -0.1080152139 0.149510253591 +1403715591562142976.0000000000 1.5973939564 0.8575690958 1.9408717209 0.5333803636 0.8301321890 -0.0897092283 0.135418576434 +1403715591612143104.0000000000 1.6320669923 0.9231859068 1.9470587724 0.5350069828 0.8331272274 -0.0732730748 0.119572605139 +1403715591662142976.0000000000 1.6645430969 0.9905600147 1.9505227793 0.5379413960 0.8345560409 -0.0569546561 0.104362043537 +1403715591712143104.0000000000 1.6953588142 1.0592721242 1.9508195173 0.5417152032 0.8344664516 -0.0388093325 0.0932963856433 +1403715591762142976.0000000000 1.7242215624 1.1292216864 1.9480432300 0.5451775021 0.8339183970 -0.0213945012 0.0830895520714 +1403715591812143104.0000000000 1.7508394726 1.1998053169 1.9419832927 0.5476313026 0.8334900979 -0.0041571923 0.0733275590943 +1403715591862142976.0000000000 1.7748301316 1.2710453642 1.9323123952 0.5494795012 0.8329922866 0.0120112476 0.0636542075541 +1403715591912143104.0000000000 1.7960486762 1.3426276714 1.9192572279 0.5509937619 0.8321950238 0.0289862571 0.0549282587495 +1403715591962142976.0000000000 1.8146833159 1.4148258502 1.9029220125 0.5525595739 0.8307350444 0.0474196520 0.0480476830272 +1403715592012143104.0000000000 1.8305963108 1.4872837739 1.8832650177 0.5532496832 0.8291501715 0.0673348143 0.0434833764106 +1403715592062142976.0000000000 1.8429165415 1.5598182442 1.8609860871 0.5539308568 0.8271641279 0.0868264916 0.0376997585472 +1403715592112143104.0000000000 1.8512657666 1.6322218491 1.8375704771 0.5552632912 0.8242408034 0.1064289920 0.0313471709401 +1403715592162142976.0000000000 1.8546634385 1.7046966964 1.8159038395 0.5590344862 0.8192816621 0.1254509836 0.0228046504467 +1403715592212143104.0000000000 1.8527084505 1.7767953421 1.7979627766 0.5653048102 0.8120465729 0.1443801324 0.01285349349 +1403715592262142976.0000000000 1.8456403947 1.8475438321 1.7832428625 0.5698414317 0.8053690360 0.1632627498 0.00259481373472 +1403715592312143104.0000000000 1.8334400299 1.9161624184 1.7721270771 0.5736376819 0.7985270459 0.1823035177 -0.00773267932705 +1403715592362142976.0000000000 1.8159193976 1.9825269040 1.7639396194 0.5753321799 0.7925906041 0.2011763641 -0.0179189182943 +1403715592412143104.0000000000 1.7930065582 2.0463605505 1.7588126119 0.5759148905 0.7867089575 0.2205574857 -0.0276667766233 +1403715592462142976.0000000000 1.7651261480 2.1071279129 1.7558827435 0.5749479956 0.7815289295 0.2392716681 -0.0373684840435 +1403715592512143104.0000000000 1.7324169192 2.1647656420 1.7542001643 0.5749477290 0.7749756601 0.2581943257 -0.0467282071905 +1403715592562142976.0000000000 1.6955307318 2.2190122169 1.7526856109 0.5752006071 0.7676960340 0.2768375072 -0.0561075355449 +1403715592612143104.0000000000 1.6540805780 2.2698938604 1.7509213154 0.5751901507 0.7601786267 0.2949523757 -0.0654816164298 +1403715592662142976.0000000000 1.6079444482 2.3172551061 1.7486599659 0.5747812158 0.7520369367 0.3139953316 -0.0739860228496 +1403715592712143104.0000000000 1.5570944090 2.3600443279 1.7468477136 0.5736498621 0.7438876694 0.3324795391 -0.0837515792086 +1403715592762142976.0000000000 1.5013323213 2.3980155522 1.7456361625 0.5704505791 0.7371561889 0.3491576755 -0.0963109941574 +1403715592812143104.0000000000 1.4408965175 2.4310015675 1.7454134501 0.5648309889 0.7327164969 0.3619157159 -0.114496741332 +1403715592862142976.0000000000 1.3763099909 2.4591766056 1.7460071530 0.5554537282 0.7316629224 0.3701166085 -0.138398771332 +1403715592912143104.0000000000 1.3085742729 2.4834498913 1.7470735434 0.5446671517 0.7309316394 0.3769861935 -0.164189044204 +1403715592962142976.0000000000 1.2385361436 2.5046302780 1.7482202347 0.5331796483 0.7297895308 0.3834046041 -0.190072651433 +1403715593012143104.0000000000 1.1667979679 2.5237883431 1.7492488295 0.5227727400 0.7266302701 0.3902520597 -0.215454038785 +1403715593062142976.0000000000 1.0943181985 2.5413532919 1.7499455472 0.5131026882 0.7216563286 0.3983464844 -0.239286132448 +1403715593112143104.0000000000 1.0218087981 2.5580704905 1.7500703024 0.5047620869 0.7143797684 0.4092546207 -0.259590904443 +1403715593162142976.0000000000 0.9495726840 2.5743176117 1.7494313010 0.4976428240 0.7053807639 0.4223125478 -0.27648093886 +1403715593212143104.0000000000 0.8778257349 2.5903373732 1.7482444919 0.4923753132 0.6946809355 0.4360141261 -0.291335941103 +1403715593262142976.0000000000 0.8066367005 2.6061431721 1.7467326319 0.4869987649 0.6839358626 0.4505762828 -0.30338911022 +1403715593312143104.0000000000 0.7359505598 2.6217568359 1.7442977153 0.4825099394 0.6725395655 0.4666918732 -0.311566023031 +1403715593362142976.0000000000 0.6659025393 2.6374168868 1.7417356800 0.4810907666 0.6589219271 0.4845602112 -0.31555501887 +1403715593412143104.0000000000 0.5960720537 2.6519648250 1.7390857704 0.4791645549 0.6452624047 0.5027733147 -0.318208661861 +1403715593462142976.0000000000 0.5264549635 2.6650620296 1.7365970762 0.4775095613 0.6307760251 0.5205871349 -0.321084506199 +1403715593512143104.0000000000 0.4568883096 2.6760058672 1.7334129544 0.4745894617 0.6170428971 0.5374135809 -0.324360215145 +1403715593562142976.0000000000 0.3870827855 2.6840162138 1.7315559424 0.4708604108 0.6038772711 0.5510137098 -0.331672438697 +1403715593612143104.0000000000 0.3174698155 2.6891278406 1.7303713819 0.4687442424 0.5888057976 0.5636564728 -0.340408502401 +1403715593662142976.0000000000 0.2485343053 2.6911638843 1.7299504352 0.4656056382 0.5746562731 0.5730843170 -0.352924812304 +1403715593712143104.0000000000 0.1803235187 2.6903310914 1.7299635011 0.4642507100 0.5589842167 0.5814000800 -0.366035340841 +1403715593762142976.0000000000 0.1135786657 2.6862422826 1.7299786390 0.4606801922 0.5444253496 0.5898307784 -0.378780216174 +1403715593812143104.0000000000 0.0488221189 2.6792652154 1.7299856765 0.4558780627 0.5297324967 0.5991532225 -0.390607334654 +1403715593862142976.0000000000 -0.0135136084 2.6695137158 1.7292664766 0.4502611475 0.5147434922 0.6107970252 -0.399037630142 +1403715593912143104.0000000000 -0.0729026872 2.6562009274 1.7280662158 0.4410879142 0.5011336811 0.6223867337 -0.40858443351 +1403715593962142976.0000000000 -0.1294348978 2.6400504532 1.7259372255 0.4300809376 0.4880308948 0.6354522776 -0.416000763987 +1403715594012143104.0000000000 -0.1835136985 2.6212790665 1.7238479645 0.4183342147 0.4749367296 0.6490360004 -0.422118298499 +1403715594062142976.0000000000 -0.2354065561 2.5996670079 1.7220221945 0.4043400307 0.4634807315 0.6616673436 -0.428825229582 +1403715594112143104.0000000000 -0.2851187490 2.5755990907 1.7202658531 0.3900906483 0.4525965678 0.6736483305 -0.434952364845 +1403715594162142976.0000000000 -0.3330875734 2.5490791432 1.7188885304 0.3766963581 0.4413140356 0.6843733884 -0.441559555469 +1403715594212143104.0000000000 -0.3795797681 2.5204232057 1.7177465059 0.3645251519 0.4293777014 0.6942284850 -0.448110492911 +1403715594262142976.0000000000 -0.4244805493 2.4898384116 1.7172198606 0.3531184223 0.4174558262 0.7032323646 -0.454425191146 +1403715594312143104.0000000000 -0.4678209223 2.4573245411 1.7168978858 0.3430941272 0.4041966004 0.7121492367 -0.460168439594 +1403715594362142976.0000000000 -0.5097784220 2.4228146100 1.7167802001 0.3347983310 0.3896245803 0.7201525483 -0.466350802763 +1403715594412143104.0000000000 -0.5501609553 2.3861736682 1.7164252713 0.3270636498 0.3738984543 0.7286204149 -0.471531129242 +1403715594462142976.0000000000 -0.5885974350 2.3474731148 1.7160283967 0.3193795287 0.3571127022 0.7373344066 -0.476240703186 +1403715594512143104.0000000000 -0.6250528020 2.3066483281 1.7159751211 0.3130128931 0.3383765274 0.7461899082 -0.480338292553 +1403715594562142976.0000000000 -0.6594215877 2.2635828041 1.7159110515 0.3055622738 0.3194394974 0.7549839406 -0.484344251365 +1403715594612143104.0000000000 -0.6912804189 2.2184649754 1.7154038688 0.2966149726 0.3008043413 0.7636702660 -0.488204906838 +1403715594662142976.0000000000 -0.7205129193 2.1707019296 1.7147984657 0.2858190721 0.2832110102 0.7732047452 -0.49015650947 +1403715594712143104.0000000000 -0.7468348388 2.1202122660 1.7138055667 0.2707479222 0.2681945782 0.7838564161 -0.490241113845 +1403715594762142976.0000000000 -0.7703216343 2.0668681107 1.7125913243 0.2500836661 0.2570128825 0.7942485938 -0.490481099937 +1403715594812143104.0000000000 -0.7922799751 2.0105161219 1.7116868386 0.2289236358 0.2462223042 0.8030712653 -0.491980780891 +1403715594862142976.0000000000 -0.8132153723 1.9515375220 1.7108039572 0.2079303026 0.2351050668 0.8103872185 -0.494735437194 +1403715594912143104.0000000000 -0.8336683119 1.8901818978 1.7097532184 0.1887314828 0.2223643130 0.8174992050 -0.496618152653 +1403715594962142976.0000000000 -0.8540861638 1.8262980769 1.7082473680 0.1712809637 0.2086803064 0.8236515574 -0.498711813778 +1403715595012143104.0000000000 -0.8744959181 1.7602269849 1.7065263413 0.1563700586 0.1931876047 0.8288857249 -0.501174030873 +1403715595062142976.0000000000 -0.8952518401 1.6914771565 1.7043219709 0.1427709654 0.1769750310 0.8337032960 -0.503224705278 +1403715595112143104.0000000000 -0.9163310890 1.6197167139 1.7026249617 0.1283258625 0.1614031331 0.8368606009 -0.507095490268 +1403715595162142976.0000000000 -0.9374847163 1.5453173524 1.7018486876 0.1120965447 0.1473623361 0.8377958300 -0.513631048346 +1403715595212143104.0000000000 -0.9592713366 1.4689266774 1.7009790583 0.0980077694 0.1312880632 0.8384736934 -0.519730494753 +1403715595262142976.0000000000 -0.9814255028 1.3907001865 1.6998219497 0.0839446219 0.1147689529 0.8385658150 -0.525917067474 +1403715595312143104.0000000000 -1.0041190109 1.3107136734 1.6979414178 0.0705494096 0.0975722819 0.8374966306 -0.533012030187 +1403715595362142976.0000000000 -1.0270915243 1.2295110561 1.6950119676 0.0582082405 0.0791528509 0.8356397497 -0.540419129606 +1403715595412143104.0000000000 -1.0500852874 1.1478200830 1.6912968616 0.0441233519 0.0619183258 0.8339744552 -0.546539896877 +1403715595462142976.0000000000 -1.0734405120 1.0652030049 1.6878681411 0.0310363562 0.0436333278 0.8306049116 -0.554281839928 +1403715595512143104.0000000000 -1.0973595380 0.9825712764 1.6841364986 0.0203151174 0.0230352657 0.8270169401 -0.561337379291 +1403715595562142976.0000000000 -1.1216395376 0.9001737369 1.6804912682 0.0116319646 0.0012098462 0.8230281861 -0.567880126952 +1403715595612143104.0000000000 -1.1462431608 0.8182798903 1.6764389821 0.0084406193 -0.0245502692 0.8169081768 -0.576183192084 +1403715595662142976.0000000000 -1.1697893057 0.7369715620 1.6725692920 0.0066033589 -0.0514924802 0.8086722947 -0.585964196778 +1403715595712143104.0000000000 -1.1920610332 0.6572368877 1.6687188699 0.0073543987 -0.0798473355 0.7984649903 -0.596677446429 +1403715595762142976.0000000000 -1.2116757330 0.5798218211 1.6654005857 0.0068564477 -0.1069670371 0.7868747595 -0.607732799033 +1403715595812143104.0000000000 -1.2284360697 0.5057380991 1.6624836546 0.0074205368 -0.1337765009 0.7745336607 -0.618179902534 +1403715595862142976.0000000000 -1.2414064293 0.4359317582 1.6612215458 0.0034652154 -0.1554312134 0.7618674551 -0.628798148108 +1403715595912143104.0000000000 -1.2504716034 0.3713029112 1.6617340967 0.0000716803 -0.1751695504 0.7476756482 -0.640544103549 +1403715595962142976.0000000000 -1.2550463276 0.3134537861 1.6643499505 0.0078804065 0.1899326582 -0.7325159023 0.653669593507 +1403715596012143104.0000000000 -1.2552814016 0.2635292206 1.6695521543 0.0203223671 0.1995372996 -0.7172737308 0.667300728774 +1403715596062142976.0000000000 -1.2519024077 0.2227068345 1.6778426166 0.0371766603 0.2048484235 -0.7024893555 0.68056133056 +1403715596112143104.0000000000 -1.2465586858 0.1921176997 1.6880818448 0.0548152905 0.2069960593 -0.6910438671 0.690366778677 +1403715596162142976.0000000000 -1.2400901761 0.1719440073 1.6996412489 0.0660902377 0.2103057777 -0.6854606329 0.693936078583 +1403715596212143104.0000000000 -1.2329496581 0.1625706582 1.7125052447 0.0738924399 0.2143322513 -0.6876454248 0.689742968914 +1403715596262142976.0000000000 -1.2254965062 0.1634947021 1.7262599510 0.0767138169 0.2198939747 -0.6987849021 0.676358847661 +1403715596312143104.0000000000 -1.2177288657 0.1735485087 1.7396204823 0.0781719834 0.2263637571 -0.7179259488 0.653629040476 +1403715596362142976.0000000000 -1.2083788189 0.1910027354 1.7535678039 0.0792447869 0.2332064131 -0.7385915948 0.627548793898 +1403715596412143104.0000000000 -1.1972431962 0.2141131174 1.7682654569 0.0836697606 0.2383439140 -0.7588465287 0.600286178143 +1403715596462142976.0000000000 -1.1837568281 0.2407753541 1.7837382710 0.0893931238 0.2434266305 -0.7762300885 0.574647017491 +1403715596512143104.0000000000 -1.1677277544 0.2692106073 1.7995555772 0.0950988203 0.2487031141 -0.7910335195 0.550789384755 +1403715596562142976.0000000000 -1.1487968181 0.2980265225 1.8158929651 0.1014768474 0.2544978227 -0.8023093098 0.530314132531 +1403715596612143104.0000000000 -1.1270543090 0.3259775595 1.8320499139 0.1073765943 0.2610497756 -0.8116899286 0.511353831976 +1403715596662142976.0000000000 -1.1022370088 0.3518339797 1.8479499369 0.1131170812 0.2683663761 -0.8190224672 0.494354338848 +1403715596712143104.0000000000 -1.0739893746 0.3747928768 1.8639835479 0.1187434607 0.2764086950 -0.8234826308 0.481014116949 +1403715596762142976.0000000000 -1.0421467078 0.3944699388 1.8798145907 0.1238215359 0.2854722265 -0.8259611180 0.47006602387 +1403715596812143104.0000000000 -1.0065278723 0.4107680246 1.8951837142 0.1299673001 0.2938141531 -0.8284165860 0.458811185921 +1403715596862142976.0000000000 -0.9670024088 0.4227884295 1.9100826717 0.1358504638 0.3008232038 -0.8310755286 0.447619835678 +1403715596912143104.0000000000 -0.9233319187 0.4297955769 1.9241854281 0.1403005691 0.3077536309 -0.8331351521 0.437594871153 +1403715596962142976.0000000000 -0.8754436744 0.4316405809 1.9372634285 0.1430722882 0.3142167164 -0.8349542716 0.428543509838 +1403715597012143104.0000000000 -0.8230633579 0.4279152966 1.9498431578 0.1453558324 0.3200384727 -0.8352405947 0.422871383389 +1403715597062142976.0000000000 -0.7658559999 0.4181288221 1.9623194262 0.1476666394 0.3242725980 -0.8345335980 0.420232696914 +1403715597112143104.0000000000 -0.7036280656 0.4022981965 1.9752975196 0.1519581023 0.3263563913 -0.8317830268 0.422536669875 +1403715597162142976.0000000000 -0.6361279848 0.3807765774 1.9888336818 0.1590969293 0.3265784330 -0.8265763132 0.429891024081 +1403715597212143104.0000000000 -0.5639906471 0.3541523962 2.0027513878 0.1701334702 0.3247891954 -0.8193112868 0.440789741439 +1403715597262142976.0000000000 -0.4884080762 0.3233325575 2.0167881532 0.1821642932 0.3230170924 -0.8104862352 0.453418339784 +1403715597312143104.0000000000 -0.4101816024 0.2890758297 2.0308319378 0.1962729581 0.3209306388 -0.8005353237 0.466501496863 +1403715597362142976.0000000000 -0.3306968048 0.2522913874 2.0438243346 0.2094220631 0.3205032265 -0.7907059473 0.477707218109 +1403715597412143104.0000000000 -0.2504100306 0.2133010922 2.0570622332 0.2239687136 0.3201950927 -0.7800503189 0.48870708813 +1403715597462142976.0000000000 -0.1701754768 0.1719656799 2.0699532955 0.2359150038 0.3230065470 -0.7667506934 0.502099846435 +1403715597512143104.0000000000 -0.0910715097 0.1299584347 2.0815788438 0.2463732649 0.3283180902 -0.7542494050 0.512460028735 +1403715597562142976.0000000000 -0.0135698888 0.0878694263 2.0921142335 0.2552199788 0.3361822319 -0.7432008895 0.519130722649 +1403715597612143104.0000000000 0.0619600661 0.0462981407 2.1008534488 0.2629531605 0.3457899273 -0.7341753177 0.521796478012 +1403715597662142976.0000000000 0.1355091543 0.0049758187 2.1083158396 0.2700262857 0.3565021306 -0.7263894726 0.521871986287 +1403715597712143104.0000000000 0.2072141841 -0.0363306389 2.1147003037 0.2749828166 0.3685384126 -0.7209940467 0.518393165104 +1403715597762142976.0000000000 0.2774805650 -0.0778343265 2.1208313681 0.2796364012 0.3794787956 -0.7160908535 0.514794343783 +1403715597812143104.0000000000 0.3463967615 -0.1194452097 2.1261757863 0.2845856499 0.3881643041 -0.7125533398 0.510497031166 +1403715597862142976.0000000000 0.4138882131 -0.1613638893 2.1312435738 0.2886248455 0.3956642924 -0.7079248758 0.508908475616 +1403715597912143104.0000000000 0.4802112090 -0.2034023748 2.1371198667 0.2933175260 0.4007774322 -0.7021501419 0.510222948314 +1403715597962142976.0000000000 0.5451167785 -0.2455000752 2.1433490961 0.2984390351 0.4037204736 -0.6957660387 0.513666760534 +1403715598012143104.0000000000 0.6079221420 -0.2871836484 2.1488067830 0.3021843061 0.4060342637 -0.6910049735 0.51607455706 +1403715598062142976.0000000000 0.6683955365 -0.3282468954 2.1538499035 0.3038071400 0.4085042570 -0.6870816010 0.518405601095 +1403715598112143104.0000000000 0.7267244422 -0.3685961992 2.1572220595 0.3028970197 0.4116008666 -0.6834850992 0.521235303094 +1403715598162142976.0000000000 0.7836499814 -0.4079790725 2.1590527541 0.3033291826 0.4130141849 -0.6795116812 0.525047202834 +1403715598212143104.0000000000 0.8387543879 -0.4463004974 2.1587780838 0.3061854900 0.4118770472 -0.6752111337 0.529809087012 +1403715598262142976.0000000000 0.8916688862 -0.4832322772 2.1557689895 0.3102966658 0.4090101205 -0.6699717146 0.536250503234 +1403715598312143104.0000000000 0.9422117977 -0.5188139592 2.1495413042 0.3146272809 0.4052637923 -0.6644467471 0.543398061246 +1403715598362142976.0000000000 0.9897425537 -0.5525248424 2.1413250895 0.3205191135 0.4000095940 -0.6583742695 0.551183403126 +1403715598412143104.0000000000 1.0336653884 -0.5841124633 2.1334261944 0.3287777615 0.3923626293 -0.6505658641 0.560999828017 +1403715598462142976.0000000000 1.0724644948 -0.6131851030 2.1256654902 0.3363084557 0.3850816234 -0.6438904608 0.569222136345 +1403715598512143104.0000000000 1.1050992490 -0.6394385441 2.1181566438 0.3436075602 0.3778974738 -0.6385273957 0.575682298506 +1403715598562142976.0000000000 1.1310845748 -0.6629836133 2.1104735419 0.3482171925 0.3727128907 -0.6355265067 0.579599816388 +1403715598612143104.0000000000 1.1503409017 -0.6839065212 2.1021968826 0.3493423274 0.3703329779 -0.6346289307 0.581428881356 +1403715598662142976.0000000000 1.1630776898 -0.7021024556 2.0924610026 0.3449229989 0.3723496626 -0.6389483278 0.578038829205 +1403715598712143104.0000000000 1.1698913909 -0.7175066589 2.0817342334 0.3372318013 0.3768786366 -0.6461152678 0.571639979495 +1403715598762142976.0000000000 1.1713958352 -0.7303777771 2.0695525856 0.3280229710 0.3830967713 -0.6554855588 0.562117849279 +1403715598812143104.0000000000 1.1682290229 -0.7408162916 2.0562814103 0.3184097518 0.3896410012 -0.6652637645 0.551560734479 +1403715598862142976.0000000000 1.1614822757 -0.7494425771 2.0423264983 0.3101583721 0.3951966880 -0.6731629684 0.542653646462 +1403715598912143104.0000000000 1.1521653351 -0.7566261476 2.0273581326 0.3022951750 0.4004137832 -0.6794587979 0.535371059527 +1403715598962142976.0000000000 1.1412844699 -0.7627589562 2.0118105534 0.2965498194 0.4040204760 -0.6838504087 0.530258689878 +1403715599012143104.0000000000 1.1289210419 -0.7678165650 1.9952477179 0.2919255747 0.4071440249 -0.6867910595 0.526622485684 +1403715599062142976.0000000000 1.1158995764 -0.7718689500 1.9786474049 0.2898792876 0.4084292407 -0.6882602890 0.524836477968 +1403715599112143104.0000000000 1.1020969206 -0.7749698350 1.9613649551 0.2881856334 0.4095165760 -0.6881386218 0.525081376408 +1403715599162142976.0000000000 1.0875736978 -0.7769659985 1.9432165659 0.2884687153 0.4092314915 -0.6888381617 0.524230267731 +1403715599212143104.0000000000 1.0720062018 -0.7777793830 1.9239775523 0.2892441027 0.4088770889 -0.6921922618 0.519641460986 +1403715599262142976.0000000000 1.0555560484 -0.7775648581 1.9036334393 0.2903463865 0.4081852526 -0.6961533069 0.514251250599 +1403715599312143104.0000000000 1.0384958500 -0.7766739380 1.8825068985 0.2928255133 0.4065079018 -0.7004187803 0.508348381344 +1403715599362142976.0000000000 1.0207688361 -0.7756056815 1.8607157334 0.2966719671 0.4036428048 -0.7045201043 0.50270234999 +1403715599412143104.0000000000 1.0024265400 -0.7749357381 1.8386029974 0.3024042720 0.3994304515 -0.7078204513 0.497993151892 +1403715599462142976.0000000000 0.9835819203 -0.7750150281 1.8159491239 0.3088689723 0.3948541266 -0.7104943055 0.493850198471 +1403715599512143104.0000000000 0.9639373378 -0.7764155827 1.7933945571 0.3145771170 0.3905555864 -0.7119415673 0.491575809157 +1403715599562142976.0000000000 0.9430730830 -0.7794402021 1.7708241132 0.3189216807 0.3874907457 -0.7132046117 0.489365983122 +1403715599612143104.0000000000 0.9210049101 -0.7845417781 1.7493813355 0.3239861876 0.3837487759 -0.7126012267 0.489866633773 +1403715599662142976.0000000000 0.8972372328 -0.7917172111 1.7285255779 0.3291464539 0.3798051660 -0.7118795945 0.490548764847 +1403715599712143104.0000000000 0.8715396545 -0.8010670297 1.7076706355 0.3306068986 0.3785630587 -0.7090880134 0.494553615343 +1403715599762142976.0000000000 0.8438860223 -0.8119360767 1.6870932337 0.3305653015 0.3780699843 -0.7056627121 0.499829776221 +1403715599812143104.0000000000 0.8137915272 -0.8241651836 1.6661266943 0.3276520489 0.3795621559 -0.7022572738 0.505382455255 +1403715599862142976.0000000000 0.7811864171 -0.8375088826 1.6444221148 0.3207226866 0.3840075840 -0.6988213839 0.511198402971 +1403715599912143104.0000000000 0.7462602378 -0.8512862959 1.6221673599 0.3115770756 0.3901479170 -0.6980171728 0.513299479187 +1403715599962142976.0000000000 0.7095672945 -0.8652227343 1.5997186450 0.3019008926 0.3965790328 -0.6989885555 0.512831279363 +1403715600012143104.0000000000 0.6719072338 -0.8789895880 1.5774724711 0.2931938728 0.4021461345 -0.7000854271 0.512051007408 +1403715600062142976.0000000000 0.6337021364 -0.8923067876 1.5551776575 0.2841858102 0.4094267216 -0.6991685645 0.512612429851 +1403715600112143104.0000000000 0.5953717644 -0.9047140623 1.5329821156 0.2747046501 0.4193410650 -0.6953607144 0.514940679466 +1403715600162142976.0000000000 0.5572112552 -0.9154547613 1.5105866614 0.2651529139 0.4318124449 -0.6890211005 0.518152359541 +1403715600212143104.0000000000 0.5200980791 -0.9237273622 1.4881073655 0.2569354082 0.4457205872 -0.6811286834 0.520942483258 +1403715600262142976.0000000000 0.4845424321 -0.9289468158 1.4659503216 0.2524280931 0.4594749950 -0.6728731036 0.521923915117 +1403715600312143104.0000000000 0.4506389134 -0.9304135063 1.4442287928 0.2520208493 0.4727759190 -0.6648497504 0.520522075775 +1403715600362142976.0000000000 0.4181884615 -0.9278021074 1.4226129088 0.2538810686 0.4867255257 -0.6558529427 0.518169454071 +1403715600412143104.0000000000 0.3876728289 -0.9206842153 1.4014992460 0.2608800034 0.4989903435 -0.6493050482 0.511227166124 +1403715600462142976.0000000000 0.3586726886 -0.9094245762 1.3803622655 0.2689238136 0.5117482801 -0.6439261848 0.501151423089 +1403715600512143104.0000000000 0.3315711619 -0.8938632843 1.3599879976 0.2810028314 0.5227549177 -0.6425427958 0.484668402556 +1403715600562142976.0000000000 0.3064310917 -0.8751748758 1.3408343106 0.2952822100 0.5323841652 -0.6415207904 0.466718965223 +1403715600612143104.0000000000 0.2835491383 -0.8545983295 1.3224235571 0.3084754829 0.5429758672 -0.6384983505 0.449822120907 +1403715600662142976.0000000000 0.2633505521 -0.8327828067 1.3059708083 0.3208144139 0.5539219510 -0.6330238305 0.435349760536 +1403715600712143104.0000000000 0.2455641150 -0.8098516341 1.2926625144 0.3326542792 0.5652683491 -0.6244627144 0.424098034035 +1403715600762142976.0000000000 0.2302112071 -0.7862448012 1.2825835835 0.3441297072 0.5769460522 -0.6131518512 0.415635423019 +1403715600812143104.0000000000 0.2172108528 -0.7621277213 1.2755506119 0.3546814645 0.5884676610 -0.6018047335 0.407109240111 +1403715600862142976.0000000000 0.2066585374 -0.7374836018 1.2719143684 0.3642847632 0.6000550743 -0.5879336442 0.40195092868 +1403715600912143104.0000000000 0.1982316387 -0.7118713417 1.2718228209 0.3735517186 0.6105085428 -0.5757584838 0.3952728185 +1403715600962142976.0000000000 0.1923071701 -0.6856724900 1.2751743490 0.3816896432 0.6199428341 -0.5634690134 0.390495287636 +1403715601012143104.0000000000 0.1882329928 -0.6589527645 1.2813438983 0.3890936314 0.6277896035 -0.5524171555 0.386421591043 +1403715601062142976.0000000000 0.1866329435 -0.6314277391 1.2906277829 0.3966321368 0.6334508081 -0.5422039301 0.383976457455 +1403715601112143104.0000000000 0.1865749037 -0.6035083574 1.3025945150 0.4014619170 0.6386230424 -0.5340053999 0.381873240543 +1403715601162142976.0000000000 0.1876829682 -0.5751157263 1.3173388792 0.4045304369 0.6429248097 -0.5269243211 0.38125263867 +1403715601212143104.0000000000 0.1901840445 -0.5459256691 1.3354267475 0.4067361510 0.6460475933 -0.5207695544 0.382082820664 +1403715601262142976.0000000000 0.1936412559 -0.5157467288 1.3558617245 0.4072240727 0.6490020310 -0.5155586690 0.383619834337 +1403715601312143104.0000000000 0.1974994734 -0.4841704221 1.3775053733 0.4071035802 0.6518104584 -0.5104477615 0.385814572138 +1403715601362142976.0000000000 0.2017636128 -0.4509477183 1.3992753469 0.4071785432 0.6544523351 -0.5059514143 0.38718334339 +1403715601412143104.0000000000 0.2063333504 -0.4158612014 1.4206042232 0.4087016533 0.6554849215 -0.5037569472 0.386692919968 +1403715601462142976.0000000000 0.2110288314 -0.3792222303 1.4407980669 0.4106114631 0.6555813144 -0.5029994860 0.385490445518 +1403715601512143104.0000000000 0.2160062594 -0.3409847981 1.4599389743 0.4122489383 0.6553364222 -0.5033496426 0.383697959228 +1403715601562142976.0000000000 0.2215818011 -0.3013404491 1.4783964632 0.4146985326 0.6541707333 -0.5037215677 0.382557657119 +1403715601612143104.0000000000 0.2274066802 -0.2603282580 1.4961379860 0.4165657793 0.6530729087 -0.5048870681 0.380864511211 +1403715601662142976.0000000000 0.2335833951 -0.2181029933 1.5131641695 0.4180796440 0.6519824313 -0.5065841741 0.378814987997 +1403715601712143104.0000000000 0.2398822862 -0.1749021725 1.5303160709 0.4211990398 0.6497921977 -0.5072472029 0.378235037837 +1403715601762142976.0000000000 0.2465102672 -0.1309355265 1.5475820201 0.4252230218 0.6471308565 -0.5062412490 0.379640400993 +1403715601812143104.0000000000 0.2532072846 -0.0861475944 1.5640253988 0.4273602626 0.6454917575 -0.5057170777 0.380728031804 +1403715601862142976.0000000000 0.2597969025 -0.0407869768 1.5803329970 0.4300142058 0.6422223083 -0.5057863432 0.383168976567 +1403715601912143104.0000000000 0.2663446201 0.0048194793 1.5962428445 0.4322959591 0.6374489795 -0.5066565002 0.387399268401 +1403715601962142976.0000000000 0.2727269885 0.0505643973 1.6125233248 0.4362055829 0.6298947370 -0.5073845441 0.394358002619 +1403715602012143104.0000000000 0.2784556550 0.0964446282 1.6288060333 0.4424314515 0.6194496455 -0.5068189825 0.404562809025 +1403715602062142976.0000000000 0.2826511916 0.1423672317 1.6439259709 0.4474666031 0.6088286777 -0.5073885553 0.41431646627 +1403715602112143104.0000000000 0.2848402770 0.1880200202 1.6577721007 0.4512211757 0.5980393701 -0.5094570605 0.423322413674 +1403715602162142976.0000000000 0.2841858818 0.2332160928 1.6698420301 0.4521825888 0.5884252787 -0.5145718427 0.429537444782 +1403715602212143104.0000000000 0.2800514608 0.2779010035 1.6804680860 0.4499425556 0.5802412606 -0.5226776473 0.433220328714 +1403715602262142976.0000000000 0.2725447464 0.3218423983 1.6900185252 0.4469992992 0.5719605396 -0.5321752568 0.435708920893 +1403715602312143104.0000000000 0.2620748361 0.3647369170 1.6977808568 0.4397622286 0.5662952940 -0.5419842344 0.438374168884 +1403715602362142976.0000000000 0.2486409277 0.4070764113 1.7039495095 0.4280149341 0.5635146659 -0.5542575479 0.438238528757 +1403715602412143104.0000000000 0.2334439684 0.4488422450 1.7094190219 0.4148837313 0.5610371084 -0.5666666094 0.438175542826 +1403715602462142976.0000000000 0.2163891718 0.4900555563 1.7151231151 0.4024078255 0.5577052707 -0.5797625583 0.436930370854 +1403715602512143104.0000000000 0.1983923052 0.5307561175 1.7215472615 0.3905456821 0.5538819407 -0.5909383330 0.437585137512 +1403715602562142976.0000000000 0.1798043707 0.5710452443 1.7276118920 0.3797342844 0.5491459716 -0.6012762792 0.438984522638 +1403715602612143104.0000000000 0.1611620576 0.6107664506 1.7318767636 0.3696001309 0.5434841292 -0.6091887318 0.443745235013 +1403715602662142976.0000000000 0.1425118351 0.6498197847 1.7339372667 0.3592764104 0.5372978653 -0.6148271224 0.451906045949 +1403715602712143104.0000000000 0.1239973286 0.6890674379 1.7332843618 0.3505529866 0.5295487016 -0.6214432244 0.458801803709 +1403715602762142976.0000000000 0.1053359254 0.7285072129 1.7283766303 0.3406230491 0.5224489752 -0.6288152689 0.464342938279 +1403715602812143104.0000000000 0.0871241788 0.7686804344 1.7191839944 0.3311426843 0.5151054333 -0.6365657049 0.468823014095 +1403715602862142976.0000000000 0.0696102315 0.8095751925 1.7076133150 0.3243004917 0.5060116012 -0.6447246946 0.472346820326 +1403715602912143104.0000000000 0.0522880799 0.8509334440 1.6926888667 0.3167267613 0.4977176744 -0.6525967384 0.47547741506 +1403715602962142976.0000000000 0.0354263818 0.8925690184 1.6744382853 0.3083356172 0.4901433989 -0.6605210933 0.477912629052 +1403715603012143104.0000000000 0.0198166952 0.9347304145 1.6539895581 0.3015091742 0.4814874112 -0.6672599190 0.481691074491 +1403715603062142976.0000000000 0.0050034765 0.9773769082 1.6319327865 0.2955614423 0.4720952100 -0.6730637877 0.486574438536 +1403715603112143104.0000000000 -0.0090811536 1.0203700442 1.6096268758 0.2903146995 0.4617345247 -0.6788037578 0.491674752589 +1403715603162142976.0000000000 -0.0228456254 1.0636130000 1.5867023937 0.2826429108 0.4529143927 -0.6852816398 0.495348980042 +1403715603212143104.0000000000 -0.0359870727 1.1073483378 1.5642925071 0.2760627332 0.4439265949 -0.6919744580 0.497885423703 +1403715603262142976.0000000000 -0.0486244784 1.1516173885 1.5415020093 0.2679103595 0.4364068634 -0.6997495244 0.498120158163 +1403715603312143104.0000000000 -0.0600886407 1.1962858076 1.5192346012 0.2601099667 0.4301338428 -0.7061709126 0.498648498162 +1403715603362142976.0000000000 -0.0703435311 1.2414653706 1.4975023827 0.2539673241 0.4242905387 -0.7123319322 0.498057582462 +1403715603412143104.0000000000 -0.0789475490 1.2870930054 1.4775157506 0.2510723983 0.4176932253 -0.7171887464 0.498131832291 +1403715603462142976.0000000000 -0.0857882941 1.3330203622 1.4591560584 0.2511990310 0.4105733006 -0.7209402810 0.49857168283 +1403715603512143104.0000000000 -0.0911052053 1.3789501001 1.4421478754 0.2532213365 0.4031897284 -0.7247516755 0.498048196993 +1403715603562142976.0000000000 -0.0956838512 1.4246169447 1.4262945201 0.2562610946 0.3960552084 -0.7285930164 0.496611256191 +1403715603612143104.0000000000 -0.0992218097 1.4694046013 1.4114276138 0.2595885894 0.3894770469 -0.7321768261 0.494811569683 +1403715603662142976.0000000000 -0.1021043137 1.5132774263 1.3973017920 0.2652363036 0.3814017447 -0.7366959251 0.491387348492 +1403715603712143104.0000000000 -0.1043246438 1.5551141520 1.3838103790 0.2701987850 0.3744459252 -0.7390226523 0.490538872062 +1403715603762142976.0000000000 -0.1063558079 1.5950038979 1.3720024641 0.2760179482 0.3675293061 -0.7407834079 0.489873702066 +1403715603812143104.0000000000 -0.1088196642 1.6325740691 1.3628314775 0.2811980036 0.3618964817 -0.7419040841 0.48942512122 +1403715603862142976.0000000000 -0.1123322201 1.6675483268 1.3564801088 0.2847181169 0.3580883547 -0.7449361672 0.485570212114 +1403715603912143104.0000000000 -0.1171090099 1.7000420063 1.3519446687 0.2840606721 0.3581843109 -0.7511403086 0.476237095171 +1403715603962142976.0000000000 -0.1221513968 1.7289744596 1.3499067807 0.2819247859 0.3594261318 -0.7568301538 0.467481966698 +1403715604012143104.0000000000 -0.1269538436 1.7540105375 1.3486936166 0.2770340679 0.3632786719 -0.7611421279 0.460373101878 +1403715604062142976.0000000000 -0.1312749382 1.7748742134 1.3479271118 0.2688241510 0.3695645519 -0.7610851116 0.460331479246 +1403715604112143104.0000000000 -0.1346307783 1.7922846553 1.3471972887 0.2603993218 0.3759582451 -0.7584227386 0.464373277391 +1403715604162142976.0000000000 -0.1366724973 1.8069632249 1.3457402914 0.2538832258 0.3807675957 -0.7547212268 0.470058736267 +1403715604212143104.0000000000 -0.1372055789 1.8193443508 1.3440573751 0.2493255085 0.3840548726 -0.7502221535 0.476975225726 +1403715604262142976.0000000000 -0.1361506729 1.8301071279 1.3420582452 0.2469856179 0.3857375175 -0.7462214056 0.483071719309 +1403715604312143104.0000000000 -0.1338478907 1.8396778140 1.3392959929 0.2454946509 0.3868757934 -0.7434224647 0.487219186648 +1403715604362142976.0000000000 -0.1303525434 1.8483043081 1.3352658674 0.2441231783 0.3877100876 -0.7421561909 0.489171698043 +1403715604412143104.0000000000 -0.1255365896 1.8561423221 1.3308608871 0.2430172912 0.3882735912 -0.7422772279 0.489091741427 +1403715604462142976.0000000000 -0.1189885670 1.8631139461 1.3264322609 0.2420464011 0.3887650800 -0.7419130439 0.489734915628 +1403715604512143104.0000000000 -0.1109665134 1.8694403171 1.3223719552 0.2436313473 0.3875850589 -0.7401874238 0.492487732143 +1403715604562142976.0000000000 -0.1017088247 1.8749201432 1.3181846737 0.2457196784 0.3861409307 -0.7368884625 0.497506196041 +1403715604612143104.0000000000 -0.0913716390 1.8797789026 1.3139779728 0.2485226130 0.3842678162 -0.7333871380 0.502710714157 +1403715604662142976.0000000000 -0.0804399692 1.8842178337 1.3096416663 0.2494477420 0.3834658231 -0.7299800962 0.50779803633 +1403715604712143104.0000000000 -0.0689698980 1.8887574608 1.3049031417 0.2501007051 0.3826946838 -0.7280124910 0.510873985647 +1403715604762142976.0000000000 -0.0573874258 1.8934613307 1.2999903487 0.2495439693 0.3830875592 -0.7263751284 0.513177261977 +1403715604812143104.0000000000 -0.0453889869 1.8986460280 1.2952234372 0.2495574781 0.3829447225 -0.7264366854 0.513190166205 +1403715604862142976.0000000000 -0.0329812655 1.9040646461 1.2907445972 0.2498119068 0.3828142632 -0.7265085594 0.513061949722 +1403715604912143104.0000000000 -0.0203749253 1.9095196539 1.2869045529 0.2489935295 0.3836287839 -0.7260900269 0.513443717733 +1403715604962142976.0000000000 -0.0078851862 1.9152451905 1.2830112369 0.2475299440 0.3848901887 -0.7269682755 0.511962494586 +1403715605012143104.0000000000 0.0047814601 1.9212546790 1.2795006983 0.2467867127 0.3858415232 -0.7282829783 0.509731832289 +1403715605062142976.0000000000 0.0182875410 1.9270713869 1.2770602741 0.2467865873 0.3861985561 -0.7286098783 0.508993812242 +1403715605112143104.0000000000 0.0327455255 1.9327767792 1.2757868648 0.2474150236 0.3862207855 -0.7281627517 0.509311611867 +1403715605162142976.0000000000 0.0476062925 1.9385462909 1.2754325122 0.2482535762 0.3866374180 -0.7266567788 0.510736326065 +1403715605212143104.0000000000 0.0630918573 1.9442792279 1.2753661345 0.2496631245 0.3866449703 -0.7254992726 0.51168818301 +1403715605262142976.0000000000 0.0791474052 1.9500835469 1.2761698710 0.2521062922 0.3860180524 -0.7249242620 0.511778560457 +1403715605312143104.0000000000 0.0956397483 1.9560022927 1.2778934271 0.2556396781 0.3847870015 -0.7245450775 0.511489735055 +1403715605362142976.0000000000 0.1122093542 1.9619114549 1.2794732039 0.2603093459 0.3827020164 -0.7246637053 0.510529847615 +1403715605412143104.0000000000 0.1286294390 1.9675324879 1.2795368153 0.2643931421 0.3811949130 -0.7244351958 0.509882684353 +1403715605462142976.0000000000 0.1447334335 1.9724888675 1.2767598615 0.2666009366 0.3809009639 -0.7251054269 0.507996571069 +1403715605512143104.0000000000 0.1605929549 1.9770482437 1.2717339424 0.2689502762 0.3804065643 -0.7262721830 0.505455548001 +1403715605562142976.0000000000 0.1760071238 1.9812352293 1.2639821443 0.2700990872 0.3806181227 -0.7280686350 0.502088030593 +1403715605612143104.0000000000 0.1910700114 1.9848307544 1.2540438130 0.2715423156 0.3805424560 -0.7292605381 0.499631141576 +1403715605662142976.0000000000 0.2058298350 1.9874628094 1.2428486594 0.2714604193 0.3814945873 -0.7288184251 0.499594659506 +1403715605712143104.0000000000 0.2201844422 1.9889381219 1.2310686715 0.2688166364 0.3840144062 -0.7270226287 0.501705739679 +1403715605762142976.0000000000 0.2346387206 1.9893534708 1.2204644358 0.2659031541 0.3863988534 -0.7241577851 0.505556071097 +1403715605812143104.0000000000 0.2489198156 1.9893562619 1.2104361475 0.2632947849 0.3885832166 -0.7225100388 0.507600417519 +1403715605862142976.0000000000 0.2632860443 1.9891240118 1.2014048522 0.2618611058 0.3899629849 -0.7210924349 0.5092968997 +1403715605912143104.0000000000 0.2779486171 1.9888266667 1.1935950602 0.2610952184 0.3911266315 -0.7197466346 0.51069954677 +1403715605962142976.0000000000 0.2927172757 1.9886102037 1.1857861335 0.2607911917 0.3918575889 -0.7179925209 0.512759518954 +1403715606012143104.0000000000 0.3074396501 1.9886585378 1.1766839425 0.2606919264 0.3924559791 -0.7169965984 0.513744977468 +1403715606062142976.0000000000 0.3221370666 1.9888122798 1.1654976090 0.2608700132 0.3930783415 -0.7160632786 0.514479965338 +1403715606112143104.0000000000 0.3369311291 1.9892778424 1.1531048964 0.2609402639 0.3941658441 -0.7149697662 0.515132700817 +1403715606162142976.0000000000 0.3518323591 1.9904462174 1.1393452233 0.2619048518 0.3945619929 -0.7147427084 0.514654780555 +1403715606212143104.0000000000 0.3669516782 1.9921010981 1.1248348465 0.2625313661 0.3948702645 -0.7149801092 0.513768624434 +1403715606262142976.0000000000 0.3820740171 1.9946730256 1.1119247832 0.2661166246 0.3933206165 -0.7158059521 0.511959640652 +1403715606312143104.0000000000 0.3972271920 1.9975565450 1.1007967939 0.2694759234 0.3923402468 -0.7166005351 0.509838729926 +1403715606362142976.0000000000 0.4123507156 2.0002233634 1.0923378946 0.2721676046 0.3915857046 -0.7173543112 0.50792541098 +1403715606412143104.0000000000 0.4273251064 2.0024849932 1.0864211378 0.2746830083 0.3908621203 -0.7181556785 0.50599255852 +1403715606462142976.0000000000 0.4420237129 2.0040988210 1.0831708256 0.2765638480 0.3904480887 -0.7176934130 0.505943566896 +1403715606512143104.0000000000 0.4565538571 2.0055308945 1.0820592148 0.2789997137 0.3898574530 -0.7169280375 0.506146732821 +1403715606562142976.0000000000 0.4705272905 2.0068402455 1.0814077394 0.2817883368 0.3893333839 -0.7169606552 0.504957689547 +1403715606612143104.0000000000 0.4837031210 2.0078504223 1.0803090927 0.2850484951 0.3886435007 -0.7166471048 0.504103671876 +1403715606662142976.0000000000 0.4960175858 2.0085184446 1.0784248528 0.2882314338 0.3880104287 -0.7164438044 0.503069401712 +1403715606712143104.0000000000 0.5077338644 2.0087868933 1.0757712802 0.2925505462 0.3864348056 -0.7166314348 0.501519397042 +1403715606762142976.0000000000 0.5186120474 2.0082750188 1.0717511388 0.2964931214 0.3849725949 -0.7167351530 0.500178618714 +1403715606812143104.0000000000 0.5284303602 2.0065289387 1.0666819441 0.3002711838 0.3835888264 -0.7155135482 0.500736648126 +1403715606862142976.0000000000 0.5370228483 2.0035625332 1.0605209565 0.3010857419 0.3839898682 -0.7122986882 0.504509401304 +1403715606912143104.0000000000 0.5444484441 1.9997994923 1.0539290244 0.3003454862 0.3852523292 -0.7084100524 0.509439328572 +1403715606962142976.0000000000 0.5503361668 1.9956488252 1.0468105755 0.2970125826 0.3883422791 -0.7039980919 0.515131523613 +1403715607012143104.0000000000 0.5544954375 1.9917651305 1.0387880173 0.2920432428 0.3924436748 -0.7024165001 0.517020083527 +1403715607062142976.0000000000 0.5574570863 1.9881823795 1.0303966992 0.2861102802 0.3969322940 -0.7014934404 0.518162729888 +1403715607112143104.0000000000 0.5596456392 1.9853905723 1.0221107697 0.2820130919 0.4004752394 -0.7014736744 0.517709264743 +1403715607162142976.0000000000 0.5613958304 1.9834605151 1.0143849676 0.2792719569 0.4030118277 -0.7015186419 0.517165578785 +1403715607212143104.0000000000 0.5630697526 1.9822941532 1.0068538126 0.2769366166 0.4051934300 -0.7021122638 0.515909646876 +1403715607262142976.0000000000 0.5643627142 1.9819443106 1.0003151365 0.2755929101 0.4061751387 -0.7026480109 0.515127243964 +1403715607312143104.0000000000 0.5651728299 1.9825121670 0.9942440118 0.2749381154 0.4068485354 -0.7030772187 0.514359530378 +1403715607362142976.0000000000 0.5658120319 1.9837337829 0.9891732707 0.2755438965 0.4064175266 -0.7028351995 0.514706749007 +1403715607412143104.0000000000 0.5659929809 1.9853350919 0.9849551165 0.2758300666 0.4060883934 -0.7024408472 0.515351188301 +1403715607462142976.0000000000 0.5657956109 1.9874878026 0.9813250041 0.2752269082 0.4061365907 -0.7018979756 0.516374331766 +1403715607512143104.0000000000 0.5654009548 1.9906606271 0.9779804633 0.2742414869 0.4063018912 -0.7026100769 0.515799825541 +1403715607562142976.0000000000 0.5646257113 1.9945466551 0.9752704036 0.2732734489 0.4064432759 -0.7028551179 0.515868363897 +1403715607612143104.0000000000 0.5639915368 1.9991765093 0.9733432427 0.2727897736 0.4059345360 -0.7035635088 0.515559192525 +1403715607662142976.0000000000 0.5632195131 2.0047194674 0.9717526629 0.2715384785 0.4058872194 -0.7043091917 0.515238762481 +1403715607712143104.0000000000 0.5626248993 2.0109467851 0.9706031932 0.2709425736 0.4055063090 -0.7041033643 0.516132935965 +1403715607762142976.0000000000 0.5618233403 2.0179463337 0.9681125656 0.2704800548 0.4051643993 -0.7047980364 0.515695721751 +1403715607812143104.0000000000 0.5608568178 2.0256102488 0.9635343519 0.2708814701 0.4039882855 -0.7059618460 0.51481507973 +1403715607862142976.0000000000 0.5598867042 2.0339958115 0.9565432984 0.2727739377 0.4018563377 -0.7079360089 0.512769412079 +1403715607912143104.0000000000 0.5590622838 2.0422467871 0.9472073460 0.2694384524 0.4071204150 -0.7058459697 0.513261488009 +1403715607962142976.0000000000 0.5596338691 2.0439254024 0.9477060443 0.2688357922 0.4085136820 -0.7019484097 0.517795634019 +1403715608012143104.0000000000 0.5590484855 2.0429628807 0.9494267197 0.2670351993 0.4108184428 -0.7032913543 0.515074441522 +1403715608062142976.0000000000 0.5587629369 2.0421894562 0.9482984544 0.2672347460 0.4109289345 -0.7028198412 0.515526208915 +1403715608112143104.0000000000 0.5589711701 2.0413735694 0.9463637460 0.2670653865 0.4111020540 -0.7045260009 0.513141593097 +1403715608162142976.0000000000 0.5597089873 2.0418331409 0.9466529061 0.2667656099 0.4109531860 -0.7054506425 0.512145466953 +1403715608212143104.0000000000 0.5589873920 2.0422244569 0.9467963936 0.2668508699 0.4111661053 -0.7042440546 0.513588705708 +1403715608262142976.0000000000 0.5583777028 2.0419208637 0.9464710038 0.2682674026 0.4100606914 -0.7037324006 0.514435164413 +1403715608312143104.0000000000 0.5590750807 2.0421390938 0.9463176611 0.2673374667 0.4106820725 -0.7045864964 0.513253137589 +1403715608362142976.0000000000 0.5592549281 2.0418605204 0.9462958898 0.2676208936 0.4104798820 -0.7049851501 0.512719476748 +1403715608412143104.0000000000 0.5590228165 2.0415835522 0.9463971774 0.2674963781 0.4105464777 -0.7044559700 0.513457947289 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_03_difficult.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_03_difficult.txt new file mode 100644 index 0000000000000000000000000000000000000000..34cd1154c526408d96d26ca019f42d6263167319 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V1_03_difficult.txt @@ -0,0 +1,2095 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1403715888384058112.0000000000 0.9080302787 2.0913569065 0.9301217440 0.3470018900 0.5477973657 -0.6209279080 0.440404663327 +1403715888434057984.0000000000 0.9082768931 2.0908487500 0.9298010705 0.3469776734 0.5477940397 -0.6209674630 0.440372108768 +1403715888484058112.0000000000 0.9084458504 2.0904659551 0.9295440871 0.3469659421 0.5478223888 -0.6209793275 0.440329354224 +1403715888534057984.0000000000 0.9085648834 2.0902215552 0.9293704457 0.3470085602 0.5478222586 -0.6209905191 0.440280146339 +1403715888584058112.0000000000 0.9086428495 2.0900649758 0.9292402184 0.3469500113 0.5478489412 -0.6210240493 0.440245792112 +1403715888634057984.0000000000 0.9086788275 2.0899940660 0.9291810783 0.3469458419 0.5478257090 -0.6210598133 0.440227536298 +1403715888684058112.0000000000 0.9086778239 2.0899783264 0.9291674663 0.3469134261 0.5478480225 -0.6210671578 0.440214952595 +1403715888734057984.0000000000 0.9086430992 2.0899988765 0.9291711056 0.3469313334 0.5478433892 -0.6210905336 0.440173624684 +1403715888784058112.0000000000 0.9085780048 2.0900376953 0.9291776708 0.3469018898 0.5478820151 -0.6210927534 0.440145621328 +1403715888834057984.0000000000 0.9085268865 2.0900926152 0.9291975119 0.3468845792 0.5478879687 -0.6211204233 0.440112806254 +1403715888884058112.0000000000 0.9085014326 2.0901411911 0.9291929812 0.3468663041 0.5479041852 -0.6211372301 0.440083301487 +1403715888934057984.0000000000 0.9084830189 2.0901784731 0.9292156044 0.3468657774 0.5479071089 -0.6211552739 0.440054608173 +1403715888984058112.0000000000 0.9084416752 2.0901902621 0.9292354240 0.3468533268 0.5479078718 -0.6211793745 0.440029451779 +1403715889034057984.0000000000 0.9084135359 2.0902050476 0.9292465834 0.3468231604 0.5479328765 -0.6211754918 0.440027574788 +1403715889084058112.0000000000 0.9084129812 2.0902437604 0.9292576563 0.3467947446 0.5479431151 -0.6211934071 0.44001193031 +1403715889134057984.0000000000 0.9084189684 2.0902615521 0.9292627463 0.3467623155 0.5479566277 -0.6212144755 0.439990915961 +1403715889184058112.0000000000 0.9084179120 2.0902798477 0.9292838453 0.3467734600 0.5479471530 -0.6212137467 0.439994961133 +1403715889234057984.0000000000 0.9084272970 2.0902796382 0.9292686118 0.3467246014 0.5479660217 -0.6212329005 0.439982923735 +1403715889284058112.0000000000 0.9084126360 2.0902873498 0.9292506407 0.3467004284 0.5479761318 -0.6212465636 0.439970088884 +1403715889334057984.0000000000 0.9083940374 2.0902986636 0.9292176270 0.3466993852 0.5480038929 -0.6212344166 0.439953485461 +1403715889384058112.0000000000 0.9083699500 2.0902892640 0.9292208258 0.3466823743 0.5480221941 -0.6212338236 0.439944931256 +1403715889434057984.0000000000 0.9083681957 2.0902539110 0.9292301297 0.3466589454 0.5480062291 -0.6212474893 0.43996398205 +1403715889484058112.0000000000 0.9083763756 2.0902451084 0.9292244666 0.3466613595 0.5479910598 -0.6212578298 0.439966372756 +1403715889534057984.0000000000 0.9083955869 2.0902757143 0.9292294379 0.3466726015 0.5479783981 -0.6212637594 0.439964912048 +1403715889584058112.0000000000 0.9083956680 2.0903121671 0.9292273365 0.3466571080 0.5479960521 -0.6212598091 0.439960709688 +1403715889634057984.0000000000 0.9084120504 2.0903374000 0.9292402831 0.3466685944 0.5480029991 -0.6212471687 0.439960855163 +1403715889684058112.0000000000 0.9084281375 2.0903407436 0.9292574707 0.3466502498 0.5479963964 -0.6212601465 0.439965207933 +1403715889734057984.0000000000 0.9083594465 2.0904471481 0.9292774502 0.3467754528 0.5480761031 -0.6212085397 0.439840108179 +1403715889784058112.0000000000 0.9082989093 2.0904168633 0.9292679480 0.3466873493 0.5480390664 -0.6213025408 0.439822937408 +1403715889834057984.0000000000 0.9082771658 2.0903808756 0.9293224840 0.3467336097 0.5479040283 -0.6212371829 0.440046977464 +1403715889884058112.0000000000 0.9082678075 2.0903636617 0.9293252771 0.3467811935 0.5478319110 -0.6212624967 0.440063530972 +1403715889934057984.0000000000 0.9083292973 2.0903213918 0.9293291141 0.3466860019 0.5476284580 -0.6213810527 0.440224346699 +1403715889984058112.0000000000 0.9083398576 2.0902702735 0.9293350593 0.3465740978 0.5476023666 -0.6214494681 0.440248340637 +1403715890034057984.0000000000 0.9083593596 2.0902520282 0.9293703648 0.3466231499 0.5475735153 -0.6215507200 0.440102646827 +1403715890084058112.0000000000 0.9083582794 2.0901820451 0.9293660618 0.3466305782 0.5476421390 -0.6214989351 0.440084541449 +1403715890134057984.0000000000 0.9083645147 2.0901224339 0.9293883854 0.3466708676 0.5475345340 -0.6216395339 0.439988106183 +1403715890184058112.0000000000 0.9083475777 2.0900749611 0.9294002145 0.3467105793 0.5476744329 -0.6215012760 0.439978014991 +1403715890234057984.0000000000 0.9083526610 2.0900477047 0.9293814480 0.3466719844 0.5476571935 -0.6214873146 0.440049601107 +1403715890284058112.0000000000 0.9083610857 2.0900757981 0.9293607969 0.3465799106 0.5477060553 -0.6216414136 0.439843603317 +1403715890334057984.0000000000 0.9083498348 2.0901235399 0.9293455502 0.3465488135 0.5478950023 -0.6215164522 0.439809374561 +1403715890384058112.0000000000 0.9083812896 2.0901576958 0.9293560273 0.3466695750 0.5478320224 -0.6215730589 0.439712648754 +1403715890434057984.0000000000 0.9084198409 2.0901995411 0.9292838525 0.3465330823 0.5480304361 -0.6215657604 0.439583290772 +1403715890484058112.0000000000 0.9084151660 2.0902734540 0.9292821109 0.3465990589 0.5481142257 -0.6214735372 0.43955719822 +1403715890534057984.0000000000 0.9084289274 2.0903358353 0.9292758274 0.3465110227 0.5480232196 -0.6215670306 0.439607880132 +1403715890584058112.0000000000 0.9084540429 2.0903822396 0.9292848382 0.3462889287 0.5480878426 -0.6216358142 0.439605060424 +1403715890634057984.0000000000 0.9084492405 2.0904005308 0.9292578381 0.3461453677 0.5482198369 -0.6215192386 0.439718354174 +1403715890684058112.0000000000 0.9084246487 2.0904927923 0.9292554171 0.3462684790 0.5480886109 -0.6215133319 0.439793353046 +1403715890734057984.0000000000 0.9083966904 2.0905919419 0.9292560156 0.3461511125 0.5483135239 -0.6213835680 0.439788754082 +1403715890784058112.0000000000 0.9084006619 2.0906935271 0.9292885164 0.3461800530 0.5483591247 -0.6213637663 0.43973709316 +1403715890834057984.0000000000 0.9084217461 2.0906836998 0.9293678865 0.3462488654 0.5482991528 -0.6212598248 0.439904526437 +1403715890884058112.0000000000 0.9084527177 2.0906308249 0.9293985113 0.3462614733 0.5482364059 -0.6212592685 0.439973586205 +1403715890934057984.0000000000 0.9084913506 2.0905631426 0.9293833653 0.3462656890 0.5481795067 -0.6213569636 0.439903199522 +1403715890984058112.0000000000 0.9084454739 2.0904929094 0.9293760381 0.3462608651 0.5482013181 -0.6212989483 0.439961754001 +1403715891034057984.0000000000 0.9084201750 2.0904111995 0.9293663564 0.3462797177 0.5481540709 -0.6213147275 0.439983501004 +1403715891084058112.0000000000 0.9084082104 2.0903417346 0.9293188360 0.3462625511 0.5481435211 -0.6213017587 0.440028465688 +1403715891134057984.0000000000 0.9083953462 2.0903248551 0.9292844303 0.3463370063 0.5481769355 -0.6213120945 0.439913635503 +1403715891184058112.0000000000 0.9083900031 2.0903248643 0.9292765451 0.3462914757 0.5481340262 -0.6212955850 0.440026248341 +1403715891234057984.0000000000 0.9084161259 2.0903420591 0.9292525434 0.3463159597 0.5481450436 -0.6213118523 0.43997028239 +1403715891284058112.0000000000 0.9084444677 2.0903453368 0.9292073619 0.3462974051 0.5481671272 -0.6213508076 0.439902354797 +1403715891334057984.0000000000 0.9083868607 2.0903312127 0.9291765401 0.3463277017 0.5481216335 -0.6213475948 0.439939728078 +1403715891384058112.0000000000 0.9083496314 2.0903567788 0.9291677111 0.3463188764 0.5481109736 -0.6213871031 0.439904153817 +1403715891434057984.0000000000 0.9083374548 2.0903801998 0.9291499630 0.3462763336 0.5481181553 -0.6213715958 0.439950597857 +1403715891484058112.0000000000 0.9083121604 2.0903990639 0.9291054848 0.3462572616 0.5481763492 -0.6213663667 0.439900485586 +1403715891534057984.0000000000 0.9082830921 2.0904379556 0.9291328856 0.3462890533 0.5481791993 -0.6213457242 0.439901066242 +1403715891584058112.0000000000 0.9082760905 2.0904549003 0.9292108297 0.3463895704 0.5480704860 -0.6213584558 0.439939401801 +1403715891634057984.0000000000 0.9082991422 2.0904643102 0.9292501690 0.3463517847 0.5480674371 -0.6213898803 0.439928564936 +1403715891684058112.0000000000 0.9083043108 2.0904897693 0.9292921179 0.3463785238 0.5480986322 -0.6213645898 0.439904369342 +1403715891734057984.0000000000 0.9083162130 2.0905061043 0.9293395507 0.3463985820 0.5480922389 -0.6213987525 0.439848281159 +1403715891784058112.0000000000 0.9083645191 2.0904978008 0.9293884537 0.3464620167 0.5479929020 -0.6214091283 0.439907428367 +1403715891834057984.0000000000 0.9083397915 2.0905179075 0.9295847475 0.3467854544 0.5477747888 -0.6212534643 0.440144024696 +1403715891884058112.0000000000 0.9083261133 2.0904648723 0.9295229803 0.3466276190 0.5479070494 -0.6212975239 0.44004152727 +1403715891934057984.0000000000 0.9084138956 2.0905486842 0.9293884212 0.3465772798 0.5479454559 -0.6214570616 0.439808011633 +1403715891984058112.0000000000 0.9084037671 2.0905330971 0.9293685871 0.3464210351 0.5479676815 -0.6214261969 0.439947006256 +1403715892034057984.0000000000 0.9083427488 2.0906219179 0.9294112936 0.3465850884 0.5479454533 -0.6214073013 0.439872166148 +1403715892084058112.0000000000 0.9083403264 2.0906877556 0.9293631307 0.3464709540 0.5479815703 -0.6214218147 0.439896584279 +1403715892134057984.0000000000 0.9082927684 2.0907287686 0.9293749674 0.3465014643 0.5479317466 -0.6215139734 0.439804407871 +1403715892184058112.0000000000 0.9080546004 2.0908258380 0.9297590810 0.3470821495 0.5475410267 -0.6213897326 0.440008642776 +1403715892234057984.0000000000 0.9079516170 2.0907454343 0.9299156920 0.3465591802 0.5478414264 -0.6213878043 0.440049659557 +1403715892284058112.0000000000 0.9081241397 2.0906565183 0.9298480849 0.3466034824 0.5476488886 -0.6216200274 0.439926428294 +1403715892334057984.0000000000 0.9081912143 2.0905067821 0.9297409405 0.3467656738 0.5476417651 -0.6215242939 0.439942742496 +1403715892384058112.0000000000 0.9083121348 2.0904555729 0.9298314899 0.3467165670 0.5476586259 -0.6216812025 0.439738711207 +1403715892434057984.0000000000 0.9083121265 2.0903011417 0.9298891861 0.3466750404 0.5476909941 -0.6215445660 0.439924247859 +1403715892484058112.0000000000 0.9084163761 2.0902366391 0.9298584288 0.3465984344 0.5477220203 -0.6216249657 0.439832372352 +1403715892534057984.0000000000 0.9083633750 2.0902306060 0.9301209556 0.3466596128 0.5476948872 -0.6215496181 0.439924420346 +1403715892584058112.0000000000 0.9082539388 2.0902864164 0.9304066773 0.3468775174 0.5475402223 -0.6215162625 0.439992304847 +1403715892634057984.0000000000 0.9081814437 2.0904211966 0.9303100765 0.3469274413 0.5475285230 -0.6215303184 0.439947645059 +1403715892684058112.0000000000 0.9081549394 2.0904847067 0.9303230929 0.3470036616 0.5474561039 -0.6216135195 0.439860097674 +1403715892734057984.0000000000 0.9082221759 2.0905521898 0.9306371712 0.3471388883 0.5474140490 -0.6215105443 0.4399512411 +1403715892784058112.0000000000 0.9084418898 2.0906235508 0.9307141032 0.3474058763 0.5472857295 -0.6214336223 0.440008795983 +1403715892834057984.0000000000 0.9087761149 2.0907221945 0.9305137728 0.3476079456 0.5471619199 -0.6213937759 0.440059456042 +1403715892884058112.0000000000 0.9090316080 2.0907853155 0.9306419994 0.3475329952 0.5471531161 -0.6215991446 0.43983950282 +1403715892934057984.0000000000 0.9089788964 2.0907483788 0.9308118686 0.3476135626 0.5470514291 -0.6216903908 0.439773354126 +1403715892984058112.0000000000 0.9087766252 2.0906691536 0.9310771633 0.3477262682 0.5470033712 -0.6213754695 0.4401889142 +1403715893034057984.0000000000 0.9086367800 2.0905954965 0.9313632205 0.3479897673 0.5468563227 -0.6214658735 0.440035739805 +1403715893084058112.0000000000 0.9084166774 2.0903981620 0.9318647108 0.3484289094 0.5465151863 -0.6215541045 0.439987433184 +1403715893134057984.0000000000 0.9082848912 2.0903825326 0.9322114962 0.3486875625 0.5462305388 -0.6215722548 0.440110343286 +1403715893184058112.0000000000 0.9080742191 2.0903422734 0.9322257435 0.3493856868 0.5458203359 -0.6212280703 0.440551344892 +1403715893234057984.0000000000 0.9078059825 2.0902236683 0.9321619156 0.3497679959 0.5455585230 -0.6210433859 0.440832575855 +1403715893284058112.0000000000 0.9077738662 2.0902508173 0.9322918540 0.3500749601 0.5454996832 -0.6209682061 0.440767631488 +1403715893334057984.0000000000 0.9076033780 2.0903059185 0.9324534633 0.3507969122 0.5449860246 -0.6206855448 0.441226941541 +1403715893384058112.0000000000 0.9074065015 2.0904118595 0.9325677879 0.3510665442 0.5448198385 -0.6205308729 0.441435228437 +1403715893434057984.0000000000 0.9073682453 2.0905580263 0.9336357726 0.3521719894 0.5441750331 -0.6201221239 0.441924172912 +1403715893484058112.0000000000 0.9071529488 2.0910095944 0.9369885813 0.3570121702 0.5418830793 -0.6174297265 0.444618456033 +1403715893534057984.0000000000 0.9070420524 2.0922856531 0.9415959665 0.3642218583 0.5382294982 -0.6137640235 0.44826908059 +1403715893584058112.0000000000 0.9074599602 2.0940546773 0.9471786137 0.3706043844 0.5345865730 -0.6106094170 0.451692070024 +1403715893634057984.0000000000 0.9073202222 2.0967926211 0.9535188349 0.3769081957 0.5306159480 -0.6085305997 0.453957527619 +1403715893684058112.0000000000 0.9062582353 2.1000662087 0.9595423836 0.3803633619 0.5288933618 -0.6077483891 0.454133703131 +1403715893734057984.0000000000 0.9046692845 2.1033181376 0.9663484683 0.3824553687 0.5276874265 -0.6082188031 0.453148715556 +1403715893784058112.0000000000 0.9021175377 2.1067930963 0.9736088221 0.3820666397 0.5279376076 -0.6087637152 0.452452985828 +1403715893834057984.0000000000 0.8988790204 2.1107922270 0.9806446072 0.3784291217 0.5306582620 -0.6097738341 0.450964610534 +1403715893884058112.0000000000 0.8948999103 2.1151410054 0.9880006383 0.3748375241 0.5329242517 -0.6128535727 0.447100738989 +1403715893934057984.0000000000 0.8906275008 2.1199294465 0.9965879007 0.3727350808 0.5341438518 -0.6148470890 0.444659377785 +1403715893984058112.0000000000 0.8858677256 2.1251728621 1.0051518638 0.3691439682 0.5363270949 -0.6176439568 0.441137076956 +1403715894034057984.0000000000 0.8810409516 2.1306964530 1.0139516747 0.3649525735 0.5387287215 -0.6212858295 0.436560307095 +1403715894084058112.0000000000 0.8768677462 2.1364871418 1.0221995058 0.3597890187 0.5420132725 -0.6246706520 0.431925978653 +1403715894134057984.0000000000 0.8733507292 2.1422839402 1.0302571483 0.3558063185 0.5443494586 -0.6247831388 0.432124472907 +1403715894184058112.0000000000 0.8713106466 2.1482073780 1.0402632001 0.3531910595 0.5456654303 -0.6211579237 0.437799209141 +1403715894234057984.0000000000 0.8703953330 2.1546915011 1.0529123539 0.3521659850 0.5458369922 -0.6168423001 0.444462229785 +1403715894284058112.0000000000 0.8700714783 2.1621621690 1.0675858551 0.3503495739 0.5466899415 -0.6117673156 0.451803093672 +1403715894334057984.0000000000 0.8701314696 2.1710425675 1.0839238124 0.3479055242 0.5479490134 -0.6081564983 0.457011267421 +1403715894384058112.0000000000 0.8705699202 2.1815897938 1.1016952379 0.3461700368 0.5484165450 -0.6055623000 0.461193993516 +1403715894434057984.0000000000 0.8709045807 2.1940703109 1.1187520059 0.3446357899 0.5486051989 -0.6049579192 0.462908656244 +1403715894484058112.0000000000 0.8710908490 2.2086257642 1.1338504615 0.3432523791 0.5488856372 -0.6068939943 0.461066200491 +1403715894534057984.0000000000 0.8713998893 2.2250311006 1.1464517413 0.3423542691 0.5490124718 -0.6101389825 0.457284684011 +1403715894584058112.0000000000 0.8719954183 2.2428170258 1.1569574393 0.3411248803 0.5491511303 -0.6126509557 0.454670934493 +1403715894634057984.0000000000 0.8733018541 2.2621747994 1.1661087874 0.3409911572 0.5488590972 -0.6149922416 0.451954936776 +1403715894684058112.0000000000 0.8749634598 2.2830307114 1.1749445876 0.3419375957 0.5480021934 -0.6181935938 0.447893912962 +1403715894734057984.0000000000 0.8777270470 2.3049179958 1.1850230261 0.3444188152 0.5462351213 -0.6197371609 0.446014263674 +1403715894784058112.0000000000 0.8812452804 2.3278334682 1.1963201526 0.3481986032 0.5436029134 -0.6208390388 0.44476116414 +1403715894834057984.0000000000 0.8855545280 2.3513270379 1.2085681653 0.3521342408 0.5409048000 -0.6209253248 0.444831670122 +1403715894884058112.0000000000 0.8907073123 2.3754986294 1.2215235895 0.3557470703 0.5386486731 -0.6202070308 0.445695936575 +1403715894934057984.0000000000 0.8961841981 2.4000824712 1.2349349610 0.3581197171 0.5369861960 -0.6190895417 0.447352470575 +1403715894984058112.0000000000 0.9017841383 2.4250829719 1.2490108307 0.3603738007 0.5355132604 -0.6185219931 0.448092418792 +1403715895034057984.0000000000 0.9073488870 2.4504054754 1.2634184299 0.3618780740 0.5344869302 -0.6183140921 0.448392310875 +1403715895084058112.0000000000 0.9128505192 2.4758779739 1.2777104445 0.3617140819 0.5343104612 -0.6180085091 0.449155581953 +1403715895134057984.0000000000 0.9182631699 2.5018961812 1.2922492529 0.3628443012 0.5333939599 -0.6187970112 0.448246757439 +1403715895184058112.0000000000 0.9235668900 2.5279573467 1.3064038641 0.3634228435 0.5328135045 -0.6194242851 0.447601565343 +1403715895234057984.0000000000 0.9284604692 2.5541676864 1.3202252941 0.3643009860 0.5320604817 -0.6205240845 0.446258104689 +1403715895284058112.0000000000 0.9332620482 2.5801314888 1.3337170008 0.3645613930 0.5317246905 -0.6205511447 0.44640802082 +1403715895334057984.0000000000 0.9381679466 2.6061516122 1.3467687350 0.3646845876 0.5315437131 -0.6209193266 0.446010787448 +1403715895384058112.0000000000 0.9430340501 2.6324109000 1.3595248580 0.3648436295 0.5313064563 -0.6208824739 0.44621466709 +1403715895434057984.0000000000 0.9473722603 2.6588737755 1.3716397909 0.3646805639 0.5311432701 -0.6209242898 0.446483974256 +1403715895484058112.0000000000 0.9515630205 2.6853854081 1.3839487973 0.3644791093 0.5311371384 -0.6215299578 0.44581255112 +1403715895534057984.0000000000 0.9554390798 2.7117251524 1.3962461019 0.3643863371 0.5310265576 -0.6218024933 0.445640047385 +1403715895584058112.0000000000 0.9592289659 2.7380130029 1.4084468674 0.3642295312 0.5307306193 -0.6229094110 0.444573642927 +1403715895634057984.0000000000 0.9634735685 2.7641897451 1.4206833166 0.3640546857 0.5307589783 -0.6223228736 0.445503460972 +1403715895684058112.0000000000 0.9678311376 2.7903178532 1.4326945471 0.3637040381 0.5307254778 -0.6227244081 0.445268628435 +1403715895734057984.0000000000 0.9720288293 2.8164277150 1.4445269148 0.3637507829 0.5304957894 -0.6232902292 0.444712126683 +1403715895784058112.0000000000 0.9760430570 2.8425314015 1.4558350980 0.3635604203 0.5303568346 -0.6236524798 0.444525627183 +1403715895834057984.0000000000 0.9801254593 2.8683253896 1.4670027290 0.3636158344 0.5301817835 -0.6237797070 0.444510605679 +1403715895884058112.0000000000 0.9841579199 2.8938792359 1.4779900764 0.3632119979 0.5304154044 -0.6238379352 0.444480341494 +1403715895934057984.0000000000 0.9882644178 2.9194605969 1.4893599843 0.3639405306 0.5299111002 -0.6239482882 0.44433101371 +1403715895984058112.0000000000 0.9919595730 2.9449987638 1.5003807377 0.3648504406 0.5290885961 -0.6250188500 0.44305851822 +1403715896034057984.0000000000 0.9956105832 2.9703840833 1.5114485587 0.3656350240 0.5285765831 -0.6258259187 0.44188204819 +1403715896084058112.0000000000 0.9996547078 2.9956149307 1.5224314108 0.3675928139 0.5274541815 -0.6271791163 0.43967484078 +1403715896134057984.0000000000 1.0038706954 3.0204644147 1.5330110819 0.3698416668 0.5259966907 -0.6291984772 0.436639323896 +1403715896184058112.0000000000 1.0081163202 3.0448639788 1.5433909182 0.3735784794 0.5234043093 -0.6309311154 0.434065635976 +1403715896234057984.0000000000 1.0123223488 3.0685081289 1.5534918924 0.3787443565 0.5194881992 -0.6338262527 0.430056978583 +1403715896284058112.0000000000 1.0164370573 3.0908614468 1.5641959075 0.3858029192 0.5143340526 -0.6361538069 0.426526580387 +1403715896334057984.0000000000 1.0202760416 3.1114779087 1.5754956001 0.3933427261 0.5086874542 -0.6390614112 0.422041569677 +1403715896384058112.0000000000 1.0233691251 3.1298121609 1.5866425043 0.3996764102 0.5039771616 -0.6418660457 0.417461096586 +1403715896434057984.0000000000 1.0259400841 3.1452246056 1.5974417631 0.4045425668 0.5002602577 -0.6434334019 0.414823388298 +1403715896484058112.0000000000 1.0277666978 3.1579109000 1.6080285601 0.4094649369 0.4965042508 -0.6452812384 0.411623757475 +1403715896534057984.0000000000 1.0286998180 3.1671610753 1.6185804241 0.4134483209 0.4936257663 -0.6456978720 0.410448957699 +1403715896584058112.0000000000 1.0287412154 3.1728597887 1.6294967654 0.4178853998 0.4902707725 -0.6460396498 0.409437581663 +1403715896634057984.0000000000 1.0276413320 3.1747294500 1.6404547853 0.4212046136 0.4877848404 -0.6456035368 0.409693417478 +1403715896684058112.0000000000 1.0252016272 3.1727889382 1.6513359748 0.4235982412 0.4859765327 -0.6451985956 0.41001233137 +1403715896734057984.0000000000 1.0211627680 3.1673713888 1.6620525225 0.4257801747 0.4846696042 -0.6454322092 0.408930166235 +1403715896784058112.0000000000 1.0156878262 3.1580766076 1.6720192634 0.4260566754 0.4848637672 -0.6469451820 0.406010798085 +1403715896834057984.0000000000 1.0090010746 3.1449001462 1.6820461360 0.4264453068 0.4851340439 -0.6492318422 0.401605994493 +1403715896884058112.0000000000 1.0012377918 3.1275393324 1.6923140213 0.4272031690 0.4846097233 -0.6517367055 0.397353916966 +1403715896934057984.0000000000 0.9924803058 3.1062714124 1.7026727212 0.4291827543 0.4833361890 -0.6547633872 0.39175655527 +1403715896984058112.0000000000 0.9828292130 3.0804504691 1.7133773690 0.4323321267 0.4809448528 -0.6582720113 0.385303698355 +1403715897034057984.0000000000 0.9721853631 3.0496807509 1.7242981432 0.4356142504 0.4782583739 -0.6618000546 0.378853322987 +1403715897084058112.0000000000 0.9610646691 3.0133314319 1.7349815307 0.4381029967 0.4762426753 -0.6643108608 0.374098594883 +1403715897134057984.0000000000 0.9494286086 2.9710827128 1.7456665255 0.4388248263 0.4753109875 -0.6652976712 0.372681158189 +1403715897184058112.0000000000 0.9373226931 2.9228653750 1.7561996870 0.4380529599 0.4756318687 -0.6651969885 0.373358937633 +1403715897234057984.0000000000 0.9244194923 2.8690142876 1.7658686767 0.4333798669 0.4794061092 -0.6637868277 0.376482032625 +1403715897284058112.0000000000 0.9112064055 2.8096147376 1.7749317817 0.4252045435 0.4859723156 -0.6601226062 0.383757930692 +1403715897334057984.0000000000 0.8977329667 2.7457527326 1.7834641210 0.4141399018 0.4948973529 -0.6552067205 0.392770805009 +1403715897384058112.0000000000 0.8841271447 2.6782214373 1.7921296618 0.4014623364 0.5048237917 -0.6491439691 0.403228271755 +1403715897434057984.0000000000 0.8706229471 2.6086658578 1.8014076848 0.3912117637 0.5123272855 -0.6451686821 0.410160310314 +1403715897484058112.0000000000 0.8576824856 2.5374934620 1.8109785635 0.3840595405 0.5173931611 -0.6413581405 0.416488081244 +1403715897534057984.0000000000 0.8451739206 2.4653922715 1.8204801518 0.3788199332 0.5212170568 -0.6388028211 0.420427394056 +1403715897584058112.0000000000 0.8335525447 2.3928566310 1.8298828198 0.3773418483 0.5218362080 -0.6386926990 0.421155241757 +1403715897634057984.0000000000 0.8226157144 2.3200084524 1.8393875498 0.3793131285 0.5199473081 -0.6401795437 0.419459770728 +1403715897684058112.0000000000 0.8119057354 2.2464270103 1.8479584401 0.3815400217 0.5180503011 -0.6414386855 0.417860634718 +1403715897734057984.0000000000 0.8013873685 2.1723149562 1.8569507508 0.3866719993 0.5137576392 -0.6443686512 0.413916530881 +1403715897784058112.0000000000 0.7913604251 2.0967100370 1.8656756184 0.3905860433 0.5106012152 -0.6458112237 0.411894167434 +1403715897834057984.0000000000 0.7815120060 2.0195077874 1.8737384293 0.3938027968 0.5078860907 -0.6463409487 0.411356845267 +1403715897884058112.0000000000 0.7718290539 1.9404907711 1.8817822898 0.3969389992 0.5053349120 -0.6455162294 0.412777004185 +1403715897934057984.0000000000 0.7619478207 1.8595339427 1.8890414887 0.3961248533 0.5059912999 -0.6428554489 0.416887007279 +1403715897984058112.0000000000 0.7523847928 1.7770183712 1.8963487065 0.3960008852 0.5061571800 -0.6406174420 0.420235054546 +1403715898034057984.0000000000 0.7424376694 1.6928750239 1.9035831812 0.3952486700 0.5066698268 -0.6363401214 0.426773271523 +1403715898084058112.0000000000 0.7318606465 1.6076073770 1.9109901545 0.3954590237 0.5056928701 -0.6316761813 0.434594159682 +1403715898134057984.0000000000 0.7206964144 1.5213894930 1.9181102392 0.3944628382 0.5044099836 -0.6274342338 0.443052953976 +1403715898184058112.0000000000 0.7085961465 1.4345900667 1.9252649276 0.3936366403 0.5013489776 -0.6251019037 0.450496401916 +1403715898234057984.0000000000 0.6952016281 1.3474799996 1.9319208800 0.3902605262 0.4988603523 -0.6241318475 0.45748716648 +1403715898284058112.0000000000 0.6803039105 1.2603623179 1.9372982778 0.3850657378 0.4964016241 -0.6255739000 0.462565779937 +1403715898334057984.0000000000 0.6632547472 1.1735584896 1.9416192951 0.3788611579 0.4934589689 -0.6287970155 0.466451264702 +1403715898384058112.0000000000 0.6445502136 1.0872333133 1.9447223033 0.3716062559 0.4904019578 -0.6337480715 0.468804961783 +1403715898434057984.0000000000 0.6247025326 1.0016609404 1.9464606896 0.3628913438 0.4876507937 -0.6404991804 0.469326513028 +1403715898484058112.0000000000 0.6041210554 0.9168487885 1.9476234742 0.3545358542 0.4836074950 -0.6481857028 0.469343598637 +1403715898534057984.0000000000 0.5830754377 0.8326707331 1.9477906027 0.3453195361 0.4798949314 -0.6561166452 0.46900556577 +1403715898584058112.0000000000 0.5620787315 0.7490449930 1.9477113254 0.3369344280 0.4750838480 -0.6630564528 0.470241075358 +1403715898634057984.0000000000 0.5413577541 0.6662013763 1.9456825883 0.3286846741 0.4694945080 -0.6702745985 0.47145864561 +1403715898684058112.0000000000 0.5208232752 0.5839125877 1.9421124548 0.3230798885 0.4614645303 -0.6749322235 0.476588256889 +1403715898734057984.0000000000 0.5003146992 0.5025940339 1.9356191966 0.3180492873 0.4533050092 -0.6795328764 0.481242443454 +1403715898784058112.0000000000 0.4792826156 0.4223587903 1.9254591480 0.3116898934 0.4470684339 -0.6844286065 0.484289901216 +1403715898834057984.0000000000 0.4583596086 0.3430378625 1.9122586886 0.3062263214 0.4413577029 -0.6889752443 0.486561333157 +1403715898884058112.0000000000 0.4377847505 0.2646476976 1.8963405012 0.3010791595 0.4367575483 -0.6926995042 0.488632357358 +1403715898934057984.0000000000 0.4175933815 0.1874850765 1.8773558820 0.2972022648 0.4324696243 -0.6966951423 0.489138749933 +1403715898984058112.0000000000 0.3980485190 0.1112738372 1.8555912628 0.2927424721 0.4298456578 -0.6993280304 0.490382362553 +1403715899034057984.0000000000 0.3794535368 0.0360249423 1.8314687921 0.2909963688 0.4264096923 -0.7012145854 0.491725525997 +1403715899084058112.0000000000 0.3610692162 -0.0383446681 1.8044537320 0.2877898391 0.4249619348 -0.7038339840 0.491123289454 +1403715899134057984.0000000000 0.3434711766 -0.1115622828 1.7764885723 0.2844478951 0.4242872454 -0.7074999650 0.488378467792 +1403715899184058112.0000000000 0.3269184704 -0.1841634870 1.7493819947 0.2795724006 0.4253651558 -0.7108112459 0.48543911027 +1403715899234057984.0000000000 0.3114820949 -0.2562308416 1.7237926514 0.2723371628 0.4287562523 -0.7131928313 0.483069903069 +1403715899284058112.0000000000 0.2976558267 -0.3273545475 1.7011581753 0.2661961393 0.4321174675 -0.7150411274 0.480760122913 +1403715899334057984.0000000000 0.2852517453 -0.3971164679 1.6808958217 0.2598553047 0.4359620181 -0.7179911895 0.476341254909 +1403715899384058112.0000000000 0.2755008722 -0.4661032591 1.6642744380 0.2536912442 0.4402870180 -0.7194764794 0.473436046401 +1403715899434057984.0000000000 0.2691545300 -0.5344232773 1.6516092596 0.2484786687 0.4444069721 -0.7192429504 0.472705376113 +1403715899484058112.0000000000 0.2666101885 -0.6016265283 1.6433188247 0.2475303969 0.4456976819 -0.7189050661 0.47250162429 +1403715899534057984.0000000000 0.2671477943 -0.6679447911 1.6370468142 0.2482100520 0.4465211916 -0.7185325643 0.471933840274 +1403715899584058112.0000000000 0.2708030453 -0.7335988866 1.6312102350 0.2496584134 0.4466933811 -0.7180861963 0.471686245973 +1403715899634057984.0000000000 0.2774124675 -0.7984269400 1.6253562994 0.2516473597 0.4465613591 -0.7186484898 0.46989457007 +1403715899684058112.0000000000 0.2867099452 -0.8625928837 1.6194182385 0.2526094961 0.4471100252 -0.7176030833 0.470453911316 +1403715899734057984.0000000000 0.2990845514 -0.9259342740 1.6131416363 0.2524280363 0.4488574928 -0.7157943079 0.47164133233 +1403715899784058112.0000000000 0.3146732403 -0.9884445869 1.6073097730 0.2520461696 0.4507063455 -0.7124380980 0.475151002372 +1403715899834057984.0000000000 0.3330171447 -1.0499935915 1.6018878738 0.2515995680 0.4524922536 -0.7076414075 0.48082435066 +1403715899884058112.0000000000 0.3537553820 -1.1101008782 1.5970043051 0.2503187250 0.4549660389 -0.7018748685 0.487563440347 +1403715899934057984.0000000000 0.3764888428 -1.1681158993 1.5924277492 0.2480786058 0.4579568491 -0.6965914538 0.493449973331 +1403715899984058112.0000000000 0.4012843845 -1.2238428276 1.5877427764 0.2443888659 0.4615163500 -0.6916776392 0.498857479024 +1403715900034057984.0000000000 0.4285433811 -1.2767747154 1.5832584585 0.2423208125 0.4636623339 -0.6878470702 0.503154322207 +1403715900084058112.0000000000 0.4577736316 -1.3264313073 1.5787765773 0.2406447072 0.4658781847 -0.6851005712 0.505652894063 +1403715900134057984.0000000000 0.4891517237 -1.3731284941 1.5744939392 0.2389673618 0.4671492034 -0.6831847735 0.507862960818 +1403715900184058112.0000000000 0.5225537754 -1.4163808543 1.5703679829 0.2369662236 0.4689003894 -0.6811140326 0.509963830392 +1403715900234057984.0000000000 0.5582691669 -1.4560088078 1.5666422937 0.2363669112 0.4699447185 -0.6795561224 0.511357136704 +1403715900284058112.0000000000 0.5962227709 -1.4923100632 1.5630671516 0.2349216247 0.4710008342 -0.6783639680 0.512632784146 +1403715900334057984.0000000000 0.6362711179 -1.5246721168 1.5599158389 0.2344516935 0.4715671333 -0.6784458039 0.512218833444 +1403715900384058112.0000000000 0.6786158380 -1.5534138666 1.5570484905 0.2333677416 0.4722749508 -0.6780237174 0.512620431399 +1403715900434057984.0000000000 0.7232129964 -1.5780910085 1.5545586231 0.2350476745 0.4712165760 -0.6794969648 0.510873177978 +1403715900484058112.0000000000 0.7700361091 -1.5983918516 1.5534187488 0.2433038126 0.4656686978 -0.6839168013 0.506175589649 +1403715900534057984.0000000000 0.8191706043 -1.6157970318 1.5538363866 0.2541026038 0.4583967838 -0.6863429976 0.504219738751 +1403715900584058112.0000000000 0.8696053140 -1.6308587569 1.5547799244 0.2639511269 0.4516634434 -0.6868993181 0.504479200114 +1403715900634057984.0000000000 0.9209909548 -1.6440131130 1.5565302604 0.2757190545 0.4433548928 -0.6873284314 0.504970364878 +1403715900684058112.0000000000 0.9729598618 -1.6556414730 1.5586813383 0.2886815590 0.4340155556 -0.6874003194 0.50574129338 +1403715900734057984.0000000000 1.0242509428 -1.6662841758 1.5608884158 0.3003615257 0.4254643263 -0.6851510005 0.509245684752 +1403715900784058112.0000000000 1.0741310698 -1.6761513685 1.5627463478 0.3084124288 0.4192439424 -0.6806946969 0.515529843984 +1403715900834057984.0000000000 1.1222114069 -1.6850880326 1.5646751488 0.3126294674 0.4153670210 -0.6745815836 0.524092302071 +1403715900884058112.0000000000 1.1680304612 -1.6927587340 1.5668197154 0.3152495548 0.4128110130 -0.6694208502 0.53111252207 +1403715900934057984.0000000000 1.2108358347 -1.6989239995 1.5688653245 0.3155827424 0.4113863701 -0.6653286839 0.537128038392 +1403715900984058112.0000000000 1.2506070396 -1.7030015122 1.5717873924 0.3168190094 0.4097084211 -0.6610346957 0.542952904077 +1403715901034057984.0000000000 1.2871895266 -1.7049391281 1.5761817223 0.3201159216 0.4067667618 -0.6569415881 0.548173647696 +1403715901084058112.0000000000 1.3199489540 -1.7046573992 1.5811600358 0.3215423010 0.4048142294 -0.6527980528 0.553706321644 +1403715901134057984.0000000000 1.3489528472 -1.7017465737 1.5870168319 0.3248899859 0.4018362629 -0.6496149535 0.557650900675 +1403715901184058112.0000000000 1.3737349131 -1.6963944857 1.5936848613 0.3269757707 0.3990734590 -0.6464453616 0.562081501353 +1403715901234057984.0000000000 1.3941562904 -1.6881403253 1.6011268282 0.3297263110 0.3963709442 -0.6445950559 0.564506730071 +1403715901284058112.0000000000 1.4097418305 -1.6772593098 1.6088127276 0.3313540447 0.3941352343 -0.6442177301 0.565548786943 +1403715901334057984.0000000000 1.4205245652 -1.6635953839 1.6167986478 0.3319629058 0.3928331691 -0.6462477438 0.563778843228 +1403715901384058112.0000000000 1.4266271710 -1.6474242399 1.6244829022 0.3310369422 0.3930130689 -0.6504737282 0.559320301352 +1403715901434057984.0000000000 1.4281626149 -1.6289770249 1.6314994399 0.3290174550 0.3944450783 -0.6573149465 0.551450501552 +1403715901484058112.0000000000 1.4253414902 -1.6089808680 1.6382080010 0.3244057390 0.3973461238 -0.6641740382 0.543828853025 +1403715901534057984.0000000000 1.4192777728 -1.5876339973 1.6454192968 0.3203078374 0.3999525815 -0.6696506581 0.537595403623 +1403715901584058112.0000000000 1.4105135580 -1.5654357249 1.6535548988 0.3165856567 0.4018865509 -0.6725968424 0.5346720581 +1403715901634057984.0000000000 1.3993760563 -1.5422698741 1.6623320131 0.3132172713 0.4036127065 -0.6733673123 0.534385803338 +1403715901684058112.0000000000 1.3858235942 -1.5177330746 1.6713059555 0.3125234259 0.4038659853 -0.6747122778 0.532902163984 +1403715901734057984.0000000000 1.3697298616 -1.4919962811 1.6788025684 0.3095012704 0.4057444890 -0.6770806270 0.530228439218 +1403715901784058112.0000000000 1.3516714479 -1.4651315953 1.6861059219 0.3067155118 0.4075551575 -0.6801836586 0.52647372112 +1403715901834057984.0000000000 1.3320739054 -1.4374604994 1.6929846719 0.3035788150 0.4099962741 -0.6832798598 0.522371124254 +1403715901884058112.0000000000 1.3109722478 -1.4091455484 1.6996945381 0.3003002678 0.4126187535 -0.6852659558 0.519592227882 +1403715901934057984.0000000000 1.2887998097 -1.3799512598 1.7058289307 0.2994715219 0.4135285884 -0.6871134162 0.516900442444 +1403715901984058112.0000000000 1.2654630735 -1.3500897220 1.7116359349 0.2986761288 0.4144649352 -0.6884205386 0.514867506929 +1403715902034057984.0000000000 1.2410268518 -1.3197014300 1.7177454422 0.2993896207 0.4143469894 -0.6881786537 0.514871409243 +1403715902084058112.0000000000 1.2155207294 -1.2888081024 1.7233222536 0.2997529929 0.4141639480 -0.6869013280 0.516510341616 +1403715902134057984.0000000000 1.1890650321 -1.2573502796 1.7277477032 0.2977982784 0.4159909281 -0.6853510005 0.518229427172 +1403715902184058112.0000000000 1.1618630994 -1.2250288618 1.7317970513 0.2958034078 0.4181775255 -0.6835414294 0.519999053286 +1403715902234057984.0000000000 1.1339890593 -1.1921042747 1.7348400383 0.2913249863 0.4215622920 -0.6827507059 0.520832468179 +1403715902284058112.0000000000 1.1057310184 -1.1577322515 1.7375334656 0.2879060088 0.4245523057 -0.6833532880 0.519512996601 +1403715902334057984.0000000000 1.0768782349 -1.1223807132 1.7400354615 0.2830168402 0.4283481694 -0.6841727689 0.518002834258 +1403715902384058112.0000000000 1.0476940291 -1.0857124178 1.7428720485 0.2799267083 0.4310044551 -0.6854967214 0.515723222811 +1403715902434057984.0000000000 1.0187928166 -1.0476681674 1.7464707848 0.2780281475 0.4327461122 -0.6865389010 0.513902217381 +1403715902484058112.0000000000 0.9901636116 -1.0079024959 1.7502705435 0.2793377089 0.4324418399 -0.6897264691 0.50915802785 +1403715902534057984.0000000000 0.9619833078 -0.9670621028 1.7544777882 0.2820305577 0.4308633965 -0.6940129364 0.503151609568 +1403715902584058112.0000000000 0.9342744914 -0.9253910135 1.7585640125 0.2843625370 0.4305633368 -0.6976583790 0.497017048822 +1403715902634057984.0000000000 0.9069529476 -0.8832688457 1.7629007199 0.2872579346 0.4312933185 -0.6999385424 0.491482440548 +1403715902684058112.0000000000 0.8802929951 -0.8409574538 1.7668109817 0.2903637854 0.4333448712 -0.7016653137 0.485352328024 +1403715902734057984.0000000000 0.8536067961 -0.7985463184 1.7682423106 0.2923721872 0.4382089968 -0.7026760078 0.478265415163 +1403715902784058112.0000000000 0.8280830629 -0.7569493088 1.7669457548 0.2942616520 0.4445996832 -0.7022694013 0.471761475644 +1403715902834057984.0000000000 0.8038168715 -0.7159656715 1.7627961078 0.2973208434 0.4512752665 -0.7012078798 0.465035976255 +1403715902884058112.0000000000 0.7811250432 -0.6756090569 1.7553127981 0.2992194191 0.4597054702 -0.6991004763 0.458690684376 +1403715902934057984.0000000000 0.7600527038 -0.6361614134 1.7459013786 0.3019582055 0.4678818687 -0.6956901738 0.453787374452 +1403715902984058112.0000000000 0.7406726667 -0.5976953807 1.7359355364 0.3032285717 0.4778394682 -0.6897506483 0.451625861788 +1403715903034057984.0000000000 0.7232487356 -0.5597181212 1.7270170920 0.3080150702 0.4863708431 -0.6831679659 0.449279033438 +1403715903084058112.0000000000 0.7073705369 -0.5225463749 1.7178553812 0.3109090809 0.4965115741 -0.6753648506 0.447988971669 +1403715903134057984.0000000000 0.6934551564 -0.4856151771 1.7091043136 0.3141672246 0.5064114346 -0.6671193595 0.446987890346 +1403715903184058112.0000000000 0.6815669036 -0.4490447824 1.7010643990 0.3162651104 0.5158516095 -0.6590322055 0.446710251756 +1403715903234057984.0000000000 0.6716263591 -0.4122484750 1.6936778396 0.3197835889 0.5225986740 -0.6541525712 0.443523951778 +1403715903284058112.0000000000 0.6635036730 -0.3752725159 1.6864674721 0.3222322293 0.5286544791 -0.6520191379 0.437677822016 +1403715903334057984.0000000000 0.6578374700 -0.3383578162 1.6798190211 0.3244758388 0.5335189005 -0.6508649075 0.431796115127 +1403715903384058112.0000000000 0.6542948390 -0.3012167202 1.6740961935 0.3266583033 0.5386657020 -0.6503224544 0.424516571744 +1403715903434057984.0000000000 0.6535073701 -0.2639984703 1.6711731562 0.3299317600 0.5436864221 -0.6489378766 0.417647866639 +1403715903484058112.0000000000 0.6558233808 -0.2267897693 1.6715437915 0.3332587515 0.5494556851 -0.6460212808 0.411938781173 +1403715903534057984.0000000000 0.6612379976 -0.1897209076 1.6755998456 0.3379639274 0.5553672442 -0.6420534674 0.406343392745 +1403715903584058112.0000000000 0.6697962117 -0.1530818684 1.6834065573 0.3433427342 0.5619210784 -0.6360035464 0.402318229161 +1403715903634057984.0000000000 0.6814065751 -0.1166046226 1.6948083813 0.3488543158 0.5692051567 -0.6297113431 0.397202442523 +1403715903684058112.0000000000 0.6959100495 -0.0804879003 1.7099821597 0.3558612576 0.5763194084 -0.6215214302 0.393611250699 +1403715903734057984.0000000000 0.7130197733 -0.0447348372 1.7285397475 0.3635985708 0.5834648490 -0.6117267057 0.391350593208 +1403715903784058112.0000000000 0.7330671719 -0.0086862132 1.7508742324 0.3761078527 0.5878157554 -0.6027535615 0.386915578618 +1403715903834057984.0000000000 0.7554942221 0.0269797507 1.7764756489 0.3879251849 0.5934570957 -0.5925305332 0.382400697818 +1403715903884058112.0000000000 0.7798414736 0.0621910979 1.8051831181 0.4015786618 0.5986542404 -0.5812165148 0.377538132817 +1403715903934057984.0000000000 0.8055377073 0.0966749406 1.8345559988 0.4136897880 0.6057359417 -0.5682001968 0.372952094257 +1403715903984058112.0000000000 0.8324063493 0.1305143595 1.8636866042 0.4251712193 0.6138034506 -0.5537222571 0.368600624381 +1403715904034057984.0000000000 0.8593452594 0.1638841636 1.8931148239 0.4375361026 0.6212736911 -0.5401851887 0.361636725929 +1403715904084058112.0000000000 0.8861963854 0.1962026925 1.9217742824 0.4484243081 0.6297631363 -0.5267262844 0.353374381304 +1403715904134057984.0000000000 0.9132949993 0.2273334481 1.9499952417 0.4586087065 0.6385480431 -0.5129385892 0.344715033949 +1403715904184058112.0000000000 0.9397865801 0.2566026487 1.9765745299 0.4657830581 0.6494498454 -0.4975555866 0.337193533875 +1403715904234057984.0000000000 0.9657673160 0.2845069161 2.0027581331 0.4722905886 0.6603983829 -0.4821586499 0.329148313137 +1403715904284058112.0000000000 0.9918551121 0.3110452043 2.0278436824 0.4771052990 0.6721355234 -0.4641365817 0.324317137088 +1403715904334057984.0000000000 1.0182369519 0.3369974261 2.0520621681 0.4831406328 0.6821372040 -0.4457537516 0.320261700324 +1403715904384058112.0000000000 1.0442467084 0.3625973267 2.0740946975 0.4887377535 0.6915910369 -0.4273852460 0.316510817321 +1403715904434057984.0000000000 1.0698212155 0.3881165300 2.0938067859 0.4957072574 0.6988042925 -0.4117206821 0.310536560875 +1403715904484058112.0000000000 1.0948194655 0.4132085102 2.1104145933 0.5010953882 0.7059847031 -0.3963650574 0.305587552511 +1403715904534057984.0000000000 1.1191798231 0.4379557584 2.1235294645 0.5051278328 0.7133284031 -0.3798009714 0.302918609518 +1403715904584058112.0000000000 1.1424833272 0.4626738167 2.1335546293 0.5096619022 0.7198117078 -0.3632433411 0.300283409252 +1403715904634057984.0000000000 1.1641079580 0.4877054716 2.1407012760 0.5143963744 0.7257967736 -0.3469493239 0.297054843443 +1403715904684058112.0000000000 1.1834588056 0.5130042464 2.1451885183 0.5206544142 0.7307318506 -0.3314830329 0.29166580602 +1403715904734057984.0000000000 1.2000640375 0.5387153010 2.1470997231 0.5281711801 0.7352524873 -0.3188532045 0.280662819986 +1403715904784058112.0000000000 1.2141625831 0.5646148154 2.1465477981 0.5359661601 0.7398464643 -0.3081395835 0.26536292435 +1403715904834057984.0000000000 1.2264152602 0.5902943087 2.1430388067 0.5427795743 0.7452294257 -0.2965412039 0.249172131683 +1403715904884058112.0000000000 1.2368097688 0.6153144837 2.1366404772 0.5506709036 0.7497356233 -0.2830798016 0.233503483968 +1403715904934057984.0000000000 1.2454543687 0.6397029574 2.1268738955 0.5588432410 0.7536059280 -0.2679115729 0.21907926953 +1403715904984058112.0000000000 1.2525351721 0.6630197040 2.1144258769 0.5668471826 0.7572909626 -0.2517163832 0.204532471374 +1403715905034057984.0000000000 1.2583367263 0.6850081681 2.0993494379 0.5752573268 0.7600103711 -0.2334077637 0.192312401255 +1403715905084058112.0000000000 1.2628118906 0.7056638145 2.0813176651 0.5834211726 0.7620660481 -0.2147484749 0.180992171719 +1403715905134057984.0000000000 1.2659582296 0.7243234649 2.0604200944 0.5921956806 0.7627082556 -0.1965410157 0.170152936729 +1403715905184058112.0000000000 1.2682911936 0.7412177063 2.0371513250 0.5994269578 0.7633502582 -0.1776392034 0.162566967818 +1403715905234057984.0000000000 1.2691096951 0.7557326485 2.0134769373 0.6045297685 0.7647612984 -0.1602542456 0.154927377316 +1403715905284058112.0000000000 1.2678062981 0.7670769395 1.9885006516 0.6032794564 0.7703835690 -0.1437749397 0.147958848523 +1403715905334057984.0000000000 1.2642682189 0.7755749264 1.9636618652 0.5997197139 0.7772928451 -0.1293804607 0.139329803487 +1403715905384058112.0000000000 1.2587004117 0.7817363306 1.9394029098 0.5953194430 0.7842707604 -0.1151948565 0.131317478863 +1403715905434057984.0000000000 1.2507607380 0.7860528803 1.9166735311 0.5922618661 0.7898513457 -0.1017236691 0.122527665784 +1403715905484058112.0000000000 1.2404524219 0.7889904650 1.8943650335 0.5881125159 0.7959339624 -0.0892335742 0.112472953997 +1403715905534057984.0000000000 1.2282871962 0.7907105766 1.8724497181 0.5845400689 0.8011138490 -0.0762137933 0.10354210063 +1403715905584058112.0000000000 1.2137818528 0.7918867589 1.8515419629 0.5818232214 0.8056257351 -0.0654290406 0.0903767374067 +1403715905634057984.0000000000 1.1972714202 0.7925856400 1.8318497114 0.5800530175 0.8092877823 -0.0569713087 0.0731167038007 +1403715905684058112.0000000000 1.1794509620 0.7927633956 1.8130654641 0.5789422604 0.8120946379 -0.0488803728 0.054211321227 +1403715905734057984.0000000000 1.1609272668 0.7922310046 1.7943484152 0.5769770811 0.8150324627 -0.0389520751 0.0360869566435 +1403715905784058112.0000000000 1.1420031414 0.7912038523 1.7759228786 0.5761638674 0.8166816606 -0.0266568861 0.0188593114896 +1403715905834057984.0000000000 1.1230041333 0.7896130641 1.7571823290 0.5734287065 0.8191631807 -0.0121879856 0.00162941025348 +1403715905884058112.0000000000 1.1045818350 0.7874993082 1.7379872139 0.5679316585 0.8229437684 0.0049631297 -0.0138763366736 +1403715905934057984.0000000000 1.0868028673 0.7856501239 1.7186667347 0.5605155835 0.8273083488 0.0232202765 -0.0290516004711 +1403715905984058112.0000000000 1.0698641670 0.7845075043 1.6992775226 0.5526842628 0.8311772675 0.0443388503 -0.0414550593834 +1403715906034057984.0000000000 1.0533053775 0.7845841241 1.6804532784 0.5459077586 0.8334917204 0.0665936007 -0.053306317433 +1403715906084058112.0000000000 1.0372320907 0.7864170363 1.6626729017 0.5422462008 0.8329343598 0.0897199631 -0.064340797289 +1403715906134057984.0000000000 1.0214907102 0.7901862886 1.6462911748 0.5426239777 0.8288798377 0.1150243463 -0.0727106135701 +1403715906184058112.0000000000 1.0055504403 0.7956770167 1.6308935854 0.5464791524 0.8216499016 0.1407549338 -0.0802497596017 +1403715906234057984.0000000000 0.9889099259 0.8019408086 1.6158850256 0.5503116970 0.8134094922 0.1667964063 -0.0877553018588 +1403715906284058112.0000000000 0.9708609167 0.8085515534 1.6012353971 0.5512836571 0.8064143433 0.1900274181 -0.0983453951274 +1403715906334057984.0000000000 0.9515354299 0.8151494871 1.5866751798 0.5505609848 0.7996949427 0.2135397403 -0.108495990778 +1403715906384058112.0000000000 0.9306996479 0.8215078718 1.5725229703 0.5488722526 0.7930055499 0.2358925700 -0.119315311512 +1403715906434057984.0000000000 0.9083023151 0.8275231501 1.5588061913 0.5471446039 0.7858408116 0.2564550971 -0.131597053501 +1403715906484058112.0000000000 0.8842679457 0.8331837015 1.5462447264 0.5467490154 0.7772651731 0.2751527367 -0.14565485347 +1403715906534057984.0000000000 0.8586401776 0.8382169279 1.5347625473 0.5460711334 0.7683093012 0.2939740370 -0.158386869939 +1403715906584058112.0000000000 0.8312092995 0.8420966175 1.5259556704 0.5433270125 0.7604116482 0.3102807367 -0.174056735583 +1403715906634057984.0000000000 0.8024576322 0.8446892091 1.5206357850 0.5392691482 0.7529955635 0.3243967325 -0.192232221851 +1403715906684058112.0000000000 0.7727519564 0.8461108823 1.5189724548 0.5346375684 0.7454134237 0.3372111733 -0.211684016418 +1403715906734057984.0000000000 0.7427442497 0.8463371540 1.5201067809 0.5286086088 0.7379497862 0.3511144538 -0.229612046843 +1403715906784058112.0000000000 0.7126572949 0.8460005557 1.5232972058 0.5211803707 0.7306010990 0.3657262925 -0.246652253707 +1403715906834057984.0000000000 0.6828469205 0.8452217987 1.5272343560 0.5142875506 0.7218405704 0.3806337756 -0.263765871938 +1403715906884058112.0000000000 0.6541634637 0.8439235588 1.5295615203 0.5077652366 0.7120628444 0.3961369802 -0.279672063322 +1403715906934057984.0000000000 0.6264097932 0.8424217123 1.5297788771 0.5023768932 0.7005778352 0.4125010003 -0.294365552989 +1403715906984058112.0000000000 0.5995970104 0.8405935347 1.5272426936 0.4968965306 0.6885638345 0.4283788715 -0.308974474989 +1403715907034057984.0000000000 0.5740945777 0.8387422550 1.5210421549 0.4914405449 0.6757346721 0.4462969526 -0.320449487114 +1403715907084058112.0000000000 0.5497566250 0.8369636723 1.5120520902 0.4857741362 0.6620789874 0.4665341432 -0.328665173615 +1403715907134057984.0000000000 0.5259647911 0.8346778382 1.5032516355 0.4801989788 0.6472030086 0.4872262880 -0.336374420387 +1403715907184058112.0000000000 0.5028567204 0.8311012661 1.4969248622 0.4741977178 0.6312423223 0.5075618340 -0.345037156995 +1403715907234057984.0000000000 0.4805464401 0.8258821128 1.4942868241 0.4654174621 0.6159118594 0.5269780574 -0.355433952291 +1403715907284058112.0000000000 0.4593175841 0.8192263598 1.4958772129 0.4553443889 0.6005192907 0.5450733856 -0.367332374509 +1403715907334057984.0000000000 0.4390731922 0.8112404941 1.5010456529 0.4455124445 0.5845569532 0.5626417399 -0.37847866895 +1403715907384058112.0000000000 0.4200143972 0.8016913745 1.5093689813 0.4362898890 0.5672513401 0.5792747545 -0.390279142086 +1403715907434057984.0000000000 0.4018611288 0.7908704705 1.5199547677 0.4283123125 0.5495334001 0.5958665474 -0.399380348583 +1403715907484058112.0000000000 0.3846362351 0.7784530070 1.5322605099 0.4196144601 0.5325935629 0.6110410651 -0.408529825695 +1403715907534057984.0000000000 0.3684082574 0.7646749272 1.5450723004 0.4109873635 0.5163158756 0.6253077655 -0.416530313433 +1403715907584058112.0000000000 0.3533655814 0.7492486994 1.5581505485 0.4015371918 0.5013095204 0.6380008969 -0.424748753845 +1403715907634057984.0000000000 0.3393779019 0.7321831940 1.5713773680 0.3914732274 0.4873901035 0.6486826116 -0.434062747273 +1403715907684058112.0000000000 0.3265262605 0.7137122656 1.5850165704 0.3822223800 0.4736092195 0.6574743387 -0.444215998594 +1403715907734057984.0000000000 0.3150558061 0.6936145187 1.5985580782 0.3722768483 0.4605476241 0.6643557869 -0.456001340509 +1403715907784058112.0000000000 0.3049751611 0.6722843851 1.6113104912 0.3626695672 0.4472745813 0.6709585803 -0.46715181418 +1403715907834057984.0000000000 0.2965739972 0.6500606012 1.6233837011 0.3534527661 0.4335388877 0.6771474196 -0.478107254835 +1403715907884058112.0000000000 0.2901043689 0.6269602420 1.6347589200 0.3423109198 0.4208921425 0.6833047749 -0.4886385404 +1403715907934057984.0000000000 0.2856395533 0.6035786546 1.6459268814 0.3293025801 0.4092288801 0.6884982327 -0.500061714206 +1403715907984058112.0000000000 0.2826580638 0.5802098388 1.6564750409 0.3162961539 0.3963598598 0.6947197928 -0.510117647206 +1403715908034057984.0000000000 0.2815516911 0.5571023494 1.6661886240 0.3026153667 0.3828694517 0.7012327024 -0.519718789203 +1403715908084058112.0000000000 0.2823635627 0.5347303437 1.6753143776 0.2896207243 0.3678074691 0.7084383934 -0.528159582466 +1403715908134057984.0000000000 0.2844407163 0.5127410943 1.6841629170 0.2764834262 0.3518196118 0.7147831261 -0.537461587815 +1403715908184058112.0000000000 0.2883929361 0.4918785322 1.6915599301 0.2629903120 0.3349418839 0.7229856712 -0.544005284397 +1403715908234057984.0000000000 0.2945885221 0.4726137097 1.6978520268 0.2488079391 0.3173983715 0.7306221237 -0.550948450958 +1403715908284058112.0000000000 0.3023625933 0.4546203292 1.7032554423 0.2344816576 0.2992799258 0.7386434050 -0.556646924488 +1403715908334057984.0000000000 0.3113847392 0.4382852934 1.7084683092 0.2197733903 0.2811361993 0.7463107065 -0.561856230476 +1403715908384058112.0000000000 0.3212053195 0.4233940824 1.7136223720 0.2048017156 0.2626243807 0.7540145436 -0.566168490794 +1403715908434057984.0000000000 0.3317995099 0.4096649038 1.7187528864 0.1899820586 0.2434242893 0.7606113551 -0.571070748047 +1403715908484058112.0000000000 0.3434442972 0.3975108286 1.7236734927 0.1748234187 0.2238455823 0.7669835920 -0.575383434922 +1403715908534057984.0000000000 0.3560066242 0.3869080038 1.7287320233 0.1607784251 0.2025648432 0.7728041124 -0.579561546515 +1403715908584058112.0000000000 0.3698679786 0.3778932483 1.7336862002 0.1455279364 0.1816074125 0.7781122680 -0.583422373508 +1403715908634057984.0000000000 0.3842305659 0.3704521078 1.7381847819 0.1331056999 0.1584358325 0.7826238758 -0.587095246727 +1403715908684058112.0000000000 0.3994394697 0.3642927342 1.7424348302 0.1196450222 0.1359977929 0.7857238096 -0.591462394366 +1403715908734057984.0000000000 0.4154126794 0.3596044986 1.7462977101 0.1063447006 0.1140673166 0.7876710141 -0.596031732003 +1403715908784058112.0000000000 0.4320125037 0.3565352978 1.7496684176 0.0911324805 0.0940411259 0.7889975899 -0.600278219406 +1403715908834057984.0000000000 0.4490882465 0.3552731764 1.7523643131 0.0763748947 0.0744715834 0.7901554469 -0.603552175407 +1403715908884058112.0000000000 0.4668750088 0.3562859134 1.7539169507 0.0613719447 0.0555260374 0.7924905750 -0.604242527528 +1403715908934057984.0000000000 0.4852638801 0.3596709781 1.7545206161 0.0464286170 0.0367392915 0.7963068437 -0.601988387429 +1403715908984058112.0000000000 0.5039860146 0.3646608714 1.7544390526 0.0340957282 0.0162680963 0.8000263245 -0.598774340204 +1403715909034057984.0000000000 0.5228364937 0.3711651669 1.7537883122 0.0231055676 -0.0042539561 0.8029292600 -0.595611148414 +1403715909084058112.0000000000 0.5420712563 0.3788019432 1.7525382055 0.0122260477 -0.0239947497 0.8055805251 -0.591873967385 +1403715909134057984.0000000000 0.5616925896 0.3870973305 1.7508897757 0.0026756653 -0.0440732151 0.8066806274 -0.589335861763 +1403715909184058112.0000000000 0.5822872102 0.3965325116 1.7487305773 0.0093251554 0.0614332103 -0.8079941327 0.58590484184 +1403715909234057984.0000000000 0.6034569716 0.4065682263 1.7461447805 0.0197752156 0.0788899277 -0.8078611902 0.583734201131 +1403715909284058112.0000000000 0.6256122537 0.4171830561 1.7433180845 0.0327425707 0.0941032366 -0.8075517138 0.581319821102 +1403715909334057984.0000000000 0.6481807966 0.4278736937 1.7400453900 0.0430298766 0.1101687427 -0.8058382530 0.580203402164 +1403715909384058112.0000000000 0.6712736773 0.4391588184 1.7358905058 0.0525114003 0.1261502730 -0.8041003591 0.578576938626 +1403715909434057984.0000000000 0.6950643891 0.4509557828 1.7309823472 0.0618492291 0.1418638802 -0.8018072221 0.577195366332 +1403715909484058112.0000000000 0.7196799330 0.4632709998 1.7249653605 0.0687657455 0.1592970272 -0.7977978313 0.577420427185 +1403715909534057984.0000000000 0.7455642853 0.4763662906 1.7175189717 0.0755144706 0.1774629419 -0.7938092591 0.57677667186 +1403715909584058112.0000000000 0.7728795150 0.4903882063 1.7091831014 0.0829430848 0.1962323184 -0.7899736524 0.574939084131 +1403715909634057984.0000000000 0.8018152283 0.5057556986 1.7009426922 0.0932073387 0.2142455266 -0.7850810205 0.573636677277 +1403715909684058112.0000000000 0.8325154629 0.5226535228 1.6928001602 0.1069920602 0.2310192348 -0.7794609353 0.57238401664 +1403715909734057984.0000000000 0.8644315394 0.5411474723 1.6836195222 0.1210676717 0.2487163094 -0.7744385163 0.568970825963 +1403715909784058112.0000000000 0.8978442467 0.5610873684 1.6745751200 0.1377792241 0.2658559964 -0.7684699027 0.56550109038 +1403715909834057984.0000000000 0.9325944352 0.5825522212 1.6649938112 0.1547430047 0.2847218666 -0.7611024182 0.561881811505 +1403715909884058112.0000000000 0.9685176338 0.6057281546 1.6557532215 0.1759862434 0.3020827325 -0.7522639736 0.558456604274 +1403715909934057984.0000000000 1.0047129935 0.6304811033 1.6467329712 0.1990882988 0.3190537395 -0.7415576336 0.555572530566 +1403715909984058112.0000000000 1.0404564479 0.6568929816 1.6373048784 0.2218596346 0.3372854302 -0.7294867386 0.552146664709 +1403715910034057984.0000000000 1.0751933729 0.6847825399 1.6270867527 0.2434458402 0.3570092015 -0.7166213497 0.547478213387 +1403715910084058112.0000000000 1.1084038092 0.7141077705 1.6159630541 0.2631675042 0.3782984119 -0.7034247966 0.541134670636 +1403715910134057984.0000000000 1.1396180156 0.7448347999 1.6034554616 0.2805920295 0.4004025226 -0.6911560940 0.532211599432 +1403715910184058112.0000000000 1.1690756441 0.7764966911 1.5904905954 0.2971311346 0.4220487219 -0.6791821373 0.521823331727 +1403715910234057984.0000000000 1.1965718388 0.8086069247 1.5766999784 0.3099898423 0.4438251365 -0.6672889767 0.511518296285 +1403715910284058112.0000000000 1.2229232976 0.8412121715 1.5635924248 0.3243610187 0.4629468089 -0.6547460055 0.50177470034 +1403715910334057984.0000000000 1.2478131913 0.8741081117 1.5514237591 0.3376453735 0.4802180092 -0.6420906250 0.493057699121 +1403715910384058112.0000000000 1.2709486520 0.9074454462 1.5398841412 0.3505496775 0.4956334623 -0.6286490104 0.486068736287 +1403715910434057984.0000000000 1.2923493716 0.9413548998 1.5284206630 0.3639717781 0.5088869697 -0.6143375697 0.480778480554 +1403715910484058112.0000000000 1.3119517593 0.9755939310 1.5171029515 0.3766158520 0.5211289023 -0.5998829214 0.476157167098 +1403715910534057984.0000000000 1.3287748363 1.0105307499 1.5063607779 0.3887573254 0.5327410052 -0.5857396032 0.471130428473 +1403715910584058112.0000000000 1.3430783250 1.0458750857 1.4959752137 0.3997299695 0.5439896855 -0.5726980682 0.465089342115 +1403715910634057984.0000000000 1.3549093366 1.0819318706 1.4859978863 0.4096235304 0.5551563967 -0.5612425889 0.457183436903 +1403715910684058112.0000000000 1.3637077284 1.1185140112 1.4772685332 0.4185313333 0.5662134441 -0.5503020064 0.448777852159 +1403715910734057984.0000000000 1.3706127595 1.1556195487 1.4690695833 0.4273850144 0.5768066504 -0.5405298091 0.438706807511 +1403715910784058112.0000000000 1.3752954318 1.1927645751 1.4619707451 0.4355721417 0.5870718576 -0.5296499616 0.430226058653 +1403715910834057984.0000000000 1.3777510698 1.2301628139 1.4555880548 0.4442873279 0.5965365284 -0.5186711250 0.421584160753 +1403715910884058112.0000000000 1.3772146445 1.2675443429 1.4496630796 0.4524666071 0.6060291817 -0.5078648084 0.412402639183 +1403715910934057984.0000000000 1.3736817780 1.3049166127 1.4433948378 0.4605519168 0.6154634958 -0.4970249220 0.402570297239 +1403715910984058112.0000000000 1.3676326963 1.3422674895 1.4375351170 0.4679717189 0.6249849831 -0.4869771970 0.391470881312 +1403715911034057984.0000000000 1.3590427120 1.3791693312 1.4322695015 0.4766698250 0.6331109120 -0.4757831703 0.381558417296 +1403715911084058112.0000000000 1.3482795002 1.4157467832 1.4275064397 0.4867201144 0.6399643251 -0.4633875547 0.372587126663 +1403715911134057984.0000000000 1.3350456023 1.4513717131 1.4232223042 0.4970624078 0.6459727132 -0.4505415989 0.364225869839 +1403715911184058112.0000000000 1.3192704344 1.4860527143 1.4186756253 0.5067201933 0.6524860455 -0.4374655957 0.355134423333 +1403715911234057984.0000000000 1.3009464006 1.5196168979 1.4143408381 0.5154803051 0.6595386306 -0.4240973204 0.345586910359 +1403715911284058112.0000000000 1.2797513435 1.5517111992 1.4097326831 0.5221316828 0.6680493732 -0.4108812474 0.335059907001 +1403715911334057984.0000000000 1.2561761706 1.5823809064 1.4053100960 0.5282292023 0.6765552060 -0.3985853506 0.323073801771 +1403715911384058112.0000000000 1.2300372867 1.6113366794 1.4008119605 0.5335581961 0.6850881253 -0.3866492552 0.310599847826 +1403715911434057984.0000000000 1.2021029200 1.6387214528 1.3957751773 0.5378379034 0.6937779879 -0.3748564260 0.298136131753 +1403715911484058112.0000000000 1.1722938520 1.6641056013 1.3902828406 0.5406238870 0.7028229023 -0.3644830987 0.284460632826 +1403715911534057984.0000000000 1.1408180951 1.6876207351 1.3841711414 0.5422840420 0.7118175133 -0.3546545355 0.271042443271 +1403715911584058112.0000000000 1.1081170811 1.7093271255 1.3776612655 0.5413700001 0.7222365508 -0.3444756009 0.258126806149 +1403715911634057984.0000000000 1.0745891230 1.7294474003 1.3711499043 0.5405157119 0.7320703052 -0.3327877651 0.247321929454 +1403715911684058112.0000000000 1.0406341924 1.7483659793 1.3651183446 0.5388855615 0.7418829167 -0.3201110957 0.238203643723 +1403715911734057984.0000000000 1.0067466837 1.7663437776 1.3611429582 0.5382934382 0.7504697881 -0.3053636354 0.231923094391 +1403715911784058112.0000000000 0.9727809107 1.7839363534 1.3602610640 0.5383383919 0.7579696116 -0.2908679815 0.225985975174 +1403715911834057984.0000000000 0.9380060956 1.8012241672 1.3631386970 0.5398073397 0.7640352237 -0.2776276958 0.218588827401 +1403715911884058112.0000000000 0.9023291462 1.8180509462 1.3696359764 0.5422912652 0.7688168864 -0.2645325820 0.211809565181 +1403715911934057984.0000000000 0.8661400147 1.8348429985 1.3791368460 0.5446560548 0.7730529650 -0.2528810123 0.204426243287 +1403715911984058112.0000000000 0.8296369353 1.8517603495 1.3922354156 0.5478905534 0.7761698646 -0.2424331333 0.196475084133 +1403715912034057984.0000000000 0.7926476862 1.8684808015 1.4082117672 0.5502852796 0.7792731245 -0.2332739375 0.188421810039 +1403715912084058112.0000000000 0.7550624534 1.8847886665 1.4256653956 0.5529405108 0.7817426205 -0.2254818843 0.179703051061 +1403715912134057984.0000000000 0.7172625627 1.9011818587 1.4437179462 0.5561897614 0.7833235533 -0.2188644592 0.170749842202 +1403715912184058112.0000000000 0.6791806821 1.9171927347 1.4611238834 0.5584140199 0.7854242500 -0.2115097946 0.162929851999 +1403715912234057984.0000000000 0.6409241960 1.9328495504 1.4782493538 0.5612476212 0.7869002229 -0.2047184884 0.154529891519 +1403715912284058112.0000000000 0.6027328691 1.9479384040 1.4947147187 0.5638879028 0.7883255632 -0.1971729362 0.147295868129 +1403715912334057984.0000000000 0.5644540467 1.9625680140 1.5105499780 0.5663095841 0.7897555466 -0.1894253042 0.140348443936 +1403715912384058112.0000000000 0.5264012152 1.9768045748 1.5257546238 0.5679432428 0.7916349105 -0.1812801667 0.133761513913 +1403715912434057984.0000000000 0.4883048814 1.9901665708 1.5404212855 0.5689132437 0.7939745250 -0.1728941213 0.126687795716 +1403715912484058112.0000000000 0.4501966708 2.0030875528 1.5546720552 0.5703737668 0.7959900083 -0.1636641215 0.119531284905 +1403715912534057984.0000000000 0.4124110579 2.0154484478 1.5686784763 0.5717674093 0.7979853164 -0.1542314391 0.111866561464 +1403715912584058112.0000000000 0.3745875296 2.0274453524 1.5822308479 0.5726728291 0.8004085692 -0.1440389589 0.103173307442 +1403715912634057984.0000000000 0.3367656346 2.0388135491 1.5954915973 0.5739418967 0.8025614079 -0.1327704062 0.0941164444975 +1403715912684058112.0000000000 0.2992081793 2.0495592354 1.6083709850 0.5753251761 0.8045655844 -0.1199302042 0.0853926710347 +1403715912734057984.0000000000 0.2615878563 2.0600199252 1.6216664933 0.5773283830 0.8061096143 -0.1062729646 0.0747347633042 +1403715912784058112.0000000000 0.2241489597 2.0697499990 1.6349116068 0.5791112147 0.8076574831 -0.0912370634 0.0632090913028 +1403715912834057984.0000000000 0.1869681159 2.0785016170 1.6472486894 0.5802520195 0.8093901100 -0.0742762478 0.0517521274953 +1403715912884058112.0000000000 0.1499532625 2.0868626523 1.6571560412 0.5817968980 0.8104499661 -0.0563008842 0.0389028574348 +1403715912934057984.0000000000 0.1133089914 2.0944937116 1.6637023656 0.5822056962 0.8117696801 -0.0372340013 0.0260795501671 +1403715912984058112.0000000000 0.0771026517 2.1014487964 1.6668926051 0.5828690828 0.8122530956 -0.0183834279 0.0130610341238 +1403715913034057984.0000000000 0.0414573651 2.1077190998 1.6665308626 0.5833164567 0.8122438875 -0.0004784452 -0.00124484281677 +1403715913084058112.0000000000 0.0064639862 2.1137070636 1.6627993936 0.5834556990 0.8118242275 0.0181721053 -0.0138074432957 +1403715913134057984.0000000000 -0.0283020842 2.1190250999 1.6567652648 0.5834441339 0.8108911687 0.0370541818 -0.0259892834918 +1403715913184058112.0000000000 -0.0626401502 2.1234675054 1.6495372860 0.5843986301 0.8086523747 0.0552793479 -0.0387784940339 +1403715913234057984.0000000000 -0.0961421482 2.1273845414 1.6424111958 0.5871484372 0.8046192151 0.0726414825 -0.0506739222176 +1403715913284058112.0000000000 -0.1287045197 2.1306867217 1.6351004978 0.5901278025 0.7998970393 0.0913433966 -0.0597518796499 +1403715913334057984.0000000000 -0.1603465783 2.1336397153 1.6280730103 0.5936056963 0.7945326651 0.1097100727 -0.0656796868123 +1403715913384058112.0000000000 -0.1913644021 2.1358415903 1.6210841711 0.5961766679 0.7897605921 0.1270487093 -0.0686309929017 +1403715913434057984.0000000000 -0.2221611259 2.1365434111 1.6148808931 0.5994874135 0.7845275380 0.1416403895 -0.0711996010837 +1403715913484058112.0000000000 -0.2528841866 2.1354988816 1.6094174900 0.6035604380 0.7790523977 0.1533862183 -0.0725591296503 +1403715913534057984.0000000000 -0.2836420377 2.1323565099 1.6040020904 0.6075537050 0.7738491633 0.1641735671 -0.07129521704 +1403715913584058112.0000000000 -0.3143034453 2.1262445957 1.5979830462 0.6118375600 0.7683750256 0.1762335384 -0.0647793188513 +1403715913634057984.0000000000 -0.3459271404 2.1171388981 1.5919819699 0.6157819523 0.7635125918 0.1853168146 -0.0593193697546 +1403715913684058112.0000000000 -0.3793277323 2.1047503949 1.5868928292 0.6189891120 0.7595555155 0.1922546584 -0.0544614034404 +1403715913734057984.0000000000 -0.4145173325 2.0878425319 1.5821870510 0.6188711374 0.7588498835 0.1958552600 -0.0527833937422 +1403715913784058112.0000000000 -0.4520930317 2.0672042528 1.5776312186 0.6164340677 0.7606499443 0.1962592527 -0.0538795698376 +1403715913834057984.0000000000 -0.4922257998 2.0429697550 1.5738995217 0.6108722077 0.7652434894 0.1953250541 -0.0555488169775 +1403715913884058112.0000000000 -0.5345291499 2.0154365612 1.5711180580 0.6046595652 0.7705459662 0.1931346514 -0.0578336463838 +1403715913934057984.0000000000 -0.5787061822 1.9848140146 1.5696677321 0.5990614420 0.7754410882 0.1901355573 -0.0605390566259 +1403715913984058112.0000000000 -0.6247828696 1.9519212429 1.5692440155 0.5952683432 0.7789103979 0.1872050962 -0.0625175471767 +1403715914034057984.0000000000 -0.6723965959 1.9167847438 1.5693667315 0.5921280680 0.7818458846 0.1848696930 -0.0626463113072 +1403715914084058112.0000000000 -0.7215042317 1.8799199820 1.5703721291 0.5909478016 0.7831809358 0.1837239314 -0.0604469568388 +1403715914134057984.0000000000 -0.7723573561 1.8413480663 1.5715716695 0.5897919487 0.7846203709 0.1819808426 -0.0583035490755 +1403715914184058112.0000000000 -0.8254322233 1.8011811587 1.5735755053 0.5890662894 0.7862046455 0.1771623511 -0.0591325923977 +1403715914234057984.0000000000 -0.8800799152 1.7591053778 1.5757422839 0.5833569294 0.7920839472 0.1682409593 -0.0631877601555 +1403715914284058112.0000000000 -0.9358054426 1.7162301116 1.5782849726 0.5766650420 0.7987809436 0.1581982818 -0.066179582846 +1403715914334057984.0000000000 -0.9923573231 1.6731345580 1.5808442231 0.5682722425 0.8066254469 0.1479826425 -0.0672546236324 +1403715914384058112.0000000000 -1.0495177221 1.6304389411 1.5836818652 0.5590971392 0.8148133891 0.1380931031 -0.0664817633072 +1403715914434057984.0000000000 -1.1069496161 1.5887427202 1.5867946934 0.5506392773 0.8223244146 0.1283835477 -0.0640047504953 +1403715914484058112.0000000000 -1.1645822203 1.5483967146 1.5902581695 0.5442384670 0.8282476828 0.1196772412 -0.0590561167182 +1403715914534057984.0000000000 -1.2228926283 1.5098717698 1.5943101690 0.5382777514 0.8336629259 0.1108191535 -0.0546104703426 +1403715914584058112.0000000000 -1.2814980836 1.4736357299 1.5992077680 0.5342692429 0.8377657947 0.1007243452 -0.0505910625336 +1403715914634057984.0000000000 -1.3407012686 1.4398582834 1.6040536675 0.5292527463 0.8424663151 0.0882607698 -0.0484981955457 +1403715914684058112.0000000000 -1.4003376001 1.4089630356 1.6090214861 0.5236166658 0.8474023206 0.0729592605 -0.0491104934774 +1403715914734057984.0000000000 -1.4596124519 1.3814224502 1.6137685375 0.5183101573 0.8518363055 0.0563201396 -0.0505720410861 +1403715914784058112.0000000000 -1.5184921305 1.3575069156 1.6185144540 0.5115213550 0.8566131588 0.0361639249 -0.0570260474546 +1403715914834057984.0000000000 -1.5758437646 1.3376554872 1.6229250254 0.5050601090 0.8605815453 0.0182449812 -0.0630936669719 +1403715914884058112.0000000000 -1.6309169058 1.3219334608 1.6273607223 0.4994454044 0.8635892103 0.0017353032 -0.0690286363141 +1403715914934057984.0000000000 -1.6827496792 1.3106334368 1.6312617692 0.4955891335 0.8654836662 -0.0107413499 -0.0722084316682 +1403715914984058112.0000000000 -1.7310038701 1.3043974647 1.6350064948 0.4937510822 0.8662123817 -0.0203844261 -0.0739625164029 +1403715915034057984.0000000000 -1.7753472473 1.3034261011 1.6390093625 0.4925221365 0.8664999110 -0.0288374534 -0.0759490003018 +1403715915084058112.0000000000 -1.8152309514 1.3075360286 1.6429655231 0.4921643232 0.8663140373 -0.0352482702 -0.0776648389739 +1403715915134057984.0000000000 -1.8504445059 1.3168599331 1.6468411380 0.4927099471 0.8658956779 -0.0388280165 -0.07716196011 +1403715915184058112.0000000000 -1.8810260167 1.3314625464 1.6511843347 0.4956206038 0.8641399776 -0.0412444060 -0.0769494324953 +1403715915234057984.0000000000 -1.9063886698 1.3516160427 1.6558055667 0.5041472711 0.8598918326 -0.0382938247 -0.0703928135785 +1403715915284058112.0000000000 -1.9274134991 1.3755146536 1.6605110300 0.5148798238 0.8544679617 -0.0321497973 -0.0612344678568 +1403715915334057984.0000000000 -1.9449802591 1.4026846069 1.6644612073 0.5256402288 0.8490242209 -0.0220352205 -0.0487305993528 +1403715915384058112.0000000000 -1.9598564768 1.4323471037 1.6665360904 0.5356492261 0.8435367165 -0.0122920356 -0.0370758729992 +1403715915434057984.0000000000 -1.9730826876 1.4638328937 1.6645618449 0.5424419063 0.8396772530 -0.0025734239 -0.0263109591454 +1403715915484058112.0000000000 -1.9855474407 1.4969895266 1.6593183991 0.5484065467 0.8359754759 0.0043688092 -0.0193952736828 +1403715915534057984.0000000000 -1.9972921522 1.5313892642 1.6504768579 0.5529834840 0.8330078645 0.0091385875 -0.0149549433901 +1403715915584058112.0000000000 -2.0084950537 1.5667400353 1.6383004392 0.5569177996 0.8303759414 0.0140221030 -0.0110336376618 +1403715915634057984.0000000000 -2.0192344598 1.6026682581 1.6231355998 0.5598651044 0.8283223714 0.0201355840 -0.0052604288659 +1403715915684058112.0000000000 -2.0302061790 1.6394829015 1.6069872681 0.5619620790 0.8267771402 0.0252477304 -0.000856962584522 +1403715915734057984.0000000000 -2.0417377650 1.6762631193 1.5902959760 0.5606547939 0.8275740391 0.0280602385 -0.000186665462225 +1403715915784058112.0000000000 -2.0539708683 1.7137211809 1.5738567245 0.5574925788 0.8296857312 0.0286134037 -0.00221025013485 +1403715915834057984.0000000000 -2.0665962615 1.7519976107 1.5575030457 0.5530352893 0.8326534640 0.0285745222 -0.00486563736728 +1403715915884058112.0000000000 -2.0796027435 1.7911791069 1.5413161978 0.5482224863 0.8358020176 0.0288459102 -0.00741662275962 +1403715915934057984.0000000000 -2.0927029940 1.8316211578 1.5256894320 0.5444680119 0.8382263309 0.0289069752 -0.00977696122667 +1403715915984058112.0000000000 -2.1059334989 1.8738883799 1.5109384735 0.5447284214 0.8380155798 0.0292596726 -0.0120294013078 +1403715916034057984.0000000000 -2.1191899843 1.9178961342 1.4965153655 0.5474185622 0.8362322532 0.0293783186 -0.0136180334489 +1403715916084058112.0000000000 -2.1322490499 1.9628879494 1.4822908693 0.5512574007 0.8337378399 0.0283621870 -0.0138592516429 +1403715916134057984.0000000000 -2.1448099593 2.0089512868 1.4675693072 0.5532226479 0.8325324182 0.0263822906 -0.0117664464046 +1403715916184058112.0000000000 -2.1568238406 2.0562811000 1.4532514801 0.5574470526 0.8298873325 0.0216280910 -0.00848672613215 +1403715916234057984.0000000000 -2.1683835122 2.1039807766 1.4388175877 0.5606468700 0.8279115139 0.0147878129 -0.00435119029801 +1403715916284058112.0000000000 -2.1792740698 2.1522418433 1.4244061069 0.5630499362 0.8263979489 0.0061752277 0.00175099530517 +1403715916334057984.0000000000 -2.1897231029 2.2010573103 1.4107932126 0.5653023074 0.8248219898 -0.0037666492 0.00937009851559 +1403715916384058112.0000000000 -2.1998439706 2.2500016746 1.3973642813 0.5671603547 0.8233005618 -0.0154907746 0.016289656155 +1403715916434057984.0000000000 -2.2095342281 2.2992223182 1.3840921009 0.5686071205 0.8217926683 -0.0287521152 0.0227171470665 +1403715916484058112.0000000000 -2.2188370348 2.3484740096 1.3705659459 0.5681467848 0.8212597859 -0.0435206095 0.0291127384639 +1403715916534057984.0000000000 -2.2274360356 2.3977771082 1.3574590471 0.5663867222 0.8212394714 -0.0589335148 0.0360368213045 +1403715916584058112.0000000000 -2.2351182592 2.4466222669 1.3446045589 0.5650651429 0.8205195714 -0.0737036826 0.0449086236277 +1403715916634057984.0000000000 -2.2422959622 2.4952540036 1.3320078442 0.5636319460 0.8194204151 -0.0906897344 0.0514255267664 +1403715916684058112.0000000000 -2.2484632794 2.5439042703 1.3196713703 0.5621451879 0.8180321171 -0.1076428385 0.0568265998353 +1403715916734057984.0000000000 -2.2538154017 2.5923721753 1.3081896355 0.5612544424 0.8161436581 -0.1235657893 0.0602866147523 +1403715916784058112.0000000000 -2.2578412449 2.6407430201 1.2973024069 0.5604657194 0.8140845556 -0.1387295527 0.0624389697555 +1403715916834057984.0000000000 -2.2601734318 2.6886938507 1.2867167308 0.5593604914 0.8122807337 -0.1521355939 0.0645802706034 +1403715916884058112.0000000000 -2.2610076193 2.7361988858 1.2777313268 0.5599524260 0.8091938417 -0.1665208132 0.0626851337321 +1403715916934057984.0000000000 -2.2588876787 2.7833636976 1.2699252875 0.5618934909 0.8053785406 -0.1778600328 0.0633002366763 +1403715916984058112.0000000000 -2.2540554970 2.8297474905 1.2626051253 0.5635604571 0.8019232842 -0.1877773474 0.0637049861826 +1403715917034057984.0000000000 -2.2461192420 2.8750396276 1.2563689946 0.5659993294 0.7982294623 -0.1957503417 0.0644692825796 +1403715917084058112.0000000000 -2.2341992836 2.9197259951 1.2512837758 0.5709150648 0.7933309371 -0.1990994504 0.0710029711526 +1403715917134057984.0000000000 -2.2181294770 2.9632972439 1.2479002051 0.5802868994 0.7852516844 -0.1995349905 0.0826601110873 +1403715917184058112.0000000000 -2.1985609389 3.0047075870 1.2445815961 0.5884440503 0.7778644407 -0.1953014576 0.102556580684 +1403715917234057984.0000000000 -2.1775587274 3.0437517956 1.2416472551 0.5949076472 0.7709392130 -0.1908276221 0.123783843316 +1403715917284058112.0000000000 -2.1568612338 3.0791021974 1.2379366491 0.5972864025 0.7662628117 -0.1899921302 0.141397479649 +1403715917334057984.0000000000 -2.1369413038 3.1115027400 1.2347223423 0.5996512186 0.7613583271 -0.1912018301 0.155543479238 +1403715917384058112.0000000000 -2.1186976064 3.1410707912 1.2316115306 0.6000536562 0.7584063816 -0.1937116303 0.16501870868 +1403715917434057984.0000000000 -2.1023357179 3.1678277918 1.2290741361 0.5987740850 0.7572693953 -0.1970032372 0.170887046479 +1403715917484058112.0000000000 -2.0883462748 3.1918755855 1.2269017206 0.5947473912 0.7589727677 -0.2040472899 0.169117066034 +1403715917534057984.0000000000 -2.0758140424 3.2134831988 1.2238402337 0.5876861682 0.7632958649 -0.2103557798 0.166597828119 +1403715917584058112.0000000000 -2.0648223993 3.2327518592 1.2199643070 0.5823423075 0.7665850187 -0.2183008897 0.159904870158 +1403715917634057984.0000000000 -2.0538087520 3.2505826807 1.2145203429 0.5789583198 0.7685699284 -0.2243561712 0.154181184155 +1403715917684058112.0000000000 -2.0421149677 3.2674114983 1.2078334020 0.5799920642 0.7673775358 -0.2291753945 0.149062274264 +1403715917734057984.0000000000 -2.0299837982 3.2826965301 1.2003470392 0.5848246684 0.7635919611 -0.2316677661 0.145730814558 +1403715917784058112.0000000000 -2.0174570724 3.2956153991 1.1916886922 0.5904152267 0.7593265378 -0.2317638052 0.145322426749 +1403715917834057984.0000000000 -2.0045242579 3.3054531277 1.1834413464 0.5962206832 0.7550521814 -0.2301014050 0.146527962094 +1403715917884058112.0000000000 -1.9916814119 3.3123253695 1.1761691091 0.6013155923 0.7514540305 -0.2276622211 0.148007809133 +1403715917934057984.0000000000 -1.9792105372 3.3152207858 1.1699810235 0.6044931586 0.7493742959 -0.2241351606 0.150962298279 +1403715917984058112.0000000000 -1.9669584821 3.3145611881 1.1647532216 0.6063877053 0.7484253739 -0.2196971023 0.154552883956 +1403715918034057984.0000000000 -1.9552529261 3.3100183330 1.1603768137 0.6063007851 0.7485985648 -0.2151792939 0.160304142519 +1403715918084058112.0000000000 -1.9439916097 3.3020030434 1.1560476362 0.6033825956 0.7501811715 -0.2120188063 0.167945464523 +1403715918134057984.0000000000 -1.9336851396 3.2907748632 1.1514014425 0.5983018185 0.7527006738 -0.2107271968 0.176268766752 +1403715918184058112.0000000000 -1.9245427404 3.2769420526 1.1472677786 0.5950213701 0.7530961555 -0.2113980818 0.184679724533 +1403715918234057984.0000000000 -1.9170371613 3.2610921896 1.1439657996 0.5941803381 0.7512989192 -0.2163935754 0.188874245013 +1403715918284058112.0000000000 -1.9112495693 3.2430336276 1.1406800332 0.5936555846 0.7489381284 -0.2245922296 0.190323559064 +1403715918334057984.0000000000 -1.9071908523 3.2226998334 1.1348958967 0.5907685936 0.7482091057 -0.2367927655 0.187362721079 +1403715918384058112.0000000000 -1.9044389504 3.2001898224 1.1256538318 0.5851508997 0.7492485648 -0.2509871329 0.18229227041 +1403715918434057984.0000000000 -1.9023168713 3.1759264330 1.1125482816 0.5785278901 0.7505564681 -0.2656797051 0.177157452147 +1403715918484058112.0000000000 -1.9000802435 3.1498060027 1.0959442677 0.5709697310 0.7522590076 -0.2794673710 0.173199135034 +1403715918534057984.0000000000 -1.8972638071 3.1217039281 1.0769464389 0.5648377503 0.7526817070 -0.2914201934 0.171763892427 +1403715918584058112.0000000000 -1.8936984090 3.0918708783 1.0549541674 0.5597622374 0.7522854109 -0.3022989906 0.171313217352 +1403715918634057984.0000000000 -1.8884746131 3.0607201325 1.0314797710 0.5554288118 0.7519826298 -0.3094536369 0.173952309912 +1403715918684058112.0000000000 -1.8816718746 3.0277615657 1.0088621821 0.5507383345 0.7524579601 -0.3135201879 0.179441904062 +1403715918734057984.0000000000 -1.8736308334 2.9931894517 0.9887841225 0.5448794100 0.7545785345 -0.3145894732 0.186416542265 +1403715918784058112.0000000000 -1.8640180607 2.9576240906 0.9724846087 0.5390430420 0.7570634540 -0.3127192217 0.196199423853 +1403715918834057984.0000000000 -1.8539287385 2.9213581511 0.9592044475 0.5304799607 0.7619354405 -0.3103182202 0.204323268296 +1403715918884058112.0000000000 -1.8433482366 2.8851072954 0.9490371799 0.5204504967 0.7681354768 -0.3078563236 0.210531835427 +1403715918934057984.0000000000 -1.8325240069 2.8496608486 0.9430433042 0.5104665325 0.7743796194 -0.3068003249 0.213620422259 +1403715918984058112.0000000000 -1.8211828182 2.8159495127 0.9408181904 0.5013991576 0.7801733141 -0.3067760877 0.21404886511 +1403715919034057984.0000000000 -1.8088890557 2.7846172533 0.9421041432 0.4928479169 0.7855173865 -0.3071046676 0.213892705527 +1403715919084058112.0000000000 -1.7954314050 2.7558639462 0.9467781118 0.4853632495 0.7903636343 -0.3053872991 0.215607140586 +1403715919134057984.0000000000 -1.7805271104 2.7300544577 0.9534806706 0.4813018142 0.7932507426 -0.3008423354 0.220444351958 +1403715919184058112.0000000000 -1.7644230047 2.7074802166 0.9606947868 0.4790658360 0.7950903143 -0.2936706421 0.228221101039 +1403715919234057984.0000000000 -1.7475244229 2.6886818108 0.9684282599 0.4790907838 0.7954061619 -0.2851197649 0.237713647535 +1403715919284058112.0000000000 -1.7304942507 2.6740886012 0.9767114508 0.4823249202 0.7937197061 -0.2760401276 0.247332867552 +1403715919334057984.0000000000 -1.7142794373 2.6632947046 0.9844090459 0.4858167281 0.7917782136 -0.2669454662 0.256533594616 +1403715919384058112.0000000000 -1.7000896848 2.6559269344 0.9904012519 0.4914891040 0.7885939401 -0.2641994024 0.258373245465 +1403715919434057984.0000000000 -1.6880007890 2.6514964532 0.9933905678 0.4977289704 0.7852343902 -0.2669493980 0.253792914346 +1403715919484058112.0000000000 -1.6773864978 2.6495287978 0.9929231928 0.5042372409 0.7815960943 -0.2707057083 0.248134579966 +1403715919534057984.0000000000 -1.6677961741 2.6495904132 0.9889060688 0.5098666697 0.7782457186 -0.2745362139 0.242898019545 +1403715919584058112.0000000000 -1.6589515660 2.6511767708 0.9813379271 0.5146719372 0.7752278945 -0.2777851022 0.238683777484 +1403715919634057984.0000000000 -1.6508407873 2.6540517754 0.9701060822 0.5179461174 0.7730654031 -0.2805081450 0.235407906823 +1403715919684058112.0000000000 -1.6433451624 2.6582007634 0.9555802334 0.5195018264 0.7719068966 -0.2818207413 0.234210728001 +1403715919734057984.0000000000 -1.6364550394 2.6635493367 0.9379653112 0.5197404070 0.7715430116 -0.2818477429 0.23484705747 +1403715919784058112.0000000000 -1.6298373561 2.6699768968 0.9179694686 0.5193973518 0.7714370392 -0.2800544497 0.238077278982 +1403715919834057984.0000000000 -1.6243600152 2.6776106554 0.8969669840 0.5192044088 0.7714354941 -0.2789599600 0.239781986468 +1403715919884058112.0000000000 -1.6201338671 2.6861948301 0.8753656348 0.5184428799 0.7718592218 -0.2776862656 0.241538112581 +1403715919934057984.0000000000 -1.6177213431 2.6962946704 0.8538886965 0.5164262808 0.7733992611 -0.2779065315 0.240677043474 +1403715919984058112.0000000000 -1.6166445877 2.7080900708 0.8339999444 0.5126808430 0.7762734470 -0.2797197727 0.237307263939 +1403715920034057984.0000000000 -1.6162443064 2.7219362950 0.8176358421 0.5095703680 0.7787054267 -0.2808263345 0.234717848362 +1403715920084058112.0000000000 -1.6166224405 2.7375816079 0.8049662266 0.5071406810 0.7807674475 -0.2822232770 0.23143151159 +1403715920134057984.0000000000 -1.6176153299 2.7549820695 0.7959549277 0.5050153779 0.7826056572 -0.2838729596 0.227824485567 +1403715920184058112.0000000000 -1.6190646493 2.7739078032 0.7904746875 0.5040688842 0.7835916345 -0.2851620394 0.224902915945 +1403715920234057984.0000000000 -1.6203435019 2.7952902865 0.7887016280 0.5047165217 0.7837670533 -0.2869938085 0.220465400195 +1403715920284058112.0000000000 -1.6212436525 2.8193237769 0.7918420099 0.5091336975 0.7818924507 -0.2874348678 0.216352190525 +1403715920334057984.0000000000 -1.6218059000 2.8449793809 0.7983554133 0.5149035063 0.7794826970 -0.2869919881 0.211935610603 +1403715920384058112.0000000000 -1.6222218389 2.8717006127 0.8071467378 0.5198662473 0.7774881866 -0.2858551727 0.208657674022 +1403715920434057984.0000000000 -1.6222908252 2.8992755644 0.8176051657 0.5266930887 0.7740045435 -0.2853593790 0.205137470218 +1403715920484058112.0000000000 -1.6219795870 2.9271216354 0.8284970396 0.5329315402 0.7707667773 -0.2842280975 0.20277311711 +1403715920534057984.0000000000 -1.6212330748 2.9551003792 0.8394992102 0.5398382342 0.7669337411 -0.2830132628 0.200725710405 +1403715920584058112.0000000000 -1.6200923334 2.9826292325 0.8502545258 0.5464555901 0.7629597857 -0.2819423834 0.199467154819 +1403715920634057984.0000000000 -1.6188487004 3.0091964534 0.8603838409 0.5526260712 0.7592198014 -0.2809568535 0.198123610616 +1403715920684058112.0000000000 -1.6176082817 3.0346362571 0.8711824848 0.5584485585 0.7558071959 -0.2795061533 0.196893373086 +1403715920734057984.0000000000 -1.6165925245 3.0585837562 0.8841279984 0.5641475311 0.7527465560 -0.2763246229 0.19686261295 +1403715920784058112.0000000000 -1.6164654046 3.0806783145 0.9003364626 0.5689873191 0.7509137539 -0.2729986384 0.194560295084 +1403715920834057984.0000000000 -1.6169191792 3.1010845324 0.9182823302 0.5715926289 0.7510984977 -0.2680011478 0.193153560915 +1403715920884058112.0000000000 -1.6185884755 3.1195096141 0.9389847160 0.5724862096 0.7529797315 -0.2635127804 0.189320042006 +1403715920934057984.0000000000 -1.6212897475 3.1356726442 0.9624377093 0.5719174538 0.7563727091 -0.2598666571 0.182428264091 +1403715920984058112.0000000000 -1.6246556333 3.1493756398 0.9877841990 0.5681215440 0.7623633153 -0.2565119950 0.173901360185 +1403715921034057984.0000000000 -1.6280745621 3.1611580147 1.0156521203 0.5642260992 0.7684466050 -0.2525635285 0.165379527651 +1403715921084058112.0000000000 -1.6309715304 3.1714033635 1.0445246963 0.5601655520 0.7746512263 -0.2469949949 0.158503956905 +1403715921134057984.0000000000 -1.6327704275 3.1807024840 1.0737442685 0.5569429489 0.7799320712 -0.2409042094 0.153250376142 +1403715921184058112.0000000000 -1.6332799697 3.1893047790 1.1035612676 0.5559915940 0.7831218525 -0.2347191917 0.150001375518 +1403715921234057984.0000000000 -1.6327569606 3.1974951815 1.1327450836 0.5546088572 0.7862057596 -0.2291111857 0.147640047911 +1403715921284058112.0000000000 -1.6309376894 3.2052224077 1.1612612515 0.5536324954 0.7885852103 -0.2231091149 0.147806457772 +1403715921334057984.0000000000 -1.6283780259 3.2123951399 1.1891897163 0.5512210755 0.7916691492 -0.2174360995 0.148784497419 +1403715921384058112.0000000000 -1.6251735847 3.2194285818 1.2168717815 0.5486910478 0.7945688295 -0.2120165359 0.150490856168 +1403715921434057984.0000000000 -1.6215074004 3.2266437625 1.2445665926 0.5461950572 0.7971131606 -0.2071653300 0.152853180488 +1403715921484058112.0000000000 -1.6175605781 3.2346192195 1.2726838352 0.5441948169 0.7990127587 -0.2044512160 0.153721543792 +1403715921534057984.0000000000 -1.6135704906 3.2433503639 1.3018916675 0.5437637137 0.7997058490 -0.2022253237 0.154584919033 +1403715921584058112.0000000000 -1.6096025550 3.2527399943 1.3329308795 0.5430884453 0.8003862162 -0.2010438866 0.154978066706 +1403715921634057984.0000000000 -1.6056338255 3.2631266453 1.3680994537 0.5436926105 0.7999959162 -0.2000522320 0.156153718639 +1403715921684058112.0000000000 -1.6019160868 3.2745976894 1.4056414938 0.5430557681 0.8003702995 -0.2009618077 0.155280933122 +1403715921734057984.0000000000 -1.5982602545 3.2867130391 1.4443305058 0.5431876825 0.8001185614 -0.2021461911 0.154577963128 +1403715921784058112.0000000000 -1.5947371270 3.2997592076 1.4838729223 0.5453011065 0.7985280264 -0.2055036390 0.150890518679 +1403715921834057984.0000000000 -1.5912152810 3.3129669471 1.5224292139 0.5463334365 0.7976018529 -0.2080183530 0.148591471047 +1403715921884058112.0000000000 -1.5876017464 3.3263934729 1.5587623107 0.5475295854 0.7965178494 -0.2107638224 0.146113927759 +1403715921934057984.0000000000 -1.5832818384 3.3403792339 1.5919658742 0.5492007079 0.7949840405 -0.2126813661 0.145415247849 +1403715921984058112.0000000000 -1.5785274194 3.3546170305 1.6222641516 0.5498807855 0.7941372290 -0.2143819295 0.144974382641 +1403715922034057984.0000000000 -1.5732864143 3.3686945357 1.6515733219 0.5501454211 0.7935332189 -0.2149192478 0.146474445038 +1403715922084058112.0000000000 -1.5675464411 3.3828337527 1.6810368609 0.5514988931 0.7922371319 -0.2147220955 0.148673197156 +1403715922134057984.0000000000 -1.5615462428 3.3970170195 1.7127100381 0.5545604552 0.7897040045 -0.2157055676 0.149336515446 +1403715922184058112.0000000000 -1.5551631990 3.4109261750 1.7470038539 0.5580652252 0.7869319673 -0.2159663206 0.150531829123 +1403715922234057984.0000000000 -1.5486131119 3.4244356641 1.7840473965 0.5621096650 0.7837300372 -0.2164256963 0.151525150307 +1403715922284058112.0000000000 -1.5420893496 3.4375297283 1.8239298395 0.5654269802 0.7811623167 -0.2161092611 0.152887384655 +1403715922334057984.0000000000 -1.5356855844 3.4496408582 1.8660488260 0.5678990616 0.7792219111 -0.2151324837 0.154989946662 +1403715922384058112.0000000000 -1.5296132871 3.4603478429 1.9083385847 0.5685580283 0.7787124086 -0.2130001139 0.158049690652 +1403715922434057984.0000000000 -1.5239259993 3.4697893608 1.9501255403 0.5676854200 0.7793678471 -0.2103869705 0.161419780381 +1403715922484058112.0000000000 -1.5190244948 3.4782148074 1.9917334801 0.5679263647 0.7793253868 -0.2095295714 0.161891767788 +1403715922534057984.0000000000 -1.5148009828 3.4857478779 2.0328145527 0.5680695784 0.7793540370 -0.2099364751 0.160719991079 +1403715922584058112.0000000000 -1.5112028265 3.4926039249 2.0733415023 0.5698142306 0.7781928371 -0.2112571174 0.158423739347 +1403715922634057984.0000000000 -1.5081665671 3.4981979868 2.1125451216 0.5717964760 0.7769304497 -0.2121186683 0.156312305542 +1403715922684058112.0000000000 -1.5051147949 3.5023262730 2.1483745374 0.5728866743 0.7761892882 -0.2125998829 0.15534586273 +1403715922734057984.0000000000 -1.5022970169 3.5050732677 2.1802932495 0.5724695343 0.7765712435 -0.2120641209 0.155706597985 +1403715922784058112.0000000000 -1.4997187085 3.5067356225 2.2082229965 0.5715762169 0.7773590229 -0.2101999621 0.157573962956 +1403715922834057984.0000000000 -1.4976190167 3.5072395774 2.2320946595 0.5698168874 0.7787093314 -0.2081315078 0.160005522949 +1403715922884058112.0000000000 -1.4960797161 3.5069776812 2.2518831628 0.5683869230 0.7798346334 -0.2061189139 0.162201244333 +1403715922934057984.0000000000 -1.4951066463 3.5061530079 2.2681772825 0.5667774388 0.7810259689 -0.2047040799 0.163884137329 +1403715922984058112.0000000000 -1.4946826934 3.5050777021 2.2827500659 0.5661310785 0.7815012064 -0.2034565801 0.165399172566 +1403715923034057984.0000000000 -1.4950730421 3.5034191462 2.2964057872 0.5654297163 0.7820410025 -0.2023138266 0.166643997349 +1403715923084058112.0000000000 -1.4964666556 3.5009163921 2.3094807621 0.5641399603 0.7829022920 -0.2018434222 0.167539067784 +1403715923134057984.0000000000 -1.4990714631 3.4976977080 2.3234508308 0.5623035087 0.7842993787 -0.2015654072 0.167513090104 +1403715923184058112.0000000000 -1.5026779196 3.4936609014 2.3394236227 0.5591033220 0.7866552490 -0.2016085022 0.167125720336 +1403715923234057984.0000000000 -1.5072707778 3.4894579847 2.3582865395 0.5554410171 0.7892472761 -0.2018666223 0.166804917732 +1403715923284058112.0000000000 -1.5129619746 3.4855161305 2.3809097088 0.5521479279 0.7917327626 -0.2034284030 0.164038968394 +1403715923334057984.0000000000 -1.5198704431 3.4816320567 2.4064445717 0.5505243935 0.7930122110 -0.2059353047 0.160141111816 +1403715923384058112.0000000000 -1.5275243092 3.4779697650 2.4321752297 0.5500159471 0.7935429314 -0.2100934910 0.153729629628 +1403715923434057984.0000000000 -1.5349732870 3.4749380540 2.4565532484 0.5506229492 0.7932026766 -0.2141853496 0.147541579729 +1403715923484058112.0000000000 -1.5422690404 3.4719755422 2.4781987788 0.5515380141 0.7925698960 -0.2185335475 0.141003076414 +1403715923534057984.0000000000 -1.5485941698 3.4691421252 2.4967989683 0.5531844679 0.7913101273 -0.2229054223 0.134641745412 +1403715923584058112.0000000000 -1.5539510767 3.4661053123 2.5114678124 0.5553390745 0.7896622936 -0.2267536263 0.128898282771 +1403715923634057984.0000000000 -1.5582675311 3.4625865104 2.5208278269 0.5573381524 0.7881084280 -0.2298552951 0.124200776329 +1403715923684058112.0000000000 -1.5614077336 3.4584970132 2.5239946745 0.5595039755 0.7864374187 -0.2321550403 0.120729139743 +1403715923734057984.0000000000 -1.5633299033 3.4536311999 2.5206984335 0.5616235795 0.7849043761 -0.2335314642 0.118182615102 +1403715923784058112.0000000000 -1.5641095464 3.4478540338 2.5112862327 0.5645854948 0.7827436724 -0.2345058975 0.116458346134 +1403715923834057984.0000000000 -1.5630967904 3.4412459186 2.4973473363 0.5676321830 0.7806640320 -0.2334918648 0.117638951985 +1403715923884058112.0000000000 -1.5607384675 3.4335791423 2.4806609518 0.5727630819 0.7771148972 -0.2316208125 0.119944519331 +1403715923934057984.0000000000 -1.5568375448 3.4249468233 2.4612564777 0.5782974833 0.7731512277 -0.2298741163 0.122340061525 +1403715923984058112.0000000000 -1.5515418187 3.4146939319 2.4388626156 0.5825507839 0.7702476691 -0.2267838639 0.126183166082 +1403715924034057984.0000000000 -1.5453424776 3.4026269550 2.4129547826 0.5853145661 0.7683754329 -0.2239054626 0.129893790182 +1403715924084058112.0000000000 -1.5381733922 3.3887009977 2.3838895234 0.5868854374 0.7672581089 -0.2204961096 0.135136757798 +1403715924134057984.0000000000 -1.5309170319 3.3723858586 2.3531797052 0.5870955666 0.7672830022 -0.2170044755 0.139659041611 +1403715924184058112.0000000000 -1.5234056247 3.3541360514 2.3222642099 0.5863101838 0.7679487744 -0.2147038941 0.142819067979 +1403715924234057984.0000000000 -1.5157361779 3.3339002132 2.2909226890 0.5835637620 0.7700584543 -0.2123613213 0.146171070871 +1403715924284058112.0000000000 -1.5083198687 3.3119885757 2.2602855660 0.5814605295 0.7716629293 -0.2117577383 0.146964745572 +1403715924334057984.0000000000 -1.5009669905 3.2883602738 2.2297693753 0.5779175993 0.7742731537 -0.2104736902 0.149040791682 +1403715924384058112.0000000000 -1.4940442747 3.2633951347 2.1998081371 0.5738090508 0.7772491566 -0.2099331764 0.150183165671 +1403715924434057984.0000000000 -1.4875194501 3.2376976723 2.1702782252 0.5695450887 0.7802576816 -0.2112561730 0.148953588909 +1403715924484058112.0000000000 -1.4810520599 3.2112839358 2.1406077554 0.5636862865 0.7844362170 -0.2119863096 0.148254498948 +1403715924534057984.0000000000 -1.4744088324 3.1846670527 2.1114762931 0.5578827050 0.7883574436 -0.2136505226 0.147013205948 +1403715924584058112.0000000000 -1.4673923617 3.1579675866 2.0829815170 0.5541428960 0.7907407397 -0.2150733139 0.146281246605 +1403715924634057984.0000000000 -1.4599976168 3.1314299362 2.0550931596 0.5520459267 0.7916993771 -0.2194445486 0.142483266143 +1403715924684058112.0000000000 -1.4515058658 3.1051162987 2.0275558178 0.5509776524 0.7911788519 -0.2260180007 0.139195956419 +1403715924734057984.0000000000 -1.4413741767 3.0788981355 2.0002260432 0.5514762500 0.7887700952 -0.2337457681 0.138125299578 +1403715924784058112.0000000000 -1.4293852720 3.0530676607 1.9730450072 0.5517180471 0.7859908353 -0.2419694213 0.138839484385 +1403715924834057984.0000000000 -1.4153970131 3.0268868208 1.9462520683 0.5527622906 0.7818779296 -0.2509094381 0.14200425068 +1403715924884058112.0000000000 -1.3995710537 3.0001381978 1.9195294525 0.5525096369 0.7779265105 -0.2606698727 0.147019259942 +1403715924934057984.0000000000 -1.3820551415 2.9723455424 1.8932862941 0.5538742987 0.7720321990 -0.2711659379 0.153813455388 +1403715924984058112.0000000000 -1.3626798150 2.9435176003 1.8673341560 0.5551074935 0.7657092330 -0.2800934348 0.1645986302 +1403715925034057984.0000000000 -1.3417420032 2.9135234532 1.8429052620 0.5576633097 0.7575887264 -0.2893208143 0.17710003111 +1403715925084058112.0000000000 -1.3198067619 2.8824301909 1.8211885741 0.5604056078 0.7488705644 -0.2970290701 0.192125386237 +1403715925134057984.0000000000 -1.2982284688 2.8491461957 1.8026197777 0.5617933351 0.7406421402 -0.3050661562 0.206814189922 +1403715925184058112.0000000000 -1.2770622459 2.8138592577 1.7873144505 0.5611890321 0.7334022344 -0.3142473837 0.220083199475 +1403715925234057984.0000000000 -1.2566647261 2.7770008923 1.7758960287 0.5593273334 0.7269130217 -0.3258485566 0.229288270945 +1403715925284058112.0000000000 -1.2373501382 2.7380268224 1.7678948490 0.5552330139 0.7216488301 -0.3384484965 0.237469748582 +1403715925334057984.0000000000 -1.2192104031 2.6971894374 1.7627559644 0.5500092814 0.7170367274 -0.3531108386 0.242200036316 +1403715925384058112.0000000000 -1.2014464851 2.6547422589 1.7597497114 0.5432042871 0.7129465194 -0.3685757542 0.246552786291 +1403715925434057984.0000000000 -1.1844018324 2.6106022805 1.7576958330 0.5359507039 0.7090522454 -0.3843157682 0.249605982681 +1403715925484058112.0000000000 -1.1676489206 2.5648269640 1.7554546724 0.5271644563 0.7059842302 -0.3997707802 0.252719658857 +1403715925534057984.0000000000 -1.1507025183 2.5175479563 1.7532959199 0.5192743335 0.7017486064 -0.4146389471 0.256861058953 +1403715925584058112.0000000000 -1.1331821271 2.4686759191 1.7510574197 0.5117565793 0.6970030355 -0.4279728148 0.262928206558 +1403715925634057984.0000000000 -1.1149016939 2.4183241582 1.7490617964 0.5054867956 0.6909463822 -0.4407566278 0.269832895441 +1403715925684058112.0000000000 -1.0955586116 2.3665308476 1.7473754825 0.5002174088 0.6837876399 -0.4525783945 0.278190230413 +1403715925734057984.0000000000 -1.0752178038 2.3135630583 1.7458735182 0.4953945660 0.6759138784 -0.4640274161 0.287059593201 +1403715925784058112.0000000000 -1.0544237873 2.2593285024 1.7438255367 0.4897838406 0.6682465616 -0.4756288937 0.295525765053 +1403715925834057984.0000000000 -1.0328122311 2.2038498165 1.7420185360 0.4851947135 0.6593956877 -0.4868176089 0.304617847041 +1403715925884058112.0000000000 -1.0107591918 2.1470125583 1.7397426648 0.4803062426 0.6503441182 -0.4973275058 0.314680462115 +1403715925934057984.0000000000 -0.9885282148 2.0887276957 1.7369337973 0.4742942847 0.6416697251 -0.5069859706 0.32599098296 +1403715925984058112.0000000000 -0.9658010129 2.0292338271 1.7342612583 0.4684994144 0.6322354523 -0.5165039219 0.33765415764 +1403715926034057984.0000000000 -0.9429069671 1.9687338522 1.7311923913 0.4641795894 0.6212194131 -0.5264889859 0.348472520084 +1403715926084058112.0000000000 -0.9199078227 1.9071867248 1.7264897328 0.4618971844 0.6077149141 -0.5370375995 0.359060149547 +1403715926134057984.0000000000 -0.8973347400 1.8445017684 1.7190003522 0.4595712652 0.5934059214 -0.5472750726 0.370342624419 +1403715926184058112.0000000000 -0.8758646243 1.7805873348 1.7080528947 0.4564646114 0.5787092307 -0.5579155105 0.381400010501 +1403715926234057984.0000000000 -0.8562401681 1.7152503523 1.6932180403 0.4521753371 0.5644678292 -0.5685425860 0.392011303683 +1403715926284058112.0000000000 -0.8384439531 1.6482777425 1.6750890919 0.4469570800 0.5502798745 -0.5790351395 0.402665786366 +1403715926334057984.0000000000 -0.8221376346 1.5797875502 1.6541802688 0.4402258742 0.5367388393 -0.5883768459 0.414638740636 +1403715926384058112.0000000000 -0.8079760433 1.5100440346 1.6316338939 0.4323444744 0.5236890214 -0.5972686868 0.42672963346 +1403715926434057984.0000000000 -0.7961494047 1.4392455812 1.6085172143 0.4239471275 0.5108206701 -0.6036789855 0.441477925358 +1403715926484058112.0000000000 -0.7872215397 1.3677921310 1.5852180372 0.4155550484 0.4979865530 -0.6092291398 0.456249109535 +1403715926534057984.0000000000 -0.7814124388 1.2956763839 1.5612904199 0.4056586805 0.4860161958 -0.6162721811 0.46844198284 +1403715926584058112.0000000000 -0.7790694582 1.2235646607 1.5365135677 0.3937313562 0.4760444722 -0.6244681876 0.477908738416 +1403715926634057984.0000000000 -0.7800482991 1.1517559140 1.5111492530 0.3802200050 0.4672187715 -0.6349114033 0.483763245003 +1403715926684058112.0000000000 -0.7837533532 1.0804911382 1.4859335511 0.3669121379 0.4583580627 -0.6464805896 0.487181913385 +1403715926734057984.0000000000 -0.7893381631 1.0093774700 1.4610465872 0.3520934869 0.4507481911 -0.6574822165 0.490482802577 +1403715926784058112.0000000000 -0.7972061713 0.9388578865 1.4369400727 0.3366270546 0.4441093345 -0.6671873144 0.494277465335 +1403715926834057984.0000000000 -0.8069266715 0.8693525050 1.4151924903 0.3199389139 0.4391041055 -0.6759411928 0.49792587781 +1403715926884058112.0000000000 -0.8180793643 0.8013703700 1.3970379596 0.3057711213 0.4331785387 -0.6844974483 0.500323513619 +1403715926934057984.0000000000 -0.8300118597 0.7348442103 1.3828987000 0.2933948347 0.4267125459 -0.6917561354 0.503298443539 +1403715926984058112.0000000000 -0.8419383783 0.6698072168 1.3723863370 0.2825818756 0.4199023524 -0.6990294549 0.505160686527 +1403715927034057984.0000000000 -0.8534573339 0.6061940274 1.3650359694 0.2743425319 0.4120413522 -0.7041869703 0.508997848864 +1403715927084058112.0000000000 -0.8644061788 0.5437567935 1.3593326071 0.2679222758 0.4030609452 -0.7072298598 0.5153498365 +1403715927134057984.0000000000 -0.8754483184 0.4827003628 1.3534646566 0.2611138838 0.3944825473 -0.7096594006 0.522098261525 +1403715927184058112.0000000000 -0.8868896700 0.4227175073 1.3469550926 0.2501589841 0.3886910540 -0.7086904237 0.533008096196 +1403715927234057984.0000000000 -0.8983584387 0.3650225337 1.3403205926 0.2390538026 0.3829088002 -0.7076142039 0.543614080649 +1403715927284058112.0000000000 -0.9095451349 0.3100886300 1.3336733788 0.2271386524 0.3779457152 -0.7061278794 0.554029319522 +1403715927334057984.0000000000 -0.9201346077 0.2584379976 1.3277657871 0.2167070640 0.3723359593 -0.7043037044 0.56423423666 +1403715927384058112.0000000000 -0.9301460474 0.2106603936 1.3235948150 0.2102169881 0.3642331949 -0.7015937478 0.575247086613 +1403715927434057984.0000000000 -0.9400370734 0.1671256097 1.3198541912 0.2046108777 0.3551361435 -0.6997602133 0.585105419715 +1403715927484058112.0000000000 -0.9496214516 0.1282953006 1.3175673376 0.2056675791 0.3414265053 -0.6990853956 0.593639956531 +1403715927534057984.0000000000 -0.9595939526 0.0940792962 1.3154635942 0.2092682678 0.3254631843 -0.7005845432 0.599551336932 +1403715927584058112.0000000000 -0.9710285905 0.0643752447 1.3136991120 0.2117001584 0.3091586620 -0.7022626052 0.605335607686 +1403715927634057984.0000000000 -0.9846466427 0.0391824096 1.3115968134 0.2139301453 0.2917511427 -0.7047071105 0.610330281151 +1403715927684058112.0000000000 -1.0007653204 0.0178704350 1.3089271535 0.2116502800 0.2754287576 -0.7083832731 0.614439823541 +1403715927734057984.0000000000 -1.0194593513 0.0001714639 1.3050564781 0.2047370995 0.2608021891 -0.7130188247 0.617793730849 +1403715927784058112.0000000000 -1.0407605760 -0.0140363205 1.2999066104 0.1925571104 0.2476500221 -0.7183599475 0.620926897113 +1403715927834057984.0000000000 -1.0646341770 -0.0246016802 1.2943463956 0.1774298829 0.2351477044 -0.7239193902 0.623830834717 +1403715927884058112.0000000000 -1.0907891037 -0.0311262901 1.2888635462 0.1615032375 0.2220004431 -0.7301580614 0.625700977271 +1403715927934057984.0000000000 -1.1192044073 -0.0331266452 1.2823389062 0.1429110889 0.2094860980 -0.7365238369 0.627076257828 +1403715927984058112.0000000000 -1.1488638501 -0.0311969032 1.2751047492 0.1248767903 0.1956735598 -0.7436819791 0.626940794007 +1403715928034057984.0000000000 -1.1794538639 -0.0253930891 1.2660531096 0.1078593063 0.1797609418 -0.7507331803 0.626459947543 +1403715928084058112.0000000000 -1.2104644840 -0.0156528472 1.2542227115 0.0940563915 0.1611486724 -0.7584358730 0.624467394801 +1403715928134057984.0000000000 -1.2417177950 -0.0025719433 1.2390244755 0.0817989165 0.1401696391 -0.7670001392 0.620783533882 +1403715928184058112.0000000000 -1.2731244925 0.0133269990 1.2205065413 0.0687075872 0.1188420780 -0.7749856031 0.616889895314 +1403715928234057984.0000000000 -1.3042502440 0.0315380837 1.1998613566 0.0575631010 0.0955785656 -0.7797637140 0.61605176526 +1403715928284058112.0000000000 -1.3354532311 0.0518297006 1.1766477544 0.0454008684 0.0728773483 -0.7814659133 0.618011876603 +1403715928334057984.0000000000 -1.3667979761 0.0741569269 1.1521207645 0.0333820798 0.0501001075 -0.7800046099 0.622871113869 +1403715928384058112.0000000000 -1.3984386839 0.0996550884 1.1267318634 0.0203622711 0.0291299693 -0.7775059667 0.627870444064 +1403715928434057984.0000000000 -1.4300783155 0.1285945760 1.1007222601 0.0094309590 0.0082487435 -0.7755732237 0.63113325841 +1403715928484058112.0000000000 -1.4617026519 0.1612801391 1.0735098657 0.0003495941 0.0119465870 0.7762315388 -0.630334637278 +1403715928534057984.0000000000 -1.4935191402 0.1976483206 1.0451297841 0.0100894321 0.0299491026 0.7801162037 -0.624835949166 +1403715928584058112.0000000000 -1.5250576314 0.2372515564 1.0170351071 0.0174637800 0.0464297994 0.7848178620 -0.617737981326 +1403715928634057984.0000000000 -1.5565970905 0.2796903694 0.9914528971 0.0250378477 0.0591856051 0.7881796733 -0.612080854895 +1403715928684058112.0000000000 -1.5881211008 0.3246291509 0.9687078920 0.0330007582 0.0677847405 0.7927098281 -0.604919256823 +1403715928734057984.0000000000 -1.6195152483 0.3717120770 0.9487305428 0.0397183990 0.0733906829 0.8005527025 -0.593423648851 +1403715928784058112.0000000000 -1.6505589329 0.4202063503 0.9326794149 0.0442724863 0.0771666824 0.8113365885 -0.577770014954 +1403715928834057984.0000000000 -1.6811168030 0.4690589865 0.9230531754 0.0460682221 0.0776352438 0.8227798839 -0.561145035192 +1403715928884058112.0000000000 -1.7110104420 0.5166675499 0.9202304304 0.0448359495 0.0755762624 0.8340944101 -0.54457734189 +1403715928934057984.0000000000 -1.7403355776 0.5622762645 0.9248911094 0.0416387761 0.0703092799 0.8435019475 -0.530874073649 +1403715928984058112.0000000000 -1.7693222813 0.6045719694 0.9366145014 0.0362032011 0.0628036335 0.8527059611 -0.517337004062 +1403715929034057984.0000000000 -1.7986913758 0.6418917305 0.9556638952 0.0304105114 0.0543753231 0.8602334686 -0.506079938898 +1403715929084058112.0000000000 -1.8287347935 0.6741296695 0.9803942998 0.0239751521 0.0463547340 0.8663799866 -0.496650933347 +1403715929134057984.0000000000 -1.8594951412 0.7011597675 1.0072920811 0.0199635315 0.0371702967 0.8716052931 -0.488389229583 +1403715929184058112.0000000000 -1.8903544501 0.7229715509 1.0342926245 0.0164216085 0.0279236386 0.8760513483 -0.481128502984 +1403715929234057984.0000000000 -1.9215045484 0.7387117603 1.0603182341 0.0157374024 0.0171942849 0.8788411573 -0.47654476277 +1403715929284058112.0000000000 -1.9529860763 0.7480033798 1.0844596552 0.0202902484 0.0037151134 0.8785879481 -0.477134908894 +1403715929334057984.0000000000 -1.9841176776 0.7509083408 1.1067903887 0.0298695848 -0.0125995074 0.8733261085 -0.486056137197 +1403715929384058112.0000000000 -2.0139320087 0.7485278759 1.1273220019 0.0437536128 -0.0311911117 0.8650543003 -0.49879233499 +1403715929434057984.0000000000 -2.0411358140 0.7418454725 1.1461044663 0.0596436591 -0.0496835596 0.8542622333 -0.514013827271 +1403715929484058112.0000000000 -2.0641032810 0.7318553871 1.1640068350 0.0755981312 -0.0666075123 0.8424326427 -0.529297274147 +1403715929534057984.0000000000 -2.0817684849 0.7193173688 1.1815324747 0.0923504826 -0.0825261036 0.8310386605 -0.542250472954 +1403715929584058112.0000000000 -2.0926116419 0.7052216547 1.1996534012 0.1066754749 -0.0947207936 0.8200724539 -0.554192642252 +1403715929634057984.0000000000 -2.0958000195 0.6911487507 1.2175322479 0.1182264026 -0.1029971616 0.8126982940 -0.561191220008 +1403715929684058112.0000000000 -2.0899336326 0.6779955651 1.2359168890 0.1177656118 -0.1002614806 0.8108679503 -0.564421884223 +1403715929734057984.0000000000 -2.0752378804 0.6652566266 1.2542695013 0.1066791417 -0.0885512641 0.8140790017 -0.563962421926 +1403715929784058112.0000000000 -2.0529618411 0.6518595991 1.2727329517 0.0899421792 -0.0727642410 0.8172293274 -0.564581257232 +1403715929834057984.0000000000 -2.0252496464 0.6379680096 1.2892331212 0.0731753203 -0.0574331706 0.8178803110 -0.567819161651 +1403715929884058112.0000000000 -1.9931602385 0.6238638910 1.3037882342 0.0527681602 -0.0399122083 0.8161735177 -0.574006381375 +1403715929934057984.0000000000 -1.9585168272 0.6099102138 1.3153594388 0.0317851779 -0.0218301021 0.8140250120 -0.579548469953 +1403715929984058112.0000000000 -1.9226685445 0.5958217320 1.3236416048 0.0134321776 -0.0058642864 0.8105354982 -0.585506099805 +1403715930034057984.0000000000 -1.8865659416 0.5818883649 1.3287390474 0.0020584091 -0.0077471847 -0.8075332059 0.589767636855 +1403715930084058112.0000000000 -1.8512120215 0.5692242387 1.3322042068 0.0178117545 -0.0215209520 -0.8046234685 0.593127864758 +1403715930134057984.0000000000 -1.8178092895 0.5578524724 1.3347026641 0.0302325072 -0.0327030136 -0.8017828741 0.595953631782 +1403715930184058112.0000000000 -1.7868787819 0.5477187365 1.3371349913 0.0417973731 -0.0433282993 -0.7992272698 0.598006195013 +1403715930234057984.0000000000 -1.7592712754 0.5390560309 1.3394960611 0.0509357940 -0.0521243991 -0.7977817806 0.598525540408 +1403715930284058112.0000000000 -1.7356718504 0.5321966295 1.3417125628 0.0571949824 -0.0590748452 -0.7964625351 0.599071220152 +1403715930334057984.0000000000 -1.7167481977 0.5271149094 1.3429478532 0.0576447313 -0.0616709624 -0.7972015430 0.597782131927 +1403715930384058112.0000000000 -1.7025102739 0.5234812775 1.3432580671 0.0544567836 -0.0612108512 -0.8007755634 0.593334802119 +1403715930434057984.0000000000 -1.6923695881 0.5209819250 1.3415061325 0.0477080682 -0.0579729516 -0.8063566563 0.58664471353 +1403715930484058112.0000000000 -1.6854796116 0.5198014705 1.3368974752 0.0404107640 -0.0547059722 -0.8127773777 0.578590667945 +1403715930534057984.0000000000 -1.6813921051 0.5188987629 1.3293778301 0.0342844852 -0.0518455868 -0.8182954457 0.571427311866 +1403715930584058112.0000000000 -1.6798789367 0.5177256879 1.3192545153 0.0291549287 -0.0495966893 -0.8246494534 0.562710793837 +1403715930634057984.0000000000 -1.6809472674 0.5157462225 1.3089188216 0.0251107327 -0.0482055943 -0.8301575018 0.554873133239 +1403715930684058112.0000000000 -1.6844873839 0.5123710343 1.3011288942 0.0237713670 -0.0486272783 -0.8347688430 0.547933653482 +1403715930734057984.0000000000 -1.6907897422 0.5064824417 1.2972433056 0.0233447710 -0.0497129803 -0.8372456201 0.544061956783 +1403715930784058112.0000000000 -1.6997791461 0.4983264118 1.2970365801 0.0224659082 -0.0506198556 -0.8391654650 0.541049198873 +1403715930834057984.0000000000 -1.7116293142 0.4875473557 1.3003575433 0.0172684646 -0.0479837585 -0.8410171969 0.538599511235 +1403715930884058112.0000000000 -1.7258617625 0.4746736076 1.3074090522 0.0078885978 -0.0421779014 -0.8430240200 0.536161632674 +1403715930934057984.0000000000 -1.7417552673 0.4596575750 1.3180295447 0.0020850706 0.0358950311 0.8439367275 -0.535236395546 +1403715930984058112.0000000000 -1.7582219713 0.4424317857 1.3298797776 0.0100772533 0.0305428317 0.8457506318 -0.532608161086 +1403715931034057984.0000000000 -1.7748089446 0.4230120754 1.3407574145 0.0157668204 0.0271388639 0.8490388426 -0.52739732 +1403715931084058112.0000000000 -1.7911770836 0.4005344439 1.3495144625 0.0194847990 0.0252842730 0.8526441536 -0.521516054838 +1403715931134057984.0000000000 -1.8069836791 0.3750761368 1.3557679760 0.0212559967 0.0245731195 0.8561955673 -0.515629222393 +1403715931184058112.0000000000 -1.8222297135 0.3462126058 1.3618110780 0.0223219227 0.0238482423 0.8585612330 -0.511669426837 +1403715931234057984.0000000000 -1.8370286630 0.3130830287 1.3702520559 0.0229056260 0.0239675982 0.8593640069 -0.510288536214 +1403715931284058112.0000000000 -1.8513346123 0.2759286096 1.3818844973 0.0230555152 0.0243658979 0.8596280295 -0.509818003909 +1403715931334057984.0000000000 -1.8649338838 0.2349137042 1.3974809805 0.0209165932 0.0261682851 0.8583245124 -0.512012449393 +1403715931384058112.0000000000 -1.8783035072 0.1896742880 1.4170487052 0.0192748114 0.0274196660 0.8565434305 -0.514985431982 +1403715931434057984.0000000000 -1.8915800038 0.1405612444 1.4391797471 0.0189979303 0.0270211996 0.8542270477 -0.518849770593 +1403715931484058112.0000000000 -1.9046415270 0.0886159751 1.4605452350 0.0176091635 0.0271699392 0.8524272852 -0.521842347048 +1403715931534057984.0000000000 -1.9176386367 0.0339214206 1.4795859276 0.0174944510 0.0261251325 0.8506049300 -0.524864434588 +1403715931584058112.0000000000 -1.9301500060 -0.0235216038 1.4954651339 0.0183954170 0.0239248382 0.8484047046 -0.52848715027 +1403715931634057984.0000000000 -1.9419057244 -0.0829715245 1.5074575998 0.0192771388 0.0213931038 0.8469416703 -0.530905390906 +1403715931684058112.0000000000 -1.9529957945 -0.1440795209 1.5159849080 0.0210384779 0.0177827186 0.8448773101 -0.534250398514 +1403715931734057984.0000000000 -1.9633094700 -0.2068868832 1.5211021255 0.0225559086 0.0144077489 0.8434482285 -0.536543319335 +1403715931784058112.0000000000 -1.9729141919 -0.2710746501 1.5234913982 0.0231983830 0.0114010042 0.8419058878 -0.539004942694 +1403715931834057984.0000000000 -1.9816296696 -0.3367979827 1.5258568224 0.0216223128 0.0099552437 0.8393696540 -0.543039549829 +1403715931884058112.0000000000 -1.9895295939 -0.4044503935 1.5292242224 0.0206955085 0.0080969587 0.8344889516 -0.550576356903 +1403715931934057984.0000000000 -1.9966218411 -0.4731131871 1.5330249740 0.0196164048 0.0066243239 0.8292719518 -0.558461587762 +1403715931984058112.0000000000 -2.0030319017 -0.5423238484 1.5373517642 0.0189570088 0.0050597456 0.8232336341 -0.567363564646 +1403715932034057984.0000000000 -2.0084664569 -0.6115819586 1.5423962267 0.0163575455 0.0049053596 0.8169882950 -0.57640133065 +1403715932084058112.0000000000 -2.0132383334 -0.6803792308 1.5486118514 0.0154399689 0.0038151571 0.8089776078 -0.587624269396 +1403715932134057984.0000000000 -2.0172138696 -0.7478321499 1.5564310548 0.0153976529 0.0024975661 0.7990110330 -0.601114002176 +1403715932184058112.0000000000 -2.0203225999 -0.8130705040 1.5654867792 0.0162075286 0.0013476336 0.7883287578 -0.615039242255 +1403715932234057984.0000000000 -2.0223819512 -0.8753604461 1.5762440650 0.0179900554 -0.0004463451 0.7756642180 -0.630889197599 +1403715932284058112.0000000000 -2.0233220825 -0.9340223741 1.5883957054 0.0177890999 -0.0005560515 0.7626001442 -0.646625284694 +1403715932334057984.0000000000 -2.0232680304 -0.9878735957 1.6010029986 0.0174271956 -0.0003794084 0.7503729261 -0.660784852071 +1403715932384058112.0000000000 -2.0222862788 -1.0357946178 1.6136617578 0.0174748176 -0.0004611787 0.7394116842 -0.673026581457 +1403715932434057984.0000000000 -2.0205104338 -1.0768010172 1.6260403237 0.0171725029 -0.0000203973 0.7307205343 -0.682460698851 +1403715932484058112.0000000000 -2.0177821122 -1.1101418424 1.6384790389 0.0156632965 0.0006014148 0.7232987772 -0.690357283089 +1403715932534057984.0000000000 -2.0145622918 -1.1354729683 1.6517459906 0.0144884268 0.0012760729 0.7155370727 -0.69842333491 +1403715932584058112.0000000000 -2.0109127753 -1.1520928498 1.6659862689 0.0135070061 0.0020145475 0.7069022803 -0.707179375091 +1403715932634057984.0000000000 -2.0066714654 -1.1592871125 1.6809100799 0.0111773719 0.0032891874 0.6986586050 -0.715360329642 +1403715932684058112.0000000000 -2.0021542634 -1.1566642288 1.6963869991 0.0100140088 0.0042456562 0.6918041299 -0.722003282463 +1403715932734057984.0000000000 -1.9972339398 -1.1433206980 1.7120032722 0.0097447552 0.0046040664 0.6854815385 -0.728010235296 +1403715932784058112.0000000000 -1.9921210326 -1.1194523970 1.7272975999 0.0104488229 0.0049578938 0.6822037152 -0.731070675321 +1403715932834057984.0000000000 -1.9869371014 -1.0844746090 1.7422748743 0.0116532202 0.0054205726 0.6841248765 -0.729251652884 +1403715932884058112.0000000000 -1.9816404662 -1.0390470211 1.7557254438 0.0144923421 0.0057268689 0.6942069023 -0.719606803618 +1403715932934057984.0000000000 -1.9759293624 -0.9833169352 1.7681769946 0.0163016100 0.0070517356 0.7114631454 -0.702498913364 +1403715932984058112.0000000000 -1.9697088363 -0.9187530008 1.7800279061 0.0177688043 0.0088579470 0.7329299226 -0.680014363746 +1403715933034057984.0000000000 -1.9627402170 -0.8471464080 1.7921023804 0.0191202108 0.0104236362 0.7536539545 -0.656910558733 +1403715933084058112.0000000000 -1.9553115184 -0.7706991270 1.8047032447 0.0205977058 0.0118316296 0.7726633097 -0.634371466065 +1403715933134057984.0000000000 -1.9474616969 -0.6908755626 1.8174692322 0.0216519581 0.0133290105 0.7906175140 -0.611782213486 +1403715933184058112.0000000000 -1.9391395182 -0.6089749905 1.8298119531 0.0221479905 0.0147228111 0.8084766283 -0.587927076186 +1403715933234057984.0000000000 -1.9303473234 -0.5267137407 1.8423985631 0.0227238947 0.0156851790 0.8240827194 -0.565796139366 +1403715933284058112.0000000000 -1.9210959093 -0.4454409995 1.8548287896 0.0224949514 0.0169467135 0.8391983118 -0.543095737062 +1403715933334057984.0000000000 -1.9112560031 -0.3665548261 1.8677006102 0.0201652874 0.0196930879 0.8532928251 -0.52066966321 +1403715933384058112.0000000000 -1.9010294336 -0.2912601155 1.8806287452 0.0154155572 0.0242176385 0.8668457361 -0.497749270533 +1403715933434057984.0000000000 -1.8911626118 -0.2210517633 1.8934221340 0.0097851902 0.0298773603 0.8798005053 -0.474302292129 +1403715933484058112.0000000000 -1.8817740233 -0.1573799798 1.9064533407 0.0038910362 0.0357960425 0.8917184796 -0.451155911264 +1403715933534057984.0000000000 -1.8731459745 -0.1025473074 1.9204044866 0.0005755306 -0.0409859619 -0.9018175608 0.430168463107 +1403715933584058112.0000000000 -1.8659918854 -0.0575821245 1.9354502285 0.0026039370 -0.0439333812 -0.9101117424 0.412019045493 +1403715933634057984.0000000000 -1.8605121643 -0.0233814937 1.9516766131 0.0034573444 -0.0464830666 -0.9169904514 0.396176580884 +1403715933684058112.0000000000 -1.8571761988 -0.0013563597 1.9692813540 0.0006104819 -0.0457308714 -0.9217397280 0.385102828506 +1403715933734057984.0000000000 -1.8556266536 0.0077838201 1.9886188188 0.0038970314 0.0433472744 0.9251553983 -0.377085289967 +1403715933784058112.0000000000 -1.8555441766 0.0024986864 2.0105283681 0.0080709995 0.0414930112 0.9265792350 -0.37371661754 +1403715933834057984.0000000000 -1.8568150425 -0.0169895983 2.0349803468 0.0125437206 0.0394366250 0.9258979064 -0.375500299116 +1403715933884058112.0000000000 -1.8590240029 -0.0511619502 2.0620069828 0.0168634174 0.0375364259 0.9215170799 -0.386151412467 +1403715933934057984.0000000000 -1.8616883694 -0.0989306469 2.0928737811 0.0195448177 0.0380719315 0.9122821129 -0.407320358605 +1403715933984058112.0000000000 -1.8647579596 -0.1591256685 2.1280601882 0.0234725946 0.0370550479 0.8969847425 -0.43987990686 +1403715934034057984.0000000000 -1.8678260966 -0.2278668040 2.1656204031 0.0257651882 0.0379295308 0.8777765808 -0.476870821106 +1403715934084058112.0000000000 -1.8710658665 -0.3018682085 2.2041420657 0.0295537682 0.0368375034 0.8553669214 -0.51586529533 +1403715934134057984.0000000000 -1.8740816815 -0.3776886603 2.2410783816 0.0312084443 0.0375556659 0.8305353092 -0.554821327274 +1403715934184058112.0000000000 -1.8768265300 -0.4537235406 2.2738561069 0.0336369724 0.0375708600 0.8034444459 -0.593240260712 +1403715934234057984.0000000000 -1.8789904759 -0.5275296010 2.2993432462 0.0356589710 0.0377431336 0.7798021927 -0.623868923709 +1403715934284058112.0000000000 -1.8805434221 -0.5978261751 2.3190550289 0.0384152427 0.0365408781 0.7583719356 -0.649662251181 +1403715934334057984.0000000000 -1.8814753402 -0.6632580558 2.3345105616 0.0389599854 0.0366439303 0.7402818416 -0.670165753299 +1403715934384058112.0000000000 -1.8819772850 -0.7225466133 2.3469338578 0.0390182298 0.0364765123 0.7232960850 -0.688469182494 +1403715934434057984.0000000000 -1.8817947957 -0.7745768610 2.3561470139 0.0399779990 0.0354735250 0.7076921215 -0.70449645118 +1403715934484058112.0000000000 -1.8807060830 -0.8179702074 2.3627914000 0.0398213824 0.0349858978 0.6933126538 -0.718684776844 +1403715934534057984.0000000000 -1.8787808396 -0.8520818156 2.3676438582 0.0389858496 0.0342122550 0.6806127126 -0.730805008567 +1403715934584058112.0000000000 -1.8761806219 -0.8754712548 2.3708427757 0.0378738428 0.0333880009 0.6686545756 -0.741857042764 +1403715934634057984.0000000000 -1.8728287855 -0.8865485945 2.3733490230 0.0362088352 0.0326632775 0.6589528601 -0.750601864277 +1403715934684058112.0000000000 -1.8684437481 -0.8841965264 2.3764028194 0.0334879872 0.0320220697 0.6521721762 -0.756653549744 +1403715934734057984.0000000000 -1.8631310738 -0.8682370229 2.3804145964 0.0293459170 0.0320952503 0.6480115187 -0.760387916572 +1403715934784058112.0000000000 -1.8572160769 -0.8375805448 2.3861366081 0.0243045223 0.0326199188 0.6463977259 -0.761915488099 +1403715934834057984.0000000000 -1.8510266156 -0.7924150843 2.3917791283 0.0204411355 0.0326924835 0.6534410668 -0.755994797408 +1403715934884058112.0000000000 -1.8450664925 -0.7341853760 2.3968920608 0.0195536699 0.0318765395 0.6712281463 -0.740306906476 +1403715934934057984.0000000000 -1.8389910623 -0.6637074066 2.4033357163 0.0184605945 0.0315721399 0.6948573212 -0.718217035166 +1403715934984058112.0000000000 -1.8330494224 -0.5832439081 2.4097046092 0.0161754560 0.0324772857 0.7197452273 -0.693289541501 +1403715935034057984.0000000000 -1.8275519434 -0.4960914443 2.4144383417 0.0149081818 0.0332604927 0.7447103437 -0.666391768926 +1403715935084058112.0000000000 -1.8224219337 -0.4037164991 2.4161662837 0.0137743612 0.0343281296 0.7693857241 -0.63771267358 +1403715935134057984.0000000000 -1.8178521289 -0.3080484861 2.4155115462 0.0144254839 0.0348232050 0.7912772357 -0.610294671457 +1403715935184058112.0000000000 -1.8132351426 -0.2102948810 2.4126340662 0.0142713522 0.0358490903 0.8112480296 -0.583427635387 +1403715935234057984.0000000000 -1.8090984972 -0.1122591675 2.4067112802 0.0151265353 0.0362240419 0.8276914747 -0.559808743561 +1403715935284058112.0000000000 -1.8055457005 -0.0159569055 2.3973935741 0.0156970579 0.0365550243 0.8415793840 -0.538666383733 +1403715935334057984.0000000000 -1.8024268210 0.0777987659 2.3850395426 0.0171155832 0.0359471485 0.8534803630 -0.519601895001 +1403715935384058112.0000000000 -1.7995601664 0.1680320316 2.3706010358 0.0182020853 0.0354112928 0.8630371917 -0.503568793888 +1403715935434057984.0000000000 -1.7967991490 0.2537850284 2.3539473982 0.0196253401 0.0344522650 0.8714021217 -0.488964446293 +1403715935484058112.0000000000 -1.7941845562 0.3341054057 2.3348289449 0.0204321024 0.0340529355 0.8780954661 -0.476834645527 +1403715935534057984.0000000000 -1.7917825780 0.4077353237 2.3134672750 0.0216481798 0.0331516561 0.8834671776 -0.466816955661 +1403715935584058112.0000000000 -1.7895520657 0.4744438530 2.2908168096 0.0229085523 0.0321220872 0.8875350654 -0.459047794263 +1403715935634057984.0000000000 -1.7871468017 0.5336217219 2.2680014291 0.0229679036 0.0321091316 0.8916764984 -0.450948446446 +1403715935684058112.0000000000 -1.7848502912 0.5847687009 2.2456824691 0.0231481543 0.0319972293 0.8957583973 -0.442783506749 +1403715935734057984.0000000000 -1.7825488583 0.6270703113 2.2240028980 0.0239359711 0.0314108176 0.8999825049 -0.434133528736 +1403715935784058112.0000000000 -1.7800363750 0.6598678732 2.2032914124 0.0238590677 0.0317874154 0.9039475618 -0.425792332688 +1403715935834057984.0000000000 -1.7774875070 0.6824963164 2.1843103689 0.0250270507 0.0312507722 0.9072554959 -0.418669919047 +1403715935884058112.0000000000 -1.7748337749 0.6946192810 2.1674902978 0.0259404360 0.0311422540 0.9096614549 -0.413368227146 +1403715935934057984.0000000000 -1.7723351903 0.6955686870 2.1530246358 0.0269724216 0.0315613577 0.9098339636 -0.412890454922 +1403715935984058112.0000000000 -1.7699258966 0.6847673884 2.1415425176 0.0281581034 0.0317561221 0.9060393803 -0.421059747763 +1403715936034057984.0000000000 -1.7674844537 0.6630413166 2.1335131154 0.0296770885 0.0321553263 0.8972690105 -0.439310400695 +1403715936084058112.0000000000 -1.7651622014 0.6325915096 2.1281111497 0.0315296020 0.0328590071 0.8842913431 -0.464709576392 +1403715936134057984.0000000000 -1.7627494454 0.5953476532 2.1245684138 0.0348555097 0.0319628587 0.8682030401 -0.493950352034 +1403715936184058112.0000000000 -1.7598907472 0.5534271371 2.1220355032 0.0375630206 0.0320481665 0.8507826059 -0.523192977723 +1403715936234057984.0000000000 -1.7565154696 0.5086748824 2.1201043479 0.0406363528 0.0319512291 0.8322018392 -0.552057881573 +1403715936284058112.0000000000 -1.7521066164 0.4624375950 2.1187509249 0.0428165874 0.0322836359 0.8127327397 -0.58016377038 +1403715936334057984.0000000000 -1.7468539939 0.4170257303 2.1162011798 0.0435766290 0.0341100960 0.7959744707 -0.602795338971 +1403715936384058112.0000000000 -1.7406795305 0.3737683302 2.1128104465 0.0416995575 0.0375533725 0.7812100281 -0.621740929301 +1403715936434057984.0000000000 -1.7337944498 0.3339606824 2.1074663489 0.0414380220 0.0398368972 0.7704162278 -0.634944680961 +1403715936484058112.0000000000 -1.7261762939 0.2987343167 2.1009872141 0.0407398925 0.0420754983 0.7629639297 -0.643782537549 +1403715936534057984.0000000000 -1.7180554588 0.2680898992 2.0942939568 0.0387290369 0.0450591269 0.7564507194 -0.651346333299 +1403715936584058112.0000000000 -1.7098596991 0.2426978209 2.0873635849 0.0359647153 0.0484153081 0.7511010857 -0.65742654059 +1403715936634057984.0000000000 -1.7015490028 0.2227494449 2.0809697137 0.0324936857 0.0517634147 0.7464848257 -0.662589702822 +1403715936684058112.0000000000 -1.6931443473 0.2088388174 2.0750124661 0.0289918112 0.0551928876 0.7430053747 -0.666375444582 +1403715936734057984.0000000000 -1.6850295913 0.2013269755 2.0682248964 0.0289599884 0.0562604832 0.7437752528 -0.665428020492 +1403715936784058112.0000000000 -1.6771195492 0.2002137016 2.0601806837 0.0298637214 0.0562888522 0.7490422668 -0.659450836556 +1403715936834057984.0000000000 -1.6695960586 0.2042981491 2.0518698671 0.0330384027 0.0549126807 0.7563345372 -0.651038500665 +1403715936884058112.0000000000 -1.6621971510 0.2127138467 2.0438808092 0.0355935875 0.0539082741 0.7627672382 -0.643438524482 +1403715936934057984.0000000000 -1.6546835963 0.2252674312 2.0358517762 0.0365150320 0.0537724835 0.7690031042 -0.635931913189 +1403715936984058112.0000000000 -1.6470650762 0.2413916274 2.0280388214 0.0359164289 0.0527751137 0.7740752581 -0.62986688461 +1403715937034057984.0000000000 -1.6392690674 0.2607427018 2.0201515853 0.0344308323 0.0501487176 0.7792245522 -0.623785797473 +1403715937084058112.0000000000 -1.6312543933 0.2829750430 2.0116355469 0.0317565510 0.0462993328 0.7854526373 -0.61637005758 +1403715937134057984.0000000000 -1.6231757566 0.3077214956 2.0025081616 0.0270506904 0.0415954844 0.7930299826 -0.607158564557 +1403715937184058112.0000000000 -1.6147421391 0.3341123244 1.9938452683 0.0217288457 0.0350670936 0.7986673611 -0.600357062529 +1403715937234057984.0000000000 -1.6061306945 0.3616680037 1.9846015276 0.0166881171 0.0269916396 0.8034685910 -0.594500783396 +1403715937284058112.0000000000 -1.5972328555 0.3902299180 1.9731987850 0.0092902758 0.0182359777 0.8074239070 -0.589616633292 +1403715937334057984.0000000000 -1.5884043545 0.4194344606 1.9594206127 0.0035854160 0.0069627061 0.8096583883 -0.586849179814 +1403715937384058112.0000000000 -1.5795461055 0.4490873813 1.9432284329 0.0033230518 0.0043148601 -0.8105513489 0.585642254406 +1403715937434057984.0000000000 -1.5707349455 0.4792209741 1.9243171029 0.0107429080 0.0155743779 -0.8111992391 0.584463705658 +1403715937484058112.0000000000 -1.5621727459 0.5095649818 1.9018658989 0.0171472970 0.0263266755 -0.8136571336 0.580495430902 +1403715937534057984.0000000000 -1.5538074833 0.5403957698 1.8754560054 0.0245181547 0.0348237713 -0.8196496548 0.571279798715 +1403715937584058112.0000000000 -1.5457624912 0.5705925423 1.8463159459 0.0291533312 0.0443602594 -0.8276283007 0.558760813295 +1403715937634057984.0000000000 -1.5374617486 0.5989411810 1.8173244928 0.0339694932 0.0542507834 -0.8351171876 0.546335253272 +1403715937684058112.0000000000 -1.5292806489 0.6253167803 1.7887152865 0.0392659004 0.0636184757 -0.8412075133 0.535519185625 +1403715937734057984.0000000000 -1.5208300567 0.6490730854 1.7604053783 0.0436716243 0.0729458865 -0.8455844725 0.527028070209 +1403715937784058112.0000000000 -1.5118623592 0.6698871380 1.7331966169 0.0494210427 0.0814385538 -0.8484619951 0.520612682735 +1403715937834057984.0000000000 -1.5025550547 0.6873420953 1.7061922122 0.0538606049 0.0910852697 -0.8504187050 0.51535476619 +1403715937884058112.0000000000 -1.4923280167 0.7010166451 1.6806784367 0.0600287467 0.0992313230 -0.8515294350 0.511319191412 +1403715937934057984.0000000000 -1.4814648324 0.7112390916 1.6554218268 0.0646084793 0.1089963932 -0.8519585629 0.508047377525 +1403715937984058112.0000000000 -1.4694641438 0.7177278147 1.6305099948 0.0691101374 0.1195140970 -0.8521793316 0.50470838744 +1403715938034057984.0000000000 -1.4562688943 0.7201102314 1.6066938545 0.0752645892 0.1293967860 -0.8519701259 0.501735605679 +1403715938084058112.0000000000 -1.4417842773 0.7180573465 1.5841939690 0.0809545429 0.1397893760 -0.8519333322 0.498111322741 +1403715938134057984.0000000000 -1.4257515456 0.7112822656 1.5645967634 0.0864414397 0.1509969637 -0.8512114351 0.495143299603 +1403715938184058112.0000000000 -1.4078843230 0.6998462944 1.5485666798 0.0924161598 0.1625759148 -0.8505256363 0.491563289253 +1403715938234057984.0000000000 -1.3878346558 0.6830255944 1.5376273972 0.0988135575 0.1740159711 -0.8474033744 0.49179451375 +1403715938284058112.0000000000 -1.3658181963 0.6610180454 1.5311721597 0.1035940031 0.1877539489 -0.8408118000 0.497043513407 +1403715938334057984.0000000000 -1.3418697704 0.6347088918 1.5294096675 0.1078637508 0.2021790798 -0.8305375294 0.507638102557 +1403715938384058112.0000000000 -1.3155686231 0.6052064400 1.5314851097 0.1119113671 0.2169891642 -0.8197162872 0.518128127983 +1403715938434057984.0000000000 -1.2871621506 0.5742878483 1.5359277679 0.1199439548 0.2284625440 -0.8100532298 0.526528326408 +1403715938484058112.0000000000 -1.2570455001 0.5424440045 1.5419582030 0.1294068763 0.2392300888 -0.7998467829 0.535040137613 +1403715938534057984.0000000000 -1.2252568437 0.5100846570 1.5474368018 0.1398741439 0.2482187531 -0.7918950931 0.540115576525 +1403715938584058112.0000000000 -1.1926267873 0.4776993588 1.5515852161 0.1495085968 0.2559898336 -0.7854089512 0.543368350116 +1403715938634057984.0000000000 -1.1595464932 0.4452273843 1.5545427197 0.1569281454 0.2624907960 -0.7811664151 0.544289602241 +1403715938684058112.0000000000 -1.1257495621 0.4124783579 1.5568870583 0.1629606723 0.2680631100 -0.7795080478 0.542174503044 +1403715938734057984.0000000000 -1.0917095630 0.3795856533 1.5577029953 0.1658734117 0.2733102338 -0.7815114850 0.53574931286 +1403715938784058112.0000000000 -1.0573446195 0.3464949512 1.5579088810 0.1660827846 0.2789033031 -0.7856380368 0.526689976432 +1403715938834057984.0000000000 -1.0215806952 0.3124501124 1.5575289768 0.1654574360 0.2837435954 -0.7914895805 0.515419880179 +1403715938884058112.0000000000 -0.9845061604 0.2772431441 1.5565379890 0.1645611911 0.2878718015 -0.7973699716 0.504232653266 +1403715938934057984.0000000000 -0.9458108471 0.2405503075 1.5552230746 0.1632877463 0.2917091530 -0.8023967371 0.494370668936 +1403715938984058112.0000000000 -0.9049491423 0.2017870659 1.5532222275 0.1626960454 0.2946363301 -0.8070088561 0.485238226077 +1403715939034057984.0000000000 -0.8619523555 0.1605388726 1.5506180347 0.1622676856 0.2971610467 -0.8107036174 0.477623445087 +1403715939084058112.0000000000 -0.8164038611 0.1163655875 1.5476340540 0.1611986416 0.2998629811 -0.8130368978 0.47230095626 +1403715939134057984.0000000000 -0.7675085201 0.0688396037 1.5457492437 0.1622367891 0.3012548812 -0.8120956184 0.47267898982 +1403715939184058112.0000000000 -0.7151361300 0.0175350178 1.5457045081 0.1663129731 0.3005312976 -0.8059159850 0.482203649248 +1403715939234057984.0000000000 -0.6596408216 -0.0369390490 1.5474308767 0.1728754056 0.2979712501 -0.7951576394 0.499050655513 +1403715939284058112.0000000000 -0.6021762125 -0.0931381061 1.5496447757 0.1800829438 0.2948427557 -0.7828193746 0.517524598034 +1403715939334057984.0000000000 -0.5437947877 -0.1499297473 1.5518058778 0.1874645338 0.2907411746 -0.7700056655 0.536113694194 +1403715939384058112.0000000000 -0.4849798929 -0.2065801935 1.5535345625 0.1952653090 0.2857012817 -0.7565733785 0.554835975496 +1403715939434057984.0000000000 -0.4271001502 -0.2619114537 1.5543024910 0.2014650184 0.2809833225 -0.7441316654 0.571601507507 +1403715939484058112.0000000000 -0.3707301633 -0.3149866691 1.5544595143 0.2070580109 0.2765620547 -0.7326007497 0.586461040136 +1403715939534057984.0000000000 -0.3164435069 -0.3653769831 1.5544709369 0.2108919414 0.2726517916 -0.7216008597 0.600398025374 +1403715939584058112.0000000000 -0.2649036953 -0.4120656797 1.5549315192 0.2146738467 0.2681346858 -0.7115468927 0.612959990015 +1403715939634057984.0000000000 -0.2167810891 -0.4543938505 1.5579675776 0.2194593285 0.2624298130 -0.6980702183 0.629020004964 +1403715939684058112.0000000000 -0.1731626957 -0.4911813973 1.5633536008 0.2245828923 0.2560536020 -0.6844309735 0.644634252835 +1403715939734057984.0000000000 -0.1350522620 -0.5213384205 1.5702917127 0.2284768715 0.2502230634 -0.6723830867 0.658094007285 +1403715939784058112.0000000000 -0.1027502863 -0.5444795960 1.5791162383 0.2317385238 0.2448395463 -0.6631427917 0.668275759626 +1403715939834057984.0000000000 -0.0767867597 -0.5601716389 1.5902551299 0.2331674098 0.2407005344 -0.6557745694 0.676502716769 +1403715939884058112.0000000000 -0.0579407402 -0.5670401857 1.6038280887 0.2338598087 0.2376131441 -0.6506243586 0.682303105338 +1403715939934057984.0000000000 -0.0463002830 -0.5647022454 1.6195649149 0.2327338167 0.2362836698 -0.6497334254 0.683996691464 +1403715939984058112.0000000000 -0.0416958703 -0.5536204938 1.6377326014 0.2300544321 0.2368725989 -0.6535065469 0.681098761751 +1403715940034057984.0000000000 -0.0436815853 -0.5342408637 1.6563057659 0.2229924367 0.2413732216 -0.6665311026 0.669140964481 +1403715940084058112.0000000000 -0.0516557223 -0.5071188454 1.6756475981 0.2149303019 0.2475580648 -0.6845072792 0.651129598889 +1403715940134057984.0000000000 -0.0644923466 -0.4736620778 1.6962029821 0.2057238199 0.2544099616 -0.7041410790 0.630189354218 +1403715940184058112.0000000000 -0.0810003228 -0.4350572774 1.7177327444 0.1972878511 0.2608471645 -0.7226739087 0.60891598952 +1403715940234057984.0000000000 -0.0998576775 -0.3925638638 1.7391833777 0.1887078199 0.2669599667 -0.7402056764 0.587551947979 +1403715940284058112.0000000000 -0.1199008206 -0.3474017678 1.7603929875 0.1813150838 0.2724635749 -0.7569078498 0.565666816822 +1403715940334057984.0000000000 -0.1401595528 -0.3008509097 1.7813711665 0.1742199306 0.2777922209 -0.7730103768 0.543078129847 +1403715940384058112.0000000000 -0.1596762356 -0.2543761895 1.8022751592 0.1677061921 0.2822536373 -0.7875631736 0.521489947192 +1403715940434057984.0000000000 -0.1780588187 -0.2087414542 1.8221293241 0.1604985218 0.2867334248 -0.8019115820 0.498960902538 +1403715940484058112.0000000000 -0.1940809722 -0.1651970268 1.8414526576 0.1538865245 0.2905467831 -0.8151400228 0.476915346351 +1403715940534057984.0000000000 -0.2068639831 -0.1246706602 1.8602914674 0.1485967547 0.2929250250 -0.8283528072 0.45381225306 +1403715940584058112.0000000000 -0.2154999584 -0.0884669763 1.8787980335 0.1437700552 0.2943080449 -0.8416411580 0.429363607054 +1403715940634057984.0000000000 -0.2194408072 -0.0578000805 1.8968310173 0.1388453488 0.2952481695 -0.8541175882 0.405010657948 +1403715940684058112.0000000000 -0.2174612673 -0.0340548082 1.9150156563 0.1357466566 0.2944077955 -0.8655533372 0.381725445447 +1403715940734057984.0000000000 -0.2093969502 -0.0193017677 1.9338289921 0.1310125466 0.2957464484 -0.8734352954 0.363978757256 +1403715940784058112.0000000000 -0.1946265914 -0.0144412268 1.9534777533 0.1251036756 0.2988436068 -0.8780378041 0.352265785378 +1403715940834057984.0000000000 -0.1717425878 -0.0206809726 1.9744760409 0.1207478295 0.3015036940 -0.8796291128 0.347517061499 +1403715940884058112.0000000000 -0.1399374102 -0.0386325628 1.9975620808 0.1184055798 0.3032330111 -0.8774280817 0.352349004532 +1403715940934057984.0000000000 -0.0984966783 -0.0682462354 2.0231563379 0.1203782891 0.3024990807 -0.8711623880 0.367531587035 +1403715940984058112.0000000000 -0.0485738602 -0.1083177258 2.0520854226 0.1270417777 0.2986613544 -0.8594297807 0.395021814845 +1403715941034057984.0000000000 0.0077705655 -0.1560188852 2.0826344358 0.1362798085 0.2934370191 -0.8435544895 0.428647119333 +1403715941084058112.0000000000 0.0690525639 -0.2094710361 2.1147627809 0.1474327996 0.2865717707 -0.8229029692 0.467943258368 +1403715941134057984.0000000000 0.1331328195 -0.2656834924 2.1483433902 0.1614836452 0.2765247012 -0.7989039928 0.509126243861 +1403715941184058112.0000000000 0.1981007110 -0.3225185245 2.1820722177 0.1743288933 0.2666486448 -0.7723216464 0.54957002439 +1403715941234057984.0000000000 0.2622383276 -0.3777759300 2.2138422490 0.1859506499 0.2567991874 -0.7486874879 0.582188610897 +1403715941284058112.0000000000 0.3243400657 -0.4298611542 2.2442182483 0.1979210343 0.2467635385 -0.7282579921 0.60792706565 +1403715941334057984.0000000000 0.3831789443 -0.4779767821 2.2724346867 0.2072836403 0.2387847824 -0.7117408473 0.627248185662 +1403715941384058112.0000000000 0.4383559107 -0.5214797496 2.2986055304 0.2152483562 0.2315980780 -0.6976290044 0.642918538929 +1403715941434057984.0000000000 0.4894861979 -0.5600550928 2.3212079849 0.2228753294 0.2250354339 -0.6854112495 0.655665356751 +1403715941484058112.0000000000 0.5361474084 -0.5940229369 2.3376695620 0.2288156271 0.2203725231 -0.6777371643 0.663137765445 +1403715941534057984.0000000000 0.5777677396 -0.6232703844 2.3482131049 0.2338058519 0.2164369606 -0.6711343571 0.669379220192 +1403715941584058112.0000000000 0.6139559465 -0.6472591598 2.3533744179 0.2384763110 0.2129686922 -0.6652689724 0.674678130363 +1403715941634057984.0000000000 0.6440377290 -0.6655972449 2.3544206628 0.2444755876 0.2083462581 -0.6578096313 0.681256201945 +1403715941684058112.0000000000 0.6668788511 -0.6772550956 2.3527025992 0.2512814594 0.2030565906 -0.6496539657 0.688168129178 +1403715941734057984.0000000000 0.6816925929 -0.6816684887 2.3492640975 0.2584643417 0.1976289480 -0.6407006984 0.695443454255 +1403715941784058112.0000000000 0.6879628354 -0.6787433829 2.3442976323 0.2645261529 0.1928670631 -0.6312999069 0.70305663921 +1403715941834057984.0000000000 0.6851945646 -0.6681978537 2.3380223939 0.2684879637 0.1895498787 -0.6237700686 0.709151576405 +1403715941884058112.0000000000 0.6724744948 -0.6489676201 2.3301134539 0.2707213967 0.1881303601 -0.6196603105 0.71227662643 +1403715941934057984.0000000000 0.6498891429 -0.6212266193 2.3198475314 0.2668254145 0.1907460981 -0.6212495828 0.711666410708 +1403715941984058112.0000000000 0.6176609396 -0.5847023998 2.3068969814 0.2602831164 0.1966785505 -0.6315848458 0.703328393864 +1403715942034057984.0000000000 0.5767580619 -0.5402857433 2.2906579667 0.2495812354 0.2063108446 -0.6490513730 0.688387505344 +1403715942084058112.0000000000 0.5283113329 -0.4889066763 2.2720941194 0.2380278622 0.2169267700 -0.6704983556 0.668369260545 +1403715942134057984.0000000000 0.4740327049 -0.4316543540 2.2505017308 0.2264374598 0.2277562265 -0.6939281047 0.644450900826 +1403715942184058112.0000000000 0.4156116186 -0.3703593514 2.2248425542 0.2149597637 0.2380779633 -0.7168184187 0.619098165123 +1403715942234057984.0000000000 0.3541568974 -0.3060323507 2.1942222417 0.2044804825 0.2472751290 -0.7383961706 0.593138970348 +1403715942284058112.0000000000 0.2905512087 -0.2398940489 2.1567195467 0.1932548766 0.2562740108 -0.7611225889 0.563620961997 +1403715942334057984.0000000000 0.2264795481 -0.1733078223 2.1145737224 0.1832335924 0.2635553416 -0.7803458116 0.536679091095 +1403715942384058112.0000000000 0.1634251112 -0.1076111877 2.0684339951 0.1752311215 0.2691392402 -0.7964949266 0.512302601372 +1403715942434057984.0000000000 0.1019797751 -0.0441788866 2.0193575547 0.1696506800 0.2727361619 -0.8087300761 0.492736538928 +1403715942484058112.0000000000 0.0429648499 0.0165291074 1.9680427971 0.1657515439 0.2752954055 -0.8203670877 0.473008146747 +1403715942534057984.0000000000 -0.0132232272 0.0732120313 1.9160605574 0.1616140393 0.2779293412 -0.8297471647 0.456240973893 +1403715942584058112.0000000000 -0.0661399024 0.1253423747 1.8641290414 0.1561107817 0.2819064279 -0.8382634345 0.439855208072 +1403715942634057984.0000000000 -0.1149636369 0.1718483518 1.8125556906 0.1496829203 0.2868881470 -0.8451807317 0.425393635588 +1403715942684058112.0000000000 -0.1590476073 0.2122547511 1.7620309827 0.1439486552 0.2915527434 -0.8505207637 0.413388694691 +1403715942734057984.0000000000 -0.1970238043 0.2454407337 1.7125721650 0.1399706096 0.2953784126 -0.8536068951 0.405604598694 +1403715942784058112.0000000000 -0.2285891269 0.2708607732 1.6646479192 0.1371853093 0.2984865234 -0.8550169931 0.401287836628 +1403715942834057984.0000000000 -0.2535966921 0.2887206581 1.6180379095 0.1358517537 0.3007814715 -0.8551239357 0.399797276163 +1403715942884058112.0000000000 -0.2718380615 0.2985969188 1.5726097729 0.1352679689 0.3030135997 -0.8539102095 0.400902343529 +1403715942934057984.0000000000 -0.2831473723 0.3009063610 1.5278270900 0.1357397426 0.3045192257 -0.8525208703 0.402555498319 +1403715942984058112.0000000000 -0.2872477795 0.2957508971 1.4852141375 0.1360878536 0.3063617579 -0.8497949107 0.406781488154 +1403715943034057984.0000000000 -0.2849421949 0.2833488825 1.4468830712 0.1355034313 0.3093643854 -0.8460560184 0.412458132254 +1403715943084058112.0000000000 -0.2755922324 0.2631457509 1.4133384372 0.1329915547 0.3140665034 -0.8411412173 0.419710531762 +1403715943134057984.0000000000 -0.2583805244 0.2362184860 1.3847858137 0.1337578933 0.3160146642 -0.8352374143 0.429676645634 +1403715943184058112.0000000000 -0.2338512358 0.2030191484 1.3616403385 0.1386295517 0.3154128861 -0.8266523320 0.444907271953 +1403715943234057984.0000000000 -0.2028487178 0.1651846964 1.3441209582 0.1492549859 0.3101562180 -0.8150660785 0.466040081197 +1403715943284058112.0000000000 -0.1664470683 0.1235808319 1.3317410572 0.1623392675 0.3038418320 -0.7995277982 0.492017685954 +1403715943334057984.0000000000 -0.1268970065 0.0806019321 1.3231067395 0.1771199769 0.2972048678 -0.7814389729 0.519279223524 +1403715943384058112.0000000000 -0.0857820625 0.0373320412 1.3175532261 0.1910667626 0.2920904599 -0.7615233087 0.546130850419 +1403715943434057984.0000000000 -0.0448988912 -0.0042902175 1.3137684280 0.2051227884 0.2869367416 -0.7411505876 0.571216031383 +1403715943484058112.0000000000 -0.0056212512 -0.0431140449 1.3092751010 0.2167966000 0.2838862350 -0.7242844868 0.589762513174 +1403715943534057984.0000000000 0.0309172167 -0.0791104381 1.3035752033 0.2249865372 0.2815467747 -0.7121013360 0.602514862091 +1403715943584058112.0000000000 0.0639224633 -0.1117429846 1.2973625187 0.2303747207 0.2795868561 -0.7025025437 0.612575590491 +1403715943634057984.0000000000 0.0932536412 -0.1403567000 1.2910334027 0.2357563640 0.2766570943 -0.6945834536 0.620833000949 +1403715943684058112.0000000000 0.1181522588 -0.1644170769 1.2854512484 0.2400981411 0.2727453781 -0.6878385470 0.628363728002 +1403715943734057984.0000000000 0.1385091321 -0.1839659761 1.2813002275 0.2454604473 0.2672725860 -0.6818022164 0.635185226044 +1403715943784058112.0000000000 0.1536724336 -0.1987093261 1.2790166784 0.2492568213 0.2615610279 -0.6744734255 0.643849721627 +1403715943834057984.0000000000 0.1625002001 -0.2075367285 1.2786178364 0.2514030031 0.2561146815 -0.6681189181 0.651781337002 +1403715943884058112.0000000000 0.1642659121 -0.2093512733 1.2815724120 0.2533294778 0.2511988886 -0.6634177044 0.65772353121 +1403715943934057984.0000000000 0.1587643573 -0.2041264517 1.2893298460 0.2529338261 0.2477607666 -0.6597170493 0.662881963136 +1403715943984058112.0000000000 0.1455487665 -0.1909560292 1.3006206905 0.2520481307 0.2461651675 -0.6621992250 0.66133700674 +1403715944034057984.0000000000 0.1249386403 -0.1700153564 1.3136924604 0.2497582480 0.2481088357 -0.6742759939 0.649164622611 +1403715944084058112.0000000000 0.0977320339 -0.1417497924 1.3275501555 0.2448940292 0.2545947382 -0.6947805143 0.626489002881 +1403715944134057984.0000000000 0.0657135508 -0.1085757739 1.3429356640 0.2387888017 0.2637964822 -0.7163250658 0.600224728081 +1403715944184058112.0000000000 0.0298516166 -0.0717502154 1.3587966607 0.2332699041 0.2743636026 -0.7374831295 0.571339127852 +1403715944234057984.0000000000 -0.0085501095 -0.0332821653 1.3736587570 0.2267844422 0.2868737884 -0.7592616806 0.538325131058 +1403715944284058112.0000000000 -0.0481203267 0.0049093990 1.3872781908 0.2200283760 0.3005115499 -0.7773696343 0.506928765996 +1403715944334057984.0000000000 -0.0874316093 0.0415498568 1.4000788661 0.2143019866 0.3146143128 -0.7897385534 0.481046266008 +1403715944384058112.0000000000 -0.1252458239 0.0757025975 1.4106346276 0.2095483288 0.3294667425 -0.7979143533 0.459210026262 +1403715944434057984.0000000000 -0.1600575972 0.1067269789 1.4195754005 0.2067430259 0.3441508244 -0.8037315496 0.439127689325 +1403715944484058112.0000000000 -0.1917420039 0.1341057062 1.4262062910 0.2044894427 0.3594871674 -0.8072518444 0.421067101501 +1403715944534057984.0000000000 -0.2189912203 0.1571094921 1.4330206619 0.2044640303 0.3740813625 -0.8082913377 0.406106769186 +1403715944584058112.0000000000 -0.2405202742 0.1749959357 1.4410648802 0.2074613400 0.3871020055 -0.8079645009 0.392816999509 +1403715944634057984.0000000000 -0.2556641483 0.1869950988 1.4496653531 0.2112674153 0.4000963935 -0.8055715962 0.382548504748 +1403715944684058112.0000000000 -0.2636949593 0.1927848365 1.4594778822 0.2169647685 0.4117082965 -0.8025164124 0.373349669519 +1403715944734057984.0000000000 -0.2644300281 0.1922609201 1.4701852501 0.2226038706 0.4237928951 -0.7981604913 0.365768955712 +1403715944784058112.0000000000 -0.2579159279 0.1854321512 1.4817115687 0.2269610228 0.4379133618 -0.7911428073 0.361681683638 +1403715944834057984.0000000000 -0.2436880144 0.1726402481 1.4950422470 0.2336972050 0.4510302902 -0.7810506390 0.363204065276 +1403715944884058112.0000000000 -0.2212736330 0.1539384515 1.5103807720 0.2419093540 0.4640233188 -0.7646531291 0.376122076245 +1403715944934057984.0000000000 -0.1913400680 0.1307132056 1.5276206043 0.2539451917 0.4748380494 -0.7433120962 0.396897712425 +1403715944984058112.0000000000 -0.1561752397 0.1051397336 1.5455878993 0.2692937110 0.4820111221 -0.7191990363 0.421780655729 +1403715945034057984.0000000000 -0.1172640230 0.0784279778 1.5638417416 0.2869635851 0.4854373898 -0.6921244012 0.450517762785 +1403715945084058112.0000000000 -0.0760759282 0.0519762164 1.5826085037 0.3049823271 0.4850003190 -0.6654850435 0.478424631106 +1403715945134057984.0000000000 -0.0340620538 0.0266111821 1.6007166608 0.3202062935 0.4823424332 -0.6431703407 0.501144310052 +1403715945184058112.0000000000 0.0066105878 0.0031085962 1.6171464649 0.3313562064 0.4800329624 -0.6247646396 0.51907664619 +1403715945234057984.0000000000 0.0446403243 -0.0178746140 1.6330708799 0.3414100857 0.4762097715 -0.6096996189 0.533788143016 +1403715945284058112.0000000000 0.0795372953 -0.0361161665 1.6488499676 0.3495253828 0.4719019982 -0.5973395191 0.54619228278 +1403715945334057984.0000000000 0.1101714564 -0.0510272969 1.6655669734 0.3580123886 0.4658763870 -0.5861054565 0.557912820683 +1403715945384058112.0000000000 0.1357005313 -0.0619863743 1.6829773293 0.3652906958 0.4592845911 -0.5749275691 0.570156699722 +1403715945434057984.0000000000 0.1550721824 -0.0686217169 1.7013924586 0.3729335602 0.4516640885 -0.5654201268 0.580706630808 +1403715945484058112.0000000000 0.1673479604 -0.0704505427 1.7211681068 0.3818371241 0.4430220353 -0.5570243686 0.589623388025 +1403715945534057984.0000000000 0.1712698883 -0.0677731547 1.7406043067 0.3878120081 0.4361369304 -0.5521789305 0.595386305708 +1403715945584058112.0000000000 0.1665402067 -0.0602238803 1.7572700286 0.3887211052 0.4355539580 -0.5606577165 0.587240646597 +1403715945634057984.0000000000 0.1537324639 -0.0485821043 1.7708576248 0.3817550150 0.4419629344 -0.5788638951 0.569076852596 +1403715945684058112.0000000000 0.1340691201 -0.0334873006 1.7838724331 0.3727704285 0.4499086163 -0.5989635172 0.547601268861 +1403715945734057984.0000000000 0.1090408073 -0.0162271487 1.7967396128 0.3616116864 0.4582275847 -0.6174930151 0.527225611264 +1403715945784058112.0000000000 0.0799599877 0.0028910032 1.8090287489 0.3487722688 0.4672690909 -0.6350540183 0.506679282161 +1403715945834057984.0000000000 0.0478846167 0.0231998668 1.8205700807 0.3329855480 0.4776937675 -0.6518763697 0.485784404853 +1403715945884058112.0000000000 0.0148975418 0.0443489743 1.8323665243 0.3179944771 0.4867095020 -0.6680369870 0.464456625838 +1403715945934057984.0000000000 -0.0171356214 0.0656717175 1.8433916727 0.3028091019 0.4957029217 -0.6824336181 0.443699918975 +1403715945984058112.0000000000 -0.0466391351 0.0870366760 1.8548737610 0.2916231562 0.5027704796 -0.6941982041 0.424578182445 +1403715946034057984.0000000000 -0.0726359855 0.1078412972 1.8661083632 0.2817295047 0.5107906153 -0.7023509984 0.407951600799 +1403715946084058112.0000000000 -0.0935956528 0.1276289232 1.8778729890 0.2745457802 0.5184071996 -0.7076050445 0.393920919582 +1403715946134057984.0000000000 -0.1091817614 0.1466135602 1.8891316718 0.2689917413 0.5257390014 -0.7124016627 0.379111878606 +1403715946184058112.0000000000 -0.1185426000 0.1640215231 1.9003300225 0.2635209948 0.5347429464 -0.7147336643 0.3657354996 +1403715946234057984.0000000000 -0.1205170287 0.1799368128 1.9122312633 0.2603761786 0.5429840305 -0.7157695390 0.353619223587 +1403715946284058112.0000000000 -0.1139492599 0.1937685415 1.9251509056 0.2594502726 0.5503749416 -0.7146694623 0.344993535114 +1403715946334057984.0000000000 -0.0987628895 0.2056371815 1.9391465373 0.2620914323 0.5575175862 -0.7092496613 0.342705617338 +1403715946384058112.0000000000 -0.0736081919 0.2151778247 1.9551059747 0.2690312760 0.5636072218 -0.6986300541 0.349120494383 +1403715946434057984.0000000000 -0.0392671693 0.2229520371 1.9732983317 0.2812243464 0.5665233944 -0.6840755646 0.363324555276 +1403715946484058112.0000000000 0.0021223795 0.2300188627 1.9925015073 0.2974148471 0.5659542459 -0.6671456626 0.382304675859 +1403715946534057984.0000000000 0.0490036691 0.2372971550 2.0118041758 0.3163616901 0.5617745679 -0.6513599104 0.400068597923 +1403715946584058112.0000000000 0.1000318039 0.2448374830 2.0322764386 0.3373887788 0.5542241279 -0.6351717078 0.419000393296 +1403715946634057984.0000000000 0.1523220131 0.2524963534 2.0528524302 0.3575030574 0.5457175141 -0.6184853523 0.438018067866 +1403715946684058112.0000000000 0.2044507892 0.2606014810 2.0736739021 0.3770272590 0.5362570076 -0.6036507722 0.453745096983 +1403715946734057984.0000000000 0.2547641647 0.2692671952 2.0933343290 0.3911959304 0.5290464506 -0.5910092964 0.466672914078 +1403715946784058112.0000000000 0.3021025241 0.2789999959 2.1116718893 0.4041054500 0.5220266827 -0.5811819755 0.475830262934 +1403715946834057984.0000000000 0.3463731179 0.2888429386 2.1281324449 0.4126918353 0.5176043601 -0.5741051533 0.481844838522 +1403715946884058112.0000000000 0.3870316217 0.2990344162 2.1433139912 0.4199347887 0.5135031341 -0.5677321890 0.487493042156 +1403715946934057984.0000000000 0.4228341858 0.3097304969 2.1576392256 0.4262769048 0.5095967289 -0.5614792156 0.493295311952 +1403715946984058112.0000000000 0.4534564448 0.3205719144 2.1706837917 0.4301919158 0.5063639321 -0.5558631178 0.499546472461 +1403715947034057984.0000000000 0.4789962173 0.3320349597 2.1834275213 0.4360274604 0.5013412244 -0.5504587810 0.505501890103 +1403715947084058112.0000000000 0.4988631315 0.3441481604 2.1959834912 0.4431456520 0.4947524331 -0.5453635054 0.511293074514 +1403715947134057984.0000000000 0.5121079535 0.3567932526 2.2098658585 0.4543381689 0.4831550000 -0.5360677200 0.522273370785 +1403715947184058112.0000000000 0.5177752777 0.3697878799 2.2229704608 0.4648515778 0.4709635638 -0.5257466382 0.53450613156 +1403715947234057984.0000000000 0.5149735028 0.3833696712 2.2338918234 0.4726414513 0.4610392113 -0.5195521455 0.542326905359 +1403715947284058112.0000000000 0.5031263141 0.3974762888 2.2414700921 0.4761757687 0.4551102130 -0.5177584634 0.545946430415 +1403715947334057984.0000000000 0.4819262361 0.4122574241 2.2451118636 0.4742732523 0.4551929584 -0.5229515774 0.542573405622 +1403715947384058112.0000000000 0.4521653463 0.4272212480 2.2443546508 0.4652858486 0.4618447747 -0.5339748379 0.533928230777 +1403715947434057984.0000000000 0.4144664658 0.4428705611 2.2387960927 0.4504965855 0.4740240831 -0.5497922998 0.519694546934 +1403715947484058112.0000000000 0.3697219080 0.4592382473 2.2310001425 0.4362103739 0.4863944475 -0.5668776940 0.501787436219 +1403715947534057984.0000000000 0.3195457255 0.4760385918 2.2208370398 0.4226183571 0.4979852805 -0.5832358700 0.482949588117 +1403715947584058112.0000000000 0.2651254761 0.4931099039 2.2078632672 0.4118113220 0.5074117908 -0.5991732294 0.462532324053 +1403715947634057984.0000000000 0.2086517606 0.5093832341 2.1911145492 0.3972359026 0.5187539963 -0.6159257610 0.440151548755 +1403715947684058112.0000000000 0.1514741027 0.5251901976 2.1721306810 0.3844324260 0.5280306216 -0.6314463249 0.417936491809 +1403715947734057984.0000000000 0.0950470987 0.5396445541 2.1502345819 0.3713679966 0.5369396152 -0.6443798714 0.398191212803 +1403715947784058112.0000000000 0.0408043870 0.5524550349 2.1260418775 0.3580827933 0.5457017782 -0.6528113420 0.384478392339 +1403715947834057984.0000000000 -0.0106194221 0.5636330501 2.0997378899 0.3452625765 0.5546214221 -0.6579143020 0.374616607502 +1403715947884058112.0000000000 -0.0581925801 0.5730326124 2.0710403843 0.3319010411 0.5638772291 -0.6620441074 0.365488398385 +1403715947934057984.0000000000 -0.1012320100 0.5814856841 2.0408543082 0.3200544032 0.5723164228 -0.6658279211 0.355938577122 +1403715947984058112.0000000000 -0.1385052754 0.5887997173 2.0102442041 0.3084563627 0.5807890024 -0.6689198937 0.346532802037 +1403715948034057984.0000000000 -0.1689790666 0.5951504958 1.9803638963 0.2978949741 0.5884294346 -0.6721384570 0.336510445083 +1403715948084058112.0000000000 -0.1917748395 0.6005768116 1.9511977642 0.2886339097 0.5950223992 -0.6753128315 0.32648336916 +1403715948134057984.0000000000 -0.2049577450 0.6047580392 1.9234791998 0.2812680963 0.6007083406 -0.6765440040 0.319884288768 +1403715948184058112.0000000000 -0.2082307740 0.6080821847 1.8975863094 0.2759093126 0.6051024893 -0.6772029976 0.314835081722 +1403715948234057984.0000000000 -0.2007584312 0.6106897617 1.8749192817 0.2766862692 0.6058054254 -0.6763109402 0.314718933595 +1403715948284058112.0000000000 -0.1821755142 0.6124073253 1.8552320446 0.2822502818 0.6038334600 -0.6731198978 0.320358446282 +1403715948334057984.0000000000 -0.1529565520 0.6135294944 1.8382074554 0.2940538723 0.5987203660 -0.6671526858 0.331622582518 +1403715948384058112.0000000000 -0.1148096060 0.6138146999 1.8231963650 0.3101261331 0.5906116819 -0.6588865306 0.347660988036 +1403715948434057984.0000000000 -0.0702119037 0.6134388246 1.8093145991 0.3273661777 0.5808970553 -0.6492241906 0.36592068425 +1403715948484058112.0000000000 -0.0207992153 0.6123036925 1.7961620397 0.3433584923 0.5710665345 -0.6378159385 0.386236698786 +1403715948534057984.0000000000 0.0310786751 0.6107669611 1.7832067965 0.3573714755 0.5611632035 -0.6270516908 0.405200770766 +1403715948584058112.0000000000 0.0853261722 0.6088202597 1.7704706819 0.3706129692 0.5506181176 -0.6155634552 0.42490863526 +1403715948634057984.0000000000 0.1394074792 0.6067285251 1.7564014757 0.3812922370 0.5410192966 -0.6065255463 0.4405009788 +1403715948684058112.0000000000 0.1924053081 0.6045775746 1.7418341406 0.3907339664 0.5316936620 -0.5974177504 0.455764027472 +1403715948734057984.0000000000 0.2433678100 0.6027423468 1.7269082976 0.4000803958 0.5219050455 -0.5884645327 0.470383135331 +1403715948784058112.0000000000 0.2904972197 0.6012125198 1.7109857254 0.4065499974 0.5140865267 -0.5813370546 0.482161147012 +1403715948834057984.0000000000 0.3333430663 0.6001589883 1.6945336865 0.4123063056 0.5075058187 -0.5758778089 0.490719984973 +1403715948884058112.0000000000 0.3717686678 0.5998122218 1.6783921429 0.4180712767 0.5019484789 -0.5707104822 0.497547663713 +1403715948934057984.0000000000 0.4050117381 0.6001384132 1.6631803206 0.4252238279 0.4974186972 -0.5658367058 0.501585643968 +1403715948984058112.0000000000 0.4324296200 0.6012227390 1.6491758733 0.4328370614 0.4940028402 -0.5593265727 0.505734176417 +1403715949034057984.0000000000 0.4536485983 0.6034385878 1.6361124304 0.4406632986 0.4917467850 -0.5526181762 0.50854115665 +1403715949084058112.0000000000 0.4680914671 0.6061459089 1.6235834975 0.4468530683 0.4921765510 -0.5470810765 0.508710992424 +1403715949134057984.0000000000 0.4754046367 0.6094795805 1.6116526447 0.4514677286 0.4955422773 -0.5441023600 0.504546690864 +1403715949184058112.0000000000 0.4753246818 0.6135491014 1.5994206426 0.4515893721 0.5042239034 -0.5447348099 0.495064926165 +1403715949234057984.0000000000 0.4682864536 0.6178268105 1.5858478260 0.4446759685 0.5194491949 -0.5496888170 0.479872922169 +1403715949284058112.0000000000 0.4561532122 0.6220312139 1.5729389710 0.4369834054 0.5358379596 -0.5557081555 0.461640152447 +1403715949334057984.0000000000 0.4395627863 0.6258841404 1.5602457268 0.4258886173 0.5545589543 -0.5626091651 0.441082961813 +1403715949384058112.0000000000 0.4205278497 0.6294145280 1.5483463997 0.4121589449 0.5735442980 -0.5702694247 0.41948149614 +1403715949434057984.0000000000 0.4004162218 0.6326083888 1.5369616454 0.3978339085 0.5914137289 -0.5778442970 0.39755999664 +1403715949484058112.0000000000 0.3810799858 0.6354347673 1.5275940785 0.3851971130 0.6071221210 -0.5824132633 0.379237003698 +1403715949534057984.0000000000 0.3640153790 0.6384051743 1.5193887920 0.3751709708 0.6208381120 -0.5851053283 0.362572111533 +1403715949584058112.0000000000 0.3502445945 0.6412648585 1.5120271998 0.3671329504 0.6336655573 -0.5842414808 0.349776000111 +1403715949634057984.0000000000 0.3406982188 0.6448496717 1.5056912388 0.3622248940 0.6446858917 -0.5828864496 0.336773832066 +1403715949684058112.0000000000 0.3359398254 0.6490496903 1.4999146451 0.3576673164 0.6555803812 -0.5805780992 0.324372510074 +1403715949734057984.0000000000 0.3366305546 0.6539831569 1.4946353836 0.3535763718 0.6663179906 -0.5771027229 0.312980082348 +1403715949784058112.0000000000 0.3433412295 0.6597017685 1.4898870476 0.3496346168 0.6771562575 -0.5716532485 0.304019080277 +1403715949834057984.0000000000 0.3574539459 0.6665920704 1.4864410790 0.3482188315 0.6866256595 -0.5637859067 0.299055681308 +1403715949884058112.0000000000 0.3784758241 0.6749684390 1.4839651202 0.3475607869 0.6959011752 -0.5541820572 0.296319593178 +1403715949934057984.0000000000 0.4070584738 0.6853377806 1.4830994583 0.3493575693 0.7040089580 -0.5422182053 0.29718696747 +1403715949984058112.0000000000 0.4426220399 0.6976412098 1.4835417536 0.3514736771 0.7117147853 -0.5281402899 0.30165568603 +1403715950034057984.0000000000 0.4845004186 0.7129500940 1.4848814613 0.3551422027 0.7185201915 -0.5136926993 0.306141406716 +1403715950084058112.0000000000 0.5324454855 0.7319031793 1.4874636727 0.3644663902 0.7220387929 -0.4968464347 0.314591564151 +1403715950134057984.0000000000 0.5855350748 0.7549005709 1.4920660725 0.3814229644 0.7200068198 -0.4788794946 0.326773822957 +1403715950184058112.0000000000 0.6420732116 0.7820004893 1.4980343663 0.4023161632 0.7134171340 -0.4640055434 0.337456002351 +1403715950234057984.0000000000 0.7005406823 0.8120930881 1.5055238791 0.4283036011 0.7014718985 -0.4499095465 0.349391758463 +1403715950284058112.0000000000 0.7583427085 0.8444902653 1.5128988313 0.4540930092 0.6875508390 -0.4402757481 0.356694054442 +1403715950334057984.0000000000 0.8142564010 0.8779635226 1.5198033621 0.4769978417 0.6738932912 -0.4317950958 0.363171979008 +1403715950384058112.0000000000 0.8675533429 0.9115389650 1.5257625851 0.4975490845 0.6602849490 -0.4249202592 0.368661725682 +1403715950434057984.0000000000 0.9174141030 0.9442982255 1.5311154617 0.5146182337 0.6477324342 -0.4181421364 0.375190513027 +1403715950484058112.0000000000 0.9626711188 0.9758517244 1.5364665500 0.5299330023 0.6354910629 -0.4111885769 0.382421333419 +1403715950534057984.0000000000 1.0027083354 1.0057404329 1.5418368037 0.5426369149 0.6240774837 -0.4051176966 0.389810370327 +1403715950584058112.0000000000 1.0365892502 1.0335059958 1.5464254208 0.5502274168 0.6165093969 -0.4012554730 0.395170847554 +1403715950634057984.0000000000 1.0634140741 1.0591601522 1.5517643468 0.5569369898 0.6099463564 -0.3987944816 0.398433925637 +1403715950684058112.0000000000 1.0828382516 1.0822093524 1.5579993333 0.5630238204 0.6038909230 -0.3959465819 0.401928146544 +1403715950734057984.0000000000 1.0944931989 1.1025332966 1.5652127463 0.5693453968 0.5973124226 -0.3929332358 0.405792017118 +1403715950784058112.0000000000 1.0978461321 1.1201504533 1.5729556969 0.5749051886 0.5918732947 -0.3896727857 0.409053966226 +1403715950834057984.0000000000 1.0922104626 1.1348026101 1.5816561083 0.5802778688 0.5870619915 -0.3871422760 0.410800038075 +1403715950884058112.0000000000 1.0775021993 1.1460818524 1.5910111957 0.5828870589 0.5848170046 -0.3850885292 0.412236063887 +1403715950934057984.0000000000 1.0536221109 1.1540843383 1.5998105561 0.5816880158 0.5872864973 -0.3871207450 0.408498655058 +1403715950984058112.0000000000 1.0205728051 1.1587011854 1.6070342210 0.5742893999 0.5968376876 -0.3951520849 0.397279862981 +1403715951034057984.0000000000 0.9793628553 1.1596214415 1.6129172261 0.5598212230 0.6123078513 -0.4065386618 0.382629860318 +1403715951084058112.0000000000 0.9318580787 1.1576932408 1.6187193061 0.5426781184 0.6291451950 -0.4179737156 0.367389107773 +1403715951134057984.0000000000 0.8793199136 1.1535443511 1.6244930061 0.5246594320 0.6465384535 -0.4275955770 0.35196950303 +1403715951184058112.0000000000 0.8233696367 1.1474854478 1.6297812914 0.5035400170 0.6658158876 -0.4354872250 0.336879105673 +1403715951234057984.0000000000 0.7652689879 1.1405567038 1.6350367114 0.4813713385 0.6854493981 -0.4427967428 0.319955937029 +1403715951284058112.0000000000 0.7075536885 1.1338983579 1.6408871872 0.4617430821 0.7028177662 -0.4478678827 0.30373487332 +1403715951334057984.0000000000 0.6508906108 1.1277344255 1.6467882908 0.4451902575 0.7175655260 -0.4518399957 0.28765599035 +1403715951384058112.0000000000 0.5970170095 1.1228286576 1.6533318201 0.4306745855 0.7309154920 -0.4532281975 0.273616786615 +1403715951434057984.0000000000 0.5469640582 1.1199310241 1.6600993658 0.4179610128 0.7431267353 -0.4530083446 0.260489321669 +1403715951484058112.0000000000 0.5018792908 1.1194142617 1.6673287771 0.4059576372 0.7545927623 -0.4522244031 0.247550498238 +1403715951534057984.0000000000 0.4623305150 1.1218489629 1.6751889442 0.3964179576 0.7644450755 -0.4508868873 0.234899008686 +1403715951584058112.0000000000 0.4290696997 1.1273656849 1.6834350800 0.3879647583 0.7738584195 -0.4474005938 0.224631256994 +1403715951634057984.0000000000 0.4024140934 1.1366449341 1.6925358469 0.3819541604 0.7817541716 -0.4438568570 0.21438872392 +1403715951684058112.0000000000 0.3836480887 1.1499490807 1.7020131664 0.3770826406 0.7893086122 -0.4381401300 0.206963337998 +1403715951734057984.0000000000 0.3725826526 1.1680630638 1.7125448616 0.3745312272 0.7952107328 -0.4334158554 0.19878869841 +1403715951784058112.0000000000 0.3693578319 1.1904271716 1.7232954608 0.3733099037 0.8006421346 -0.4270011368 0.19308525904 +1403715951834057984.0000000000 0.3751910037 1.2184763239 1.7352450765 0.3765979526 0.8036469837 -0.4205932266 0.188220204567 +1403715951884058112.0000000000 0.3902162268 1.2521058116 1.7490901585 0.3879267258 0.8029621072 -0.4114601695 0.188322167513 +1403715951934057984.0000000000 0.4135416585 1.2912570146 1.7662314418 0.4109741959 0.7960262875 -0.4003232828 0.192830570971 +1403715951984058112.0000000000 0.4430572868 1.3343117902 1.7845690602 0.4384041938 0.7863314947 -0.3865517728 0.200155615172 +1403715952034057984.0000000000 0.4771933363 1.3803086070 1.8029570434 0.4677615030 0.7746209046 -0.3716035501 0.207538989044 +1403715952084058112.0000000000 0.5140034340 1.4276381238 1.8216989259 0.4994592954 0.7599147716 -0.3565536816 0.214334841206 +1403715952134057984.0000000000 0.5518212202 1.4749066875 1.8401628018 0.5290102965 0.7453199308 -0.3404988853 0.22069620767 +1403715952184058112.0000000000 0.5888049223 1.5208579975 1.8575689732 0.5530416447 0.7334286143 -0.3255084601 0.224213401337 +1403715952234057984.0000000000 0.6248635896 1.5644886328 1.8741221488 0.5733514192 0.7227293807 -0.3132297338 0.225427430176 +1403715952284058112.0000000000 0.6598251866 1.6049844572 1.8895702086 0.5893735436 0.7142399006 -0.3025713261 0.225722801442 +1403715952334057984.0000000000 0.6928720339 1.6416938296 1.9043173505 0.6025449952 0.7071844422 -0.2931250559 0.225626672095 +1403715952384058112.0000000000 0.7235922957 1.6740253409 1.9187707167 0.6137868151 0.7009367532 -0.2846160620 0.225714666795 +1403715952434057984.0000000000 0.7515557473 1.7014261418 1.9329752311 0.6246742838 0.6941722612 -0.2771209139 0.226077221237 +1403715952484058112.0000000000 0.7760870648 1.7237692067 1.9464048231 0.6324532393 0.6903809770 -0.2700588011 0.224600201718 +1403715952534057984.0000000000 0.7971580253 1.7404275200 1.9597298824 0.6391045317 0.6874545649 -0.2619280782 0.224377585108 +1403715952584058112.0000000000 0.8144213293 1.7514911275 1.9737293594 0.6464496545 0.6840099044 -0.2542349332 0.222705845473 +1403715952634057984.0000000000 0.8278524760 1.7563055932 1.9884462867 0.6551815366 0.6788653689 -0.2473066577 0.220722409662 +1403715952684058112.0000000000 0.8372884650 1.7541986181 2.0039758113 0.6653202471 0.6714155916 -0.2405041933 0.220698448628 +1403715952734057984.0000000000 0.8421466861 1.7444169117 2.0200463589 0.6766350338 0.6620702956 -0.2334072936 0.222146325771 +1403715952784058112.0000000000 0.8420056591 1.7267816095 2.0360507789 0.6868935162 0.6531084864 -0.2268951302 0.223931244559 +1403715952834057984.0000000000 0.8369210658 1.7010900792 2.0518371259 0.6940355584 0.6467560965 -0.2222263942 0.225025831961 +1403715952884058112.0000000000 0.8262673645 1.6664891447 2.0646106267 0.6905605149 0.6515077083 -0.2215998438 0.222614892974 +1403715952934057984.0000000000 0.8099186107 1.6229978971 2.0744542114 0.6748784212 0.6688267235 -0.2250345128 0.215799440645 +1403715952984058112.0000000000 0.7889794842 1.5721807020 2.0815742927 0.6513980496 0.6929421583 -0.2297650822 0.206687573896 +1403715953034057984.0000000000 0.7645416503 1.5161722305 2.0863423250 0.6252197787 0.7182764623 -0.2342787756 0.195684969716 +1403715953084058112.0000000000 0.7374493250 1.4558340474 2.0878957704 0.5967616944 0.7436470509 -0.2390030329 0.183690212129 +1403715953134057984.0000000000 0.7089830708 1.3927479554 2.0853143236 0.5665369339 0.7681383172 -0.2430846802 0.17294295701 +1403715953184058112.0000000000 0.6804323972 1.3288446334 2.0803857136 0.5381184911 0.7892277637 -0.2477576002 0.16175351049 +1403715953234057984.0000000000 0.6528984905 1.2653475869 2.0736854544 0.5131721787 0.8062602642 -0.2511116151 0.153432910568 +1403715953284058112.0000000000 0.6272144602 1.2043010493 2.0651727144 0.4931185451 0.8192521227 -0.2534942531 0.14628986151 +1403715953334057984.0000000000 0.6037534007 1.1468559708 2.0545734531 0.4769166464 0.8294581812 -0.2549018269 0.139909601859 +1403715953384058112.0000000000 0.5823068821 1.0925756739 2.0413354363 0.4607666935 0.8397095731 -0.2543716698 0.133704676766 +1403715953434057984.0000000000 0.5635537832 1.0429556384 2.0262823453 0.4469552883 0.8485446109 -0.2536873418 0.125879887703 +1403715953484058112.0000000000 0.5486674591 0.9994158277 2.0109781365 0.4353454638 0.8565240500 -0.2505876448 0.118518822492 +1403715953534057984.0000000000 0.5378657081 0.9626209953 1.9966509337 0.4252786885 0.8640311563 -0.2454303489 0.11114019017 +1403715953584058112.0000000000 0.5315994398 0.9329659003 1.9837592835 0.4162343422 0.8712350589 -0.2385299653 0.103932190144 +1403715953634057984.0000000000 0.5302527850 0.9116120527 1.9728415031 0.4090585888 0.8777273214 -0.2298428585 0.0971497842862 +1403715953684058112.0000000000 0.5338319928 0.8992225624 1.9636053196 0.4031153442 0.8835949055 -0.2203041375 0.0906870948729 +1403715953734057984.0000000000 0.5424414929 0.8960999964 1.9560904017 0.3983619931 0.8885057992 -0.2112232962 0.0851462650322 +1403715953784058112.0000000000 0.5566062769 0.9031440213 1.9502443742 0.3955472926 0.8922391344 -0.2015229891 0.0827052066774 +1403715953834057984.0000000000 0.5760469329 0.9205295006 1.9468432180 0.3975296576 0.8937138073 -0.1902859514 0.0838871785003 +1403715953884058112.0000000000 0.6004254035 0.9480967326 1.9454198791 0.4039931374 0.8931291915 -0.1755990576 0.0909657253186 +1403715953934057984.0000000000 0.6284729982 0.9851711466 1.9441098830 0.4156944477 0.8898118194 -0.1571850568 0.103565970301 +1403715953984058112.0000000000 0.6589993383 1.0309462455 1.9425638128 0.4348697254 0.8818808211 -0.1359744674 0.121183676807 +1403715954034057984.0000000000 0.6895259065 1.0836980373 1.9397036073 0.4567517890 0.8709007422 -0.1146743203 0.140568491128 +1403715954084058112.0000000000 0.7179103024 1.1429291462 1.9351676442 0.4812177018 0.8571880948 -0.1008806820 0.153235705796 +1403715954134057984.0000000000 0.7435054838 1.2068832544 1.9292776343 0.5072812724 0.8413132102 -0.0899085274 0.163628389381 +1403715954184058112.0000000000 0.7654934903 1.2743065176 1.9231609979 0.5341044476 0.8238921707 -0.0831849450 0.170336123496 +1403715954234057984.0000000000 0.7828611553 1.3436333111 1.9174691914 0.5599785088 0.8061560637 -0.0808520824 0.173203381625 +1403715954284058112.0000000000 0.7955426014 1.4131328519 1.9118706579 0.5831981130 0.7895306910 -0.0820082810 0.172614862923 +1403715954334057984.0000000000 0.8032965962 1.4812088914 1.9065098045 0.6042709899 0.7741746201 -0.0870222378 0.167144722924 +1403715954384058112.0000000000 0.8063068789 1.5467739310 1.9013226345 0.6238032326 0.7597714731 -0.0954583212 0.156539274914 +1403715954434057984.0000000000 0.8051504201 1.6082206823 1.8963561299 0.6424377911 0.7451140938 -0.1030831747 0.146466825099 +1403715954484058112.0000000000 0.8005424498 1.6644560928 1.8919104357 0.6601455199 0.7301006544 -0.1089004716 0.138930249398 +1403715954534057984.0000000000 0.7928234601 1.7138653848 1.8878982336 0.6762012344 0.7155224428 -0.1117090196 0.135279781861 +1403715954584058112.0000000000 0.7822744962 1.7556292592 1.8844066087 0.6908031260 0.7016009390 -0.1124386481 0.133808497519 +1403715954634057984.0000000000 0.7683145805 1.7885903285 1.8810052732 0.7022786725 0.6903295508 -0.1128239999 0.132365110557 +1403715954684058112.0000000000 0.7508047075 1.8120649511 1.8775610042 0.7112965824 0.6813411752 -0.1129122513 0.130698884335 +1403715954734057984.0000000000 0.7299793931 1.8250402911 1.8726283636 0.7133714800 0.6793239899 -0.1128968925 0.129901270116 +1403715954784058112.0000000000 0.7060070316 1.8280869772 1.8671030001 0.7103541038 0.6826119655 -0.1131074855 0.129014140565 +1403715954834057984.0000000000 0.6789101733 1.8214482322 1.8611838347 0.7014808393 0.6918272122 -0.1145127963 0.127226412472 +1403715954884058112.0000000000 0.6492123107 1.8054044216 1.8553901682 0.6896348195 0.7035786177 -0.1158087593 0.126369599683 +1403715954934057984.0000000000 0.6167799404 1.7809549146 1.8495392941 0.6724028334 0.7200817542 -0.1184991484 0.123752368681 +1403715954984058112.0000000000 0.5819323934 1.7492775468 1.8439393993 0.6514944870 0.7388341812 -0.1209959617 0.12263345075 +1403715955034057984.0000000000 0.5449078761 1.7123201217 1.8394979748 0.6310963430 0.7562184494 -0.1241409318 0.120166932236 +1403715955084058112.0000000000 0.5064024921 1.6712976479 1.8357073056 0.6104571758 0.7727829723 -0.1278139281 0.117524950273 +1403715955134057984.0000000000 0.4664188623 1.6274735739 1.8322436596 0.5888522083 0.7892896194 -0.1336378139 0.111426694513 +1403715955184058112.0000000000 0.4257860284 1.5823888625 1.8289721846 0.5666062789 0.8052448820 -0.1405235745 0.103880362489 +1403715955234057984.0000000000 0.3855527117 1.5372790179 1.8256626108 0.5434878101 0.8207562414 -0.1473747332 0.0962334688947 +1403715955284058112.0000000000 0.3467639627 1.4937943617 1.8232147956 0.5228578966 0.8337349598 -0.1523646100 0.0910530746123 +1403715955334057984.0000000000 0.3098619419 1.4531050388 1.8215360798 0.5045105080 0.8446582347 -0.1558273910 0.087974076237 +1403715955384058112.0000000000 0.2747872276 1.4161660933 1.8207116292 0.4887987529 0.8534603632 -0.1597292234 0.0846626412941 +1403715955434057984.0000000000 0.2416443015 1.3836552720 1.8204425336 0.4739576335 0.8615449425 -0.1628190448 0.0812061102733 +1403715955484058112.0000000000 0.2107024548 1.3562139622 1.8210493580 0.4604235040 0.8686994914 -0.1664373774 0.0752993364067 +1403715955534057984.0000000000 0.1825222364 1.3348798532 1.8226842483 0.4471801571 0.8755130968 -0.1706056333 0.0663358296972 +1403715955584058112.0000000000 0.1579358034 1.3204688248 1.8255607253 0.4354479022 0.8815140257 -0.1733016528 0.0573121626465 +1403715955634057984.0000000000 0.1375536637 1.3137319900 1.8293951528 0.4253657040 0.8869722292 -0.1728612735 0.049631266334 +1403715955684058112.0000000000 0.1222612018 1.3157344689 1.8344260441 0.4186022878 0.8912757915 -0.1686939589 0.0440674067852 +1403715955734057984.0000000000 0.1124110544 1.3275666040 1.8414036138 0.4203017140 0.8923785462 -0.1584684228 0.0435288238005 +1403715955784058112.0000000000 0.1071987350 1.3493656598 1.8517917979 0.4345795726 0.8876975810 -0.1451264657 0.0455182243529 +1403715955834057984.0000000000 0.1058483326 1.3802907368 1.8657972069 0.4605244784 0.8764973940 -0.1323617510 0.0463669070917 +1403715955884058112.0000000000 0.1069973896 1.4167172801 1.8802800506 0.4894810083 0.8627687435 -0.1172636979 0.0478295189193 +1403715955934057984.0000000000 0.1093381992 1.4563332296 1.8952189439 0.5180716549 0.8478607587 -0.1028724601 0.0463805050967 +1403715955984058112.0000000000 0.1125130119 1.4981867548 1.9103326819 0.5472017590 0.8312875213 -0.0862130377 0.045810521446 +1403715956034057984.0000000000 0.1160713092 1.5410286098 1.9256061977 0.5748642382 0.8141790639 -0.0668277061 0.0466649459168 +1403715956084058112.0000000000 0.1192881779 1.5832715215 1.9406587397 0.5980538234 0.7987020866 -0.0470025077 0.0468760649255 +1403715956134057984.0000000000 0.1217822133 1.6236718485 1.9546062471 0.6152362260 0.7865520671 -0.0279069825 0.0451822117566 +1403715956184058112.0000000000 0.1231522883 1.6611327209 1.9677405745 0.6294973445 0.7758034209 -0.0092467529 0.042150242349 +1403715956234057984.0000000000 0.1229038638 1.6944141069 1.9799360006 0.6394620671 0.7678840566 0.0084834848 0.0370185203835 +1403715956284058112.0000000000 0.1210502404 1.7228856477 1.9916728983 0.6452609263 0.7630011002 0.0245702677 0.0293931979907 +1403715956334057984.0000000000 0.1172844169 1.7461985873 2.0044964140 0.6529807673 0.7560925446 0.0396278030 0.0192306737874 +1403715956384058112.0000000000 0.1117475299 1.7636859713 2.0182645097 0.6626722536 0.7469434197 0.0537073922 0.00751851622914 +1403715956434057984.0000000000 0.1048708106 1.7748187112 2.0333255110 0.6752221589 0.7345721225 0.0666770628 -0.00574476463561 +1403715956484058112.0000000000 0.0970478613 1.7787317463 2.0489782153 0.6885422375 0.7206282356 0.0789343308 -0.0193366139821 +1403715956534057984.0000000000 0.0890964931 1.7748629355 2.0643075880 0.6988724541 0.7088128937 0.0901741437 -0.0320967051135 +1403715956584058112.0000000000 0.0816246212 1.7626950027 2.0796369952 0.7062872172 0.6995055095 0.0997074243 -0.0436902561801 +1403715956634057984.0000000000 0.0750345575 1.7414222689 2.0946764817 0.7101425453 0.6937608618 0.1068044602 -0.0546464936966 +1403715956684058112.0000000000 0.0695876882 1.7109659359 2.1078197034 0.7074995501 0.6948787776 0.1131122969 -0.0615912287795 +1403715956734057984.0000000000 0.0652781696 1.6710844817 2.1200602980 0.6986634866 0.7023984875 0.1168472970 -0.0696592170841 +1403715956784058112.0000000000 0.0625168874 1.6231567754 2.1318868462 0.6863729847 0.7133003387 0.1198378362 -0.075720840419 +1403715956834057984.0000000000 0.0611857240 1.5680040930 2.1430780626 0.6718300185 0.7262166477 0.1213001002 -0.0808708388207 +1403715956884058112.0000000000 0.0610256610 1.5071144879 2.1535223721 0.6545396955 0.7412813778 0.1226622526 -0.0838670238999 +1403715956934057984.0000000000 0.0620910572 1.4415744796 2.1629703801 0.6357657431 0.7571387536 0.1240483105 -0.0845863138117 +1403715956984058112.0000000000 0.0640601691 1.3724274506 2.1704527226 0.6141944723 0.7746191123 0.1253149651 -0.0838244629999 +1403715957034057984.0000000000 0.0667366036 1.3009157184 2.1751348351 0.5924992106 0.7913903735 0.1267226630 -0.0811623617646 +1403715957084058112.0000000000 0.0694496162 1.2283741116 2.1770906062 0.5723209477 0.8063023524 0.1273302209 -0.0781809701525 +1403715957134057984.0000000000 0.0716736496 1.1562291639 2.1763677218 0.5527360915 0.8200971543 0.1269814264 -0.0761524002788 +1403715957184058112.0000000000 0.0730935367 1.0850001764 2.1722662738 0.5331490765 0.8332039375 0.1262124355 -0.0747909215113 +1403715957234057984.0000000000 0.0737842894 1.0157168682 2.1648741342 0.5135168198 0.8457284478 0.1251223031 -0.0734048887561 +1403715957284058112.0000000000 0.0732280191 0.9498700773 2.1542524355 0.4931267165 0.8580822117 0.1231981678 -0.0730969966613 +1403715957334057984.0000000000 0.0715762763 0.8883078220 2.1405491318 0.4716387454 0.8703803736 0.1213669558 -0.072560051227 +1403715957384058112.0000000000 0.0687536685 0.8319020882 2.1244497452 0.4511683657 0.8814441148 0.1205574195 -0.0704931694535 +1403715957434057984.0000000000 0.0643288577 0.7822999407 2.1070714025 0.4336858300 0.8904172819 0.1202364673 -0.0679474565183 +1403715957484058112.0000000000 0.0579666582 0.7406852389 2.0884155941 0.4169980751 0.8985834123 0.1198537029 -0.0655404184926 +1403715957534057984.0000000000 0.0492644758 0.7081243055 2.0690283022 0.4032950986 0.9050216362 0.1194416334 -0.0634239510547 +1403715957584058112.0000000000 0.0384005901 0.6853811246 2.0486907657 0.3917037128 0.9101064842 0.1210453073 -0.0601865626906 +1403715957634057984.0000000000 0.0247921412 0.6732373874 2.0281607483 0.3824977194 0.9140546109 0.1217561641 -0.05809560702 +1403715957684058112.0000000000 0.0084884006 0.6723399862 2.0076315301 0.3792469563 0.9152241299 0.1246293404 -0.0548093584725 +1403715957734057984.0000000000 -0.0112745469 0.6837880705 1.9880794200 0.3850198591 0.9125884284 0.1269414970 -0.0531782359366 +1403715957784058112.0000000000 -0.0348545947 0.7074004332 1.9705316582 0.3998812360 0.9060366463 0.1274455742 -0.0543159124546 +1403715957834057984.0000000000 -0.0623112173 0.7433288704 1.9567450610 0.4263458141 0.8936514924 0.1276767906 -0.0575751164603 +1403715957884058112.0000000000 -0.0930822995 0.7883161011 1.9457548490 0.4576352230 0.8776439552 0.1277103231 -0.0632547542167 +1403715957934057984.0000000000 -0.1260896195 0.8388522667 1.9360156698 0.4894321117 0.8595398465 0.1299083248 -0.069074507354 +1403715957984058112.0000000000 -0.1608310940 0.8927123655 1.9272002036 0.5203985676 0.8401171673 0.1330393622 -0.0754254873852 +1403715958034057984.0000000000 -0.1968426527 0.9478500138 1.9187775594 0.5494338767 0.8200617201 0.1365137085 -0.0835774950341 +1403715958084058112.0000000000 -0.2333318580 1.0027019293 1.9098759753 0.5773359021 0.7989263829 0.1421554646 -0.0905080918306 +1403715958134057984.0000000000 -0.2700460674 1.0556091305 1.9000209560 0.6002818901 0.7798390041 0.1465280696 -0.100211301576 +1403715958184058112.0000000000 -0.3063051078 1.1056082415 1.8896758180 0.6212287413 0.7609828168 0.1510474028 -0.110293633388 +1403715958234057984.0000000000 -0.3411909644 1.1512366097 1.8781844424 0.6385121466 0.7440277046 0.1568880532 -0.118790370332 +1403715958284058112.0000000000 -0.3742858862 1.1918992434 1.8659206959 0.6516988163 0.7297266227 0.1635761224 -0.126611852071 +1403715958334057984.0000000000 -0.4052060471 1.2267941595 1.8531335985 0.6629150129 0.7165277179 0.1699132135 -0.135134063548 +1403715958384058112.0000000000 -0.4337523468 1.2551935956 1.8400152542 0.6730473747 0.7039143312 0.1763447969 -0.142878823609 +1403715958434057984.0000000000 -0.4597756055 1.2759650051 1.8280948024 0.6837123763 0.6899962923 0.1806381789 -0.154312512348 +1403715958484058112.0000000000 -0.4818416621 1.2886766451 1.8161747916 0.6932561299 0.6766284546 0.1855369804 -0.164760133839 +1403715958534057984.0000000000 -0.4996328104 1.2924929976 1.8038407939 0.6982294047 0.6673176614 0.1902241754 -0.176004546048 +1403715958584058112.0000000000 -0.5128563584 1.2870236478 1.7901346341 0.6968084649 0.6642443018 0.1962782279 -0.186312447053 +1403715958634057984.0000000000 -0.5208355435 1.2722887920 1.7762940530 0.6917463879 0.6646436759 0.2024079182 -0.196892746157 +1403715958684058112.0000000000 -0.5234798743 1.2488834984 1.7623724941 0.6821396640 0.6690070929 0.2086934378 -0.208715206526 +1403715958734057984.0000000000 -0.5205510558 1.2179307718 1.7481807406 0.6687173659 0.6767213470 0.2164824855 -0.219090475496 +1403715958784058112.0000000000 -0.5121803915 1.1798937296 1.7337010036 0.6502531387 0.6883887137 0.2252166357 -0.229279963087 +1403715958834057984.0000000000 -0.4987432336 1.1358139991 1.7194094143 0.6278019369 0.7023169987 0.2331356164 -0.241378014138 +1403715958884058112.0000000000 -0.4803352453 1.0877108036 1.7049922486 0.6024329681 0.7176902746 0.2412550716 -0.252569156989 +1403715958934057984.0000000000 -0.4571675696 1.0373685227 1.6910214058 0.5778881589 0.7314045525 0.2494992178 -0.262379108832 +1403715958984058112.0000000000 -0.4298031467 0.9862683700 1.6769086994 0.5539551008 0.7438394154 0.2587728020 -0.26995056451 +1403715959034057984.0000000000 -0.3986265801 0.9357752002 1.6614962288 0.5295759281 0.7562051342 0.2725356645 -0.270974986056 +1403715959084058112.0000000000 -0.3643818184 0.8871143111 1.6463073578 0.5086133985 0.7654598347 0.2873908190 -0.26979653365 +1403715959134057984.0000000000 -0.3283230881 0.8416952606 1.6312339602 0.4929692408 0.7708448779 0.3047428505 -0.264407444812 +1403715959184058112.0000000000 -0.2913733433 0.7996370755 1.6161051511 0.4805828505 0.7734988492 0.3246140848 -0.255666482046 +1403715959234057984.0000000000 -0.2547002131 0.7609991733 1.6017452992 0.4698277961 0.7746410950 0.3440298193 -0.246650561278 +1403715959284058112.0000000000 -0.2190348435 0.7250702584 1.5872342527 0.4574059796 0.7762417265 0.3623985346 -0.238528518049 +1403715959334057984.0000000000 -0.1853237229 0.6921540651 1.5723625980 0.4406184165 0.7801247627 0.3801780998 -0.229620073369 +1403715959384058112.0000000000 -0.1550447475 0.6631038709 1.5576590105 0.4218740263 0.7854901120 0.3951643194 -0.221071822046 +1403715959434057984.0000000000 -0.1297162474 0.6385888950 1.5439222943 0.4053514892 0.7900098913 0.4072847218 -0.213760841117 +1403715959484058112.0000000000 -0.1098416687 0.6185468612 1.5309583686 0.3900166594 0.7944303908 0.4170254518 -0.207019641657 +1403715959534057984.0000000000 -0.0974854076 0.6037058146 1.5199521906 0.3774390872 0.7974536331 0.4250721958 -0.202289562074 +1403715959584058112.0000000000 -0.0940772686 0.5949929765 1.5124211597 0.3701122593 0.7968520095 0.4346173731 -0.197867454165 +1403715959634057984.0000000000 -0.1006691450 0.5924444889 1.5101242889 0.3670962169 0.7942945632 0.4419268946 -0.197578172564 +1403715959684058112.0000000000 -0.1181438042 0.5961163274 1.5138424848 0.3719773442 0.7876145594 0.4480792127 -0.201298734248 +1403715959734057984.0000000000 -0.1464007636 0.6053095985 1.5237370328 0.3850689625 0.7774190925 0.4493269457 -0.213182421087 +1403715959784058112.0000000000 -0.1833713644 0.6190868175 1.5383559625 0.4057168131 0.7627521345 0.4477217611 -0.230539093157 +1403715959834057984.0000000000 -0.2266478368 0.6357856199 1.5548917061 0.4286066573 0.7460498067 0.4440712388 -0.250013507868 +1403715959884058112.0000000000 -0.2736395525 0.6542154499 1.5718325378 0.4541837692 0.7264490560 0.4394569567 -0.269937874502 +1403715959934057984.0000000000 -0.3226100097 0.6735301872 1.5884131624 0.4799501467 0.7059246833 0.4330911098 -0.289396421365 +1403715959984058112.0000000000 -0.3719043732 0.6927747285 1.6039714904 0.5048977298 0.6850706856 0.4250104854 -0.308419398604 +1403715960034057984.0000000000 -0.4194489166 0.7112590950 1.6171542779 0.5267127704 0.6657682327 0.4174980806 -0.324070471521 +1403715960084058112.0000000000 -0.4641372286 0.7280536949 1.6291871072 0.5451541296 0.6483304030 0.4095140104 -0.338781550276 +1403715960134057984.0000000000 -0.5048254091 0.7428892377 1.6394686304 0.5594011307 0.6342476826 0.4035741152 -0.349182166876 +1403715960184058112.0000000000 -0.5403550822 0.7551992189 1.6494739330 0.5723826404 0.6213396618 0.3982685802 -0.357347555925 +1403715960234057984.0000000000 -0.5693257927 0.7642353714 1.6592115769 0.5838694708 0.6098270034 0.3937031907 -0.363600418926 +1403715960284058112.0000000000 -0.5911086285 0.7697684008 1.6687700879 0.5923865790 0.6011304774 0.3899398163 -0.368330326998 +1403715960334057984.0000000000 -0.6054089583 0.7716143176 1.6786354324 0.6011105145 0.5926297283 0.3860056152 -0.372096519157 +1403715960384058112.0000000000 -0.6119071331 0.7695307280 1.6887040706 0.6088105117 0.5845523995 0.3815532806 -0.376915570428 +1403715960434057984.0000000000 -0.6096583132 0.7630127444 1.6989613407 0.6148775917 0.5782650244 0.3778847932 -0.38044472907 +1403715960484058112.0000000000 -0.5981347706 0.7517028025 1.7083526226 0.6160899675 0.5772316923 0.3771437737 -0.380787735361 +1403715960534057984.0000000000 -0.5775042422 0.7356565534 1.7169282193 0.6119987401 0.5821425476 0.3802336028 -0.37681560972 +1403715960584058112.0000000000 -0.5481853818 0.7152260823 1.7240717162 0.6008284202 0.5945823819 0.3882561117 -0.367061564862 +1403715960634057984.0000000000 -0.5108456434 0.6903475842 1.7296752913 0.5833229517 0.6124322092 0.3993519365 -0.353806661857 +1403715960684058112.0000000000 -0.4673490305 0.6622192406 1.7358114679 0.5645532784 0.6304752695 0.4095764575 -0.340628325035 +1403715960734057984.0000000000 -0.4195445451 0.6314718602 1.7419514432 0.5468544857 0.6465632953 0.4204041524 -0.325831897256 +1403715960784058112.0000000000 -0.3682734684 0.5983310881 1.7479178387 0.5263282232 0.6642542969 0.4309409128 -0.309894756612 +1403715960834057984.0000000000 -0.3151511778 0.5633257631 1.7528141180 0.5001922589 0.6849591956 0.4430421774 -0.290434559818 +1403715960884058112.0000000000 -0.2621515365 0.5271642749 1.7585279533 0.4758977009 0.7026536344 0.4542271408 -0.271066325854 +1403715960934057984.0000000000 -0.2112476530 0.4904389384 1.7649593116 0.4513149165 0.7194537722 0.4629394799 -0.253748209575 +1403715960984058112.0000000000 -0.1647090513 0.4545444043 1.7725345193 0.4325838398 0.7315623712 0.4696571117 -0.238976810648 +1403715961034057984.0000000000 -0.1231916422 0.4196504379 1.7801384651 0.4148842536 0.7424431725 0.4751897572 -0.225485889557 +1403715961084058112.0000000000 -0.0882659382 0.3864438526 1.7880568222 0.3986984791 0.7518650803 0.4798425127 -0.213282879651 +1403715961134057984.0000000000 -0.0610140237 0.3551747435 1.7968050816 0.3822552062 0.7613499794 0.4828921621 -0.202589057036 +1403715961184058112.0000000000 -0.0433011943 0.3267806906 1.8069804013 0.3666093002 0.7703756004 0.4841908577 -0.194108909384 +1403715961234057984.0000000000 -0.0360267600 0.3020673739 1.8190152815 0.3548527737 0.7778438630 0.4823966868 -0.190609208498 +1403715961284058112.0000000000 -0.0399726015 0.2816310811 1.8334668122 0.3488131942 0.7829484763 0.4774009132 -0.193415116008 +1403715961334057984.0000000000 -0.0554422393 0.2659654330 1.8510949799 0.3512211239 0.7834979409 0.4705278403 -0.203416445396 +1403715961384058112.0000000000 -0.0814677816 0.2551319749 1.8713146030 0.3600049474 0.7798976973 0.4631624091 -0.218258109647 +1403715961434057984.0000000000 -0.1162945804 0.2489201097 1.8935952415 0.3730486926 0.7726115110 0.4565067070 -0.23560083294 +1403715961484058112.0000000000 -0.1580746028 0.2467202854 1.9172902809 0.3881744415 0.7617601601 0.4523822188 -0.253756555859 +1403715961534057984.0000000000 -0.2051171296 0.2482043565 1.9423344882 0.4047321288 0.7481878966 0.4496095013 -0.272503342269 +1403715961584058112.0000000000 -0.2556628021 0.2529721322 1.9677601478 0.4227317836 0.7315459977 0.4492191173 -0.290414319646 +1403715961634057984.0000000000 -0.3085725832 0.2598001205 1.9933701378 0.4403542175 0.7131034080 0.4502015374 -0.308042640495 +1403715961684058112.0000000000 -0.3626936662 0.2679198256 2.0185963005 0.4576098385 0.6934203030 0.4511970626 -0.325856916125 +1403715961734057984.0000000000 -0.4166814552 0.2767436801 2.0420022187 0.4753901523 0.6721877856 0.4532315822 -0.341685406319 +1403715961784058112.0000000000 -0.4688767044 0.2856625561 2.0626188324 0.4934154146 0.6502273051 0.4553870383 -0.35548322841 +1403715961834057984.0000000000 -0.5187858043 0.2942561288 2.0800452057 0.5082526621 0.6301306165 0.4562282000 -0.369419094231 +1403715961884058112.0000000000 -0.5654304075 0.3020239130 2.0932034572 0.5210159011 0.6119528281 0.4573289349 -0.380665748682 +1403715961934057984.0000000000 -0.6080019388 0.3088371423 2.1026915555 0.5317034219 0.5959022933 0.4580673493 -0.390341173115 +1403715961984058112.0000000000 -0.6457126846 0.3137933316 2.1110486990 0.5433606488 0.5783601906 0.4548041007 -0.404242409032 +1403715962034057984.0000000000 -0.6773427860 0.3165288736 2.1176282093 0.5545390293 0.5598732295 0.4494623226 -0.420728002947 +1403715962084058112.0000000000 -0.7009098173 0.3167758222 2.1222546531 0.5632602355 0.5422914405 0.4433487472 -0.438291899284 +1403715962134057984.0000000000 -0.7153072341 0.3147147158 2.1238511623 0.5683968759 0.5277889745 0.4400302769 -0.452478889289 +1403715962184058112.0000000000 -0.7201577306 0.3103870447 2.1223566742 0.5694747929 0.5166817656 0.4395057696 -0.464298494308 +1403715962234057984.0000000000 -0.7146753768 0.3039118234 2.1180046287 0.5656189832 0.5101919143 0.4419170585 -0.473802374235 +1403715962284058112.0000000000 -0.6985610731 0.2954353862 2.1110512348 0.5568684583 0.5082104043 0.4476337618 -0.480878072259 +1403715962334057984.0000000000 -0.6724569908 0.2854951023 2.1020739380 0.5434091266 0.5105902248 0.4545294478 -0.487244419689 +1403715962384058112.0000000000 -0.6360165639 0.2750044714 2.0918614001 0.5286359320 0.5154419579 0.4617647333 -0.491565835457 +1403715962434057984.0000000000 -0.5895531638 0.2641335290 2.0799674687 0.5101352859 0.5232086711 0.4698781938 -0.495206178803 +1403715962484058112.0000000000 -0.5347483368 0.2536395398 2.0662274612 0.4888055108 0.5325630361 0.4787685751 -0.498223279902 +1403715962534057984.0000000000 -0.4724977585 0.2443775603 2.0496928975 0.4638168615 0.5446034949 0.4895630404 -0.498607041507 +1403715962584058112.0000000000 -0.4041172154 0.2370486374 2.0303927148 0.4347791663 0.5589429671 0.5023703395 -0.496159125783 +1403715962634057984.0000000000 -0.3314417053 0.2330179954 2.0088641741 0.4084443823 0.5707658156 0.5145786416 -0.492552933117 +1403715962684058112.0000000000 -0.2559108636 0.2324891829 1.9854907191 0.3842863937 0.5805136329 0.5250904031 -0.489497659121 +1403715962734057984.0000000000 -0.1784954045 0.2361593304 1.9592350841 0.3628693617 0.5880644006 0.5355175378 -0.485517305327 +1403715962784058112.0000000000 -0.0998097010 0.2442214685 1.9299475260 0.3431380409 0.5941158961 0.5478773898 -0.47865744806 +1403715962834057984.0000000000 -0.0211424625 0.2570072860 1.8978290891 0.3283924112 0.5969451853 0.5620197569 -0.468986847305 +1403715962884058112.0000000000 0.0564215546 0.2741910666 1.8636184196 0.3170406760 0.5971235719 0.5769996627 -0.458257611802 +1403715962934057984.0000000000 0.1328343482 0.2955354033 1.8259821946 0.3085254400 0.5945883827 0.5965158032 -0.442092303188 +1403715962984058112.0000000000 0.2068580300 0.3205963990 1.7842611447 0.3047791337 0.5880239708 0.6195034269 -0.421370375618 +1403715963034057984.0000000000 0.2771346901 0.3473510282 1.7391843651 0.2979840427 0.5823194110 0.6417764617 -0.400290628222 +1403715963084058112.0000000000 0.3422140167 0.3747160587 1.6906743606 0.2895657499 0.5766553479 0.6623042834 -0.380753624427 +1403715963134057984.0000000000 0.4020692028 0.4018570877 1.6398663178 0.2784987943 0.5718984048 0.6808164120 -0.363124839823 +1403715963184058112.0000000000 0.4557784648 0.4284279005 1.5868640990 0.2665063639 0.5674314856 0.6967465317 -0.348626071615 +1403715963234057984.0000000000 0.5020661032 0.4535686459 1.5317225226 0.2550502700 0.5619616794 0.7110703782 -0.336938195976 +1403715963284058112.0000000000 0.5404439947 0.4765057363 1.4741596138 0.2424739205 0.5573006024 0.7235203467 -0.327323608048 +1403715963334057984.0000000000 0.5689193714 0.4967614181 1.4156282557 0.2344025662 0.5494851711 0.7337596378 -0.323602035708 +1403715963384058112.0000000000 0.5847409353 0.5129001232 1.3596069035 0.2339121799 0.5385421826 0.7377124603 -0.333223251949 +1403715963434057984.0000000000 0.5882968144 0.5249117267 1.3067928036 0.2451965558 0.5207719650 0.7362818254 -0.355758742753 +1403715963484058112.0000000000 0.5831041774 0.5331338749 1.2563681536 0.2593893963 0.5009026311 0.7305151088 -0.384917356125 +1403715963534057984.0000000000 0.5716577278 0.5383664721 1.2083145296 0.2759700996 0.4785176421 0.7213197040 -0.417802889964 +1403715963584058112.0000000000 0.5563683203 0.5409372049 1.1618277854 0.2887526152 0.4579955604 0.7114251527 -0.448035987487 +1403715963634057984.0000000000 0.5396294474 0.5422649913 1.1173881369 0.2992297446 0.4382418105 0.7031583000 -0.473258999438 +1403715963684058112.0000000000 0.5231052318 0.5428227519 1.0761052405 0.3071924778 0.4206125776 0.6964957539 -0.493570163264 +1403715963734057984.0000000000 0.5080855343 0.5430887353 1.0380712624 0.3115313660 0.4061891734 0.6920751248 -0.508911176031 +1403715963784058112.0000000000 0.4956009290 0.5433597843 1.0032216696 0.3110297206 0.3966788678 0.6897419490 -0.519771519463 +1403715963834057984.0000000000 0.4855446826 0.5438659444 0.9720637677 0.3091747540 0.3891447403 0.6885454529 -0.528093270075 +1403715963884058112.0000000000 0.4784451027 0.5449034865 0.9443276616 0.3061604676 0.3843329656 0.6894506073 -0.532176474166 +1403715963934057984.0000000000 0.4744650739 0.5468517321 0.9191323456 0.3009220201 0.3823862416 0.6929885071 -0.531971455082 +1403715963984058112.0000000000 0.4727201208 0.5494016616 0.8977480325 0.2931045067 0.3831337750 0.6971068897 -0.530415161004 +1403715964034057984.0000000000 0.4730436021 0.5532754079 0.8785951500 0.2886596600 0.3822110558 0.7043346704 -0.523930321292 +1403715964084058112.0000000000 0.4745343362 0.5574640965 0.8620819696 0.2820984802 0.3832211788 0.7170324198 -0.509339262665 +1403715964134057984.0000000000 0.4765546667 0.5616704593 0.8499843569 0.2810750936 0.3802638194 0.7325508328 -0.489658551111 +1403715964184058112.0000000000 0.4792006010 0.5638328480 0.8456598870 0.2761707950 0.3803633124 0.7438680216 -0.475093473996 +1403715964234057984.0000000000 0.4810374572 0.5629989835 0.8496249283 0.2736329473 0.3799665535 0.7494058034 -0.468125378642 +1403715964284058112.0000000000 0.4814653180 0.5583158173 0.8626287409 0.2693936373 0.3823644715 0.7466391682 -0.473026882588 +1403715964334057984.0000000000 0.4800867655 0.5511962158 0.8796922194 0.2676547689 0.3830171767 0.7430194435 -0.479145983596 +1403715964384058112.0000000000 0.4777010781 0.5422250166 0.8977350015 0.2665723230 0.3835997620 0.7376627579 -0.487487512442 +1403715964434057984.0000000000 0.4749417555 0.5320937379 0.9142349372 0.2651568910 0.3845933191 0.7346723112 -0.491971947507 +1403715964484058112.0000000000 0.4717167418 0.5207822007 0.9293931095 0.2653207338 0.3839552594 0.7331128456 -0.49470074048 +1403715964534057984.0000000000 0.4678995836 0.5082867879 0.9436634521 0.2676622338 0.3818648418 0.7323656205 -0.496162039138 +1403715964584058112.0000000000 0.4640159670 0.4946679709 0.9574185855 0.2675470813 0.3819363096 0.7326974779 -0.495678949092 +1403715964634057984.0000000000 0.4599353838 0.4796361911 0.9734602138 0.2655928280 0.3832591387 0.7303718372 -0.499129103341 +1403715964684058112.0000000000 0.4554281136 0.4638326366 0.9918020903 0.2616930417 0.3861490451 0.7266243009 -0.5044034023 +1403715964734057984.0000000000 0.4505012301 0.4479745168 1.0125105968 0.2580055159 0.3888429513 0.7225092394 -0.510112450246 +1403715964784058112.0000000000 0.4454332313 0.4321413264 1.0375514393 0.2527420291 0.3921965993 0.7164467651 -0.51865916263 +1403715964834057984.0000000000 0.4393501030 0.4165001938 1.0662498434 0.2474192928 0.3948820655 0.7100480693 -0.52790490357 +1403715964884058112.0000000000 0.4325642959 0.4023402816 1.0959353684 0.2457054937 0.3945341185 0.7039220905 -0.537089685422 +1403715964934057984.0000000000 0.4253573778 0.3899790625 1.1231895462 0.2472969306 0.3915914811 0.6993778801 -0.544399596643 +1403715964984058112.0000000000 0.4179960060 0.3794373835 1.1481374163 0.2489132866 0.3880996163 0.6946157293 -0.552204538354 +1403715965034057984.0000000000 0.4107542362 0.3712909457 1.1697407968 0.2537270247 0.3820054867 0.6899569625 -0.560048029131 +1403715965084058112.0000000000 0.4044467774 0.3651959299 1.1874405553 0.2591212763 0.3752880982 0.6847287135 -0.568473039321 +1403715965134057984.0000000000 0.3998301566 0.3616377736 1.2014077841 0.2639885429 0.3694483641 0.6795369524 -0.576235616558 +1403715965184058112.0000000000 0.3973640039 0.3611705936 1.2094223775 0.2658866778 0.3662343094 0.6848069118 -0.571153393302 +1403715965234057984.0000000000 0.3972218544 0.3638610365 1.2140543166 0.2638775888 0.3662558500 0.6980686297 -0.555810632061 +1403715965284058112.0000000000 0.3990049063 0.3695426827 1.2166205587 0.2604296327 0.3678589758 0.7155887642 -0.53365616352 +1403715965334057984.0000000000 0.4019519396 0.3763604431 1.2187203969 0.2522427740 0.3733076277 0.7349208319 -0.50685931862 +1403715965384058112.0000000000 0.4046216208 0.3829993344 1.2215543787 0.2419344795 0.3801696865 0.7526694257 -0.4800285957 +1403715965434057984.0000000000 0.4054857808 0.3884347580 1.2263747385 0.2324259869 0.3871997407 0.7670040897 -0.455806151562 +1403715965484058112.0000000000 0.4030192561 0.3912689973 1.2328742808 0.2250450100 0.3929530457 0.7784582232 -0.434678550314 +1403715965534057984.0000000000 0.3963996893 0.3904668670 1.2411745706 0.2203694772 0.3969976791 0.7866150908 -0.418409888991 +1403715965584058112.0000000000 0.3843062540 0.3849736972 1.2514623579 0.2179749350 0.3996958774 0.7910793635 -0.408562815184 +1403715965634057984.0000000000 0.3662494859 0.3744031370 1.2650603639 0.2205871273 0.3993716850 0.7901039769 -0.409364485643 +1403715965684058112.0000000000 0.3418220238 0.3583942948 1.2823378381 0.2297715478 0.3951743786 0.7823498572 -0.423049580172 +1403715965734057984.0000000000 0.3123111201 0.3376146043 1.3024367802 0.2427142710 0.3881033990 0.7690235994 -0.446170637684 +1403715965784058112.0000000000 0.2801792066 0.3134943050 1.3236393322 0.2558536634 0.3801561693 0.7524722424 -0.473081086468 +1403715965834057984.0000000000 0.2475993185 0.2881743389 1.3449926877 0.2685884987 0.3717664347 0.7333121735 -0.50189958427 +1403715965884058112.0000000000 0.2157917639 0.2626655798 1.3655167589 0.2798917875 0.3633677318 0.7146293381 -0.528137659978 +1403715965934057984.0000000000 0.1862825583 0.2382266242 1.3846307429 0.2895084031 0.3554402127 0.6977780201 -0.550411640855 +1403715965984058112.0000000000 0.1596187913 0.2157012693 1.4017673620 0.2988539875 0.3473345225 0.6839371384 -0.567692711211 +1403715966034057984.0000000000 0.1368474857 0.1950703735 1.4172305493 0.3041682496 0.3414256473 0.6736929106 -0.580558408423 +1403715966084058112.0000000000 0.1187712815 0.1771020674 1.4333711622 0.3110789788 0.3337213249 0.6610846531 -0.595673591509 +1403715966134057984.0000000000 0.1068499207 0.1625915465 1.4506882288 0.3166152614 0.3264611429 0.6470801987 -0.611935547948 +1403715966184058112.0000000000 0.1016369104 0.1526925645 1.4670538223 0.3197554257 0.3214769898 0.6389149653 -0.621447246264 +1403715966234057984.0000000000 0.1035142175 0.1479239214 1.4822380030 0.3198530382 0.3203622705 0.6389754768 -0.621910274589 +1403715966284058112.0000000000 0.1124511143 0.1482956242 1.4960207110 0.3163181585 0.3241246987 0.6480507424 -0.612304040147 +1403715966334057984.0000000000 0.1277654270 0.1530082233 1.5085855847 0.3072249951 0.3331259273 0.6650912469 -0.593543218508 +1403715966384058112.0000000000 0.1484942856 0.1615618779 1.5217811004 0.2981569058 0.3427069597 0.6825668196 -0.572500599203 +1403715966434057984.0000000000 0.1730151029 0.1724661578 1.5348895405 0.2891099291 0.3526116134 0.7006534400 -0.548785254925 +1403715966484058112.0000000000 0.2004232706 0.1850002059 1.5472690034 0.2775629836 0.3645760354 0.7201982611 -0.520919926034 +1403715966534057984.0000000000 0.2292289267 0.1978648565 1.5590194774 0.2642184744 0.3773603750 0.7399285030 -0.490197465867 +1403715966584058112.0000000000 0.2573402201 0.2094757149 1.5716366217 0.2528809913 0.3882472107 0.7551696423 -0.46371771475 +1403715966634057984.0000000000 0.2834130424 0.2186368106 1.5849184954 0.2431613698 0.3981228206 0.7670803072 -0.440407277785 +1403715966684058112.0000000000 0.3057220842 0.2243758611 1.5987961379 0.2357800375 0.4060647148 0.7751753718 -0.422637391075 +1403715966734057984.0000000000 0.3237742177 0.2265627359 1.6127458457 0.2303172761 0.4125033867 0.7805818408 -0.409251631776 +1403715966784058112.0000000000 0.3371072371 0.2247756979 1.6259027018 0.2252344621 0.4180487783 0.7854473786 -0.396959785724 +1403715966834057984.0000000000 0.3442696357 0.2181978746 1.6397856793 0.2236108634 0.4210052030 0.7880750446 -0.389474678117 +1403715966884058112.0000000000 0.3444056575 0.2064499858 1.6553705023 0.2276598570 0.4202559642 0.7865620609 -0.390993655198 +1403715966934057984.0000000000 0.3375779767 0.1889521587 1.6738030603 0.2371388806 0.4168008655 0.7781280102 -0.405658710691 +1403715966984058112.0000000000 0.3257077384 0.1672396976 1.6932971500 0.2491095483 0.4113686981 0.7663741340 -0.425900121951 +1403715967034057984.0000000000 0.3098525999 0.1420096172 1.7135091273 0.2646698935 0.4024461810 0.7526804128 -0.448841971117 +1403715967084058112.0000000000 0.2921690822 0.1140482570 1.7346848705 0.2785774437 0.3942973957 0.7351982767 -0.475823145247 +1403715967134057984.0000000000 0.2742249456 0.0852688317 1.7555120364 0.2929097120 0.3848941591 0.7174105708 -0.501380553923 +1403715967184058112.0000000000 0.2574981890 0.0564698611 1.7757065127 0.3059107346 0.3758953385 0.6998927402 -0.52466319591 +1403715967234057984.0000000000 0.2432683888 0.0283883990 1.7958415891 0.3191981195 0.3662646363 0.6810688829 -0.547821096153 +1403715967284058112.0000000000 0.2331717231 0.0019843170 1.8158867738 0.3306264063 0.3569369741 0.6616692931 -0.570504971549 +1403715967334057984.0000000000 0.2284806177 -0.0216304199 1.8357236359 0.3413777105 0.3482114159 0.6431916500 -0.590351225951 +1403715967384058112.0000000000 0.2306907136 -0.0415482420 1.8544133764 0.3459773543 0.3437730002 0.6301722282 -0.604154580729 +1403715967434057984.0000000000 0.2399922020 -0.0572853349 1.8715960891 0.3488638130 0.3419777193 0.6241263853 -0.609763507196 +1403715967484058112.0000000000 0.2569617790 -0.0688824682 1.8876097932 0.3455094967 0.3445160291 0.6242778495 -0.610089386897 +1403715967534057984.0000000000 0.2820167096 -0.0760869917 1.9030579204 0.3366521999 0.3489647272 0.6286567215 -0.608012863326 +1403715967584058112.0000000000 0.3143608918 -0.0789780849 1.9177649833 0.3231621177 0.3549418319 0.6373317727 -0.602819005307 +1403715967634057984.0000000000 0.3526183391 -0.0775922988 1.9315460500 0.3061427417 0.3614936417 0.6506755199 -0.593481538537 +1403715967684058112.0000000000 0.3959973777 -0.0721319004 1.9450628221 0.2860141578 0.3678575566 0.6663989485 -0.582055977541 +1403715967734057984.0000000000 0.4425920973 -0.0634277584 1.9591881456 0.2631951371 0.3741962784 0.6812253052 -0.571522133042 +1403715967784058112.0000000000 0.4910349165 -0.0510834633 1.9720658237 0.2396988792 0.3796859752 0.6979510219 -0.557895490812 +1403715967834057984.0000000000 0.5400686112 -0.0351475463 1.9839936477 0.2151360382 0.3847614250 0.7147698800 -0.542935677119 +1403715967884058112.0000000000 0.5873675590 -0.0169975958 1.9949119368 0.1944663473 0.3865415377 0.7286798877 -0.530842821124 +1403715967934057984.0000000000 0.6315214338 0.0028676288 2.0030526536 0.1778534511 0.3862392122 0.7419814775 -0.518315452142 +1403715967984058112.0000000000 0.6718238590 0.0242441812 2.0074519694 0.1679065051 0.3824417615 0.7564409875 -0.5033316372 +1403715968034057984.0000000000 0.7079603946 0.0467517765 2.0082444744 0.1630042022 0.3759618662 0.7723583230 -0.485329708748 +1403715968084058112.0000000000 0.7384536954 0.0687777469 2.0064888944 0.1617887253 0.3681211350 0.7873736025 -0.467283691557 +1403715968134057984.0000000000 0.7631271906 0.0888931802 2.0033572817 0.1617150312 0.3604591366 0.8000854290 -0.451420830078 +1403715968184058112.0000000000 0.7823151066 0.1062183227 1.9992788280 0.1632379960 0.3534621673 0.8081190400 -0.441997138152 +1403715968234057984.0000000000 0.7952594297 0.1192693492 1.9952401891 0.1675429679 0.3468122794 0.8094355704 -0.443243335195 +1403715968284058112.0000000000 0.8027389275 0.1283081964 1.9908911988 0.1758960829 0.3390869309 0.8039198328 -0.455843749266 +1403715968334057984.0000000000 0.8068169748 0.1345843225 1.9848263078 0.1843641483 0.3325523334 0.7946697693 -0.473200553865 +1403715968384058112.0000000000 0.8080463199 0.1385019039 1.9764155411 0.1939276106 0.3257224812 0.7840900554 -0.491426222456 +1403715968434057984.0000000000 0.8077707846 0.1411492324 1.9652419646 0.2016065963 0.3204787728 0.7712541608 -0.511678762505 +1403715968484058112.0000000000 0.8060841837 0.1436037103 1.9504169872 0.2100065899 0.3147447842 0.7585270264 -0.530537183715 +1403715968534057984.0000000000 0.8036799160 0.1461964753 1.9335347604 0.2169470366 0.3101435179 0.7453303046 -0.548842161949 +1403715968584058112.0000000000 0.8008571161 0.1492139758 1.9134213023 0.2249987125 0.3044788352 0.7325693350 -0.565694606365 +1403715968634057984.0000000000 0.7986516981 0.1533938564 1.8909784177 0.2324634068 0.2990602557 0.7201160324 -0.581340371756 +1403715968684058112.0000000000 0.7981863432 0.1601759318 1.8678614929 0.2396326894 0.2935558349 0.7085193344 -0.59531630148 +1403715968734057984.0000000000 0.8002177809 0.1705432756 1.8444373424 0.2465551262 0.2883420449 0.6981143191 -0.607211521925 +1403715968784058112.0000000000 0.8060751304 0.1851259784 1.8212595307 0.2513597383 0.2839608243 0.6888910980 -0.61774880596 +1403715968834057984.0000000000 0.8160530721 0.2044240117 1.7986772940 0.2562304453 0.2797908196 0.6808603899 -0.626491967699 +1403715968884058112.0000000000 0.8306593072 0.2286287761 1.7762776758 0.2586642487 0.2773064977 0.6756040626 -0.632260281418 +1403715968934057984.0000000000 0.8500196625 0.2579516648 1.7539677003 0.2591518060 0.2762912129 0.6737191623 -0.634512409176 +1403715968984058112.0000000000 0.8744154085 0.2927717562 1.7303734013 0.2563998710 0.2780016086 0.6783698552 -0.629911542502 +1403715969034057984.0000000000 0.9034939274 0.3326528672 1.7049909166 0.2500862321 0.2824927056 0.6912464753 -0.616305977729 +1403715969084058112.0000000000 0.9365774703 0.3770694761 1.6786151746 0.2408963812 0.2896088690 0.7102980242 -0.594619503024 +1403715969134057984.0000000000 0.9725748679 0.4250054142 1.6509140549 0.2299330829 0.2983803658 0.7346755512 -0.56422670018 +1403715969184058112.0000000000 1.0103904873 0.4749022090 1.6229640817 0.2161681038 0.3082581951 0.7608885312 -0.528485457912 +1403715969234057984.0000000000 1.0476275060 0.5248783815 1.5967348713 0.2039682269 0.3169152014 0.7830166472 -0.49481981343 +1403715969284058112.0000000000 1.0827743470 0.5728362749 1.5724534819 0.1932055580 0.3245450382 0.8010799860 -0.464341454731 +1403715969334057984.0000000000 1.1144052462 0.6171519976 1.5501778334 0.1847964484 0.3303695900 0.8143272782 -0.439974193172 +1403715969384058112.0000000000 1.1415209701 0.6568430721 1.5289855295 0.1788718486 0.3344841822 0.8255206994 -0.41790042888 +1403715969434057984.0000000000 1.1634045046 0.6905277007 1.5090256924 0.1736736478 0.3381058153 0.8345297932 -0.39885078161 +1403715969484058112.0000000000 1.1787922473 0.7173851401 1.4902973055 0.1732003833 0.3381577317 0.8418810248 -0.383258810425 +1403715969534057984.0000000000 1.1874443637 0.7369047782 1.4726433801 0.1781684078 0.3337871807 0.8476929224 -0.371831744003 +1403715969584058112.0000000000 1.1885651529 0.7471031685 1.4565034675 0.1901220189 0.3235344944 0.8512337435 -0.366851690438 +1403715969634057984.0000000000 1.1835270443 0.7468798058 1.4431116368 0.2050620218 0.3109754673 0.8517923694 -0.368366102349 +1403715969684058112.0000000000 1.1740456933 0.7369965251 1.4312845895 0.2203300886 0.2983324035 0.8501017525 -0.373870886003 +1403715969734057984.0000000000 1.1606429085 0.7171441317 1.4218283290 0.2368090444 0.2849974424 0.8458439672 -0.383726357471 +1403715969784058112.0000000000 1.1451193111 0.6873162352 1.4149442211 0.2503010675 0.2743943528 0.8382029229 -0.399340675058 +1403715969834057984.0000000000 1.1287423139 0.6480988107 1.4105970168 0.2609094036 0.2665061146 0.8267078953 -0.421253878154 +1403715969884058112.0000000000 1.1131563051 0.6014231660 1.4083124195 0.2639203526 0.2649717189 0.8126511123 -0.446916329253 +1403715969934057984.0000000000 1.0991885329 0.5492865488 1.4076363065 0.2610600669 0.2679514414 0.7955877222 -0.476539445201 +1403715969984058112.0000000000 1.0871793163 0.4938548363 1.4083583468 0.2573411329 0.2706521470 0.7761590484 -0.508035518645 +1403715970034057984.0000000000 1.0772309549 0.4373358124 1.4083585943 0.2543950637 0.2718008790 0.7590810006 -0.534044444105 +1403715970084058112.0000000000 1.0699054061 0.3810716363 1.4083123037 0.2524034427 0.2716349919 0.7430780011 -0.557083492412 +1403715970134057984.0000000000 1.0653654004 0.3265275458 1.4076047113 0.2522140105 0.2696822023 0.7288463007 -0.576578418398 +1403715970184058112.0000000000 1.0641623730 0.2745279718 1.4071766264 0.2528160562 0.2671808099 0.7143244272 -0.595347855601 +1403715970234057984.0000000000 1.0666462880 0.2258622245 1.4078372329 0.2530806417 0.2643823699 0.6982187556 -0.615258255197 +1403715970284058112.0000000000 1.0736056003 0.1821314689 1.4086975440 0.2530202070 0.2616372538 0.6831548674 -0.633108323545 +1403715970334057984.0000000000 1.0854438787 0.1443317910 1.4098224081 0.2521278036 0.2598763929 0.6703360749 -0.64772322625 +1403715970384058112.0000000000 1.1020290319 0.1131095166 1.4111851687 0.2527020177 0.2577541400 0.6612303133 -0.657631330072 +1403715970434057984.0000000000 1.1242762561 0.0890626009 1.4134417745 0.2485622455 0.2584326699 0.6554391926 -0.664702061089 +1403715970484058112.0000000000 1.1521488296 0.0730801206 1.4155274222 0.2416917270 0.2616551203 0.6560174423 -0.665404254968 +1403715970534057984.0000000000 1.1857633598 0.0650249522 1.4171174498 0.2293810398 0.2686670980 0.6630629582 -0.659962000844 +1403715970584058112.0000000000 1.2237547255 0.0645123969 1.4184988162 0.2128629185 0.2789497340 0.6760788623 -0.647914960336 +1403715970634057984.0000000000 1.2644070299 0.0712562125 1.4191839641 0.1984656012 0.2891425945 0.6936703464 -0.629149756148 +1403715970684058112.0000000000 1.3065605508 0.0843449701 1.4200310045 0.1847217030 0.2996609032 0.7126542255 -0.606799135138 +1403715970734057984.0000000000 1.3492094213 0.1027328808 1.4206924574 0.1699821997 0.3112352170 0.7331396637 -0.58029727295 +1403715970784058112.0000000000 1.3907129437 0.1253098865 1.4217759293 0.1536407236 0.3242469290 0.7541191723 -0.550057025333 +1403715970834057984.0000000000 1.4290379202 0.1499897199 1.4239619265 0.1380596553 0.3368426275 0.7734292810 -0.518925546904 +1403715970884058112.0000000000 1.4625478820 0.1749913066 1.4279937847 0.1239832461 0.3485129613 0.7898218691 -0.489232343076 +1403715970934057984.0000000000 1.4899418508 0.1990754628 1.4336417339 0.1120895822 0.3574923248 0.8034967718 -0.462631712 +1403715970984058112.0000000000 1.5096045552 0.2211173111 1.4406959694 0.1035188245 0.3627543717 0.8153273206 -0.43924307521 +1403715971034057984.0000000000 1.5201628058 0.2401904534 1.4488361106 0.1008148431 0.3625496454 0.8263214234 -0.419031057659 +1403715971084058112.0000000000 1.5209397930 0.2547528005 1.4587741284 0.1025029745 0.3570927933 0.8372409974 -0.40125476877 +1403715971134057984.0000000000 1.5117231789 0.2636071323 1.4715667978 0.1098674469 0.3457699233 0.8459929468 -0.390727831391 +1403715971184058112.0000000000 1.4927396232 0.2648437288 1.4873650803 0.1202375903 0.3315247696 0.8515358546 -0.387970278893 +1403715971234057984.0000000000 1.4648210502 0.2576968447 1.5054872054 0.1357619065 0.3109700611 0.8544085362 -0.393512870363 +1403715971284058112.0000000000 1.4296832257 0.2418270837 1.5268450883 0.1518059545 0.2884169006 0.8529593879 -0.407714270377 +1403715971334057984.0000000000 1.3896863159 0.2177048816 1.5501579940 0.1684773398 0.2634603220 0.8485372349 -0.426835572108 +1403715971384058112.0000000000 1.3476743941 0.1866712205 1.5747822491 0.1831373870 0.2377639417 0.8415476738 -0.449139753522 +1403715971434057984.0000000000 1.3052174973 0.1494318612 1.6007413467 0.1944197592 0.2132876657 0.8323115870 -0.473251255683 +1403715971484058112.0000000000 1.2638487019 0.1080009036 1.6261134283 0.2033051068 0.1890367341 0.8218694248 -0.497456324898 +1403715971534057984.0000000000 1.2253011250 0.0631461753 1.6510806281 0.2086040154 0.1660811312 0.8110005084 -0.520749073887 +1403715971584058112.0000000000 1.1908936799 0.0160556917 1.6759127317 0.2096319857 0.1453869027 0.8007365470 -0.541976070902 +1403715971634057984.0000000000 1.1612828830 -0.0321681476 1.7006789036 0.2070449053 0.1274067520 0.7912574350 -0.561080741378 +1403715971684058112.0000000000 1.1369930222 -0.0803550162 1.7248939904 0.2005863191 0.1123685665 0.7832994296 -0.577564228036 +1403715971734057984.0000000000 1.1183690820 -0.1280874640 1.7486039964 0.1886223949 0.1011042328 0.7754368108 -0.594051579138 +1403715971784058112.0000000000 1.1047712455 -0.1740071792 1.7712870734 0.1745013656 0.0922123411 0.7687394350 -0.608346807907 +1403715971834057984.0000000000 1.0959598112 -0.2171120204 1.7931702839 0.1555943016 0.0865899525 0.7639460091 -0.620225030655 +1403715971884058112.0000000000 1.0911723575 -0.2570074917 1.8134819723 0.1361025051 0.0820594513 0.7614404975 -0.62845105083 +1403715971934057984.0000000000 1.0895197407 -0.2929221496 1.8317992607 0.1188657495 0.0767708901 0.7605505401 -0.633671870927 +1403715971984058112.0000000000 1.0906555124 -0.3246832326 1.8489229756 0.1031780571 0.0711796905 0.7611945692 -0.636294403514 +1403715972034057984.0000000000 1.0938716173 -0.3525518925 1.8648288908 0.0907164351 0.0645377705 0.7621936620 -0.637703870245 +1403715972084058112.0000000000 1.0987784948 -0.3760772964 1.8805871439 0.0797402518 0.0580477210 0.7606381181 -0.641639780253 +1403715972134057984.0000000000 1.1047255836 -0.3953761785 1.8968072601 0.0722499850 0.0515434890 0.7560497909 -0.648468906074 +1403715972184058112.0000000000 1.1116902072 -0.4098051167 1.9139786858 0.0666200165 0.0455922807 0.7482390643 -0.658499369807 +1403715972234057984.0000000000 1.1196464519 -0.4186967574 1.9316904954 0.0620993596 0.0408428617 0.7385430179 -0.670096814571 +1403715972284058112.0000000000 1.1285800275 -0.4210360740 1.9490308684 0.0592285304 0.0365826801 0.7297888089 -0.680119094767 +1403715972334057984.0000000000 1.1386404614 -0.4163198193 1.9660754991 0.0572928166 0.0331435404 0.7223470478 -0.688355853745 +1403715972384058112.0000000000 1.1498313856 -0.4041610380 1.9824778567 0.0542541955 0.0318968793 0.7179744777 -0.693218378817 +1403715972434057984.0000000000 1.1620680713 -0.3841347257 1.9976389285 0.0527096483 0.0308005250 0.7175898932 -0.693785100619 +1403715972484058112.0000000000 1.1752235517 -0.3563647872 2.0114168243 0.0516459028 0.0304126480 0.7208882291 -0.690454873786 +1403715972534057984.0000000000 1.1892925222 -0.3210328906 2.0233872819 0.0507416971 0.0310031910 0.7300189194 -0.680835119284 +1403715972584058112.0000000000 1.2044810446 -0.2788039884 2.0337659818 0.0470369743 0.0338348461 0.7454042096 -0.664089821182 +1403715972634057984.0000000000 1.2201607005 -0.2309587228 2.0431658443 0.0436792345 0.0372406980 0.7615390267 -0.645572277693 +1403715972684058112.0000000000 1.2363355094 -0.1788015332 2.0507254008 0.0389179198 0.0417647043 0.7787829195 -0.624690538873 +1403715972734057984.0000000000 1.2526187905 -0.1238935456 2.0559976468 0.0339780451 0.0468269380 0.7957472625 -0.602859042039 +1403715972784058112.0000000000 1.2685690245 -0.0675762973 2.0585152267 0.0302018766 0.0518071968 0.8113037290 -0.581541159539 +1403715972834057984.0000000000 1.2838309042 -0.0114783805 2.0592573442 0.0270710158 0.0564461463 0.8229173936 -0.56470165223 +1403715972884058112.0000000000 1.2979005342 0.0437513985 2.0587935581 0.0258315438 0.0600496500 0.8287812274 -0.555741349955 +1403715972934057984.0000000000 1.3106769669 0.0969016309 2.0577462207 0.0253570286 0.0638899879 0.8278108544 -0.556780279684 +1403715972984058112.0000000000 1.3223774520 0.1485263556 2.0551130373 0.0246001428 0.0677057446 0.8245511664 -0.561182803661 +1403715973034057984.0000000000 1.3329523984 0.1987792841 2.0522053127 0.0206792484 0.0740809555 0.8191599340 -0.568384890121 +1403715973084058112.0000000000 1.3416215960 0.2483307702 2.0487051207 0.0178548674 0.0796610670 0.8145227634 -0.574358760741 +1403715973134057984.0000000000 1.3481344525 0.2979787958 2.0448139430 0.0189862575 0.0820903359 0.8112338223 -0.578619377745 +1403715973184058112.0000000000 1.3525154667 0.3481436002 2.0404808007 0.0221599703 0.0824668798 0.8096406124 -0.580680831619 +1403715973234057984.0000000000 1.3552282481 0.3986084797 2.0365785363 0.0234603877 0.0839164035 0.8089440649 -0.581392421116 +1403715973284058112.0000000000 1.3565557284 0.4493548349 2.0329616126 0.0241696053 0.0854351681 0.8090224017 -0.581033059104 +1403715973334057984.0000000000 1.3561934625 0.5007863938 2.0292901734 0.0238208354 0.0873524399 0.8114360526 -0.577385184698 +1403715973384058112.0000000000 1.3540471804 0.5525748589 2.0254161541 0.0240999777 0.0884308423 0.8155936925 -0.571319618025 +1403715973434057984.0000000000 1.3499416642 0.6040810559 2.0214545963 0.0258910671 0.0884044428 0.8211342263 -0.563252065702 +1403715973484058112.0000000000 1.3441875482 0.6548387185 2.0176894386 0.0272001441 0.0884936363 0.8266409462 -0.555061955597 +1403715973534057984.0000000000 1.3368538610 0.7041802741 2.0147545217 0.0270763564 0.0893142449 0.8322415687 -0.546501425333 +1403715973584058112.0000000000 1.3281038114 0.7513613564 2.0131317434 0.0251127474 0.0911495533 0.8370004433 -0.538972510153 +1403715973634057984.0000000000 1.3176930329 0.7962210920 2.0122162068 0.0218341056 0.0934113629 0.8412320928 -0.532096001816 +1403715973684058112.0000000000 1.3054309676 0.8386398038 2.0113136093 0.0169859529 0.0966865363 0.8453457194 -0.525122657815 +1403715973734057984.0000000000 1.2908940928 0.8781253498 2.0104644074 0.0125386814 0.0994070582 0.8487716553 -0.519179829541 +1403715973784058112.0000000000 1.2737296080 0.9139033094 2.0097793731 0.0085958799 0.1015532700 0.8513678571 -0.514573431246 +1403715973834057984.0000000000 1.2533805440 0.9460340491 2.0094199004 0.0065338157 0.1024057614 0.8531515691 -0.511471181469 +1403715973884058112.0000000000 1.2300360897 0.9745847547 2.0091227889 0.0059339739 0.1019131206 0.8550780510 -0.508350303016 +1403715973934057984.0000000000 1.2037722886 0.9993102337 2.0089567703 0.0054340549 0.1011307909 0.8564508366 -0.506196600815 +1403715973984058112.0000000000 1.1743802217 1.0198181277 2.0090328393 0.0095697965 0.0969690521 0.8559684900 -0.50776310025 +1403715974034057984.0000000000 1.1421918199 1.0361925003 2.0099039417 0.0155387622 0.0914928389 0.8534762242 -0.512802049572 +1403715974084058112.0000000000 1.1081509702 1.0489892832 2.0113413133 0.0212966502 0.0860998505 0.8501798289 -0.518967751432 +1403715974134057984.0000000000 1.0722931826 1.0585699176 2.0131551991 0.0264401154 0.0811892161 0.8456767763 -0.526820673082 +1403715974184058112.0000000000 1.0352184745 1.0653571241 2.0150807447 0.0296327692 0.0777123359 0.8411941992 -0.534298616 +1403715974234057984.0000000000 0.9971648420 1.0699197368 2.0162013795 0.0320233079 0.0748259544 0.8374701683 -0.540388102629 +1403715974284058112.0000000000 0.9585231063 1.0726736936 2.0158739386 0.0345794133 0.0717995919 0.8355272679 -0.543638912683 +1403715974334057984.0000000000 0.9195973481 1.0742151925 2.0136356812 0.0362926991 0.0692193191 0.8352918749 -0.544223308641 +1403715974384058112.0000000000 0.8803718916 1.0743115853 2.0093852570 0.0366844680 0.0675450307 0.8356497669 -0.543857872717 +1403715974434057984.0000000000 0.8405785454 1.0729348716 2.0034652119 0.0372142461 0.0661271192 0.8364802860 -0.542718191328 +1403715974484058112.0000000000 0.8004019963 1.0697307484 1.9970807373 0.0373315960 0.0650328032 0.8363090261 -0.543106158485 +1403715974534057984.0000000000 0.7597629581 1.0646759789 1.9906180457 0.0379484926 0.0638696196 0.8346151785 -0.545800409941 +1403715974584058112.0000000000 0.7188971052 1.0578719721 1.9839354429 0.0381661436 0.0630743320 0.8323765758 -0.549285181152 +1403715974634057984.0000000000 0.6780353896 1.0497882309 1.9767955268 0.0390555584 0.0617784273 0.8299436500 -0.553038540385 +1403715974684058112.0000000000 0.6372133045 1.0404189725 1.9695041749 0.0385213666 0.0616313699 0.8276770905 -0.556478492296 +1403715974734057984.0000000000 0.5961714150 1.0304139690 1.9613856834 0.0391949748 0.0607029004 0.8259452747 -0.559100451648 +1403715974784058112.0000000000 0.5553295497 1.0197275947 1.9528003741 0.0395126116 0.0600234259 0.8246313326 -0.561087432724 +1403715974834057984.0000000000 0.5146758718 1.0085790741 1.9437153519 0.0385952711 0.0597651652 0.8244813466 -0.561399179957 +1403715974884058112.0000000000 0.4739933274 0.9966827413 1.9345550431 0.0386955171 0.0589259304 0.8238353187 -0.562428448218 +1403715974934057984.0000000000 0.4336114381 0.9844623889 1.9250523778 0.0383314006 0.0579421916 0.8233073257 -0.563328016015 +1403715974984058112.0000000000 0.3933367732 0.9719387175 1.9156625718 0.0378722388 0.0568287819 0.8226970802 -0.564363089899 +1403715975034057984.0000000000 0.3531342884 0.9593243194 1.9062774478 0.0389271461 0.0544912584 0.8221931754 -0.565255484211 +1403715975084058112.0000000000 0.3134181768 0.9462099492 1.8972924688 0.0390758383 0.0521165161 0.8217198762 -0.566156685666 +1403715975134057984.0000000000 0.2739182248 0.9327501740 1.8886306460 0.0406423232 0.0491832490 0.8216159983 -0.56645949624 +1403715975184058112.0000000000 0.2349709701 0.9188709283 1.8804870407 0.0415680828 0.0466888966 0.8214327919 -0.56686895299 +1403715975234057984.0000000000 0.1967208894 0.9046161447 1.8727344266 0.0430782398 0.0435502310 0.8217161575 -0.566595269197 +1403715975284058112.0000000000 0.1592777879 0.8897875136 1.8663365480 0.0437605616 0.0411113420 0.8214522775 -0.567107597044 +1403715975334057984.0000000000 0.1228588375 0.8741954376 1.8616100884 0.0443326465 0.0384593048 0.8197432001 -0.569716231362 +1403715975384058112.0000000000 0.0872728490 0.8583285668 1.8582965892 0.0451122350 0.0360095421 0.8178531252 -0.572524641122 +1403715975434057984.0000000000 0.0529140384 0.8425591608 1.8564746508 0.0464814948 0.0332658755 0.8154359546 -0.576018277625 +1403715975484058112.0000000000 0.0198231634 0.8271201142 1.8557553508 0.0490263098 0.0297749709 0.8128893502 -0.579586728996 +1403715975534057984.0000000000 -0.0115460117 0.8125302293 1.8565778859 0.0490923344 0.0282638877 0.8119703194 -0.580943453119 +1403715975584058112.0000000000 -0.0412909058 0.7987977675 1.8581383868 0.0481722241 0.0275865029 0.8130361403 -0.579560744208 +1403715975634057984.0000000000 -0.0696208748 0.7854665370 1.8612110501 0.0461289212 0.0279925364 0.8145085916 -0.577636819038 +1403715975684058112.0000000000 -0.0965283012 0.7722713821 1.8653100461 0.0442729687 0.0284548087 0.8157146661 -0.576055389343 +1403715975734057984.0000000000 -0.1222541565 0.7589770987 1.8703822532 0.0439124551 0.0283358834 0.8166985242 -0.574693217829 +1403715975784058112.0000000000 -0.1466075138 0.7455122811 1.8759987122 0.0426645180 0.0289933301 0.8176013655 -0.573469382631 +1403715975834057984.0000000000 -0.1700381684 0.7317380220 1.8820226621 0.0426217216 0.0291046621 0.8179754488 -0.572933218293 +1403715975884058112.0000000000 -0.1923420647 0.7179576967 1.8876968298 0.0426957356 0.0291174634 0.8191657100 -0.571223937712 +1403715975934057984.0000000000 -0.2134755723 0.7037525756 1.8937136341 0.0426978138 0.0293231757 0.8199804263 -0.570043111156 +1403715975984058112.0000000000 -0.2335078097 0.6889247566 1.8998861973 0.0427975071 0.0295212193 0.8208337833 -0.568795895923 +1403715976034057984.0000000000 -0.2526048539 0.6738769962 1.9055048311 0.0440723354 0.0292036510 0.8219999107 -0.567028149974 +1403715976084058112.0000000000 -0.2704132436 0.6587137755 1.9113506227 0.0440557357 0.0297936866 0.8224102526 -0.566403394026 +1403715976134057984.0000000000 -0.2870108633 0.6428837556 1.9174909306 0.0447946995 0.0304411413 0.8221047665 -0.566754377741 +1403715976184058112.0000000000 -0.3025359003 0.6266845859 1.9235426851 0.0466237415 0.0306210894 0.8212536961 -0.567830029422 +1403715976234057984.0000000000 -0.3169868147 0.6102123184 1.9297604541 0.0485129196 0.0306579171 0.8202421651 -0.569130371118 +1403715976284058112.0000000000 -0.3301897928 0.5933390276 1.9357733220 0.0492659238 0.0316429124 0.8196687603 -0.569837449002 +1403715976334057984.0000000000 -0.3425548872 0.5760919234 1.9414378765 0.0523624722 0.0309790117 0.8190362677 -0.570506848803 +1403715976384058112.0000000000 -0.3534686018 0.5584221525 1.9469589580 0.0552965602 0.0298443149 0.8178733834 -0.571956935395 +1403715976434057984.0000000000 -0.3623915889 0.5405627234 1.9517006680 0.0577381987 0.0268831435 0.8178380973 -0.571912968608 +1403715976484058112.0000000000 -0.3693219436 0.5226672490 1.9556702528 0.0589724677 0.0223793750 0.8179015460 -0.571890262744 +1403715976534057984.0000000000 -0.3741864988 0.5044746804 1.9591599491 0.0587577447 0.0176609271 0.8177432997 -0.572303691105 +1403715976584058112.0000000000 -0.3766104313 0.4863914299 1.9620030846 0.0575336219 0.0110381562 0.8175964975 -0.5728036389 +1403715976634057984.0000000000 -0.3765841060 0.4683407562 1.9640947334 0.0531006116 0.0050239044 0.8181764429 -0.572487898311 +1403715976684058112.0000000000 -0.3741996754 0.4501658258 1.9661043996 0.0460590465 -0.0000943908 0.8180303819 -0.573327872696 +1403715976734057984.0000000000 -0.3700312639 0.4322182762 1.9672211241 0.0386174119 -0.0044881574 0.8188929743 -0.572628019457 +1403715976784058112.0000000000 -0.3644473659 0.4138273053 1.9682066929 0.0324542269 -0.0084083181 0.8189939050 -0.572821967929 +1403715976834057984.0000000000 -0.3576412267 0.3951269277 1.9685661245 0.0276411781 -0.0125362153 0.8192326098 -0.572657611229 +1403715976884058112.0000000000 -0.3496226804 0.3761908442 1.9687732793 0.0235947059 -0.0160466740 0.8188767071 -0.573259742792 +1403715976934057984.0000000000 -0.3404564249 0.3573026069 1.9684437050 0.0206844772 -0.0193884841 0.8191988462 -0.572808423006 +1403715976984058112.0000000000 -0.3298974958 0.3383204620 1.9684166045 0.0171018846 -0.0230654893 0.8190381711 -0.573020054672 +1403715977034057984.0000000000 -0.3180445796 0.3193879690 1.9678739240 0.0140833133 -0.0281369414 0.8187957148 -0.57322207757 +1403715977084058112.0000000000 -0.3047857548 0.3006823972 1.9670625299 0.0098834024 -0.0334823314 0.8185167697 -0.573420918245 +1403715977134057984.0000000000 -0.2900585377 0.2823371861 1.9661055902 0.0054911051 -0.0404739585 0.8184250932 -0.573159727486 +1403715977184058112.0000000000 -0.2738005227 0.2641876488 1.9651276866 0.0005669509 -0.0491210792 0.8177777643 -0.573433803017 +1403715977234057984.0000000000 -0.2558083288 0.2462575198 1.9637229050 0.0062601830 0.0583745228 -0.8172747235 0.573249728742 +1403715977284058112.0000000000 -0.2364818104 0.2289316265 1.9615300077 0.0133414580 0.0693673020 -0.8168270176 0.572541532318 +1403715977334057984.0000000000 -0.2155116889 0.2117119592 1.9600328850 0.0209250811 0.0821036096 -0.8152711086 0.572847412351 +1403715977384058112.0000000000 -0.1930091169 0.1952426635 1.9586679087 0.0300994347 0.0953640008 -0.8136988347 0.572620238666 +1403715977434057984.0000000000 -0.1690433506 0.1794112824 1.9569094604 0.0410807779 0.1084862509 -0.8122241907 0.571694819927 +1403715977484058112.0000000000 -0.1440696225 0.1641059148 1.9545609726 0.0503073826 0.1241193847 -0.8097908604 0.571228770267 +1403715977534057984.0000000000 -0.1175215174 0.1494575658 1.9525287930 0.0613080716 0.1393890969 -0.8077908920 0.569461038942 +1403715977584058112.0000000000 -0.0896249919 0.1349632068 1.9508173031 0.0727469167 0.1552915532 -0.8043889767 0.568815254491 +1403715977634057984.0000000000 -0.0602849740 0.1209616081 1.9492523911 0.0854424313 0.1711648715 -0.8007227582 0.567666488509 +1403715977684058112.0000000000 -0.0299962183 0.1078140824 1.9471404190 0.0980929843 0.1871304111 -0.7970856760 0.56569815343 +1403715977734057984.0000000000 0.0007444006 0.0961726916 1.9444358071 0.1112402835 0.2035187097 -0.7935541700 0.562563341719 +1403715977784058112.0000000000 0.0322577381 0.0849264226 1.9421133006 0.1231399027 0.2207875230 -0.7886662972 0.560441705851 +1403715977834057984.0000000000 0.0645589975 0.0743735131 1.9397385373 0.1354660432 0.2380392147 -0.7830145954 0.558457184373 +1403715977884058112.0000000000 0.0973026287 0.0645378356 1.9370960240 0.1459623103 0.2566529398 -0.7757228472 0.557743970706 +1403715977934057984.0000000000 0.1309198586 0.0557342611 1.9345326651 0.1559304154 0.2756048368 -0.7674519888 0.557445176066 +1403715977984058112.0000000000 0.1651440225 0.0487871276 1.9319005437 0.1647897493 0.2959310031 -0.7579159865 0.55752357554 +1403715978034057984.0000000000 0.2002314695 0.0437137079 1.9294007426 0.1744185340 0.3159466325 -0.7483204159 0.556572057871 +1403715978084058112.0000000000 0.2359260095 0.0410042318 1.9269280930 0.1845679017 0.3363945798 -0.7367582865 0.556741056236 +1403715978134057984.0000000000 0.2722090458 0.0404969620 1.9239101660 0.1932508233 0.3573305596 -0.7252855994 0.555814528259 +1403715978184058112.0000000000 0.3093220239 0.0422475209 1.9204428141 0.2012517161 0.3775877233 -0.7136631017 0.554626212251 +1403715978234057984.0000000000 0.3474904680 0.0468834689 1.9163520849 0.2093888271 0.3970132965 -0.7026956000 0.552046787247 +1403715978284058112.0000000000 0.3864536408 0.0547334009 1.9127121334 0.2187959001 0.4149116600 -0.6910316525 0.549956292622 +1403715978334057984.0000000000 0.4258189347 0.0666571160 1.9098992688 0.2313728387 0.4298266381 -0.6812545307 0.54553454063 +1403715978384058112.0000000000 0.4660250739 0.0823396720 1.9073739406 0.2462186517 0.4424415766 -0.6716064951 0.540894206526 +1403715978434057984.0000000000 0.5067870652 0.1014790800 1.9041550862 0.2611220696 0.4542649968 -0.6641333389 0.53327805649 +1403715978484058112.0000000000 0.5480954303 0.1237535081 1.9008532723 0.2779637570 0.4643410747 -0.6578032665 0.523849576441 +1403715978534057984.0000000000 0.5889312387 0.1492332356 1.8971905716 0.2968483992 0.4736592052 -0.6510995904 0.513417285057 +1403715978584058112.0000000000 0.6294942068 0.1770960728 1.8935086212 0.3159409764 0.4824332919 -0.6432509122 0.503654328111 +1403715978634057984.0000000000 0.6688820647 0.2071075332 1.8890440664 0.3333164624 0.4926011972 -0.6340496533 0.494191494886 +1403715978684058112.0000000000 0.7067665386 0.2387147798 1.8840466909 0.3486272269 0.5038937535 -0.6252563834 0.483326594339 +1403715978734057984.0000000000 0.7428159214 0.2713416561 1.8786164180 0.3611720057 0.5169147831 -0.6148680200 0.473593926543 +1403715978784058112.0000000000 0.7768775550 0.3048851134 1.8730047070 0.3712948339 0.5310571027 -0.6034700257 0.464696059791 +1403715978834057984.0000000000 0.8089784299 0.3394492355 1.8674488551 0.3798878801 0.5463151192 -0.5923277364 0.454282777264 +1403715978884058112.0000000000 0.8399747396 0.3746734475 1.8624383925 0.3870539623 0.5624028058 -0.5800135032 0.444383449751 +1403715978934057984.0000000000 0.8699860582 0.4106236916 1.8583398655 0.3947243282 0.5781687656 -0.5671598911 0.433870074049 +1403715978984058112.0000000000 0.8988469711 0.4473308160 1.8547639390 0.4013136074 0.5944126447 -0.5531064372 0.423903603962 +1403715979034057984.0000000000 0.9264846727 0.4851364426 1.8519516699 0.4097776542 0.6092477737 -0.5375859909 0.414609125137 +1403715979084058112.0000000000 0.9537224950 0.5244142740 1.8504941112 0.4209752209 0.6219039861 -0.5211225732 0.405520109437 +1403715979134057984.0000000000 0.9791557529 0.5649205431 1.8506189645 0.4348687358 0.6323847861 -0.5050211225 0.394882679637 +1403715979184058112.0000000000 1.0031219441 0.6062885690 1.8529430573 0.4498661675 0.6416901638 -0.4865117159 0.386213043941 +1403715979234057984.0000000000 1.0252191486 0.6481881883 1.8571714968 0.4680529735 0.6483154586 -0.4669439717 0.37759344205 +1403715979284058112.0000000000 1.0452307757 0.6900985847 1.8626358797 0.4854771970 0.6547174403 -0.4456853159 0.370164238902 +1403715979334057984.0000000000 1.0625128234 0.7315180074 1.8672303813 0.4972403799 0.6641513334 -0.4225722436 0.364811882967 +1403715979384058112.0000000000 1.0764789525 0.7726897805 1.8716192867 0.5064558855 0.6744743802 -0.4002153783 0.358349546537 +1403715979434057984.0000000000 1.0870256123 0.8133676109 1.8748756681 0.5109997836 0.6867613861 -0.3791921874 0.351356378447 +1403715979484058112.0000000000 1.0939811015 0.8540633177 1.8784743869 0.5155130980 0.6978755860 -0.3598675404 0.343090754255 +1403715979534057984.0000000000 1.0973780296 0.8950810829 1.8827016397 0.5198737646 0.7080692425 -0.3417927405 0.333986435697 +1403715979584058112.0000000000 1.0968718813 0.9364598136 1.8874649296 0.5242524295 0.7176176641 -0.3258111635 0.322538934214 +1403715979634057984.0000000000 1.0926996697 0.9781408881 1.8926483698 0.5284242690 0.7265904121 -0.3098626695 0.311157983883 +1403715979684058112.0000000000 1.0846240145 1.0203317350 1.8984199721 0.5333948167 0.7348859227 -0.2940117621 0.2983114711 +1403715979734057984.0000000000 1.0729213160 1.0626375222 1.9046702445 0.5395379568 0.7418522598 -0.2763100073 0.286717278366 +1403715979784058112.0000000000 1.0574756558 1.1052581079 1.9112920616 0.5469682430 0.7474982856 -0.2586024778 0.274220372382 +1403715979834057984.0000000000 1.0383233516 1.1477403209 1.9180035987 0.5548258745 0.7521264426 -0.2407199913 0.261778435256 +1403715979884058112.0000000000 1.0152960365 1.1899032857 1.9252116273 0.5637266137 0.7556635968 -0.2227105653 0.248162925332 +1403715979934057984.0000000000 0.9886480290 1.2312746430 1.9322855198 0.5720301280 0.7588180743 -0.2039896523 0.235297438326 +1403715979984058112.0000000000 0.9581984692 1.2716392420 1.9398855918 0.5809913809 0.7610016133 -0.1847144616 0.221824542235 +1403715980034057984.0000000000 0.9239027472 1.3104925096 1.9476469432 0.5898043860 0.7625759098 -0.1655491209 0.207851525301 +1403715980084058112.0000000000 0.8860116537 1.3475048902 1.9549062153 0.5967927944 0.7646723776 -0.1461565026 0.19430077808 +1403715980134057984.0000000000 0.8443204582 1.3824611718 1.9614570410 0.6026461219 0.7668977200 -0.1269420889 0.180475053297 +1403715980184058112.0000000000 0.7989921315 1.4150284994 1.9676086096 0.6075177521 0.7693968948 -0.1084228604 0.164909316315 +1403715980234057984.0000000000 0.7502802684 1.4451952517 1.9734769173 0.6115426344 0.7720042792 -0.0914599294 0.147173640878 +1403715980284058112.0000000000 0.6982028602 1.4724894568 1.9785700613 0.6134271491 0.7755930652 -0.0751583085 0.128505870096 +1403715980334057984.0000000000 0.6433512044 1.4969752195 1.9830032268 0.6146945834 0.7788003600 -0.0579622823 0.110729138571 +1403715980384058112.0000000000 0.5858271406 1.5186978876 1.9874026226 0.6163651137 0.7809700587 -0.0406665850 0.0923365736352 +1403715980434057984.0000000000 0.5262264247 1.5375912249 1.9919384265 0.6192732900 0.7814058732 -0.0232214582 0.0732544713366 +1403715980484058112.0000000000 0.4649799745 1.5531990062 1.9965231566 0.6228132791 0.7804596717 -0.0051415357 0.054404823242 +1403715980534057984.0000000000 0.4018946358 1.5652178011 2.0009612081 0.6263900976 0.7787428942 0.0115287459 0.032588931079 +1403715980584058112.0000000000 0.3380435267 1.5736822006 2.0046589142 0.6279533349 0.7776275922 0.0289494223 0.0114833820038 +1403715980634057984.0000000000 0.2738518384 1.5784863787 2.0075261223 0.6279640307 0.7767640178 0.0471897915 -0.00848294267204 +1403715980684058112.0000000000 0.2097775278 1.5799569279 2.0098259936 0.6271466881 0.7755922067 0.0662318124 -0.0275155876651 +1403715980734057984.0000000000 0.1462874248 1.5777630896 2.0114699866 0.6255750703 0.7741028196 0.0852757405 -0.0463541166199 +1403715980784058112.0000000000 0.0833577838 1.5719137972 2.0123420755 0.6220707414 0.7732016318 0.1038829157 -0.0662990880352 +1403715980834057984.0000000000 0.0216526945 1.5630043064 2.0126714474 0.6176129393 0.7721060902 0.1234225572 -0.0846954255911 +1403715980884058112.0000000000 -0.0390284483 1.5508428653 2.0132338201 0.6135155499 0.7696904498 0.1425332589 -0.104209172858 +1403715980934057984.0000000000 -0.0980626941 1.5360381684 2.0136359847 0.6093666968 0.7663026659 0.1625540558 -0.122591321478 +1403715980984058112.0000000000 -0.1553390515 1.5184074307 2.0144385297 0.6058901055 0.7612016538 0.1824954182 -0.142002269644 +1403715981034057984.0000000000 -0.2102427122 1.4979094601 2.0152709415 0.6025998681 0.7549262400 0.2020588580 -0.161653917366 +1403715981084058112.0000000000 -0.2625759279 1.4748305845 2.0161767374 0.5993470455 0.7474571191 0.2219660396 -0.181168572006 +1403715981134057984.0000000000 -0.3121388112 1.4495024880 2.0167731873 0.5947816911 0.7398387194 0.2423494066 -0.200350129178 +1403715981184058112.0000000000 -0.3585435526 1.4221155246 2.0173457543 0.5910432951 0.7307305317 0.2641671426 -0.216602017853 +1403715981234057984.0000000000 -0.4016648922 1.3917297319 2.0181164022 0.5851194260 0.7217438840 0.2854460939 -0.235035211797 +1403715981284058112.0000000000 -0.4414096141 1.3590552848 2.0195648823 0.5782082249 0.7121710769 0.3065744543 -0.253967930649 +1403715981334057984.0000000000 -0.4774116773 1.3248508042 2.0213321702 0.5710334565 0.7016040660 0.3278724658 -0.27234568517 +1403715981384058112.0000000000 -0.5098993153 1.2891632976 2.0236602040 0.5624638850 0.6906356834 0.3486001094 -0.291778502514 +1403715981434057984.0000000000 -0.5383596299 1.2521226066 2.0263550990 0.5540387534 0.6783220714 0.3690951807 -0.310948508058 +1403715981484058112.0000000000 -0.5626155175 1.2136091476 2.0298686213 0.5450907365 0.6648485296 0.3884337405 -0.331619889283 +1403715981534057984.0000000000 -0.5824821007 1.1742041166 2.0341349262 0.5377367501 0.6491550759 0.4071329282 -0.351681182099 +1403715981584058112.0000000000 -0.5974177918 1.1340971858 2.0386306800 0.5305981822 0.6324004709 0.4253506324 -0.370960985845 +1403715981634057984.0000000000 -0.6069113628 1.0934782173 2.0430247670 0.5224035611 0.6154008483 0.4444343594 -0.388399813849 +1403715981684058112.0000000000 -0.6108154089 1.0524261562 2.0470856939 0.5134018688 0.5985651824 0.4637610949 -0.403811701692 +1403715981734057984.0000000000 -0.6091264760 1.0110370758 2.0498523444 0.5025059861 0.5828848935 0.4849291131 -0.415423507033 +1403715981784058112.0000000000 -0.6019706803 0.9693568530 2.0514449119 0.4875995509 0.5698645536 0.5069198055 -0.424892197285 +1403715981834057984.0000000000 -0.5890859500 0.9275578832 2.0518501077 0.4692727298 0.5593411017 0.5309079275 -0.430182995424 +1403715981884058112.0000000000 -0.5721948889 0.8861379229 2.0524671817 0.4513444360 0.5481508080 0.5534895942 -0.43527940543 +1403715981934057984.0000000000 -0.5519617086 0.8449453128 2.0534013938 0.4342919596 0.5361107230 0.5737859184 -0.441299791945 +1403715981984058112.0000000000 -0.5290485105 0.8043165075 2.0548290578 0.4204745128 0.5217787814 0.5918682449 -0.447928641707 +1403715982034057984.0000000000 -0.5035605025 0.7640685289 2.0566156818 0.4069830263 0.5076569180 0.6077782286 -0.455252561399 +1403715982084058112.0000000000 -0.4756838434 0.7241388702 2.0589219163 0.3949409296 0.4925278335 0.6217945306 -0.463475519328 +1403715982134057984.0000000000 -0.4454566353 0.6847124274 2.0610311160 0.3832883829 0.4772593257 0.6348797160 -0.471424753112 +1403715982184058112.0000000000 -0.4133125468 0.6458096902 2.0635271843 0.3722719818 0.4615574899 0.6469781246 -0.479372048991 +1403715982234057984.0000000000 -0.3790906368 0.6072853670 2.0663410058 0.3610273870 0.4460326312 0.6580860659 -0.487480099702 +1403715982284058112.0000000000 -0.3427441959 0.5690240953 2.0691969897 0.3482580531 0.4314704872 0.6688201781 -0.495206135369 +1403715982334057984.0000000000 -0.3047280836 0.5311880828 2.0721301646 0.3370101647 0.4158439550 0.6789593267 -0.502505907038 +1403715982384058112.0000000000 -0.2648743701 0.4937821119 2.0751436478 0.3245133120 0.4009776657 0.6884062372 -0.509906731138 +1403715982434057984.0000000000 -0.2231547358 0.4572981141 2.0778447831 0.3127942385 0.3846536669 0.6979529347 -0.516781406311 +1403715982484058112.0000000000 -0.1794801139 0.4215185292 2.0802469920 0.3002014638 0.3681428006 0.7073366563 -0.523473795037 +1403715982534057984.0000000000 -0.1339300606 0.3868246945 2.0823908867 0.2892275763 0.3499467761 0.7160568128 -0.53023325421 +1403715982584058112.0000000000 -0.0861806533 0.3530511517 2.0839160804 0.2764494027 0.3319517614 0.7244918052 -0.537117659474 +1403715982634057984.0000000000 -0.0364530726 0.3203602456 2.0853485739 0.2633210617 0.3129916043 0.7323208438 -0.544430395845 +1403715982684058112.0000000000 0.0149945092 0.2884158012 2.0865681923 0.2486735620 0.2944678836 0.7402055535 -0.550949964802 +1403715982734057984.0000000000 0.0679621689 0.2574608050 2.0872239902 0.2339448457 0.2752390999 0.7477622488 -0.557103999493 +1403715982784058112.0000000000 0.1226308593 0.2277287432 2.0880712053 0.2190122240 0.2551222324 0.7550350598 -0.562910606414 +1403715982834057984.0000000000 0.1787475207 0.1998884662 2.0889421627 0.2030611365 0.2355757204 0.7617949006 -0.568277031255 +1403715982884058112.0000000000 0.2360483895 0.1740568225 2.0898660657 0.1882135633 0.2148761652 0.7683759153 -0.572714886269 +1403715982934057984.0000000000 0.2944877427 0.1500046014 2.0906982253 0.1743052298 0.1940417780 0.7746581906 -0.576081732876 +1403715982984058112.0000000000 0.3540651742 0.1273922502 2.0917914847 0.1586449416 0.1747060931 0.7791051458 -0.580779420585 +1403715983034057984.0000000000 0.4146095331 0.1065758376 2.0921721915 0.1430515978 0.1553531683 0.7832245428 -0.584774271838 +1403715983084058112.0000000000 0.4759349523 0.0875176077 2.0923989485 0.1279340728 0.1354817348 0.7870311771 -0.58809820505 +1403715983134057984.0000000000 0.5380734682 0.0701249047 2.0927906319 0.1116782468 0.1161432292 0.7901944656 -0.591296394469 +1403715983184058112.0000000000 0.6010069487 0.0547835395 2.0932360065 0.0953699456 0.0958100172 0.7925387410 -0.59464893681 +1403715983234057984.0000000000 0.6643346363 0.0413794851 2.0936626533 0.0778612936 0.0759116269 0.7942619021 -0.597765066534 +1403715983284058112.0000000000 0.7278834127 0.0298296440 2.0937580456 0.0608507935 0.0548389894 0.7959098077 -0.599847850812 +1403715983334057984.0000000000 0.7913429987 0.0202857825 2.0936301941 0.0454358403 0.0322033522 0.7961330676 -0.602553455893 +1403715983384058112.0000000000 0.8550905939 0.0133747014 2.0932808165 0.0282395168 0.0099868739 0.7971063244 -0.603095597479 +1403715983434057984.0000000000 0.9187769118 0.0088526460 2.0933661446 0.0099441896 -0.0123794908 0.7959818357 -0.605112203321 +1403715983484058112.0000000000 0.9821751866 0.0062386846 2.0944011301 0.0099223087 0.0338778439 -0.7920032352 0.609495459242 +1403715983534057984.0000000000 1.0449876623 0.0061128770 2.0960167994 0.0309249928 0.0545537415 -0.7865020806 0.614395647279 +1403715983584058112.0000000000 1.1068857601 0.0085157319 2.0981682483 0.0519268975 0.0745764494 -0.7796420267 0.619596853353 +1403715983634057984.0000000000 1.1673408470 0.0139431297 2.1004500961 0.0733406284 0.0939421741 -0.7723660619 0.623896374899 +1403715983684058112.0000000000 1.2257272635 0.0229457587 2.1021623484 0.0940893154 0.1128963183 -0.7657912048 0.626071443783 +1403715983734057984.0000000000 1.2818611861 0.0355343302 2.1041939869 0.1142284981 0.1308672918 -0.7584099339 0.628203768196 +1403715983784058112.0000000000 1.3352140001 0.0518035252 2.1056752792 0.1329553479 0.1488203019 -0.7526767690 0.627417783218 +1403715983834057984.0000000000 1.3854624176 0.0716824518 2.1071285314 0.1503706229 0.1668607545 -0.7468770893 0.62587600841 +1403715983884058112.0000000000 1.4322836928 0.0951622944 2.1090099338 0.1677699691 0.1843680957 -0.7410303198 0.623486734348 +1403715983934057984.0000000000 1.4752370133 0.1219866992 2.1108421928 0.1832052176 0.2020115369 -0.7357072323 0.619969398912 +1403715983984058112.0000000000 1.5144934453 0.1521603077 2.1129814233 0.1993092855 0.2183946153 -0.7306697166 0.615387167497 +1403715984034057984.0000000000 1.5496667814 0.1854873612 2.1149729009 0.2135585001 0.2351765600 -0.7267004299 0.609090500479 +1403715984084058112.0000000000 1.5806810935 0.2218838752 2.1172019057 0.2278939417 0.2511659898 -0.7235437293 0.601219151949 +1403715984134057984.0000000000 1.6074903595 0.2606418645 2.1194985093 0.2399637049 0.2678393366 -0.7207098377 0.592669250065 +1403715984184058112.0000000000 1.6304070026 0.3013820732 2.1222036322 0.2537185558 0.2828055161 -0.7178551051 0.58337979271 +1403715984234057984.0000000000 1.6491878121 0.3436821837 2.1251337119 0.2661016230 0.2980801702 -0.7142936078 0.574563121198 +1403715984284058112.0000000000 1.6638437396 0.3871839562 2.1286229028 0.2774532488 0.3131687316 -0.7094589030 0.567109429611 +1403715984334057984.0000000000 1.6745412952 0.4317572177 2.1331729396 0.2901528705 0.3268146550 -0.7032901851 0.560701710884 +1403715984384058112.0000000000 1.6811783921 0.4772383699 2.1377946467 0.3015226557 0.3410645721 -0.6965834804 0.554554326053 +1403715984434057984.0000000000 1.6837174375 0.5233869330 2.1425249883 0.3109360187 0.3562360681 -0.6885175386 0.549871125954 +1403715984484058112.0000000000 1.6820624597 0.5702686805 2.1472304403 0.3195855574 0.3718996409 -0.6811899877 0.543632163553 +1403715984534057984.0000000000 1.6763562879 0.6178323384 2.1515958823 0.3273171478 0.3884567407 -0.6749829773 0.535128793575 +1403715984584058112.0000000000 1.6669336141 0.6658399110 2.1551274049 0.3320428927 0.4072678390 -0.6699804507 0.524410736409 +1403715984634057984.0000000000 1.6544520659 0.7141898524 2.1583395739 0.3354279458 0.4272297859 -0.6642112049 0.513601283512 +1403715984684058112.0000000000 1.6394210986 0.7633255991 2.1615623256 0.3411042254 0.4464943941 -0.6577621725 0.501636908372 +1403715984734057984.0000000000 1.6221231703 0.8129293870 2.1648574860 0.3495262707 0.4645486030 -0.6502849612 0.489035224439 +1403715984784058112.0000000000 1.6032239602 0.8628774483 2.1683436122 0.3623276148 0.4798651379 -0.6416214339 0.476203826686 +1403715984834057984.0000000000 1.5831695871 0.9123521725 2.1724819074 0.3768918522 0.4931757008 -0.6319047003 0.464140829629 +1403715984884058112.0000000000 1.5612108206 0.9608031491 2.1766062653 0.3907512193 0.5064321121 -0.6211392197 0.452798045737 +1403715984934057984.0000000000 1.5377691167 1.0077404226 2.1804714531 0.4031914802 0.5194524968 -0.6094416147 0.442929624269 +1403715984984058112.0000000000 1.5128414709 1.0529341672 2.1839932476 0.4137254119 0.5321179401 -0.5968384252 0.435276550703 +1403715985034057984.0000000000 1.4863076227 1.0963714579 2.1871482544 0.4215528288 0.5450397083 -0.5834529459 0.429892531746 +1403715985084058112.0000000000 1.4580501221 1.1381095699 2.1900289075 0.4271848558 0.5563504653 -0.5716614878 0.425664659126 +1403715985134057984.0000000000 1.4282491451 1.1781751010 2.1927401375 0.4304105332 0.5662195036 -0.5626713573 0.421358743062 +1403715985184058112.0000000000 1.3971389924 1.2169016376 2.1960598005 0.4331157316 0.5736621068 -0.5545736233 0.419250100309 +1403715985234057984.0000000000 1.3647393116 1.2544843258 2.1992941941 0.4333988053 0.5800906362 -0.5475083526 0.419398299012 +1403715985284058112.0000000000 1.3309830567 1.2910258967 2.2022512203 0.4290819115 0.5875125993 -0.5398514845 0.423412368196 +1403715985334057984.0000000000 1.2959951043 1.3273790122 2.2055538014 0.4251581086 0.5925778596 -0.5343497746 0.427273192951 +1403715985384058112.0000000000 1.2597883445 1.3639953765 2.2091624488 0.4215610630 0.5952009401 -0.5315090748 0.430720575829 +1403715985434057984.0000000000 1.2219349313 1.4014797089 2.2132752373 0.4212386049 0.5933855004 -0.5341334004 0.430294313484 +1403715985484058112.0000000000 1.1827260460 1.4392415508 2.2166832650 0.4193020593 0.5902419348 -0.5407831006 0.428198411496 +1403715985534057984.0000000000 1.1421419472 1.4774436974 2.2193824351 0.4150745025 0.5871691098 -0.5504190790 0.424245720517 +1403715985584058112.0000000000 1.1008035916 1.5159050406 2.2215399504 0.4080878297 0.5845274732 -0.5621451526 0.419266960023 +1403715985634057984.0000000000 1.0586475882 1.5544646194 2.2228014994 0.3986998007 0.5826759041 -0.5752051984 0.413117706408 +1403715985684058112.0000000000 1.0167338259 1.5933652517 2.2229592228 0.3888902456 0.5814288909 -0.5880200769 0.406124624811 +1403715985734057984.0000000000 0.9754733445 1.6323367957 2.2214536419 0.3793734664 0.5803730388 -0.6008457478 0.397777948235 +1403715985784058112.0000000000 0.9361809003 1.6716065039 2.2189967101 0.3739345742 0.5766610657 -0.6138837570 0.388306170945 +1403715985834057984.0000000000 0.8992201117 1.7100916431 2.2146398243 0.3706284254 0.5718009077 -0.6248539800 0.381098144706 +1403715985884058112.0000000000 0.8647886626 1.7473676875 2.2073610969 0.3695189447 0.5659362151 -0.6326917066 0.377985653617 +1403715985934057984.0000000000 0.8332488944 1.7833838202 2.1972317071 0.3710746402 0.5591809078 -0.6376782796 0.378135869028 +1403715985984058112.0000000000 0.8043667841 1.8177617311 2.1840171486 0.3733390379 0.5528703670 -0.6403482881 0.380665719421 +1403715986034057984.0000000000 0.7771861974 1.8508897572 2.1672887886 0.3760914893 0.5470484969 -0.6419645177 0.383633538387 +1403715986084058112.0000000000 0.7521139282 1.8824304352 2.1476354981 0.3792336150 0.5415691382 -0.6422054060 0.387887806374 +1403715986134057984.0000000000 0.7290841278 1.9122082893 2.1256858590 0.3827083668 0.5365118820 -0.6430831100 0.390042843857 +1403715986184058112.0000000000 0.7078096678 1.9398440589 2.1023242539 0.3860979236 0.5324954556 -0.6429957567 0.392343522908 +1403715986234057984.0000000000 0.6878798252 1.9648227639 2.0785686365 0.3878288326 0.5300975126 -0.6424249419 0.394810863389 +1403715986284058112.0000000000 0.6695640446 1.9872829188 2.0547301180 0.3873483577 0.5297829334 -0.6407527525 0.398405827579 +1403715986334057984.0000000000 0.6521377143 2.0073610158 2.0311561034 0.3857878667 0.5308558984 -0.6357207743 0.406471197283 +1403715986384058112.0000000000 0.6353903369 2.0257798074 2.0085080902 0.3859761465 0.5309369070 -0.6291553664 0.416283485222 +1403715986434057984.0000000000 0.6187473586 2.0430554277 1.9854699152 0.3855723248 0.5314162143 -0.6239071009 0.42387582959 +1403715986484058112.0000000000 0.6021583532 2.0597023389 1.9614301188 0.3833607666 0.5338594515 -0.6214694414 0.42638520386 +1403715986534057984.0000000000 0.5850663008 2.0758225951 1.9356219935 0.3777785686 0.5388251422 -0.6220213028 0.424311581357 +1403715986584058112.0000000000 0.5676661144 2.0915915419 1.9087675780 0.3701947117 0.5448750792 -0.6250803750 0.418738042543 +1403715986634057984.0000000000 0.5509358003 2.1069973751 1.8812255463 0.3617979815 0.5517605960 -0.6292169600 0.410790071086 +1403715986684058112.0000000000 0.5359326959 2.1219554335 1.8534997456 0.3542797346 0.5576551183 -0.6335408416 0.402656976472 +1403715986734057984.0000000000 0.5235723288 2.1365155445 1.8267255145 0.3491165218 0.5618151178 -0.6364974475 0.396676728533 +1403715986784058112.0000000000 0.5149544143 2.1506311572 1.8014034017 0.3466732292 0.5643605513 -0.6370400794 0.394328261032 +1403715986834057984.0000000000 0.5102049196 2.1641341149 1.7778097173 0.3470365198 0.5646557927 -0.6362581373 0.394848163649 +1403715986884058112.0000000000 0.5086454753 2.1771830796 1.7554676453 0.3494526258 0.5637480356 -0.6338127492 0.397935187697 +1403715986934057984.0000000000 0.5100292938 2.1896488109 1.7341159747 0.3538057545 0.5602566698 -0.6319341049 0.401986615567 +1403715986984058112.0000000000 0.5137645472 2.2013432400 1.7136000260 0.3594109290 0.5544964061 -0.6292384660 0.409165580949 +1403715987034057984.0000000000 0.5194545940 2.2125532356 1.6942380886 0.3687028024 0.5441184033 -0.6286073974 0.415747695849 +1403715987084058112.0000000000 0.5261353209 2.2229268833 1.6750560348 0.3756505312 0.5340386051 -0.6279977333 0.423448100318 +1403715987134057984.0000000000 0.5329684602 2.2327166897 1.6564474083 0.3840710687 0.5213607004 -0.6315280974 0.426432522711 +1403715987184058112.0000000000 0.5394289720 2.2410656669 1.6379942695 0.3904719995 0.5093606452 -0.6345899479 0.43055655692 +1403715987234057984.0000000000 0.5449457496 2.2477601450 1.6196142251 0.3947081428 0.4986083727 -0.6376327750 0.434763863441 +1403715987284058112.0000000000 0.5490327698 2.2524395282 1.6014165650 0.3973560312 0.4888117334 -0.6407917750 0.438813371274 +1403715987334057984.0000000000 0.5514238970 2.2551920241 1.5828442525 0.3959019394 0.4830822247 -0.6435391705 0.442437062932 +1403715987384058112.0000000000 0.5520280684 2.2557828940 1.5640151372 0.3901177502 0.4819281076 -0.6443028017 0.447691120918 +1403715987434057984.0000000000 0.5506684504 2.2550615241 1.5452709220 0.3830501457 0.4830954062 -0.6443304907 0.452470588097 +1403715987484058112.0000000000 0.5477961930 2.2534307336 1.5269252853 0.3748128462 0.4859472168 -0.6441247848 0.456589415561 +1403715987534057984.0000000000 0.5436851870 2.2515956864 1.5092312178 0.3674745227 0.4892819641 -0.6450729746 0.45765324448 +1403715987584058112.0000000000 0.5385653001 2.2493038435 1.4921606080 0.3615309700 0.4924643197 -0.6461571246 0.45744422806 +1403715987634057984.0000000000 0.5327030117 2.2466983702 1.4758513121 0.3573491506 0.4948808374 -0.6467546530 0.457277771347 +1403715987684058112.0000000000 0.5265162901 2.2441369613 1.4605573200 0.3548045635 0.4968021390 -0.6463118316 0.457801674049 +1403715987734057984.0000000000 0.5200458832 2.2417668477 1.4454873713 0.3521280979 0.4993530294 -0.6461342301 0.457343318856 +1403715987784058112.0000000000 0.5133842930 2.2393365818 1.4303018216 0.3483747410 0.5027469482 -0.6466205603 0.455809605936 +1403715987834057984.0000000000 0.5066267249 2.2373671250 1.4146579083 0.3438306865 0.5071699249 -0.6489472218 0.451028413296 +1403715987884058112.0000000000 0.5000310370 2.2355481594 1.3993667512 0.3389710217 0.5117169074 -0.6513170828 0.446128356764 +1403715987934057984.0000000000 0.4943433818 2.2338416863 1.3845531469 0.3357690774 0.5153984074 -0.6536632823 0.440849091843 +1403715987984058112.0000000000 0.4899253063 2.2319915715 1.3701542049 0.3325650833 0.5190960206 -0.6548823603 0.437114265302 +1403715988034057984.0000000000 0.4873586205 2.2301708141 1.3571208659 0.3322040259 0.5208396398 -0.6546639777 0.435639335944 +1403715988084058112.0000000000 0.4867215880 2.2284668243 1.3453212980 0.3346753777 0.5208896801 -0.6526553666 0.436700475266 +1403715988134057984.0000000000 0.4878403012 2.2265734508 1.3346058498 0.3384245517 0.5196139460 -0.6492157269 0.440441948304 +1403715988184058112.0000000000 0.4900486275 2.2246704716 1.3245543707 0.3420799266 0.5186854825 -0.6451768262 0.444627436203 +1403715988234057984.0000000000 0.4930235596 2.2228342566 1.3147228293 0.3454217764 0.5175467508 -0.6413495569 0.448887405617 +1403715988284058112.0000000000 0.4960400610 2.2213953522 1.3054689871 0.3488825615 0.5160371063 -0.6372577165 0.453750224222 +1403715988334057984.0000000000 0.4988927060 2.2206621629 1.2967997161 0.3514466326 0.5151242522 -0.6337532834 0.457699732375 +1403715988384058112.0000000000 0.5019484317 2.2207061442 1.2894173283 0.3557319896 0.5128257535 -0.6314396368 0.460161366425 +1403715988434057984.0000000000 0.5047282236 2.2212805280 1.2824378886 0.3591843844 0.5107432348 -0.6309887121 0.460414130159 +1403715988484058112.0000000000 0.5067568760 2.2222727667 1.2760615817 0.3633172524 0.5080270627 -0.6311996574 0.459887018955 +1403715988534057984.0000000000 0.5079279126 2.2237435328 1.2699791826 0.3678908488 0.5045926651 -0.6335027791 0.456855332243 +1403715988584058112.0000000000 0.5082686715 2.2251807454 1.2643205038 0.3709944517 0.5020439295 -0.6355100199 0.454358915743 +1403715988634057984.0000000000 0.5076761458 2.2262765150 1.2591552500 0.3746010487 0.4991580157 -0.6384906140 0.450383242861 +1403715988684058112.0000000000 0.5057840326 2.2268639926 1.2542749835 0.3778187728 0.4963996714 -0.6423863373 0.445174274683 +1403715988734057984.0000000000 0.5028989382 2.2263808639 1.2496517912 0.3783414644 0.4954855334 -0.6454057043 0.441365267526 +1403715988784058112.0000000000 0.4992721960 2.2245015589 1.2451359107 0.3764726114 0.4963732883 -0.6485770582 0.437298217505 +1403715988834057984.0000000000 0.4949929007 2.2209701617 1.2406575670 0.3719447062 0.4992582691 -0.6502523120 0.43539665471 +1403715988884058112.0000000000 0.4904882098 2.2161237414 1.2367186276 0.3665479057 0.5026808129 -0.6509792259 0.434949055236 +1403715988934057984.0000000000 0.4861734157 2.2100155632 1.2336268294 0.3618399647 0.5054176220 -0.6512459149 0.435320141579 +1403715988984058112.0000000000 0.4822116467 2.2029311562 1.2315689828 0.3583730553 0.5072745050 -0.6508730486 0.436584017589 +1403715989034057984.0000000000 0.4786250372 2.1950595474 1.2300515904 0.3549170295 0.5091655585 -0.6499881562 0.438519934538 +1403715989084058112.0000000000 0.4752632085 2.1869035574 1.2287554129 0.3527071346 0.5100020304 -0.6502161727 0.438992636653 +1403715989134057984.0000000000 0.4724667553 2.1781571587 1.2280158131 0.3513525057 0.5103079768 -0.6493374682 0.441019316964 +1403715989184058112.0000000000 0.4701963282 2.1692556436 1.2275665934 0.3505246446 0.5103093157 -0.6495451438 0.441370572266 +1403715989234057984.0000000000 0.4686000220 2.1600380551 1.2271519934 0.3491848357 0.5106790204 -0.6496049890 0.441916560996 +1403715989284058112.0000000000 0.4676588527 2.1506766920 1.2268646596 0.3492087341 0.5099511956 -0.6497401383 0.442539027495 +1403715989334057984.0000000000 0.4670436764 2.1410977865 1.2264028880 0.3489137825 0.5097300277 -0.6494809425 0.443406107964 +1403715989384058112.0000000000 0.4670055424 2.1313070209 1.2261418118 0.3491215183 0.5091239507 -0.6490856234 0.44451639097 +1403715989434057984.0000000000 0.4674100909 2.1215687041 1.2255487348 0.3480021435 0.5096079751 -0.6493612025 0.444437001699 +1403715989484058112.0000000000 0.4682416859 2.1119178603 1.2255427596 0.3482519914 0.5091412898 -0.6497285270 0.444239280935 +1403715989534057984.0000000000 0.4693907459 2.1021360554 1.2250942988 0.3478058638 0.5091686689 -0.6502757568 0.443756451016 +1403715989584058112.0000000000 0.4713870579 2.0919544539 1.2249686619 0.3481939977 0.5087289549 -0.6491674323 0.445575397904 +1403715989634057984.0000000000 0.4742932372 2.0813341096 1.2252650033 0.3496668046 0.5074868520 -0.6468727288 0.449161322318 +1403715989684058112.0000000000 0.4771955388 2.0710718870 1.2252553155 0.3514180157 0.5063077970 -0.6441016800 0.453090298733 +1403715989734057984.0000000000 0.4803159050 2.0610804753 1.2244292896 0.3533798149 0.5050093481 -0.6416788451 0.456438960278 +1403715989784058112.0000000000 0.4833992245 2.0512392691 1.2225738877 0.3543508097 0.5045821190 -0.6393752266 0.459381876528 +1403715989834057984.0000000000 0.4862404612 2.0417280524 1.2196502800 0.3546267104 0.5047837602 -0.6376255665 0.46137499791 +1403715989884058112.0000000000 0.4885096190 2.0326996099 1.2158255747 0.3546919293 0.5052195073 -0.6359759864 0.46312139819 +1403715989934057984.0000000000 0.4903088637 2.0240647853 1.2112488871 0.3531682369 0.5067300028 -0.6340104194 0.465325357959 +1403715989984058112.0000000000 0.4914325602 2.0165167866 1.2066491485 0.3526516243 0.5077757505 -0.6334192822 0.465382242899 +1403715990034057984.0000000000 0.4920431077 2.0094990508 1.2022578848 0.3518861520 0.5091001498 -0.6327077047 0.465482689099 +1403715990084058112.0000000000 0.4924671904 2.0032115311 1.1976825489 0.3517828972 0.5098771448 -0.6324478230 0.465063266219 +1403715990134057984.0000000000 0.4922971832 1.9974801728 1.1923864092 0.3511261130 0.5108303447 -0.6325042429 0.464436426733 +1403715990184058112.0000000000 0.4919037920 1.9924613177 1.1861672226 0.3508976293 0.5118841084 -0.6326280125 0.463278869706 +1403715990234057984.0000000000 0.4912582474 1.9880807474 1.1789522038 0.3495425836 0.5133452171 -0.6325485840 0.462794726856 +1403715990284058112.0000000000 0.4903830495 1.9846915041 1.1715609162 0.3492533710 0.5141521381 -0.6322787267 0.462485971169 +1403715990334057984.0000000000 0.4894402435 1.9821500569 1.1640125374 0.3485290218 0.5151086723 -0.6318590660 0.462541562851 +1403715990384058112.0000000000 0.4884537509 1.9803185202 1.1554506056 0.3478142552 0.5160666423 -0.6314450538 0.462577137977 +1403715990434057984.0000000000 0.4874332066 1.9793414272 1.1449923645 0.3468999561 0.5172197606 -0.6314864499 0.461918827557 +1403715990484058112.0000000000 0.4866054633 1.9792006244 1.1324689789 0.3453155030 0.5186204566 -0.6312779850 0.46182045333 +1403715990534057984.0000000000 0.4858902906 1.9801190031 1.1184268672 0.3450509325 0.5190793816 -0.6315835605 0.46108421755 +1403715990584058112.0000000000 0.4854599253 1.9820907493 1.1026160414 0.3438488593 0.5201352371 -0.6320235392 0.460188594991 +1403715990634057984.0000000000 0.4852526550 1.9850573436 1.0857948949 0.3422276014 0.5213956890 -0.6328961213 0.458769336332 +1403715990684058112.0000000000 0.4853578402 1.9890634222 1.0683854310 0.3402189012 0.5229756611 -0.6338081344 0.457203243656 +1403715990734057984.0000000000 0.4860457049 1.9941157886 1.0506253729 0.3390092964 0.5240614761 -0.6349970734 0.455204331042 +1403715990784058112.0000000000 0.4876220030 1.9998949908 1.0331482921 0.3379630617 0.5248191033 -0.6353855858 0.454566865358 +1403715990834057984.0000000000 0.4897115286 2.0067291530 1.0162321794 0.3366077398 0.5260919796 -0.6365408910 0.452480002366 +1403715990884058112.0000000000 0.4927940836 2.0145015573 1.0002991155 0.3349558148 0.5273069027 -0.6369983520 0.451647132201 +1403715990934057984.0000000000 0.4971475371 2.0234361272 0.9856261691 0.3340608593 0.5280748650 -0.6375413102 0.450645489289 +1403715990984058112.0000000000 0.5029294163 2.0333262372 0.9723537318 0.3336154913 0.5287238520 -0.6366998168 0.451403517511 +1403715991034057984.0000000000 0.5100363603 2.0444385758 0.9615898323 0.3348679777 0.5281655529 -0.6353145747 0.453078334648 +1403715991084058112.0000000000 0.5182305131 2.0565838653 0.9527652926 0.3371277635 0.5269426312 -0.6332658044 0.45568712464 +1403715991134057984.0000000000 0.5260491384 2.0678607835 0.9494551144 0.3462115650 0.5202246775 -0.6327151908 0.457356889644 +1403715991184058112.0000000000 0.5292482684 2.0738490315 0.9500868319 0.3436784600 0.5224687112 -0.6307056340 0.459480103155 +1403715991234057984.0000000000 0.5300530120 2.0764089158 0.9521918676 0.3389632089 0.5264796439 -0.6278057780 0.462366772849 +1403715991284058112.0000000000 0.5301698974 2.0776886366 0.9520617582 0.3377333784 0.5270332864 -0.6257602936 0.465398898895 +1403715991334057984.0000000000 0.5295337389 2.0764551057 0.9504757293 0.3425239302 0.5231743507 -0.6269985022 0.464584582461 +1403715991384058112.0000000000 0.5284551714 2.0741813694 0.9474804678 0.3501189322 0.5178653144 -0.6324415314 0.457438475393 +1403715991434057984.0000000000 0.5285486955 2.0746069045 0.9477379394 0.3474625729 0.5198734297 -0.6305897538 0.459736815984 +1403715991484058112.0000000000 0.5288202165 2.0756148471 0.9484402991 0.3486912370 0.5189673515 -0.6311967571 0.458996691923 +1403715991534057984.0000000000 0.5282101945 2.0744713643 0.9469509245 0.3484637395 0.5191997094 -0.6312645099 0.458813472524 +1403715991584058112.0000000000 0.5280758853 2.0748208264 0.9472676596 0.3495330802 0.5184672148 -0.6309121948 0.459312720744 +1403715991634057984.0000000000 0.5282601434 2.0747579831 0.9473675575 0.3489869563 0.5187720375 -0.6315522910 0.45850341458 +1403715991684058112.0000000000 0.5283004940 2.0747816694 0.9465108997 0.3485686186 0.5190873930 -0.6314258000 0.458638916468 +1403715991734057984.0000000000 0.5282217395 2.0750212693 0.9468171251 0.3497297040 0.5182748002 -0.6313805323 0.45873629584 +1403715991784058112.0000000000 0.5283465581 2.0748004700 0.9468611189 0.3487342667 0.5189405597 -0.6313042224 0.45884647283 +1403715991834057984.0000000000 0.5283991288 2.0749576427 0.9466085885 0.3494798490 0.5183980451 -0.6317253612 0.458312524438 +1403715991884058112.0000000000 0.5283537215 2.0748500734 0.9466692302 0.3491323190 0.5186452337 -0.6312075595 0.459010634074 +1403715991934057984.0000000000 0.5283533271 2.0748006744 0.9467583644 0.3492502013 0.5185416005 -0.6316664241 0.458406407264 +1403715991984058112.0000000000 0.5283192962 2.0747641353 0.9466431844 0.3492013668 0.5186184788 -0.6313718887 0.458762266349 +1403715992034057984.0000000000 0.5284034268 2.0748294262 0.9467454950 0.3493238368 0.5184812379 -0.6315800015 0.458537637066 +1403715992084058112.0000000000 0.5283392514 2.0747666347 0.9467666082 0.3491449195 0.5186415959 -0.6316122819 0.458448083917 +1403715992134057984.0000000000 0.5282755717 2.0748243926 0.9468594031 0.3493086494 0.5184948343 -0.6314449157 0.458719841071 +1403715992184058112.0000000000 0.5283276292 2.0749799590 0.9468538660 0.3492297276 0.5186042986 -0.6316462159 0.458378922713 +1403715992234057984.0000000000 0.5282799900 2.0749634708 0.9469204409 0.3490981963 0.5186630930 -0.6315509269 0.4585438606 +1403715992284058112.0000000000 0.5282910444 2.0750055052 0.9469279684 0.3493331372 0.5184832585 -0.6315224814 0.458607485136 +1403715992334057984.0000000000 0.5283796926 2.0750968234 0.9468251591 0.3491500152 0.5186158199 -0.6316290180 0.458450304644 +1403715992384058112.0000000000 0.5283875556 2.0750806849 0.9468381357 0.3492586363 0.5184998646 -0.6315946972 0.458545999711 +1403715992434057984.0000000000 0.5284115832 2.0750746994 0.9468478921 0.3492577434 0.5184843652 -0.6316545713 0.45848172741 +1403715992484058112.0000000000 0.5284218129 2.0750721843 0.9468235395 0.3492164255 0.5185053184 -0.6316604800 0.458481363736 +1403715992534057984.0000000000 0.5283951169 2.0750080522 0.9468122005 0.3493415535 0.5184216010 -0.6316779021 0.458456705318 +1403715992584058112.0000000000 0.5283370055 2.0749423376 0.9467566626 0.3492776544 0.5184469041 -0.6317335632 0.458400079394 +1403715992634057984.0000000000 0.5283120408 2.0748834996 0.9466928671 0.3492355324 0.5184379112 -0.6317108020 0.458473704621 +1403715992684058112.0000000000 0.5283235330 2.0748265476 0.9466536820 0.3492983145 0.5184608369 -0.6317193427 0.458388176234 +1403715992734057984.0000000000 0.5283806583 2.0747942639 0.9466122894 0.3493493957 0.5183982976 -0.6317842050 0.458330582688 +1403715992784058112.0000000000 0.5283731983 2.0747836712 0.9465596750 0.3493205201 0.5183632762 -0.6318486916 0.458303304699 +1403715992834057984.0000000000 0.5283660810 2.0747567779 0.9465261779 0.3492242880 0.5183625617 -0.6319096228 0.458293442906 +1403715992884058112.0000000000 0.5283252852 2.0747799224 0.9465473880 0.3492551589 0.5183391187 -0.6319426494 0.458250891818 +1403715992934057984.0000000000 0.5282533591 2.0748493346 0.9465938900 0.3492574870 0.5183429795 -0.6319436463 0.458243375622 +1403715992984058112.0000000000 0.5281824301 2.0749275528 0.9467025946 0.3492327825 0.5183722325 -0.6319992040 0.458152483744 +1403715993034057984.0000000000 0.5281265467 2.0750304730 0.9468108270 0.3492099886 0.5183848862 -0.6320291445 0.458114237085 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_01_easy.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_01_easy.txt new file mode 100644 index 0000000000000000000000000000000000000000..2d37a8d427f1154f0fe53c56bdb7aa4c63806d0e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_01_easy.txt @@ -0,0 +1,2241 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1413393213505760512.0000000000 -1.0805520923 0.4272539299 1.3077239102 0.4340338472 0.5668555860 0.5560183037 -0.425597239215 +1413393213555760384.0000000000 -1.0818362344 0.4271738049 1.3075269095 0.4340269706 0.5668909070 0.5559887051 -0.42559587414 +1413393213605760512.0000000000 -1.0827582610 0.4271218722 1.3073925543 0.4339999222 0.5669556090 0.5559333401 -0.425609593765 +1413393213655760384.0000000000 -1.0833468104 0.4270903424 1.3073260358 0.4340064265 0.5669887467 0.5559014958 -0.425600410938 +1413393213705760512.0000000000 -1.0836815634 0.4270210800 1.3072699609 0.4339531497 0.5670011669 0.5558911148 -0.425651746225 +1413393213755760384.0000000000 -1.0838215671 0.4269766590 1.3072619064 0.4338671409 0.5670360002 0.5559042586 -0.425675855264 +1413393213805760512.0000000000 -1.0838427606 0.4269659294 1.3071936351 0.4338748089 0.5670543975 0.5558931866 -0.42565799141 +1413393213855760384.0000000000 -1.0837980369 0.4269336509 1.3072017875 0.4338701315 0.5670693422 0.5558668007 -0.425677307328 +1413393213905760512.0000000000 -1.0836660433 0.4269000753 1.3072289116 0.4337524706 0.5671400686 0.5559162393 -0.425638428462 +1413393213955760384.0000000000 -1.0835189941 0.4268026346 1.3073096465 0.4336432103 0.5671484807 0.5559856856 -0.425647840799 +1413393214005760512.0000000000 -1.0834673236 0.4267965040 1.3075277790 0.4334920450 0.5672226280 0.5560400413 -0.425632012058 +1413393214055760384.0000000000 -1.0833864065 0.4269143662 1.3074919164 0.4337779712 0.5673547272 0.5558013904 -0.425476320775 +1413393214105760512.0000000000 -1.0833093800 0.4269814763 1.3075714677 0.4334948485 0.5675069359 0.5559143266 -0.425414333891 +1413393214155760384.0000000000 -1.0832362302 0.4269947222 1.3075344194 0.4335965389 0.5674042077 0.5558702795 -0.4255052749 +1413393214205760512.0000000000 -1.0831150302 0.4269364770 1.3075835202 0.4333725687 0.5675167425 0.5558485675 -0.425611717053 +1413393214255760384.0000000000 -1.0831404480 0.4270055863 1.3075213271 0.4335557183 0.5673786539 0.5559041627 -0.42553667771 +1413393214305760512.0000000000 -1.0830906000 0.4268867899 1.3074635006 0.4334626367 0.5674634781 0.5558566890 -0.425580409455 +1413393214355760384.0000000000 -1.0830453377 0.4268671210 1.3074224895 0.4334422053 0.5674672406 0.5558053352 -0.425663264716 +1413393214405760512.0000000000 -1.0830525035 0.4268792002 1.3073977778 0.4334629979 0.5674402703 0.5558743357 -0.425587936748 +1413393214455760384.0000000000 -1.0830122896 0.4268638912 1.3074088938 0.4334012344 0.5674383974 0.5557994161 -0.425751152995 +1413393214505760512.0000000000 -1.0829995601 0.4269309007 1.3073674297 0.4334497028 0.5674314454 0.5558475204 -0.425648263203 +1413393214555760384.0000000000 -1.0829379888 0.4269039954 1.3073921917 0.4333340751 0.5674813620 0.5557587287 -0.425815357435 +1413393214605760512.0000000000 -1.0828938491 0.4269072140 1.3073438279 0.4333704501 0.5674730114 0.5558053075 -0.425728663078 +1413393214655760384.0000000000 -1.0828553864 0.4268626309 1.3073771738 0.4333176904 0.5674966139 0.5557631335 -0.425805955572 +1413393214705760512.0000000000 -1.0828332511 0.4267989358 1.3073699465 0.4332858446 0.5675006672 0.5557236752 -0.425884451929 +1413393214755760384.0000000000 -1.0828353008 0.4267854846 1.3073348892 0.4333191039 0.5675008579 0.5557370955 -0.425832844098 +1413393214805760512.0000000000 -1.0828251845 0.4267529226 1.3073045093 0.4332431308 0.5675604492 0.5556659634 -0.42592354143 +1413393214855760384.0000000000 -1.0828168470 0.4267637437 1.3072708732 0.4332783523 0.5675651555 0.5556609071 -0.425888036901 +1413393214905760512.0000000000 -1.0828046704 0.4267812342 1.3072570903 0.4332842255 0.5675512474 0.5556898504 -0.425862831938 +1413393214955760384.0000000000 -1.0827778435 0.4267739326 1.3073209192 0.4332416330 0.5675851873 0.5556571863 -0.425903549929 +1413393215005760512.0000000000 -1.0827527069 0.4267790700 1.3074221515 0.4332413185 0.5676195303 0.5556454754 -0.425873378451 +1413393215055760384.0000000000 -1.0827627160 0.4268520382 1.3075236758 0.4333306578 0.5677054647 0.5557656469 -0.425510977643 +1413393215105760512.0000000000 -1.0827694502 0.4268106428 1.3075738635 0.4329515930 0.5677993072 0.5557424350 -0.425801844503 +1413393215155760384.0000000000 -1.0828128926 0.4267997095 1.3074968751 0.4331195830 0.5676568278 0.5557177510 -0.425853183377 +1413393215205760512.0000000000 -1.0828451156 0.4268325310 1.3074818968 0.4330456406 0.5676539106 0.5558567865 -0.425750800154 +1413393215255760384.0000000000 -1.0828908908 0.4267974347 1.3074335051 0.4330517665 0.5676838152 0.5557561135 -0.425836113815 +1413393215305760512.0000000000 -1.0829122985 0.4268325807 1.3074305312 0.4330712848 0.5676948327 0.5557721877 -0.425780594478 +1413393215355760384.0000000000 -1.0829049253 0.4268206880 1.3074204099 0.4330754561 0.5677369309 0.5557120082 -0.425798767653 +1413393215405760512.0000000000 -1.0827963978 0.4268420018 1.3075139815 0.4329184124 0.5678667205 0.5557771133 -0.425700406764 +1413393215455760384.0000000000 -1.0828033518 0.4268708502 1.3075877444 0.4328332775 0.5678780230 0.5559427360 -0.425555612298 +1413393215505760512.0000000000 -1.0828634367 0.4268548333 1.3076682902 0.4326959068 0.5680572241 0.5558987762 -0.425513563856 +1413393215555760384.0000000000 -1.0829841078 0.4269053259 1.3078268144 0.4326405036 0.5680960642 0.5559729642 -0.425421108513 +1413393215605760512.0000000000 -1.0832777849 0.4269262720 1.3078929066 0.4326793435 0.5680721778 0.5560380320 -0.425328453603 +1413393215655760384.0000000000 -1.0835861753 0.4269080846 1.3080416842 0.4323705641 0.5683270854 0.5560092953 -0.425339491269 +1413393215705760512.0000000000 -1.0837540263 0.4269697466 1.3081247730 0.4319169812 0.5686589021 0.5563416521 -0.42492204059 +1413393215755760384.0000000000 -1.0836644442 0.4269669760 1.3081051975 0.4316269966 0.5688937321 0.5566246599 -0.42453155986 +1413393215805760512.0000000000 -1.0834218098 0.4269596555 1.3081933282 0.4313833752 0.5690061855 0.5568978683 -0.424270089491 +1413393215855760384.0000000000 -1.0831927050 0.4270278344 1.3081553480 0.4311269476 0.5691694265 0.5570545860 -0.424106009467 +1413393215905760512.0000000000 -1.0831000770 0.4270291368 1.3081091303 0.4309666125 0.5692336044 0.5570911312 -0.42413483006 +1413393215955760384.0000000000 -1.0830998860 0.4270229793 1.3081836752 0.4307834798 0.5693623978 0.5570170206 -0.42424532079 +1413393216005760512.0000000000 -1.0829252420 0.4270245999 1.3082812275 0.4310151322 0.5691864590 0.5570473791 -0.424206256763 +1413393216055760384.0000000000 -1.0829511362 0.4269258692 1.3083536600 0.4312135493 0.5690177926 0.5571826608 -0.424053191334 +1413393216105760512.0000000000 -1.0830211396 0.4269187106 1.3082270060 0.4311597962 0.5690934060 0.5572259258 -0.423949517067 +1413393216155760384.0000000000 -1.0831647735 0.4267859313 1.3081528412 0.4313871700 0.5688433790 0.5570675821 -0.424261745379 +1413393216205760512.0000000000 -1.0832169731 0.4266568173 1.3082068371 0.4313146630 0.5688819464 0.5573056680 -0.423970971781 +1413393216255760384.0000000000 -1.0834716705 0.4267247085 1.3083560026 0.4304888456 0.5693449432 0.5578549436 -0.423466115951 +1413393216305760512.0000000000 -1.0837909291 0.4268240813 1.3084776323 0.4295746985 0.5699985710 0.5583479070 -0.422865016547 +1413393216355760384.0000000000 -1.0838860112 0.4270628645 1.3083509299 0.4292148155 0.5704396164 0.5584109131 -0.422552408881 +1413393216405760512.0000000000 -1.0835605908 0.4270659546 1.3082195150 0.4286948923 0.5706840594 0.5587773361 -0.422265653696 +1413393216455760384.0000000000 -1.0836449687 0.4270113583 1.3086239947 0.4289594518 0.5704120396 0.5589462109 -0.422141003812 +1413393216505760512.0000000000 -1.0836635030 0.4273069916 1.3084448912 0.4279402003 0.5716150414 0.5597094780 -0.42053386265 +1413393216555760384.0000000000 -1.0835685469 0.4278807966 1.3084198996 0.4280652202 0.5723419860 0.5597030479 -0.419424983158 +1413393216605760512.0000000000 -1.0834307885 0.4284221393 1.3083468183 0.4275494497 0.5734661467 0.5590012154 -0.41935150869 +1413393216655760384.0000000000 -1.0837075318 0.4289965403 1.3089934750 0.4287019902 0.5732646155 0.5584181962 -0.419227148922 +1413393216705760512.0000000000 -1.0835403970 0.4296675636 1.3103210707 0.4310916762 0.5725834285 0.5583096717 -0.417849846967 +1413393216755760384.0000000000 -1.0830214422 0.4305898635 1.3115702771 0.4334131631 0.5723343178 0.5583203577 -0.415770173237 +1413393216805760512.0000000000 -1.0823327517 0.4313704669 1.3144443749 0.4357973830 0.5716789976 0.5583211847 -0.414175348605 +1413393216855760384.0000000000 -1.0813902441 0.4318974856 1.3187701123 0.4379924483 0.5710414127 0.5579707199 -0.413210595092 +1413393216905760512.0000000000 -1.0800141965 0.4322670612 1.3244894800 0.4407466347 0.5700685726 0.5570987821 -0.412801615212 +1413393216955760384.0000000000 -1.0781515326 0.4323498610 1.3305808069 0.4429857569 0.5692332165 0.5578141102 -0.41058565841 +1413393217005760512.0000000000 -1.0758244621 0.4320747088 1.3384751256 0.4440367753 0.5693405900 0.5582532661 -0.40870028835 +1413393217055760384.0000000000 -1.0726201019 0.4310094681 1.3483766273 0.4432032502 0.5703622801 0.5593584171 -0.406664369872 +1413393217105760512.0000000000 -1.0687948180 0.4291543897 1.3610226825 0.4428610995 0.5711485464 0.5595743068 -0.405635279161 +1413393217155760384.0000000000 -1.0642930568 0.4265552581 1.3749294652 0.4418408869 0.5723721664 0.5597211078 -0.404819731745 +1413393217205760512.0000000000 -1.0591715166 0.4233033803 1.3887412835 0.4414978318 0.5729765136 0.5598697797 -0.404132910273 +1413393217255760384.0000000000 -1.0539143201 0.4195340910 1.4013986269 0.4426665781 0.5726518091 0.5599502620 -0.403202071295 +1413393217305760512.0000000000 -1.0482770694 0.4151309385 1.4121524007 0.4430594691 0.5727874204 0.5603230077 -0.402058459561 +1413393217355760384.0000000000 -1.0419796505 0.4098454965 1.4216631986 0.4423416727 0.5731715463 0.5607924978 -0.401646607712 +1413393217405760512.0000000000 -1.0350684134 0.4039491444 1.4301216846 0.4421009596 0.5737071147 0.5612387386 -0.400522117192 +1413393217455760384.0000000000 -1.0275168963 0.3973211937 1.4376670954 0.4416671182 0.5742209530 0.5616653001 -0.399665540765 +1413393217505760512.0000000000 -1.0195815455 0.3896760972 1.4444353846 0.4416699211 0.5739964751 0.5621292574 -0.399332474676 +1413393217555760384.0000000000 -1.0113345445 0.3813409278 1.4501744125 0.4419904201 0.5743148243 0.5617519800 -0.399050954293 +1413393217605760512.0000000000 -1.0021357857 0.3721497518 1.4547029126 0.4423515926 0.5739231069 0.5620059623 -0.398856658756 +1413393217655760384.0000000000 -0.9927690613 0.3618970262 1.4590606382 0.4421220180 0.5738217748 0.5622219791 -0.398952551264 +1413393217705760512.0000000000 -0.9830792487 0.3508759533 1.4650279529 0.4424194773 0.5738746316 0.5621413557 -0.398660268214 +1413393217755760384.0000000000 -0.9730882733 0.3387413500 1.4730978735 0.4424080353 0.5736546602 0.5620189947 -0.399161760088 +1413393217805760512.0000000000 -0.9627910654 0.3257988289 1.4829801197 0.4420202661 0.5738779948 0.5620217960 -0.399266367596 +1413393217855760384.0000000000 -0.9521787000 0.3120200560 1.4945676189 0.4415429930 0.5745024639 0.5613556913 -0.399833080498 +1413393217905760512.0000000000 -0.9414238312 0.2974897488 1.5077924753 0.4413947197 0.5743626141 0.5611994950 -0.400416552725 +1413393217955760384.0000000000 -0.9304516342 0.2822880266 1.5223933202 0.4417069791 0.5741958546 0.5606215410 -0.401120372106 +1413393218005760512.0000000000 -0.9190460370 0.2665903258 1.5367245367 0.4407541482 0.5750402703 0.5601041747 -0.401681194372 +1413393218055760384.0000000000 -0.9073339582 0.2501550042 1.5494816645 0.4389435475 0.5762204850 0.5585988513 -0.404061676194 +1413393218105760512.0000000000 -0.8954847841 0.2334147674 1.5602615073 0.4364963521 0.5782198998 0.5569695599 -0.406100469699 +1413393218155760384.0000000000 -0.8833414451 0.2163587578 1.5694315006 0.4327784369 0.5808883021 0.5543506232 -0.409837762567 +1413393218205760512.0000000000 -0.8708232278 0.1991630202 1.5764367756 0.4287346472 0.5832396837 0.5516713363 -0.414339004188 +1413393218255760384.0000000000 -0.8577702902 0.1826558480 1.5810006615 0.4237974330 0.5869889930 0.5487230527 -0.418022331133 +1413393218305760512.0000000000 -0.8444519815 0.1670308288 1.5828556004 0.4194803011 0.5901595152 0.5468608635 -0.42034654695 +1413393218355760384.0000000000 -0.8309823709 0.1526585796 1.5825448438 0.4192231456 0.5900262221 0.5472101544 -0.420335649635 +1413393218405760512.0000000000 -0.8174148748 0.1398817332 1.5800220927 0.4230293534 0.5880490547 0.5485115120 -0.417587830885 +1413393218455760384.0000000000 -0.8034269996 0.1280075931 1.5759587011 0.4269456235 0.5856938346 0.5506925751 -0.41402639331 +1413393218505760512.0000000000 -0.7890345115 0.1166922843 1.5711325312 0.4311566510 0.5827269920 0.5528971960 -0.410898875503 +1413393218555760384.0000000000 -0.7744945248 0.1058025318 1.5664524702 0.4353689310 0.5804823302 0.5546439789 -0.407264305927 +1413393218605760512.0000000000 -0.7596503394 0.0946186494 1.5626385890 0.4385550341 0.5780753548 0.5558657935 -0.405600278376 +1413393218655760384.0000000000 -0.7444938303 0.0827973290 1.5595361991 0.4404815862 0.5765148061 0.5566807727 -0.404614838929 +1413393218705760512.0000000000 -0.7290223749 0.0707052282 1.5574865005 0.4407269939 0.5768927392 0.5562657826 -0.4043796031 +1413393218755760384.0000000000 -0.7130638548 0.0580894672 1.5555841271 0.4401409673 0.5769322636 0.5578802299 -0.402734082373 +1413393218805760512.0000000000 -0.6966373710 0.0449454585 1.5538455189 0.4362270353 0.5796139452 0.5596542581 -0.400675379407 +1413393218855760384.0000000000 -0.6800777890 0.0314626918 1.5527515883 0.4286623569 0.5854661200 0.5609300560 -0.398541689589 +1413393218905760512.0000000000 -0.6638095384 0.0178116186 1.5520208783 0.4212664707 0.5904782519 0.5629229880 -0.396216739012 +1413393218955760384.0000000000 -0.6482655187 0.0043700340 1.5517880768 0.4153207318 0.5944928323 0.5647686235 -0.393857034976 +1413393219005760512.0000000000 -0.6340715003 -0.0085079698 1.5526210299 0.4115738687 0.5975342607 0.5654215307 -0.392247690235 +1413393219055760384.0000000000 -0.6214314823 -0.0209701309 1.5546728273 0.4087865416 0.5990972814 0.5658005444 -0.392231761573 +1413393219105760512.0000000000 -0.6104268712 -0.0328139758 1.5578789197 0.4089937403 0.5986253085 0.5658484999 -0.39266695244 +1413393219155760384.0000000000 -0.6010684461 -0.0440899610 1.5617766324 0.4093414109 0.5983032504 0.5651226062 -0.393839142184 +1413393219205760512.0000000000 -0.5929663467 -0.0549445400 1.5661450663 0.4094407323 0.5976860295 0.5650437523 -0.394785074258 +1413393219255760384.0000000000 -0.5861263665 -0.0652169166 1.5713790155 0.4102802899 0.5963995236 0.5648149747 -0.396183967856 +1413393219305760512.0000000000 -0.5805364948 -0.0748281151 1.5772139666 0.4107231327 0.5955120177 0.5646172905 -0.397340232507 +1413393219355760384.0000000000 -0.5761097332 -0.0838746755 1.5831216181 0.4104512110 0.5949975006 0.5648772650 -0.398021925418 +1413393219405760512.0000000000 -0.5728983554 -0.0924853566 1.5892966724 0.4097254239 0.5948837673 0.5643691351 -0.39965717765 +1413393219455760384.0000000000 -0.5710263148 -0.1002865106 1.5940369687 0.4105336413 0.5940771901 0.5640741377 -0.400443240318 +1413393219505760512.0000000000 -0.5706133581 -0.1075799194 1.5968400716 0.4113314372 0.5932496763 0.5638326940 -0.401190682214 +1413393219555760384.0000000000 -0.5713265577 -0.1143033276 1.5980542829 0.4123485985 0.5921001176 0.5632759337 -0.402624274767 +1413393219605760512.0000000000 -0.5728134207 -0.1203829444 1.5982328874 0.4137894224 0.5909614761 0.5627516715 -0.403550992982 +1413393219655760384.0000000000 -0.5750879639 -0.1259408582 1.5993336343 0.4150938578 0.5896761962 0.5617879630 -0.405429842824 +1413393219705760512.0000000000 -0.5781298242 -0.1309184350 1.6025777240 0.4175960073 0.5877242468 0.5609186427 -0.406895638521 +1413393219755760384.0000000000 -0.5819904334 -0.1352100005 1.6088706994 0.4205280169 0.5854571546 0.5600979840 -0.408272403494 +1413393219805760512.0000000000 -0.5855547568 -0.1389727651 1.6187271491 0.4244845602 0.5824939256 0.5600256612 -0.40851553647 +1413393219855760384.0000000000 -0.5893156625 -0.1425012384 1.6321565422 0.4257315619 0.5816672304 0.5599089504 -0.408555794945 +1413393219905760512.0000000000 -0.5923112971 -0.1457925119 1.6484563840 0.4276555872 0.5801568148 0.5599712838 -0.408608529487 +1413393219955760384.0000000000 -0.5955696827 -0.1489695603 1.6654440026 0.4298131178 0.5785246980 0.5602423030 -0.40828717781 +1413393220005760512.0000000000 -0.5988311054 -0.1522463888 1.6807399818 0.4310036747 0.5776558968 0.5599633104 -0.408644819178 +1413393220055760384.0000000000 -0.6015346989 -0.1556038975 1.6938045136 0.4325531273 0.5766838864 0.5595522788 -0.408943436805 +1413393220105760512.0000000000 -0.6034444983 -0.1591696788 1.7049586963 0.4332609903 0.5763951138 0.5592299755 -0.40904207812 +1413393220155760384.0000000000 -0.6052210909 -0.1627874630 1.7154601188 0.4340945074 0.5759663806 0.5591443267 -0.40887933306 +1413393220205760512.0000000000 -0.6068713801 -0.1665544911 1.7262980538 0.4352648623 0.5750936216 0.5592512158 -0.40871738837 +1413393220255760384.0000000000 -0.6083018016 -0.1705799394 1.7374442147 0.4356194314 0.5751518216 0.5587021097 -0.40900861324 +1413393220305760512.0000000000 -0.6093502820 -0.1747308040 1.7487383823 0.4368856880 0.5743915668 0.5589300496 -0.408414523704 +1413393220355760384.0000000000 -0.6098833491 -0.1793998390 1.7603809129 0.4369745177 0.5742261443 0.5586173292 -0.408979566247 +1413393220405760512.0000000000 -0.6100182071 -0.1842443939 1.7722391554 0.4370765575 0.5745287308 0.5583428992 -0.408820287156 +1413393220455760384.0000000000 -0.6095139000 -0.1894146150 1.7842274924 0.4367414987 0.5748507870 0.5587269276 -0.408200509876 +1413393220505760512.0000000000 -0.6084820681 -0.1949464739 1.7959663357 0.4351752699 0.5760125317 0.5594866793 -0.407193692901 +1413393220555760384.0000000000 -0.6069952310 -0.2005827916 1.8063523617 0.4337199193 0.5774651407 0.5597968969 -0.406261587021 +1413393220605760512.0000000000 -0.6053321416 -0.2063835334 1.8143041793 0.4330975777 0.5782009382 0.5599597429 -0.405654100976 +1413393220655760384.0000000000 -0.6039614788 -0.2123218200 1.8194437223 0.4335031267 0.5776568953 0.5598007977 -0.406214989139 +1413393220705760512.0000000000 -0.6024317628 -0.2184862686 1.8221733297 0.4333789172 0.5781164450 0.5588256387 -0.407035619654 +1413393220755760384.0000000000 -0.6008463156 -0.2247789596 1.8220126926 0.4313277576 0.5797288273 0.5576232709 -0.408567179326 +1413393220805760512.0000000000 -0.5987134703 -0.2312300986 1.8209273296 0.4268663910 0.5824492456 0.5572793551 -0.409850803335 +1413393220855760384.0000000000 -0.5967305848 -0.2371630966 1.8216604226 0.4232398494 0.5856636624 0.5556011921 -0.411306965461 +1413393220905760512.0000000000 -0.5944535318 -0.2422765151 1.8252607322 0.4208539049 0.5872024283 0.5551063601 -0.412228368591 +1413393220955760384.0000000000 -0.5925009942 -0.2468386028 1.8322739106 0.4192394534 0.5882438569 0.5551915334 -0.412273946388 +1413393221005760512.0000000000 -0.5905544265 -0.2500241797 1.8418242180 0.4204599874 0.5886530980 0.5543920806 -0.41152199227 +1413393221055760384.0000000000 -0.5889253913 -0.2525397392 1.8535628994 0.4206706134 0.5889695790 0.5546899879 -0.410451077882 +1413393221105760512.0000000000 -0.5874200488 -0.2544965315 1.8662669159 0.4202189184 0.5895327289 0.5553026850 -0.409275152208 +1413393221155760384.0000000000 -0.5861131201 -0.2555414581 1.8798078929 0.4208115426 0.5901102490 0.5552255607 -0.407936412204 +1413393221205760512.0000000000 -0.5849368993 -0.2560575811 1.8936662877 0.4209726303 0.5904809439 0.5563648985 -0.405675238598 +1413393221255760384.0000000000 -0.5840846141 -0.2561973539 1.9080332454 0.4203936798 0.5910290627 0.5570762928 -0.404499449919 +1413393221305760512.0000000000 -0.5836833384 -0.2553731998 1.9219425078 0.4210976430 0.5913320538 0.5585762451 -0.401242763934 +1413393221355760384.0000000000 -0.5839073519 -0.2541942448 1.9362891867 0.4203578133 0.5921121308 0.5595357743 -0.399527534286 +1413393221405760512.0000000000 -0.5847275611 -0.2527586281 1.9509481399 0.4203802852 0.5919679494 0.5610658201 -0.397566985779 +1413393221455760384.0000000000 -0.5864380715 -0.2509076310 1.9656073721 0.4218087575 0.5913816490 0.5621185672 -0.395433728584 +1413393221505760512.0000000000 -0.5887222147 -0.2490446303 1.9783141886 0.4221943668 0.5910498041 0.5632015364 -0.393974713812 +1413393221555760384.0000000000 -0.5917260098 -0.2471484714 1.9876111376 0.4236491166 0.5899756565 0.5650206911 -0.391409975957 +1413393221605760512.0000000000 -0.5959272881 -0.2453954912 1.9951694362 0.4250664683 0.5889906628 0.5659092166 -0.390070833557 +1413393221655760384.0000000000 -0.6009962649 -0.2440820159 2.0024465053 0.4262449690 0.5877624600 0.5664818212 -0.389806186801 +1413393221705760512.0000000000 -0.6069081622 -0.2431389802 2.0102762282 0.4288386859 0.5856298851 0.5654435299 -0.391674142137 +1413393221755760384.0000000000 -0.6132076786 -0.2425493839 2.0184670678 0.4309521590 0.5839261895 0.5634627313 -0.394740664755 +1413393221805760512.0000000000 -0.6195516767 -0.2425460236 2.0265163197 0.4327395461 0.5816567354 0.5625194072 -0.397471815229 +1413393221855760384.0000000000 -0.6259026754 -0.2427479718 2.0344617145 0.4343605326 0.5799904414 0.5621330555 -0.398683387567 +1413393221905760512.0000000000 -0.6321649974 -0.2431919891 2.0424389522 0.4344883256 0.5795385151 0.5614629938 -0.400142863311 +1413393221955760384.0000000000 -0.6381829683 -0.2441095883 2.0498812155 0.4342704013 0.5786386562 0.5608613029 -0.402518475449 +1413393222005760512.0000000000 -0.6438695148 -0.2450374267 2.0548071032 0.4339520252 0.5785552596 0.5609459906 -0.40286355877 +1413393222055760384.0000000000 -0.6494525853 -0.2460332440 2.0567963490 0.4338792905 0.5782145644 0.5606286359 -0.403871528393 +1413393222105760512.0000000000 -0.6548837915 -0.2475383340 2.0560207230 0.4332455081 0.5775736727 0.5605975547 -0.40550877182 +1413393222155760384.0000000000 -0.6607077047 -0.2490616301 2.0522433273 0.4332242457 0.5769928801 0.5610639884 -0.405713162392 +1413393222205760512.0000000000 -0.6661793960 -0.2506017774 2.0454424382 0.4329853627 0.5766753181 0.5615023019 -0.405813279901 +1413393222255760384.0000000000 -0.6711859158 -0.2523553143 2.0356586033 0.4315168653 0.5770135726 0.5623563038 -0.405714086035 +1413393222305760512.0000000000 -0.6758620980 -0.2541031480 2.0235025769 0.4299457189 0.5777566464 0.5640691481 -0.403942981847 +1413393222355760384.0000000000 -0.6804310058 -0.2559297774 2.0108752337 0.4270346874 0.5797080684 0.5662690666 -0.401147448525 +1413393222405760512.0000000000 -0.6851120767 -0.2580990615 1.9990657908 0.4234825222 0.5815198812 0.5686857187 -0.398865559386 +1413393222455760384.0000000000 -0.6904359992 -0.2602037721 1.9883562987 0.4221365013 0.5821962621 0.5711926927 -0.395710998585 +1413393222505760512.0000000000 -0.6963893005 -0.2626649285 1.9792433140 0.4194061781 0.5837494139 0.5722965790 -0.394729914199 +1413393222555760384.0000000000 -0.7029959226 -0.2655133194 1.9726794749 0.4167192466 0.5848816353 0.5722921041 -0.395904394743 +1413393222605760512.0000000000 -0.7103508039 -0.2681178816 1.9676864002 0.4155234389 0.5853785671 0.5729310727 -0.395502453587 +1413393222655760384.0000000000 -0.7188125531 -0.2707008937 1.9649756589 0.4138294353 0.5860864020 0.5737287301 -0.395073755129 +1413393222705760512.0000000000 -0.7288275099 -0.2731012846 1.9648148953 0.4145430554 0.5848482764 0.5747748734 -0.394639574456 +1413393222755760384.0000000000 -0.7397747007 -0.2756518146 1.9670068701 0.4123896342 0.5859503726 0.5751829062 -0.394666409636 +1413393222805760512.0000000000 -0.7519173647 -0.2780824095 1.9709988080 0.4106705567 0.5866346780 0.5762675685 -0.393859287019 +1413393222855760384.0000000000 -0.7650966330 -0.2805726954 1.9771572507 0.4087541673 0.5873341313 0.5775555281 -0.392922716158 +1413393222905760512.0000000000 -0.7798222985 -0.2831801917 1.9855670286 0.4069110508 0.5876857835 0.5782171981 -0.393336609635 +1413393222955760384.0000000000 -0.7959631706 -0.2856727800 1.9954291932 0.4051502277 0.5877992512 0.5798143135 -0.392633028558 +1413393223005760512.0000000000 -0.8136774129 -0.2880254156 2.0068018941 0.4063322538 0.5860135735 0.5804391024 -0.393157270733 +1413393223055760384.0000000000 -0.8325470634 -0.2904403141 2.0188070966 0.4073173604 0.5843127081 0.5799816428 -0.395338489177 +1413393223105760512.0000000000 -0.8525661306 -0.2926660398 2.0309425171 0.4080135009 0.5830001889 0.5794133867 -0.397386323498 +1413393223155760384.0000000000 -0.8737925537 -0.2945497702 2.0428364856 0.4098281028 0.5811742179 0.5798240410 -0.397594688066 +1413393223205760512.0000000000 -0.8959645268 -0.2965316917 2.0545314098 0.4120989901 0.5786802766 0.5805735904 -0.397791234268 +1413393223255760384.0000000000 -0.9191063168 -0.2986591625 2.0655745798 0.4136468354 0.5771752399 0.5810367775 -0.397694985274 +1413393223305760512.0000000000 -0.9429829173 -0.3012259088 2.0755901824 0.4146066440 0.5761352559 0.5804868435 -0.399004413734 +1413393223355760384.0000000000 -0.9676005368 -0.3041254912 2.0822075896 0.4157808255 0.5749356808 0.5806516515 -0.399272998981 +1413393223405760512.0000000000 -0.9928934211 -0.3073102359 2.0843451521 0.4171001285 0.5738346412 0.5800870408 -0.400300277843 +1413393223455760384.0000000000 -1.0187052796 -0.3106481762 2.0810834138 0.4192961820 0.5722289822 0.5796170412 -0.400984774419 +1413393223505760512.0000000000 -1.0448740820 -0.3144459778 2.0726122406 0.4216387648 0.5707141476 0.5783820643 -0.402467764434 +1413393223555760384.0000000000 -1.0713004232 -0.3186596196 2.0598510703 0.4235660367 0.5697041133 0.5765791652 -0.404457046073 +1413393223605760512.0000000000 -1.0978750871 -0.3229880528 2.0435854402 0.4261235399 0.5686370308 0.5748955285 -0.405667089169 +1413393223655760384.0000000000 -1.1237978305 -0.3275125899 2.0244757699 0.4284303761 0.5680694236 0.5734339839 -0.406100983639 +1413393223705760512.0000000000 -1.1494914754 -0.3324857254 2.0050651035 0.4296887130 0.5686083632 0.5720540602 -0.405963411368 +1413393223755760384.0000000000 -1.1748742745 -0.3379020161 1.9880059546 0.4310592263 0.5691467643 0.5708242018 -0.405486910732 +1413393223805760512.0000000000 -1.1997530867 -0.3439036141 1.9748485314 0.4321859341 0.5699553991 0.5690611909 -0.40562978485 +1413393223855760384.0000000000 -1.2243644786 -0.3505822460 1.9660759121 0.4321200826 0.5715341846 0.5686779515 -0.404012744328 +1413393223905760512.0000000000 -1.2485576260 -0.3576045774 1.9597708114 0.4340967734 0.5720327869 0.5680311056 -0.402093453216 +1413393223955760384.0000000000 -1.2728154643 -0.3653972597 1.9581165977 0.4346482970 0.5730865530 0.5673823865 -0.40091132214 +1413393224005760512.0000000000 -1.2971073458 -0.3738405398 1.9588409644 0.4358091792 0.5735357960 0.5659979684 -0.400965521983 +1413393224055760384.0000000000 -1.3212630091 -0.3828489263 1.9596783387 0.4352347693 0.5754420952 0.5649693826 -0.400308240474 +1413393224105760512.0000000000 -1.3451349786 -0.3923773184 1.9591826477 0.4362226519 0.5757964362 0.5634982967 -0.400796621337 +1413393224155760384.0000000000 -1.3680796329 -0.4022815116 1.9561396444 0.4370611825 0.5762044740 0.5626597809 -0.400474590677 +1413393224205760512.0000000000 -1.3904281067 -0.4127301804 1.9508259375 0.4377833592 0.5765487281 0.5617618735 -0.400450860943 +1413393224255760384.0000000000 -1.4125858487 -0.4234828595 1.9430359250 0.4395272946 0.5759415221 0.5613454868 -0.399997956026 +1413393224305760512.0000000000 -1.4339903540 -0.4349379837 1.9329967348 0.4406712518 0.5755708203 0.5601850668 -0.400898702439 +1413393224355760384.0000000000 -1.4551757244 -0.4466858019 1.9192301705 0.4414357805 0.5754100110 0.5598357222 -0.400776415354 +1413393224405760512.0000000000 -1.4763799442 -0.4585504320 1.9031622523 0.4419057550 0.5770232139 0.5582308237 -0.400177288032 +1413393224455760384.0000000000 -1.4977511631 -0.4707681774 1.8850063212 0.4430527324 0.5788863327 0.5550464182 -0.400647430822 +1413393224505760512.0000000000 -1.5187561142 -0.4831376480 1.8646665832 0.4440263383 0.5820268573 0.5512655718 -0.400239450408 +1413393224555760384.0000000000 -1.5393631965 -0.4955926026 1.8423253003 0.4438044823 0.5870704734 0.5461489858 -0.400133885132 +1413393224605760512.0000000000 -1.5598406141 -0.5079621960 1.8194467753 0.4453089830 0.5916483665 0.5400858741 -0.399949207678 +1413393224655760384.0000000000 -1.5800731165 -0.5200567758 1.7971438857 0.4464400965 0.5973189641 0.5334158312 -0.399210278483 +1413393224705760512.0000000000 -1.5983602397 -0.5318647100 1.7757372582 0.4461686266 0.6040404008 0.5281858799 -0.396343824302 +1413393224755760384.0000000000 -1.6159030889 -0.5430708566 1.7543939430 0.4459182001 0.6108747488 0.5225641361 -0.39359334813 +1413393224805760512.0000000000 -1.6322535538 -0.5536359594 1.7337005598 0.4471344394 0.6171293394 0.5175225451 -0.389092003062 +1413393224855760384.0000000000 -1.6471934458 -0.5633964010 1.7149215562 0.4477810104 0.6235312630 0.5122183143 -0.3851406618 +1413393224905760512.0000000000 -1.6619265705 -0.5726531484 1.6994793110 0.4495655232 0.6274684530 0.5079872317 -0.382260582923 +1413393224955760384.0000000000 -1.6754373217 -0.5813062770 1.6860941046 0.4503330138 0.6319833062 0.5045777025 -0.37841593441 +1413393225005760512.0000000000 -1.6885541061 -0.5892962263 1.6763932123 0.4519467357 0.6345083780 0.5028706780 -0.374518821421 +1413393225055760384.0000000000 -1.7021144150 -0.5968373481 1.6696058100 0.4534333150 0.6361296068 0.5023796526 -0.370610357121 +1413393225105760512.0000000000 -1.7166655002 -0.6034583943 1.6658484830 0.4550435193 0.6376793943 0.5011087725 -0.367682449498 +1413393225155760384.0000000000 -1.7307425041 -0.6097583761 1.6626308073 0.4567313659 0.6383668030 0.5002101020 -0.365614740095 +1413393225205760512.0000000000 -1.7447389965 -0.6159947265 1.6594722921 0.4560819788 0.6400234462 0.4991261657 -0.365009982791 +1413393225255760384.0000000000 -1.7586655621 -0.6214774654 1.6560118120 0.4566544677 0.6409736800 0.4989524235 -0.362857985635 +1413393225305760512.0000000000 -1.7727078724 -0.6265295978 1.6527467219 0.4565818715 0.6427102874 0.4978625080 -0.361371559881 +1413393225355760384.0000000000 -1.7870441872 -0.6306644232 1.6507413461 0.4580946415 0.6444601496 0.4954977438 -0.359586430298 +1413393225405760512.0000000000 -1.8014098284 -0.6340702837 1.6492343962 0.4579663616 0.6488980651 0.4907597287 -0.358263871285 +1413393225455760384.0000000000 -1.8167042569 -0.6364406035 1.6490939099 0.4584808220 0.6536228579 0.4856957799 -0.355910248425 +1413393225505760512.0000000000 -1.8321911884 -0.6377827219 1.6502503860 0.4598420643 0.6594004480 0.4778189555 -0.354154444928 +1413393225555760384.0000000000 -1.8474438368 -0.6378237142 1.6514248559 0.4609735925 0.6664179478 0.4699139233 -0.350101943047 +1413393225605760512.0000000000 -1.8628377518 -0.6363991922 1.6536114699 0.4630932420 0.6734868466 0.4606548061 -0.34605962809 +1413393225655760384.0000000000 -1.8783239642 -0.6333074641 1.6570160053 0.4668071492 0.6801722484 0.4504947169 -0.341337527962 +1413393225705760512.0000000000 -1.8932745799 -0.6285968039 1.6607989196 0.4713815636 0.6869895921 0.4404286469 -0.334465736294 +1413393225755760384.0000000000 -1.9081000312 -0.6224090097 1.6651406221 0.4778220530 0.6924597672 0.4312719696 -0.325868140019 +1413393225805760512.0000000000 -1.9225551259 -0.6148306398 1.6698783056 0.4851058095 0.6975715940 0.4216772626 -0.31662992746 +1413393225855760384.0000000000 -1.9360766196 -0.6063094072 1.6737286125 0.4935129576 0.7021208774 0.4127043931 -0.305198817327 +1413393225905760512.0000000000 -1.9493330340 -0.5974575428 1.6734927954 0.5018032707 0.7061494792 0.4036513281 -0.29429916063 +1413393225955760384.0000000000 -1.9624539318 -0.5882432620 1.6681272336 0.5097364977 0.7101194711 0.3953341830 -0.282152305433 +1413393226005760512.0000000000 -1.9757124114 -0.5791796560 1.6589132611 0.5177233797 0.7135330244 0.3861535221 -0.271511661855 +1413393226055760384.0000000000 -1.9890877595 -0.5706253069 1.6479116946 0.5239916759 0.7177725784 0.3758198685 -0.262668375988 +1413393226105760512.0000000000 -2.0022646476 -0.5632737706 1.6370951135 0.5280591481 0.7225659687 0.3654449244 -0.25593351527 +1413393226155760384.0000000000 -2.0157191319 -0.5564333771 1.6275365010 0.5314758455 0.7271625101 0.3547697581 -0.250811738556 +1413393226205760512.0000000000 -2.0290299045 -0.5503346641 1.6205949453 0.5340323526 0.7317813409 0.3451334209 -0.245333318552 +1413393226255760384.0000000000 -2.0427395307 -0.5448132431 1.6180031350 0.5348306304 0.7364032074 0.3365291339 -0.241691238955 +1413393226305760512.0000000000 -2.0562428743 -0.5396125801 1.6180568998 0.5355471432 0.7403548160 0.3288432610 -0.238591939304 +1413393226355760384.0000000000 -2.0694886336 -0.5349526184 1.6197215286 0.5334458534 0.7453981376 0.3221737293 -0.236688035669 +1413393226405760512.0000000000 -2.0822503840 -0.5303179681 1.6212137790 0.5311733995 0.7499450081 0.3180761194 -0.232948249029 +1413393226455760384.0000000000 -2.0949696123 -0.5256563392 1.6213141624 0.5275239271 0.7549231806 0.3143887729 -0.230150379355 +1413393226505760512.0000000000 -2.1078984341 -0.5206862746 1.6188513224 0.5241941932 0.7590797829 0.3117386300 -0.22767818855 +1413393226555760384.0000000000 -2.1210976107 -0.5151614131 1.6144086542 0.5217060560 0.7621823268 0.3093703170 -0.226254058259 +1413393226605760512.0000000000 -2.1343627095 -0.5088949692 1.6071746342 0.5193044378 0.7649585778 0.3076089949 -0.224806542278 +1413393226655760384.0000000000 -2.1478821217 -0.5013793204 1.5995787846 0.5190307279 0.7660901597 0.3065310947 -0.223050798388 +1413393226705760512.0000000000 -2.1618854244 -0.4924801241 1.5920365252 0.5227889085 0.7639526241 0.3082789367 -0.219162593716 +1413393226755760384.0000000000 -2.1763623076 -0.4825221442 1.5853136088 0.5277149481 0.7610239825 0.3094296241 -0.215899836394 +1413393226805760512.0000000000 -2.1911757413 -0.4722284961 1.5786974601 0.5312553521 0.7586187320 0.3118310567 -0.21219510477 +1413393226855760384.0000000000 -2.2067152197 -0.4619104275 1.5726344931 0.5337816024 0.7566190750 0.3137962827 -0.210087289848 +1413393226905760512.0000000000 -2.2227938070 -0.4514869768 1.5670655582 0.5360715547 0.7547683342 0.3164134901 -0.20696510141 +1413393226955760384.0000000000 -2.2396763169 -0.4414122688 1.5621256180 0.5368521166 0.7538506922 0.3180885357 -0.205714905238 +1413393227005760512.0000000000 -2.2573254085 -0.4317069215 1.5576036099 0.5373501968 0.7530153446 0.3195919447 -0.205142988392 +1413393227055760384.0000000000 -2.2758028978 -0.4221767563 1.5537660737 0.5377899942 0.7524293646 0.3197259461 -0.205930310722 +1413393227105760512.0000000000 -2.2949968075 -0.4130092934 1.5506041978 0.5387408291 0.7514588450 0.3193311432 -0.207594663197 +1413393227155760384.0000000000 -2.3147767514 -0.4043016404 1.5479863705 0.5385382306 0.7514078591 0.3178818418 -0.210508760197 +1413393227205760512.0000000000 -2.3349374578 -0.3957693751 1.5459225635 0.5382781657 0.7512553179 0.3168023993 -0.213326752653 +1413393227255760384.0000000000 -2.3553906032 -0.3874793060 1.5449523851 0.5375057994 0.7516824900 0.3139755785 -0.217899715152 +1413393227305760512.0000000000 -2.3756419334 -0.3791611685 1.5438248545 0.5363291943 0.7525802600 0.3128214777 -0.219355124715 +1413393227355760384.0000000000 -2.3959767540 -0.3707949084 1.5433007620 0.5363934161 0.7526477811 0.3115326085 -0.220795956924 +1413393227405760512.0000000000 -2.4161168325 -0.3624295562 1.5426066436 0.5349837937 0.7537747493 0.3106636894 -0.221594313512 +1413393227455760384.0000000000 -2.4361464436 -0.3538079999 1.5423219378 0.5339613152 0.7547004424 0.3093790379 -0.222704213946 +1413393227505760512.0000000000 -2.4560099949 -0.3448693966 1.5422515535 0.5337523077 0.7550453571 0.3085415820 -0.223197390011 +1413393227555760384.0000000000 -2.4756951108 -0.3352615975 1.5426362305 0.5345069846 0.7553747822 0.3060731371 -0.223674890457 +1413393227605760512.0000000000 -2.4950825810 -0.3250838044 1.5432366675 0.5353043103 0.7562306897 0.3025482976 -0.223671560294 +1413393227655760384.0000000000 -2.5138934580 -0.3143164703 1.5436058757 0.5362602161 0.7575202477 0.2989842827 -0.221802735698 +1413393227705760512.0000000000 -2.5320918112 -0.3028162497 1.5438119839 0.5368448192 0.7598086183 0.2942293406 -0.218900887885 +1413393227755760384.0000000000 -2.5497104113 -0.2906985612 1.5437276340 0.5380093762 0.7621785053 0.2882538376 -0.215730300045 +1413393227805760512.0000000000 -2.5666014574 -0.2779831264 1.5434684898 0.5397047850 0.7644573145 0.2825258330 -0.210957135781 +1413393227855760384.0000000000 -2.5830223850 -0.2647976555 1.5431406112 0.5411215585 0.7674269808 0.2737820030 -0.208054567149 +1413393227905760512.0000000000 -2.5988821163 -0.2509406102 1.5424877870 0.5430364216 0.7702198887 0.2657505569 -0.203099505834 +1413393227955760384.0000000000 -2.6140390416 -0.2366048293 1.5419617809 0.5458251810 0.7726592520 0.2564464927 -0.198261817737 +1413393228005760512.0000000000 -2.6280423903 -0.2215022321 1.5408815196 0.5479609755 0.7759586372 0.2462702353 -0.192296474068 +1413393228055760384.0000000000 -2.6410830432 -0.2057253763 1.5395307939 0.5511563508 0.7785884565 0.2366157410 -0.184498464637 +1413393228105760512.0000000000 -2.6535158793 -0.1896508268 1.5381086580 0.5533477934 0.7817563219 0.2260991298 -0.177601960251 +1413393228155760384.0000000000 -2.6650061921 -0.1729343301 1.5362906863 0.5553459513 0.7850423704 0.2166626138 -0.168394366836 +1413393228205760512.0000000000 -2.6759269201 -0.1560754327 1.5346594535 0.5563198726 0.7885332458 0.2071713040 -0.160634897936 +1413393228255760384.0000000000 -2.6862090309 -0.1389766526 1.5330218422 0.5579983697 0.7908393936 0.2002452515 -0.152028655947 +1413393228305760512.0000000000 -2.6961940314 -0.1217542320 1.5317297854 0.5594980924 0.7928619292 0.1934610949 -0.144584406204 +1413393228355760384.0000000000 -2.7058981643 -0.1043054897 1.5310239727 0.5611744715 0.7943760043 0.1873390399 -0.137673746501 +1413393228405760512.0000000000 -2.7153681584 -0.0864310548 1.5305970728 0.5629285415 0.7958729836 0.1808792819 -0.130308620391 +1413393228455760384.0000000000 -2.7245491678 -0.0682605082 1.5304827343 0.5647879702 0.7973273124 0.1730693295 -0.12381725532 +1413393228505760512.0000000000 -2.7337546851 -0.0500908403 1.5308487291 0.5678627184 0.7975646862 0.1655688289 -0.118361595456 +1413393228555760384.0000000000 -2.7427770334 -0.0319843556 1.5310487325 0.5700866127 0.7983012572 0.1579570878 -0.112986349631 +1413393228605760512.0000000000 -2.7515225817 -0.0139842634 1.5307481134 0.5706566283 0.8000835830 0.1507206793 -0.107240615334 +1413393228655760384.0000000000 -2.7604169133 0.0036193396 1.5308401306 0.5709221692 0.8015677955 0.1441813945 -0.10367579922 +1413393228705760512.0000000000 -2.7690834446 0.0210612760 1.5308639607 0.5708240731 0.8030204672 0.1396872975 -0.0990225518966 +1413393228755760384.0000000000 -2.7778566171 0.0383462761 1.5312265157 0.5701993522 0.8045524555 0.1354426905 -0.0960381319164 +1413393228805760512.0000000000 -2.7869400614 0.0556462164 1.5312695420 0.5673330964 0.8073243539 0.1317459022 -0.0948871047174 +1413393228855760384.0000000000 -2.7961189415 0.0735623451 1.5305429583 0.5645886083 0.8098576525 0.1284991741 -0.0941182679415 +1413393228905760512.0000000000 -2.8050176403 0.0916839715 1.5291919175 0.5603510405 0.8132439782 0.1261206362 -0.0934586991438 +1413393228955760384.0000000000 -2.8138115258 0.1106279423 1.5276569639 0.5589637703 0.8144508350 0.1247070067 -0.0931531179722 +1413393229005760512.0000000000 -2.8224761096 0.1305493391 1.5254535011 0.5590402676 0.8146158887 0.1252265940 -0.0905164802414 +1413393229055760384.0000000000 -2.8309462067 0.1517323468 1.5223814007 0.5603267061 0.8138305113 0.1281872602 -0.0853340945058 +1413393229105760512.0000000000 -2.8398276782 0.1734583741 1.5184417864 0.5630688403 0.8118613944 0.1311717603 -0.081415764801 +1413393229155760384.0000000000 -2.8490534705 0.1954026163 1.5139194875 0.5652835061 0.8102477034 0.1335803501 -0.0781633352452 +1413393229205760512.0000000000 -2.8588558925 0.2175444280 1.5088919927 0.5672599231 0.8086882370 0.1364631489 -0.0749488088239 +1413393229255760384.0000000000 -2.8696684990 0.2399215333 1.5030374064 0.5690677378 0.8071556754 0.1392001990 -0.072697524655 +1413393229305760512.0000000000 -2.8812368690 0.2622566969 1.4964171478 0.5710018693 0.8056211503 0.1409014927 -0.0712614674299 +1413393229355760384.0000000000 -2.8939096259 0.2844701243 1.4891746141 0.5727457702 0.8041920025 0.1420445566 -0.0711396495055 +1413393229405760512.0000000000 -2.9077291776 0.3066642191 1.4813397095 0.5742331553 0.8029753082 0.1418885628 -0.0731749520616 +1413393229455760384.0000000000 -2.9227006289 0.3286310553 1.4738141467 0.5756239882 0.8019414697 0.1397461658 -0.0775752053224 +1413393229505760512.0000000000 -2.9381916714 0.3503600990 1.4666541605 0.5760969002 0.8015625631 0.1365679475 -0.0834207096382 +1413393229555760384.0000000000 -2.9539789763 0.3717570824 1.4596074304 0.5748495624 0.8022532374 0.1346523550 -0.0883542133736 +1413393229605760512.0000000000 -2.9695654860 0.3930358462 1.4529499501 0.5727837221 0.8036574415 0.1317740028 -0.0932155388478 +1413393229655760384.0000000000 -2.9848600108 0.4142931860 1.4467262050 0.5695798559 0.8057590129 0.1298930867 -0.0972573233285 +1413393229705760512.0000000000 -2.9995111708 0.4357639061 1.4409969511 0.5664064180 0.8078581367 0.1295845802 -0.0987767041043 +1413393229755760384.0000000000 -3.0136704018 0.4576604328 1.4361148194 0.5633195427 0.8098826232 0.1295460312 -0.0998952210756 +1413393229805760512.0000000000 -3.0273769379 0.4801787960 1.4316527741 0.5592125995 0.8125965841 0.1298703605 -0.10050746052 +1413393229855760384.0000000000 -3.0406193386 0.5036371608 1.4279268698 0.5548918155 0.8154173751 0.1311347393 -0.099966282056 +1413393229905760512.0000000000 -3.0535291368 0.5282365045 1.4252560656 0.5514961503 0.8176272557 0.1320041689 -0.0995618721449 +1413393229955760384.0000000000 -3.0662175009 0.5542941892 1.4238436966 0.5501412174 0.8183890760 0.1336940259 -0.0985386659639 +1413393230005760512.0000000000 -3.0786448092 0.5818526658 1.4231860393 0.5502824049 0.8181708422 0.1366945098 -0.0953958008124 +1413393230055760384.0000000000 -3.0911225005 0.6110773190 1.4231376094 0.5537246041 0.8156046891 0.1410062016 -0.0910785654486 +1413393230105760512.0000000000 -3.1040970936 0.6412443017 1.4231961819 0.5571353023 0.8130050853 0.1448610522 -0.0873971499119 +1413393230155760384.0000000000 -3.1176500605 0.6720681657 1.4230104673 0.5600299413 0.8107666260 0.1477235734 -0.0848627651534 +1413393230205760512.0000000000 -3.1319962900 0.7031931769 1.4221227499 0.5620989907 0.8090210532 0.1505414269 -0.0828669955305 +1413393230255760384.0000000000 -3.1474017264 0.7346177531 1.4208224698 0.5646300586 0.8069905637 0.1522216263 -0.0823875202629 +1413393230305760512.0000000000 -3.1637619973 0.7661100751 1.4188847096 0.5669102454 0.8051639731 0.1526794372 -0.0837421007241 +1413393230355760384.0000000000 -3.1808288559 0.7972511957 1.4157769171 0.5666119582 0.8052508530 0.1516632494 -0.0867191520881 +1413393230405760512.0000000000 -3.1984744563 0.8284864648 1.4124388801 0.5673987357 0.8046262679 0.1499938160 -0.0902058695961 +1413393230455760384.0000000000 -3.2163878772 0.8599234705 1.4086849574 0.5669835672 0.8051083184 0.1475243299 -0.0925570219652 +1413393230505760512.0000000000 -3.2343223698 0.8916269962 1.4051894622 0.5662955199 0.8061513116 0.1431532003 -0.094533635495 +1413393230555760384.0000000000 -3.2518960529 0.9237204818 1.4021658043 0.5654835548 0.8076732313 0.1373596395 -0.0949980532584 +1413393230605760512.0000000000 -3.2688712199 0.9560778900 1.3997651051 0.5652327076 0.8091529288 0.1296461821 -0.0947385432453 +1413393230655760384.0000000000 -3.2853643182 0.9894314912 1.3981497248 0.5643743545 0.8112392237 0.1214419927 -0.0928673910838 +1413393230705760512.0000000000 -3.3013696643 1.0239901196 1.3976195695 0.5648377074 0.8125506500 0.1125335450 -0.0897552603401 +1413393230755760384.0000000000 -3.3162592682 1.0590661983 1.3991813030 0.5652016247 0.8139941451 0.1028785279 -0.085887506361 +1413393230805760512.0000000000 -3.3301229944 1.0944794713 1.4010911813 0.5657515164 0.8152500307 0.0933007077 -0.0811639519993 +1413393230855760384.0000000000 -3.3430659015 1.1309251808 1.4031008040 0.5663719231 0.8164974262 0.0835437963 -0.0746674750956 +1413393230905760512.0000000000 -3.3548153794 1.1682015726 1.4057864746 0.5673023215 0.8174684052 0.0746031849 -0.0659382083395 +1413393230955760384.0000000000 -3.3656535433 1.2059005980 1.4092552157 0.5684130180 0.8181153007 0.0675958813 -0.0549981144316 +1413393231005760512.0000000000 -3.3758527487 1.2439537002 1.4130444239 0.5694673253 0.8185196033 0.0624426877 -0.0428197988586 +1413393231055760384.0000000000 -3.3858346346 1.2822403064 1.4171651599 0.5704852798 0.8186324877 0.0584997584 -0.0310672491272 +1413393231105760512.0000000000 -3.3963990606 1.3207021276 1.4218735974 0.5722011697 0.8179777868 0.0552052952 -0.0212258603689 +1413393231155760384.0000000000 -3.4077998575 1.3591916798 1.4269282084 0.5733122544 0.8175407453 0.0526490509 -0.0129717480233 +1413393231205760512.0000000000 -3.4204626391 1.3976934310 1.4322803461 0.5732736080 0.8178578214 0.0490628436 -0.00766757151337 +1413393231255760384.0000000000 -3.4341316749 1.4363692247 1.4377340203 0.5735842915 0.8177936150 0.0469900129 -0.00256954307916 +1413393231305760512.0000000000 -3.4492666467 1.4746396277 1.4426700111 0.5743105245 0.8174936466 0.0432345018 -0.00152878831228 +1413393231355760384.0000000000 -3.4653040729 1.5126975733 1.4447740518 0.5746714549 0.8174548210 0.0389190577 -0.00237518321997 +1413393231405760512.0000000000 -3.4823139662 1.5509994327 1.4445857076 0.5757258522 0.8168914280 0.0346969310 -0.0049255347306 +1413393231455760384.0000000000 -3.4999435885 1.5894439314 1.4424981493 0.5785590776 0.8150495287 0.0297401856 -0.00889836236366 +1413393231505760512.0000000000 -3.5178112586 1.6278905276 1.4391383895 0.5837078707 0.8114677106 0.0248883701 -0.0136325138581 +1413393231555760384.0000000000 -3.5357472675 1.6658917517 1.4338087468 0.5910848655 0.8061227425 0.0211027209 -0.0184250089182 +1413393231605760512.0000000000 -3.5531506685 1.7029720820 1.4266958899 0.5979678644 0.8010068459 0.0176106281 -0.0226347451544 +1413393231655760384.0000000000 -3.5695562722 1.7386301178 1.4181664708 0.6026291994 0.7974971027 0.0142621709 -0.0251596826367 +1413393231705760512.0000000000 -3.5846896246 1.7727460810 1.4088270415 0.6046477826 0.7960102453 0.0120169005 -0.0249868451894 +1413393231755760384.0000000000 -3.5984039501 1.8053987158 1.3994866338 0.6038897287 0.7966793911 0.0085922952 -0.0233519993647 +1413393231805760512.0000000000 -3.6110554381 1.8365574702 1.3912714971 0.6014728024 0.7985775535 0.0042286852 -0.0220562275485 +1413393231855760384.0000000000 -3.6226896595 1.8660742291 1.3842057745 0.5980551299 0.8011375473 -0.0019378761 -0.022470794852 +1413393231905760512.0000000000 -3.6326959079 1.8945745689 1.3776856944 0.5926048475 0.8051520215 -0.0094394414 -0.0214619183316 +1413393231955760384.0000000000 -3.6409803442 1.9221914831 1.3725057833 0.5882865771 0.8081995402 -0.0175768413 -0.0205781690735 +1413393232005760512.0000000000 -3.6472701023 1.9492947099 1.3684420632 0.5847690896 0.8105701405 -0.0261040508 -0.0184319739865 +1413393232055760384.0000000000 -3.6511464077 1.9761964695 1.3649189237 0.5816644226 0.8126506260 -0.0331251909 -0.012968471323 +1413393232105760512.0000000000 -3.6530743420 2.0029193640 1.3630686487 0.5797122737 0.8138077765 -0.0401261596 -0.00636191932565 +1413393232155760384.0000000000 -3.6530776404 2.0292846674 1.3614772759 0.5781103397 0.8145792622 -0.0474075660 0.00125829618738 +1413393232205760512.0000000000 -3.6512013500 2.0555689495 1.3598211833 0.5783911607 0.8139265961 -0.0534373593 0.0114721430464 +1413393232255760384.0000000000 -3.6480853120 2.0816226399 1.3572394355 0.5783005530 0.8133171635 -0.0605550652 0.0204143582903 +1413393232305760512.0000000000 -3.6437454963 2.1074705700 1.3533175250 0.5783866577 0.8123831502 -0.0682544147 0.0290486896508 +1413393232355760384.0000000000 -3.6383980424 2.1332900215 1.3482153385 0.5778899788 0.8115967764 -0.0780247445 0.0355806711447 +1413393232405760512.0000000000 -3.6319295911 2.1587352652 1.3414239983 0.5757925740 0.8118692137 -0.0868790755 0.0422293491692 +1413393232455760384.0000000000 -3.6243657102 2.1841282129 1.3329629519 0.5741775464 0.8116201025 -0.0959073481 0.0489360291472 +1413393232505760512.0000000000 -3.6159276522 2.2095040499 1.3229608375 0.5721186760 0.8116079308 -0.1048134160 0.0546528605172 +1413393232555760384.0000000000 -3.6067141634 2.2349811284 1.3117908762 0.5709208480 0.8110905335 -0.1123667705 0.0596258393877 +1413393232605760512.0000000000 -3.5969369785 2.2602670326 1.2984117698 0.5698990928 0.8106951473 -0.1180052602 0.0637429269106 +1413393232655760384.0000000000 -3.5863139660 2.2853440534 1.2850391647 0.5692519150 0.8100577752 -0.1236899358 0.0667791723594 +1413393232705760512.0000000000 -3.5746709606 2.3103907492 1.2724381341 0.5692375119 0.8091926375 -0.1277924154 0.0696062430151 +1413393232755760384.0000000000 -3.5620447277 2.3352789168 1.2602172605 0.5687132673 0.8089026680 -0.1300001707 0.0730865847073 +1413393232805760512.0000000000 -3.5483678649 2.3602148120 1.2486461574 0.5678593578 0.8089117865 -0.1321777787 0.0756736832266 +1413393232855760384.0000000000 -3.5336884940 2.3858962519 1.2380429787 0.5681364219 0.8083000052 -0.1336765840 0.077476955516 +1413393232905760512.0000000000 -3.5182706250 2.4112283750 1.2274638354 0.5665047642 0.8091956878 -0.1341942530 0.0791618176362 +1413393232955760384.0000000000 -3.5016336135 2.4368097879 1.2184034105 0.5656278168 0.8096381790 -0.1326083215 0.0834639149412 +1413393233005760512.0000000000 -3.4843649728 2.4627233076 1.2109640707 0.5641620842 0.8105932831 -0.1309466805 0.0866754803394 +1413393233055760384.0000000000 -3.4666014658 2.4890272516 1.2057122788 0.5630091627 0.8114682543 -0.1282143964 0.0900056862269 +1413393233105760512.0000000000 -3.4484635823 2.5155952769 1.2021059034 0.5611112650 0.8127992267 -0.1265655568 0.0921559828529 +1413393233155760384.0000000000 -3.4301049111 2.5426918971 1.2005841998 0.5606235866 0.8131772571 -0.1253197559 0.0934820917906 +1413393233205760512.0000000000 -3.4114988739 2.5706006504 1.2011840793 0.5608184929 0.8130410600 -0.1239789831 0.0952683817551 +1413393233255760384.0000000000 -3.3922727488 2.5993800379 1.2045700142 0.5634863470 0.8107713257 -0.1241651899 0.0985697712006 +1413393233305760512.0000000000 -3.3728612761 2.6284938592 1.2099141957 0.5662058446 0.8082629048 -0.1252675867 0.102127615908 +1413393233355760384.0000000000 -3.3534378936 2.6580589959 1.2173571115 0.5701578172 0.8046131041 -0.1273422077 0.106309822187 +1413393233405760512.0000000000 -3.3339498854 2.6875559982 1.2265676614 0.5742914071 0.8004022869 -0.1318807129 0.110240810945 +1413393233455760384.0000000000 -3.3149411452 2.7167322732 1.2377524595 0.5776840053 0.7964970931 -0.1381952275 0.113029420215 +1413393233505760512.0000000000 -3.2959671919 2.7452715394 1.2511669821 0.5789760941 0.7937790522 -0.1435156881 0.118763403587 +1413393233555760384.0000000000 -3.2774740841 2.7726373926 1.2658600265 0.5788894940 0.7917508500 -0.1513654099 0.122906704242 +1413393233605760512.0000000000 -3.2589020607 2.7994119363 1.2809415208 0.5756976061 0.7915957243 -0.1581304521 0.130166185212 +1413393233655760384.0000000000 -3.2409410815 2.8252156746 1.2972539466 0.5705665728 0.7924960224 -0.1658759598 0.137437282263 +1413393233705760512.0000000000 -3.2235539890 2.8508486718 1.3154086913 0.5645874718 0.7936567068 -0.1747466981 0.1442692275 +1413393233755760384.0000000000 -3.2062223650 2.8770129868 1.3365069330 0.5622195778 0.7919896957 -0.1815054700 0.154004001798 +1413393233805760512.0000000000 -3.1901523187 2.9027371552 1.3593327983 0.5623301799 0.7888065883 -0.1895745148 0.160095091677 +1413393233855760384.0000000000 -3.1749878530 2.9281984130 1.3824104899 0.5639669965 0.7848543884 -0.1954230242 0.166597291475 +1413393233905760512.0000000000 -3.1610928516 2.9533351424 1.4055792417 0.5666681270 0.7804178252 -0.2026310871 0.169634591231 +1413393233955760384.0000000000 -3.1476040863 2.9777505434 1.4282285308 0.5683727216 0.7762781740 -0.2094440712 0.174578999072 +1413393234005760512.0000000000 -3.1351286200 3.0013423816 1.4506879976 0.5681481119 0.7734081313 -0.2190633287 0.17623519367 +1413393234055760384.0000000000 -3.1233837587 3.0240412978 1.4733535514 0.5669901815 0.7710269410 -0.2292871209 0.17738942038 +1413393234105760512.0000000000 -3.1119679605 3.0456151014 1.4951976374 0.5640062379 0.7696973025 -0.2393236067 0.179408019138 +1413393234155760384.0000000000 -3.1007617802 3.0662389453 1.5149922625 0.5601675528 0.7690280968 -0.2483952925 0.181955703037 +1413393234205760512.0000000000 -3.0896664765 3.0862196230 1.5330773161 0.5587220206 0.7670301221 -0.2566837792 0.183324665554 +1413393234255760384.0000000000 -3.0784018959 3.1056332575 1.5497027583 0.5634899183 0.7601568379 -0.2661420261 0.183872552629 +1413393234305760512.0000000000 -3.0668892421 3.1240841449 1.5645579594 0.5713565337 0.7507643834 -0.2765248591 0.182862118619 +1413393234355760384.0000000000 -3.0551033607 3.1408187158 1.5782737832 0.5806686510 0.7399151851 -0.2879856765 0.180038014866 +1413393234405760512.0000000000 -3.0425335208 3.1547167286 1.5898366082 0.5884839028 0.7295891454 -0.2988514202 0.179092723721 +1413393234455760384.0000000000 -3.0295106225 3.1652131997 1.5990756077 0.5936581019 0.7213107483 -0.3090118309 0.178304657034 +1413393234505760512.0000000000 -3.0158166944 3.1717272753 1.6059609851 0.5959453251 0.7151747578 -0.3168219803 0.181653703504 +1413393234555760384.0000000000 -3.0010546994 3.1736912104 1.6123070066 0.5957943968 0.7107119585 -0.3230893301 0.188496243037 +1413393234605760512.0000000000 -2.9853925083 3.1707535442 1.6181043023 0.5914525741 0.7095248267 -0.3246811814 0.203323641841 +1413393234655760384.0000000000 -2.9685052650 3.1640707378 1.6265444673 0.5817780476 0.7121614054 -0.3230023159 0.223673735516 +1413393234705760512.0000000000 -2.9533365496 3.1525472777 1.6395055971 0.5692476333 0.7163228527 -0.3208339488 0.244753508472 +1413393234755760384.0000000000 -2.9402967266 3.1379723627 1.6569940799 0.5557691582 0.7207431073 -0.3221711969 0.260491335779 +1413393234805760512.0000000000 -2.9288417656 3.1221872763 1.6754759093 0.5406784532 0.7259069799 -0.3248095102 0.274271123011 +1413393234855760384.0000000000 -2.9193948543 3.1061864437 1.6924452652 0.5276279007 0.7294198906 -0.3320759544 0.281568787501 +1413393234905760512.0000000000 -2.9112051588 3.0908672423 1.7066422816 0.5195905001 0.7291058502 -0.3426450719 0.284648425599 +1413393234955760384.0000000000 -2.9040981448 3.0761056110 1.7163444926 0.5141522621 0.7268260534 -0.3539982437 0.286455202242 +1413393235005760512.0000000000 -2.8979230672 3.0618754916 1.7212163304 0.5111990583 0.7225077101 -0.3676873414 0.285419254176 +1413393235055760384.0000000000 -2.8921100906 3.0478620485 1.7211973174 0.5098735704 0.7165873381 -0.3816029458 0.284448098412 +1413393235105760512.0000000000 -2.8863592461 3.0337107419 1.7161564761 0.5083431187 0.7103107626 -0.3948433605 0.284858938544 +1413393235155760384.0000000000 -2.8804807774 3.0191914330 1.7065247043 0.5051366075 0.7049126175 -0.4068313714 0.287094835728 +1413393235205760512.0000000000 -2.8737161603 3.0042141315 1.6942490965 0.5003466618 0.7005165295 -0.4150982434 0.294318294251 +1413393235255760384.0000000000 -2.8669424210 2.9885456162 1.6808785083 0.4920896822 0.6986278459 -0.4215023039 0.303484242513 +1413393235305760512.0000000000 -2.8600604619 2.9728386973 1.6679154962 0.4827303931 0.6976514076 -0.4262146043 0.313998395212 +1413393235355760384.0000000000 -2.8535940008 2.9576940598 1.6558976181 0.4733863273 0.6975450675 -0.4307560368 0.322157571171 +1413393235405760512.0000000000 -2.8474056335 2.9435026127 1.6450574450 0.4642292828 0.6984042251 -0.4346384894 0.328347521377 +1413393235455760384.0000000000 -2.8410767479 2.9308492810 1.6355161316 0.4566826226 0.6989801854 -0.4380297871 0.333163005449 +1413393235505760512.0000000000 -2.8345018173 2.9199715971 1.6269317457 0.4490823750 0.7004975460 -0.4404325254 0.337116299002 +1413393235555760384.0000000000 -2.8268830614 2.9111778738 1.6200136191 0.4436936025 0.7004822504 -0.4388007018 0.346286800344 +1413393235605760512.0000000000 -2.8189362382 2.9046203917 1.6135491022 0.4389044527 0.6999755644 -0.4354430282 0.357472320333 +1413393235655760384.0000000000 -2.8110319985 2.9010930223 1.6077734436 0.4361152707 0.6978346780 -0.4343719412 0.366266637252 +1413393235705760512.0000000000 -2.8036088280 2.9010605962 1.6027633859 0.4359310946 0.6948806934 -0.4334839805 0.37309052709 +1413393235755760384.0000000000 -2.7971568760 2.9045790961 1.5982025430 0.4373455608 0.6915494946 -0.4355022450 0.375267839825 +1413393235805760512.0000000000 -2.7917615797 2.9114485163 1.5943654400 0.4407090198 0.6878085217 -0.4387701691 0.374400502107 +1413393235855760384.0000000000 -2.7873276933 2.9215934742 1.5918052805 0.4487581054 0.6816947952 -0.4450991543 0.368503883205 +1413393235905760512.0000000000 -2.7835144327 2.9336538595 1.5897508188 0.4573478370 0.6745535955 -0.4531931282 0.361145941965 +1413393235955760384.0000000000 -2.7799561404 2.9466737935 1.5878798363 0.4648744511 0.6673474689 -0.4616339315 0.354165517482 +1413393236005760512.0000000000 -2.7763993473 2.9595966098 1.5866594088 0.4704116705 0.6602072617 -0.4684921808 0.35121832014 +1413393236055760384.0000000000 -2.7729548723 2.9721010608 1.5856482606 0.4745506922 0.6529474632 -0.4765808636 0.348327333617 +1413393236105760512.0000000000 -2.7686857003 2.9836439074 1.5849432433 0.4759008333 0.6466799979 -0.4842796752 0.347558014337 +1413393236155760384.0000000000 -2.7646753835 2.9935861294 1.5869968653 0.4753177852 0.6405900289 -0.4919176816 0.3489045892 +1413393236205760512.0000000000 -2.7617463120 3.0012180571 1.5880972061 0.4693092938 0.6372365200 -0.4984154749 0.353921486605 +1413393236255760384.0000000000 -2.7597011411 3.0074544664 1.5912172344 0.4608371215 0.6353257892 -0.5034028750 0.361352784067 +1413393236305760512.0000000000 -2.7584519547 3.0124293922 1.5936990611 0.4506333075 0.6335960080 -0.5077711832 0.371017717002 +1413393236355760384.0000000000 -2.7565571083 3.0172337622 1.5974650868 0.4421235183 0.6299953388 -0.5135106942 0.379393508859 +1413393236405760512.0000000000 -2.7548802372 3.0224930131 1.6021124202 0.4353944750 0.6255027530 -0.5208620115 0.384552625805 +1413393236455760384.0000000000 -2.7530376927 3.0279110884 1.6075615864 0.4302232690 0.6197460000 -0.5284922988 0.389254061503 +1413393236505760512.0000000000 -2.7512381612 3.0335588743 1.6129009221 0.4240609700 0.6146086122 -0.5380238744 0.391099550048 +1413393236555760384.0000000000 -2.7490505647 3.0392813293 1.6184128756 0.4167504587 0.6102008797 -0.5476736947 0.392463330349 +1413393236605760512.0000000000 -2.7464739083 3.0451311692 1.6236604151 0.4080530134 0.6067377772 -0.5583687098 0.391900997587 +1413393236655760384.0000000000 -2.7429185568 3.0511890730 1.6278964095 0.4007269091 0.6027050930 -0.5683706789 0.391304595594 +1413393236705760512.0000000000 -2.7383937639 3.0575083004 1.6296285629 0.3967303549 0.5975956649 -0.5764448126 0.391402382313 +1413393236755760384.0000000000 -2.7330269032 3.0638145764 1.6290395798 0.3959483523 0.5906585623 -0.5842597380 0.391136707208 +1413393236805760512.0000000000 -2.7261143087 3.0699216957 1.6263569742 0.3976368090 0.5823699748 -0.5913586617 0.391184245287 +1413393236855760384.0000000000 -2.7177140397 3.0751884761 1.6226590013 0.3986261389 0.5753458325 -0.5961119611 0.393350866619 +1413393236905760512.0000000000 -2.7079154121 3.0794328947 1.6205791711 0.3988773466 0.5700149781 -0.5988805404 0.396638230013 +1413393236955760384.0000000000 -2.6972308845 3.0823552608 1.6207171924 0.3992555190 0.5657841255 -0.5988313491 0.402348566816 +1413393237005760512.0000000000 -2.6852529431 3.0840316431 1.6253443451 0.3987656416 0.5634581316 -0.5966621455 0.409261751293 +1413393237055760384.0000000000 -2.6739852618 3.0847978842 1.6329110970 0.3968411022 0.5629142919 -0.5940373759 0.415649173712 +1413393237105760512.0000000000 -2.6622233671 3.0849546102 1.6434876391 0.3936485284 0.5639614602 -0.5901375269 0.422759987241 +1413393237155760384.0000000000 -2.6503961693 3.0848492029 1.6553856382 0.3906375770 0.5654815959 -0.5845074589 0.43125848233 +1413393237205760512.0000000000 -2.6387015872 3.0851850425 1.6657692354 0.3868495329 0.5681087815 -0.5791235970 0.438424122014 +1413393237255760384.0000000000 -2.6266966132 3.0863682557 1.6729574903 0.3842843889 0.5700161791 -0.5752170143 0.443319806183 +1413393237305760512.0000000000 -2.6148344487 3.0885122467 1.6767504049 0.3810626514 0.5725038545 -0.5728641337 0.44593416184 +1413393237355760384.0000000000 -2.6034904822 3.0921209256 1.6776504945 0.3791788391 0.5748357344 -0.5707343505 0.447269032629 +1413393237405760512.0000000000 -2.5922421115 3.0971608315 1.6752486389 0.3794678544 0.5754442981 -0.5690810922 0.448346649125 +1413393237455760384.0000000000 -2.5812952743 3.1039813952 1.6707603963 0.3818686698 0.5751186807 -0.5689761082 0.446856812008 +1413393237505760512.0000000000 -2.5706849270 3.1126311262 1.6661480704 0.3873834892 0.5730448498 -0.5705110124 0.442798845051 +1413393237555760384.0000000000 -2.5606321176 3.1224726821 1.6616867821 0.3937304396 0.5704251352 -0.5737464169 0.436355995853 +1413393237605760512.0000000000 -2.5510659050 3.1328312048 1.6578464157 0.4006700470 0.5672156980 -0.5766944632 0.430294505501 +1413393237655760384.0000000000 -2.5422606186 3.1432004476 1.6537657850 0.4057984484 0.5652037056 -0.5808273698 0.422506753781 +1413393237705760512.0000000000 -2.5337497225 3.1530733341 1.6500011631 0.4105229170 0.5633935211 -0.5834230563 0.416744780912 +1413393237755760384.0000000000 -2.5257044479 3.1620698771 1.6463130936 0.4132616513 0.5629685203 -0.5852732251 0.411990903608 +1413393237805760512.0000000000 -2.5177605458 3.1698048534 1.6429443836 0.4144783743 0.5633976582 -0.5863031342 0.408704527506 +1413393237855760384.0000000000 -2.5095718256 3.1761045878 1.6395566138 0.4130874582 0.5655207032 -0.5862374671 0.407272290098 +1413393237905760512.0000000000 -2.5008076973 3.1811979034 1.6371106076 0.4099961616 0.5687517965 -0.5856545999 0.406734841197 +1413393237955760384.0000000000 -2.4920269959 3.1852574320 1.6349797981 0.4074048719 0.5710508254 -0.5848464237 0.407279861788 +1413393238005760512.0000000000 -2.4833870189 3.1879439645 1.6308188836 0.3992477582 0.5771082124 -0.5830610635 0.409374077048 +1413393238055760384.0000000000 -2.4741027348 3.1902455136 1.6273177186 0.3921365421 0.5823607336 -0.5809068011 0.411864294059 +1413393238105760512.0000000000 -2.4642185474 3.1925810965 1.6249711558 0.3860824560 0.5863792885 -0.5800018753 0.413155529818 +1413393238155760384.0000000000 -2.4533291034 3.1951038415 1.6243420613 0.3819975979 0.5881192500 -0.5786621645 0.416345628401 +1413393238205760512.0000000000 -2.4415517047 3.1982596275 1.6246394974 0.3783769383 0.5894712297 -0.5781468764 0.418450416567 +1413393238255760384.0000000000 -2.4288123925 3.2023585698 1.6273072225 0.3759883147 0.5901476947 -0.5776251785 0.420366077043 +1413393238305760512.0000000000 -2.4147878612 3.2074556369 1.6316223830 0.3735019017 0.5898619902 -0.5785237390 0.421745711685 +1413393238355760384.0000000000 -2.3987589069 3.2138825379 1.6391968466 0.3723974709 0.5890598840 -0.5799329180 0.421908031735 +1413393238405760512.0000000000 -2.3802204731 3.2214876476 1.6493277250 0.3727048960 0.5875410495 -0.5809076173 0.422413205111 +1413393238455760384.0000000000 -2.3599050780 3.2304396483 1.6623026071 0.3761500435 0.5838223890 -0.5828577542 0.421828639546 +1413393238505760512.0000000000 -2.3389644532 3.2404179518 1.6751232334 0.3816515041 0.5786914153 -0.5867048335 0.418611769573 +1413393238555760384.0000000000 -2.3176611974 3.2508297708 1.6864259780 0.3895211480 0.5719602357 -0.5902841200 0.415571199311 +1413393238605760512.0000000000 -2.2960948379 3.2609890755 1.6951974626 0.3977453974 0.5650574658 -0.5942864923 0.411499968679 +1413393238655760384.0000000000 -2.2741132377 3.2701867230 1.7010689740 0.4045998665 0.5589684479 -0.5983839127 0.407173077797 +1413393238705760512.0000000000 -2.2518835647 3.2780400567 1.7039334281 0.4098624750 0.5542798167 -0.6014914321 0.403726012864 +1413393238755760384.0000000000 -2.2299336972 3.2842221112 1.7040480157 0.4137543526 0.5505572617 -0.6038721336 0.401288529031 +1413393238805760512.0000000000 -2.2076064085 3.2883405972 1.7024652971 0.4153807176 0.5486876985 -0.6044052476 0.401366373421 +1413393238855760384.0000000000 -2.1852341900 3.2903026047 1.7001393551 0.4141260232 0.5489815113 -0.6037323160 0.403269423195 +1413393238905760512.0000000000 -2.1627773833 3.2901286408 1.6977294003 0.4106450870 0.5509217445 -0.6017592482 0.40711380612 +1413393238955760384.0000000000 -2.1402574257 3.2880786742 1.6964322068 0.4046987577 0.5548966665 -0.5980294940 0.413121446078 +1413393239005760512.0000000000 -2.1174638513 3.2847075387 1.6958108000 0.3986084009 0.5582500736 -0.5940534869 0.420200729161 +1413393239055760384.0000000000 -2.0948157049 3.2809515886 1.6950083242 0.3925461370 0.5623503974 -0.5904006043 0.425554564557 +1413393239105760512.0000000000 -2.0719126946 3.2771964668 1.6945547185 0.3879630670 0.5650954302 -0.5874549911 0.430172577945 +1413393239155760384.0000000000 -2.0489611905 3.2737482921 1.6944411781 0.3847019372 0.5668016053 -0.5854589826 0.433564458131 +1413393239205760512.0000000000 -2.0259664253 3.2710850069 1.6942409909 0.3816250254 0.5690392536 -0.5836397922 0.43579956498 +1413393239255760384.0000000000 -2.0027207213 3.2692336924 1.6945961290 0.3804804504 0.5692611954 -0.5828235663 0.437599141712 +1413393239305760512.0000000000 -1.9793826733 3.2681492770 1.6948345843 0.3784730183 0.5700508967 -0.5823967082 0.438878370185 +1413393239355760384.0000000000 -1.9559217255 3.2684009489 1.6953632698 0.3771667346 0.5709940993 -0.5823488375 0.438840317634 +1413393239405760512.0000000000 -1.9320694263 3.2695733275 1.6964802680 0.3766743053 0.5708203789 -0.5826975018 0.439026404797 +1413393239455760384.0000000000 -1.9078747737 3.2720295448 1.6984439710 0.3766820091 0.5706353353 -0.5835943615 0.438068030475 +1413393239505760512.0000000000 -1.8832572822 3.2753241424 1.7010993987 0.3752246091 0.5717681063 -0.5822586324 0.439616435526 +1413393239555760384.0000000000 -1.8583291934 3.2802148620 1.7046254085 0.3764123697 0.5709566355 -0.5836043261 0.437867832516 +1413393239605760512.0000000000 -1.8331898525 3.2863353193 1.7089642699 0.3790404316 0.5697384438 -0.5854966700 0.434649406224 +1413393239655760384.0000000000 -1.8075162034 3.2936067946 1.7142213065 0.3846638347 0.5663270886 -0.5888784935 0.429568950055 +1413393239705760512.0000000000 -1.7814686247 3.3012220421 1.7201734037 0.3925185929 0.5608971836 -0.5942825191 0.422080313679 +1413393239755760384.0000000000 -1.7552189455 3.3083979784 1.7262659562 0.3988976369 0.5569250523 -0.5979837035 0.416089715911 +1413393239805760512.0000000000 -1.7287333087 3.3144309544 1.7319601165 0.4026290080 0.5544228610 -0.6005068384 0.412185286206 +1413393239855760384.0000000000 -1.7022716833 3.3189463816 1.7368289032 0.4035601342 0.5536969768 -0.6026542931 0.409104728571 +1413393239905760512.0000000000 -1.6754235850 3.3219934182 1.7410350471 0.4015442466 0.5553354898 -0.6020971584 0.409687348724 +1413393239955760384.0000000000 -1.6480478789 3.3238035925 1.7453946516 0.4004086268 0.5562214732 -0.6013718529 0.410661051013 +1413393240005760512.0000000000 -1.6200959979 3.3243406122 1.7499551373 0.3981530997 0.5580087636 -0.5985159407 0.414582920116 +1413393240055760384.0000000000 -1.5916558930 3.3241023786 1.7549888222 0.3953853368 0.5603666963 -0.5950591438 0.419003838226 +1413393240105760512.0000000000 -1.5628556126 3.3231551296 1.7603575018 0.3917317108 0.5631185529 -0.5901343160 0.425658608642 +1413393240155760384.0000000000 -1.5339459295 3.3222875551 1.7652389512 0.3884535326 0.5657422794 -0.5858351126 0.431087864742 +1413393240205760512.0000000000 -1.5052985797 3.3220340976 1.7685614341 0.3866570336 0.5675559456 -0.5825086547 0.434810595729 +1413393240255760384.0000000000 -1.4771626420 3.3224246531 1.7694200522 0.3844041675 0.5695233611 -0.5809774665 0.4362817445 +1413393240305760512.0000000000 -1.4494928336 3.3237618968 1.7678431026 0.3847878505 0.5697273555 -0.5811027414 0.435509648991 +1413393240355760384.0000000000 -1.4218018189 3.3259514365 1.7639939636 0.3864064162 0.5689001663 -0.5819521374 0.434021188526 +1413393240405760512.0000000000 -1.3940022606 3.3289061442 1.7579485163 0.3898518679 0.5667706295 -0.5840851079 0.430849348737 +1413393240455760384.0000000000 -1.3660943834 3.3321552148 1.7497134410 0.3935741405 0.5644757593 -0.5854987763 0.428553025952 +1413393240505760512.0000000000 -1.3386206609 3.3355532416 1.7396521473 0.3979313810 0.5615452983 -0.5884160493 0.424363107327 +1413393240555760384.0000000000 -1.3115333807 3.3385614710 1.7300561716 0.4014703408 0.5589261031 -0.5903510955 0.421792319445 +1413393240605760512.0000000000 -1.2849267799 3.3409458217 1.7228003160 0.4042232656 0.5567743350 -0.5921178082 0.419526390908 +1413393240655760384.0000000000 -1.2578296060 3.3422817381 1.7174278950 0.4045270127 0.5559433851 -0.5932341045 0.418757860681 +1413393240705760512.0000000000 -1.2287589137 3.3425227526 1.7168998592 0.4034575128 0.5557378610 -0.5937700259 0.419302541796 +1413393240755760384.0000000000 -1.1988129953 3.3418284341 1.7218125695 0.4014634420 0.5559258419 -0.5921821793 0.423194789137 +1413393240805760512.0000000000 -1.1693152912 3.3405791251 1.7281659526 0.3998791660 0.5558286161 -0.5900156384 0.427823267996 +1413393240855760384.0000000000 -1.1404590634 3.3390435076 1.7339286409 0.3976744856 0.5561677583 -0.5870858503 0.433431231554 +1413393240905760512.0000000000 -1.1123261646 3.3375805500 1.7381010726 0.3980933204 0.5542852604 -0.5850114380 0.438236438184 +1413393240955760384.0000000000 -1.0860116647 3.3362051941 1.7387381137 0.3983463938 0.5524615660 -0.5828990303 0.443097155323 +1413393241005760512.0000000000 -1.0609581804 3.3352029550 1.7361874230 0.3990173765 0.5506842959 -0.5810429375 0.447125311625 +1413393241055760384.0000000000 -1.0363916936 3.3345173117 1.7313691844 0.4010142191 0.5478470813 -0.5806829673 0.449286615789 +1413393241105760512.0000000000 -1.0129768974 3.3343549126 1.7235399427 0.4035934506 0.5447456279 -0.5828024620 0.448002028871 +1413393241155760384.0000000000 -0.9909463866 3.3344741385 1.7135239542 0.4065658214 0.5413368602 -0.5863285322 0.444834226368 +1413393241205760512.0000000000 -0.9702097743 3.3345510843 1.7013513473 0.4090951898 0.5385081149 -0.5903367776 0.440627535297 +1413393241255760384.0000000000 -0.9506571294 3.3342022453 1.6888083709 0.4105794320 0.5362541020 -0.5944620802 0.436429723225 +1413393241305760512.0000000000 -0.9322504071 3.3330394855 1.6763662631 0.4102001214 0.5353448559 -0.5986693676 0.432130459377 +1413393241355760384.0000000000 -0.9148275014 3.3307111509 1.6634230079 0.4048025305 0.5380517006 -0.6034421763 0.427191782184 +1413393241405760512.0000000000 -0.8976996643 3.3275179353 1.6518755982 0.4012041551 0.5396190378 -0.6070122818 0.423535842334 +1413393241455760384.0000000000 -0.8805588400 3.3228946670 1.6409843207 0.3962685124 0.5418336004 -0.6085956139 0.423082727585 +1413393241505760512.0000000000 -0.8632481284 3.3173630914 1.6312046328 0.3917955195 0.5443584075 -0.6076886189 0.425305463859 +1413393241555760384.0000000000 -0.8455728922 3.3110350803 1.6224731737 0.3886909211 0.5458553291 -0.6052785968 0.429650029489 +1413393241605760512.0000000000 -0.8276534254 3.3042408907 1.6143210927 0.3862862393 0.5470637313 -0.6015908979 0.435422331473 +1413393241655760384.0000000000 -0.8098851730 3.2977129132 1.6064031717 0.3842746139 0.5484382133 -0.5986053731 0.439568145574 +1413393241705760512.0000000000 -0.7923349013 3.2913640514 1.5986733870 0.3824471476 0.5496381078 -0.5953213391 0.444099800669 +1413393241755760384.0000000000 -0.7750427600 3.2856777888 1.5912221576 0.3811035579 0.5504343914 -0.5942336025 0.445722430004 +1413393241805760512.0000000000 -0.7580111441 3.2807338454 1.5839959355 0.3788340091 0.5524563998 -0.5932187913 0.446506646663 +1413393241855760384.0000000000 -0.7410026203 3.2767190818 1.5774538583 0.3776152771 0.5539156680 -0.5926199012 0.446526357556 +1413393241905760512.0000000000 -0.7238631127 3.2736000041 1.5722251260 0.3781340317 0.5538096437 -0.5913156562 0.447945674548 +1413393241955760384.0000000000 -0.7070787030 3.2715756292 1.5677610908 0.3801246899 0.5536237125 -0.5883038966 0.450449253898 +1413393242005760512.0000000000 -0.6905186769 3.2706871983 1.5631534739 0.3821097182 0.5531627549 -0.5865758817 0.451588158489 +1413393242055760384.0000000000 -0.6743356930 3.2708381677 1.5593045392 0.3850157130 0.5522534891 -0.5835825083 0.454103997553 +1413393242105760512.0000000000 -0.6588278382 3.2721997025 1.5557876737 0.3879114128 0.5515717440 -0.5807540653 0.456089972133 +1413393242155760384.0000000000 -0.6441634135 3.2746387609 1.5533260061 0.3931255316 0.5487163307 -0.5787544034 0.457609052945 +1413393242205760512.0000000000 -0.6308957081 3.2781391623 1.5516730103 0.3993921778 0.5454528156 -0.5766351859 0.458758080744 +1413393242255760384.0000000000 -0.6192750609 3.2821007815 1.5500430637 0.4031150768 0.5435838317 -0.5750888063 0.459660437285 +1413393242305760512.0000000000 -0.6094708088 3.2865265594 1.5487474449 0.4058040548 0.5421011921 -0.5750833341 0.459051767766 +1413393242355760384.0000000000 -0.6017029910 3.2916458894 1.5475499256 0.4076286321 0.5415227337 -0.5774377769 0.455145735919 +1413393242405760512.0000000000 -0.5957574694 3.2971210116 1.5466550563 0.4085580759 0.5417149353 -0.5820699765 0.448129188779 +1413393242455760384.0000000000 -0.5914197490 3.3026361721 1.5459182963 0.4083122501 0.5425520399 -0.5885555722 0.438771841425 +1413393242505760512.0000000000 -0.5883466331 3.3076581175 1.5453602834 0.4073919864 0.5437143978 -0.5961138237 0.427848959708 +1413393242555760384.0000000000 -0.5858041891 3.3117418729 1.5450558496 0.4058026469 0.5454043055 -0.6021208089 0.418699040915 +1413393242605760512.0000000000 -0.5832582454 3.3144962525 1.5452827681 0.4041409738 0.5466629636 -0.6068775619 0.411739362287 +1413393242655760384.0000000000 -0.5801010608 3.3157458317 1.5460336691 0.4025125098 0.5481111550 -0.6093820743 0.407690236271 +1413393242705760512.0000000000 -0.5761434675 3.3153892290 1.5477690714 0.4028388657 0.5477044888 -0.6111680243 0.40523362067 +1413393242755760384.0000000000 -0.5715549720 3.3135878672 1.5504193251 0.4056002854 0.5464229168 -0.6122160124 0.402618875156 +1413393242805760512.0000000000 -0.5663999104 3.3100931832 1.5533411119 0.4071443498 0.5470277014 -0.6107178142 0.402514501194 +1413393242855760384.0000000000 -0.5606866821 3.3050132861 1.5566991197 0.4076939777 0.5498983972 -0.6069646511 0.403721792427 +1413393242905760512.0000000000 -0.5544861074 3.2983788274 1.5598412894 0.4048126868 0.5568474874 -0.5992442852 0.408599866651 +1413393242955760384.0000000000 -0.5482365450 3.2909122627 1.5630814975 0.4013159436 0.5647295059 -0.5929015634 0.410480005121 +1413393243005760512.0000000000 -0.5418634444 3.2831485052 1.5669381830 0.3983025290 0.5734286089 -0.5864701366 0.410594087488 +1413393243055760384.0000000000 -0.5349762454 3.2755844921 1.5711811871 0.3972818640 0.5824202881 -0.5791272507 0.409347476005 +1413393243105760512.0000000000 -0.5273991331 3.2684012366 1.5755816347 0.3973541072 0.5910212705 -0.5725323124 0.406214626214 +1413393243155760384.0000000000 -0.5191932560 3.2619664278 1.5811337141 0.4008150325 0.5985064473 -0.5648809676 0.402550412684 +1413393243205760512.0000000000 -0.5101823243 3.2563596495 1.5877064424 0.4076087437 0.6044864061 -0.5551265321 0.400357128399 +1413393243255760384.0000000000 -0.5002075434 3.2509337003 1.5952099914 0.4158762258 0.6074643074 -0.5453510071 0.400782184186 +1413393243305760512.0000000000 -0.4899667995 3.2457022335 1.6013078797 0.4239073934 0.6098264240 -0.5358233761 0.401631129254 +1413393243355760384.0000000000 -0.4797626039 3.2407851591 1.6045798856 0.4310958150 0.6114987354 -0.5288068353 0.400735605832 +1413393243405760512.0000000000 -0.4699439140 3.2357910065 1.6058792464 0.4371188157 0.6123731904 -0.5226361791 0.400970872962 +1413393243455760384.0000000000 -0.4611314730 3.2310685036 1.6048757663 0.4416413743 0.6140256527 -0.5177329285 0.399847482401 +1413393243505760512.0000000000 -0.4529634732 3.2264385972 1.6014231286 0.4456202089 0.6150417780 -0.5139222927 0.39878580445 +1413393243555760384.0000000000 -0.4456953944 3.2218792615 1.5949795861 0.4482263407 0.6164823928 -0.5111940143 0.397143911734 +1413393243605760512.0000000000 -0.4396311946 3.2172753475 1.5874431526 0.4495585834 0.6181271451 -0.5092746240 0.395544270566 +1413393243655760384.0000000000 -0.4347355367 3.2127555234 1.5796654070 0.4498625042 0.6199544905 -0.5078135840 0.394215069411 +1413393243705760512.0000000000 -0.4312148399 3.2083665248 1.5722931748 0.4486961290 0.6225236682 -0.5069187499 0.392644173904 +1413393243755760384.0000000000 -0.4287830715 3.2043655107 1.5661861444 0.4473621701 0.6247399079 -0.5069225657 0.390636210106 +1413393243805760512.0000000000 -0.4272587411 3.2005695423 1.5611964362 0.4455348351 0.6268275606 -0.5068259259 0.389504044722 +1413393243855760384.0000000000 -0.4269491984 3.1973199472 1.5576327099 0.4457898038 0.6274470032 -0.5071046837 0.387848615743 +1413393243905760512.0000000000 -0.4273419995 3.1941460147 1.5547260525 0.4449776974 0.6283228618 -0.5068062327 0.387753365791 +1413393243955760384.0000000000 -0.4283454881 3.1914232727 1.5527692470 0.4449889632 0.6286606837 -0.5064515629 0.387656267576 +1413393244005760512.0000000000 -0.4300777044 3.1890773226 1.5514693426 0.4446249589 0.6291036121 -0.5063778449 0.387451634901 +1413393244055760384.0000000000 -0.4322350349 3.1870484096 1.5510784421 0.4441086993 0.6293109624 -0.5055555190 0.388778591238 +1413393244105760512.0000000000 -0.4351754110 3.1855462570 1.5511577095 0.4429606338 0.6300575783 -0.5052990455 0.389212280885 +1413393244155760384.0000000000 -0.4389138392 3.1847294048 1.5515138866 0.4425270759 0.6310907340 -0.5043566796 0.389253917616 +1413393244205760512.0000000000 -0.4436591979 3.1850001538 1.5519879419 0.4439317825 0.6325430234 -0.5024673391 0.387737629202 +1413393244255760384.0000000000 -0.4491599749 3.1861221255 1.5525123899 0.4449334146 0.6358152828 -0.4992326446 0.385408808016 +1413393244305760512.0000000000 -0.4554656104 3.1882430122 1.5531161556 0.4462090375 0.6399164346 -0.4950686784 0.382506804132 +1413393244355760384.0000000000 -0.4624403301 3.1913362735 1.5537578856 0.4486722830 0.6444826588 -0.4901920040 0.378215658385 +1413393244405760512.0000000000 -0.4693775305 3.1951565392 1.5536992974 0.4525380814 0.6472629000 -0.4854240998 0.374997955318 +1413393244455760384.0000000000 -0.4769837418 3.1991980698 1.5523546796 0.4574507355 0.6485920612 -0.4814040020 0.371910405302 +1413393244505760512.0000000000 -0.4855505113 3.2034337174 1.5479484260 0.4616276968 0.6502097823 -0.4783196348 0.36788236642 +1413393244555760384.0000000000 -0.4947127680 3.2076111222 1.5402110552 0.4656427043 0.6508343070 -0.4760999245 0.364582553955 +1413393244605760512.0000000000 -0.5043901439 3.2118840174 1.5306245685 0.4681102725 0.6524123805 -0.4745675863 0.360577959014 +1413393244655760384.0000000000 -0.5143783777 3.2162579636 1.5214148954 0.4703135474 0.6537122343 -0.4734408009 0.356818286956 +1413393244705760512.0000000000 -0.5248769954 3.2203450410 1.5156304400 0.4727502861 0.6543385165 -0.4715062244 0.355007258054 +1413393244755760384.0000000000 -0.5378441960 3.2235869194 1.5102071331 0.4748980012 0.6545446094 -0.4725885526 0.350290312023 +1413393244805760512.0000000000 -0.5511279729 3.2262735531 1.5076095141 0.4779927951 0.6536434725 -0.4736905647 0.346251855724 +1413393244855760384.0000000000 -0.5648134493 3.2282387494 1.5083585651 0.4793334976 0.6537568245 -0.4749252359 0.34247252849 +1413393244905760512.0000000000 -0.5773373545 3.2298029005 1.5139833778 0.4809576372 0.6529854312 -0.4757308527 0.340543585505 +1413393244955760384.0000000000 -0.5889602813 3.2303488266 1.5233465935 0.4813807691 0.6528818127 -0.4754232575 0.340573956862 +1413393245005760512.0000000000 -0.6015058744 3.2295468767 1.5323717521 0.4781735398 0.6552011611 -0.4749938551 0.341236489632 +1413393245055760384.0000000000 -0.6141577651 3.2279898295 1.5411883308 0.4744936908 0.6573688717 -0.4759564763 0.340862635914 +1413393245105760512.0000000000 -0.6269107402 3.2258454447 1.5481193087 0.4700414837 0.6602986320 -0.4765473059 0.340542780581 +1413393245155760384.0000000000 -0.6393329504 3.2232241955 1.5525592473 0.4658361500 0.6627653192 -0.4782210810 0.339180498676 +1413393245205760512.0000000000 -0.6515411713 3.2201013570 1.5546604366 0.4615418585 0.6652493968 -0.4798802702 0.337842092099 +1413393245255760384.0000000000 -0.6634028876 3.2167632152 1.5542409693 0.4588264772 0.6668781594 -0.4798112734 0.338427135813 +1413393245305760512.0000000000 -0.6743710744 3.2134709945 1.5507983369 0.4565816552 0.6680819094 -0.4795545829 0.339451257724 +1413393245355760384.0000000000 -0.6845623060 3.2104016258 1.5447798265 0.4555953330 0.6686063106 -0.4781660028 0.34169543135 +1413393245405760512.0000000000 -0.6940513575 3.2074204141 1.5369139646 0.4551197367 0.6686792766 -0.4768811322 0.343974470148 +1413393245455760384.0000000000 -0.7030635418 3.2046326873 1.5271914072 0.4552014483 0.6683768684 -0.4747942618 0.347324649628 +1413393245505760512.0000000000 -0.7120718800 3.2022779627 1.5154427935 0.4553417507 0.6680260736 -0.4732487764 0.34991520499 +1413393245555760384.0000000000 -0.7207509451 3.2004257659 1.5036171832 0.4560604839 0.6671159276 -0.4711565110 0.353520460935 +1413393245605760512.0000000000 -0.7292487375 3.1990505198 1.4921250767 0.4566152052 0.6660644494 -0.4695395122 0.356922050427 +1413393245655760384.0000000000 -0.7377597875 3.1982705145 1.4813180342 0.4569020412 0.6652149965 -0.4682234007 0.359856054827 +1413393245705760512.0000000000 -0.7463646170 3.1980442726 1.4709397737 0.4560681236 0.6648488058 -0.4673007838 0.362778044482 +1413393245755760384.0000000000 -0.7552738764 3.1985196748 1.4611995143 0.4543593487 0.6647108336 -0.4681614779 0.364063072193 +1413393245805760512.0000000000 -0.7644370243 3.1998077550 1.4523470302 0.4530435815 0.6642132361 -0.4698486575 0.364437277615 +1413393245855760384.0000000000 -0.7738538613 3.2018970766 1.4447324848 0.4534216837 0.6625781457 -0.4724390283 0.363593649862 +1413393245905760512.0000000000 -0.7836228188 3.2046434653 1.4376343956 0.4532714358 0.6613321600 -0.4762957460 0.361008506731 +1413393245955760384.0000000000 -0.7935526516 3.2080696741 1.4313356440 0.4543790221 0.6593926368 -0.4808826282 0.35706155303 +1413393246005760512.0000000000 -0.8034931807 3.2118539349 1.4252676319 0.4553184291 0.6576095801 -0.4869323186 0.350901247257 +1413393246055760384.0000000000 -0.8129705616 3.2154464130 1.4197039986 0.4567548841 0.6555354968 -0.4930447089 0.34431831703 +1413393246105760512.0000000000 -0.8216745445 3.2184333858 1.4140917748 0.4567432027 0.6541279937 -0.4989383867 0.338471122632 +1413393246155760384.0000000000 -0.8295108319 3.2206735095 1.4088992976 0.4578396853 0.6530801230 -0.5025142943 0.333689315792 +1413393246205760512.0000000000 -0.8361189951 3.2221773723 1.4042235715 0.4598448771 0.6532551376 -0.5016521746 0.331881770969 +1413393246255760384.0000000000 -0.8415782577 3.2226093487 1.3993607474 0.4613696963 0.6552154569 -0.4971608273 0.332658714314 +1413393246305760512.0000000000 -0.8462577128 3.2223097093 1.3944322478 0.4625389892 0.6592208085 -0.4883847303 0.336104097396 +1413393246355760384.0000000000 -0.8501452779 3.2216034222 1.3895348496 0.4640796350 0.6636270215 -0.4780486426 0.340145210143 +1413393246405760512.0000000000 -0.8533841698 3.2206423171 1.3852387871 0.4666187897 0.6669186263 -0.4686864909 0.34324834184 +1413393246455760384.0000000000 -0.8563625331 3.2197287696 1.3820381864 0.4700164607 0.6692803427 -0.4599775055 0.345787570516 +1413393246505760512.0000000000 -0.8594286183 3.2188708017 1.3788776892 0.4732184090 0.6711429918 -0.4532853937 0.346646468079 +1413393246555760384.0000000000 -0.8628755021 3.2180416600 1.3755831972 0.4752670971 0.6731724092 -0.4477665533 0.347080981387 +1413393246605760512.0000000000 -0.8668797931 3.2172058367 1.3720952735 0.4758635668 0.6758125629 -0.4436293893 0.346445104647 +1413393246655760384.0000000000 -0.8715863077 3.2164462539 1.3683472264 0.4751395525 0.6785043081 -0.4418836697 0.344402572586 +1413393246705760512.0000000000 -0.8767172796 3.2158890905 1.3648965913 0.4744623745 0.6806714545 -0.4401111814 0.343327794064 +1413393246755760384.0000000000 -0.8821308113 3.2158346484 1.3617825356 0.4744508837 0.6820211054 -0.4389416059 0.342160543119 +1413393246805760512.0000000000 -0.8878612887 3.2160237112 1.3581290606 0.4746261528 0.6827786954 -0.4375596948 0.342176535817 +1413393246855760384.0000000000 -0.8940310626 3.2166215053 1.3534673615 0.4747512867 0.6836182732 -0.4363565409 0.341862898711 +1413393246905760512.0000000000 -0.9005968638 3.2178111086 1.3480122652 0.4757321385 0.6839589412 -0.4345847996 0.342074774143 +1413393246955760384.0000000000 -0.9077224194 3.2196321865 1.3418359201 0.4781963654 0.6833676189 -0.4329335592 0.341914414449 +1413393247005760512.0000000000 -0.9156389727 3.2217945917 1.3343569822 0.4787790126 0.6840467548 -0.4317174470 0.341278098227 +1413393247055760384.0000000000 -0.9243285578 3.2243519825 1.3260269283 0.4792245333 0.6847240339 -0.4309246736 0.340295121583 +1413393247105760512.0000000000 -0.9336627611 3.2273962810 1.3169483089 0.4798093851 0.6853811506 -0.4299936028 0.339324526004 +1413393247155760384.0000000000 -0.9436624204 3.2310502772 1.3071230220 0.4802190960 0.6862415837 -0.4300507451 0.336925014401 +1413393247205760512.0000000000 -0.9543323722 3.2350509505 1.2961635125 0.4798217260 0.6878351994 -0.4312462615 0.332686807217 +1413393247255760384.0000000000 -0.9653729739 3.2392298444 1.2841482137 0.4776745499 0.6904758833 -0.4339360013 0.326756217469 +1413393247305760512.0000000000 -0.9764460251 3.2435589609 1.2712852509 0.4743718090 0.6938207429 -0.4373067230 0.319917166732 +1413393247355760384.0000000000 -0.9870214972 3.2481036722 1.2579090681 0.4701109263 0.6976337720 -0.4406933366 0.313196775408 +1413393247405760512.0000000000 -0.9965049726 3.2530331915 1.2450742661 0.4680563951 0.6998196288 -0.4439843248 0.306681622303 +1413393247455760384.0000000000 -1.0044789768 3.2582106862 1.2323551395 0.4660510020 0.7022253166 -0.4457740556 0.30159834147 +1413393247505760512.0000000000 -1.0106654096 3.2637276660 1.2206470581 0.4663596173 0.7025035737 -0.4486874761 0.29610299733 +1413393247555760384.0000000000 -1.0149177127 3.2688984003 1.2090439654 0.4658677063 0.7036075505 -0.4496225497 0.292819497154 +1413393247605760512.0000000000 -1.0172282839 3.2742422446 1.1983415114 0.4670134184 0.7035952331 -0.4517342754 0.28772966371 +1413393247655760384.0000000000 -1.0175110797 3.2791536430 1.1875122154 0.4685043461 0.7035251993 -0.4523001147 0.284570866263 +1413393247705760512.0000000000 -1.0151716741 3.2835406803 1.1760281660 0.4696623641 0.7037371749 -0.4514073633 0.283553601268 +1413393247755760384.0000000000 -1.0106110481 3.2878087062 1.1652603607 0.4729041901 0.7028076731 -0.4511726976 0.280831263461 +1413393247805760512.0000000000 -1.0040074586 3.2913796492 1.1541947537 0.4742961376 0.7030969785 -0.4513393995 0.27747172685 +1413393247855760384.0000000000 -0.9950703560 3.2942332530 1.1445222144 0.4787390060 0.7011069703 -0.4507655851 0.27580494493 +1413393247905760512.0000000000 -0.9826608688 3.2968890033 1.1382639772 0.4886656133 0.6956297378 -0.4480337514 0.276714553101 +1413393247955760384.0000000000 -0.9675795745 3.2982521092 1.1342011538 0.4978535761 0.6905639263 -0.4409629343 0.284279740884 +1413393248005760512.0000000000 -0.9514185177 3.2983823253 1.1289234047 0.5053198377 0.6860658403 -0.4343993989 0.291997750929 +1413393248055760384.0000000000 -0.9360558739 3.2966382539 1.1234003707 0.5108015578 0.6831904167 -0.4276249075 0.299114629356 +1413393248105760512.0000000000 -0.9211556025 3.2932141409 1.1179312770 0.5126477234 0.6824020521 -0.4224533803 0.305045721782 +1413393248155760384.0000000000 -0.9075480273 3.2878661020 1.1128650028 0.5139522753 0.6818261219 -0.4191146338 0.308721755024 +1413393248205760512.0000000000 -0.8938044553 3.2816018487 1.1091117210 0.5122427304 0.6834413206 -0.4162114751 0.311902796545 +1413393248255760384.0000000000 -0.8817219179 3.2736377381 1.1068582155 0.5084947336 0.6858773406 -0.4165176233 0.312279440743 +1413393248305760512.0000000000 -0.8697595071 3.2649873031 1.1064398644 0.5027329980 0.6897004801 -0.4164976068 0.313213224541 +1413393248355760384.0000000000 -0.8589905716 3.2556085927 1.1072751479 0.5010015280 0.6905928819 -0.4166207811 0.31385675899 +1413393248405760512.0000000000 -0.8490967364 3.2455276411 1.1090137984 0.5003817718 0.6899271815 -0.4166807135 0.316221045559 +1413393248455760384.0000000000 -0.8402287319 3.2353780190 1.1126518991 0.5030889636 0.6871767435 -0.4159988273 0.318801809096 +1413393248505760512.0000000000 -0.8326157740 3.2247617391 1.1176279501 0.5074625742 0.6830596787 -0.4155342741 0.321313675656 +1413393248555760384.0000000000 -0.8254494729 3.2137757832 1.1234116088 0.5107648141 0.6791834399 -0.4157785893 0.323971178301 +1413393248605760512.0000000000 -0.8191850234 3.2024080307 1.1316698693 0.5136154884 0.6759708335 -0.4155202694 0.326504927962 +1413393248655760384.0000000000 -0.8149648860 3.1900343486 1.1404569386 0.5148795785 0.6740023168 -0.4165238268 0.32730383178 +1413393248705760512.0000000000 -0.8128116502 3.1760059208 1.1488050909 0.5124054302 0.6743561115 -0.4178250190 0.328795929808 +1413393248755760384.0000000000 -0.8124408631 3.1611715449 1.1575205036 0.5080872446 0.6762700841 -0.4197003767 0.329177336712 +1413393248805760512.0000000000 -0.8136696424 3.1455865316 1.1668166558 0.5025779859 0.6788371008 -0.4224339341 0.328854268778 +1413393248855760384.0000000000 -0.8160585234 3.1294771319 1.1758249185 0.4940412685 0.6833716413 -0.4259095950 0.327913771792 +1413393248905760512.0000000000 -0.8194872080 3.1132065398 1.1835807675 0.4840729909 0.6888910186 -0.4312367405 0.324248943795 +1413393248955760384.0000000000 -0.8230755826 3.0969896534 1.1893857920 0.4743724041 0.6937511969 -0.4364293571 0.321262377543 +1413393249005760512.0000000000 -0.8261931226 3.0814983168 1.1935029472 0.4669340952 0.6971534799 -0.4409479583 0.318613361684 +1413393249055760384.0000000000 -0.8287799532 3.0667056638 1.1956291074 0.4617901760 0.6989231092 -0.4443539646 0.317499409343 +1413393249105760512.0000000000 -0.8307138254 3.0528458877 1.1959736514 0.4589542976 0.6991710965 -0.4469973834 0.317354800983 +1413393249155760384.0000000000 -0.8315898051 3.0400367752 1.1942420181 0.4581050899 0.6980771443 -0.4488537251 0.318368278375 +1413393249205760512.0000000000 -0.8315245420 3.0282101054 1.1912388893 0.4592643432 0.6958614044 -0.4494355669 0.320719254287 +1413393249255760384.0000000000 -0.8305537200 3.0172118014 1.1879802259 0.4602147853 0.6938061826 -0.4494651023 0.323753693706 +1413393249305760512.0000000000 -0.8289746601 3.0069998281 1.1850733285 0.4614912226 0.6916199878 -0.4499481606 0.325936031712 +1413393249355760384.0000000000 -0.8268750586 2.9975262116 1.1825290455 0.4615002595 0.6909294929 -0.4489267581 0.328783686109 +1413393249405760512.0000000000 -0.8242310156 2.9889214360 1.1805158873 0.4614115209 0.6903996663 -0.4476493613 0.331749541912 +1413393249455760384.0000000000 -0.8214261544 2.9810148960 1.1780821974 0.4596655302 0.6913524410 -0.4449406572 0.335808299805 +1413393249505760512.0000000000 -0.8186620650 2.9742479835 1.1754554909 0.4578492750 0.6929103195 -0.4411848577 0.340007723156 +1413393249555760384.0000000000 -0.8158793847 2.9686169799 1.1717517025 0.4540603442 0.6956934375 -0.4362783065 0.345689288524 +1413393249605760512.0000000000 -0.8135290965 2.9647058159 1.1668611127 0.4515197432 0.6980854439 -0.4312977705 0.35041242503 +1413393249655760384.0000000000 -0.8117728215 2.9629450853 1.1611957819 0.4519769204 0.6986577521 -0.4272906857 0.353577260108 +1413393249705760512.0000000000 -0.8105205009 2.9638387587 1.1550703954 0.4551890893 0.6975522364 -0.4267543659 0.352284660002 +1413393249755760384.0000000000 -0.8099184492 2.9665633837 1.1475079850 0.4583133756 0.6965373219 -0.4273815613 0.349470470746 +1413393249805760512.0000000000 -0.8101696680 2.9709181105 1.1390313153 0.4624090063 0.6948986623 -0.4284035182 0.346069625282 +1413393249855760384.0000000000 -0.8109791317 2.9764331288 1.1300680531 0.4663150527 0.6929181426 -0.4290979864 0.343932605881 +1413393249905760512.0000000000 -0.8126117597 2.9829401383 1.1208780155 0.4695000543 0.6915871265 -0.4296889377 0.341532373631 +1413393249955760384.0000000000 -0.8150636472 2.9902945776 1.1116432552 0.4706526686 0.6915683754 -0.4302552369 0.339263435714 +1413393250005760512.0000000000 -0.8179415761 2.9981591988 1.1026281145 0.4695031115 0.6923031260 -0.4326969595 0.336238830721 +1413393250055760384.0000000000 -0.8211246547 3.0065551004 1.0937022432 0.4664897998 0.6942341167 -0.4346921731 0.333869693962 +1413393250105760512.0000000000 -0.8243831782 3.0158028348 1.0852163892 0.4632677844 0.6961451437 -0.4365390303 0.331961705451 +1413393250155760384.0000000000 -0.8273068253 3.0259960805 1.0775060987 0.4613548678 0.6966485718 -0.4386476509 0.330787985994 +1413393250205760512.0000000000 -0.8299132943 3.0371942963 1.0700990790 0.4605294446 0.6964933069 -0.4407138134 0.329516370907 +1413393250255760384.0000000000 -0.8318257700 3.0492141656 1.0632993120 0.4616201050 0.6946757816 -0.4414926817 0.330781875444 +1413393250305760512.0000000000 -0.8334043090 3.0620106339 1.0565836427 0.4624555737 0.6928131605 -0.4421786639 0.332600054326 +1413393250355760384.0000000000 -0.8346613656 3.0756544485 1.0505933903 0.4652717073 0.6894372826 -0.4431411888 0.334401492939 +1413393250405760512.0000000000 -0.8360541135 3.0898601223 1.0450378430 0.4689944972 0.6854840821 -0.4448966200 0.334996615483 +1413393250455760384.0000000000 -0.8377286174 3.1048970608 1.0404549345 0.4748806606 0.6806057889 -0.4459601695 0.335236700851 +1413393250505760512.0000000000 -0.8398616297 3.1201420717 1.0364342352 0.4818347572 0.6750439973 -0.4477483464 0.334174036574 +1413393250555760384.0000000000 -0.8424906887 3.1350219630 1.0329321972 0.4892970454 0.6694786509 -0.4492437841 0.332515803804 +1413393250605760512.0000000000 -0.8459778246 3.1489857642 1.0291012076 0.4943328683 0.6658054350 -0.4507440436 0.330405728255 +1413393250655760384.0000000000 -0.8501074030 3.1614785505 1.0246283105 0.4951864174 0.6651105345 -0.4513709053 0.3296705851 +1413393250705760512.0000000000 -0.8549081095 3.1727313161 1.0203751751 0.4948062104 0.6655302675 -0.4528530944 0.327353558177 +1413393250755760384.0000000000 -0.8604232293 3.1827908777 1.0167143760 0.4932206427 0.6672360724 -0.4536165196 0.325209893018 +1413393250805760512.0000000000 -0.8666485277 3.1915321620 1.0127907576 0.4894059646 0.6704298016 -0.4562442956 0.320697405212 +1413393250855760384.0000000000 -0.8729019247 3.1992064512 1.0093604087 0.4856148032 0.6736577164 -0.4580282928 0.31713345309 +1413393250905760512.0000000000 -0.8785590868 3.2057638715 1.0066304347 0.4812965895 0.6770230211 -0.4583458188 0.316089437097 +1413393250955760384.0000000000 -0.8835233132 3.2112390692 1.0046940194 0.4767804824 0.6796413044 -0.4595612997 0.315549490298 +1413393251005760512.0000000000 -0.8874039219 3.2159146932 1.0034135975 0.4718743200 0.6813340634 -0.4616608278 0.316208475986 +1413393251055760384.0000000000 -0.8898422573 3.2199411997 1.0033983679 0.4683284703 0.6808002333 -0.4637843443 0.31950519277 +1413393251105760512.0000000000 -0.8906171615 3.2235032585 1.0043345712 0.4657013169 0.6777704322 -0.4677278666 0.324006431222 +1413393251155760384.0000000000 -0.8900279965 3.2266350783 1.0069266165 0.4638565631 0.6726993788 -0.4724350270 0.330329804746 +1413393251205760512.0000000000 -0.8886153205 3.2291291156 1.0097756882 0.4620375897 0.6654883886 -0.4791757786 0.337693712691 +1413393251255760384.0000000000 -0.8868389301 3.2308450908 1.0135310491 0.4595071378 0.6572106842 -0.4866115307 0.346607162325 +1413393251305760512.0000000000 -0.8842564770 3.2322798503 1.0166590828 0.4560587157 0.6486186930 -0.4947450614 0.355712753685 +1413393251355760384.0000000000 -0.8811897714 3.2332051818 1.0214416279 0.4531320699 0.6382404217 -0.5034275696 0.365897763701 +1413393251405760512.0000000000 -0.8789924000 3.2336207713 1.0267474675 0.4491931615 0.6282016935 -0.5122925727 0.375691969506 +1413393251455760384.0000000000 -0.8774579399 3.2335232535 1.0321920306 0.4463406297 0.6170444459 -0.5209245000 0.385582493559 +1413393251505760512.0000000000 -0.8762253719 3.2329148579 1.0379071069 0.4431996779 0.6057998681 -0.5293962176 0.395373507079 +1413393251555760384.0000000000 -0.8758448835 3.2317848562 1.0444226706 0.4392705403 0.5953839786 -0.5367146790 0.405581883021 +1413393251605760512.0000000000 -0.8768384608 3.2304562527 1.0514004391 0.4359519377 0.5849207289 -0.5441722248 0.414355208312 +1413393251655760384.0000000000 -0.8790381770 3.2288330012 1.0587895922 0.4324817060 0.5745222241 -0.5512653263 0.423072485482 +1413393251705760512.0000000000 -0.8828926802 3.2267821559 1.0661082089 0.4281970131 0.5647817443 -0.5583037968 0.43123748644 +1413393251755760384.0000000000 -0.8885966776 3.2243868071 1.0733886810 0.4226118730 0.5561272478 -0.5657624018 0.438217518734 +1413393251805760512.0000000000 -0.8960907455 3.2217132577 1.0804447455 0.4150988335 0.5487109894 -0.5742971568 0.443612425673 +1413393251855760384.0000000000 -0.9052807432 3.2190310663 1.0875123774 0.4060004641 0.5428163890 -0.5843757728 0.446115396612 +1413393251905760512.0000000000 -0.9158793124 3.2163373348 1.0942694421 0.3945591811 0.5387341689 -0.5955555652 0.446544641281 +1413393251955760384.0000000000 -0.9272791481 3.2134234842 1.1012019663 0.3818807017 0.5352064214 -0.6059806119 0.447781993966 +1413393252005760512.0000000000 -0.9389320819 3.2104765456 1.1086544190 0.3695525100 0.5315458370 -0.6143562735 0.451061342542 +1413393252055760384.0000000000 -0.9505830004 3.2079498710 1.1166257909 0.3586258266 0.5271898169 -0.6225829223 0.453705761876 +1413393252105760512.0000000000 -0.9617863927 3.2059107724 1.1258713024 0.3511270490 0.5204777192 -0.6304851891 0.456400225205 +1413393252155760384.0000000000 -0.9725553183 3.2042071094 1.1360536678 0.3454153614 0.5129597557 -0.6371977776 0.45993424467 +1413393252205760512.0000000000 -0.9826758877 3.2027772462 1.1461917435 0.3405659976 0.5049619855 -0.6440532382 0.462842976491 +1413393252255760384.0000000000 -0.9921034376 3.2012263842 1.1561907100 0.3355547253 0.4963901821 -0.6498112830 0.467701945677 +1413393252305760512.0000000000 -1.0009587640 3.1999000035 1.1663938312 0.3309923617 0.4880838134 -0.6548735101 0.472608647148 +1413393252355760384.0000000000 -1.0093381811 3.1988385056 1.1764476509 0.3264614027 0.4796817016 -0.6603652588 0.476703411611 +1413393252405760512.0000000000 -1.0174267802 3.1977618639 1.1858879332 0.3218495206 0.4704375085 -0.6672300372 0.479484633879 +1413393252455760384.0000000000 -1.0253009846 3.1969133623 1.1936170090 0.3168656048 0.4626628114 -0.6750929709 0.479362902323 +1413393252505760512.0000000000 -1.0328127901 3.1964759240 1.1996235773 0.3144413049 0.4550754541 -0.6816009702 0.4790126453 +1413393252555760384.0000000000 -1.0396885962 3.1956374641 1.2028327328 0.3115651502 0.4490716951 -0.6857637001 0.480614104455 +1413393252605760512.0000000000 -1.0458100743 3.1943581586 1.2036247041 0.3093092486 0.4446722820 -0.6884524383 0.482314825045 +1413393252655760384.0000000000 -1.0512212074 3.1924882111 1.2024990117 0.3067621844 0.4408115566 -0.6905439101 0.484490703673 +1413393252705760512.0000000000 -1.0561927983 3.1902133506 1.1993025870 0.3031623230 0.4373841365 -0.6928201094 0.486608691999 +1413393252755760384.0000000000 -1.0606734214 3.1872662571 1.1957275528 0.2993028803 0.4341497304 -0.6936389052 0.490710573197 +1413393252805760512.0000000000 -1.0647753455 3.1840112873 1.1924800760 0.2946902697 0.4309189334 -0.6943464996 0.4953276252 +1413393252855760384.0000000000 -1.0684761776 3.1805033732 1.1898269058 0.2895559628 0.4275713592 -0.6949870374 0.500332984123 +1413393252905760512.0000000000 -1.0717757560 3.1772383884 1.1879665834 0.2853960920 0.4239593751 -0.6955356244 0.505012588014 +1413393252955760384.0000000000 -1.0747632718 3.1742345692 1.1869258035 0.2808709702 0.4215392255 -0.6953533420 0.509803794916 +1413393253005760512.0000000000 -1.0774073172 3.1718246605 1.1864617727 0.2760896822 0.4198730137 -0.6959747507 0.512933023058 +1413393253055760384.0000000000 -1.0795128820 3.1702518948 1.1869921452 0.2711369389 0.4192669824 -0.6967370812 0.515031452925 +1413393253105760512.0000000000 -1.0809533921 3.1696485180 1.1882592983 0.2664554752 0.4187518653 -0.6985737130 0.515405784392 +1413393253155760384.0000000000 -1.0816835713 3.1704694845 1.1895414245 0.2630700359 0.4186547284 -0.7028904179 0.511338865154 +1413393253205760512.0000000000 -1.0812683218 3.1719430923 1.1909131538 0.2606468538 0.4181896774 -0.7073439058 0.506798983948 +1413393253255760384.0000000000 -1.0798027257 3.1739316849 1.1924398393 0.2595064832 0.4169895257 -0.7125072152 0.501108360486 +1413393253305760512.0000000000 -1.0767176457 3.1760422125 1.1943430137 0.2590653606 0.4164440922 -0.7162262995 0.496466861924 +1413393253355760384.0000000000 -1.0718881221 3.1778822360 1.1967421514 0.2592743522 0.4157108517 -0.7186362011 0.493480808758 +1413393253405760512.0000000000 -1.0653830908 3.1791575770 1.1996950943 0.2606963732 0.4134809636 -0.7204727251 0.491924736189 +1413393253455760384.0000000000 -1.0572838540 3.1799588005 1.2031527485 0.2623703910 0.4122791532 -0.7209386449 0.491360507288 +1413393253505760512.0000000000 -1.0477391267 3.1800384038 1.2073271926 0.2640848080 0.4108137729 -0.7204510833 0.492383483373 +1413393253555760384.0000000000 -1.0367655631 3.1793012564 1.2121844855 0.2658420689 0.4091361175 -0.7199640349 0.493545763068 +1413393253605760512.0000000000 -1.0244975344 3.1781966621 1.2182817413 0.2687483339 0.4080147411 -0.7174047417 0.496617297937 +1413393253655760384.0000000000 -1.0111649604 3.1764649171 1.2248748332 0.2705558430 0.4072160033 -0.7145846453 0.500343329222 +1413393253705760512.0000000000 -0.9971205543 3.1742268684 1.2319361627 0.2723815922 0.4066123335 -0.7123471217 0.503027093465 +1413393253755760384.0000000000 -0.9824783127 3.1716984527 1.2392595570 0.2731239361 0.4076394706 -0.7093700083 0.505991668771 +1413393253805760512.0000000000 -0.9675417049 3.1687605434 1.2469781593 0.2737259168 0.4066277278 -0.7082931506 0.507985064979 +1413393253855760384.0000000000 -0.9523717974 3.1658166111 1.2551871437 0.2736910358 0.4053237198 -0.7086937477 0.508487041225 +1413393253905760512.0000000000 -0.9370535872 3.1626971595 1.2637572280 0.2730587346 0.4031223373 -0.7095383058 0.509398371847 +1413393253955760384.0000000000 -0.9214914175 3.1594420515 1.2725789002 0.2714995846 0.3996237841 -0.7115410967 0.510194153661 +1413393254005760512.0000000000 -0.9056155608 3.1558841225 1.2822052627 0.2706623843 0.3946724571 -0.7137257703 0.511440172564 +1413393254055760384.0000000000 -0.8897016793 3.1518967575 1.2924236967 0.2675898867 0.3898743592 -0.7163759835 0.513029323556 +1413393254105760512.0000000000 -0.8738450871 3.1476291271 1.3032420979 0.2647189524 0.3837189789 -0.7194521951 0.514851590719 +1413393254155760384.0000000000 -0.8577571397 3.1428154308 1.3143905053 0.2617044211 0.3766435783 -0.7222459405 0.517697993288 +1413393254205760512.0000000000 -0.8416882784 3.1375415931 1.3256090101 0.2572214407 0.3692735314 -0.7256744921 0.520452419535 +1413393254255760384.0000000000 -0.8260398288 3.1325600803 1.3376141194 0.2535082636 0.3620167212 -0.7287252002 0.523103275146 +1413393254305760512.0000000000 -0.8106858063 3.1272399360 1.3497463229 0.2466885975 0.3571244667 -0.7306628951 0.527009093795 +1413393254355760384.0000000000 -0.7954792500 3.1220339367 1.3617409629 0.2388861443 0.3539623829 -0.7325950521 0.530045782184 +1413393254405760512.0000000000 -0.7803005455 3.1172091748 1.3735550019 0.2299535057 0.3530893589 -0.7342721859 0.532253367212 +1413393254455760384.0000000000 -0.7648268669 3.1127823190 1.3851914335 0.2214681996 0.3521077194 -0.7374870002 0.532057247877 +1413393254505760512.0000000000 -0.7484511347 3.1088773955 1.3969235551 0.2137664815 0.3518286625 -0.7399323657 0.531996783599 +1413393254555760384.0000000000 -0.7307941023 3.1057609436 1.4092164787 0.2107885963 0.3495685152 -0.7426631897 0.530868540748 +1413393254605760512.0000000000 -0.7119287222 3.1031369334 1.4209512225 0.2085790275 0.3473452193 -0.7455725797 0.529119661667 +1413393254655760384.0000000000 -0.6915251832 3.1007469187 1.4327066667 0.2094231461 0.3442998305 -0.7474578804 0.528115791853 +1413393254705760512.0000000000 -0.6696028062 3.0984584801 1.4452143974 0.2127344225 0.3407126247 -0.7465522224 0.530394901984 +1413393254755760384.0000000000 -0.6468338461 3.0960844239 1.4578406197 0.2167736633 0.3366363112 -0.7448967528 0.533679679695 +1413393254805760512.0000000000 -0.6236978643 3.0938917099 1.4699383014 0.2203132264 0.3341747687 -0.7430127062 0.536396704604 +1413393254855760384.0000000000 -0.6004277531 3.0921117561 1.4812899094 0.2233544356 0.3328480755 -0.7415338206 0.538007943806 +1413393254905760512.0000000000 -0.5771931436 3.0902945658 1.4923782841 0.2263635636 0.3310939665 -0.7396168827 0.540465715203 +1413393254955760384.0000000000 -0.5542950730 3.0888653040 1.5025704672 0.2285879803 0.3307015225 -0.7385054070 0.541289019054 +1413393255005760512.0000000000 -0.5318839951 3.0877114822 1.5121170931 0.2298343017 0.3311315688 -0.7377746559 0.54149481531 +1413393255055760384.0000000000 -0.5097546291 3.0868043981 1.5216591267 0.2326263263 0.3302598917 -0.7373575026 0.541403093425 +1413393255105760512.0000000000 -0.4880479000 3.0860911697 1.5309873637 0.2358310625 0.3291976800 -0.7371188036 0.540988416463 +1413393255155760384.0000000000 -0.4669709585 3.0854779809 1.5399057302 0.2400658425 0.3273617436 -0.7375162634 0.539696619639 +1413393255205760512.0000000000 -0.4466959908 3.0847538778 1.5482218313 0.2443018486 0.3255670916 -0.7382033977 0.537939047853 +1413393255255760384.0000000000 -0.4273313124 3.0836355192 1.5558313782 0.2476126877 0.3242763160 -0.7386369652 0.536608107819 +1413393255305760512.0000000000 -0.4091003529 3.0822338652 1.5622882796 0.2502305971 0.3235034989 -0.7391895800 0.535097093357 +1413393255355760384.0000000000 -0.3920548982 3.0801970383 1.5677858739 0.2516545352 0.3229560459 -0.7398550329 0.533838849927 +1413393255405760512.0000000000 -0.3761252146 3.0774348856 1.5725238307 0.2530878543 0.3221892980 -0.7400120270 0.53340678122 +1413393255455760384.0000000000 -0.3614505805 3.0740197584 1.5766429857 0.2536994402 0.3217561390 -0.7403414065 0.532920428269 +1413393255505760512.0000000000 -0.3480080639 3.0697247445 1.5807713260 0.2537385508 0.3210220307 -0.7406199265 0.532957529365 +1413393255555760384.0000000000 -0.3359342439 3.0645078865 1.5847238652 0.2522049456 0.3209599920 -0.7410325652 0.533149215818 +1413393255605760512.0000000000 -0.3250074751 3.0584987196 1.5886065397 0.2500019308 0.3208638883 -0.7416740417 0.533352618542 +1413393255655760384.0000000000 -0.3151566845 3.0517017679 1.5922261808 0.2476525120 0.3205921026 -0.7422885459 0.533757109236 +1413393255705760512.0000000000 -0.3062897486 3.0443720770 1.5951138571 0.2448604629 0.3204689676 -0.7433091902 0.533698831078 +1413393255755760384.0000000000 -0.2984258026 3.0365417136 1.5970647266 0.2410857527 0.3208604058 -0.7452651526 0.532452920088 +1413393255805760512.0000000000 -0.2913363310 3.0281324739 1.5985820171 0.2371906387 0.3209419873 -0.7467995683 0.532003051179 +1413393255855760384.0000000000 -0.2848928348 3.0193514712 1.5990239960 0.2323131049 0.3218833756 -0.7496733574 0.529539017394 +1413393255905760512.0000000000 -0.2788781186 3.0099981448 1.5995044920 0.2261180732 0.3242542680 -0.7513770033 0.528358198125 +1413393255955760384.0000000000 -0.2725542107 2.9999111276 1.6000805822 0.2197665259 0.3267671732 -0.7513671285 0.529502905396 +1413393256005760512.0000000000 -0.2657011783 2.9895731296 1.6003211415 0.2147391868 0.3286182132 -0.7514585564 0.530289722391 +1413393256055760384.0000000000 -0.2579834434 2.9789022018 1.6001242076 0.2108503650 0.3299332628 -0.7508763697 0.531856036016 +1413393256105760512.0000000000 -0.2495226671 2.9680395238 1.5988192179 0.2082162763 0.3300016067 -0.7507687191 0.533002112744 +1413393256155760384.0000000000 -0.2403270164 2.9574604057 1.5967892668 0.2067700844 0.3298020005 -0.7507809808 0.53367095812 +1413393256205760512.0000000000 -0.2302106718 2.9471095769 1.5945626003 0.2070176626 0.3287748362 -0.7511707826 0.533660238116 +1413393256255760384.0000000000 -0.2191920685 2.9367543253 1.5923237345 0.2074691328 0.3273867775 -0.7522423292 0.532828241657 +1413393256305760512.0000000000 -0.2072615037 2.9264429805 1.5906611373 0.2083991986 0.3262785297 -0.7530397639 0.532018053376 +1413393256355760384.0000000000 -0.1945772493 2.9161446986 1.5892846420 0.2101646465 0.3250096811 -0.7542850879 0.530333418422 +1413393256405760512.0000000000 -0.1811694565 2.9055109968 1.5885173373 0.2113419771 0.3239912949 -0.7560946934 0.527906264619 +1413393256455760384.0000000000 -0.1669026920 2.8945518784 1.5896505874 0.2148976715 0.3217542846 -0.7577584889 0.525447660279 +1413393256505760512.0000000000 -0.1520686952 2.8829058450 1.5923485608 0.2183070559 0.3201131895 -0.7587639262 0.523590373872 +1413393256555760384.0000000000 -0.1369588160 2.8702751523 1.5964922427 0.2197232731 0.3201458243 -0.7594870459 0.521926969494 +1413393256605760512.0000000000 -0.1214938570 2.8565943728 1.6016489824 0.2187041025 0.3229054829 -0.7581005147 0.522670234792 +1413393256655760384.0000000000 -0.1054791649 2.8419449029 1.6070661240 0.2162338398 0.3265573539 -0.7555117616 0.525171590242 +1413393256705760512.0000000000 -0.0888770697 2.8269034905 1.6112948480 0.2142268749 0.3299188429 -0.7532503992 0.527137780206 +1413393256755760384.0000000000 -0.0714451576 2.8116199976 1.6135138936 0.2128466410 0.3330168430 -0.7513268840 0.528492197757 +1413393256805760512.0000000000 -0.0530480585 2.7960343381 1.6131921028 0.2121157558 0.3355033142 -0.7492190536 0.530203019665 +1413393256855760384.0000000000 -0.0341446476 2.7807535550 1.6103270317 0.2120026664 0.3377253747 -0.7475633485 0.531173682301 +1413393256905760512.0000000000 -0.0149272588 2.7660743424 1.6057893973 0.2142152728 0.3384070507 -0.7467065426 0.531057270124 +1413393256955760384.0000000000 0.0048664610 2.7514987595 1.6000238920 0.2169729360 0.3381431420 -0.7466559622 0.530176229835 +1413393257005760512.0000000000 0.0254480904 2.7369141461 1.5939287619 0.2205521148 0.3373796267 -0.7466448391 0.529200563518 +1413393257055760384.0000000000 0.0464017043 2.7220998065 1.5875069921 0.2221583519 0.3375200737 -0.7461452994 0.529143703217 +1413393257105760512.0000000000 0.0678087498 2.7075014380 1.5810170602 0.2251324035 0.3364794112 -0.7457389549 0.529122308994 +1413393257155760384.0000000000 0.0894535554 2.6926882615 1.5742851465 0.2268807293 0.3357999665 -0.7464583970 0.527791037016 +1413393257205760512.0000000000 0.1113126856 2.6774456647 1.5679394082 0.2279065984 0.3353216660 -0.7463438595 0.527815124894 +1413393257255760384.0000000000 0.1332865621 2.6620908662 1.5616363410 0.2284726133 0.3349344721 -0.7471171178 0.52672115652 +1413393257305760512.0000000000 0.1555395028 2.6462665554 1.5560972025 0.2292830048 0.3342370619 -0.7462554353 0.528031926587 +1413393257355760384.0000000000 0.1778481260 2.6302163315 1.5502459229 0.2292046435 0.3341732805 -0.7462000749 0.528184530551 +1413393257405760512.0000000000 0.2002314507 2.6137985655 1.5446253479 0.2290981419 0.3336813025 -0.7459985793 0.528826010499 +1413393257455760384.0000000000 0.2226443276 2.5973465614 1.5387021458 0.2285009410 0.3335334899 -0.7464782894 0.528500609761 +1413393257505760512.0000000000 0.2449638225 2.5807152036 1.5329271022 0.2293404268 0.3320675140 -0.7472277193 0.528000824141 +1413393257555760384.0000000000 0.2671457116 2.5635829336 1.5269351668 0.2287378441 0.3313155879 -0.7471143043 0.528894314694 +1413393257605760512.0000000000 0.2894274182 2.5461513202 1.5209010920 0.2293664260 0.3294456456 -0.7472251479 0.529633068741 +1413393257655760384.0000000000 0.3116544327 2.5283605870 1.5145245108 0.2296372075 0.3275267115 -0.7479142855 0.529733166508 +1413393257705760512.0000000000 0.3337318618 2.5102543925 1.5075185295 0.2283807158 0.3267237436 -0.7486613477 0.529716934321 +1413393257755760384.0000000000 0.3557323007 2.4917838631 1.5007703477 0.2275445988 0.3255350405 -0.7485862277 0.530913413537 +1413393257805760512.0000000000 0.3773370219 2.4730949947 1.4937229070 0.2248203080 0.3258059906 -0.7484134846 0.5321499241 +1413393257855760384.0000000000 0.3988446465 2.4541532845 1.4868896567 0.2204488885 0.3273566192 -0.7480084072 0.533594747107 +1413393257905760512.0000000000 0.4205713378 2.4350916741 1.4809058699 0.2163057154 0.3285658272 -0.7473433581 0.535475713581 +1413393257955760384.0000000000 0.4427578771 2.4161371967 1.4759192996 0.2129554994 0.3298030990 -0.7464661493 0.537278474378 +1413393258005760512.0000000000 0.4654396273 2.3973934633 1.4717959563 0.2108839977 0.3300775086 -0.7457317124 0.538944330127 +1413393258055760384.0000000000 0.4885961101 2.3791333394 1.4680078687 0.2091612814 0.3304583747 -0.7452800420 0.540005999957 +1413393258105760512.0000000000 0.5124099263 2.3614915249 1.4647996501 0.2094696990 0.3300010596 -0.7450000780 0.540552152647 +1413393258155760384.0000000000 0.5367383202 2.3447235535 1.4618608716 0.2104419260 0.3311048319 -0.7442330323 0.540556176317 +1413393258205760512.0000000000 0.5616691135 2.3288326862 1.4593022934 0.2124520940 0.3331289167 -0.7433504618 0.539740051834 +1413393258255760384.0000000000 0.5872673953 2.3135906924 1.4577863673 0.2164962981 0.3352588107 -0.7403463588 0.540941911632 +1413393258305760512.0000000000 0.6130889677 2.2991810620 1.4569789691 0.2215121658 0.3382082294 -0.7351336831 0.544174624512 +1413393258355760384.0000000000 0.6391536406 2.2859370960 1.4568724050 0.2286183924 0.3412328042 -0.7284936268 0.548261652614 +1413393258405760512.0000000000 0.6650911755 2.2741119626 1.4566177954 0.2367047702 0.3450444021 -0.7234750742 0.549089272645 +1413393258455760384.0000000000 0.6902227798 2.2638858951 1.4558436409 0.2446533609 0.3503200294 -0.7192265229 0.547844703079 +1413393258505760512.0000000000 0.7142181882 2.2554469830 1.4550479636 0.2555660831 0.3550744027 -0.7152545395 0.544994577382 +1413393258555760384.0000000000 0.7372442458 2.2480963455 1.4542646599 0.2659644057 0.3621653901 -0.7102531502 0.541885253297 +1413393258605760512.0000000000 0.7592397253 2.2415780309 1.4537701560 0.2748735957 0.3717085254 -0.7046410230 0.538292027823 +1413393258655760384.0000000000 0.7797200663 2.2360318099 1.4534069107 0.2819190312 0.3830726799 -0.7000798082 0.532602331907 +1413393258705760512.0000000000 0.7986675746 2.2315425617 1.4525948869 0.2879792436 0.3961761251 -0.6960479917 0.525004406009 +1413393258755760384.0000000000 0.8165777224 2.2274904506 1.4520632820 0.2937264908 0.4088035112 -0.6927096813 0.516485948809 +1413393258805760512.0000000000 0.8339169652 2.2238038710 1.4521340389 0.3010871893 0.4205759951 -0.6890281535 0.507644108046 +1413393258855760384.0000000000 0.8506920074 2.2203268453 1.4527151222 0.3095521770 0.4319614438 -0.6845453117 0.498983443599 +1413393258905760512.0000000000 0.8667586595 2.2167128547 1.4530121534 0.3156066556 0.4444221169 -0.6792177165 0.491471987501 +1413393258955760384.0000000000 0.8822600523 2.2130225258 1.4533406374 0.3208932508 0.4576064613 -0.6731404662 0.484257948715 +1413393259005760512.0000000000 0.8977685995 2.2093692711 1.4541565151 0.3270142676 0.4702303053 -0.6661400538 0.477705513426 +1413393259055760384.0000000000 0.9130341686 2.2055883834 1.4551125282 0.3333954273 0.4820858912 -0.6588585905 0.47153583136 +1413393259105760512.0000000000 0.9281650251 2.2020265314 1.4563263991 0.3408102110 0.4937994091 -0.6514079664 0.464411676099 +1413393259155760384.0000000000 0.9434677507 2.1982091595 1.4578481707 0.3474647423 0.5054072757 -0.6432110747 0.458378939211 +1413393259205760512.0000000000 0.9590242261 2.1942090470 1.4596668076 0.3550503451 0.5157618548 -0.6350250806 0.452407016586 +1413393259255760384.0000000000 0.9745561067 2.1903188698 1.4613067890 0.3621158909 0.5267560089 -0.6264382993 0.446066414112 +1413393259305760512.0000000000 0.9905585160 2.1863089230 1.4631826048 0.3696577765 0.5370916871 -0.6182136369 0.438973287368 +1413393259355760384.0000000000 1.0068757052 2.1821361623 1.4648777521 0.3761859915 0.5473231416 -0.6102176351 0.431921192338 +1413393259405760512.0000000000 1.0234466272 2.1779135498 1.4670707347 0.3837267694 0.5573961460 -0.6011583011 0.425055290324 +1413393259455760384.0000000000 1.0405460352 2.1734529275 1.4695137160 0.3914459074 0.5667231859 -0.5920639481 0.418396000803 +1413393259505760512.0000000000 1.0580306210 2.1688497299 1.4720636206 0.3978968151 0.5767806201 -0.5825793028 0.411829572458 +1413393259555760384.0000000000 1.0759540238 2.1643271449 1.4750138049 0.4046808398 0.5871468030 -0.5724902629 0.404656580968 +1413393259605760512.0000000000 1.0940305591 2.1597457584 1.4783646519 0.4112672516 0.5974793610 -0.5616675042 0.398004115077 +1413393259655760384.0000000000 1.1123263651 2.1551214639 1.4817471799 0.4176320655 0.6077234015 -0.5514134783 0.390126775763 +1413393259705760512.0000000000 1.1308201111 2.1505191758 1.4854972847 0.4244083748 0.6179121684 -0.5403606826 0.382194212603 +1413393259755760384.0000000000 1.1496236245 2.1457004059 1.4894892710 0.4309236438 0.6274036789 -0.5297067241 0.374272926225 +1413393259805760512.0000000000 1.1687468077 2.1407120759 1.4938854673 0.4374686759 0.6363506173 -0.5185391191 0.367146062774 +1413393259855760384.0000000000 1.1881702731 2.1358226571 1.4987375427 0.4441395607 0.6447840108 -0.5074887079 0.359789996257 +1413393259905760512.0000000000 1.2082189618 2.1308572991 1.5037404813 0.4501610432 0.6526982241 -0.4968185493 0.352861718731 +1413393259955760384.0000000000 1.2284464476 2.1258933364 1.5084520121 0.4557845448 0.6604125778 -0.4864632764 0.345643105746 +1413393260005760512.0000000000 1.2489091690 2.1208827830 1.5131591998 0.4616935265 0.6675427046 -0.4761114056 0.338443133414 +1413393260055760384.0000000000 1.2696814566 2.1157820858 1.5176886579 0.4662307240 0.6746238303 -0.4662585080 0.33183520496 +1413393260105760512.0000000000 1.2906485645 2.1109204185 1.5229443863 0.4724592681 0.6805951152 -0.4560240196 0.324984034493 +1413393260155760384.0000000000 1.3117207465 2.1059808633 1.5278888061 0.4776413233 0.6868900345 -0.4460946766 0.31786850469 +1413393260205760512.0000000000 1.3330978965 2.1009465992 1.5328476345 0.4828419198 0.6926010234 -0.4362766016 0.311175560992 +1413393260255760384.0000000000 1.3545186387 2.0958556451 1.5371289124 0.4877060794 0.6986126858 -0.4259019406 0.304451362854 +1413393260305760512.0000000000 1.3764951381 2.0908346199 1.5410306729 0.4954558896 0.7020393071 -0.4142534084 0.300097294817 +1413393260355760384.0000000000 1.3988307858 2.0854057148 1.5437346086 0.5042148980 0.7035631513 -0.4006024125 0.300472853871 +1413393260405760512.0000000000 1.4207426354 2.0794669960 1.5444183527 0.5115441095 0.7047176114 -0.3865581205 0.303757356744 +1413393260455760384.0000000000 1.4420302326 2.0730208513 1.5436344747 0.5184857400 0.7044631705 -0.3718681565 0.310834768167 +1413393260505760512.0000000000 1.4617533212 2.0662272131 1.5413094730 0.5249147797 0.7030976830 -0.3581830102 0.319097247544 +1413393260555760384.0000000000 1.4787437967 2.0589246594 1.5369624582 0.5282658569 0.7025137077 -0.3460778562 0.328085038369 +1413393260605760512.0000000000 1.4925488956 2.0518565645 1.5313478052 0.5306676325 0.7020754280 -0.3358584533 0.335679991237 +1413393260655760384.0000000000 1.5021534209 2.0449499434 1.5244446897 0.5288043065 0.7048307536 -0.3274357472 0.341123798115 +1413393260705760512.0000000000 1.5071681697 2.0389031462 1.5180679610 0.5268469586 0.7081088557 -0.3199835955 0.344419263884 +1413393260755760384.0000000000 1.5072527712 2.0340295252 1.5115076810 0.5202605272 0.7148848818 -0.3197275686 0.340650659115 +1413393260805760512.0000000000 1.5029041385 2.0304947423 1.5054939856 0.5123008348 0.7225257475 -0.3231186050 0.333314815179 +1413393260855760384.0000000000 1.4945736796 2.0291582196 1.5015199994 0.5077837739 0.7279689849 -0.3307851988 0.320621191064 +1413393260905760512.0000000000 1.4835629278 2.0295164221 1.4990119646 0.5050956091 0.7315213193 -0.3389809990 0.307972185923 +1413393260955760384.0000000000 1.4706789268 2.0311849341 1.4972831863 0.5030277912 0.7340146922 -0.3476774277 0.295475682754 +1413393261005760512.0000000000 1.4569643361 2.0339829985 1.4962767287 0.5013350996 0.7356316381 -0.3552039039 0.285200626947 +1413393261055760384.0000000000 1.4431574807 2.0375545593 1.4955805774 0.4993390878 0.7368653621 -0.3614676291 0.277544711147 +1413393261105760512.0000000000 1.4296745426 2.0419266671 1.4949500575 0.4968028765 0.7381618354 -0.3669490088 0.271389814712 +1413393261155760384.0000000000 1.4170501241 2.0470232486 1.4941244331 0.4932481901 0.7399134636 -0.3703977605 0.268402288312 +1413393261205760512.0000000000 1.4052000198 2.0530201848 1.4930752412 0.4900928440 0.7415621885 -0.3728655509 0.266206321851 +1413393261255760384.0000000000 1.3946299183 2.0600789801 1.4923665342 0.4885682002 0.7419249697 -0.3744410376 0.265786309607 +1413393261305760512.0000000000 1.3850589335 2.0684157294 1.4924549976 0.4902851186 0.7411743134 -0.3730932409 0.266613152557 +1413393261355760384.0000000000 1.3761612953 2.0779688073 1.4932360440 0.4941557927 0.7402507948 -0.3697176944 0.266735149177 +1413393261405760512.0000000000 1.3678227674 2.0883995827 1.4940753626 0.4978088315 0.7400208122 -0.3655616548 0.266308545352 +1413393261455760384.0000000000 1.3599162659 2.0998364317 1.4949605083 0.5014643641 0.7408432283 -0.3596763470 0.265174900851 +1413393261505760512.0000000000 1.3519191464 2.1124384737 1.4965547256 0.5054628919 0.7423244711 -0.3557210779 0.258697041522 +1413393261555760384.0000000000 1.3445737883 2.1259853937 1.4988869842 0.5102771055 0.7436209089 -0.3525583401 0.24969548691 +1413393261605760512.0000000000 1.3373613638 2.1396934127 1.5006554629 0.5149306918 0.7454542766 -0.3499727240 0.238040745691 +1413393261655760384.0000000000 1.3305363462 2.1532129952 1.5022384023 0.5183852255 0.7488186162 -0.3454378401 0.226318661683 +1413393261705760512.0000000000 1.3247854424 2.1665719127 1.5041963060 0.5211171100 0.7529683431 -0.3399473855 0.214269472968 +1413393261755760384.0000000000 1.3206799335 2.1798382078 1.5061541603 0.5238103702 0.7573939202 -0.3328767934 0.202904376807 +1413393261805760512.0000000000 1.3183536678 2.1927924785 1.5078954587 0.5262731856 0.7623460884 -0.3236101071 0.192721234582 +1413393261855760384.0000000000 1.3182749865 2.2052579263 1.5100744276 0.5297856829 0.7664119193 -0.3120794812 0.185866343241 +1413393261905760512.0000000000 1.3210020586 2.2172654279 1.5126869455 0.5342649555 0.7689264392 -0.2986514203 0.184717128699 +1413393261955760384.0000000000 1.3255174601 2.2289779367 1.5159126476 0.5390969297 0.7704928926 -0.2866313591 0.18318751813 +1413393262005760512.0000000000 1.3314875669 2.2401752280 1.5189101381 0.5420538940 0.7724728197 -0.2757005158 0.182900367662 +1413393262055760384.0000000000 1.3385425045 2.2513058783 1.5223281338 0.5454733482 0.7733250529 -0.2667986746 0.182333913963 +1413393262105760512.0000000000 1.3463518131 2.2621592470 1.5257557905 0.5476807167 0.7745088395 -0.2593109817 0.181492988415 +1413393262155760384.0000000000 1.3549067181 2.2728433314 1.5298382264 0.5497943467 0.7750272065 -0.2541662613 0.180162474091 +1413393262205760512.0000000000 1.3640777228 2.2831760901 1.5343580859 0.5502924724 0.7761403229 -0.2495917851 0.180245207438 +1413393262255760384.0000000000 1.3734944990 2.2934932041 1.5397591712 0.5509084382 0.7767917211 -0.2468164656 0.17937710846 +1413393262305760512.0000000000 1.3830086729 2.3034289623 1.5447709384 0.5495701065 0.7785825330 -0.2447267169 0.178579874304 +1413393262355760384.0000000000 1.3929480197 2.3133434509 1.5496642675 0.5486580785 0.7797409293 -0.2425132341 0.179348062037 +1413393262405760512.0000000000 1.4027516503 2.3234561779 1.5546743028 0.5487278459 0.7800391637 -0.2421619240 0.17830944118 +1413393262455760384.0000000000 1.4128061004 2.3338152943 1.5597714232 0.5481416403 0.7806942189 -0.2417304708 0.17783041967 +1413393262505760512.0000000000 1.4229576063 2.3443894825 1.5643240211 0.5480027603 0.7809263132 -0.2412544058 0.177885861294 +1413393262555760384.0000000000 1.4331600618 2.3550282384 1.5667327380 0.5475712611 0.7813626185 -0.2406319547 0.178141614606 +1413393262605760512.0000000000 1.4434786454 2.3658359453 1.5659920068 0.5470228779 0.7818328358 -0.2398435767 0.178825184637 +1413393262655760384.0000000000 1.4538091022 2.3770360836 1.5626973937 0.5468019693 0.7819794230 -0.2398408452 0.178863516065 +1413393262705760512.0000000000 1.4639389896 2.3881234217 1.5568485564 0.5470228885 0.7818806135 -0.2396912024 0.178820561076 +1413393262755760384.0000000000 1.4738585919 2.3992377403 1.5485098701 0.5466867989 0.7821999458 -0.2392271747 0.179073023311 +1413393262805760512.0000000000 1.4836174326 2.4105989883 1.5386730927 0.5464175617 0.7824623757 -0.2392089207 0.178772400076 +1413393262855760384.0000000000 1.4934220465 2.4225399348 1.5284758814 0.5463776789 0.7825611995 -0.2395711718 0.177974870778 +1413393262905760512.0000000000 1.5030617693 2.4348876744 1.5185552469 0.5469165248 0.7824147523 -0.2395811451 0.176947295009 +1413393262955760384.0000000000 1.5126846627 2.4474112173 1.5089928776 0.5463516266 0.7829314680 -0.2406553093 0.174937813778 +1413393263005760512.0000000000 1.5220456778 2.4598530381 1.4999907733 0.5464918206 0.7830840461 -0.2410504658 0.173264940419 +1413393263055760384.0000000000 1.5317423553 2.4726257973 1.4917719490 0.5473835256 0.7825723541 -0.2428141480 0.170273532721 +1413393263105760512.0000000000 1.5417565280 2.4855631468 1.4838018964 0.5468026439 0.7831999712 -0.2437741497 0.167865534273 +1413393263155760384.0000000000 1.5525775040 2.4992723188 1.4771977808 0.5476230553 0.7827855134 -0.2449835848 0.165344708288 +1413393263205760512.0000000000 1.5637042063 2.5126717861 1.4714101870 0.5476768752 0.7829613090 -0.2458623676 0.163013267184 +1413393263255760384.0000000000 1.5753926700 2.5258427056 1.4666979713 0.5486857214 0.7823538114 -0.2463271227 0.161831522247 +1413393263305760512.0000000000 1.5878974219 2.5390232197 1.4628316889 0.5495584490 0.7818017944 -0.2463791673 0.161458265009 +1413393263355760384.0000000000 1.6007053854 2.5516728202 1.4595186223 0.5498682372 0.7816460324 -0.2468176838 0.16048499201 +1413393263405760512.0000000000 1.6143244627 2.5642306037 1.4563168728 0.5495996776 0.7816148790 -0.2480998286 0.159577098577 +1413393263455760384.0000000000 1.6288564820 2.5768479759 1.4519895616 0.5493795044 0.7816892327 -0.2471429169 0.161444982057 +1413393263505760512.0000000000 1.6439231960 2.5893954763 1.4458015483 0.5495587999 0.7814847629 -0.2459772332 0.163590621625 +1413393263555760384.0000000000 1.6596349759 2.6020009961 1.4377113278 0.5517281338 0.7796660868 -0.2446634795 0.166903089598 +1413393263605760512.0000000000 1.6752886554 2.6143768851 1.4275151625 0.5545853506 0.7775417365 -0.2425138349 0.170443470856 +1413393263655760384.0000000000 1.6909576077 2.6266144796 1.4155267901 0.5592578338 0.7740585666 -0.2400637595 0.174451718622 +1413393263705760512.0000000000 1.7059318653 2.6384590081 1.4019100494 0.5641326543 0.7706477506 -0.2380227508 0.176639641369 +1413393263755760384.0000000000 1.7197848433 2.6493926443 1.3865416498 0.5676834070 0.7689509243 -0.2339028160 0.178155825224 +1413393263805760512.0000000000 1.7323918985 2.6594617794 1.3711933643 0.5711207512 0.7677994575 -0.2285885752 0.179031683829 +1413393263855760384.0000000000 1.7434429398 2.6685053572 1.3559320069 0.5736227767 0.7680359062 -0.2231730313 0.176837651272 +1413393263905760512.0000000000 1.7531288365 2.6763323663 1.3411437567 0.5755407221 0.7689602446 -0.2166756080 0.17465594863 +1413393263955760384.0000000000 1.7613983398 2.6831196799 1.3272582830 0.5780768386 0.7696791664 -0.2101429027 0.171058791148 +1413393264005760512.0000000000 1.7683747146 2.6887629142 1.3137089699 0.5780338616 0.7721438174 -0.2043862935 0.16702401946 +1413393264055760384.0000000000 1.7739771101 2.6932253567 1.3011304039 0.5772445607 0.7748760709 -0.2010606556 0.161029204289 +1413393264105760512.0000000000 1.7787248414 2.6967436725 1.2891837032 0.5732670091 0.7795537313 -0.1980949120 0.156266829941 +1413393264155760384.0000000000 1.7827698440 2.6992939476 1.2779261886 0.5686600288 0.7841306758 -0.1969372349 0.151593470771 +1413393264205760512.0000000000 1.7862707504 2.7010547587 1.2669964919 0.5630184841 0.7891308766 -0.1964753017 0.147241644851 +1413393264255760384.0000000000 1.7898469094 2.7027757495 1.2568288830 0.5574217413 0.7936565288 -0.1951430514 0.145977759248 +1413393264305760512.0000000000 1.7932487514 2.7043874206 1.2471751169 0.5529571450 0.7970533943 -0.1955238678 0.143926021034 +1413393264355760384.0000000000 1.7970127626 2.7066662854 1.2377202118 0.5486016393 0.8000107739 -0.1950565840 0.144816891602 +1413393264405760512.0000000000 1.8007244100 2.7096196638 1.2292112270 0.5448571077 0.8024658149 -0.1952170269 0.145153920193 +1413393264455760384.0000000000 1.8046136758 2.7139837433 1.2218545878 0.5440020558 0.8028487803 -0.1957648109 0.145505113086 +1413393264505760512.0000000000 1.8086177895 2.7192147735 1.2148664441 0.5436627110 0.8026407091 -0.1972619012 0.145898906773 +1413393264555760384.0000000000 1.8126988510 2.7254046386 1.2082733748 0.5437972509 0.8020936347 -0.1982618960 0.147046154807 +1413393264605760512.0000000000 1.8166276269 2.7327279520 1.2026518033 0.5463599607 0.7998800099 -0.2001250847 0.147080636287 +1413393264655760384.0000000000 1.8205816071 2.7407942173 1.1970733460 0.5476520159 0.7984938706 -0.2023037929 0.14682637172 +1413393264705760512.0000000000 1.8242488908 2.7497144259 1.1919920298 0.5501919928 0.7967022928 -0.2035637209 0.145313589277 +1413393264755760384.0000000000 1.8276503417 2.7589221098 1.1863772366 0.5509584424 0.7965920139 -0.2036243808 0.14290930588 +1413393264805760512.0000000000 1.8315007508 2.7684851901 1.1809473740 0.5525367917 0.7957929170 -0.2025307142 0.14282169632 +1413393264855760384.0000000000 1.8354023929 2.7782022200 1.1749184600 0.5524882566 0.7962477215 -0.2006080941 0.143187586364 +1413393264905760512.0000000000 1.8396446567 2.7881804903 1.1687945960 0.5526208981 0.7964043534 -0.1987101295 0.144445606514 +1413393264955760384.0000000000 1.8438712180 2.7985369033 1.1623972536 0.5519759448 0.7969303770 -0.1976201427 0.145501923637 +1413393265005760512.0000000000 1.8479704818 2.8092380622 1.1557707085 0.5515466991 0.7973628401 -0.1962047042 0.146671244602 +1413393265055760384.0000000000 1.8520693587 2.8204413705 1.1496521116 0.5528227785 0.7964439431 -0.1951711136 0.148230419987 +1413393265105760512.0000000000 1.8561392358 2.8320126477 1.1437014586 0.5542588405 0.7953255992 -0.1946700313 0.149525609354 +1413393265155760384.0000000000 1.8598956721 2.8442590715 1.1389914930 0.5597912887 0.7914012998 -0.1931009846 0.151755413726 +1413393265205760512.0000000000 1.8633559620 2.8568022228 1.1353188604 0.5679293347 0.7853161294 -0.1920653225 0.154420722546 +1413393265255760384.0000000000 1.8661540601 2.8686341399 1.1313937792 0.5745623764 0.7802262893 -0.1906627402 0.157393559776 +1413393265305760512.0000000000 1.8675239862 2.8795769286 1.1281856697 0.5813761920 0.7751921649 -0.1908565993 0.157011430581 +1413393265355760384.0000000000 1.8677609719 2.8890999690 1.1253121212 0.5859962837 0.7716149360 -0.1945293461 0.152895649152 +1413393265405760512.0000000000 1.8670884101 2.8967567424 1.1223858637 0.5869656124 0.7706747046 -0.1990136714 0.148072374806 +1413393265455760384.0000000000 1.8656996541 2.9025160225 1.1192000371 0.5844526652 0.7725105260 -0.2027868107 0.143248311395 +1413393265505760512.0000000000 1.8639868366 2.9065076684 1.1167296483 0.5808080824 0.7752565725 -0.2066758970 0.13756559083 +1413393265555760384.0000000000 1.8622738817 2.9089833555 1.1142766492 0.5760589771 0.7793016443 -0.2063278023 0.135180768159 +1413393265605760512.0000000000 1.8607563433 2.9100914667 1.1128528344 0.5722068959 0.7834014497 -0.2010007620 0.135868063047 +1413393265655760384.0000000000 1.8592501034 2.9101753714 1.1116219680 0.5686874378 0.7874806784 -0.1932812068 0.138243098284 +1413393265705760512.0000000000 1.8574282767 2.9100747309 1.1116121067 0.5669907015 0.7906324320 -0.1852066709 0.13827650139 +1413393265755760384.0000000000 1.8551629985 2.9098682245 1.1122973594 0.5656143589 0.7938655165 -0.1762742227 0.137059611616 +1413393265805760512.0000000000 1.8526387488 2.9095790679 1.1142924643 0.5652945903 0.7961846964 -0.1678808765 0.135454666758 +1413393265855760384.0000000000 1.8492925054 2.9094778785 1.1174344156 0.5653198438 0.7985683102 -0.1594664404 0.13142519764 +1413393265905760512.0000000000 1.8452269725 2.9095641150 1.1212306733 0.5655350088 0.8008277486 -0.1512036320 0.126422041454 +1413393265955760384.0000000000 1.8403980058 2.9097229299 1.1259931393 0.5656507114 0.8032031102 -0.1429651101 0.12027058544 +1413393266005760512.0000000000 1.8345472628 2.9101941442 1.1319606393 0.5668219338 0.8050726794 -0.1337149122 0.11265521982 +1413393266055760384.0000000000 1.8281266568 2.9109026886 1.1381364892 0.5674288570 0.8074204645 -0.1248725207 0.102486776103 +1413393266105760512.0000000000 1.8214664397 2.9119171680 1.1451921172 0.5691898074 0.8089586476 -0.1129764680 0.0940488562588 +1413393266155760384.0000000000 1.8141191191 2.9129252047 1.1529709528 0.5710177718 0.8105092649 -0.0993884121 0.0844711739093 +1413393266205760512.0000000000 1.8060123788 2.9139171372 1.1615125694 0.5722944769 0.8123589749 -0.0850152941 0.0729679890127 +1413393266255760384.0000000000 1.7975060262 2.9146017094 1.1708285535 0.5732548232 0.8141758904 -0.0692368038 0.0608505717465 +1413393266305760512.0000000000 1.7885471279 2.9148044874 1.1811674924 0.5747227027 0.8153460271 -0.0521070449 0.046792381413 +1413393266355760384.0000000000 1.7794310512 2.9147704549 1.1920548076 0.5754084836 0.8165595782 -0.0325308040 0.032821929898 +1413393266405760512.0000000000 1.7702027585 2.9149783293 1.2034785098 0.5761545658 0.8170543215 -0.0126236910 0.0175725506214 +1413393266455760384.0000000000 1.7605866929 2.9146298086 1.2157280567 0.5757952461 0.8175325364 0.0099087378 0.00148436637691 +1413393266505760512.0000000000 1.7509499725 2.9141956937 1.2292727857 0.5759268084 0.8167069590 0.0321729209 -0.0162159670457 +1413393266555760384.0000000000 1.7416714042 2.9132515673 1.2428982079 0.5768380641 0.8143506475 0.0540821461 -0.0341466294964 +1413393266605760512.0000000000 1.7326896474 2.9124341109 1.2553170499 0.5801208828 0.8093831651 0.0749871120 -0.0523028333986 +1413393266655760384.0000000000 1.7245283121 2.9113743419 1.2646286982 0.5812797114 0.8052645522 0.0941360214 -0.0692914683163 +1413393266705760512.0000000000 1.7172679927 2.9097547852 1.2703305128 0.5818168392 0.8012165084 0.1111833267 -0.0847321673882 +1413393266755760384.0000000000 1.7109135361 2.9074853969 1.2726243875 0.5813286317 0.7975821700 0.1269193249 -0.0990514461185 +1413393266805760512.0000000000 1.7054937898 2.9047398774 1.2731690858 0.5805191758 0.7940296283 0.1411192047 -0.112248857371 +1413393266855760384.0000000000 1.7016349122 2.9017237334 1.2749605669 0.5820320181 0.7890970447 0.1535654094 -0.122401997163 +1413393266905760512.0000000000 1.6991561224 2.8987934946 1.2809819432 0.5834459094 0.7846461386 0.1647325119 -0.129555036572 +1413393266955760384.0000000000 1.6980940325 2.8954311674 1.2891476430 0.5789384101 0.7852452061 0.1734672124 -0.134645496696 +1413393267005760512.0000000000 1.6986142926 2.8912263422 1.3023033974 0.5757255067 0.7854977698 0.1800173986 -0.13830087071 +1413393267055760384.0000000000 1.7001243715 2.8868707204 1.3195726512 0.5695082288 0.7883618795 0.1847714907 -0.141440519594 +1413393267105760512.0000000000 1.7033025887 2.8818311690 1.3389522259 0.5680401817 0.7884328901 0.1876619195 -0.143132573685 +1413393267155760384.0000000000 1.7075224790 2.8765188928 1.3568076801 0.5649728340 0.7901697065 0.1884858761 -0.144605000801 +1413393267205760512.0000000000 1.7123553670 2.8714139086 1.3718071540 0.5625006059 0.7918239518 0.1886907536 -0.144926523313 +1413393267255760384.0000000000 1.7177992822 2.8665601111 1.3838398744 0.5611724999 0.7928831529 0.1874450164 -0.145897556971 +1413393267305760512.0000000000 1.7239928549 2.8624039127 1.3925987612 0.5594835566 0.7945328876 0.1860929988 -0.145137990177 +1413393267355760384.0000000000 1.7306493986 2.8588067971 1.3994424330 0.5596632678 0.7950034822 0.1838546735 -0.144720244142 +1413393267405760512.0000000000 1.7377688158 2.8558106037 1.4033304566 0.5601755257 0.7952411526 0.1825612643 -0.143060387157 +1413393267455760384.0000000000 1.7454918529 2.8532474968 1.4051178122 0.5606728783 0.7956500611 0.1811553761 -0.140604528832 +1413393267505760512.0000000000 1.7539416592 2.8511614209 1.4045388234 0.5624876820 0.7952558556 0.1805753460 -0.136265461855 +1413393267555760384.0000000000 1.7626935213 2.8492733598 1.4015095107 0.5632671427 0.7955574771 0.1804471950 -0.131366800797 +1413393267605760512.0000000000 1.7716555228 2.8471356847 1.3965692838 0.5641631569 0.7956688297 0.1804517675 -0.126760425357 +1413393267655760384.0000000000 1.7808792499 2.8445380123 1.3897905686 0.5649934911 0.7957223208 0.1803241667 -0.122847621339 +1413393267705760512.0000000000 1.7903278243 2.8414479851 1.3808432483 0.5660994057 0.7954322037 0.1802716244 -0.119671273408 +1413393267755760384.0000000000 1.7995790518 2.8385441084 1.3692450196 0.5665673046 0.7955048523 0.1811411243 -0.115591576149 +1413393267805760512.0000000000 1.8083076431 2.8350476774 1.3569080381 0.5667634821 0.7955131842 0.1816884502 -0.113698004418 +1413393267855760384.0000000000 1.8164513952 2.8315452923 1.3446148417 0.5682090858 0.7944494659 0.1835300329 -0.110928841577 +1413393267905760512.0000000000 1.8237721553 2.8279004237 1.3331355406 0.5685777343 0.7941408393 0.1847576349 -0.109198460635 +1413393267955760384.0000000000 1.8299531440 2.8239250320 1.3232141882 0.5687843332 0.7938317450 0.1843820888 -0.110990037051 +1413393268005760512.0000000000 1.8353231285 2.8196964723 1.3146391829 0.5675281903 0.7946888382 0.1820515589 -0.115059261216 +1413393268055760384.0000000000 1.8401007640 2.8153452185 1.3071531018 0.5656818173 0.7959795960 0.1789841936 -0.119938412124 +1413393268105760512.0000000000 1.8448785400 2.8111081547 1.3004916599 0.5639956727 0.7970313709 0.1775175526 -0.123034115269 +1413393268155760384.0000000000 1.8495361041 2.8068633110 1.2945767641 0.5614626768 0.7986903015 0.1755527871 -0.126628132195 +1413393268205760512.0000000000 1.8544990560 2.8031623516 1.2890237925 0.5604023420 0.7993761472 0.1752397169 -0.127428536782 +1413393268255760384.0000000000 1.8596170831 2.7998529267 1.2833945491 0.5601538482 0.7993877330 0.1772591017 -0.125642864777 +1413393268305760512.0000000000 1.8648554854 2.7970384797 1.2780140793 0.5604698050 0.7991234768 0.1802545535 -0.121587673941 +1413393268355760384.0000000000 1.8698240643 2.7946230475 1.2733014418 0.5606531643 0.7988795138 0.1845112523 -0.115823786527 +1413393268405760512.0000000000 1.8744652601 2.7922963694 1.2694871496 0.5602655398 0.7989127829 0.1894683006 -0.109282446854 +1413393268455760384.0000000000 1.8780108844 2.7903020504 1.2675012742 0.5604082388 0.7986987328 0.1916511816 -0.106267420495 +1413393268505760512.0000000000 1.8804917717 2.7886403430 1.2666369756 0.5595779192 0.7994234034 0.1924041098 -0.103804783451 +1413393268555760384.0000000000 1.8813710646 2.7869910786 1.2676517675 0.5581636840 0.8007176709 0.1900725082 -0.10572111869 +1413393268605760512.0000000000 1.8811378378 2.7857856958 1.2707402573 0.5582592581 0.8011405652 0.1863490344 -0.108602177312 +1413393268655760384.0000000000 1.8802588191 2.7848092450 1.2749888157 0.5591425332 0.8009164144 0.1832345747 -0.110984753097 +1413393268705760512.0000000000 1.8789030696 2.7841169976 1.2804584883 0.5603103017 0.8004524310 0.1804477526 -0.112990618994 +1413393268755760384.0000000000 1.8772850658 2.7836451940 1.2865484926 0.5600153321 0.8010313463 0.1774886976 -0.115019008578 +1413393268805760512.0000000000 1.8753710271 2.7834202447 1.2930540164 0.5585473363 0.8022923118 0.1756115172 -0.116243341647 +1413393268855760384.0000000000 1.8734361328 2.7838968818 1.3002711755 0.5587915499 0.8024851225 0.1730614628 -0.117555782476 +1413393268905760512.0000000000 1.8714597867 2.7847195463 1.3061616708 0.5576203495 0.8034552482 0.1717228036 -0.118450363767 +1413393268955760384.0000000000 1.8693748431 2.7868704212 1.3108948854 0.5595465946 0.8022971737 0.1709435729 -0.118343349755 +1413393269005760512.0000000000 1.8676590874 2.7892734685 1.3131050700 0.5629326464 0.8000964645 0.1722741905 -0.115213221475 +1413393269055760384.0000000000 1.8659138238 2.7919567772 1.3128982332 0.5665744296 0.7975018175 0.1755149513 -0.110357458461 +1413393269105760512.0000000000 1.8641238007 2.7945296372 1.3117157354 0.5699195203 0.7949141231 0.1805826526 -0.103407847094 +1413393269155760384.0000000000 1.8613921529 2.7963484628 1.3109549089 0.5716397070 0.7931147838 0.1851517152 -0.0995782481468 +1413393269205760512.0000000000 1.8572301428 2.7970965979 1.3114385712 0.5742172330 0.7902889697 0.1886915109 -0.100565538357 +1413393269255760384.0000000000 1.8515375768 2.7963917624 1.3131721996 0.5750336662 0.7882754664 0.1908451501 -0.107406706302 +1413393269305760512.0000000000 1.8449756394 2.7945735227 1.3155902213 0.5760949118 0.7856990880 0.1929837248 -0.116399646103 +1413393269355760384.0000000000 1.8378797413 2.7920903794 1.3185969548 0.5788971013 0.7815649793 0.1951184790 -0.12634519515 +1413393269405760512.0000000000 1.8310002317 2.7884650637 1.3208976784 0.5799577586 0.7785064284 0.1971731916 -0.136746011368 +1413393269455760384.0000000000 1.8248275399 2.7841278335 1.3211385408 0.5802073629 0.7763781561 0.1996619338 -0.143984328956 +1413393269505760512.0000000000 1.8194641355 2.7790288481 1.3183545833 0.5785802886 0.7759102321 0.2012346486 -0.150707589429 +1413393269555760384.0000000000 1.8152557149 2.7732523110 1.3118654937 0.5754877660 0.7767130518 0.2034806188 -0.155326443695 +1413393269605760512.0000000000 1.8121686783 2.7669814370 1.3016813076 0.5719262165 0.7781948576 0.2051288994 -0.158856227661 +1413393269655760384.0000000000 1.8101536259 2.7604420242 1.2887328336 0.5694248265 0.7791208533 0.2061307345 -0.161975872512 +1413393269705760512.0000000000 1.8091747575 2.7536833651 1.2728853091 0.5667515022 0.7803560335 0.2073055375 -0.163895118192 +1413393269755760384.0000000000 1.8093303315 2.7468239538 1.2556077613 0.5633138775 0.7822962129 0.2091678905 -0.164130753673 +1413393269805760512.0000000000 1.8104921084 2.7400830902 1.2378623271 0.5596867642 0.7845406416 0.2114076952 -0.162952428922 +1413393269855760384.0000000000 1.8124599431 2.7338429506 1.2205170430 0.5571150899 0.7861133300 0.2142833189 -0.160409688683 +1413393269905760512.0000000000 1.8149786558 2.7281218649 1.2035665799 0.5558145957 0.7867249594 0.2179790360 -0.156904790553 +1413393269955760384.0000000000 1.8180699667 2.7227993921 1.1869963781 0.5547835517 0.7872185944 0.2218026129 -0.152662032905 +1413393270005760512.0000000000 1.8212423186 2.7180006480 1.1709875631 0.5538568353 0.7876561889 0.2257278638 -0.147943453884 +1413393270055760384.0000000000 1.8238184768 2.7134111713 1.1563084248 0.5535842159 0.7875292861 0.2273417148 -0.147166178936 +1413393270105760512.0000000000 1.8261145420 2.7088501273 1.1419558245 0.5512661979 0.7889575312 0.2280320968 -0.14714943395 +1413393270155760384.0000000000 1.8279771451 2.7046898333 1.1281647662 0.5499405322 0.7897342877 0.2283472273 -0.147454093355 +1413393270205760512.0000000000 1.8293343578 2.7008899282 1.1150074154 0.5489975111 0.7901069949 0.2286344207 -0.148522628329 +1413393270255760384.0000000000 1.8304568946 2.6975647942 1.1020192665 0.5480542351 0.7906156040 0.2287879769 -0.149062348152 +1413393270305760512.0000000000 1.8309946392 2.6950372851 1.0894854427 0.5473836397 0.7907884820 0.2289196502 -0.150401201642 +1413393270355760384.0000000000 1.8311753784 2.6936640541 1.0773831132 0.5480111666 0.7904299712 0.2282634773 -0.150996711395 +1413393270405760512.0000000000 1.8308918221 2.6935661921 1.0661798960 0.5473197426 0.7914784913 0.2256986368 -0.151865145765 +1413393270455760384.0000000000 1.8302828580 2.6951153519 1.0568478165 0.5481231676 0.7919447712 0.2219857911 -0.152009148118 +1413393270505760512.0000000000 1.8301928019 2.6970628726 1.0480102657 0.5484338431 0.7931238224 0.2174483574 -0.151298162366 +1413393270555760384.0000000000 1.8309400198 2.6992356408 1.0386093386 0.5488005810 0.7947256477 0.2133339341 -0.147369263633 +1413393270605760512.0000000000 1.8325607093 2.7010525343 1.0288789440 0.5503952899 0.7956791540 0.2085767576 -0.143022532669 +1413393270655760384.0000000000 1.8348025243 2.7027669126 1.0193850813 0.5506321334 0.7977808125 0.2037268204 -0.137278591041 +1413393270705760512.0000000000 1.8368383741 2.7060392289 1.0113949053 0.5534886816 0.7981142736 0.2003404243 -0.128559714093 +1413393270755760384.0000000000 1.8373573059 2.7106337455 1.0082205562 0.5561141967 0.7981743840 0.1957105911 -0.123903258601 +1413393270805760512.0000000000 1.8373549452 2.7160693132 1.0083569924 0.5575907085 0.7987754050 0.1927619452 -0.117869786586 +1413393270855760384.0000000000 1.8368835289 2.7214575998 1.0131817767 0.5595144595 0.7988738903 0.1900259637 -0.11240200258 +1413393270905760512.0000000000 1.8354020450 2.7269595580 1.0216999128 0.5599062045 0.7996202004 0.1886355189 -0.107374197908 +1413393270955760384.0000000000 1.8333835353 2.7324703018 1.0304760664 0.5632972155 0.7981996330 0.1871606717 -0.102686298498 +1413393271005760512.0000000000 1.8300518226 2.7385681739 1.0399441105 0.5637494004 0.7985722435 0.1869066666 -0.0976467282442 +1413393271055760384.0000000000 1.8255229088 2.7442596191 1.0482719420 0.5644789388 0.7987469294 0.1848930810 -0.0958197216173 +1413393271105760512.0000000000 1.8200053620 2.7500277212 1.0542032033 0.5660574760 0.7982438901 0.1828773522 -0.0945595037676 +1413393271155760384.0000000000 1.8133487798 2.7556497391 1.0578423369 0.5677821981 0.7975999383 0.1799692567 -0.0952301447801 +1413393271205760512.0000000000 1.8060598363 2.7611550767 1.0586319117 0.5694981274 0.7967531919 0.1792521144 -0.0934072459897 +1413393271255760384.0000000000 1.7981300337 2.7661691793 1.0573120896 0.5727823221 0.7947622587 0.1789213648 -0.0908873409682 +1413393271305760512.0000000000 1.7897993381 2.7708145825 1.0537043625 0.5760948997 0.7928990873 0.1787361371 -0.08648177417 +1413393271355760384.0000000000 1.7807092250 2.7748082424 1.0483989263 0.5783114156 0.7921389142 0.1772598902 -0.0815523055223 +1413393271405760512.0000000000 1.7705307302 2.7781532861 1.0435867738 0.5810214638 0.7914248244 0.1731269821 -0.0780247008914 +1413393271455760384.0000000000 1.7593751439 2.7804506828 1.0394906439 0.5825146798 0.7920368406 0.1658596398 -0.076451754259 +1413393271505760512.0000000000 1.7474747070 2.7816389244 1.0368822847 0.5834244107 0.7933136427 0.1568422494 -0.0752989382642 +1413393271555760384.0000000000 1.7346308250 2.7817553482 1.0353468144 0.5853802689 0.7937411371 0.1469026286 -0.0756608599553 +1413393271605760512.0000000000 1.7211621799 2.7807520765 1.0342739450 0.5868456038 0.7941355572 0.1389851011 -0.0751271971133 +1413393271655760384.0000000000 1.7076571261 2.7787891571 1.0335427528 0.5866048144 0.7956879216 0.1319729613 -0.0732028739325 +1413393271705760512.0000000000 1.6943805069 2.7758046610 1.0332986269 0.5847866653 0.7984506206 0.1254276762 -0.0690583848911 +1413393271755760384.0000000000 1.6811523807 2.7723549644 1.0335047826 0.5804990230 0.8030752820 0.1182549503 -0.0640838708209 +1413393271805760512.0000000000 1.6678785624 2.7682329297 1.0350011782 0.5771409602 0.8069438838 0.1104685732 -0.0595531256686 +1413393271855760384.0000000000 1.6543510523 2.7641176905 1.0367905368 0.5740604347 0.8103946750 0.1038130484 -0.0542027575969 +1413393271905760512.0000000000 1.6404594646 2.7602338029 1.0392226531 0.5743044209 0.8112937660 0.0978398622 -0.0490328326714 +1413393271955760384.0000000000 1.6261034077 2.7564510219 1.0420130217 0.5749534968 0.8116879162 0.0929957838 -0.0440793310854 +1413393272005760512.0000000000 1.6110583053 2.7529705224 1.0457194123 0.5768157834 0.8110492478 0.0886074516 -0.0403904585417 +1413393272055760384.0000000000 1.5957318838 2.7492067501 1.0493804592 0.5768416041 0.8115920624 0.0850019751 -0.0366981229934 +1413393272105760512.0000000000 1.5799423943 2.7450482117 1.0536678148 0.5776011394 0.8114728467 0.0821151420 -0.0338503515078 +1413393272155760384.0000000000 1.5638614885 2.7408748766 1.0584561768 0.5786147497 0.8112681142 0.0779113807 -0.0312863411393 +1413393272205760512.0000000000 1.5475099547 2.7367801984 1.0642382479 0.5812525208 0.8099922850 0.0716732688 -0.0303471224195 +1413393272255760384.0000000000 1.5308899079 2.7324468838 1.0702020148 0.5818564788 0.8102255788 0.0631717400 -0.0314146590636 +1413393272305760512.0000000000 1.5146734014 2.7280353428 1.0766018212 0.5830793947 0.8099857650 0.0546250617 -0.0309448326456 +1413393272355760384.0000000000 1.4989578588 2.7233590526 1.0827846635 0.5835764954 0.8102025443 0.0461110881 -0.0297334632606 +1413393272405760512.0000000000 1.4840907815 2.7185263785 1.0884807220 0.5830819248 0.8110682559 0.0390891874 -0.0256083714199 +1413393272455760384.0000000000 1.4700850280 2.7138746483 1.0944054542 0.5836560304 0.8111027248 0.0333116585 -0.0186639052862 +1413393272505760512.0000000000 1.4566582145 2.7090166646 1.1006578597 0.5840748458 0.8111744291 0.0266776075 -0.011871202541 +1413393272555760384.0000000000 1.4437816522 2.7038449774 1.1067296294 0.5841431443 0.8113740097 0.0209179731 -0.00338254677344 +1413393272605760512.0000000000 1.4312610921 2.6986125457 1.1131937796 0.5841786192 0.8114610564 0.0151823049 0.0059826704008 +1413393272655760384.0000000000 1.4187636572 2.6932061687 1.1198468122 0.5835993376 0.8118654119 0.0086039722 0.0145718175576 +1413393272705760512.0000000000 1.4059654947 2.6873820444 1.1264093348 0.5824716760 0.8125098587 0.0019763166 0.0234642360254 +1413393272755760384.0000000000 1.3925673311 2.6814975893 1.1332221430 0.5819411702 0.8126153054 -0.0058677306 0.0310871297284 +1413393272805760512.0000000000 1.3787980144 2.6753306986 1.1400013625 0.5811119653 0.8127640560 -0.0137576645 0.039168861289 +1413393272855760384.0000000000 1.3646782625 2.6691319969 1.1471297070 0.5810766612 0.8121522997 -0.0217669321 0.0477991269069 +1413393272905760512.0000000000 1.3497340980 2.6628666989 1.1546477724 0.5807889250 0.8116365237 -0.0309090036 0.0545436650975 +1413393272955760384.0000000000 1.3340307507 2.6564581925 1.1623758488 0.5798329246 0.8114614148 -0.0403570060 0.0607903270863 +1413393273005760512.0000000000 1.3176936838 2.6499912339 1.1700652361 0.5790162932 0.8110071611 -0.0507970332 0.0665370438761 +1413393273055760384.0000000000 1.3006050019 2.6434763553 1.1776302808 0.5768723607 0.8113531149 -0.0630812637 0.0703218075761 +1413393273105760512.0000000000 1.2833107691 2.6372353289 1.1849080437 0.5737044454 0.8121333077 -0.0746622270 0.0756852148176 +1413393273155760384.0000000000 1.2657646282 2.6311779536 1.1925419035 0.5717837858 0.8118007916 -0.0868956851 0.0805724327928 +1413393273205760512.0000000000 1.2483084468 2.6253891783 1.1997104693 0.5687611644 0.8118976070 -0.0991256838 0.086643594016 +1413393273255760384.0000000000 1.2310506061 2.6200809121 1.2066624283 0.5648173637 0.8123304345 -0.1113628284 0.0932680611978 +1413393273305760512.0000000000 1.2140298340 2.6153757718 1.2138048205 0.5618335588 0.8117715291 -0.1243666450 0.0995136898243 +1413393273355760384.0000000000 1.1973977407 2.6110806690 1.2207445798 0.5587853436 0.8109565400 -0.1361451287 0.107577571262 +1413393273405760512.0000000000 1.1810038392 2.6075223922 1.2280704211 0.5584089419 0.8080570449 -0.1478279333 0.115629442217 +1413393273455760384.0000000000 1.1648597181 2.6040904195 1.2344338710 0.5547017649 0.8072770595 -0.1585051342 0.124442049475 +1413393273505760512.0000000000 1.1491976778 2.6015570520 1.2418159974 0.5546432773 0.8037040292 -0.1690769180 0.133580179191 +1413393273555760384.0000000000 1.1336326598 2.5998434827 1.2498601109 0.5557709703 0.7991710790 -0.1793107857 0.142449489982 +1413393273605760512.0000000000 1.1180021400 2.5985969265 1.2583407072 0.5571448663 0.7944820237 -0.1890858474 0.150447513009 +1413393273655760384.0000000000 1.1023090740 2.5975268621 1.2672359828 0.5585548676 0.7894648449 -0.1994199410 0.158093028432 +1413393273705760512.0000000000 1.0866332033 2.5963895620 1.2763293373 0.5589962130 0.7850246246 -0.2089907084 0.166079668828 +1413393273755760384.0000000000 1.0706396520 2.5952219922 1.2854631260 0.5586611131 0.7812979935 -0.2181512820 0.172861864798 +1413393273805760512.0000000000 1.0547538651 2.5937749129 1.2942498458 0.5571223672 0.7779154641 -0.2283414253 0.179784293397 +1413393273855760384.0000000000 1.0385201745 2.5919091138 1.3028256177 0.5546352513 0.7752177884 -0.2397512957 0.184218443296 +1413393273905760512.0000000000 1.0221286144 2.5898142582 1.3113249597 0.5513707251 0.7731435173 -0.2508523079 0.187916324186 +1413393273955760384.0000000000 1.0063207471 2.5875401795 1.3200084308 0.5476746997 0.7707620352 -0.2621541557 0.19301167612 +1413393274005760512.0000000000 0.9907360122 2.5852681535 1.3290138447 0.5436836089 0.7687483117 -0.2726432987 0.197736689268 +1413393274055760384.0000000000 0.9756530653 2.5829182506 1.3384052274 0.5400439520 0.7665320600 -0.2826400566 0.202226925469 +1413393274105760512.0000000000 0.9615725503 2.5804742676 1.3483503214 0.5370952156 0.7632990066 -0.2930325793 0.207449423542 +1413393274155760384.0000000000 0.9480929824 2.5781431831 1.3587857680 0.5349649751 0.7594786060 -0.3028321411 0.212831897854 +1413393274205760512.0000000000 0.9352004817 2.5757006310 1.3694560021 0.5330120512 0.7556529561 -0.3123901457 0.217483700677 +1413393274255760384.0000000000 0.9231402964 2.5731622913 1.3801138690 0.5300518868 0.7522253535 -0.3219880815 0.222543681434 +1413393274305760512.0000000000 0.9120332916 2.5705398468 1.3912008120 0.5277441388 0.7482705272 -0.3307706543 0.228403407157 +1413393274355760384.0000000000 0.9016473318 2.5677366592 1.4022990528 0.5249934833 0.7448766106 -0.3389008814 0.233852239823 +1413393274405760512.0000000000 0.8924224574 2.5646773375 1.4132909561 0.5218884835 0.7411463954 -0.3472078557 0.240377071071 +1413393274455760384.0000000000 0.8839585474 2.5612831098 1.4230346140 0.5193205245 0.7368932920 -0.3556485730 0.246593920517 +1413393274505760512.0000000000 0.8757571190 2.5572691576 1.4305600030 0.5171475335 0.7321959172 -0.3638512463 0.253100450343 +1413393274555760384.0000000000 0.8682330813 2.5530373025 1.4352005882 0.5140093268 0.7278856767 -0.3731156790 0.258382552814 +1413393274605760512.0000000000 0.8612811454 2.5484246236 1.4370479157 0.5112770840 0.7230470254 -0.3816633873 0.26482409512 +1413393274655760384.0000000000 0.8549866191 2.5436729237 1.4362449808 0.5076217027 0.7187874382 -0.3903931244 0.270662213858 +1413393274705760512.0000000000 0.8498657970 2.5388294694 1.4335238706 0.5043066648 0.7141311715 -0.3985210372 0.277258797222 +1413393274755760384.0000000000 0.8454867375 2.5336023172 1.4290779449 0.5013577222 0.7092981735 -0.4048962575 0.285649358711 +1413393274805760512.0000000000 0.8417444296 2.5280812113 1.4242891214 0.4993513256 0.7037440715 -0.4103948426 0.294904405945 +1413393274855760384.0000000000 0.8382540997 2.5221157189 1.4198902502 0.4971094803 0.6982272966 -0.4157609794 0.304144069134 +1413393274905760512.0000000000 0.8348390469 2.5159088998 1.4163829477 0.4948665204 0.6925306036 -0.4208976649 0.313613848258 +1413393274955760384.0000000000 0.8311104056 2.5097033254 1.4135218154 0.4926749605 0.6872265441 -0.4261270288 0.32156930162 +1413393275005760512.0000000000 0.8271807386 2.5034312165 1.4115649479 0.4909030122 0.6810180542 -0.4321700551 0.329329145434 +1413393275055760384.0000000000 0.8224874777 2.4971530958 1.4099571721 0.4884058987 0.6756132342 -0.4386583119 0.335537361929 +1413393275105760512.0000000000 0.8170477581 2.4906613443 1.4084804415 0.4856308155 0.6702420066 -0.4450451697 0.341867167984 +1413393275155760384.0000000000 0.8108878865 2.4838418354 1.4070702296 0.4824494399 0.6648828803 -0.4524160053 0.347121090668 +1413393275205760512.0000000000 0.8039831783 2.4769525290 1.4055684798 0.4789901791 0.6598154946 -0.4605729540 0.350833971456 +1413393275255760384.0000000000 0.7965602349 2.4696789039 1.4047085114 0.4750080659 0.6545070295 -0.4690589006 0.354924827959 +1413393275305760512.0000000000 0.7885815443 2.4619411584 1.4038920042 0.4696137168 0.6496263189 -0.4781010654 0.35898185751 +1413393275355760384.0000000000 0.7802609276 2.4541657869 1.4035211711 0.4655915113 0.6436880498 -0.4872781991 0.362560609763 +1413393275405760512.0000000000 0.7717779654 2.4459735516 1.4034406957 0.4610758020 0.6374891115 -0.4966772513 0.3665084522 +1413393275455760384.0000000000 0.7630511947 2.4375734912 1.4040772259 0.4573145365 0.6306523989 -0.5056793918 0.37071460612 +1413393275505760512.0000000000 0.7540641809 2.4286789610 1.4054925732 0.4531414930 0.6243162661 -0.5138196335 0.375341672947 +1413393275555760384.0000000000 0.7448506549 2.4192446977 1.4073224665 0.4486409731 0.6178057481 -0.5218485594 0.380409537051 +1413393275605760512.0000000000 0.7354273047 2.4094206236 1.4099236596 0.4453725647 0.6102040296 -0.5302710363 0.384846656351 +1413393275655760384.0000000000 0.7258623146 2.3990382960 1.4129928346 0.4412790390 0.6036711733 -0.5377509915 0.389458335996 +1413393275705760512.0000000000 0.7164207676 2.3878109503 1.4169749991 0.4371320186 0.5963339799 -0.5452355021 0.394993202485 +1413393275755760384.0000000000 0.7064965849 2.3758567986 1.4206014124 0.4297637898 0.5917772860 -0.5533500200 0.398630761642 +1413393275805760512.0000000000 0.6961218961 2.3638120581 1.4243020057 0.4217333527 0.5890256938 -0.5620769113 0.399072997104 +1413393275855760384.0000000000 0.6859276162 2.3515469260 1.4285673265 0.4146353868 0.5864869780 -0.5712755803 0.397183499188 +1413393275905760512.0000000000 0.6762873805 2.3391346062 1.4333633101 0.4084323949 0.5847525440 -0.5801644302 0.393264128749 +1413393275955760384.0000000000 0.6680704699 2.3261659063 1.4385696854 0.4031760469 0.5834195447 -0.5875597151 0.389672030337 +1413393276005760512.0000000000 0.6615971866 2.3125750888 1.4437415922 0.3993462278 0.5820417614 -0.5930214209 0.387395886158 +1413393276055760384.0000000000 0.6570507753 2.2980800257 1.4490791653 0.3959987154 0.5817073188 -0.5936006466 0.390435506914 +1413393276105760512.0000000000 0.6550836381 2.2826386771 1.4557874974 0.3943786678 0.5814746985 -0.5885163745 0.400001397786 +1413393276155760384.0000000000 0.6540954310 2.2669305527 1.4628375387 0.3932842725 0.5814666727 -0.5819659357 0.410535795275 +1413393276205760512.0000000000 0.6538417514 2.2516324130 1.4703434783 0.3927809872 0.5817310886 -0.5749317776 0.420434879299 +1413393276255760384.0000000000 0.6538105219 2.2372245348 1.4776920167 0.3926458366 0.5822085326 -0.5690932921 0.427779495133 +1413393276305760512.0000000000 0.6536811032 2.2238295778 1.4844595228 0.3920405167 0.5832882461 -0.5642975092 0.433182844083 +1413393276355760384.0000000000 0.6534447581 2.2118298040 1.4902985572 0.3924164840 0.5841987919 -0.5618994537 0.434729891467 +1413393276405760512.0000000000 0.6529202772 2.2011365347 1.4939354195 0.3936237017 0.5848128501 -0.5607527679 0.434293270736 +1413393276455760384.0000000000 0.6523246688 2.1916334120 1.4951538442 0.3950661044 0.5853473918 -0.5608587816 0.43212108392 +1413393276505760512.0000000000 0.6522174494 2.1833149131 1.4935544731 0.3967275161 0.5859656520 -0.5624162157 0.427714312197 +1413393276555760384.0000000000 0.6520628432 2.1757589083 1.4890049524 0.3983366834 0.5863011646 -0.5656439671 0.421456680468 +1413393276605760512.0000000000 0.6517647639 2.1686902675 1.4829498532 0.4003042659 0.5862820412 -0.5683475295 0.415945848088 +1413393276655760384.0000000000 0.6521072819 2.1617962199 1.4767835274 0.4011670641 0.5870319855 -0.5706184274 0.410917321382 +1413393276705760512.0000000000 0.6534548846 2.1549275784 1.4712367806 0.4024566251 0.5871303628 -0.5720273402 0.407543033399 +1413393276755760384.0000000000 0.6555016708 2.1478381682 1.4656064304 0.4014081381 0.5887565584 -0.5723966149 0.405708438122 +1413393276805760512.0000000000 0.6584762355 2.1407826680 1.4612850970 0.4025525143 0.5886192527 -0.5727097453 0.404329563951 +1413393276855760384.0000000000 0.6623946877 2.1333968535 1.4576435917 0.4025814706 0.5888516755 -0.5723441231 0.404479997642 +1413393276905760512.0000000000 0.6671285830 2.1258267093 1.4545273144 0.4027945381 0.5892702889 -0.5716384459 0.404656117985 +1413393276955760384.0000000000 0.6727339043 2.1182496432 1.4519575349 0.4031613698 0.5895667486 -0.5705830297 0.405347955684 +1413393277005760512.0000000000 0.6792289931 2.1105317984 1.4495297148 0.4028714083 0.5896818622 -0.5705894866 0.40545969892 +1413393277055760384.0000000000 0.6864377163 2.1029995990 1.4474901133 0.4028084778 0.5897257197 -0.5703835823 0.405748043534 +1413393277105760512.0000000000 0.6943048636 2.0955764591 1.4458896033 0.4027006829 0.5897716916 -0.5699734895 0.406364040184 +1413393277155760384.0000000000 0.7029319314 2.0881784132 1.4451263632 0.4035090790 0.5889187489 -0.5697166421 0.407158541765 +1413393277205760512.0000000000 0.7121093385 2.0808777391 1.4451450298 0.4046815924 0.5877823029 -0.5691267735 0.408459898779 +1413393277255760384.0000000000 0.7218540147 2.0735403741 1.4459512885 0.4060359375 0.5867945854 -0.5676795844 0.410544542599 +1413393277305760512.0000000000 0.7318502857 2.0661350081 1.4471520406 0.4063528416 0.5861901845 -0.5668750876 0.412202705903 +1413393277355760384.0000000000 0.7420929836 2.0586276237 1.4487558621 0.4058158499 0.5858644571 -0.5659114539 0.414512436759 +1413393277405760512.0000000000 0.7523692014 2.0514359693 1.4506652687 0.4054116084 0.5859567111 -0.5654307261 0.415432611347 +1413393277455760384.0000000000 0.7627660978 2.0443488929 1.4529137716 0.4046848794 0.5859814733 -0.5656782767 0.415769104926 +1413393277505760512.0000000000 0.7731668289 2.0375509261 1.4556076309 0.4033930051 0.5865311270 -0.5653916944 0.416638395266 +1413393277555760384.0000000000 0.7836614820 2.0313631918 1.4590002810 0.4040313497 0.5859236229 -0.5657516985 0.416385869371 +1413393277605760512.0000000000 0.7945303089 2.0255150714 1.4631235718 0.4070948112 0.5831431053 -0.5658347348 0.417191786089 +1413393277655760384.0000000000 0.8052209897 2.0197823332 1.4659424259 0.4092412037 0.5806204408 -0.5669404286 0.417109207848 +1413393277705760512.0000000000 0.8162482745 2.0139837817 1.4672608506 0.4122494640 0.5762454155 -0.5689027392 0.417541942696 +1413393277755760384.0000000000 0.8277266068 2.0075420633 1.4662166334 0.4140125236 0.5711153585 -0.5712453717 0.419642232055 +1413393277805760512.0000000000 0.8387426924 2.0006732434 1.4632543020 0.4146580193 0.5659374106 -0.5744249626 0.421674680955 +1413393277855760384.0000000000 0.8493290554 1.9931937797 1.4578396533 0.4137684522 0.5608187557 -0.5781490975 0.424289538314 +1413393277905760512.0000000000 0.8592095352 1.9849620958 1.4499014269 0.4125318627 0.5548902496 -0.5816462749 0.428487904124 +1413393277955760384.0000000000 0.8681456035 1.9760037389 1.4415257732 0.4112109127 0.5480086255 -0.5857909483 0.432944680694 +1413393278005760512.0000000000 0.8761398825 1.9661735454 1.4338251337 0.4095119561 0.5402557102 -0.5909942958 0.437206436104 +1413393278055760384.0000000000 0.8827879903 1.9553660055 1.4266124233 0.4051777208 0.5336529531 -0.5975211805 0.440470179531 +1413393278105760512.0000000000 0.8881936917 1.9435285726 1.4199427125 0.3980528740 0.5281186535 -0.6049100068 0.443540844834 +1413393278155760384.0000000000 0.8926975798 1.9309048090 1.4144442251 0.3910784803 0.5217740152 -0.6123800045 0.446990189412 +1413393278205760512.0000000000 0.8962811754 1.9176342644 1.4100682592 0.3841109322 0.5154166679 -0.6200957339 0.449761860361 +1413393278255760384.0000000000 0.8992355117 1.9034079905 1.4065711324 0.3767110748 0.5083605275 -0.6288337898 0.451914156713 +1413393278305760512.0000000000 0.9016655803 1.8888982314 1.4042753571 0.3719469766 0.5000773304 -0.6388956256 0.450988347805 +1413393278355760384.0000000000 0.9034869213 1.8738033628 1.4028695083 0.3683081224 0.4925538982 -0.6482388500 0.448916671083 +1413393278405760512.0000000000 0.9052592218 1.8577429810 1.4022577772 0.3656914771 0.4854911307 -0.6572172233 0.445683325952 +1413393278455760384.0000000000 0.9066235808 1.8403329090 1.4017173677 0.3629901163 0.4796396445 -0.6653169677 0.442196019174 +1413393278505760512.0000000000 0.9083218978 1.8211710563 1.4019638638 0.3607881268 0.4752642209 -0.6714871738 0.439386872015 +1413393278555760384.0000000000 0.9103718955 1.7999888599 1.4026399611 0.3588188577 0.4716028293 -0.6768697780 0.436677343566 +1413393278605760512.0000000000 0.9125152621 1.7764559436 1.4043166019 0.3577880583 0.4684200971 -0.6802120139 0.435754442538 +1413393278655760384.0000000000 0.9147141005 1.7507967036 1.4055149820 0.3557845290 0.4675169199 -0.6816787338 0.436072703099 +1413393278705760512.0000000000 0.9176263526 1.7222928495 1.4069063018 0.3517385221 0.4687239653 -0.6796053350 0.441264597485 +1413393278755760384.0000000000 0.9209213214 1.6913541167 1.4094168177 0.3454902701 0.4726844768 -0.6732416274 0.45160997531 +1413393278805760512.0000000000 0.9243870489 1.6591312370 1.4123280456 0.3406806746 0.4758508147 -0.6661686697 0.462300750165 +1413393278855760384.0000000000 0.9282320692 1.6261126936 1.4161441646 0.3353589179 0.4796938958 -0.6600845659 0.470867846 +1413393278905760512.0000000000 0.9317840979 1.5934052183 1.4205762800 0.3314986135 0.4829794147 -0.6553590858 0.476806064184 +1413393278955760384.0000000000 0.9354662864 1.5611327034 1.4254853199 0.3287069151 0.4854216311 -0.6521127177 0.480693881185 +1413393279005760512.0000000000 0.9391813058 1.5297895876 1.4315322356 0.3264514900 0.4879208176 -0.6498429023 0.482770030925 +1413393279055760384.0000000000 0.9428259328 1.4994759172 1.4377273490 0.3253769329 0.4901362678 -0.6485071487 0.48304737712 +1413393279105760512.0000000000 0.9467379860 1.4699682783 1.4438313774 0.3238336657 0.4924314947 -0.6478906795 0.482577089565 +1413393279155760384.0000000000 0.9508687140 1.4415014152 1.4483527787 0.3240501839 0.4936875869 -0.6475596538 0.481591673182 +1413393279205760512.0000000000 0.9551854394 1.4139097638 1.4498433406 0.3229385174 0.4961162982 -0.6470395161 0.480540526205 +1413393279255760384.0000000000 0.9599374208 1.3873594186 1.4484316498 0.3218876207 0.4985089569 -0.6474593115 0.47819830557 +1413393279305760512.0000000000 0.9650599636 1.3617563216 1.4443780729 0.3210266255 0.5006837850 -0.6483642425 0.47526988346 +1413393279355760384.0000000000 0.9705214055 1.3371783498 1.4393473748 0.3196608801 0.5033836059 -0.6497134330 0.471480987931 +1413393279405760512.0000000000 0.9763772031 1.3135409337 1.4342534542 0.3176862994 0.5064831314 -0.6512887949 0.467304139046 +1413393279455760384.0000000000 0.9837097153 1.2903815643 1.4298796886 0.3171902820 0.5084469660 -0.6510967787 0.465773542133 +1413393279505760512.0000000000 0.9923044673 1.2680414995 1.4263843710 0.3179341593 0.5093860602 -0.6504647210 0.465122950126 +1413393279555760384.0000000000 1.0021775667 1.2466459714 1.4239048224 0.3195149130 0.5101237824 -0.6487107246 0.465680515773 +1413393279605760512.0000000000 1.0132708375 1.2259989265 1.4224111245 0.3216141950 0.5105174892 -0.6456384997 0.468067442348 +1413393279655760384.0000000000 1.0254493963 1.2062998857 1.4217743963 0.3244148327 0.5101026872 -0.6423708187 0.471073238578 +1413393279705760512.0000000000 1.0383259404 1.1876517711 1.4208792040 0.3266154203 0.5104080278 -0.6398323013 0.472673924157 +1413393279755760384.0000000000 1.0520816549 1.1698733467 1.4202405054 0.3291762605 0.5098161440 -0.6375986781 0.47455075024 +1413393279805760512.0000000000 1.0660080410 1.1530679797 1.4188402196 0.3321547452 0.5088538655 -0.6357359236 0.476005046486 +1413393279855760384.0000000000 1.0801592227 1.1374205964 1.4165740748 0.3358697216 0.5079662397 -0.6338030882 0.476922923342 +1413393279905760512.0000000000 1.0942811110 1.1224976368 1.4138621425 0.3386163538 0.5067804393 -0.6328404152 0.477520219616 +1413393279955760384.0000000000 1.1081498348 1.1086226028 1.4119323685 0.3422727727 0.5052863483 -0.6316874730 0.478023003333 +1413393280005760512.0000000000 1.1214927982 1.0958374565 1.4101222027 0.3447510212 0.5052141209 -0.6313057025 0.476821282469 +1413393280055760384.0000000000 1.1343583882 1.0837981602 1.4087416615 0.3466648097 0.5050694058 -0.6312171925 0.475702912585 +1413393280105760512.0000000000 1.1466944579 1.0729950158 1.4084334744 0.3505089260 0.5042808953 -0.6316928901 0.473083886795 +1413393280155760384.0000000000 1.1584652869 1.0628476830 1.4091317879 0.3547963571 0.5031486719 -0.6323834276 0.470161843873 +1413393280205760512.0000000000 1.1695563828 1.0531023376 1.4108681917 0.3599198583 0.5015060963 -0.6326831326 0.46761243006 +1413393280255760384.0000000000 1.1799007991 1.0433609082 1.4125793416 0.3632765626 0.5010728220 -0.6339223650 0.463787237052 +1413393280305760512.0000000000 1.1896914890 1.0332482703 1.4152180035 0.3663017733 0.5004201742 -0.6337935818 0.462286010807 +1413393280355760384.0000000000 1.1987317211 1.0228523080 1.4187815572 0.3702751571 0.4991837301 -0.6334558231 0.460918248543 +1413393280405760512.0000000000 1.2070641695 1.0119944782 1.4234111688 0.3754163425 0.4967086384 -0.6329269136 0.460159342391 +1413393280455760384.0000000000 1.2144614233 1.0006304601 1.4285270080 0.3811642489 0.4937029335 -0.6339026335 0.457316826759 +1413393280505760512.0000000000 1.2207264787 0.9883167861 1.4338581506 0.3851629049 0.4925616267 -0.6344169163 0.45447525446 +1413393280555760384.0000000000 1.2257170171 0.9745092019 1.4372392729 0.3846501278 0.4939467152 -0.6368193704 0.450024456253 +1413393280605760512.0000000000 1.2296842902 0.9595199672 1.4389762905 0.3851535738 0.4948731313 -0.6384068905 0.446311495071 +1413393280655760384.0000000000 1.2326317280 0.9432444611 1.4382029434 0.3851480579 0.4959901229 -0.6403411052 0.44228728285 +1413393280705760512.0000000000 1.2346654974 0.9255122862 1.4352662965 0.3857655736 0.4959868878 -0.6424629248 0.438660825334 +1413393280755760384.0000000000 1.2358459971 0.9064968906 1.4300169526 0.3874045249 0.4955385753 -0.6446770711 0.43445451839 +1413393280805760512.0000000000 1.2361203650 0.8857479912 1.4222556377 0.3886367670 0.4953678607 -0.6469941468 0.430082224636 +1413393280855760384.0000000000 1.2360571431 0.8628558063 1.4126834253 0.3880756212 0.4959786285 -0.6494655283 0.42614204195 +1413393280905760512.0000000000 1.2358808077 0.8375656711 1.4034277743 0.3873048224 0.4973710467 -0.6496048545 0.42500652863 +1413393280955760384.0000000000 1.2356776732 0.8098581033 1.3950026078 0.3858571160 0.4992736999 -0.6487844733 0.42534546658 +1413393281005760512.0000000000 1.2364863887 0.7791872279 1.3891198456 0.3806492162 0.5030177530 -0.6465257874 0.429049788025 +1413393281055760384.0000000000 1.2380838725 0.7465307348 1.3855023098 0.3742580812 0.5084352412 -0.6419660086 0.435090953722 +1413393281105760512.0000000000 1.2395192434 0.7126798999 1.3837961205 0.3681359600 0.5128254123 -0.6387019165 0.439938488106 +1413393281155760384.0000000000 1.2419508841 0.6777841047 1.3837250508 0.3625921329 0.5163961631 -0.6351615833 0.445456744325 +1413393281205760512.0000000000 1.2445174606 0.6430581847 1.3851367469 0.3591304368 0.5188926788 -0.6321968782 0.449558477284 +1413393281255760384.0000000000 1.2475461037 0.6083919426 1.3870907950 0.3551885733 0.5212589577 -0.6301075333 0.452873793571 +1413393281305760512.0000000000 1.2510108460 0.5743337375 1.3902418960 0.3523270024 0.5226776648 -0.6283842455 0.455858511068 +1413393281355760384.0000000000 1.2551404915 0.5410729939 1.3944303684 0.3504090378 0.5231861378 -0.6274403020 0.458048511478 +1413393281405760512.0000000000 1.2598302215 0.5086953673 1.3986971831 0.3486023576 0.5236976695 -0.6262824340 0.460420959708 +1413393281455760384.0000000000 1.2650292448 0.4773325896 1.4031228806 0.3479703813 0.5226465726 -0.6268782744 0.461281695842 +1413393281505760512.0000000000 1.2706072573 0.4468681427 1.4073441309 0.3466639059 0.5219963998 -0.6275593864 0.462074789888 +1413393281555760384.0000000000 1.2766772102 0.4175490391 1.4118420719 0.3463335505 0.5209549884 -0.6283184635 0.462466085508 +1413393281605760512.0000000000 1.2835285927 0.3890670153 1.4165995250 0.3463062528 0.5191168161 -0.6287277954 0.463994687336 +1413393281655760384.0000000000 1.2909095042 0.3613607447 1.4220633550 0.3462507052 0.5170962612 -0.6282754114 0.466896041078 +1413393281705760512.0000000000 1.2985748472 0.3349540731 1.4281887813 0.3473576279 0.5146676547 -0.6280162766 0.469100671404 +1413393281755760384.0000000000 1.3066537465 0.3093197506 1.4349569970 0.3480519801 0.5120032744 -0.6268979888 0.472981371541 +1413393281805760512.0000000000 1.3149642775 0.2847443331 1.4425506395 0.3498091536 0.5087060417 -0.6246278075 0.478217336923 +1413393281855760384.0000000000 1.3229810708 0.2618714134 1.4508926744 0.3549523948 0.5034327173 -0.6244646306 0.480216848594 +1413393281905760512.0000000000 1.3301337231 0.2397913272 1.4587292080 0.3567675989 0.4999622244 -0.6251226033 0.481639268899 +1413393281955760384.0000000000 1.3361224054 0.2189145583 1.4665877598 0.3583528070 0.4972816943 -0.6277887589 0.479766043383 +1413393282005760512.0000000000 1.3411646850 0.1986589651 1.4740965436 0.3571477975 0.4964271050 -0.6312983825 0.47693598364 +1413393282055760384.0000000000 1.3455552122 0.1790970491 1.4821934249 0.3562820624 0.4956565481 -0.6356456234 0.472591070421 +1413393282105760512.0000000000 1.3493830424 0.1599993610 1.4905560236 0.3561345171 0.4947261271 -0.6400757103 0.467672267744 +1413393282155760384.0000000000 1.3529449059 0.1411385089 1.4995621942 0.3574770355 0.4927357116 -0.6447381441 0.462314192965 +1413393282205760512.0000000000 1.3565268872 0.1220554997 1.5087666306 0.3578985759 0.4920178892 -0.6481139441 0.458012359554 +1413393282255760384.0000000000 1.3601666733 0.1024192277 1.5183520396 0.3582858784 0.4912304828 -0.6511608508 0.454217336216 +1413393282305760512.0000000000 1.3639985924 0.0817592055 1.5283420565 0.3576250668 0.4913063951 -0.6522028484 0.453159775573 +1413393282355760384.0000000000 1.3682750847 0.0601176573 1.5389897669 0.3559898119 0.4926455258 -0.6497367677 0.456523572802 +1413393282405760512.0000000000 1.3726897456 0.0379251185 1.5499755612 0.3539112743 0.4942122690 -0.6463696411 0.461202049152 +1413393282455760384.0000000000 1.3771638089 0.0154572988 1.5606230349 0.3507029498 0.4966793714 -0.6419754536 0.467102301405 +1413393282505760512.0000000000 1.3814242512 -0.0066393703 1.5698957327 0.3480302441 0.4991343994 -0.6388988495 0.470688921294 +1413393282555760384.0000000000 1.3859938900 -0.0283327636 1.5770640521 0.3461247743 0.5009074961 -0.6360728836 0.474025956826 +1413393282605760512.0000000000 1.3908917385 -0.0492805962 1.5812832073 0.3449712245 0.5022657138 -0.6330621517 0.477447713511 +1413393282655760384.0000000000 1.3958628008 -0.0692333906 1.5830814846 0.3446704058 0.5031737105 -0.6303967743 0.480227482925 +1413393282705760512.0000000000 1.4007159660 -0.0879401515 1.5829470600 0.3453251119 0.5037787744 -0.6280946964 0.482135422849 +1413393282755760384.0000000000 1.4052266197 -0.1049881242 1.5826442651 0.3485814290 0.5042146713 -0.6256089031 0.482568184794 +1413393282805760512.0000000000 1.4091698497 -0.1203076467 1.5824933755 0.3548982124 0.5042543410 -0.6231032961 0.481162239524 +1413393282855760384.0000000000 1.4121017246 -0.1339881805 1.5825037533 0.3611431261 0.5064238009 -0.6207114726 0.477313150958 +1413393282905760512.0000000000 1.4140379479 -0.1467506630 1.5822989334 0.3645894821 0.5112770604 -0.6192350167 0.471400330072 +1413393282955760384.0000000000 1.4150763291 -0.1586012665 1.5822814255 0.3668377386 0.5184257215 -0.6170205685 0.464704705083 +1413393283005760512.0000000000 1.4157010692 -0.1697344375 1.5822897778 0.3683325411 0.5266163315 -0.6150300261 0.45688559339 +1413393283055760384.0000000000 1.4161887377 -0.1801948542 1.5829504703 0.3692852149 0.5359979389 -0.6116192339 0.449729421196 +1413393283105760512.0000000000 1.4166017623 -0.1897706878 1.5841328555 0.3711784112 0.5455536872 -0.6068688617 0.44306652553 +1413393283155760384.0000000000 1.4172093836 -0.1988668774 1.5860909590 0.3736772312 0.5549236960 -0.6001417875 0.43846875995 +1413393283205760512.0000000000 1.4181937264 -0.2071303499 1.5883827001 0.3769600047 0.5638860673 -0.5932184385 0.433619121118 +1413393283255760384.0000000000 1.4200636627 -0.2146967391 1.5907669927 0.3799030745 0.5734875928 -0.5851119328 0.429452745875 +1413393283305760512.0000000000 1.4224065712 -0.2212268393 1.5933665248 0.3842393071 0.5819329587 -0.5776355525 0.424324586878 +1413393283355760384.0000000000 1.4253551427 -0.2266099462 1.5960289935 0.3882539608 0.5907208357 -0.5696867732 0.41924305196 +1413393283405760512.0000000000 1.4290168318 -0.2305974811 1.5984661691 0.3937641583 0.5990334936 -0.5612316243 0.413675869443 +1413393283455760384.0000000000 1.4335338868 -0.2336935577 1.6000921058 0.3990593148 0.6069798584 -0.5533033203 0.407654940452 +1413393283505760512.0000000000 1.4384308462 -0.2357628291 1.6001662219 0.4047496605 0.6148532356 -0.5450111832 0.40136768825 +1413393283555760384.0000000000 1.4439904390 -0.2364788515 1.5987208140 0.4117698865 0.6219496257 -0.5368609907 0.39421377496 +1413393283605760512.0000000000 1.4498802702 -0.2366884081 1.5942511040 0.4179163734 0.6284515965 -0.5295144814 0.387309836696 +1413393283655760384.0000000000 1.4563613745 -0.2361052121 1.5861203544 0.4245577849 0.6348391664 -0.5206193238 0.381687620732 +1413393283705760512.0000000000 1.4628007638 -0.2347732966 1.5761376497 0.4323744608 0.6403347013 -0.5115784354 0.375913953486 +1413393283755760384.0000000000 1.4696750462 -0.2328534985 1.5647517568 0.4398582299 0.6453984972 -0.5015220018 0.372103747681 +1413393283805760512.0000000000 1.4770271122 -0.2298449602 1.5529442408 0.4473033060 0.6507002103 -0.4919464320 0.366739276338 +1413393283855760384.0000000000 1.4841493477 -0.2264267034 1.5409394982 0.4535328455 0.6567858834 -0.4815931183 0.361950728462 +1413393283905760512.0000000000 1.4909438525 -0.2224378769 1.5292667072 0.4585787272 0.6634939251 -0.4714356752 0.356692818155 +1413393283955760384.0000000000 1.4973705802 -0.2177553999 1.5179944358 0.4630000754 0.6709450047 -0.4611065664 0.35049174779 +1413393284005760512.0000000000 1.5030379323 -0.2123521053 1.5072044044 0.4657096415 0.6794576126 -0.4520355318 0.342221800055 +1413393284055760384.0000000000 1.5083358718 -0.2060893391 1.4974423286 0.4697145059 0.6867628501 -0.4424119648 0.334659116125 +1413393284105760512.0000000000 1.5132905152 -0.1989172931 1.4884425540 0.4733260763 0.6945995882 -0.4321278321 0.326740530442 +1413393284155760384.0000000000 1.5181396714 -0.1908029291 1.4805482139 0.4781302928 0.7012999433 -0.4216204608 0.319070524606 +1413393284205760512.0000000000 1.5231384826 -0.1819190011 1.4735913718 0.4827515827 0.7076294900 -0.4111133797 0.31176466016 +1413393284255760384.0000000000 1.5280322917 -0.1719753138 1.4678236486 0.4878400540 0.7139625141 -0.3990741194 0.30497451936 +1413393284305760512.0000000000 1.5325638634 -0.1612355424 1.4628238444 0.4930422625 0.7199513151 -0.3875567343 0.29728640895 +1413393284355760384.0000000000 1.5369105994 -0.1495710728 1.4587052871 0.4994335265 0.7248455318 -0.3755091258 0.29009998966 +1413393284405760512.0000000000 1.5406808786 -0.1370226286 1.4549099063 0.5058600321 0.7297875763 -0.3632444710 0.282080087353 +1413393284455760384.0000000000 1.5439993413 -0.1238470621 1.4515395188 0.5120317180 0.7346036574 -0.3503710726 0.274629018417 +1413393284505760512.0000000000 1.5465182108 -0.1102020840 1.4482527711 0.5181227099 0.7393119153 -0.3377688224 0.266231049973 +1413393284555760384.0000000000 1.5482796423 -0.0961343892 1.4449360873 0.5225281860 0.7450506937 -0.3252859807 0.257007372263 +1413393284605760512.0000000000 1.5490713002 -0.0817995822 1.4418965724 0.5270501720 0.7502987451 -0.3131901556 0.247349622398 +1413393284655760384.0000000000 1.5490647201 -0.0671363600 1.4387964166 0.5311282792 0.7557037826 -0.3028111754 0.234776353434 +1413393284705760512.0000000000 1.5483314001 -0.0523615033 1.4356967225 0.5340689522 0.7618278507 -0.2931980059 0.220053651279 +1413393284755760384.0000000000 1.5474706430 -0.0372168298 1.4332695814 0.5376075106 0.7670514233 -0.2836726683 0.20528052946 +1413393284805760512.0000000000 1.5467874356 -0.0220142520 1.4311420244 0.5410938316 0.7721725385 -0.2725950615 0.191465319692 +1413393284855760384.0000000000 1.5463434558 -0.0069139977 1.4289107685 0.5440210692 0.7774417914 -0.2604559654 0.17829197189 +1413393284905760512.0000000000 1.5463754839 0.0079163529 1.4271611395 0.5468919988 0.7822496092 -0.2478294757 0.166057946413 +1413393284955760384.0000000000 1.5470862958 0.0227681910 1.4257755654 0.5498165224 0.7866848857 -0.2341915246 0.154864495743 +1413393285005760512.0000000000 1.5485438797 0.0376746987 1.4247211757 0.5528853193 0.7906910346 -0.2205975850 0.143046205507 +1413393285055760384.0000000000 1.5510374297 0.0524390299 1.4238654886 0.5553797029 0.7945088881 -0.2067387288 0.132544748252 +1413393285105760512.0000000000 1.5544207391 0.0673049648 1.4237502012 0.5582523414 0.7976690977 -0.1933815856 0.121168874905 +1413393285155760384.0000000000 1.5589025520 0.0820614552 1.4240547690 0.5611330135 0.8004555910 -0.1790456900 0.111100084925 +1413393285205760512.0000000000 1.5641996273 0.0966223942 1.4243976527 0.5632221507 0.8032863455 -0.1654906695 0.100621540705 +1413393285255760384.0000000000 1.5704268038 0.1110721677 1.4247946722 0.5658447197 0.8053178808 -0.1520203357 0.0904028848863 +1413393285305760512.0000000000 1.5775488326 0.1253020022 1.4251466821 0.5675800955 0.8076558728 -0.1380431413 0.0805538166063 +1413393285355760384.0000000000 1.5857302186 0.1394586533 1.4256874497 0.5699006004 0.8090862783 -0.1244977758 0.0713652838406 +1413393285405760512.0000000000 1.5947044239 0.1534172828 1.4261758894 0.5713254450 0.8108762563 -0.1104713603 0.0621531294073 +1413393285455760384.0000000000 1.6044784145 0.1674886264 1.4267414424 0.5723638756 0.8125427774 -0.0965269088 0.0534451557236 +1413393285505760512.0000000000 1.6150948961 0.1814444597 1.4273803573 0.5736544330 0.8136899731 -0.0827633902 0.0444909017327 +1413393285555760384.0000000000 1.6265036426 0.1953444062 1.4282286295 0.5750052189 0.8145091535 -0.0676415929 0.0369925947337 +1413393285605760512.0000000000 1.6385120420 0.2092551941 1.4293870991 0.5767066780 0.8147035465 -0.0528683821 0.0295376547326 +1413393285655760384.0000000000 1.6508582229 0.2228968872 1.4309832724 0.5792490418 0.8139801788 -0.0374587812 0.0224422766472 +1413393285705760512.0000000000 1.6636828620 0.2365094777 1.4328605571 0.5813996157 0.8131575184 -0.0217388054 0.0166361505862 +1413393285755760384.0000000000 1.6768089136 0.2498507644 1.4349928753 0.5835869710 0.8119148973 -0.0044707598 0.0141583550766 +1413393285805760512.0000000000 1.6895684389 0.2625304933 1.4377425544 0.5850477594 0.8108525074 0.0113057506 0.01046472727 +1413393285855760384.0000000000 1.7017851772 0.2745905304 1.4409761879 0.5854394869 0.8103535867 0.0238870931 0.00413260917864 +1413393285905760512.0000000000 1.7136318398 0.2862477228 1.4445867887 0.5842817389 0.8109268788 0.0314777913 -0.00464709854334 +1413393285955760384.0000000000 1.7251092474 0.2975412810 1.4483370918 0.5831970177 0.8113491599 0.0379205129 -0.0124825449663 +1413393286005760512.0000000000 1.7365708217 0.3086673253 1.4521447050 0.5821371743 0.8117844130 0.0417793301 -0.0194130051152 +1413393286055760384.0000000000 1.7480223803 0.3197871061 1.4557773759 0.5802860475 0.8128277928 0.0438587749 -0.0256025442629 +1413393286105760512.0000000000 1.7595010707 0.3311029910 1.4597041672 0.5791139729 0.8134337052 0.0447747927 -0.0307868742839 +1413393286155760384.0000000000 1.7712282754 0.3427407534 1.4640776442 0.5792293671 0.8131878921 0.0451952307 -0.0342955327799 +1413393286205760512.0000000000 1.7833260406 0.3544506903 1.4684351542 0.5790939670 0.8132049459 0.0450325507 -0.0363312902246 +1413393286255760384.0000000000 1.7959506043 0.3663865504 1.4720767819 0.5798520181 0.8126488374 0.0449413676 -0.0367937170983 +1413393286305760512.0000000000 1.8091151581 0.3780983433 1.4735117309 0.5799701650 0.8126188504 0.0441289170 -0.0365766365544 +1413393286355760384.0000000000 1.8227708103 0.3896096002 1.4725828214 0.5807013561 0.8122061205 0.0439285217 -0.0343138153921 +1413393286405760512.0000000000 1.8368764761 0.4009127757 1.4694957812 0.5814691509 0.8117894186 0.0435646116 -0.0315228643861 +1413393286455760384.0000000000 1.8512635805 0.4116332131 1.4628604057 0.5823392591 0.8113318565 0.0427007492 -0.0282533526792 +1413393286505760512.0000000000 1.8655837483 0.4213801399 1.4533225616 0.5826971528 0.8112374064 0.0408465583 -0.0262575169402 +1413393286555760384.0000000000 1.8797533457 0.4310665774 1.4431419469 0.5829728363 0.8112091682 0.0383828027 -0.0246803180889 +1413393286605760512.0000000000 1.8937338625 0.4403617938 1.4336467411 0.5819699899 0.8120766315 0.0354818267 -0.0241560630114 +1413393286655760384.0000000000 1.9079893716 0.4495187994 1.4257274222 0.5812173714 0.8127465613 0.0337962965 -0.0220727149994 +1413393286705760512.0000000000 1.9223762408 0.4586262023 1.4198048201 0.5804579662 0.8133956777 0.0329856984 -0.019182402689 +1413393286755760384.0000000000 1.9367787102 0.4675584113 1.4155704651 0.5796461248 0.8140413178 0.0337017355 -0.0145360227746 +1413393286805760512.0000000000 1.9511270390 0.4763113127 1.4130638713 0.5788973175 0.8145636220 0.0360433852 -0.00805455914976 +1413393286855760384.0000000000 1.9647503397 0.4847712526 1.4119110600 0.5780078828 0.8150707946 0.0395471976 -0.00158313981626 +1413393286905760512.0000000000 1.9769430213 0.4928473003 1.4116218385 0.5777718979 0.8149630196 0.0447336889 0.00371588364662 +1413393286955760384.0000000000 1.9873421058 0.5008609580 1.4122106055 0.5776013325 0.8147217417 0.0506087850 0.00662835725364 +1413393287005760512.0000000000 1.9958174248 0.5092283903 1.4133857048 0.5772813035 0.8145301150 0.0568113538 0.00771093360162 +1413393287055760384.0000000000 2.0019751217 0.5176015939 1.4152377635 0.5781528676 0.8134773738 0.0629020357 0.0060957322401 +1413393287105760512.0000000000 2.0058690736 0.5256763076 1.4173123475 0.5777427507 0.8132782252 0.0691704242 0.00270092371524 +1413393287155760384.0000000000 2.0072902413 0.5332795758 1.4207058445 0.5771362454 0.8131639829 0.0752789185 -0.00334299423851 +1413393287205760512.0000000000 2.0063003586 0.5403892700 1.4246983683 0.5760701195 0.8133901423 0.0797916932 -0.013152167576 +1413393287255760384.0000000000 2.0032317709 0.5469069498 1.4289672017 0.5746208018 0.8136178196 0.0847931624 -0.0254381105965 +1413393287305760512.0000000000 1.9987806946 0.5534168155 1.4340455830 0.5740220014 0.8129222443 0.0905957945 -0.0380600679634 +1413393287355760384.0000000000 1.9932058886 0.5600283310 1.4399731279 0.5741466619 0.8113078806 0.0975416601 -0.0511933399534 +1413393287405760512.0000000000 1.9870362785 0.5663878011 1.4459750331 0.5742741841 0.8092807696 0.1059121655 -0.06368995622 +1413393287455760384.0000000000 1.9804218749 0.5726643260 1.4524786681 0.5731844111 0.8077123830 0.1154731406 -0.0756722600714 +1413393287505760512.0000000000 1.9737362926 0.5788447561 1.4590642178 0.5717782128 0.8059602287 0.1268091939 -0.0861232452285 +1413393287555760384.0000000000 1.9670288824 0.5847856667 1.4655954324 0.5694951723 0.8044841821 0.1389529338 -0.0957733346087 +1413393287605760512.0000000000 1.9603949533 0.5904676133 1.4717851297 0.5667869355 0.8028758033 0.1513332361 -0.106024836398 +1413393287655760384.0000000000 1.9538467603 0.5963618725 1.4777192660 0.5636271850 0.8013399153 0.1632561367 -0.116302065077 +1413393287705760512.0000000000 1.9474329757 0.6024290462 1.4843930413 0.5617178259 0.7985346712 0.1749745185 -0.127276788663 +1413393287755760384.0000000000 1.9412802139 0.6087872082 1.4909323467 0.5598209277 0.7954196006 0.1866630963 -0.138076342514 +1413393287805760512.0000000000 1.9355084834 0.6154448199 1.4966244444 0.5577053570 0.7921985255 0.1987312813 -0.147959821234 +1413393287855760384.0000000000 1.9300472673 0.6222182867 1.5019058877 0.5565365893 0.7879245474 0.2099255045 -0.159289720155 +1413393287905760512.0000000000 1.9253182011 0.6292349760 1.5062050921 0.5545877597 0.7839918630 0.2219626095 -0.168883911389 +1413393287955760384.0000000000 1.9211053999 0.6368127696 1.5103053531 0.5532865099 0.7793970200 0.2339514385 -0.177991706306 +1413393288005760512.0000000000 1.9173878241 0.6450447587 1.5142554377 0.5520247657 0.7747574119 0.2447124093 -0.187444518315 +1413393288055760384.0000000000 1.9144098689 0.6539385666 1.5174129267 0.5495317482 0.7713145346 0.2552828140 -0.194729123139 +1413393288105760512.0000000000 1.9125407106 0.6633610725 1.5194898326 0.5475066566 0.7683306013 0.2645455066 -0.199800458131 +1413393288155760384.0000000000 1.9114802429 0.6733673777 1.5207810601 0.5442541252 0.7669488141 0.2723398501 -0.203489483518 +1413393288205760512.0000000000 1.9109907088 0.6843005046 1.5214232674 0.5410866102 0.7665048932 0.2786568160 -0.205050988731 +1413393288255760384.0000000000 1.9108267384 0.6958029071 1.5213291891 0.5363647101 0.7678945874 0.2837708927 -0.205243467488 +1413393288305760512.0000000000 1.9107324330 0.7080606814 1.5207242155 0.5315414081 0.7696881532 0.2886777562 -0.204227890721 +1413393288355760384.0000000000 1.9103624985 0.7215336987 1.5199413644 0.5273412199 0.7718437612 0.2910070611 -0.203674584521 +1413393288405760512.0000000000 1.9093936716 0.7363441019 1.5194106277 0.5261574063 0.7722692006 0.2922413493 -0.20335599156 +1413393288455760384.0000000000 1.9076077990 0.7524585668 1.5194495029 0.5290131778 0.7701829547 0.2920563997 -0.204123328903 +1413393288505760512.0000000000 1.9055091476 0.7696444277 1.5193811523 0.5325843419 0.7680962541 0.2904039300 -0.205055164922 +1413393288555760384.0000000000 1.9031895913 0.7877664616 1.5192430118 0.5377337006 0.7651663200 0.2882150100 -0.205657671859 +1413393288605760512.0000000000 1.9007128804 0.8058071897 1.5186777191 0.5425688358 0.7616986810 0.2872818256 -0.207131191225 +1413393288655760384.0000000000 1.8985134962 0.8235638498 1.5183141151 0.5471555038 0.7579941827 0.2868061057 -0.209303443409 +1413393288705760512.0000000000 1.8967106218 0.8405186989 1.5175293275 0.5505658465 0.7542679201 0.2878660337 -0.212344767079 +1413393288755760384.0000000000 1.8955953193 0.8567012294 1.5156710058 0.5511859249 0.7520175460 0.2910198703 -0.214408772506 +1413393288805760512.0000000000 1.8950016530 0.8725942613 1.5129796933 0.5513456737 0.7505102333 0.2938842732 -0.215370313256 +1413393288855760384.0000000000 1.8947546524 0.8882449264 1.5092878890 0.5499420476 0.7503098843 0.2972407884 -0.215050541633 +1413393288905760512.0000000000 1.8946168757 0.9036427011 1.5060306811 0.5482580525 0.7502026001 0.2996848372 -0.216328835377 +1413393288955760384.0000000000 1.8949655366 0.9188718266 1.5008215892 0.5460665275 0.7509285727 0.3020122566 -0.216116225816 +1413393289005760512.0000000000 1.8952418963 0.9342394527 1.4939883461 0.5453240223 0.7505311056 0.3039442397 -0.216662570241 +1413393289055760384.0000000000 1.8957828078 0.9492863110 1.4843452997 0.5444623751 0.7503524969 0.3060495968 -0.216484403006 +1413393289105760512.0000000000 1.8965348210 0.9637427196 1.4733143635 0.5444971364 0.7497386024 0.3063916832 -0.218034476696 +1413393289155760384.0000000000 1.8970119223 0.9780347735 1.4617787314 0.5448735972 0.7485205198 0.3069675934 -0.220455644326 +1413393289205760512.0000000000 1.8975156686 0.9921623315 1.4506081401 0.5441604916 0.7480061442 0.3075561171 -0.223126427151 +1413393289255760384.0000000000 1.8985893618 1.0060293426 1.4404647318 0.5446509199 0.7466976724 0.3090179917 -0.224289639417 +1413393289305760512.0000000000 1.9000005033 1.0196680829 1.4317088569 0.5451235360 0.7457052720 0.3102269793 -0.2247736619 +1413393289355760384.0000000000 1.9017783644 1.0329468599 1.4244873826 0.5444829659 0.7454648140 0.3118477971 -0.224880996044 +1413393289405760512.0000000000 1.9039068754 1.0460691420 1.4183117230 0.5442050555 0.7451900794 0.3142082802 -0.223172040459 +1413393289455760384.0000000000 1.9061418454 1.0588662141 1.4140071670 0.5432260426 0.7456534762 0.3153480521 -0.22240046352 +1413393289505760512.0000000000 1.9084632420 1.0713098078 1.4119614659 0.5415075870 0.7468214563 0.3159294719 -0.22184637566 +1413393289555760384.0000000000 1.9106372061 1.0835735733 1.4116277946 0.5408655137 0.7471733370 0.3170979214 -0.22055704224 +1413393289605760512.0000000000 1.9127775268 1.0956514707 1.4120034038 0.5404158982 0.7476765343 0.3175702919 -0.219270533167 +1413393289655760384.0000000000 1.9145707518 1.1074583040 1.4124887118 0.5397023668 0.7482197574 0.3179310417 -0.218651326701 +1413393289705760512.0000000000 1.9161565601 1.1188383410 1.4130235087 0.5390249480 0.7487956800 0.3178819222 -0.218422111338 +1413393289755760384.0000000000 1.9172742957 1.1303413588 1.4140215667 0.5395596482 0.7488389108 0.3171773223 -0.217977563024 +1413393289805760512.0000000000 1.9180148014 1.1415657644 1.4155638586 0.5404276018 0.7485591679 0.3162806550 -0.218091097169 +1413393289855760384.0000000000 1.9183503504 1.1527865078 1.4177968507 0.5418987522 0.7479917743 0.3148523353 -0.218453781901 +1413393289905760512.0000000000 1.9183852103 1.1639695718 1.4203641746 0.5438255462 0.7472575285 0.3136988883 -0.217837023712 +1413393289955760384.0000000000 1.9181266258 1.1748270177 1.4235804042 0.5455030644 0.7466294244 0.3123536998 -0.217729363025 +1413393290005760512.0000000000 1.9179040040 1.1851841304 1.4264967186 0.5462466721 0.7467272562 0.3111216854 -0.217293062281 +1413393290055760384.0000000000 1.9177900123 1.1948481530 1.4279940165 0.5462211336 0.7474183653 0.3095879306 -0.21717176086 +1413393290105760512.0000000000 1.9176731528 1.2043015075 1.4272870498 0.5465507809 0.7479167409 0.3078394425 -0.217112114531 +1413393290155760384.0000000000 1.9175461291 1.2131324680 1.4237376184 0.5466927300 0.7484538268 0.3062318686 -0.217177279743 +1413393290205760512.0000000000 1.9176923016 1.2213932397 1.4173960975 0.5460579337 0.7497164990 0.3042790671 -0.217163886115 +1413393290255760384.0000000000 1.9179691213 1.2293125244 1.4089121838 0.5457280696 0.7506310517 0.3029099526 -0.216747454364 +1413393290305760512.0000000000 1.9183470541 1.2369354522 1.3977204829 0.5446108587 0.7521083534 0.3023933977 -0.215151737861 +1413393290355760384.0000000000 1.9185366091 1.2444920263 1.3853170209 0.5432484614 0.7535708612 0.3025230003 -0.213288303964 +1413393290405760512.0000000000 1.9185676532 1.2517499874 1.3727131562 0.5412396226 0.7548078748 0.3038580673 -0.212120291399 +1413393290455760384.0000000000 1.9183135683 1.2586380917 1.3600323995 0.5388936023 0.7554939427 0.3063495054 -0.212067367605 +1413393290505760512.0000000000 1.9177637823 1.2652763777 1.3475610211 0.5364629550 0.7557391688 0.3096530757 -0.212557708433 +1413393290555760384.0000000000 1.9167013168 1.2722562239 1.3356899660 0.5347767022 0.7556071246 0.3125440774 -0.213044483037 +1413393290605760512.0000000000 1.9150600001 1.2795837565 1.3244206296 0.5337135220 0.7550260160 0.3150412556 -0.214090165512 +1413393290655760384.0000000000 1.9127947016 1.2872645769 1.3132840633 0.5319146864 0.7551859181 0.3168069388 -0.215393497992 +1413393290705760512.0000000000 1.9099026521 1.2953316898 1.3018277776 0.5304539747 0.7551242981 0.3190613546 -0.215883596342 +1413393290755760384.0000000000 1.9062566116 1.3039895036 1.2905275176 0.5306526615 0.7541064317 0.3204330785 -0.216919073933 +1413393290805760512.0000000000 1.9025711840 1.3124746212 1.2789498521 0.5310763542 0.7529947329 0.3220727442 -0.217315406205 +1413393290855760384.0000000000 1.8985917761 1.3210167188 1.2669094853 0.5315948734 0.7521629084 0.3228330871 -0.217799558471 +1413393290905760512.0000000000 1.8938849675 1.3295485145 1.2549221103 0.5315024289 0.7518418929 0.3220987948 -0.220207407998 +1413393290955760384.0000000000 1.8881357857 1.3384178932 1.2436424013 0.5312947565 0.7515746222 0.3193618725 -0.225542597792 +1413393291005760512.0000000000 1.8821103107 1.3480966756 1.2320231099 0.5314841360 0.7511870857 0.3165643314 -0.230281565892 +1413393291055760384.0000000000 1.8760431169 1.3584569839 1.2201364394 0.5323000128 0.7505646812 0.3127871425 -0.235528255706 +1413393291105760512.0000000000 1.8705564556 1.3693334767 1.2073205021 0.5330511630 0.7498916632 0.3098759743 -0.239782884311 +1413393291155760384.0000000000 1.8655785813 1.3810622798 1.1950493185 0.5355841562 0.7482037820 0.3069806640 -0.243112287141 +1413393291205760512.0000000000 1.8617310374 1.3932121536 1.1825738405 0.5374555553 0.7470252722 0.3048461694 -0.245282656917 +1413393291255760384.0000000000 1.8590128650 1.4059067344 1.1702842488 0.5392431678 0.7459885762 0.3032940136 -0.246435775469 +1413393291305760512.0000000000 1.8578599499 1.4190926232 1.1572976507 0.5403890053 0.7457611197 0.3037956794 -0.243984139696 +1413393291355760384.0000000000 1.8576513032 1.4326150418 1.1440863001 0.5402909304 0.7463493306 0.3056974294 -0.239994726841 +1413393291405760512.0000000000 1.8582501422 1.4461181154 1.1311775975 0.5403035283 0.7463144282 0.3089554530 -0.235867334887 +1413393291455760384.0000000000 1.8598712654 1.4589933433 1.1185471532 0.5392874023 0.7464542088 0.3132293008 -0.232083211391 +1413393291505760512.0000000000 1.8619556311 1.4715315754 1.1070731804 0.5384668609 0.7459420455 0.3175644289 -0.229731882832 +1413393291555760384.0000000000 1.8642206533 1.4842487530 1.0969912026 0.5379555312 0.7453869424 0.3211648534 -0.227717565041 +1413393291605760512.0000000000 1.8662707774 1.4969540991 1.0882771437 0.5379152705 0.7443569033 0.3242514642 -0.226805974712 +1413393291655760384.0000000000 1.8680745097 1.5098255140 1.0807181616 0.5378332831 0.7434370682 0.3272439803 -0.225716775195 +1413393291705760512.0000000000 1.8696538503 1.5226002165 1.0743333885 0.5370604677 0.7431551409 0.3296010358 -0.225054766125 +1413393291755760384.0000000000 1.8709740466 1.5351683443 1.0694305771 0.5367405417 0.7425817869 0.3317589731 -0.224539226903 +1413393291805760512.0000000000 1.8718338668 1.5472404032 1.0663939995 0.5365275875 0.7415964125 0.3342574839 -0.22459929494 +1413393291855760384.0000000000 1.8720917600 1.5586329134 1.0662713550 0.5354372332 0.7404296820 0.3378530362 -0.225668299102 +1413393291905760512.0000000000 1.8715028605 1.5697997709 1.0703039510 0.5348641767 0.7388178837 0.3412987822 -0.227120207121 +1413393291955760384.0000000000 1.8705798625 1.5805191140 1.0780872622 0.5349573407 0.7371851272 0.3440991303 -0.227979210319 +1413393292005760512.0000000000 1.8692857184 1.5905352759 1.0887088539 0.5365310371 0.7344773911 0.3462764517 -0.229717276771 +1413393292055760384.0000000000 1.8679461590 1.5998883861 1.1005220669 0.5389961368 0.7313417144 0.3481837508 -0.231063924033 +1413393292105760512.0000000000 1.8661418786 1.6086189006 1.1124496056 0.5410550790 0.7284986240 0.3490996364 -0.233834557321 +1413393292155760384.0000000000 1.8640355820 1.6168767141 1.1242187393 0.5437863871 0.7254283121 0.3500258065 -0.235652421983 +1413393292205760512.0000000000 1.8620783279 1.6237033776 1.1360006628 0.5458117995 0.7223909186 0.3516829647 -0.237823322352 +1413393292255760384.0000000000 1.8602445381 1.6293014322 1.1471687520 0.5479088640 0.7192156876 0.3535524815 -0.239844354125 +1413393292305760512.0000000000 1.8588194343 1.6333171216 1.1580371668 0.5487365181 0.7172175770 0.3547307866 -0.242184330576 +1413393292355760384.0000000000 1.8579418029 1.6356935526 1.1678158629 0.5487075088 0.7158637333 0.3557903460 -0.244688403711 +1413393292405760512.0000000000 1.8571263847 1.6368802371 1.1780768209 0.5480952276 0.7151112533 0.3558518886 -0.248147033508 +1413393292455760384.0000000000 1.8565890025 1.6370754699 1.1886344060 0.5485227369 0.7136649514 0.3565304151 -0.250382122728 +1413393292505760512.0000000000 1.8565893800 1.6358826272 1.1981081938 0.5467062222 0.7137597463 0.3584811565 -0.25129781455 +1413393292555760384.0000000000 1.8570464431 1.6338011963 1.2074291716 0.5456150994 0.7135040140 0.3602458104 -0.251871279524 +1413393292605760512.0000000000 1.8582203080 1.6302427689 1.2163358352 0.5434521318 0.7138989788 0.3629697934 -0.251517310647 +1413393292655760384.0000000000 1.8600488604 1.6253175619 1.2251927956 0.5419388248 0.7138045603 0.3665084889 -0.249913759944 +1413393292705760512.0000000000 1.8614674081 1.6196236341 1.2341503557 0.5405314157 0.7136474205 0.3695875996 -0.248873771516 +1413393292755760384.0000000000 1.8624939912 1.6127999291 1.2428842518 0.5394946910 0.7127352194 0.3727830383 -0.24897146803 +1413393292805760512.0000000000 1.8639231742 1.6046786574 1.2524635642 0.5393692834 0.7115056541 0.3747279947 -0.2498387685 +1413393292855760384.0000000000 1.8652025741 1.5951345065 1.2629611483 0.5398014917 0.7096816921 0.3761636623 -0.251926863411 +1413393292905760512.0000000000 1.8662840985 1.5842083908 1.2742889332 0.5399689544 0.7079006762 0.3776075767 -0.254406522969 +1413393292955760384.0000000000 1.8672685783 1.5718421418 1.2861262380 0.5389797268 0.7071207754 0.3779724580 -0.258104405609 +1413393293005760512.0000000000 1.8683364153 1.5582161851 1.2977230515 0.5370246622 0.7069798520 0.3791848335 -0.260773585898 +1413393293055760384.0000000000 1.8697407708 1.5434661991 1.3092829116 0.5352313928 0.7068374038 0.3801166969 -0.263475876457 +1413393293105760512.0000000000 1.8714171356 1.5277921061 1.3205619077 0.5331181541 0.7069771735 0.3814870076 -0.265397763769 +1413393293155760384.0000000000 1.8731263504 1.5111683897 1.3322124435 0.5305338687 0.7075955235 0.3816248782 -0.268709585908 +1413393293205760512.0000000000 1.8752015203 1.4939424851 1.3438417190 0.5287696665 0.7077713804 0.3825133082 -0.270454953531 +1413393293255760384.0000000000 1.8773464237 1.4759492719 1.3553841087 0.5263297108 0.7085673326 0.3820385121 -0.273780835623 +1413393293305760512.0000000000 1.8799143921 1.4574624597 1.3647539178 0.5238323118 0.7093798456 0.3826175690 -0.275651482231 +1413393293355760384.0000000000 1.8827777162 1.4386522652 1.3718713794 0.5221322764 0.7098819880 0.3811155766 -0.279636132094 +1413393293405760512.0000000000 1.8861789400 1.4196000013 1.3754097727 0.5200341928 0.7107362991 0.3800124623 -0.282858409639 +1413393293455760384.0000000000 1.8900018636 1.4008439562 1.3768718835 0.5181213162 0.7117022559 0.3785766267 -0.285849503005 +1413393293505760512.0000000000 1.8943004211 1.3824498830 1.3753192464 0.5167658439 0.7125189070 0.3785876371 -0.286253857022 +1413393293555760384.0000000000 1.8989590826 1.3644791794 1.3723461462 0.5168140504 0.7123741995 0.3800019358 -0.284648495573 +1413393293605760512.0000000000 1.9042479354 1.3466165515 1.3681279263 0.5176912587 0.7116214676 0.3824482500 -0.281645137598 +1413393293655760384.0000000000 1.9101040044 1.3288703565 1.3637738452 0.5184452239 0.7111398212 0.3855806915 -0.277168242881 +1413393293705760512.0000000000 1.9162189407 1.3110757474 1.3598806384 0.5191059649 0.7103543632 0.3895828111 -0.272306645463 +1413393293755760384.0000000000 1.9221580438 1.2928716281 1.3570800933 0.5197145143 0.7095531123 0.3928303717 -0.268543299354 +1413393293805760512.0000000000 1.9280199135 1.2741413202 1.3553008018 0.5203981986 0.7088806103 0.3949590922 -0.265859569424 +1413393293855760384.0000000000 1.9336331885 1.2544638543 1.3545234614 0.5201799480 0.7085320682 0.3967620127 -0.264527948096 +1413393293905760512.0000000000 1.9387466561 1.2339906455 1.3546081772 0.5201406585 0.7080834384 0.3982247546 -0.263606874984 +1413393293955760384.0000000000 1.9433155877 1.2128536064 1.3555425864 0.5201900053 0.7076907256 0.3999917899 -0.261883109955 +1413393294005760512.0000000000 1.9470115235 1.1908122038 1.3575806397 0.5202039828 0.7072062440 0.4007331140 -0.262030754264 +1413393294055760384.0000000000 1.9500367046 1.1680114052 1.3601342824 0.5201934932 0.7069081173 0.4013004640 -0.261987749512 +1413393294105760512.0000000000 1.9521930409 1.1445110230 1.3640760522 0.5224227079 0.7050513828 0.4001289808 -0.264336642549 +1413393294155760384.0000000000 1.9537991345 1.1202514591 1.3690250355 0.5249998241 0.7030674641 0.3977062153 -0.268143789839 +1413393294205760512.0000000000 1.9551735508 1.0952063028 1.3744210315 0.5271009946 0.7015880827 0.3947903097 -0.272175155224 +1413393294255760384.0000000000 1.9569819021 1.0695606152 1.3791514689 0.5277884031 0.7014731214 0.3937409815 -0.272658946178 +1413393294305760512.0000000000 1.9592712565 1.0431471328 1.3832461164 0.5275060459 0.7020781486 0.3939809693 -0.271298066031 +1413393294355760384.0000000000 1.9617780633 1.0160099250 1.3867277340 0.5262912604 0.7036189989 0.3941021178 -0.269483458579 +1413393294405760512.0000000000 1.9643770836 0.9881171838 1.3899862789 0.5253988597 0.7048980904 0.3947985669 -0.266849792801 +1413393294455760384.0000000000 1.9668666173 0.9596866573 1.3929091162 0.5250017577 0.7060444721 0.3954752105 -0.263578670926 +1413393294505760512.0000000000 1.9688162204 0.9304497450 1.3956795734 0.5235129928 0.7079341184 0.3958815761 -0.260847097102 +1413393294555760384.0000000000 1.9701279889 0.9005246210 1.3986217708 0.5220610809 0.7098451132 0.3952113627 -0.259576813008 +1413393294605760512.0000000000 1.9708341642 0.8700451219 1.4015373210 0.5204097562 0.7119432878 0.3934527167 -0.25981801398 +1413393294655760384.0000000000 1.9711504522 0.8389996830 1.4044444947 0.5188191646 0.7138097144 0.3909424895 -0.261660726875 +1413393294705760512.0000000000 1.9712534450 0.8075330079 1.4072351289 0.5164658241 0.7160649070 0.3884784292 -0.263815487878 +1413393294755760384.0000000000 1.9710051099 0.7760378367 1.4100496834 0.5150853603 0.7177628240 0.3854105219 -0.266387555515 +1413393294805760512.0000000000 1.9705025364 0.7445802382 1.4127090169 0.5133347212 0.7196490565 0.3820306913 -0.269527828586 +1413393294855760384.0000000000 1.9699826059 0.7133994201 1.4149527782 0.5114385719 0.7212802488 0.3806013743 -0.270791402745 +1413393294905760512.0000000000 1.9692986863 0.6829634070 1.4173394119 0.5107852717 0.7223122660 0.3800759718 -0.270010466772 +1413393294955760384.0000000000 1.9684065831 0.6532746817 1.4199910779 0.5114226437 0.7222403268 0.3809680674 -0.26772956798 +1413393295005760512.0000000000 1.9673368151 0.6238279611 1.4227096698 0.5123567709 0.7214639323 0.3833802383 -0.264574992305 +1413393295055760384.0000000000 1.9661160757 0.5949589842 1.4259100209 0.5141994710 0.7205952990 0.3852770543 -0.260581869041 +1413393295105760512.0000000000 1.9643923263 0.5661081802 1.4294440948 0.5156056688 0.7197000665 0.3873331662 -0.257207361761 +1413393295155760384.0000000000 1.9618628599 0.5368136817 1.4335684754 0.5156733415 0.7195169183 0.3877544687 -0.256949180168 +1413393295205760512.0000000000 1.9586997052 0.5076102133 1.4380387188 0.5156931879 0.7198439228 0.3862469275 -0.258260670163 +1413393295255760384.0000000000 1.9550690418 0.4782135466 1.4423990580 0.5141757615 0.7210933477 0.3845702013 -0.260294891261 +1413393295305760512.0000000000 1.9509547591 0.4489905793 1.4469202556 0.5125398310 0.7223030657 0.3825545726 -0.263122028416 +1413393295355760384.0000000000 1.9463968510 0.4201586347 1.4517361201 0.5112027969 0.7235304489 0.3805981114 -0.265180066377 +1413393295405760512.0000000000 1.9414301458 0.3916749664 1.4568713046 0.5080374058 0.7255920774 0.3781979282 -0.269036166134 +1413393295455760384.0000000000 1.9360792856 0.3641798144 1.4624242121 0.5066763557 0.7266124805 0.3757994677 -0.272191355125 +1413393295505760512.0000000000 1.9306371824 0.3375890866 1.4675987924 0.5045393544 0.7281648382 0.3731039749 -0.275698081624 +1413393295555760384.0000000000 1.9250852706 0.3119494503 1.4715521270 0.5027566862 0.7290355193 0.3710753425 -0.279367171017 +1413393295605760512.0000000000 1.9198894849 0.2876709807 1.4730170624 0.5016485396 0.7299129236 0.3693448358 -0.281354329854 +1413393295655760384.0000000000 1.9151879957 0.2644696394 1.4723697861 0.5007115222 0.7303808866 0.3683444030 -0.283115052188 +1413393295705760512.0000000000 1.9118119679 0.2420021715 1.4693558182 0.5000500801 0.7306010052 0.3682987767 -0.283774734051 +1413393295755760384.0000000000 1.9086571278 0.2211762494 1.4638511030 0.5003637125 0.7303742081 0.3689480338 -0.282961162767 +1413393295805760512.0000000000 1.9055637779 0.2017507000 1.4568341066 0.5017725314 0.7292197761 0.3711237995 -0.28058861389 +1413393295855760384.0000000000 1.9028966631 0.1837644780 1.4494121396 0.5046246543 0.7270555292 0.3756269124 -0.275042975433 +1413393295905760512.0000000000 1.9002582335 0.1670454346 1.4425904069 0.5080472868 0.7246415441 0.3803717517 -0.268514277879 +1413393295955760384.0000000000 1.8972855813 0.1509884094 1.4368623169 0.5112817235 0.7220151632 0.3857247615 -0.261727934487 +1413393296005760512.0000000000 1.8936855886 0.1350362685 1.4324733031 0.5139385690 0.7198375156 0.3892924533 -0.257201252431 +1413393296055760384.0000000000 1.8893536966 0.1189412995 1.4291713103 0.5158129131 0.7183316533 0.3923433626 -0.252988854311 +1413393296105760512.0000000000 1.8839730137 0.1022129346 1.4270878999 0.5165801961 0.7173788982 0.3947080068 -0.250435634177 +1413393296155760384.0000000000 1.8773752688 0.0849797521 1.4262136393 0.5166989459 0.7173360622 0.3951394999 -0.249631626258 +1413393296205760512.0000000000 1.8697513741 0.0671926737 1.4259821891 0.5163709101 0.7176390179 0.3960757048 -0.247950316085 +1413393296255760384.0000000000 1.8608253165 0.0486367232 1.4264837456 0.5152504917 0.7183080312 0.3967299272 -0.247297124664 +1413393296305760512.0000000000 1.8504987471 0.0296541841 1.4278489855 0.5150400036 0.7186923813 0.3968590541 -0.246410119378 +1413393296355760384.0000000000 1.8387969391 0.0099610444 1.4300442700 0.5135870698 0.7200538934 0.3953728313 -0.247852852594 +1413393296405760512.0000000000 1.8257882706 -0.0101047079 1.4329205067 0.5113928986 0.7221026025 0.3925312911 -0.250926922129 +1413393296455760384.0000000000 1.8119807512 -0.0301972670 1.4346500263 0.5088854464 0.7248381482 0.3888902259 -0.25379057032 +1413393296505760512.0000000000 1.7976726837 -0.0501902077 1.4337427070 0.5070481548 0.7277952503 0.3842322984 -0.256089404819 +1413393296555760384.0000000000 1.7832422008 -0.0697650356 1.4300827859 0.5064844643 0.7306384574 0.3789181698 -0.25702519831 +1413393296605760512.0000000000 1.7683797625 -0.0887634526 1.4236097428 0.5065575474 0.7334071853 0.3730032305 -0.257646932437 +1413393296655760384.0000000000 1.7531700715 -0.1068038188 1.4141118958 0.5070343192 0.7363482721 0.3672264257 -0.256616783542 +1413393296705760512.0000000000 1.7375631350 -0.1241551658 1.4035181798 0.5078156072 0.7390057382 0.3610959648 -0.256131864749 +1413393296755760384.0000000000 1.7216414347 -0.1407998197 1.3925388175 0.5080023424 0.7417356271 0.3559183277 -0.255115706295 +1413393296805760512.0000000000 1.7053595045 -0.1564150926 1.3824508124 0.5088129903 0.7436707239 0.3513378777 -0.254214261938 +1413393296855760384.0000000000 1.6890230958 -0.1709253454 1.3730451775 0.5104669289 0.7448502287 0.3478513342 -0.252232235492 +1413393296905760512.0000000000 1.6726923322 -0.1845174277 1.3642013310 0.5119039481 0.7457587477 0.3455086279 -0.249844003693 +1413393296955760384.0000000000 1.6562162565 -0.1969825685 1.3561668329 0.5138839831 0.7462103174 0.3433194207 -0.247437243497 +1413393297005760512.0000000000 1.6396436458 -0.2083196155 1.3488141914 0.5153459464 0.7469916135 0.3414336934 -0.244632618159 +1413393297055760384.0000000000 1.6229157837 -0.2186365147 1.3420920417 0.5171583967 0.7478694934 0.3389244945 -0.241595945002 +1413393297105760512.0000000000 1.6060575380 -0.2281435960 1.3356160338 0.5185250915 0.7491593097 0.3356530778 -0.239225979875 +1413393297155760384.0000000000 1.5892573434 -0.2372523232 1.3293570339 0.5193165178 0.7505250504 0.3327195977 -0.237318714895 +1413393297205760512.0000000000 1.5722802869 -0.2457745636 1.3235748044 0.5195789940 0.7518310020 0.3292629917 -0.237431454739 +1413393297255760384.0000000000 1.5552315348 -0.2534569477 1.3181030449 0.5199047883 0.7528925111 0.3257245613 -0.238233893465 +1413393297305760512.0000000000 1.5384104727 -0.2602579388 1.3126633349 0.5207119246 0.7534088221 0.3231314097 -0.238370154387 +1413393297355760384.0000000000 1.5218072564 -0.2660674019 1.3073109947 0.5214538004 0.7538156988 0.3217812457 -0.237286021882 +1413393297405760512.0000000000 1.5050589386 -0.2708695873 1.3024066084 0.5227328356 0.7536586587 0.3205776944 -0.236598712208 +1413393297455760384.0000000000 1.4885455668 -0.2747693053 1.2975204715 0.5236234788 0.7537894034 0.3203585614 -0.234500276938 +1413393297505760512.0000000000 1.4719937213 -0.2778843041 1.2928071066 0.5248996643 0.7531990472 0.3212777131 -0.232276061729 +1413393297555760384.0000000000 1.4552261637 -0.2804877086 1.2881480956 0.5257447185 0.7527291070 0.3211597190 -0.232051324954 +1413393297605760512.0000000000 1.4383503220 -0.2823394772 1.2835682243 0.5262928295 0.7524139252 0.3209174805 -0.23216613344 +1413393297655760384.0000000000 1.4215452466 -0.2839178969 1.2793294365 0.5260471669 0.7523965311 0.3197321094 -0.234403959793 +1413393297705760512.0000000000 1.4047844234 -0.2849107450 1.2753912844 0.5253914710 0.7525870923 0.3182307608 -0.237288123613 +1413393297755760384.0000000000 1.3881940061 -0.2851221817 1.2716723469 0.5256346811 0.7521339071 0.3164888775 -0.240494403916 +1413393297805760512.0000000000 1.3719990456 -0.2844869045 1.2678008070 0.5254878288 0.7518555056 0.3150505924 -0.243554849564 +1413393297855760384.0000000000 1.3564797546 -0.2830263491 1.2638654831 0.5262069169 0.7510502754 0.3134615538 -0.246519002593 +1413393297905760512.0000000000 1.3417500592 -0.2807500362 1.2596238552 0.5259628646 0.7507315423 0.3134763931 -0.247987434082 +1413393297955760384.0000000000 1.3277048234 -0.2774918103 1.2555735507 0.5255397962 0.7505044929 0.3138336176 -0.24911721978 +1413393298005760512.0000000000 1.3145730768 -0.2733241837 1.2513884324 0.5252881454 0.7503301744 0.3140944676 -0.249843269088 +1413393298055760384.0000000000 1.3022808132 -0.2684955787 1.2473423467 0.5247256970 0.7501979011 0.3149491358 -0.250345948372 +1413393298105760512.0000000000 1.2909886120 -0.2625566621 1.2431223904 0.5237623962 0.7506722616 0.3164321830 -0.249067825253 +1413393298155760384.0000000000 1.2803333091 -0.2557603738 1.2385150494 0.5220130820 0.7513924062 0.3190035179 -0.24728232782 +1413393298205760512.0000000000 1.2702068818 -0.2478652204 1.2334906946 0.5206841114 0.7519177828 0.3225466545 -0.243867504507 +1413393298255760384.0000000000 1.2601948186 -0.2388400424 1.2285056444 0.5207495002 0.7516538381 0.3262480778 -0.239580169057 +1413393298305760512.0000000000 1.2499989845 -0.2291774409 1.2234221800 0.5206351368 0.7511598313 0.3310630352 -0.234723728802 +1413393298355760384.0000000000 1.2395511674 -0.2187834644 1.2182574336 0.5209956517 0.7503594061 0.3359965274 -0.229413657576 +1413393298405760512.0000000000 1.2284369384 -0.2078084417 1.2131795335 0.5229001779 0.7485248743 0.3408279339 -0.223879959013 +1413393298455760384.0000000000 1.2161333539 -0.1968217118 1.2086784898 0.5261049317 0.7455317085 0.3450073545 -0.219922708598 +1413393298505760512.0000000000 1.2026165290 -0.1860303527 1.2047136190 0.5292446404 0.7426427592 0.3479588149 -0.217500588393 +1413393298555760384.0000000000 1.1876851699 -0.1757261617 1.2012542124 0.5320206521 0.7402643235 0.3492484623 -0.21676777576 +1413393298605760512.0000000000 1.1715752746 -0.1663228171 1.1984468603 0.5329247843 0.7391307369 0.3490170284 -0.218778522535 +1413393298655760384.0000000000 1.1541180200 -0.1579787290 1.1961539175 0.5319625957 0.7393241004 0.3474929962 -0.222854860691 +1413393298705760512.0000000000 1.1356618559 -0.1502320243 1.1945965690 0.5302961163 0.7402843665 0.3443948157 -0.228379720458 +1413393298755760384.0000000000 1.1166925075 -0.1428236014 1.1931018593 0.5282414226 0.7414524369 0.3413690761 -0.233829932322 +1413393298805760512.0000000000 1.0974221214 -0.1352640146 1.1918709735 0.5268155880 0.7423865889 0.3385689627 -0.238114565799 +1413393298855760384.0000000000 1.0780323423 -0.1277319058 1.1910872133 0.5255574167 0.7432170891 0.3361153241 -0.241752454429 +1413393298905760512.0000000000 1.0588556073 -0.1198383995 1.1906108676 0.5248414454 0.7439210703 0.3339405552 -0.244144637235 +1413393298955760384.0000000000 1.0400230441 -0.1115940233 1.1899307241 0.5236925778 0.7451905985 0.3319823061 -0.24540742497 +1413393299005760512.0000000000 1.0213278972 -0.1029790090 1.1897706905 0.5232597583 0.7459703697 0.3300422880 -0.246575588738 +1413393299055760384.0000000000 1.0030684388 -0.0937598933 1.1897511163 0.5232768869 0.7466626482 0.3292474257 -0.245504220237 +1413393299105760512.0000000000 0.9849512116 -0.0838333415 1.1902662530 0.5248603348 0.7462716650 0.3288816051 -0.243797294373 +1413393299155760384.0000000000 0.9671401593 -0.0732444675 1.1906827424 0.5283642737 0.7446318487 0.3297577287 -0.24003009102 +1413393299205760512.0000000000 0.9493843723 -0.0623897112 1.1914720658 0.5338352512 0.7416856357 0.3307501793 -0.235640958193 +1413393299255760384.0000000000 0.9314412949 -0.0519609503 1.1930682737 0.5400661181 0.7379585296 0.3307549066 -0.233124405671 +1413393299305760512.0000000000 0.9134216657 -0.0422863788 1.1951925510 0.5469325733 0.7336755087 0.3298093343 -0.231971574055 +1413393299355760384.0000000000 0.8956944520 -0.0338369406 1.1976378463 0.5526751307 0.7301959755 0.3270358634 -0.23326290173 +1413393299405760512.0000000000 0.8784153750 -0.0269144212 1.1996353551 0.5566157056 0.7278298627 0.3243580040 -0.235020281075 +1413393299455760384.0000000000 0.8620252610 -0.0215683318 1.2015606923 0.5578754429 0.7273234904 0.3216741516 -0.237278887928 +1413393299505760512.0000000000 0.8464428565 -0.0175275026 1.2033950646 0.5576334467 0.7279066796 0.3192121815 -0.239374994828 +1413393299555760384.0000000000 0.8318334232 -0.0150097149 1.2051016636 0.5555131463 0.7297792409 0.3172746741 -0.241172521262 +1413393299605760512.0000000000 0.8182765966 -0.0137963398 1.2069558750 0.5525683367 0.7320836845 0.3158159685 -0.24286207263 +1413393299655760384.0000000000 0.8057764488 -0.0134499019 1.2089785250 0.5488782790 0.7348966776 0.3143043183 -0.244688176242 +1413393299705760512.0000000000 0.7944435675 -0.0135912893 1.2115040381 0.5457314298 0.7372807334 0.3142079208 -0.244678787679 +1413393299755760384.0000000000 0.7841015693 -0.0142202307 1.2148641965 0.5444285720 0.7381536115 0.3142280213 -0.244923511428 +1413393299805760512.0000000000 0.7747250335 -0.0153295335 1.2183947854 0.5446233935 0.7378157628 0.3155031205 -0.243866849611 +1413393299855760384.0000000000 0.7663009580 -0.0166574953 1.2221031948 0.5446081071 0.7376533498 0.3173763381 -0.241954138605 +1413393299905760512.0000000000 0.7585474133 -0.0183456092 1.2257547881 0.5436870904 0.7379933779 0.3208711521 -0.238352314248 +1413393299955760384.0000000000 0.7514348859 -0.0202808388 1.2295255442 0.5434106742 0.7380185378 0.3252637562 -0.232888312272 +1413393300005760512.0000000000 0.7444300110 -0.0228768431 1.2337901320 0.5440844148 0.7371817365 0.3293741629 -0.228140083423 +1413393300055760384.0000000000 0.7372166175 -0.0261877977 1.2379269026 0.5440365915 0.7367465110 0.3334261893 -0.223731405902 +1413393300105760512.0000000000 0.7295142757 -0.0301764799 1.2422881058 0.5438024698 0.7367226506 0.3355237945 -0.221229277376 +1413393300155760384.0000000000 0.7209575643 -0.0354010060 1.2471281176 0.5426438633 0.7372161938 0.3357422889 -0.222096908365 +1413393300205760512.0000000000 0.7115593209 -0.0418290746 1.2522675431 0.5398646906 0.7385563159 0.3347131637 -0.225937562462 +1413393300255760384.0000000000 0.7014750548 -0.0493806170 1.2576327576 0.5363081545 0.7396672338 0.3334093562 -0.232602983254 +1413393300305760512.0000000000 0.6910922482 -0.0578261231 1.2632757754 0.5316978161 0.7401778615 0.3332598804 -0.241603016938 +1413393300355760384.0000000000 0.6808394690 -0.0666493132 1.2689789651 0.5269547065 0.7400379273 0.3343031989 -0.250806647981 +1413393300405760512.0000000000 0.6705115655 -0.0751881658 1.2751017038 0.5217514383 0.7393041588 0.3369910878 -0.260080380182 +1413393300455760384.0000000000 0.6602072220 -0.0832438817 1.2819209466 0.5163658746 0.7377209750 0.3410081521 -0.269902735784 +1413393300505760512.0000000000 0.6505145890 -0.0904502264 1.2886702665 0.5124230311 0.7347743762 0.3468800361 -0.27785516695 +1413393300555760384.0000000000 0.6416293919 -0.0969322868 1.2949714780 0.5084265152 0.7309609150 0.3541438672 -0.28597332158 +1413393300605760512.0000000000 0.6336570063 -0.1025083882 1.3009666628 0.5049965572 0.7261834328 0.3632217281 -0.292755999631 +1413393300655760384.0000000000 0.6266089271 -0.1068875257 1.3064743892 0.5024978201 0.7204055273 0.3738952429 -0.2978492309 +1413393300705760512.0000000000 0.6201671994 -0.1102358881 1.3121628752 0.5000041731 0.7140611944 0.3862653358 -0.301515385923 +1413393300755760384.0000000000 0.6141104980 -0.1127241400 1.3181945056 0.4977885143 0.7072305360 0.3988195284 -0.304917279988 +1413393300805760512.0000000000 0.6088545898 -0.1143479642 1.3234768323 0.4969760498 0.7003204091 0.4103699988 -0.306859242276 +1413393300855760384.0000000000 0.6040490285 -0.1154743625 1.3269474925 0.4974197652 0.6932209660 0.4201765735 -0.308982065166 +1413393300905760512.0000000000 0.5991033674 -0.1160261231 1.3278747404 0.4988003245 0.6863625267 0.4281156551 -0.311161861691 +1413393300955760384.0000000000 0.5942363507 -0.1165140785 1.3255728372 0.5003173347 0.6803189539 0.4338351191 -0.314063329515 +1413393301005760512.0000000000 0.5895082576 -0.1171496005 1.3201360497 0.5022079789 0.6746174747 0.4376754907 -0.317991467854 +1413393301055760384.0000000000 0.5846085682 -0.1181342194 1.3127252985 0.5037865411 0.6695017048 0.4404093428 -0.322499921139 +1413393301105760512.0000000000 0.5798858107 -0.1198697008 1.3035279873 0.5042790704 0.6649712419 0.4434616844 -0.326890809237 +1413393301155760384.0000000000 0.5754100884 -0.1223312647 1.2919321916 0.5041812959 0.6605545214 0.4467848048 -0.331439712898 +1413393301205760512.0000000000 0.5714864199 -0.1256859989 1.2786702025 0.5027595150 0.6565099925 0.4507662138 -0.336210232255 +1413393301255760384.0000000000 0.5686647164 -0.1300743667 1.2647467979 0.5001726711 0.6526895415 0.4556458820 -0.340896599713 +1413393301305760512.0000000000 0.5670641489 -0.1354397029 1.2515194477 0.4978162804 0.6480990992 0.4610378040 -0.34581881367 +1413393301355760384.0000000000 0.5666668377 -0.1419538693 1.2387540331 0.4945622871 0.6432506671 0.4677734426 -0.350463592783 +1413393301405760512.0000000000 0.5675466831 -0.1494323890 1.2271470364 0.4904071902 0.6384872717 0.4743275958 -0.356157442106 +1413393301455760384.0000000000 0.5697505470 -0.1576558717 1.2159617413 0.4857413808 0.6336486523 0.4815404698 -0.361474027207 +1413393301505760512.0000000000 0.5731230468 -0.1666418785 1.2054542247 0.4799964232 0.6289035309 0.4900812259 -0.365929193359 +1413393301555760384.0000000000 0.5774360192 -0.1761930340 1.1954808288 0.4730519898 0.6247459240 0.4999939520 -0.36867383068 +1413393301605760512.0000000000 0.5824123537 -0.1862885064 1.1863270193 0.4659553939 0.6203233504 0.5106042710 -0.370631609933 +1413393301655760384.0000000000 0.5878364371 -0.1968729384 1.1781987047 0.4592616569 0.6153603136 0.5213428010 -0.372306458153 +1413393301705760512.0000000000 0.5932600260 -0.2075083653 1.1710819093 0.4544706240 0.6101950092 0.5302806181 -0.374060113753 +1413393301755760384.0000000000 0.5985867896 -0.2185521259 1.1644516069 0.4499059827 0.6056795239 0.5383006320 -0.375458853549 +1413393301805760512.0000000000 0.6035305743 -0.2300543476 1.1583955064 0.4470309044 0.6009971776 0.5450801377 -0.376634314113 +1413393301855760384.0000000000 0.6079073966 -0.2421137664 1.1531073996 0.4449039598 0.5972355670 0.5492458021 -0.37907676381 +1413393301905760512.0000000000 0.6118641350 -0.2547540515 1.1481442259 0.4432923477 0.5939342668 0.5530676303 -0.380591877954 +1413393301955760384.0000000000 0.6154453316 -0.2681923835 1.1436550616 0.4422129989 0.5909935151 0.5563998233 -0.38156724874 +1413393302005760512.0000000000 0.6183610055 -0.2822791496 1.1399593479 0.4422043752 0.5883956106 0.5581368878 -0.383052359854 +1413393302055760384.0000000000 0.6209377720 -0.2973026163 1.1370354755 0.4423042940 0.5862275445 0.5593740691 -0.384453935445 +1413393302105760512.0000000000 0.6229735185 -0.3132716731 1.1347765799 0.4414535769 0.5853303987 0.5599391713 -0.385973040827 +1413393302155760384.0000000000 0.6245514150 -0.3300538124 1.1332811716 0.4408296388 0.5851950941 0.5594407793 -0.387610559489 +1413393302205760512.0000000000 0.6256887024 -0.3476531543 1.1325302530 0.4404414808 0.5855502675 0.5588188502 -0.388411738859 +1413393302255760384.0000000000 0.6267083594 -0.3660987086 1.1323686449 0.4393121241 0.5865977675 0.5577266676 -0.389677919509 +1413393302305760512.0000000000 0.6273804677 -0.3851389506 1.1330272173 0.4395100045 0.5874342363 0.5555539703 -0.391294978159 +1413393302355760384.0000000000 0.6280199649 -0.4048643839 1.1339350843 0.4379404610 0.5898058767 0.5530753164 -0.392994751609 +1413393302405760512.0000000000 0.6284621951 -0.4247717392 1.1353918285 0.4376238851 0.5915715208 0.5510552971 -0.393530850702 +1413393302455760384.0000000000 0.6288282232 -0.4448625659 1.1378048829 0.4370086338 0.5940718206 0.5481999363 -0.394434982961 +1413393302505760512.0000000000 0.6291014200 -0.4650324835 1.1409293517 0.4361332382 0.5968223119 0.5457149814 -0.394697460883 +1413393302555760384.0000000000 0.6292557118 -0.4851957771 1.1449099840 0.4348984115 0.6000251302 0.5423256474 -0.39587385225 +1413393302605760512.0000000000 0.6293113863 -0.5051101565 1.1495467443 0.4330361707 0.6035458358 0.5392895770 -0.396710034114 +1413393302655760384.0000000000 0.6293130283 -0.5243721672 1.1547545095 0.4321418733 0.6064202384 0.5371311807 -0.39622971937 +1413393302705760512.0000000000 0.6293035029 -0.5430732592 1.1606702597 0.4319214160 0.6084157543 0.5357242786 -0.395314631245 +1413393302755760384.0000000000 0.6290691054 -0.5611523231 1.1672835480 0.4313040328 0.6103881181 0.5342458304 -0.39494881856 +1413393302805760512.0000000000 0.6285585989 -0.5783473066 1.1747409932 0.4313852539 0.6116503540 0.5326763684 -0.395027206311 +1413393302855760384.0000000000 0.6278508260 -0.5947604435 1.1827443251 0.4307111883 0.6130206452 0.5316639860 -0.395002489602 +1413393302905760512.0000000000 0.6267558658 -0.6103916577 1.1910333680 0.4306582572 0.6135111112 0.5312526674 -0.394852105603 +1413393302955760384.0000000000 0.6254049534 -0.6250544444 1.1994813641 0.4303053924 0.6143328598 0.5309958631 -0.394304197411 +1413393303005760512.0000000000 0.6237200252 -0.6386610192 1.2080834256 0.4316687789 0.6136216704 0.5317084010 -0.392958887428 +1413393303055760384.0000000000 0.6218237049 -0.6515455438 1.2169702716 0.4329388699 0.6124774655 0.5322831160 -0.392568431654 +1413393303105760512.0000000000 0.6196760184 -0.6635016913 1.2258172074 0.4344227508 0.6115929308 0.5324696779 -0.3920548466 +1413393303155760384.0000000000 0.6174593642 -0.6750219678 1.2344876861 0.4349704711 0.6109494758 0.5331565914 -0.391516891513 +1413393303205760512.0000000000 0.6151355302 -0.6859419145 1.2435525217 0.4355767798 0.6102273348 0.5330856333 -0.392065270484 +1413393303255760384.0000000000 0.6128111134 -0.6961155210 1.2524995746 0.4357593010 0.6100342828 0.5335643187 -0.391511332111 +1413393303305760512.0000000000 0.6101852947 -0.7055216722 1.2613498445 0.4376804975 0.6087561274 0.5353266412 -0.388943629078 +1413393303355760384.0000000000 0.6073633953 -0.7143596366 1.2703274071 0.4405786796 0.6068397926 0.5379381475 -0.385043429587 +1413393303405760512.0000000000 0.6042649206 -0.7231280927 1.2796983443 0.4433912138 0.6051058274 0.5402474920 -0.381292298142 +1413393303455760384.0000000000 0.6009168424 -0.7320969293 1.2897961611 0.4450409377 0.6042243483 0.5417135811 -0.378679147568 +1413393303505760512.0000000000 0.5972139976 -0.7415219693 1.3008979717 0.4472655872 0.6027999745 0.5424940723 -0.377207988785 +1413393303555760384.0000000000 0.5931269850 -0.7513502563 1.3127959725 0.4490049455 0.6026125149 0.5420362426 -0.376097630313 +1413393303605760512.0000000000 0.5884312793 -0.7618166602 1.3256495432 0.4510671229 0.6017978140 0.5412483516 -0.376069227105 +1413393303655760384.0000000000 0.5834640790 -0.7730007187 1.3391933943 0.4525116572 0.6014191342 0.5397046406 -0.377156633232 +1413393303705760512.0000000000 0.5786512741 -0.7846286663 1.3531275577 0.4529420251 0.6022287588 0.5380233823 -0.377749763854 +1413393303755760384.0000000000 0.5738824839 -0.7968870187 1.3675161715 0.4522122528 0.6033719343 0.5370185661 -0.378229357661 +1413393303805760512.0000000000 0.5691898038 -0.8095216725 1.3825666838 0.4523566912 0.6037253766 0.5357932458 -0.379229074963 +1413393303855760384.0000000000 0.5646551255 -0.8224332869 1.3979705843 0.4510287767 0.6052962453 0.5339735129 -0.380869774962 +1413393303905760512.0000000000 0.5602304536 -0.8356030836 1.4137610465 0.4494169605 0.6066758804 0.5324892019 -0.382653918783 +1413393303955760384.0000000000 0.5558123275 -0.8486469016 1.4288950482 0.4472327161 0.6083045745 0.5304174946 -0.385494129285 +1413393304005760512.0000000000 0.5514674467 -0.8613506627 1.4416717787 0.4446050788 0.6105711171 0.5287173716 -0.387281778287 +1413393304055760384.0000000000 0.5470436114 -0.8735171669 1.4517096232 0.4428778219 0.6118126208 0.5273535596 -0.38915649163 +1413393304105760512.0000000000 0.5429495383 -0.8849386095 1.4579180242 0.4404560459 0.6134804761 0.5274835772 -0.389103139216 +1413393304155760384.0000000000 0.5391272588 -0.8953553159 1.4605135552 0.4381769104 0.6153954097 0.5289110323 -0.386707389054 +1413393304205760512.0000000000 0.5350511134 -0.9050373238 1.4604222240 0.4360352481 0.6165240804 0.5311267965 -0.384285891956 +1413393304255760384.0000000000 0.5305598109 -0.9137177393 1.4582402032 0.4355563858 0.6165773567 0.5344330445 -0.380137236962 +1413393304305760512.0000000000 0.5253724994 -0.9216934919 1.4540209070 0.4358635412 0.6160574667 0.5373347750 -0.376520266033 +1413393304355760384.0000000000 0.5199559617 -0.9292995136 1.4487479871 0.4363466081 0.6149442267 0.5406202723 -0.373061599286 +1413393304405760512.0000000000 0.5136657652 -0.9364619009 1.4435970690 0.4369157149 0.6137973891 0.5429653902 -0.370871956746 +1413393304455760384.0000000000 0.5062788136 -0.9434060241 1.4387536781 0.4384282531 0.6119064151 0.5449620350 -0.369279821256 +1413393304505760512.0000000000 0.4979267783 -0.9504085481 1.4344057916 0.4393659971 0.6102535395 0.5461079438 -0.369207599943 +1413393304555760384.0000000000 0.4887319766 -0.9573287132 1.4306030357 0.4414374107 0.6075410288 0.5468729032 -0.370076935965 +1413393304605760512.0000000000 0.4789371116 -0.9641721941 1.4267495883 0.4442953733 0.6047196304 0.5477977745 -0.369909972878 +1413393304655760384.0000000000 0.4687453556 -0.9714466878 1.4233200783 0.4458158824 0.6025539832 0.5482783951 -0.370901196828 +1413393304705760512.0000000000 0.4578538348 -0.9791585867 1.4205818259 0.4482198875 0.5998066637 0.5482773410 -0.372455173231 +1413393304755760384.0000000000 0.4466543347 -0.9875847559 1.4182667248 0.4471637074 0.5994485823 0.5485042153 -0.373964091501 +1413393304805760512.0000000000 0.4349430824 -0.9964866284 1.4168704130 0.4465859772 0.5983369111 0.5486670298 -0.376189309003 +1413393304855760384.0000000000 0.4229153808 -1.0059542324 1.4160346312 0.4441914008 0.5986385067 0.5483984902 -0.378926158694 +1413393304905760512.0000000000 0.4106353742 -1.0153820402 1.4153375421 0.4433725751 0.5980287917 0.5498577111 -0.378733179761 +1413393304955760384.0000000000 0.3978117115 -1.0251830695 1.4153890121 0.4423546971 0.5977117454 0.5501975394 -0.379928491981 +1413393305005760512.0000000000 0.3848625013 -1.0348448667 1.4154411122 0.4422797421 0.5970600776 0.5518081378 -0.378702617463 +1413393305055760384.0000000000 0.3716555379 -1.0449102718 1.4157495214 0.4406168486 0.5976686684 0.5524186043 -0.378791025747 +1413393305105760512.0000000000 0.3579451467 -1.0550613522 1.4169504971 0.4399783934 0.5979930400 0.5524208806 -0.379017820264 +1413393305155760384.0000000000 0.3437741823 -1.0652134684 1.4186119291 0.4384999285 0.5993499552 0.5521360114 -0.379002993195 +1413393305205760512.0000000000 0.3287713806 -1.0752439126 1.4210076410 0.4396801891 0.5988817825 0.5524900469 -0.377858028855 +1413393305255760384.0000000000 0.3135315993 -1.0852341743 1.4238914606 0.4424411781 0.5975904944 0.5541370877 -0.37425057498 +1413393305305760512.0000000000 0.2977512116 -1.0956190315 1.4280990148 0.4446378996 0.5975546271 0.5533767926 -0.37282667745 +1413393305355760384.0000000000 0.2814249883 -1.1064911413 1.4327199204 0.4470034690 0.5980863616 0.5519533024 -0.371252144365 +1413393305405760512.0000000000 0.2646961046 -1.1180541411 1.4374471411 0.4478610245 0.6000055691 0.5500891074 -0.369886190155 +1413393305455760384.0000000000 0.2478943723 -1.1304688737 1.4425080675 0.4468525196 0.6032319048 0.5473670220 -0.369896523395 +1413393305505760512.0000000000 0.2306686782 -1.1434613829 1.4477970389 0.4470791478 0.6053183928 0.5449541077 -0.369776823915 +1413393305555760384.0000000000 0.2129862335 -1.1569075213 1.4532846720 0.4473004992 0.6074233032 0.5424941249 -0.369674611623 +1413393305605760512.0000000000 0.1951565439 -1.1709792775 1.4589064244 0.4468847312 0.6095061605 0.5405658861 -0.369573808904 +1413393305655760384.0000000000 0.1766630178 -1.1849648292 1.4648172678 0.4482408977 0.6111823496 0.5387403147 -0.367824831092 +1413393305705760512.0000000000 0.1576166136 -1.1990076800 1.4710671843 0.4504709252 0.6130662671 0.5363340830 -0.365474279647 +1413393305755760384.0000000000 0.1380622050 -1.2130136517 1.4775023669 0.4552497409 0.6135512349 0.5344613316 -0.361460427339 +1413393305805760512.0000000000 0.1181646712 -1.2274473679 1.4845079618 0.4604481833 0.6142864125 0.5319799019 -0.35726328925 +1413393305855760384.0000000000 0.0980468069 -1.2424407701 1.4917583570 0.4666905446 0.6137370185 0.5307325267 -0.351922992534 +1413393305905760512.0000000000 0.0777418069 -1.2586527516 1.4988027156 0.4717586036 0.6137143480 0.5303971127 -0.345655061812 +1413393305955760384.0000000000 0.0569380370 -1.2767496015 1.5068534756 0.4754154042 0.6143255930 0.5279546328 -0.343290205222 +1413393306005760512.0000000000 0.0359109585 -1.2967765899 1.5153355935 0.4758016252 0.6167411062 0.5246828092 -0.34344020022 +1413393306055760384.0000000000 0.0145606652 -1.3185335329 1.5243008537 0.4754564787 0.6189810180 0.5209170972 -0.345613966698 +1413393306105760512.0000000000 -0.0068318166 -1.3415050068 1.5329379839 0.4743687274 0.6214546251 0.5180819994 -0.346928668803 +1413393306155760384.0000000000 -0.0282911717 -1.3656953588 1.5413848148 0.4731920492 0.6231631569 0.5160989867 -0.34842330633 +1413393306205760512.0000000000 -0.0497886595 -1.3908409396 1.5498849777 0.4717700454 0.6247727543 0.5143145536 -0.350103655622 +1413393306255760384.0000000000 -0.0712707498 -1.4165225965 1.5582442892 0.4703268503 0.6262953367 0.5133148371 -0.350791509521 +1413393306305760512.0000000000 -0.0927061004 -1.4427400886 1.5663311890 0.4678995873 0.6286333200 0.5125032806 -0.351042038077 +1413393306355760384.0000000000 -0.1143571686 -1.4690591783 1.5742755590 0.4653527978 0.6322168330 0.5105777436 -0.35079768717 +1413393306405760512.0000000000 -0.1363807653 -1.4950822630 1.5812223700 0.4632421066 0.6368896403 0.5075977355 -0.349460835575 +1413393306455760384.0000000000 -0.1589797147 -1.5206947318 1.5863378619 0.4620199231 0.6426631081 0.5029135110 -0.347274704941 +1413393306505760512.0000000000 -0.1820979413 -1.5457321804 1.5893606319 0.4623587384 0.6486849220 0.4964127716 -0.344973374566 +1413393306555760384.0000000000 -0.2057155763 -1.5698239988 1.5894813995 0.4647732930 0.6544864056 0.4892008868 -0.341051056807 +1413393306605760512.0000000000 -0.2296368352 -1.5930919895 1.5875976592 0.4692134774 0.6597387544 0.4802997070 -0.337484340491 +1413393306655760384.0000000000 -0.2540405088 -1.6156727757 1.5836746955 0.4738756616 0.6650408037 0.4710062095 -0.33364013134 +1413393306705760512.0000000000 -0.2785779900 -1.6381708945 1.5791700725 0.4754677371 0.6721552295 0.4589035741 -0.333983963932 +1413393306755760384.0000000000 -0.3029966745 -1.6599808668 1.5749499140 0.4765224376 0.6786936832 0.4483879436 -0.333540856369 +1413393306805760512.0000000000 -0.3271396046 -1.6809654431 1.5714692398 0.4777250250 0.6839366161 0.4382857217 -0.334537190477 +1413393306855760384.0000000000 -0.3507581731 -1.7007185326 1.5684261575 0.4779367860 0.6891874481 0.4303654292 -0.333740448901 +1413393306905760512.0000000000 -0.3736919957 -1.7187217146 1.5658135915 0.4794596071 0.6936170737 0.4228701000 -0.331955898976 +1413393306955760384.0000000000 -0.3960451115 -1.7349861986 1.5641104682 0.4804604974 0.6984865601 0.4154252871 -0.329690865269 +1413393307005760512.0000000000 -0.4177239862 -1.7491418457 1.5631202546 0.4825792796 0.7029974601 0.4088344743 -0.325217131561 +1413393307055760384.0000000000 -0.4385588797 -1.7613179139 1.5622710426 0.4857474740 0.7070253113 0.4028468463 -0.31918492928 +1413393307105760512.0000000000 -0.4586702050 -1.7714420736 1.5612503527 0.4901766192 0.7104346596 0.3973149219 -0.311689475727 +1413393307155760384.0000000000 -0.4782722359 -1.7797870783 1.5601150893 0.4951006709 0.7135659764 0.3925272628 -0.302690057614 +1413393307205760512.0000000000 -0.4974927443 -1.7865539966 1.5593986487 0.4995743131 0.7172135206 0.3870404100 -0.293649438237 +1413393307255760384.0000000000 -0.5163549455 -1.7921190237 1.5593645659 0.5044190270 0.7205361338 0.3807894560 -0.285286724697 +1413393307305760512.0000000000 -0.5349584308 -1.7966499983 1.5598019029 0.5098193551 0.7234411905 0.3742953391 -0.276803302324 +1413393307355760384.0000000000 -0.5531941143 -1.8003941480 1.5602818279 0.5126005140 0.7284531272 0.3668120620 -0.268413236846 +1413393307405760512.0000000000 -0.5712688419 -1.8031893508 1.5614754542 0.5164843653 0.7329104063 0.3586126882 -0.259775242738 +1413393307455760384.0000000000 -0.5892416467 -1.8049446853 1.5636256212 0.5204910069 0.7376471983 0.3495250020 -0.250595282477 +1413393307505760512.0000000000 -0.6070739511 -1.8060777504 1.5663633710 0.5234201355 0.7430738703 0.3398322364 -0.241633267591 +1413393307555760384.0000000000 -0.6247639226 -1.8067761165 1.5695113379 0.5246913524 0.7495198284 0.3301355926 -0.232227263915 +1413393307605760512.0000000000 -0.6428191841 -1.8069207646 1.5732979582 0.5259653171 0.7557655185 0.3194476499 -0.223902133293 +1413393307655760384.0000000000 -0.6612914112 -1.8065398036 1.5776165980 0.5255769514 0.7630139786 0.3080615920 -0.216047661825 +1413393307705760512.0000000000 -0.6800250840 -1.8054540688 1.5821742612 0.5254674595 0.7696310978 0.2971792015 -0.207933750423 +1413393307755760384.0000000000 -0.6992633594 -1.8031274242 1.5871083784 0.5277975039 0.7743817519 0.2868171813 -0.198742551541 +1413393307805760512.0000000000 -0.7189981331 -1.7996754046 1.5925333867 0.5343344163 0.7757080392 0.2777260475 -0.188764435108 +1413393307855760384.0000000000 -0.7392706211 -1.7956404551 1.5980892797 0.5402943408 0.7770638166 0.2681139157 -0.179913252787 +1413393307905760512.0000000000 -0.7599741846 -1.7910896589 1.6039003435 0.5467142848 0.7777993756 0.2587234862 -0.170861873347 +1413393307955760384.0000000000 -0.7810890204 -1.7864109657 1.6098627280 0.5517313133 0.7792193939 0.2494904266 -0.16175358166 +1413393308005760512.0000000000 -0.8026903585 -1.7817217089 1.6162832753 0.5562957534 0.7807858596 0.2393340159 -0.153713060695 +1413393308055760384.0000000000 -0.8247171054 -1.7773180893 1.6224719185 0.5597511504 0.7828542948 0.2296942158 -0.145115023131 +1413393308105760512.0000000000 -0.8473900887 -1.7730235128 1.6288355246 0.5629367306 0.7848813523 0.2198648166 -0.136831877107 +1413393308155760384.0000000000 -0.8705339613 -1.7689279820 1.6351042576 0.5646765953 0.7877845659 0.2097003343 -0.128691842522 +1413393308205760512.0000000000 -0.8943691551 -1.7650837423 1.6416134015 0.5665891038 0.7902585934 0.1998364572 -0.120555105524 +1413393308255760384.0000000000 -0.9188551858 -1.7614578762 1.6483119244 0.5687797085 0.7924253305 0.1894476286 -0.11252259703 +1413393308305760512.0000000000 -0.9440292647 -1.7580050112 1.6552770593 0.5714248815 0.7942610870 0.1773986358 -0.105606129527 +1413393308355760384.0000000000 -0.9696165266 -1.7550045998 1.6621848522 0.5732186033 0.7963300915 0.1654525162 -0.0995202647623 +1413393308405760512.0000000000 -0.9956011316 -1.7523325942 1.6691676858 0.5746798710 0.7984760471 0.1526602120 -0.094201420669 +1413393308455760384.0000000000 -1.0217840742 -1.7500268803 1.6750954541 0.5743312137 0.8016632316 0.1398691054 -0.0889738923317 +1413393308505760512.0000000000 -1.0480567847 -1.7477292294 1.6795612854 0.5727619707 0.8054434211 0.1267535997 -0.0844875453714 +1413393308555760384.0000000000 -1.0740828863 -1.7456576361 1.6815910848 0.5714828541 0.8087866500 0.1138345385 -0.0794556487461 +1413393308605760512.0000000000 -1.0995510502 -1.7438860669 1.6812187231 0.5707832273 0.8115308621 0.1005636893 -0.0742368624491 +1413393308655760384.0000000000 -1.1246879732 -1.7415721834 1.6782508160 0.5690413945 0.8147812299 0.0865057003 -0.0695715643738 +1413393308705760512.0000000000 -1.1494572624 -1.7380387101 1.6733064737 0.5678673817 0.8173667786 0.0721478435 -0.0650605460967 +1413393308755760384.0000000000 -1.1734208021 -1.7338867720 1.6670356415 0.5682577494 0.8186316119 0.0580455263 -0.0596333050384 +1413393308805760512.0000000000 -1.1963189806 -1.7294883029 1.6587593378 0.5707161651 0.8181833317 0.0445873271 -0.053582319318 +1413393308855760384.0000000000 -1.2177718632 -1.7251140961 1.6476248959 0.5743038218 0.8167407573 0.0331345565 -0.0448526117074 +1413393308905760512.0000000000 -1.2381472937 -1.7202407171 1.6347291862 0.5773689612 0.8153796796 0.0218687239 -0.0363705879873 +1413393308955760384.0000000000 -1.2574332607 -1.7147661654 1.6213775135 0.5801972386 0.8139360103 0.0113475077 -0.0273965238829 +1413393309005760512.0000000000 -1.2755393595 -1.7092117282 1.6081131098 0.5826760032 0.8125109266 0.0014624805 -0.0176785369422 +1413393309055760384.0000000000 -1.2927040260 -1.7043068612 1.5948978080 0.5832168855 0.8122076981 -0.0089289972 -0.00984848266145 +1413393309105760512.0000000000 -1.3088371383 -1.6996692879 1.5825661347 0.5855064750 0.8104488987 -0.0187487787 -0.00179823318596 +1413393309155760384.0000000000 -1.3239712815 -1.6954843466 1.5705305768 0.5856355828 0.8100542849 -0.0284629438 0.0057341502289 +1413393309205760512.0000000000 -1.3384283485 -1.6916644261 1.5596532244 0.5868478166 0.8087654139 -0.0369145987 0.0120605908304 +1413393309255760384.0000000000 -1.3521643091 -1.6887361995 1.5491620595 0.5866464723 0.8084823305 -0.0430521788 0.0186747909716 +1413393309305760512.0000000000 -1.3654162543 -1.6864374869 1.5397359408 0.5868142974 0.8079773550 -0.0468687231 0.0249979380322 +1413393309355760384.0000000000 -1.3781648785 -1.6843570352 1.5304841488 0.5868154310 0.8076561642 -0.0481175073 0.0319980593549 +1413393309405760512.0000000000 -1.3910149393 -1.6830780220 1.5216378992 0.5860094144 0.8079892398 -0.0485113549 0.0373229566349 +1413393309455760384.0000000000 -1.4039105521 -1.6823616480 1.5137615093 0.5851195699 0.8084500360 -0.0478857646 0.0418399544204 +1413393309505760512.0000000000 -1.4171028213 -1.6820751898 1.5074012033 0.5825745618 0.8102003559 -0.0467799632 0.0446530892762 +1413393309555760384.0000000000 -1.4307340076 -1.6819986205 1.5020178083 0.5795354223 0.8123987527 -0.0456813009 0.0453892025425 +1413393309605760512.0000000000 -1.4446116559 -1.6823700912 1.4967852673 0.5740470865 0.8163252588 -0.0442114332 0.046134189631 +1413393309655760384.0000000000 -1.4589158964 -1.6824788158 1.4925556587 0.5699377825 0.8193251995 -0.0422062180 0.0457796536502 +1413393309705760512.0000000000 -1.4735442382 -1.6817062152 1.4891229958 0.5663966987 0.8219198034 -0.0412593298 0.0440486581112 +1413393309755760384.0000000000 -1.4881934861 -1.6798425864 1.4867622527 0.5646944641 0.8232204743 -0.0420793870 0.0407128732084 +1413393309805760512.0000000000 -1.5030537785 -1.6770930349 1.4850105599 0.5643730781 0.8236172864 -0.0439361674 0.0347448900921 +1413393309855760384.0000000000 -1.5173344265 -1.6734802589 1.4835123337 0.5636627300 0.8241946430 -0.0460483762 0.0294459558741 +1413393309905760512.0000000000 -1.5306743292 -1.6689167417 1.4823085050 0.5636699199 0.8242403485 -0.0475029541 0.0254467797695 +1413393309955760384.0000000000 -1.5431504161 -1.6636013576 1.4809671080 0.5628112563 0.8248600739 -0.0490680890 0.0210159706596 +1413393310005760512.0000000000 -1.5544508942 -1.6573745754 1.4800408639 0.5627772233 0.8248712787 -0.0509618300 0.0164943159985 +1413393310055760384.0000000000 -1.5643092559 -1.6500536860 1.4793654848 0.5633952150 0.8244532468 -0.0515635773 0.0142784114223 +1413393310105760512.0000000000 -1.5727715931 -1.6417247304 1.4792805015 0.5654182996 0.8231071706 -0.0512898279 0.0128874252721 +1413393310155760384.0000000000 -1.5794770355 -1.6324921951 1.4794099057 0.5683392728 0.8211774189 -0.0494787648 0.0144903279631 +1413393310205760512.0000000000 -1.5845005810 -1.6228365813 1.4792701775 0.5709893371 0.8194889128 -0.0450439983 0.01949710016 +1413393310255760384.0000000000 -1.5887792315 -1.6129230299 1.4790746358 0.5733617288 0.8179354870 -0.0400510786 0.0251749501549 +1413393310305760512.0000000000 -1.5923643276 -1.6028380473 1.4783483142 0.5747044687 0.8169955455 -0.0356056490 0.0310691186893 +1413393310355760384.0000000000 -1.5958138110 -1.5925046670 1.4776100370 0.5752599534 0.8165798803 -0.0314759194 0.0358127295162 +1413393310405760512.0000000000 -1.5992334533 -1.5817543293 1.4769709371 0.5762430917 0.8158019750 -0.0286455569 0.0398806829709 +1413393310455760384.0000000000 -1.6030409809 -1.5710356406 1.4763393245 0.5767271670 0.8154022226 -0.0278218654 0.0416044953933 +1413393310505760512.0000000000 -1.6077844661 -1.5602969540 1.4761457974 0.5771238326 0.8151808193 -0.0294123542 0.0392839292213 +1413393310555760384.0000000000 -1.6127363075 -1.5494544637 1.4757747993 0.5776779606 0.8148208374 -0.0310979611 0.0372571275221 +1413393310605760512.0000000000 -1.6179878846 -1.5386495159 1.4751403632 0.5773587381 0.8151048918 -0.0340267416 0.0332127030586 +1413393310655760384.0000000000 -1.6231467353 -1.5278663446 1.4748593403 0.5774536439 0.8150533838 -0.0379234289 0.0282326788161 +1413393310705760512.0000000000 -1.6278365131 -1.5172341137 1.4746649777 0.5774671934 0.8150096713 -0.0417246189 0.0234506368462 +1413393310755760384.0000000000 -1.6318229506 -1.5066980898 1.4739538686 0.5764082064 0.8156962640 -0.0451348805 0.018868676335 +1413393310805760512.0000000000 -1.6347677769 -1.4958941154 1.4734229282 0.5758730244 0.8159734343 -0.0482156592 0.0152598977015 +1413393310855760384.0000000000 -1.6362807614 -1.4848939739 1.4728537208 0.5749287970 0.8165207377 -0.0507008700 0.0134233034704 +1413393310905760512.0000000000 -1.6361690110 -1.4736809106 1.4715968316 0.5740272755 0.8171395412 -0.0501509677 0.0161411769053 +1413393310955760384.0000000000 -1.6344412385 -1.4621562125 1.4691929603 0.5721020993 0.8185008967 -0.0472293116 0.0229098712826 +1413393311005760512.0000000000 -1.6318003587 -1.4503363730 1.4665603010 0.5704224059 0.8195967704 -0.0450075545 0.0292187069943 +1413393311055760384.0000000000 -1.6286786551 -1.4380729405 1.4635801535 0.5684265748 0.8208495548 -0.0435779030 0.0346150803977 +1413393311105760512.0000000000 -1.6254332554 -1.4250011639 1.4595362643 0.5664398220 0.8220764364 -0.0433529718 0.0381677955187 +1413393311155760384.0000000000 -1.6219968380 -1.4112828337 1.4534916678 0.5665989659 0.8218038037 -0.0432349262 0.0416516656222 +1413393311205760512.0000000000 -1.6189095858 -1.3972562989 1.4450869999 0.5663942476 0.8218339229 -0.0458116069 0.0410835249192 +1413393311255760384.0000000000 -1.6158949708 -1.3823914006 1.4343181633 0.5664763764 0.8217125764 -0.0484208354 0.0393494535092 +1413393311305760512.0000000000 -1.6125649853 -1.3672411026 1.4218648351 0.5660090627 0.8219808144 -0.0493038726 0.039375244474 +1413393311355760384.0000000000 -1.6087774991 -1.3513382457 1.4093274236 0.5653361448 0.8223777370 -0.0488265870 0.0413021240067 +1413393311405760512.0000000000 -1.6046553778 -1.3346825446 1.3970312278 0.5649303789 0.8225855457 -0.0481132921 0.0434948057109 +1413393311455760384.0000000000 -1.6003618812 -1.3170873498 1.3850239265 0.5642592974 0.8229851297 -0.0470590513 0.0457424022132 +1413393311505760512.0000000000 -1.5960513595 -1.2985854973 1.3740215660 0.5633847393 0.8235282257 -0.0467653961 0.0470307862332 +1413393311555760384.0000000000 -1.5917179660 -1.2792101435 1.3638882606 0.5626812359 0.8239359647 -0.0454067516 0.0495739825757 +1413393311605760512.0000000000 -1.5875628688 -1.2586918888 1.3550041103 0.5625895760 0.8239483177 -0.0442845421 0.0513908364458 +1413393311655760384.0000000000 -1.5838329770 -1.2372234604 1.3476123948 0.5640748549 0.8229291577 -0.0434413338 0.0521537143247 +1413393311705760512.0000000000 -1.5805905049 -1.2146093118 1.3420971574 0.5670906795 0.8208717868 -0.0426411714 0.0525300044476 +1413393311755760384.0000000000 -1.5778022656 -1.1910999150 1.3377249706 0.5701212454 0.8188052128 -0.0413750888 0.0529895375458 +1413393311805760512.0000000000 -1.5756933636 -1.1672374968 1.3341176427 0.5734688061 0.8165623632 -0.0395335129 0.0528822912966 +1413393311855760384.0000000000 -1.5743488428 -1.1432788228 1.3314013096 0.5762851361 0.8147325934 -0.0382660436 0.0513999323037 +1413393311905760512.0000000000 -1.5736397342 -1.1193714004 1.3288393850 0.5782361944 0.8135430562 -0.0355938183 0.0502362345906 +1413393311955760384.0000000000 -1.5738182914 -1.0956018723 1.3266830904 0.5799217196 0.8126222454 -0.0335191512 0.0470356457795 +1413393312005760512.0000000000 -1.5744144104 -1.0719190260 1.3252752794 0.5836774749 0.8101615833 -0.0303464466 0.0451431875832 +1413393312055760384.0000000000 -1.5754306845 -1.0487698258 1.3237539728 0.5874769186 0.8075875126 -0.0259495338 0.044720256938 +1413393312105760512.0000000000 -1.5771911494 -1.0263003615 1.3223346975 0.5914071368 0.8048513556 -0.0216214760 0.0445466680124 +1413393312155760384.0000000000 -1.5798713687 -1.0047161032 1.3208757059 0.5933116737 0.8035950339 -0.0186206278 0.043238311735 +1413393312205760512.0000000000 -1.5833489567 -0.9841532730 1.3193490221 0.5931888656 0.8038329440 -0.0166488201 0.0412599646583 +1413393312255760384.0000000000 -1.5875025904 -0.9643949551 1.3178184052 0.5918246120 0.8049662115 -0.0162492225 0.0388457177723 +1413393312305760512.0000000000 -1.5925166573 -0.9450819253 1.3173908563 0.5920013680 0.8050414942 -0.0191849928 0.032779702337 +1413393312355760384.0000000000 -1.5979617150 -0.9265364181 1.3173940030 0.5906386221 0.8061944314 -0.0229367603 0.025893278988 +1413393312405760512.0000000000 -1.6034635176 -0.9086480055 1.3170142935 0.5873308708 0.8086794997 -0.0269921252 0.0187440698508 +1413393312455760384.0000000000 -1.6087679776 -0.8910465375 1.3168693251 0.5854355331 0.8100490235 -0.0307070076 0.0119539005629 +1413393312505760512.0000000000 -1.6132196109 -0.8739480088 1.3163538754 0.5824145466 0.8121530680 -0.0339928809 0.00672116276651 +1413393312555760384.0000000000 -1.6163426585 -0.8568138374 1.3164251536 0.5818538663 0.8125080775 -0.0353910717 0.0049167384765 +1413393312605760512.0000000000 -1.6181644792 -0.8396031812 1.3167315147 0.5829379778 0.8117910589 -0.0334252065 0.00783239078747 +1413393312655760384.0000000000 -1.6189097956 -0.8227419336 1.3166319492 0.5835452661 0.8114261042 -0.0298114614 0.0131862290281 +1413393312705760512.0000000000 -1.6190376651 -0.8063268765 1.3161735218 0.5827990199 0.8119889978 -0.0254924028 0.0192173677812 +1413393312755760384.0000000000 -1.6190447363 -0.7900259762 1.3164065519 0.5828484983 0.8119458234 -0.0233230306 0.0220826639992 +1413393312805760512.0000000000 -1.6190630396 -0.7737143208 1.3167770889 0.5829972614 0.8118381034 -0.0217115864 0.0237000876133 +1413393312855760384.0000000000 -1.6192339693 -0.7575865408 1.3175911630 0.5835766175 0.8114589367 -0.0205717998 0.0234419821602 +1413393312905760512.0000000000 -1.6194442270 -0.7416072815 1.3189420989 0.5863407972 0.8095244757 -0.0196697821 0.0220837593985 +1413393312955760384.0000000000 -1.6198384197 -0.7263331291 1.3206307864 0.5882580017 0.8082175459 -0.0194154679 0.0189726508649 +1413393313005760512.0000000000 -1.6203235617 -0.7114947415 1.3238065002 0.5939194237 0.8041533850 -0.0187040257 0.0157229449185 +1413393313055760384.0000000000 -1.6206314960 -0.6981275819 1.3255201088 0.5919937045 0.8056567704 -0.0162223499 0.0140519565932 +1413393313105760512.0000000000 -1.6204675184 -0.6863174630 1.3277719652 0.5893565478 0.8076489128 -0.0114359263 0.0152089739424 +1413393313155760384.0000000000 -1.6204804912 -0.6753768781 1.3291427863 0.5851874020 0.8107056151 -0.0063706003 0.0164780372732 +1413393313205760512.0000000000 -1.6206334663 -0.6643311748 1.3328528034 0.5824768859 0.8126711455 -0.0011195724 0.0168829264763 +1413393313255760384.0000000000 -1.6208850494 -0.6530077619 1.3375625671 0.5793528450 0.8148885740 0.0035125292 0.0171626065206 +1413393313305760512.0000000000 -1.6218538114 -0.6422902302 1.3424639984 0.5782451691 0.8157390385 0.0051427775 0.0132626312446 +1413393313355760384.0000000000 -1.6229476953 -0.6319553295 1.3470593888 0.5773836064 0.8163899264 0.0064719617 0.00968363842262 +1413393313405760512.0000000000 -1.6237982246 -0.6220044861 1.3512153616 0.5773441195 0.8164385412 0.0072179723 0.00705528342121 +1413393313455760384.0000000000 -1.6244964572 -0.6116956750 1.3561476096 0.5787132355 0.8155003347 0.0062433510 0.00334897670059 +1413393313505760512.0000000000 -1.6249409212 -0.6004474257 1.3601489597 0.5818707535 0.8132690434 0.0044295401 -0.000518083127149 +1413393313555760384.0000000000 -1.6245901767 -0.5884837869 1.3634945084 0.5864314431 0.8099883594 0.0012548656 -0.00393008196689 +1413393313605760512.0000000000 -1.6232613458 -0.5778738513 1.3644133549 0.5908155224 0.8067640533 -0.0033694307 -0.0075781052557 +1413393313655760384.0000000000 -1.6205491029 -0.5673371488 1.3646400233 0.5961529182 0.8027498673 -0.0092005825 -0.0104736818107 +1413393313705760512.0000000000 -1.6160324019 -0.5574268104 1.3633439644 0.6011769717 0.7989524969 -0.0133748447 -0.00907028052465 +1413393313755760384.0000000000 -1.6096987432 -0.5487840981 1.3614677504 0.6053096965 0.7958289734 -0.0156185508 -0.00353231479372 +1413393313805760512.0000000000 -1.6020962290 -0.5427668633 1.3598358950 0.6088013687 0.7931260274 -0.0175546524 0.00195762784312 +1413393313855760384.0000000000 -1.5933357452 -0.5384648371 1.3583427353 0.6086353573 0.7931713037 -0.0191065165 0.00878782768192 +1413393313905760512.0000000000 -1.5836666215 -0.5368020055 1.3558272343 0.6029412493 0.7973572100 -0.0209735467 0.0156025595757 +1413393313955760384.0000000000 -1.5733118283 -0.5363912158 1.3535981460 0.5951471610 0.8029651283 -0.0246905813 0.0209101566312 +1413393314005760512.0000000000 -1.5624523708 -0.5369636835 1.3517933861 0.5879804624 0.8079504826 -0.0289455601 0.0256348992187 +1413393314055760384.0000000000 -1.5512710575 -0.5379879188 1.3506184260 0.5811047805 0.8126015713 -0.0339178453 0.0290774846812 +1413393314105760512.0000000000 -1.5403088335 -0.5388449851 1.3506042959 0.5773656299 0.8150353496 -0.0378910903 0.0305053043774 +1413393314155760384.0000000000 -1.5293172315 -0.5395128003 1.3509419998 0.5757194040 0.8160520711 -0.0394554351 0.0323952729953 +1413393314205760512.0000000000 -1.5183391461 -0.5397302778 1.3517707726 0.5753074455 0.8163056217 -0.0390225287 0.03381889123 +1413393314255760384.0000000000 -1.5075545916 -0.5393361726 1.3528243699 0.5753213651 0.8163889000 -0.0357430242 0.0351699750098 +1413393314305760512.0000000000 -1.4971954776 -0.5385596827 1.3545549574 0.5758719204 0.8162252960 -0.0319873292 0.0335351807313 +1413393314355760384.0000000000 -1.4873682271 -0.5378868103 1.3558081233 0.5758653112 0.8165197145 -0.0258007151 0.0317651115897 +1413393314405760512.0000000000 -1.4781491521 -0.5372742872 1.3564212697 0.5746784040 0.8176658341 -0.0173886099 0.0294100661679 +1413393314455760384.0000000000 -1.4696095821 -0.5364842366 1.3569771079 0.5736892330 0.8186417562 -0.0083793448 0.0252215275318 +1413393314505760512.0000000000 -1.4618776924 -0.5355114167 1.3570318627 0.5724624113 0.8196928044 0.0018655817 0.0196726642518 +1413393314555760384.0000000000 -1.4553184491 -0.5338379357 1.3571677422 0.5727900955 0.8194846479 0.0137801435 0.0129044956887 +1413393314605760512.0000000000 -1.4495670810 -0.5317082429 1.3569153082 0.5717920258 0.8199610681 0.0261189414 0.00596045026433 +1413393314655760384.0000000000 -1.4447861615 -0.5293581043 1.3565792726 0.5704762807 0.8203723102 0.0392836624 -0.0016969643851 +1413393314705760512.0000000000 -1.4407155382 -0.5262329679 1.3562782326 0.5691705513 0.8205334525 0.0518640259 -0.00893642579366 +1413393314755760384.0000000000 -1.4374440063 -0.5223336042 1.3555790808 0.5670540035 0.8211674094 0.0622014882 -0.0162732220212 +1413393314805760512.0000000000 -1.4351594629 -0.5173253282 1.3543924233 0.5653342223 0.8213946991 0.0719656407 -0.022998087315 +1413393314855760384.0000000000 -1.4339444085 -0.5116309299 1.3527130510 0.5637664437 0.8214231406 0.0805161474 -0.0307988822402 +1413393314905760512.0000000000 -1.4337597193 -0.5049461067 1.3504349260 0.5617350794 0.8216283391 0.0890091893 -0.0381829437846 +1413393314955760384.0000000000 -1.4346612176 -0.4971951321 1.3483490830 0.5605504230 0.8210318876 0.0978237633 -0.0460475195442 +1413393315005760512.0000000000 -1.4363289528 -0.4881897149 1.3458866563 0.5590578076 0.8206063376 0.1054619431 -0.0541976467671 +1413393315055760384.0000000000 -1.4385940172 -0.4775870821 1.3430879843 0.5581959608 0.8199528844 0.1110750046 -0.0612933928807 +1413393315105760512.0000000000 -1.4412762361 -0.4656047497 1.3396724206 0.5577033413 0.8191451434 0.1158595069 -0.0674150711821 +1413393315155760384.0000000000 -1.4442261385 -0.4522618160 1.3353364266 0.5567920422 0.8187511474 0.1213076013 -0.0700974053488 +1413393315205760512.0000000000 -1.4475848333 -0.4373456235 1.3310635931 0.5586539456 0.8166966684 0.1259110796 -0.0711246854146 +1413393315255760384.0000000000 -1.4513821760 -0.4212351335 1.3256078581 0.5598711508 0.8152616665 0.1305594159 -0.0696200298392 +1413393315305760512.0000000000 -1.4558607450 -0.4040651456 1.3197174565 0.5624484568 0.8130932949 0.1343454121 -0.0669502616317 +1413393315355760384.0000000000 -1.4612984378 -0.3859277237 1.3138979220 0.5666342418 0.8099499948 0.1375369690 -0.0631682205839 +1413393315405760512.0000000000 -1.4677418797 -0.3673060496 1.3079636694 0.5711465458 0.8066427253 0.1404353838 -0.0582841299008 +1413393315455760384.0000000000 -1.4756729168 -0.3485497061 1.3024642674 0.5762276172 0.8029965986 0.1424780438 -0.0534621628176 +1413393315505760512.0000000000 -1.4856423373 -0.3301267539 1.2975257490 0.5798790451 0.8006182282 0.1414852527 -0.05227493657 +1413393315555760384.0000000000 -1.4973839074 -0.3121232912 1.2931421086 0.5832780890 0.7983833782 0.1406838112 -0.0507810755541 +1413393315605760512.0000000000 -1.5111630157 -0.2949601281 1.2903466850 0.5854961921 0.7971508280 0.1379568645 -0.0520832978637 +1413393315655760384.0000000000 -1.5269056548 -0.2785578871 1.2909595583 0.5889170948 0.7950058462 0.1343411236 -0.0556311276942 +1413393315705760512.0000000000 -1.5436762979 -0.2633047672 1.2935875466 0.5897746972 0.7946953309 0.1316738850 -0.057333460381 +1413393315755760384.0000000000 -1.5618055672 -0.2488571902 1.3002651610 0.5900909058 0.7948319725 0.1273936121 -0.0616905669147 +1413393315805760512.0000000000 -1.5806025991 -0.2359012728 1.3100668670 0.5882940410 0.7963749352 0.1240365078 -0.0656660389304 +1413393315855760384.0000000000 -1.5999607291 -0.2240313699 1.3235235781 0.5882253930 0.7966299077 0.1192310703 -0.07180270991 +1413393315905760512.0000000000 -1.6192125819 -0.2124174024 1.3382811232 0.5858879578 0.7984474153 0.1167484658 -0.0747450440358 +1413393315955760384.0000000000 -1.6384886135 -0.2012377716 1.3539451751 0.5853812944 0.7987706647 0.1152647912 -0.0775125371084 +1413393316005760512.0000000000 -1.6573133045 -0.1901733399 1.3693119325 0.5851041027 0.7989860648 0.1150107037 -0.0777624284284 +1413393316055760384.0000000000 -1.6759717670 -0.1793732501 1.3847957026 0.5853879870 0.7987579077 0.1147197578 -0.0783969824844 +1413393316105760512.0000000000 -1.6943015782 -0.1689847680 1.4003528182 0.5851085143 0.7988604858 0.1164952331 -0.0768037197746 +1413393316155760384.0000000000 -1.7124503258 -0.1587324933 1.4172203810 0.5864882657 0.7978054848 0.1183498341 -0.0743723025325 +1413393316205760512.0000000000 -1.7306260419 -0.1489892783 1.4350809843 0.5879036679 0.7966852340 0.1202045273 -0.0721996316773 +1413393316255760384.0000000000 -1.7491183469 -0.1400774335 1.4536193922 0.5885837708 0.7959876362 0.1222616871 -0.0708865824568 +1413393316305760512.0000000000 -1.7678312023 -0.1318506023 1.4723770266 0.5891527324 0.7954446948 0.1232033573 -0.0706238501382 +1413393316355760384.0000000000 -1.7870445317 -0.1245371524 1.4912096446 0.5883602225 0.7958181948 0.1236949734 -0.0721470922222 +1413393316405760512.0000000000 -1.8064735896 -0.1178474361 1.5103244296 0.5879873622 0.7958889049 0.1244054237 -0.073177890128 +1413393316455760384.0000000000 -1.8261627565 -0.1119091402 1.5292825933 0.5863971197 0.7968883254 0.1244517351 -0.0749611931833 +1413393316505760512.0000000000 -1.8460028334 -0.1064272946 1.5483178765 0.5850337250 0.7976947576 0.1243571562 -0.0771615959298 +1413393316555760384.0000000000 -1.8658804790 -0.1012903450 1.5668783359 0.5837064614 0.7984745345 0.1249649644 -0.0781597232342 +1413393316605760512.0000000000 -1.8858648679 -0.0963963075 1.5847683727 0.5823447178 0.7992567292 0.1257369158 -0.0790793172037 +1413393316655760384.0000000000 -1.9060412409 -0.0917981272 1.6014692498 0.5803904905 0.8004115966 0.1268387797 -0.0800004906719 +1413393316705760512.0000000000 -1.9263848057 -0.0872010250 1.6164872183 0.5784458154 0.8015571606 0.1281500127 -0.0805241037536 +1413393316755760384.0000000000 -1.9468669740 -0.0826511037 1.6292835455 0.5765032722 0.8026471625 0.1299407133 -0.0807274465753 +1413393316805760512.0000000000 -1.9677075685 -0.0779507409 1.6395566372 0.5755039777 0.8030292250 0.1314213247 -0.0816558076629 +1413393316855760384.0000000000 -1.9885905901 -0.0731521728 1.6462871987 0.5741581803 0.8036244031 0.1333437135 -0.0821562955551 +1413393316905760512.0000000000 -2.0096231953 -0.0682166540 1.6495736683 0.5738400970 0.8034783823 0.1353551720 -0.0825167237731 +1413393316955760384.0000000000 -2.0309451360 -0.0630383694 1.6499289562 0.5728482144 0.8038201597 0.1367590536 -0.083755807873 +1413393317005760512.0000000000 -2.0525367013 -0.0574022657 1.6487211692 0.5737941824 0.8028153321 0.1382066324 -0.0845381899401 +1413393317055760384.0000000000 -2.0744024463 -0.0515159455 1.6458304946 0.5761141109 0.8009250505 0.1394105029 -0.0847130829794 +1413393317105760512.0000000000 -2.0965903554 -0.0459014736 1.6411612561 0.5794677683 0.7982583383 0.1401770428 -0.0857387166656 +1413393317155760384.0000000000 -2.1190881252 -0.0404578134 1.6359707258 0.5830059829 0.7954779194 0.1408297951 -0.086520936402 +1413393317205760512.0000000000 -2.1415484199 -0.0353030463 1.6309643615 0.5866988155 0.7927042465 0.1412938713 -0.0862584454206 +1413393317255760384.0000000000 -2.1643314628 -0.0308167073 1.6264389115 0.5891335442 0.7908936725 0.1410153888 -0.0867382619722 +1413393317305760512.0000000000 -2.1873322298 -0.0270302001 1.6224340807 0.5914606659 0.7891877119 0.1407547842 -0.0868626889489 +1413393317355760384.0000000000 -2.2104761109 -0.0239461157 1.6191621596 0.5931224080 0.7880572307 0.1398180785 -0.0873070172176 +1413393317405760512.0000000000 -2.2335362667 -0.0219514617 1.6160636970 0.5942410221 0.7874133670 0.1392143186 -0.0864706339648 +1413393317455760384.0000000000 -2.2566535938 -0.0210189042 1.6132914249 0.5945591907 0.7872832570 0.1389402533 -0.0859072060013 +1413393317505760512.0000000000 -2.2798676225 -0.0210564999 1.6098947457 0.5951414865 0.7869768597 0.1385362304 -0.0853331484472 +1413393317555760384.0000000000 -2.3030624187 -0.0223955497 1.6045496121 0.5960360015 0.7864985508 0.1374420770 -0.085268927656 +1413393317605760512.0000000000 -2.3264278215 -0.0251589493 1.5966411372 0.5951286968 0.7872783748 0.1369853782 -0.0851445880443 +1413393317655760384.0000000000 -2.3498265725 -0.0287364453 1.5863032072 0.5949873138 0.7876040213 0.1356365715 -0.0852802588361 +1413393317705760512.0000000000 -2.3731992971 -0.0332511276 1.5739788044 0.5946431657 0.7881135931 0.1336154665 -0.0861590215037 +1413393317755760384.0000000000 -2.3963751971 -0.0387373661 1.5613275719 0.5941493884 0.7886485384 0.1326243335 -0.0862019334021 +1413393317805760512.0000000000 -2.4193272361 -0.0451709451 1.5495097378 0.5934585500 0.7894332503 0.1310906011 -0.0861240210686 +1413393317855760384.0000000000 -2.4418628927 -0.0524719739 1.5383025369 0.5925357762 0.7903527256 0.1306637701 -0.0846811802101 +1413393317905760512.0000000000 -2.4640515134 -0.0606479351 1.5274936526 0.5918949169 0.7911152755 0.1307752564 -0.0818221275861 +1413393317955760384.0000000000 -2.4862046705 -0.0696907420 1.5167451360 0.5899482098 0.7929346972 0.1297875283 -0.0798177497589 +1413393318005760512.0000000000 -2.5083545607 -0.0793857906 1.5060683750 0.5889706568 0.7940795136 0.1290111049 -0.0768597833371 +1413393318055760384.0000000000 -2.5308882778 -0.0898500399 1.4951478245 0.5861922938 0.7965861779 0.1266782311 -0.0760373699237 +1413393318105760512.0000000000 -2.5536061649 -0.1008086130 1.4843067433 0.5844505829 0.7983297570 0.1241055375 -0.0753984799572 +1413393318155760384.0000000000 -2.5765513136 -0.1122172092 1.4729967996 0.5818112038 0.8006803987 0.1209195675 -0.0760597161706 +1413393318205760512.0000000000 -2.5996496175 -0.1237370658 1.4614941027 0.5795950858 0.8027286629 0.1168562826 -0.07772283785 +1413393318255760384.0000000000 -2.6228635983 -0.1353216932 1.4499482827 0.5783739976 0.8039460219 0.1123823343 -0.0807745241732 +1413393318305760512.0000000000 -2.6457889025 -0.1467449326 1.4381579083 0.5783276260 0.8042845916 0.1081561186 -0.0834608089435 +1413393318355760384.0000000000 -2.6682176625 -0.1581243098 1.4257763256 0.5781570440 0.8046498620 0.1043274640 -0.0859582004485 +1413393318405760512.0000000000 -2.6899744815 -0.1694333121 1.4127325803 0.5778016569 0.8050665912 0.1020442683 -0.0871779575664 +1413393318455760384.0000000000 -2.7109388859 -0.1802772429 1.3993628358 0.5780281295 0.8050168947 0.0999442880 -0.0885574399558 +1413393318505760512.0000000000 -2.7308849913 -0.1907301607 1.3850628888 0.5781423790 0.8051087044 0.0982052404 -0.0889218449177 +1413393318555760384.0000000000 -2.7498595314 -0.2013933168 1.3701872351 0.5787592969 0.8047724539 0.0974979039 -0.0887306735784 +1413393318605760512.0000000000 -2.7678178415 -0.2118986339 1.3553277060 0.5783782015 0.8051080634 0.0967544922 -0.0889844401141 +1413393318655760384.0000000000 -2.7848059767 -0.2221667001 1.3411217075 0.5788120532 0.8048840512 0.0959847838 -0.0890235505584 +1413393318705760512.0000000000 -2.8009199562 -0.2322995156 1.3278567114 0.5784797150 0.8051118004 0.0954208176 -0.0897277869843 +1413393318755760384.0000000000 -2.8160164792 -0.2421629375 1.3161009840 0.5788477499 0.8047979656 0.0951052773 -0.0905013986718 +1413393318805760512.0000000000 -2.8298901759 -0.2518848601 1.3055152377 0.5798292846 0.8040767854 0.0959771222 -0.0897046034559 +1413393318855760384.0000000000 -2.8427000898 -0.2613536697 1.2965451124 0.5822778836 0.8023035294 0.0968159256 -0.0888154800514 +1413393318905760512.0000000000 -2.8546654352 -0.2708088028 1.2893934017 0.5870704445 0.7987566472 0.0974821042 -0.0885062206171 +1413393318955760384.0000000000 -2.8656458732 -0.2807213345 1.2831977933 0.5917105416 0.7952481668 0.0983613511 -0.0882271660691 +1413393319005760512.0000000000 -2.8754133812 -0.2914812267 1.2777224813 0.5951852940 0.7926208920 0.0990448561 -0.0877308600287 +1413393319055760384.0000000000 -2.8842574498 -0.3033611226 1.2727631867 0.5955114029 0.7922575838 0.1002790358 -0.0873968247152 +1413393319105760512.0000000000 -2.8923319681 -0.3162757467 1.2688082688 0.5927360857 0.7942081826 0.1004497478 -0.0883580418716 +1413393319155760384.0000000000 -2.8994176235 -0.3300401845 1.2658120775 0.5881322143 0.7975317826 0.1007924536 -0.0887943443445 +1413393319205760512.0000000000 -2.9057142863 -0.3444863142 1.2648622216 0.5845924635 0.7999529426 0.1012316297 -0.0898838052296 +1413393319255760384.0000000000 -2.9111131555 -0.3592482998 1.2646904412 0.5797874209 0.8033233586 0.1020460099 -0.0900263289731 +1413393319305760512.0000000000 -2.9155832123 -0.3740782318 1.2643527214 0.5753366823 0.8063980319 0.1024652536 -0.0906133979264 +1413393319355760384.0000000000 -2.9193126842 -0.3888316178 1.2627694876 0.5713840059 0.8091374767 0.1028630582 -0.0907527012099 +1413393319405760512.0000000000 -2.9224485456 -0.4031078464 1.2591171577 0.5682578023 0.8112872336 0.1038123803 -0.0901059615811 +1413393319455760384.0000000000 -2.9252734210 -0.4163021313 1.2536743574 0.5655642297 0.8131149686 0.1042844732 -0.0900327641617 +1413393319505760512.0000000000 -2.9276555428 -0.4287677904 1.2467833901 0.5610221340 0.8161353545 0.1048014627 -0.0905201731367 +1413393319555760384.0000000000 -2.9298023115 -0.4399404211 1.2384234397 0.5555792453 0.8197232041 0.1037324771 -0.0928716541267 +1413393319605760512.0000000000 -2.9315298752 -0.4496714566 1.2288182171 0.5510182230 0.8226246059 0.1027342452 -0.0954638707284 +1413393319655760384.0000000000 -2.9323805426 -0.4583915869 1.2182234250 0.5462175556 0.8256645825 0.1016186423 -0.0979695398133 +1413393319705760512.0000000000 -2.9321047108 -0.4655667611 1.2074742359 0.5433445144 0.8274316349 0.1013224810 -0.0993347022938 +1413393319755760384.0000000000 -2.9311200574 -0.4698314580 1.1959471443 0.5455658075 0.8259441311 0.1042450621 -0.0964738774176 +1413393319805760512.0000000000 -2.9294876252 -0.4717536814 1.1827066771 0.5483918831 0.8240833437 0.1095581877 -0.0902772877037 +1413393319855760384.0000000000 -2.9279565817 -0.4712777839 1.1684761250 0.5530398805 0.8208627317 0.1142534086 -0.0853078240598 +1413393319905760512.0000000000 -2.9265404902 -0.4695457977 1.1534597970 0.5577647644 0.8175059518 0.1186212894 -0.0806937178993 +1413393319955760384.0000000000 -2.9254167874 -0.4673135520 1.1368455492 0.5621811405 0.8143120659 0.1220887249 -0.077088052011 +1413393320005760512.0000000000 -2.9248317157 -0.4643448217 1.1194322562 0.5662386492 0.8113385893 0.1247862182 -0.0743766463727 +1413393320055760384.0000000000 -2.9248265727 -0.4612990481 1.1015690044 0.5694985515 0.8089461337 0.1262601679 -0.0730473994205 +1413393320105760512.0000000000 -2.9253172077 -0.4583161382 1.0835340798 0.5735237378 0.8060400121 0.1268712481 -0.0726202966671 +1413393320155760384.0000000000 -2.9265225540 -0.4548506318 1.0658115665 0.5787642415 0.8023281090 0.1266879391 -0.0724687822105 +1413393320205760512.0000000000 -2.9284131098 -0.4515968634 1.0484107263 0.5837582242 0.7988215319 0.1253572949 -0.0734577734299 +1413393320255760384.0000000000 -2.9308269286 -0.4490339581 1.0324336749 0.5867980930 0.7967486816 0.1243785832 -0.0734132444165 +1413393320305760512.0000000000 -2.9337633083 -0.4473720680 1.0187435100 0.5854141601 0.7980095324 0.1228004820 -0.0734240360324 +1413393320355760384.0000000000 -2.9373126068 -0.4464510820 1.0090899244 0.5834934567 0.7996340554 0.1213117151 -0.0735134763751 +1413393320405760512.0000000000 -2.9414495999 -0.4465035460 1.0034283050 0.5788524162 0.8031681072 0.1197556436 -0.0742257214851 +1413393320455760384.0000000000 -2.9459927138 -0.4468800954 1.0014113689 0.5739547779 0.8068766029 0.1188096046 -0.0735550029843 +1413393320505760512.0000000000 -2.9510391027 -0.4469193252 1.0022810892 0.5704592837 0.8095325853 0.1186750292 -0.0717595740658 +1413393320555760384.0000000000 -2.9565729855 -0.4468314847 1.0036197527 0.5689867908 0.8106970091 0.1187440017 -0.0701730248472 +1413393320605760512.0000000000 -2.9625826600 -0.4464217240 1.0021292439 0.5683456748 0.8113467922 0.1180948372 -0.068943355405 +1413393320655760384.0000000000 -2.9689757537 -0.4456320512 0.9947660118 0.5671488865 0.8123353394 0.1187245619 -0.0660145077848 +1413393320705760512.0000000000 -2.9761855059 -0.4444909372 0.9813183903 0.5667816967 0.8126977323 0.1186089452 -0.0649062576888 +1413393320755760384.0000000000 -2.9841030661 -0.4432380951 0.9610407520 0.5682009467 0.8117961696 0.1181076910 -0.0646934041854 +1413393320805760512.0000000000 -2.9925608244 -0.4420202482 0.9340892439 0.5703245630 0.8103753956 0.1169400473 -0.0659290252334 +1413393320855760384.0000000000 -2.9952413351 -0.4430346464 0.9261549605 0.5854086724 0.8000152068 0.1130937441 -0.0669489372375 +1413393320905760512.0000000000 -2.9900833100 -0.4459609339 0.9436582747 0.5897353911 0.7969162564 0.1150412871 -0.0624672006264 +1413393320955760384.0000000000 -2.9847547519 -0.4499899052 0.9513694592 0.5749904556 0.8075239044 0.1195534725 -0.0547547904124 +1413393321005760512.0000000000 -2.9802627922 -0.4539433853 0.9526212259 0.5647377300 0.8143194798 0.1254143255 -0.0471839814358 +1413393321055760384.0000000000 -2.9775167230 -0.4572419985 0.9473476781 0.5630128029 0.8151887522 0.1278091939 -0.0463539853612 +1413393321105760512.0000000000 -2.9761231580 -0.4595786990 0.9330802608 0.5687946278 0.8113039212 0.1251061689 -0.0510594289274 +1413393321155760384.0000000000 -2.9742106819 -0.4613911817 0.9266386578 0.5901035982 0.7964966901 0.1099039593 -0.0727453490719 +1413393321205760512.0000000000 -2.9714087436 -0.4631595802 0.9384642730 0.6008250630 0.7886575761 0.1126579225 -0.0658533510303 +1413393321255760384.0000000000 -2.9720419152 -0.4641751172 0.9410204274 0.5960385963 0.7924161384 0.1161222151 -0.0577086343401 +1413393321305760512.0000000000 -2.9724203179 -0.4638321318 0.9309808460 0.5832989510 0.8026692120 0.1126706924 -0.0528184141476 +1413393321355760384.0000000000 -2.9715430487 -0.4626623309 0.9288923119 0.5838870579 0.8022979008 0.1056630954 -0.0650330087238 +1413393321405760512.0000000000 -2.9694206274 -0.4634202291 0.9337895454 0.5888988892 0.7986780834 0.1065556221 -0.0629072080731 +1413393321455760384.0000000000 -2.9711543921 -0.4644426423 0.9335037895 0.5919447732 0.7965027345 0.1053561315 -0.0639129489065 +1413393321505760512.0000000000 -2.9713543761 -0.4639758143 0.9313748725 0.5911867908 0.7969596557 0.1083625133 -0.06009202415 +1413393321555760384.0000000000 -2.9707488073 -0.4635080173 0.9323754683 0.5884076990 0.7990787177 0.1061871207 -0.0630387038044 +1413393321605760512.0000000000 -2.9708707503 -0.4635680226 0.9315992683 0.5890776692 0.7985583704 0.1067947813 -0.0623450343308 +1413393321655760384.0000000000 -2.9712777656 -0.4641928029 0.9319170019 0.5905810139 0.7974631337 0.1068392377 -0.0620644317546 +1413393321705760512.0000000000 -2.9707208019 -0.4639898334 0.9320624347 0.5910484742 0.7971157053 0.1066957306 -0.0623239489462 +1413393321755760384.0000000000 -2.9708708517 -0.4639568395 0.9315485788 0.5895548638 0.7982198641 0.1065933735 -0.0625137095616 +1413393321805760512.0000000000 -2.9709248219 -0.4640198434 0.9317088918 0.5903980048 0.7976059004 0.1066874263 -0.0622319583756 +1413393321855760384.0000000000 -2.9707694231 -0.4641894975 0.9317111766 0.5906142222 0.7974490633 0.1064465002 -0.0626017142992 +1413393321905760512.0000000000 -2.9707135690 -0.4641217871 0.9317932345 0.5907793120 0.7973303463 0.1064925639 -0.0624776537306 +1413393321955760384.0000000000 -2.9710488937 -0.4641914066 0.9316062530 0.5901557584 0.7977867509 0.1064677528 -0.0625867277978 +1413393322005760512.0000000000 -2.9707429938 -0.4641372474 0.9317764682 0.5909067572 0.7972348767 0.1065008652 -0.0624765658557 +1413393322055760384.0000000000 -2.9709203930 -0.4642166657 0.9317456384 0.5908324101 0.7972813621 0.1063791511 -0.0627930655624 +1413393322105760512.0000000000 -2.9709121141 -0.4641252254 0.9316926485 0.5907271951 0.7973615699 0.1065167284 -0.0625307472753 +1413393322155760384.0000000000 -2.9708751111 -0.4641453272 0.9317085294 0.5906803100 0.7973909773 0.1064606416 -0.0626939592358 +1413393322205760512.0000000000 -2.9709237076 -0.4641897782 0.9317905564 0.5909284326 0.7971975059 0.1065146544 -0.0627244175379 +1413393322255760384.0000000000 -2.9709631319 -0.4641280559 0.9317502793 0.5908650880 0.7972642419 0.1063972545 -0.0626721678629 +1413393322305760512.0000000000 -2.9709049681 -0.4640995773 0.9317072454 0.5907861092 0.7973219340 0.1064185589 -0.0626466048786 +1413393322355760384.0000000000 -2.9709603754 -0.4642173767 0.9317002069 0.5909382754 0.7971992594 0.1064566010 -0.0627079554243 +1413393322405760512.0000000000 -2.9708979306 -0.4642441799 0.9316147700 0.5908701901 0.7972582487 0.1064183655 -0.0626644629391 +1413393322455760384.0000000000 -2.9708747336 -0.4642449460 0.9315398030 0.5908890685 0.7972549816 0.1063772332 -0.0625978219236 +1413393322505760512.0000000000 -2.9708861320 -0.4643313659 0.9315282733 0.5909326881 0.7972114682 0.1064108688 -0.0626830125899 +1413393322555760384.0000000000 -2.9708119069 -0.4643344298 0.9314937063 0.5909823449 0.7971623221 0.1065017495 -0.0626855455971 +1413393322605760512.0000000000 -2.9708060348 -0.4643322914 0.9314504898 0.5909459676 0.7972020461 0.1064347435 -0.0626371012811 +1413393322655760384.0000000000 -2.9707447579 -0.4643138841 0.9314634243 0.5909319584 0.7972192298 0.1063926603 -0.0626220569442 +1413393322705760512.0000000000 -2.9707135414 -0.4643391395 0.9315317667 0.5909080391 0.7972291084 0.1064176907 -0.062679447719 +1413393322755760384.0000000000 -2.9707380468 -0.4643364347 0.9315618540 0.5909073240 0.7972227874 0.1064331013 -0.0627403906436 +1413393322805760512.0000000000 -2.9707339326 -0.4643153315 0.9315406756 0.5909739478 0.7971763959 0.1064418687 -0.0626874432451 +1413393322855760384.0000000000 -2.9707318661 -0.4642623863 0.9315151272 0.5909679022 0.7971800583 0.1064447054 -0.0626930446853 +1413393322905760512.0000000000 -2.9707769198 -0.4642346755 0.9315022783 0.5909449615 0.7971965401 0.1064323970 -0.0627206002679 +1413393322955760384.0000000000 -2.9707604282 -0.4642094687 0.9315318159 0.5909958360 0.7971625146 0.1063960397 -0.0627353952431 +1413393323005760512.0000000000 -2.9707611612 -0.4642161774 0.9315469138 0.5910014994 0.7971524524 0.1064177720 -0.0627730289875 +1413393323055760384.0000000000 -2.9707313327 -0.4642425476 0.9315355683 0.5910248368 0.7971275458 0.1064412236 -0.0628298008719 +1413393323105760512.0000000000 -2.9706668618 -0.4643030909 0.9315335754 0.5910136180 0.7971284669 0.1064802325 -0.0628575421541 +1413393323155760384.0000000000 -2.9706400621 -0.4643520599 0.9316013317 0.5910510305 0.7970976685 0.1064788076 -0.0628987268585 +1413393323205760512.0000000000 -2.9706265091 -0.4643730777 0.9316424742 0.5910707855 0.7970802483 0.1064953310 -0.0629058725028 +1413393323255760384.0000000000 -2.9706219127 -0.4643869543 0.9316914180 0.5910514491 0.7970946126 0.1065006061 -0.0628966133061 +1413393323305760512.0000000000 -2.9706557568 -0.4644120751 0.9317771794 0.5910570235 0.7970931399 0.1064715311 -0.0629121154791 +1413393323355760384.0000000000 -2.9706567765 -0.4644153132 0.9318426760 0.5910509887 0.7970956485 0.1064999841 -0.0628888638486 +1413393323405760512.0000000000 -2.9707035513 -0.4643361805 0.9319041021 0.5910038485 0.7971370988 0.1064556700 -0.062881532808 +1413393323455760384.0000000000 -2.9707427269 -0.4643246750 0.9317924940 0.5910151588 0.7971222675 0.1064629479 -0.0629508808077 +1413393323505760512.0000000000 -2.9707899022 -0.4643677380 0.9315864884 0.5910582495 0.7970860975 0.1064542715 -0.0630189419346 +1413393323555760384.0000000000 -2.9708414608 -0.4643948258 0.9314300587 0.5910204641 0.7971097036 0.1064931286 -0.0630090866653 +1413393323605760512.0000000000 -2.9708754153 -0.4643748174 0.9312876345 0.5910070697 0.7971226451 0.1064601821 -0.0630266753925 +1413393323655760384.0000000000 -2.9708864274 -0.4643667443 0.9311920265 0.5909944901 0.7971340550 0.1064526070 -0.0630131214291 +1413393323705760512.0000000000 -2.9708781710 -0.4643701849 0.9311185574 0.5910122189 0.7971174534 0.1064792140 -0.0630119002839 +1413393323755760384.0000000000 -2.9708300611 -0.4643689489 0.9310657747 0.5909788592 0.7971451568 0.1064571106 -0.0630116700181 +1413393323805760512.0000000000 -2.9708217068 -0.4643838941 0.9310476473 0.5909678705 0.7971521496 0.1064523466 -0.0630343095945 +1413393323855760384.0000000000 -2.9708253803 -0.4643854435 0.9310427602 0.5909862041 0.7971339281 0.1065065370 -0.0630013083356 +1413393323905760512.0000000000 -2.9708316784 -0.4643761279 0.9310449071 0.5909640899 0.7971526518 0.1064594823 -0.0630513498292 +1413393323955760384.0000000000 -2.9708187837 -0.4643851439 0.9310860007 0.5909804759 0.7971386149 0.1065116171 -0.0629871514913 +1413393324005760512.0000000000 -2.9708022696 -0.4643819564 0.9311411237 0.5909741441 0.7971456499 0.1064636073 -0.0630386713193 +1413393324055760384.0000000000 -2.9707757255 -0.4643803041 0.9311773449 0.5909713059 0.7971469647 0.1065067679 -0.0629757150176 +1413393324105760512.0000000000 -2.9707500474 -0.4643977593 0.9311839106 0.5909464625 0.7971637817 0.1064944829 -0.063016733612 +1413393324155760384.0000000000 -2.9707542291 -0.4644328318 0.9311802949 0.5909552165 0.7971575172 0.1065270228 -0.0629588619591 +1413393324205760512.0000000000 -2.9707583959 -0.4644604682 0.9312306213 0.5909749626 0.7971452834 0.1064961320 -0.0629806682168 +1413393324255760384.0000000000 -2.9707775239 -0.4644825679 0.9312591118 0.5909428882 0.7971656627 0.1065257216 -0.0629736431772 +1413393324305760512.0000000000 -2.9707740490 -0.4644756048 0.9312617192 0.5909235711 0.7971792332 0.1065204493 -0.0629920401822 +1413393324355760384.0000000000 -2.9707854689 -0.4644429564 0.9312483940 0.5909155311 0.7971850571 0.1065269263 -0.0629828064834 +1413393324405760512.0000000000 -2.9708334684 -0.4644442764 0.9312139223 0.5909176391 0.7971768046 0.1065593220 -0.0630126722189 +1413393324455760384.0000000000 -2.9708754010 -0.4644491840 0.9311843886 0.5909223824 0.7971751519 0.1065316186 -0.0630359378434 +1413393324505760512.0000000000 -2.9708822434 -0.4644756013 0.9311198106 0.5908861865 0.7971939687 0.1066015194 -0.0630191003066 +1413393324555760384.0000000000 -2.9708753570 -0.4645007892 0.9310679677 0.5908536747 0.7972150749 0.1066184159 -0.0630283503374 +1413393324605760512.0000000000 -2.9708418975 -0.4644965461 0.9310345059 0.5908602596 0.7972065425 0.1066585984 -0.0630065521153 +1413393324655760384.0000000000 -2.9708586777 -0.4644782819 0.9310539133 0.5908483280 0.7972124842 0.1066806835 -0.063005874603 +1413393324705760512.0000000000 -2.9708752459 -0.4644821407 0.9310684307 0.5908352616 0.7972179593 0.1067091618 -0.0630109022 +1413393324755760384.0000000000 -2.9708551405 -0.4644915927 0.9310839718 0.5908383709 0.7972121070 0.1067331049 -0.0630152383532 +1413393324805760512.0000000000 -2.9708264855 -0.4645017228 0.9311131598 0.5908398517 0.7972086496 0.1067365208 -0.0630393034499 +1413393324855760384.0000000000 -2.9707659318 -0.4644767571 0.9311508624 0.5908107523 0.7972279775 0.1067590459 -0.0630294608855 +1413393324905760512.0000000000 -2.9707075092 -0.4644681525 0.9311836765 0.5908178771 0.7972236740 0.1067383984 -0.0630520734221 +1413393324955760384.0000000000 -2.9706776068 -0.4644986208 0.9312193638 0.5907812083 0.7972489500 0.1067517622 -0.0630534454809 +1413393325005760512.0000000000 -2.9706511120 -0.4645091274 0.9312142024 0.5907805227 0.7972468936 0.1067537799 -0.0630824470932 +1413393325055760384.0000000000 -2.9706241658 -0.4645118248 0.9311938115 0.5907917693 0.7972386533 0.1067422149 -0.0631008279749 +1413393325105760512.0000000000 -2.9706576477 -0.4645311052 0.9311481018 0.5907786066 0.7972329199 0.1068179181 -0.0631683613574 +1413393325155760384.0000000000 -2.9707091698 -0.4645516687 0.9310934234 0.5907048074 0.7972911051 0.1067952635 -0.0631624564838 +1413393325205760512.0000000000 -2.9707682528 -0.4646001238 0.9310575138 0.5906780355 0.7973054359 0.1068091089 -0.0632085002303 +1413393325255760384.0000000000 -2.9708339983 -0.4646416966 0.9310151836 0.5907066364 0.7972815174 0.1068227019 -0.0632199499178 +1413393325305760512.0000000000 -2.9709321784 -0.4646794980 0.9310052958 0.5906992630 0.7972770285 0.1068621479 -0.0632787631922 +1413393325355760384.0000000000 -2.9710356287 -0.4647183245 0.9310146351 0.5906733247 0.7972977766 0.1068386176 -0.0632991997062 +1413393325405760512.0000000000 -2.9711603003 -0.4647505950 0.9310668263 0.5906812667 0.7972907101 0.1068235451 -0.0633395205082 +1413393325455760384.0000000000 -2.9712838138 -0.4647519531 0.9311527960 0.5906977919 0.7973099620 0.1066759084 -0.0631917219542 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_02_medium.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_02_medium.txt new file mode 100644 index 0000000000000000000000000000000000000000..1a537a7340ef6d3a7a14684a189c6239d7e199f2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_02_medium.txt @@ -0,0 +1,2310 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1413393887255760384.0000000000 -1.0015689347 0.4141769115 1.3066970514 0.4134526643 0.5539092534 0.5832203034 -0.426726506144 +1413393887305760512.0000000000 -1.0027620519 0.4140434295 1.3065348813 0.4134223843 0.5539398609 0.5832670628 -0.426652195718 +1413393887355760384.0000000000 -1.0036602084 0.4139507385 1.3064876562 0.4134479154 0.5540319114 0.5831752378 -0.42663345443 +1413393887405760512.0000000000 -1.0042670068 0.4139217677 1.3063770302 0.4134436852 0.5541313235 0.5831565583 -0.426533965843 +1413393887455760384.0000000000 -1.0046488641 0.4138853406 1.3064192335 0.4133100632 0.5541927127 0.5831801917 -0.426551395251 +1413393887505760512.0000000000 -1.0048077485 0.4138484092 1.3064169974 0.4132240486 0.5541575597 0.5832649471 -0.426564515897 +1413393887555760384.0000000000 -1.0048687556 0.4138832521 1.3065311577 0.4131578907 0.5541708025 0.5832452355 -0.426638341424 +1413393887605760512.0000000000 -1.0048283979 0.4140305739 1.3066988386 0.4133851147 0.5541721281 0.5831950694 -0.426485064676 +1413393887655760384.0000000000 -1.0046467253 0.4140420566 1.3070645117 0.4133934840 0.5542450580 0.5828560534 -0.426845480252 +1413393887705760512.0000000000 -1.0044945897 0.4139995671 1.3068919150 0.4132057358 0.5543854918 0.5829076769 -0.42677439763 +1413393887755760384.0000000000 -1.0044440076 0.4140094801 1.3069943763 0.4132768958 0.5543515986 0.5828154230 -0.426875503374 +1413393887805760512.0000000000 -1.0042420762 0.4139805240 1.3067851678 0.4132096625 0.5543802023 0.5830126726 -0.426634023123 +1413393887855760384.0000000000 -1.0041235173 0.4139112598 1.3068017733 0.4131375062 0.5544545995 0.5829280708 -0.426722816722 +1413393887905760512.0000000000 -1.0039619892 0.4139265665 1.3065399419 0.4129984274 0.5545791085 0.5830808689 -0.426486824738 +1413393887955760384.0000000000 -1.0038449911 0.4138327474 1.3065811472 0.4129184977 0.5546279859 0.5829809114 -0.426637279761 +1413393888005760512.0000000000 -1.0037483812 0.4138314616 1.3063460576 0.4129582436 0.5546043031 0.5830724228 -0.426504520355 +1413393888055760384.0000000000 -1.0037815965 0.4137857839 1.3063605555 0.4128046054 0.5547716955 0.5830842657 -0.426419350832 +1413393888105760512.0000000000 -1.0037707171 0.4137491940 1.3062369105 0.4127226935 0.5547742756 0.5831448960 -0.426412372791 +1413393888155760384.0000000000 -1.0037652803 0.4137692930 1.3063151557 0.4128571343 0.5547641744 0.5829950478 -0.426500259865 +1413393888205760512.0000000000 -1.0037872369 0.4137185192 1.3061853794 0.4126933747 0.5548269671 0.5831102407 -0.426419584777 +1413393888255760384.0000000000 -1.0037993975 0.4136953173 1.3062700691 0.4126898252 0.5549183202 0.5830525105 -0.426383086046 +1413393888305760512.0000000000 -1.0037677772 0.4136519845 1.3062613802 0.4126953662 0.5549096247 0.5830796996 -0.42635185824 +1413393888355760384.0000000000 -1.0037583751 0.4136133894 1.3064282619 0.4126247319 0.5549605116 0.5830110005 -0.426447927041 +1413393888405760512.0000000000 -1.0037393082 0.4137123863 1.3065923362 0.4128851676 0.5548962836 0.5828873473 -0.426448464771 +1413393888455760384.0000000000 -1.0037349021 0.4137138645 1.3066596116 0.4126396667 0.5550228893 0.5830100103 -0.426353639251 +1413393888505760512.0000000000 -1.0036625530 0.4138278599 1.3067487905 0.4125873879 0.5550400865 0.5830337851 -0.42634933463 +1413393888555760384.0000000000 -1.0034912114 0.4138996760 1.3069164486 0.4127200841 0.5548990855 0.5828926203 -0.42659738663 +1413393888605760512.0000000000 -1.0034034794 0.4140050280 1.3069153862 0.4126771881 0.5549121213 0.5828975075 -0.426615250282 +1413393888655760384.0000000000 -1.0035507214 0.4139806751 1.3071863277 0.4126219799 0.5549586060 0.5828023949 -0.426738111546 +1413393888705760512.0000000000 -1.0036068411 0.4140295662 1.3072233083 0.4126683051 0.5548978897 0.5828460991 -0.426712580964 +1413393888755760384.0000000000 -1.0037007870 0.4140089642 1.3074204986 0.4127127405 0.5548782759 0.5826742380 -0.42692976602 +1413393888805760512.0000000000 -1.0037276022 0.4139918914 1.3073720623 0.4127454976 0.5547988322 0.5826806355 -0.426992607637 +1413393888855760384.0000000000 -1.0037414006 0.4139462377 1.3072795454 0.4125514441 0.5549658337 0.5826919512 -0.426947677569 +1413393888905760512.0000000000 -1.0037191583 0.4141080626 1.3071521811 0.4126874787 0.5548919366 0.5826769456 -0.426932735515 +1413393888955760384.0000000000 -1.0036212516 0.4140177539 1.3073493522 0.4127004833 0.5548733323 0.5825918640 -0.427060436233 +1413393889005760512.0000000000 -1.0035699720 0.4138960939 1.3077822374 0.4129722094 0.5546397121 0.5822865187 -0.427517431416 +1413393889055760384.0000000000 -1.0034789532 0.4138708704 1.3077337401 0.4131110112 0.5545017669 0.5824278928 -0.427369667485 +1413393889105760512.0000000000 -1.0035506365 0.4136699004 1.3079488624 0.4127938910 0.5547108212 0.5823144111 -0.42755939365 +1413393889155760384.0000000000 -1.0036481401 0.4136440280 1.3084684324 0.4129423822 0.5547408763 0.5819975612 -0.427808354162 +1413393889205760512.0000000000 -1.0035937412 0.4138235194 1.3087838196 0.4128172241 0.5546720314 0.5820596927 -0.427933863027 +1413393889255760384.0000000000 -1.0037358386 0.4138864839 1.3094702870 0.4131433935 0.5543906461 0.5818917406 -0.428212038723 +1413393889305760512.0000000000 -1.0037740181 0.4140024090 1.3094881255 0.4125670485 0.5544984452 0.5824079363 -0.427926279321 +1413393889355760384.0000000000 -1.0037625757 0.4143053200 1.3092636718 0.4116525339 0.5553536808 0.5829383503 -0.426974660106 +1413393889405760512.0000000000 -1.0034717564 0.4146225509 1.3093363637 0.4106381299 0.5561874250 0.5833279752 -0.426333610972 +1413393889455760384.0000000000 -1.0028233740 0.4150270286 1.3093176181 0.4102355951 0.5568558702 0.5836601527 -0.42539290361 +1413393889505760512.0000000000 -1.0019988383 0.4153375562 1.3091772244 0.4085503066 0.5583643110 0.5843136953 -0.424138478106 +1413393889555760384.0000000000 -1.0008560730 0.4160801191 1.3090515189 0.4054826051 0.5610672247 0.5868988383 -0.419925207583 +1413393889605760512.0000000000 -0.9998563216 0.4171713576 1.3099825148 0.4027055861 0.5636930671 0.5894545791 -0.415477600093 +1413393889655760384.0000000000 -0.9986161515 0.4190115648 1.3122965886 0.4007624433 0.5661639527 0.5924582079 -0.409684164505 +1413393889705760512.0000000000 -0.9979749399 0.4211939707 1.3171381173 0.4016068261 0.5663673901 0.5955658178 -0.404031302337 +1413393889755760384.0000000000 -0.9977117647 0.4234769859 1.3250910732 0.4016388124 0.5669316505 0.5993223189 -0.397602221021 +1413393889805760512.0000000000 -0.9987136208 0.4255244307 1.3377333103 0.4027304937 0.5668051748 0.6016513919 -0.393135658331 +1413393889855760384.0000000000 -1.0009432447 0.4271657782 1.3542762033 0.4050392236 0.5654641601 0.6049723748 -0.38755894607 +1413393889905760512.0000000000 -1.0046833825 0.4280030634 1.3754402363 0.4092812217 0.5623530529 0.6078626654 -0.383080808033 +1413393889955760384.0000000000 -1.0104781987 0.4275245676 1.4008962637 0.4159938343 0.5578582020 0.6087626451 -0.380987399015 +1413393890005760512.0000000000 -1.0177548870 0.4250496073 1.4296801558 0.4228650312 0.5527084736 0.6090305249 -0.380500102956 +1413393890055760384.0000000000 -1.0261330334 0.4202013271 1.4612158895 0.4265665048 0.5505797078 0.6065418187 -0.383418863034 +1413393890105760512.0000000000 -1.0351103533 0.4129912904 1.4940688847 0.4266108852 0.5510700383 0.6027883956 -0.38855001695 +1413393890155760384.0000000000 -1.0443979859 0.4040595862 1.5254815943 0.4262669039 0.5518279341 0.5986037124 -0.394279156528 +1413393890205760512.0000000000 -1.0538482785 0.3938602042 1.5525261114 0.4249641566 0.5532638123 0.5950439406 -0.399032991566 +1413393890255760384.0000000000 -1.0636441578 0.3826886991 1.5746393018 0.4238529459 0.5543404966 0.5919483627 -0.403301909171 +1413393890305760512.0000000000 -1.0735950562 0.3708621897 1.5916572038 0.4221833705 0.5559382947 0.5893547505 -0.406638404783 +1413393890355760384.0000000000 -1.0835374506 0.3585698211 1.6033480253 0.4205927496 0.5573788451 0.5876401968 -0.408790363277 +1413393890405760512.0000000000 -1.0934684606 0.3458286240 1.6096311930 0.4189960473 0.5587140674 0.5860679434 -0.410859183938 +1413393890455760384.0000000000 -1.1035351801 0.3328223206 1.6117159823 0.4189237256 0.5590194678 0.5833260303 -0.41440425811 +1413393890505760512.0000000000 -1.1137896604 0.3194662608 1.6116257710 0.4214425765 0.5572424147 0.5786071504 -0.420809709296 +1413393890555760384.0000000000 -1.1237971964 0.3061850792 1.6124012038 0.4257293371 0.5538016622 0.5727335319 -0.428992484601 +1413393890605760512.0000000000 -1.1325836080 0.2933454584 1.6134021826 0.4308078227 0.5502640852 0.5683802190 -0.434232636941 +1413393890655760384.0000000000 -1.1393812728 0.2808462953 1.6137468780 0.4325275661 0.5490649090 0.5680729740 -0.434443007311 +1413393890705760512.0000000000 -1.1442158502 0.2684792862 1.6139555128 0.4310574983 0.5502934834 0.5705112879 -0.431141955286 +1413393890755760384.0000000000 -1.1473299598 0.2561635612 1.6148721555 0.4287969278 0.5519707293 0.5740314504 -0.42655527493 +1413393890805760512.0000000000 -1.1492255195 0.2437813751 1.6168883906 0.4257516845 0.5542712906 0.5773106054 -0.422174495219 +1413393890855760384.0000000000 -1.1503586842 0.2315483037 1.6199941058 0.4236894632 0.5560561779 0.5801524347 -0.417985547964 +1413393890905760512.0000000000 -1.1509619738 0.2190584431 1.6243578997 0.4217288830 0.5575330993 0.5819701320 -0.415466434232 +1413393890955760384.0000000000 -1.1513934352 0.2063544646 1.6296774429 0.4209461318 0.5580900467 0.5837318534 -0.413033869248 +1413393891005760512.0000000000 -1.1518354591 0.1933222582 1.6360258369 0.4201847551 0.5587386796 0.5848601009 -0.411332617218 +1413393891055760384.0000000000 -1.1523292935 0.1798784353 1.6432459317 0.4199364699 0.5585765492 0.5861959696 -0.409902287259 +1413393891105760512.0000000000 -1.1530699261 0.1660750141 1.6518774480 0.4201011369 0.5584602285 0.5858741545 -0.410351901569 +1413393891155760384.0000000000 -1.1537056632 0.1519106207 1.6611898102 0.4190232220 0.5589656416 0.5859192483 -0.410701333505 +1413393891205760512.0000000000 -1.1544733199 0.1376033261 1.6707249928 0.4191217284 0.5586615444 0.5855484566 -0.41154253802 +1413393891255760384.0000000000 -1.1548958621 0.1230843207 1.6773294719 0.4196613254 0.5581203462 0.5844571376 -0.413274612568 +1413393891305760512.0000000000 -1.1558591587 0.1083807052 1.6806178299 0.4240898309 0.5545365850 0.5810088730 -0.418408509347 +1413393891355760384.0000000000 -1.1572438617 0.0934628965 1.6818264754 0.4355209507 0.5455186840 0.5715253428 -0.431381095389 +1413393891405760512.0000000000 -1.1573360854 0.0785049163 1.6810312975 0.4500182974 0.5334425685 0.5575139217 -0.449556209205 +1413393891455760384.0000000000 -1.1537136376 0.0632877556 1.6781489585 0.4634762726 0.5207354224 0.5429417657 -0.468229221266 +1413393891505760512.0000000000 -1.1451141820 0.0484709363 1.6738861984 0.4740905822 0.5107888348 0.5313832928 -0.481627119555 +1413393891555760384.0000000000 -1.1304503283 0.0340326467 1.6691211863 0.4794317984 0.5045967329 0.5244034361 -0.490436870572 +1413393891605760512.0000000000 -1.1087303912 0.0205572031 1.6640609547 0.4838770460 0.5008431598 0.5231545181 -0.491251955647 +1413393891655760384.0000000000 -1.0798337348 0.0073467323 1.6604153861 0.4837642952 0.5007025347 0.5226420033 -0.492051231854 +1413393891705760512.0000000000 -1.0437707624 -0.0052635224 1.6576638709 0.4840225211 0.5005756678 0.5231907349 -0.491342706066 +1413393891755760384.0000000000 -1.0018197591 -0.0175088143 1.6571472245 0.4832666292 0.5010583274 0.5242014885 -0.490516785763 +1413393891805760512.0000000000 -0.9534842568 -0.0291300252 1.6586472608 0.4825171236 0.5022608215 0.5257358639 -0.488378023716 +1413393891855760384.0000000000 -0.8979433981 -0.0403674279 1.6614388194 0.4799982145 0.5050917554 0.5290463944 -0.484348991298 +1413393891905760512.0000000000 -0.8359549320 -0.0512312899 1.6651667445 0.4741069862 0.5111151352 0.5355006279 -0.476679097204 +1413393891955760384.0000000000 -0.7680953784 -0.0617686191 1.6692540402 0.4644624316 0.5203532139 0.5448853994 -0.465410661496 +1413393892005760512.0000000000 -0.6955688333 -0.0721162188 1.6740569439 0.4518639242 0.5315650065 0.5563867330 -0.451321882038 +1413393892055760384.0000000000 -0.6197550929 -0.0824669140 1.6803318986 0.4400785931 0.5415060558 0.5670692982 -0.437646472045 +1413393892105760512.0000000000 -0.5423520666 -0.0929058419 1.6883672718 0.4305791452 0.5494027409 0.5752806508 -0.426392308574 +1413393892155760384.0000000000 -0.4645175623 -0.1034406016 1.6979334682 0.4239970650 0.5550524789 0.5814488902 -0.417205492132 +1413393892205760512.0000000000 -0.3867558681 -0.1144054161 1.7080390529 0.4194391605 0.5588571146 0.5855688297 -0.410924155724 +1413393892255760384.0000000000 -0.3095932063 -0.1255536814 1.7170437148 0.4177182386 0.5609122870 0.5882269615 -0.406051623831 +1413393892305760512.0000000000 -0.2338112072 -0.1371618908 1.7244609365 0.4163721628 0.5628848504 0.5888149289 -0.403846315749 +1413393892355760384.0000000000 -0.1594388466 -0.1490391141 1.7293075309 0.4147741920 0.5648539575 0.5901969295 -0.400711817597 +1413393892405760512.0000000000 -0.0862167207 -0.1611614067 1.7314249636 0.4130242324 0.5669392020 0.5912487558 -0.398014865888 +1413393892455760384.0000000000 -0.0143886162 -0.1735463241 1.7305205082 0.4119597956 0.5686265134 0.5919991025 -0.395588267935 +1413393892505760512.0000000000 0.0558371886 -0.1863383185 1.7271183795 0.4121430079 0.5693068739 0.5925873371 -0.39353280981 +1413393892555760384.0000000000 0.1245688787 -0.1997809922 1.7209748821 0.4106343257 0.5713312778 0.5928612561 -0.391759559669 +1413393892605760512.0000000000 0.1923397679 -0.2135885611 1.7125989075 0.4085427139 0.5733753960 0.5944136111 -0.388594859956 +1413393892655760384.0000000000 0.2583301210 -0.2277642765 1.7023916224 0.4048035872 0.5764181226 0.5972819339 -0.383575931386 +1413393892705760512.0000000000 0.3221486573 -0.2422960603 1.6917950652 0.3995531225 0.5806345703 0.6015594226 -0.375961512783 +1413393892755760384.0000000000 0.3835300632 -0.2573762612 1.6813375010 0.3918103004 0.5858270627 0.6068746721 -0.367415940724 +1413393892805760512.0000000000 0.4416617179 -0.2730140918 1.6712286556 0.3840332079 0.5904822143 0.6132038950 -0.357533541057 +1413393892855760384.0000000000 0.4951791830 -0.2893188206 1.6627751295 0.3772310506 0.5949061281 0.6179497221 -0.349172699589 +1413393892905760512.0000000000 0.5437140123 -0.3065223476 1.6556880191 0.3698587257 0.5990853858 0.6226017751 -0.341567348028 +1413393892955760384.0000000000 0.5865284766 -0.3247375434 1.6500288347 0.3634109707 0.6020806708 0.6270432738 -0.335034423582 +1413393893005760512.0000000000 0.6231183999 -0.3436934889 1.6458620326 0.3589751884 0.6041213584 0.6307082506 -0.329213154546 +1413393893055760384.0000000000 0.6530060022 -0.3638571408 1.6434428306 0.3561522123 0.6048763017 0.6329148235 -0.326648262853 +1413393893105760512.0000000000 0.6758146102 -0.3848728178 1.6424058627 0.3547801908 0.6050529925 0.6338661208 -0.325968761424 +1413393893155760384.0000000000 0.6915362802 -0.4067824488 1.6434709283 0.3560562881 0.6038390777 0.6328352040 -0.328818935914 +1413393893205760512.0000000000 0.7006522699 -0.4293065099 1.6461787402 0.3598676085 0.6006640663 0.6316977899 -0.332649794883 +1413393893255760384.0000000000 0.7034779586 -0.4527027389 1.6503768017 0.3632829259 0.5985775745 0.6294645168 -0.336904771609 +1413393893305760512.0000000000 0.7004052534 -0.4771380358 1.6561215698 0.3648827856 0.5982853755 0.6257745361 -0.342522104594 +1413393893355760384.0000000000 0.6922990642 -0.5022075112 1.6629043938 0.3636057815 0.5999959010 0.6220182836 -0.347690968034 +1413393893405760512.0000000000 0.6786736594 -0.5273461451 1.6708027770 0.3630888234 0.6015717462 0.6174253966 -0.353643634346 +1413393893455760384.0000000000 0.6604881293 -0.5524219449 1.6789417349 0.3616481070 0.6033210516 0.6136437370 -0.358686101634 +1413393893505760512.0000000000 0.6380716559 -0.5773041734 1.6872784649 0.3590795981 0.6049645514 0.6111821046 -0.362679154049 +1413393893555760384.0000000000 0.6113633234 -0.6013856885 1.6958537760 0.3575886418 0.6058880373 0.6088728006 -0.366475049946 +1413393893605760512.0000000000 0.5803123592 -0.6246311525 1.7046755875 0.3562885042 0.6066169738 0.6064016092 -0.370609548227 +1413393893655760384.0000000000 0.5454248848 -0.6467593867 1.7131852402 0.3530924020 0.6083094661 0.6049179948 -0.373308945238 +1413393893705760512.0000000000 0.5061034103 -0.6674212564 1.7221234074 0.3507060609 0.6100385188 0.6026488143 -0.376394302612 +1413393893755760384.0000000000 0.4624908519 -0.6864679355 1.7317968815 0.3504108226 0.6103382074 0.5998169383 -0.380682503548 +1413393893805760512.0000000000 0.4150678444 -0.7035296616 1.7418397614 0.3519579369 0.6093691756 0.5978667192 -0.38386222083 +1413393893855760384.0000000000 0.3637050786 -0.7188334861 1.7529752900 0.3573719813 0.6066770660 0.5938633518 -0.389300043574 +1413393893905760512.0000000000 0.3093177883 -0.7322986903 1.7640601898 0.3642554862 0.6019764268 0.5909679708 -0.394587353874 +1413393893955760384.0000000000 0.2522617141 -0.7439436499 1.7754465663 0.3723012964 0.5966947220 0.5869626115 -0.401026241169 +1413393894005760512.0000000000 0.1935179475 -0.7540784030 1.7866665278 0.3781522063 0.5931260324 0.5837810008 -0.405465364324 +1413393894055760384.0000000000 0.1336460406 -0.7629883301 1.7977803401 0.3820608471 0.5898395972 0.5824327117 -0.408522820744 +1413393894105760512.0000000000 0.0725086838 -0.7705246933 1.8094142229 0.3846852315 0.5879909179 0.5808586217 -0.410958896558 +1413393894155760384.0000000000 0.0107174331 -0.7768386104 1.8211360333 0.3848557575 0.5874907140 0.5800456965 -0.412659298813 +1413393894205760512.0000000000 -0.0518085610 -0.7817527380 1.8330815887 0.3842698575 0.5874464753 0.5794774892 -0.414064191725 +1413393894255760384.0000000000 -0.1151372824 -0.7848413910 1.8448357491 0.3842962256 0.5875926628 0.5787241004 -0.414885151918 +1413393894305760512.0000000000 -0.1789831013 -0.7865434075 1.8557309498 0.3832805496 0.5884139188 0.5775644565 -0.416274403573 +1413393894355760384.0000000000 -0.2432044565 -0.7866879465 1.8637047964 0.3834981902 0.5882821402 0.5770996935 -0.416904311992 +1413393894405760512.0000000000 -0.3079928299 -0.7855516187 1.8666271608 0.3843671933 0.5875802519 0.5776866518 -0.416280483151 +1413393894455760384.0000000000 -0.3733822856 -0.7832537866 1.8645552131 0.3860145646 0.5862309306 0.5784931646 -0.415537856769 +1413393894505760512.0000000000 -0.4393005105 -0.7798160617 1.8584292187 0.3881519300 0.5845782279 0.5789614390 -0.415222864002 +1413393894555760384.0000000000 -0.5059573181 -0.7752062024 1.8496986516 0.3915818944 0.5825474905 0.5791403316 -0.414606461075 +1413393894605760512.0000000000 -0.5728842418 -0.7695618119 1.8384140472 0.3940041817 0.5809103942 0.5800241074 -0.413371326475 +1413393894655760384.0000000000 -0.6404355422 -0.7629268628 1.8266063023 0.3969945932 0.5788726647 0.5800626826 -0.413314668512 +1413393894705760512.0000000000 -0.7079929279 -0.7554170787 1.8149164791 0.3990435586 0.5775266551 0.5801360259 -0.41312152258 +1413393894755760384.0000000000 -0.7754257086 -0.7471995168 1.8040092600 0.4005492799 0.5758123988 0.5805487012 -0.413477401214 +1413393894805760512.0000000000 -0.8427451907 -0.7382535195 1.7938173889 0.4000023937 0.5756392117 0.5806822684 -0.41406000313 +1413393894855760384.0000000000 -0.9100758498 -0.7286242813 1.7847354078 0.4010416804 0.5745005604 0.5802643750 -0.415220341201 +1413393894905760512.0000000000 -0.9771529292 -0.7187085570 1.7766602479 0.4030028513 0.5723002103 0.5798796231 -0.41689422384 +1413393894955760384.0000000000 -1.0440720269 -0.7082608225 1.7697719645 0.4064143594 0.5693749280 0.5785187018 -0.419470703962 +1413393895005760512.0000000000 -1.1105970449 -0.6973354709 1.7637546427 0.4100980571 0.5662475880 0.5766960703 -0.422616723748 +1413393895055760384.0000000000 -1.1763756513 -0.6861443340 1.7586098080 0.4132407731 0.5631222106 0.5747818076 -0.426323014867 +1413393895105760512.0000000000 -1.2411569220 -0.6745462169 1.7535188108 0.4148917502 0.5614571372 0.5749549121 -0.426682045169 +1413393895155760384.0000000000 -1.3048594637 -0.6626590655 1.7489243160 0.4147584953 0.5610352369 0.5763108497 -0.425535730725 +1413393895205760512.0000000000 -1.3673639643 -0.6505196900 1.7449775057 0.4127747079 0.5618624461 0.5781388279 -0.423890466774 +1413393895255760384.0000000000 -1.4291583271 -0.6381500413 1.7415920856 0.4121014685 0.5622143745 0.5793345012 -0.422443975622 +1413393895305760512.0000000000 -1.4902936491 -0.6258845312 1.7375171834 0.4124369790 0.5615439810 0.5792209880 -0.423163257968 +1413393895355760384.0000000000 -1.5502098591 -0.6136121186 1.7322669888 0.4141337808 0.5601816218 0.5786593695 -0.424079115646 +1413393895405760512.0000000000 -1.6092144136 -0.6011761500 1.7251309569 0.4158947953 0.5590061251 0.5771392128 -0.425974178162 +1413393895455760384.0000000000 -1.6665215296 -0.5883234032 1.7147803569 0.4173626651 0.5584351426 0.5767627722 -0.425797254416 +1413393895505760512.0000000000 -1.7226775727 -0.5750584763 1.7031098481 0.4192879749 0.5589781228 0.5747676967 -0.42589100396 +1413393895555760384.0000000000 -1.7777970731 -0.5613187167 1.6906532165 0.4202625593 0.5618705481 0.5726601864 -0.423958935901 +1413393895605760512.0000000000 -1.8319006765 -0.5473791190 1.6790187169 0.4211795002 0.5657927347 0.5691219443 -0.422595104577 +1413393895655760384.0000000000 -1.8847148654 -0.5328498697 1.6683522276 0.4244247569 0.5691493034 0.5661385895 -0.418831462099 +1413393895705760512.0000000000 -1.9365347111 -0.5177912755 1.6594693204 0.4312936492 0.5710169140 0.5609726964 -0.416215215923 +1413393895755760384.0000000000 -1.9870213488 -0.5025819702 1.6512864739 0.4363044157 0.5753562344 0.5550382479 -0.41296029319 +1413393895805760512.0000000000 -2.0365504036 -0.4869398469 1.6442465839 0.4427307811 0.5799991499 0.5474579815 -0.409731863572 +1413393895855760384.0000000000 -2.0853926030 -0.4706162892 1.6385126483 0.4492394175 0.5862595575 0.5393405996 -0.404469275286 +1413393895905760512.0000000000 -2.1311937491 -0.4539577373 1.6328246680 0.4566156063 0.5935465569 0.5306642211 -0.396988862894 +1413393895955760384.0000000000 -2.1746170688 -0.4372842919 1.6286564105 0.4624240939 0.6029958062 0.5202709680 -0.389715453769 +1413393896005760512.0000000000 -2.2160233662 -0.4203123104 1.6243738910 0.4696760600 0.6123605331 0.5112183133 -0.378252312955 +1413393896055760384.0000000000 -2.2558429515 -0.4036492183 1.6199612579 0.4772100617 0.6225151795 0.4998592552 -0.367268475787 +1413393896105760512.0000000000 -2.2945679274 -0.3870248868 1.6163954504 0.4863354318 0.6322294932 0.4875149716 -0.355095576175 +1413393896155760384.0000000000 -2.3319077571 -0.3713354325 1.6140009848 0.4946458442 0.6418513389 0.4735669762 -0.345089360306 +1413393896205760512.0000000000 -2.3683107947 -0.3558906339 1.6123291746 0.5045855211 0.6502308006 0.4593049676 -0.334114208927 +1413393896255760384.0000000000 -2.4026054665 -0.3410571287 1.6116151669 0.5171505450 0.6565654315 0.4429621637 -0.324440548413 +1413393896305760512.0000000000 -2.4347660340 -0.3276610499 1.6112795014 0.5284859687 0.6628758173 0.4272513768 -0.314252275514 +1413393896355760384.0000000000 -2.4649116117 -0.3154679867 1.6117733060 0.5391802799 0.6694668557 0.4105225527 -0.304253165277 +1413393896405760512.0000000000 -2.4925281691 -0.3050557757 1.6142331334 0.5478026911 0.6775050178 0.3913287247 -0.29624481698 +1413393896455760384.0000000000 -2.5173811846 -0.2969645677 1.6184718121 0.5525314385 0.6877411772 0.3693157100 -0.292107838045 +1413393896505760512.0000000000 -2.5389124939 -0.2907931042 1.6230690946 0.5543417969 0.6995304285 0.3490705990 -0.28550318508 +1413393896555760384.0000000000 -2.5565898469 -0.2860077361 1.6286546993 0.5531510448 0.7133464882 0.3280934286 -0.278415896823 +1413393896605760512.0000000000 -2.5716751562 -0.2815171877 1.6339712745 0.5512895975 0.7267419984 0.3087852008 -0.269402203518 +1413393896655760384.0000000000 -2.5845059232 -0.2768243586 1.6399983625 0.5491626999 0.7392735059 0.2903192175 -0.26001877691 +1413393896705760512.0000000000 -2.5947591598 -0.2718022333 1.6467996556 0.5467238542 0.7512453447 0.2709067088 -0.251660514343 +1413393896755760384.0000000000 -2.6023765350 -0.2660547365 1.6541379462 0.5434246739 0.7629061172 0.2511786529 -0.244076144839 +1413393896805760512.0000000000 -2.6071912973 -0.2591633345 1.6620560150 0.5406629300 0.7732002903 0.2317445385 -0.236937494064 +1413393896855760384.0000000000 -2.6088336373 -0.2508197107 1.6695760077 0.5359358077 0.7842025686 0.2128933160 -0.229075483964 +1413393896905760512.0000000000 -2.6069635569 -0.2406764827 1.6768131094 0.5294363022 0.7958409587 0.1951378216 -0.219671575109 +1413393896955760384.0000000000 -2.6019818581 -0.2280525100 1.6833443482 0.5222218883 0.8072397901 0.1810296240 -0.207066404737 +1413393897005760512.0000000000 -2.5940569576 -0.2131043344 1.6878487696 0.5127574459 0.8191263093 0.1733789743 -0.189872647977 +1413393897055760384.0000000000 -2.5840366182 -0.1951044048 1.6896774132 0.5031791256 0.8301126336 0.1726758459 -0.167053390551 +1413393897105760512.0000000000 -2.5732085619 -0.1726734222 1.6900496981 0.4984781939 0.8367803863 0.1762944611 -0.142261513606 +1413393897155760384.0000000000 -2.5626893443 -0.1464078284 1.6891813312 0.4984641890 0.8391906553 0.1823431234 -0.1185051969 +1413393897205760512.0000000000 -2.5535338607 -0.1163452869 1.6876220579 0.5043994711 0.8368562348 0.1899500209 -0.0957695426753 +1413393897255760384.0000000000 -2.5469010827 -0.0831453057 1.6864511589 0.5167613868 0.8293407334 0.1986158850 -0.0755205091997 +1413393897305760512.0000000000 -2.5436695872 -0.0479711709 1.6863949660 0.5333663769 0.8179980393 0.2071909033 -0.0589189727284 +1413393897355760384.0000000000 -2.5447672185 -0.0120195036 1.6874788785 0.5485097974 0.8072352687 0.2124918420 -0.04853287768 +1413393897405760512.0000000000 -2.5509459510 0.0239888514 1.6895104625 0.5596487760 0.7997706486 0.2119321451 -0.0473806185571 +1413393897455760384.0000000000 -2.5618727571 0.0595095697 1.6922202453 0.5673691549 0.7952737239 0.2068277370 -0.0534250252457 +1413393897505760512.0000000000 -2.5765170652 0.0937182059 1.6951585857 0.5725105780 0.7924352425 0.2010751820 -0.0620225424416 +1413393897555760384.0000000000 -2.5939056837 0.1268464121 1.6979340901 0.5756520322 0.7906678639 0.1965312896 -0.0696025790565 +1413393897605760512.0000000000 -2.6134734659 0.1585897448 1.7003429024 0.5749121331 0.7915855547 0.1924225886 -0.076432298207 +1413393897655760384.0000000000 -2.6348242742 0.1891502324 1.7028029997 0.5735011280 0.7925768684 0.1905391607 -0.0813215353386 +1413393897705760512.0000000000 -2.6577803581 0.2190295351 1.7054914840 0.5712897200 0.7939504617 0.1900092142 -0.0846594275659 +1413393897755760384.0000000000 -2.6821533257 0.2486944921 1.7089230651 0.5699559833 0.7947166956 0.1903297632 -0.085732910892 +1413393897805760512.0000000000 -2.7079782269 0.2778087110 1.7129085154 0.5692686423 0.7947074756 0.1923589539 -0.0858561232757 +1413393897855760384.0000000000 -2.7349411025 0.3070769910 1.7174291192 0.5696448067 0.7944363742 0.1932455633 -0.0838557922625 +1413393897905760512.0000000000 -2.7630911128 0.3363979301 1.7224608659 0.5697994474 0.7948055587 0.1928064790 -0.080239486792 +1413393897955760384.0000000000 -2.7925340379 0.3657419250 1.7281658682 0.5710426812 0.7947906382 0.1919209863 -0.073378693776 +1413393898005760512.0000000000 -2.8234590393 0.3948589596 1.7343984075 0.5733805964 0.7944876520 0.1893722109 -0.0645153339893 +1413393898055760384.0000000000 -2.8559992345 0.4236439703 1.7409195145 0.5773085418 0.7934877187 0.1851263257 -0.053106792747 +1413393898105760512.0000000000 -2.8911260875 0.4519365902 1.7496679084 0.5858714107 0.7893347832 0.1784907688 -0.0429690062053 +1413393898155760384.0000000000 -2.9285306924 0.4782568999 1.7595607950 0.5983944445 0.7827326473 0.1670455759 -0.0367350958478 +1413393898205760512.0000000000 -2.9682012977 0.5022541470 1.7707362351 0.6124280228 0.7751469477 0.1514559182 -0.0337673091039 +1413393898255760384.0000000000 -3.0101619292 0.5232968865 1.7835814112 0.6282260251 0.7654481519 0.1353251146 -0.0332911634957 +1413393898305760512.0000000000 -3.0536718912 0.5400290320 1.7972636563 0.6426450917 0.7559480752 0.1194407045 -0.0358289240726 +1413393898355760384.0000000000 -3.0983431990 0.5521250187 1.8114684499 0.6562121352 0.7464301170 0.1019359826 -0.0428575483782 +1413393898405760512.0000000000 -3.1430234627 0.5587096173 1.8260651732 0.6700250028 0.7355886114 0.0857548946 -0.0512053564226 +1413393898455760384.0000000000 -3.1868643261 0.5589756815 1.8407355149 0.6829191628 0.7244272340 0.0701992762 -0.062439261539 +1413393898505760512.0000000000 -3.2286286545 0.5527137524 1.8530646698 0.6893977457 0.7184796327 0.0564516618 -0.0730135294414 +1413393898555760384.0000000000 -3.2681466840 0.5396240348 1.8605156083 0.6811276639 0.7257381469 0.0450394265 -0.0856778709483 +1413393898605760512.0000000000 -3.3043271431 0.5207715987 1.8627948060 0.6620517456 0.7428570639 0.0395513908 -0.0910305238149 +1413393898655760384.0000000000 -3.3368326838 0.4968267302 1.8625948812 0.6384157202 0.7629321971 0.0345011477 -0.095757515246 +1413393898705760512.0000000000 -3.3655303344 0.4688111266 1.8592444067 0.6115217426 0.7846987718 0.0325692315 -0.0960637343247 +1413393898755760384.0000000000 -3.3904419838 0.4386485062 1.8534509369 0.5814658023 0.8073856810 0.0313571754 -0.0950926406421 +1413393898805760512.0000000000 -3.4114964114 0.4084002744 1.8461497358 0.5490631938 0.8301598308 0.0316549830 -0.091445210634 +1413393898855760384.0000000000 -3.4289014491 0.3804766044 1.8397661800 0.5175425776 0.8507181372 0.0322712258 -0.0859470726423 +1413393898905760512.0000000000 -3.4431563747 0.3571628706 1.8362136880 0.4911094022 0.8668234688 0.0322179012 -0.0799414532289 +1413393898955760384.0000000000 -3.4543026567 0.3399811923 1.8348169183 0.4686199802 0.8798438069 0.0342361586 -0.0714008051075 +1413393899005760512.0000000000 -3.4628469561 0.3301176887 1.8356872742 0.4505967185 0.8898544879 0.0386391341 -0.0602379029224 +1413393899055760384.0000000000 -3.4694860610 0.3303552125 1.8393827434 0.4436844832 0.8938569164 0.0462965482 -0.0449502173753 +1413393899105760512.0000000000 -3.4753282967 0.3410051132 1.8473985334 0.4502672414 0.8906301483 0.0568694946 -0.0283409739121 +1413393899155760384.0000000000 -3.4821885622 0.3622323336 1.8608574837 0.4744368291 0.8776962881 0.0657852893 -0.0152058134415 +1413393899205760512.0000000000 -3.4909664732 0.3912366016 1.8790204213 0.5111968489 0.8564635628 0.0714325284 -0.0067335874752 +1413393899255760384.0000000000 -3.5020002590 0.4238366165 1.9001290103 0.5528179220 0.8299862647 0.0741544610 -0.00403255733234 +1413393899305760512.0000000000 -3.5151075043 0.4571137502 1.9236284901 0.5963381796 0.7993861063 0.0729207968 -0.0067220480981 +1413393899355760384.0000000000 -3.5295702856 0.4877073100 1.9474121728 0.6343123623 0.7697752656 0.0703317801 -0.0121370588106 +1413393899405760512.0000000000 -3.5447474783 0.5135651743 1.9709353263 0.6648193424 0.7437413024 0.0668523943 -0.0198714492383 +1413393899455760384.0000000000 -3.5597390144 0.5326711319 1.9940416988 0.6886895604 0.7217752352 0.0628939137 -0.0281345836269 +1413393899505760512.0000000000 -3.5745485859 0.5434316787 2.0181733314 0.7101943424 0.7004979104 0.0565252986 -0.0416120674714 +1413393899555760384.0000000000 -3.5880264297 0.5450220042 2.0412411264 0.7265912799 0.6829458560 0.0510551074 -0.0551674340861 +1413393899605760512.0000000000 -3.5991841806 0.5366971109 2.0622545734 0.7359408402 0.6720159077 0.0451981860 -0.0688681609252 +1413393899655760384.0000000000 -3.6073778937 0.5179734812 2.0796190748 0.7349939606 0.6717292389 0.0404400201 -0.0832364833656 +1413393899705760512.0000000000 -3.6119461625 0.4891493164 2.0931556291 0.7235782075 0.6825380406 0.0383115391 -0.0954391259158 +1413393899755760384.0000000000 -3.6124062464 0.4514041107 2.1027686163 0.6993983267 0.7059201059 0.0369380144 -0.105614240475 +1413393899805760512.0000000000 -3.6083199147 0.4061262818 2.1105623305 0.6704064725 0.7323872179 0.0363417819 -0.113328723495 +1413393899855760384.0000000000 -3.5996251636 0.3549108203 2.1162201640 0.6351862714 0.7620061305 0.0350781479 -0.12105610762 +1413393899905760512.0000000000 -3.5863453478 0.3003901209 2.1194395827 0.5951026018 0.7930234439 0.0343547645 -0.125644183786 +1413393899955760384.0000000000 -3.5683772134 0.2449211051 2.1203420364 0.5514640537 0.8237816163 0.0338463664 -0.126986887798 +1413393900005760512.0000000000 -3.5456233539 0.1915515205 2.1210228248 0.5134277898 0.8483261332 0.0325310519 -0.125205459542 +1413393900055760384.0000000000 -3.5184690102 0.1427664459 2.1214095392 0.4839629043 0.8662132704 0.0312262439 -0.120330374614 +1413393900105760512.0000000000 -3.4873665472 0.1005311150 2.1211633663 0.4625180628 0.8788951833 0.0308794621 -0.11254668885 +1413393900155760384.0000000000 -3.4525933645 0.0660060247 2.1197312701 0.4487267683 0.8874178567 0.0343883962 -0.0997560685531 +1413393900205760512.0000000000 -3.4151496249 0.0396780411 2.1170139034 0.4392627066 0.8934331824 0.0392857811 -0.0853349320877 +1413393900255760384.0000000000 -3.3755108522 0.0221755679 2.1132968453 0.4364961450 0.8958831795 0.0481431644 -0.0674290725987 +1413393900305760512.0000000000 -3.3350746322 0.0138794322 2.1087020001 0.4406289568 0.8944671015 0.0592855428 -0.0475389444671 +1413393900355760384.0000000000 -3.2953072983 0.0143679281 2.1037783102 0.4519410924 0.8887934065 0.0702457635 -0.0293438619894 +1413393900405760512.0000000000 -3.2576571588 0.0233880451 2.0993222214 0.4729905256 0.8773966974 0.0789059710 -0.0151276545058 +1413393900455760384.0000000000 -3.2224455599 0.0382264303 2.0940396574 0.4979281553 0.8630145925 0.0851699672 -0.00440930151183 +1413393900505760512.0000000000 -3.1903140014 0.0570011372 2.0884389076 0.5266008717 0.8454828489 0.0885932909 0.0012259682726 +1413393900555760384.0000000000 -3.1612500313 0.0787431808 2.0815660070 0.5575169769 0.8252478277 0.0901373875 0.00401182628704 +1413393900605760512.0000000000 -3.1348400248 0.1009625212 2.0731816337 0.5918729718 0.8010843401 0.0891282795 0.0025327998543 +1413393900655760384.0000000000 -3.1106239724 0.1214833644 2.0626881502 0.6235658308 0.7769401903 0.0867655561 -0.00115481264364 +1413393900705760512.0000000000 -3.0880268555 0.1386634494 2.0498614797 0.6520244832 0.7536715884 0.0823895683 -0.00742760197806 +1413393900755760384.0000000000 -3.0666881567 0.1501549421 2.0340687856 0.6730086992 0.7353935901 0.0776629840 -0.0149672751776 +1413393900805760512.0000000000 -3.0461663742 0.1550165804 2.0174338481 0.6864212914 0.7232503887 0.0717310991 -0.0242762284836 +1413393900855760384.0000000000 -3.0259073651 0.1521878202 2.0000974538 0.6907548877 0.7193052156 0.0649455844 -0.0352102681183 +1413393900905760512.0000000000 -3.0051417738 0.1417364839 1.9819070387 0.6853649348 0.7243883822 0.0591714021 -0.0451123388339 +1413393900955760384.0000000000 -2.9836735466 0.1237451261 1.9631500080 0.6702868044 0.7380715471 0.0535759296 -0.0556382148785 +1413393901005760512.0000000000 -2.9606729664 0.0996986460 1.9452334045 0.6503500684 0.7553024427 0.0480609019 -0.0652162426723 +1413393901055760384.0000000000 -2.9357994921 0.0709912557 1.9284408383 0.6271412888 0.7741848644 0.0436367212 -0.0736711352857 +1413393901105760512.0000000000 -2.9079950867 0.0391228568 1.9111113442 0.6010599053 0.7946374068 0.0449828845 -0.0724908408149 +1413393901155760384.0000000000 -2.8777840727 0.0060390220 1.8939050079 0.5717780686 0.8162258687 0.0486154930 -0.0669455401876 +1413393901205760512.0000000000 -2.8456422062 -0.0262787248 1.8779029646 0.5456452415 0.8342813523 0.0561612911 -0.055604002101 +1413393901255760384.0000000000 -2.8126100514 -0.0559405451 1.8641387461 0.5241072187 0.8481357676 0.0636380349 -0.0439037994345 +1413393901305760512.0000000000 -2.7796914991 -0.0815769257 1.8524656511 0.5065195027 0.8587542852 0.0698470203 -0.0331732549078 +1413393901355760384.0000000000 -2.7478257215 -0.1020720298 1.8433056066 0.4942861796 0.8657540210 0.0743612317 -0.02493100321 +1413393901405760512.0000000000 -2.7173077037 -0.1170883395 1.8354301877 0.4840214639 0.8714088899 0.0775632883 -0.0188070580834 +1413393901455760384.0000000000 -2.6886601290 -0.1260321902 1.8287647884 0.4752651014 0.8761520671 0.0793076615 -0.013817871175 +1413393901505760512.0000000000 -2.6621230433 -0.1284119032 1.8231836499 0.4695806063 0.8790056274 0.0823321972 -0.00803557604283 +1413393901555760384.0000000000 -2.6379152897 -0.1239741609 1.8185639585 0.4658596033 0.8806796334 0.0858640766 -0.0023608723486 +1413393901605760512.0000000000 -2.6165259077 -0.1120891033 1.8155288448 0.4669119192 0.8796892695 0.0901422393 0.00379809086784 +1413393901655760384.0000000000 -2.5984779004 -0.0925547115 1.8147980899 0.4771124764 0.8734788255 0.0962963780 0.0111997240822 +1413393901705760512.0000000000 -2.5845186714 -0.0660516619 1.8167377452 0.4962909748 0.8619566991 0.1022018696 0.0167539582448 +1413393901755760384.0000000000 -2.5746494578 -0.0346625576 1.8203905787 0.5178613725 0.8486568489 0.1058412298 0.0199696210085 +1413393901805760512.0000000000 -2.5693091128 -0.0001670340 1.8254863914 0.5406837896 0.8343553624 0.1057872655 0.0179227038345 +1413393901855760384.0000000000 -2.5675007283 0.0354672914 1.8303367814 0.5576291333 0.8236398398 0.1024156888 0.0133488084149 +1413393901905760512.0000000000 -2.5687683983 0.0710899231 1.8341154964 0.5666638685 0.8181391780 0.0974131847 0.00714262602232 +1413393901955760384.0000000000 -2.5722677497 0.1065802594 1.8368935791 0.5701305739 0.8162508792 0.0931547722 0.00279629173196 +1413393902005760512.0000000000 -2.5780660559 0.1420770293 1.8396270987 0.5710722868 0.8159504043 0.0900075945 -0.000117861458965 +1413393902055760384.0000000000 -2.5860108445 0.1775870553 1.8427375160 0.5704450968 0.8166457660 0.0876169906 -0.00231245022642 +1413393902105760512.0000000000 -2.5956573752 0.2132505612 1.8461610031 0.5694860368 0.8174355249 0.0864778552 -0.00252924514367 +1413393902155760384.0000000000 -2.6072447876 0.2491128223 1.8500850658 0.5705074944 0.8167252546 0.0864672969 -0.00211279604685 +1413393902205760512.0000000000 -2.6206222518 0.2847134024 1.8538025636 0.5700179082 0.8170344971 0.0867909101 -0.00124610284308 +1413393902255760384.0000000000 -2.6359150671 0.3204667921 1.8580304718 0.5705889275 0.8166410464 0.0867499081 -0.000361442656894 +1413393902305760512.0000000000 -2.6532775792 0.3561785548 1.8620160107 0.5704668084 0.8167207451 0.0868033149 0.000171793095613 +1413393902355760384.0000000000 -2.6724018195 0.3920985063 1.8649224347 0.5706931809 0.8165198151 0.0871987015 0.00103500265621 +1413393902405760512.0000000000 -2.6933107740 0.4287636235 1.8660366425 0.5726767486 0.8151438703 0.0870624706 0.00139231624426 +1413393902455760384.0000000000 -2.7159212509 0.4650235873 1.8652948399 0.5753883823 0.8131962260 0.0873899552 0.00176163360562 +1413393902505760512.0000000000 -2.7403316626 0.5004463845 1.8635238923 0.5790832889 0.8105938931 0.0871629162 0.00164652575319 +1413393902555760384.0000000000 -2.7667407304 0.5351669758 1.8617419202 0.5800297964 0.8099510083 0.0868479453 0.00149458787279 +1413393902605760512.0000000000 -2.7952678448 0.5692072225 1.8620590621 0.5798577324 0.8101129383 0.0864932455 0.000977718039736 +1413393902655760384.0000000000 -2.8257002892 0.6028213261 1.8647906885 0.5786198350 0.8110430923 0.0860631307 0.00115175496678 +1413393902705760512.0000000000 -2.8582907766 0.6365876049 1.8715549861 0.5778405985 0.8116366073 0.0857009155 0.00127026461673 +1413393902755760384.0000000000 -2.8927752314 0.6689932890 1.8812889873 0.5762891669 0.8128336838 0.0848067606 0.000109721361903 +1413393902805760512.0000000000 -2.9295255339 0.7012396637 1.8944167850 0.5725325619 0.8159238844 0.0802954779 -0.00522652324804 +1413393902855760384.0000000000 -2.9680601602 0.7334100016 1.9099502939 0.5677689243 0.8197363612 0.0741025994 -0.013399681206 +1413393902905760512.0000000000 -3.0078125758 0.7658841232 1.9263177339 0.5591687850 0.8260768337 0.0659746748 -0.0239724199807 +1413393902955760384.0000000000 -3.0475250207 0.7993862444 1.9427597055 0.5502669008 0.8322749299 0.0586088037 -0.0330119234113 +1413393903005760512.0000000000 -3.0867560075 0.8344578410 1.9593754367 0.5429000485 0.8371739612 0.0517040051 -0.0415450592598 +1413393903055760384.0000000000 -3.1249168506 0.8717461379 1.9764092687 0.5385883057 0.8399424989 0.0458744482 -0.0481120621066 +1413393903105760512.0000000000 -3.1613996907 0.9115723663 1.9935760881 0.5390163176 0.8397040616 0.0446505898 -0.0486294473478 +1413393903155760384.0000000000 -3.1964876478 0.9537014683 2.0111789091 0.5448501239 0.8359862239 0.0454166007 -0.0469330184625 +1413393903205760512.0000000000 -3.2301459775 0.9975536444 2.0281081990 0.5510142549 0.8320406681 0.0474989460 -0.0428423569111 +1413393903255760384.0000000000 -3.2626564302 1.0431289125 2.0444000190 0.5573593921 0.8279795633 0.0485293857 -0.0380164369483 +1413393903305760512.0000000000 -3.2939654980 1.0898529611 2.0598400597 0.5630546412 0.8244067469 0.0478745765 -0.0321093692184 +1413393903355760384.0000000000 -3.3241865116 1.1373571648 2.0732707392 0.5662401296 0.8226560940 0.0447434906 -0.0246391293556 +1413393903405760512.0000000000 -3.3534440073 1.1859240780 2.0840980158 0.5694584862 0.8210083373 0.0369798442 -0.0171707249548 +1413393903455760384.0000000000 -3.3819255722 1.2346014239 2.0904242339 0.5716702752 0.8200227501 0.0254266068 -0.0104533962945 +1413393903505760512.0000000000 -3.4097239301 1.2833908833 2.0917236158 0.5736650774 0.8190070865 0.0106606340 -0.00470340928609 +1413393903555760384.0000000000 -3.4368315363 1.3315516051 2.0875895833 0.5764088699 0.8171425857 -0.0054536012 0.00103324818493 +1413393903605760512.0000000000 -3.4632980350 1.3795240657 2.0822700751 0.5826415483 0.8124011745 -0.0225728068 0.00486068786705 +1413393903655760384.0000000000 -3.4885606616 1.4264050921 2.0769680876 0.5896628604 0.8066387613 -0.0394516305 0.0086711409045 +1413393903705760512.0000000000 -3.5124478063 1.4719384750 2.0715596396 0.5943019699 0.8022216621 -0.0556799206 0.0120548727188 +1413393903755760384.0000000000 -3.5344134528 1.5162302174 2.0669434238 0.5981111869 0.7981320971 -0.0706741031 0.0159164939054 +1413393903805760512.0000000000 -3.5546613148 1.5585583741 2.0629699982 0.5982386480 0.7966723416 -0.0842028835 0.0182640253156 +1413393903855760384.0000000000 -3.5729498125 1.5987981650 2.0598588476 0.5963223120 0.7966019570 -0.0975034725 0.0178352222295 +1413393903905760512.0000000000 -3.5888668682 1.6371632155 2.0579005738 0.5937681714 0.7969907556 -0.1094606152 0.0162316930965 +1413393903955760384.0000000000 -3.6019033724 1.6736717561 2.0575167942 0.5919071082 0.7969156443 -0.1198277039 0.0145860399534 +1413393904005760512.0000000000 -3.6116887680 1.7083608449 2.0584377068 0.5908367408 0.7965352214 -0.1274144825 0.0144615509955 +1413393904055760384.0000000000 -3.6181363823 1.7412242468 2.0585592810 0.5885455070 0.7974557239 -0.1320347231 0.0156648198055 +1413393904105760512.0000000000 -3.6211843023 1.7723439661 2.0566273460 0.5881882042 0.7973449747 -0.1337307281 0.0197919214287 +1413393904155760384.0000000000 -3.6212366948 1.8015288427 2.0519251854 0.5855286915 0.7993429696 -0.1324790882 0.0256175629345 +1413393904205760512.0000000000 -3.6186137572 1.8289446327 2.0452333886 0.5825727694 0.8016339481 -0.1303306394 0.031716022271 +1413393904255760384.0000000000 -3.6133363570 1.8547807308 2.0387128419 0.5794121402 0.8040999542 -0.1276917813 0.037411821897 +1413393904305760512.0000000000 -3.6052334418 1.8795206249 2.0362228324 0.5786353299 0.8048231512 -0.1249787704 0.0426750188846 +1413393904355760384.0000000000 -3.5946832650 1.9032339868 2.0381637693 0.5789783326 0.8046548497 -0.1234514186 0.0455456954001 +1413393904405760512.0000000000 -3.5814916658 1.9254616407 2.0444152039 0.5786944769 0.8046957655 -0.1235762053 0.0480244603477 +1413393904455760384.0000000000 -3.5654781963 1.9478870540 2.0547679636 0.5784862924 0.8043788556 -0.1253901301 0.0510448966901 +1413393904505760512.0000000000 -3.5467164228 1.9707164328 2.0701557947 0.5782920042 0.8038291846 -0.1280382885 0.0551651746721 +1413393904555760384.0000000000 -3.5252236916 1.9927534140 2.0879194346 0.5776851501 0.8032756558 -0.1304488305 0.0633339619079 +1413393904605760512.0000000000 -3.5016881758 2.0132185376 2.1036796914 0.5705794574 0.8070333486 -0.1310308483 0.0772474847958 +1413393904655760384.0000000000 -3.4767073435 2.0330197497 2.1168229631 0.5584417127 0.8136625253 -0.1310774608 0.094418471885 +1413393904705760512.0000000000 -3.4512955429 2.0525029500 2.1275921364 0.5449847680 0.8203311690 -0.1346442267 0.109175583967 +1413393904755760384.0000000000 -3.4256991882 2.0725283877 2.1357804991 0.5315578988 0.8261663736 -0.1399016836 0.123785469213 +1413393904805760512.0000000000 -3.4003604621 2.0943576382 2.1428418000 0.5208576418 0.8297565404 -0.1470200633 0.136368990639 +1413393904855760384.0000000000 -3.3753231481 2.1185541138 2.1486709241 0.5132769245 0.8308959559 -0.1549704714 0.148804778968 +1413393904905760512.0000000000 -3.3509454178 2.1456974649 2.1535038049 0.5105797159 0.8287188516 -0.1640314012 0.160084721789 +1413393904955760384.0000000000 -3.3267206014 2.1761529288 2.1576727042 0.5143724013 0.8220554122 -0.1729363967 0.172449803754 +1413393905005760512.0000000000 -3.3030436699 2.2098798762 2.1606020395 0.5221899113 0.8123542677 -0.1831590628 0.183986406997 +1413393905055760384.0000000000 -3.2804733028 2.2457088835 2.1613454512 0.5296042070 0.8024737427 -0.1933830509 0.195341423865 +1413393905105760512.0000000000 -3.2594035575 2.2822436214 2.1589887826 0.5349077563 0.7935806435 -0.2044462945 0.205682199405 +1413393905155760384.0000000000 -3.2399867540 2.3190901397 2.1529528105 0.5388294504 0.7851707225 -0.2169195248 0.214745616092 +1413393905205760512.0000000000 -3.2223679189 2.3564050964 2.1434592047 0.5414506014 0.7775781528 -0.2311195038 0.220878331892 +1413393905255760384.0000000000 -3.2062880474 2.3940166015 2.1316866055 0.5429670205 0.7703770422 -0.2458437459 0.226421906976 +1413393905305760512.0000000000 -3.1917794305 2.4316060086 2.1188735562 0.5436038484 0.7634057930 -0.2615116642 0.23090712557 +1413393905355760384.0000000000 -3.1787223186 2.4689693475 2.1064400694 0.5428899836 0.7572005212 -0.2767972624 0.23516188446 +1413393905405760512.0000000000 -3.1668087069 2.5058801437 2.0943233262 0.5408319392 0.7517870001 -0.2908508993 0.240255851942 +1413393905455760384.0000000000 -3.1557542442 2.5423725612 2.0833719991 0.5387582269 0.7458964164 -0.3049189775 0.245769253719 +1413393905505760512.0000000000 -3.1455965091 2.5780266018 2.0733657300 0.5353555251 0.7406722619 -0.3188231219 0.251298386707 +1413393905555760384.0000000000 -3.1364064309 2.6127640420 2.0642757823 0.5320035954 0.7350505160 -0.3349002498 0.253997511935 +1413393905605760512.0000000000 -3.1276804657 2.6463630514 2.0556030456 0.5277859319 0.7294607201 -0.3525780610 0.254985840153 +1413393905655760384.0000000000 -3.1188308682 2.6786481834 2.0478384034 0.5243830182 0.7229204293 -0.3695479355 0.256598570627 +1413393905705760512.0000000000 -3.1096483500 2.7092560921 2.0411717847 0.5220851866 0.7152495175 -0.3859528232 0.258622512438 +1413393905755760384.0000000000 -3.0997315371 2.7378356355 2.0358744758 0.5208358191 0.7062891086 -0.4021145421 0.261131460405 +1413393905805760512.0000000000 -3.0893098522 2.7642696240 2.0314374617 0.5187299631 0.6980534668 -0.4183391212 0.26197893549 +1413393905855760384.0000000000 -3.0781031185 2.7880957221 2.0274532973 0.5139241300 0.6917386698 -0.4356918008 0.259908168648 +1413393905905760512.0000000000 -3.0652057969 2.8091625722 2.0238341385 0.5063836262 0.6874031448 -0.4523189869 0.257798513771 +1413393905955760384.0000000000 -3.0502038809 2.8271488572 2.0208074302 0.4967053048 0.6847264055 -0.4674994860 0.256666749837 +1413393906005760512.0000000000 -3.0320772909 2.8421176197 2.0193056652 0.4877978152 0.6814757607 -0.4801970416 0.258949570765 +1413393906055760384.0000000000 -3.0100237931 2.8538846899 2.0188821622 0.4763299045 0.6809713707 -0.4871890043 0.268392787799 +1413393906105760512.0000000000 -2.9848989412 2.8627081533 2.0190943728 0.4654024327 0.6806005753 -0.4894416854 0.28395469547 +1413393906155760384.0000000000 -2.9572224533 2.8697871618 2.0192888542 0.4577292335 0.6783919462 -0.4892378938 0.301520479055 +1413393906205760512.0000000000 -2.9277207810 2.8757846441 2.0178033201 0.4522189990 0.6748352785 -0.4865486958 0.321505350565 +1413393906255760384.0000000000 -2.8970841426 2.8814606817 2.0148081556 0.4499486584 0.6692441084 -0.4831994688 0.340847182112 +1413393906305760512.0000000000 -2.8652115617 2.8875014139 2.0098691565 0.4484837952 0.6633161660 -0.4804703878 0.357801838691 +1413393906355760384.0000000000 -2.8330954604 2.8940249330 2.0020435254 0.4466190511 0.6578885260 -0.4795143955 0.371187358509 +1413393906405760512.0000000000 -2.8017800119 2.9012561759 1.9915836716 0.4448543514 0.6529690950 -0.4809506568 0.380029515562 +1413393906455760384.0000000000 -2.7722683247 2.9089354782 1.9783784078 0.4442533583 0.6474310529 -0.4827443791 0.387852871462 +1413393906505760512.0000000000 -2.7440093388 2.9172158346 1.9618160202 0.4432887020 0.6418723624 -0.4868449389 0.393035624942 +1413393906555760384.0000000000 -2.7164239561 2.9265259442 1.9427055979 0.4438812443 0.6356484679 -0.4920927447 0.395935849352 +1413393906605760512.0000000000 -2.6900486391 2.9362824450 1.9208239883 0.4454615557 0.6285733115 -0.4995905029 0.396066817383 +1413393906655760384.0000000000 -2.6649503970 2.9460642951 1.8971961094 0.4482862801 0.6202002408 -0.5084769888 0.394768570492 +1413393906705760512.0000000000 -2.6411654191 2.9560556095 1.8732915258 0.4528102009 0.6117003383 -0.5189860046 0.389151827946 +1413393906755760384.0000000000 -2.6186470850 2.9652176465 1.8502288264 0.4582171269 0.6034627699 -0.5283883449 0.38298238454 +1413393906805760512.0000000000 -2.5969808461 2.9727598397 1.8282214476 0.4642624598 0.5952392358 -0.5351965790 0.379097932405 +1413393906855760384.0000000000 -2.5764637909 2.9777216043 1.8067018243 0.4671788145 0.5897480425 -0.5388931113 0.378860681911 +1413393906905760512.0000000000 -2.5572368770 2.9801999511 1.7854992245 0.4695758226 0.5856147547 -0.5399635212 0.38077985984 +1413393906955760384.0000000000 -2.5391465236 2.9801717978 1.7646688051 0.4709602733 0.5826265714 -0.5398454855 0.383809263975 +1413393907005760512.0000000000 -2.5224429905 2.9777714931 1.7440745838 0.4706792046 0.5816876648 -0.5389268162 0.386857123097 +1413393907055760384.0000000000 -2.5075960884 2.9726217302 1.7226813732 0.4642873144 0.5858211323 -0.5350854875 0.39361708762 +1413393907105760512.0000000000 -2.4946013194 2.9655909446 1.7012223140 0.4568456024 0.5907847179 -0.5311610292 0.40016680743 +1413393907155760384.0000000000 -2.4834079890 2.9571546579 1.6802673383 0.4491933567 0.5959692863 -0.5281329605 0.405119135724 +1413393907205760512.0000000000 -2.4735459268 2.9476711025 1.6597788568 0.4407335169 0.6014219849 -0.5239503060 0.411730057064 +1413393907255760384.0000000000 -2.4650400836 2.9377771238 1.6398980360 0.4300620730 0.6083962899 -0.5176638345 0.420624205435 +1413393907305760512.0000000000 -2.4582105197 2.9282075234 1.6199036701 0.4172186978 0.6165066601 -0.5099882815 0.430998896828 +1413393907355760384.0000000000 -2.4527556213 2.9203414744 1.6012996338 0.4057980346 0.6231931943 -0.5020039409 0.441531698751 +1413393907405760512.0000000000 -2.4492458036 2.9154909405 1.5843059675 0.3976737600 0.6274044584 -0.4995354350 0.445739358156 +1413393907455760384.0000000000 -2.4471749658 2.9153042650 1.5710496393 0.3976211884 0.6274077301 -0.5031997949 0.441641140788 +1413393907505760512.0000000000 -2.4473114151 2.9187133997 1.5618830987 0.4013627477 0.6252231253 -0.5085256772 0.435207564255 +1413393907555760384.0000000000 -2.4476825037 2.9256657029 1.5585739827 0.4105817171 0.6192762013 -0.5172469917 0.424706003728 +1413393907605760512.0000000000 -2.4486090329 2.9340535943 1.5591889056 0.4184507014 0.6143449314 -0.5224235279 0.417795372466 +1413393907655760384.0000000000 -2.4502692295 2.9428401908 1.5592980649 0.4231995893 0.6111631055 -0.5276113507 0.411105860677 +1413393907705760512.0000000000 -2.4528774442 2.9515789460 1.5573479426 0.4251566735 0.6098369440 -0.5322499304 0.405031747344 +1413393907755760384.0000000000 -2.4553382825 2.9601191003 1.5521956229 0.4262452179 0.6091678963 -0.5351644531 0.401034283416 +1413393907805760512.0000000000 -2.4578989952 2.9681455964 1.5427186595 0.4286252304 0.6074584712 -0.5361813766 0.399730095209 +1413393907855760384.0000000000 -2.4609050780 2.9755439443 1.5276800584 0.4310599178 0.6053773785 -0.5366771394 0.399603834908 +1413393907905760512.0000000000 -2.4640694186 2.9823706054 1.5072340790 0.4346619051 0.6027914882 -0.5361668642 0.400295570386 +1413393907955760384.0000000000 -2.4676135308 2.9880485044 1.4812774040 0.4353129590 0.6020002025 -0.5337729464 0.40396141589 +1413393908005760512.0000000000 -2.4719947447 2.9928309494 1.4524962267 0.4347085892 0.6017058528 -0.5315117297 0.408011997876 +1413393908055760384.0000000000 -2.4770000511 2.9972524509 1.4248476134 0.4328571170 0.6025481254 -0.5288177093 0.412216330551 +1413393908105760512.0000000000 -2.4839340786 3.0014866393 1.3988358953 0.4293243203 0.6044623394 -0.5283649702 0.413686314153 +1413393908155760384.0000000000 -2.4923788082 3.0058228114 1.3749134210 0.4244402246 0.6073738761 -0.5299794825 0.412394493756 +1413393908205760512.0000000000 -2.5017436670 3.0103428101 1.3550174295 0.4202275706 0.6098092388 -0.5305724928 0.412352168772 +1413393908255760384.0000000000 -2.5116173520 3.0154035175 1.3394774479 0.4188098518 0.6103958760 -0.5311473602 0.412186443823 +1413393908305760512.0000000000 -2.5225816816 3.0209961268 1.3271679348 0.4208050926 0.6087542676 -0.5293459153 0.414890609247 +1413393908355760384.0000000000 -2.5337439272 3.0270875309 1.3174512205 0.4266708608 0.6041855890 -0.5266770072 0.418954747719 +1413393908405760512.0000000000 -2.5463599998 3.0334641435 1.3071898512 0.4287963101 0.6022824476 -0.5260205230 0.420347459933 +1413393908455760384.0000000000 -2.5602045095 3.0402471306 1.2969569711 0.4291560070 0.6015841046 -0.5273953523 0.419256280944 +1413393908505760512.0000000000 -2.5750558054 3.0470799572 1.2865986521 0.4275867569 0.6021142174 -0.5297678441 0.417101985025 +1413393908555760384.0000000000 -2.5909946755 3.0538581240 1.2761187198 0.4245808603 0.6036050339 -0.5320384966 0.415122986886 +1413393908605760512.0000000000 -2.6079756686 3.0610022528 1.2662947122 0.4234720933 0.6037824637 -0.5358455535 0.411081093578 +1413393908655760384.0000000000 -2.6257334043 3.0681855871 1.2565567720 0.4228356258 0.6034337361 -0.5412072423 0.405182033945 +1413393908705760512.0000000000 -2.6439746867 3.0756501613 1.2488362579 0.4305251797 0.5972068507 -0.5511376178 0.392733208834 +1413393908755760384.0000000000 -2.6621535544 3.0819508908 1.2427334778 0.4408420870 0.5888580862 -0.5600092490 0.381174565874 +1413393908805760512.0000000000 -2.6803378072 3.0856796883 1.2389312975 0.4515427135 0.5798412925 -0.5653945072 0.374462687893 +1413393908855760384.0000000000 -2.6978425844 3.0855356407 1.2396960287 0.4601643359 0.5724626083 -0.5651638034 0.375666369762 +1413393908905760512.0000000000 -2.7164496343 3.0809869228 1.2435088417 0.4609077788 0.5711764835 -0.5596425351 0.38486579095 +1413393908955760384.0000000000 -2.7348759470 3.0728448167 1.2486382935 0.4525255366 0.5769457934 -0.5526548427 0.396139893144 +1413393909005760512.0000000000 -2.7546726028 3.0624356738 1.2562607239 0.4419821718 0.5839802232 -0.5478228203 0.404362481297 +1413393909055760384.0000000000 -2.7755080713 3.0506231910 1.2663149556 0.4307076275 0.5910051881 -0.5434309800 0.41217299434 +1413393909105760512.0000000000 -2.7978292885 3.0384651443 1.2779190432 0.4212763323 0.5964314791 -0.5409565805 0.41732687504 +1413393909155760384.0000000000 -2.8209977544 3.0266584085 1.2907726403 0.4142347944 0.5999389641 -0.5394306184 0.421304382086 +1413393909205760512.0000000000 -2.8446925850 3.0155740840 1.3035843155 0.4096111208 0.6015256064 -0.5388644823 0.424276730857 +1413393909255760384.0000000000 -2.8692237011 3.0055048150 1.3146893766 0.4079818921 0.6011428708 -0.5382876308 0.427111754905 +1413393909305760512.0000000000 -2.8947724061 2.9961873160 1.3233989037 0.4061071909 0.6008219912 -0.5375622984 0.430251856176 +1413393909355760384.0000000000 -2.9204903386 2.9878176244 1.3293829169 0.4042371508 0.6005165693 -0.5374360444 0.432590654308 +1413393909405760512.0000000000 -2.9468581648 2.9804689400 1.3326247021 0.4025490580 0.6000552613 -0.5381807350 0.433877212835 +1413393909455760384.0000000000 -2.9740145419 2.9743097586 1.3329424840 0.4013093279 0.5995939146 -0.5395050821 0.434018694651 +1413393909505760512.0000000000 -3.0019177417 2.9693291779 1.3309059444 0.4007523542 0.5988849750 -0.5408877632 0.433791153637 +1413393909555760384.0000000000 -3.0307450946 2.9653026630 1.3254203501 0.3984622270 0.5994666992 -0.5432207561 0.432179060518 +1413393909605760512.0000000000 -3.0603360254 2.9621372846 1.3164245578 0.3938705686 0.6013696380 -0.5469771244 0.428994824013 +1413393909655760384.0000000000 -3.0899919057 2.9598785675 1.3042205615 0.3868232794 0.6046468341 -0.5521705677 0.424119818742 +1413393909705760512.0000000000 -3.1190632489 2.9585003931 1.2900611615 0.3788869654 0.6079888726 -0.5579626471 0.418893641257 +1413393909755760384.0000000000 -3.1469392932 2.9582992562 1.2741131153 0.3701957743 0.6114869331 -0.5640154454 0.413431247771 +1413393909805760512.0000000000 -3.1732454653 2.9594836258 1.2566467912 0.3636557484 0.6133003396 -0.5694669079 0.409053335067 +1413393909855760384.0000000000 -3.1972077758 2.9616929648 1.2373222741 0.3572153063 0.6150195335 -0.5741379332 0.405603047449 +1413393909905760512.0000000000 -3.2187707528 2.9650214400 1.2160147643 0.3510029341 0.6163072185 -0.5789412977 0.402230439615 +1413393909955760384.0000000000 -3.2376249947 2.9696294060 1.1930123404 0.3460496661 0.6169409735 -0.5827457495 0.400051065761 +1413393910005760512.0000000000 -3.2538522343 2.9755552683 1.1688782909 0.3413366174 0.6174594484 -0.5862925779 0.398113245514 +1413393910055760384.0000000000 -3.2666033125 2.9831243962 1.1455261609 0.3369322855 0.6180689155 -0.5897775505 0.395764944882 +1413393910105760512.0000000000 -3.2753411680 2.9925942349 1.1254460424 0.3343920771 0.6172450436 -0.5938456568 0.393113000039 +1413393910155760384.0000000000 -3.2797310792 3.0035793232 1.1091699622 0.3319162170 0.6162985807 -0.5984497493 0.389699347952 +1413393910205760512.0000000000 -3.2789304451 3.0158143151 1.0972216573 0.3302486039 0.6153884123 -0.6014197359 0.38797843107 +1413393910255760384.0000000000 -3.2733160969 3.0290896432 1.0895035735 0.3276707992 0.6153126621 -0.6041031194 0.386110860244 +1413393910305760512.0000000000 -3.2623893223 3.0433667302 1.0857113397 0.3258055959 0.6146140964 -0.6071496974 0.384017540074 +1413393910355760384.0000000000 -3.2461041321 3.0587932716 1.0853952941 0.3230696197 0.6142912688 -0.6128734019 0.377701537101 +1413393910405760512.0000000000 -3.2240177001 3.0750918016 1.0893145086 0.3222056820 0.6127266817 -0.6202710666 0.368799831768 +1413393910455760384.0000000000 -3.1969107746 3.0916199167 1.0963465286 0.3245511555 0.6096365941 -0.6271133631 0.360192449157 +1413393910505760512.0000000000 -3.1642327114 3.1075123705 1.1038916442 0.3261898520 0.6080566854 -0.6319869474 0.352788528827 +1413393910555760384.0000000000 -3.1258304207 3.1222181073 1.1098988092 0.3284483740 0.6070390927 -0.6347050043 0.347526636406 +1413393910605760512.0000000000 -3.0823854658 3.1354510090 1.1140682834 0.3325322913 0.6062632511 -0.6338554822 0.346546350893 +1413393910655760384.0000000000 -3.0338227604 3.1472822099 1.1160365737 0.3382330851 0.6054176686 -0.6304608496 0.348693194399 +1413393910705760512.0000000000 -2.9807886579 3.1578943240 1.1156110798 0.3465474495 0.6029577096 -0.6274215860 0.350269923128 +1413393910755760384.0000000000 -2.9237067169 3.1671189991 1.1126969236 0.3552373552 0.6008377044 -0.6226607313 0.353686426275 +1413393910805760512.0000000000 -2.8629296098 3.1748027738 1.1064522162 0.3618312638 0.6006585739 -0.6167324020 0.357671019941 +1413393910855760384.0000000000 -2.7990188299 3.1813337064 1.0975663047 0.3677741597 0.6015620464 -0.6099440011 0.36170925794 +1413393910905760512.0000000000 -2.7322702337 3.1866619962 1.0867874696 0.3742822973 0.6023997916 -0.6020783777 0.366781788194 +1413393910955760384.0000000000 -2.6630978662 3.1908967946 1.0742546078 0.3826808059 0.6023842140 -0.5918265979 0.374739826483 +1413393911005760512.0000000000 -2.5919987033 3.1945252683 1.0599586094 0.3913402135 0.6022765853 -0.5820780401 0.381183561219 +1413393911055760384.0000000000 -2.5201118003 3.1977133906 1.0434333682 0.3992370059 0.6029092978 -0.5728082317 0.386006374803 +1413393911105760512.0000000000 -2.4478223620 3.2004884911 1.0262362001 0.4067439591 0.6034533119 -0.5651065085 0.388661917473 +1413393911155760384.0000000000 -2.3755149532 3.2027252510 1.0087354362 0.4120403406 0.6050425394 -0.5590283864 0.38940152334 +1413393911205760512.0000000000 -2.3030303259 3.2043676795 0.9913577201 0.4160243569 0.6067704308 -0.5529409556 0.391164515868 +1413393911255760384.0000000000 -2.2307700390 3.2053220709 0.9738231232 0.4184336219 0.6085200203 -0.5484941763 0.392136235941 +1413393911305760512.0000000000 -2.1589722245 3.2057094863 0.9564179505 0.4212035015 0.6092387175 -0.5446381638 0.393427332634 +1413393911355760384.0000000000 -2.0868508949 3.2058161457 0.9411744256 0.4261258515 0.6074209466 -0.5383327111 0.399567822215 +1413393911405760512.0000000000 -2.0154181297 3.2056416428 0.9266178218 0.4304579888 0.6048320982 -0.5320551081 0.407187198683 +1413393911455760384.0000000000 -1.9456160401 3.2054856513 0.9137761525 0.4350556060 0.6016214856 -0.5258024680 0.415102363733 +1413393911505760512.0000000000 -1.8786576380 3.2053482486 0.9019584727 0.4372630828 0.5994733708 -0.5213819647 0.42141846296 +1413393911555760384.0000000000 -1.8138617748 3.2055232464 0.8917377646 0.4367949300 0.5984525345 -0.5189178880 0.426367187531 +1413393911605760512.0000000000 -1.7530702647 3.2062705196 0.8861775346 0.4376174633 0.5963754959 -0.5171827753 0.430522009469 +1413393911655760384.0000000000 -1.6950016870 3.2080290500 0.8853797948 0.4399280128 0.5932271722 -0.5148767086 0.435254914519 +1413393911705760512.0000000000 -1.6399552959 3.2103430006 0.8873899444 0.4391588147 0.5916401879 -0.5141957028 0.438980868423 +1413393911755760384.0000000000 -1.5906571123 3.2133849863 0.8916190119 0.4340348823 0.5931452501 -0.5186609673 0.436787401678 +1413393911805760512.0000000000 -1.5449770281 3.2173996256 0.8991648198 0.4263688256 0.5970456710 -0.5240244802 0.43260193648 +1413393911855760384.0000000000 -1.5026875596 3.2223912920 0.9103543480 0.4176848079 0.6014393466 -0.5310110291 0.426423968091 +1413393911905760512.0000000000 -1.4626951024 3.2289728695 0.9254007279 0.4127684226 0.6031751391 -0.5422942432 0.414389834109 +1413393911955760384.0000000000 -1.4239186149 3.2365564719 0.9438136426 0.4087869686 0.6041252103 -0.5565347992 0.397737302569 +1413393912005760512.0000000000 -1.3840068150 3.2442704515 0.9656622565 0.4019658887 0.6063430391 -0.5714181622 0.379806302098 +1413393912055760384.0000000000 -1.3426454168 3.2512978882 0.9915422940 0.3935862957 0.6091307690 -0.5850328685 0.363023521104 +1413393912105760512.0000000000 -1.2983669519 3.2570776498 1.0208654150 0.3863987205 0.6111161291 -0.5949812714 0.351041866849 +1413393912155760384.0000000000 -1.2509840282 3.2612864294 1.0512355225 0.3792499982 0.6126830526 -0.6034166356 0.341580561324 +1413393912205760512.0000000000 -1.1999343832 3.2637412083 1.0819767634 0.3730964772 0.6139933813 -0.6095029163 0.335137794682 +1413393912255760384.0000000000 -1.1445079967 3.2643631145 1.1129568187 0.3683011757 0.6148718681 -0.6132785399 0.331928098039 +1413393912305760512.0000000000 -1.0843702116 3.2632954167 1.1442882288 0.3653979836 0.6145545564 -0.6161455352 0.33041139548 +1413393912355760384.0000000000 -1.0190300704 3.2605301228 1.1764739414 0.3654743604 0.6129238549 -0.6166176550 0.33246880678 +1413393912405760512.0000000000 -0.9484890422 3.2559714692 1.2101696247 0.3701087498 0.6089998487 -0.6144617902 0.33848989055 +1413393912455760384.0000000000 -0.8732280156 3.2497123283 1.2448103818 0.3778920327 0.6032918394 -0.6098138376 0.348372862955 +1413393912505760512.0000000000 -0.7946894704 3.2419138165 1.2793502606 0.3872828072 0.5973257094 -0.6030165719 0.359979219051 +1413393912555760384.0000000000 -0.7143708143 3.2328324481 1.3116961398 0.3959687833 0.5918036654 -0.5974408123 0.368838203076 +1413393912605760512.0000000000 -0.6327969699 3.2223157058 1.3407961113 0.4022753058 0.5881168986 -0.5923290383 0.37608430207 +1413393912655760384.0000000000 -0.5515622588 3.2106844140 1.3663073024 0.4073981696 0.5858827490 -0.5863333166 0.383381503972 +1413393912705760512.0000000000 -0.4701217434 3.1979746704 1.3884063911 0.4115885209 0.5840406650 -0.5804163361 0.390651081959 +1413393912755760384.0000000000 -0.3885578545 3.1843841316 1.4074610330 0.4153953619 0.5825368977 -0.5742983342 0.397842782327 +1413393912805760512.0000000000 -0.3068738440 3.1696217513 1.4232732579 0.4172019327 0.5810601067 -0.5694256278 0.405050804397 +1413393912855760384.0000000000 -0.2257396992 3.1537270803 1.4364393293 0.4172722126 0.5789921372 -0.5665247560 0.411948669828 +1413393912905760512.0000000000 -0.1456392163 3.1369436846 1.4462679111 0.4156283251 0.5762012556 -0.5661427518 0.418004297941 +1413393912955760384.0000000000 -0.0669957670 3.1195304947 1.4529993904 0.4129145476 0.5723848912 -0.5687553897 0.422367635436 +1413393913005760512.0000000000 0.0106260955 3.1015997636 1.4579467369 0.4116319038 0.5654097214 -0.5749688267 0.424596126918 +1413393913055760384.0000000000 0.0870856606 3.0830787187 1.4612000483 0.4109447305 0.5568162035 -0.5829679231 0.425709460335 +1413393913105760512.0000000000 0.1620607240 3.0635400325 1.4627246083 0.4112460737 0.5458586735 -0.5913416628 0.42805375051 +1413393913155760384.0000000000 0.2359791266 3.0428247443 1.4630932807 0.4131966380 0.5318687881 -0.5997187606 0.432112877365 +1413393913205760512.0000000000 0.3076706891 3.0206140285 1.4612110761 0.4137997410 0.5177494668 -0.6084018424 0.436523151962 +1413393913255760384.0000000000 0.3768570639 2.9966942418 1.4575065390 0.4134564611 0.5029353901 -0.6187071838 0.439671660349 +1413393913305760512.0000000000 0.4432282341 2.9706970477 1.4511390564 0.4098726867 0.4891256807 -0.6294866188 0.443291152476 +1413393913355760384.0000000000 0.5064384800 2.9424923888 1.4420516209 0.4031562869 0.4766943031 -0.6411616814 0.446250207789 +1413393913405760512.0000000000 0.5670485457 2.9119025087 1.4321129707 0.3977680299 0.4622078044 -0.6529226426 0.449262242753 +1413393913455760384.0000000000 0.6254101364 2.8782133519 1.4235950490 0.3928017679 0.4460292874 -0.6642422349 0.453372803839 +1413393913505760512.0000000000 0.6808852793 2.8411493637 1.4164273554 0.3872208426 0.4294332482 -0.6734807004 0.460511509701 +1413393913555760384.0000000000 0.7327922501 2.8006781054 1.4107826931 0.3803957524 0.4124914633 -0.6807579571 0.470869905743 +1413393913605760512.0000000000 0.7817953029 2.7567054040 1.4070032114 0.3721433782 0.3963334484 -0.6867593808 0.482483840794 +1413393913655760384.0000000000 0.8268239121 2.7098767520 1.4044899797 0.3633052964 0.3799242713 -0.6912600219 0.495808825827 +1413393913705760512.0000000000 0.8673040930 2.6604397252 1.4043288954 0.3528356504 0.3647539108 -0.6955202341 0.508638567541 +1413393913755760384.0000000000 0.9032471219 2.6087090397 1.4076923758 0.3430581549 0.3487104960 -0.6996644146 0.520751187606 +1413393913805760512.0000000000 0.9339255305 2.5558761401 1.4120551209 0.3328204444 0.3332250819 -0.7045093277 0.530903196198 +1413393913855760384.0000000000 0.9595934972 2.5020264847 1.4169456542 0.3220290480 0.3183276186 -0.7094974681 0.539979779399 +1413393913905760512.0000000000 0.9799378390 2.4477315297 1.4233903513 0.3122034315 0.3031062047 -0.7154425656 0.546623802462 +1413393913955760384.0000000000 0.9948216832 2.3931403397 1.4296154431 0.2994269041 0.2902809537 -0.7208086953 0.553638258934 +1413393914005760512.0000000000 1.0044493996 2.3378814276 1.4372971454 0.2841579722 0.2782604554 -0.7233217690 0.564474077667 +1413393914055760384.0000000000 1.0092040446 2.2830829988 1.4459851862 0.2685150832 0.2663457970 -0.7247939353 0.575876130643 +1413393914105760512.0000000000 1.0089757478 2.2291719341 1.4545728469 0.2487463997 0.2566124376 -0.7272284404 0.586015427291 +1413393914155760384.0000000000 1.0045027525 2.1764873040 1.4630078795 0.2261417731 0.2486095586 -0.7317723699 0.592926963834 +1413393914205760512.0000000000 0.9963332412 2.1257552525 1.4704415205 0.2013001456 0.2420893283 -0.7411452644 0.592937353833 +1413393914255760384.0000000000 0.9853365399 2.0775903331 1.4792493203 0.1797134088 0.2334427886 -0.7502760697 0.591855872979 +1413393914305760512.0000000000 0.9726034161 2.0315201548 1.4889603509 0.1605819674 0.2230443190 -0.7591882069 0.58999824575 +1413393914355760384.0000000000 0.9588614531 1.9873033712 1.5002688817 0.1439630647 0.2113683948 -0.7668551327 0.588669043747 +1413393914405760512.0000000000 0.9446778718 1.9445917915 1.5126412837 0.1292282610 0.1985157142 -0.7739150468 0.587321945959 +1413393914455760384.0000000000 0.9304502760 1.9036033705 1.5259481661 0.1190252425 0.1829357060 -0.7812878925 0.584770679927 +1413393914505760512.0000000000 0.9159949773 1.8638524131 1.5396202983 0.1097621578 0.1679510123 -0.7878641776 0.582249743511 +1413393914555760384.0000000000 0.9015147592 1.8247942031 1.5545816790 0.1035773438 0.1512381592 -0.7919862584 0.582371461889 +1413393914605760512.0000000000 0.8865689668 1.7863150605 1.5699958439 0.0978007054 0.1350484652 -0.7951239182 0.583073656411 +1413393914655760384.0000000000 0.8711302398 1.7483668397 1.5854997903 0.0918815237 0.1198858588 -0.7976991544 0.583833217243 +1413393914705760512.0000000000 0.8548210553 1.7106681574 1.6009410846 0.0866037738 0.1034094154 -0.8009338591 0.583362008186 +1413393914755760384.0000000000 0.8375949090 1.6733798581 1.6166910824 0.0831925324 0.0860116897 -0.8041779853 0.582218824659 +1413393914805760512.0000000000 0.8188692742 1.6363730774 1.6318897568 0.0782676886 0.0702303678 -0.8079606464 0.579777076356 +1413393914855760384.0000000000 0.7983980786 1.5990565112 1.6467696300 0.0719826219 0.0552878108 -0.8118372304 0.57678598413 +1413393914905760512.0000000000 0.7763210994 1.5615815441 1.6609207210 0.0621139730 0.0457351097 -0.8149926543 0.57431448481 +1413393914955760384.0000000000 0.7527075653 1.5238769940 1.6744560292 0.0493697732 0.0412501027 -0.8184463180 0.570969945813 +1413393915005760512.0000000000 0.7280519237 1.4857095605 1.6876937486 0.0368410927 0.0385408109 -0.8227528041 0.565893243522 +1413393915055760384.0000000000 0.7030864953 1.4467574532 1.7014084990 0.0263238515 0.0369768538 -0.8257841617 0.562156815727 +1413393915105760512.0000000000 0.6781261740 1.4067776343 1.7152845958 0.0183407391 0.0360207197 -0.8284431305 0.558612660641 +1413393915155760384.0000000000 0.6534938463 1.3654491874 1.7291138713 0.0116169197 0.0353605001 -0.8307438472 0.555409166759 +1413393915205760512.0000000000 0.6295849867 1.3227444928 1.7426359774 0.0073581013 0.0348520105 -0.8322751851 0.55321714728 +1413393915255760384.0000000000 0.6062219727 1.2784857212 1.7545630471 0.0036849009 0.0349596194 -0.8327597766 0.552517330995 +1413393915305760512.0000000000 0.5838408792 1.2327438013 1.7643702516 0.0022728094 0.0359042693 -0.8323086766 0.553143728766 +1413393915355760384.0000000000 0.5624341235 1.1857971812 1.7714687074 0.0009076304 0.0408699099 -0.8297665123 0.556611499758 +1413393915405760512.0000000000 0.5420676872 1.1378807129 1.7762709237 0.0010792725 -0.0495002694 0.8255181262 -0.56219959247 +1413393915455760384.0000000000 0.5229572778 1.0893303872 1.7804514441 0.0047163551 -0.0617352018 0.8196241562 -0.569546102931 +1413393915505760512.0000000000 0.5056098798 1.0398330955 1.7850165245 0.0072406550 -0.0732583071 0.8137343949 -0.576556265988 +1413393915555760384.0000000000 0.4904757435 0.9899468113 1.7901439505 0.0070087059 -0.0820407215 0.8096248202 -0.581143569737 +1413393915605760512.0000000000 0.4778172365 0.9406525817 1.7960110113 0.0025718172 -0.0875653927 0.8061460833 -0.585195847697 +1413393915655760384.0000000000 0.4672428273 0.8920761222 1.8022268788 0.0033766854 0.0906001300 -0.8044947151 0.586999546696 +1413393915705760512.0000000000 0.4584406678 0.8442427349 1.8083092843 0.0069467176 0.0944655937 -0.8030041691 0.588398078791 +1413393915755760384.0000000000 0.4512274743 0.7973138798 1.8145611620 0.0093364212 0.0987864469 -0.8013666541 0.589886052433 +1413393915805760512.0000000000 0.4456735347 0.7513428015 1.8205107735 0.0096084808 0.1035262190 -0.8001224778 0.590757157852 +1413393915855760384.0000000000 0.4419670523 0.7066477316 1.8261866774 0.0096106924 0.1080152694 -0.7998419789 0.590333079614 +1413393915905760512.0000000000 0.4402324346 0.6630139301 1.8318439199 0.0099678117 0.1117114952 -0.8000111912 0.589409262269 +1413393915955760384.0000000000 0.4406026660 0.6202759423 1.8380699041 0.0101641908 0.1146961325 -0.7991729867 0.589969510808 +1413393916005760512.0000000000 0.4431446039 0.5786292997 1.8445333741 0.0091074931 0.1182364500 -0.7972128071 0.591936597607 +1413393916055760384.0000000000 0.4480377600 0.5382913918 1.8512474911 0.0084176999 0.1211258053 -0.7956167395 0.593507948882 +1413393916105760512.0000000000 0.4552618235 0.4991987106 1.8583075652 0.0063738617 0.1240987298 -0.7935686227 0.595657384898 +1413393916155760384.0000000000 0.4650761997 0.4616102163 1.8657778696 0.0048172367 0.1259208858 -0.7914558894 0.598095560845 +1413393916205760512.0000000000 0.4772675569 0.4257746704 1.8737001379 0.0033253530 0.1254425795 -0.7896159580 0.600632783094 +1413393916255760384.0000000000 0.4922929251 0.3918269637 1.8822569815 0.0073938314 0.1181613042 -0.7892375140 0.602567327292 +1413393916305760512.0000000000 0.5091254129 0.3592372111 1.8899059914 0.0104937104 0.1084854481 -0.7901283977 0.603173196245 +1413393916355760384.0000000000 0.5275417797 0.3271941718 1.8983156245 0.0122616124 0.0967394124 -0.7925194778 0.602000013463 +1413393916405760512.0000000000 0.5469781430 0.2958622338 1.9073577393 0.0118563221 0.0836754242 -0.7960031470 0.599363696697 +1413393916455760384.0000000000 0.5669032663 0.2649397254 1.9171545290 0.0080667015 0.0702516047 -0.7989887959 0.597173797495 +1413393916505760512.0000000000 0.5870119657 0.2361336563 1.9278237790 0.0033392060 0.0551593497 -0.8018531919 0.594960296616 +1413393916555760384.0000000000 0.6069717659 0.2085376899 1.9383657285 0.0047356405 -0.0397566360 0.8042508341 -0.592939777313 +1413393916605760512.0000000000 0.6268293635 0.1815104642 1.9486282534 0.0155320964 -0.0234598472 0.8079718742 -0.588548927475 +1413393916655760384.0000000000 0.6470952513 0.1551793587 1.9596447127 0.0265281587 -0.0058423398 0.8117402093 -0.583386626897 +1413393916705760512.0000000000 0.6675565858 0.1283964060 1.9718800490 0.0382790722 0.0134075277 0.8156005391 -0.577192092273 +1413393916755760384.0000000000 0.6882538447 0.1027765224 1.9836052870 0.0506633039 0.0327490324 0.8179717302 -0.572086513583 +1413393916805760512.0000000000 0.7090928843 0.0780721949 1.9943843886 0.0627949892 0.0525951402 0.8176533942 -0.569853900193 +1413393916855760384.0000000000 0.7293728219 0.0517884054 2.0053860160 0.0766282438 0.0721720226 0.8151688347 -0.569577986195 +1413393916905760512.0000000000 0.7500222824 0.0253048042 2.0170089727 0.0877227332 0.0932229388 0.8116269746 -0.569978824048 +1413393916955760384.0000000000 0.7706786074 -0.0014037399 2.0294318031 0.0969715129 0.1155430767 0.8073153355 -0.570515794782 +1413393917005760512.0000000000 0.7910382966 -0.0284423010 2.0432590907 0.1036523411 0.1403335580 0.8003282706 -0.573617768106 +1413393917055760384.0000000000 0.8106668857 -0.0551875083 2.0573655587 0.1100800374 0.1648285896 0.7931129044 -0.575921732826 +1413393917105760512.0000000000 0.8291542637 -0.0809320466 2.0714467835 0.1176354228 0.1880217117 0.7857880277 -0.577362034431 +1413393917155760384.0000000000 0.8459195160 -0.1057632940 2.0855343632 0.1272559014 0.2098826724 0.7783961190 -0.577801593311 +1413393917205760512.0000000000 0.8611102514 -0.1291650740 2.0999120639 0.1371507044 0.2309949627 0.7714780307 -0.576760487212 +1413393917255760384.0000000000 0.8750339933 -0.1504020359 2.1136751592 0.1450909474 0.2522179501 0.7659551176 -0.573277838807 +1413393917305760512.0000000000 0.8870794187 -0.1694304752 2.1268491103 0.1550664934 0.2719195263 0.7625840027 -0.566109346935 +1413393917355760384.0000000000 0.8971944487 -0.1864827367 2.1391800382 0.1653129355 0.2915036749 0.7593056739 -0.557810124003 +1413393917405760512.0000000000 0.9052629572 -0.2019818737 2.1501145922 0.1744335388 0.3123803953 0.7542399298 -0.550557496965 +1413393917455760384.0000000000 0.9108825280 -0.2159511156 2.1584335509 0.1854398808 0.3327832515 0.7489609542 -0.542148362708 +1413393917505760512.0000000000 0.9141333950 -0.2285782840 2.1641270033 0.1973716916 0.3526350365 0.7429251037 -0.533624621468 +1413393917555760384.0000000000 0.9152976656 -0.2394606465 2.1674366002 0.2079927214 0.3739525454 0.7360454489 -0.52453371553 +1413393917605760512.0000000000 0.9136812679 -0.2488740661 2.1678898554 0.2225722327 0.3929058174 0.7293119475 -0.513994847482 +1413393917655760384.0000000000 0.9091859727 -0.2572539379 2.1659800606 0.2385496696 0.4107560261 0.7223739901 -0.502542894292 +1413393917705760512.0000000000 0.9021735077 -0.2644740102 2.1621585048 0.2568777123 0.4270394507 0.7137187995 -0.492195716911 +1413393917755760384.0000000000 0.8929477270 -0.2706379396 2.1568126760 0.2761726819 0.4422397149 0.7024949004 -0.484410568972 +1413393917805760512.0000000000 0.8815865338 -0.2760482887 2.1516340985 0.2968375048 0.4556351107 0.6890714439 -0.479024724633 +1413393917855760384.0000000000 0.8687447585 -0.2810311071 2.1476005572 0.3147299265 0.4704640973 0.6736036618 -0.475254366951 +1413393917905760512.0000000000 0.8551294363 -0.2851422799 2.1442842363 0.3286764505 0.4870848634 0.6576355284 -0.471418750629 +1413393917955760384.0000000000 0.8410013451 -0.2882566644 2.1412008979 0.3398844328 0.5044492895 0.6428898419 -0.46551276866 +1413393918005760512.0000000000 0.8260562766 -0.2902498521 2.1391186635 0.3496415630 0.5219050118 0.6274980333 -0.460013211036 +1413393918055760384.0000000000 0.8108012206 -0.2906482432 2.1377840137 0.3583251693 0.5391462329 0.6124791567 -0.453644899882 +1413393918105760512.0000000000 0.7954822967 -0.2892884042 2.1369310775 0.3664069932 0.5559195575 0.5976782819 -0.446631875613 +1413393918155760384.0000000000 0.7798121589 -0.2861466448 2.1361280306 0.3735293882 0.5724829629 0.5838053265 -0.438075785844 +1413393918205760512.0000000000 0.7637665056 -0.2811467682 2.1361889591 0.3779528208 0.5901447397 0.5690007848 -0.430254527462 +1413393918255760384.0000000000 0.7468436432 -0.2737438150 2.1359084100 0.3851760739 0.6052314110 0.5556240956 -0.420257296777 +1413393918305760512.0000000000 0.7292363330 -0.2637917043 2.1365221596 0.3911437777 0.6206909127 0.5408604406 -0.411362759386 +1413393918355760384.0000000000 0.7106771959 -0.2511335620 2.1377064523 0.3980797052 0.6350367256 0.5260502156 -0.401910532386 +1413393918405760512.0000000000 0.6916302595 -0.2356760867 2.1392521519 0.4053270950 0.6487540218 0.5113493124 -0.391599343651 +1413393918455760384.0000000000 0.6721129666 -0.2172147557 2.1410520212 0.4129623796 0.6622009820 0.4964093416 -0.380170616963 +1413393918505760512.0000000000 0.6517907373 -0.1956897308 2.1436457590 0.4204899988 0.6756460212 0.4803112545 -0.368770543613 +1413393918555760384.0000000000 0.6306957332 -0.1710447049 2.1470268685 0.4275829416 0.6891514890 0.4632666819 -0.357249261234 +1413393918605760512.0000000000 0.6090450365 -0.1429645667 2.1512916313 0.4375754925 0.7009243799 0.4445164693 -0.345886990953 +1413393918655760384.0000000000 0.5870543612 -0.1115844679 2.1555976444 0.4503672375 0.7106783786 0.4249534532 -0.333946337305 +1413393918705760512.0000000000 0.5649280794 -0.0772821877 2.1608075766 0.4620715222 0.7207393715 0.4025301093 -0.32402805102 +1413393918755760384.0000000000 0.5436455820 -0.0403607203 2.1658769111 0.4712423441 0.7323609869 0.3784631504 -0.313597961943 +1413393918805760512.0000000000 0.5233598955 -0.0005053153 2.1712887627 0.4814183229 0.7428702547 0.3517455898 -0.30439320474 +1413393918855760384.0000000000 0.5039764948 0.0426995525 2.1773988515 0.4916276261 0.7527568867 0.3220840995 -0.296515058032 +1413393918905760512.0000000000 0.4871653055 0.0889324769 2.1832921512 0.5073097446 0.7586649824 0.2934252293 -0.284545079669 +1413393918955760384.0000000000 0.4731289473 0.1376998266 2.1885868148 0.5238263813 0.7630970859 0.2662468385 -0.269075046732 +1413393919005760512.0000000000 0.4626822040 0.1882004802 2.1937405464 0.5402577872 0.7664277546 0.2409489361 -0.250307072568 +1413393919055760384.0000000000 0.4557486954 0.2397796485 2.1993497785 0.5550748705 0.7697100619 0.2152228268 -0.230472218534 +1413393919105760512.0000000000 0.4522116461 0.2917949260 2.2048078259 0.5680146080 0.7726253205 0.1908329153 -0.209743456711 +1413393919155760384.0000000000 0.4521593604 0.3432920345 2.2102570729 0.5778407380 0.7761869751 0.1653239676 -0.190530435764 +1413393919205760512.0000000000 0.4553980572 0.3940503604 2.2164358090 0.5885335587 0.7773865524 0.1392529190 -0.172936471021 +1413393919255760384.0000000000 0.4621944185 0.4434858198 2.2226740234 0.5986924181 0.7774100991 0.1134103446 -0.156009679743 +1413393919305760512.0000000000 0.4724337385 0.4912241741 2.2291042958 0.6106946123 0.7743745278 0.0867895019 -0.140938864701 +1413393919355760384.0000000000 0.4859962472 0.5360396113 2.2336879034 0.6212617378 0.7707110986 0.0610824463 -0.127699609996 +1413393919405760512.0000000000 0.5028771499 0.5768189665 2.2360007124 0.6300402263 0.7667736713 0.0358075975 -0.1175808923 +1413393919455760384.0000000000 0.5228984318 0.6141474643 2.2348634343 0.6330729097 0.7661661519 0.0124932012 -0.109781776859 +1413393919505760512.0000000000 0.5466246428 0.6482913741 2.2308213433 0.6327420063 0.7676730583 -0.0077336152 -0.101271023558 +1413393919555760384.0000000000 0.5744259420 0.6787899276 2.2246062430 0.6307846633 0.7698306019 -0.0268309658 -0.0935502650685 +1413393919605760512.0000000000 0.6061463644 0.7054975159 2.2151300275 0.6282278334 0.7721853739 -0.0435019002 -0.0846588590899 +1413393919655760384.0000000000 0.6417862583 0.7290227846 2.2032878662 0.6277580595 0.7727771499 -0.0569078326 -0.0741403666481 +1413393919705760512.0000000000 0.6809633053 0.7496259035 2.1895472875 0.6289017365 0.7720440480 -0.0664058495 -0.0634102265934 +1413393919755760384.0000000000 0.7238954344 0.7671594127 2.1742285041 0.6331171330 0.7694008648 -0.0696329483 -0.0483348496276 +1413393919805760512.0000000000 0.7697838935 0.7812281416 2.1570492363 0.6388790419 0.7656165482 -0.0684885840 -0.0312119339425 +1413393919855760384.0000000000 0.8179562263 0.7912995157 2.1375965350 0.6441938436 0.7620559772 -0.0640951121 -0.0132964699442 +1413393919905760512.0000000000 0.8674904103 0.7966717618 2.1156128712 0.6471011748 0.7601694942 -0.0582653427 0.00274947252204 +1413393919955760384.0000000000 0.9175289840 0.7970900451 2.0906455735 0.6466484407 0.7608246595 -0.0522817258 0.0160702439831 +1413393920005760512.0000000000 0.9673478998 0.7935966508 2.0630979183 0.6429293315 0.7640481451 -0.0473130932 0.0251749446045 +1413393920055760384.0000000000 1.0165980588 0.7863548430 2.0340188783 0.6388263672 0.7675119777 -0.0435402755 0.0305037859738 +1413393920105760512.0000000000 1.0650983273 0.7754723077 2.0032335956 0.6353621377 0.7704216956 -0.0405835739 0.0334415680862 +1413393920155760384.0000000000 1.1128631997 0.7615837037 1.9706280492 0.6314880135 0.7736656408 -0.0373858776 0.035590184256 +1413393920205760512.0000000000 1.1598483543 0.7447359148 1.9365823025 0.6284139756 0.7762527710 -0.0350865195 0.0360062063814 +1413393920255760384.0000000000 1.2060243105 0.7250668955 1.9018578685 0.6262463724 0.7780750034 -0.0328601730 0.0365373671398 +1413393920305760512.0000000000 1.2509794955 0.7023453249 1.8675852817 0.6238211904 0.7801377625 -0.0309128090 0.0357294311238 +1413393920355760384.0000000000 1.2952175049 0.6767779091 1.8338373907 0.6210066950 0.7824547343 -0.0283903221 0.0361837424857 +1413393920405760512.0000000000 1.3383455070 0.6484865681 1.8007354499 0.6144951255 0.7876571406 -0.0264789375 0.0359281982845 +1413393920455760384.0000000000 1.3805052342 0.6180811066 1.7685182152 0.6058444058 0.7944215935 -0.0249731787 0.0349746780546 +1413393920505760512.0000000000 1.4219396018 0.5861287270 1.7372734957 0.5977647127 0.8005890699 -0.0225416989 0.0350194404262 +1413393920555760384.0000000000 1.4624071883 0.5534727014 1.7076047790 0.5915335463 0.8052716265 -0.0208371037 0.0345179115393 +1413393920605760512.0000000000 1.5018295402 0.5205059367 1.6790622840 0.5870134577 0.8086311407 -0.0180633468 0.034707263825 +1413393920655760384.0000000000 1.5401829059 0.4876018563 1.6513912218 0.5836962454 0.8110745364 -0.0156706380 0.0348025951259 +1413393920705760512.0000000000 1.5775261884 0.4550272343 1.6245529754 0.5817482101 0.8124909867 -0.0133008862 0.0353624525222 +1413393920755760384.0000000000 1.6135800057 0.4225459732 1.5983928883 0.5813800274 0.8127750824 -0.0107707258 0.0357480168392 +1413393920805760512.0000000000 1.6483296500 0.3903294063 1.5723344490 0.5800485484 0.8137695838 -0.0096541941 0.0350648338736 +1413393920855760384.0000000000 1.6820943749 0.3584172886 1.5465062697 0.5792748192 0.8142728400 -0.0071776193 0.0367274767911 +1413393920905760512.0000000000 1.7145688276 0.3264259560 1.5202742415 0.5748470603 0.8173372522 -0.0046740778 0.0385853129428 +1413393920955760384.0000000000 1.7456471308 0.2948666084 1.4944017029 0.5693902328 0.8210872275 -0.0020998716 0.0400764033631 +1413393921005760512.0000000000 1.7755627360 0.2640001734 1.4683017637 0.5607613909 0.8269342166 -0.0010130265 0.0415383879189 +1413393921055760384.0000000000 1.8038316911 0.2342600904 1.4422143344 0.5510579190 0.8333508990 0.0010313016 0.0431321864882 +1413393921105760512.0000000000 1.8305178251 0.2064503686 1.4171334615 0.5421463623 0.8391211626 0.0026209548 0.0441149286324 +1413393921155760384.0000000000 1.8555353044 0.1815908095 1.3935829520 0.5360625557 0.8429672418 0.0034335199 0.0450707950021 +1413393921205760512.0000000000 1.8789300383 0.1595364684 1.3711614886 0.5312016135 0.8458931906 0.0054703912 0.0475355731755 +1413393921255760384.0000000000 1.9002257629 0.1408006360 1.3501196035 0.5280876433 0.8477697820 0.0067189674 0.048628111127 +1413393921305760512.0000000000 1.9196131813 0.1257498995 1.3303724635 0.5264382050 0.8487531161 0.0068288508 0.0493389413168 +1413393921355760384.0000000000 1.9367638774 0.1141393196 1.3119180104 0.5250181565 0.8497242537 0.0060558198 0.0478325727792 +1413393921405760512.0000000000 1.9521357340 0.1063948691 1.2952930466 0.5268528239 0.8486929926 0.0048152842 0.0460773196317 +1413393921455760384.0000000000 1.9657787677 0.1024607580 1.2805987097 0.5331659243 0.8448577439 0.0028337272 0.0440619991245 +1413393921505760512.0000000000 1.9776966916 0.1015692445 1.2670336263 0.5421931908 0.8391798647 0.0020920016 0.0424184153143 +1413393921555760384.0000000000 1.9882896086 0.1032808970 1.2543146976 0.5528654174 0.8322835893 0.0006406485 0.0405394482776 +1413393921605760512.0000000000 1.9978012281 0.1066637568 1.2411203845 0.5617534158 0.8262869484 0.0000461056 0.0410240985998 +1413393921655760384.0000000000 2.0059296729 0.1110528649 1.2269300668 0.5675630993 0.8223567827 -0.0011024187 0.0400029370215 +1413393921705760512.0000000000 2.0131299075 0.1154737131 1.2094605876 0.5717050836 0.8194656729 -0.0018852910 0.0403206402002 +1413393921755760384.0000000000 2.0191892504 0.1197691038 1.1887526154 0.5749674753 0.8171742674 -0.0030906567 0.0403616993868 +1413393921805760512.0000000000 2.0242703531 0.1240977185 1.1652846094 0.5784658860 0.8146763273 -0.0034829468 0.0408358851196 +1413393921855760384.0000000000 2.0283466718 0.1286214740 1.1398766189 0.5828011080 0.8115437765 -0.0038266586 0.0415322058418 +1413393921905760512.0000000000 2.0312131378 0.1332906344 1.1133014403 0.5900141244 0.8063040443 -0.0050432720 0.041613538505 +1413393921955760384.0000000000 2.0330372251 0.1375530843 1.0863377596 0.5976874990 0.8005795610 -0.0054035135 0.0425772476637 +1413393922005760512.0000000000 2.0338851626 0.1405816825 1.0593521168 0.6024765478 0.7969754068 -0.0063541485 0.0425656573946 +1413393922055760384.0000000000 2.0337765234 0.1418378119 1.0312727001 0.6005110349 0.7984088017 -0.0071327041 0.0433475137521 +1413393922105760512.0000000000 2.0325701010 0.1418820148 1.0031780538 0.5962592235 0.8015412036 -0.0079173014 0.0440902891595 +1413393922155760384.0000000000 2.0302367297 0.1405928447 0.9744702225 0.5880826698 0.8074980006 -0.0084409193 0.0451054701596 +1413393922205760512.0000000000 2.0268742722 0.1382367846 0.9447659890 0.5738555220 0.8176320953 -0.0097222109 0.0455310362924 +1413393922255760384.0000000000 2.0226494238 0.1359930405 0.9152911201 0.5605970614 0.8266987080 -0.0106405112 0.0467649493974 +1413393922305760512.0000000000 2.0172365314 0.1346930586 0.8860009888 0.5467146653 0.8359429946 -0.0126107656 0.0462963625539 +1413393922355760384.0000000000 2.0109382431 0.1353756601 0.8575552802 0.5341627533 0.8440111761 -0.0142495093 0.0459591023754 +1413393922405760512.0000000000 2.0038562705 0.1390712076 0.8306175698 0.5242587160 0.8501840827 -0.0161048719 0.045612029849 +1413393922455760384.0000000000 1.9957156778 0.1467163158 0.8057985955 0.5184364690 0.8538768293 -0.0211770375 0.0408597734028 +1413393922505760512.0000000000 1.9871561908 0.1585537945 0.7828610787 0.5184148418 0.8540144339 -0.0276016687 0.0338163632759 +1413393922555760384.0000000000 1.9787048921 0.1749711038 0.7620112261 0.5239074124 0.8506627396 -0.0348956170 0.0260042803908 +1413393922605760512.0000000000 1.9707698296 0.1950464542 0.7428885064 0.5324317573 0.8452384708 -0.0421275798 0.0177092741047 +1413393922655760384.0000000000 1.9642234641 0.2178621273 0.7241584204 0.5393367013 0.8406584193 -0.0479115519 0.0106690157052 +1413393922705760512.0000000000 1.9596372231 0.2431691502 0.7060030975 0.5461005613 0.8361020687 -0.0516457430 0.00634230686545 +1413393922755760384.0000000000 1.9568955193 0.2701122586 0.6878546803 0.5494304217 0.8338343874 -0.0532526977 0.00325211832586 +1413393922805760512.0000000000 1.9565835667 0.2988124384 0.6698815853 0.5504155695 0.8332121061 -0.0528247739 0.00313534241717 +1413393922855760384.0000000000 1.9587276316 0.3287094525 0.6519497309 0.5474353459 0.8353449824 -0.0496369803 0.00703367892955 +1413393922905760512.0000000000 1.9628985557 0.3604379078 0.6358700912 0.5426103754 0.8386526998 -0.0457969360 0.0117588348942 +1413393922955760384.0000000000 1.9690173141 0.3944427457 0.6225846371 0.5373540831 0.8421808734 -0.0400656557 0.0194089967583 +1413393923005760512.0000000000 1.9765386658 0.4304713531 0.6125159243 0.5315823596 0.8458405536 -0.0328601191 0.0299025991228 +1413393923055760384.0000000000 1.9844557312 0.4694133301 0.6062690916 0.5270410271 0.8485152449 -0.0265371183 0.0393117832309 +1413393923105760512.0000000000 1.9920722334 0.5120881842 0.6036491968 0.5239668273 0.8502012215 -0.0229492024 0.0457163085087 +1413393923155760384.0000000000 1.9990371639 0.5584702813 0.6040532313 0.5207030734 0.8519854351 -0.0202574058 0.0507815446107 +1413393923205760512.0000000000 2.0050197323 0.6090142052 0.6078902917 0.5196023076 0.8525062011 -0.0188919425 0.0537560561314 +1413393923255760384.0000000000 2.0100555082 0.6632483883 0.6134214751 0.5210896586 0.8515061472 -0.0189150413 0.0551821544379 +1413393923305760512.0000000000 2.0136077869 0.7211498953 0.6200686605 0.5249731238 0.8492812293 -0.0226741214 0.0510930232988 +1413393923355760384.0000000000 2.0158828098 0.7825658618 0.6277765145 0.5312464864 0.8457306573 -0.0293545104 0.0406833954651 +1413393923405760512.0000000000 2.0175455059 0.8464176339 0.6360965988 0.5368119509 0.8425210960 -0.0366863667 0.0254016282429 +1413393923455760384.0000000000 2.0193743837 0.9117105504 0.6446520619 0.5433318781 0.8385167522 -0.0400386775 0.00877672494582 +1413393923505760512.0000000000 2.0225396120 0.9785262881 0.6532928703 0.5505025356 0.8338810268 -0.0391483154 -0.00753664048826 +1413393923555760384.0000000000 2.0276400504 1.0457839727 0.6618795390 0.5578342846 0.8289907231 -0.0329111338 -0.0226307139536 +1413393923605760512.0000000000 2.0347169791 1.1130040594 0.6700031622 0.5626226028 0.8256064775 -0.0212782658 -0.0371077693455 +1413393923655760384.0000000000 2.0446713801 1.1803423276 0.6773095052 0.5659916278 0.8231510398 -0.0023455699 -0.0455010022631 +1413393923705760512.0000000000 2.0570126677 1.2475439749 0.6845293075 0.5681263687 0.8210632356 0.0211699266 -0.0513753493496 +1413393923755760384.0000000000 2.0713521650 1.3143744247 0.6907386345 0.5660004093 0.8211381702 0.0481310443 -0.0553086308308 +1413393923805760512.0000000000 2.0869609481 1.3812747557 0.6962593260 0.5621865722 0.8213874205 0.0742237905 -0.0613171466628 +1413393923855760384.0000000000 2.1035843318 1.4482877591 0.7020763313 0.5586019051 0.8205738635 0.0992554340 -0.069071014074 +1413393923905760512.0000000000 2.1208423002 1.5153763447 0.7086016410 0.5549074321 0.8190444448 0.1233321150 -0.0776732170953 +1413393923955760384.0000000000 2.1382911437 1.5823907740 0.7154672555 0.5507544234 0.8171617257 0.1451799836 -0.0885384187075 +1413393924005760512.0000000000 2.1557767609 1.6497909233 0.7220955998 0.5451986597 0.8157081426 0.1659428593 -0.0992049141663 +1413393924055760384.0000000000 2.1732218300 1.7179440123 0.7287079398 0.5400870036 0.8136558016 0.1854363899 -0.109011974019 +1413393924105760512.0000000000 2.1902608399 1.7871414387 0.7349489846 0.5353623587 0.8108255009 0.2064162793 -0.115505288051 +1413393924155760384.0000000000 2.2063646134 1.8577934647 0.7411533974 0.5332793602 0.8058112603 0.2289795494 -0.117684759588 +1413393924205760512.0000000000 2.2210325702 1.9292772063 0.7476599047 0.5341766641 0.7981643874 0.2528702562 -0.11681410763 +1413393924255760384.0000000000 2.2334878785 2.0008974102 0.7544722139 0.5377174202 0.7878805998 0.2777437888 -0.113853081536 +1413393924305760512.0000000000 2.2431200878 2.0720333506 0.7615710524 0.5406433775 0.7780573859 0.3001164944 -0.110731804072 +1413393924355760384.0000000000 2.2491847220 2.1420532889 0.7690261945 0.5432923939 0.7685505713 0.3207026107 -0.106363666423 +1413393924405760512.0000000000 2.2511824464 2.2104585883 0.7772866464 0.5466164610 0.7589807540 0.3390377842 -0.101054641185 +1413393924455760384.0000000000 2.2482384110 2.2768325205 0.7862407565 0.5496688388 0.7502667416 0.3551828263 -0.0938570397413 +1413393924505760512.0000000000 2.2392096382 2.3400015647 0.7969065750 0.5531216593 0.7421873457 0.3679463325 -0.0884865540376 +1413393924555760384.0000000000 2.2247533683 2.3985858507 0.8092369559 0.5569167183 0.7346719096 0.3781049680 -0.0844842429845 +1413393924605760512.0000000000 2.2037595014 2.4530344304 0.8229580988 0.5640494252 0.7255833750 0.3856306381 -0.0816457153612 +1413393924655760384.0000000000 2.1767003262 2.5015139963 0.8386952931 0.5722161138 0.7164034829 0.3912240922 -0.0792368500837 +1413393924705760512.0000000000 2.1424947555 2.5437551092 0.8569791268 0.5816341093 0.7067593060 0.3952500818 -0.077268486586 +1413393924755760384.0000000000 2.1013174054 2.5780986294 0.8794841871 0.5902846067 0.6989723777 0.3963742491 -0.0767408162623 +1413393924805760512.0000000000 2.0534661334 2.6045215134 0.9055587319 0.5956296669 0.6951774169 0.3952345599 -0.0757845740726 +1413393924855760384.0000000000 1.9985403924 2.6218544132 0.9362116831 0.5957122095 0.6982611246 0.3883577868 -0.0820767613595 +1413393924905760512.0000000000 1.9370452476 2.6308271813 0.9716152746 0.5905799684 0.7070991366 0.3775485995 -0.0931835121562 +1413393924955760384.0000000000 1.8691238509 2.6322560591 1.0119636987 0.5792475110 0.7211784237 0.3636734005 -0.110071159076 +1413393925005760512.0000000000 1.7974069776 2.6268434353 1.0566069158 0.5679184075 0.7334077498 0.3509302370 -0.128178484195 +1413393925055760384.0000000000 1.7227119498 2.6169070037 1.1045988725 0.5566980403 0.7437047978 0.3405356048 -0.145003336339 +1413393925105760512.0000000000 1.6454195319 2.6040783121 1.1548785576 0.5456874632 0.7520009002 0.3326783870 -0.161384415152 +1413393925155760384.0000000000 1.5657733218 2.5898269761 1.2071948214 0.5331216072 0.7595765578 0.3270254189 -0.178547417049 +1413393925205760512.0000000000 1.4847903296 2.5745914637 1.2600219491 0.5180093123 0.7669450849 0.3231832081 -0.197520133341 +1413393925255760384.0000000000 1.4032944695 2.5596923656 1.3123528581 0.5026848889 0.7724751540 0.3230850656 -0.214955993968 +1413393925305760512.0000000000 1.3215583421 2.5467060914 1.3647477970 0.4897387371 0.7751879010 0.3257505090 -0.230491417168 +1413393925355760384.0000000000 1.2402010181 2.5370025717 1.4163151061 0.4813061779 0.7746616265 0.3324073160 -0.240310432252 +1413393925405760512.0000000000 1.1592130108 2.5311600425 1.4676485500 0.4791239447 0.7707322078 0.3412268571 -0.244900676564 +1413393925455760384.0000000000 1.0783041341 2.5286014178 1.5193110251 0.4799177147 0.7655561492 0.3483202423 -0.24955115361 +1413393925505760512.0000000000 0.9976479707 2.5290838173 1.5706662046 0.4830251395 0.7595346988 0.3552199536 -0.252215265944 +1413393925555760384.0000000000 0.9171448787 2.5318398483 1.6211679934 0.4848699506 0.7547752777 0.3607854040 -0.255047649472 +1413393925605760512.0000000000 0.8366319288 2.5368615103 1.6699946673 0.4857304391 0.7512996798 0.3640107530 -0.25905772192 +1413393925655760384.0000000000 0.7557468114 2.5441049658 1.7151416439 0.4869224089 0.7480056027 0.3673006903 -0.261695221339 +1413393925705760512.0000000000 0.6749489628 2.5529589237 1.7532854983 0.4878166708 0.7453048763 0.3709150448 -0.262635805987 +1413393925755760384.0000000000 0.5941069128 2.5631581151 1.7839937140 0.4900035579 0.7423209850 0.3736738068 -0.263104455774 +1413393925805760512.0000000000 0.5133664245 2.5743622645 1.8066137028 0.4925175607 0.7393519521 0.3754287944 -0.264269490611 +1413393925855760384.0000000000 0.4330193681 2.5865032999 1.8223193000 0.4956804054 0.7363860081 0.3763142028 -0.26537558968 +1413393925905760512.0000000000 0.3530635323 2.5995794782 1.8320478753 0.5005973496 0.7323943497 0.3769546484 -0.266281811514 +1413393925955760384.0000000000 0.2733631977 2.6132229733 1.8369914150 0.5065838373 0.7277142355 0.3757357171 -0.269494857486 +1413393926005760512.0000000000 0.1941606447 2.6274247916 1.8374468594 0.5136834162 0.7225793714 0.3736812624 -0.272709944999 +1413393926055760384.0000000000 0.1157565650 2.6416596628 1.8359258743 0.5215648798 0.7168025375 0.3693964469 -0.278765965234 +1413393926105760512.0000000000 0.0391910625 2.6556474409 1.8340010065 0.5284341315 0.7116045295 0.3648569023 -0.285054035412 +1413393926155760384.0000000000 -0.0348648290 2.6692083502 1.8320056314 0.5324363150 0.7085269826 0.3613174082 -0.289742671845 +1413393926205760512.0000000000 -0.1062744428 2.6824940195 1.8303437805 0.5335830660 0.7077452887 0.3584285406 -0.29311209338 +1413393926255760384.0000000000 -0.1747940788 2.6954623019 1.8290621365 0.5328795343 0.7085525097 0.3566800196 -0.294571054995 +1413393926305760512.0000000000 -0.2404354452 2.7081439809 1.8284197473 0.5295755151 0.7114135673 0.3558927192 -0.294585950858 +1413393926355760384.0000000000 -0.3035790410 2.7207232869 1.8284061422 0.5246305521 0.7153688003 0.3564026600 -0.293236095036 +1413393926405760512.0000000000 -0.3641801016 2.7332895912 1.8291206699 0.5195706081 0.7185447568 0.3593901609 -0.290823877861 +1413393926455760384.0000000000 -0.4228728503 2.7461595653 1.8311534580 0.5179184739 0.7183483602 0.3623033339 -0.290641328732 +1413393926505760512.0000000000 -0.4794921572 2.7589496023 1.8327613242 0.5190322478 0.7153696015 0.3648064668 -0.292861914267 +1413393926555760384.0000000000 -0.5343035509 2.7718533457 1.8307726597 0.5220512771 0.7102096115 0.3687247117 -0.295138710916 +1413393926605760512.0000000000 -0.5875526317 2.7847744248 1.8245345382 0.5252797136 0.7040622025 0.3735159087 -0.298099821313 +1413393926655760384.0000000000 -0.6391912445 2.7973772018 1.8147652588 0.5265358559 0.6984493436 0.3796437203 -0.301328977225 +1413393926705760512.0000000000 -0.6885317553 2.8095572285 1.8046554717 0.5268526611 0.6927019911 0.3879018651 -0.303516668568 +1413393926755760384.0000000000 -0.7357874605 2.8209075663 1.7971445795 0.5243035597 0.6882377322 0.3960812852 -0.307496693953 +1413393926805760512.0000000000 -0.7804603370 2.8313041483 1.7926437735 0.5205202320 0.6842359119 0.4047586779 -0.311528999669 +1413393926855760384.0000000000 -0.8232447293 2.8411268055 1.7924944663 0.5150670596 0.6804584815 0.4145322114 -0.315982950307 +1413393926905760512.0000000000 -0.8634171259 2.8501541102 1.7959144048 0.5068991874 0.6783336315 0.4254295453 -0.319259142505 +1413393926955760384.0000000000 -0.9016800811 2.8585570949 1.8033891931 0.4973558159 0.6769316989 0.4357750567 -0.323265784401 +1413393927005760512.0000000000 -0.9377872819 2.8668028444 1.8145618595 0.4867296894 0.6767965597 0.4464308204 -0.325177103821 +1413393927055760384.0000000000 -0.9733261946 2.8755175293 1.8296497029 0.4745802779 0.6787285406 0.4546168955 -0.327756931656 +1413393927105760512.0000000000 -1.0088624109 2.8853279119 1.8482535790 0.4640438192 0.6801739737 0.4604640687 -0.331661786782 +1413393927155760384.0000000000 -1.0446480117 2.8962555392 1.8685578199 0.4538586779 0.6819988350 0.4635395844 -0.337669873199 +1413393927205760512.0000000000 -1.0805247116 2.9091353223 1.8894850692 0.4456300874 0.6833864420 0.4651174017 -0.343602384657 +1413393927255760384.0000000000 -1.1163559012 2.9238988271 1.9102299907 0.4359490678 0.6861972679 0.4666836171 -0.348264441589 +1413393927305760512.0000000000 -1.1523803797 2.9410054687 1.9304628011 0.4267651370 0.6885875744 0.4709249054 -0.349211116248 +1413393927355760384.0000000000 -1.1891133621 2.9609083528 1.9503325313 0.4205085617 0.6884587927 0.4785981739 -0.346613369882 +1413393927405760512.0000000000 -1.2269304955 2.9838674732 1.9703270602 0.4189342477 0.6849969184 0.4878331090 -0.342479452785 +1413393927455760384.0000000000 -1.2664427733 3.0094673309 1.9908814068 0.4242423644 0.6765906955 0.4985512831 -0.337179573911 +1413393927505760512.0000000000 -1.3078857818 3.0368442940 2.0122904620 0.4331752572 0.6659099887 0.5085574148 -0.332103055231 +1413393927555760384.0000000000 -1.3510620597 3.0648528582 2.0342314682 0.4418431115 0.6552602925 0.5181498271 -0.327000566642 +1413393927605760512.0000000000 -1.3958778476 3.0922978155 2.0567846948 0.4501888117 0.6434173757 0.5283707018 -0.322751476967 +1413393927655760384.0000000000 -1.4422866609 3.1185095810 2.0800644508 0.4586515790 0.6305348768 0.5380441381 -0.320270204071 +1413393927705760512.0000000000 -1.4902213063 3.1426212673 2.1042829662 0.4678950842 0.6163214068 0.5466385857 -0.320013078293 +1413393927755760384.0000000000 -1.5394200957 3.1641864147 2.1294142381 0.4783101968 0.6015847379 0.5544210955 -0.319268550993 +1413393927805760512.0000000000 -1.5896122799 3.1823180834 2.1558092601 0.4885347418 0.5878625975 0.5602006821 -0.319259405944 +1413393927855760384.0000000000 -1.6405202174 3.1959972371 2.1835701721 0.4960352859 0.5773315980 0.5636991507 -0.320749884761 +1413393927905760512.0000000000 -1.6914664091 3.2046364058 2.2124816782 0.4997465566 0.5708694881 0.5648373418 -0.324530713485 +1413393927955760384.0000000000 -1.7420511033 3.2085841048 2.2416690080 0.5025339266 0.5661562571 0.5657135625 -0.326947871017 +1413393928005760512.0000000000 -1.7920883057 3.2079528104 2.2697041071 0.5049561915 0.5626966633 0.5656735060 -0.329249441068 +1413393928055760384.0000000000 -1.8412596253 3.2030314309 2.2952782450 0.5072198147 0.5597808790 0.5662994871 -0.329663947146 +1413393928105760512.0000000000 -1.8894592289 3.1935718092 2.3189216955 0.5097306512 0.5573145950 0.5660167839 -0.330454392914 +1413393928155760384.0000000000 -1.9365242840 3.1793009364 2.3407315099 0.5113403943 0.5558061899 0.5654999506 -0.331391439743 +1413393928205760512.0000000000 -1.9825326302 3.1604418930 2.3606547461 0.5117674063 0.5558295554 0.5651456168 -0.33129753842 +1413393928255760384.0000000000 -2.0277448982 3.1366822845 2.3786783276 0.5080575347 0.5596036785 0.5637560159 -0.333017145008 +1413393928305760512.0000000000 -2.0719444380 3.1080899117 2.3951478532 0.4991373069 0.5678043184 0.5599240001 -0.339035866655 +1413393928355760384.0000000000 -2.1153881126 3.0753385684 2.4111755882 0.4891563892 0.5766864612 0.5525053081 -0.350566166219 +1413393928405760512.0000000000 -2.1581608772 3.0398509931 2.4253254891 0.4809610904 0.5840723385 0.5438698220 -0.362962187574 +1413393928455760384.0000000000 -2.1992541911 3.0024779689 2.4362634846 0.4733095114 0.5908705023 0.5357810719 -0.373883402857 +1413393928505760512.0000000000 -2.2390020125 2.9642008681 2.4445533985 0.4678930821 0.5957892754 0.5279305483 -0.383927778596 +1413393928555760384.0000000000 -2.2777933363 2.9259341763 2.4507831246 0.4659000486 0.5982186240 0.5204169767 -0.392731196694 +1413393928605760512.0000000000 -2.3150539012 2.8878204556 2.4557808832 0.4681052474 0.5972418493 0.5127596726 -0.401568386395 +1413393928655760384.0000000000 -2.3498368981 2.8499876064 2.4599903275 0.4700160233 0.5966322114 0.5064516863 -0.408193130394 +1413393928705760512.0000000000 -2.3817376015 2.8128227365 2.4639986426 0.4726082953 0.5958337001 0.5035745699 -0.409922253165 +1413393928755760384.0000000000 -2.4104341624 2.7760979670 2.4680097505 0.4741739332 0.5961259161 0.5023283421 -0.409217802618 +1413393928805760512.0000000000 -2.4361296480 2.7401081015 2.4721422556 0.4795286992 0.5942324043 0.5038571631 -0.403816834076 +1413393928855760384.0000000000 -2.4586605127 2.7041431125 2.4765183752 0.4839473030 0.5930003441 0.5058874069 -0.397773216004 +1413393928905760512.0000000000 -2.4787115043 2.6682956034 2.4813199232 0.4907249538 0.5907475350 0.5079153181 -0.390164579752 +1413393928955760384.0000000000 -2.4959205156 2.6323362412 2.4864138695 0.4977379547 0.5899105670 0.5089717040 -0.38106463477 +1413393929005760512.0000000000 -2.5104490583 2.5953829555 2.4921469058 0.5042032466 0.5910817793 0.5083770629 -0.371421833199 +1413393929055760384.0000000000 -2.5225975417 2.5569615391 2.4986844531 0.5086062644 0.5954038342 0.5051537483 -0.362813495689 +1413393929105760512.0000000000 -2.5324707136 2.5169651319 2.5061639033 0.5139644340 0.6000796221 0.5006583557 -0.353675301021 +1413393929155760384.0000000000 -2.5401279966 2.4749386741 2.5147149078 0.5190937041 0.6055296682 0.4945792807 -0.345350376277 +1413393929205760512.0000000000 -2.5457867615 2.4310951102 2.5235219788 0.5223444097 0.6134629701 0.4880505708 -0.335598185819 +1413393929255760384.0000000000 -2.5494234729 2.3853976854 2.5331739390 0.5243174007 0.6235682997 0.4791595765 -0.326588332875 +1413393929305760512.0000000000 -2.5514433200 2.3374789090 2.5432662500 0.5243787995 0.6354047530 0.4687905878 -0.318626833954 +1413393929355760384.0000000000 -2.5523531732 2.2877655918 2.5543148731 0.5238170129 0.6485133759 0.4563432330 -0.311122149567 +1413393929405760512.0000000000 -2.5525538429 2.2366640365 2.5660821013 0.5233778536 0.6616364065 0.4423805107 -0.304322808351 +1413393929455760384.0000000000 -2.5519933162 2.1846524767 2.5782028765 0.5242661062 0.6735974889 0.4283544225 -0.29651974903 +1413393929505760512.0000000000 -2.5503815877 2.1321377764 2.5906135134 0.5256916553 0.6853354357 0.4148577045 -0.286106115158 +1413393929555760384.0000000000 -2.5480560077 2.0789454143 2.6034552676 0.5272272699 0.6966076884 0.4010998066 -0.275477911082 +1413393929605760512.0000000000 -2.5451965927 2.0254564118 2.6168640260 0.5302970059 0.7065335537 0.3873061779 -0.263797929603 +1413393929655760384.0000000000 -2.5419952849 1.9716437674 2.6304601102 0.5335626142 0.7159935792 0.3735076590 -0.251308893714 +1413393929705760512.0000000000 -2.5387971661 1.9175857916 2.6447193888 0.5375082340 0.7241908621 0.3592228398 -0.239982176655 +1413393929755760384.0000000000 -2.5356538968 1.8631409037 2.6593829417 0.5404109951 0.7327789537 0.3440232936 -0.229431765362 +1413393929805760512.0000000000 -2.5326404558 1.8085178435 2.6746034233 0.5421460058 0.7416508032 0.3268452203 -0.221819738848 +1413393929855760384.0000000000 -2.5296137275 1.7538552205 2.6901744875 0.5422534925 0.7511270393 0.3074509233 -0.217355125304 +1413393929905760512.0000000000 -2.5265032831 1.6995000050 2.7066563238 0.5419441453 0.7600804560 0.2860646418 -0.216197281327 +1413393929955760384.0000000000 -2.5227046217 1.6459842306 2.7232418199 0.5411664372 0.7684218497 0.2653060859 -0.215126541938 +1413393930005760512.0000000000 -2.5178025709 1.5937924288 2.7392024716 0.5408620611 0.7757188675 0.2457168976 -0.212959328763 +1413393930055760384.0000000000 -2.5116129724 1.5433142411 2.7531247533 0.5406093934 0.7822998178 0.2275296156 -0.209711117683 +1413393930105760512.0000000000 -2.5038008792 1.4943594106 2.7648315571 0.5406248892 0.7878240442 0.2114721645 -0.205760851979 +1413393930155760384.0000000000 -2.4943561005 1.4472660800 2.7743010560 0.5419340916 0.7914234611 0.1988232055 -0.201061380241 +1413393930205760512.0000000000 -2.4832822669 1.4018193427 2.7811110664 0.5433700833 0.7940196927 0.1887245255 -0.196633500824 +1413393930255760384.0000000000 -2.4704248814 1.3579184318 2.7852062183 0.5452017743 0.7955487348 0.1828517643 -0.190846713732 +1413393930305760512.0000000000 -2.4557492851 1.3157279134 2.7862173312 0.5477429825 0.7961224493 0.1802211112 -0.183540245976 +1413393930355760384.0000000000 -2.4390901168 1.2752253898 2.7837272308 0.5520588768 0.7952072087 0.1841400279 -0.170202649481 +1413393930405760512.0000000000 -2.4212900643 1.2355389336 2.7786898102 0.5555343324 0.7940362774 0.1895796407 -0.157947952173 +1413393930455760384.0000000000 -2.4029731354 1.1967972861 2.7700405609 0.5585377727 0.7926956456 0.1957804588 -0.146079368541 +1413393930505760512.0000000000 -2.3848005383 1.1585793090 2.7565143450 0.5606879652 0.7915025344 0.2009715455 -0.136978763108 +1413393930555760384.0000000000 -2.3672325979 1.1203416550 2.7380331329 0.5622407790 0.7903845845 0.2032139681 -0.133722093342 +1413393930605760512.0000000000 -2.3504925906 1.0822972106 2.7147137233 0.5635902244 0.7893119141 0.2021494928 -0.135971849015 +1413393930655760384.0000000000 -2.3340207309 1.0445100031 2.6859936456 0.5649765876 0.7880196253 0.1999269002 -0.140910468516 +1413393930705760512.0000000000 -2.3174629572 1.0068826682 2.6526897895 0.5666523724 0.7863709310 0.1973955122 -0.146836165763 +1413393930755760384.0000000000 -2.3008192539 0.9698526365 2.6174024199 0.5688999783 0.7841628479 0.1948084226 -0.153268134967 +1413393930805760512.0000000000 -2.2836663989 0.9335035313 2.5815695328 0.5709813231 0.7818912376 0.1940873187 -0.157976371202 +1413393930855760384.0000000000 -2.2655828819 0.8974365211 2.5469633188 0.5721005842 0.7802939817 0.1935543867 -0.162415895261 +1413393930905760512.0000000000 -2.2459908112 0.8617917676 2.5148111403 0.5721234177 0.7796507951 0.1949703875 -0.16372532069 +1413393930955760384.0000000000 -2.2248879602 0.8262128970 2.4857813147 0.5709048812 0.7797347826 0.1985169342 -0.163316601358 +1413393931005760512.0000000000 -2.2028724638 0.7910590408 2.4614278389 0.5694025495 0.7800707776 0.2001650869 -0.164937128971 +1413393931055760384.0000000000 -2.1794909314 0.7566199677 2.4412015977 0.5677155511 0.7808484964 0.2029026399 -0.163722928756 +1413393931105760512.0000000000 -2.1555101043 0.7225041285 2.4259846052 0.5666872937 0.7808484010 0.2040384028 -0.165860230583 +1413393931155760384.0000000000 -2.1302317356 0.6886847246 2.4140908110 0.5635857894 0.7826325515 0.2055428368 -0.166161035078 +1413393931205760512.0000000000 -2.1042245401 0.6556841661 2.4055602678 0.5605956653 0.7844186150 0.2066832134 -0.166439135109 +1413393931255760384.0000000000 -2.0779955692 0.6235305721 2.3986764806 0.5568768497 0.7864000810 0.2075464915 -0.16848602521 +1413393931305760512.0000000000 -2.0510900901 0.5924077856 2.3906682922 0.5534028515 0.7884617501 0.2073366185 -0.170542895294 +1413393931355760384.0000000000 -2.0237134271 0.5623455564 2.3803748706 0.5503027017 0.7902293927 0.2064235612 -0.173475522289 +1413393931405760512.0000000000 -1.9959683105 0.5336505426 2.3673915437 0.5462926480 0.7923990351 0.2050598304 -0.177816135194 +1413393931455760384.0000000000 -1.9674622501 0.5067842992 2.3522130033 0.5437047972 0.7937759686 0.2030518340 -0.181864669056 +1413393931505760512.0000000000 -1.9379602355 0.4814581689 2.3354642980 0.5412698320 0.7949541637 0.2012005069 -0.185992480155 +1413393931555760384.0000000000 -1.9066137324 0.4568324678 2.3154648476 0.5398184477 0.7954757991 0.2003080140 -0.188920607845 +1413393931605760512.0000000000 -1.8740464849 0.4339302227 2.2922917231 0.5376079123 0.7965502217 0.2001064950 -0.190900150833 +1413393931655760384.0000000000 -1.8401534415 0.4131124427 2.2673863979 0.5375643487 0.7961719483 0.2003106663 -0.192380967807 +1413393931705760512.0000000000 -1.8053237924 0.3949075955 2.2406553391 0.5372743376 0.7960921032 0.2007600965 -0.193051891995 +1413393931755760384.0000000000 -1.7694782996 0.3787585109 2.2119348373 0.5372481529 0.7956732023 0.2019727301 -0.193586140277 +1413393931805760512.0000000000 -1.7325518530 0.3651303223 2.1816498077 0.5374353787 0.7953136774 0.2031938028 -0.19326574152 +1413393931855760384.0000000000 -1.6942541869 0.3535166267 2.1506330290 0.5375440717 0.7950112305 0.2046040697 -0.192719197175 +1413393931905760512.0000000000 -1.6545864504 0.3440862595 2.1201626087 0.5373883845 0.7948899498 0.2058896829 -0.192283983904 +1413393931955760384.0000000000 -1.6136796780 0.3369821748 2.0912098390 0.5379836932 0.7942732962 0.2073667484 -0.191578987404 +1413393932005760512.0000000000 -1.5715963049 0.3321419602 2.0636643982 0.5385228877 0.7938006085 0.2091986859 -0.190025269789 +1413393932055760384.0000000000 -1.5283401794 0.3293124837 2.0373978608 0.5386990380 0.7935551681 0.2122587430 -0.187135692987 +1413393932105760512.0000000000 -1.4842279213 0.3287043636 2.0124883526 0.5388723370 0.7933877623 0.2156945311 -0.183380294394 +1413393932155760384.0000000000 -1.4393507639 0.3299059483 1.9884927124 0.5394386001 0.7930153398 0.2203602229 -0.177690854526 +1413393932205760512.0000000000 -1.3940586807 0.3328885292 1.9654029106 0.5406605509 0.7922177281 0.2253425322 -0.171166536475 +1413393932255760384.0000000000 -1.3489443237 0.3375636818 1.9433414698 0.5426862027 0.7907895704 0.2311416053 -0.163453660351 +1413393932305760512.0000000000 -1.3044137173 0.3433046804 1.9223720984 0.5439439179 0.7898018064 0.2361617483 -0.156734646735 +1413393932355760384.0000000000 -1.2606834095 0.3500192938 1.9024915063 0.5453014228 0.7888859471 0.2400549319 -0.150595320004 +1413393932405760512.0000000000 -1.2183586597 0.3573215401 1.8835969552 0.5458292492 0.7885031318 0.2427788309 -0.14625895213 +1413393932455760384.0000000000 -1.1774682803 0.3653199326 1.8652396148 0.5462144415 0.7883346643 0.2448938228 -0.14214519524 +1413393932505760512.0000000000 -1.1382956451 0.3740709878 1.8474358314 0.5468265347 0.7881606575 0.2460483964 -0.138721683776 +1413393932555760384.0000000000 -1.1011133160 0.3833832723 1.8305313191 0.5484341753 0.7872479516 0.2468931621 -0.136030822425 +1413393932605760512.0000000000 -1.0659906271 0.3931305308 1.8149228264 0.5513853043 0.7855129236 0.2465497604 -0.134747573742 +1413393932655760384.0000000000 -1.0328222184 0.4031606992 1.8003714942 0.5549535341 0.7834492058 0.2454877693 -0.134051005656 +1413393932705760512.0000000000 -1.0015059065 0.4128941626 1.7866583450 0.5574812833 0.7820432567 0.2442439386 -0.134044253268 +1413393932755760384.0000000000 -0.9718124976 0.4224735852 1.7738976625 0.5599282607 0.7808149164 0.2425668437 -0.134051242036 +1413393932805760512.0000000000 -0.9436403844 0.4318748925 1.7620371506 0.5626289647 0.7793692015 0.2411032677 -0.13379652493 +1413393932855760384.0000000000 -0.9167825556 0.4409811726 1.7504533179 0.5643978930 0.7784589464 0.2411381730 -0.131563933736 +1413393932905760512.0000000000 -0.8916137293 0.4495919364 1.7400120675 0.5668592983 0.7770837710 0.2409335252 -0.129469630527 +1413393932955760384.0000000000 -0.8682872663 0.4578950087 1.7315495113 0.5729643876 0.7730834337 0.2394812731 -0.129238287068 +1413393933005760512.0000000000 -0.8466803812 0.4650445910 1.7243637112 0.5817890396 0.7666451916 0.2378324734 -0.131195952879 +1413393933055760384.0000000000 -0.8261662815 0.4703598750 1.7176974774 0.5897111391 0.7604498089 0.2369998921 -0.133371330157 +1413393933105760512.0000000000 -0.8066163370 0.4733540663 1.7120605166 0.5977835728 0.7539550077 0.2356855743 -0.136597791215 +1413393933155760384.0000000000 -0.7873991817 0.4737415132 1.7068086469 0.6023759430 0.7502538232 0.2338438696 -0.139926654756 +1413393933205760512.0000000000 -0.7683482728 0.4712915868 1.7028500518 0.6046837062 0.7484339091 0.2310786090 -0.144246232473 +1413393933255760384.0000000000 -0.7493887254 0.4656991338 1.7001351669 0.6037704113 0.7490684241 0.2270610560 -0.15100020962 +1413393933305760512.0000000000 -0.7301755403 0.4575509992 1.6990658938 0.6018905813 0.7505274638 0.2207826291 -0.160285011666 +1413393933355760384.0000000000 -0.7100441729 0.4469374857 1.6987103849 0.5991630658 0.7524363095 0.2151703300 -0.168952507584 +1413393933405760512.0000000000 -0.6884787635 0.4342786292 1.6995328891 0.5942249389 0.7559384721 0.2088211109 -0.178458656332 +1413393933455760384.0000000000 -0.6650019590 0.4200841418 1.7004266691 0.5862755610 0.7617162383 0.2028198086 -0.186904960122 +1413393933505760512.0000000000 -0.6394694369 0.4047815771 1.7012069111 0.5759245052 0.7688984130 0.1976007136 -0.19509011451 +1413393933555760384.0000000000 -0.6117246865 0.3896894599 1.7009472723 0.5657035278 0.7759249587 0.1933373977 -0.201347033072 +1413393933605760512.0000000000 -0.5817456446 0.3756346337 1.6985394856 0.5570095242 0.7820153138 0.1903399129 -0.204849106713 +1413393933655760384.0000000000 -0.5491752939 0.3630337615 1.6941261361 0.5519079198 0.7858778224 0.1900098615 -0.204181166834 +1413393933705760512.0000000000 -0.5143162895 0.3521703452 1.6877749843 0.5499009007 0.7878335223 0.1937697388 -0.198445531481 +1413393933755760384.0000000000 -0.4772716651 0.3427747850 1.6794281087 0.5506117480 0.7881794311 0.2002015641 -0.188465437411 +1413393933805760512.0000000000 -0.4385458594 0.3343310393 1.6689132559 0.5521283947 0.7877940435 0.2073075990 -0.177646672357 +1413393933855760384.0000000000 -0.3992608860 0.3265110404 1.6566379538 0.5526650259 0.7876978160 0.2131136463 -0.169340171071 +1413393933905760512.0000000000 -0.3599401766 0.3194374138 1.6430707701 0.5536364676 0.7871952533 0.2170208411 -0.163438824985 +1413393933955760384.0000000000 -0.3210572513 0.3136020743 1.6298551714 0.5569033500 0.7850414264 0.2199918096 -0.158657559912 +1413393934005760512.0000000000 -0.2826590703 0.3085452930 1.6195153395 0.5666450876 0.7779133238 0.2230265767 -0.154994682151 +1413393934055760384.0000000000 -0.2444736348 0.3029395000 1.6126828811 0.5764766705 0.7706982496 0.2251319079 -0.15170524229 +1413393934105760512.0000000000 -0.2068016417 0.2962192861 1.6100398474 0.5854392552 0.7637088665 0.2267701638 -0.150282861745 +1413393934155760384.0000000000 -0.1691469891 0.2876142404 1.6101762665 0.5899984183 0.7599751142 0.2287644122 -0.148346000538 +1413393934205760512.0000000000 -0.1317729844 0.2765781257 1.6126979445 0.5927014701 0.7576608179 0.2301694855 -0.147231315609 +1413393934255760384.0000000000 -0.0950418110 0.2630007212 1.6159239327 0.5908090108 0.7586977153 0.2300757971 -0.149624921583 +1413393934305760512.0000000000 -0.0588265113 0.2478347436 1.6189272697 0.5874818956 0.7608850532 0.2292503080 -0.152850431787 +1413393934355760384.0000000000 -0.0228900981 0.2314742984 1.6191953953 0.5805363054 0.7658204318 0.2273369226 -0.157526467394 +1413393934405760512.0000000000 0.0128407146 0.2144558062 1.6164041433 0.5725887351 0.7713990801 0.2245778821 -0.163249424412 +1413393934455760384.0000000000 0.0488349753 0.1971368023 1.6100770433 0.5656870384 0.7761757948 0.2219681511 -0.168164949095 +1413393934505760512.0000000000 0.0850237409 0.1800341100 1.6001962528 0.5595343847 0.7803509974 0.2193516380 -0.172795984132 +1413393934555760384.0000000000 0.1216408673 0.1630964795 1.5874431991 0.5541507654 0.7838586840 0.2164247686 -0.177884266494 +1413393934605760512.0000000000 0.1586095689 0.1473376010 1.5723989166 0.5500155372 0.7865583685 0.2134697321 -0.182317073341 +1413393934655760384.0000000000 0.1963712976 0.1323605124 1.5559017421 0.5467637158 0.7885572115 0.2093054579 -0.18819720662 +1413393934705760512.0000000000 0.2352040385 0.1184493098 1.5373442999 0.5438115086 0.7902518298 0.2054210335 -0.193838302675 +1413393934755760384.0000000000 0.2747576885 0.1055157230 1.5162598698 0.5383398945 0.7927743866 0.2015141509 -0.20270909444 +1413393934805760512.0000000000 0.3154834961 0.0937416776 1.4932068022 0.5307346963 0.7958067044 0.1985842772 -0.213486899327 +1413393934855760384.0000000000 0.3580062439 0.0837306405 1.4680131067 0.5222388295 0.7984918494 0.1998511251 -0.223017710658 +1413393934905760512.0000000000 0.4026333744 0.0758518285 1.4400303533 0.5126170819 0.8011519779 0.2062187408 -0.229897948233 +1413393934955760384.0000000000 0.4492835527 0.0710919371 1.4098016219 0.5040653268 0.8025527264 0.2192555669 -0.231849658123 +1413393935005760512.0000000000 0.4978891634 0.0695687289 1.3769018301 0.5000987854 0.8003825998 0.2402996173 -0.227035223543 +1413393935055760384.0000000000 0.5472741315 0.0712282861 1.3418418168 0.4980483641 0.7956216689 0.2667285674 -0.21860891653 +1413393935105760512.0000000000 0.5961720486 0.0758579501 1.3070030760 0.4961595434 0.7890985926 0.2934379408 -0.212234053888 +1413393935155760384.0000000000 0.6435652581 0.0829007547 1.2746965934 0.4934935742 0.7816115118 0.3185967766 -0.209865744736 +1413393935205760512.0000000000 0.6883546391 0.0919105415 1.2466639828 0.4898297995 0.7734848579 0.3421607269 -0.211456801694 +1413393935255760384.0000000000 0.7298276982 0.1029754790 1.2238263447 0.4853584091 0.7651236697 0.3632465679 -0.216944499223 +1413393935305760512.0000000000 0.7675396298 0.1158520741 1.2051096178 0.4802870076 0.7566420048 0.3825629514 -0.224639388881 +1413393935355760384.0000000000 0.8014898174 0.1300620490 1.1908157869 0.4747183318 0.7483290284 0.3991041936 -0.235291337125 +1413393935405760512.0000000000 0.8319742203 0.1458172445 1.1805955396 0.4714883144 0.7376598877 0.4168738500 -0.244484872025 +1413393935455760384.0000000000 0.8594535468 0.1623297846 1.1742709523 0.4693133867 0.7258552845 0.4343269663 -0.253454408978 +1413393935505760512.0000000000 0.8832773032 0.1794792906 1.1719987479 0.4687308685 0.7123880871 0.4517058785 -0.262214388548 +1413393935555760384.0000000000 0.9037671427 0.1964288401 1.1729295088 0.4660408746 0.6997895500 0.4692671645 -0.26997929053 +1413393935605760512.0000000000 0.9209705872 0.2135555379 1.1760033938 0.4653324074 0.6863214434 0.4869205358 -0.274475898443 +1413393935655760384.0000000000 0.9344631476 0.2305361685 1.1801386325 0.4640931985 0.6746078474 0.5030089254 -0.276593160098 +1413393935705760512.0000000000 0.9445071264 0.2469239072 1.1846577483 0.4656506714 0.6618410027 0.5184983848 -0.276216155084 +1413393935755760384.0000000000 0.9511160532 0.2616792614 1.1892920646 0.4680594462 0.6496078039 0.5323888467 -0.274758388136 +1413393935805760512.0000000000 0.9540116894 0.2739730518 1.1941907137 0.4723007428 0.6360813529 0.5460237653 -0.272379456943 +1413393935855760384.0000000000 0.9532022074 0.2826448419 1.1997479020 0.4765672967 0.6221246049 0.5588604587 -0.27114493419 +1413393935905760512.0000000000 0.9488135816 0.2864528244 1.2060161291 0.4774025819 0.6108154019 0.5690388004 -0.274200954095 +1413393935955760384.0000000000 0.9411027172 0.2840100213 1.2137257787 0.4704372476 0.6058354294 0.5736123256 -0.287438912472 +1413393936005760512.0000000000 0.9305408345 0.2761612339 1.2227004150 0.4593458748 0.6030213473 0.5756750833 -0.306536817414 +1413393936055760384.0000000000 0.9177076716 0.2643965431 1.2322783578 0.4468938709 0.5995825891 0.5783026501 -0.326117512533 +1413393936105760512.0000000000 0.9030769977 0.2493772558 1.2426329637 0.4332660615 0.5949809395 0.5810167178 -0.347415853478 +1413393936155760384.0000000000 0.8868054896 0.2321790174 1.2534546593 0.4187211402 0.5893238808 0.5842672073 -0.368784219632 +1413393936205760512.0000000000 0.8691203576 0.2138739203 1.2649169251 0.4016354804 0.5836245951 0.5884339086 -0.389636764273 +1413393936255760384.0000000000 0.8504090124 0.1955627798 1.2763577077 0.3850695831 0.5759952623 0.5944659795 -0.408118944907 +1413393936305760512.0000000000 0.8300499648 0.1778007798 1.2881912962 0.3681363564 0.5674070374 0.6019969105 -0.424410882035 +1413393936355760384.0000000000 0.8087956889 0.1611501602 1.2994372993 0.3519572351 0.5568555934 0.6111549122 -0.438779700969 +1413393936405760512.0000000000 0.7864513647 0.1463124734 1.3105488041 0.3378158944 0.5445877205 0.6210554886 -0.451214711854 +1413393936455760384.0000000000 0.7627872558 0.1334662053 1.3218465948 0.3260277306 0.5303057666 0.6320107139 -0.461567081102 +1413393936505760512.0000000000 0.7374835590 0.1227349327 1.3336747989 0.3198383447 0.5116010298 0.6433468190 -0.471245891169 +1413393936555760384.0000000000 0.7107210090 0.1140438435 1.3457471454 0.3161233884 0.4914316882 0.6537858528 -0.480754571253 +1413393936605760512.0000000000 0.6829895665 0.1069065604 1.3583212431 0.3136435678 0.4710058780 0.6621057771 -0.491321804083 +1413393936655760384.0000000000 0.6547298894 0.1010255754 1.3716537132 0.3117578542 0.4507325760 0.6682010281 -0.503144682269 +1413393936705760512.0000000000 0.6264550750 0.0964493780 1.3854382410 0.3098464202 0.4317394340 0.6729019227 -0.514586493695 +1413393936755760384.0000000000 0.5989051545 0.0931189693 1.3992715369 0.3064058899 0.4145009152 0.6775495526 -0.524624652236 +1413393936805760512.0000000000 0.5725199060 0.0911541170 1.4131287730 0.3022893327 0.3981988237 0.6826400454 -0.532974131239 +1413393936855760384.0000000000 0.5477129599 0.0905253264 1.4272838765 0.2974122389 0.3820632573 0.6881359256 -0.540409636811 +1413393936905760512.0000000000 0.5244068201 0.0912931300 1.4420208405 0.2932848230 0.3651769023 0.6935295643 -0.547399841109 +1413393936955760384.0000000000 0.5033079546 0.0933233101 1.4569625049 0.2874833899 0.3483217412 0.6998795701 -0.553347858475 +1413393937005760512.0000000000 0.4845502974 0.0965613960 1.4727044745 0.2834651831 0.3294474621 0.7059197918 -0.55927552 +1413393937055760384.0000000000 0.4687215839 0.1011395667 1.4889169528 0.2781095465 0.3107522035 0.7123848492 -0.564443066034 +1413393937105760512.0000000000 0.4559534482 0.1067409090 1.5058580880 0.2712679109 0.2926417227 0.7186562859 -0.5694801888 +1413393937155760384.0000000000 0.4463338626 0.1136053989 1.5235733934 0.2630700719 0.2757631810 0.7243511655 -0.574512135866 +1413393937205760512.0000000000 0.4401029612 0.1217114682 1.5421433265 0.2541847728 0.2590808472 0.7293149903 -0.579971431029 +1413393937255760384.0000000000 0.4370004660 0.1310225001 1.5613545045 0.2448142311 0.2436499966 0.7344156917 -0.584238190413 +1413393937305760512.0000000000 0.4371332039 0.1415274876 1.5816273337 0.2344898399 0.2296029283 0.7389210523 -0.588466387153 +1413393937355760384.0000000000 0.4400422888 0.1535126095 1.6022964369 0.2247390313 0.2168770468 0.7439161724 -0.590800679467 +1413393937405760512.0000000000 0.4453081086 0.1667658881 1.6235236464 0.2161000837 0.2066104485 0.7480600656 -0.592468576883 +1413393937455760384.0000000000 0.4527566064 0.1816658522 1.6433126782 0.2078934538 0.1988828938 0.7540078091 -0.590506672436 +1413393937505760512.0000000000 0.4621104317 0.1978747272 1.6590994257 0.1983805083 0.1952268730 0.7627611072 -0.583718369888 +1413393937555760384.0000000000 0.4729736764 0.2145305416 1.6706129314 0.1873179966 0.1949474348 0.7701864043 -0.577685354139 +1413393937605760512.0000000000 0.4845425662 0.2312738526 1.6765113453 0.1780360033 0.1954462598 0.7762602549 -0.572297088706 +1413393937655760384.0000000000 0.4966359971 0.2477627355 1.6776573841 0.1680179052 0.1976517600 0.7814420114 -0.567496385936 +1413393937705760512.0000000000 0.5088277645 0.2645308665 1.6752994167 0.1601417805 0.2001292050 0.7863567146 -0.562090765653 +1413393937755760384.0000000000 0.5207496601 0.2811243689 1.6713401914 0.1540978433 0.2024348406 0.7918453255 -0.555207141919 +1413393937805760512.0000000000 0.5320952556 0.2968853724 1.6680819762 0.1485978422 0.2049536137 0.7969206695 -0.548479848436 +1413393937855760384.0000000000 0.5422291897 0.3113185212 1.6662213803 0.1442352825 0.2078084371 0.8004779678 -0.543366229993 +1413393937905760512.0000000000 0.5505994042 0.3239749449 1.6666522213 0.1444262518 0.2075952494 0.8015786438 -0.54177204432 +1413393937955760384.0000000000 0.5576597119 0.3356294199 1.6681629082 0.1487116026 0.2045897110 0.7999024384 -0.544227892054 +1413393938005760512.0000000000 0.5636665683 0.3456968267 1.6705143213 0.1548389407 0.2010977471 0.7979433927 -0.546690900421 +1413393938055760384.0000000000 0.5691944751 0.3545961556 1.6734790627 0.1633785181 0.1956065938 0.7956579155 -0.549521611711 +1413393938105760512.0000000000 0.5749473415 0.3622387919 1.6772114092 0.1739882566 0.1875038949 0.7928212418 -0.553177055376 +1413393938155760384.0000000000 0.5816427220 0.3687387368 1.6820751322 0.1862596672 0.1765065936 0.7891941609 -0.55796535306 +1413393938205760512.0000000000 0.5904785461 0.3741740510 1.6878484966 0.1981318409 0.1629512320 0.7855526814 -0.563114246246 +1413393938255760384.0000000000 0.6026031009 0.3786275319 1.6944647024 0.2061436701 0.1503583937 0.7823973823 -0.568112204531 +1413393938305760512.0000000000 0.6189662206 0.3822418409 1.7022265397 0.2076462190 0.1409614219 0.7800919051 -0.573122626317 +1413393938355760384.0000000000 0.6400663363 0.3851794783 1.7114136751 0.2015701340 0.1349023370 0.7782896727 -0.579168391651 +1413393938405760512.0000000000 0.6655746448 0.3877735311 1.7216514299 0.1890594389 0.1318474625 0.7776018010 -0.584985652994 +1413393938455760384.0000000000 0.6950861988 0.3906188448 1.7330265343 0.1702191528 0.1313350832 0.7771979346 -0.591388118202 +1413393938505760512.0000000000 0.7272271320 0.3942948314 1.7444061107 0.1514202817 0.1292101368 0.7781215911 -0.595737717718 +1413393938555760384.0000000000 0.7610778132 0.3989720735 1.7555712514 0.1340822226 0.1254846819 0.7796558875 -0.598675412324 +1413393938605760512.0000000000 0.7958942223 0.4044478383 1.7651396369 0.1185052444 0.1195015673 0.7814460441 -0.600847703303 +1413393938655760384.0000000000 0.8312635764 0.4114106879 1.7717027806 0.1033404157 0.1131192873 0.7839215623 -0.601657518391 +1413393938705760512.0000000000 0.8666558207 0.4196626783 1.7746141900 0.0894308845 0.1065713056 0.7871141041 -0.600912689908 +1413393938755760384.0000000000 0.9017874075 0.4292314504 1.7748451199 0.0771146316 0.0987782770 0.7886182081 -0.601977995771 +1413393938805760512.0000000000 0.9363079037 0.4406084215 1.7725295551 0.0676684635 0.0891254123 0.7883279879 -0.604993077195 +1413393938855760384.0000000000 0.9701353419 0.4534469554 1.7691255382 0.0619839275 0.0772253638 0.7870476075 -0.608892682966 +1413393938905760512.0000000000 1.0035758762 0.4678485884 1.7655682816 0.0566033093 0.0650465163 0.7866079650 -0.611402425175 +1413393938955760384.0000000000 1.0365921630 0.4840943933 1.7624162290 0.0514927556 0.0528418044 0.7871096256 -0.612384419393 +1413393939005760512.0000000000 1.0694239832 0.5020694301 1.7599461517 0.0455076163 0.0412502522 0.7883104900 -0.612204250975 +1413393939055760384.0000000000 1.1018598978 0.5214651096 1.7590765546 0.0405925499 0.0299695412 0.7880334281 -0.613561233799 +1413393939105760512.0000000000 1.1344091829 0.5417901475 1.7618303010 0.0346669815 0.0191655308 0.7803683471 -0.624064200009 +1413393939155760384.0000000000 1.1669012399 0.5642427998 1.7657120902 0.0288399398 0.0083499312 0.7716686833 -0.635315653677 +1413393939205760512.0000000000 1.1994589019 0.5898166773 1.7679561604 0.0224717169 -0.0011490489 0.7700292433 -0.637611689131 +1413393939255760384.0000000000 1.2316036554 0.6188225078 1.7680430850 0.0177026416 -0.0092663745 0.7754454269 -0.631098360585 +1413393939305760512.0000000000 1.2632561181 0.6505912433 1.7667716297 0.0133141202 -0.0152014671 0.7858007631 -0.618149504846 +1413393939355760384.0000000000 1.2943317977 0.6849782179 1.7634132615 0.0103431253 -0.0200045510 0.8013381581 -0.597787582745 +1413393939405760512.0000000000 1.3254305649 0.7202320325 1.7584597466 0.0046181801 -0.0208761842 0.8197790533 -0.572280666361 +1413393939455760384.0000000000 1.3563147719 0.7547411624 1.7515926525 0.0026671064 0.0189743571 -0.8384969275 0.544569337149 +1413393939505760512.0000000000 1.3868252759 0.7866274003 1.7431559716 0.0108557008 0.0144153177 -0.8554106276 0.517635982684 +1413393939555760384.0000000000 1.4165173890 0.8142152331 1.7332355997 0.0187451920 0.0090599050 -0.8691618946 0.494089199231 +1413393939605760512.0000000000 1.4446696698 0.8364453186 1.7216548321 0.0246895227 0.0035891682 -0.8803640984 0.473641847454 +1413393939655760384.0000000000 1.4711291491 0.8521253754 1.7087286636 0.0286353208 -0.0010625043 -0.8894835623 0.456067847922 +1413393939705760512.0000000000 1.4950480234 0.8596924725 1.6948241893 0.0255890196 -0.0005705217 -0.8952027562 0.444923478591 +1413393939755760384.0000000000 1.5167860624 0.8580318805 1.6809341989 0.0193113593 0.0023616498 -0.8961633649 0.443297549534 +1413393939805760512.0000000000 1.5369179504 0.8465509027 1.6681860401 0.0114303505 0.0065414100 -0.8899908608 0.455788135757 +1413393939855760384.0000000000 1.5561214946 0.8253996228 1.6578744305 0.0052369324 0.0088341696 -0.8751201369 0.48379673202 +1413393939905760512.0000000000 1.5746156009 0.7973873141 1.6508133228 0.0020003953 0.0078286964 -0.8526422659 0.522432652477 +1413393939955760384.0000000000 1.5925972980 0.7659867897 1.6464610684 0.0004543585 -0.0067105171 0.8246619055 -0.565585982969 +1413393940005760512.0000000000 1.6102199537 0.7348825266 1.6432871347 0.0008873135 -0.0045042225 0.7961079076 -0.605137277031 +1413393940055760384.0000000000 1.6276458665 0.7060350382 1.6417457609 0.0030864907 -0.0000531566 -0.7678924454 0.64057135672 +1413393940105760512.0000000000 1.6442216498 0.6818338447 1.6403638803 0.0074372083 -0.0042084086 -0.7432142374 0.66899893462 +1413393940155760384.0000000000 1.6595697335 0.6644187134 1.6386679558 0.0143907484 -0.0092303504 -0.7240166371 0.689570602744 +1413393940205760512.0000000000 1.6729638345 0.6558216982 1.6371012287 0.0189716723 -0.0122144992 -0.7086747723 0.705174410153 +1413393940255760384.0000000000 1.6845134962 0.6551270992 1.6341691626 0.0226638669 -0.0145249751 -0.7024196769 0.711253802605 +1413393940305760512.0000000000 1.6938276270 0.6625998052 1.6298293586 0.0242438017 -0.0153712304 -0.7089149930 0.704709511794 +1413393940355760384.0000000000 1.7006570854 0.6790923213 1.6236258456 0.0212516732 -0.0133658966 -0.7268638045 0.686322612798 +1413393940405760512.0000000000 1.7049474857 0.7029462506 1.6178630019 0.0161081802 -0.0106572114 -0.7505270788 0.660557381609 +1413393940455760384.0000000000 1.7072533644 0.7324661362 1.6120983280 0.0128519918 -0.0096803108 -0.7774751801 0.628707771698 +1413393940505760512.0000000000 1.7078793165 0.7653032491 1.6058815754 0.0113074980 -0.0100737970 -0.8070633738 0.590270590252 +1413393940555760384.0000000000 1.7074515847 0.7987950234 1.6014791755 0.0139331987 -0.0135563667 -0.8332162994 0.552605364963 +1413393940605760512.0000000000 1.7056820547 0.8297390053 1.5996429028 0.0188876112 -0.0198586875 -0.8533797720 0.520568780757 +1413393940655760384.0000000000 1.7019023650 0.8556404445 1.6004870643 0.0239880394 -0.0266834079 -0.8673421503 0.496417328457 +1413393940705760512.0000000000 1.6957689229 0.8746511868 1.6038093830 0.0309210250 -0.0350547561 -0.8765579959 0.479021016438 +1413393940755760384.0000000000 1.6866952287 0.8860840547 1.6095359605 0.0400359658 -0.0460594941 -0.8818687301 0.467528809042 +1413393940805760512.0000000000 1.6734055211 0.8886679435 1.6177857250 0.0455470358 -0.0540129784 -0.8814353861 0.46699007029 +1413393940855760384.0000000000 1.6548318745 0.8826627074 1.6284743504 0.0423237748 -0.0550684791 -0.8737892702 0.481319511229 +1413393940905760512.0000000000 1.6316806421 0.8700551523 1.6403621593 0.0324509846 -0.0500003715 -0.8623963678 0.502712046068 +1413393940955760384.0000000000 1.6055002644 0.8522839534 1.6537021628 0.0225736427 -0.0438332241 -0.8469282555 0.529416290921 +1413393941005760512.0000000000 1.5767281547 0.8311393484 1.6683177202 0.0130920743 -0.0375213543 -0.8273801986 0.560234551329 +1413393941055760384.0000000000 1.5464045587 0.8087194262 1.6845768342 0.0077327394 -0.0338287279 -0.8043369229 0.593159284164 +1413393941105760512.0000000000 1.5146765695 0.7873041685 1.7012262304 0.0027109810 -0.0294490740 -0.7810387379 0.623781927102 +1413393941155760384.0000000000 1.4819504140 0.7689946928 1.7177153396 0.0003559082 -0.0259014180 -0.7604495725 0.648880141082 +1413393941205760512.0000000000 1.4484267592 0.7553751308 1.7331067981 0.0009972902 0.0228035626 0.7440369809 -0.667748436113 +1413393941255760384.0000000000 1.4140723307 0.7473771182 1.7464620873 0.0020432756 0.0197260062 0.7359978661 -0.676693321054 +1413393941305760512.0000000000 1.3789606635 0.7457589123 1.7565453201 0.0028254027 0.0164163647 0.7411565928 -0.671125491311 +1413393941355760384.0000000000 1.3433402623 0.7501104523 1.7649801542 0.0024388527 0.0137156497 0.7542954527 -0.656387311745 +1413393941405760512.0000000000 1.3072852595 0.7594028719 1.7721622864 0.0017188047 0.0113538974 0.7725447643 -0.634856457676 +1413393941455760384.0000000000 1.2708684133 0.7720648775 1.7788842258 0.0008910257 0.0094003809 0.7922369262 -0.61014055073 +1413393941505760512.0000000000 1.2336477335 0.7867455335 1.7849995799 0.0007310101 0.0070552077 0.8134531073 -0.581587252127 +1413393941555760384.0000000000 1.1958605907 0.8013292809 1.7918458955 0.0005684284 0.0051202026 0.8324371758 -0.554095487074 +1413393941605760512.0000000000 1.1576928769 0.8139959751 1.7998356908 0.0001576602 0.0035012987 0.8484612426 -0.529245912538 +1413393941655760384.0000000000 1.1190759399 0.8228309079 1.8092008842 0.0002037965 0.0018759141 0.8602548195 -0.509860848623 +1413393941705760512.0000000000 1.0798951254 0.8267336113 1.8183386926 0.0011387541 0.0018229001 0.8691184728 -0.494599292842 +1413393941755760384.0000000000 1.0401890100 0.8250494197 1.8257318332 0.0037137531 0.0025001289 0.8760568291 -0.482187089732 +1413393941805760512.0000000000 1.0001580149 0.8175340661 1.8312220119 0.0070072359 0.0031552667 0.8804820633 -0.474017171793 +1413393941855760384.0000000000 0.9600813993 0.8026843277 1.8358608737 0.0103942809 0.0043688590 0.8798082568 -0.475195016052 +1413393941905760512.0000000000 0.9201681009 0.7802771266 1.8407124503 0.0127785402 0.0060204210 0.8717451517 -0.489755912572 +1413393941955760384.0000000000 0.8803127579 0.7519468375 1.8457024760 0.0153825071 0.0077112779 0.8593980434 -0.511017531692 +1413393942005760512.0000000000 0.8407349055 0.7189411299 1.8517452703 0.0174766690 0.0095651965 0.8423676467 -0.538534883522 +1413393942055760384.0000000000 0.8013809857 0.6832038341 1.8593372769 0.0197402288 0.0113014384 0.8207603625 -0.57081961097 +1413393942105760512.0000000000 0.7622225468 0.6474949971 1.8674030832 0.0225394716 0.0126378218 0.7982628075 -0.601754724043 +1413393942155760384.0000000000 0.7236563252 0.6138150132 1.8753272459 0.0252454176 0.0135858962 0.7771990970 -0.628601348936 +1413393942205760512.0000000000 0.6857295951 0.5837713747 1.8831154553 0.0279260778 0.0141595313 0.7586606103 -0.65073321739 +1413393942255760384.0000000000 0.6484165120 0.5586805627 1.8901138092 0.0316804788 0.0135704789 0.7459676156 -0.665089847939 +1413393942305760512.0000000000 0.6120637367 0.5394178674 1.8974527264 0.0336277811 0.0138144764 0.7370677057 -0.674840373551 +1413393942355760384.0000000000 0.5766500907 0.5266858540 1.9047307972 0.0355463441 0.0136251903 0.7335625365 -0.678554947396 +1413393942405760512.0000000000 0.5423623490 0.5208584533 1.9112431895 0.0374338355 0.0129943387 0.7366342289 -0.675129519419 +1413393942455760384.0000000000 0.5092780777 0.5215591552 1.9171022669 0.0391154434 0.0128208967 0.7460728688 -0.664590762195 +1413393942505760512.0000000000 0.4776065537 0.5279240851 1.9228163034 0.0403746927 0.0120197766 0.7590721864 -0.649642074543 +1413393942555760384.0000000000 0.4472117784 0.5386587694 1.9275140002 0.0412403515 0.0113652781 0.7763830369 -0.62880795474 +1413393942605760512.0000000000 0.4178366900 0.5526188604 1.9304033595 0.0413113380 0.0117035731 0.7964192619 -0.603218665983 +1413393942655760384.0000000000 0.3896480339 0.5678898442 1.9318466570 0.0400526354 0.0127069404 0.8154782562 -0.577260369061 +1413393942705760512.0000000000 0.3624378314 0.5833896724 1.9319438379 0.0399776332 0.0124847073 0.8321864292 -0.552911989298 +1413393942755760384.0000000000 0.3362427726 0.5963650805 1.9313996978 0.0387868336 0.0129136153 0.8458346723 -0.531876420924 +1413393942805760512.0000000000 0.3106404725 0.6056724141 1.9291381947 0.0387359131 0.0119389693 0.8566357905 -0.514326853828 +1413393942855760384.0000000000 0.2857584110 0.6110289414 1.9243792646 0.0383381196 0.0113089810 0.8643624924 -0.501278143646 +1413393942905760512.0000000000 0.2615755239 0.6118430878 1.9174786998 0.0380556512 0.0103802922 0.8702341985 -0.491056470027 +1413393942955760384.0000000000 0.2380578110 0.6071204474 1.9090574091 0.0367108601 0.0102718611 0.8740628795 -0.484314860708 +1413393943005760512.0000000000 0.2150059001 0.5962199404 1.8997326862 0.0367278497 0.0092415212 0.8731689212 -0.485944126806 +1413393943055760384.0000000000 0.1927255594 0.5781322374 1.8919098777 0.0362003514 0.0080765024 0.8640242998 -0.502081979411 +1413393943105760512.0000000000 0.1711601389 0.5543633017 1.8859627107 0.0368850730 0.0062113267 0.8497230166 -0.525900851685 +1413393943155760384.0000000000 0.1506208552 0.5268490861 1.8822437097 0.0360296748 0.0056690076 0.8307590367 -0.555435997921 +1413393943205760512.0000000000 0.1310787483 0.4980937710 1.8795012108 0.0356384980 0.0043019269 0.8106307843 -0.584456262153 +1413393943255760384.0000000000 0.1123506882 0.4700861421 1.8774474300 0.0364232199 0.0032244846 0.7901131346 -0.611869419323 +1413393943305760512.0000000000 0.0947315738 0.4444881706 1.8754790253 0.0347458905 0.0042813042 0.7725880411 -0.633941726253 +1413393943355760384.0000000000 0.0782431230 0.4228442065 1.8742378116 0.0329021799 0.0042830383 0.7561580559 -0.653547317838 +1413393943405760512.0000000000 0.0624866287 0.4064139948 1.8726931596 0.0313231024 0.0054578593 0.7442279848 -0.667168480747 +1413393943455760384.0000000000 0.0474643728 0.3955408585 1.8712217923 0.0304295130 0.0061941866 0.7367499180 -0.675451874783 +1413393943505760512.0000000000 0.0332858703 0.3900856574 1.8680093532 0.0314459140 0.0059856275 0.7398076609 -0.672056509246 +1413393943555760384.0000000000 0.0195177661 0.3916435226 1.8620579809 0.0341626871 0.0059828885 0.7534097626 -0.656636006867 +1413393943605760512.0000000000 0.0066422489 0.3983160195 1.8560932128 0.0369348701 0.0056222035 0.7688875571 -0.638291571841 +1413393943655760384.0000000000 -0.0051801749 0.4089781383 1.8490751610 0.0388737157 0.0056683518 0.7890610664 -0.613057368839 +1413393943705760512.0000000000 -0.0160405981 0.4214775404 1.8428367013 0.0407114616 0.0062684979 0.8086034871 -0.586910285742 +1413393943755760384.0000000000 -0.0254773123 0.4343320935 1.8377490271 0.0407063501 0.0080081707 0.8264952403 -0.561412931904 +1413393943805760512.0000000000 -0.0340379814 0.4457412162 1.8336276755 0.0413813992 0.0095178390 0.8419480671 -0.53788515771 +1413393943855760384.0000000000 -0.0421790551 0.4538005245 1.8313189486 0.0434767285 0.0127073978 0.8525972559 -0.520601781899 +1413393943905760512.0000000000 -0.0498828131 0.4570583976 1.8312732695 0.0460952246 0.0180652653 0.8596098648 -0.50854671052 +1413393943955760384.0000000000 -0.0573369200 0.4537827642 1.8336611214 0.0511199498 0.0229487568 0.8620458355 -0.50372322034 +1413393944005760512.0000000000 -0.0641873791 0.4439761438 1.8401185775 0.0542737193 0.0312485160 0.8579359408 -0.509925303478 +1413393944055760384.0000000000 -0.0705564656 0.4296382433 1.8474757537 0.0575579548 0.0408615547 0.8495293217 -0.522797615438 +1413393944105760512.0000000000 -0.0764070076 0.4107900860 1.8566996664 0.0580556174 0.0532943311 0.8381864364 -0.539659853483 +1413393944155760384.0000000000 -0.0822070800 0.3894992998 1.8674901209 0.0560331565 0.0685653173 0.8242265997 -0.559293835925 +1413393944205760512.0000000000 -0.0886129760 0.3673593374 1.8793175397 0.0541398702 0.0842785720 0.8084775699 -0.579939665544 +1413393944255760384.0000000000 -0.0961262768 0.3456397358 1.8917939139 0.0558563442 0.0973384013 0.7912689274 -0.601081349735 +1413393944305760512.0000000000 -0.1048391617 0.3259954141 1.9044091301 0.0589633771 0.1095316063 0.7742558119 -0.620527263774 +1413393944355760384.0000000000 -0.1148186827 0.3093867522 1.9160386153 0.0648638227 0.1197347252 0.7590207692 -0.6366661229 +1413393944405760512.0000000000 -0.1255897786 0.2968709909 1.9265699692 0.0728960180 0.1276303453 0.7474701725 -0.64783100173 +1413393944455760384.0000000000 -0.1363505625 0.2891824624 1.9363644224 0.0788954493 0.1352122729 0.7402151401 -0.653891960232 +1413393944505760512.0000000000 -0.1473016886 0.2868852003 1.9440941477 0.0895709275 0.1385669843 0.7401069002 -0.651934058053 +1413393944555760384.0000000000 -0.1580215959 0.2900961886 1.9495476601 0.1007360057 0.1401868777 0.7486698060 -0.64007297875 +1413393944605760512.0000000000 -0.1683415654 0.2977718981 1.9536412354 0.1116054142 0.1412161230 0.7621255038 -0.621905904875 +1413393944655760384.0000000000 -0.1776538151 0.3087830090 1.9573118122 0.1178762105 0.1438107062 0.7783911763 -0.599608919543 +1413393944705760512.0000000000 -0.1858698679 0.3219011518 1.9608959696 0.1214001142 0.1465827737 0.7957085635 -0.574998595349 +1413393944755760384.0000000000 -0.1934468770 0.3349561133 1.9654408666 0.1235273224 0.1496841805 0.8110121574 -0.551901193453 +1413393944805760512.0000000000 -0.2005848641 0.3466945407 1.9713453873 0.1232933587 0.1530253715 0.8241212894 -0.531230725547 +1413393944855760384.0000000000 -0.2080363980 0.3557538329 1.9786227955 0.1230357194 0.1558992053 0.8342399708 -0.514394129611 +1413393944905760512.0000000000 -0.2161256980 0.3611615100 1.9873659567 0.1223994559 0.1584350657 0.8417462434 -0.501378065756 +1413393944955760384.0000000000 -0.2252334061 0.3618721179 1.9980218591 0.1207685833 0.1622114389 0.8465552086 -0.492388745991 +1413393945005760512.0000000000 -0.2361413041 0.3569787679 2.0109366239 0.1216565005 0.1655897927 0.8464919062 -0.491152897945 +1413393945055760384.0000000000 -0.2490915975 0.3461906859 2.0265129768 0.1265784284 0.1674736495 0.8388280836 -0.502292667986 +1413393945105760512.0000000000 -0.2635618803 0.3309453914 2.0428194661 0.1344374889 0.1688129054 0.8248671462 -0.522515986063 +1413393945155760384.0000000000 -0.2788301236 0.3132295423 2.0582866121 0.1438743374 0.1708178403 0.8066963242 -0.54714027547 +1413393945205760512.0000000000 -0.2942418224 0.2944482279 2.0716430652 0.1548420003 0.1731484321 0.7854861348 -0.573633251714 +1413393945255760384.0000000000 -0.3088288326 0.2766465920 2.0820439755 0.1659429094 0.1766064944 0.7636003283 -0.598487790723 +1413393945305760512.0000000000 -0.3217697678 0.2612866168 2.0885151391 0.1759696899 0.1814099337 0.7441955267 -0.618302613818 +1413393945355760384.0000000000 -0.3329448593 0.2492131501 2.0904916971 0.1857679244 0.1879284057 0.7301261161 -0.630150019566 +1413393945405760512.0000000000 -0.3417231041 0.2410695447 2.0878683980 0.1936847014 0.1969072380 0.7221102417 -0.634248038909 +1413393945455760384.0000000000 -0.3477755125 0.2368639242 2.0811824791 0.1995212357 0.2078763422 0.7192970233 -0.632131707074 +1413393945505760512.0000000000 -0.3512613623 0.2363752036 2.0702824495 0.2012753089 0.2225052749 0.7225568836 -0.622809122213 +1413393945555760384.0000000000 -0.3525350759 0.2396876027 2.0566939571 0.2026936282 0.2377157718 0.7296777002 -0.608257312965 +1413393945605760512.0000000000 -0.3521271923 0.2460038293 2.0428161009 0.2056895783 0.2514944723 0.7377184985 -0.591788598061 +1413393945655760384.0000000000 -0.3502129714 0.2552091674 2.0290727718 0.2103268598 0.2644017812 0.7455123976 -0.574513337736 +1413393945705760512.0000000000 -0.3473540703 0.2661258986 2.0158470095 0.2151259682 0.2769726184 0.7536478468 -0.555897391091 +1413393945755760384.0000000000 -0.3439719683 0.2780812418 2.0031813023 0.2197994551 0.2899641447 0.7615789235 -0.536289602397 +1413393945805760512.0000000000 -0.3406218332 0.2894004763 1.9910816523 0.2240275439 0.3029208642 0.7690139165 -0.516399269833 +1413393945855760384.0000000000 -0.3378766285 0.2991598697 1.9800302938 0.2279153215 0.3163266721 0.7747213532 -0.497794001253 +1413393945905760512.0000000000 -0.3367677023 0.3064997398 1.9706179909 0.2339651552 0.3275380292 0.7775799490 -0.483061661191 +1413393945955760384.0000000000 -0.3378926888 0.3102398892 1.9648434425 0.2414491015 0.3374935472 0.7725705931 -0.480557088948 +1413393946005760512.0000000000 -0.3416191682 0.3108458827 1.9619142647 0.2542626796 0.3438913056 0.7619119746 -0.486394287216 +1413393946055760384.0000000000 -0.3468446956 0.3088332531 1.9611098870 0.2686880373 0.3484284408 0.7469081466 -0.498530421129 +1413393946105760512.0000000000 -0.3526149996 0.3054835661 1.9612103568 0.2844211398 0.3519717715 0.7293850464 -0.513047698947 +1413393946155760384.0000000000 -0.3576787361 0.3016406385 1.9620515555 0.3003678150 0.3551057530 0.7101947043 -0.528490834234 +1413393946205760512.0000000000 -0.3610030448 0.2980370744 1.9630223042 0.3159467844 0.3587434151 0.6908372892 -0.542424770276 +1413393946255760384.0000000000 -0.3614192982 0.2956454719 1.9625348791 0.3287377175 0.3646166641 0.6749025651 -0.550901741707 +1413393946305760512.0000000000 -0.3583933426 0.2949725931 1.9599642591 0.3386333698 0.3735981349 0.6648281353 -0.55114011374 +1413393946355760384.0000000000 -0.3512212374 0.2957298936 1.9569441464 0.3413532059 0.3880131901 0.6574471167 -0.548349379379 +1413393946405760512.0000000000 -0.3401266770 0.2983978351 1.9519399353 0.3404738213 0.4062538304 0.6548724162 -0.538681279363 +1413393946455760384.0000000000 -0.3262807752 0.3025868247 1.9467230108 0.3371852452 0.4262183052 0.6530921124 -0.527365868692 +1413393946505760512.0000000000 -0.3106938179 0.3087236343 1.9412516085 0.3357513167 0.4458974897 0.6524835184 -0.512554134 +1413393946555760384.0000000000 -0.2937588667 0.3164990119 1.9356168098 0.3342191217 0.4659712554 0.6534952894 -0.494077194915 +1413393946605760512.0000000000 -0.2767538854 0.3255550396 1.9296161384 0.3341591392 0.4847695662 0.6560307371 -0.472186201968 +1413393946655760384.0000000000 -0.2605497966 0.3354956758 1.9233246099 0.3351985268 0.5034283332 0.6584454106 -0.447941404854 +1413393946705760512.0000000000 -0.2467248368 0.3456773360 1.9176094948 0.3388714654 0.5202727467 0.6599064169 -0.423090911991 +1413393946755760384.0000000000 -0.2355419966 0.3555874661 1.9135930144 0.3452213862 0.5349696201 0.6587740387 -0.400807267867 +1413393946805760512.0000000000 -0.2285543605 0.3642486779 1.9125652367 0.3541421269 0.5479160036 0.6528601561 -0.384896120396 +1413393946855760384.0000000000 -0.2255432986 0.3712958778 1.9139464302 0.3653556903 0.5587466557 0.6434982872 -0.374469422927 +1413393946905760512.0000000000 -0.2267356770 0.3763833177 1.9178775833 0.3808936729 0.5654201020 0.6300483427 -0.371832225781 +1413393946955760384.0000000000 -0.2315345570 0.3796216016 1.9241056879 0.4005640863 0.5683234681 0.6120719412 -0.376729063445 +1413393947005760512.0000000000 -0.2388553535 0.3812205725 1.9313944177 0.4237562374 0.5675593612 0.5902164287 -0.387235832711 +1413393947055760384.0000000000 -0.2465316732 0.3818180919 1.9366885140 0.4462337050 0.5661629412 0.5679799185 -0.397157168854 +1413393947105760512.0000000000 -0.2533175966 0.3815580017 1.9381506806 0.4661582350 0.5656735968 0.5470734040 -0.404253104516 +1413393947155760384.0000000000 -0.2582811514 0.3803742881 1.9353317971 0.4813727550 0.5686679786 0.5288266701 -0.40649643771 +1413393947205760512.0000000000 -0.2600914781 0.3782714577 1.9276446297 0.4914386279 0.5756340018 0.5144470717 -0.403085327717 +1413393947255760384.0000000000 -0.2583100042 0.3750305229 1.9163181043 0.4990748957 0.5841571139 0.5019971317 -0.397093936619 +1413393947305760512.0000000000 -0.2536215039 0.3708108739 1.9017258776 0.5048332750 0.5942574891 0.4904333242 -0.389199891564 +1413393947355760384.0000000000 -0.2461367502 0.3655689652 1.8846754193 0.5101289642 0.6046224001 0.4782906020 -0.381363728222 +1413393947405760512.0000000000 -0.2359820700 0.3591610636 1.8650189810 0.5120946399 0.6172531394 0.4657417537 -0.373954891107 +1413393947455760384.0000000000 -0.2232551757 0.3516078290 1.8428085127 0.5072882157 0.6346951960 0.4516323020 -0.368576909576 +1413393947505760512.0000000000 -0.2081742025 0.3437470828 1.8193051222 0.4999179981 0.6536116262 0.4369806342 -0.363210355961 +1413393947555760384.0000000000 -0.1908092559 0.3363811326 1.7960775410 0.4927043557 0.6716048295 0.4217751304 -0.35818306803 +1413393947605760512.0000000000 -0.1715072606 0.3305008829 1.7733907700 0.4853258517 0.6894795479 0.4061529770 -0.352301759697 +1413393947655760384.0000000000 -0.1503371335 0.3264080561 1.7509507129 0.4764483624 0.7077757177 0.3921363136 -0.343918017802 +1413393947705760512.0000000000 -0.1276000319 0.3252730273 1.7285220711 0.4679323498 0.7252029138 0.3824204255 -0.329961616 +1413393947755760384.0000000000 -0.1038514009 0.3279041209 1.7067326480 0.4636869190 0.7397743007 0.3761480655 -0.310227429467 +1413393947805760512.0000000000 -0.0796239142 0.3343242213 1.6860344478 0.4641531826 0.7505041839 0.3729451765 -0.286735397843 +1413393947855760384.0000000000 -0.0561435468 0.3445864521 1.6676666780 0.4698112318 0.7570122900 0.3702305855 -0.262943174056 +1413393947905760512.0000000000 -0.0343674225 0.3578149494 1.6520131514 0.4782690856 0.7607978723 0.3657553550 -0.242215398961 +1413393947955760384.0000000000 -0.0149363561 0.3733216101 1.6389642950 0.4900765394 0.7613011517 0.3598255464 -0.225324472885 +1413393948005760512.0000000000 0.0018062551 0.3909169753 1.6281492206 0.5099546506 0.7548550620 0.3561628061 -0.208058033413 +1413393948055760384.0000000000 0.0156860630 0.4087121152 1.6189232088 0.5298319328 0.7469900225 0.3521917776 -0.192989588002 +1413393948105760512.0000000000 0.0270244945 0.4253756080 1.6107935996 0.5462972586 0.7405040504 0.3472162209 -0.180704046813 +1413393948155760384.0000000000 0.0358040014 0.4398046735 1.6042186814 0.5592624265 0.7362393923 0.3389884712 -0.17396526073 +1413393948205760512.0000000000 0.0421640959 0.4517047051 1.5991757833 0.5708315292 0.7326033732 0.3283864510 -0.172063946504 +1413393948255760384.0000000000 0.0466831498 0.4607232721 1.5952887239 0.5813775311 0.7292269145 0.3165240740 -0.17332277407 +1413393948305760512.0000000000 0.0501289626 0.4662705127 1.5926961083 0.5903921961 0.7265633492 0.3027741937 -0.178523225354 +1413393948355760384.0000000000 0.0535557020 0.4687996256 1.5911093645 0.6002751138 0.7227001944 0.2888805341 -0.184179949526 +1413393948405760512.0000000000 0.0578205605 0.4679737200 1.5899495591 0.6101366345 0.7184796414 0.2761073086 -0.187843142633 +1413393948455760384.0000000000 0.0634236015 0.4633274243 1.5886545985 0.6166713569 0.7165896142 0.2647534296 -0.190056265 +1413393948505760512.0000000000 0.0707269966 0.4549946175 1.5870933643 0.6197278426 0.7175774019 0.2550075536 -0.189713523751 +1413393948555760384.0000000000 0.0802109367 0.4425931650 1.5848813379 0.6153663514 0.7245538557 0.2470964769 -0.187854451095 +1413393948605760512.0000000000 0.0916782867 0.4272806012 1.5806294082 0.6052161763 0.7362368490 0.2431186109 -0.18044950306 +1413393948655760384.0000000000 0.1043454834 0.4102519819 1.5754941557 0.5899141795 0.7518424075 0.2410179020 -0.169247233314 +1413393948705760512.0000000000 0.1182636535 0.3909303854 1.5709558730 0.5738727078 0.7673131047 0.2391768913 -0.157146839857 +1413393948755760384.0000000000 0.1326088596 0.3706384271 1.5661102111 0.5581747459 0.7820477533 0.2365294235 -0.144554821338 +1413393948805760512.0000000000 0.1460374583 0.3507508546 1.5626852227 0.5435183403 0.7955935274 0.2320072083 -0.133384437908 +1413393948855760384.0000000000 0.1577263814 0.3324785271 1.5602197642 0.5304681398 0.8077454132 0.2248538148 -0.12486657708 +1413393948905760512.0000000000 0.1672714157 0.3172380488 1.5608125360 0.5224580366 0.8164713100 0.2156592228 -0.117912253679 +1413393948955760384.0000000000 0.1752650146 0.3042395139 1.5628196670 0.5197495310 0.8217923178 0.2046466005 -0.11241699267 +1413393949005760512.0000000000 0.1814743583 0.2944367368 1.5664873751 0.5264510499 0.8211986398 0.1919269207 -0.10791729789 +1413393949055760384.0000000000 0.1868245498 0.2871274817 1.5708976800 0.5379550055 0.8171198665 0.1807807349 -0.1011823194 +1413393949105760512.0000000000 0.1905490710 0.2831912885 1.5774570394 0.5523313835 0.8108674238 0.1685378905 -0.0949686439709 +1413393949155760384.0000000000 0.1934717675 0.2804639199 1.5856171910 0.5676726210 0.8033255840 0.1571139133 -0.0879262171134 +1413393949205760512.0000000000 0.1961958928 0.2770443624 1.5939909684 0.5829964506 0.7951993146 0.1451604877 -0.0818634320156 +1413393949255760384.0000000000 0.1983991574 0.2730644604 1.6021560490 0.5964091814 0.7878607278 0.1332656766 -0.0762353024349 +1413393949305760512.0000000000 0.2003100868 0.2683148913 1.6113559566 0.6109604766 0.7790428449 0.1221078876 -0.0700657240497 +1413393949355760384.0000000000 0.2021574352 0.2613113581 1.6205311903 0.6230012954 0.7716310719 0.1106329512 -0.0649247640929 +1413393949405760512.0000000000 0.2040796450 0.2513041803 1.6298992619 0.6350145812 0.7637669449 0.0986794248 -0.0606539918881 +1413393949455760384.0000000000 0.2060892929 0.2377794578 1.6391788494 0.6445090022 0.7574748574 0.0860101444 -0.0586706192927 +1413393949505760512.0000000000 0.2085157955 0.2198292795 1.6472588368 0.6471855998 0.7564840065 0.0725064774 -0.0602126077161 +1413393949555760384.0000000000 0.2116579160 0.1973457877 1.6531234087 0.6394452353 0.7638331092 0.0596287178 -0.0641341432736 +1413393949605760512.0000000000 0.2162520450 0.1709843157 1.6576768269 0.6275847924 0.7740117337 0.0482343193 -0.0686776154312 +1413393949655760384.0000000000 0.2224723006 0.1418991872 1.6616827408 0.6145866849 0.7844332541 0.0386940298 -0.0738271535424 +1413393949705760512.0000000000 0.2310328833 0.1110348460 1.6657625229 0.6015326069 0.7942256282 0.0281419411 -0.0810691399574 +1413393949755760384.0000000000 0.2426344428 0.0796159810 1.6705940286 0.5902146008 0.8022135765 0.0161196082 -0.0885452477574 +1413393949805760512.0000000000 0.2578848288 0.0479881414 1.6763078542 0.5804858090 0.8085421719 0.0029794912 -0.0963685865454 +1413393949855760384.0000000000 0.2775079479 0.0169756390 1.6830399510 0.5725074520 0.8130093219 -0.0123135659 -0.105353861439 +1413393949905760512.0000000000 0.3021544754 -0.0131361111 1.6895838400 0.5647282701 0.8171314313 -0.0258211620 -0.112745166378 +1413393949955760384.0000000000 0.3323815743 -0.0420189788 1.6967638139 0.5582518872 0.8202651133 -0.0369165202 -0.118983801075 +1413393950005760512.0000000000 0.3690667837 -0.0676768493 1.7045734383 0.5530840671 0.8233649844 -0.0433519132 -0.119535470837 +1413393950055760384.0000000000 0.4125220933 -0.0901336252 1.7122231859 0.5496807272 0.8273071996 -0.0397319478 -0.108790017904 +1413393950105760512.0000000000 0.4622666039 -0.1118393251 1.7189452125 0.5484159296 0.8312254148 -0.0267017415 -0.0871280374693 +1413393950155760384.0000000000 0.5166329130 -0.1316073264 1.7255995999 0.5430009843 0.8371287263 -0.0124736467 -0.0648832402746 +1413393950205760512.0000000000 0.5741008088 -0.1487872066 1.7330706114 0.5376729011 0.8420673002 0.0027051210 -0.042698895437 +1413393950255760384.0000000000 0.6331650759 -0.1632761556 1.7410574175 0.5320288680 0.8462632598 0.0174235250 -0.0219134539596 +1413393950305760512.0000000000 0.6921929433 -0.1743278358 1.7500026219 0.5270205987 0.8493775032 0.0276959212 -0.00633100637419 +1413393950355760384.0000000000 0.7497857848 -0.1822482857 1.7583680794 0.5221721756 0.8522565882 0.0315289610 0.000922747699294 +1413393950405760512.0000000000 0.8060185529 -0.1867523125 1.7654049734 0.5188358039 0.8542579300 0.0322178735 0.00384788629881 +1413393950455760384.0000000000 0.8608103585 -0.1878840081 1.7713419620 0.5180630789 0.8547529748 0.0313805938 0.00482252370296 +1413393950505760512.0000000000 0.9141589040 -0.1852448397 1.7756251708 0.5216587106 0.8526703094 0.0285254198 0.00343998298096 +1413393950555760384.0000000000 0.9665796149 -0.1786915553 1.7778090200 0.5282483390 0.8487048099 0.0254916974 0.00200284277539 +1413393950605760512.0000000000 1.0180281299 -0.1687496852 1.7781939378 0.5378014703 0.8427497051 0.0232693367 0.00102522785826 +1413393950655760384.0000000000 1.0686965607 -0.1557661577 1.7765706839 0.5490229559 0.8355470429 0.0208549876 5.00376337105e-05 +1413393950705760512.0000000000 1.1186859728 -0.1411201366 1.7726232508 0.5597964168 0.8284090811 0.0191383668 -0.00029828472843 +1413393950755760384.0000000000 1.1680837548 -0.1256949855 1.7658054548 0.5676536435 0.8230552258 0.0186816720 0.000656860896146 +1413393950805760512.0000000000 1.2168743679 -0.1103466884 1.7558100277 0.5736306889 0.8189042232 0.0183716064 0.00248798696636 +1413393950855760384.0000000000 1.2647057010 -0.0946233668 1.7423694412 0.5778535697 0.8159228150 0.0184153928 0.00401064771572 +1413393950905760512.0000000000 1.3120276032 -0.0788465065 1.7255711785 0.5797060994 0.8145276105 0.0203980894 0.0083383483076 +1413393950955760384.0000000000 1.3586261835 -0.0632262108 1.7067593451 0.5803825846 0.8137897710 0.0249003397 0.0167999135136 +1413393951005760512.0000000000 1.4035375778 -0.0478501700 1.6874111466 0.5790623165 0.8143166593 0.0303591269 0.0255643394829 +1413393951055760384.0000000000 1.4461868189 -0.0325000580 1.6689543782 0.5771869582 0.8152673008 0.0341224196 0.0320952325251 +1413393951105760512.0000000000 1.4859258271 -0.0170850866 1.6521139656 0.5749289005 0.8168880525 0.0332369998 0.0323414722674 +1413393951155760384.0000000000 1.5229789796 -0.0011082363 1.6374345019 0.5750765778 0.8170257623 0.0302811932 0.028963472642 +1413393951205760512.0000000000 1.5577352187 0.0153362004 1.6239887176 0.5756707912 0.8168529880 0.0266450618 0.0253845774004 +1413393951255760384.0000000000 1.5905587943 0.0320195960 1.6116861893 0.5765671766 0.8164292200 0.0229789489 0.0220360490397 +1413393951305760512.0000000000 1.6218221550 0.0489497502 1.6005624184 0.5768178871 0.8163861027 0.0197658849 0.0201038853411 +1413393951355760384.0000000000 1.6516323262 0.0659434689 1.5906717303 0.5761279039 0.8169585841 0.0170000366 0.0191391990676 +1413393951405760512.0000000000 1.6802079712 0.0830310608 1.5818087148 0.5736955684 0.8187036604 0.0148201525 0.0194441353385 +1413393951455760384.0000000000 1.7076656510 0.1002933143 1.5731307838 0.5692826464 0.8217582374 0.0135919450 0.0211169800642 +1413393951505760512.0000000000 1.7337927308 0.1178632018 1.5634766320 0.5644260491 0.8250705286 0.0128478938 0.0227330059137 +1413393951555760384.0000000000 1.7586516803 0.1366078920 1.5520374932 0.5603297038 0.8278103527 0.0122616325 0.0247041553223 +1413393951605760512.0000000000 1.7822195636 0.1568727009 1.5385621288 0.5578030498 0.8294477376 0.0119340097 0.0270145828956 +1413393951655760384.0000000000 1.8043755520 0.1783424390 1.5233896104 0.5580099151 0.8292486768 0.0112105045 0.0290842115741 +1413393951705760512.0000000000 1.8252480912 0.2004320179 1.5067593113 0.5601312080 0.8277135971 0.0113292542 0.0318571645562 +1413393951755760384.0000000000 1.8448144075 0.2230051609 1.4883740011 0.5625637529 0.8259335692 0.0113503160 0.0350276108964 +1413393951805760512.0000000000 1.8625850328 0.2468220747 1.4698026395 0.5656251054 0.8238167514 0.0095243096 0.0361038487387 +1413393951855760384.0000000000 1.8785962559 0.2716487658 1.4520021284 0.5688978418 0.8215830336 0.0067628679 0.0362053614816 +1413393951905760512.0000000000 1.8930902201 0.2971332688 1.4346565846 0.5711248186 0.8200360229 0.0039986807 0.0366247621408 +1413393951955760384.0000000000 1.9060814492 0.3234533584 1.4183327256 0.5724697333 0.8190980269 0.0009939680 0.0368217177743 +1413393952005760512.0000000000 1.9176093226 0.3505282057 1.4031810479 0.5740202442 0.8179782024 -0.0015985860 0.037548157886 +1413393952055760384.0000000000 1.9277795390 0.3779367771 1.3896293705 0.5753063985 0.8170162002 -0.0040734603 0.0386067780713 +1413393952105760512.0000000000 1.9363085674 0.4056495647 1.3790285167 0.5768122823 0.8159679544 -0.0072972803 0.0378237759993 +1413393952155760384.0000000000 1.9438088600 0.4333802058 1.3713674696 0.5779670218 0.8150615309 -0.0091185727 0.0393150630213 +1413393952205760512.0000000000 1.9498132250 0.4611040492 1.3674939336 0.5786105458 0.8146030584 -0.0124728033 0.0384203419963 +1413393952255760384.0000000000 1.9546726512 0.4883657231 1.3667861924 0.5794879770 0.8139792475 -0.0157916437 0.0371765123844 +1413393952305760512.0000000000 1.9584553039 0.5150074872 1.3691246012 0.5797537213 0.8138091302 -0.0176998304 0.0358753151665 +1413393952355760384.0000000000 1.9609610741 0.5407684262 1.3740986931 0.5804844843 0.8134039534 -0.0174153933 0.0332937866267 +1413393952405760512.0000000000 1.9625916826 0.5663892971 1.3794007840 0.5810312365 0.8131764621 -0.0143240192 0.0306849516003 +1413393952455760384.0000000000 1.9635479413 0.5921589317 1.3850100865 0.5820812049 0.8125708738 -0.0083902085 0.0289767195633 +1413393952505760512.0000000000 1.9635730822 0.6173540055 1.3903921679 0.5820503128 0.8127385943 -0.0009266891 0.025933605694 +1413393952555760384.0000000000 1.9626851597 0.6422175220 1.3958315747 0.5816793252 0.8130745897 0.0076884499 0.0223553557667 +1413393952605760512.0000000000 1.9610324556 0.6668624528 1.4014678730 0.5819170157 0.8128443710 0.0174526745 0.0187621840593 +1413393952655760384.0000000000 1.9582944428 0.6914483838 1.4071895200 0.5814163329 0.8130352577 0.0273547820 0.0134325528699 +1413393952705760512.0000000000 1.9544290071 0.7157177032 1.4126878592 0.5812354638 0.8128346472 0.0375043224 0.00765491498624 +1413393952755760384.0000000000 1.9493443551 0.7396323600 1.4180047860 0.5804527843 0.8129416765 0.0469064762 0.000422151699111 +1413393952805760512.0000000000 1.9435491535 0.7632273399 1.4230799500 0.5798045383 0.8128506677 0.0553436650 -0.00612928247586 +1413393952855760384.0000000000 1.9372391247 0.7866696006 1.4282059391 0.5788060586 0.8129983482 0.0621253769 -0.0125566713109 +1413393952905760512.0000000000 1.9302403653 0.8097543256 1.4341014070 0.5781065157 0.8130855491 0.0648968516 -0.0217518979476 +1413393952955760384.0000000000 1.9227428291 0.8327380671 1.4404211159 0.5766458250 0.8137042619 0.0659887339 -0.0317876332173 +1413393953005760512.0000000000 1.9151586500 0.8559558274 1.4472782257 0.5751377114 0.8143758152 0.0657375022 -0.0410758487918 +1413393953055760384.0000000000 1.9079621007 0.8795205910 1.4541442346 0.5735904629 0.8150461126 0.0653843566 -0.0491802910403 +1413393953105760512.0000000000 1.9015620536 0.9035483365 1.4599333352 0.5723575703 0.8155382910 0.0647254585 -0.055809700541 +1413393953155760384.0000000000 1.8961559361 0.9278168206 1.4619418954 0.5712424651 0.8160188874 0.0639916721 -0.0608299880048 +1413393953205760512.0000000000 1.8917381537 0.9522615751 1.4589317392 0.5706076843 0.8161768733 0.0634615264 -0.0650754703946 +1413393953255760384.0000000000 1.8885549115 0.9773320222 1.4515627719 0.5703420186 0.8161401038 0.0622102584 -0.068957933363 +1413393953305760512.0000000000 1.8865034374 1.0031228904 1.4427301500 0.5696148993 0.8163607478 0.0593423295 -0.0746490717124 +1413393953355760384.0000000000 1.8863814359 1.0296346918 1.4349813966 0.5704409203 0.8155554781 0.0565453421 -0.079177287705 +1413393953405760512.0000000000 1.8884986636 1.0567934633 1.4300018791 0.5732097017 0.8134725334 0.0541154628 -0.0822471395011 +1413393953455760384.0000000000 1.8930198643 1.0844319027 1.4283378273 0.5762165699 0.8112932297 0.0524881880 -0.0838018510505 +1413393953505760512.0000000000 1.9005161291 1.1125244486 1.4308907620 0.5814228005 0.8077948976 0.0538642202 -0.0807067301336 +1413393953555760384.0000000000 1.9107076411 1.1400822162 1.4359390514 0.5868361693 0.8042966035 0.0572944823 -0.0738080369928 +1413393953605760512.0000000000 1.9229497455 1.1668724698 1.4422816262 0.5926204875 0.8005326545 0.0636411277 -0.0624358376929 +1413393953655760384.0000000000 1.9360710386 1.1928004355 1.4499287446 0.5970732962 0.7974664189 0.0690622615 -0.0527370249183 +1413393953705760512.0000000000 1.9497784565 1.2174184243 1.4582084404 0.6018478862 0.7940007252 0.0734707269 -0.0440910714215 +1413393953755760384.0000000000 1.9632755324 1.2407444294 1.4654295982 0.6062640894 0.7906931337 0.0762401641 -0.037890097785 +1413393953805760512.0000000000 1.9763300100 1.2619666824 1.4703639789 0.6088780188 0.7886163389 0.0784535944 -0.0345956909932 +1413393953855760384.0000000000 1.9887097336 1.2807576678 1.4727321625 0.6108791910 0.7868193880 0.0813911861 -0.0334266279866 +1413393953905760512.0000000000 2.0003214657 1.2969324404 1.4725781225 0.6121054212 0.7854574057 0.0845120935 -0.0352324178938 +1413393953955760384.0000000000 2.0113522538 1.3107318810 1.4697195532 0.6099118286 0.7865654370 0.0891089274 -0.037174907372 +1413393954005760512.0000000000 2.0219501024 1.3221277618 1.4649909047 0.6025500253 0.7914627488 0.0947468851 -0.0392837380447 +1413393954055760384.0000000000 2.0316533650 1.3313254452 1.4607252531 0.5954248940 0.7958721409 0.1013910534 -0.0421495586084 +1413393954105760512.0000000000 2.0404116462 1.3392107753 1.4569686650 0.5859198867 0.8018965256 0.1071159267 -0.0467549672748 +1413393954155760384.0000000000 2.0485285838 1.3462253304 1.4538082320 0.5747860429 0.8086894913 0.1145550169 -0.0501942185796 +1413393954205760512.0000000000 2.0555079454 1.3528971033 1.4515829610 0.5628208001 0.8156538654 0.1222929652 -0.054643841836 +1413393954255760384.0000000000 2.0612747013 1.3599768604 1.4508649533 0.5509763072 0.8220288185 0.1307373213 -0.0600123596196 +1413393954305760512.0000000000 2.0656267333 1.3684035381 1.4520256312 0.5411269779 0.8265640113 0.1401195745 -0.0658789331262 +1413393954355760384.0000000000 2.0683593975 1.3787642304 1.4541800737 0.5326953778 0.8297438063 0.1500957840 -0.0723332987509 +1413393954405760512.0000000000 2.0694984051 1.3912845736 1.4569680369 0.5261772913 0.8311931874 0.1613326700 -0.0789120581717 +1413393954455760384.0000000000 2.0688889531 1.4062348679 1.4603678758 0.5212705334 0.8311333585 0.1734292789 -0.0861200133635 +1413393954505760512.0000000000 2.0666982211 1.4231616697 1.4643402964 0.5177557628 0.8297723570 0.1863153531 -0.093238376633 +1413393954555760384.0000000000 2.0625443477 1.4425478150 1.4687660123 0.5137568721 0.8283056046 0.1997174188 -0.100382540612 +1413393954605760512.0000000000 2.0566740402 1.4642984184 1.4739322034 0.5104572279 0.8263454313 0.2119376876 -0.108023438088 +1413393954655760384.0000000000 2.0487619372 1.4891959696 1.4793126283 0.5087281099 0.8234340195 0.2235377497 -0.114817247022 +1413393954705760512.0000000000 2.0386861686 1.5174295436 1.4844758764 0.5059853608 0.8214217907 0.2340725275 -0.120229398688 +1413393954755760384.0000000000 2.0267218948 1.5487028246 1.4900228913 0.5036478208 0.8197454485 0.2424575422 -0.124782260197 +1413393954805760512.0000000000 2.0127827976 1.5825851607 1.4952859407 0.5014269204 0.8183358449 0.2495764301 -0.128876273934 +1413393954855760384.0000000000 1.9967819499 1.6192376402 1.5005335304 0.4997551911 0.8170853319 0.2554703306 -0.131724028081 +1413393954905760512.0000000000 1.9784410907 1.6588170375 1.5059232743 0.4986804586 0.8158191105 0.2605423270 -0.13369620395 +1413393954955760384.0000000000 1.9577136168 1.7011919030 1.5117335096 0.5003899340 0.8132834553 0.2641842120 -0.135597335441 +1413393955005760512.0000000000 1.9341857030 1.7462834205 1.5187430666 0.5062075109 0.8085257245 0.2661840915 -0.138514036049 +1413393955055760384.0000000000 1.9080051520 1.7934529290 1.5266056504 0.5155617259 0.8011950429 0.2683675047 -0.142342869535 +1413393955105760512.0000000000 1.8798473442 1.8416493937 1.5338754161 0.5234965327 0.7944220156 0.2709526574 -0.146388862037 +1413393955155760384.0000000000 1.8498285014 1.8904350957 1.5405157516 0.5307369242 0.7877045247 0.2743395853 -0.150258746597 +1413393955205760512.0000000000 1.8180299603 1.9394058339 1.5473480155 0.5353220431 0.7827268048 0.2755821962 -0.157554791642 +1413393955255760384.0000000000 1.7848613725 1.9879341644 1.5542370700 0.5371257944 0.7792409299 0.2766444742 -0.166575175305 +1413393955305760512.0000000000 1.7508735042 2.0365623037 1.5612497445 0.5381255024 0.7761359601 0.2773727022 -0.17634709851 +1413393955355760384.0000000000 1.7166502658 2.0848297164 1.5677712973 0.5373306395 0.7734201491 0.2811612407 -0.184513992879 +1413393955405760512.0000000000 1.6822411438 2.1326467306 1.5741156958 0.5363615824 0.7700584414 0.2872617880 -0.19185128346 +1413393955455760384.0000000000 1.6473836570 2.1805601356 1.5814682018 0.5385269365 0.7633307209 0.2957078868 -0.199679229747 +1413393955505760512.0000000000 1.6124126543 2.2278515494 1.5896549732 0.5420902652 0.7541685874 0.3057937704 -0.209423150841 +1413393955555760384.0000000000 1.5779718181 2.2741096986 1.5970406649 0.5462770356 0.7432155957 0.3173179383 -0.22027551993 +1413393955605760512.0000000000 1.5444722841 2.3191373791 1.6021454905 0.5518448924 0.7298037941 0.3317877629 -0.229718343348 +1413393955655760384.0000000000 1.5120287440 2.3627524553 1.6040130811 0.5563192141 0.7163449938 0.3482257580 -0.236849326149 +1413393955705760512.0000000000 1.4805997291 2.4052172943 1.6025682484 0.5590325351 0.7045024864 0.3669158317 -0.237763840451 +1413393955755760384.0000000000 1.4503229446 2.4458825706 1.5982593526 0.5613838764 0.6934397245 0.3861536237 -0.234253859421 +1413393955805760512.0000000000 1.4208873420 2.4838473491 1.5914495198 0.5624496684 0.6839266222 0.4042574333 -0.2290647803 +1413393955855760384.0000000000 1.3915735534 2.5184321927 1.5822227317 0.5600776345 0.6782209957 0.4201023457 -0.223256228236 +1413393955905760512.0000000000 1.3616694908 2.5484985676 1.5725217322 0.5522569713 0.6780246873 0.4313016296 -0.221976722561 +1413393955955760384.0000000000 1.3299158413 2.5736262572 1.5647027606 0.5397544112 0.6826739832 0.4358046789 -0.229555418419 +1413393956005760512.0000000000 1.2965744845 2.5949574235 1.5584278779 0.5260516865 0.6888528390 0.4370480513 -0.240292301642 +1413393956055760384.0000000000 1.2616935409 2.6136225852 1.5539721707 0.5137981990 0.6936990710 0.4368732948 -0.252853186257 +1413393956105760512.0000000000 1.2254285894 2.6306182007 1.5508082432 0.5037510716 0.6965894714 0.4365300659 -0.265404347832 +1413393956155760384.0000000000 1.1881144885 2.6462588321 1.5484841765 0.4951526236 0.6973775948 0.4379891338 -0.276864386077 +1413393956205760512.0000000000 1.1500971039 2.6610738371 1.5468439875 0.4884290552 0.6956060058 0.4414744765 -0.287523267487 +1413393956255760384.0000000000 1.1112459915 2.6757268017 1.5466838363 0.4870815966 0.6890230423 0.4460186700 -0.298439460366 +1413393956305760512.0000000000 1.0720241576 2.6900301790 1.5472058628 0.4882486067 0.6794893870 0.4521675661 -0.308953011095 +1413393956355760384.0000000000 1.0329942915 2.7037350451 1.5487052796 0.4900732216 0.6681992494 0.4588766501 -0.320577947765 +1413393956405760512.0000000000 0.9947881713 2.7166648209 1.5508266875 0.4915413741 0.6562134501 0.4665401689 -0.33183016185 +1413393956455760384.0000000000 0.9577210309 2.7284607380 1.5529930441 0.4919142748 0.6440585301 0.4751426451 -0.342707488748 +1413393956505760512.0000000000 0.9220934719 2.7390133120 1.5544600314 0.4885148903 0.6334098020 0.4854870642 -0.352771222228 +1413393956555760384.0000000000 0.8880325726 2.7483175495 1.5555722096 0.4815575481 0.6245974185 0.4972027314 -0.36162112307 +1413393956605760512.0000000000 0.8553992364 2.7565778478 1.5563175739 0.4723216788 0.6166041550 0.5097645091 -0.369934714594 +1413393956655760384.0000000000 0.8238286222 2.7640342478 1.5567620218 0.4611016038 0.6090357255 0.5238656657 -0.37686278707 +1413393956705760512.0000000000 0.7933008762 2.7708315010 1.5564743510 0.4484545615 0.6023223078 0.5383401391 -0.382473840161 +1413393956755760384.0000000000 0.7640318715 2.7770372341 1.5559199065 0.4350633934 0.5959223664 0.5529110570 -0.387150797582 +1413393956805760512.0000000000 0.7351731203 2.7826806817 1.5562509433 0.4226533641 0.5883170774 0.5662209293 -0.393244210908 +1413393956855760384.0000000000 0.7062530607 2.7880355053 1.5575524926 0.4100243174 0.5810864135 0.5773954637 -0.401040045053 +1413393956905760512.0000000000 0.6770807185 2.7933161745 1.5594442018 0.3980442805 0.5730295254 0.5872569413 -0.410276977921 +1413393956955760384.0000000000 0.6477878737 2.7989220129 1.5614330863 0.3864652189 0.5647998949 0.5960585273 -0.419952313157 +1413393957005760512.0000000000 0.6182106826 2.8051301120 1.5633366199 0.3767030883 0.5553258928 0.6053369137 -0.42810647852 +1413393957055760384.0000000000 0.5884493272 2.8118946096 1.5652261575 0.3669342344 0.5452503855 0.6150836740 -0.435583928419 +1413393957105760512.0000000000 0.5582375132 2.8194225792 1.5667396709 0.3594453455 0.5325200989 0.6266055798 -0.441119978193 +1413393957155760384.0000000000 0.5270606561 2.8272261239 1.5681621520 0.3523644423 0.5187285788 0.6382005681 -0.446609444788 +1413393957205760512.0000000000 0.4948334158 2.8348909897 1.5699621493 0.3447808636 0.5039410153 0.6494492631 -0.453194509949 +1413393957255760384.0000000000 0.4624529663 2.8428284017 1.5718901287 0.3361786604 0.4887264745 0.6607797395 -0.45989181049 +1413393957305760512.0000000000 0.4297157004 2.8508187938 1.5739278507 0.3265050030 0.4733861153 0.6719388614 -0.466688585004 +1413393957355760384.0000000000 0.3965280904 2.8588753931 1.5764702298 0.3171423695 0.4574832069 0.6822623472 -0.473970381295 +1413393957405760512.0000000000 0.3626422813 2.8671334248 1.5786556702 0.3082294414 0.4419673577 0.6916195633 -0.480959297457 +1413393957455760384.0000000000 0.3281218224 2.8749979226 1.5806805477 0.2999818119 0.4260605328 0.6993161900 -0.489326272932 +1413393957505760512.0000000000 0.2929461518 2.8827151316 1.5810125759 0.2926040012 0.4106379635 0.7061983000 -0.497034528511 +1413393957555760384.0000000000 0.2579694129 2.8904141429 1.5791020670 0.2847239663 0.3956936845 0.7122602521 -0.505018914864 +1413393957605760512.0000000000 0.2234073479 2.8981848247 1.5745914862 0.2767954818 0.3802119584 0.7177482191 -0.5134789401 +1413393957655760384.0000000000 0.1892787373 2.9059891626 1.5675604982 0.2689242031 0.3643187405 0.7214532838 -0.52388623529 +1413393957705760512.0000000000 0.1556231275 2.9139495714 1.5579172100 0.2624176539 0.3468842076 0.7239826639 -0.535403981931 +1413393957755760384.0000000000 0.1227483016 2.9224622079 1.5451176123 0.2551223726 0.3294770391 0.7272940313 -0.545344705425 +1413393957805760512.0000000000 0.0908222529 2.9320551131 1.5293233876 0.2503095255 0.3104358130 0.7322898524 -0.552020216575 +1413393957855760384.0000000000 0.0603561320 2.9422757046 1.5113511304 0.2458232620 0.2913087390 0.7388494950 -0.555708166424 +1413393957905760512.0000000000 0.0319050562 2.9538317423 1.4929238070 0.2427047752 0.2726885655 0.7463400479 -0.556517628795 +1413393957955760384.0000000000 0.0057009594 2.9662780248 1.4747030991 0.2407655926 0.2540494579 0.7549199137 -0.554605018234 +1413393958005760512.0000000000 -0.0181791094 2.9791491953 1.4586905072 0.2381735858 0.2387389502 0.7639027284 -0.550208758767 +1413393958055760384.0000000000 -0.0394215550 2.9915259829 1.4463774902 0.2346663462 0.2266270668 0.7721871685 -0.545251185547 +1413393958105760512.0000000000 -0.0578480927 3.0027488973 1.4393037838 0.2297675858 0.2182543096 0.7781805580 -0.542224060631 +1413393958155760384.0000000000 -0.0738589112 3.0118820647 1.4370261997 0.2232859133 0.2131335121 0.7825891518 -0.540621611171 +1413393958205760512.0000000000 -0.0881643558 3.0179787867 1.4398488168 0.2178264520 0.2092366331 0.7853805089 -0.5403231667 +1413393958255760384.0000000000 -0.1006143768 3.0211160702 1.4469252311 0.2100545669 0.2088761901 0.7859339463 -0.542729811357 +1413393958305760512.0000000000 -0.1111836980 3.0220942006 1.4572183071 0.2005341489 0.2115073846 0.7863857199 -0.544654184725 +1413393958355760384.0000000000 -0.1203088319 3.0218100619 1.4700380762 0.1897336125 0.2166224180 0.7859137902 -0.547188631654 +1413393958405760512.0000000000 -0.1286652531 3.0207970896 1.4817554217 0.1810306515 0.2213546367 0.7865476503 -0.547332460027 +1413393958455760384.0000000000 -0.1366849232 3.0192799079 1.4909290003 0.1749120513 0.2248825068 0.7874769171 -0.54654710454 +1413393958505760512.0000000000 -0.1449641244 3.0169997210 1.4974662989 0.1698617169 0.2282955360 0.7898936349 -0.54322756827 +1413393958555760384.0000000000 -0.1536164124 3.0142788976 1.5006112507 0.1659824691 0.2312174966 0.7935447486 -0.537842933602 +1413393958605760512.0000000000 -0.1625221521 3.0111350229 1.5004927986 0.1630784797 0.2337949253 0.7974819517 -0.531759230297 +1413393958655760384.0000000000 -0.1721149334 3.0070193449 1.4972000810 0.1615448111 0.2357601682 0.8009087260 -0.526180225543 +1413393958705760512.0000000000 -0.1826713524 3.0016052631 1.4912555880 0.1609003438 0.2372608704 0.8034718968 -0.52177703073 +1413393958755760384.0000000000 -0.1946774282 2.9939803881 1.4838059890 0.1620847685 0.2380516910 0.8025965492 -0.5223970707 +1413393958805760512.0000000000 -0.2080134849 2.9844645449 1.4747348228 0.1653027449 0.2377593098 0.7990815163 -0.526891111534 +1413393958855760384.0000000000 -0.2221963063 2.9734707631 1.4639068688 0.1692289269 0.2371153731 0.7943854060 -0.533000653684 +1413393958905760512.0000000000 -0.2370435674 2.9611194065 1.4503857121 0.1734765945 0.2362543146 0.7897726275 -0.538840390835 +1413393958955760384.0000000000 -0.2523050719 2.9476664596 1.4338943023 0.1760930242 0.2365792073 0.7856526087 -0.543848787754 +1413393959005760512.0000000000 -0.2677165873 2.9332148100 1.4155450218 0.1767675424 0.2382407667 0.7811848651 -0.549313006999 +1413393959055760384.0000000000 -0.2826689646 2.9183915331 1.3957866501 0.1738654856 0.2425015847 0.7757251981 -0.556070311478 +1413393959105760512.0000000000 -0.2977366113 2.9037150255 1.3755017859 0.1696163978 0.2475042481 0.7699664166 -0.563137320781 +1413393959155760384.0000000000 -0.3131653088 2.8899685955 1.3558875191 0.1666263732 0.2514305721 0.7638007782 -0.570637091691 +1413393959205760512.0000000000 -0.3291621926 2.8777090335 1.3365821638 0.1674936383 0.2522909793 0.7590347579 -0.576334433415 +1413393959255760384.0000000000 -0.3456525780 2.8674243172 1.3173662400 0.1731245919 0.2502131789 0.7565833288 -0.578794356799 +1413393959305760512.0000000000 -0.3619305498 2.8589075739 1.2981440585 0.1775545329 0.2488832897 0.7576964915 -0.576565280592 +1413393959355760384.0000000000 -0.3780378435 2.8518122686 1.2795600146 0.1811447162 0.2477796068 0.7606937290 -0.571958834916 +1413393959405760512.0000000000 -0.3939805792 2.8457504766 1.2623174700 0.1841153916 0.2467779252 0.7636078329 -0.567543175184 +1413393959455760384.0000000000 -0.4095083739 2.8405134521 1.2464491763 0.1860747137 0.2464063532 0.7660358787 -0.563781112266 +1413393959505760512.0000000000 -0.4246844691 2.8358793531 1.2322738323 0.1894531396 0.2450711488 0.7664328753 -0.562697332135 +1413393959555760384.0000000000 -0.4391550141 2.8315309353 1.2194301040 0.1917858430 0.2439163768 0.7653845891 -0.563834569962 +1413393959605760512.0000000000 -0.4531571101 2.8274499963 1.2096278417 0.1965423520 0.2408414734 0.7583986104 -0.572885709626 +1413393959655760384.0000000000 -0.4660425833 2.8243297853 1.2018092821 0.2026166938 0.2366386485 0.7483624289 -0.585578603181 +1413393959705760512.0000000000 -0.4768308130 2.8231734149 1.1946359738 0.2062480062 0.2340446298 0.7395479072 -0.596450973835 +1413393959755760384.0000000000 -0.4853591431 2.8245100649 1.1876644397 0.2096488326 0.2318794328 0.7328073296 -0.604377955723 +1413393959805760512.0000000000 -0.4912296309 2.8288068895 1.1793317411 0.2105600081 0.2318130308 0.7335931168 -0.603132108785 +1413393959855760384.0000000000 -0.4943592529 2.8359406791 1.1697087012 0.2074018799 0.2350306502 0.7415154712 -0.593211479646 +1413393959905760512.0000000000 -0.4955322596 2.8452697767 1.1608898694 0.2050726361 0.2378556535 0.7502660730 -0.581782366259 +1413393959955760384.0000000000 -0.4949850735 2.8559971924 1.1530589842 0.2029256535 0.2401526840 0.7594133461 -0.569595678777 +1413393960005760512.0000000000 -0.4931654632 2.8673447911 1.1465322789 0.2001134029 0.2428071746 0.7671927518 -0.558940590326 +1413393960055760384.0000000000 -0.4904073605 2.8787102953 1.1410579223 0.1977783417 0.2450335626 0.7738743980 -0.549509505712 +1413393960105760512.0000000000 -0.4871177150 2.8894844232 1.1368890940 0.1960347508 0.2465799433 0.7794433310 -0.541513436468 +1413393960155760384.0000000000 -0.4836058763 2.8994166196 1.1333073986 0.1936846503 0.2483570373 0.7852983931 -0.533021080252 +1413393960205760512.0000000000 -0.4802274501 2.9081038194 1.1301402614 0.1913007231 0.2504827855 0.7910211999 -0.524354716564 +1413393960255760384.0000000000 -0.4770727561 2.9151522276 1.1266162880 0.1877520648 0.2529134223 0.7981272231 -0.513592152178 +1413393960305760512.0000000000 -0.4748099249 2.9197267070 1.1240532362 0.1855394216 0.2543845043 0.8025220120 -0.506776151044 +1413393960355760384.0000000000 -0.4738258716 2.9212754839 1.1227140517 0.1846341248 0.2546110876 0.8036496282 -0.505203631427 +1413393960405760512.0000000000 -0.4740895190 2.9194848763 1.1232353492 0.1858067599 0.2516011183 0.8003073470 -0.511547530095 +1413393960455760384.0000000000 -0.4748240568 2.9148419597 1.1238113262 0.1865568861 0.2467435424 0.7959192028 -0.520410198887 +1413393960505760512.0000000000 -0.4757680821 2.9082018126 1.1225057186 0.1861186084 0.2399176602 0.7918030748 -0.529950253038 +1413393960555760384.0000000000 -0.4761909184 2.9005795754 1.1167041533 0.1834753711 0.2314617413 0.7900874779 -0.537144326851 +1413393960605760512.0000000000 -0.4758610124 2.8920547345 1.1055879606 0.1787184393 0.2210993470 0.7894355660 -0.544027835093 +1413393960655760384.0000000000 -0.4747004705 2.8828455683 1.0887464694 0.1722018011 0.2095135365 0.7899512878 -0.549934160225 +1413393960705760512.0000000000 -0.4727385480 2.8735269486 1.0658196723 0.1644296422 0.1968874291 0.7919003443 -0.554158892131 +1413393960755760384.0000000000 -0.4702475300 2.8638752743 1.0380267138 0.1556464536 0.1838361202 0.7950223999 -0.556702654987 +1413393960805760512.0000000000 -0.4672170936 2.8540037612 1.0069167281 0.1458335232 0.1708200380 0.7987800291 -0.558125042652 +1413393960855760384.0000000000 -0.4639932714 2.8440070864 0.9731435383 0.1359663195 0.1600706868 0.8054043628 -0.55426920142 +1413393960905760512.0000000000 -0.4608541201 2.8332021718 0.9399021102 0.1264344616 0.1512352431 0.8134037765 -0.547281028873 +1413393960955760384.0000000000 -0.4579691854 2.8205503998 0.9103189279 0.1153479829 0.1457869674 0.8194104720 -0.542224567237 +1413393961005760512.0000000000 -0.4560343845 2.8057853549 0.8841843067 0.1059592380 0.1420690023 0.8245385318 -0.537331599661 +1413393961055760384.0000000000 -0.4553457838 2.7890635619 0.8617003518 0.1001374709 0.1376784167 0.8268657452 -0.536013227332 +1413393961105760512.0000000000 -0.4561013587 2.7698326678 0.8435117133 0.0985375877 0.1327228204 0.8250686062 -0.540311754369 +1413393961155760384.0000000000 -0.4579440454 2.7487077624 0.8290244640 0.0990890618 0.1282780085 0.8210858402 -0.547306270247 +1413393961205760512.0000000000 -0.4604687041 2.7255726640 0.8202595893 0.0985844934 0.1259481982 0.8138577951 -0.558617613774 +1413393961255760384.0000000000 -0.4630865441 2.7023685021 0.8183700968 0.0953115121 0.1273738256 0.7991587747 -0.579686878499 +1413393961305760512.0000000000 -0.4658634346 2.6798109900 0.8205818057 0.0909017149 0.1299101664 0.7821435117 -0.60258754884 +1413393961355760384.0000000000 -0.4687444447 2.6598253611 0.8269968700 0.0855123379 0.1331954503 0.7631118087 -0.626583577413 +1413393961405760512.0000000000 -0.4724126138 2.6433377662 0.8347399329 0.0838922081 0.1337021949 0.7471404665 -0.645652339757 +1413393961455760384.0000000000 -0.4770103593 2.6316220983 0.8457175664 0.0854824372 0.1323501421 0.7387577985 -0.655296198665 +1413393961505760512.0000000000 -0.4818864904 2.6257786018 0.8581461681 0.0894891531 0.1298487214 0.7418142676 -0.651799504007 +1413393961555760384.0000000000 -0.4864658101 2.6269705492 0.8722747107 0.0971729541 0.1257504245 0.7505139332 -0.641461677573 +1413393961605760512.0000000000 -0.4894601706 2.6348249911 0.8884737123 0.1020508051 0.1232542381 0.7623782499 -0.627035429663 +1413393961655760384.0000000000 -0.4919921799 2.6452384481 0.9086389332 0.1069572678 0.1208597193 0.7757857080 -0.610007874004 +1413393961705760512.0000000000 -0.4936685207 2.6580546935 0.9352848482 0.1099967745 0.1193982700 0.7839044209 -0.599281754742 +1413393961755760384.0000000000 -0.4945274737 2.6716522996 0.9681942694 0.1132488647 0.1175363844 0.7863745835 -0.595797706796 +1413393961805760512.0000000000 -0.4939586127 2.6868673860 1.0051180853 0.1138565401 0.1178013107 0.7903022322 -0.590408266568 +1413393961855760384.0000000000 -0.4920167540 2.7033852448 1.0457998608 0.1141111915 0.1180434549 0.7938999380 -0.585463292783 +1413393961905760512.0000000000 -0.4889203762 2.7208663892 1.0892463338 0.1137929275 0.1187895519 0.7981075454 -0.579624497331 +1413393961955760384.0000000000 -0.4847406032 2.7387109682 1.1361613682 0.1134499859 0.1189963502 0.8017459210 -0.574606341345 +1413393962005760512.0000000000 -0.4797239733 2.7566369102 1.1853963983 0.1128550814 0.1196540350 0.8056785821 -0.569059456395 +1413393962055760384.0000000000 -0.4738951644 2.7737440699 1.2381855187 0.1110703131 0.1206387585 0.8094623113 -0.563808870165 +1413393962105760512.0000000000 -0.4677932253 2.7892505711 1.2955795361 0.1104061792 0.1206099821 0.8129675597 -0.558880537113 +1413393962155760384.0000000000 -0.4613135334 2.8029857956 1.3560995179 0.1088275622 0.1217933612 0.8165666852 -0.553662160095 +1413393962205760512.0000000000 -0.4543172447 2.8151216101 1.4201355418 0.1070508152 0.1222814641 0.8195298358 -0.549507247246 +1413393962255760384.0000000000 -0.4473465953 2.8253850495 1.4865541996 0.1060180883 0.1222970016 0.8217940483 -0.546313234807 +1413393962305760512.0000000000 -0.4404824196 2.8336821670 1.5542840153 0.1051128978 0.1228326853 0.8244703723 -0.542320952328 +1413393962355760384.0000000000 -0.4335732786 2.8402693772 1.6206705690 0.1044961222 0.1230215654 0.8287533596 -0.535830312529 +1413393962405760512.0000000000 -0.4267903715 2.8450309116 1.6835600935 0.1040462829 0.1234453742 0.8339726763 -0.527660104345 +1413393962455760384.0000000000 -0.4204257495 2.8477742967 1.7404952394 0.1040215511 0.1253215674 0.8409465026 -0.516026163494 +1413393962505760512.0000000000 -0.4149563460 2.8475749098 1.7915980628 0.1048882640 0.1288763486 0.8473300606 -0.504401731978 +1413393962555760384.0000000000 -0.4106293239 2.8441510233 1.8369465452 0.1073456305 0.1342577219 0.8524156647 -0.493800885349 +1413393962605760512.0000000000 -0.4076959659 2.8367717537 1.8769039058 0.1128410570 0.1401758921 0.8548464872 -0.486677612454 +1413393962655760384.0000000000 -0.4062685209 2.8249990986 1.9129698774 0.1223615793 0.1462830661 0.8544329773 -0.483294109037 +1413393962705760512.0000000000 -0.4064799585 2.8080116453 1.9465973741 0.1352919731 0.1529669455 0.8511627724 -0.48354847794 +1413393962755760384.0000000000 -0.4076787069 2.7862726763 1.9783000858 0.1504786169 0.1604574749 0.8447684960 -0.487827605519 +1413393962805760512.0000000000 -0.4097030866 2.7598838714 2.0083347461 0.1687553121 0.1679468437 0.8362468105 -0.493970418388 +1413393962855760384.0000000000 -0.4117918995 2.7294190544 2.0362069913 0.1885135384 0.1766011227 0.8269213791 -0.499475446991 +1413393962905760512.0000000000 -0.4132048973 2.6954259445 2.0623449413 0.2087587866 0.1857826087 0.8161934528 -0.505700345004 +1413393962955760384.0000000000 -0.4130885704 2.6590821913 2.0855149482 0.2281389186 0.1972415326 0.8055354556 -0.510059841056 +1413393963005760512.0000000000 -0.4111975654 2.6199948805 2.1058155181 0.2455890232 0.2110600274 0.7951754038 -0.512675115128 +1413393963055760384.0000000000 -0.4068308238 2.5785004060 2.1235002006 0.2614461553 0.2264240865 0.7845671398 -0.514618736626 +1413393963105760512.0000000000 -0.4002070329 2.5347171928 2.1387211661 0.2775174826 0.2417447754 0.7734142525 -0.51611423579 +1413393963155760384.0000000000 -0.3907981045 2.4887597316 2.1515370747 0.2903983805 0.2589332160 0.7619716462 -0.517708007122 +1413393963205760512.0000000000 -0.3780293568 2.4407879505 2.1617259267 0.2987601364 0.2787233175 0.7501450844 -0.519940424916 +1413393963255760384.0000000000 -0.3620951687 2.3916753363 2.1694975356 0.3054665996 0.2990600322 0.7375732122 -0.522722689684 +1413393963305760512.0000000000 -0.3435578697 2.3418473743 2.1743273698 0.3116357730 0.3187553112 0.7260436556 -0.523582664602 +1413393963355760384.0000000000 -0.3230705180 2.2913848559 2.1762918564 0.3188043204 0.3375450381 0.7150729104 -0.522587681904 +1413393963405760512.0000000000 -0.3004253558 2.2408599536 2.1747996555 0.3260961183 0.3553572229 0.7056886304 -0.519024202375 +1413393963455760384.0000000000 -0.2758465898 2.1904960153 2.1706161584 0.3343442009 0.3719980964 0.6971933120 -0.513568746454 +1413393963505760512.0000000000 -0.2492473027 2.1397597917 2.1641365159 0.3413176844 0.3882272247 0.6882857749 -0.508964195639 +1413393963555760384.0000000000 -0.2210550199 2.0888172415 2.1552055159 0.3480397685 0.4032076738 0.6798448861 -0.504086125712 +1413393963605760512.0000000000 -0.1914758678 2.0376666744 2.1443351558 0.3553982056 0.4166931566 0.6707574788 -0.500143312707 +1413393963655760384.0000000000 -0.1601274805 1.9867361005 2.1309361190 0.3633516444 0.4284405616 0.6622170426 -0.495865764308 +1413393963705760512.0000000000 -0.1271156014 1.9359273392 2.1149582728 0.3714201096 0.4393500261 0.6538063501 -0.491483380514 +1413393963755760384.0000000000 -0.0926992247 1.8852542434 2.0967669574 0.3801025526 0.4492960924 0.6460450008 -0.48608736642 +1413393963805760512.0000000000 -0.0564225918 1.8346644398 2.0770144297 0.3890821388 0.4585545107 0.6388902308 -0.479752147511 +1413393963855760384.0000000000 -0.0180611426 1.7841376425 2.0545689476 0.3970023446 0.4681145884 0.6328358918 -0.471992165812 +1413393963905760512.0000000000 0.0222480202 1.7336209303 2.0299148057 0.4044038598 0.4778714043 0.6273181883 -0.463215208981 +1413393963955760384.0000000000 0.0640976183 1.6831241733 2.0029114173 0.4113273497 0.4879782312 0.6224514130 -0.453035645083 +1413393964005760512.0000000000 0.1073038195 1.6318785330 1.9734924130 0.4172682078 0.4982447631 0.6175555920 -0.443017482234 +1413393964055760384.0000000000 0.1514627379 1.5798597273 1.9432591861 0.4233524982 0.5083515921 0.6114821917 -0.434097742723 +1413393964105760512.0000000000 0.1968404866 1.5267836346 1.9116809798 0.4291332628 0.5186158789 0.6040163456 -0.426669037013 +1413393964155760384.0000000000 0.2426924673 1.4726339600 1.8783888040 0.4327059349 0.5302529305 0.5950457213 -0.421328842132 +1413393964205760512.0000000000 0.2890757145 1.4177212174 1.8446338809 0.4355337674 0.5421117154 0.5846978381 -0.41779619869 +1413393964255760384.0000000000 0.3361771203 1.3624496079 1.8111939692 0.4370094774 0.5549844329 0.5737108948 -0.414573039548 +1413393964305760512.0000000000 0.3841189324 1.3069971124 1.7784268616 0.4370952150 0.5682183820 0.5631477144 -0.411023472772 +1413393964355760384.0000000000 0.4324349540 1.2518180217 1.7466202836 0.4384595568 0.5796658366 0.5537863316 -0.406277533037 +1413393964405760512.0000000000 0.4812694987 1.1971902939 1.7163352365 0.4393805087 0.5914122544 0.5436657754 -0.401999799386 +1413393964455760384.0000000000 0.5306591375 1.1433783725 1.6873141986 0.4409671783 0.6018181788 0.5341346117 -0.397571432363 +1413393964505760512.0000000000 0.5801102329 1.0905905596 1.6597028788 0.4424579191 0.6117135476 0.5250244118 -0.392920974971 +1413393964555760384.0000000000 0.6296997111 1.0390178480 1.6339172702 0.4443494344 0.6210200104 0.5146129938 -0.389950244846 +1413393964605760512.0000000000 0.6796851044 0.9890356326 1.6089912314 0.4453987670 0.6303464594 0.5043736181 -0.387156987332 +1413393964655760384.0000000000 0.7300731843 0.9409788271 1.5853062309 0.4468086042 0.6390055957 0.4936203299 -0.38519201681 +1413393964705760512.0000000000 0.7804818523 0.8955235503 1.5631845180 0.4502663639 0.6462104746 0.4829802886 -0.382625489079 +1413393964755760384.0000000000 0.8314647707 0.8523849533 1.5421431766 0.4511423223 0.6548130818 0.4727694737 -0.379709701777 +1413393964805760512.0000000000 0.8830641662 0.8118190871 1.5220239809 0.4504083355 0.6643290390 0.4632685586 -0.375741269786 +1413393964855760384.0000000000 0.9354395323 0.7741657867 1.5025785441 0.4491063848 0.6737781514 0.4555835305 -0.369824424051 +1413393964905760512.0000000000 0.9882944336 0.7398592731 1.4838962512 0.4458047290 0.6849681149 0.4479746352 -0.362485242999 +1413393964955760384.0000000000 1.0414561173 0.7086975248 1.4660812670 0.4387636913 0.6979162067 0.4410950267 -0.354731685939 +1413393965005760512.0000000000 1.0944051426 0.6810423275 1.4495324406 0.4288539476 0.7122963050 0.4322968577 -0.34905256399 +1413393965055760384.0000000000 1.1461248196 0.6579666156 1.4344719676 0.4184495491 0.7266771194 0.4221720631 -0.344399605242 +1413393965105760512.0000000000 1.1966509943 0.6399959555 1.4206325244 0.4068351217 0.7412658264 0.4111931896 -0.34048541701 +1413393965155760384.0000000000 1.2453704198 0.6285337776 1.4085707123 0.3973159379 0.7543493129 0.4000280072 -0.33626589646 +1413393965205760512.0000000000 1.2926129984 0.6240694104 1.3972167684 0.3905285714 0.7655540443 0.3912374461 -0.329162119531 +1413393965255760384.0000000000 1.3369760920 0.6279793229 1.3873045138 0.3854307255 0.7753446821 0.3871744062 -0.316827648802 +1413393965305760512.0000000000 1.3798643460 0.6392311029 1.3795457013 0.3837609740 0.7819549857 0.3870173293 -0.302475622335 +1413393965355760384.0000000000 1.4195400131 0.6581779297 1.3725350886 0.3859475222 0.7851087596 0.3921171805 -0.284416705699 +1413393965405760512.0000000000 1.4553705828 0.6844316783 1.3672541760 0.3945010330 0.7830576659 0.4019494839 -0.263867844373 +1413393965455760384.0000000000 1.4862340905 0.7169791801 1.3641427575 0.4070533269 0.7769464405 0.4142905197 -0.242950988631 +1413393965505760512.0000000000 1.5118569858 0.7543438199 1.3629316547 0.4254005972 0.7651773760 0.4296078477 -0.221302987682 +1413393965555760384.0000000000 1.5310534903 0.7947667730 1.3631893875 0.4438065753 0.7514462355 0.4452594854 -0.200270490693 +1413393965605760512.0000000000 1.5433383814 0.8357735353 1.3652181557 0.4598349647 0.7386511289 0.4567428307 -0.185289777441 +1413393965655760384.0000000000 1.5483642256 0.8761084880 1.3685829177 0.4731832135 0.7274185558 0.4651767467 -0.174844174949 +1413393965705760512.0000000000 1.5455027368 0.9142461238 1.3743068300 0.4838045220 0.7196695824 0.4665547437 -0.17417103011 +1413393965755760384.0000000000 1.5354423267 0.9493210042 1.3819752193 0.4903232538 0.7167166701 0.4605492258 -0.183833436128 +1413393965805760512.0000000000 1.5190191605 0.9822345653 1.3912916777 0.4992301168 0.7122670454 0.4518896340 -0.198092668052 +1413393965855760384.0000000000 1.4980039683 1.0132303004 1.4010785407 0.5091332455 0.7067568589 0.4422149068 -0.213831842608 +1413393965905760512.0000000000 1.4746127937 1.0424755036 1.4076394926 0.5166832541 0.7019996519 0.4365929413 -0.222758854573 +1413393965955760384.0000000000 1.4491907345 1.0703318998 1.4103707725 0.5248098929 0.6959313884 0.4361910026 -0.223587764051 +1413393966005760512.0000000000 1.4218148316 1.0961836836 1.4102822139 0.5317730102 0.6902863689 0.4379986180 -0.221086872357 +1413393966055760384.0000000000 1.3918648660 1.1191399392 1.4103122043 0.5360990786 0.6866029584 0.4399358923 -0.218244280547 +1413393966105760512.0000000000 1.3593001812 1.1378294674 1.4132036412 0.5360263373 0.6867451749 0.4384120470 -0.221024223813 +1413393966155760384.0000000000 1.3248724208 1.1526374600 1.4190034932 0.5330835452 0.6894837135 0.4358519583 -0.224649088618 +1413393966205760512.0000000000 1.2878556963 1.1644449890 1.4282003692 0.5313672622 0.6911581827 0.4339313599 -0.227272466517 +1413393966255760384.0000000000 1.2489092055 1.1732330278 1.4409434949 0.5295283214 0.6925598818 0.4331925979 -0.228702295641 +1413393966305760512.0000000000 1.2077153251 1.1800414276 1.4562082970 0.5309663487 0.6910126798 0.4361792595 -0.224329816438 +1413393966355760384.0000000000 1.1638531786 1.1843685807 1.4752338916 0.5359117222 0.6863356329 0.4401560666 -0.219099662537 +1413393966405760512.0000000000 1.1177892172 1.1849448599 1.4989256507 0.5449694648 0.6782397015 0.4432754227 -0.215652705357 +1413393966455760384.0000000000 1.0697095158 1.1808245295 1.5257018364 0.5530784789 0.6713887060 0.4425871380 -0.217848633269 +1413393966505760512.0000000000 1.0195619433 1.1721043579 1.5544938121 0.5605671210 0.6653537737 0.4383096533 -0.225728833952 +1413393966555760384.0000000000 0.9685057051 1.1590321949 1.5821933837 0.5667039485 0.6601984952 0.4322036195 -0.237032936324 +1413393966605760512.0000000000 0.9175350837 1.1422815571 1.6070084722 0.5716369092 0.6559386585 0.4263757568 -0.247344768154 +1413393966655760384.0000000000 0.8669240599 1.1220354473 1.6283960714 0.5751767646 0.6529091478 0.4212392813 -0.25581009008 +1413393966705760512.0000000000 0.8179650468 1.0978783837 1.6463453255 0.5781606002 0.6503715528 0.4166292725 -0.262996602548 +1413393966755760384.0000000000 0.7706594287 1.0702205327 1.6612209599 0.5801758864 0.6487651946 0.4127875156 -0.268525846094 +1413393966805760512.0000000000 0.7252571580 1.0390685154 1.6729055716 0.5815979699 0.6475993182 0.4103377927 -0.2719959932 +1413393966855760384.0000000000 0.6819142155 1.0044806147 1.6814265363 0.5793071366 0.6498726218 0.4083227069 -0.274483850147 +1413393966905760512.0000000000 0.6406932839 0.9665792256 1.6867956020 0.5714323932 0.6570742100 0.4068667611 -0.276003516733 +1413393966955760384.0000000000 0.6015722698 0.9257022777 1.6900292277 0.5607194447 0.6670412386 0.4031344870 -0.279521512212 +1413393967005760512.0000000000 0.5641784304 0.8828410747 1.6910587966 0.5475328276 0.6799005839 0.3973204774 -0.282983103599 +1413393967055760384.0000000000 0.5279791494 0.8391629851 1.6904231471 0.5364815269 0.6910505275 0.3911470811 -0.285728368699 +1413393967105760512.0000000000 0.4930960953 0.7951841253 1.6876988242 0.5277571659 0.7002147393 0.3854916536 -0.287346267982 +1413393967155760384.0000000000 0.4596100692 0.7515528747 1.6833059362 0.5225372952 0.7069439521 0.3804502767 -0.287128212993 +1413393967205760512.0000000000 0.4274099588 0.7085541941 1.6775234395 0.5189368238 0.7125321019 0.3752659494 -0.286667130678 +1413393967255760384.0000000000 0.3966922466 0.6667872799 1.6704581281 0.5201116904 0.7153800925 0.3695158352 -0.284909108647 +1413393967305760512.0000000000 0.3675661237 0.6261321886 1.6614732920 0.5226502135 0.7179638901 0.3631448456 -0.281940468783 +1413393967355760384.0000000000 0.3398259380 0.5870330999 1.6507344166 0.5279516562 0.7195346008 0.3563457939 -0.276685167939 +1413393967405760512.0000000000 0.3137844886 0.5490463377 1.6384148284 0.5344293866 0.7211866466 0.3475970822 -0.271019039885 +1413393967455760384.0000000000 0.2892159871 0.5118500669 1.6245941969 0.5407972214 0.7235704166 0.3365123917 -0.265976742852 +1413393967505760512.0000000000 0.2662960964 0.4750971167 1.6096524516 0.5451220451 0.7275446402 0.3239056920 -0.26192719444 +1413393967555760384.0000000000 0.2456553646 0.4389148837 1.5945374151 0.5493652475 0.7320160158 0.3123677374 -0.254512817175 +1413393967605760512.0000000000 0.2271699192 0.4029520042 1.5802543746 0.5515304059 0.7379716115 0.2997495765 -0.247714156456 +1413393967655760384.0000000000 0.2110940463 0.3673562319 1.5668674976 0.5534974841 0.7439823755 0.2873023378 -0.239975262965 +1413393967705760512.0000000000 0.1969389780 0.3329824597 1.5549447638 0.5567432696 0.7491669244 0.2758329346 -0.229569256289 +1413393967755760384.0000000000 0.1850528695 0.2988092592 1.5445531806 0.5590644197 0.7546743955 0.2643810476 -0.2191259753 +1413393967805760512.0000000000 0.1757594401 0.2644135533 1.5368292391 0.5611952252 0.7598921426 0.2532582846 -0.208528396463 +1413393967855760384.0000000000 0.1688577781 0.2295807463 1.5313630284 0.5613206006 0.7659184230 0.2432236920 -0.197814024713 +1413393967905760512.0000000000 0.1639962507 0.1941451918 1.5282313486 0.5551554316 0.7756456937 0.2350178370 -0.186929989483 +1413393967955760384.0000000000 0.1598940132 0.1596559188 1.5288120597 0.5460804508 0.7862561753 0.2290353748 -0.176465762044 +1413393968005760512.0000000000 0.1562848297 0.1265641752 1.5332840951 0.5357116488 0.7967071799 0.2241815698 -0.167371809543 +1413393968055760384.0000000000 0.1529624439 0.0959690280 1.5429885271 0.5313329422 0.8023955364 0.2212556691 -0.157774004685 +1413393968105760512.0000000000 0.1492657609 0.0674520985 1.5574027821 0.5295302708 0.8056710747 0.2182753394 -0.151154516979 +1413393968155760384.0000000000 0.1448244487 0.0414640697 1.5760251894 0.5296218059 0.8072171742 0.2147053644 -0.147657654655 +1413393968205760512.0000000000 0.1395575458 0.0176450645 1.5969028909 0.5293916577 0.8087140676 0.2094966687 -0.147774068441 +1413393968255760384.0000000000 0.1340022586 -0.0044562552 1.6175267491 0.5274334570 0.8108619468 0.2048442094 -0.149518231557 +1413393968305760512.0000000000 0.1285090290 -0.0245956190 1.6361052728 0.5251318643 0.8128164920 0.2032294461 -0.149210145577 +1413393968355760384.0000000000 0.1232430971 -0.0419359367 1.6517670756 0.5243802495 0.8135158958 0.2071835298 -0.142450784808 +1413393968405760512.0000000000 0.1175934143 -0.0568642534 1.6649535844 0.5247195619 0.8130659648 0.2144717694 -0.132646064375 +1413393968455760384.0000000000 0.1108191762 -0.0696510848 1.6762746936 0.5262139946 0.8116252657 0.2213825417 -0.123907344789 +1413393968505760512.0000000000 0.1023873888 -0.0806122556 1.6860774675 0.5315909700 0.8074510538 0.2269327564 -0.118048127454 +1413393968555760384.0000000000 0.0921135107 -0.0901404221 1.6935293092 0.5370803623 0.8032474127 0.2308867202 -0.114147276751 +1413393968605760512.0000000000 0.0798560254 -0.0981818024 1.6980224269 0.5399581668 0.8009743517 0.2338919794 -0.110362167179 +1413393968655760384.0000000000 0.0656480895 -0.1050848414 1.6999306547 0.5408289481 0.8005653265 0.2346140761 -0.107496242839 +1413393968705760512.0000000000 0.0495377075 -0.1113154812 1.6997321670 0.5398568235 0.8020446134 0.2325484727 -0.105831262191 +1413393968755760384.0000000000 0.0313250789 -0.1166522050 1.6974079386 0.5393038228 0.8035075315 0.2294029984 -0.104409280586 +1413393968805760512.0000000000 0.0110328028 -0.1203710575 1.6930980237 0.5426233733 0.8029092591 0.2240387099 -0.103456526419 +1413393968855760384.0000000000 -0.0109744617 -0.1227245442 1.6870104536 0.5496529104 0.8002734959 0.2165684706 -0.102674764911 +1413393968905760512.0000000000 -0.0345910612 -0.1239184693 1.6792694918 0.5588965624 0.7965792662 0.2061913447 -0.102865127833 +1413393968955760384.0000000000 -0.0593857702 -0.1247671920 1.6688740961 0.5669558486 0.7940526437 0.1921211475 -0.105503219926 +1413393969005760512.0000000000 -0.0846763795 -0.1253718391 1.6559193397 0.5733101009 0.7928281631 0.1762103569 -0.108115410842 +1413393969055760384.0000000000 -0.1095146059 -0.1263450397 1.6405843544 0.5796907042 0.7914905931 0.1606182395 -0.108180911421 +1413393969105760512.0000000000 -0.1334106349 -0.1281393233 1.6239964758 0.5858181947 0.7902211698 0.1459012432 -0.105263349471 +1413393969155760384.0000000000 -0.1560379708 -0.1303717305 1.6060947598 0.5916661295 0.7890647050 0.1336352858 -0.0972095313936 +1413393969205760512.0000000000 -0.1776546859 -0.1329838309 1.5883298186 0.5952377962 0.7894537973 0.1221151801 -0.0868478596623 +1413393969255760384.0000000000 -0.1982036961 -0.1367595765 1.5719146905 0.5983875370 0.7899272161 0.1102328295 -0.0761319387993 +1413393969305760512.0000000000 -0.2182116002 -0.1414832909 1.5557931300 0.5978802826 0.7929016763 0.0975043387 -0.0658711123574 +1413393969355760384.0000000000 -0.2377099473 -0.1475164968 1.5407872756 0.5970445681 0.7957326370 0.0838440415 -0.0575980111527 +1413393969405760512.0000000000 -0.2568076554 -0.1547147827 1.5271887837 0.5954734415 0.7987378092 0.0683577761 -0.0525024476939 +1413393969455760384.0000000000 -0.2753252291 -0.1630800551 1.5153320085 0.5943471559 0.8009480918 0.0507619936 -0.0515444719601 +1413393969505760512.0000000000 -0.2928330651 -0.1724488148 1.5047057694 0.5933084484 0.8025053368 0.0309333415 -0.054894424052 +1413393969555760384.0000000000 -0.3081380444 -0.1826163399 1.4944033028 0.5925507906 0.8035366178 0.0130976338 -0.0551445047695 +1413393969605760512.0000000000 -0.3209605440 -0.1938870928 1.4841017175 0.5883614494 0.8067736140 -0.0029121714 -0.0542094072249 +1413393969655760384.0000000000 -0.3304609743 -0.2048182857 1.4751012177 0.5848167060 0.8094057586 -0.0174653374 -0.0504648421281 +1413393969705760512.0000000000 -0.3364499882 -0.2149081118 1.4692652989 0.5808777260 0.8121790029 -0.0296728366 -0.0454517033322 +1413393969755760384.0000000000 -0.3393833576 -0.2252274575 1.4659382350 0.5765066548 0.8150432933 -0.0402235652 -0.0415520370325 +1413393969805760512.0000000000 -0.3386235810 -0.2348014708 1.4683888179 0.5728461412 0.8172686012 -0.0493466629 -0.0385258221444 +1413393969855760384.0000000000 -0.3340477597 -0.2443610863 1.4748825361 0.5708537578 0.8183157514 -0.0566898040 -0.0356592815912 +1413393969905760512.0000000000 -0.3255093291 -0.2531357159 1.4854636952 0.5704599737 0.8184277335 -0.0613099780 -0.0315047630512 +1413393969955760384.0000000000 -0.3128134537 -0.2617643725 1.5003881235 0.5719036274 0.8176491983 -0.0618628753 -0.0234310524837 +1413393970005760512.0000000000 -0.2965763362 -0.2698000687 1.5179915350 0.5708676671 0.8189071226 -0.0580372087 -0.0115288131212 +1413393970055760384.0000000000 -0.2773015380 -0.2768450763 1.5381994621 0.5705749209 0.8197792454 -0.0487364995 0.0055679548717 +1413393970105760512.0000000000 -0.2562997860 -0.2835128520 1.5587564758 0.5679349421 0.8218561187 -0.0385497927 0.0227230122609 +1413393970155760384.0000000000 -0.2351223413 -0.2892941414 1.5785334898 0.5645305122 0.8240567735 -0.0303538120 0.036254391824 +1413393970205760512.0000000000 -0.2146202378 -0.2944471563 1.5964273721 0.5608395206 0.8263310613 -0.0246258722 0.0450508130473 +1413393970255760384.0000000000 -0.1950771538 -0.2986321812 1.6118546243 0.5585715831 0.8276653676 -0.0211616259 0.0501997153509 +1413393970305760512.0000000000 -0.1766434575 -0.3014707368 1.6243764896 0.5573056302 0.8284011897 -0.0189364737 0.0529463255756 +1413393970355760384.0000000000 -0.1595362611 -0.3026977734 1.6344671156 0.5558931416 0.8293204770 -0.0176685907 0.0538347696862 +1413393970405760512.0000000000 -0.1438661766 -0.3025313088 1.6437471188 0.5550582255 0.8298603339 -0.0161120134 0.0546131433635 +1413393970455760384.0000000000 -0.1296136297 -0.3003421994 1.6528784379 0.5557943645 0.8293501917 -0.0144053847 0.05534770854 +1413393970505760512.0000000000 -0.1166236203 -0.2961033285 1.6631271500 0.5607885843 0.8259679840 -0.0129344451 0.0559084365697 +1413393970555760384.0000000000 -0.1051934918 -0.2903755496 1.6741671564 0.5672311741 0.8216115505 -0.0120949953 0.0552898396642 +1413393970605760512.0000000000 -0.0951786214 -0.2836613575 1.6848306688 0.5728146223 0.8176792998 -0.0098892238 0.0564462075729 +1413393970655760384.0000000000 -0.0865682463 -0.2759841266 1.6948663602 0.5793082273 0.8128855677 -0.0065417261 0.0598016501477 +1413393970705760512.0000000000 -0.0792374933 -0.2679968757 1.7017906946 0.5847333243 0.8085717195 -0.0019105419 0.065536735376 +1413393970755760384.0000000000 -0.0732002782 -0.2604138884 1.7042467294 0.5876531182 0.8055458928 0.0051509201 0.0757172066698 +1413393970805760512.0000000000 -0.0692537350 -0.2534874582 1.7029916125 0.5875997462 0.8041766527 0.0140975938 0.0884743318814 +1413393970855760384.0000000000 -0.0684020271 -0.2473314588 1.6986838634 0.5857439921 0.8039183879 0.0218067028 0.100715783312 +1413393970905760512.0000000000 -0.0716510349 -0.2417180334 1.6925798218 0.5841994704 0.8035694030 0.0280615565 0.110452444272 +1413393970955760384.0000000000 -0.0800598728 -0.2364075083 1.6868111562 0.5841016901 0.8028066400 0.0313301890 0.115521139791 +1413393971005760512.0000000000 -0.0943073722 -0.2308603724 1.6821727339 0.5857047713 0.8017180326 0.0311540612 0.11501105002 +1413393971055760384.0000000000 -0.1145413280 -0.2256448827 1.6794025237 0.5899685928 0.7998832641 0.0264930850 0.106873475862 +1413393971105760512.0000000000 -0.1398600871 -0.2208742875 1.6789410149 0.5962617164 0.7968579486 0.0200691514 0.0953236825135 +1413393971155760384.0000000000 -0.1692653489 -0.2171182323 1.6819893789 0.6072836290 0.7896630181 0.0160178052 0.0859205541774 +1413393971205760512.0000000000 -0.2024111840 -0.2151110785 1.6890308969 0.6205014422 0.7804312216 0.0119924851 0.0759028910048 +1413393971255760384.0000000000 -0.2384389064 -0.2155712527 1.6991814000 0.6335257629 0.7706112533 0.0097938393 0.0686111120301 +1413393971305760512.0000000000 -0.2767418350 -0.2198615251 1.7112095694 0.6470118931 0.7597860701 0.0091394502 0.0633814507109 +1413393971355760384.0000000000 -0.3166546082 -0.2281803943 1.7215009358 0.6585983674 0.7500370192 0.0092837031 0.0600539190744 +1413393971405760512.0000000000 -0.3581649901 -0.2414124584 1.7281760599 0.6664562869 0.7432820626 0.0091762684 0.0573026098216 +1413393971455760384.0000000000 -0.4014601228 -0.2598870012 1.7307892856 0.6666943559 0.7434699715 0.0073165330 0.0521297001664 +1413393971505760512.0000000000 -0.4460556555 -0.2834419505 1.7288358103 0.6592588399 0.7505629805 0.0035939634 0.0449452741077 +1413393971555760384.0000000000 -0.4916868224 -0.3119909428 1.7241404562 0.6466902799 0.7619541881 -0.0028374187 0.0347770935524 +1413393971605760512.0000000000 -0.5381290488 -0.3444765558 1.7194434236 0.6333606121 0.7735171623 -0.0143710159 0.0178608123461 +1413393971655760384.0000000000 -0.5843395436 -0.3799387107 1.7157855699 0.6211728638 0.7831617627 -0.0282489385 -0.00198095702906 +1413393971705760512.0000000000 -0.6285453837 -0.4174930590 1.7144394016 0.6130269776 0.7885247373 -0.0439430454 -0.0222636973064 +1413393971755760384.0000000000 -0.6693950466 -0.4568077900 1.7153421602 0.6064587076 0.7915902415 -0.0611090457 -0.0431092817178 +1413393971805760512.0000000000 -0.7053697767 -0.4976582653 1.7176504117 0.6006089093 0.7936872909 -0.0759946161 -0.0596174522468 +1413393971855760384.0000000000 -0.7354796824 -0.5397884804 1.7207603097 0.5954048635 0.7955532873 -0.0872915469 -0.0704854695055 +1413393971905760512.0000000000 -0.7588541783 -0.5828532768 1.7248965670 0.5919041210 0.7975697092 -0.0916634103 -0.0716232478956 +1413393971955760384.0000000000 -0.7754091918 -0.6266234310 1.7298040342 0.5886129350 0.8008131368 -0.0900982347 -0.0641517003813 +1413393972005760512.0000000000 -0.7858489409 -0.6705954998 1.7362506549 0.5861713102 0.8037709390 -0.0865788227 -0.0534750429636 +1413393972055760384.0000000000 -0.7910772898 -0.7147757905 1.7435692257 0.5837997831 0.8068589782 -0.0807097484 -0.0405257837965 +1413393972105760512.0000000000 -0.7924257903 -0.7591416718 1.7506117385 0.5800334887 0.8101813571 -0.0782107527 -0.0324098557302 +1413393972155760384.0000000000 -0.7909784158 -0.8038340801 1.7536893050 0.5721977472 0.8158112197 -0.0786625630 -0.0292231597924 +1413393972205760512.0000000000 -0.7867928768 -0.8485140004 1.7515625790 0.5626250338 0.8224638594 -0.0791363788 -0.0272709542948 +1413393972255760384.0000000000 -0.7796246014 -0.8921639191 1.7447178250 0.5544456131 0.8283037459 -0.0773219929 -0.0228970738922 +1413393972305760512.0000000000 -0.7687252164 -0.9338189946 1.7350404072 0.5531846131 0.8301500309 -0.0689472010 -0.00916480151951 +1413393972355760384.0000000000 -0.7553596783 -0.9731842918 1.7255715914 0.5572987543 0.8282860171 -0.0574995798 0.00736007030456 +1413393972405760512.0000000000 -0.7406183126 -1.0116745928 1.7167102301 0.5603467970 0.8266383174 -0.0468303535 0.0220788879662 +1413393972455760384.0000000000 -0.7255029449 -1.0490121390 1.7088955836 0.5635957277 0.8244785214 -0.0366440480 0.035386963505 +1413393972505760512.0000000000 -0.7106945329 -1.0856275325 1.7010219450 0.5610854390 0.8260039966 -0.0278399563 0.0461027608744 +1413393972555760384.0000000000 -0.6968174179 -1.1209284720 1.6935148087 0.5533626908 0.8309102043 -0.0218784268 0.0538451413256 +1413393972605760512.0000000000 -0.6843533245 -1.1537422010 1.6877186079 0.5469284792 0.8348952741 -0.0181362233 0.0590778928151 +1413393972655760384.0000000000 -0.6736497583 -1.1840482494 1.6829445396 0.5435802625 0.8369110861 -0.0167595019 0.0618017087588 +1413393972705760512.0000000000 -0.6646843726 -1.2114813892 1.6786419148 0.5425519805 0.8374199539 -0.0159111757 0.0641249079352 +1413393972755760384.0000000000 -0.6575469064 -1.2368550359 1.6736662061 0.5424228473 0.8373719107 -0.0159093559 0.0658227184003 +1413393972805760512.0000000000 -0.6522278694 -1.2596945367 1.6685352023 0.5448091877 0.8356840490 -0.0161799414 0.0674783573437 +1413393972855760384.0000000000 -0.6486028810 -1.2804682951 1.6630357822 0.5473300507 0.8338743816 -0.0170420626 0.0692307694866 +1413393972905760512.0000000000 -0.6467641861 -1.2990528100 1.6566588792 0.5491824692 0.8324312039 -0.0169540140 0.0718990109402 +1413393972955760384.0000000000 -0.6466233797 -1.3149343068 1.6501680100 0.5513351339 0.8306806710 -0.0170222054 0.0755608197355 +1413393973005760512.0000000000 -0.6485934000 -1.3285274945 1.6439436312 0.5531427899 0.8290824800 -0.0158697085 0.0800215452298 +1413393973055760384.0000000000 -0.6532632848 -1.3403755872 1.6384664710 0.5578069222 0.8257033881 -0.0149857687 0.0827090025119 +1413393973105760512.0000000000 -0.6605239123 -1.3507059787 1.6328468147 0.5639315681 0.8213932007 -0.0148309333 0.0841096894725 +1413393973155760384.0000000000 -0.6703966322 -1.3596926349 1.6276658828 0.5715922376 0.8160527281 -0.0145515171 0.0844305172465 +1413393973205760512.0000000000 -0.6829302167 -1.3685429199 1.6222084470 0.5804739963 0.8097944868 -0.0139209698 0.0841964098964 +1413393973255760384.0000000000 -0.6980211355 -1.3777330594 1.6172558427 0.5912939410 0.8019821109 -0.0131936065 0.083797958161 +1413393973305760512.0000000000 -0.7157773671 -1.3874956087 1.6122815470 0.6035095285 0.7929690842 -0.0126511306 0.0825604592377 +1413393973355760384.0000000000 -0.7357951701 -1.3983009279 1.6069726334 0.6144695557 0.7846746058 -0.0120643916 0.0810393645199 +1413393973405760512.0000000000 -0.7583161402 -1.4107175541 1.6020892024 0.6254523309 0.7761785680 -0.0114806688 0.0788949083218 +1413393973455760384.0000000000 -0.7832095882 -1.4257950841 1.5972321414 0.6348337691 0.7686891663 -0.0100414086 0.0774740038512 +1413393973505760512.0000000000 -0.8103334468 -1.4441321186 1.5924783762 0.6442962783 0.7608426673 -0.0083762310 0.0770102597934 +1413393973555760384.0000000000 -0.8397526968 -1.4667394232 1.5867667420 0.6505124082 0.7557098286 -0.0077723035 0.0753382573114 +1413393973605760512.0000000000 -0.8714498307 -1.4937893629 1.5810462548 0.6542841901 0.7527728867 -0.0082511475 0.07195205473 +1413393973655760384.0000000000 -0.9056835578 -1.5252344347 1.5760890196 0.6556229004 0.7523602958 -0.0125345242 0.0628926349534 +1413393973705760512.0000000000 -0.9418579878 -1.5616556504 1.5710597112 0.6512063889 0.7570892475 -0.0207497265 0.0481202572994 +1413393973755760384.0000000000 -0.9790359579 -1.6027110807 1.5662129903 0.6420498318 0.7654528129 -0.0313996703 0.0294629490921 +1413393973805760512.0000000000 -1.0158594366 -1.6476501680 1.5619473042 0.6305137653 0.7749129885 -0.0433064523 0.0093168256978 +1413393973855760384.0000000000 -1.0512500657 -1.6956543688 1.5588306042 0.6161631263 0.7853057719 -0.0584170565 -0.0150097948967 +1413393973905760512.0000000000 -1.0832683618 -1.7456099681 1.5570176891 0.6011346458 0.7947256968 -0.0738232657 -0.0399791182274 +1413393973955760384.0000000000 -1.1100740414 -1.7966828072 1.5554142843 0.5827914797 0.8057553650 -0.0865953248 -0.0601134994526 +1413393974005760512.0000000000 -1.1305897840 -1.8484030693 1.5533538905 0.5580845876 0.8214334046 -0.0928916552 -0.0718324110522 +1413393974055760384.0000000000 -1.1440456003 -1.8993881518 1.5514998475 0.5303309823 0.8387460525 -0.0961907202 -0.0774690516119 +1413393974105760512.0000000000 -1.1498805401 -1.9489899770 1.5504869889 0.5005382209 0.8567364194 -0.0962431618 -0.0787492907972 +1413393974155760384.0000000000 -1.1476700977 -1.9936431078 1.5510901690 0.4719474006 0.8734147601 -0.0935820824 -0.0751977512106 +1413393974205760512.0000000000 -1.1371444617 -2.0316495991 1.5535181840 0.4475944691 0.8881684985 -0.0834981723 -0.0619997154456 +1413393974255760384.0000000000 -1.1191288970 -2.0607958904 1.5585774815 0.4292225760 0.8998140786 -0.0668128747 -0.0404801678917 +1413393974305760512.0000000000 -1.0954086638 -2.0799273258 1.5666401825 0.4163991904 0.9077009068 -0.0490783908 -0.0167955225297 +1413393974355760384.0000000000 -1.0684139095 -2.0873867987 1.5783539480 0.4066426797 0.9129883723 -0.0327911283 0.00432493362813 +1413393974405760512.0000000000 -1.0398701314 -2.0828611978 1.5914907174 0.4002155537 0.9159361200 -0.0175394503 0.0241019159965 +1413393974455760384.0000000000 -1.0111766437 -2.0666177665 1.6064766239 0.3993577491 0.9157402902 -0.0010248927 0.0439551903125 +1413393974505760512.0000000000 -0.9840337178 -2.0382751975 1.6242343963 0.4039062550 0.9125057527 0.0162946377 0.0626695569052 +1413393974555760384.0000000000 -0.9599144481 -1.9983304434 1.6439523066 0.4142152383 0.9061051877 0.0329454101 0.0794589522873 +1413393974605760512.0000000000 -0.9405733108 -1.9474931024 1.6657526389 0.4299240488 0.8970199094 0.0461434991 0.0916044314135 +1413393974655760384.0000000000 -0.9268083385 -1.8874656197 1.6888904674 0.4506410031 0.8852696812 0.0569606575 0.0998787334061 +1413393974705760512.0000000000 -0.9190724268 -1.8200805520 1.7127315090 0.4757031751 0.8708309997 0.0653618894 0.105298065774 +1413393974755760384.0000000000 -0.9175922937 -1.7477624922 1.7363844257 0.4999737551 0.8565347380 0.0703024184 0.106920796451 +1413393974805760512.0000000000 -0.9219843086 -1.6722277975 1.7581619554 0.5222767172 0.8428168637 0.0734735894 0.10718393851 +1413393974855760384.0000000000 -0.9325353758 -1.5952061400 1.7774917561 0.5429250573 0.8308338183 0.0700432685 0.100207230219 +1413393974905760512.0000000000 -0.9483821619 -1.5174354239 1.7939698305 0.5603649801 0.8211694663 0.0621523503 0.0883678784447 +1413393974955760384.0000000000 -0.9679793701 -1.4395695939 1.8066102282 0.5757165934 0.8122148813 0.0537811155 0.0772332977972 +1413393975005760512.0000000000 -0.9909892459 -1.3625356018 1.8155011380 0.5891189606 0.8041435492 0.0447145141 0.0655180491446 +1413393975055760384.0000000000 -1.0166794522 -1.2874967196 1.8198546846 0.5985434153 0.7984835351 0.0354644532 0.0539638461568 +1413393975105760512.0000000000 -1.0442453070 -1.2145042444 1.8205711220 0.6055175596 0.7941489497 0.0271068516 0.044058474962 +1413393975155760384.0000000000 -1.0734631976 -1.1439823429 1.8183278779 0.6092075799 0.7920818793 0.0185477534 0.0335916942478 +1413393975205760512.0000000000 -1.1033922155 -1.0757570002 1.8135785816 0.6094157102 0.7923039866 0.0123425283 0.0267310117824 +1413393975255760384.0000000000 -1.1339199262 -1.0102930131 1.8083792324 0.6078455645 0.7937415080 0.0072861760 0.0210973880118 +1413393975305760512.0000000000 -1.1646818705 -0.9471327393 1.8038258030 0.6056988198 0.7954854366 0.0042516774 0.0177139235998 +1413393975355760384.0000000000 -1.1953757809 -0.8857329108 1.8016366096 0.6071928964 0.7942944816 0.0051587518 0.0196583409678 +1413393975405760512.0000000000 -1.2263218810 -0.8269057980 1.8000254098 0.6101904875 0.7918922299 0.0070753163 0.0228955237922 +1413393975455760384.0000000000 -1.2576915502 -0.7708799264 1.7991210175 0.6138919092 0.7888014496 0.0113580469 0.0282841244283 +1413393975505760512.0000000000 -1.2900232168 -0.7174099328 1.7992677207 0.6181227213 0.7852871808 0.0145628777 0.0321911112339 +1413393975555760384.0000000000 -1.3233585961 -0.6676747471 1.7996559941 0.6216555318 0.7822674235 0.0175764596 0.0359603381806 +1413393975605760512.0000000000 -1.3580728008 -0.6211217530 1.8007946616 0.6245294173 0.7798545628 0.0192263705 0.0376857336445 +1413393975655760384.0000000000 -1.3943479487 -0.5783247118 1.8023023226 0.6262648040 0.7785055301 0.0190466736 0.0368613502321 +1413393975705760512.0000000000 -1.4322565560 -0.5392882751 1.8039785581 0.6258610031 0.7791975480 0.0144784186 0.0306522668923 +1413393975755760384.0000000000 -1.4711193793 -0.5035602194 1.8058431557 0.6243564402 0.7807646195 0.0079010386 0.0228739606075 +1413393975805760512.0000000000 -1.5103333116 -0.4712029878 1.8079556364 0.6225449492 0.7824223706 0.0009521614 0.0158780829001 +1413393975855760384.0000000000 -1.5494615969 -0.4417706995 1.8110473061 0.6226834456 0.7823983994 -0.0070863962 0.00823736569779 +1413393975905760512.0000000000 -1.5879946384 -0.4155775008 1.8143060953 0.6224597092 0.7824941900 -0.0156847220 0.000861700227961 +1413393975955760384.0000000000 -1.6250222319 -0.3918265094 1.8170331418 0.6200769359 0.7842757884 -0.0203734346 -0.00100221603062 +1413393976005760512.0000000000 -1.6603974693 -0.3708170485 1.8189223506 0.6154195437 0.7878519257 -0.0234107734 0.000253368288498 +1413393976055760384.0000000000 -1.6942708912 -0.3523092319 1.8176863734 0.6097767343 0.7921922437 -0.0240572821 0.0050030454934 +1413393976105760512.0000000000 -1.7270833078 -0.3359011394 1.8142531967 0.6043897815 0.7962468465 -0.0246070631 0.00992189139751 +1413393976155760384.0000000000 -1.7592145419 -0.3211351314 1.8092019187 0.6008955461 0.7987985815 -0.0259795198 0.0130550190643 +1413393976205760512.0000000000 -1.7909016264 -0.3081916093 1.8015843718 0.5974275860 0.8012849796 -0.0288972710 0.0136970308288 +1413393976255760384.0000000000 -1.8219931819 -0.2965827782 1.7922142562 0.5959743283 0.8022458932 -0.0328582486 0.0116817092079 +1413393976305760512.0000000000 -1.8522292463 -0.2858938015 1.7814408037 0.5962861744 0.8018534872 -0.0375176982 0.00813668317635 +1413393976355760384.0000000000 -1.8811860904 -0.2763872144 1.7712705290 0.5994612018 0.7992870665 -0.0420901419 0.00385651779892 +1413393976405760512.0000000000 -1.9086935354 -0.2686550485 1.7630281975 0.6032611483 0.7962901888 -0.0446976656 -0.000202183439193 +1413393976455760384.0000000000 -1.9344514120 -0.2629451376 1.7573502098 0.6053230176 0.7946636827 -0.0454236233 -0.0055109140529 +1413393976505760512.0000000000 -1.9583052329 -0.2603018529 1.7537705580 0.6034224639 0.7961521359 -0.0436111570 -0.011007883448 +1413393976555760384.0000000000 -1.9799080329 -0.2589475882 1.7523766667 0.6006135447 0.7984496733 -0.0388555921 -0.015222750113 +1413393976605760512.0000000000 -1.9990334571 -0.2589931513 1.7511942375 0.5967955250 0.8014647597 -0.0336379653 -0.0189163319633 +1413393976655760384.0000000000 -2.0158910650 -0.2602575384 1.7484897364 0.5934460490 0.8040471434 -0.0286156217 -0.0226080577621 +1413393976705760512.0000000000 -2.0309586965 -0.2622658738 1.7443655535 0.5918783623 0.8050823951 -0.0258921742 -0.0291879544904 +1413393976755760384.0000000000 -2.0437099294 -0.2648522514 1.7378687978 0.5902634093 0.8061067782 -0.0232618781 -0.0352115725214 +1413393976805760512.0000000000 -2.0539769621 -0.2677787991 1.7285563771 0.5868913646 0.8083765112 -0.0211575298 -0.0404759339966 +1413393976855760384.0000000000 -2.0612637505 -0.2711503395 1.7172379200 0.5802131354 0.8131505414 -0.0178035139 -0.0426842983575 +1413393976905760512.0000000000 -2.0653542087 -0.2752317587 1.7054381174 0.5703671219 0.8202365358 -0.0126714455 -0.0416269872482 +1413393976955760384.0000000000 -2.0666654377 -0.2788075685 1.6947170040 0.5615159051 0.8265052137 -0.0077365149 -0.039104555429 +1413393977005760512.0000000000 -2.0652938935 -0.2823739809 1.6844448448 0.5534971026 0.8322274299 -0.0003057462 -0.0322237321752 +1413393977055760384.0000000000 -2.0618283683 -0.2840402346 1.6750092417 0.5492784953 0.8352871872 0.0074970499 -0.0230704088734 +1413393977105760512.0000000000 -2.0571944833 -0.2834393017 1.6677242116 0.5474943611 0.8365651560 0.0147022835 -0.0138746983522 +1413393977155760384.0000000000 -2.0524231195 -0.2798850788 1.6650220737 0.5496573190 0.8351135027 0.0202116789 -0.00733193664091 +1413393977205760512.0000000000 -2.0476969206 -0.2735984621 1.6668684223 0.5535053074 0.8324779354 0.0247262513 -0.000987032480601 +1413393977255760384.0000000000 -2.0437924011 -0.2653042075 1.6728532760 0.5582803030 0.8291966016 0.0273590524 0.00275344835705 +1413393977305760512.0000000000 -2.0409198549 -0.2555295064 1.6820657766 0.5633722084 0.8256630720 0.0293671648 0.00546040049669 +1413393977355760384.0000000000 -2.0389060984 -0.2453880143 1.6940735316 0.5671082668 0.8230510819 0.0302061268 0.00791961082192 +1413393977405760512.0000000000 -2.0377896935 -0.2346731369 1.7096088597 0.5703731593 0.8207367681 0.0308263326 0.0107402912047 +1413393977455760384.0000000000 -2.0378577321 -0.2236491406 1.7266371583 0.5720665422 0.8195524072 0.0304103729 0.0122037816863 +1413393977505760512.0000000000 -2.0388553967 -0.2124417055 1.7440410441 0.5726863909 0.8190196199 0.0312787594 0.0160872347167 +1413393977555760384.0000000000 -2.0411443242 -0.2011885538 1.7613147645 0.5726498904 0.8190116283 0.0308397319 0.0184652849743 +1413393977605760512.0000000000 -2.0447146904 -0.1900339432 1.7767947950 0.5722398766 0.8192845381 0.0300204841 0.0203258426506 +1413393977655760384.0000000000 -2.0495163238 -0.1790228166 1.7893938031 0.5719813471 0.8194603309 0.0290804949 0.0218272664309 +1413393977705760512.0000000000 -2.0554798620 -0.1675853187 1.7986536301 0.5718501224 0.8195376479 0.0280954442 0.0235823497622 +1413393977755760384.0000000000 -2.0627423374 -0.1555275246 1.8056814000 0.5712585876 0.8199881242 0.0261951534 0.0244318680571 +1413393977805760512.0000000000 -2.0715081769 -0.1430599450 1.8111120658 0.5715141452 0.8198525910 0.0242168710 0.0250370522965 +1413393977855760384.0000000000 -2.0816149580 -0.1304869723 1.8155306649 0.5717089477 0.8197111716 0.0229642139 0.0263651126433 +1413393977905760512.0000000000 -2.0931185113 -0.1178198457 1.8202295375 0.5721581352 0.8194152918 0.0211512412 0.0273179950247 +1413393977955760384.0000000000 -2.1059934481 -0.1050905219 1.8254268235 0.5720048242 0.8195586937 0.0188111710 0.0279314966472 +1413393978005760512.0000000000 -2.1201690068 -0.0921080103 1.8312618264 0.5715156471 0.8199662029 0.0158147863 0.0278421222937 +1413393978055760384.0000000000 -2.1355885237 -0.0789335424 1.8376655089 0.5707626470 0.8205829990 0.0118249223 0.0270871521795 +1413393978105760512.0000000000 -2.1522199352 -0.0654732449 1.8446672646 0.5699934694 0.8212130926 0.0074890029 0.0256985655023 +1413393978155760384.0000000000 -2.1699013235 -0.0517554644 1.8520076150 0.5698476866 0.8214118128 0.0029413509 0.0234007757174 +1413393978205760512.0000000000 -2.1880758027 -0.0375478103 1.8596021325 0.5703849583 0.8210979898 -0.0020081750 0.0213320801288 +1413393978255760384.0000000000 -2.2062956919 -0.0229025852 1.8674730205 0.5715556599 0.8202828726 -0.0079951341 0.0199051364839 +1413393978305760512.0000000000 -2.2244202273 -0.0079541465 1.8756144014 0.5730509287 0.8191550543 -0.0145952936 0.0196114134587 +1413393978355760384.0000000000 -2.2420498365 0.0074506690 1.8844623213 0.5761481448 0.8167845757 -0.0234432422 0.0191490609141 +1413393978405760512.0000000000 -2.2589259475 0.0228435383 1.8933063724 0.5783134021 0.8149190399 -0.0322493810 0.0205071900633 +1413393978455760384.0000000000 -2.2748816849 0.0381391883 1.9029039038 0.5819441652 0.8117796999 -0.0431097209 0.0222768800777 +1413393978505760512.0000000000 -2.2897063538 0.0528856949 1.9125179478 0.5846115078 0.8090790987 -0.0545819861 0.0253220015189 +1413393978555760384.0000000000 -2.3029970903 0.0669536031 1.9226043822 0.5879306236 0.8056278627 -0.0660332362 0.0306747526779 +1413393978605760512.0000000000 -2.3147481604 0.0798009087 1.9319062704 0.5876472237 0.8044152139 -0.0786243058 0.0374849654684 +1413393978655760384.0000000000 -2.3250628487 0.0912359835 1.9412414954 0.5869650758 0.8031718108 -0.0914451941 0.0449979835593 +1413393978705760512.0000000000 -2.3339984573 0.1015791766 1.9500756969 0.5842003893 0.8030927417 -0.1045128741 0.0531884616864 +1413393978755760384.0000000000 -2.3415999891 0.1106685104 1.9588802768 0.5801307870 0.8035066265 -0.1184627374 0.0615788195746 +1413393978805760512.0000000000 -2.3482177883 0.1188940564 1.9681914656 0.5763556616 0.8034983705 -0.1319451754 0.0692458715444 +1413393978855760384.0000000000 -2.3533276707 0.1264405209 1.9782511498 0.5735811159 0.8022703609 -0.1464613608 0.076915806622 +1413393978905760512.0000000000 -2.3568675582 0.1333369539 1.9887802187 0.5718669640 0.7999876563 -0.1602740969 0.0854408511014 +1413393978955760384.0000000000 -2.3589021304 0.1397012757 1.9997559884 0.5706483165 0.7970309453 -0.1744428395 0.0931228587363 +1413393979005760512.0000000000 -2.3593505366 0.1451643762 2.0108334211 0.5691172833 0.7938645508 -0.1896879618 0.0995141695713 +1413393979055760384.0000000000 -2.3578034819 0.1496074366 2.0217268844 0.5676522694 0.7902710353 -0.2046308068 0.106624691252 +1413393979105760512.0000000000 -2.3542434100 0.1531159465 2.0328370535 0.5665163404 0.7859781725 -0.2199539101 0.113656613923 +1413393979155760384.0000000000 -2.3484594570 0.1554334395 2.0436224544 0.5643191413 0.7818847070 -0.2347731492 0.122807899079 +1413393979205760512.0000000000 -2.3407323130 0.1566088645 2.0528914209 0.5619466785 0.7774959040 -0.2486461848 0.133757708308 +1413393979255760384.0000000000 -2.3311898507 0.1566310237 2.0596924561 0.5594959227 0.7728382650 -0.2625130411 0.144125750141 +1413393979305760512.0000000000 -2.3202429241 0.1552028419 2.0633812114 0.5573485381 0.7674097421 -0.2770786921 0.153858029071 +1413393979355760384.0000000000 -2.3080749790 0.1520266705 2.0641644169 0.5557146690 0.7612248096 -0.2921121553 0.162445328466 +1413393979405760512.0000000000 -2.2944561862 0.1472636126 2.0619990824 0.5536843708 0.7549446007 -0.3076453037 0.169842970007 +1413393979455760384.0000000000 -2.2795142811 0.1404064430 2.0567482252 0.5519286801 0.7481189691 -0.3229055553 0.177270252771 +1413393979505760512.0000000000 -2.2633641852 0.1313139067 2.0489699346 0.5501188720 0.7410580592 -0.3385026169 0.183352551151 +1413393979555760384.0000000000 -2.2450928160 0.1202500340 2.0391384786 0.5478215117 0.7338502585 -0.3539868008 0.189865042158 +1413393979605760512.0000000000 -2.2242931400 0.1074074389 2.0272927001 0.5444374874 0.7270678018 -0.3686253128 0.197675523768 +1413393979655760384.0000000000 -2.2015302367 0.0919466414 2.0140481671 0.5401305823 0.7208044802 -0.3814273777 0.207877393946 +1413393979705760512.0000000000 -2.1768423993 0.0738679432 2.0015863784 0.5356735003 0.7142704800 -0.3932115660 0.219673045324 +1413393979755760384.0000000000 -2.1505274538 0.0533520415 1.9902152386 0.5302218127 0.7086064527 -0.4039479012 0.231447224374 +1413393979805760512.0000000000 -2.1224427796 0.0300327740 1.9801202395 0.5235065019 0.7037002552 -0.4128477493 0.245567972759 +1413393979855760384.0000000000 -2.0930931298 0.0044376416 1.9713769646 0.5149479121 0.6997402453 -0.4220509261 0.258969597977 +1413393979905760512.0000000000 -2.0626138153 -0.0229974535 1.9640818721 0.5063012234 0.6956727467 -0.4316181840 0.270932175896 +1413393979955760384.0000000000 -2.0311896620 -0.0520322369 1.9577582937 0.4972438011 0.6915596602 -0.4415972573 0.281932085642 +1413393980005760512.0000000000 -1.9989294640 -0.0822507894 1.9523757831 0.4884760403 0.6868609843 -0.4522221495 0.291733223709 +1413393980055760384.0000000000 -1.9660276023 -0.1138095781 1.9466103117 0.4766691335 0.6841513855 -0.4622845087 0.301689330045 +1413393980105760512.0000000000 -1.9322634829 -0.1461348818 1.9411209695 0.4633401274 0.6825006519 -0.4715111849 0.311746674291 +1413393980155760384.0000000000 -1.8973862022 -0.1783970068 1.9358529862 0.4490097902 0.6817159669 -0.4788989444 0.322969580459 +1413393980205760512.0000000000 -1.8615032223 -0.2099806301 1.9306032242 0.4338610735 0.6819088312 -0.4861225058 0.332339922561 +1413393980255760384.0000000000 -1.8246100828 -0.2401379781 1.9257654227 0.4207799833 0.6820054014 -0.4919489683 0.340292595758 +1413393980305760512.0000000000 -1.7865052086 -0.2685099356 1.9214241437 0.4102280778 0.6818211498 -0.4968725394 0.346338741055 +1413393980355760384.0000000000 -1.7470792994 -0.2946088634 1.9176678080 0.4026015077 0.6812649712 -0.5006095283 0.350970319384 +1413393980405760512.0000000000 -1.7053674992 -0.3181108991 1.9144919950 0.3984732038 0.6798921210 -0.5021907020 0.356048182838 +1413393980455760384.0000000000 -1.6617686046 -0.3387525600 1.9121756043 0.3977744915 0.6773472714 -0.5031046564 0.360363472738 +1413393980505760512.0000000000 -1.6165874002 -0.3567130998 1.9100444410 0.4004468658 0.6735466649 -0.5017781037 0.366327630103 +1413393980555760384.0000000000 -1.5700617693 -0.3721466851 1.9085282530 0.4064116749 0.6684653400 -0.4992558014 0.372461118142 +1413393980605760512.0000000000 -1.5225478083 -0.3854045072 1.9071520507 0.4130297878 0.6632463054 -0.4953743618 0.379624781142 +1413393980655760384.0000000000 -1.4745513894 -0.3964453401 1.9057935116 0.4181729622 0.6593737907 -0.4917963831 0.385349056584 +1413393980705760512.0000000000 -1.4267544312 -0.4052744605 1.9046427690 0.4220430840 0.6567454591 -0.4896802225 0.388301837255 +1413393980755760384.0000000000 -1.3795446526 -0.4121671580 1.9037726525 0.4221143772 0.6566515228 -0.4895685628 0.388523940593 +1413393980805760512.0000000000 -1.3331151809 -0.4169162731 1.9032849884 0.4204397061 0.6580690829 -0.4921608133 0.384646941247 +1413393980855760384.0000000000 -1.2875023770 -0.4198550776 1.9031961667 0.4182530546 0.6598327316 -0.4962226334 0.378745622778 +1413393980905760512.0000000000 -1.2418290694 -0.4208518161 1.9034513657 0.4146358506 0.6624172748 -0.5018786263 0.370672780167 +1413393980955760384.0000000000 -1.1954783413 -0.4200494327 1.9051767363 0.4138530964 0.6631493439 -0.5075612423 0.36240881282 +1413393981005760512.0000000000 -1.1477681965 -0.4180261662 1.9078866264 0.4147027657 0.6624241307 -0.5137175499 0.35399175999 +1413393981055760384.0000000000 -1.0981517381 -0.4149650171 1.9121433741 0.4178007967 0.6604295785 -0.5181372856 0.347575918789 +1413393981105760512.0000000000 -1.0466807439 -0.4115383361 1.9181616556 0.4224334452 0.6572769859 -0.5216946656 0.342595423307 +1413393981155760384.0000000000 -0.9931330377 -0.4079710160 1.9271785778 0.4284893407 0.6530528256 -0.5231689637 0.340900465304 +1413393981205760512.0000000000 -0.9378939229 -0.4046736666 1.9393209169 0.4350291610 0.6486019674 -0.5238414492 0.340081244805 +1413393981255760384.0000000000 -0.8809054094 -0.4019702170 1.9548479519 0.4390702500 0.6462301444 -0.5241763822 0.338884989961 +1413393981305760512.0000000000 -0.8223290806 -0.4001017047 1.9732130475 0.4405350301 0.6459756277 -0.5243045053 0.337267195776 +1413393981355760384.0000000000 -0.7626803696 -0.3991338161 1.9924987232 0.4407650785 0.6464713290 -0.5252470155 0.334539293962 +1413393981405760512.0000000000 -0.7020292808 -0.3992499507 2.0112724692 0.4390595481 0.6487173706 -0.5247114412 0.333272245881 +1413393981455760384.0000000000 -0.6404619838 -0.4006271918 2.0283164674 0.4357703174 0.6521048466 -0.5221354508 0.335019507814 +1413393981505760512.0000000000 -0.5776314595 -0.4028306002 2.0430998950 0.4324820168 0.6556304073 -0.5181263607 0.338604708362 +1413393981555760384.0000000000 -0.5137725789 -0.4055220528 2.0544549549 0.4288380993 0.6595358372 -0.5129835554 0.34345048539 +1413393981605760512.0000000000 -0.4490196190 -0.4080096659 2.0626494884 0.4266090270 0.6623806448 -0.5087803740 0.346985807361 +1413393981655760384.0000000000 -0.3830157599 -0.4097196412 2.0676552399 0.4243810479 0.6649987252 -0.5056282454 0.349310032959 +1413393981705760512.0000000000 -0.3158929826 -0.4104100325 2.0699063679 0.4227819909 0.6672476007 -0.5027118313 0.351164978544 +1413393981755760384.0000000000 -0.2477563749 -0.4100681889 2.0693622978 0.4212692227 0.6692699744 -0.4993267685 0.353952993465 +1413393981805760512.0000000000 -0.1785432932 -0.4082083349 2.0664297687 0.4215802396 0.6701871098 -0.4954402800 0.357292972794 +1413393981855760384.0000000000 -0.1091004039 -0.4048942087 2.0610411734 0.4221169484 0.6724057014 -0.4898306289 0.360213560944 +1413393981905760512.0000000000 -0.0392556364 -0.3995347998 2.0535302577 0.4241766280 0.6749399474 -0.4828454432 0.362478321529 +1413393981955760384.0000000000 0.0308628053 -0.3917566182 2.0456738353 0.4278391994 0.6778383777 -0.4745100372 0.363770501478 +1413393982005760512.0000000000 0.1001672550 -0.3817620736 2.0383152537 0.4332168097 0.6808198454 -0.4656350078 0.36330644558 +1413393982055760384.0000000000 0.1683851030 -0.3696131464 2.0312200016 0.4382748384 0.6851081699 -0.4566534123 0.360568471404 +1413393982105760512.0000000000 0.2358892907 -0.3549432694 2.0249119207 0.4447470315 0.6899905239 -0.4459843361 0.356666688703 +1413393982155760384.0000000000 0.3024258433 -0.3378856653 2.0192660291 0.4523638303 0.6950308156 -0.4344759718 0.351468007545 +1413393982205760512.0000000000 0.3677591557 -0.3184604878 2.0143580714 0.4598280565 0.7011973807 -0.4227331929 0.343768874922 +1413393982255760384.0000000000 0.4317283700 -0.2968249366 2.0104908899 0.4684386693 0.7077319966 -0.4095383142 0.334602754385 +1413393982305760512.0000000000 0.4945698033 -0.2732811709 2.0073326899 0.4767154051 0.7149531468 -0.3951591433 0.324705515625 +1413393982355760384.0000000000 0.5553618970 -0.2483666810 2.0045261510 0.4831015148 0.7241328163 -0.3804999677 0.312192833535 +1413393982405760512.0000000000 0.6144407839 -0.2221843025 2.0026491975 0.4886758986 0.7341216280 -0.3643090930 0.299232662172 +1413393982455760384.0000000000 0.6715408913 -0.1948456820 2.0007309809 0.4941539574 0.7442628295 -0.3468047948 0.285676637698 +1413393982505760512.0000000000 0.7264420132 -0.1665597140 1.9989463284 0.4994684545 0.7545423095 -0.3279247192 0.271408446271 +1413393982555760384.0000000000 0.7799732318 -0.1367296682 1.9981060413 0.5054521227 0.7642929593 -0.3078445157 0.256137030042 +1413393982605760512.0000000000 0.8323934109 -0.1054610165 1.9977191771 0.5115041792 0.7736669043 -0.2857201711 0.241178315219 +1413393982655760384.0000000000 0.8837246647 -0.0727056812 1.9969850947 0.5177278501 0.7823973605 -0.2617340573 0.226511648086 +1413393982705760512.0000000000 0.9338207834 -0.0386929082 1.9957643525 0.5232872042 0.7907362573 -0.2362826783 0.212313846226 +1413393982755760384.0000000000 0.9821437157 -0.0032479067 1.9946234009 0.5290809842 0.7983203635 -0.2088683923 0.197817855687 +1413393982805760512.0000000000 1.0290302462 0.0335583604 1.9936565592 0.5347259055 0.8046984758 -0.1805804396 0.184171859505 +1413393982855760384.0000000000 1.0740391362 0.0717127521 1.9929094656 0.5405972479 0.8097265617 -0.1519013615 0.170362810372 +1413393982905760512.0000000000 1.1164337062 0.1105810004 1.9918776726 0.5455905591 0.8141945655 -0.1224437203 0.156287192885 +1413393982955760384.0000000000 1.1562072594 0.1501269959 1.9902865734 0.5491403983 0.8182772508 -0.0944257688 0.141247788923 +1413393983005760512.0000000000 1.1930583275 0.1903723889 1.9882492675 0.5522566859 0.8214300415 -0.0674907652 0.125340481892 +1413393983055760384.0000000000 1.2269398532 0.2313646095 1.9859803632 0.5545901215 0.8238529772 -0.0399239562 0.110009757218 +1413393983105760512.0000000000 1.2575614362 0.2731411770 1.9838876802 0.5570571547 0.8248873070 -0.0125326536 0.0953477309326 +1413393983155760384.0000000000 1.2850674113 0.3157736362 1.9816102419 0.5584020528 0.8253678526 0.0153550925 0.0819711926725 +1413393983205760512.0000000000 1.3089708017 0.3589360885 1.9790138128 0.5594455705 0.8248874294 0.0429496996 0.0688237297805 +1413393983255760384.0000000000 1.3289776352 0.4024822818 1.9763836433 0.5607910109 0.8231011035 0.0700138364 0.0558218446672 +1413393983305760512.0000000000 1.3447379163 0.4460629773 1.9736756642 0.5611320524 0.8209717122 0.0966690641 0.0423244548452 +1413393983355760384.0000000000 1.3561085257 0.4898857002 1.9713949949 0.5628964652 0.8167872645 0.1230135463 0.0295601323215 +1413393983405760512.0000000000 1.3626249734 0.5333984803 1.9698025254 0.5653143055 0.8112504691 0.1484406376 0.0160558255105 +1413393983455760384.0000000000 1.3640505338 0.5762123781 1.9688222545 0.5674105824 0.8051693366 0.1724688079 0.00144242970826 +1413393983505760512.0000000000 1.3602796736 0.6180765601 1.9692003131 0.5709745641 0.7972596555 0.1953939590 -0.0136487969036 +1413393983555760384.0000000000 1.3513950850 0.6581920231 1.9703278714 0.5732931132 0.7893712297 0.2176768015 -0.0290667867684 +1413393983605760512.0000000000 1.3375763793 0.6961594813 1.9725044568 0.5759237572 0.7803263781 0.2396644731 -0.0443115092776 +1413393983655760384.0000000000 1.3192016749 0.7315186837 1.9752636729 0.5769225233 0.7718106929 0.2606460846 -0.0594329453823 +1413393983705760512.0000000000 1.2962731686 0.7639997175 1.9791485782 0.5779580173 0.7627507325 0.2799738402 -0.0760953290222 +1413393983755760384.0000000000 1.2693287803 0.7931467339 1.9834199334 0.5767599475 0.7547879185 0.2985475660 -0.0922632744819 +1413393983805760512.0000000000 1.2385810885 0.8187487783 1.9883951049 0.5742538223 0.7475904840 0.3153460271 -0.109077490946 +1413393983855760384.0000000000 1.2042792610 0.8407879427 1.9943451121 0.5713816131 0.7401415903 0.3315226269 -0.12572281538 +1413393983905760512.0000000000 1.1667857588 0.8593587386 2.0011065546 0.5681520079 0.7327806351 0.3466514540 -0.141663707738 +1413393983955760384.0000000000 1.1265482223 0.8745428732 2.0084789757 0.5663109024 0.7235974409 0.3629791966 -0.154741100412 +1413393984005760512.0000000000 1.0836984796 0.8859267107 2.0159772105 0.5634864165 0.7148485663 0.3785881568 -0.167766483902 +1413393984055760384.0000000000 1.0382322736 0.8936315326 2.0239265047 0.5612520701 0.7048915090 0.3947565376 -0.179697942082 +1413393984105760512.0000000000 0.9903149220 0.8971206573 2.0325672637 0.5588983760 0.6942896966 0.4108857855 -0.191747995335 +1413393984155760384.0000000000 0.9402156261 0.8962036204 2.0418239173 0.5561732195 0.6833712409 0.4270123682 -0.203311422296 +1413393984205760512.0000000000 0.8882841261 0.8906735283 2.0516716775 0.5530876133 0.6721507071 0.4427326433 -0.215163485609 +1413393984255760384.0000000000 0.8346984056 0.8804307414 2.0622832300 0.5494513886 0.6610589260 0.4577854987 -0.227016970976 +1413393984305760512.0000000000 0.7795127143 0.8654089990 2.0736528922 0.5443453316 0.6513928357 0.4707499174 -0.240354007203 +1413393984355760384.0000000000 0.7232731024 0.8459902674 2.0854514854 0.5388623816 0.6424807265 0.4822925267 -0.253455654007 +1413393984405760512.0000000000 0.6661573363 0.8222481791 2.0981158524 0.5346244679 0.6330176678 0.4927301567 -0.26586143621 +1413393984455760384.0000000000 0.6086263665 0.7944132038 2.1111192761 0.5304613293 0.6240114402 0.5028441316 -0.276348113564 +1413393984505760512.0000000000 0.5507919888 0.7624086291 2.1247241741 0.5271963767 0.6153010430 0.5112747275 -0.286472965526 +1413393984555760384.0000000000 0.4930490976 0.7261697600 2.1384801927 0.5246257936 0.6063632839 0.5191228911 -0.295977648851 +1413393984605760512.0000000000 0.4356601353 0.6858730266 2.1515877904 0.5191596067 0.6007214599 0.5259432613 -0.304943792034 +1413393984655760384.0000000000 0.3786598051 0.6413774442 2.1634917450 0.5096440637 0.5994865420 0.5301429195 -0.315954584093 +1413393984705760512.0000000000 0.3222394462 0.5935064971 2.1734698594 0.4975352447 0.6019440086 0.5305135249 -0.329662692192 +1413393984755760384.0000000000 0.2659211150 0.5437345922 2.1807704118 0.4872919735 0.6045354500 0.5296666035 -0.341374737433 +1413393984805760512.0000000000 0.2096108617 0.4927610667 2.1853085114 0.4779183432 0.6078406937 0.5278133764 -0.351478004962 +1413393984855760384.0000000000 0.1538599124 0.4411232551 2.1870445481 0.4661353372 0.6148083695 0.5244948371 -0.360046777607 +1413393984905760512.0000000000 0.0986804983 0.3899791860 2.1857139476 0.4540912787 0.6249295046 0.5188523027 -0.366137286819 +1413393984955760384.0000000000 0.0436543613 0.3398766635 2.1817688244 0.4436943679 0.6362719734 0.5112522819 -0.370019442733 +1413393985005760512.0000000000 -0.0111070949 0.2917036944 2.1755115798 0.4371393242 0.6472112113 0.5021972666 -0.371247578639 +1413393985055760384.0000000000 -0.0657876332 0.2461892488 2.1665199459 0.4359456953 0.6567335800 0.4933527950 -0.367770818967 +1413393985105760512.0000000000 -0.1208536017 0.2034148428 2.1555143664 0.4401659298 0.6641314656 0.4836245912 -0.362340455258 +1413393985155760384.0000000000 -0.1762343599 0.1636842597 2.1427505716 0.4502675847 0.6687675680 0.4741664238 -0.353801137236 +1413393985205760512.0000000000 -0.2311091977 0.1261814253 2.1277994992 0.4621950383 0.6727206059 0.4638958690 -0.344417414937 +1413393985255760384.0000000000 -0.2852567710 0.0904889575 2.1110153946 0.4746747739 0.6767062600 0.4534377820 -0.333386674181 +1413393985305760512.0000000000 -0.3387018309 0.0560745693 2.0936497183 0.4875172851 0.6806080427 0.4427606697 -0.321033609385 +1413393985355760384.0000000000 -0.3911734137 0.0222945715 2.0762609802 0.4991947647 0.6853099289 0.4323498328 -0.30696662746 +1413393985405760512.0000000000 -0.4431040107 -0.0112529491 2.0599666993 0.5099812945 0.6903652465 0.4207876742 -0.293687995764 +1413393985455760384.0000000000 -0.4940153888 -0.0451226720 2.0440865354 0.5187361319 0.6968150685 0.4082200591 -0.280567227422 +1413393985505760512.0000000000 -0.5443396857 -0.0795204573 2.0291842526 0.5271744923 0.7028962916 0.3950036035 -0.268320724217 +1413393985555760384.0000000000 -0.5940018662 -0.1149814192 2.0148829516 0.5317361818 0.7113040855 0.3806179155 -0.257746257582 +1413393985605760512.0000000000 -0.6431591908 -0.1511861252 2.0010337619 0.5328942048 0.7216579139 0.3655596419 -0.248193009534 +1413393985655760384.0000000000 -0.6915431418 -0.1880733339 1.9873324017 0.5305915439 0.7337364458 0.3505875997 -0.23914802247 +1413393985705760512.0000000000 -0.7393941561 -0.2252783945 1.9741196564 0.5264489303 0.7464141970 0.3350533707 -0.23120685352 +1413393985755760384.0000000000 -0.7867028266 -0.2620584055 1.9610027491 0.5219138916 0.7588122696 0.3201015134 -0.22213700809 +1413393985805760512.0000000000 -0.8338446950 -0.2979181396 1.9485131715 0.5180137058 0.7699316770 0.3055111947 -0.213377419916 +1413393985855760384.0000000000 -0.8810295361 -0.3321189150 1.9374410789 0.5141812216 0.7804182431 0.2906186691 -0.205197042859 +1413393985905760512.0000000000 -0.9286117550 -0.3637717966 1.9279742460 0.5112992518 0.7898689014 0.2743058930 -0.198586179457 +1413393985955760384.0000000000 -0.9761834869 -0.3923084763 1.9200243519 0.5095890029 0.7980568919 0.2586112396 -0.191166085066 +1413393986005760512.0000000000 -1.0240747417 -0.4170750985 1.9143677757 0.5098800986 0.8045548881 0.2421833966 -0.1845560065 +1413393986055760384.0000000000 -1.0716645669 -0.4387505433 1.9092504359 0.5111178947 0.8098594628 0.2267165687 -0.177442231924 +1413393986105760512.0000000000 -1.1179388522 -0.4579671969 1.9050744988 0.5124415544 0.8149033829 0.2094294529 -0.17168411151 +1413393986155760384.0000000000 -1.1631367731 -0.4739595950 1.9025139124 0.5144963324 0.8188818070 0.1923865550 -0.166473792438 +1413393986205760512.0000000000 -1.2069372199 -0.4868228384 1.9008309564 0.5161198680 0.8227179771 0.1732690938 -0.163503006281 +1413393986255760384.0000000000 -1.2487673812 -0.4961187952 1.8995739666 0.5185347020 0.8257125953 0.1534391764 -0.160551835437 +1413393986305760512.0000000000 -1.2884052994 -0.5016253386 1.8991385028 0.5204432276 0.8286445173 0.1338033237 -0.156792159799 +1413393986355760384.0000000000 -1.3249743561 -0.5038143384 1.8991115301 0.5226041486 0.8310283204 0.1149833023 -0.15184095189 +1413393986405760512.0000000000 -1.3588519348 -0.5012525847 1.8995953180 0.5255440730 0.8326395470 0.0957099281 -0.14613152225 +1413393986455760384.0000000000 -1.3888906764 -0.4956876280 1.9001803817 0.5275303893 0.8345104909 0.0783283553 -0.138450704952 +1413393986505760512.0000000000 -1.4145832145 -0.4870662819 1.9017308693 0.5325538199 0.8344219296 0.0645004698 -0.126357278128 +1413393986555760384.0000000000 -1.4357066520 -0.4759969116 1.9039470498 0.5407371463 0.8324083205 0.0549623492 -0.108068805216 +1413393986605760512.0000000000 -1.4535311260 -0.4617895511 1.9062779342 0.5504944217 0.8289946517 0.0493094106 -0.0853952057344 +1413393986655760384.0000000000 -1.4690202411 -0.4449746232 1.9090602024 0.5590666461 0.8256220067 0.0451185445 -0.0612952214104 +1413393986705760512.0000000000 -1.4829440183 -0.4270668204 1.9131864117 0.5692363113 0.8202861603 0.0385924483 -0.0401405030543 +1413393986755760384.0000000000 -1.4961396209 -0.4087189433 1.9179827761 0.5781454760 0.8150660578 0.0317460638 -0.0201821053372 +1413393986805760512.0000000000 -1.5090040783 -0.3907540557 1.9236471798 0.5868924081 0.8092957233 0.0244218579 -0.00114301148898 +1413393986855760384.0000000000 -1.5222369851 -0.3742044103 1.9294812024 0.5942473494 0.8039257511 0.0174417945 0.0164090892271 +1413393986905760512.0000000000 -1.5366138690 -0.3593593725 1.9354052797 0.5994364456 0.7997667681 0.0107357926 0.0305582566578 +1413393986955760384.0000000000 -1.5526602764 -0.3464332601 1.9409612520 0.6001533517 0.7988751400 0.0031110514 0.0400597876736 +1413393987005760512.0000000000 -1.5704590543 -0.3353490322 1.9456682601 0.5966946215 0.8011487563 -0.0050563780 0.0457234292935 +1413393987055760384.0000000000 -1.5898077179 -0.3257157320 1.9486669998 0.5925426601 0.8038920560 -0.0122926650 0.049996486258 +1413393987105760512.0000000000 -1.6105968466 -0.3170866944 1.9498211465 0.5881587857 0.8068019833 -0.0181857162 0.053000774967 +1413393987155760384.0000000000 -1.6325830792 -0.3091149395 1.9485322947 0.5842828434 0.8093488277 -0.0230997492 0.05508571175 +1413393987205760512.0000000000 -1.6556917694 -0.3015070906 1.9456297459 0.5811783074 0.8113502090 -0.0273580326 0.0565168243213 +1413393987255760384.0000000000 -1.6799166097 -0.2936106724 1.9424650082 0.5774013108 0.8138677552 -0.0301023147 0.0576268505929 +1413393987305760512.0000000000 -1.7051105369 -0.2853792483 1.9404991496 0.5747911778 0.8155712000 -0.0324823804 0.0583405058192 +1413393987355760384.0000000000 -1.7313797115 -0.2769757917 1.9396943241 0.5726342716 0.8170350275 -0.0339183363 0.0582520496859 +1413393987405760512.0000000000 -1.7585288807 -0.2681533425 1.9402287308 0.5708221726 0.8182693378 -0.0343939003 0.0584328481274 +1413393987455760384.0000000000 -1.7868002222 -0.2589959575 1.9422670149 0.5700919533 0.8188535655 -0.0347476042 0.057154239926 +1413393987505760512.0000000000 -1.8156861293 -0.2493889690 1.9450919562 0.5697540011 0.8190828031 -0.0350061495 0.0570816029635 +1413393987555760384.0000000000 -1.8449742239 -0.2391880996 1.9488356743 0.5710649217 0.8180635632 -0.0350100175 0.0585761082474 +1413393987605760512.0000000000 -1.8746483555 -0.2286237846 1.9526697171 0.5721042321 0.8170867165 -0.0358664885 0.0614787799823 +1413393987655760384.0000000000 -1.9049364456 -0.2174093072 1.9567858935 0.5733979307 0.8158476108 -0.0380546335 0.064492898879 +1413393987705760512.0000000000 -1.9357728379 -0.2058776169 1.9612454104 0.5738126140 0.8151091437 -0.0419077217 0.0676750374581 +1413393987755760384.0000000000 -1.9672883355 -0.1941519056 1.9659184582 0.5748852501 0.8138558762 -0.0474381707 0.0699655768937 +1413393987805760512.0000000000 -1.9995959941 -0.1829767219 1.9699068974 0.5742692283 0.8138522419 -0.0527677019 0.071238693156 +1413393987855760384.0000000000 -2.0326402538 -0.1717783621 1.9731692674 0.5741555190 0.8135571640 -0.0590997574 0.0705506879215 +1413393987905760512.0000000000 -2.0661475014 -0.1607582685 1.9735754799 0.5727517708 0.8142108416 -0.0645650060 0.0696238062196 +1413393987955760384.0000000000 -2.0998676317 -0.1498054449 1.9708277741 0.5723302743 0.8141552976 -0.0688619174 0.0696221579295 +1413393988005760512.0000000000 -2.1336681407 -0.1386607353 1.9644731793 0.5724959590 0.8137031289 -0.0723027655 0.0700564419319 +1413393988055760384.0000000000 -2.1675950601 -0.1273380146 1.9552419531 0.5721824841 0.8135936353 -0.0750365856 0.0710078320911 +1413393988105760512.0000000000 -2.2014189791 -0.1158895582 1.9436618976 0.5729350423 0.8127175338 -0.0766509633 0.0732139150946 +1413393988155760384.0000000000 -2.2352176910 -0.1043948324 1.9290171629 0.5748533262 0.8110359242 -0.0769349430 0.0764551999298 +1413393988205760512.0000000000 -2.2692142377 -0.0933606550 1.9114747036 0.5765368319 0.8094601945 -0.0765964603 0.0806997972306 +1413393988255760384.0000000000 -2.3036586717 -0.0827592449 1.8922845667 0.5787869256 0.8075145401 -0.0753993292 0.0850934977982 +1413393988305760512.0000000000 -2.3387469098 -0.0724192607 1.8717025801 0.5803001439 0.8061414223 -0.0741856298 0.0887932575917 +1413393988355760384.0000000000 -2.3747425024 -0.0625138998 1.8513421765 0.5822345475 0.8044486141 -0.0722312203 0.0929946764095 +1413393988405760512.0000000000 -2.4117495669 -0.0528763636 1.8312270308 0.5828601471 0.8036106270 -0.0694048115 0.0983208073839 +1413393988455760384.0000000000 -2.4498675683 -0.0438475614 1.8114817581 0.5819384033 0.8036945970 -0.0647995736 0.105941987585 +1413393988505760512.0000000000 -2.4895660182 -0.0353851420 1.7919382737 0.5789364400 0.8049554878 -0.0588721312 0.115815945369 +1413393988555760384.0000000000 -2.5317748488 -0.0270604818 1.7736399326 0.5767189048 0.8055844791 -0.0532520516 0.124872618453 +1413393988605760512.0000000000 -2.5770001949 -0.0187034672 1.7568513248 0.5758695980 0.8053016706 -0.0488555954 0.132198926957 +1413393988655760384.0000000000 -2.6261544943 -0.0103736073 1.7417831170 0.5756395566 0.8056164527 -0.0514134018 0.130299248447 +1413393988705760512.0000000000 -2.6783521884 -0.0022138784 1.7275645988 0.5741894127 0.8070260404 -0.0559227800 0.126048130058 +1413393988755760384.0000000000 -2.7336854994 0.0057331479 1.7148330487 0.5732302073 0.8085576093 -0.0656892550 0.115441082843 +1413393988805760512.0000000000 -2.7904498580 0.0137090053 1.7028280247 0.5701289245 0.8110997985 -0.0779229768 0.104871998372 +1413393988855760384.0000000000 -2.8481188135 0.0221043614 1.6931155245 0.5638405368 0.8154158079 -0.0945911257 0.0907382401104 +1413393988905760512.0000000000 -2.9051428384 0.0316994694 1.6876259952 0.5568435665 0.8192900892 -0.1135124478 0.076183439281 +1413393988955760384.0000000000 -2.9599704690 0.0425912988 1.6857001379 0.5496324391 0.8223595943 -0.1316255637 0.0656017567713 +1413393989005760512.0000000000 -3.0118155419 0.0543241512 1.6874349764 0.5426400211 0.8246462784 -0.1492851721 0.0566944471246 +1413393989055760384.0000000000 -3.0598949483 0.0667515878 1.6928790416 0.5352191643 0.8268677405 -0.1653806135 0.0497939608318 +1413393989105760512.0000000000 -3.1032035107 0.0806449970 1.7025906390 0.5274726112 0.8289313955 -0.1811233890 0.0428917702749 +1413393989155760384.0000000000 -3.1407320966 0.0958758754 1.7160388823 0.5194809091 0.8311433477 -0.1945070273 0.0388244376235 +1413393989205760512.0000000000 -3.1716201607 0.1131858100 1.7340662067 0.5120857722 0.8333595145 -0.2044215812 0.038625103654 +1413393989255760384.0000000000 -3.1953940804 0.1329877075 1.7554283252 0.5072135729 0.8348746604 -0.2091172109 0.0445946747743 +1413393989305760512.0000000000 -3.2117447026 0.1553493991 1.7798233896 0.5129306119 0.8318789646 -0.2010057694 0.0669048296209 +1413393989355760384.0000000000 -3.2235357061 0.1800242811 1.8061337414 0.5243602043 0.8249858013 -0.1894877929 0.0924076840238 +1413393989405760512.0000000000 -3.2324384000 0.2066104474 1.8340982102 0.5391377578 0.8148230670 -0.1783617020 0.116537337259 +1413393989455760384.0000000000 -3.2403422049 0.2343899048 1.8611599062 0.5548047655 0.8030626322 -0.1682370003 0.1377620873 +1413393989505760512.0000000000 -3.2488920197 0.2623190105 1.8860151182 0.5679292979 0.7926072350 -0.1603920978 0.153311638611 +1413393989555760384.0000000000 -3.2588452914 0.2893771745 1.9075427385 0.5782026418 0.7840449796 -0.1554221054 0.16370444133 +1413393989605760512.0000000000 -3.2709046812 0.3151492350 1.9248641791 0.5829656411 0.7796823980 -0.1531496700 0.169680871238 +1413393989655760384.0000000000 -3.2849507317 0.3396262796 1.9386220342 0.5847461590 0.7777233155 -0.1521582367 0.173396208038 +1413393989705760512.0000000000 -3.3006406861 0.3632489690 1.9487659595 0.5825524583 0.7785584273 -0.1544082587 0.175035705578 +1413393989755760384.0000000000 -3.3180322243 0.3860248899 1.9560293722 0.5796585235 0.7797312651 -0.1588073206 0.175486139942 +1413393989805760512.0000000000 -3.3371176276 0.4079136732 1.9607863401 0.5768803389 0.7805642357 -0.1657527511 0.174512389278 +1413393989855760384.0000000000 -3.3575103366 0.4290421071 1.9637244112 0.5762110524 0.7795167557 -0.1761698783 0.171168410179 +1413393989905760512.0000000000 -3.3787752275 0.4491644123 1.9644776648 0.5757184769 0.7778064577 -0.1884743282 0.167459778357 +1413393989955760384.0000000000 -3.4002954018 0.4687970546 1.9636486129 0.5770583803 0.7740498152 -0.2026907254 0.163606170866 +1413393990005760512.0000000000 -3.4217662653 0.4869278702 1.9607554436 0.5789327863 0.7687773764 -0.2191580395 0.16058620155 +1413393990055760384.0000000000 -3.4421105551 0.5032752010 1.9555291588 0.5796868233 0.7631254879 -0.2340958015 0.163712651737 +1413393990105760512.0000000000 -3.4613655667 0.5174334179 1.9479888244 0.5791205842 0.7574478862 -0.2487859061 0.170286880086 +1413393990155760384.0000000000 -3.4797245360 0.5291565194 1.9381720620 0.5773356544 0.7516318822 -0.2638773549 0.179169744418 +1413393990205760512.0000000000 -3.4973155458 0.5387730706 1.9262099568 0.5744409716 0.7457033465 -0.2796940799 0.188984949041 +1413393990255760384.0000000000 -3.5143158117 0.5458780124 1.9120017739 0.5696097083 0.7403844353 -0.2963323767 0.198903973423 +1413393990305760512.0000000000 -3.5308861359 0.5502215593 1.8960726509 0.5633399880 0.7352777036 -0.3146296815 0.207419671324 +1413393990355760384.0000000000 -3.5470075595 0.5520739096 1.8795944543 0.5552084040 0.7308615460 -0.3337486175 0.214934615647 +1413393990405760512.0000000000 -3.5621305898 0.5514971217 1.8642615675 0.5475343888 0.7253643411 -0.3528424734 0.222609197376 +1413393990455760384.0000000000 -3.5760495456 0.5486427611 1.8506612596 0.5410148567 0.7184235547 -0.3727476267 0.228538241068 +1413393990505760512.0000000000 -3.5887856120 0.5434619568 1.8379671552 0.5335671580 0.7119136665 -0.3924642718 0.233359839616 +1413393990555760384.0000000000 -3.6000985491 0.5359162617 1.8261866452 0.5242819656 0.7067534059 -0.4118594902 0.236642777315 +1413393990605760512.0000000000 -3.6096956982 0.5258582232 1.8144951170 0.5103362442 0.7048834770 -0.4313855981 0.237913151089 +1413393990655760384.0000000000 -3.6168655244 0.5134713190 1.8029881987 0.4917094532 0.7067079147 -0.4489735116 0.239183032208 +1413393990705760512.0000000000 -3.6211652404 0.4990331080 1.7908313319 0.4662446653 0.7143558621 -0.4622414356 0.242166202326 +1413393990755760384.0000000000 -3.6208370002 0.4834427707 1.7797287542 0.4402701528 0.7234943590 -0.4690250195 0.25046683621 +1413393990805760512.0000000000 -3.6158262200 0.4680255598 1.7701533076 0.4157162767 0.7325764215 -0.4721750912 0.259927773078 +1413393990855760384.0000000000 -3.6054373367 0.4544472067 1.7621236876 0.3938452764 0.7408853898 -0.4726117867 0.269467691133 +1413393990905760512.0000000000 -3.5893831251 0.4440619258 1.7569518324 0.3793446111 0.7457291432 -0.4707106604 0.280030686152 +1413393990955760384.0000000000 -3.5667416804 0.4378375290 1.7546594040 0.3742092660 0.7466330650 -0.4632068962 0.296556677303 +1413393991005760512.0000000000 -3.5386127750 0.4368252735 1.7555249936 0.3799208993 0.7427901601 -0.4520201686 0.315595715285 +1413393991055760384.0000000000 -3.5056619950 0.4414207230 1.7589758427 0.3929188742 0.7349201382 -0.4394033064 0.335308638419 +1413393991105760512.0000000000 -3.4699876002 0.4516860115 1.7645852390 0.4133248721 0.7224419084 -0.4270113955 0.353414073117 +1413393991155760384.0000000000 -3.4340543264 0.4665841565 1.7719838627 0.4388808424 0.7064859428 -0.4142966721 0.369620733092 +1413393991205760512.0000000000 -3.3993622814 0.4848851831 1.7802040579 0.4666963612 0.6880026741 -0.4039575200 0.381661039223 +1413393991255760384.0000000000 -3.3679573220 0.5051752315 1.7886719308 0.4939417213 0.6692928724 -0.3932179174 0.391724771227 +1413393991305760512.0000000000 -3.3413129457 0.5261993574 1.7963595203 0.5186577846 0.6514420789 -0.3834259469 0.399502019401 +1413393991355760384.0000000000 -3.3209385508 0.5472231654 1.8027326557 0.5382536944 0.6381886219 -0.3801138881 0.398135247621 +1413393991405760512.0000000000 -3.3069555687 0.5671243161 1.8077310489 0.5514341537 0.6301021519 -0.3806556687 0.392419309088 +1413393991455760384.0000000000 -3.2994754346 0.5851502148 1.8101322432 0.5529744404 0.6324613208 -0.3886410143 0.378378260271 +1413393991505760512.0000000000 -3.2980241501 0.6007740629 1.8114345083 0.5470625766 0.6409733616 -0.4020053218 0.358144395866 +1413393991555760384.0000000000 -3.3012141250 0.6139617684 1.8133240018 0.5402213959 0.6495143898 -0.4164187090 0.335987142172 +1413393991605760512.0000000000 -3.3072458859 0.6244157967 1.8152128720 0.5303343936 0.6593679990 -0.4318626506 0.312208142005 +1413393991655760384.0000000000 -3.3145110752 0.6316760132 1.8177414315 0.5183756096 0.6693592813 -0.4468085681 0.289148721882 +1413393991705760512.0000000000 -3.3210743788 0.6358742571 1.8212431882 0.5053509175 0.6787754162 -0.4586742729 0.27111306849 +1413393991755760384.0000000000 -3.3252633093 0.6370900413 1.8265559724 0.4942813239 0.6858519047 -0.4674478514 0.2584291854 +1413393991805760512.0000000000 -3.3259235263 0.6353641870 1.8336316972 0.4851204325 0.6911916324 -0.4724723542 0.25235325985 +1413393991855760384.0000000000 -3.3215384839 0.6313421050 1.8438336654 0.4832778433 0.6919658600 -0.4698842808 0.258523765691 +1413393991905760512.0000000000 -3.3129251540 0.6251436819 1.8556349881 0.4849455419 0.6910941637 -0.4587446997 0.277073959076 +1413393991955760384.0000000000 -3.3012009253 0.6176576653 1.8694599309 0.4915645554 0.6864286885 -0.4423747358 0.302464107922 +1413393992005760512.0000000000 -3.2891014669 0.6095691865 1.8848073202 0.5021130807 0.6784675531 -0.4266359612 0.324878423797 +1413393992055760384.0000000000 -3.2783383121 0.6009519897 1.8997317892 0.5115301306 0.6707215709 -0.4124904766 0.343978351859 +1413393992105760512.0000000000 -3.2701708831 0.5916511731 1.9136440261 0.5184787226 0.6644111100 -0.4022674411 0.357657094157 +1413393992155760384.0000000000 -3.2657870412 0.5817533257 1.9250575096 0.5185033282 0.6639277053 -0.3989903858 0.362161528538 +1413393992205760512.0000000000 -3.2652227253 0.5712025421 1.9333218699 0.5074166292 0.6721723238 -0.4025969149 0.358648094506 +1413393992255760384.0000000000 -3.2678897930 0.5604910479 1.9404733621 0.4924920110 0.6831432773 -0.4092173270 0.351152475595 +1413393992305760512.0000000000 -3.2726687741 0.5502511313 1.9476694686 0.4775799821 0.6936496338 -0.4181613957 0.340453511409 +1413393992355760384.0000000000 -3.2784875628 0.5417795319 1.9562764056 0.4675967749 0.7003773564 -0.4322330816 0.322489345533 +1413393992405760512.0000000000 -3.2836858385 0.5344422681 1.9653972943 0.4610822312 0.7043516527 -0.4460627789 0.30384193697 +1413393992455760384.0000000000 -3.2871724246 0.5276736079 1.9739752081 0.4595311756 0.7043824541 -0.4585750343 0.287028561191 +1413393992505760512.0000000000 -3.2876733148 0.5208566858 1.9817170449 0.4621429513 0.7015240360 -0.4665894505 0.276734898744 +1413393992555760384.0000000000 -3.2847033232 0.5135833602 1.9879503316 0.4687437875 0.6964846714 -0.4687690154 0.274670665381 +1413393992605760512.0000000000 -3.2781870463 0.5054211729 1.9914700976 0.4777337197 0.6902042083 -0.4657984031 0.280036589789 +1413393992655760384.0000000000 -3.2688793449 0.4956481091 1.9935969259 0.4885665485 0.6830117255 -0.4553319418 0.295754176978 +1413393992705760512.0000000000 -3.2583322973 0.4848577769 1.9951670582 0.5013669537 0.6742157892 -0.4408118428 0.315830914644 +1413393992755760384.0000000000 -3.2480308960 0.4731055235 1.9963010144 0.5134195546 0.6652899295 -0.4250699908 0.336311126218 +1413393992805760512.0000000000 -3.2399632913 0.4602089203 1.9967393006 0.5222515575 0.6580341366 -0.4113039616 0.353657230802 +1413393992855760384.0000000000 -3.2353810684 0.4463288880 1.9965960667 0.5255777072 0.6548633989 -0.4011880696 0.366019310117 +1413393992905760512.0000000000 -3.2352468611 0.4316292073 1.9957213097 0.5234609501 0.6563049421 -0.3968486847 0.371165162899 +1413393992955760384.0000000000 -3.2395868506 0.4161617648 1.9938682911 0.5140720395 0.6633300300 -0.3986970488 0.369815998531 +1413393993005760512.0000000000 -3.2480292642 0.4003744193 1.9919133847 0.5006202516 0.6734796816 -0.4035382141 0.364638714062 +1413393993055760384.0000000000 -3.2596651804 0.3846876659 1.9904628328 0.4862635097 0.6841204659 -0.4090362584 0.358073074336 +1413393993105760512.0000000000 -3.2732780066 0.3702788302 1.9903378924 0.4748764971 0.6920598683 -0.4155852602 0.350477306926 +1413393993155760384.0000000000 -3.2886700345 0.3571660706 1.9903555498 0.4620737463 0.7010279209 -0.4251680772 0.338052974101 +1413393993205760512.0000000000 -3.3042972649 0.3456369511 1.9907300098 0.4481935005 0.7101271542 -0.4366489534 0.322768806613 +1413393993255760384.0000000000 -3.3184733357 0.3355632465 1.9908150507 0.4310771686 0.7203134893 -0.4480227947 0.307565484511 +1413393993305760512.0000000000 -3.3300501287 0.3276312144 1.9918953963 0.4144694386 0.7297706892 -0.4581643933 0.292805762325 +1413393993355760384.0000000000 -3.3373122060 0.3219538021 1.9944005879 0.4009819674 0.7370601659 -0.4642125310 0.283659125822 +1413393993405760512.0000000000 -3.3392407672 0.3188322283 1.9983316585 0.3907591598 0.7425752299 -0.4659654898 0.280651864942 +1413393993455760384.0000000000 -3.3352036468 0.3190664079 2.0041318578 0.3862549305 0.7454363150 -0.4635649097 0.28326560568 +1413393993505760512.0000000000 -3.3245919009 0.3232889248 2.0124739626 0.3910441450 0.7432511457 -0.4582691064 0.290949543971 +1413393993555760384.0000000000 -3.3087225539 0.3313541859 2.0235284864 0.4042615874 0.7360165463 -0.4507388040 0.302798188779 +1413393993605760512.0000000000 -3.2894574048 0.3428811228 2.0366065980 0.4236550332 0.7248139676 -0.4413331904 0.316837719348 +1413393993655760384.0000000000 -3.2678136152 0.3571335679 2.0511645428 0.4469521336 0.7104736694 -0.4297153671 0.332874839303 +1413393993705760512.0000000000 -3.2460470080 0.3732676657 2.0660221513 0.4706700091 0.6944187569 -0.4179011236 0.348727663887 +1413393993755760384.0000000000 -3.2253361355 0.3905083363 2.0792388115 0.4930586215 0.6781408346 -0.4059495591 0.363625026134 +1413393993805760512.0000000000 -3.2074876664 0.4075796677 2.0867432231 0.5109657191 0.6642588959 -0.3957185406 0.375607494194 +1413393993855760384.0000000000 -3.1930915098 0.4240859088 2.0882313134 0.5254071734 0.6522510243 -0.3872737457 0.385402321379 +1413393993905760512.0000000000 -3.1827383002 0.4398212053 2.0837233676 0.5369325905 0.6422524502 -0.3805554628 0.392928394455 +1413393993955760384.0000000000 -3.1774616765 0.4546799257 2.0747472040 0.5478124491 0.6325271804 -0.3748345634 0.399136488911 +1413393994005760512.0000000000 -3.1785146156 0.4682378441 2.0635417594 0.5573833517 0.6242424423 -0.3717314731 0.401821956141 +1413393994055760384.0000000000 -3.1872763891 0.4802039874 2.0541458347 0.5666397267 0.6170910892 -0.3720301581 0.399639298889 +1413393994105760512.0000000000 -3.2047848270 0.4893004579 2.0484591722 0.5720622047 0.6133277971 -0.3762655385 0.393697970243 +1413393994155760384.0000000000 -3.2319592108 0.4949906811 2.0475754164 0.5758527998 0.6117479315 -0.3823221142 0.384691853761 +1413393994205760512.0000000000 -3.2673152731 0.4970481553 2.0505272140 0.5773227619 0.6122292954 -0.3904054332 0.373439842873 +1413393994255760384.0000000000 -3.3089507110 0.4953868297 2.0576177075 0.5731468789 0.6172853283 -0.3999616414 0.361236991679 +1413393994305760512.0000000000 -3.3561991049 0.4900797362 2.0680699971 0.5644156738 0.6264406889 -0.4122550409 0.345040275367 +1413393994355760384.0000000000 -3.4070996505 0.4804800721 2.0812451585 0.5465358433 0.6416453337 -0.4236289898 0.331855867307 +1413393994405760512.0000000000 -3.4611773566 0.4673775468 2.0930529911 0.5256166204 0.6583737473 -0.4357238092 0.316884741359 +1413393994455760384.0000000000 -3.5163083553 0.4520035929 2.0993720976 0.4992234137 0.6777637306 -0.4485704071 0.300327985105 +1413393994505760512.0000000000 -3.5712484148 0.4347052184 2.1004723086 0.4711613129 0.6964873726 -0.4604432250 0.284436976385 +1413393994555760384.0000000000 -3.6247662516 0.4166293048 2.0963258436 0.4436392740 0.7131479211 -0.4713198629 0.269187339904 +1413393994605760512.0000000000 -3.6753868298 0.3983639311 2.0867750418 0.4172573786 0.7273876765 -0.4814053543 0.255053588303 +1413393994655760384.0000000000 -3.7213790235 0.3805214843 2.0728552417 0.3940972829 0.7382512726 -0.4905740632 0.242918666681 +1413393994705760512.0000000000 -3.7609810675 0.3643447079 2.0560932620 0.3740602475 0.7467124228 -0.4980745873 0.233283506468 +1413393994755760384.0000000000 -3.7911782052 0.3505902762 2.0388173888 0.3593960267 0.7525371315 -0.5010464242 0.231246281169 +1413393994805760512.0000000000 -3.8105404365 0.3399755509 2.0230846749 0.3531854030 0.7552953869 -0.4974499313 0.23944209195 +1413393994855760384.0000000000 -3.8192336248 0.3338157776 2.0111435592 0.3602895701 0.7520620368 -0.4888681379 0.256128995209 +1413393994905760512.0000000000 -3.8194836972 0.3319452156 2.0019500184 0.3747791753 0.7447111591 -0.4780527148 0.276426230735 +1413393994955760384.0000000000 -3.8139103328 0.3341881058 1.9935885554 0.3929782819 0.7344699802 -0.4688766678 0.293728766894 +1413393995005760512.0000000000 -3.8037717967 0.3397312636 1.9852438367 0.4112725412 0.7230149133 -0.4627390572 0.306556514902 +1413393995055760384.0000000000 -3.7913076162 0.3478463191 1.9765432300 0.4296281244 0.7109944408 -0.4591832757 0.314733695634 +1413393995105760512.0000000000 -3.7772511281 0.3576603038 1.9669769149 0.4479458735 0.6990154583 -0.4574812270 0.318485180862 +1413393995155760384.0000000000 -3.7624089899 0.3684634807 1.9558850644 0.4628066242 0.6901140874 -0.4566008386 0.317912329318 +1413393995205760512.0000000000 -3.7474888181 0.3799133879 1.9432232339 0.4780237911 0.6821556762 -0.4584111717 0.309864625534 +1413393995255760384.0000000000 -3.7322236468 0.3906495547 1.9288634469 0.4905293048 0.6778829299 -0.4575636145 0.300817674214 +1413393995305760512.0000000000 -3.7169596050 0.3999058922 1.9126269316 0.4994527615 0.6774380067 -0.4553485422 0.290314297211 +1413393995355760384.0000000000 -3.7014999725 0.4074238928 1.8961139983 0.5075371845 0.6793468374 -0.4504838990 0.279209845023 +1413393995405760512.0000000000 -3.6851530719 0.4126468675 1.8795853735 0.5138862690 0.6836974130 -0.4428622441 0.268982867251 +1413393995455760384.0000000000 -3.6675922996 0.4155960574 1.8641655336 0.5200593149 0.6890818349 -0.4328699088 0.259476734868 +1413393995505760512.0000000000 -3.6489328861 0.4158566675 1.8493080855 0.5248066521 0.6963321288 -0.4202820215 0.251122612884 +1413393995555760384.0000000000 -3.6287235373 0.4136835632 1.8357961735 0.5300509019 0.7036511596 -0.4051974471 0.244409729281 +1413393995605760512.0000000000 -3.6073174588 0.4091892748 1.8229919374 0.5351365870 0.7114871644 -0.3876785674 0.238998277314 +1413393995655760384.0000000000 -3.5853504171 0.4024453896 1.8107592495 0.5403645918 0.7198250520 -0.3674278566 0.234210957624 +1413393995705760512.0000000000 -3.5629261066 0.3936247638 1.7992155713 0.5465435885 0.7274122751 -0.3443828256 0.231434563689 +1413393995755760384.0000000000 -3.5405054522 0.3833082555 1.7888506402 0.5532581413 0.7343851081 -0.3205082073 0.227724463062 +1413393995805760512.0000000000 -3.5189123880 0.3714078550 1.7794866865 0.5602818708 0.7408310407 -0.2968823902 0.221617780805 +1413393995855760384.0000000000 -3.4984034561 0.3579623243 1.7709540406 0.5681729094 0.7460304931 -0.2744031575 0.21288718976 +1413393995905760512.0000000000 -3.4792061486 0.3427412651 1.7627589948 0.5757308220 0.7507727914 -0.2533088505 0.201764373496 +1413393995955760384.0000000000 -3.4608982285 0.3256775198 1.7547584466 0.5828378134 0.7547864454 -0.2325173990 0.19113650699 +1413393996005760512.0000000000 -3.4436874898 0.3063352525 1.7466405170 0.5891655753 0.7580857054 -0.2138041518 0.180215906331 +1413393996055760384.0000000000 -3.4274201496 0.2847853974 1.7383346741 0.5940716865 0.7609846900 -0.1977091940 0.169977079403 +1413393996105760512.0000000000 -3.4121317306 0.2610225473 1.7302485295 0.5984605286 0.7628583204 -0.1846745903 0.160584788797 +1413393996155760384.0000000000 -3.3978870733 0.2353109365 1.7227944795 0.6023977846 0.7640784495 -0.1759604062 0.149462261269 +1413393996205760512.0000000000 -3.3845108836 0.2073083633 1.7148939141 0.6031923327 0.7670085859 -0.1702672955 0.137353147101 +1413393996255760384.0000000000 -3.3714313742 0.1766870290 1.7056590395 0.5981167634 0.7736647588 -0.1663140133 0.126644491702 +1413393996305760512.0000000000 -3.3581253753 0.1439605920 1.6961317342 0.5919103707 0.7804046001 -0.1621657831 0.119637084754 +1413393996355760384.0000000000 -3.3444888223 0.1095953801 1.6854475074 0.5841877086 0.7876714607 -0.1582249218 0.115166250404 +1413393996405760512.0000000000 -3.3303730646 0.0743797297 1.6730681000 0.5774304632 0.7936557581 -0.1540354025 0.113831861112 +1413393996455760384.0000000000 -3.3159806835 0.0385708813 1.6580576619 0.5706436898 0.7992861372 -0.1508174557 0.112967009116 +1413393996505760512.0000000000 -3.3014087001 0.0025634963 1.6404618926 0.5644728903 0.8041416402 -0.1488576963 0.112106935098 +1413393996555760384.0000000000 -3.2864899336 -0.0330147544 1.6202523702 0.5577801211 0.8089817467 -0.1478968887 0.112055256083 +1413393996605760512.0000000000 -3.2713997087 -0.0680947604 1.5982879058 0.5518473923 0.8131492041 -0.1471008835 0.112312766854 +1413393996655760384.0000000000 -3.2563830177 -0.1020652567 1.5762988936 0.5468490307 0.8168707584 -0.1456863940 0.111596488741 +1413393996705760512.0000000000 -3.2413148007 -0.1345618114 1.5553429212 0.5436354781 0.8195299317 -0.1434751163 0.110661868192 +1413393996755760384.0000000000 -3.2261730527 -0.1652864709 1.5358893825 0.5419632628 0.8213541377 -0.1404246550 0.109243390951 +1413393996805760512.0000000000 -3.2107709283 -0.1941368110 1.5178939932 0.5426193075 0.8218885171 -0.1348050026 0.109046613163 +1413393996855760384.0000000000 -3.1956879481 -0.2211768092 1.5013134764 0.5436860734 0.8223504999 -0.1281885402 0.108225723065 +1413393996905760512.0000000000 -3.1808704046 -0.2466100645 1.4859235083 0.5448472999 0.8228188418 -0.1210830616 0.107002175331 +1413393996955760384.0000000000 -3.1666313280 -0.2706020355 1.4715330489 0.5451913398 0.8239444915 -0.1131833156 0.105220791493 +1413393997005760512.0000000000 -3.1528172005 -0.2929165043 1.4584747803 0.5455351642 0.8250193996 -0.1056784501 0.102793190944 +1413393997055760384.0000000000 -3.1393524802 -0.3135042600 1.4467082271 0.5454677182 0.8262205067 -0.0997401072 0.0993808518067 +1413393997105760512.0000000000 -3.1261341173 -0.3321881507 1.4357075088 0.5452285382 0.8273126888 -0.0936188749 0.0975451808779 +1413393997155760384.0000000000 -3.1134032051 -0.3489970258 1.4260262656 0.5461429845 0.8274956206 -0.0892258524 0.0949609692417 +1413393997205760512.0000000000 -3.1011364271 -0.3636684869 1.4179351344 0.5494101110 0.8259769371 -0.0854675314 0.0927681539927 +1413393997255760384.0000000000 -3.0894041273 -0.3767793179 1.4105826842 0.5532480338 0.8239744806 -0.0819614555 0.0909119807198 +1413393997305760512.0000000000 -3.0782506938 -0.3886655094 1.4034086544 0.5567791656 0.8220773481 -0.0783332960 0.0897200606916 +1413393997355760384.0000000000 -3.0677754576 -0.3996505456 1.3950132338 0.5601091310 0.8202172911 -0.0753188959 0.0885913129144 +1413393997405760512.0000000000 -3.0578407151 -0.4097054503 1.3831312186 0.5625908823 0.8188504849 -0.0733654203 0.0871372352723 +1413393997455760384.0000000000 -3.0484107394 -0.4192826194 1.3666109210 0.5641296401 0.8180440046 -0.0714962390 0.0863136342799 +1413393997505760512.0000000000 -3.0394713248 -0.4285850693 1.3464941771 0.5650964251 0.8175839184 -0.0703749041 0.085263940581 +1413393997555760384.0000000000 -3.0313184199 -0.4378136017 1.3245327432 0.5670918208 0.8163158594 -0.0691982294 0.0851286644224 +1413393997605760512.0000000000 -3.0242493384 -0.4468538027 1.3030814535 0.5689882946 0.8151520855 -0.0683828964 0.0842803513346 +1413393997655760384.0000000000 -3.0180242398 -0.4554708610 1.2830808563 0.5712376568 0.8136000749 -0.0676922496 0.0846180644546 +1413393997705760512.0000000000 -3.0129642894 -0.4640288766 1.2645289844 0.5714040269 0.8135352691 -0.0677929203 0.0840352541958 +1413393997755760384.0000000000 -3.0087253610 -0.4723440429 1.2478768629 0.5707357270 0.8140237521 -0.0676677299 0.0839472411132 +1413393997805760512.0000000000 -3.0052859963 -0.4804529483 1.2329330924 0.5691654565 0.8150119532 -0.0679029250 0.084825657442 +1413393997855760384.0000000000 -3.0029329746 -0.4884142243 1.2197024768 0.5677035098 0.8159579535 -0.0681078965 0.0853619202648 +1413393997905760512.0000000000 -3.0016069724 -0.4960247511 1.2075849658 0.5663042346 0.8168159367 -0.0684460470 0.0861764355211 +1413393997955760384.0000000000 -3.0012584951 -0.5031517848 1.1965179074 0.5650189133 0.8175403912 -0.0691094776 0.0872078928903 +1413393998005760512.0000000000 -3.0019340209 -0.5096949460 1.1865331672 0.5642237433 0.8179578691 -0.0693713239 0.0882276108604 +1413393998055760384.0000000000 -3.0035769574 -0.5156490242 1.1771389765 0.5626482054 0.8188722760 -0.0700019315 0.0893024194033 +1413393998105760512.0000000000 -3.0062146348 -0.5209317070 1.1684444452 0.5617601452 0.8192601230 -0.0709340790 0.090591095889 +1413393998155760384.0000000000 -3.0098098133 -0.5254180890 1.1602348599 0.5613235421 0.8192715562 -0.0723490137 0.0920631226649 +1413393998205760512.0000000000 -3.0144563867 -0.5292582169 1.1528754121 0.5619413232 0.8185109019 -0.0737875628 0.0939002036034 +1413393998255760384.0000000000 -3.0201326161 -0.5327132644 1.1462070882 0.5619452405 0.8181850283 -0.0755162910 0.09533150538 +1413393998305760512.0000000000 -3.0269612125 -0.5355332703 1.1408316908 0.5629922139 0.8171715643 -0.0777493726 0.0960491361814 +1413393998355760384.0000000000 -3.0349777138 -0.5377887121 1.1365388265 0.5631845290 0.8168006324 -0.0797063030 0.0964718526083 +1413393998405760512.0000000000 -3.0441395945 -0.5395111168 1.1331849474 0.5604364712 0.8184793287 -0.0822452844 0.09611588555 +1413393998455760384.0000000000 -3.0544479605 -0.5404481041 1.1314876505 0.5570839833 0.8206559474 -0.0860915216 0.093645616148 +1413393998505760512.0000000000 -3.0655723858 -0.5403241414 1.1317323073 0.5553876495 0.8217046523 -0.0913641547 0.0894349727635 +1413393998555760384.0000000000 -3.0770472353 -0.5391723023 1.1328949378 0.5549611428 0.8218736691 -0.0959878607 0.0856045128438 +1413393998605760512.0000000000 -3.0889647616 -0.5370786437 1.1342719333 0.5568262416 0.8205123606 -0.1019758883 0.0794035324581 +1413393998655760384.0000000000 -3.1005893693 -0.5343602607 1.1347237303 0.5597955419 0.8183510955 -0.1071428640 0.0738298210765 +1413393998705760512.0000000000 -3.1116289696 -0.5314342799 1.1340958855 0.5627352408 0.8161886230 -0.1123621404 0.0673790009214 +1413393998755760384.0000000000 -3.1213692407 -0.5284136586 1.1324165335 0.5649797458 0.8144893136 -0.1165781625 0.061762260914 +1413393998805760512.0000000000 -3.1295522462 -0.5253832667 1.1302426862 0.5675998857 0.8125905729 -0.1188322047 0.0583595556683 +1413393998855760384.0000000000 -3.1359437936 -0.5227406172 1.1267157077 0.5691007676 0.8115715847 -0.1188665620 0.0578499752311 +1413393998905760512.0000000000 -3.1406357068 -0.5207066127 1.1220690917 0.5692040532 0.8116332508 -0.1169030074 0.0599324522691 +1413393998955760384.0000000000 -3.1434856905 -0.5189486097 1.1166687701 0.5693634997 0.8117263283 -0.1119916037 0.0662076566934 +1413393999005760512.0000000000 -3.1450523000 -0.5171918587 1.1110747148 0.5705904793 0.8109897655 -0.1059592904 0.0741264734236 +1413393999055760384.0000000000 -3.1460289944 -0.5154921739 1.1050769059 0.5719716138 0.8099811395 -0.0996430617 0.0827664603577 +1413393999105760512.0000000000 -3.1469894227 -0.5142216529 1.0981177760 0.5710059925 0.8105008015 -0.0931870111 0.0914154702121 +1413393999155760384.0000000000 -3.1485169454 -0.5134137942 1.0903749756 0.5671579459 0.8129876940 -0.0889116523 0.0973529245476 +1413393999205760512.0000000000 -3.1508196211 -0.5127408637 1.0823503441 0.5630542316 0.8156610424 -0.0868793012 0.100593157078 +1413393999255760384.0000000000 -3.1542080817 -0.5113583305 1.0741709424 0.5588605395 0.8185164134 -0.0870309247 0.100654838517 +1413393999305760512.0000000000 -3.1587135156 -0.5089887057 1.0664187900 0.5551741733 0.8211766854 -0.0905691298 0.0961650735197 +1413393999355760384.0000000000 -3.1639237499 -0.5055899634 1.0594234271 0.5536667862 0.8223777280 -0.0962097615 0.0888349269241 +1413393999405760512.0000000000 -3.1692411270 -0.5010946911 1.0525251285 0.5531017579 0.8228467492 -0.1015770865 0.0817543162826 +1413393999455760384.0000000000 -3.1742233321 -0.4961949860 1.0451858558 0.5520969960 0.8235156099 -0.1056920056 0.0764208555827 +1413393999505760512.0000000000 -3.1785234308 -0.4905224473 1.0385939801 0.5530375788 0.8227966353 -0.1093160713 0.0721465860116 +1413393999555760384.0000000000 -3.1818851431 -0.4838555234 1.0325001812 0.5542715697 0.8218278936 -0.1128227690 0.0682126320626 +1413393999605760512.0000000000 -3.1841478008 -0.4761789479 1.0265257720 0.5572707378 0.8196288940 -0.1160784346 0.0646807383106 +1413393999655760384.0000000000 -3.1849736841 -0.4678008180 1.0210107170 0.5593454231 0.8181238874 -0.1179595791 0.0623822110506 +1413393999705760512.0000000000 -3.1843491593 -0.4594888777 1.0151884395 0.5611027361 0.8168238929 -0.1196521299 0.0603805873664 +1413393999755760384.0000000000 -3.1821163228 -0.4513098111 1.0078765178 0.5622347291 0.8160046235 -0.1208241898 0.0585668766173 +1413393999805760512.0000000000 -3.1784493665 -0.4431278140 0.9984241816 0.5638193412 0.8149225866 -0.1213459386 0.0573069934234 +1413393999855760384.0000000000 -3.1733724603 -0.4352326930 0.9864594828 0.5636677571 0.8150235645 -0.1221478158 0.0556341620456 +1413393999905760512.0000000000 -3.1668321222 -0.4276409754 0.9728376729 0.5641575018 0.8147565571 -0.1221554259 0.0545538059776 +1413393999955760384.0000000000 -3.1584641143 -0.4203430420 0.9572406636 0.5646695900 0.8146436832 -0.1192309607 0.0573402263305 +1413394000005760512.0000000000 -3.1483252728 -0.4133453589 0.9413046618 0.5679961578 0.8125874740 -0.1115505881 0.0681060064154 +1413394000055760384.0000000000 -3.1421882771 -0.4091724191 0.9339073092 0.5717548578 0.8095240688 -0.0995237649 0.0886689619846 +1413394000105760512.0000000000 -3.1455155820 -0.4095720548 0.9414178044 0.5715047046 0.8098952964 -0.1038077505 0.0817063795856 +1413394000155760384.0000000000 -3.1465873842 -0.4100254516 0.9505229520 0.5772430439 0.8053394803 -0.0981084090 0.0927012932507 +1413394000205760512.0000000000 -3.1478390841 -0.4112750024 0.9542755897 0.5795662815 0.8029769509 -0.0923866115 0.103902145181 +1413394000255760384.0000000000 -3.1496493295 -0.4136647470 0.9489815267 0.5774258796 0.8036719512 -0.0875064634 0.114163774432 +1413394000305760512.0000000000 -3.1509003359 -0.4157206110 0.9359811578 0.5755304536 0.8041453705 -0.0935855899 0.11557100604 +1413394000355760384.0000000000 -3.1477539500 -0.4174516139 0.9333945997 0.5809524519 0.8006357124 -0.1159966641 0.0895627074003 +1413394000405760512.0000000000 -3.1439619748 -0.4186671526 0.9390927463 0.5812834403 0.8005019551 -0.1079290856 0.0982725514553 +1413394000455760384.0000000000 -3.1451635325 -0.4181923736 0.9379800481 0.5787149237 0.8023321177 -0.1071163170 0.0993896601803 +1413394000505760512.0000000000 -3.1456610310 -0.4179705555 0.9326722320 0.5766909942 0.8037642624 -0.1081889918 0.0984156982467 +1413394000555760384.0000000000 -3.1443424208 -0.4185838879 0.9348748099 0.5790650969 0.8020868544 -0.1082212423 0.0981246874209 +1413394000605760512.0000000000 -3.1450013618 -0.4185981763 0.9360118440 0.5809722938 0.8007562934 -0.1105998329 0.0950169955684 +1413394000655760384.0000000000 -3.1449600822 -0.4184296777 0.9336519459 0.5792931463 0.8019049077 -0.1072124785 0.0993652564861 +1413394000705760512.0000000000 -3.1453766143 -0.4179983103 0.9346057052 0.5792019798 0.8020213054 -0.1096628203 0.0962338716346 +1413394000755760384.0000000000 -3.1446858523 -0.4182395860 0.9340542586 0.5789179342 0.8022174761 -0.1082478994 0.0978955501842 +1413394000805760512.0000000000 -3.1453489060 -0.4182132923 0.9344235142 0.5802368083 0.8012748930 -0.1095485998 0.0963477883671 +1413394000855760384.0000000000 -3.1451143522 -0.4183008021 0.9343067084 0.5796813905 0.8016655375 -0.1083213531 0.0978178714515 +1413394000905760512.0000000000 -3.1450554903 -0.4182433729 0.9342659449 0.5795805875 0.8017515368 -0.1095854821 0.0962903830896 +1413394000955760384.0000000000 -3.1450314768 -0.4183220956 0.9342914045 0.5795428496 0.8017730790 -0.1087866758 0.09723926411 +1413394001005760512.0000000000 -3.1451481914 -0.4183750905 0.9343119520 0.5799391615 0.8015003400 -0.1094383321 0.0963899651463 +1413394001055760384.0000000000 -3.1448525156 -0.4183759859 0.9342504167 0.5797080156 0.8016537897 -0.1090208039 0.0969756791123 +1413394001105760512.0000000000 -3.1451198629 -0.4183160527 0.9341681367 0.5795214152 0.8018001262 -0.1095533285 0.0962785293653 +1413394001155760384.0000000000 -3.1449788985 -0.4184480123 0.9341790995 0.5798402620 0.8015675341 -0.1090906207 0.096819395901 +1413394001205760512.0000000000 -3.1450547069 -0.4184399031 0.9341907373 0.5797374633 0.8016303791 -0.1096230259 0.0963119983403 +1413394001255760384.0000000000 -3.1451091018 -0.4183719755 0.9341238195 0.5796072598 0.8017464778 -0.1092423879 0.0965614331044 +1413394001305760512.0000000000 -3.1451210740 -0.4183400614 0.9342167011 0.5797230532 0.8016589331 -0.1095294148 0.0962675636718 +1413394001355760384.0000000000 -3.1450489814 -0.4183371877 0.9341993187 0.5797160723 0.8016479218 -0.1093802501 0.0965704196788 +1413394001405760512.0000000000 -3.1451384095 -0.4182646388 0.9341907592 0.5797289609 0.8016679157 -0.1094913594 0.0962004523802 +1413394001455760384.0000000000 -3.1450000852 -0.4182419062 0.9340549049 0.5796488423 0.8017066022 -0.1094159828 0.0964462870652 +1413394001505760512.0000000000 -3.1450364703 -0.4181805742 0.9340411520 0.5797630351 0.8016221962 -0.1095867373 0.0962674645348 +1413394001555760384.0000000000 -3.1449971064 -0.4181457674 0.9339629348 0.5795847038 0.8017475720 -0.1095423992 0.0963476244346 +1413394001605760512.0000000000 -3.1450174506 -0.4181787898 0.9339736848 0.5796251778 0.8017175910 -0.1096947232 0.0961801707652 +1413394001655760384.0000000000 -3.1450660537 -0.4182705834 0.9339515258 0.5796669569 0.8016877213 -0.1096607509 0.096216091837 +1413394001705760512.0000000000 -3.1451042767 -0.4183527552 0.9339848275 0.5796109304 0.8017414375 -0.1096896978 0.096072925127 +1413394001755760384.0000000000 -3.1451130388 -0.4184537255 0.9339829059 0.5796285309 0.8017345803 -0.1096722586 0.0960438681223 +1413394001805760512.0000000000 -3.1451847827 -0.4186281197 0.9339683181 0.5796004518 0.8017666467 -0.1096782560 0.0959387337877 +1413394001855760384.0000000000 -3.1452219244 -0.4188213878 0.9339060583 0.5795467051 0.8018096586 -0.1096866011 0.0958944076569 +1413394001905760512.0000000000 -3.1452684966 -0.4190022737 0.9338709177 0.5795139454 0.8018331430 -0.1097533380 0.0958196367848 +1413394001955760384.0000000000 -3.1452834859 -0.4190473151 0.9337880057 0.5794836865 0.8018538602 -0.1097888521 0.095788579758 +1413394002005760512.0000000000 -3.1452552639 -0.4190436225 0.9336732924 0.5794292048 0.8018761340 -0.1098833841 0.0958232974201 +1413394002055760384.0000000000 -3.1451841471 -0.4190499919 0.9336258256 0.5794292569 0.8018633391 -0.1099216061 0.0958861944283 +1413394002105760512.0000000000 -3.1451344045 -0.4192156682 0.9336651431 0.5794340110 0.8018520667 -0.1099726228 0.0958932333677 +1413394002155760384.0000000000 -3.1450918099 -0.4193418155 0.9336302334 0.5793600812 0.8019086573 -0.1100053498 0.0958291430982 +1413394002205760512.0000000000 -3.1450415954 -0.4194915345 0.9336469871 0.5793110509 0.8019440191 -0.1100419907 0.0957875609263 +1413394002255760384.0000000000 -3.1449718332 -0.4195988215 0.9336496130 0.5793642652 0.8019082198 -0.1100160489 0.0957952204856 +1413394002305760512.0000000000 -3.1449317427 -0.4196455408 0.9336445507 0.5792889765 0.8019668565 -0.1100175458 0.095757936803 +1413394002355760384.0000000000 -3.1449274286 -0.4196514120 0.9336359700 0.5792911096 0.8019587583 -0.1100947947 0.095724064541 +1413394002405760512.0000000000 -3.1449618226 -0.4195287960 0.9335917785 0.5792560710 0.8019865988 -0.1100615657 0.0957410636064 +1413394002455760384.0000000000 -3.1450375201 -0.4192223920 0.9335525081 0.5792096374 0.8020242799 -0.1100791790 0.0956860742218 +1413394002505760512.0000000000 -3.1451665299 -0.4187147620 0.9335354000 0.5791715479 0.8020506827 -0.1100834585 0.0956904002491 +1413394002555760384.0000000000 -3.1453752275 -0.4179139563 0.9335777088 0.5791339693 0.8020733958 -0.1100941049 0.0957152099598 +1413394002605760512.0000000000 -3.1456715509 -0.4167314108 0.9336547292 0.5791123472 0.8020884335 -0.1101461216 0.0956601597234 +1413394002655760384.0000000000 -3.1460736165 -0.4151301515 0.9337574871 0.5790445857 0.8021347630 -0.1101292880 0.0957012524967 diff --git a/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_03_difficult.txt b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_03_difficult.txt new file mode 100644 index 0000000000000000000000000000000000000000..77ae6c7866a195ab8e1c3f21dcae3b3f87846936 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/data/euroc_groundtruth/V2_03_difficult.txt @@ -0,0 +1,1891 @@ +#timestamp [ns] p_RS_R_x [m] p_RS_R_y [m] p_RS_R_z [m] q_RS_w [] q_RS_x [] q_RS_y [] q_RS_z [] +1413394882805760512.0000000000 -1.0516909472 0.3626874258 1.3107838438 0.4152901805 0.5441961050 0.5791644582 -0.442666009146 +1413394882855760384.0000000000 -1.0524840899 0.3624194883 1.3108103715 0.4152349552 0.5443537473 0.5790717028 -0.442645335272 +1413394882905760512.0000000000 -1.0530694460 0.3622540670 1.3107938757 0.4153789040 0.5443891228 0.5789917527 -0.442571349537 +1413394882955760384.0000000000 -1.0534169549 0.3620659482 1.3108053606 0.4153947965 0.5444578098 0.5789449888 -0.442533113241 +1413394883005760512.0000000000 -1.0536540915 0.3619357957 1.3107673967 0.4152786315 0.5445172644 0.5789738708 -0.442531201001 +1413394883055760384.0000000000 -1.0537739491 0.3618562739 1.3107816247 0.4152438132 0.5444944474 0.5790165703 -0.442536081822 +1413394883105760512.0000000000 -1.0538496231 0.3617891972 1.3107729630 0.4152169809 0.5444929750 0.5790003899 -0.442584237659 +1413394883155760384.0000000000 -1.0539150620 0.3618298018 1.3107757320 0.4153023290 0.5444512746 0.5789843287 -0.442576470513 +1413394883205760512.0000000000 -1.0539355144 0.3618857821 1.3107835791 0.4153506940 0.5445012250 0.5788961301 -0.442585005934 +1413394883255760384.0000000000 -1.0539289489 0.3619250764 1.3108281365 0.4153164038 0.5445720170 0.5788427482 -0.442599904928 +1413394883305760512.0000000000 -1.0538682254 0.3619768252 1.3108420942 0.4152855653 0.5445895821 0.5788611809 -0.442583121581 +1413394883355760384.0000000000 -1.0537763530 0.3619736470 1.3108937394 0.4151420980 0.5446119878 0.5789003205 -0.442638950069 +1413394883405760512.0000000000 -1.0537504572 0.3620159636 1.3109193000 0.4151482978 0.5445570329 0.5789296309 -0.442662412318 +1413394883455760384.0000000000 -1.0536604323 0.3620838178 1.3109501662 0.4151437946 0.5445224733 0.5789556951 -0.442675060214 +1413394883505760512.0000000000 -1.0536265807 0.3621469739 1.3109590898 0.4152084182 0.5445154651 0.5789238065 -0.442664776009 +1413394883555760384.0000000000 -1.0536178611 0.3622453987 1.3109944468 0.4152263606 0.5445533024 0.5789288568 -0.442594791113 +1413394883605760512.0000000000 -1.0535971490 0.3621801556 1.3110306855 0.4150874625 0.5444592176 0.5793990233 -0.442225429644 +1413394883655760384.0000000000 -1.0533996202 0.3620593003 1.3111322672 0.4149151440 0.5443669380 0.5794130987 -0.442482226887 +1413394883705760512.0000000000 -1.0534077049 0.3620627616 1.3111433231 0.4148036185 0.5446236218 0.5789798327 -0.442837918452 +1413394883755760384.0000000000 -1.0534149083 0.3619905960 1.3110741633 0.4149284736 0.5445467454 0.5791114181 -0.442643388501 +1413394883805760512.0000000000 -1.0533409820 0.3619397211 1.3109213383 0.4150488472 0.5445291435 0.5791659090 -0.442480865375 +1413394883855760384.0000000000 -1.0532858608 0.3619579215 1.3109170595 0.4149995282 0.5446501366 0.5789633491 -0.442643265811 +1413394883905760512.0000000000 -1.0532719821 0.3620016256 1.3108576409 0.4150728944 0.5446571054 0.5788372151 -0.442730853061 +1413394883955760384.0000000000 -1.0532320114 0.3619605492 1.3107426356 0.4150111453 0.5446376826 0.5790432855 -0.442543125058 +1413394884005760512.0000000000 -1.0532444836 0.3620117745 1.3107359875 0.4151764537 0.5446208399 0.5788908681 -0.442608196772 +1413394884055760384.0000000000 -1.0532893379 0.3619823082 1.3107697633 0.4150292788 0.5446848197 0.5788445003 -0.442728121323 +1413394884105760512.0000000000 -1.0533811005 0.3620331840 1.3106866452 0.4151826518 0.5446311124 0.5788915364 -0.442588868122 +1413394884155760384.0000000000 -1.0534098886 0.3620235232 1.3107124583 0.4149884142 0.5447331804 0.5789127924 -0.442617619384 +1413394884205760512.0000000000 -1.0534141008 0.3620858337 1.3107577661 0.4151878597 0.5446809913 0.5787959002 -0.44264767569 +1413394884255760384.0000000000 -1.0533472943 0.3620700874 1.3107997519 0.4150078721 0.5447130166 0.5789104588 -0.442627243027 +1413394884305760512.0000000000 -1.0534000235 0.3620518172 1.3108405604 0.4150195813 0.5447184950 0.5789323003 -0.442580953069 +1413394884355760384.0000000000 -1.0534103906 0.3619822565 1.3108836242 0.4150125494 0.5446452531 0.5790730612 -0.442493527502 +1413394884405760512.0000000000 -1.0533487800 0.3619475221 1.3109225898 0.4149333208 0.5446780454 0.5789693078 -0.442663197845 +1413394884455760384.0000000000 -1.0533760241 0.3619929246 1.3109961925 0.4150101701 0.5447527401 0.5789552764 -0.442517568821 +1413394884505760512.0000000000 -1.0534521810 0.3619327938 1.3109816047 0.4148812539 0.5448201796 0.5790506516 -0.442430627304 +1413394884555760384.0000000000 -1.0534067341 0.3619125989 1.3109888376 0.4149849642 0.5447440796 0.5790288958 -0.442455540217 +1413394884605760512.0000000000 -1.0534338585 0.3619850351 1.3109701009 0.4149986417 0.5448391803 0.5789140682 -0.442475871286 +1413394884655760384.0000000000 -1.0534646570 0.3620143308 1.3109519086 0.4149889204 0.5448562297 0.5788680922 -0.442524142518 +1413394884705760512.0000000000 -1.0534137411 0.3620463035 1.3109770944 0.4150744143 0.5447931291 0.5789195665 -0.442454305718 +1413394884755760384.0000000000 -1.0534522823 0.3621100969 1.3109431811 0.4151182273 0.5448174574 0.5789118957 -0.442393278048 +1413394884805760512.0000000000 -1.0534258053 0.3620586182 1.3110501867 0.4149605458 0.5447752807 0.5789308936 -0.442568253904 +1413394884855760384.0000000000 -1.0534062806 0.3621667127 1.3110278275 0.4151400336 0.5447314632 0.5789201584 -0.442467892243 +1413394884905760512.0000000000 -1.0534547846 0.3622885968 1.3110121347 0.4150388017 0.5448929457 0.5788051872 -0.44251443616 +1413394884955760384.0000000000 -1.0534285758 0.3622017245 1.3109602256 0.4151313312 0.5447220529 0.5787968510 -0.442648922061 +1413394885005760512.0000000000 -1.0533699119 0.3622263996 1.3108884276 0.4151448499 0.5447808241 0.5787498377 -0.442625386308 +1413394885055760384.0000000000 -1.0533713350 0.3621491373 1.3108425785 0.4150228932 0.5447526998 0.5787968358 -0.442712905955 +1413394885105760512.0000000000 -1.0533575240 0.3621894316 1.3108452656 0.4150224392 0.5447976701 0.5787759182 -0.442685339923 +1413394885155760384.0000000000 -1.0533514449 0.3621727798 1.3108349639 0.4151749449 0.5447550210 0.5786980118 -0.442696672032 +1413394885205760512.0000000000 -1.0533852842 0.3620886659 1.3108367480 0.4149420957 0.5447625103 0.5788359865 -0.442725383712 +1413394885255760384.0000000000 -1.0533972351 0.3621593289 1.3108645227 0.4151269645 0.5447825598 0.5787065381 -0.442696632637 +1413394885305760512.0000000000 -1.0533497702 0.3620781267 1.3108801793 0.4150651824 0.5447420456 0.5787625008 -0.442731256828 +1413394885355760384.0000000000 -1.0533220515 0.3620594995 1.3109289507 0.4148862948 0.5447454286 0.5788643363 -0.442761629502 +1413394885405760512.0000000000 -1.0533677116 0.3620887830 1.3109482068 0.4151047118 0.5447776486 0.5786780631 -0.442760760659 +1413394885455760384.0000000000 -1.0533369665 0.3620486046 1.3109462663 0.4150655272 0.5447690607 0.5787095837 -0.442766864635 +1413394885505760512.0000000000 -1.0532949588 0.3619941871 1.3109026217 0.4148286429 0.5448111177 0.5788200133 -0.44279276793 +1413394885555760384.0000000000 -1.0532191549 0.3620787082 1.3108909976 0.4150074847 0.5447413619 0.5787848370 -0.442756986104 +1413394885605760512.0000000000 -1.0531823677 0.3621691480 1.3108936481 0.4151007569 0.5447341305 0.5787150100 -0.442769721038 +1413394885655760384.0000000000 -1.0531268899 0.3621316634 1.3108932844 0.4148802963 0.5448261663 0.5787444714 -0.442824598602 +1413394885705760512.0000000000 -1.0531336009 0.3620797209 1.3108739823 0.4149087961 0.5447390537 0.5788315309 -0.442791275 +1413394885755760384.0000000000 -1.0532049717 0.3620665170 1.3108522875 0.4149839364 0.5447841830 0.5787557770 -0.442764358391 +1413394885805760512.0000000000 -1.0532689344 0.3620460990 1.3108845339 0.4149392735 0.5448097306 0.5787244174 -0.442815769215 +1413394885855760384.0000000000 -1.0533467597 0.3620191834 1.3108524079 0.4149170678 0.5447427490 0.5788136424 -0.44280236179 +1413394885905760512.0000000000 -1.0535091812 0.3621341409 1.3108752438 0.4149905271 0.5448675142 0.5788421711 -0.442542648094 +1413394885955760384.0000000000 -1.0536246483 0.3618815309 1.3109155525 0.4146028072 0.5445773435 0.5792676525 -0.442706467021 +1413394886005760512.0000000000 -1.0537817991 0.3620562589 1.3110474497 0.4149565310 0.5451871142 0.5785699621 -0.442536876224 +1413394886055760384.0000000000 -1.0539318912 0.3619107961 1.3110697914 0.4149560221 0.5450619073 0.5787737329 -0.442425115748 +1413394886105760512.0000000000 -1.0540470308 0.3618165675 1.3112012482 0.4148253097 0.5449248932 0.5789239396 -0.442519937809 +1413394886155760384.0000000000 -1.0540408701 0.3617345870 1.3113095608 0.4147593276 0.5450261438 0.5788488110 -0.44255537142 +1413394886205760512.0000000000 -1.0539770806 0.3618328924 1.3114110606 0.4148576488 0.5450172220 0.5788673130 -0.442449989205 +1413394886255760384.0000000000 -1.0538705815 0.3618864790 1.3113959067 0.4147372419 0.5450931569 0.5789106542 -0.442412618429 +1413394886305760512.0000000000 -1.0539004274 0.3618911086 1.3113852166 0.4146369807 0.5450593582 0.5791276167 -0.442264257935 +1413394886355760384.0000000000 -1.0538123075 0.3621217111 1.3112855727 0.4142826192 0.5453521753 0.5794075791 -0.441868502566 +1413394886405760512.0000000000 -1.0537022281 0.3620667407 1.3113099113 0.4140423078 0.5454387140 0.5796157868 -0.441713839803 +1413394886455760384.0000000000 -1.0536486053 0.3619792554 1.3114412615 0.4140627025 0.5453887320 0.5795602369 -0.44182931229 +1413394886505760512.0000000000 -1.0536126652 0.3619280846 1.3113087007 0.4136262482 0.5456263991 0.5797716458 -0.441667293502 +1413394886555760384.0000000000 -1.0536319299 0.3619925723 1.3115191055 0.4132539431 0.5458367493 0.5801914101 -0.441204430241 +1413394886605760512.0000000000 -1.0537375832 0.3619670379 1.3116050350 0.4125355542 0.5462111037 0.5803818318 -0.441162981183 +1413394886655760384.0000000000 -1.0538248491 0.3619970699 1.3118009488 0.4118661485 0.5466689123 0.5804874400 -0.441082427737 +1413394886705760512.0000000000 -1.0538499908 0.3621227645 1.3119520033 0.4121806988 0.5465139978 0.5808120266 -0.440552960976 +1413394886755760384.0000000000 -1.0538092380 0.3620040223 1.3122732055 0.4112490890 0.5471173772 0.5812302341 -0.440122911653 +1413394886805760512.0000000000 -1.0538282177 0.3621303787 1.3124838682 0.4110418608 0.5472493791 0.5815577723 -0.439719527933 +1413394886855760384.0000000000 -1.0540560505 0.3620775982 1.3125581265 0.4104192037 0.5476852247 0.5821768921 -0.438938535749 +1413394886905760512.0000000000 -1.0544685551 0.3621226574 1.3126479545 0.4106117723 0.5476773767 0.5830110001 -0.437659270784 +1413394886955760384.0000000000 -1.0542288267 0.3622781060 1.3116537241 0.4079756916 0.5494609392 0.5843041320 -0.436161888166 +1413394887005760512.0000000000 -1.0535534404 0.3626217364 1.3119436113 0.4088803967 0.5490143687 0.5838300100 -0.436511813725 +1413394887055760384.0000000000 -1.0527502251 0.3634153838 1.3122520944 0.4079036238 0.5503385690 0.5856590099 -0.43329622353 +1413394887105760512.0000000000 -1.0517147079 0.3644783423 1.3142466434 0.4071695037 0.5514150245 0.5875114977 -0.430098484261 +1413394887155760384.0000000000 -1.0503618696 0.3657780914 1.3185425048 0.4072773397 0.5521629363 0.5881604776 -0.428145434281 +1413394887205760512.0000000000 -1.0489197685 0.3672190946 1.3242968042 0.4093477962 0.5519465916 0.5876145516 -0.427198408881 +1413394887255760384.0000000000 -1.0470636101 0.3683691263 1.3307904080 0.4107757476 0.5519858011 0.5883404244 -0.424771121401 +1413394887305760512.0000000000 -1.0453782215 0.3691837793 1.3390872755 0.4136831335 0.5509675068 0.5874600843 -0.424489953625 +1413394887355760384.0000000000 -1.0433251778 0.3697251429 1.3488714334 0.4141261115 0.5516348030 0.5885727829 -0.421640471467 +1413394887405760512.0000000000 -1.0410955026 0.3699239358 1.3619801313 0.4133753009 0.5534031220 0.5894810387 -0.418781506463 +1413394887455760384.0000000000 -1.0389283673 0.3699616106 1.3792016535 0.4159883086 0.5524664423 0.5896701100 -0.417161501872 +1413394887505760512.0000000000 -1.0366925539 0.3695079701 1.3995651691 0.4167390289 0.5525882247 0.5893884332 -0.41664866558 +1413394887555760384.0000000000 -1.0342397629 0.3687337894 1.4221268319 0.4159871450 0.5538926574 0.5905026215 -0.414082447558 +1413394887605760512.0000000000 -1.0316666836 0.3672509952 1.4467588024 0.4151634148 0.5551327687 0.5918663426 -0.411292086736 +1413394887655760384.0000000000 -1.0294855467 0.3649732833 1.4707999973 0.4127196495 0.5572257639 0.5945196426 -0.407072884832 +1413394887705760512.0000000000 -1.0280120486 0.3619505795 1.4939283415 0.4091298420 0.5603407382 0.5965745423 -0.403397874228 +1413394887755760384.0000000000 -1.0270853971 0.3580518060 1.5155134639 0.4055617185 0.5634565003 0.5983010772 -0.400090346984 +1413394887805760512.0000000000 -1.0274008021 0.3534719803 1.5354023558 0.4024022686 0.5656603678 0.6001704256 -0.397361576898 +1413394887855760384.0000000000 -1.0290374221 0.3484354691 1.5527521391 0.4014293881 0.5663096431 0.6027592315 -0.393483345799 +1413394887905760512.0000000000 -1.0321724094 0.3424838360 1.5676518607 0.3987995039 0.5685747756 0.6038370570 -0.391232013997 +1413394887955760384.0000000000 -1.0370168345 0.3356053310 1.5807928256 0.3978558505 0.5691171156 0.6043618887 -0.390593316003 +1413394888005760512.0000000000 -1.0436560303 0.3280042639 1.5927049621 0.3973907180 0.5694871867 0.6038132297 -0.391375197162 +1413394888055760384.0000000000 -1.0523298666 0.3196808893 1.6050609533 0.3996466256 0.5678368516 0.6022715787 -0.393843661968 +1413394888105760512.0000000000 -1.0628819605 0.3106521658 1.6181872242 0.4029105121 0.5652481422 0.6006380016 -0.39672616245 +1413394888155760384.0000000000 -1.0746689428 0.3009313421 1.6325527615 0.4057978655 0.5626209896 0.5985783201 -0.400611668735 +1413394888205760512.0000000000 -1.0874063906 0.2908997213 1.6471576888 0.4082782804 0.5605327261 0.5974009686 -0.402770395513 +1413394888255760384.0000000000 -1.1011218962 0.2800015970 1.6622930587 0.4097749217 0.5591853042 0.5961724991 -0.404937847722 +1413394888305760512.0000000000 -1.1149618778 0.2685069075 1.6769878082 0.4101518770 0.5580785621 0.5981393268 -0.403178747045 +1413394888355760384.0000000000 -1.1295612128 0.2561469078 1.6927259363 0.4092381344 0.5580996670 0.5982991009 -0.403840435082 +1413394888405760512.0000000000 -1.1447562702 0.2432545830 1.7083026508 0.4085055561 0.5583999300 0.5997027407 -0.402081274808 +1413394888455760384.0000000000 -1.1607039668 0.2293716903 1.7242885494 0.4072864884 0.5586086148 0.6007275636 -0.401497853141 +1413394888505760512.0000000000 -1.1772782575 0.2147546697 1.7401305027 0.4043323119 0.5603438030 0.6010931078 -0.401518716501 +1413394888555760384.0000000000 -1.1948023772 0.1995678315 1.7536093404 0.4017018788 0.5623944456 0.6006373664 -0.401973683438 +1413394888605760512.0000000000 -1.2131034515 0.1838246667 1.7623602885 0.3991439048 0.5637381888 0.6008383055 -0.402339071409 +1413394888655760384.0000000000 -1.2324560295 0.1678010296 1.7668175312 0.3980038199 0.5640973458 0.6000193163 -0.404183081992 +1413394888705760512.0000000000 -1.2532079409 0.1517128178 1.7684512016 0.3994514993 0.5631001233 0.5979849146 -0.407149594941 +1413394888755760384.0000000000 -1.2743647677 0.1353656468 1.7691104176 0.3989952253 0.5629775285 0.5948350957 -0.412347331092 +1413394888805760512.0000000000 -1.2967323749 0.1194139565 1.7701097268 0.4005216105 0.5621612201 0.5902463947 -0.418528846852 +1413394888855760384.0000000000 -1.3192369402 0.1034802110 1.7713531397 0.4005692412 0.5617328597 0.5874708181 -0.422940321126 +1413394888905760512.0000000000 -1.3420087925 0.0881489752 1.7734995055 0.4003739363 0.5613593069 0.5845103353 -0.427696279683 +1413394888955760384.0000000000 -1.3646074635 0.0734847132 1.7765590172 0.3998201136 0.5617764936 0.5816532525 -0.431544368364 +1413394889005760512.0000000000 -1.3868795959 0.0596236632 1.7797826772 0.3997424703 0.5612167415 0.5809050586 -0.433348634869 +1413394889055760384.0000000000 -1.4087626957 0.0470783285 1.7840455483 0.3997246604 0.5610410921 0.5789428092 -0.436209023747 +1413394889105760512.0000000000 -1.4302633493 0.0353434193 1.7884917786 0.3991722436 0.5616700664 0.5776277912 -0.437646422779 +1413394889155760384.0000000000 -1.4513063084 0.0245882656 1.7936682396 0.4010093692 0.5597404881 0.5780567438 -0.437872667356 +1413394889205760512.0000000000 -1.4720871573 0.0152687297 1.7999014637 0.4067979586 0.5558199272 0.5773609553 -0.438444930138 +1413394889255760384.0000000000 -1.4925275007 0.0065285457 1.8083462662 0.4151815845 0.5499577508 0.5722592232 -0.444623555007 +1413394889305760512.0000000000 -1.5116132017 -0.0014722857 1.8188938257 0.4269930442 0.5410226293 0.5649584702 -0.453644554422 +1413394889355760384.0000000000 -1.5285345225 -0.0089244699 1.8308661006 0.4420147748 0.5290900342 0.5544672757 -0.466103759676 +1413394889405760512.0000000000 -1.5412490417 -0.0160080396 1.8442504265 0.4554406124 0.5176131590 0.5422060610 -0.480273936002 +1413394889455760384.0000000000 -1.5490681505 -0.0222082058 1.8575155581 0.4687896009 0.5064302470 0.5318447049 -0.49082168338 +1413394889505760512.0000000000 -1.5502095193 -0.0279754787 1.8694050528 0.4750933270 0.5007822308 0.5271381750 -0.495609556328 +1413394889555760384.0000000000 -1.5449692141 -0.0331143349 1.8790392012 0.4738846276 0.5027825528 0.5320121115 -0.489495840192 +1413394889605760512.0000000000 -1.5332517541 -0.0381294278 1.8870757886 0.4619575668 0.5135120949 0.5430392609 -0.477502770752 +1413394889655760384.0000000000 -1.5162667170 -0.0428946286 1.8952330465 0.4473128716 0.5266122017 0.5572152452 -0.460545279404 +1413394889705760512.0000000000 -1.4955944954 -0.0474437183 1.9038424560 0.4300919097 0.5409492690 0.5724392500 -0.441257456157 +1413394889755760384.0000000000 -1.4727602537 -0.0520414816 1.9124895511 0.4119137187 0.5551909841 0.5880734013 -0.419832983769 +1413394889805760512.0000000000 -1.4498112051 -0.0571881837 1.9218274494 0.3938558039 0.5679562865 0.6007574620 -0.401738390313 +1413394889855760384.0000000000 -1.4288273109 -0.0623667759 1.9319434086 0.3780353474 0.5787720152 0.6113085175 -0.385245541143 +1413394889905760512.0000000000 -1.4110230505 -0.0677074426 1.9421982086 0.3637611943 0.5886915135 0.6193044439 -0.370920613055 +1413394889955760384.0000000000 -1.3974361023 -0.0736490574 1.9510170307 0.3507121335 0.5967040471 0.6256148619 -0.359932388375 +1413394890005760512.0000000000 -1.3886311567 -0.0792752097 1.9569178218 0.3407525047 0.6030871106 0.6316898767 -0.348053971773 +1413394890055760384.0000000000 -1.3853892679 -0.0854044911 1.9603105073 0.3313845616 0.6085713685 0.6364967482 -0.338669531013 +1413394890105760512.0000000000 -1.3880867913 -0.0917539994 1.9619648835 0.3237741868 0.6137366623 0.6376782666 -0.334460780354 +1413394890155760384.0000000000 -1.3981890728 -0.0981209396 1.9634434021 0.3245589467 0.6146890063 0.6338105828 -0.339268419879 +1413394890205760512.0000000000 -1.4158238905 -0.1044263873 1.9645825943 0.3345580556 0.6101797565 0.6258488256 -0.352228362978 +1413394890255760384.0000000000 -1.4396825303 -0.1107018158 1.9647615002 0.3449614638 0.6057562861 0.6134462493 -0.371139609279 +1413394890305760512.0000000000 -1.4685114278 -0.1160265531 1.9623859343 0.3582506720 0.5988391547 0.5998347583 -0.391466966149 +1413394890355760384.0000000000 -1.5013089185 -0.1203098655 1.9584989362 0.3728758484 0.5901968558 0.5846459404 -0.413304243248 +1413394890405760512.0000000000 -1.5348945976 -0.1232990476 1.9531954867 0.3869696536 0.5808773541 0.5691667217 -0.43460928388 +1413394890455760384.0000000000 -1.5684747003 -0.1244839598 1.9462179378 0.4014183779 0.5698275577 0.5557266568 -0.453131022252 +1413394890505760512.0000000000 -1.6000641235 -0.1237213720 1.9382708213 0.4160405576 0.5575718827 0.5423929535 -0.470992286651 +1413394890555760384.0000000000 -1.6283751616 -0.1202722804 1.9300239204 0.4310111341 0.5457525382 0.5310482804 -0.484119089887 +1413394890605760512.0000000000 -1.6517583908 -0.1155658611 1.9212369301 0.4419497192 0.5352052483 0.5239669695 -0.493654132765 +1413394890655760384.0000000000 -1.6697470436 -0.1084408269 1.9125761220 0.4532806721 0.5246524130 0.5207988421 -0.498041207049 +1413394890705760512.0000000000 -1.6818693973 -0.0995814115 1.9050524928 0.4615021403 0.5172183735 0.5177837060 -0.501399005212 +1413394890755760384.0000000000 -1.6871735715 -0.0895864173 1.8973165859 0.4645725391 0.5136149329 0.5208457951 -0.499090887904 +1413394890805760512.0000000000 -1.6855002777 -0.0780971006 1.8878451959 0.4608864943 0.5168855367 0.5318943532 -0.487341131339 +1413394890855760384.0000000000 -1.6778758255 -0.0661676384 1.8783386936 0.4482454915 0.5268654596 0.5457213571 -0.472944993907 +1413394890905760512.0000000000 -1.6658140163 -0.0537453009 1.8689559978 0.4322545534 0.5390549689 0.5620188023 -0.454654382357 +1413394890955760384.0000000000 -1.6510222298 -0.0410512798 1.8602136625 0.4146760814 0.5521037093 0.5792236990 -0.433272602597 +1413394891005760512.0000000000 -1.6353097239 -0.0282999399 1.8518418784 0.3961368260 0.5649117225 0.5959845500 -0.41079529826 +1413394891055760384.0000000000 -1.6207196634 -0.0158489212 1.8447777883 0.3786246048 0.5761754197 0.6092965860 -0.391692436227 +1413394891105760512.0000000000 -1.6092173481 -0.0034153485 1.8390797699 0.3654079297 0.5840762185 0.6206656406 -0.374307598765 +1413394891155760384.0000000000 -1.6019028299 0.0083228023 1.8343591790 0.3531572975 0.5915371379 0.6281787846 -0.361600818992 +1413394891205760512.0000000000 -1.6000873972 0.0195531516 1.8300914230 0.3444121479 0.5963529798 0.6343152530 -0.351265648365 +1413394891255760384.0000000000 -1.6045704088 0.0301503019 1.8261255204 0.3391216679 0.5989969273 0.6390232483 -0.343290640215 +1413394891305760512.0000000000 -1.6159217563 0.0398612135 1.8234193328 0.3364632484 0.6005029128 0.6407831458 -0.339978961486 +1413394891355760384.0000000000 -1.6344175618 0.0488206017 1.8219499275 0.3386947867 0.5987825754 0.6415248306 -0.339398233084 +1413394891405760512.0000000000 -1.6604754268 0.0569541146 1.8226644904 0.3490876563 0.5924272629 0.6385847123 -0.345510219201 +1413394891455760384.0000000000 -1.6926023500 0.0634866638 1.8251749795 0.3594922948 0.5866486403 0.6322600183 -0.356168403996 +1413394891505760512.0000000000 -1.7294524390 0.0690736112 1.8278602083 0.3717925698 0.5787124419 0.6260516184 -0.367316710516 +1413394891555760384.0000000000 -1.7699650292 0.0734224962 1.8313935819 0.3832934490 0.5718242522 0.6180686864 -0.379597491324 +1413394891605760512.0000000000 -1.8130173377 0.0766805319 1.8344353894 0.3950068560 0.5634240099 0.6132090014 -0.387940316674 +1413394891655760384.0000000000 -1.8571579751 0.0787948374 1.8375574300 0.4026421801 0.5576347581 0.6087415502 -0.395419367761 +1413394891705760512.0000000000 -1.9020442383 0.0798711279 1.8404537718 0.4088633155 0.5529780036 0.6055208148 -0.400488026833 +1413394891755760384.0000000000 -1.9471412045 0.0799116792 1.8436739694 0.4124301882 0.5501647564 0.6032764311 -0.404076265647 +1413394891805760512.0000000000 -1.9916673778 0.0784233789 1.8487078725 0.4141907276 0.5479040067 0.6023856064 -0.406667950292 +1413394891855760384.0000000000 -2.0366660149 0.0760427758 1.8580150294 0.4204834890 0.5430627694 0.5991184713 -0.411501544682 +1413394891905760512.0000000000 -2.0810505377 0.0719115130 1.8709323204 0.4284764781 0.5363942066 0.5941875296 -0.419082739419 +1413394891955760384.0000000000 -2.1243694605 0.0662969671 1.8871375071 0.4365630671 0.5295410097 0.5881641637 -0.427857364152 +1413394892005760512.0000000000 -2.1656678957 0.0594449334 1.9047501517 0.4442579489 0.5230215184 0.5828853711 -0.435118386534 +1413394892055760384.0000000000 -2.2039028285 0.0506137207 1.9225667183 0.4485715910 0.5167162851 0.5794387136 -0.442762448321 +1413394892105760512.0000000000 -2.2385195699 0.0406393126 1.9403168449 0.4511931981 0.5101583865 0.5780147345 -0.449513164856 +1413394892155760384.0000000000 -2.2689920439 0.0289874465 1.9575863305 0.4510813892 0.5036427214 0.5798508875 -0.454579517543 +1413394892205760512.0000000000 -2.2952653306 0.0155540551 1.9747200534 0.4476973875 0.4968650941 0.5846121101 -0.459261154699 +1413394892255760384.0000000000 -2.3181701497 0.0008351431 1.9911004295 0.4430858294 0.4892300817 0.5903527207 -0.464556282955 +1413394892305760512.0000000000 -2.3372645430 -0.0150736254 2.0054539874 0.4369555316 0.4818569097 0.5961475327 -0.470629260964 +1413394892355760384.0000000000 -2.3530076401 -0.0317798842 2.0149253793 0.4296572908 0.4738407758 0.6041554477 -0.475253328954 +1413394892405760512.0000000000 -2.3654236975 -0.0491715871 2.0204214717 0.4219067337 0.4650592411 0.6109314487 -0.482159076786 +1413394892455760384.0000000000 -2.3745585060 -0.0669819688 2.0218223454 0.4127099384 0.4563651523 0.6183645526 -0.488903502382 +1413394892505760512.0000000000 -2.3800103036 -0.0852696923 2.0205537299 0.4034123986 0.4461872956 0.6269399131 -0.495097646223 +1413394892555760384.0000000000 -2.3816005710 -0.1038073252 2.0191187606 0.3922058103 0.4365654827 0.6364035784 -0.500575336025 +1413394892605760512.0000000000 -2.3791032605 -0.1226907200 2.0179603147 0.3781450034 0.4274174783 0.6480884126 -0.504283714906 +1413394892655760384.0000000000 -2.3735503930 -0.1415655048 2.0176164638 0.3635281772 0.4176892511 0.6602801337 -0.507358944818 +1413394892705760512.0000000000 -2.3651343854 -0.1604720292 2.0193326005 0.3480015252 0.4071960833 0.6726639508 -0.510499262926 +1413394892755760384.0000000000 -2.3545015836 -0.1793928810 2.0221321875 0.3318625672 0.3960105642 0.6861265715 -0.512126153766 +1413394892805760512.0000000000 -2.3422649730 -0.1984313802 2.0267524933 0.3167262110 0.3833872675 0.6972219395 -0.51631412675 +1413394892855760384.0000000000 -2.3284861785 -0.2172210900 2.0324166565 0.3020177916 0.3703486129 0.7081872870 -0.519709462157 +1413394892905760512.0000000000 -2.3133587436 -0.2354346140 2.0380921355 0.2876139335 0.3577125066 0.7196993406 -0.520915393341 +1413394892955760384.0000000000 -2.2976347498 -0.2535841525 2.0437219812 0.2729257884 0.3461088256 0.7317067776 -0.5199282513 +1413394893005760512.0000000000 -2.2817570850 -0.2719208348 2.0499160829 0.2603458187 0.3338174548 0.7428253738 -0.518648653276 +1413394893055760384.0000000000 -2.2661287703 -0.2909541623 2.0568166445 0.2500475403 0.3200152929 0.7525094809 -0.518455322137 +1413394893105760512.0000000000 -2.2511056834 -0.3105609021 2.0640304249 0.2428060936 0.3048491773 0.7608977402 -0.518793609192 +1413394893155760384.0000000000 -2.2361459608 -0.3313186103 2.0715426678 0.2363971179 0.2891328894 0.7691032441 -0.518650918053 +1413394893205760512.0000000000 -2.2208849292 -0.3535394166 2.0797114294 0.2266014659 0.2757719037 0.7754130995 -0.520899374047 +1413394893255760384.0000000000 -2.2063632152 -0.3770293037 2.0880692324 0.2197964840 0.2627790566 0.7805670443 -0.522830529356 +1413394893305760512.0000000000 -2.1921233443 -0.4024613388 2.0976182239 0.2131997675 0.2521782576 0.7817765236 -0.528939932897 +1413394893355760384.0000000000 -2.1781818937 -0.4291207033 2.1075104837 0.2093033656 0.2423616602 0.7820213730 -0.534691966492 +1413394893405760512.0000000000 -2.1648677427 -0.4572039230 2.1177869561 0.2116521589 0.2308436290 0.7802601290 -0.541395154786 +1413394893455760384.0000000000 -2.1508468366 -0.4858211480 2.1267916302 0.2152581833 0.2202671149 0.7802653921 -0.54436406057 +1413394893505760512.0000000000 -2.1354275941 -0.5156355234 2.1353880698 0.2178952699 0.2108871508 0.7785240484 -0.549498468668 +1413394893555760384.0000000000 -2.1187111374 -0.5460990586 2.1408577177 0.2213825328 0.2030995391 0.7783497200 -0.551282200629 +1413394893605760512.0000000000 -2.1002888956 -0.5771205368 2.1438996509 0.2269716278 0.1958404322 0.7767670865 -0.553862165772 +1413394893655760384.0000000000 -2.0799514041 -0.6088771640 2.1436430382 0.2343680570 0.1892734743 0.7761521627 -0.553926877952 +1413394893705760512.0000000000 -2.0571023149 -0.6416567970 2.1421820511 0.2450707290 0.1817539584 0.7731630874 -0.555989817025 +1413394893755760384.0000000000 -2.0309896411 -0.6756643763 2.1393593396 0.2515991976 0.1789483086 0.7709307716 -0.557082661733 +1413394893805760512.0000000000 -2.0012855373 -0.7107877408 2.1360282669 0.2584454304 0.1768856438 0.7678879929 -0.55880717505 +1413394893855760384.0000000000 -1.9673158438 -0.7468209109 2.1321313430 0.2598548708 0.1798927857 0.7658764307 -0.559952966488 +1413394893905760512.0000000000 -1.9287573721 -0.7837237725 2.1277728823 0.2597835070 0.1821841998 0.7643549099 -0.561322561893 +1413394893955760384.0000000000 -1.8854205158 -0.8212851182 2.1235156786 0.2564696700 0.1845997226 0.7622476489 -0.564911296162 +1413394894005760512.0000000000 -1.8373466865 -0.8590415768 2.1189735138 0.2518842506 0.1847888724 0.7604311104 -0.569343414258 +1413394894055760384.0000000000 -1.7854541407 -0.8970399584 2.1136760442 0.2470711733 0.1823274098 0.7581464549 -0.575262117472 +1413394894105760512.0000000000 -1.7292178048 -0.9349067250 2.1071187309 0.2387201230 0.1801892094 0.7575028020 -0.580287908396 +1413394894155760384.0000000000 -1.6684398416 -0.9716888481 2.0997009195 0.2253805962 0.1786163241 0.7573031135 -0.586337607476 +1413394894205760512.0000000000 -1.6038942743 -1.0074309918 2.0918016554 0.2060329972 0.1790664822 0.7580513885 -0.592320598439 +1413394894255760384.0000000000 -1.5364726227 -1.0415542880 2.0831407936 0.1852540608 0.1778490216 0.7593065355 -0.597916585922 +1413394894305760512.0000000000 -1.4675911915 -1.0739595972 2.0731783332 0.1668709293 0.1740579457 0.7634338568 -0.59918834329 +1413394894355760384.0000000000 -1.3976688400 -1.1042105129 2.0629537980 0.1506258532 0.1681881122 0.7659824408 -0.601909886624 +1413394894405760512.0000000000 -1.3271444517 -1.1325946077 2.0515092961 0.1347488309 0.1609830836 0.7699692955 -0.602556622605 +1413394894455760384.0000000000 -1.2567681320 -1.1583217481 2.0389062605 0.1207702180 0.1529847620 0.7749610286 -0.601203477335 +1413394894505760512.0000000000 -1.1872172369 -1.1821296810 2.0249694100 0.1106254383 0.1428936950 0.7799933276 -0.599127543347 +1413394894555760384.0000000000 -1.1183051544 -1.2040498573 2.0100050732 0.1021250527 0.1318228691 0.7840566525 -0.597869860744 +1413394894605760512.0000000000 -1.0500307767 -1.2243058640 1.9941399175 0.0912319102 0.1228944721 0.7876916061 -0.596754238362 +1413394894655760384.0000000000 -0.9827515794 -1.2433494056 1.9778664117 0.0831305755 0.1123018895 0.7898533997 -0.597167648121 +1413394894705760512.0000000000 -0.9171218503 -1.2612612424 1.9610014844 0.0794649594 0.1007147361 0.7903339662 -0.599094386589 +1413394894755760384.0000000000 -0.8527244325 -1.2778619714 1.9428448888 0.0795325072 0.0889086237 0.7914432459 -0.599489303911 +1413394894805760512.0000000000 -0.7888252522 -1.2935086611 1.9255949987 0.0760553684 0.0813845990 0.7930862181 -0.598837522768 +1413394894855760384.0000000000 -0.7253326814 -1.3078271255 1.9089360207 0.0746306031 0.0734598189 0.7951610936 -0.597287839623 +1413394894905760512.0000000000 -0.6619241173 -1.3211749173 1.8930090293 0.0687316574 0.0705050201 0.7979745359 -0.594593677617 +1413394894955760384.0000000000 -0.5991901813 -1.3346185739 1.8772591571 0.0632502341 0.0693203475 0.8003167451 -0.592188487533 +1413394895005760512.0000000000 -0.5368330288 -1.3471820230 1.8630360326 0.0541097699 0.0725076580 0.8024993050 -0.589753879006 +1413394895055760384.0000000000 -0.4758684692 -1.3587386720 1.8481464542 0.0484581557 0.0750033294 0.8041707309 -0.58765274043 +1413394895105760512.0000000000 -0.4161663854 -1.3694003040 1.8342005669 0.0454756247 0.0760562994 0.8064566068 -0.584615384897 +1413394895155760384.0000000000 -0.3581562861 -1.3801174674 1.8217898498 0.0431026324 0.0781070655 0.8083048166 -0.581966298727 +1413394895205760512.0000000000 -0.3016762587 -1.3902211169 1.8110721756 0.0421882066 0.0803058863 0.8092289717 -0.580447750659 +1413394895255760384.0000000000 -0.2471764911 -1.3995383749 1.8028109585 0.0432078002 0.0822413347 0.8081108248 -0.581658270513 +1413394895305760512.0000000000 -0.1945882098 -1.4087376187 1.7954869994 0.0467709925 0.0833464974 0.8078179168 -0.58163222819 +1413394895355760384.0000000000 -0.1440875517 -1.4177757188 1.7876229039 0.0592300294 0.0780560758 0.8075803850 -0.581560808918 +1413394895405760512.0000000000 -0.0949766904 -1.4277547594 1.7816840167 0.0722099503 0.0730888900 0.8069077803 -0.581673079492 +1413394895455760384.0000000000 -0.0457958882 -1.4376805116 1.7787222016 0.0837171722 0.0687148817 0.8063062174 -0.581498051564 +1413394895505760512.0000000000 0.0039462706 -1.4475678544 1.7794778651 0.0915135093 0.0674654462 0.8070692953 -0.579407321171 +1413394895555760384.0000000000 0.0547783379 -1.4566239734 1.7828431186 0.0983230545 0.0664831352 0.8086188423 -0.576236182113 +1413394895605760512.0000000000 0.1070556616 -1.4661310398 1.7914394589 0.0987420439 0.0694205446 0.8081939108 -0.576414260195 +1413394895655760384.0000000000 0.1606287245 -1.4759417297 1.8034906836 0.0966922146 0.0738333976 0.8085535775 -0.575708569744 +1413394895705760512.0000000000 0.2155186281 -1.4862762013 1.8198704083 0.0914014294 0.0793461152 0.8096847047 -0.574247900856 +1413394895755760384.0000000000 0.2709797973 -1.4963277307 1.8394740553 0.0871388312 0.0834248904 0.8106700263 -0.572940852307 +1413394895805760512.0000000000 0.3265496697 -1.5070904639 1.8605020923 0.0829230901 0.0870502021 0.8105354763 -0.573217467534 +1413394895855760384.0000000000 0.3815038943 -1.5185775036 1.8805547440 0.0801085919 0.0891317099 0.8100902507 -0.57392677019 +1413394895905760512.0000000000 0.4360840821 -1.5300981575 1.8971540361 0.0783412111 0.0899759636 0.8098746273 -0.57434316284 +1413394895955760384.0000000000 0.4901421379 -1.5422554139 1.9106585428 0.0772697759 0.0896715782 0.8092084103 -0.57547383828 +1413394896005760512.0000000000 0.5433684274 -1.5544561287 1.9213640067 0.0767863484 0.0891062471 0.8084220028 -0.576730265244 +1413394896055760384.0000000000 0.5958490640 -1.5668099462 1.9293573120 0.0758181296 0.0887971907 0.8083921088 -0.576947890644 +1413394896105760512.0000000000 0.6481148491 -1.5792627792 1.9341674381 0.0743199215 0.0878833089 0.8082407821 -0.577494512086 +1413394896155760384.0000000000 0.6994692001 -1.5921352070 1.9359244408 0.0742916550 0.0868080953 0.8086156551 -0.577135882546 +1413394896205760512.0000000000 0.7500374902 -1.6055984720 1.9350694262 0.0731641040 0.0870695453 0.8088209902 -0.576952783131 +1413394896255760384.0000000000 0.8006389492 -1.6191145984 1.9324343862 0.0644522689 0.0914218603 0.8085781559 -0.577658475522 +1413394896305760512.0000000000 0.8502276716 -1.6326836931 1.9284725441 0.0521223885 0.0989771250 0.8076816951 -0.578910238975 +1413394896355760384.0000000000 0.8980537829 -1.6463364709 1.9245332800 0.0387221329 0.1082718907 0.8070016706 -0.579246146082 +1413394896405760512.0000000000 0.9434639707 -1.6597368105 1.9206354986 0.0273111744 0.1148219463 0.8068361885 -0.578865602181 +1413394896455760384.0000000000 0.9853053169 -1.6729827257 1.9172507826 0.0157515094 0.1220381725 0.8059422333 -0.579064496353 +1413394896505760512.0000000000 1.0231918910 -1.6858975614 1.9123776370 0.0064030719 0.1285657656 0.8055330967 -0.578399753325 +1413394896555760384.0000000000 1.0572722836 -1.6987329153 1.9057158057 0.0057058699 -0.1364690378 -0.8044477246 0.57810682681 +1413394896605760512.0000000000 1.0864210004 -1.7110610714 1.8970003416 0.0166489477 -0.1441098554 -0.8031216695 0.577884716902 +1413394896655760384.0000000000 1.1100782035 -1.7232982390 1.8864786682 0.0287717291 -0.1532903039 -0.8011213907 0.577822453408 +1413394896705760512.0000000000 1.1279440225 -1.7353976927 1.8736296266 0.0405565524 -0.1606490247 -0.7988391287 0.578275975082 +1413394896755760384.0000000000 1.1387835716 -1.7462878014 1.8584786317 0.0515268267 -0.1694378370 -0.7967594666 0.577763063866 +1413394896805760512.0000000000 1.1426675541 -1.7563718172 1.8417909815 0.0619313183 -0.1771090730 -0.7938478611 0.57844832225 +1413394896855760384.0000000000 1.1380844814 -1.7654386980 1.8242057488 0.0681963401 -0.1820043110 -0.7900669253 0.581393105828 +1413394896905760512.0000000000 1.1237584058 -1.7730997560 1.8067358322 0.0691713102 -0.1856923802 -0.7861855150 0.585359723357 +1413394896955760384.0000000000 1.1011444971 -1.7785919059 1.7905030288 0.0727915350 -0.1888388982 -0.7840189360 0.586818175408 +1413394897005760512.0000000000 1.0692476846 -1.7812137373 1.7756653925 0.0769300759 -0.1914341671 -0.7826148292 0.587323379601 +1413394897055760384.0000000000 1.0270995978 -1.7818740383 1.7627528845 0.0804975916 -0.1944828131 -0.7819799548 0.58668894949 +1413394897105760512.0000000000 0.9749993255 -1.7809019177 1.7507048319 0.0782750877 -0.1938411507 -0.7837153508 0.584883636131 +1413394897155760384.0000000000 0.9138032726 -1.7781028300 1.7400399399 0.0739404352 -0.1908826150 -0.7845880884 0.585250519706 +1413394897205760512.0000000000 0.8431344537 -1.7734485504 1.7306776658 0.0670054384 -0.1871034756 -0.7861249087 0.585243700186 +1413394897255760384.0000000000 0.7636276705 -1.7677281072 1.7219115575 0.0518518852 -0.1775678722 -0.7902331368 0.584219669476 +1413394897305760512.0000000000 0.6765554004 -1.7605481537 1.7136537912 0.0259041703 -0.1596744569 -0.7949160460 0.584757660522 +1413394897355760384.0000000000 0.5834840153 -1.7522069717 1.7068856719 0.0010481205 0.1415562605 0.7981465626 -0.585596098998 +1413394897405760512.0000000000 0.4867564180 -1.7432414044 1.7020468506 0.0235829074 0.1266651451 0.7992705145 -0.586997812669 +1413394897455760384.0000000000 0.3883727815 -1.7336437434 1.6989780663 0.0415154460 0.1132687686 0.7997332624 -0.588109992072 +1413394897505760512.0000000000 0.2888931897 -1.7235734735 1.6971889180 0.0551030927 0.1035514597 0.7998743022 -0.58859310653 +1413394897555760384.0000000000 0.1897745119 -1.7129112320 1.6966615773 0.0638928754 0.0971312862 0.8008906771 -0.587415812781 +1413394897605760512.0000000000 0.0913865861 -1.7022392646 1.6973998494 0.0695961833 0.0921652400 0.8014066584 -0.58686396006 +1413394897655760384.0000000000 -0.0062695815 -1.6915494378 1.7000128708 0.0733603946 0.0887695708 0.8002823901 -0.588460968829 +1413394897705760512.0000000000 -0.1027682834 -1.6805439599 1.7046208392 0.0748232456 0.0873329503 0.7977811243 -0.591878125481 +1413394897755760384.0000000000 -0.1981057384 -1.6685982163 1.7092662362 0.0761596172 0.0856493684 0.7966786389 -0.593436639186 +1413394897805760512.0000000000 -0.2922550470 -1.6561207061 1.7159801862 0.0783972542 0.0833338296 0.7935981663 -0.597587896307 +1413394897855760384.0000000000 -0.3846579659 -1.6427208069 1.7237102678 0.0776208019 0.0827834483 0.7916290860 -0.60037097026 +1413394897905760512.0000000000 -0.4759336740 -1.6283952403 1.7325498110 0.0793096922 0.0810508503 0.7895267045 -0.603148667656 +1413394897955760384.0000000000 -0.5658005765 -1.6129596709 1.7430470580 0.0804165450 0.0802704030 0.7865704831 -0.606956931652 +1413394898005760512.0000000000 -0.6538541847 -1.5960450105 1.7533397594 0.0811604713 0.0791085527 0.7869184039 -0.60655934613 +1413394898055760384.0000000000 -0.7403395432 -1.5777758689 1.7639300656 0.0820908332 0.0782563334 0.7887348103 -0.604180801109 +1413394898105760512.0000000000 -0.8248044840 -1.5584064733 1.7752818070 0.0843048655 0.0764101368 0.7897879652 -0.602734726605 +1413394898155760384.0000000000 -0.9072856470 -1.5381235946 1.7866489218 0.0884700071 0.0720806552 0.7917682053 -0.600067117908 +1413394898205760512.0000000000 -0.9874232703 -1.5170181878 1.7991714128 0.0908357848 0.0688455077 0.7924781051 -0.599155747055 +1413394898255760384.0000000000 -1.0656448996 -1.4953967575 1.8119276071 0.0985468970 0.0621933411 0.7926782935 -0.59839921493 +1413394898305760512.0000000000 -1.1407981617 -1.4730583608 1.8247698433 0.1063188884 0.0535535114 0.7928023854 -0.59773965332 +1413394898355760384.0000000000 -1.2121335755 -1.4500638548 1.8380380327 0.1127411504 0.0436388332 0.7930459711 -0.59704536933 +1413394898405760512.0000000000 -1.2794829692 -1.4266425537 1.8510095283 0.1191428853 0.0317227917 0.7937378376 -0.595633177861 +1413394898455760384.0000000000 -1.3415331780 -1.4030054270 1.8643250568 0.1205986955 0.0204167611 0.7954298396 -0.593574326225 +1413394898505760512.0000000000 -1.3982409405 -1.3789734740 1.8782752896 0.1199720934 0.0076403870 0.7972032042 -0.591620970295 +1413394898555760384.0000000000 -1.4494811855 -1.3545224124 1.8922359475 0.1170387300 -0.0052362218 0.7999221784 -0.58855673147 +1413394898605760512.0000000000 -1.4955017349 -1.3304042277 1.9070135799 0.1147512104 -0.0183456024 0.8017101886 -0.586307404058 +1413394898655760384.0000000000 -1.5363221848 -1.3066965507 1.9224638270 0.1119348763 -0.0291238155 0.8033961642 -0.584103578324 +1413394898705760512.0000000000 -1.5715121777 -1.2833831677 1.9381293106 0.1070664386 -0.0368825017 0.8068502485 -0.57980094458 +1413394898755760384.0000000000 -1.6012271733 -1.2608163136 1.9543560451 0.0994537164 -0.0409234763 0.8115137844 -0.574351464826 +1413394898805760512.0000000000 -1.6262545585 -1.2394099373 1.9711146073 0.0962623015 -0.0456852295 0.8157251375 -0.568541053224 +1413394898855760384.0000000000 -1.6462685185 -1.2192857406 1.9885075930 0.0946316834 -0.0512135111 0.8179347755 -0.565159025201 +1413394898905760512.0000000000 -1.6621069506 -1.2010410351 2.0056329376 0.1003453903 -0.0598152826 0.8193410681 -0.561278138442 +1413394898955760384.0000000000 -1.6723373965 -1.1844573339 2.0234418361 0.1044166208 -0.0664265055 0.8200689611 -0.558723176243 +1413394899005760512.0000000000 -1.6771342078 -1.1695877529 2.0404432270 0.1087055684 -0.0713851346 0.8218786734 -0.554619426434 +1413394899055760384.0000000000 -1.6757323940 -1.1565747386 2.0560879853 0.1082306071 -0.0717789057 0.8242373605 -0.551150340529 +1413394899105760512.0000000000 -1.6687253988 -1.1453623192 2.0689164002 0.1052152368 -0.0698231701 0.8289799176 -0.544836466402 +1413394899155760384.0000000000 -1.6564537194 -1.1366481327 2.0793607463 0.1017133844 -0.0671495740 0.8329724109 -0.539724267326 +1413394899205760512.0000000000 -1.6393236264 -1.1305507302 2.0866009343 0.1000436269 -0.0661130197 0.8352124671 -0.536694024665 +1413394899255760384.0000000000 -1.6177469130 -1.1274812234 2.0911028681 0.1020388603 -0.0682001834 0.8357573159 -0.535206983295 +1413394899305760512.0000000000 -1.5907962454 -1.1270215899 2.0940359655 0.1002202192 -0.0673463685 0.8353200901 -0.536340117177 +1413394899355760384.0000000000 -1.5589506351 -1.1291156398 2.0948371217 0.0957651991 -0.0643348815 0.8344838153 -0.538819832262 +1413394899405760512.0000000000 -1.5216751083 -1.1333500846 2.0937049448 0.0835898936 -0.0564156541 0.8340441714 -0.542402363448 +1413394899455760384.0000000000 -1.4798863134 -1.1395704520 2.0902525355 0.0667697546 -0.0475124404 0.8340478834 -0.545571714897 +1413394899505760512.0000000000 -1.4351707800 -1.1474438905 2.0839303693 0.0511524676 -0.0427274012 0.8339432399 -0.547810612265 +1413394899555760384.0000000000 -1.3882112848 -1.1572912247 2.0751380768 0.0373741340 -0.0427247414 0.8334168726 -0.549721826948 +1413394899605760512.0000000000 -1.3393016167 -1.1689336554 2.0647029772 0.0261890033 -0.0471808629 0.8329857103 -0.550656797578 +1413394899655760384.0000000000 -1.2886867567 -1.1821251511 2.0535359233 0.0167537700 -0.0556997089 0.8322187084 -0.551388134619 +1413394899705760512.0000000000 -1.2364088155 -1.1971436006 2.0430015762 0.0070062573 -0.0665281985 0.8323057644 -0.550265413813 +1413394899755760384.0000000000 -1.1825080537 -1.2139300721 2.0335064337 0.0021303716 0.0790426201 -0.8310794808 0.550503971196 +1413394899805760512.0000000000 -1.1266037193 -1.2323772518 2.0250037700 0.0132550050 0.0931233309 -0.8286097218 0.551867990566 +1413394899855760384.0000000000 -1.0696647707 -1.2525640782 2.0177173316 0.0231428697 0.1076678366 -0.8240144694 0.555762718084 +1413394899905760512.0000000000 -1.0109835080 -1.2735813651 2.0108131247 0.0349020984 0.1215367446 -0.8195014890 0.558952567547 +1413394899955760384.0000000000 -0.9505461488 -1.2958002111 2.0066956645 0.0511608456 0.1325238016 -0.8142656952 0.56284224038 +1413394900005760512.0000000000 -0.8892450304 -1.3188369091 2.0056058977 0.0665017639 0.1434238162 -0.8097864299 0.565024833413 +1413394900055760384.0000000000 -0.8270863622 -1.3430957892 2.0086408126 0.0816909869 0.1541101954 -0.8040701806 0.568372918929 +1413394900105760512.0000000000 -0.7653511212 -1.3667358443 2.0149972221 0.0945411113 0.1660768079 -0.7975896259 0.572128709944 +1413394900155760384.0000000000 -0.7033738383 -1.3905484736 2.0238575758 0.1092891608 0.1756251166 -0.7905793698 0.576364431366 +1413394900205760512.0000000000 -0.6420799320 -1.4138797003 2.0333464264 0.1230282807 0.1853051923 -0.7846188230 0.578704873364 +1413394900255760384.0000000000 -0.5817251861 -1.4368681443 2.0410882559 0.1354200828 0.1943936336 -0.7794204716 0.579979521122 +1413394900305760512.0000000000 -0.5227566311 -1.4595664616 2.0461854686 0.1427243786 0.2060147967 -0.7727522625 0.583130856813 +1413394900355760384.0000000000 -0.4649777291 -1.4808015996 2.0491746970 0.1504280410 0.2173329714 -0.7664212807 0.585436763908 +1413394900405760512.0000000000 -0.4086298410 -1.5008922789 2.0498165827 0.1548048232 0.2306371591 -0.7592056179 0.588599012246 +1413394900455760384.0000000000 -0.3534743591 -1.5198474086 2.0473799927 0.1550215036 0.2464590431 -0.7540486072 0.588758839872 +1413394900505760512.0000000000 -0.2991433395 -1.5370255604 2.0426874865 0.1526754875 0.2639386014 -0.7493139778 0.587839410778 +1413394900555760384.0000000000 -0.2449778962 -1.5522579039 2.0370420997 0.1507123064 0.2800612026 -0.7444199176 0.58710349147 +1413394900605760512.0000000000 -0.1908159035 -1.5656542675 2.0298059384 0.1470186959 0.2961828654 -0.7392221938 0.586695629338 +1413394900655760384.0000000000 -0.1357170647 -1.5765143038 2.0220375743 0.1449021352 0.3119550498 -0.7319102184 0.588213269442 +1413394900705760512.0000000000 -0.0794810819 -1.5842143807 2.0151726882 0.1445280516 0.3261020556 -0.7252351789 0.588899844549 +1413394900755760384.0000000000 -0.0213243445 -1.5875504648 2.0108209831 0.1468427342 0.3390598624 -0.7182696136 0.589545912756 +1413394900805760512.0000000000 0.0382254940 -1.5849846836 2.0091090113 0.1500103083 0.3533866381 -0.7134652776 0.586158757575 +1413394900855760384.0000000000 0.1005857223 -1.5780977159 2.0126163166 0.1582159972 0.3645075077 -0.7087643124 0.582885172741 +1413394900905760512.0000000000 0.1653293742 -1.5664085715 2.0200315925 0.1664997564 0.3759190111 -0.7045450927 0.578427990861 +1413394900955760384.0000000000 0.2322146148 -1.5495848601 2.0324294621 0.1763588015 0.3880273267 -0.6972522565 0.576343350561 +1413394901005760512.0000000000 0.3018151343 -1.5284538354 2.0496591960 0.1862203387 0.4003604071 -0.6904191222 0.573022657115 +1413394901055760384.0000000000 0.3725101658 -1.5028327947 2.0679061145 0.1970172878 0.4119464687 -0.6830014760 0.570081817841 +1413394901105760512.0000000000 0.4441711215 -1.4726340674 2.0865291626 0.2105992713 0.4227580939 -0.6740390386 0.567974396812 +1413394901155760384.0000000000 0.5160097624 -1.4381714447 2.1036348734 0.2269605715 0.4320368135 -0.6656700483 0.564549800786 +1413394901205760512.0000000000 0.5874268961 -1.3996272848 2.1197423923 0.2477428229 0.4373232447 -0.6586954628 0.559903706627 +1413394901255760384.0000000000 0.6580225420 -1.3578684897 2.1338486989 0.2701832946 0.4403895180 -0.6533772250 0.553313890652 +1413394901305760512.0000000000 0.7270278909 -1.3129402118 2.1460724709 0.2928823503 0.4432292644 -0.6475867742 0.546259203949 +1413394901355760384.0000000000 0.7939962193 -1.2659798497 2.1565144699 0.3164206327 0.4444398875 -0.6436822642 0.536678965902 +1413394901405760512.0000000000 0.8589856314 -1.2178891655 2.1660063629 0.3396574320 0.4442829040 -0.6382700490 0.529015004174 +1413394901455760384.0000000000 0.9208206215 -1.1692589813 2.1733479560 0.3603603148 0.4449808501 -0.6305342788 0.52398378779 +1413394901505760512.0000000000 0.9786332821 -1.1208152667 2.1775183024 0.3775176941 0.4468005314 -0.6234855608 0.518763367218 +1413394901555760384.0000000000 1.0320886850 -1.0726835367 2.1782983215 0.3894220808 0.4516897639 -0.6182544493 0.511945540129 +1413394901605760512.0000000000 1.0813342769 -1.0247382462 2.1752325923 0.3964001491 0.4611943118 -0.6144152402 0.502653599596 +1413394901655760384.0000000000 1.1261762319 -0.9774967170 2.1687861627 0.3971414053 0.4753544827 -0.6101572397 0.493988828554 +1413394901705760512.0000000000 1.1673110684 -0.9305951803 2.1597433334 0.3971814974 0.4909775168 -0.6053388093 0.48451301542 +1413394901755760384.0000000000 1.2051932907 -0.8841971896 2.1503028463 0.3956710935 0.5083261986 -0.5961238468 0.479254860047 +1413394901805760512.0000000000 1.2397940266 -0.8377582104 2.1416426420 0.3951608835 0.5256345526 -0.5848021434 0.474934360095 +1413394901855760384.0000000000 1.2715204255 -0.7906182539 2.1343355699 0.3968910792 0.5425679557 -0.5707704395 0.471506723288 +1413394901905760512.0000000000 1.3007832395 -0.7426715078 2.1294891710 0.4013166705 0.5576152579 -0.5551167224 0.46888759694 +1413394901955760384.0000000000 1.3268554279 -0.6932596038 2.1265347292 0.4070383945 0.5718883796 -0.5400894048 0.464291784899 +1413394902005760512.0000000000 1.3506027972 -0.6426098282 2.1250815536 0.4134451102 0.5847864280 -0.5267258900 0.45787313892 +1413394902055760384.0000000000 1.3713490919 -0.5902524709 2.1253263359 0.4212600587 0.5958384886 -0.5149221110 0.449857397466 +1413394902105760512.0000000000 1.3897627739 -0.5364496568 2.1274771370 0.4283030718 0.6065707401 -0.5028186096 0.442495041537 +1413394902155760384.0000000000 1.4054742728 -0.4815501129 2.1297414274 0.4354694039 0.6158397080 -0.4920007989 0.434790830508 +1413394902205760512.0000000000 1.4186558346 -0.4253059772 2.1304380949 0.4453986811 0.6228526666 -0.4810310454 0.426946956865 +1413394902255760384.0000000000 1.4292063358 -0.3685147206 2.1288314065 0.4544310182 0.6294542777 -0.4695965554 0.420426969953 +1413394902305760512.0000000000 1.4375158088 -0.3108422292 2.1261279004 0.4645139936 0.6344013712 -0.4572076576 0.415599335573 +1413394902355760384.0000000000 1.4429719335 -0.2526628888 2.1219177733 0.4744366805 0.6380084824 -0.4442772685 0.41288342336 +1413394902405760512.0000000000 1.4448788813 -0.1941079034 2.1167662646 0.4845388827 0.6403784705 -0.4320748242 0.410425184343 +1413394902455760384.0000000000 1.4422287992 -0.1349526340 2.1111729930 0.4957398919 0.6421145471 -0.4253733126 0.401233613762 +1413394902505760512.0000000000 1.4350450796 -0.0758787240 2.1065885325 0.5074960687 0.6427145326 -0.4246883613 0.38601239046 +1413394902555760384.0000000000 1.4239036757 -0.0180484855 2.1030307782 0.5199241289 0.6410016316 -0.4260708151 0.370485450623 +1413394902605760512.0000000000 1.4089885779 0.0379298267 2.1004815525 0.5306639341 0.6391612844 -0.4311043327 0.352161462917 +1413394902655760384.0000000000 1.3917145145 0.0910266186 2.0981790941 0.5384250370 0.6379133378 -0.4371318546 0.33478469896 +1413394902705760512.0000000000 1.3721083735 0.1404109431 2.0961689403 0.5436424831 0.6372321109 -0.4451168935 0.316637077006 +1413394902755760384.0000000000 1.3514358219 0.1854843015 2.0952341932 0.5472906806 0.6359975503 -0.4533195643 0.300801262366 +1413394902805760512.0000000000 1.3297390891 0.2255187097 2.0936666362 0.5476193745 0.6368675025 -0.4585535692 0.290243740691 +1413394902855760384.0000000000 1.3082593239 0.2601647835 2.0921926040 0.5443402765 0.6396176928 -0.4627988226 0.283549149471 +1413394902905760512.0000000000 1.2869625685 0.2897371776 2.0897506327 0.5372006062 0.6444940716 -0.4649245202 0.282644813928 +1413394902955760384.0000000000 1.2659311847 0.3149326284 2.0856702406 0.5306913310 0.6485586980 -0.4663755056 0.283252915535 +1413394903055760384.0000000000 1.2263165891 0.3535820496 2.0700179952 0.5171284592 0.6531358024 -0.4716143709 0.289087643348 +1413394903155760384.0000000000 1.1878203392 0.3787455344 2.0425581779 0.4994828950 0.6552771044 -0.4887228418 0.286842705765 +1413394903255760384.0000000000 1.1540609570 0.3925598581 2.0028799550 0.4761469555 0.6570772955 -0.5138140537 0.278439621377 +1413394903355760384.0000000000 1.1330764082 0.3945972807 1.9578866294 0.4558584709 0.6539469334 -0.5273548560 0.294012446516 +1413394903455760384.0000000000 1.1238920632 0.3882272831 1.9223669916 0.4517029738 0.6417871105 -0.5298574484 0.321441771809 +1413394903555760384.0000000000 1.1234629423 0.3760438727 1.9000204606 0.4521656672 0.6293237342 -0.5298352828 0.344633747619 +1413394903605760512.0000000000 1.1254080029 0.3679883953 1.8936312964 0.4503646237 0.6260494103 -0.5276753157 0.356079489369 +1413394903655760384.0000000000 1.1274152677 0.3589223138 1.8914855420 0.4485724846 0.6234312958 -0.5261841655 0.365029272103 +1413394903705760512.0000000000 1.1293440855 0.3491742347 1.8933621844 0.4467543118 0.6217133211 -0.5247777855 0.37214433632 +1413394903755760384.0000000000 1.1314930192 0.3390197580 1.8991891217 0.4428068764 0.6221530395 -0.5238658080 0.377375517014 +1413394903805760512.0000000000 1.1329862847 0.3288498603 1.9087627571 0.4401375490 0.6223095036 -0.5218222631 0.383029170373 +1413394903855760384.0000000000 1.1338878005 0.3185514457 1.9193420869 0.4337513472 0.6260602582 -0.5180558090 0.389264050091 +1413394903905760512.0000000000 1.1346075964 0.3084646653 1.9297016278 0.4269643315 0.6289174467 -0.5156735656 0.395278482388 +1413394903955760384.0000000000 1.1344370159 0.2990969014 1.9379560400 0.4204174175 0.6298023863 -0.5161043424 0.400292964056 +1413394904005760512.0000000000 1.1339344892 0.2909948681 1.9441591157 0.4168518099 0.6270041286 -0.5213120071 0.401664265955 +1413394904055760384.0000000000 1.1338946395 0.2838563872 1.9482327379 0.4133548703 0.6220307706 -0.5313435294 0.399861882922 +1413394904105760512.0000000000 1.1338657972 0.2774585750 1.9503789233 0.4107099441 0.6144597258 -0.5452824256 0.395504315312 +1413394904155760384.0000000000 1.1344388026 0.2711132086 1.9499409460 0.4065227860 0.6063594721 -0.5598620630 0.391946278774 +1413394904205760512.0000000000 1.1358736833 0.2643737468 1.9470793400 0.3994708050 0.5980441193 -0.5757216829 0.388986955017 +1413394904255760384.0000000000 1.1387673078 0.2572079538 1.9416379977 0.3906286386 0.5900531549 -0.5913041979 0.386789201843 +1413394904305760512.0000000000 1.1437298773 0.2485367472 1.9336807649 0.3787662947 0.5820802802 -0.6054288722 0.388811679464 +1413394904355760384.0000000000 1.1505518247 0.2390381260 1.9240110979 0.3673772634 0.5722148297 -0.6203464628 0.390863660364 +1413394904405760512.0000000000 1.1597879667 0.2282017470 1.9120919238 0.3548842466 0.5614462638 -0.6339029258 0.396235214411 +1413394904455760384.0000000000 1.1715721880 0.2162656477 1.8986433565 0.3425051106 0.5498370759 -0.6461940454 0.403488159467 +1413394904505760512.0000000000 1.1866359022 0.2025122327 1.8853548166 0.3307234354 0.5367324598 -0.6557759471 0.415329005867 +1413394904555760384.0000000000 1.2039122757 0.1879541421 1.8738730701 0.3224586626 0.5203094926 -0.6631142146 0.430787628819 +1413394904605760512.0000000000 1.2230427153 0.1730389718 1.8635613469 0.3157683769 0.5024082123 -0.6702216115 0.445734575554 +1413394904655760384.0000000000 1.2440186366 0.1574021876 1.8545981745 0.3105645899 0.4832051204 -0.6759344358 0.461708875412 +1413394904705760512.0000000000 1.2662502298 0.1413639636 1.8462759358 0.3043489155 0.4641264399 -0.6828100943 0.475109209072 +1413394904755760384.0000000000 1.2889715373 0.1250365077 1.8393682944 0.2958032958 0.4467421843 -0.6891569084 0.487836639143 +1413394904805760512.0000000000 1.3117142528 0.1087591369 1.8332521903 0.2878615444 0.4290855661 -0.6943150875 0.500946970695 +1413394904855760384.0000000000 1.3341887244 0.0922157642 1.8279498763 0.2784754917 0.4118212735 -0.6994063435 0.513503072881 +1413394904905760512.0000000000 1.3561721240 0.0760787409 1.8242220020 0.2706135454 0.3929027602 -0.7035930598 0.526642702656 +1413394904955760384.0000000000 1.3774966635 0.0607194970 1.8219492704 0.2640206229 0.3736759880 -0.7051805893 0.541645366563 +1413394905005760512.0000000000 1.3973163256 0.0463639695 1.8210431140 0.2591389391 0.3526094140 -0.7058950772 0.556979130112 +1413394905055760384.0000000000 1.4152430741 0.0335695450 1.8216156223 0.2553116026 0.3310731535 -0.7059138541 0.571744858474 +1413394905105760512.0000000000 1.4303471162 0.0226616417 1.8227534258 0.2508131428 0.3104214115 -0.7067690939 0.584130775316 +1413394905155760384.0000000000 1.4422570616 0.0141189284 1.8243031780 0.2460962834 0.2910035704 -0.7102050037 0.591914177892 +1413394905205760512.0000000000 1.4502570387 0.0084875769 1.8236030119 0.2394850068 0.2750655066 -0.7212153092 0.588926460999 +1413394905255760384.0000000000 1.4545617938 0.0054517062 1.8220740413 0.2307167558 0.2623402447 -0.7367823467 0.578877489776 +1413394905305760512.0000000000 1.4559912390 0.0041224313 1.8186140746 0.2189833313 0.2547031452 -0.7584392315 0.558518164968 +1413394905355760384.0000000000 1.4550083939 0.0034318916 1.8145986669 0.2039052628 0.2523384826 -0.7808571311 0.53386334849 +1413394905405760512.0000000000 1.4533942075 0.0020014848 1.8110608100 0.1918593293 0.2493268334 -0.8038166513 0.50488109391 +1413394905455760384.0000000000 1.4519231220 -0.0029723779 1.8084449828 0.1756167729 0.2516695666 -0.8218413427 0.479997901766 +1413394905505760512.0000000000 1.4518446003 -0.0125328659 1.8072691506 0.1633136293 0.2517819051 -0.8369565443 0.457644265376 +1413394905555760384.0000000000 1.4539854876 -0.0279596322 1.8069556858 0.1516907545 0.2531255638 -0.8485174994 0.439244142909 +1413394905605760512.0000000000 1.4592836038 -0.0509840778 1.8090265861 0.1409421310 0.2572718942 -0.8525772305 0.432502663792 +1413394905655760384.0000000000 1.4697420839 -0.0832001824 1.8153780286 0.1347755619 0.2608854838 -0.8456642599 0.445675074225 +1413394905705760512.0000000000 1.4847903197 -0.1220416821 1.8240850518 0.1330842157 0.2631866185 -0.8322326169 0.469478718034 +1413394905755760384.0000000000 1.5039862011 -0.1654875433 1.8360358587 0.1392855934 0.2612054587 -0.8125412579 0.502143342051 +1413394905805760512.0000000000 1.5252207036 -0.2111103892 1.8490790314 0.1463806245 0.2590411306 -0.7893053179 0.537091724478 +1413394905855760384.0000000000 1.5477813896 -0.2566027615 1.8635797186 0.1573221283 0.2539380240 -0.7628428327 0.573442273001 +1413394905905760512.0000000000 1.5699348241 -0.2995601711 1.8778564167 0.1673549808 0.2498162208 -0.7387232652 0.603218122863 +1413394905955760384.0000000000 1.5905400247 -0.3387438421 1.8923875966 0.1779686945 0.2448548189 -0.7159268617 0.629143854818 +1413394906005760512.0000000000 1.6087771366 -0.3725629161 1.9070604757 0.1904911284 0.2386583047 -0.6981368221 0.647580358913 +1413394906055760384.0000000000 1.6232402104 -0.4000489517 1.9220368884 0.2029483842 0.2328163117 -0.6824501388 0.662472887293 +1413394906105760512.0000000000 1.6328036548 -0.4206196902 1.9369228077 0.2166271725 0.2259509390 -0.6729634751 0.670178336321 +1413394906155760384.0000000000 1.6373245841 -0.4349404655 1.9533356417 0.2313317601 0.2179700509 -0.6717701277 0.669103556435 +1413394906205760512.0000000000 1.6349572872 -0.4429398890 1.9698968213 0.2391638583 0.2119899047 -0.6787387186 0.661191864038 +1413394906255760384.0000000000 1.6263954733 -0.4457451019 1.9852270654 0.2416285141 0.2094268656 -0.6974120488 0.641383257751 +1413394906305760512.0000000000 1.6115998417 -0.4449967734 1.9990245119 0.2360497238 0.2091073779 -0.7191591310 0.619164579601 +1413394906355760384.0000000000 1.5912968986 -0.4417672886 2.0101468645 0.2258977660 0.2085231150 -0.7419339205 0.595837534375 +1413394906405760512.0000000000 1.5667473322 -0.4378117671 2.0190551329 0.2107142687 0.2090332283 -0.7635298714 0.573521352601 +1413394906455760384.0000000000 1.5388237656 -0.4340676862 2.0238524467 0.1888684675 0.2115913153 -0.7856722440 0.549797182835 +1413394906505760512.0000000000 1.5087355532 -0.4321778508 2.0265756689 0.1612823727 0.2150865181 -0.8051575075 0.528627632737 +1413394906555760384.0000000000 1.4785789782 -0.4319845951 2.0276302336 0.1383450051 0.2136707245 -0.8224771367 0.508661813643 +1413394906605760512.0000000000 1.4497734381 -0.4355358422 2.0272853940 0.1161914094 0.2110314512 -0.8354271995 0.493990563927 +1413394906655760384.0000000000 1.4232353234 -0.4437149061 2.0261080267 0.0970019706 0.2054139302 -0.8423590187 0.488699313145 +1413394906705760512.0000000000 1.4002846004 -0.4568567853 2.0254473529 0.0838944372 0.1959073567 -0.8421878767 0.495279326624 +1413394906755760384.0000000000 1.3810055912 -0.4745478543 2.0250554573 0.0759154900 0.1847766430 -0.8339287276 0.514448547433 +1413394906805760512.0000000000 1.3642681070 -0.4957767901 2.0247583728 0.0710953736 0.1709813364 -0.8193805151 0.542518572913 +1413394906855760384.0000000000 1.3495667763 -0.5181920514 2.0228468189 0.0667109208 0.1585986482 -0.8009589741 0.573463899174 +1413394906905760512.0000000000 1.3365037241 -0.5395352475 2.0206117559 0.0662429542 0.1460896594 -0.7793063311 0.605765073875 +1413394906955760384.0000000000 1.3240868162 -0.5580472954 2.0189186077 0.0658083675 0.1340903182 -0.7559548756 0.637354902251 +1413394907005760512.0000000000 1.3125089567 -0.5715204469 2.0173123741 0.0658325826 0.1245472279 -0.7343181625 0.664026276082 +1413394907055760384.0000000000 1.3009085386 -0.5780378724 2.0177371054 0.0697252712 0.1145330725 -0.7120705589 0.689185084697 +1413394907105760512.0000000000 1.2884840023 -0.5764749695 2.0182779290 0.0760321995 0.1052224425 -0.6966154351 0.705602067635 +1413394907155760384.0000000000 1.2746807511 -0.5658718539 2.0181188053 0.0823979869 0.0975407552 -0.6926199271 0.709911268645 +1413394907205760512.0000000000 1.2585226281 -0.5455920974 2.0140830535 0.0819846229 0.0957548556 -0.7042131667 0.698708340542 +1413394907255760384.0000000000 1.2403780021 -0.5166800700 2.0096448540 0.0827435879 0.0940211028 -0.7240656014 0.678264355316 +1413394907305760512.0000000000 1.2203430164 -0.4813576595 2.0047541576 0.0820956021 0.0937883018 -0.7492632403 0.650437286218 +1413394907355760384.0000000000 1.1988802554 -0.4416181550 1.9994315013 0.0829246444 0.0926687300 -0.7782669062 0.615497061382 +1413394907405760512.0000000000 1.1763951616 -0.3994963919 1.9945631495 0.0905672645 0.0845187986 -0.8066226698 0.577939453406 +1413394907455760384.0000000000 1.1528764065 -0.3580056919 1.9890199812 0.1044774503 0.0689886790 -0.8327429165 0.539318328566 +1413394907505760512.0000000000 1.1274250136 -0.3203430773 1.9822888080 0.1165519554 0.0518193936 -0.8517559422 0.508175370327 +1413394907555760384.0000000000 1.0988747991 -0.2878354957 1.9735106663 0.1259843925 0.0336270137 -0.8677339198 0.479619642295 +1413394907605760512.0000000000 1.0660175857 -0.2626798472 1.9635293286 0.1254287921 0.0210430882 -0.8779616793 0.461528001558 +1413394907655760384.0000000000 1.0289260190 -0.2456257390 1.9517915940 0.1172134924 0.0136621179 -0.8847993729 0.450782002081 +1413394907705760512.0000000000 0.9870639374 -0.2385354988 1.9399971398 0.0987472466 0.0141557425 -0.8834137010 0.457852409796 +1413394907755760384.0000000000 0.9421647037 -0.2402443869 1.9287955194 0.0741900610 0.0215832477 -0.8742649635 0.479260651298 +1413394907805760512.0000000000 0.8955931366 -0.2487227518 1.9184583427 0.0502194677 0.0309727870 -0.8564923524 0.512776307851 +1413394907855760384.0000000000 0.8488537429 -0.2604331881 1.9063920013 0.0293132873 0.0400829205 -0.8345204400 0.548734658906 +1413394907905760512.0000000000 0.8032493253 -0.2733406766 1.8931377685 0.0132327472 0.0476481967 -0.8101872383 0.584081486337 +1413394907955760384.0000000000 0.7596203719 -0.2846815796 1.8788363528 0.0039705338 0.0527175226 -0.7888170462 0.612350198275 +1413394908005760512.0000000000 0.7176157962 -0.2933179074 1.8631872501 0.0022090359 -0.0567201677 0.7703746345 -0.635059733604 +1413394908055760384.0000000000 0.6774963992 -0.2979391085 1.8464963245 0.0036692592 -0.0582482822 0.7588147487 -0.648686250278 +1413394908105760512.0000000000 0.6388302127 -0.2979079793 1.8265728928 0.0056866168 -0.0606346918 0.7601497633 -0.646887497087 +1413394908155760384.0000000000 0.6020062591 -0.2932087440 1.8047004293 0.0066416524 -0.0626525557 0.7727754881 -0.631544607093 +1413394908205760512.0000000000 0.5670601015 -0.2852214501 1.7821101811 0.0063395958 -0.0637798733 0.7916104656 -0.607655171961 +1413394908255760384.0000000000 0.5339020935 -0.2753139958 1.7592482819 0.0098261582 -0.0676580421 0.8118204666 -0.579890822403 +1413394908305760512.0000000000 0.5032000260 -0.2653018871 1.7381073156 0.0100475240 -0.0694070098 0.8308709742 -0.552028204487 +1413394908355760384.0000000000 0.4750980155 -0.2573915007 1.7193918311 0.0093176358 -0.0710249349 0.8473804817 -0.526132074185 +1413394908405760512.0000000000 0.4498258217 -0.2536581157 1.7045403488 0.0063219603 -0.0705749904 0.8607231235 -0.504117950627 +1413394908455760384.0000000000 0.4278064205 -0.2561773912 1.6939676806 0.0002711281 0.0672721456 -0.8712651696 0.486180408067 +1413394908505760512.0000000000 0.4081916464 -0.2660440563 1.6880496933 0.0076055071 0.0636626879 -0.8787341661 0.472985712052 +1413394908555760384.0000000000 0.3907192712 -0.2843412269 1.6885790965 0.0128579936 0.0628314430 -0.8783957420 0.473611446394 +1413394908605760512.0000000000 0.3743592027 -0.3128752654 1.6956909346 0.0110913247 0.0687312342 -0.8676481998 0.492280002928 +1413394908655760384.0000000000 0.3599656713 -0.3477081702 1.7086943773 0.0096141015 0.0750032262 -0.8498829189 0.52151808151 +1413394908705760512.0000000000 0.3475986256 -0.3848045789 1.7265565304 0.0116240429 0.0783847207 -0.8268647341 0.556790291508 +1413394908755760384.0000000000 0.3366259971 -0.4215179640 1.7475129133 0.0109470681 0.0836427633 -0.8012890094 0.592300576741 +1413394908805760512.0000000000 0.3273723395 -0.4553075359 1.7691631279 0.0130136943 0.0861907107 -0.7791583080 0.620736768901 +1413394908855760384.0000000000 0.3198059272 -0.4859012816 1.7930863088 0.0156784782 0.0879477123 -0.7574092468 0.646800292231 +1413394908905760512.0000000000 0.3135347801 -0.5102816388 1.8194036943 0.0223561958 0.0867003780 -0.7395074483 0.667167129592 +1413394908955760384.0000000000 0.3081336158 -0.5284243254 1.8498890406 0.0317816390 0.0833100482 -0.7222983650 0.68580932866 +1413394909005760512.0000000000 0.3032195680 -0.5396599858 1.8806886698 0.0441013578 0.0780257994 -0.7151584981 0.693192157671 +1413394909055760384.0000000000 0.2971706538 -0.5438446743 1.9081933083 0.0524554183 0.0745174367 -0.7215256110 0.686364606784 +1413394909105760512.0000000000 0.2901490978 -0.5423349198 1.9356305186 0.0596129626 0.0712389597 -0.7376283063 0.668786802441 +1413394909155760384.0000000000 0.2816000896 -0.5350130654 1.9605821317 0.0655004902 0.0677335489 -0.7594931295 0.643655217029 +1413394909205760512.0000000000 0.2705044753 -0.5242077452 1.9823026682 0.0619374932 0.0658154434 -0.7827024857 0.615799393726 +1413394909255760384.0000000000 0.2579502811 -0.5114047396 2.0005070401 0.0565769139 0.0618777380 -0.8070823517 0.584455538048 +1413394909305760512.0000000000 0.2439368621 -0.4983389710 2.0166772022 0.0496634194 0.0560399238 -0.8264782468 0.557966647113 +1413394909355760384.0000000000 0.2289542224 -0.4869428163 2.0315985215 0.0449018776 0.0445414304 -0.8415244587 0.536503930744 +1413394909405760512.0000000000 0.2133613286 -0.4793193827 2.0455912276 0.0403195198 0.0310211326 -0.8506267280 0.523303158113 +1413394909455760384.0000000000 0.1965184595 -0.4762378161 2.0589942999 0.0349204799 0.0158968383 -0.8529021887 0.520658916302 +1413394909505760512.0000000000 0.1785302868 -0.4780834023 2.0721375823 0.0297544315 -0.0000582693 -0.8487940399 0.527885734032 +1413394909555760384.0000000000 0.1590199371 -0.4832294599 2.0850123492 0.0268813916 -0.0169641346 -0.8400877274 0.541518438483 +1413394909605760512.0000000000 0.1378414584 -0.4912608014 2.0988649090 0.0245587693 -0.0321906569 -0.8282321778 0.558920466731 +1413394909655760384.0000000000 0.1145503635 -0.5004928848 2.1129488266 0.0222545403 -0.0448998393 -0.8159341770 0.575968886937 +1413394909705760512.0000000000 0.0884856017 -0.5100346169 2.1274707177 0.0156060858 -0.0532225812 -0.8024380790 0.594152283808 +1413394909755760384.0000000000 0.0601171321 -0.5185033319 2.1433186774 0.0066159305 -0.0570224888 -0.7863029890 0.615168492948 +1413394909805760512.0000000000 0.0299504495 -0.5244988948 2.1592691446 0.0057677149 0.0560168677 0.7699911058 -0.635564741775 +1413394909855760384.0000000000 -0.0012681186 -0.5268498505 2.1761836298 0.0173508309 0.0539394632 0.7529333187 -0.655653033637 +1413394909905760512.0000000000 -0.0327865600 -0.5242973346 2.1923009656 0.0257558532 0.0524705037 0.7416330781 -0.668254337589 +1413394909955760384.0000000000 -0.0644448140 -0.5157198732 2.2055219086 0.0351835718 0.0481779362 0.7401622587 -0.669776704197 +1413394910005760512.0000000000 -0.0959133049 -0.5013122080 2.2151953985 0.0437678129 0.0444137773 0.7519864360 -0.656222671783 +1413394910055760384.0000000000 -0.1264524050 -0.4820024541 2.2235828008 0.0516956253 0.0401247573 0.7685860801 -0.63639060625 +1413394910105760512.0000000000 -0.1557888126 -0.4600040089 2.2305063983 0.0555728297 0.0373039585 0.7880185683 -0.612002296849 +1413394910155760384.0000000000 -0.1839185624 -0.4367398403 2.2353705913 0.0559277229 0.0368030744 0.8070068707 -0.586734636865 +1413394910205760512.0000000000 -0.2106645498 -0.4135753447 2.2382701863 0.0533769631 0.0380771159 0.8249738379 -0.561354789612 +1413394910255760384.0000000000 -0.2365191541 -0.3920526255 2.2392820091 0.0498773237 0.0390750247 0.8411022240 -0.537152160744 +1413394910305760512.0000000000 -0.2618175786 -0.3734866486 2.2389116943 0.0464626642 0.0399792915 0.8541676673 -0.5163724171 +1413394910355760384.0000000000 -0.2865916989 -0.3589112312 2.2368397867 0.0421759047 0.0412658091 0.8639384573 -0.500128651473 +1413394910405760512.0000000000 -0.3113474342 -0.3488410449 2.2320750015 0.0382982674 0.0417705037 0.8715117215 -0.487089095634 +1413394910455760384.0000000000 -0.3365404425 -0.3444432204 2.2257007926 0.0364431134 0.0414471595 0.8763313191 -0.478536781962 +1413394910505760512.0000000000 -0.3620726788 -0.3478937310 2.2203234493 0.0367270528 0.0389785032 0.8725034784 -0.485663958045 +1413394910555760384.0000000000 -0.3881757367 -0.3580344925 2.2153563403 0.0390073895 0.0349386251 0.8610653452 -0.505790655707 +1413394910605760512.0000000000 -0.4141489602 -0.3734805176 2.2108325773 0.0428004899 0.0296221252 0.8422888139 -0.536507410657 +1413394910655760384.0000000000 -0.4392861462 -0.3921108163 2.2077122573 0.0424710111 0.0270982848 0.8178744731 -0.573186917476 +1413394910705760512.0000000000 -0.4636312153 -0.4106289792 2.2040887830 0.0426344059 0.0241567465 0.7936066220 -0.606454687897 +1413394910755760384.0000000000 -0.4868063051 -0.4268222128 2.2005698903 0.0392524046 0.0236557038 0.7708405799 -0.635377412921 +1413394910805760512.0000000000 -0.5089879512 -0.4387501900 2.1970801804 0.0321972209 0.0257458212 0.7517015756 -0.658213668122 +1413394910855760384.0000000000 -0.5306430838 -0.4455030780 2.1928173060 0.0252208079 0.0271606330 0.7385906778 -0.673134475101 +1413394910905760512.0000000000 -0.5522031023 -0.4461432868 2.1879150267 0.0184822284 0.0292661684 0.7296004445 -0.682997137593 +1413394910955760384.0000000000 -0.5736299112 -0.4402177584 2.1830681258 0.0109708745 0.0319705083 0.7232860103 -0.689720866592 +1413394911005760512.0000000000 -0.5952976354 -0.4272901204 2.1772687842 0.0018372639 0.0345909856 0.7237982530 -0.689141623397 +1413394911055760384.0000000000 -0.6182288817 -0.4075694501 2.1681387714 0.0048732494 -0.0364069287 -0.7373885371 0.674469370941 +1413394911105760512.0000000000 -0.6432197044 -0.3817102407 2.1559185692 0.0021477727 0.0308851102 0.7560447542 -0.653787294723 +1413394911155760384.0000000000 -0.6693026153 -0.3511710186 2.1420894447 0.0097203571 0.0257676947 0.7806420228 -0.624371342047 +1413394911205760512.0000000000 -0.6960373722 -0.3181665206 2.1280858606 0.0185193974 0.0200934809 0.8043923450 -0.593469661659 +1413394911255760384.0000000000 -0.7225091893 -0.2846346950 2.1139169077 0.0247178327 0.0162520508 0.8248819780 -0.564530443784 +1413394911305760512.0000000000 -0.7490720558 -0.2531763955 2.0992381938 0.0294392903 0.0154054204 0.8409422154 -0.540103871074 +1413394911355760384.0000000000 -0.7754085097 -0.2249389236 2.0830007922 0.0347519216 0.0147828621 0.8540450475 -0.518826394607 +1413394911405760512.0000000000 -0.8010325917 -0.2017013405 2.0664599721 0.0378584914 0.0158646160 0.8629247567 -0.503662498906 +1413394911455760384.0000000000 -0.8258351758 -0.1841288918 2.0491493006 0.0406851066 0.0165301050 0.8677863282 -0.494993299319 +1413394911505760512.0000000000 -0.8498625881 -0.1720197279 2.0299163302 0.0430940215 0.0172549829 0.8709030549 -0.489257641656 +1413394911555760384.0000000000 -0.8732912073 -0.1665679312 2.0106715909 0.0456247359 0.0196429128 0.8678710629 -0.494299866155 +1413394911605760512.0000000000 -0.8956431831 -0.1673954761 1.9915802496 0.0477005434 0.0223489760 0.8585722714 -0.509979250684 +1413394911655760384.0000000000 -0.9173607953 -0.1739416897 1.9734810827 0.0508013988 0.0248943385 0.8433369449 -0.534398996287 +1413394911705760512.0000000000 -0.9380904935 -0.1841763779 1.9577664088 0.0539591678 0.0279047894 0.8223415230 -0.565742123665 +1413394911755760384.0000000000 -0.9569815295 -0.1951271771 1.9438999596 0.0553216285 0.0299140747 0.7997517528 -0.597027469607 +1413394911805760512.0000000000 -0.9744957067 -0.2040740390 1.9327080546 0.0585859264 0.0301487954 0.7774899260 -0.625434372509 +1413394911855760384.0000000000 -0.9903453085 -0.2079677938 1.9233175528 0.0605705948 0.0322647987 0.7585227288 -0.648022727712 +1413394911905760512.0000000000 -1.0039644059 -0.2059452255 1.9156924499 0.0623376117 0.0331259292 0.7463495860 -0.661799811444 +1413394911955760384.0000000000 -1.0158016352 -0.1983428231 1.9081489495 0.0652065400 0.0335557634 0.7472729300 -0.660458390743 +1413394912005760512.0000000000 -1.0258765696 -0.1858476066 1.9016613808 0.0666556186 0.0358805110 0.7573959386 -0.648553012193 +1413394912055760384.0000000000 -1.0340802235 -0.1697716729 1.8970018781 0.0675498513 0.0382811597 0.7758877774 -0.626074857578 +1413394912105760512.0000000000 -1.0403489958 -0.1505759623 1.8941960571 0.0674174296 0.0417926662 0.7975260530 -0.598047203827 +1413394912155760384.0000000000 -1.0456851259 -0.1303804315 1.8931856631 0.0692549971 0.0459275911 0.8168377630 -0.570850655379 +1413394912205760512.0000000000 -1.0499887591 -0.1114860840 1.8939781864 0.0717091657 0.0515663235 0.8316747463 -0.548193237955 +1413394912255760384.0000000000 -1.0538696732 -0.0958133603 1.8964990555 0.0764450898 0.0575107825 0.8420506971 -0.53084770096 +1413394912305760512.0000000000 -1.0569961749 -0.0844280400 1.9003589186 0.0813446380 0.0656277531 0.8488176050 -0.518251600476 +1413394912355760384.0000000000 -1.0596630654 -0.0774197808 1.9045282524 0.0878911222 0.0735983698 0.8520797335 -0.510703983068 +1413394912405760512.0000000000 -1.0618984148 -0.0760418270 1.9100662955 0.0916095575 0.0862918352 0.8533695413 -0.505887175219 +1413394912455760384.0000000000 -1.0644170123 -0.0814042420 1.9180174355 0.0948338367 0.1007578828 0.8520503738 -0.504841116633 +1413394912505760512.0000000000 -1.0669386676 -0.0909011958 1.9273267662 0.0993786434 0.1142083636 0.8472187653 -0.509215768348 +1413394912555760384.0000000000 -1.0699688365 -0.1054995788 1.9390514564 0.1018336321 0.1295533668 0.8388283706 -0.51885720688 +1413394912605760512.0000000000 -1.0738466433 -0.1232460734 1.9513644970 0.1058363666 0.1439989686 0.8280606861 -0.531392943739 +1413394912655760384.0000000000 -1.0786900316 -0.1434881101 1.9649240264 0.1095937055 0.1590022122 0.8156459067 -0.54537076478 +1413394912705760512.0000000000 -1.0841946983 -0.1647555703 1.9778674424 0.1125882305 0.1730485318 0.8053784428 -0.555647064144 +1413394912755760384.0000000000 -1.0908191434 -0.1865734260 1.9907326063 0.1167447919 0.1859852555 0.7964239864 -0.563461597866 +1413394912805760512.0000000000 -1.0981386906 -0.2086427658 2.0035181055 0.1195634859 0.1979239172 0.7894674017 -0.56857006377 +1413394912855760384.0000000000 -1.1058297565 -0.2306615275 2.0157790676 0.1223470325 0.2063595916 0.7848382788 -0.571380607561 +1413394912905760512.0000000000 -1.1147864799 -0.2521953985 2.0273102011 0.1278715838 0.2113772596 0.7821667541 -0.571999721139 +1413394912955760384.0000000000 -1.1248470967 -0.2729938080 2.0376700433 0.1382730825 0.2117664195 0.7823201494 -0.56921939715 +1413394913005760512.0000000000 -1.1352878753 -0.2937257217 2.0482488271 0.1486320781 0.2097510002 0.7821578909 -0.567575595876 +1413394913055760384.0000000000 -1.1456434430 -0.3142079244 2.0590685843 0.1578318895 0.2075267674 0.7820830546 -0.566010451431 +1413394913105760512.0000000000 -1.1555711043 -0.3347679801 2.0697884830 0.1658439333 0.2052975402 0.7821903939 -0.564381871947 +1413394913155760384.0000000000 -1.1641607147 -0.3558319229 2.0809018293 0.1700980843 0.2019953945 0.7825692957 -0.563781695066 +1413394913205760512.0000000000 -1.1712276816 -0.3772839476 2.0922507137 0.1713325998 0.1976264187 0.7832636312 -0.563992041541 +1413394913255760384.0000000000 -1.1764528071 -0.3991564725 2.1040255982 0.1701257659 0.1911052348 0.7841856465 -0.565321930249 +1413394913305760512.0000000000 -1.1794904998 -0.4214203282 2.1167836622 0.1655365839 0.1817400348 0.7837870977 -0.570303414531 +1413394913355760384.0000000000 -1.1810496143 -0.4440352003 2.1299712152 0.1603922081 0.1699698641 0.7825211737 -0.577100682305 +1413394913405760512.0000000000 -1.1805095761 -0.4665670019 2.1419145571 0.1535451512 0.1561176737 0.7832489914 -0.581869552405 +1413394913455760384.0000000000 -1.1777221157 -0.4888132377 2.1514491672 0.1456895193 0.1391240418 0.7849745788 -0.585861737618 +1413394913505760512.0000000000 -1.1733303525 -0.5103749256 2.1576797943 0.1390176764 0.1195966551 0.7866417312 -0.589546870456 +1413394913555760384.0000000000 -1.1669643934 -0.5312319584 2.1608232281 0.1340725583 0.0972365221 0.7889623872 -0.591699213714 +1413394913605760512.0000000000 -1.1582841735 -0.5513089028 2.1611887771 0.1287103417 0.0733907536 0.7912462255 -0.593276373895 +1413394913655760384.0000000000 -1.1470630274 -0.5708596309 2.1585225419 0.1232010064 0.0485977443 0.7938317081 -0.593541060485 +1413394913705760512.0000000000 -1.1328583654 -0.5896695192 2.1527909065 0.1141574139 0.0262984620 0.7982453306 -0.590830659226 +1413394913755760384.0000000000 -1.1154701782 -0.6079487509 2.1436909512 0.1016776141 0.0058756133 0.8039047406 -0.585972958426 +1413394913805760512.0000000000 -1.0947242185 -0.6259637835 2.1322452383 0.0848298218 -0.0121233351 0.8088891568 -0.58168312512 +1413394913855760384.0000000000 -1.0711963247 -0.6441418130 2.1182608415 0.0643737903 -0.0266832490 0.8134184381 -0.577489795506 +1413394913905760512.0000000000 -1.0454489664 -0.6628869908 2.1022636189 0.0434489478 -0.0399228081 0.8168489337 -0.573825912486 +1413394913955760384.0000000000 -1.0177311438 -0.6825941010 2.0850811669 0.0216644040 -0.0522063056 0.8180567427 -0.572353318356 +1413394914005760512.0000000000 -0.9889567419 -0.7024110635 2.0658036809 0.0015120922 -0.0647904070 0.8179466110 -0.571632100458 +1413394914055760384.0000000000 -0.9595268012 -0.7230205431 2.0449597945 0.0151710045 0.0786347094 -0.8167130259 0.5714597593 +1413394914105760512.0000000000 -0.9291949181 -0.7437902974 2.0240366598 0.0293219637 0.0946643948 -0.8141199100 0.572177985347 +1413394914155760384.0000000000 -0.8985550376 -0.7647658284 2.0050604107 0.0394684219 0.1133746383 -0.8109336901 0.572691003414 +1413394914205760512.0000000000 -0.8669622418 -0.7860819074 1.9895222801 0.0477157665 0.1333428426 -0.8062588502 0.574360129555 +1413394914255760384.0000000000 -0.8341056072 -0.8070333075 1.9776377152 0.0549950485 0.1539536561 -0.8023086653 0.574085901312 +1413394914305760512.0000000000 -0.7994026482 -0.8274494274 1.9702756350 0.0636918175 0.1737415862 -0.7970560263 0.574855551043 +1413394914355760384.0000000000 -0.7628618792 -0.8475240580 1.9660894154 0.0708451518 0.1931220197 -0.7920793936 0.574713045123 +1413394914405760512.0000000000 -0.7240310562 -0.8667981769 1.9666962601 0.0787325678 0.2122908686 -0.7864963162 0.574593173 +1413394914455760384.0000000000 -0.6834360794 -0.8849817259 1.9703986567 0.0876594517 0.2291018924 -0.7817445922 0.573326727056 +1413394914505760512.0000000000 -0.6402656322 -0.9030428625 1.9781028935 0.0947537378 0.2449825223 -0.7757587837 0.573762670855 +1413394914555760384.0000000000 -0.5947250630 -0.9190553500 1.9875317517 0.1057091231 0.2562656550 -0.7733032086 0.570224204152 +1413394914605760512.0000000000 -0.5473778929 -0.9336937893 1.9971414864 0.1198619376 0.2622676515 -0.7710574567 0.567731620943 +1413394914655760384.0000000000 -0.4988618287 -0.9471430539 2.0039650732 0.1340641714 0.2668487728 -0.7698697222 0.564020514979 +1413394914705760512.0000000000 -0.4496945889 -0.9597651747 2.0081175999 0.1461959184 0.2720325860 -0.7676390456 0.561565064157 +1413394914755760384.0000000000 -0.3994602470 -0.9716782622 2.0096641208 0.1589738876 0.2762619903 -0.7662300951 0.557940908334 +1413394914805760512.0000000000 -0.3489979787 -0.9827105727 2.0086178021 0.1693437641 0.2822404796 -0.7635709513 0.555537940674 +1413394914855760384.0000000000 -0.2981225913 -0.9938020107 2.0047964787 0.1768895466 0.2894021842 -0.7610639404 0.552935930042 +1413394914905760512.0000000000 -0.2473186722 -1.0045450110 1.9980763823 0.1809742099 0.2987098984 -0.7563027161 0.553197011607 +1413394914955760384.0000000000 -0.1965587786 -1.0143169777 1.9878112982 0.1847638699 0.3085708101 -0.7508216232 0.55399752491 +1413394915005760512.0000000000 -0.1456172181 -1.0230782647 1.9741788938 0.1867005306 0.3199394372 -0.7442287039 0.55579250141 +1413394915055760384.0000000000 -0.0942985775 -1.0294651251 1.9589287957 0.1879279085 0.3334738344 -0.7353764076 0.559195709974 +1413394915105760512.0000000000 -0.0421210579 -1.0335790200 1.9436587464 0.1901856248 0.3478263395 -0.7260714670 0.561842051136 +1413394915155760384.0000000000 0.0109259447 -1.0349048975 1.9286495925 0.1914544018 0.3644051285 -0.7179075366 0.561393697175 +1413394915205760512.0000000000 0.0652576316 -1.0337226976 1.9150256525 0.1927343684 0.3816453965 -0.7086916602 0.561209751594 +1413394915255760384.0000000000 0.1211599973 -1.0289855582 1.9022167044 0.1954578424 0.3988283487 -0.6998140251 0.559457335672 +1413394915305760512.0000000000 0.1784419763 -1.0201054749 1.8911234175 0.2005452018 0.4152750968 -0.6900349168 0.55783512759 +1413394915355760384.0000000000 0.2367699757 -1.0072992423 1.8809276937 0.2057942414 0.4303844092 -0.6803443747 0.556371748319 +1413394915405760512.0000000000 0.2966422079 -0.9897343443 1.8721250149 0.2139772083 0.4445982176 -0.6699466853 0.554723010231 +1413394915455760384.0000000000 0.3575085502 -0.9679042456 1.8641990827 0.2218003984 0.4583019868 -0.6594984863 0.553015025734 +1413394915505760512.0000000000 0.4195018400 -0.9409776888 1.8574067149 0.2312777866 0.4706913240 -0.6488428206 0.551328629021 +1413394915555760384.0000000000 0.4828910140 -0.9081825529 1.8526421234 0.2481822019 0.4802081185 -0.6388782095 0.547394182502 +1413394915605760512.0000000000 0.5467984121 -0.8698325823 1.8493179280 0.2723809943 0.4861298061 -0.6303678641 0.540483821682 +1413394915655760384.0000000000 0.6100471792 -0.8269355434 1.8465253267 0.2996451941 0.4903145569 -0.6234005217 0.530260485527 +1413394915705760512.0000000000 0.6715064794 -0.7802263279 1.8440948739 0.3270144537 0.4955731293 -0.6149953331 0.518892629454 +1413394915755760384.0000000000 0.7304494112 -0.7311402085 1.8414758677 0.3515325624 0.5028754569 -0.6053351846 0.507060594782 +1413394915805760512.0000000000 0.7863790854 -0.6807103219 1.8400759559 0.3730848897 0.5108582170 -0.5910599086 0.500479501757 +1413394915855760384.0000000000 0.8386424470 -0.6287822046 1.8394404831 0.3937174489 0.5189214904 -0.5753288163 0.494675459573 +1413394915905760512.0000000000 0.8870823331 -0.5762310109 1.8392197964 0.4109491036 0.5281920854 -0.5593636388 0.489128076041 +1413394915955760384.0000000000 0.9313323122 -0.5234799385 1.8390106275 0.4247071623 0.5383057068 -0.5445509452 0.483026976949 +1413394916005760512.0000000000 0.9712929150 -0.4702604038 1.8389316502 0.4378138975 0.5478696474 -0.5322933189 0.474153628369 +1413394916055760384.0000000000 1.0064820264 -0.4172018021 1.8392093949 0.4482414531 0.5575907422 -0.5205939313 0.46599798562 +1413394916105760512.0000000000 1.0371854803 -0.3640891171 1.8406805174 0.4597488259 0.5645368055 -0.5105704595 0.457435261169 +1413394916155760384.0000000000 1.0625367725 -0.3115378378 1.8415395117 0.4648362633 0.5750498123 -0.5033769415 0.447053259159 +1413394916205760512.0000000000 1.0834144358 -0.2593142960 1.8413364105 0.4648009894 0.5889045035 -0.5003431841 0.432213169824 +1413394916255760384.0000000000 1.1005985705 -0.2075640390 1.8416440487 0.4634330003 0.6025327265 -0.4972650781 0.418224353553 +1413394916305760512.0000000000 1.1146306384 -0.1559846557 1.8422919439 0.4606053144 0.6173413603 -0.4950108428 0.402115225643 +1413394916355760384.0000000000 1.1265546862 -0.1044518313 1.8439208678 0.4629439510 0.6280687989 -0.4935904263 0.384162690916 +1413394916405760512.0000000000 1.1369425055 -0.0533596455 1.8449928401 0.4684081882 0.6361255113 -0.4933510146 0.364064389218 +1413394916455760384.0000000000 1.1461664983 -0.0030449147 1.8443436414 0.4776562646 0.6412055501 -0.4948055574 0.340393001964 +1413394916505760512.0000000000 1.1552911064 0.0453503894 1.8416791980 0.4875472442 0.6454170306 -0.4945896782 0.317986778773 +1413394916555760384.0000000000 1.1652239011 0.0914877351 1.8374944940 0.5025856114 0.6453217205 -0.4930651874 0.29640226266 +1413394916605760512.0000000000 1.1760251555 0.1346805986 1.8313920738 0.5211136238 0.6425583414 -0.4905103979 0.273786264234 +1413394916655760384.0000000000 1.1878917436 0.1736206179 1.8224493369 0.5386882410 0.6410941389 -0.4846550458 0.252829528968 +1413394916705760512.0000000000 1.2001854358 0.2073370608 1.8086744247 0.5483805264 0.6469916595 -0.4750536971 0.234530543182 +1413394916755760384.0000000000 1.2139551956 0.2352560174 1.7916130302 0.5531436061 0.6580850668 -0.4598442274 0.222484791498 +1413394916855760384.0000000000 1.2466308757 0.2744894677 1.7488791057 0.5509380522 0.6891092239 -0.4246016481 0.20324660044 +1413394916955760384.0000000000 1.2867371878 0.2958758701 1.6942451965 0.5411572512 0.7233353724 -0.3851855628 0.188591756643 +1413394917055760384.0000000000 1.3371171874 0.3053748357 1.6354758411 0.5301653471 0.7565263920 -0.3322359201 0.190294025976 +1413394917155760384.0000000000 1.3939816733 0.3117440447 1.5801806456 0.5205423226 0.7850603946 -0.2826276836 0.18121109134 +1413394917255760384.0000000000 1.4560111793 0.3212021555 1.5287665158 0.5108082140 0.8087384354 -0.2351824471 0.172355238339 +1413394917355760384.0000000000 1.5205763700 0.3397992975 1.4832751683 0.5071271037 0.8233519031 -0.1989301069 0.159187175621 +1413394917455760384.0000000000 1.5865059097 0.3696745459 1.4417932757 0.5071673610 0.8309354015 -0.1760533712 0.146057649783 +1413394917555760384.0000000000 1.6540085083 0.4123832248 1.4040115857 0.5141878579 0.8307160454 -0.1535962515 0.148087441092 +1413394917655760384.0000000000 1.7209944519 0.4713942502 1.3711603792 0.5222705691 0.8272385811 -0.1356732381 0.156532919978 +1413394917755760384.0000000000 1.7809743458 0.5433580357 1.3482502946 0.5274586212 0.8236859093 -0.1262710139 0.165482799128 +1413394917855760384.0000000000 1.8288394900 0.6249574976 1.3372078640 0.5310498838 0.8198553435 -0.1101976724 0.183520324809 +1413394917955760384.0000000000 1.8592552604 0.7181526752 1.3341824856 0.5300567582 0.8204661490 -0.0927308290 0.193070258727 +1413394918055760384.0000000000 1.8701033148 0.8199432512 1.3268069506 0.5314313519 0.8225419470 -0.0831332954 0.18464646967 +1413394918155760384.0000000000 1.8616073881 0.9313606298 1.3141615881 0.5383878687 0.8246801732 -0.0886302501 0.148948962674 +1413394918255760384.0000000000 1.8415814902 1.0490133335 1.3012718326 0.5462582933 0.8254037707 -0.0926308145 0.108305237442 +1413394918355760384.0000000000 1.8172206118 1.1708464521 1.2895555599 0.5457218551 0.8295622351 -0.1019885697 0.0601039649205 +1413394918455760384.0000000000 1.7981121776 1.2963669438 1.2797013060 0.5475865156 0.8300303925 -0.1038035158 0.0205763341352 +1413394918555760384.0000000000 1.7913568128 1.4250044004 1.2712138801 0.5526139989 0.8286388112 -0.0893009060 -0.000914845100387 +1413394918655760384.0000000000 1.7976598315 1.5556837195 1.2628436571 0.5558411978 0.8291086011 -0.0597941068 -0.00664494525927 +1413394918755760384.0000000000 1.8140950618 1.6874935727 1.2549274687 0.5598633730 0.8282727445 -0.0226535996 -0.00201960261763 +1413394918855760384.0000000000 1.8354681032 1.8206953677 1.2515682329 0.5702273079 0.8213498854 0.0132686723 0.00700895718084 +1413394918955760384.0000000000 1.8550037225 1.9540017927 1.2602387433 0.5883406277 0.8074267090 0.0423087898 0.0112863478868 +1413394919055760384.0000000000 1.8666782998 2.0810529962 1.2870903194 0.6034470622 0.7952780316 0.0580067589 -0.00443975871781 +1413394919155760384.0000000000 1.8720929834 2.1953606087 1.3311221670 0.6144384990 0.7852080569 0.0716887613 -0.0278273216219 +1413394919255760384.0000000000 1.8746036455 2.2940742128 1.3913641993 0.6230809111 0.7751736318 0.0907169988 -0.0514436093804 +1413394919355760384.0000000000 1.8767969202 2.3765675974 1.4587677558 0.6327102737 0.7622524913 0.1197341573 -0.0656702411376 +1413394919455760384.0000000000 1.8787388146 2.4417447315 1.5281268711 0.6391557257 0.7498743048 0.1569036439 -0.0674517000646 +1413394919555760384.0000000000 1.8767735855 2.4862570821 1.5944407790 0.6252818138 0.7525800966 0.1950507749 -0.067831015772 +1413394919655760384.0000000000 1.8675987616 2.5111261856 1.6536777012 0.5963244472 0.7669709053 0.2209950318 -0.0855218105561 +1413394919755760384.0000000000 1.8498561132 2.5246889596 1.7044895941 0.5648723988 0.7818038992 0.2365893695 -0.117163588444 +1413394919855760384.0000000000 1.8253964022 2.5351921321 1.7460788296 0.5334353398 0.7940189390 0.2495696543 -0.150650756669 +1413394919955760384.0000000000 1.7961097860 2.5487899869 1.7768660302 0.5104610499 0.7961973700 0.2723723547 -0.176953567278 +1413394920055760384.0000000000 1.7630134310 2.5680296982 1.7965691690 0.4930198908 0.7904236416 0.3033581798 -0.200338884936 +1413394920155760384.0000000000 1.7253121526 2.5942133043 1.8038176588 0.4773082920 0.7805444446 0.3370359210 -0.222112476885 +1413394920255760384.0000000000 1.6820629692 2.6286689598 1.7982373749 0.4648121807 0.7664362512 0.3739284799 -0.238123080593 +1413394920355760384.0000000000 1.6310101849 2.6716241499 1.7837665396 0.4663755811 0.7428067413 0.4103777211 -0.249643923428 +1413394920455760384.0000000000 1.5700965304 2.7190900577 1.7682231571 0.4736996584 0.7165987442 0.4413725802 -0.259393752466 +1413394920555760384.0000000000 1.4990343598 2.7666760195 1.7555011135 0.4839154958 0.6900995727 0.4686674914 -0.264460120345 +1413394920655760384.0000000000 1.4186605822 2.8097774145 1.7462857378 0.4940949375 0.6685792667 0.4906365259 -0.261051252167 +1413394920755760384.0000000000 1.3284934995 2.8417849834 1.7414010319 0.4981584229 0.6567359978 0.5047389705 -0.256465566111 +1413394920855760384.0000000000 1.2292134508 2.8589887289 1.7384926184 0.4909064786 0.6589218109 0.5069374539 -0.260475131732 +1413394920955760384.0000000000 1.1203100031 2.8646524355 1.7308786074 0.4854286657 0.6636365536 0.5034560545 -0.265476056056 +1413394921055760384.0000000000 1.0003984611 2.8611439010 1.7166018798 0.4759977512 0.6750707869 0.4924317169 -0.274256408506 +1413394921155760384.0000000000 0.8729835824 2.8516181222 1.6971435002 0.4729568165 0.6838276989 0.4722952967 -0.292623786719 +1413394921255760384.0000000000 0.7409092563 2.8408368984 1.6684430866 0.4680137054 0.6940720571 0.4495973578 -0.311591666988 +1413394921355760384.0000000000 0.6081098501 2.8324311773 1.6290627796 0.4453017758 0.7158489121 0.4195696794 -0.336493607098 +1413394921455760384.0000000000 0.4763702409 2.8364406463 1.5804119535 0.4227748406 0.7354175823 0.3925486767 -0.355426434256 +1413394921555760384.0000000000 0.3492153221 2.8603475052 1.5181522058 0.4199091019 0.7428501499 0.3895024995 -0.346609007132 +1413394921655760384.0000000000 0.2250547872 2.9066533522 1.4521439037 0.4502336922 0.7294383010 0.4055335099 -0.317414492055 +1413394921755760384.0000000000 0.1020843364 2.9643572835 1.3878574654 0.4857243630 0.7084301471 0.4223650684 -0.289493210288 +1413394921855760384.0000000000 -0.0219450838 3.0206175068 1.3309971273 0.5113683265 0.6869331853 0.4319915203 -0.282857844102 +1413394921955760384.0000000000 -0.1462615737 3.0675051176 1.2850845292 0.5239987598 0.6665409691 0.4299444451 -0.310316306972 +1413394922055760384.0000000000 -0.2615943107 3.1054889079 1.2518600415 0.5193299748 0.6515003304 0.4313659940 -0.346073801427 +1413394922155760384.0000000000 -0.3618409845 3.1390303274 1.2332422802 0.5081075209 0.6361107683 0.4495547707 -0.367546386024 +1413394922255760384.0000000000 -0.4441054300 3.1701583638 1.2245330850 0.4871524301 0.6265218350 0.4840465964 -0.368580781672 +1413394922355760384.0000000000 -0.5162302955 3.2010013679 1.2307960792 0.4722142808 0.6140650711 0.5240051099 -0.354057066373 +1413394922455760384.0000000000 -0.5869968818 3.2273185460 1.2574511419 0.4652400336 0.6004702452 0.5516492476 -0.344485563466 +1413394922555760384.0000000000 -0.6605880924 3.2434410360 1.3060044251 0.4529963840 0.5963412292 0.5621492489 -0.350941072581 +1413394922655760384.0000000000 -0.7366603217 3.2516296153 1.3636957947 0.4357665736 0.6007446848 0.5601339258 -0.368053395754 +1413394922755760384.0000000000 -0.8147037626 3.2575585429 1.4196222561 0.4202267706 0.6067935587 0.5602340925 -0.375963828071 +1413394922855760384.0000000000 -0.8958512066 3.2646530653 1.4749238760 0.4080706534 0.6125559900 0.5634652954 -0.375180439004 +1413394922955760384.0000000000 -0.9822793490 3.2738688092 1.5301018031 0.4029445883 0.6153945441 0.5663710130 -0.371684125948 +1413394923055760384.0000000000 -1.0758965737 3.2845814815 1.5787764901 0.3979544890 0.6187584911 0.5692995358 -0.36697165133 +1413394923155760384.0000000000 -1.1774943437 3.2969913910 1.6165791471 0.4010540629 0.6178019637 0.5709168028 -0.362671168671 +1413394923255760384.0000000000 -1.2888263296 3.3109164697 1.6535958765 0.4236506125 0.6033636230 0.5724246185 -0.358890725785 +1413394923355760384.0000000000 -1.4048992346 3.3198379854 1.6926733496 0.4354430055 0.5959293286 0.5704734839 -0.360302135098 +1413394923455760384.0000000000 -1.5217090345 3.3203407161 1.7310938811 0.4225429454 0.6001034126 0.5727585172 -0.365076751566 +1413394923555760384.0000000000 -1.6416486938 3.3154720514 1.7693517592 0.4042322400 0.6003984192 0.5830964752 -0.368939744396 +1413394923655760384.0000000000 -1.7683289049 3.3080819628 1.8049596736 0.3967777142 0.5860321023 0.5976822249 -0.37670914334 +1413394923755760384.0000000000 -1.9012118011 3.2979730203 1.8313038888 0.3992681096 0.5596803209 0.6143771801 -0.387148027971 +1413394923855760384.0000000000 -2.0370849272 3.2818550708 1.8474120339 0.3975772817 0.5328764405 0.6300086977 -0.401327852304 +1413394923955760384.0000000000 -2.1734843426 3.2593952506 1.8536001986 0.3914676955 0.5072113018 0.6445130609 -0.417244116764 +1413394924055760384.0000000000 -2.3076892426 3.2300973346 1.8501300434 0.3807890496 0.4829589443 0.6586454014 -0.433516543122 +1413394924155760384.0000000000 -2.4387457865 3.1933808300 1.8458888369 0.3616900483 0.4629201824 0.6704029520 -0.453260516283 +1413394924255760384.0000000000 -2.5655828601 3.1509662834 1.8459209148 0.3327638197 0.4471725481 0.6815123143 -0.474179204517 +1413394924355760384.0000000000 -2.6891972993 3.1069810044 1.8489694661 0.3007282698 0.4314372075 0.6930916865 -0.492999348721 +1413394924455760384.0000000000 -2.8128063700 3.0655217297 1.8533210582 0.2817733265 0.4062495565 0.7059415192 -0.507160390627 +1413394924555760384.0000000000 -2.9357463960 3.0264096500 1.8591898762 0.2662434439 0.3788647961 0.7185410854 -0.518916759692 +1413394924655760384.0000000000 -3.0569334520 2.9892489613 1.8659590591 0.2548847256 0.3454868766 0.7352349071 -0.524501883773 +1413394924755760384.0000000000 -3.1756503266 2.9523482828 1.8754112495 0.2460930943 0.3090974510 0.7490469752 -0.531813485751 +1413394924855760384.0000000000 -3.2905932513 2.9138322680 1.8883505268 0.2455876183 0.2685309425 0.7569353604 -0.542795278996 +1413394924905760512.0000000000 -3.3448284354 2.8938590055 1.8958900671 0.2462344882 0.2487692904 0.7589327873 -0.549093290178 +1413394924955760384.0000000000 -3.3966726322 2.8737292379 1.9036395235 0.2495846042 0.2299923524 0.7609185330 -0.553004547266 +1413394925005760512.0000000000 -3.4454067826 2.8528981833 1.9125366764 0.2522584901 0.2141829321 0.7613090626 -0.557583928126 +1413394925055760384.0000000000 -3.4902367718 2.8318529724 1.9213933500 0.2578071254 0.1989318066 0.7624591528 -0.559122225175 +1413394925105760512.0000000000 -3.5296578038 2.8105601513 1.9293558107 0.2562666575 0.1901703854 0.7673299464 -0.556208034963 +1413394925155760384.0000000000 -3.5637619225 2.7879452984 1.9385375482 0.2522002684 0.1822667168 0.7731241725 -0.552677919199 +1413394925205760512.0000000000 -3.5929132951 2.7642823056 1.9483501084 0.2501381581 0.1730519944 0.7795865004 -0.54747492864 +1413394925255760384.0000000000 -3.6171347005 2.7390375229 1.9585808372 0.2469220893 0.1650426655 0.7857370695 -0.542593455528 +1413394925305760512.0000000000 -3.6370557365 2.7117030820 1.9684187088 0.2450210243 0.1569412618 0.7905095749 -0.538914417974 +1413394925355760384.0000000000 -3.6528763677 2.6820944964 1.9769016693 0.2443613594 0.1495433404 0.7936645018 -0.536675855535 +1413394925405760512.0000000000 -3.6644517597 2.6500377425 1.9833403951 0.2404779573 0.1468583679 0.7954779929 -0.536486471982 +1413394925455760384.0000000000 -3.6717228598 2.6154975126 1.9875707322 0.2338669163 0.1471782706 0.7962140119 -0.538226782535 +1413394925505760512.0000000000 -3.6754144367 2.5785988745 1.9894117464 0.2269331356 0.1496864134 0.7967226208 -0.539748455436 +1413394925555760384.0000000000 -3.6757394199 2.5393127498 1.9891112975 0.2204896559 0.1518165019 0.7965818608 -0.542027121499 +1413394925605760512.0000000000 -3.6726420098 2.4985736921 1.9860896102 0.2146654193 0.1529604504 0.7968335343 -0.543671019031 +1413394925655760384.0000000000 -3.6662215689 2.4566346976 1.9809521158 0.2076366646 0.1555618325 0.7968085111 -0.545695637109 +1413394925705760512.0000000000 -3.6564442079 2.4129306274 1.9751877553 0.1951447923 0.1628746224 0.7959479988 -0.549415280703 +1413394925755760384.0000000000 -3.6442993696 2.3680877807 1.9698551193 0.1822358891 0.1715515884 0.7947859316 -0.552879241934 +1413394925805760512.0000000000 -3.6306198936 2.3222245674 1.9649673200 0.1708615927 0.1794964428 0.7934967406 -0.555832947801 +1413394925855760384.0000000000 -3.6161881578 2.2758383535 1.9601445534 0.1625778555 0.1860903091 0.7925940935 -0.557434696373 +1413394925905760512.0000000000 -3.6009954832 2.2291950732 1.9554592078 0.1555862121 0.1899860745 0.7924058851 -0.558382606643 +1413394925955760384.0000000000 -3.5858390713 2.1825501373 1.9510803932 0.1510502491 0.1914105425 0.7923100219 -0.559276904265 +1413394926005760512.0000000000 -3.5707045914 2.1357767130 1.9466425579 0.1490512333 0.1894370499 0.7935778711 -0.558687297566 +1413394926055760384.0000000000 -3.5557152637 2.0886305964 1.9420331390 0.1504384053 0.1836709192 0.7955271754 -0.557467302053 +1413394926105760512.0000000000 -3.5406649710 2.0414399638 1.9372410072 0.1535683746 0.1771499405 0.7981702770 -0.554940412799 +1413394926155760384.0000000000 -3.5252915569 1.9938541142 1.9328310887 0.1573163545 0.1709720681 0.8000397194 -0.553133405232 +1413394926205760512.0000000000 -3.5093137211 1.9455923042 1.9285347432 0.1619090981 0.1642472453 0.8023974430 -0.55042404544 +1413394926255760384.0000000000 -3.4920512658 1.8959896085 1.9250650040 0.1634559535 0.1603411464 0.8040178988 -0.548751388619 +1413394926305760512.0000000000 -3.4734555837 1.8452635130 1.9225313732 0.1601847368 0.1607670775 0.8056042264 -0.547262850223 +1413394926355760384.0000000000 -3.4537782771 1.7933335568 1.9201042607 0.1549933597 0.1624563024 0.8078693200 -0.544914828286 +1413394926405760512.0000000000 -3.4337083693 1.7400371993 1.9180820795 0.1505550950 0.1645302300 0.8097333587 -0.5427659298 +1413394926455760384.0000000000 -3.4131062125 1.6851817959 1.9165933610 0.1451032672 0.1658251373 0.8116414264 -0.541003937783 +1413394926505760512.0000000000 -3.3921663576 1.6284547809 1.9157297401 0.1389852523 0.1649859969 0.8127110193 -0.541261045738 +1413394926555760384.0000000000 -3.3708992043 1.5701345803 1.9154009928 0.1314630313 0.1619000460 0.8128091056 -0.543918380288 +1413394926605760512.0000000000 -3.3491730855 1.5104535880 1.9156398913 0.1201781814 0.1573257820 0.8132368655 -0.547221713456 +1413394926655760384.0000000000 -3.3274949816 1.4497366715 1.9167111370 0.1063954031 0.1515334318 0.8127038370 -0.552476343827 +1413394926705760512.0000000000 -3.3058172033 1.3885737027 1.9182845233 0.0869902279 0.1465623867 0.8118059274 -0.55850094297 +1413394926755760384.0000000000 -3.2852234707 1.3275338489 1.9199926044 0.0663996514 0.1401118409 0.8113188253 -0.563667918215 +1413394926805760512.0000000000 -3.2663001512 1.2667652647 1.9221581918 0.0439974018 0.1334077209 0.8111466629 -0.567721498523 +1413394926855760384.0000000000 -3.2500112222 1.2062442602 1.9252523686 0.0197444471 0.1274618426 0.8102763385 -0.571678135619 +1413394926905760512.0000000000 -3.2372234775 1.1467797594 1.9267618935 0.0002486601 -0.1185110556 -0.8099540875 0.574394850279 +1413394926955760384.0000000000 -3.2286401571 1.0877593874 1.9263755499 0.0181503605 -0.1096149255 -0.8102288056 0.575486242291 +1413394927005760512.0000000000 -3.2248609791 1.0293174801 1.9233630685 0.0311839619 -0.0998114078 -0.8106113256 0.576172302485 +1413394927055760384.0000000000 -3.2264158786 0.9705556465 1.9169760059 0.0338758080 -0.0858724617 -0.8107213094 0.57810838821 +1413394927105760512.0000000000 -3.2328545939 0.9116944929 1.9071897529 0.0254000309 -0.0664573116 -0.8109284600 0.58080400899 +1413394927155760384.0000000000 -3.2425474917 0.8536116854 1.8944966449 0.0156545804 -0.0483067621 -0.8120987813 0.581306253362 +1413394927205760512.0000000000 -3.2550782232 0.7957346977 1.8827765108 0.0045109666 -0.0312105945 -0.8115597452 0.583417800433 +1413394927255760384.0000000000 -3.2694119336 0.7379412379 1.8729336447 0.0070485831 0.0155361370 0.8113747573 -0.584277287953 +1413394927305760512.0000000000 -3.2842813905 0.6804567035 1.8680321767 0.0146902637 0.0049912998 0.8113036568 -0.584419078742 +1413394927355760384.0000000000 -3.2989600436 0.6245051855 1.8658232997 0.0207743238 -0.0031986718 0.8130045347 -0.581877841631 +1413394927405760512.0000000000 -3.3125816296 0.5675730649 1.8683900686 0.0214773598 -0.0065883724 0.8153931060 -0.578471606082 +1413394927455760384.0000000000 -3.3253448620 0.5099622106 1.8754804292 0.0206108797 -0.0079016255 0.8166805960 -0.576667633962 +1413394927505760512.0000000000 -3.3370380085 0.4526305749 1.8857192796 0.0183243947 -0.0072217867 0.8185373017 -0.574115622619 +1413394927555760384.0000000000 -3.3478559582 0.3957845236 1.8989672593 0.0160290325 -0.0059591435 0.8207358028 -0.57105192465 +1413394927605760512.0000000000 -3.3582290144 0.3387691736 1.9160850301 0.0142019577 -0.0043114821 0.8217792622 -0.569612640025 +1413394927655760384.0000000000 -3.3680837362 0.2817351460 1.9353327803 0.0123738078 -0.0038221809 0.8214544978 -0.570126992802 +1413394927705760512.0000000000 -3.3774170012 0.2245083618 1.9546788568 0.0110813492 -0.0048966623 0.8221964491 -0.56907488569 +1413394927755760384.0000000000 -3.3863515575 0.1665009679 1.9749257982 0.0092004015 -0.0057999539 0.8210281125 -0.570784155008 +1413394927805760512.0000000000 -3.3952971222 0.1079996284 1.9930133160 0.0109284955 -0.0091804985 0.8196665705 -0.572663076963 +1413394927855760384.0000000000 -3.4036776160 0.0491878546 2.0086017566 0.0118741392 -0.0117731571 0.8184450066 -0.574341508873 +1413394927905760512.0000000000 -3.4116177722 -0.0094925877 2.0211851738 0.0118707048 -0.0130027931 0.8183978718 -0.57438222221 +1413394927955760384.0000000000 -3.4190108838 -0.0687179608 2.0310990184 0.0112367342 -0.0137974571 0.8186542208 -0.574011004018 +1413394928005760512.0000000000 -3.4260211521 -0.1282839005 2.0385961083 0.0101497864 -0.0139991926 0.8181495396 -0.574745452562 +1413394928055760384.0000000000 -3.4329387734 -0.1876442463 2.0432491219 0.0129455903 -0.0167544027 0.8161388421 -0.577467827732 +1413394928105760512.0000000000 -3.4393998634 -0.2472992610 2.0459245425 0.0181922815 -0.0211461881 0.8129959407 -0.5816007909 +1413394928155760384.0000000000 -3.4449503215 -0.3068776764 2.0467110356 0.0245103412 -0.0261865627 0.8084674798 -0.587446883688 +1413394928205760512.0000000000 -3.4490851193 -0.3659518972 2.0462223771 0.0294791483 -0.0297875150 0.8023235677 -0.595416305137 +1413394928255760384.0000000000 -3.4513664716 -0.4241662149 2.0452303536 0.0345635889 -0.0338183855 0.7965199371 -0.602675422568 +1413394928305760512.0000000000 -3.4516516994 -0.4809361361 2.0453005728 0.0385338720 -0.0357762357 0.7904685033 -0.610241548102 +1413394928355760384.0000000000 -3.4495398086 -0.5352222509 2.0461767209 0.0406144325 -0.0366971625 0.7864939816 -0.615167459343 +1413394928405760512.0000000000 -3.4447660762 -0.5868315246 2.0481692069 0.0392436786 -0.0351407555 0.7844856604 -0.617905583135 +1413394928455760384.0000000000 -3.4374687074 -0.6352853919 2.0507596280 0.0325829957 -0.0294175227 0.7864191214 -0.616131417141 +1413394928505760512.0000000000 -3.4283022205 -0.6810646882 2.0542787135 0.0236411107 -0.0219402492 0.7894554198 -0.612959919965 +1413394928555760384.0000000000 -3.4181400601 -0.7246526015 2.0586773456 0.0174388971 -0.0164920315 0.7917455758 -0.610379259892 +1413394928605760512.0000000000 -3.4072424802 -0.7661749974 2.0631461110 0.0124663503 -0.0115363701 0.7947090874 -0.60675280684 +1413394928655760384.0000000000 -3.3960304746 -0.8062101019 2.0681703421 0.0089461778 -0.0075966394 0.7965385949 -0.604473757728 +1413394928705760512.0000000000 -3.3849296667 -0.8449319341 2.0730708261 0.0077091925 -0.0050556885 0.7982498778 -0.602255876626 +1413394928755760384.0000000000 -3.3738210837 -0.8824064860 2.0779217121 0.0078042595 -0.0035732317 0.7992473069 -0.600940985426 +1413394928805760512.0000000000 -3.3628932363 -0.9186245073 2.0816265889 0.0086340599 -0.0028005412 0.8002795665 -0.599558358612 +1413394928855760384.0000000000 -3.3524839127 -0.9539235273 2.0830297722 0.0133087369 -0.0045152905 0.8003075081 -0.599425043008 +1413394928905760512.0000000000 -3.3420762042 -0.9887538305 2.0819191111 0.0194746242 -0.0075685712 0.8001822922 -0.599392821877 +1413394928955760384.0000000000 -3.3311125847 -1.0231333343 2.0782590793 0.0228015414 -0.0087700357 0.8004749480 -0.598868127229 +1413394929005760512.0000000000 -3.3195330030 -1.0559562908 2.0722744128 0.0244102850 -0.0086552131 0.8007618351 -0.598422683932 +1413394929055760384.0000000000 -3.3069915780 -1.0873282709 2.0647975151 0.0245403824 -0.0081636792 0.7996897304 -0.599856198596 +1413394929105760512.0000000000 -3.2936237739 -1.1177402983 2.0569632544 0.0237365761 -0.0070335855 0.7970124833 -0.603455222107 +1413394929155760384.0000000000 -3.2795641207 -1.1469810529 2.0493334134 0.0233334343 -0.0061914282 0.7929668450 -0.608786333393 +1413394929205760512.0000000000 -3.2646001503 -1.1742326131 2.0423979629 0.0213011019 -0.0046432877 0.7892182208 -0.613725755389 +1413394929255760384.0000000000 -3.2491666430 -1.1993625284 2.0363700388 0.0177612252 -0.0017231797 0.7866490348 -0.6171425002 +1413394929305760512.0000000000 -3.2335502233 -1.2219393893 2.0314673282 0.0117343299 0.0024151637 0.7840808730 -0.620543034015 +1413394929355760384.0000000000 -3.2181865460 -1.2419039467 2.0270998050 0.0066040035 0.0059487772 0.7830515519 -0.62189329164 +1413394929405760512.0000000000 -3.2034928632 -1.2595491470 2.0236868192 0.0028774895 0.0089714342 0.7832930787 -0.621581198439 +1413394929455760384.0000000000 -3.1895065883 -1.2745266620 2.0208687752 0.0001764260 -0.0110176419 -0.7855441595 0.618707486578 +1413394929505760512.0000000000 -3.1765814797 -1.2871698517 2.0180698235 0.0025351994 -0.0126095536 -0.7907954395 0.611945377245 +1413394929555760384.0000000000 -3.1647854552 -1.2980114816 2.0152381645 0.0038343360 -0.0138145400 -0.7980433268 0.602429502047 +1413394929605760512.0000000000 -3.1541821654 -1.3075362232 2.0128545642 0.0045286757 -0.0144577607 -0.8050793232 0.592973648392 +1413394929655760384.0000000000 -3.1450936605 -1.3166158612 2.0110885052 0.0018382358 -0.0134223561 -0.8104130895 0.585702215842 +1413394929705760512.0000000000 -3.1369589139 -1.3260380247 2.0099930336 0.0026117036 0.0112029882 0.8135812047 -0.581337505658 +1413394929755760384.0000000000 -3.1294083866 -1.3357282955 2.0084306170 0.0066027963 0.0089449249 0.8156025973 -0.578505656519 +1413394929805760512.0000000000 -3.1224550545 -1.3462707674 2.0057265962 0.0103890495 0.0070547297 0.8160638636 -0.577825292818 +1413394929855760384.0000000000 -3.1157183996 -1.3571067300 2.0005628134 0.0131717102 0.0054938932 0.8150598101 -0.579201026547 +1413394929905760512.0000000000 -3.1089744232 -1.3686686206 1.9938873552 0.0144607406 0.0051404142 0.8124447736 -0.582836128762 +1413394929955760384.0000000000 -3.1020799992 -1.3801823257 1.9854267186 0.0153540329 0.0050278652 0.8079450919 -0.58903624906 +1413394930005760512.0000000000 -3.0952387832 -1.3914874070 1.9745002080 0.0168594920 0.0047130088 0.8027977764 -0.595994358379 +1413394930055760384.0000000000 -3.0885645006 -1.4012227037 1.9610532650 0.0185474520 0.0038738424 0.7980985255 -0.602228967286 +1413394930105760512.0000000000 -3.0818807717 -1.4095354603 1.9459214863 0.0204998045 0.0028582942 0.7942032169 -0.607299628247 +1413394930155760384.0000000000 -3.0750625448 -1.4164883836 1.9316182692 0.0224341550 0.0022930635 0.7892462576 -0.613662607199 +1413394930205760512.0000000000 -3.0676802097 -1.4214933311 1.9180905989 0.0241998322 0.0010378157 0.7843881338 -0.619797181799 +1413394930255760384.0000000000 -3.0596051551 -1.4245064162 1.9068642990 0.0237166441 0.0016457355 0.7781530099 -0.627624653394 +1413394930305760512.0000000000 -3.0506165027 -1.4244997841 1.8974802190 0.0184895492 0.0051634591 0.7728442260 -0.634305350412 +1413394930355760384.0000000000 -3.0416723219 -1.4211122489 1.8882163261 0.0117491000 0.0100185832 0.7724531894 -0.634883971114 +1413394930405760512.0000000000 -3.0330607957 -1.4144852926 1.8779416645 0.0046483395 0.0150050741 0.7807697268 -0.624621384845 +1413394930455760384.0000000000 -3.0254536088 -1.4052153178 1.8669869164 0.0010968363 -0.0193720299 -0.7945069839 0.606944951313 +1413394930505760512.0000000000 -3.0189866978 -1.3945916319 1.8551183827 0.0063629630 -0.0234794418 -0.8117658790 0.583476123031 +1413394930555760384.0000000000 -3.0138128282 -1.3834432500 1.8410885421 0.0110830749 -0.0275185319 -0.8294315510 0.557820040962 +1413394930605760512.0000000000 -3.0102376671 -1.3729262081 1.8245208548 0.0151864560 -0.0314264772 -0.8460596709 0.531944340497 +1413394930655760384.0000000000 -3.0085279248 -1.3645552633 1.8049858019 0.0173577031 -0.0347947163 -0.8594213973 0.509787112199 +1413394930705760512.0000000000 -3.0094449296 -1.3607478829 1.7841958498 0.0115112999 -0.0314427214 -0.8679784447 0.495471759886 +1413394930755760384.0000000000 -3.0125427320 -1.3636342530 1.7636192815 0.0025140084 -0.0260463193 -0.8702055705 0.491993428962 +1413394930805760512.0000000000 -3.0170432811 -1.3732973574 1.7442109750 0.0085373088 0.0189804400 0.8643939059 -0.502384347531 +1413394930855760384.0000000000 -3.0222184226 -1.3877629363 1.7257666707 0.0187878164 0.0127045907 0.8543754493 -0.519161056907 +1413394930905760512.0000000000 -3.0271390790 -1.4063187987 1.7093884852 0.0259164145 0.0088728649 0.8405374429 -0.541060457677 +1413394930955760384.0000000000 -3.0313227635 -1.4273871778 1.6956493861 0.0311211922 0.0053007402 0.8239727328 -0.565749334132 +1413394931005760512.0000000000 -3.0343664172 -1.4488738837 1.6844282595 0.0339588708 0.0038752315 0.8081946459 -0.587922777216 +1413394931055760384.0000000000 -3.0362629776 -1.4694526256 1.6757749242 0.0361506942 0.0030439347 0.7954943657 -0.604874016535 +1413394931105760512.0000000000 -3.0369607752 -1.4873673886 1.6703035350 0.0369286857 0.0029047407 0.7866426948 -0.616296280455 +1413394931155760384.0000000000 -3.0365951671 -1.5022538151 1.6675417811 0.0387787252 0.0028128500 0.7811846199 -0.623088186384 +1413394931205760512.0000000000 -3.0349098439 -1.5136148702 1.6686048792 0.0402248639 0.0030049155 0.7771123092 -0.628067981736 +1413394931255760384.0000000000 -3.0316001727 -1.5210714976 1.6737287087 0.0394569079 0.0041724728 0.7737412186 -0.632258071945 +1413394931305760512.0000000000 -3.0268738049 -1.5264266803 1.6844971345 0.0404469309 0.0044893117 0.7690586298 -0.637881427716 +1413394931355760384.0000000000 -3.0209174912 -1.5286534836 1.7014642591 0.0398692199 0.0062665227 0.7638567275 -0.644122718038 +1413394931405760512.0000000000 -3.0137149207 -1.5265733238 1.7207412679 0.0372338833 0.0086559407 0.7623602067 -0.646022931342 +1413394931455760384.0000000000 -3.0058955486 -1.5199747218 1.7380216332 0.0377118312 0.0099460341 0.7679931628 -0.639269423715 +1413394931505760512.0000000000 -2.9972274191 -1.5100180866 1.7524116513 0.0383456636 0.0114672694 0.7790821722 -0.625642933894 +1413394931555760384.0000000000 -2.9878838997 -1.4973184294 1.7638066217 0.0402112737 0.0115856395 0.7909377782 -0.61046396896 +1413394931605760512.0000000000 -2.9778327112 -1.4834272167 1.7730192295 0.0419304758 0.0109874293 0.8003861977 -0.597915584467 +1413394931655760384.0000000000 -2.9668770213 -1.4687009051 1.7800875750 0.0442691460 0.0076370242 0.8077090461 -0.58786734506 +1413394931705760512.0000000000 -2.9547761461 -1.4536885680 1.7850635296 0.0473188589 0.0004615290 0.8128921781 -0.580488604 +1413394931755760384.0000000000 -2.9411781853 -1.4390807846 1.7884390194 0.0514128867 -0.0110604892 0.8162361473 -0.575319852288 +1413394931805760512.0000000000 -2.9253188033 -1.4249561749 1.7901258454 0.0543526355 -0.0251128864 0.8180628354 -0.572003786138 +1413394931855760384.0000000000 -2.9065003611 -1.4113487400 1.7905550239 0.0526706374 -0.0397419765 0.8191824206 -0.569724969637 +1413394931905760512.0000000000 -2.8842869535 -1.3985712744 1.7893702112 0.0441863141 -0.0521851209 0.8199934019 -0.568273792832 +1413394931955760384.0000000000 -2.8587887820 -1.3872211581 1.7881288474 0.0301231370 -0.0634690170 0.8199243039 -0.568144714275 +1413394932005760512.0000000000 -2.8304078734 -1.3767997887 1.7884511294 0.0126770288 -0.0747387224 0.8176382646 -0.570719795124 +1413394932055760384.0000000000 -2.7996769113 -1.3665452258 1.7921280727 0.0060917038 0.0871505544 -0.8128616076 0.575867761664 +1413394932105760512.0000000000 -2.7668929469 -1.3562319164 1.8000739520 0.0273817888 0.0995695904 -0.8058124700 0.583097245333 +1413394932155760384.0000000000 -2.7329096467 -1.3455503134 1.8116403571 0.0496434127 0.1121998879 -0.7993760905 0.588170538819 +1413394932205760512.0000000000 -2.6983724687 -1.3343742580 1.8270738362 0.0725619974 0.1242520400 -0.7923403945 0.592868354981 +1413394932255760384.0000000000 -2.6640508518 -1.3223473896 1.8451378160 0.0973194334 0.1352591849 -0.7867272673 0.594385470632 +1413394932305760512.0000000000 -2.6310540489 -1.3096008895 1.8658065921 0.1190221305 0.1482654054 -0.7788082972 0.597753074638 +1413394932355760384.0000000000 -2.5999789473 -1.2958590256 1.8867710426 0.1384411730 0.1627050863 -0.7713752087 0.599450901976 +1413394932405760512.0000000000 -2.5712725418 -1.2814786564 1.9075074782 0.1532367785 0.1790397053 -0.7622677243 0.602835956214 +1413394932455760384.0000000000 -2.5447981935 -1.2656550755 1.9261431204 0.1666830045 0.1956822040 -0.7524105212 0.606468184314 +1413394932505760512.0000000000 -2.5210601909 -1.2480521393 1.9420589614 0.1778249160 0.2129137360 -0.7428708530 0.609252768531 +1413394932555760384.0000000000 -2.5000009424 -1.2283754017 1.9550828971 0.1884258588 0.2291734778 -0.7338862321 0.611053361909 +1413394932605760512.0000000000 -2.4818039145 -1.2064816253 1.9646351612 0.1972887169 0.2459816947 -0.7258247313 0.611349840499 +1413394932655760384.0000000000 -2.4660669245 -1.1821851438 1.9710813309 0.2061599102 0.2622245583 -0.7201115222 0.608420716385 +1413394932705760512.0000000000 -2.4528000181 -1.1555335981 1.9753718864 0.2140412477 0.2778880172 -0.7161913613 0.603352739446 +1413394932755760384.0000000000 -2.4418801892 -1.1265923440 1.9789206266 0.2201927301 0.2945683283 -0.7143209931 0.595390779562 +1413394932805760512.0000000000 -2.4331365513 -1.0955182333 1.9828578854 0.2255690915 0.3102018875 -0.7155340470 0.583870192309 +1413394932855760384.0000000000 -2.4263031679 -1.0626744855 1.9872209892 0.2299209874 0.3254123646 -0.7190662490 0.569374096819 +1413394932905760512.0000000000 -2.4209073074 -1.0285652083 1.9920668308 0.2345163974 0.3393116912 -0.7223691798 0.555024687358 +1413394932955760384.0000000000 -2.4162876934 -0.9941094294 1.9963757645 0.2383555946 0.3521674702 -0.7251365426 0.541610263922 +1413394933005760512.0000000000 -2.4115814301 -0.9599572318 1.9996847052 0.2434134616 0.3637345610 -0.7263685348 0.529939437537 +1413394933055760384.0000000000 -2.4063306861 -0.9263272690 2.0012811051 0.2492193740 0.3744788856 -0.7258222358 0.520420358827 +1413394933105760512.0000000000 -2.4006169740 -0.8932614088 2.0007591570 0.2546527684 0.3854192638 -0.7233625404 0.513176961529 +1413394933155760384.0000000000 -2.3944760547 -0.8607697743 1.9982802809 0.2615211618 0.3963444316 -0.7191910620 0.507229720872 +1413394933205760512.0000000000 -2.3873580927 -0.8292657992 1.9938015489 0.2692768081 0.4060385181 -0.7133186100 0.503784957144 +1413394933255760384.0000000000 -2.3800816380 -0.7982792847 1.9867474891 0.2781950100 0.4152425282 -0.7067243491 0.500721353199 +1413394933305760512.0000000000 -2.3726643333 -0.7678662379 1.9769912577 0.2859118473 0.4247757086 -0.6989811345 0.499244816339 +1413394933355760384.0000000000 -2.3650130437 -0.7381346362 1.9643499729 0.2930758637 0.4339418231 -0.6912002269 0.498039434749 +1413394933405760512.0000000000 -2.3571965504 -0.7089852534 1.9491408434 0.3005359719 0.4424141940 -0.6836632130 0.496540453279 +1413394933455760384.0000000000 -2.3497400068 -0.6800934048 1.9307957761 0.3071397345 0.4508560033 -0.6764551812 0.494775136481 +1413394933505760512.0000000000 -2.3423165163 -0.6512870328 1.9101052328 0.3139671229 0.4585606770 -0.6698404615 0.492402789765 +1413394933555760384.0000000000 -2.3348266504 -0.6226689529 1.8871473028 0.3206467687 0.4663578437 -0.6634412897 0.489429940241 +1413394933605760512.0000000000 -2.3273023333 -0.5941865315 1.8644805295 0.3280576493 0.4737204005 -0.6562807210 0.487096269866 +1413394933655760384.0000000000 -2.3200138182 -0.5658394621 1.8430424976 0.3370650783 0.4798887826 -0.6479076049 0.486116883865 +1413394933705760512.0000000000 -2.3130808173 -0.5378309993 1.8229222592 0.3460224941 0.4854884431 -0.6387521565 0.486379571776 +1413394933755760384.0000000000 -2.3068922748 -0.5098286517 1.8043304729 0.3553180969 0.4897492203 -0.6303410223 0.486379426844 +1413394933805760512.0000000000 -2.3021010188 -0.4819612743 1.7864853404 0.3625378144 0.4937329008 -0.6231858329 0.486244355675 +1413394933855760384.0000000000 -2.2993630531 -0.4539916877 1.7691494904 0.3675519744 0.4983286278 -0.6180230484 0.484377576414 +1413394933905760512.0000000000 -2.2987314111 -0.4257479241 1.7518450835 0.3701806871 0.5054013821 -0.6145397118 0.479454528001 +1413394933955760384.0000000000 -2.3002217762 -0.3972079703 1.7341805510 0.3693724284 0.5153768562 -0.6131275585 0.471195609388 +1413394934005760512.0000000000 -2.3031666845 -0.3683176432 1.7175079127 0.3694579702 0.5256941129 -0.6112392299 0.462096431259 +1413394934055760384.0000000000 -2.3066752539 -0.3390567654 1.7019318938 0.3710478401 0.5359759121 -0.6083594451 0.452716365444 +1413394934105760512.0000000000 -2.3096285155 -0.3096863325 1.6888037423 0.3768675698 0.5436434562 -0.6022137513 0.446946557428 +1413394934155760384.0000000000 -2.3120337729 -0.2804382851 1.6774699034 0.3862080119 0.5497064918 -0.5923884629 0.444681968889 +1413394934205760512.0000000000 -2.3147222394 -0.2511638661 1.6652178498 0.3966806875 0.5551444397 -0.5817318911 0.442772052018 +1413394934255760384.0000000000 -2.3186795662 -0.2217874095 1.6503252225 0.4059404361 0.5618690949 -0.5711525873 0.439659191372 +1413394934305760512.0000000000 -2.3239215994 -0.1923347736 1.6319436277 0.4130457299 0.5708582192 -0.5612226900 0.434215627064 +1413394934355760384.0000000000 -2.3304594035 -0.1628184901 1.6106639205 0.4195204936 0.5809164016 -0.5533687746 0.424643013626 +1413394934405760512.0000000000 -2.3382354033 -0.1333589496 1.5867006817 0.4254570414 0.5909481108 -0.5478024108 0.411921297031 +1413394934455760384.0000000000 -2.3466389741 -0.1045524788 1.5602124766 0.4309741387 0.6000030065 -0.5429023359 0.399392961487 +1413394934505760512.0000000000 -2.3552973964 -0.0769686357 1.5306484763 0.4347377842 0.6081260677 -0.5379693785 0.389582715989 +1413394934555760384.0000000000 -2.3627445008 -0.0504848045 1.4991433309 0.4367507650 0.6156912188 -0.5323151511 0.383162722914 +1413394934605760512.0000000000 -2.3698839641 -0.0249900041 1.4669776009 0.4376822572 0.6229941300 -0.5261048110 0.378848628943 +1413394934655760384.0000000000 -2.3763543263 -0.0003832276 1.4367268674 0.4377409766 0.6293222548 -0.5200631655 0.376657192789 +1413394934705760512.0000000000 -2.3829554540 0.0233388601 1.4105453252 0.4389585856 0.6337455957 -0.5147161432 0.375165526091 +1413394934755760384.0000000000 -2.3907882141 0.0465176748 1.3875617423 0.4424348338 0.6356589349 -0.5118561158 0.371742455338 +1413394934805760512.0000000000 -2.3985539511 0.0690634865 1.3689539363 0.4451650794 0.6368186239 -0.5092014768 0.370140443995 +1413394934855760384.0000000000 -2.4054563383 0.0911152477 1.3544596026 0.4476158408 0.6370611452 -0.5069631287 0.369839887752 +1413394934905760512.0000000000 -2.4120134150 0.1125978303 1.3434902082 0.4492280459 0.6373553840 -0.5056826662 0.369130489627 +1413394934955760384.0000000000 -2.4182012352 0.1337345461 1.3365273778 0.4505716820 0.6374057378 -0.5044322808 0.369116727799 +1413394935005760512.0000000000 -2.4237234860 0.1543682285 1.3343550159 0.4525874253 0.6360057219 -0.5032870887 0.370625755289 +1413394935055760384.0000000000 -2.4296147329 0.1745666570 1.3354535603 0.4556174843 0.6336719247 -0.5028904255 0.3714482735 +1413394935105760512.0000000000 -2.4346468021 0.1939875310 1.3391046248 0.4585574481 0.6298122368 -0.5035546057 0.373489454044 +1413394935155760384.0000000000 -2.4403655582 0.2123429122 1.3424606567 0.4611222706 0.6245738413 -0.5059168210 0.375928102828 +1413394935205760512.0000000000 -2.4468603582 0.2294322907 1.3444338455 0.4618744377 0.6196465514 -0.5083351851 0.379875630612 +1413394935255760384.0000000000 -2.4544313690 0.2452859488 1.3443948202 0.4622104259 0.6144211026 -0.5110497492 0.384286852166 +1413394935305760512.0000000000 -2.4633998134 0.2599205141 1.3419671941 0.4625763530 0.6094819767 -0.5127475057 0.389416015544 +1413394935355760384.0000000000 -2.4737167354 0.2733444505 1.3371590474 0.4624906649 0.6051412087 -0.5129267355 0.395995790915 +1413394935405760512.0000000000 -2.4852370488 0.2859247867 1.3292497425 0.4616887368 0.6015968622 -0.5135509456 0.401484933677 +1413394935455760384.0000000000 -2.4984842226 0.2977373556 1.3186230396 0.4588784636 0.6001717734 -0.5146054317 0.405469663103 +1413394935505760512.0000000000 -2.5134319608 0.3089375752 1.3050149497 0.4539080401 0.6006017184 -0.5171946774 0.407129871982 +1413394935555760384.0000000000 -2.5302528212 0.3198254849 1.2888376996 0.4473970481 0.6024875059 -0.5209753306 0.406730121231 +1413394935605760512.0000000000 -2.5486365132 0.3305337228 1.2720675467 0.4415178902 0.6041898728 -0.5245683458 0.406010592096 +1413394935655760384.0000000000 -2.5683008092 0.3409742499 1.2567560051 0.4364675238 0.6052140518 -0.5276114884 0.406002671655 +1413394935705760512.0000000000 -2.5888042200 0.3514949644 1.2448720387 0.4330937147 0.6054915429 -0.5298292203 0.406313700362 +1413394935755760384.0000000000 -2.6111409960 0.3618818886 1.2357857467 0.4310274203 0.6047208003 -0.5309009190 0.408255227434 +1413394935805760512.0000000000 -2.6323888536 0.3723828700 1.2306108936 0.4303013263 0.6035103296 -0.5309100762 0.410792577248 +1413394935855760384.0000000000 -2.6533359403 0.3834613642 1.2311444776 0.4305947394 0.6018348268 -0.5318471165 0.411730076972 +1413394935905760512.0000000000 -2.6757287900 0.3946369279 1.2325253454 0.4291864669 0.6012982812 -0.5337523628 0.411518856042 +1413394935955760384.0000000000 -2.6988514646 0.4058727825 1.2325140683 0.4270812842 0.6017507379 -0.5357600394 0.410437335385 +1413394936005760512.0000000000 -2.7228299458 0.4172326860 1.2288886292 0.4231104270 0.6044641783 -0.5378591830 0.407808929534 +1413394936055760384.0000000000 -2.7480120511 0.4289812957 1.2212862986 0.4171612234 0.6106075012 -0.5405886759 0.401122022226 +1413394936105760512.0000000000 -2.7736965548 0.4413534867 1.2103872166 0.4109843927 0.6193547568 -0.5421365201 0.391892214439 +1413394936205760512.0000000000 -2.8229153040 0.4687952734 1.1832937436 0.4089665410 0.6378397410 -0.5353057601 0.373302258627 +1413394936255760384.0000000000 -2.8452466071 0.4838472454 1.1685597581 0.4154715459 0.6460313092 -0.5241610954 0.367807134533 +1413394936305760512.0000000000 -2.8669846795 0.4997538564 1.1528985755 0.4255245172 0.6545570620 -0.5087417514 0.362857779537 +1413394936405760512.0000000000 -2.9085222669 0.5342649332 1.1238309850 0.4527512040 0.6714010740 -0.4695933536 0.351737156509 +1413394936505760512.0000000000 -2.9499832236 0.5708422399 1.0974631696 0.4754124287 0.6942708901 -0.4230015134 0.336215218938 +1413394936605760512.0000000000 -2.9937647730 0.6093765027 1.0746381695 0.4900018953 0.7196951522 -0.3765434767 0.316468071937 +1413394936705760512.0000000000 -3.0405039768 0.6506791251 1.0558133073 0.5010803082 0.7411308758 -0.3422655606 0.287224364813 +1413394936805760512.0000000000 -3.0882863809 0.6949612231 1.0412056059 0.5100912906 0.7573347086 -0.3128618116 0.261473710316 +1413394936905760512.0000000000 -3.1375550629 0.7423966277 1.0291030648 0.5154753751 0.7717810898 -0.2846976680 0.239971508619 +1413394937005760512.0000000000 -3.1885422721 0.7938923512 1.0175961297 0.5175244084 0.7865563402 -0.2564312143 0.218496321802 +1413394937105760512.0000000000 -3.2407356668 0.8507887533 1.0077348144 0.5182459758 0.8012540418 -0.2260376895 0.195755030257 +1413394937205760512.0000000000 -3.2927396143 0.9144897993 0.9992241086 0.5214993741 0.8118943095 -0.1957878567 0.174737369127 +1413394937255760384.0000000000 -3.3186081009 0.9488748113 0.9952298824 0.5225848002 0.8162063957 -0.1859524208 0.161659962044 +1413394937305760512.0000000000 -3.3439648149 0.9852435895 0.9916777882 0.5232249692 0.8199519084 -0.1791687069 0.14769249784 +1413394937355760384.0000000000 -3.3681638612 1.0240128411 0.9890496364 0.5248333995 0.8221289947 -0.1736393645 0.136026431159 +1413394937455760384.0000000000 -3.4124476738 1.1059842369 0.9838813086 0.5296617566 0.8230693083 -0.1652632665 0.121257536263 +1413394937555760384.0000000000 -3.4509313286 1.1941724048 0.9790123283 0.5344569988 0.8221191481 -0.1591843436 0.114613121024 +1413394937655760384.0000000000 -3.4847728228 1.2875662035 0.9744223922 0.5394870361 0.8195684873 -0.1567608030 0.112637840776 +1413394937755760384.0000000000 -3.5145324487 1.3854033223 0.9727608838 0.5450706856 0.8155233945 -0.1597863893 0.110850577471 +1413394937855760384.0000000000 -3.5399053644 1.4850285102 0.9729327878 0.5478890215 0.8119955866 -0.1677547714 0.111081609854 +1413394937955760384.0000000000 -3.5591487238 1.5858474637 0.9756150321 0.5465104488 0.8090921672 -0.1852873055 0.111197161409 +1413394938055760384.0000000000 -3.5714895090 1.6875966569 0.9844741063 0.5417223979 0.8070492811 -0.2083716791 0.108579670496 +1413394938155760384.0000000000 -3.5742279059 1.7897282433 1.0042955516 0.5357761860 0.8054876794 -0.2297695408 0.106486783398 +1413394938255760384.0000000000 -3.5622343591 1.8931418303 1.0379879561 0.5314022507 0.8024910060 -0.2477601366 0.110610794549 +1413394938355760384.0000000000 -3.5337171802 1.9960157694 1.0887969049 0.5306718452 0.7972293699 -0.2552479103 0.132895556134 +1413394938455760384.0000000000 -3.4937906554 2.0986547039 1.1521042229 0.5354383088 0.7870585782 -0.2641645279 0.155118387367 +1413394938555760384.0000000000 -3.4465951065 2.1995272750 1.2143948825 0.5337917638 0.7796435278 -0.2726434829 0.181350086087 +1413394938655760384.0000000000 -3.3961284724 2.2985984064 1.2644031918 0.5222783803 0.7757403401 -0.2887255658 0.205157904609 +1413394938755760384.0000000000 -3.3433845659 2.3978809208 1.3028004841 0.5077973392 0.7707512179 -0.3134347423 0.223255648916 +1413394938855760384.0000000000 -3.2882097661 2.4986574540 1.3318887162 0.4964478209 0.7603561940 -0.3468562168 0.234710000277 +1413394938955760384.0000000000 -3.2282056216 2.6007265480 1.3526906863 0.4958872019 0.7378390297 -0.3914025039 0.237683674563 +1413394939055760384.0000000000 -3.1600104028 2.6985089674 1.3646566197 0.5012381146 0.7057709712 -0.4374546103 0.243477211692 +1413394939155760384.0000000000 -3.0829058347 2.7860607498 1.3660586476 0.5014224563 0.6746484780 -0.4762500858 0.258090695707 +1413394939255760384.0000000000 -2.9988828884 2.8601503280 1.3565215305 0.4910120434 0.6526361850 -0.5035912695 0.281725072773 +1413394939355760384.0000000000 -2.9097081560 2.9212102213 1.3392101750 0.4764024578 0.6378109005 -0.5209004685 0.308059499608 +1413394939455760384.0000000000 -2.8173482684 2.9700826293 1.3249025132 0.4545546846 0.6361167257 -0.5227323481 0.339832962216 +1413394939555760384.0000000000 -2.7230442106 3.0130342930 1.3264453939 0.4369239651 0.6375362500 -0.5164953186 0.368615741087 +1413394939655760384.0000000000 -2.6288153574 3.0574659995 1.3465829436 0.4383145795 0.6275356572 -0.5237921157 0.373792921179 +1413394939755760384.0000000000 -2.5347998272 3.0998984995 1.3792485044 0.4449061839 0.6111369778 -0.5422127107 0.366845278439 +1413394939855760384.0000000000 -2.4398408770 3.1352967376 1.4171904139 0.4512047660 0.5910247748 -0.5661641004 0.355755795691 +1413394939955760384.0000000000 -2.3430946955 3.1576610897 1.4455151712 0.4348138585 0.5878905959 -0.5780110318 0.362249641596 +1413394940055760384.0000000000 -2.2445252175 3.1693948560 1.4587732529 0.4012198231 0.5978417229 -0.5812923767 0.379087193971 +1413394940155760384.0000000000 -2.1418467399 3.1775012009 1.4637886819 0.3838875331 0.5911187025 -0.5934383687 0.388638577628 +1413394940255760384.0000000000 -2.0333053974 3.1830011059 1.4592917268 0.3780295251 0.5708309533 -0.6079142517 0.402101931662 +1413394940355760384.0000000000 -1.9183193683 3.1839103837 1.4454720476 0.3732116975 0.5443311591 -0.6225372557 0.420551998382 +1413394940455760384.0000000000 -1.8027654348 3.1801861727 1.4246713825 0.3642911032 0.5158460178 -0.6394861224 0.438465936386 +1413394940555760384.0000000000 -1.6886265730 3.1706390297 1.4032956291 0.3462115473 0.4924925930 -0.6528423968 0.459766696581 +1413394940655760384.0000000000 -1.5760699121 3.1571190262 1.3845150336 0.3151035358 0.4790150648 -0.6605864640 0.484644047763 +1413394940755760384.0000000000 -1.4643368347 3.1464087059 1.3739564401 0.2862361481 0.4696400468 -0.6666603476 0.503061700934 +1413394940855760384.0000000000 -1.3508846148 3.1448597423 1.3790349336 0.2759893985 0.4579605839 -0.6741617572 0.509517301625 +1413394940955760384.0000000000 -1.2350441141 3.1516932493 1.4005093428 0.2832918284 0.4417797794 -0.6868429736 0.502815170847 +1413394941005760512.0000000000 -1.1766981649 3.1560322053 1.4142418455 0.2884154137 0.4325950717 -0.6962005756 0.49495738356 +1413394941055760384.0000000000 -1.1184169529 3.1596304625 1.4282839784 0.2929509283 0.4233854184 -0.7062346650 0.485960017932 +1413394941105760512.0000000000 -1.0603372593 3.1619029360 1.4421311028 0.2970972413 0.4133734703 -0.7175426801 0.475382062715 +1413394941205760512.0000000000 -0.9445865551 3.1585345302 1.4711105988 0.2999637826 0.3961703124 -0.7360302120 0.459706797578 +1413394941305760512.0000000000 -0.8291123895 3.1411782872 1.5026621895 0.2965932483 0.3873527602 -0.7469773429 0.451680344423 +1413394941405760512.0000000000 -0.7135973934 3.1079362272 1.5351612990 0.2853890825 0.3889703668 -0.7521088930 0.448984786338 +1413394941505760512.0000000000 -0.5947907574 3.0585081311 1.5695666615 0.2619621478 0.4044749131 -0.7416576303 0.466604583358 +1413394941605760512.0000000000 -0.4703360859 2.9996520035 1.6058657201 0.2383710983 0.4198201988 -0.7280988766 0.48662331021 +1413394941705760512.0000000000 -0.3375117623 2.9383337724 1.6439920397 0.2250973419 0.4214261060 -0.7203497745 0.502819476772 +1413394941755760384.0000000000 -0.2676275334 2.9083130346 1.6637623455 0.2242316145 0.4165748352 -0.7183013672 0.510126195757 +1413394941805760512.0000000000 -0.1957927416 2.8792906141 1.6833205706 0.2258500074 0.4100288371 -0.7180810173 0.515002698476 +1413394941855760384.0000000000 -0.1223885117 2.8518883284 1.7034857274 0.2357049589 0.3975725789 -0.7223526919 0.514379048279 +1413394941905760512.0000000000 -0.0484302736 2.8251372336 1.7239117286 0.2496954673 0.3828512883 -0.7287661840 0.509879312801 +1413394941955760384.0000000000 0.0256474597 2.7981160240 1.7449039371 0.2658583533 0.3658561411 -0.7368257683 0.502549905128 +1413394942005760512.0000000000 0.0986366371 2.7695958013 1.7662267650 0.2816040193 0.3493019185 -0.7448856354 0.49379422454 +1413394942055760384.0000000000 0.1701072540 2.7380254602 1.7883225427 0.2958129278 0.3341172652 -0.7518987781 0.485292275142 +1413394942105760512.0000000000 0.2393234797 2.7026067513 1.8112140560 0.3101754104 0.3182734578 -0.7586921093 0.476318700215 +1413394942155760384.0000000000 0.3052666093 2.6622603114 1.8347766538 0.3210471896 0.3037801170 -0.7653386750 0.46787076756 +1413394942205760512.0000000000 0.3673148394 2.6156423516 1.8593695171 0.3287610630 0.2901475788 -0.7709421739 0.461929334842 +1413394942255760384.0000000000 0.4249834583 2.5619512895 1.8855397907 0.3332994358 0.2767017210 -0.7767459752 0.457179760776 +1413394942305760512.0000000000 0.4776343304 2.5011326297 1.9119366457 0.3344021547 0.2645112593 -0.7827477757 0.453337525775 +1413394942355760384.0000000000 0.5250384187 2.4326814580 1.9396840592 0.3309709191 0.2529612361 -0.7873736797 0.454435421351 +1413394942405760512.0000000000 0.5668773292 2.3574109551 1.9671674190 0.3237218913 0.2437608187 -0.7915837165 0.457362022981 +1413394942455760384.0000000000 0.6044694097 2.2738909026 1.9950804477 0.3138851649 0.2339962836 -0.7941800965 0.464757804502 +1413394942505760512.0000000000 0.6374643873 2.1845825135 2.0202241247 0.3019066823 0.2238477827 -0.7965045868 0.473629568839 +1413394942555760384.0000000000 0.6661133625 2.0904351701 2.0413512611 0.2899594022 0.2123367240 -0.7985035327 0.48293764503 +1413394942605760512.0000000000 0.6907860887 1.9915954482 2.0580389611 0.2762343792 0.2003761217 -0.8006327129 0.492474605115 +1413394942655760384.0000000000 0.7114135615 1.8889151080 2.0702270393 0.2624530829 0.1871045679 -0.8015510433 0.503613130193 +1413394942705760512.0000000000 0.7276963303 1.7830265371 2.0777700690 0.2462779447 0.1745904271 -0.8012350063 0.516611867254 +1413394942755760384.0000000000 0.7396575353 1.6744074092 2.0805121419 0.2238658099 0.1663288585 -0.7978393924 0.534482098799 +1413394942805760512.0000000000 0.7476782021 1.5640938630 2.0792766105 0.1962127419 0.1612882048 -0.7904677030 0.55735759208 +1413394942855760384.0000000000 0.7521980153 1.4535581900 2.0735518354 0.1657904952 0.1579929405 -0.7802778958 0.58199497236 +1413394942905760512.0000000000 0.7540709878 1.3442502035 2.0626370532 0.1337098055 0.1556338467 -0.7681330682 0.606524017057 +1413394942955760384.0000000000 0.7544482278 1.2378746086 2.0472843173 0.1034487964 0.1517484498 -0.7554665208 0.628920575637 +1413394943005760512.0000000000 0.7539858118 1.1354490609 2.0277525948 0.0771684683 0.1448023747 -0.7448431869 0.646750281502 +1413394943055760384.0000000000 0.7533608039 1.0379705835 2.0049086371 0.0547082465 0.1354246478 -0.7368284262 0.660114416491 +1413394943105760512.0000000000 0.7536359988 0.9458926201 1.9803086682 0.0348435701 0.1233460410 -0.7311295209 0.670090518827 +1413394943155760384.0000000000 0.7547563619 0.8600737517 1.9538099175 0.0167131382 0.1098350633 -0.7268902625 0.677707515154 +1413394943205760512.0000000000 0.7569869837 0.7814223493 1.9255114715 0.0002890402 0.0955692095 -0.7235218207 0.683653872722 +1413394943255760384.0000000000 0.7604735654 0.7101092841 1.8949385108 0.0155716230 -0.0803531503 0.7213130425 -0.687756054557 +1413394943305760512.0000000000 0.7657903652 0.6462172566 1.8637842394 0.0294473601 -0.0641171217 0.7200066858 -0.690371074166 +1413394943355760384.0000000000 0.7735357342 0.5907634425 1.8338128535 0.0422467237 -0.0479608023 0.7200621170 -0.69095985665 +1413394943405760512.0000000000 0.7837108990 0.5446248944 1.8064347999 0.0548345647 -0.0323504560 0.7213235587 -0.689665819164 +1413394943455760384.0000000000 0.7965117274 0.5075598210 1.7817276701 0.0684558790 -0.0182625048 0.7239144558 -0.686242037633 +1413394943505760512.0000000000 0.8124159563 0.4783876395 1.7602754147 0.0821577870 -0.0044517664 0.7274020749 -0.681260964086 +1413394943555760384.0000000000 0.8318539012 0.4562111459 1.7417125618 0.0940541720 0.0089607251 0.7339456930 -0.672604815502 +1413394943605760512.0000000000 0.8549732332 0.4408233332 1.7254030734 0.1030861734 0.0221145375 0.7427246916 -0.66124444846 +1413394943655760384.0000000000 0.8822176250 0.4316683894 1.7113874730 0.1086417094 0.0347542404 0.7540217874 -0.646869589536 +1413394943705760512.0000000000 0.9129182191 0.4265317850 1.6986852534 0.1077720074 0.0496924185 0.7645896533 -0.633497056012 +1413394943755760384.0000000000 0.9459206391 0.4243193073 1.6856873394 0.1075696451 0.0629061765 0.7728073021 -0.622286476035 +1413394943805760512.0000000000 0.9813373098 0.4243466178 1.6719775339 0.1041679467 0.0753487861 0.7779405234 -0.615044828748 +1413394943855760384.0000000000 1.0183108340 0.4252389236 1.6575745552 0.0965390651 0.0880063366 0.7803065977 -0.611601755348 +1413394943905760512.0000000000 1.0560980295 0.4274870826 1.6420187944 0.0880756557 0.0998674863 0.7815599265 -0.609453234748 +1413394943955760384.0000000000 1.0940537916 0.4316380633 1.6240238499 0.0789695752 0.1100478064 0.7835558611 -0.606377356999 +1413394944005760512.0000000000 1.1309568806 0.4375581772 1.6050689349 0.0749807672 0.1156663457 0.7856279430 -0.603148336801 +1413394944055760384.0000000000 1.1665877382 0.4446632458 1.5863707240 0.0764512353 0.1171414970 0.7881690203 -0.599351878073 +1413394944105760512.0000000000 1.2010271860 0.4531016629 1.5689785996 0.0787552283 0.1161691487 0.7904685277 -0.596206214043 +1413394944155760384.0000000000 1.2343665626 0.4625707635 1.5537716703 0.0817111626 0.1147971702 0.7921757261 -0.593803430921 +1413394944205760512.0000000000 1.2668677856 0.4729813238 1.5406509992 0.0839798648 0.1146459240 0.7932492716 -0.592080473854 +1413394944255760384.0000000000 1.2983320643 0.4842206124 1.5290113328 0.0848457471 0.1167858604 0.7958044610 -0.588096524341 +1413394944305760512.0000000000 1.3290585043 0.4958798025 1.5195012348 0.0858048577 0.1191261634 0.7995291738 -0.582408433844 +1413394944355760384.0000000000 1.3582344318 0.5066446247 1.5147123798 0.0870677294 0.1213853656 0.8043870679 -0.575018476726 +1413394944405760512.0000000000 1.3862573601 0.5173685227 1.5143398524 0.0902056269 0.1234206590 0.8099581987 -0.566213742435 +1413394944455760384.0000000000 1.4125880738 0.5267191723 1.5170847492 0.0951335890 0.1254937303 0.8157972739 -0.556485158666 +1413394944505760512.0000000000 1.4376126054 0.5345771736 1.5196380015 0.1004566156 0.1305697949 0.8205585011 -0.547305895595 +1413394944555760384.0000000000 1.4614018900 0.5404303040 1.5203982830 0.1034137454 0.1413604437 0.8236695008 -0.539343467242 +1413394944605760512.0000000000 1.4836809300 0.5438833517 1.5185489974 0.1054559572 0.1554004626 0.8262462427 -0.53108086371 +1413394944655760384.0000000000 1.5043336299 0.5451590735 1.5137233296 0.1079261366 0.1717084713 0.8291594712 -0.520924871035 +1413394944705760512.0000000000 1.5225691604 0.5436826559 1.5063533557 0.1116860740 0.1892340497 0.8316424638 -0.509987752461 +1413394944755760384.0000000000 1.5379018273 0.5391186532 1.4962742753 0.1173360148 0.2077122689 0.8328060673 -0.499521698429 +1413394944805760512.0000000000 1.5504840060 0.5314631388 1.4843489460 0.1240505338 0.2270025445 0.8324641871 -0.489984374311 +1413394944855760384.0000000000 1.5594627163 0.5201395592 1.4709389482 0.1317357597 0.2461889886 0.8302534225 -0.482406390903 +1413394944905760512.0000000000 1.5644462331 0.5051039570 1.4565565742 0.1412883376 0.2654431945 0.8259557044 -0.476838222592 +1413394944955760384.0000000000 1.5652922111 0.4863552329 1.4409056524 0.1523069408 0.2850196305 0.8197873941 -0.472773766665 +1413394945005760512.0000000000 1.5617183068 0.4640955791 1.4244388816 0.1657357492 0.3027809041 0.8116196843 -0.471305499204 +1413394945055760384.0000000000 1.5537207039 0.4387558410 1.4075328072 0.1827877325 0.3175177536 0.8018572717 -0.472012750647 +1413394945105760512.0000000000 1.5419099651 0.4104801670 1.3896524758 0.2018207319 0.3316213931 0.7912362651 -0.47248366814 +1413394945155760384.0000000000 1.5268562350 0.3795432190 1.3718662954 0.2207286553 0.3446590611 0.7803764385 -0.472759565239 +1413394945205760512.0000000000 1.5091287762 0.3461915724 1.3549115735 0.2391310852 0.3574502762 0.7690357104 -0.472895020369 +1413394945255760384.0000000000 1.4892747826 0.3106408320 1.3387159630 0.2569436763 0.3707297393 0.7565854785 -0.473410837719 +1413394945305760512.0000000000 1.4671706598 0.2730918746 1.3240185249 0.2750012879 0.3828365751 0.7445604770 -0.472694557311 +1413394945355760384.0000000000 1.4437846430 0.2337320035 1.3113198504 0.2930707259 0.3942932366 0.7306870032 -0.474066341964 +1413394945405760512.0000000000 1.4196625304 0.1928226571 1.3000727601 0.3117162184 0.4050018991 0.7136807524 -0.479026350502 +1413394945455760384.0000000000 1.3959229162 0.1506874009 1.2899542650 0.3259959927 0.4184454778 0.6949668264 -0.485439084698 +1413394945505760512.0000000000 1.3732095556 0.1079911754 1.2806598162 0.3324046098 0.4369681907 0.6752344915 -0.492569139504 +1413394945555760384.0000000000 1.3514610220 0.0658781023 1.2716286979 0.3356777597 0.4575907031 0.6556584399 -0.498039356226 +1413394945605760512.0000000000 1.3309594732 0.0255989147 1.2625301324 0.3383473016 0.4781970225 0.6379625052 -0.499852531339 +1413394945655760384.0000000000 1.3112176965 -0.0124343493 1.2539275921 0.3405468650 0.4991732744 0.6199113095 -0.500563525654 +1413394945705760512.0000000000 1.2920156476 -0.0474445313 1.2457175645 0.3437366226 0.5193255657 0.6034733309 -0.497961876088 +1413394945755760384.0000000000 1.2738182399 -0.0788128573 1.2379517220 0.3470370452 0.5393695721 0.5870356345 -0.493998904696 +1413394945805760512.0000000000 1.2552936002 -0.1060025261 1.2299204684 0.3523948772 0.5584121907 0.5711495760 -0.487628790853 +1413394945855760384.0000000000 1.2359851709 -0.1289551145 1.2218617259 0.3589302691 0.5770330998 0.5544003799 -0.480460281812 +1413394945905760512.0000000000 1.2178794960 -0.1473663192 1.2133786271 0.3656508453 0.5955465695 0.5365752000 -0.472980758285 +1413394945955760384.0000000000 1.2014641854 -0.1605223495 1.2049173620 0.3746540945 0.6127230597 0.5194242439 -0.463036949416 +1413394946005760512.0000000000 1.1853213537 -0.1682628001 1.1968700595 0.3871186060 0.6275675158 0.5040557107 -0.449695495328 +1413394946055760384.0000000000 1.1706912416 -0.1707998941 1.1889979921 0.4028009765 0.6402657814 0.4908679213 -0.432272814779 +1413394946155760384.0000000000 1.1441609791 -0.1624751729 1.1765025703 0.4344034526 0.6635176165 0.4631027935 -0.395694093442 +1413394946205760512.0000000000 1.1339557077 -0.1536499011 1.1711260044 0.4493876415 0.6742655756 0.4468435205 -0.37914054056 +1413394946255760384.0000000000 1.1246182783 -0.1423424643 1.1663775704 0.4620706487 0.6859287482 0.4281368440 -0.364268185482 +1413394946355760384.0000000000 1.1102042510 -0.1130454369 1.1572422226 0.4796127483 0.7114612634 0.3861483053 -0.338650215955 +1413394946455760384.0000000000 1.1021898514 -0.0745260375 1.1486965131 0.4917132415 0.7369688571 0.3422884121 -0.312943500771 +1413394946555760384.0000000000 1.1023124997 -0.0265385735 1.1420846214 0.5037245981 0.7586309241 0.2972428469 -0.287031949868 +1413394946655760384.0000000000 1.1133028727 0.0307073590 1.1353653769 0.5263565527 0.7704264630 0.2587631874 -0.249866879422 +1413394946755760384.0000000000 1.1324533771 0.0953912835 1.1291337653 0.5547456384 0.7748887959 0.2234758309 -0.204604945327 +1413394946855760384.0000000000 1.1592257660 0.1597163118 1.1237303050 0.5745201959 0.7810294472 0.1845312707 -0.160834564834 +1413394946955760384.0000000000 1.1914185992 0.2209762581 1.1209008246 0.5891085705 0.7864528010 0.1417238765 -0.119822480761 +1413394947055760384.0000000000 1.2277687012 0.2764227279 1.1224801225 0.6001287208 0.7899771548 0.0985116087 -0.0779556045424 +1413394947155760384.0000000000 1.2660531297 0.3236982149 1.1326341776 0.6014037724 0.7961119573 0.0555229434 -0.0379006163932 +1413394947255760384.0000000000 1.3042490677 0.3631302363 1.1580239260 0.5937491306 0.8045270459 0.0140746891 -0.000324685075509 +1413394947355760384.0000000000 1.3407037996 0.3950227557 1.2012302921 0.5969835072 0.8011809453 -0.0238537023 0.0339232361668 +1413394947455760384.0000000000 1.3716812968 0.4214258813 1.2598110866 0.6015745758 0.7949951547 -0.0521465119 0.0580644048624 +1413394947555760384.0000000000 1.3959396740 0.4401675477 1.3230497229 0.5951252613 0.7973585735 -0.0717011680 0.0700297882599 +1413394947655760384.0000000000 1.4149717407 0.4523346324 1.3773952299 0.5717794909 0.8127073095 -0.0818875840 0.076612443892 +1413394947755760384.0000000000 1.4302068674 0.4641493895 1.4184636850 0.5417410529 0.8329205067 -0.0836809974 0.0758785328417 +1413394947855760384.0000000000 1.4419024494 0.4824611720 1.4524243237 0.5195194186 0.8486441746 -0.0735885716 0.0669877653886 +1413394947955760384.0000000000 1.4518217220 0.5159542108 1.4936346972 0.5114370130 0.8559852530 -0.0535293802 0.0534418724163 +1413394948055760384.0000000000 1.4600501388 0.5657057485 1.5457968737 0.5063999560 0.8610459766 -0.0289807052 0.0363184448774 +1413394948155760384.0000000000 1.4680358956 0.6316584535 1.5971258759 0.4969530843 0.8674935602 -0.0052768448 0.0215571322991 +1413394948255760384.0000000000 1.4757338185 0.7151942255 1.6407045250 0.5064125654 0.8619794393 0.0177081658 0.0149726645553 +1413394948355760384.0000000000 1.4805728539 0.8164607686 1.6805861048 0.5457212045 0.8371195269 0.0359950342 0.011118550658 +1413394948455760384.0000000000 1.4812505147 0.9217300843 1.7157937663 0.5970109937 0.8008792506 0.0462742564 0.00538448383897 +1413394948555760384.0000000000 1.4783591397 1.0180385412 1.7476568958 0.6451055789 0.7624456034 0.0501545675 -0.000115466913101 +1413394948655760384.0000000000 1.4722013558 1.0950796156 1.7796229918 0.6744781681 0.7366387601 0.0491356499 -0.0053127994631 +1413394948755760384.0000000000 1.4635290861 1.1414024676 1.8137143482 0.6906199728 0.7216115125 0.0478810249 -0.00531842140235 +1413394948855760384.0000000000 1.4527400579 1.1568366725 1.8482939583 0.6732894426 0.7379185353 0.0464045698 -0.00204390649553 +1413394948955760384.0000000000 1.4389134015 1.1485200473 1.8833719895 0.6343690026 0.7717276513 0.0447896287 0.00250798335216 +1413394949055760384.0000000000 1.4218634352 1.1255870868 1.9086510024 0.5808767556 0.8127377109 0.0439179346 0.0105272528963 +1413394949155760384.0000000000 1.4000186355 1.0970900466 1.9198763916 0.5273197153 0.8484331029 0.0427888008 0.0162575020595 +1413394949255760384.0000000000 1.3726173644 1.0791978790 1.9226085643 0.4907057483 0.8701070594 0.0413110323 0.0203708680564 +1413394949355760384.0000000000 1.3384235412 1.0829139338 1.9180823666 0.4688949922 0.8820919758 0.0387674450 0.0234161856134 +1413394949455760384.0000000000 1.2970334999 1.1127936741 1.9094164557 0.4678600109 0.8827128616 0.0362999259 0.0246440556093 +1413394949555760384.0000000000 1.2478753163 1.1719704740 1.9099654908 0.5105749370 0.8587190829 0.0356334004 0.0253974637132 +1413394949655760384.0000000000 1.1919290767 1.2481112125 1.9197327443 0.5730336892 0.8184815365 0.0342488734 0.0233961556223 +1413394949755760384.0000000000 1.1305389772 1.3212229980 1.9325974248 0.6234193940 0.7810743617 0.0304543710 0.018537311658 +1413394949855760384.0000000000 1.0645762066 1.3795056175 1.9439048602 0.6478362194 0.7613325610 0.0246237348 0.00863921503337 +1413394949955760384.0000000000 0.9961102485 1.4174245074 1.9530983997 0.6478207340 0.7614601607 0.0192511404 -0.0116667815732 +1413394950055760384.0000000000 0.9290835633 1.4362758044 1.9637955188 0.6449318370 0.7630899633 0.0195147868 -0.0370918662486 +1413394950155760384.0000000000 0.8679177741 1.4372795715 1.9741676358 0.6331588570 0.7706579155 0.0236223023 -0.0681045217145 +1413394950255760384.0000000000 0.8182812684 1.4249712136 1.9794770365 0.5955396346 0.7972709132 0.0320891068 -0.0930694563142 +1413394950355760384.0000000000 0.7851794564 1.4106448726 1.9813343097 0.5511910213 0.8283887258 0.0566025467 -0.0821993228059 +1413394950455760384.0000000000 0.7625922422 1.4045824238 1.9858122200 0.5173410345 0.8497523216 0.0838960963 -0.0569270668337 +1413394950555760384.0000000000 0.7400894479 1.4145829492 1.9954454303 0.4962941666 0.8614232185 0.1007477653 -0.0386267614094 +1413394950655760384.0000000000 0.7106823030 1.4452998994 2.0117902342 0.4951299780 0.8614798736 0.1087282081 -0.0296126505907 +1413394950755760384.0000000000 0.6706772328 1.4970981409 2.0374895594 0.5318143287 0.8384651583 0.1154069130 -0.0288260750041 +1413394950855760384.0000000000 0.6204927280 1.5574406292 2.0696397248 0.5888951294 0.7980276232 0.1210436216 -0.0412659758247 +1413394950955760384.0000000000 0.5647056857 1.6100207435 2.1031640460 0.6440206772 0.7515844208 0.1297243137 -0.0594123571583 +1413394951055760384.0000000000 0.5072498228 1.6405837578 2.1368947738 0.6826147519 0.7122578512 0.1425165376 -0.0800930109781 +1413394951155760384.0000000000 0.4522546782 1.6387487119 2.1713703696 0.6946917015 0.6940728201 0.1544869629 -0.108628442745 +1413394951255760384.0000000000 0.4054860527 1.6028984627 2.2039162248 0.6729321884 0.7065217548 0.1695441129 -0.138723010773 +1413394951355760384.0000000000 0.3711853666 1.5411869093 2.2330513462 0.6170733284 0.7481218617 0.1883520834 -0.155105383925 +1413394951455760384.0000000000 0.3473694760 1.4682146164 2.2601783076 0.5423679256 0.7991608198 0.2090518694 -0.153219885431 +1413394951555760384.0000000000 0.3256958407 1.4023974798 2.2916937592 0.4755340137 0.8387186603 0.2235292314 -0.143014311662 +1413394951655760384.0000000000 0.2981539640 1.3579453239 2.3290685544 0.4313387921 0.8625685961 0.2273581055 -0.135020574063 +1413394951755760384.0000000000 0.2584967870 1.3471732262 2.3705395106 0.4088792668 0.8746656276 0.2276057886 -0.126385877414 +1413394951855760384.0000000000 0.2019339558 1.3802286195 2.4234498054 0.4434255653 0.8580841115 0.2287174412 -0.121465047206 +1413394951955760384.0000000000 0.1311192427 1.4414812381 2.4819464892 0.5040597379 0.8244668416 0.2246441717 -0.125352318581 +1413394952055760384.0000000000 0.0533244432 1.5126176346 2.5416318627 0.5673228500 0.7832943717 0.2141824232 -0.1368232464 +1413394952155760384.0000000000 -0.0238209811 1.5791993570 2.5895304203 0.6128655720 0.7490827211 0.2050563156 -0.145680386943 +1413394952255760384.0000000000 -0.0954315893 1.6319848517 2.6196139846 0.6225794877 0.7411990206 0.1992859200 -0.152656200119 +1413394952355760384.0000000000 -0.1612223889 1.6701202303 2.6301146163 0.5945360110 0.7620218585 0.2014462179 -0.158962385873 +1413394952455760384.0000000000 -0.2225447903 1.7002721318 2.6324372994 0.5586270232 0.7842291300 0.2057167867 -0.174931770576 +1413394952555760384.0000000000 -0.2781028714 1.7320245054 2.6391327442 0.5314976624 0.7976627031 0.2189496691 -0.182497915813 +1413394952655760384.0000000000 -0.3278650654 1.7719166727 2.6571693762 0.5248188294 0.7977666499 0.2414687512 -0.172703244843 +1413394952755760384.0000000000 -0.3790338344 1.8220984487 2.6889767201 0.5368245760 0.7859569324 0.2573325556 -0.16694619167 +1413394952855760384.0000000000 -0.4342430424 1.8766640528 2.7234931341 0.5677536320 0.7608919072 0.2613764646 -0.174303363871 +1413394952955760384.0000000000 -0.4894436576 1.9271570887 2.7521002138 0.6058911047 0.7286704291 0.2578537382 -0.188273271145 +1413394953055760384.0000000000 -0.5381065250 1.9643186345 2.7684844623 0.6351628272 0.7022108471 0.2520057240 -0.199903037237 +1413394953155760384.0000000000 -0.5755794223 1.9828517509 2.7767823261 0.6529408820 0.6853616566 0.2471000105 -0.207097052439 +1413394953255760384.0000000000 -0.5970663672 1.9758101538 2.7940379539 0.6637560892 0.6750750353 0.2432351235 -0.211040814857 +1413394953355760384.0000000000 -0.5988012114 1.9379544873 2.8337816893 0.6765919958 0.6631155730 0.2376776708 -0.214500193038 +1413394953455760384.0000000000 -0.5806097404 1.8700381094 2.8792778960 0.6678961771 0.6728737141 0.2376684762 -0.211351264326 +1413394953555760384.0000000000 -0.5477219684 1.7805767854 2.8980374811 0.6157122540 0.7220333479 0.2524503311 -0.189301598141 +1413394953655760384.0000000000 -0.5083317693 1.6797848277 2.8802976005 0.5532753752 0.7717183308 0.2680649461 -0.1627217312 +1413394953755760384.0000000000 -0.4715563645 1.5791229480 2.8262165662 0.5015056120 0.8069697528 0.2777074090 -0.142023006179 +1413394953855760384.0000000000 -0.4447930657 1.4873133115 2.7419333111 0.4672224837 0.8277015935 0.2833420675 -0.127790827745 +1413394953955760384.0000000000 -0.4347871453 1.4121921101 2.6474882931 0.4691363295 0.8267285143 0.2834674159 -0.126796262213 +1413394954055760384.0000000000 -0.4429098367 1.3544441919 2.5576471001 0.5078937321 0.8031241065 0.2784844367 -0.139578096214 +1413394954155760384.0000000000 -0.4629728438 1.3057926099 2.4728289774 0.5554983189 0.7701706494 0.2724639722 -0.154990878167 +1413394954255760384.0000000000 -0.4868516488 1.2546537206 2.3921118645 0.6003368569 0.7348049866 0.2649112615 -0.171695408779 +1413394954355760384.0000000000 -0.5071156310 1.1915709079 2.3159762527 0.6307172914 0.7080610571 0.2587187733 -0.184146230115 +1413394954455760384.0000000000 -0.5189028952 1.1096296352 2.2520732141 0.6350233514 0.7038037283 0.2542153560 -0.191781667703 +1413394954555760384.0000000000 -0.5202483906 1.0082504470 2.1997992297 0.6022539068 0.7316589250 0.2562202484 -0.190569235464 +1413394954655760384.0000000000 -0.5132731661 0.8946117017 2.1506757154 0.5411792706 0.7792475855 0.2595877738 -0.180311910992 +1413394954755760384.0000000000 -0.5057089792 0.7850698762 2.1012045215 0.4801526294 0.8213799974 0.2572758757 -0.169107883323 +1413394954855760384.0000000000 -0.5048544840 0.6945142261 2.0474715323 0.4487132857 0.8424113495 0.2533805505 -0.157473178988 +1413394954955760384.0000000000 -0.5152746075 0.6317189053 1.9918859865 0.4732260126 0.8304106432 0.2539610045 -0.148253542248 +1413394955055760384.0000000000 -0.5366986007 0.5862167216 1.9329686973 0.5220337293 0.7988139301 0.2572325481 -0.152343384322 +1413394955155760384.0000000000 -0.5656533534 0.5451811917 1.8752673144 0.5667772278 0.7621657560 0.2646983470 -0.166738476332 +1413394955255760384.0000000000 -0.5957918647 0.4974015495 1.8216168516 0.5985645016 0.7278734830 0.2771005246 -0.187446070642 +1413394955355760384.0000000000 -0.6221959582 0.4348275658 1.7768485381 0.5942136931 0.7177277121 0.2907774797 -0.217314232085 +1413394955455760384.0000000000 -0.6406020434 0.3600712721 1.7440797450 0.5401345979 0.7430581468 0.3009821360 -0.255986250592 +1413394955555760384.0000000000 -0.6487796189 0.2904377088 1.7223380588 0.4721431839 0.7766763585 0.3145485514 -0.273703958423 +1413394955655760384.0000000000 -0.6515611537 0.2445338636 1.7147686111 0.4262186811 0.7977269337 0.3357980221 -0.263076155262 +1413394955755760384.0000000000 -0.6624044261 0.2310723508 1.7162231454 0.4227855902 0.7961188164 0.3642549557 -0.234020302669 +1413394955855760384.0000000000 -0.6893133764 0.2430206013 1.7256252682 0.4508006032 0.7779945444 0.3812237775 -0.214876095687 +1413394955905760512.0000000000 -0.7094506695 0.2545939636 1.7327940413 0.4683955502 0.7671146449 0.3830362037 -0.213129061295 +1413394955955760384.0000000000 -0.7335058020 0.2683997153 1.7415970042 0.4866198955 0.7560849599 0.3808098324 -0.215686073295 +1413394956005760512.0000000000 -0.7607741125 0.2834305032 1.7522593276 0.5062576614 0.7438370639 0.3758668810 -0.221661206696 +1413394956105760512.0000000000 -0.8205290259 0.3126454714 1.7768440579 0.5489111089 0.7140867931 0.3626142300 -0.239348212339 +1413394956205760512.0000000000 -0.8787812120 0.3327801269 1.8027865775 0.5772490660 0.6884098986 0.3520393409 -0.262571189908 +1413394956305760512.0000000000 -0.9267672157 0.3380578369 1.8280723886 0.5862293016 0.6706677538 0.3508187867 -0.28890508631 +1413394956405760512.0000000000 -0.9602426559 0.3290760016 1.8476130742 0.5736297519 0.6640023954 0.3612986238 -0.315456860805 +1413394956505760512.0000000000 -0.9778559243 0.3106696851 1.8540518266 0.5396009708 0.6712647365 0.3891962846 -0.326742555987 +1413394956605760512.0000000000 -0.9832819459 0.2903579864 1.8475344417 0.4987850640 0.6828715480 0.4292162545 -0.31729058554 +1413394956655760384.0000000000 -0.9841621792 0.2813359927 1.8409300930 0.4757082139 0.6908676515 0.4499714656 -0.306478814107 +1413394956705760512.0000000000 -0.9855840580 0.2733267231 1.8349594552 0.4535513739 0.6986721137 0.4679507062 -0.295246617753 +1413394956755760384.0000000000 -0.9895886234 0.2667353793 1.8302429043 0.4341763126 0.7051346935 0.4826061930 -0.285249463111 +1413394956805760512.0000000000 -0.9978750955 0.2620746405 1.8276062698 0.4207247479 0.7084590763 0.4934048822 -0.27861810056 +1413394956855760384.0000000000 -1.0120126747 0.2598066593 1.8277306668 0.4172255640 0.7064836412 0.4999776078 -0.277175188516 +1413394956905760512.0000000000 -1.0321630956 0.2595476784 1.8306051845 0.4224674154 0.7005022492 0.5013362621 -0.281921680737 +1413394956955760384.0000000000 -1.0571693559 0.2607432306 1.8347486489 0.4306536237 0.6933508336 0.5005784228 -0.288484523975 +1413394957005760512.0000000000 -1.0858553822 0.2630594701 1.8394352593 0.4397059192 0.6859417332 0.4989299327 -0.295316043477 +1413394957055760384.0000000000 -1.1181129433 0.2663215140 1.8456216651 0.4518361376 0.6771355802 0.4947062847 -0.304297884648 +1413394957105760512.0000000000 -1.1527585982 0.2697108615 1.8533566667 0.4653597353 0.6674323922 0.4879868324 -0.315979698573 +1413394957155760384.0000000000 -1.1885184378 0.2730317320 1.8623031635 0.4795233314 0.6571049008 0.4792961588 -0.329462768909 +1413394957205760512.0000000000 -1.2240783742 0.2761787715 1.8723421636 0.4949470489 0.6457043903 0.4696872656 -0.342763959132 +1413394957255760384.0000000000 -1.2578634069 0.2784679414 1.8829082373 0.5080229934 0.6348675163 0.4603940747 -0.356220677108 +1413394957305760512.0000000000 -1.2888894077 0.2799994624 1.8948557675 0.5210626975 0.6237338896 0.4492527720 -0.370973917006 +1413394957355760384.0000000000 -1.3159175445 0.2804071640 1.9078679707 0.5334662970 0.6125272243 0.4371301711 -0.386188196439 +1413394957405760512.0000000000 -1.3373939843 0.2796355292 1.9206624510 0.5432046851 0.6030205217 0.4277833812 -0.397864674476 +1413394957455760384.0000000000 -1.3525993810 0.2777722000 1.9327273436 0.5466166779 0.5993255698 0.4226252736 -0.404236251429 +1413394957505760512.0000000000 -1.3611063552 0.2745139882 1.9434485500 0.5414664394 0.6028331326 0.4231933562 -0.405356253791 +1413394957555760384.0000000000 -1.3627817680 0.2701668829 1.9536142809 0.5282263573 0.6128078763 0.4301635820 -0.400503077321 +1413394957605760512.0000000000 -1.3583065938 0.2647477164 1.9624083229 0.5096440989 0.6263313166 0.4421794149 -0.390447614051 +1413394957655760384.0000000000 -1.3492858556 0.2591002229 1.9708343785 0.4899084323 0.6393820640 0.4574682586 -0.376700274123 +1413394957705760512.0000000000 -1.3376474116 0.2537839776 1.9772606242 0.4687170985 0.6517625020 0.4740116584 -0.361694443169 +1413394957755760384.0000000000 -1.3251070752 0.2489042707 1.9808816696 0.4463130837 0.6633565345 0.4908806215 -0.346119856186 +1413394957805760512.0000000000 -1.3137496717 0.2450022876 1.9838000735 0.4269132400 0.6714914274 0.5050603464 -0.334302849038 +1413394957855760384.0000000000 -1.3050465309 0.2423401705 1.9863999934 0.4133983193 0.6749347051 0.5148945052 -0.32931538359 +1413394957905760512.0000000000 -1.3000619082 0.2410571373 1.9891103213 0.4070986530 0.6731817245 0.5212071683 -0.330817382066 +1413394957955760384.0000000000 -1.2987131686 0.2409847937 1.9914297022 0.4047022874 0.6678822654 0.5249057556 -0.338560608937 +1413394958005760512.0000000000 -1.3011795677 0.2424226482 1.9936680757 0.4074915361 0.6584782491 0.5254795383 -0.352460349952 +1413394958055760384.0000000000 -1.3059354576 0.2454203622 1.9957174511 0.4143236803 0.6451033082 0.5235383914 -0.371598119491 +1413394958105760512.0000000000 -1.3120613383 0.2500163599 1.9977616341 0.4250039573 0.6273014698 0.5209136838 -0.393081971428 +1413394958155760384.0000000000 -1.3179776652 0.2556907385 2.0002826001 0.4366213237 0.6074649011 0.5176423031 -0.415204358901 +1413394958205760512.0000000000 -1.3223959290 0.2621703380 2.0027934738 0.4471377050 0.5865368998 0.5145109954 -0.437402301715 +1413394958255760384.0000000000 -1.3232729571 0.2697790996 2.0049817686 0.4549964423 0.5664988112 0.5140260243 -0.455888781097 +1413394958305760512.0000000000 -1.3200023758 0.2785595309 2.0081997593 0.4618593951 0.5469930747 0.5149190318 -0.471532465618 +1413394958355760384.0000000000 -1.3118487418 0.2884116288 2.0123243460 0.4646827038 0.5308563539 0.5170024777 -0.484736995034 +1413394958405760512.0000000000 -1.2972952125 0.2995022614 2.0144107871 0.4595443266 0.5217708333 0.5283287201 -0.487281205163 +1413394958455760384.0000000000 -1.2768462980 0.3115734457 2.0143913381 0.4425083832 0.5233057361 0.5480917302 -0.479513182996 +1413394958505760512.0000000000 -1.2515875610 0.3246451108 2.0141503254 0.4212283123 0.5283836505 0.5720789582 -0.464868898081 +1413394958555760384.0000000000 -1.2228388768 0.3384471278 2.0138639274 0.3948431521 0.5365809579 0.5971576659 -0.446746553268 +1413394958605760512.0000000000 -1.1931984990 0.3528029657 2.0138030749 0.3674767667 0.5447818832 0.6220973568 -0.425638819104 +1413394958655760384.0000000000 -1.1647614137 0.3674096986 2.0147371953 0.3405803814 0.5519901966 0.6443492966 -0.405124438494 +1413394958705760512.0000000000 -1.1405314578 0.3818555757 2.0174972302 0.3189460990 0.5553360646 0.6616262723 -0.390033225553 +1413394958755760384.0000000000 -1.1218793309 0.3957127643 2.0213420817 0.3031206642 0.5554581832 0.6753410864 -0.378811940979 +1413394958805760512.0000000000 -1.1101703932 0.4088372130 2.0264652295 0.2938921736 0.5506610212 0.6864383412 -0.373098155489 +1413394958855760384.0000000000 -1.1060242276 0.4210011338 2.0324405227 0.2906033770 0.5430863515 0.6945344218 -0.371791378422 +1413394958905760512.0000000000 -1.1094950419 0.4317102942 2.0391354234 0.2950523494 0.5306327967 0.7010510854 -0.37403251446 +1413394958955760384.0000000000 -1.1202872014 0.4404764370 2.0475245380 0.3069317427 0.5127754976 0.7042046293 -0.38334062457 +1413394959005760512.0000000000 -1.1365096531 0.4465926972 2.0568718050 0.3216931011 0.4937063803 0.7025821001 -0.398931010915 +1413394959055760384.0000000000 -1.1563850960 0.4496783031 2.0673797754 0.3365496942 0.4741294279 0.6971178700 -0.419478562306 +1413394959105760512.0000000000 -1.1777242426 0.4500681789 2.0781968136 0.3469816108 0.4566134705 0.6901985173 -0.441286649557 +1413394959155760384.0000000000 -1.1995954371 0.4479696192 2.0902639974 0.3552026267 0.4408920193 0.6801505863 -0.465661358947 +1413394959205760512.0000000000 -1.2197711003 0.4442823288 2.1031629039 0.3604964562 0.4263468486 0.6684722980 -0.491340469012 +1413394959255760384.0000000000 -1.2373955439 0.4402024951 2.1170912196 0.3647618493 0.4112970937 0.6563092512 -0.516760738451 +1413394959305760512.0000000000 -1.2514313818 0.4366192746 2.1310142860 0.3672847612 0.3977258819 0.6462615276 -0.53783088886 +1413394959355760384.0000000000 -1.2605260516 0.4342913172 2.1434973960 0.3644129618 0.3887046059 0.6430978990 -0.550033648824 +1413394959405760512.0000000000 -1.2644878986 0.4339755944 2.1523848982 0.3534031553 0.3874814613 0.6534809202 -0.545826908309 +1413394959455760384.0000000000 -1.2637574682 0.4352474926 2.1600032715 0.3362870156 0.3913335321 0.6713655598 -0.53201258901 +1413394959505760512.0000000000 -1.2593491852 0.4378827889 2.1663432688 0.3156676078 0.3974875139 0.6937345216 -0.510969716465 +1413394959555760384.0000000000 -1.2534134669 0.4407906060 2.1727572028 0.2940984758 0.4038536584 0.7174928950 -0.485399067504 +1413394959605760512.0000000000 -1.2479672073 0.4427234960 2.1798217735 0.2725743128 0.4082461093 0.7388906883 -0.46160471072 +1413394959655760384.0000000000 -1.2450053360 0.4431534930 2.1879828357 0.2543101467 0.4103452707 0.7565839577 -0.441048549651 +1413394959705760512.0000000000 -1.2456199898 0.4410743061 2.1972988960 0.2405077459 0.4086046182 0.7707059310 -0.425688451858 +1413394959755760384.0000000000 -1.2513454543 0.4357840254 2.2061803824 0.2337206822 0.4005419645 0.7814586828 -0.417448325403 +1413394959805760512.0000000000 -1.2628384089 0.4263675189 2.2142523921 0.2361019096 0.3859014167 0.7879625455 -0.417673331468 +1413394959855760384.0000000000 -1.2793615916 0.4122037141 2.2217860625 0.2452405945 0.3653038407 0.7898816023 -0.427196920715 +1413394959905760512.0000000000 -1.2989450763 0.3933890534 2.2282135056 0.2527891481 0.3463004267 0.7863974960 -0.444693871606 +1413394959955760384.0000000000 -1.3205550319 0.3698176278 2.2340321242 0.2573271634 0.3300984305 0.7771966473 -0.469875652279 +1413394960005760512.0000000000 -1.3426566901 0.3426959561 2.2384597065 0.2594837407 0.3142777571 0.7634940413 -0.50097358079 +1413394960055760384.0000000000 -1.3636742443 0.3137945115 2.2415925819 0.2587058176 0.2982258263 0.7478410230 -0.53372882702 +1413394960105760512.0000000000 -1.3827285000 0.2849924707 2.2424685967 0.2569402088 0.2816773836 0.7333740658 -0.562851721413 +1413394960155760384.0000000000 -1.3985538559 0.2575523481 2.2418359850 0.2508885332 0.2665002142 0.7236552841 -0.585111621373 +1413394960205760512.0000000000 -1.4110185712 0.2323957751 2.2400671339 0.2439062526 0.2515057042 0.7193968788 -0.599768915032 +1413394960255760384.0000000000 -1.4194508026 0.2105675051 2.2379045716 0.2323626584 0.2389415066 0.7217078444 -0.606673172874 +1413394960305760512.0000000000 -1.4242298559 0.1917118884 2.2356339857 0.2193221753 0.2271020975 0.7289363631 -0.607432464796 +1413394960355760384.0000000000 -1.4255855836 0.1762633583 2.2317658516 0.2036140881 0.2170543545 0.7412272240 -0.601673426894 +1413394960405760512.0000000000 -1.4246204691 0.1637187485 2.2257416060 0.1876192900 0.2066326807 0.7575722752 -0.590073033698 +1413394960455760384.0000000000 -1.4220987700 0.1531352392 2.2173483234 0.1707569024 0.1966241574 0.7758815945 -0.574620546422 +1413394960505760512.0000000000 -1.4185619580 0.1436922871 2.2053939515 0.1535442310 0.1871956764 0.7967042889 -0.5537546604 +1413394960555760384.0000000000 -1.4148245880 0.1339209361 2.1913601527 0.1359677729 0.1773261621 0.8165295069 -0.532304200012 +1413394960605760512.0000000000 -1.4120748703 0.1222194200 2.1761046735 0.1200028911 0.1669592028 0.8332792207 -0.513195548514 +1413394960655760384.0000000000 -1.4112323717 0.1068287132 2.1593921621 0.1068131436 0.1559286819 0.8472675894 -0.496401884051 +1413394960705760512.0000000000 -1.4121295190 0.0872734612 2.1435795203 0.0974779577 0.1421268729 0.8562229773 -0.487011512086 +1413394960755760384.0000000000 -1.4156619629 0.0616576560 2.1298547421 0.0944618752 0.1246039240 0.8578355153 -0.489560052505 +1413394960805760512.0000000000 -1.4209828139 0.0293633489 2.1194725542 0.0934522362 0.1087627050 0.8518879582 -0.503710492441 +1413394960855760384.0000000000 -1.4269750274 -0.0082861908 2.1121648530 0.0929380614 0.0942274334 0.8392407986 -0.527407422741 +1413394960905760512.0000000000 -1.4332166792 -0.0491734524 2.1067433896 0.0904872557 0.0845925938 0.8234500909 -0.553702173942 +1413394960955760384.0000000000 -1.4390604927 -0.0915529002 2.1028262691 0.0881263334 0.0771145645 0.8066934390 -0.579251921709 +1413394961005760512.0000000000 -1.4442854735 -0.1333810540 2.1001770484 0.0858082316 0.0723232658 0.7904415930 -0.602169727517 +1413394961055760384.0000000000 -1.4484977446 -0.1728161312 2.0974219236 0.0832509643 0.0696746149 0.7784421764 -0.618257634795 +1413394961105760512.0000000000 -1.4518178162 -0.2094707976 2.0943689899 0.0807637937 0.0680408563 0.7703570246 -0.628806572868 +1413394961155760384.0000000000 -1.4543039579 -0.2430761421 2.0900450632 0.0794511005 0.0678848789 0.7692506498 -0.630343242731 +1413394961205760512.0000000000 -1.4558308328 -0.2727759361 2.0834958054 0.0782811312 0.0691164238 0.7768923279 -0.620913275154 +1413394961255760384.0000000000 -1.4563246940 -0.2991442730 2.0761180393 0.0772426372 0.0695672345 0.7912355415 -0.602611228546 +1413394961305760512.0000000000 -1.4559544242 -0.3232881583 2.0675002593 0.0756367926 0.0702482281 0.8090406885 -0.57861682168 +1413394961355760384.0000000000 -1.4548524705 -0.3474019160 2.0589068144 0.0730054128 0.0712446757 0.8262040024 -0.55405897905 +1413394961405760512.0000000000 -1.4536687745 -0.3729412244 2.0510385235 0.0735148812 0.0707604109 0.8404280571 -0.532230408167 +1413394961455760384.0000000000 -1.4530656122 -0.4018057218 2.0443925405 0.0805227372 0.0652070722 0.8479083502 -0.519918797663 +1413394961505760512.0000000000 -1.4524402006 -0.4354463133 2.0401361757 0.0902666260 0.0575645490 0.8480348826 -0.519013580528 +1413394961555760384.0000000000 -1.4507313278 -0.4735108446 2.0371597923 0.1009369441 0.0488464229 0.8424690067 -0.526945664175 +1413394961605760512.0000000000 -1.4469673076 -0.5153569310 2.0365758167 0.1078448952 0.0432234524 0.8316588236 -0.542996144379 +1413394961655760384.0000000000 -1.4398440044 -0.5596874726 2.0374843432 0.1072496434 0.0435828559 0.8181816523 -0.563184545691 +1413394961705760512.0000000000 -1.4302636748 -0.6048353160 2.0399328689 0.1040004758 0.0453741763 0.8015742712 -0.587029618464 +1413394961755760384.0000000000 -1.4182121179 -0.6491285673 2.0429148225 0.0980421684 0.0499033146 0.7839032744 -0.611058956929 +1413394961805760512.0000000000 -1.4042976511 -0.6907630383 2.0456364719 0.0916816344 0.0553283007 0.7684489711 -0.630887815582 +1413394961855760384.0000000000 -1.3887942684 -0.7288439640 2.0473373878 0.0849969320 0.0615764628 0.7576011671 -0.644223821597 +1413394961905760512.0000000000 -1.3719027184 -0.7624544228 2.0491401634 0.0790724653 0.0676339381 0.7501549292 -0.653024331752 +1413394961955760384.0000000000 -1.3539143598 -0.7909987956 2.0504915821 0.0735072783 0.0733586494 0.7477095182 -0.655854911556 +1413394962005760512.0000000000 -1.3353975942 -0.8143035216 2.0513323279 0.0694488857 0.0781627787 0.7509848955 -0.651988588143 +1413394962055760384.0000000000 -1.3159803610 -0.8322511207 2.0507393748 0.0639359479 0.0836341487 0.7626526479 -0.638183721475 +1413394962105760512.0000000000 -1.2970949899 -0.8461697034 2.0487336711 0.0660904637 0.0842177004 0.7776384983 -0.619530302349 +1413394962155760384.0000000000 -1.2785435761 -0.8577775703 2.0473066700 0.0684405391 0.0840108447 0.7918850364 -0.600979333896 +1413394962205760512.0000000000 -1.2601294256 -0.8680061282 2.0470438048 0.0717129218 0.0837432524 0.8042935582 -0.583914545719 +1413394962255760384.0000000000 -1.2417319414 -0.8780042855 2.0478218492 0.0752566047 0.0832161948 0.8133148986 -0.570903130219 +1413394962305760512.0000000000 -1.2232243623 -0.8886257764 2.0503779957 0.0779040795 0.0825176304 0.8186477042 -0.562972229724 +1413394962355760384.0000000000 -1.2047372480 -0.9010512137 2.0549422693 0.0817643364 0.0818459121 0.8177246313 -0.563863695752 +1413394962405760512.0000000000 -1.1860875631 -0.9159226311 2.0635955685 0.0871980186 0.0791865433 0.8064683669 -0.579426242169 +1413394962455760384.0000000000 -1.1663505837 -0.9311883511 2.0744306581 0.0900690724 0.0780060576 0.7897272134 -0.601775328164 +1413394962505760512.0000000000 -1.1455296378 -0.9450584554 2.0871250538 0.0938067253 0.0758616583 0.7691393115 -0.627590652141 +1413394962555760384.0000000000 -1.1230990514 -0.9552404661 2.0997057324 0.0945862045 0.0751156329 0.7505433797 -0.649688946172 +1413394962605760512.0000000000 -1.0987833107 -0.9604797883 2.1110523246 0.0925378002 0.0759053277 0.7386494073 -0.663379370973 +1413394962655760384.0000000000 -1.0725709411 -0.9596379265 2.1202638609 0.0887009439 0.0779528868 0.7362391797 -0.666338772867 +1413394962705760512.0000000000 -1.0448465147 -0.9527637367 2.1267557289 0.0839601614 0.0804167638 0.7459601123 -0.655764703452 +1413394962755760384.0000000000 -1.0158551981 -0.9406089235 2.1317478162 0.0767292047 0.0845364837 0.7618495637 -0.637613875647 +1413394962805760512.0000000000 -0.9864749536 -0.9247114989 2.1351035763 0.0715603411 0.0868901997 0.7795202117 -0.616179722395 +1413394962855760384.0000000000 -0.9569262495 -0.9068497149 2.1365078065 0.0669030126 0.0866764011 0.7968824254 -0.594129269117 +1413394962905760512.0000000000 -0.9278365556 -0.8883351149 2.1360036624 0.0654904385 0.0825756275 0.8107533555 -0.575822250944 +1413394962955760384.0000000000 -0.8990529881 -0.8702940813 2.1352183891 0.0657055169 0.0758293863 0.8183190099 -0.565938766388 +1413394963005760512.0000000000 -0.8707766211 -0.8539457856 2.1343428507 0.0672235572 0.0690156571 0.8171048041 -0.568381536913 +1413394963055760384.0000000000 -0.8424887162 -0.8400218159 2.1343623292 0.0695682687 0.0620345103 0.8072500001 -0.582803065213 +1413394963105760512.0000000000 -0.8142273688 -0.8272947004 2.1338931080 0.0717312119 0.0556754972 0.7917210766 -0.604096523051 +1413394963155760384.0000000000 -0.7851364231 -0.8127474285 2.1307466848 0.0705600378 0.0518792652 0.7751938771 -0.625623110017 +1413394963205760512.0000000000 -0.7553102311 -0.7949997703 2.1239419364 0.0695202780 0.0489384960 0.7618354578 -0.642167182096 +1413394963255760384.0000000000 -0.7245355866 -0.7739256073 2.1126911408 0.0675902866 0.0472917586 0.7564032636 -0.648882998316 +1413394963305760512.0000000000 -0.6930761701 -0.7488120652 2.0961986431 0.0659419689 0.0464742611 0.7614591688 -0.643173175819 +1413394963355760384.0000000000 -0.6610402234 -0.7200505769 2.0748959744 0.0657539677 0.0454276312 0.7749898871 -0.626899849257 +1413394963405760512.0000000000 -0.6283202453 -0.6885803412 2.0501544310 0.0654090761 0.0451316339 0.7930672484 -0.603928081684 +1413394963455760384.0000000000 -0.5950008876 -0.6562043843 2.0240457864 0.0641422739 0.0456094476 0.8115866771 -0.578906393621 +1413394963505760512.0000000000 -0.5614943306 -0.6240287340 1.9962838612 0.0639707551 0.0457028261 0.8281245585 -0.555003342146 +1413394963555760384.0000000000 -0.5276434935 -0.5932348084 1.9679862236 0.0646957706 0.0460408464 0.8412978520 -0.534707978168 +1413394963605760512.0000000000 -0.4936605572 -0.5663304567 1.9423330993 0.0653483862 0.0466792245 0.8476792914 -0.524395325431 +1413394963655760384.0000000000 -0.4597963418 -0.5450143888 1.9204826475 0.0671900822 0.0468658729 0.8448982239 -0.528617133763 +1413394963705760512.0000000000 -0.4258012046 -0.5281883577 1.9017290979 0.0695748381 0.0469152835 0.8346682564 -0.544322698234 +1413394963755760384.0000000000 -0.3913203559 -0.5147134421 1.8850755853 0.0731598692 0.0457390358 0.8184122460 -0.568117038738 +1413394963805760512.0000000000 -0.3556289992 -0.5022171965 1.8700570509 0.0739437987 0.0464486282 0.7992494898 -0.594621806341 +1413394963855760384.0000000000 -0.3190454535 -0.4885668277 1.8547335213 0.0731101768 0.0484096043 0.7831631362 -0.6156028869 +1413394963905760512.0000000000 -0.2811722162 -0.4723385994 1.8380764588 0.0676391887 0.0536375188 0.7734914067 -0.627900470163 +1413394963955760384.0000000000 -0.2427407795 -0.4523621606 1.8180633988 0.0627593182 0.0587882420 0.7775361438 -0.622930779224 +1413394964005760512.0000000000 -0.2042570511 -0.4300198639 1.7965029088 0.0603496645 0.0625792809 0.7887545810 -0.608529344054 +1413394964055760384.0000000000 -0.1658001772 -0.4057691165 1.7734448685 0.0603005531 0.0650833873 0.8060522541 -0.585156183956 +1413394964105760512.0000000000 -0.1273257608 -0.3809746737 1.7518772115 0.0601281034 0.0667524734 0.8228668692 -0.561087189385 +1413394964155760384.0000000000 -0.0895586118 -0.3574511987 1.7309036028 0.0620326456 0.0674616745 0.8378663532 -0.538127166734 +1413394964205760512.0000000000 -0.0522114601 -0.3374163586 1.7129539586 0.0640690586 0.0679414584 0.8473269928 -0.522796405123 +1413394964255760384.0000000000 -0.0159998568 -0.3225254730 1.6993911473 0.0694976744 0.0652339490 0.8477814795 -0.52170985061 +1413394964305760512.0000000000 0.0200830510 -0.3130420673 1.6901049110 0.0742044508 0.0630867249 0.8409763317 -0.532233571046 +1413394964355760384.0000000000 0.0565567893 -0.3077448640 1.6847600805 0.0771816288 0.0612237036 0.8270773076 -0.553387550889 +1413394964405760512.0000000000 0.0937256402 -0.3045997160 1.6822845472 0.0775087606 0.0614086905 0.8093003000 -0.579011562225 +1413394964455760384.0000000000 0.1317659635 -0.3014957949 1.6819078710 0.0742226347 0.0633370723 0.7899297877 -0.605384461487 +1413394964505760512.0000000000 0.1700224675 -0.2960672261 1.6811865154 0.0702175415 0.0656422735 0.7744538045 -0.625285449657 +1413394964555760384.0000000000 0.2090690045 -0.2872278350 1.6789405768 0.0625520794 0.0702769605 0.7688916862 -0.632419133977 +1413394964605760512.0000000000 0.2481791072 -0.2744579765 1.6747842544 0.0526860447 0.0756406836 0.7754081795 -0.624695784224 +1413394964655760384.0000000000 0.2867242168 -0.2586749442 1.6697035046 0.0428426228 0.0818932072 0.7893638161 -0.60692897287 +1413394964705760512.0000000000 0.3241734845 -0.2410602986 1.6643044922 0.0348020907 0.0864535567 0.8076213088 -0.582290665023 +1413394964755760384.0000000000 0.3596048296 -0.2231469539 1.6602926768 0.0278681957 0.0903746659 0.8252099373 -0.556852173252 +1413394964805760512.0000000000 0.3923524261 -0.2065930596 1.6577171583 0.0224027398 0.0943204027 0.8410549147 -0.532192079422 +1413394964855760384.0000000000 0.4220355154 -0.1934720918 1.6567943645 0.0181361423 0.0978013959 0.8525751027 -0.513051324481 +1413394964905760512.0000000000 0.4481932352 -0.1846796063 1.6585360896 0.0123797810 0.1029215995 0.8608519183 -0.498184564284 +1413394964955760384.0000000000 0.4706609900 -0.1814188265 1.6619447295 0.0057336427 0.1100688717 0.8651185378 -0.489307556042 +1413394965005760512.0000000000 0.4879700760 -0.1847393256 1.6682984671 0.0048532319 0.1127697639 0.8626098004 -0.493116374475 +1413394965055760384.0000000000 0.4995359738 -0.1949817390 1.6775735743 0.0121024216 0.1098111574 0.8529187119 -0.510220258375 +1413394965105760512.0000000000 0.5073068244 -0.2096840251 1.6889244157 0.0231163948 0.1021734831 0.8373356481 -0.536558686501 +1413394965155760384.0000000000 0.5129066683 -0.2263282276 1.7025481850 0.0319653166 0.0918624355 0.8189056604 -0.565626228862 +1413394965205760512.0000000000 0.5175014908 -0.2434138057 1.7176546304 0.0366104086 0.0816813548 0.7981188970 -0.595813780052 +1413394965255760384.0000000000 0.5217365200 -0.2588610799 1.7322088361 0.0378613661 0.0700604044 0.7823308084 -0.617751214413 +1413394965305760512.0000000000 0.5259783947 -0.2708218297 1.7454159295 0.0388882179 0.0564010426 0.7730380485 -0.630649510033 +1413394965355760384.0000000000 0.5304419595 -0.2789189048 1.7561770409 0.0379810463 0.0411607287 0.7739236692 -0.630797422994 +1413394965405760512.0000000000 0.5352374805 -0.2829922226 1.7650448613 0.0359557924 0.0256689982 0.7818803540 -0.621861235021 +1413394965455760384.0000000000 0.5408757698 -0.2843309553 1.7741732303 0.0301762967 0.0115149143 0.7905136863 -0.611592110447 +1413394965505760512.0000000000 0.5470313571 -0.2840029475 1.7846514709 0.0233379364 -0.0030491508 0.7964871852 -0.604197159183 +1413394965555760384.0000000000 0.5543100903 -0.2829875089 1.7973003207 0.0125063865 -0.0154846439 0.7978515260 -0.602525317735 +1413394965605760512.0000000000 0.5627032377 -0.2806742507 1.8125865775 0.0028787584 0.0269369789 -0.7939786798 0.607341722508 +1413394965655760384.0000000000 0.5714206443 -0.2765106589 1.8298648462 0.0210684619 0.0386959756 -0.7849321111 0.618013205688 +1413394965705760512.0000000000 0.5799639786 -0.2701815355 1.8474431009 0.0390325202 0.0511701787 -0.7747961264 0.628926893821 +1413394965755760384.0000000000 0.5873801509 -0.2602762229 1.8620610007 0.0541132169 0.0670937775 -0.7697224292 0.632532660688 +1413394965805760512.0000000000 0.5931018222 -0.2467719596 1.8718739952 0.0636819362 0.0862555341 -0.7707637366 0.628034916375 +1413394965855760384.0000000000 0.5977029937 -0.2305731569 1.8770248635 0.0710245460 0.1054735052 -0.7758663464 0.617950051408 +1413394965905760512.0000000000 0.6012989013 -0.2125680296 1.8795902924 0.0760849492 0.1256628895 -0.7798951271 0.608427078119 +1413394965955760384.0000000000 0.6048267310 -0.1934797037 1.8825010136 0.0837688020 0.1430750386 -0.7770484525 0.607213326284 +1413394966005760512.0000000000 0.6085676676 -0.1733453335 1.8859533500 0.0957819429 0.1566894309 -0.7673705555 0.614342471393 +1413394966055760384.0000000000 0.6119551118 -0.1510830066 1.8890691765 0.1098712484 0.1672280392 -0.7535822280 0.626160456484 +1413394966105760512.0000000000 0.6145149058 -0.1255517659 1.8897191907 0.1245757668 0.1769293834 -0.7414166494 0.635199357418 +1413394966155760384.0000000000 0.6151216112 -0.0964209368 1.8856508059 0.1342454865 0.1887996631 -0.7400736315 0.631366657737 +1413394966205760512.0000000000 0.6142296253 -0.0637543229 1.8772235691 0.1396987646 0.2027307382 -0.7483650026 0.615901230617 +1413394966255760384.0000000000 0.6121560403 -0.0279999807 1.8667319131 0.1441883716 0.2168497349 -0.7615920627 0.59343359858 +1413394966305760512.0000000000 0.6088503774 0.0100634818 1.8535928039 0.1455355716 0.2322122667 -0.7795466627 0.563208541576 +1413394966355760384.0000000000 0.6055003304 0.0483248622 1.8388400938 0.1453866233 0.2478482627 -0.7982616937 0.529350769117 +1413394966405760512.0000000000 0.6033665779 0.0850761194 1.8241678961 0.1458408320 0.2621445083 -0.8135972219 0.498066530764 +1413394966455760384.0000000000 0.6033278586 0.1182687319 1.8108100831 0.1467392566 0.2754769945 -0.8244177011 0.472139248651 +1413394966505760512.0000000000 0.6071177248 0.1456293296 1.8007263197 0.1520053071 0.2857552463 -0.8262272477 0.461071427212 +1413394966555760384.0000000000 0.6155378460 0.1660445533 1.7953426362 0.1616133332 0.2932049011 -0.8179885512 0.467767834029 +1413394966605760512.0000000000 0.6274130013 0.1808711113 1.7918835888 0.1737719467 0.2980507154 -0.8040750405 0.484182208221 +1413394966655760384.0000000000 0.6419137708 0.1914530543 1.7909319503 0.1878001514 0.3010926729 -0.7841156133 0.509153228858 +1413394966705760512.0000000000 0.6575715581 0.2004805848 1.7909165874 0.2026395042 0.3034382593 -0.7624542401 0.534346316429 +1413394966755760384.0000000000 0.6731168477 0.2097262216 1.7909876285 0.2177614168 0.3049445259 -0.7410416582 0.557176868013 +1413394966805760512.0000000000 0.6873461836 0.2203810847 1.7899190493 0.2319533827 0.3073813490 -0.7241119391 0.572168012244 +1413394966855760384.0000000000 0.6991643644 0.2329990380 1.7878921022 0.2428130553 0.3120954704 -0.7130671128 0.578941732944 +1413394966905760512.0000000000 0.7079782754 0.2480966097 1.7836554803 0.2483247093 0.3213446143 -0.7100931917 0.575187045014 +1413394966955760384.0000000000 0.7139690510 0.2650633704 1.7777274013 0.2479552737 0.3353722804 -0.7136710129 0.562776421929 +1413394967005760512.0000000000 0.7178386708 0.2834544325 1.7713885978 0.2439961401 0.3524664010 -0.7216881006 0.54350676649 +1413394967055760384.0000000000 0.7212427639 0.3024841583 1.7658855883 0.2389579867 0.3698557011 -0.7312491842 0.520941908059 +1413394967105760512.0000000000 0.7245198061 0.3217514700 1.7603448184 0.2331667141 0.3874843638 -0.7387970639 0.499667939311 +1413394967155760384.0000000000 0.7292450753 0.3402899866 1.7579862469 0.2312444559 0.4030398123 -0.7409134435 0.484904300441 +1413394967205760512.0000000000 0.7375575372 0.3571996263 1.7598493565 0.2375060950 0.4128738148 -0.7360162920 0.48104686443 +1413394967255760384.0000000000 0.7493991024 0.3724657586 1.7647851561 0.2493367171 0.4193775299 -0.7242052590 0.487319640238 +1413394967305760512.0000000000 0.7639351604 0.3866685831 1.7722255354 0.2659983933 0.4224118799 -0.7083689493 0.499025540478 +1413394967355760384.0000000000 0.7798441451 0.4005619272 1.7819927269 0.2854963303 0.4225039810 -0.6888033315 0.515298168007 +1413394967405760512.0000000000 0.7950211960 0.4150543144 1.7935092457 0.3063344565 0.4209354643 -0.6670943131 0.532876827252 +1413394967455760384.0000000000 0.8079804216 0.4312290326 1.8052289216 0.3256506706 0.4199301950 -0.6494244650 0.54392842937 +1413394967505760512.0000000000 0.8167738611 0.4496836136 1.8157843571 0.3410029766 0.4224700884 -0.6391968734 0.54466811128 +1413394967555760384.0000000000 0.8212027191 0.4699204414 1.8239713644 0.3495424547 0.4307311943 -0.6387090315 0.533236798905 +1413394967605760512.0000000000 0.8208110762 0.4914791454 1.8302961406 0.3476543629 0.4470977673 -0.6442607593 0.513972863482 +1413394967655760384.0000000000 0.8171465232 0.5135164236 1.8356352246 0.3398501914 0.4668526378 -0.6530879796 0.489925048319 +1413394967705760512.0000000000 0.8121720459 0.5354074091 1.8416982972 0.3307274417 0.4868381351 -0.6603339624 0.466440829748 +1413394967755760384.0000000000 0.8080675463 0.5564792490 1.8517141860 0.3290319430 0.5011407268 -0.6609139808 0.451429576301 +1413394967805760512.0000000000 0.8056006405 0.5766771766 1.8643103932 0.3334795328 0.5112686132 -0.6552324136 0.445046391441 +1413394967855760384.0000000000 0.8053019394 0.5962569009 1.8792647304 0.3437853562 0.5177807587 -0.6437218836 0.446471557073 +1413394967905760512.0000000000 0.8063726374 0.6157337117 1.8953353365 0.3584638788 0.5222368668 -0.6278959930 0.452237685919 +1413394967955760384.0000000000 0.8078798523 0.6352854127 1.9127286259 0.3755261439 0.5249414070 -0.6100621995 0.45960934192 +1413394968005760512.0000000000 0.8080916569 0.6552933360 1.9304633947 0.3908791861 0.5293705840 -0.5937871923 0.463030254935 +1413394968055760384.0000000000 0.8056927272 0.6753361057 1.9449173159 0.3988946413 0.5387307784 -0.5836900379 0.458211908562 +1413394968105760512.0000000000 0.8006390582 0.6956613331 1.9552725825 0.3999248873 0.5523272179 -0.5799940524 0.445647425732 +1413394968155760384.0000000000 0.7935634475 0.7154549346 1.9608896774 0.3948326692 0.5684050288 -0.5811082674 0.428177612843 +1413394968205760512.0000000000 0.7865259401 0.7347963261 1.9640934345 0.3891754212 0.5821766795 -0.5832884536 0.411566987695 +1413394968255760384.0000000000 0.7809808387 0.7536451054 1.9655698915 0.3851836550 0.5932796986 -0.5836008284 0.398826809774 +1413394968305760512.0000000000 0.7774791250 0.7722100189 1.9663709833 0.3854546314 0.6000324261 -0.5808108169 0.392485171318 +1413394968355760384.0000000000 0.7754877015 0.7909858151 1.9649885928 0.3885442124 0.6050822088 -0.5757087842 0.389189300145 +1413394968405760512.0000000000 0.7747540100 0.8095016180 1.9615239246 0.3931309708 0.6099025021 -0.5690082804 0.386906390029 +1413394968455760384.0000000000 0.7760428067 0.8281197016 1.9573298319 0.3989690614 0.6133606517 -0.5625484474 0.384904719742 +1413394968505760512.0000000000 0.7785559507 0.8468519634 1.9532690238 0.4049115289 0.6170905252 -0.5563521573 0.381730552249 +1413394968555760384.0000000000 0.7819507769 0.8654100589 1.9486942220 0.4075609891 0.6225070388 -0.5524392141 0.375752500277 +1413394968605760512.0000000000 0.7869827795 0.8834930657 1.9440857838 0.4067690837 0.6283810168 -0.5505012421 0.369627640632 +1413394968655760384.0000000000 0.7937377188 0.9012496370 1.9397492711 0.4040740979 0.6345385783 -0.5485977195 0.364863615985 +1413394968705760512.0000000000 0.8026785723 0.9186441290 1.9359118586 0.4005232222 0.6407723015 -0.5441926381 0.364480971634 +1413394968755760384.0000000000 0.8141930385 0.9359269979 1.9328769789 0.3970593683 0.6455287886 -0.5369769680 0.370529589872 +1413394968805760512.0000000000 0.8278929531 0.9542595621 1.9306581487 0.3959313655 0.6482127993 -0.5302688200 0.376660987131 +1413394968855760384.0000000000 0.8431732238 0.9740643943 1.9297626355 0.3987180993 0.6477332591 -0.5262172232 0.380211699349 +1413394968905760512.0000000000 0.8598887447 0.9957802422 1.9296621304 0.4042723408 0.6454611639 -0.5240656406 0.381181013101 +1413394968955760384.0000000000 0.8774098675 1.0193067281 1.9309772146 0.4140373546 0.6415267879 -0.5219700070 0.380215414222 +1413394969005760512.0000000000 0.8950548674 1.0437862252 1.9326444864 0.4251857358 0.6378336307 -0.5184096412 0.378994450512 +1413394969055760384.0000000000 0.9124065509 1.0688390692 1.9343378011 0.4363184224 0.6349696419 -0.5138144651 0.377404933232 +1413394969155760384.0000000000 0.9470556905 1.1189825605 1.9318913464 0.4536899701 0.6338801579 -0.5039108320 0.372068850902 +1413394969255760384.0000000000 0.9794958939 1.1664723377 1.9129031941 0.4664858334 0.6338306214 -0.4936057589 0.370139251315 +1413394969355760384.0000000000 1.0083344027 1.2096670976 1.8789209726 0.4780984904 0.6316226206 -0.4840475340 0.371715863878 +1413394969455760384.0000000000 1.0304710275 1.2485012900 1.8366144674 0.4863746639 0.6290008453 -0.4732668943 0.379230892448 +1413394969555760384.0000000000 1.0438585574 1.2828662871 1.7908501654 0.4736398792 0.6390664115 -0.4665567492 0.386761149002 +1413394969655760384.0000000000 1.0475471049 1.3165384468 1.7455215100 0.4458412535 0.6578248190 -0.4656955162 0.389383834191 +1413394969755760384.0000000000 1.0458126017 1.3554371628 1.7064440743 0.4214875254 0.6720132812 -0.4623469674 0.396209158929 +1413394969855760384.0000000000 1.0410416519 1.4066644564 1.6744535597 0.4095122799 0.6784962692 -0.4633203907 0.396581291609 +1413394969955760384.0000000000 1.0350358826 1.4728342906 1.6512455876 0.4080136599 0.6781856949 -0.4779179063 0.381029515065 +1413394970055760384.0000000000 1.0313871006 1.5501162209 1.6415850396 0.4097637223 0.6752418331 -0.4935844028 0.364028290183 +1413394970155760384.0000000000 1.0345749701 1.6343227110 1.6480877936 0.4133185867 0.6713880552 -0.5039093083 0.352818982273 +1413394970255760384.0000000000 1.0458285976 1.7223905493 1.6648349314 0.4260183625 0.6625921207 -0.5040694216 0.354110229395 +1413394970355760384.0000000000 1.0634180854 1.8115335417 1.6802100617 0.4562352088 0.6415075875 -0.4996561800 0.361470816634 +1413394970455760384.0000000000 1.0802120994 1.8966831929 1.6886642927 0.4910939457 0.6155851216 -0.4979820846 0.363174252855 +1413394970555760384.0000000000 1.0887806974 1.9715354375 1.6842412653 0.5107498642 0.6009820054 -0.5030915551 0.353346986103 +1413394970655760384.0000000000 1.0886876508 2.0317604242 1.6711955260 0.5243392720 0.5903164364 -0.5130865419 0.336655659922 +1413394970755760384.0000000000 1.0838964604 2.0720105895 1.6536880840 0.5287217355 0.5855156900 -0.5113982863 0.340729358749 +1413394970855760384.0000000000 1.0719390311 2.0909437808 1.6317118969 0.5006647684 0.6064519360 -0.5013261968 0.360864078728 +1413394970955760384.0000000000 1.0525856293 2.0969608437 1.6169290641 0.4593512214 0.6355170913 -0.4977986972 0.370554907014 +1413394971055760384.0000000000 1.0308499273 2.1010762416 1.6205466771 0.4307670289 0.6528115291 -0.4962947555 0.376786929229 +1413394971155760384.0000000000 1.0092340643 2.1104448575 1.6391157133 0.4141380814 0.6610009857 -0.5039035890 0.37101013396 +1413394971255760384.0000000000 0.9914843704 2.1265557895 1.6592789692 0.3967641379 0.6699136969 -0.5174804537 0.354975826792 +1413394971355760384.0000000000 0.9826858608 2.1481760485 1.6701344315 0.3781613375 0.6791846473 -0.5306545862 0.337798649811 +1413394971455760384.0000000000 0.9899650014 2.1757044742 1.6734825048 0.3649150723 0.6853757843 -0.5402833466 0.324331512022 +1413394971555760384.0000000000 1.0197665716 2.2108086525 1.6784179399 0.3664627443 0.6814225964 -0.5516817041 0.311473272465 +1413394971655760384.0000000000 1.0747466193 2.2501044593 1.6921038507 0.3911486450 0.6642970506 -0.5557111686 0.311283252398 +1413394971755760384.0000000000 1.1480355787 2.2858374395 1.7094285091 0.4245301283 0.6383448611 -0.5534556792 0.325540810805 +1413394971855760384.0000000000 1.2318660497 2.3126288104 1.7266974594 0.4501766179 0.6116492173 -0.5506192019 0.346474735425 +1413394971955760384.0000000000 1.3187447401 2.3271317025 1.7440291582 0.4701566853 0.5824120770 -0.5513240586 0.368497823866 +1413394972055760384.0000000000 1.4012206997 2.3274952411 1.7542962413 0.4750848984 0.5566910443 -0.5554603956 0.394782433098 +1413394972155760384.0000000000 1.4743152948 2.3142149612 1.7549443402 0.4690547671 0.5301806419 -0.5685656441 0.419081401213 +1413394972255760384.0000000000 1.5340865157 2.2876551523 1.7461363536 0.4546412043 0.5018148641 -0.5884696231 0.441799411771 +1413394972355760384.0000000000 1.5791043339 2.2487899824 1.7309651371 0.4341955879 0.4707617419 -0.6120019046 0.464016424896 +1413394972455760384.0000000000 1.6080548855 2.1992106196 1.7094910754 0.4075878255 0.4380119120 -0.6416783748 0.479861014071 +1413394972555760384.0000000000 1.6209221352 2.1398792927 1.6808131032 0.3666682981 0.4112406068 -0.6785041734 0.485867892766 +1413394972655760384.0000000000 1.6192501114 2.0718363235 1.6543929973 0.3177722782 0.3859496131 -0.7116835143 0.493528368804 +1413394972755760384.0000000000 1.6127313167 1.9945383478 1.6332779425 0.2644255287 0.3611106135 -0.7319092494 0.513796764535 +1413394972855760384.0000000000 1.6038673027 1.9137113633 1.6198072362 0.2131064448 0.3338572593 -0.7438658124 0.538320189811 +1413394972955760384.0000000000 1.5963537094 1.8351191933 1.6113394412 0.1719440020 0.2989100016 -0.7544169107 0.558518751707 +1413394973005760512.0000000000 1.5937156397 1.7976869745 1.6080009680 0.1550191443 0.2790139606 -0.7608828236 0.564958054658 +1413394973055760384.0000000000 1.5917722118 1.7615089887 1.6051970805 0.1402764761 0.2575146446 -0.7678304596 0.569600828156 +1413394973105760512.0000000000 1.5907656763 1.7265550556 1.6023802701 0.1266346396 0.2352611184 -0.7745826085 0.573269270818 +1413394973155760384.0000000000 1.5907239545 1.6928518631 1.5990681429 0.1149464426 0.2120334387 -0.7821703257 0.574489963194 +1413394973205760512.0000000000 1.5912796208 1.6602597358 1.5956264918 0.1051630421 0.1873989689 -0.7902593279 0.573857609202 +1413394973255760384.0000000000 1.5921937933 1.6278964329 1.5921861607 0.0942746496 0.1636672482 -0.7970158429 0.573664595768 +1413394973305760512.0000000000 1.5932451087 1.5955168151 1.5892510301 0.0828742305 0.1401723900 -0.8027325654 0.573675859158 +1413394973355760384.0000000000 1.5941036029 1.5631218985 1.5866462622 0.0715397734 0.1167474744 -0.8075100651 0.573741738826 +1413394973405760512.0000000000 1.5947080713 1.5301441941 1.5845944079 0.0592772651 0.0933363729 -0.8103939730 0.575357398421 +1413394973455760384.0000000000 1.5947600989 1.4970325779 1.5824808414 0.0459678451 0.0711450376 -0.8129156556 0.57618875183 +1413394973505760512.0000000000 1.5942301295 1.4635059925 1.5813470398 0.0325679981 0.0485033535 -0.8143486254 0.57742797512 +1413394973555760384.0000000000 1.5932144208 1.4296387417 1.5801535873 0.0185908630 0.0257832796 -0.8159482701 0.577250398738 +1413394973605760512.0000000000 1.5913033735 1.3954062303 1.5795467975 0.0045745877 0.0032890651 -0.8172638061 0.576236172442 +1413394973655760384.0000000000 1.5883858524 1.3606584262 1.5792780995 0.0125481336 0.0172056665 0.8177651634 -0.575157932184 +1413394973705760512.0000000000 1.5848100842 1.3253388778 1.5803691597 0.0289400631 0.0385265855 0.8155766664 -0.576639294721 +1413394973755760384.0000000000 1.5805599055 1.2902666377 1.5815913150 0.0467644103 0.0584015378 0.8129817731 -0.577462541554 +1413394973805760512.0000000000 1.5760448354 1.2547645641 1.5834812761 0.0622619878 0.0803901075 0.8090369526 -0.578895573336 +1413394973855760384.0000000000 1.5711357884 1.2197176715 1.5852869091 0.0770832669 0.1018683634 0.8053486734 -0.578873492805 +1413394973905760512.0000000000 1.5658627950 1.1849616928 1.5872472787 0.0909219599 0.1241127808 0.8013453522 -0.57807857719 +1413394973955760384.0000000000 1.5602140693 1.1509825226 1.5895833283 0.1044038492 0.1458179026 0.7975637392 -0.575959249832 +1413394974005760512.0000000000 1.5540602776 1.1177192653 1.5923802585 0.1174947330 0.1671607987 0.7930441234 -0.573875660208 +1413394974055760384.0000000000 1.5471794414 1.0852074978 1.5957983157 0.1310139636 0.1884003573 0.7876749278 -0.571759437931 +1413394974105760512.0000000000 1.5401131092 1.0538636393 1.5989516412 0.1431142248 0.2100364325 0.7822084704 -0.56881712743 +1413394974155760384.0000000000 1.5323399702 1.0232634041 1.6028508759 0.1547533408 0.2310747660 0.7752482484 -0.567138439287 +1413394974205760512.0000000000 1.5236456559 0.9936583915 1.6070370271 0.1656597876 0.2529668776 0.7678634505 -0.564756863661 +1413394974255760384.0000000000 1.5142384838 0.9650007223 1.6114751356 0.1762073653 0.2744326616 0.7601474555 -0.561972885929 +1413394974305760512.0000000000 1.5037557771 0.9378391984 1.6162995957 0.1867020099 0.2955368420 0.7531393738 -0.557298320591 +1413394974355760384.0000000000 1.4922943249 0.9121230636 1.6216596914 0.1957862441 0.3173389021 0.7453718122 -0.552616168344 +1413394974405760512.0000000000 1.4793132564 0.8877176048 1.6274972707 0.2044782030 0.3388937930 0.7377702234 -0.546840707086 +1413394974455760384.0000000000 1.4650883697 0.8655931918 1.6337361387 0.2143913902 0.3583846238 0.7297825382 -0.541307897775 +1413394974505760512.0000000000 1.4491575827 0.8451492933 1.6397296801 0.2248722609 0.3779669653 0.7208668171 -0.535653312679 +1413394974555760384.0000000000 1.4315992369 0.8267642388 1.6466893237 0.2358242509 0.3956285986 0.7115924763 -0.5305667557 +1413394974605760512.0000000000 1.4120450934 0.8105383693 1.6541773211 0.2497646173 0.4104653737 0.7009080397 -0.52712781455 +1413394974655760384.0000000000 1.3908399006 0.7962084878 1.6615454146 0.2654327183 0.4232107346 0.6890932113 -0.524965420077 +1413394974705760512.0000000000 1.3687631678 0.7841249663 1.6686996329 0.2809720190 0.4347876853 0.6786105306 -0.521058673307 +1413394974755760384.0000000000 1.3467418288 0.7745844548 1.6747260134 0.2951563176 0.4464345572 0.6699589616 -0.514523006431 +1413394974805760512.0000000000 1.3244588702 0.7668155493 1.6798851739 0.3076005815 0.4579517752 0.6626502253 -0.506514296695 +1413394974855760384.0000000000 1.3022750697 0.7609590252 1.6838172504 0.3198760628 0.4683918757 0.6562439119 -0.497626650629 +1413394974905760512.0000000000 1.2799028572 0.7564598136 1.6851009045 0.3326237635 0.4777298335 0.6510481103 -0.487105734168 +1413394974955760384.0000000000 1.2575067843 0.7526727979 1.6833828228 0.3441107534 0.4868604338 0.6458721942 -0.476868761987 +1413394975005760512.0000000000 1.2356927243 0.7492468095 1.6778463948 0.3546580187 0.4952838654 0.6398206661 -0.468552129099 +1413394975055760384.0000000000 1.2137440148 0.7461504473 1.6695545919 0.3665823839 0.5011390849 0.6329812545 -0.462397777813 +1413394975105760512.0000000000 1.1925906353 0.7432051294 1.6589696473 0.3793299123 0.5052788202 0.6242375950 -0.459488363777 +1413394975155760384.0000000000 1.1721613219 0.7401377372 1.6456459454 0.3905500922 0.5093557322 0.6154121110 -0.4574880295 +1413394975205760512.0000000000 1.1528427078 0.7369767794 1.6302973967 0.3995979777 0.5141451138 0.6062633682 -0.456531473665 +1413394975255760384.0000000000 1.1348254230 0.7338484869 1.6126448074 0.4073302454 0.5191552105 0.5979286609 -0.455017862415 +1413394975305760512.0000000000 1.1183944169 0.7306153632 1.5933199646 0.4136053087 0.5247304040 0.5906086169 -0.452515318492 +1413394975355760384.0000000000 1.1038640630 0.7274077980 1.5740170736 0.4198502541 0.5299299744 0.5844742044 -0.44865341945 +1413394975405760512.0000000000 1.0913283374 0.7243498473 1.5543269449 0.4246637506 0.5354799585 0.5807035528 -0.442385913766 +1413394975455760384.0000000000 1.0803083233 0.7212443111 1.5351892255 0.4277426483 0.5420216199 0.5783393776 -0.434479406524 +1413394975505760512.0000000000 1.0710201005 0.7177866529 1.5170574148 0.4301208174 0.5484347302 0.5772240561 -0.425473639867 +1413394975555760384.0000000000 1.0633991903 0.7136612057 1.4996071816 0.4311169528 0.5545413726 0.5770869846 -0.416644514296 +1413394975605760512.0000000000 1.0567191660 0.7086655807 1.4836414419 0.4310070263 0.5600046563 0.5778637210 -0.408290641773 +1413394975655760384.0000000000 1.0505253450 0.7025975142 1.4691069855 0.4298988365 0.5648011033 0.5782970639 -0.402193000833 +1413394975755760384.0000000000 1.0378103713 0.6870491578 1.4448187455 0.4283291320 0.5713651881 0.5790973140 -0.393347527493 +1413394975805760512.0000000000 1.0308889167 0.6777081027 1.4350161636 0.4265571774 0.5739321161 0.5799588054 -0.390254640586 +1413394975855760384.0000000000 1.0234313588 0.6673935921 1.4269623626 0.4261399487 0.5748248471 0.5796806335 -0.389809571989 +1413394975955760384.0000000000 1.0057557169 0.6440290744 1.4177329054 0.4346683770 0.5687139424 0.5754131483 -0.395635643711 +1413394976055760384.0000000000 0.9882977612 0.6169828416 1.4125395060 0.4444438617 0.5601030357 0.5676678585 -0.408053238759 +1413394976155760384.0000000000 0.9751671719 0.5867733931 1.4065255044 0.4491584350 0.5547803933 0.5656123502 -0.412986785283 +1413394976255760384.0000000000 0.9679997505 0.5537064119 1.3994215891 0.4491839331 0.5533034399 0.5677135757 -0.412056299068 +1413394976355760384.0000000000 0.9662855887 0.5172089167 1.3930975768 0.4515098767 0.5497924075 0.5683399823 -0.413348284663 +1413394976455760384.0000000000 0.9705716587 0.4769847774 1.3892249297 0.4593067240 0.5424891601 0.5627385021 -0.421981306214 +1413394976505760512.0000000000 0.9760688922 0.4557782252 1.3883586636 0.4637235493 0.5383116430 0.5586229059 -0.427926972519 +1413394976605760512.0000000000 0.9953726157 0.4106616796 1.3880485585 0.4701324062 0.5320935096 0.5497934800 -0.439976302773 +1413394976705760512.0000000000 1.0289751089 0.3630565888 1.3892528198 0.4638779473 0.5354128402 0.5424795439 -0.451515542343 +1413394976755760384.0000000000 1.0520163248 0.3394829546 1.3891966529 0.4535738408 0.5427996239 0.5424037268 -0.453252177502 +1413394976805760512.0000000000 1.0780131760 0.3164870723 1.3891410556 0.4414686406 0.5525178896 0.5446593889 -0.450750009619 +1413394976855760384.0000000000 1.1070219627 0.2946635296 1.3894253394 0.4242589602 0.5650837239 0.5499798931 -0.445204264114 +1413394976905760512.0000000000 1.1376676739 0.2747219825 1.3894430859 0.4038110208 0.5807209863 0.5564961683 -0.435903441313 +1413394976955760384.0000000000 1.1684270267 0.2570448366 1.3893858534 0.3835993957 0.5966709560 0.5642778618 -0.422404744952 +1413394977005760512.0000000000 1.1978346429 0.2419877556 1.3906169242 0.3641488304 0.6113348867 0.5714557432 -0.408783095484 +1413394977105760512.0000000000 1.2452801063 0.2212181941 1.3980544002 0.3316141652 0.6382437565 0.5784770932 -0.384761231581 +1413394977155760384.0000000000 1.2617504303 0.2161773032 1.4037807642 0.3174103809 0.6498763335 0.5809916153 -0.373309716073 +1413394977205760512.0000000000 1.2709332592 0.2150889368 1.4110277809 0.3064874941 0.6596696622 0.5821511743 -0.363319918236 +1413394977305760512.0000000000 1.2639334933 0.2265030076 1.4313442772 0.3069928870 0.6634920833 0.5912911134 -0.340453288821 +1413394977405760512.0000000000 1.2267308006 0.2517205259 1.4609273338 0.3316241399 0.6490427580 0.6057825360 -0.319055554884 +1413394977505760512.0000000000 1.1558350730 0.2806998355 1.4997239625 0.3513857759 0.6363192841 0.6149475070 -0.305721063797 +1413394977605760512.0000000000 1.0539864318 0.3065567455 1.5465975075 0.3598208991 0.6316558493 0.6167619440 -0.301901495735 +1413394977705760512.0000000000 0.9237151132 0.3285080163 1.5978099006 0.3648165465 0.6295454060 0.6158607434 -0.302153957338 +1413394977805760512.0000000000 0.7652142198 0.3458588543 1.6545957814 0.3776474644 0.6218285638 0.6117110069 -0.310678731156 +1413394977905760512.0000000000 0.5838921954 0.3576416480 1.7153049256 0.4012047114 0.6075851988 0.6010719198 -0.329526255339 +1413394978005760512.0000000000 0.3892983006 0.3629871818 1.7755014567 0.4263931241 0.5916419793 0.5886244791 -0.348812119324 +1413394978105760512.0000000000 0.1901403880 0.3612885425 1.8328931580 0.4468341424 0.5776380070 0.5787858414 -0.36287812261 +1413394978155760384.0000000000 0.0905818978 0.3574231773 1.8593885660 0.4535450410 0.5727404432 0.5764133955 -0.366077694122 +1413394978205760512.0000000000 -0.0082972957 0.3515604083 1.8827299768 0.4577756010 0.5696200160 0.5749816996 -0.367927413533 +1413394978255760384.0000000000 -0.1066129630 0.3434171587 1.9027651870 0.4609858785 0.5672425750 0.5740367101 -0.36906603257 +1413394978305760512.0000000000 -0.2038788651 0.3331466074 1.9198306725 0.4623205638 0.5657862365 0.5742167927 -0.369351737335 +1413394978355760384.0000000000 -0.3004424204 0.3206762365 1.9342009844 0.4630963634 0.5650278402 0.5743361586 -0.369355215192 +1413394978405760512.0000000000 -0.3957761504 0.3056657474 1.9453296025 0.4635428677 0.5643986085 0.5743290641 -0.369767963329 +1413394978455760384.0000000000 -0.4898112632 0.2883255356 1.9531996461 0.4622270028 0.5641666291 0.5746980563 -0.37119315263 +1413394978505760512.0000000000 -0.5830107266 0.2687062661 1.9584742248 0.4605261140 0.5647222221 0.5743531600 -0.372991900374 +1413394978555760384.0000000000 -0.6755291273 0.2465318958 1.9631581617 0.4573136880 0.5661592399 0.5736367635 -0.375857379043 +1413394978605760512.0000000000 -0.7675252572 0.2222771523 1.9681498922 0.4539764353 0.5676649420 0.5721811554 -0.379829745062 +1413394978655760384.0000000000 -0.8583485864 0.1961796902 1.9734062557 0.4489287167 0.5706951563 0.5700882426 -0.384407910293 +1413394978705760512.0000000000 -0.9483825439 0.1686198417 1.9797684611 0.4431296088 0.5741967160 0.5668946398 -0.390595376988 +1413394978755760384.0000000000 -1.0375697819 0.1403604886 1.9870375074 0.4378937630 0.5773344071 0.5638523973 -0.396237944649 +1413394978805760512.0000000000 -1.1256126018 0.1117452890 1.9951320349 0.4334915455 0.5803401305 0.5606501063 -0.401200537459 +1413394978855760384.0000000000 -1.2129382807 0.0834011230 2.0036277127 0.4307503000 0.5823318384 0.5581866269 -0.404686914222 +1413394978905760512.0000000000 -1.2992621586 0.0554396412 2.0126429204 0.4288046677 0.5840333065 0.5557569810 -0.40763443411 +1413394978955760384.0000000000 -1.3847681200 0.0280809259 2.0210836342 0.4288673495 0.5847668079 0.5530642387 -0.410171335905 +1413394979005760512.0000000000 -1.4696990723 0.0015433239 2.0286240028 0.4315012247 0.5839341182 0.5487181194 -0.414410501947 +1413394979055760384.0000000000 -1.5536744322 -0.0239994745 2.0335962342 0.4364224817 0.5817683871 0.5433931728 -0.41929085489 +1413394979105760512.0000000000 -1.6356566789 -0.0488095426 2.0362575593 0.4421461471 0.5787197233 0.5374160613 -0.425175544339 +1413394979155760384.0000000000 -1.7149945909 -0.0730415507 2.0365477222 0.4474188007 0.5755126962 0.5295494138 -0.43379600228 +1413394979205760512.0000000000 -1.7912246854 -0.0964869243 2.0355818661 0.4524820490 0.5723062675 0.5197273628 -0.444532338475 +1413394979255760384.0000000000 -1.8635047602 -0.1189440848 2.0325416151 0.4559572956 0.5692361217 0.5112255983 -0.454666438273 +1413394979305760512.0000000000 -1.9316821434 -0.1397332611 2.0284745049 0.4588353702 0.5660030665 0.5020980123 -0.4658414084 +1413394979355760384.0000000000 -1.9953892643 -0.1587639309 2.0236991191 0.4608057759 0.5632802677 0.4927887372 -0.477003812833 +1413394979405760512.0000000000 -2.0530446246 -0.1755360298 2.0204519429 0.4631437449 0.5586744841 0.4836309654 -0.489368758445 +1413394979455760384.0000000000 -2.1036550158 -0.1892375581 2.0184379745 0.4667539604 0.5530232233 0.4748608819 -0.50081253753 +1413394979505760512.0000000000 -2.1461680113 -0.2000213421 2.0186977119 0.4717892036 0.5460168820 0.4658938588 -0.512077556879 +1413394979555760384.0000000000 -2.1795131229 -0.2073779158 2.0211037104 0.4783614549 0.5374859567 0.4599648402 -0.520299443117 +1413394979605760512.0000000000 -2.2036145989 -0.2113044523 2.0254883840 0.4853986883 0.5293128783 0.4559269216 -0.525686819746 +1413394979655760384.0000000000 -2.2197434114 -0.2123094373 2.0322905895 0.4902619584 0.5234142464 0.4557728314 -0.52721140439 +1413394979705760512.0000000000 -2.2261794832 -0.2104007410 2.0409042575 0.4938962434 0.5191913141 0.4600101343 -0.52430673887 +1413394979755760384.0000000000 -2.2211378283 -0.2056561195 2.0496820637 0.4950975990 0.5193318355 0.4705158015 -0.513602660284 +1413394979805760512.0000000000 -2.2059325123 -0.1985567625 2.0586499853 0.4940122060 0.5238267482 0.4885500637 -0.492824830432 +1413394979855760384.0000000000 -2.1826826453 -0.1899479230 2.0693982332 0.4909304871 0.5312254778 0.5100346833 -0.465458236978 +1413394979905760512.0000000000 -2.1531391201 -0.1813235322 2.0816965918 0.4868348363 0.5390266581 0.5304083628 -0.437160236891 +1413394979955760384.0000000000 -2.1195703526 -0.1737816966 2.0957297931 0.4825815166 0.5458542563 0.5462240883 -0.413276488624 +1413394980005760512.0000000000 -2.0836190827 -0.1683042227 2.1101884037 0.4783077234 0.5521322565 0.5566292898 -0.395645708691 +1413394980055760384.0000000000 -2.0463749706 -0.1652785939 2.1239410149 0.4759221386 0.5560872825 0.5624556544 -0.384588987101 +1413394980105760512.0000000000 -2.0089149142 -0.1649516273 2.1365095752 0.4764448720 0.5578095650 0.5638413585 -0.379383309568 +1413394980155760384.0000000000 -1.9714482014 -0.1673741171 2.1478569432 0.4798158480 0.5570632155 0.5616633402 -0.379462275087 +1413394980205760512.0000000000 -1.9330876850 -0.1722859938 2.1573635940 0.4833167146 0.5555422076 0.5579824955 -0.38266609941 +1413394980255760384.0000000000 -1.8935785622 -0.1798443893 2.1645032660 0.4861536745 0.5546402609 0.5524576932 -0.388354584077 +1413394980305760512.0000000000 -1.8531650099 -0.1900429250 2.1699604011 0.4879069994 0.5541407741 0.5467055385 -0.394952929683 +1413394980355760384.0000000000 -1.8114077309 -0.2022728172 2.1725100210 0.4878806602 0.5550414868 0.5424874720 -0.399510640729 +1413394980405760512.0000000000 -1.7674914053 -0.2163379687 2.1722001837 0.4863153201 0.5571293805 0.5410064109 -0.400520069729 +1413394980455760384.0000000000 -1.7214495412 -0.2322503511 2.1711640412 0.4824023684 0.5611596518 0.5412992674 -0.39922788394 +1413394980505760512.0000000000 -1.6737103568 -0.2501273671 2.1699101163 0.4749877276 0.5678300195 0.5417547887 -0.398067175886 +1413394980555760384.0000000000 -1.6240749512 -0.2695262740 2.1696065248 0.4655872044 0.5755581478 0.5420270498 -0.397703471094 +1413394980605760512.0000000000 -1.5733052458 -0.2898669338 2.1700545216 0.4571297434 0.5826676650 0.5422859681 -0.396808163601 +1413394980655760384.0000000000 -1.5220213422 -0.3104926678 2.1718192762 0.4492607515 0.5886936527 0.5424532786 -0.396672410274 +1413394980705760512.0000000000 -1.4708195253 -0.3312024200 2.1748934986 0.4439381217 0.5929497645 0.5419924448 -0.396955552517 +1413394980755760384.0000000000 -1.4199547594 -0.3515517995 2.1788337660 0.4400432729 0.5955518637 0.5427036328 -0.396424851146 +1413394980805760512.0000000000 -1.3690852411 -0.3715257343 2.1836896229 0.4367335560 0.5977260867 0.5428230971 -0.39664897782 +1413394980855760384.0000000000 -1.3186077756 -0.3910769974 2.1890290350 0.4346326878 0.5992223752 0.5427554602 -0.396791484506 +1413394980905760512.0000000000 -1.2683203483 -0.4098954670 2.1944928344 0.4326684277 0.6001018977 0.5430158774 -0.397252439777 +1413394980955760384.0000000000 -1.2187317626 -0.4278520134 2.1987451403 0.4319514500 0.6005779369 0.5433257003 -0.396889493435 +1413394981005760512.0000000000 -1.1700286982 -0.4453082767 2.2005184823 0.4293048431 0.6022394611 0.5431586973 -0.397471524391 +1413394981055760384.0000000000 -1.1221651783 -0.4620617508 2.2001632403 0.4269564633 0.6037209000 0.5424188114 -0.398761941955 +1413394981105760512.0000000000 -1.0752354139 -0.4779267140 2.1972776635 0.4237861228 0.6058538296 0.5410838870 -0.400717714265 +1413394981155760384.0000000000 -1.0290278637 -0.4927438953 2.1920237861 0.4207945036 0.6079671237 0.5399406492 -0.402208972475 +1413394981205760512.0000000000 -0.9831662374 -0.5064854577 2.1838958558 0.4174390933 0.6101785320 0.5390601361 -0.403535540066 +1413394981255760384.0000000000 -0.9382447066 -0.5183586841 2.1729002689 0.4151521525 0.6120838569 0.5383931777 -0.403899527812 +1413394981305760512.0000000000 -0.8942370025 -0.5286247565 2.1600506491 0.4143137190 0.6132903493 0.5378828158 -0.403610166065 +1413394981355760384.0000000000 -0.8513186370 -0.5370339053 2.1460706474 0.4159464797 0.6129281543 0.5389957545 -0.400987755885 +1413394981405760512.0000000000 -0.8091810332 -0.5432388401 2.1326081654 0.4206560848 0.6108526818 0.5414318310 -0.395928063985 +1413394981455760384.0000000000 -0.7682826405 -0.5483310701 2.1197151561 0.4251682802 0.6094037903 0.5434200707 -0.390581080779 +1413394981505760512.0000000000 -0.7286546210 -0.5526724794 2.1084706127 0.4296767779 0.6079443764 0.5448826318 -0.385855438382 +1413394981555760384.0000000000 -0.6901192842 -0.5568791831 2.0985151196 0.4320948941 0.6078739769 0.5452312501 -0.382761171865 +1413394981605760512.0000000000 -0.6527429157 -0.5610191752 2.0892094895 0.4319410884 0.6096069779 0.5453212933 -0.380040676359 +1413394981655760384.0000000000 -0.6164180176 -0.5648029577 2.0799235634 0.4300704003 0.6126611516 0.5460734072 -0.376151030867 +1413394981705760512.0000000000 -0.5816114756 -0.5681268096 2.0704973747 0.4287268801 0.6162341192 0.5462406428 -0.371577626939 +1413394981755760384.0000000000 -0.5486385589 -0.5710060998 2.0616019854 0.4270429440 0.6212428982 0.5444021862 -0.367855739491 +1413394981805760512.0000000000 -0.5174488853 -0.5736454920 2.0526231012 0.4245914821 0.6276550721 0.5408231855 -0.365077342361 +1413394981855760384.0000000000 -0.4883542837 -0.5755245827 2.0448798591 0.4231034684 0.6339808910 0.5356708845 -0.36346717663 +1413394981905760512.0000000000 -0.4612916614 -0.5762978047 2.0371359148 0.4225254107 0.6404408485 0.5295368124 -0.361799061898 +1413394981955760384.0000000000 -0.4367260428 -0.5755640279 2.0305261560 0.4224899437 0.6470857036 0.5219070668 -0.36110296763 +1413394982005760512.0000000000 -0.4138438842 -0.5733726853 2.0245180000 0.4231286077 0.6539814260 0.5136477856 -0.359772745221 +1413394982055760384.0000000000 -0.3932481174 -0.5693773740 2.0196599075 0.4238557099 0.6616391095 0.5032491826 -0.359611298803 +1413394982105760512.0000000000 -0.3746750934 -0.5630251303 2.0156858288 0.4263160331 0.6686300733 0.4916462915 -0.359822718987 +1413394982155760384.0000000000 -0.3577592951 -0.5542480607 2.0126815250 0.4289280682 0.6757502632 0.4785776324 -0.361034269781 +1413394982205760512.0000000000 -0.3421680907 -0.5425954322 2.0103841337 0.4319972259 0.6828637797 0.4649842014 -0.361752881906 +1413394982255760384.0000000000 -0.3276644548 -0.5277666124 2.0090523301 0.4346788674 0.6909946284 0.4501311169 -0.36188766677 +1413394982305760512.0000000000 -0.3134067780 -0.5094844782 2.0078416054 0.4382715263 0.6985371396 0.4365663532 -0.359685631006 +1413394982355760384.0000000000 -0.2992716173 -0.4872176229 2.0074088131 0.4418851598 0.7061897808 0.4235031266 -0.355919373975 +1413394982405760512.0000000000 -0.2852953875 -0.4607792004 2.0081514473 0.4469983668 0.7134920259 0.4101891709 -0.350523084992 +1413394982455760384.0000000000 -0.2709905432 -0.4304348845 2.0103225546 0.4521306134 0.7205439464 0.3963876241 -0.345356600107 +1413394982505760512.0000000000 -0.2558433225 -0.3959971319 2.0137186341 0.4570910973 0.7277356620 0.3819960787 -0.339922830677 +1413394982555760384.0000000000 -0.2396287169 -0.3575320333 2.0182724719 0.4622576205 0.7347177060 0.3689026202 -0.33229300572 +1413394982605760512.0000000000 -0.2223929476 -0.3154944979 2.0242826601 0.4669655243 0.7416395734 0.3539423169 -0.326555934845 +1413394982655760384.0000000000 -0.2036866134 -0.2696489863 2.0306335479 0.4733671322 0.7472683570 0.3411850826 -0.31797216891 +1413394982705760512.0000000000 -0.1836643334 -0.2201778473 2.0377287358 0.4794278555 0.7523386640 0.3291874704 -0.309469021576 +1413394982755760384.0000000000 -0.1623075656 -0.1671888327 2.0455354858 0.4855433960 0.7572654472 0.3174245239 -0.300063867562 +1413394982805760512.0000000000 -0.1396340893 -0.1107157528 2.0535269521 0.4925909035 0.7613747866 0.3062199998 -0.289641067308 +1413394982855760384.0000000000 -0.1154019661 -0.0512865677 2.0613710800 0.4993445564 0.7652827326 0.2953311131 -0.278885078176 +1413394982905760512.0000000000 -0.0899543101 0.0107942277 2.0697081982 0.5058082010 0.7688776569 0.2847973375 -0.268096417504 +1413394983005760512.0000000000 -0.0351069584 0.1415940146 2.0866706089 0.5188903055 0.7737468734 0.2682226706 -0.245204457161 +1413394983105760512.0000000000 0.0237043620 0.2778415990 2.1041416096 0.5301823792 0.7755850288 0.2591166141 -0.224127392724 +1413394983205760512.0000000000 0.0844170588 0.4168312961 2.1231721758 0.5393069550 0.7749262634 0.2548454883 -0.209024093724 +1413394983305760512.0000000000 0.1455781872 0.5566849287 2.1426943365 0.5454219976 0.7734340269 0.2527767447 -0.201043696659 +1413394983405760512.0000000000 0.2072134951 0.6962709188 2.1614646111 0.5505010944 0.7706216649 0.2571701198 -0.192235075016 +1413394983505760512.0000000000 0.2689391537 0.8340618116 2.1786990354 0.5554974626 0.7660667097 0.2713015085 -0.175954132893 +1413394983605760512.0000000000 0.3270324252 0.9668396267 2.1901455587 0.5587689329 0.7617909358 0.2830333511 -0.165360127823 +1413394983705760512.0000000000 0.3790360129 1.0942653674 2.1908456430 0.5625788816 0.7568176356 0.2924295592 -0.158798681748 +1413394983805760512.0000000000 0.4247067461 1.2146458111 2.1803278354 0.5661953668 0.7524334555 0.2993783404 -0.153750807755 +1413394983905760512.0000000000 0.4624432120 1.3271642479 2.1594213288 0.5670129919 0.7509194307 0.3016388649 -0.153721406517 +1413394984005760512.0000000000 0.4924314601 1.4310753264 2.1289538544 0.5664776192 0.7505896122 0.3022552363 -0.156077266511 +1413394984105760512.0000000000 0.5141651756 1.5253645147 2.0935026420 0.5650490959 0.7488370464 0.3067786598 -0.160777644459 +1413394984205760512.0000000000 0.5287187364 1.6096000371 2.0595052363 0.5624553823 0.7460520473 0.3150287516 -0.16675482406 +1413394984305760512.0000000000 0.5360231549 1.6860165800 2.0271905325 0.5567634112 0.7458673467 0.3233434160 -0.170720357407 +1413394984405760512.0000000000 0.5361150040 1.7549619844 1.9977842955 0.5488009209 0.7482286624 0.3305422151 -0.172375352179 +1413394984505760512.0000000000 0.5273146823 1.8176242974 1.9714076200 0.5413666076 0.7491466528 0.3394517997 -0.174567936775 +1413394984605760512.0000000000 0.5092082850 1.8735001650 1.9484102500 0.5349187628 0.7469799479 0.3511088441 -0.180569804132 +1413394984705760512.0000000000 0.4820115239 1.9226614153 1.9293637686 0.5288821015 0.7418007989 0.3659164922 -0.190053724657 +1413394984805760512.0000000000 0.4446662055 1.9666983763 1.9138366784 0.5219423984 0.7353667753 0.3827614741 -0.20076227845 +1413394984905760512.0000000000 0.3965418896 2.0061130608 1.9021600026 0.5148309679 0.7274772627 0.3976271063 -0.218216844034 +1413394985005760512.0000000000 0.3401131658 2.0412904584 1.8949108013 0.5115472137 0.7147143659 0.4143479924 -0.236259527936 +1413394985105760512.0000000000 0.2767122926 2.0728972105 1.8918096835 0.5088796493 0.7019338277 0.4318181396 -0.248723739121 +1413394985205760512.0000000000 0.2075840347 2.0999962855 1.8928014721 0.5050702782 0.6941838783 0.4441325856 -0.256435184196 +1413394985305760512.0000000000 0.1317656291 2.1216445702 1.9029298841 0.4983964492 0.6919761794 0.4498228224 -0.265385333077 +1413394985405760512.0000000000 0.0501334726 2.1371536967 1.9283035155 0.4808503148 0.7003948448 0.4422189181 -0.287528197791 +1413394985505760512.0000000000 -0.0367387981 2.1548345674 1.9673404118 0.4618564392 0.7104136705 0.4327116641 -0.307833822045 +1413394985605760512.0000000000 -0.1272637601 2.1830569367 2.0204764470 0.4631074031 0.7076450690 0.4339064409 -0.310636749318 +1413394985705760512.0000000000 -0.2194610090 2.2192845823 2.0741248933 0.4750788112 0.6978386978 0.4466561765 -0.296343609694 +1413394985805760512.0000000000 -0.3134793230 2.2569941103 2.1169278867 0.4873643606 0.6877695522 0.4586322758 -0.281256926454 +1413394985905760512.0000000000 -0.4121718303 2.2917184532 2.1449616434 0.4944865548 0.6820020831 0.4650137411 -0.272246995203 +1413394986005760512.0000000000 -0.5158260070 2.3214235876 2.1610361743 0.4977009844 0.6801345120 0.4662152360 -0.268987229155 +1413394986105760512.0000000000 -0.6248156411 2.3451141277 2.1732577850 0.5000390366 0.6796472221 0.4647705641 -0.268382074775 +1413394986205760512.0000000000 -0.7399371586 2.3615063967 2.1889120431 0.4938808709 0.6862992267 0.4550809913 -0.279242454158 +1413394986305760512.0000000000 -0.8598877795 2.3739849166 2.2106743001 0.4827524709 0.6962275795 0.4406968591 -0.296653818166 +1413394986405760512.0000000000 -0.9812900698 2.3889048931 2.2363494639 0.4751023255 0.7026660913 0.4314260972 -0.307261561353 +1413394986505760512.0000000000 -1.1023908804 2.4087424247 2.2655414093 0.4760292999 0.7029349076 0.4298961706 -0.307356314073 +1413394986605760512.0000000000 -1.2232791395 2.4335649009 2.2963843108 0.4847016491 0.6974997979 0.4375385926 -0.29515813266 +1413394986705760512.0000000000 -1.3458422043 2.4599172785 2.3269827139 0.4942548112 0.6902939292 0.4493163989 -0.278066982074 +1413394986805760512.0000000000 -1.4726220683 2.4831200428 2.3583713427 0.5030026910 0.6833894867 0.4563444270 -0.267800048973 +1413394986905760512.0000000000 -1.6055761490 2.4993708859 2.3924587651 0.5058241273 0.6823202521 0.4521328299 -0.272317700296 +1413394987005760512.0000000000 -1.7413030337 2.5096240486 2.4244616173 0.5038757105 0.6854295402 0.4400873892 -0.287434694742 +1413394987105760512.0000000000 -1.8751670633 2.5156692726 2.4445501404 0.4963987482 0.6918906631 0.4270871014 -0.304092421843 +1413394987205760512.0000000000 -2.0070525393 2.5226513455 2.4519393771 0.4921606400 0.6955381957 0.4179998489 -0.315088319421 +1413394987305760512.0000000000 -2.1351184859 2.5334673337 2.4510980103 0.5007565539 0.6904229168 0.4180824632 -0.312675748312 +1413394987405760512.0000000000 -2.2582868910 2.5454634767 2.4449037414 0.5196464971 0.6772012746 0.4282274417 -0.296626380989 +1413394987505760512.0000000000 -2.3774785439 2.5520685633 2.4417620779 0.5358309539 0.6650932645 0.4361000004 -0.28346592048 +1413394987605760512.0000000000 -2.4942304756 2.5482241626 2.4441585317 0.5461476485 0.6568966609 0.4387769034 -0.278719127195 +1413394987705760512.0000000000 -2.6073444187 2.5308219750 2.4521262538 0.5554697723 0.6494944019 0.4372445039 -0.280049277262 +1413394987805760512.0000000000 -2.7149057879 2.4986872748 2.4643303432 0.5631169475 0.6434205789 0.4331364468 -0.285135196901 +1413394987905760512.0000000000 -2.8145321236 2.4509848242 2.4813072904 0.5686701188 0.6397744557 0.4301236526 -0.286873814399 +1413394988005760512.0000000000 -2.9052424207 2.3874207777 2.5037006904 0.5737348694 0.6363373330 0.4258349816 -0.290805203978 +1413394988105760512.0000000000 -2.9854262360 2.3080990724 2.5299552863 0.5753595436 0.6357075473 0.4182077601 -0.299899281809 +1413394988205760512.0000000000 -3.0535042143 2.2142024532 2.5580989525 0.5674424285 0.6426138164 0.4087471030 -0.313021371681 +1413394988305760512.0000000000 -3.1084588235 2.1108879590 2.5878531032 0.5538972963 0.6562967363 0.3924174382 -0.329364438376 +1413394988405760512.0000000000 -3.1490811550 2.0056388891 2.6122809711 0.5392957954 0.6760068671 0.3689695738 -0.340640887503 +1413394988505760512.0000000000 -3.1742138410 1.9049198722 2.6270155812 0.5291133960 0.6985653080 0.3409725981 -0.340269322607 +1413394988605760512.0000000000 -3.1836917115 1.8131276964 2.6332983397 0.5288142762 0.7197370624 0.3113578481 -0.324638741728 +1413394988705760512.0000000000 -3.1770924356 1.7299008917 2.6313978228 0.5382729025 0.7355208025 0.2884413788 -0.293382007759 +1413394988805760512.0000000000 -3.1575609296 1.6518173138 2.6227779979 0.5524751848 0.7436739858 0.2714599888 -0.26082493641 +1413394988905760512.0000000000 -3.1288005687 1.5752902501 2.6078635153 0.5676171234 0.7451702182 0.2592014655 -0.235258894124 +1413394989005760512.0000000000 -3.0915276983 1.4947667646 2.5894645799 0.5781218668 0.7451932598 0.2543255739 -0.21396405088 +1413394989105760512.0000000000 -3.0478054116 1.4098557596 2.5718429123 0.5803031432 0.7481560465 0.2553343219 -0.19574262702 +1413394989205760512.0000000000 -3.0011846532 1.3197437278 2.5576235466 0.5773068443 0.7525939335 0.2572424473 -0.184785015961 +1413394989305760512.0000000000 -2.9547496978 1.2257507441 2.5484934048 0.5720934985 0.7568289307 0.2570911970 -0.18391061671 +1413394989405760512.0000000000 -2.9076309395 1.1282784550 2.5422637172 0.5657868366 0.7607031119 0.2556169643 -0.189409605605 +1413394989505760512.0000000000 -2.8594434150 1.0295909799 2.5356276346 0.5602005403 0.7634694070 0.2546441745 -0.196076932733 +1413394989605760512.0000000000 -2.8091620782 0.9311599609 2.5223118082 0.5542504795 0.7662220433 0.2539001274 -0.203088433165 +1413394989705760512.0000000000 -2.7569814003 0.8338132428 2.4991226691 0.5463311533 0.7681630842 0.2571409161 -0.212899732938 +1413394989805760512.0000000000 -2.7026907625 0.7381310330 2.4665457640 0.5340121588 0.7680892854 0.2682716783 -0.230000370842 +1413394989905760512.0000000000 -2.6459607124 0.6462212192 2.4245839731 0.5143508746 0.7674798222 0.2897769386 -0.24989443001 +1413394990005760512.0000000000 -2.5866914147 0.5622088488 2.3762337276 0.4996060192 0.7576717528 0.3251777041 -0.265681767168 +1413394990105760512.0000000000 -2.5260532456 0.4865851905 2.3210331652 0.4921272180 0.7373523212 0.3703751573 -0.277388894157 +1413394990155760384.0000000000 -2.4960657542 0.4508810321 2.2901979967 0.4883646296 0.7254492365 0.3936579231 -0.283296370293 +1413394990205760512.0000000000 -2.4667733991 0.4163794445 2.2577894120 0.4837265765 0.7130690813 0.4164632291 -0.289999074597 +1413394990255760384.0000000000 -2.4387866119 0.3831114154 2.2248919137 0.4790494008 0.6995266368 0.4395546101 -0.296590459726 +1413394990355760384.0000000000 -2.3869794751 0.3186056737 2.1610848418 0.4689355791 0.6718712967 0.4819216282 -0.310547786362 +1413394990405760512.0000000000 -2.3626715223 0.2868201988 2.1297538494 0.4621488769 0.6597444457 0.5007699602 -0.316836123081 +1413394990455760384.0000000000 -2.3404578461 0.2551892615 2.0998204578 0.4555044796 0.6495862613 0.5156496948 -0.323510046988 +1413394990505760512.0000000000 -2.3203166900 0.2237120187 2.0713028179 0.4483247516 0.6415913245 0.5274048332 -0.330468805402 +1413394990555760384.0000000000 -2.3025336878 0.1922108531 2.0443084507 0.4414429213 0.6357574987 0.5357708727 -0.337476105823 +1413394990605760512.0000000000 -2.2867482080 0.1607190619 2.0181973342 0.4351986795 0.6320133232 0.5417468186 -0.343033020563 +1413394990655760384.0000000000 -2.2731574733 0.1295189973 1.9931158808 0.4295048757 0.6290183809 0.5466829553 -0.347849370588 +1413394990705760512.0000000000 -2.2619080042 0.0990407179 1.9688957703 0.4264258948 0.6263777072 0.5504994649 -0.350374461691 +1413394990755760384.0000000000 -2.2534820386 0.0685750833 1.9457825063 0.4242447721 0.6249127407 0.5519882515 -0.353283752783 +1413394990805760512.0000000000 -2.2477716772 0.0385672173 1.9232544463 0.4228636723 0.6238730275 0.5532583223 -0.354787244791 +1413394990855760384.0000000000 -2.2447056646 0.0089089078 1.9021707369 0.4222303588 0.6237740710 0.5535232995 -0.355301828615 +1413394990905760512.0000000000 -2.2440008005 -0.0204371562 1.8820781151 0.4223898170 0.6237790368 0.5533852835 -0.355318566557 +1413394990955760384.0000000000 -2.2451205017 -0.0494469802 1.8630836552 0.4228254303 0.6245140217 0.5522679596 -0.355247790903 +1413394991005760512.0000000000 -2.2485794148 -0.0780663697 1.8450313567 0.4242394537 0.6249864838 0.5511067925 -0.354533615111 +1413394991055760384.0000000000 -2.2538907793 -0.1064972101 1.8279170439 0.4257713825 0.6257634130 0.5499649150 -0.353096974114 +1413394991105760512.0000000000 -2.2612377739 -0.1350977748 1.8122026787 0.4259903482 0.6279773250 0.5466435315 -0.354058684289 +1413394991155760384.0000000000 -2.2705345905 -0.1634977629 1.7976562629 0.4263464835 0.6301605887 0.5425547159 -0.356034673568 +1413394991205760512.0000000000 -2.2818094956 -0.1913314338 1.7838658041 0.4269925004 0.6322487666 0.5384857805 -0.357731695403 +1413394991255760384.0000000000 -2.2948158912 -0.2183204530 1.7705143386 0.4273743812 0.6359994927 0.5338406299 -0.357589101457 +1413394991305760512.0000000000 -2.3095544939 -0.2442514274 1.7578994105 0.4281871471 0.6405275663 0.5281323166 -0.357010448127 +1413394991355760384.0000000000 -2.3257355546 -0.2686843566 1.7452834669 0.4301307426 0.6461031762 0.5213611008 -0.354571336347 +1413394991405760512.0000000000 -2.3437357891 -0.2920272237 1.7336477614 0.4327288319 0.6525205446 0.5134635268 -0.35116648989 +1413394991455760384.0000000000 -2.3631633090 -0.3139138107 1.7228819122 0.4363069591 0.6589901785 0.5046910456 -0.347354473855 +1413394991505760512.0000000000 -2.3836768607 -0.3340930747 1.7127122778 0.4409593093 0.6657109795 0.4950311171 -0.342531710095 +1413394991555760384.0000000000 -2.4052032259 -0.3527860058 1.7027462123 0.4461247468 0.6727992203 0.4847075083 -0.336708406251 +1413394991605760512.0000000000 -2.4277047529 -0.3698694623 1.6929996296 0.4522646188 0.6789295952 0.4747370237 -0.33035749979 +1413394991655760384.0000000000 -2.4512643230 -0.3851587052 1.6844539865 0.4601388652 0.6836608813 0.4645942361 -0.32408674749 +1413394991705760512.0000000000 -2.4758232268 -0.3991703675 1.6766663222 0.4703938386 0.6865384153 0.4546328662 -0.317338301908 +1413394991755760384.0000000000 -2.5009164520 -0.4124744516 1.6701098715 0.4815631250 0.6876393217 0.4440071938 -0.313219941499 +1413394991805760512.0000000000 -2.5260536790 -0.4253626912 1.6638821088 0.4913166414 0.6880747753 0.4339026721 -0.31127083486 +1413394991855760384.0000000000 -2.5511234455 -0.4381981879 1.6584896087 0.4999942690 0.6883063896 0.4234350847 -0.31135634571 +1413394991905760512.0000000000 -2.5754972566 -0.4512847566 1.6535571134 0.5058813387 0.6889108656 0.4144777791 -0.312560491789 +1413394991955760384.0000000000 -2.5989048520 -0.4641417072 1.6488253932 0.5101570026 0.6898735060 0.4068216814 -0.313545049361 +1413394992005760512.0000000000 -2.6210246507 -0.4768476107 1.6440989407 0.5127450847 0.6924114743 0.3989525715 -0.313840204602 +1413394992055760384.0000000000 -2.6414316728 -0.4892563780 1.6390132887 0.5119812643 0.6970945921 0.3914255670 -0.31419793164 +1413394992105760512.0000000000 -2.6599455613 -0.5007930398 1.6343762134 0.5103810005 0.7027018764 0.3835486160 -0.314025104786 +1413394992155760384.0000000000 -2.6766488058 -0.5114249083 1.6303565148 0.5069288809 0.7100238460 0.3752164866 -0.313212126181 +1413394992205760512.0000000000 -2.6914320722 -0.5205965412 1.6264619436 0.5033435423 0.7175690013 0.3682527165 -0.31004829225 +1413394992255760384.0000000000 -2.7045457036 -0.5276338264 1.6232686539 0.5012024192 0.7243261078 0.3616490099 -0.305545116285 +1413394992305760512.0000000000 -2.7161612690 -0.5323137496 1.6211542300 0.5017228323 0.7297773592 0.3554032041 -0.298977872154 +1413394992355760384.0000000000 -2.7261982453 -0.5347102264 1.6193363183 0.5045571564 0.7338837978 0.3501875747 -0.290181511753 +1413394992405760512.0000000000 -2.7349622535 -0.5349874787 1.6184674789 0.5095488319 0.7366961476 0.3451899766 -0.280147557731 +1413394992455760384.0000000000 -2.7428099364 -0.5333910983 1.6181140210 0.5159923596 0.7384468550 0.3418224519 -0.267592112347 +1413394992505760512.0000000000 -2.7499238570 -0.5306926955 1.6176985267 0.5231821162 0.7389482281 0.3413324195 -0.252444387648 +1413394992555760384.0000000000 -2.7566982186 -0.5275601264 1.6177593471 0.5304022839 0.7384499041 0.3415332280 -0.238160052185 +1413394992605760512.0000000000 -2.7637243170 -0.5247694913 1.6185815192 0.5366579035 0.7376390713 0.3407097859 -0.227604342895 +1413394992655760384.0000000000 -2.7714473234 -0.5228232205 1.6208466215 0.5410256846 0.7373641775 0.3368807971 -0.223822712982 +1413394992705760512.0000000000 -2.7796039614 -0.5217324921 1.6233186845 0.5444965400 0.7371691822 0.3320822343 -0.223218512515 +1413394992755760384.0000000000 -2.7880677808 -0.5212263403 1.6260740207 0.5456813663 0.7387275933 0.3249049065 -0.225721489992 +1413394992805760512.0000000000 -2.7963006893 -0.5211702125 1.6287453284 0.5454588117 0.7413612867 0.3167684769 -0.229163390323 +1413394992855760384.0000000000 -2.8040313105 -0.5211404995 1.6312670743 0.5443618289 0.7449424103 0.3087009596 -0.231159516779 +1413394992905760512.0000000000 -2.8110838736 -0.5212310588 1.6335442662 0.5427671893 0.7486436075 0.3009274512 -0.233193474014 +1413394992955760384.0000000000 -2.8171057352 -0.5210700597 1.6345750727 0.5414966081 0.7516220045 0.2954905764 -0.233518960888 +1413394993005760512.0000000000 -2.8223609495 -0.5204291793 1.6335986153 0.5405002455 0.7541626807 0.2913200052 -0.232875052919 +1413394993055760384.0000000000 -2.8266164534 -0.5192987265 1.6294035655 0.5406046047 0.7556071638 0.2893636431 -0.230376121432 +1413394993105760512.0000000000 -2.8300905439 -0.5173534463 1.6222065841 0.5418047850 0.7559262580 0.2897182984 -0.22602295219 +1413394993155760384.0000000000 -2.8330400130 -0.5150833807 1.6120051823 0.5428914786 0.7561728889 0.2908401090 -0.221095987128 +1413394993205760512.0000000000 -2.8356961691 -0.5125728374 1.5994283898 0.5436807955 0.7560354771 0.2929796744 -0.21675899122 +1413394993255760384.0000000000 -2.8375753073 -0.5100259642 1.5843790277 0.5453327575 0.7552624124 0.2956599110 -0.211603612813 +1413394993305760512.0000000000 -2.8394984886 -0.5071429913 1.5675482477 0.5476679359 0.7537862902 0.2990596279 -0.205983978898 +1413394993355760384.0000000000 -2.8413940466 -0.5047373264 1.5499523078 0.5494523832 0.7522969611 0.3026088930 -0.201442842646 +1413394993405760512.0000000000 -2.8437727870 -0.5027113113 1.5323217721 0.5512113804 0.7507507981 0.3062766952 -0.196809144093 +1413394993455760384.0000000000 -2.8467761629 -0.5012688547 1.5152290678 0.5526910192 0.7494162656 0.3090800243 -0.19333245143 +1413394993505760512.0000000000 -2.8506943925 -0.5006682789 1.4988164286 0.5535980626 0.7482016256 0.3119823160 -0.190763065055 +1413394993555760384.0000000000 -2.8552587380 -0.5011210695 1.4830302169 0.5543507985 0.7470927845 0.3139877114 -0.18962932454 +1413394993605760512.0000000000 -2.8610098170 -0.5026326348 1.4676795711 0.5544109203 0.7468478826 0.3143716799 -0.189782029406 +1413394993655760384.0000000000 -2.8674984264 -0.5048188558 1.4524709574 0.5535834844 0.7476060249 0.3133233875 -0.190942431374 +1413394993705760512.0000000000 -2.8749284931 -0.5074703117 1.4373377991 0.5530691560 0.7492552397 0.3091592168 -0.192747692864 +1413394993755760384.0000000000 -2.8828458946 -0.5104510897 1.4213288667 0.5525723324 0.7517675392 0.3024862801 -0.194965214514 +1413394993805760512.0000000000 -2.8909105174 -0.5132871761 1.4033793643 0.5514415771 0.7557558149 0.2938225898 -0.195993930985 +1413394993855760384.0000000000 -2.8990395037 -0.5156830805 1.3835764270 0.5512659205 0.7601128393 0.2831390635 -0.195362808877 +1413394993905760512.0000000000 -2.9070742203 -0.5177123259 1.3614596412 0.5508184857 0.7652208783 0.2705857781 -0.194471951361 +1413394993955760384.0000000000 -2.9146852712 -0.5189077452 1.3382916537 0.5508917175 0.7704341728 0.2566974092 -0.192499197271 +1413394994005760512.0000000000 -2.9216161088 -0.5191539613 1.3147057205 0.5512265182 0.7756965425 0.2414864993 -0.190074906797 +1413394994055760384.0000000000 -2.9274880940 -0.5183491402 1.2924347014 0.5522789529 0.7806511874 0.2260340969 -0.18568863414 +1413394994105760512.0000000000 -2.9316714017 -0.5170549916 1.2711010027 0.5542195796 0.7848479253 0.2119217778 -0.17872759116 +1413394994155760384.0000000000 -2.9339758628 -0.5149550619 1.2530939517 0.5572365841 0.7881569260 0.1976074065 -0.171018602167 +1413394994205760512.0000000000 -2.9347702997 -0.5109852630 1.2390603787 0.5613809749 0.7907606729 0.1837763051 -0.160546656395 +1413394994305760512.0000000000 -2.9311448022 -0.5016906374 1.2168213118 0.5692806077 0.7951585298 0.1596858437 -0.134695707061 +1413394994405760512.0000000000 -2.9221027191 -0.4923326584 1.2018976044 0.5747374038 0.7995687182 0.1417732516 -0.101326831234 +1413394994505760512.0000000000 -2.9128888424 -0.4834536281 1.1965479949 0.5800368365 0.8010050731 0.1299878609 -0.0710724789617 +1413394994605760512.0000000000 -2.9079243345 -0.4767421124 1.2003687480 0.5836781074 0.8013434820 0.1208352406 -0.0506688791461 +1413394994705760512.0000000000 -2.9093453757 -0.4731645240 1.2133450704 0.5867163095 0.8007237786 0.1146409886 -0.038247173902 +1413394994805760512.0000000000 -2.9180790826 -0.4729582377 1.2340165587 0.5919480713 0.7978216170 0.1094975050 -0.0329915855082 +1413394994905760512.0000000000 -2.9336782503 -0.4772766645 1.2559786482 0.5954194153 0.7958184890 0.1042970383 -0.0356480043226 +1413394995005760512.0000000000 -2.9537507005 -0.4861337028 1.2676857190 0.5964395878 0.7952163327 0.1006973589 -0.0418430899709 +1413394995105760512.0000000000 -2.9765638756 -0.4996762106 1.2601830826 0.5953168539 0.7960919661 0.0928652579 -0.0566698233366 +1413394995205760512.0000000000 -2.9989221498 -0.5176415121 1.2324141556 0.5867811249 0.8019909996 0.0845017749 -0.0731969815987 +1413394995305760512.0000000000 -3.0173238354 -0.5366133869 1.1905940468 0.5704644557 0.8132654231 0.0851407174 -0.0769461806626 +1413394995405760512.0000000000 -3.0309525930 -0.5525487776 1.1468232744 0.5563712869 0.8227924044 0.0895705814 -0.0737615168015 +1413394995505760512.0000000000 -3.0412719808 -0.5619673417 1.1036377249 0.5497651298 0.8271376159 0.0944914123 -0.0683596330881 +1413394995605760512.0000000000 -3.0508356904 -0.5639418001 1.0621357314 0.5494162274 0.8273999606 0.0970567882 -0.0642735886216 +1413394995705760512.0000000000 -3.0614184645 -0.5576160571 1.0258186379 0.5591564418 0.8208321519 0.0972465834 -0.064200887166 +1413394995805760512.0000000000 -3.0721821852 -0.5476319606 0.9973598697 0.5718028099 0.8120979465 0.0950731246 -0.0670788551836 +1413394995905760512.0000000000 -3.0815844152 -0.5378631723 0.9726135082 0.5798451066 0.8064299331 0.0923975266 -0.0700935976447 +1413394996005760512.0000000000 -3.0880693126 -0.5291928367 0.9324195187 0.5828549190 0.8046953715 0.0937209715 -0.0629434825486 +1413394996105760512.0000000000 -3.0900969240 -0.5341508110 0.9481661635 0.5927029403 0.7975684729 0.0928983390 -0.0629098894794 +1413394996205760512.0000000000 -3.0876083396 -0.5418297830 0.9407332269 0.5787708141 0.8072655468 0.0887577462 -0.0739509578961 +1413394996305760512.0000000000 -3.0919597927 -0.5455830303 0.9375798534 0.5948631415 0.7950364334 0.1023816858 -0.0597737635613 +1413394996405760512.0000000000 -3.0894872651 -0.5446586174 0.9352394422 0.5925761484 0.7966920149 0.1012009582 -0.0623995817633 +1413394996505760512.0000000000 -3.0905534214 -0.5439866432 0.9356600232 0.5894808286 0.7989075944 0.1036277715 -0.0593320595056 +1413394996605760512.0000000000 -3.0900155446 -0.5445191068 0.9358524246 0.5925416616 0.7966667484 0.1023375343 -0.061184150745 +1413394996705760512.0000000000 -3.0901584401 -0.5441941842 0.9348702590 0.5906338892 0.7980700010 0.1026618036 -0.0607983270676 +1413394996805760512.0000000000 -3.0902424466 -0.5446793090 0.9349542695 0.5916870627 0.7973076450 0.1025088492 -0.0608183759095 +1413394996905760512.0000000000 -3.0901361813 -0.5447374725 0.9347789240 0.5913097967 0.7975761144 0.1025899639 -0.0608306287721 +1413394997005760512.0000000000 -3.0900340499 -0.5449309088 0.9347444111 0.5913153476 0.7975453183 0.1026911704 -0.0610094133951 +1413394997105760512.0000000000 -3.0900072015 -0.5451555866 0.9347591409 0.5913273499 0.7975387214 0.1026711983 -0.0610129340612 +1413394997205760512.0000000000 -3.0898809744 -0.5451847454 0.9346310881 0.5910227816 0.7977775110 0.1026076587 -0.0609490200684 +1413394997305760512.0000000000 -3.0897054376 -0.5452911230 0.9346090718 0.5911311486 0.7976639151 0.1027081298 -0.0612150614496 +1413394997405760512.0000000000 -3.0897855259 -0.5451238265 0.9345891339 0.5910920387 0.7977128296 0.1026272529 -0.0610908359033 +1413394997505760512.0000000000 -3.0903243183 -0.5446490399 0.9346981523 0.5911032503 0.7977071319 0.1026683130 -0.060987676578 +1413394997605760512.0000000000 -3.0914405346 -0.5436055880 0.9347371540 0.5910447184 0.7977423555 0.1026996318 -0.0610414674311 diff --git a/slahmr/third-party/DROID-SLAM/demo.py b/slahmr/third-party/DROID-SLAM/demo.py new file mode 100644 index 0000000000000000000000000000000000000000..382f080ad6c7caf2a97bf5d0b59a027a523d2fb0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/demo.py @@ -0,0 +1,134 @@ +import sys +sys.path.append('droid_slam') + +from tqdm import tqdm +import numpy as np +import torch +import lietorch +import cv2 +import os +import glob +import time +import argparse + +from torch.multiprocessing import Process +from droid import Droid + +import torch.nn.functional as F + + +def show_image(image): + image = image.permute(1, 2, 0).cpu().numpy() + cv2.imshow('image', image / 255.0) + cv2.waitKey(1) + +def image_stream(imagedir, calib, stride): + """ image generator """ + + calib = np.loadtxt(calib, delimiter=" ") + fx, fy, cx, cy = calib[:4] + + K = np.eye(3) + K[0,0] = fx + K[0,2] = cx + K[1,1] = fy + K[1,2] = cy + + image_list = sorted(os.listdir(imagedir))[::stride] + + for t, imfile in enumerate(image_list): + image = cv2.imread(os.path.join(imagedir, imfile)) + if len(calib) > 4: + image = cv2.undistort(image, K, calib[4:]) + + h0, w0, _ = image.shape + h1 = int(h0 * np.sqrt((384 * 512) / (h0 * w0))) + w1 = int(w0 * np.sqrt((384 * 512) / (h0 * w0))) + + image = cv2.resize(image, (w1, h1)) + image = image[:h1-h1%8, :w1-w1%8] + image = torch.as_tensor(image).permute(2, 0, 1) + + intrinsics = torch.as_tensor([fx, fy, cx, cy]) + intrinsics[0::2] *= (w1 / w0) + intrinsics[1::2] *= (h1 / h0) + + yield t, image[None], intrinsics + + +def save_reconstruction(droid, reconstruction_path): + + from pathlib import Path + import random + import string + + t = droid.video.counter.value + tstamps = droid.video.tstamp[:t].cpu().numpy() + images = droid.video.images[:t].cpu().numpy() + disps = droid.video.disps_up[:t].cpu().numpy() + poses = droid.video.poses[:t].cpu().numpy() + intrinsics = droid.video.intrinsics[:t].cpu().numpy() + + Path("reconstructions/{}".format(reconstruction_path)).mkdir(parents=True, exist_ok=True) + np.save("reconstructions/{}/tstamps.npy".format(reconstruction_path), tstamps) + np.save("reconstructions/{}/images.npy".format(reconstruction_path), images) + np.save("reconstructions/{}/disps.npy".format(reconstruction_path), disps) + np.save("reconstructions/{}/poses.npy".format(reconstruction_path), poses) + np.save("reconstructions/{}/intrinsics.npy".format(reconstruction_path), intrinsics) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument("--imagedir", type=str, help="path to image directory") + parser.add_argument("--calib", type=str, help="path to calibration file") + parser.add_argument("--t0", default=0, type=int, help="starting frame") + parser.add_argument("--stride", default=3, type=int, help="frame stride") + + parser.add_argument("--weights", default="droid.pth") + parser.add_argument("--buffer", type=int, default=512) + parser.add_argument("--image_size", default=[240, 320]) + parser.add_argument("--disable_vis", action="store_true") + + parser.add_argument("--beta", type=float, default=0.3, help="weight for translation / rotation components of flow") + parser.add_argument("--filter_thresh", type=float, default=2.4, help="how much motion before considering new keyframe") + parser.add_argument("--warmup", type=int, default=8, help="number of warmup frames") + parser.add_argument("--keyframe_thresh", type=float, default=4.0, help="threshold to create a new keyframe") + parser.add_argument("--frontend_thresh", type=float, default=16.0, help="add edges between frames whithin this distance") + parser.add_argument("--frontend_window", type=int, default=25, help="frontend optimization window") + parser.add_argument("--frontend_radius", type=int, default=2, help="force edges between frames within radius") + parser.add_argument("--frontend_nms", type=int, default=1, help="non-maximal supression of edges") + + parser.add_argument("--backend_thresh", type=float, default=22.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=3) + parser.add_argument("--upsample", action="store_true") + parser.add_argument("--reconstruction_path", help="path to saved reconstruction") + args = parser.parse_args() + + args.stereo = False + torch.multiprocessing.set_start_method('spawn') + + droid = None + + # need high resolution depths + if args.reconstruction_path is not None: + args.upsample = True + + tstamps = [] + for (t, image, intrinsics) in tqdm(image_stream(args.imagedir, args.calib, args.stride)): + if t < args.t0: + continue + + if not args.disable_vis: + show_image(image[0]) + + if droid is None: + args.image_size = [image.shape[2], image.shape[3]] + droid = Droid(args) + + droid.track(t, image, intrinsics=intrinsics) + + if args.reconstruction_path is not None: + save_reconstruction(droid, args.reconstruction_path) + + traj_est = droid.terminate(image_stream(args.imagedir, args.calib, args.stride)) diff --git a/slahmr/third-party/DROID-SLAM/dist/droid_backends-0.0.0-py3.10-linux-x86_64.egg b/slahmr/third-party/DROID-SLAM/dist/droid_backends-0.0.0-py3.10-linux-x86_64.egg new file mode 100644 index 0000000000000000000000000000000000000000..fd11a85ce1c58777417eedba9aaeaf2db4eee834 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/dist/droid_backends-0.0.0-py3.10-linux-x86_64.egg differ diff --git a/slahmr/third-party/DROID-SLAM/dist/lietorch-0.2-py3.10-linux-x86_64.egg b/slahmr/third-party/DROID-SLAM/dist/lietorch-0.2-py3.10-linux-x86_64.egg new file mode 100644 index 0000000000000000000000000000000000000000..deb93626751ba56fc6c4d648a41d022b623c4e35 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/dist/lietorch-0.2-py3.10-linux-x86_64.egg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b451626220b072156ef90a02bb5936edbf3d185f9d809ac94f4213fd172d6226 +size 3447692 diff --git a/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/PKG-INFO b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/PKG-INFO new file mode 100644 index 0000000000000000000000000000000000000000..04485a5acbd5c88ab164cb4c51ad589223079a06 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/PKG-INFO @@ -0,0 +1,11 @@ +Metadata-Version: 2.1 +Name: droid-backends +Version: 0.0.0 +Summary: UNKNOWN +Home-page: UNKNOWN +License: UNKNOWN +Platform: UNKNOWN +License-File: LICENSE + +UNKNOWN + diff --git a/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/SOURCES.txt b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/SOURCES.txt new file mode 100644 index 0000000000000000000000000000000000000000..b4a53a4a43dc70181de369d77ae8b74c29c990cc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/SOURCES.txt @@ -0,0 +1,11 @@ +LICENSE +README.md +setup.py +droid_backends.egg-info/PKG-INFO +droid_backends.egg-info/SOURCES.txt +droid_backends.egg-info/dependency_links.txt +droid_backends.egg-info/top_level.txt +src/altcorr_kernel.cu +src/correlation_kernels.cu +src/droid.cpp +src/droid_kernels.cu \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/dependency_links.txt b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/dependency_links.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b137891791fe96927ad78e64b0aad7bded08bdc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/dependency_links.txt @@ -0,0 +1 @@ + diff --git a/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/top_level.txt b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/top_level.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b2748a1ed3025be542ae7fb4f846586e0314930 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_backends.egg-info/top_level.txt @@ -0,0 +1 @@ +droid_backends diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/__init__.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..8b137891791fe96927ad78e64b0aad7bded08bdc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/__init__.py @@ -0,0 +1 @@ + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/augmentation.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/augmentation.py new file mode 100644 index 0000000000000000000000000000000000000000..ba5341457c2ca025605f3f2a60821016aba0e8fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/augmentation.py @@ -0,0 +1,58 @@ +import torch +import torchvision.transforms as transforms +import numpy as np +import torch.nn.functional as F + + +class RGBDAugmentor: + """ perform augmentation on RGB-D video """ + + def __init__(self, crop_size): + self.crop_size = crop_size + self.augcolor = transforms.Compose([ + transforms.ToPILImage(), + transforms.ColorJitter(brightness=0.25, contrast=0.25, saturation=0.25, hue=0.4/3.14), + transforms.RandomGrayscale(p=0.1), + transforms.ToTensor()]) + + self.max_scale = 0.25 + + def spatial_transform(self, images, depths, poses, intrinsics): + """ cropping and resizing """ + ht, wd = images.shape[2:] + + max_scale = self.max_scale + min_scale = np.log2(np.maximum( + (self.crop_size[0] + 1) / float(ht), + (self.crop_size[1] + 1) / float(wd))) + + scale = 2 ** np.random.uniform(min_scale, max_scale) + intrinsics = scale * intrinsics + depths = depths.unsqueeze(dim=1) + + images = F.interpolate(images, scale_factor=scale, mode='bilinear', + align_corners=False, recompute_scale_factor=True) + + depths = F.interpolate(depths, scale_factor=scale, recompute_scale_factor=True) + + # always perform center crop (TODO: try non-center crops) + y0 = (images.shape[2] - self.crop_size[0]) // 2 + x0 = (images.shape[3] - self.crop_size[1]) // 2 + + intrinsics = intrinsics - torch.tensor([0.0, 0.0, x0, y0]) + images = images[:, :, y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]] + depths = depths[:, :, y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]] + + depths = depths.squeeze(dim=1) + return images, poses, depths, intrinsics + + def color_transform(self, images): + """ color jittering """ + num, ch, ht, wd = images.shape + images = images.permute(1, 2, 3, 0).reshape(ch, ht, wd*num) + images = 255 * self.augcolor(images[[2,1,0]] / 255.0) + return images[[2,1,0]].reshape(ch, ht, wd, num).permute(3,0,1,2).contiguous() + + def __call__(self, images, poses, depths, intrinsics): + images = self.color_transform(images) + return self.spatial_transform(images, depths, poses, intrinsics) diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/base.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/base.py new file mode 100644 index 0000000000000000000000000000000000000000..f676697b8a94ff9f5b5d2b0eaf618c64411bec1d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/base.py @@ -0,0 +1,157 @@ + +import numpy as np +import torch +import torch.utils.data as data +import torch.nn.functional as F + +import csv +import os +import cv2 +import math +import random +import json +import pickle +import os.path as osp + +from .augmentation import RGBDAugmentor +from .rgbd_utils import * + +class RGBDDataset(data.Dataset): + def __init__(self, name, datapath, n_frames=4, crop_size=[384,512], fmin=8.0, fmax=75.0, do_aug=True): + """ Base class for RGBD dataset """ + self.aug = None + self.root = datapath + self.name = name + + self.n_frames = n_frames + self.fmin = fmin # exclude very easy examples + self.fmax = fmax # exclude very hard examples + + if do_aug: + self.aug = RGBDAugmentor(crop_size=crop_size) + + # building dataset is expensive, cache so only needs to be performed once + cur_path = osp.dirname(osp.abspath(__file__)) + if not os.path.isdir(osp.join(cur_path, 'cache')): + os.mkdir(osp.join(cur_path, 'cache')) + + cache_path = osp.join(cur_path, 'cache', '{}.pickle'.format(self.name)) + + if osp.isfile(cache_path): + scene_info = pickle.load(open(cache_path, 'rb'))[0] + else: + scene_info = self._build_dataset() + with open(cache_path, 'wb') as cachefile: + pickle.dump((scene_info,), cachefile) + + self.scene_info = scene_info + self._build_dataset_index() + + def _build_dataset_index(self): + self.dataset_index = [] + for scene in self.scene_info: + if not self.__class__.is_test_scene(scene): + graph = self.scene_info[scene]['graph'] + for i in graph: + if len(graph[i][0]) > self.n_frames: + self.dataset_index.append((scene, i)) + else: + print("Reserving {} for validation".format(scene)) + + @staticmethod + def image_read(image_file): + return cv2.imread(image_file) + + @staticmethod + def depth_read(depth_file): + return np.load(depth_file) + + def build_frame_graph(self, poses, depths, intrinsics, f=16, max_flow=256): + """ compute optical flow distance between all pairs of frames """ + def read_disp(fn): + depth = self.__class__.depth_read(fn)[f//2::f, f//2::f] + depth[depth < 0.01] = np.mean(depth) + return 1.0 / depth + + poses = np.array(poses) + intrinsics = np.array(intrinsics) / f + + disps = np.stack(list(map(read_disp, depths)), 0) + d = f * compute_distance_matrix_flow(poses, disps, intrinsics) + + # uncomment for nice visualization + # import matplotlib.pyplot as plt + # plt.imshow(d) + # plt.show() + + graph = {} + for i in range(d.shape[0]): + j, = np.where(d[i] < max_flow) + graph[i] = (j, d[i,j]) + + return graph + + def __getitem__(self, index): + """ return training video """ + + index = index % len(self.dataset_index) + scene_id, ix = self.dataset_index[index] + + frame_graph = self.scene_info[scene_id]['graph'] + images_list = self.scene_info[scene_id]['images'] + depths_list = self.scene_info[scene_id]['depths'] + poses_list = self.scene_info[scene_id]['poses'] + intrinsics_list = self.scene_info[scene_id]['intrinsics'] + + inds = [ ix ] + while len(inds) < self.n_frames: + # get other frames within flow threshold + k = (frame_graph[ix][1] > self.fmin) & (frame_graph[ix][1] < self.fmax) + frames = frame_graph[ix][0][k] + + # prefer frames forward in time + if np.count_nonzero(frames[frames > ix]): + ix = np.random.choice(frames[frames > ix]) + + elif np.count_nonzero(frames): + ix = np.random.choice(frames) + + inds += [ ix ] + + images, depths, poses, intrinsics = [], [], [], [] + for i in inds: + images.append(self.__class__.image_read(images_list[i])) + depths.append(self.__class__.depth_read(depths_list[i])) + poses.append(poses_list[i]) + intrinsics.append(intrinsics_list[i]) + + images = np.stack(images).astype(np.float32) + depths = np.stack(depths).astype(np.float32) + poses = np.stack(poses).astype(np.float32) + intrinsics = np.stack(intrinsics).astype(np.float32) + + images = torch.from_numpy(images).float() + images = images.permute(0, 3, 1, 2) + + disps = torch.from_numpy(1.0 / depths) + poses = torch.from_numpy(poses) + intrinsics = torch.from_numpy(intrinsics) + + if self.aug is not None: + images, poses, disps, intrinsics = \ + self.aug(images, poses, disps, intrinsics) + + # scale scene + if len(disps[disps>0.01]) > 0: + s = disps[disps>0.01].mean() + disps = disps / s + poses[...,:3] *= s + + return images, poses, disps, intrinsics + + def __len__(self): + return len(self.dataset_index) + + def __imul__(self, x): + self.dataset_index *= x + return self diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/factory.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/factory.py new file mode 100644 index 0000000000000000000000000000000000000000..830dca09d712c626c80b734713b1efe19bf7656e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/factory.py @@ -0,0 +1,82 @@ + +import pickle +import os +import os.path as osp + +# RGBD-Dataset +from .tartan import TartanAir + +from .stream import ImageStream +from .stream import StereoStream +from .stream import RGBDStream + +# streaming datasets for inference +from .tartan import TartanAirStream +from .tartan import TartanAirTestStream + +def dataset_factory(dataset_list, **kwargs): + """ create a combined dataset """ + + from torch.utils.data import ConcatDataset + + dataset_map = { 'tartan': (TartanAir, ) } + db_list = [] + for key in dataset_list: + # cache datasets for faster future loading + db = dataset_map[key][0](**kwargs) + + print("Dataset {} has {} images".format(key, len(db))) + db_list.append(db) + + return ConcatDataset(db_list) + + +def create_datastream(dataset_path, **kwargs): + """ create data_loader to stream images 1 by 1 """ + + from torch.utils.data import DataLoader + + if osp.isfile(osp.join(dataset_path, 'calibration.txt')): + db = ETH3DStream(dataset_path, **kwargs) + + elif osp.isdir(osp.join(dataset_path, 'image_left')): + db = TartanAirStream(dataset_path, **kwargs) + + elif osp.isfile(osp.join(dataset_path, 'rgb.txt')): + db = TUMStream(dataset_path, **kwargs) + + elif osp.isdir(osp.join(dataset_path, 'mav0')): + db = EurocStream(dataset_path, **kwargs) + + elif osp.isfile(osp.join(dataset_path, 'calib.txt')): + db = KITTIStream(dataset_path, **kwargs) + + else: + # db = TartanAirStream(dataset_path, **kwargs) + db = TartanAirTestStream(dataset_path, **kwargs) + + stream = DataLoader(db, shuffle=False, batch_size=1, num_workers=4) + return stream + + +def create_imagestream(dataset_path, **kwargs): + """ create data_loader to stream images 1 by 1 """ + from torch.utils.data import DataLoader + + db = ImageStream(dataset_path, **kwargs) + return DataLoader(db, shuffle=False, batch_size=1, num_workers=4) + +def create_stereostream(dataset_path, **kwargs): + """ create data_loader to stream images 1 by 1 """ + from torch.utils.data import DataLoader + + db = StereoStream(dataset_path, **kwargs) + return DataLoader(db, shuffle=False, batch_size=1, num_workers=4) + +def create_rgbdstream(dataset_path, **kwargs): + """ create data_loader to stream images 1 by 1 """ + from torch.utils.data import DataLoader + + db = RGBDStream(dataset_path, **kwargs) + return DataLoader(db, shuffle=False, batch_size=1, num_workers=4) + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/rgbd_utils.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/rgbd_utils.py new file mode 100644 index 0000000000000000000000000000000000000000..1e67486459915cb09093b6f467222f6a0df227ea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/rgbd_utils.py @@ -0,0 +1,190 @@ +import numpy as np +import os.path as osp + +import torch +from lietorch import SE3 + +import geom.projective_ops as pops +from scipy.spatial.transform import Rotation + + +def parse_list(filepath, skiprows=0): + """ read list data """ + data = np.loadtxt(filepath, delimiter=' ', dtype=np.unicode_, skiprows=skiprows) + return data + +def associate_frames(tstamp_image, tstamp_depth, tstamp_pose, max_dt=1.0): + """ pair images, depths, and poses """ + associations = [] + for i, t in enumerate(tstamp_image): + if tstamp_pose is None: + j = np.argmin(np.abs(tstamp_depth - t)) + if (np.abs(tstamp_depth[j] - t) < max_dt): + associations.append((i, j)) + + else: + j = np.argmin(np.abs(tstamp_depth - t)) + k = np.argmin(np.abs(tstamp_pose - t)) + + if (np.abs(tstamp_depth[j] - t) < max_dt) and \ + (np.abs(tstamp_pose[k] - t) < max_dt): + associations.append((i, j, k)) + + return associations + +def loadtum(datapath, frame_rate=-1): + """ read video data in tum-rgbd format """ + if osp.isfile(osp.join(datapath, 'groundtruth.txt')): + pose_list = osp.join(datapath, 'groundtruth.txt') + + elif osp.isfile(osp.join(datapath, 'pose.txt')): + pose_list = osp.join(datapath, 'pose.txt') + + else: + return None, None, None, None + + image_list = osp.join(datapath, 'rgb.txt') + depth_list = osp.join(datapath, 'depth.txt') + + calib_path = osp.join(datapath, 'calibration.txt') + intrinsic = None + if osp.isfile(calib_path): + intrinsic = np.loadtxt(calib_path, delimiter=' ') + intrinsic = intrinsic.astype(np.float64) + + image_data = parse_list(image_list) + depth_data = parse_list(depth_list) + pose_data = parse_list(pose_list, skiprows=1) + pose_vecs = pose_data[:,1:].astype(np.float64) + + tstamp_image = image_data[:,0].astype(np.float64) + tstamp_depth = depth_data[:,0].astype(np.float64) + tstamp_pose = pose_data[:,0].astype(np.float64) + associations = associate_frames(tstamp_image, tstamp_depth, tstamp_pose) + + # print(len(tstamp_image)) + # print(len(associations)) + + indicies = range(len(associations))[::5] + + # indicies = [ 0 ] + # for i in range(1, len(associations)): + # t0 = tstamp_image[associations[indicies[-1]][0]] + # t1 = tstamp_image[associations[i][0]] + # if t1 - t0 > 1.0 / frame_rate: + # indicies += [ i ] + + images, poses, depths, intrinsics, tstamps = [], [], [], [], [] + for ix in indicies: + (i, j, k) = associations[ix] + images += [ osp.join(datapath, image_data[i,1]) ] + depths += [ osp.join(datapath, depth_data[j,1]) ] + poses += [ pose_vecs[k] ] + tstamps += [ tstamp_image[i] ] + + if intrinsic is not None: + intrinsics += [ intrinsic ] + + return images, depths, poses, intrinsics, tstamps + + +def all_pairs_distance_matrix(poses, beta=2.5): + """ compute distance matrix between all pairs of poses """ + poses = np.array(poses, dtype=np.float32) + poses[:,:3] *= beta # scale to balence rot + trans + poses = SE3(torch.from_numpy(poses)) + + r = (poses[:,None].inv() * poses[None,:]).log() + return r.norm(dim=-1).cpu().numpy() + +def pose_matrix_to_quaternion(pose): + """ convert 4x4 pose matrix to (t, q) """ + q = Rotation.from_matrix(pose[:3, :3]).as_quat() + return np.concatenate([pose[:3, 3], q], axis=0) + +def compute_distance_matrix_flow(poses, disps, intrinsics): + """ compute flow magnitude between all pairs of frames """ + if not isinstance(poses, SE3): + poses = torch.from_numpy(poses).float().cuda()[None] + poses = SE3(poses).inv() + + disps = torch.from_numpy(disps).float().cuda()[None] + intrinsics = torch.from_numpy(intrinsics).float().cuda()[None] + + N = poses.shape[1] + + ii, jj = torch.meshgrid(torch.arange(N), torch.arange(N)) + ii = ii.reshape(-1).cuda() + jj = jj.reshape(-1).cuda() + + MAX_FLOW = 100.0 + matrix = np.zeros((N, N), dtype=np.float32) + + s = 2048 + for i in range(0, ii.shape[0], s): + flow1, val1 = pops.induced_flow(poses, disps, intrinsics, ii[i:i+s], jj[i:i+s]) + flow2, val2 = pops.induced_flow(poses, disps, intrinsics, jj[i:i+s], ii[i:i+s]) + + flow = torch.stack([flow1, flow2], dim=2) + val = torch.stack([val1, val2], dim=2) + + mag = flow.norm(dim=-1).clamp(max=MAX_FLOW) + mag = mag.view(mag.shape[1], -1) + val = val.view(val.shape[1], -1) + + mag = (mag * val).mean(-1) / val.mean(-1) + mag[val.mean(-1) < 0.7] = np.inf + + i1 = ii[i:i+s].cpu().numpy() + j1 = jj[i:i+s].cpu().numpy() + matrix[i1, j1] = mag.cpu().numpy() + + return matrix + + +def compute_distance_matrix_flow2(poses, disps, intrinsics, beta=0.4): + """ compute flow magnitude between all pairs of frames """ + # if not isinstance(poses, SE3): + # poses = torch.from_numpy(poses).float().cuda()[None] + # poses = SE3(poses).inv() + + # disps = torch.from_numpy(disps).float().cuda()[None] + # intrinsics = torch.from_numpy(intrinsics).float().cuda()[None] + + N = poses.shape[1] + + ii, jj = torch.meshgrid(torch.arange(N), torch.arange(N)) + ii = ii.reshape(-1) + jj = jj.reshape(-1) + + MAX_FLOW = 128.0 + matrix = np.zeros((N, N), dtype=np.float32) + + s = 2048 + for i in range(0, ii.shape[0], s): + flow1a, val1a = pops.induced_flow(poses, disps, intrinsics, ii[i:i+s], jj[i:i+s], tonly=True) + flow1b, val1b = pops.induced_flow(poses, disps, intrinsics, ii[i:i+s], jj[i:i+s]) + flow2a, val2a = pops.induced_flow(poses, disps, intrinsics, jj[i:i+s], ii[i:i+s], tonly=True) + flow2b, val2b = pops.induced_flow(poses, disps, intrinsics, ii[i:i+s], jj[i:i+s]) + + flow1 = flow1a + beta * flow1b + val1 = val1a * val2b + + flow2 = flow2a + beta * flow2b + val2 = val2a * val2b + + flow = torch.stack([flow1, flow2], dim=2) + val = torch.stack([val1, val2], dim=2) + + mag = flow.norm(dim=-1).clamp(max=MAX_FLOW) + mag = mag.view(mag.shape[1], -1) + val = val.view(val.shape[1], -1) + + mag = (mag * val).mean(-1) / val.mean(-1) + mag[val.mean(-1) < 0.8] = np.inf + + i1 = ii[i:i+s].cpu().numpy() + j1 = jj[i:i+s].cpu().numpy() + matrix[i1, j1] = mag.cpu().numpy() + + return matrix diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/stream.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/stream.py new file mode 100644 index 0000000000000000000000000000000000000000..1b17d706f6f7edb39c1ce8c806c09011375e0255 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/stream.py @@ -0,0 +1,234 @@ + +import numpy as np +import torch +import torch.utils.data as data +import torch.nn.functional as F + +import csv +import os +import cv2 +import math +import random +import json +import pickle +import os.path as osp + +from .rgbd_utils import * + +class RGBDStream(data.Dataset): + def __init__(self, datapath, frame_rate=-1, image_size=[384,512], crop_size=[0,0]): + self.datapath = datapath + self.frame_rate = frame_rate + self.image_size = image_size + self.crop_size = crop_size + self._build_dataset_index() + + @staticmethod + def image_read(image_file): + return cv2.imread(image_file) + + @staticmethod + def depth_read(depth_file): + return np.load(depth_file) + + def __len__(self): + return len(self.images) + + def __getitem__(self, index): + """ return training video """ + image = self.__class__.image_read(self.images[index]) + image = torch.from_numpy(image).float() + image = image.permute(2, 0, 1) + + try: + tstamp = self.tstamps[index] + except: + tstamp = index + + pose = torch.from_numpy(self.poses[index]).float() + intrinsic = torch.from_numpy(self.intrinsics[index]).float() + + # resize image + sx = self.image_size[1] / image.shape[2] + sy = self.image_size[0] / image.shape[1] + + image = F.interpolate(image[None], self.image_size, mode='bilinear', align_corners=False)[0] + + fx, fy, cx, cy = intrinsic.unbind(dim=0) + fx, cx = sx * fx, sx * cx + fy, cy = sy * fy, sy * cy + + # crop image + if self.crop_size[0] > 0: + cy = cy - self.crop_size[0] + image = image[:,self.crop_size[0]:-self.crop_size[0],:] + + if self.crop_size[1] > 0: + cx = cx - self.crop_size[1] + image = image[:,:,self.crop_size[1]:-self.crop_size[1]] + + intrinsic = torch.stack([fx, fy, cx, cy]) + + return tstamp, image, pose, intrinsic + + +class ImageStream(data.Dataset): + def __init__(self, datapath, intrinsics, rate=1, image_size=[384,512]): + rgb_list = osp.join(datapath, 'rgb.txt') + if os.path.isfile(rgb_list): + rgb_list = np.loadtxt(rgb_list, delimiter=' ', dtype=np.unicode_) + self.timestamps = rgb_list[:,0].astype(np.float) + self.images = [os.path.join(datapath, x) for x in rgb_list[:,1]] + self.images = self.images[::rate] + self.timestamps = self.timestamps[::rate] + + else: + import glob + self.images = sorted(glob.glob(osp.join(datapath, '*.jpg'))) + sorted(glob.glob(osp.join(datapath, '*.png'))) + self.images = self.images[::rate] + + self.intrinsics = intrinsics + self.image_size = image_size + + def __len__(self): + return len(self.images) + + @staticmethod + def image_read(imfile): + return cv2.imread(imfile) + + def __getitem__(self, index): + """ return training video """ + image = self.__class__.image_read(self.images[index]) + + try: + tstamp = self.timestamps[index] + except: + tstamp = index + + ht0, wd0 = image.shape[:2] + ht1, wd1 = self.image_size + + intrinsics = torch.as_tensor(self.intrinsics) + intrinsics[0] *= wd1 / wd0 + intrinsics[1] *= ht1 / ht0 + intrinsics[2] *= wd1 / wd0 + intrinsics[3] *= ht1 / ht0 + + # resize image + ikwargs = {'mode': 'bilinear', 'align_corners': True} + image = torch.from_numpy(image).float().permute(2, 0, 1) + image = F.interpolate(image[None], self.image_size, **ikwargs)[0] + + return tstamp, image, intrinsics + + + +class StereoStream(data.Dataset): + def __init__(self, datapath, intrinsics, rate=1, image_size=[384,512], + map_left=None, map_right=None, left_root='image_left', right_root='image_right'): + import glob + self.intrinsics = intrinsics + self.image_size = image_size + + imgs = sorted(glob.glob(osp.join(datapath, left_root, '*.png')))[::rate] + self.images_l = [] + self.images_r = [] + self.tstamps = [] + + for img_l in imgs: + img_r = img_l.replace(left_root, right_root) + if os.path.isfile(img_r): + t = np.float(img_l.split('/')[-1].replace('.png', '')) + self.tstamps.append(t) + self.images_l += [ img_l ] + self.images_r += [ img_r ] + + self.map_left = map_left + self.map_right = map_right + + def __len__(self): + return len(self.images_l) + + @staticmethod + def image_read(imfile, imap=None): + image = cv2.imread(imfile) + if imap is not None: + image = cv2.remap(image, imap[0], imap[1], interpolation=cv2.INTER_LINEAR) + return image + + def __getitem__(self, index): + """ return training video """ + tstamp = self.tstamps[index] + image_l = self.__class__.image_read(self.images_l[index], self.map_left) + image_r = self.__class__.image_read(self.images_r[index], self.map_right) + + ht0, wd0 = image_l.shape[:2] + ht1, wd1 = self.image_size + + intrinsics = torch.as_tensor(self.intrinsics) + intrinsics[0] *= wd1 / wd0 + intrinsics[1] *= ht1 / ht0 + intrinsics[2] *= wd1 / wd0 + intrinsics[3] *= ht1 / ht0 + + image_l = torch.from_numpy(image_l).float().permute(2, 0, 1) + image_r = torch.from_numpy(image_r).float().permute(2, 0, 1) + + # resize image + ikwargs = {'mode': 'bilinear', 'align_corners': True} + image_l = F.interpolate(image_l[None], self.image_size, **ikwargs)[0] + image_r = F.interpolate(image_r[None], self.image_size, **ikwargs)[0] + + return tstamp, image_l, image_r, intrinsics + + + +# class RGBDStream(data.Dataset): +# def __init__(self, datapath, intrinsics=None, rate=1, image_size=[384,512]): +# assoc_file = osp.join(datapath, 'associated.txt') +# assoc_list = np.loadtxt(assoc_file, delimiter=' ', dtype=np.unicode_) + +# self.intrinsics = intrinsics +# self.image_size = image_size + +# self.timestamps = assoc_list[:,0].astype(np.float)[::rate] +# self.images = [os.path.join(datapath, x) for x in assoc_list[:,1]][::rate] +# self.depths = [os.path.join(datapath, x) for x in assoc_list[:,3]][::rate] + +# def __len__(self): +# return len(self.images) + +# @staticmethod +# def image_read(imfile): +# return cv2.imread(imfile) + +# @staticmethod +# def depth_read(depth_file): +# depth = cv2.imread(depth_file, cv2.IMREAD_ANYDEPTH) +# return depth.astype(np.float32) / 5000.0 + +# def __getitem__(self, index): +# """ return training video """ +# tstamp = self.timestamps[index] +# image = self.__class__.image_read(self.images[index]) +# depth = self.__class__.depth_read(self.depths[index]) + +# ht0, wd0 = image.shape[:2] +# ht1, wd1 = self.image_size + +# intrinsics = torch.as_tensor(self.intrinsics) +# intrinsics[0] *= wd1 / wd0 +# intrinsics[1] *= ht1 / ht0 +# intrinsics[2] *= wd1 / wd0 +# intrinsics[3] *= ht1 / ht0 + +# # resize image +# ikwargs = {'mode': 'bilinear', 'align_corners': True} +# image = torch.from_numpy(image).float().permute(2, 0, 1) +# image = F.interpolate(image[None], self.image_size, **ikwargs)[0] + +# depth = torch.from_numpy(depth).float()[None,None] +# depth = F.interpolate(depth, self.image_size, mode='nearest').squeeze() + +# return tstamp, image, depth, intrinsics diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan.py b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan.py new file mode 100644 index 0000000000000000000000000000000000000000..49780ca91919e83cae8513dba7f9f9702b65b65a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan.py @@ -0,0 +1,138 @@ + +import numpy as np +import torch +import glob +import cv2 +import os +import os.path as osp + +from lietorch import SE3 +from .base import RGBDDataset +from .stream import RGBDStream + +cur_path = osp.dirname(osp.abspath(__file__)) +test_split = osp.join(cur_path, 'tartan_test.txt') +test_split = open(test_split).read().split() + + +class TartanAir(RGBDDataset): + + # scale depths to balance rot & trans + DEPTH_SCALE = 5.0 + + def __init__(self, mode='training', **kwargs): + self.mode = mode + self.n_frames = 2 + super(TartanAir, self).__init__(name='TartanAir', **kwargs) + + @staticmethod + def is_test_scene(scene): + # print(scene, any(x in scene for x in test_split)) + return any(x in scene for x in test_split) + + def _build_dataset(self): + from tqdm import tqdm + print("Building TartanAir dataset") + + scene_info = {} + scenes = glob.glob(osp.join(self.root, '*/*/*/*')) + for scene in tqdm(sorted(scenes)): + images = sorted(glob.glob(osp.join(scene, 'image_left/*.png'))) + depths = sorted(glob.glob(osp.join(scene, 'depth_left/*.npy'))) + + poses = np.loadtxt(osp.join(scene, 'pose_left.txt'), delimiter=' ') + poses = poses[:, [1, 2, 0, 4, 5, 3, 6]] + poses[:,:3] /= TartanAir.DEPTH_SCALE + intrinsics = [TartanAir.calib_read()] * len(images) + + # graph of co-visible frames based on flow + graph = self.build_frame_graph(poses, depths, intrinsics) + + scene = '/'.join(scene.split('/')) + scene_info[scene] = {'images': images, 'depths': depths, + 'poses': poses, 'intrinsics': intrinsics, 'graph': graph} + + return scene_info + + @staticmethod + def calib_read(): + return np.array([320.0, 320.0, 320.0, 240.0]) + + @staticmethod + def image_read(image_file): + return cv2.imread(image_file) + + @staticmethod + def depth_read(depth_file): + depth = np.load(depth_file) / TartanAir.DEPTH_SCALE + depth[depth==np.nan] = 1.0 + depth[depth==np.inf] = 1.0 + return depth + + +class TartanAirStream(RGBDStream): + def __init__(self, datapath, **kwargs): + super(TartanAirStream, self).__init__(datapath=datapath, **kwargs) + + def _build_dataset_index(self): + """ build list of images, poses, depths, and intrinsics """ + self.root = 'datasets/TartanAir' + + scene = osp.join(self.root, self.datapath) + image_glob = osp.join(scene, 'image_left/*.png') + images = sorted(glob.glob(image_glob)) + + poses = np.loadtxt(osp.join(scene, 'pose_left.txt'), delimiter=' ') + poses = poses[:, [1, 2, 0, 4, 5, 3, 6]] + + poses = SE3(torch.as_tensor(poses)) + poses = poses[[0]].inv() * poses + poses = poses.data.cpu().numpy() + + intrinsic = self.calib_read(self.datapath) + intrinsics = np.tile(intrinsic[None], (len(images), 1)) + + self.images = images[::int(self.frame_rate)] + self.poses = poses[::int(self.frame_rate)] + self.intrinsics = intrinsics[::int(self.frame_rate)] + + @staticmethod + def calib_read(datapath): + return np.array([320.0, 320.0, 320.0, 240.0]) + + @staticmethod + def image_read(image_file): + return cv2.imread(image_file) + + +class TartanAirTestStream(RGBDStream): + def __init__(self, datapath, **kwargs): + super(TartanAirTestStream, self).__init__(datapath=datapath, **kwargs) + + def _build_dataset_index(self): + """ build list of images, poses, depths, and intrinsics """ + self.root = 'datasets/mono' + image_glob = osp.join(self.root, self.datapath, '*.png') + images = sorted(glob.glob(image_glob)) + + poses = np.loadtxt(osp.join(self.root, 'mono_gt', self.datapath + '.txt'), delimiter=' ') + poses = poses[:, [1, 2, 0, 4, 5, 3, 6]] + + poses = SE3(torch.as_tensor(poses)) + poses = poses[[0]].inv() * poses + poses = poses.data.cpu().numpy() + + intrinsic = self.calib_read(self.datapath) + intrinsics = np.tile(intrinsic[None], (len(images), 1)) + + self.images = images[::int(self.frame_rate)] + self.poses = poses[::int(self.frame_rate)] + self.intrinsics = intrinsics[::int(self.frame_rate)] + + @staticmethod + def calib_read(datapath): + return np.array([320.0, 320.0, 320.0, 240.0]) + + @staticmethod + def image_read(image_file): + return cv2.imread(image_file) \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan_test.txt b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan_test.txt new file mode 100644 index 0000000000000000000000000000000000000000..d52d88da87b3b2096624162da3872116eefb6003 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/data_readers/tartan_test.txt @@ -0,0 +1,32 @@ +abandonedfactory/abandonedfactory/Easy/P011 +abandonedfactory/abandonedfactory/Hard/P011 +abandonedfactory_night/abandonedfactory_night/Easy/P013 +abandonedfactory_night/abandonedfactory_night/Hard/P014 +amusement/amusement/Easy/P008 +amusement/amusement/Hard/P007 +carwelding/carwelding/Easy/P007 +endofworld/endofworld/Easy/P009 +gascola/gascola/Easy/P008 +gascola/gascola/Hard/P009 +hospital/hospital/Easy/P036 +hospital/hospital/Hard/P049 +japanesealley/japanesealley/Easy/P007 +japanesealley/japanesealley/Hard/P005 +neighborhood/neighborhood/Easy/P021 +neighborhood/neighborhood/Hard/P017 +ocean/ocean/Easy/P013 +ocean/ocean/Hard/P009 +office2/office2/Easy/P011 +office2/office2/Hard/P010 +office/office/Hard/P007 +oldtown/oldtown/Easy/P007 +oldtown/oldtown/Hard/P008 +seasidetown/seasidetown/Easy/P009 +seasonsforest/seasonsforest/Easy/P011 +seasonsforest/seasonsforest/Hard/P006 +seasonsforest_winter/seasonsforest_winter/Easy/P009 +seasonsforest_winter/seasonsforest_winter/Hard/P018 +soulcity/soulcity/Easy/P012 +soulcity/soulcity/Hard/P009 +westerndesert/westerndesert/Easy/P013 +westerndesert/westerndesert/Hard/P007 diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/depth_video.py b/slahmr/third-party/DROID-SLAM/droid_slam/depth_video.py new file mode 100644 index 0000000000000000000000000000000000000000..d209ece074e7d18f268df363b52690513d2aded9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/depth_video.py @@ -0,0 +1,193 @@ +import numpy as np +import torch +import lietorch +import droid_backends + +from torch.multiprocessing import Process, Queue, Lock, Value +from collections import OrderedDict + +from droid_net import cvx_upsample +import geom.projective_ops as pops + +class DepthVideo: + def __init__(self, image_size=[480, 640], buffer=1024, stereo=False, device="cuda:0"): + + # current keyframe count + self.counter = Value('i', 0) + self.ready = Value('i', 0) + self.ht = ht = image_size[0] + self.wd = wd = image_size[1] + + ### state attributes ### + self.tstamp = torch.zeros(buffer, device="cuda", dtype=torch.float).share_memory_() + self.images = torch.zeros(buffer, 3, ht, wd, device="cuda", dtype=torch.uint8) + self.dirty = torch.zeros(buffer, device="cuda", dtype=torch.bool).share_memory_() + self.red = torch.zeros(buffer, device="cuda", dtype=torch.bool).share_memory_() + self.poses = torch.zeros(buffer, 7, device="cuda", dtype=torch.float).share_memory_() + self.disps = torch.ones(buffer, ht//8, wd//8, device="cuda", dtype=torch.float).share_memory_() + self.disps_sens = torch.zeros(buffer, ht//8, wd//8, device="cuda", dtype=torch.float).share_memory_() + self.disps_up = torch.zeros(buffer, ht, wd, device="cuda", dtype=torch.float).share_memory_() + self.intrinsics = torch.zeros(buffer, 4, device="cuda", dtype=torch.float).share_memory_() + + self.stereo = stereo + c = 1 if not self.stereo else 2 + + ### feature attributes ### + self.fmaps = torch.zeros(buffer, c, 128, ht//8, wd//8, dtype=torch.half, device="cuda").share_memory_() + self.nets = torch.zeros(buffer, 128, ht//8, wd//8, dtype=torch.half, device="cuda").share_memory_() + self.inps = torch.zeros(buffer, 128, ht//8, wd//8, dtype=torch.half, device="cuda").share_memory_() + + # initialize poses to identity transformation + self.poses[:] = torch.as_tensor([0, 0, 0, 0, 0, 0, 1], dtype=torch.float, device="cuda") + + def get_lock(self): + return self.counter.get_lock() + + def __item_setter(self, index, item): + if isinstance(index, int) and index >= self.counter.value: + self.counter.value = index + 1 + + elif isinstance(index, torch.Tensor) and index.max().item() > self.counter.value: + self.counter.value = index.max().item() + 1 + + # self.dirty[index] = True + self.tstamp[index] = item[0] + self.images[index] = item[1] + + if item[2] is not None: + self.poses[index] = item[2] + + if item[3] is not None: + self.disps[index] = item[3] + + if item[4] is not None: + depth = item[4][3::8,3::8] + self.disps_sens[index] = torch.where(depth>0, 1.0/depth, depth) + + if item[5] is not None: + self.intrinsics[index] = item[5] + + if len(item) > 6: + self.fmaps[index] = item[6] + + if len(item) > 7: + self.nets[index] = item[7] + + if len(item) > 8: + self.inps[index] = item[8] + + def __setitem__(self, index, item): + with self.get_lock(): + self.__item_setter(index, item) + + def __getitem__(self, index): + """ index the depth video """ + + with self.get_lock(): + # support negative indexing + if isinstance(index, int) and index < 0: + index = self.counter.value + index + + item = ( + self.poses[index], + self.disps[index], + self.intrinsics[index], + self.fmaps[index], + self.nets[index], + self.inps[index]) + + return item + + def append(self, *item): + with self.get_lock(): + self.__item_setter(self.counter.value, item) + + + ### geometric operations ### + + @staticmethod + def format_indicies(ii, jj): + """ to device, long, {-1} """ + + if not isinstance(ii, torch.Tensor): + ii = torch.as_tensor(ii) + + if not isinstance(jj, torch.Tensor): + jj = torch.as_tensor(jj) + + ii = ii.to(device="cuda", dtype=torch.long).reshape(-1) + jj = jj.to(device="cuda", dtype=torch.long).reshape(-1) + + return ii, jj + + def upsample(self, ix, mask): + """ upsample disparity """ + + disps_up = cvx_upsample(self.disps[ix].unsqueeze(-1), mask) + self.disps_up[ix] = disps_up.squeeze() + + def normalize(self): + """ normalize depth and poses """ + + with self.get_lock(): + s = self.disps[:self.counter.value].mean() + self.disps[:self.counter.value] /= s + self.poses[:self.counter.value,:3] *= s + self.dirty[:self.counter.value] = True + + + def reproject(self, ii, jj): + """ project points from ii -> jj """ + ii, jj = DepthVideo.format_indicies(ii, jj) + Gs = lietorch.SE3(self.poses[None]) + + coords, valid_mask = \ + pops.projective_transform(Gs, self.disps[None], self.intrinsics[None], ii, jj) + + return coords, valid_mask + + def distance(self, ii=None, jj=None, beta=0.3, bidirectional=True): + """ frame distance metric """ + + return_matrix = False + if ii is None: + return_matrix = True + N = self.counter.value + ii, jj = torch.meshgrid(torch.arange(N), torch.arange(N)) + + ii, jj = DepthVideo.format_indicies(ii, jj) + + if bidirectional: + + poses = self.poses[:self.counter.value].clone() + + d1 = droid_backends.frame_distance( + poses, self.disps, self.intrinsics[0], ii, jj, beta) + + d2 = droid_backends.frame_distance( + poses, self.disps, self.intrinsics[0], jj, ii, beta) + + d = .5 * (d1 + d2) + + else: + d = droid_backends.frame_distance( + self.poses, self.disps, self.intrinsics[0], ii, jj, beta) + + if return_matrix: + return d.reshape(N, N) + + return d + + def ba(self, target, weight, eta, ii, jj, t0=1, t1=None, itrs=2, lm=1e-4, ep=0.1, motion_only=False): + """ dense bundle adjustment (DBA) """ + + with self.get_lock(): + + # [t0, t1] window of bundle adjustment optimization + if t1 is None: + t1 = max(ii.max().item(), jj.max().item()) + 1 + + droid_backends.ba(self.poses, self.disps, self.intrinsics[0], self.disps_sens, + target, weight, eta, ii, jj, t0, t1, itrs, lm, ep, motion_only) + + self.disps.clamp_(min=0.001) diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/droid.py b/slahmr/third-party/DROID-SLAM/droid_slam/droid.py new file mode 100644 index 0000000000000000000000000000000000000000..fe99c5ca2d423778a7c5e87a9bb8cbd5d94d55a3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/droid.py @@ -0,0 +1,89 @@ +import torch +import lietorch +import numpy as np + +from droid_net import DroidNet +from depth_video import DepthVideo +from motion_filter import MotionFilter +from droid_frontend import DroidFrontend +from droid_backend import DroidBackend +from trajectory_filler import PoseTrajectoryFiller + +from collections import OrderedDict +from torch.multiprocessing import Process + + +class Droid: + def __init__(self, args): + super(Droid, self).__init__() + self.load_weights(args.weights) + self.args = args + self.disable_vis = args.disable_vis + + # store images, depth, poses, intrinsics (shared between processes) + self.video = DepthVideo(args.image_size, args.buffer, stereo=args.stereo) + + # filter incoming frames so that there is enough motion + self.filterx = MotionFilter(self.net, self.video, thresh=args.filter_thresh) + + # frontend process + self.frontend = DroidFrontend(self.net, self.video, self.args) + + # backend process + self.backend = DroidBackend(self.net, self.video, self.args) + + # visualizer + if not self.disable_vis: + from visualization import droid_visualization + self.visualizer = Process(target=droid_visualization, args=(self.video,)) + self.visualizer.start() + + # post processor - fill in poses for non-keyframes + self.traj_filler = PoseTrajectoryFiller(self.net, self.video) + + + def load_weights(self, weights): + """ load trained model weights """ + + print(weights) + self.net = DroidNet() + state_dict = OrderedDict([ + (k.replace("module.", ""), v) for (k, v) in torch.load(weights).items()]) + + state_dict["update.weight.2.weight"] = state_dict["update.weight.2.weight"][:2] + state_dict["update.weight.2.bias"] = state_dict["update.weight.2.bias"][:2] + state_dict["update.delta.2.weight"] = state_dict["update.delta.2.weight"][:2] + state_dict["update.delta.2.bias"] = state_dict["update.delta.2.bias"][:2] + + self.net.load_state_dict(state_dict) + self.net.to("cuda:0").eval() + + def track(self, tstamp, image, depth=None, intrinsics=None): + """ main thread - update map """ + + with torch.no_grad(): + # check there is enough motion + self.filterx.track(tstamp, image, depth, intrinsics) + + # local bundle adjustment + self.frontend() + + # global bundle adjustment + # self.backend() + + def terminate(self, stream=None): + """ terminate the visualization process, return poses [t, q] """ + + del self.frontend + + torch.cuda.empty_cache() + print("#" * 32) + self.backend(7) + + torch.cuda.empty_cache() + print("#" * 32) + self.backend(12) + + camera_trajectory = self.traj_filler(stream) + return camera_trajectory.inv().data.cpu().numpy() + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/droid_backend.py b/slahmr/third-party/DROID-SLAM/droid_slam/droid_backend.py new file mode 100644 index 0000000000000000000000000000000000000000..665eee0e4c4d7b8c1ec4bfc196512cc42adb301d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/droid_backend.py @@ -0,0 +1,41 @@ +import torch +import lietorch +import numpy as np + +from lietorch import SE3 +from factor_graph import FactorGraph + + +class DroidBackend: + def __init__(self, net, video, args): + self.video = video + self.update_op = net.update + + # global optimization window + self.t0 = 0 + self.t1 = 0 + + self.upsample = args.upsample + self.beta = args.beta + self.backend_thresh = args.backend_thresh + self.backend_radius = args.backend_radius + self.backend_nms = args.backend_nms + + @torch.no_grad() + def __call__(self, steps=12): + """ main update """ + + t = self.video.counter.value + if not self.video.stereo and not torch.any(self.video.disps_sens): + self.video.normalize() + + graph = FactorGraph(self.video, self.update_op, corr_impl="alt", max_factors=16*t, upsample=self.upsample) + + graph.add_proximity_factors(rad=self.backend_radius, + nms=self.backend_nms, + thresh=self.backend_thresh, + beta=self.beta) + + graph.update_lowmem(steps=steps) + graph.clear_edges() + self.video.dirty[:t] = True diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/droid_frontend.py b/slahmr/third-party/DROID-SLAM/droid_slam/droid_frontend.py new file mode 100644 index 0000000000000000000000000000000000000000..5d2c56d616486dc35e41356c85aba687cd0acd4a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/droid_frontend.py @@ -0,0 +1,119 @@ +import torch +import lietorch +import numpy as np + +from lietorch import SE3 +from factor_graph import FactorGraph + + +class DroidFrontend: + def __init__(self, net, video, args): + self.video = video + self.update_op = net.update + self.graph = FactorGraph(video, net.update, max_factors=48, upsample=args.upsample) + + # local optimization window + self.t0 = 0 + self.t1 = 0 + + # frontent variables + self.is_initialized = False + self.count = 0 + + self.max_age = 25 + self.iters1 = 4 + self.iters2 = 2 + + self.warmup = args.warmup + self.beta = args.beta + self.frontend_nms = args.frontend_nms + self.keyframe_thresh = args.keyframe_thresh + self.frontend_window = args.frontend_window + self.frontend_thresh = args.frontend_thresh + self.frontend_radius = args.frontend_radius + + def __update(self): + """ add edges, perform update """ + + self.count += 1 + self.t1 += 1 + + if self.graph.corr is not None: + self.graph.rm_factors(self.graph.age > self.max_age, store=True) + + self.graph.add_proximity_factors(self.t1-5, max(self.t1-self.frontend_window, 0), + rad=self.frontend_radius, nms=self.frontend_nms, thresh=self.frontend_thresh, beta=self.beta, remove=True) + + self.video.disps[self.t1-1] = torch.where(self.video.disps_sens[self.t1-1] > 0, + self.video.disps_sens[self.t1-1], self.video.disps[self.t1-1]) + + for itr in range(self.iters1): + self.graph.update(None, None, use_inactive=True) + + # set initial pose for next frame + poses = SE3(self.video.poses) + d = self.video.distance([self.t1-3], [self.t1-2], beta=self.beta, bidirectional=True) + + if d.item() < self.keyframe_thresh: + self.graph.rm_keyframe(self.t1 - 2) + + with self.video.get_lock(): + self.video.counter.value -= 1 + self.t1 -= 1 + + else: + for itr in range(self.iters2): + self.graph.update(None, None, use_inactive=True) + + # set pose for next itration + self.video.poses[self.t1] = self.video.poses[self.t1-1] + self.video.disps[self.t1] = self.video.disps[self.t1-1].mean() + + # update visualization + self.video.dirty[self.graph.ii.min():self.t1] = True + + def __initialize(self): + """ initialize the SLAM system """ + + self.t0 = 0 + self.t1 = self.video.counter.value + + self.graph.add_neighborhood_factors(self.t0, self.t1, r=3) + + for itr in range(8): + self.graph.update(1, use_inactive=True) + + self.graph.add_proximity_factors(0, 0, rad=2, nms=2, thresh=self.frontend_thresh, remove=False) + + for itr in range(8): + self.graph.update(1, use_inactive=True) + + + # self.video.normalize() + self.video.poses[self.t1] = self.video.poses[self.t1-1].clone() + self.video.disps[self.t1] = self.video.disps[self.t1-4:self.t1].mean() + + # initialization complete + self.is_initialized = True + self.last_pose = self.video.poses[self.t1-1].clone() + self.last_disp = self.video.disps[self.t1-1].clone() + self.last_time = self.video.tstamp[self.t1-1].clone() + + with self.video.get_lock(): + self.video.ready.value = 1 + self.video.dirty[:self.t1] = True + + self.graph.rm_factors(self.graph.ii < self.warmup-4, store=True) + + def __call__(self): + """ main update """ + + # do initialization + if not self.is_initialized and self.video.counter.value == self.warmup: + self.__initialize() + + # do update + elif self.is_initialized and self.t1 < self.video.counter.value: + self.__update() + + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/droid_net.py b/slahmr/third-party/DROID-SLAM/droid_slam/droid_net.py new file mode 100644 index 0000000000000000000000000000000000000000..0e360314e148058f39aefcfb9cd4e7a36b288007 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/droid_net.py @@ -0,0 +1,222 @@ +import numpy as np +import torch +import torch.nn as nn +import torch.nn.functional as F +from collections import OrderedDict + +from modules.extractor import BasicEncoder +from modules.corr import CorrBlock +from modules.gru import ConvGRU +from modules.clipping import GradientClip + +from lietorch import SE3 +from geom.ba import BA + +import geom.projective_ops as pops +from geom.graph_utils import graph_to_edge_list, keyframe_indicies + +from torch_scatter import scatter_mean + + +def cvx_upsample(data, mask): + """ upsample pixel-wise transformation field """ + batch, ht, wd, dim = data.shape + data = data.permute(0, 3, 1, 2) + mask = mask.view(batch, 1, 9, 8, 8, ht, wd) + mask = torch.softmax(mask, dim=2) + + up_data = F.unfold(data, [3,3], padding=1) + up_data = up_data.view(batch, dim, 9, 1, 1, ht, wd) + + up_data = torch.sum(mask * up_data, dim=2) + up_data = up_data.permute(0, 4, 2, 5, 3, 1) + up_data = up_data.reshape(batch, 8*ht, 8*wd, dim) + + return up_data + +def upsample_disp(disp, mask): + batch, num, ht, wd = disp.shape + disp = disp.view(batch*num, ht, wd, 1) + mask = mask.view(batch*num, -1, ht, wd) + return cvx_upsample(disp, mask).view(batch, num, 8*ht, 8*wd) + + +class GraphAgg(nn.Module): + def __init__(self): + super(GraphAgg, self).__init__() + self.conv1 = nn.Conv2d(128, 128, 3, padding=1) + self.conv2 = nn.Conv2d(128, 128, 3, padding=1) + self.relu = nn.ReLU(inplace=True) + + self.eta = nn.Sequential( + nn.Conv2d(128, 1, 3, padding=1), + GradientClip(), + nn.Softplus()) + + self.upmask = nn.Sequential( + nn.Conv2d(128, 8*8*9, 1, padding=0)) + + def forward(self, net, ii): + batch, num, ch, ht, wd = net.shape + net = net.view(batch*num, ch, ht, wd) + + _, ix = torch.unique(ii, return_inverse=True) + net = self.relu(self.conv1(net)) + + net = net.view(batch, num, 128, ht, wd) + net = scatter_mean(net, ix, dim=1) + net = net.view(-1, 128, ht, wd) + + net = self.relu(self.conv2(net)) + + eta = self.eta(net).view(batch, -1, ht, wd) + upmask = self.upmask(net).view(batch, -1, 8*8*9, ht, wd) + + return .01 * eta, upmask + + +class UpdateModule(nn.Module): + def __init__(self): + super(UpdateModule, self).__init__() + cor_planes = 4 * (2*3 + 1)**2 + + self.corr_encoder = nn.Sequential( + nn.Conv2d(cor_planes, 128, 1, padding=0), + nn.ReLU(inplace=True), + nn.Conv2d(128, 128, 3, padding=1), + nn.ReLU(inplace=True)) + + self.flow_encoder = nn.Sequential( + nn.Conv2d(4, 128, 7, padding=3), + nn.ReLU(inplace=True), + nn.Conv2d(128, 64, 3, padding=1), + nn.ReLU(inplace=True)) + + self.weight = nn.Sequential( + nn.Conv2d(128, 128, 3, padding=1), + nn.ReLU(inplace=True), + nn.Conv2d(128, 2, 3, padding=1), + GradientClip(), + nn.Sigmoid()) + + self.delta = nn.Sequential( + nn.Conv2d(128, 128, 3, padding=1), + nn.ReLU(inplace=True), + nn.Conv2d(128, 2, 3, padding=1), + GradientClip()) + + self.gru = ConvGRU(128, 128+128+64) + self.agg = GraphAgg() + + def forward(self, net, inp, corr, flow=None, ii=None, jj=None): + """ RaftSLAM update operator """ + + batch, num, ch, ht, wd = net.shape + + if flow is None: + flow = torch.zeros(batch, num, 4, ht, wd, device=net.device) + + output_dim = (batch, num, -1, ht, wd) + net = net.view(batch*num, -1, ht, wd) + inp = inp.view(batch*num, -1, ht, wd) + corr = corr.view(batch*num, -1, ht, wd) + flow = flow.view(batch*num, -1, ht, wd) + + corr = self.corr_encoder(corr) + flow = self.flow_encoder(flow) + net = self.gru(net, inp, corr, flow) + + ### update variables ### + delta = self.delta(net).view(*output_dim) + weight = self.weight(net).view(*output_dim) + + delta = delta.permute(0,1,3,4,2)[...,:2].contiguous() + weight = weight.permute(0,1,3,4,2)[...,:2].contiguous() + + net = net.view(*output_dim) + + if ii is not None: + eta, upmask = self.agg(net, ii.to(net.device)) + return net, delta, weight, eta, upmask + + else: + return net, delta, weight + + +class DroidNet(nn.Module): + def __init__(self): + super(DroidNet, self).__init__() + self.fnet = BasicEncoder(output_dim=128, norm_fn='instance') + self.cnet = BasicEncoder(output_dim=256, norm_fn='none') + self.update = UpdateModule() + + + def extract_features(self, images): + """ run feeature extraction networks """ + + # normalize images + images = images[:, :, [2,1,0]] / 255.0 + mean = torch.as_tensor([0.485, 0.456, 0.406], device=images.device) + std = torch.as_tensor([0.229, 0.224, 0.225], device=images.device) + images = images.sub_(mean[:, None, None]).div_(std[:, None, None]) + + fmaps = self.fnet(images) + net = self.cnet(images) + + net, inp = net.split([128,128], dim=2) + net = torch.tanh(net) + inp = torch.relu(inp) + return fmaps, net, inp + + + def forward(self, Gs, images, disps, intrinsics, graph=None, num_steps=12, fixedp=2): + """ Estimates SE3 or Sim3 between pair of frames """ + + u = keyframe_indicies(graph) + ii, jj, kk = graph_to_edge_list(graph) + + ii = ii.to(device=images.device, dtype=torch.long) + jj = jj.to(device=images.device, dtype=torch.long) + + fmaps, net, inp = self.extract_features(images) + net, inp = net[:,ii], inp[:,ii] + corr_fn = CorrBlock(fmaps[:,ii], fmaps[:,jj], num_levels=4, radius=3) + + ht, wd = images.shape[-2:] + coords0 = pops.coords_grid(ht//8, wd//8, device=images.device) + + coords1, _ = pops.projective_transform(Gs, disps, intrinsics, ii, jj) + target = coords1.clone() + + Gs_list, disp_list, residual_list = [], [], [] + for step in range(num_steps): + Gs = Gs.detach() + disps = disps.detach() + coords1 = coords1.detach() + target = target.detach() + + # extract motion features + corr = corr_fn(coords1) + resd = target - coords1 + flow = coords1 - coords0 + + motion = torch.cat([flow, resd], dim=-1) + motion = motion.permute(0,1,4,2,3).clamp(-64.0, 64.0) + + net, delta, weight, eta, upmask = \ + self.update(net, inp, corr, motion, ii, jj) + + target = coords1 + delta + + for i in range(2): + Gs, disps = BA(target, weight, eta, Gs, disps, intrinsics, ii, jj, fixedp=2) + + coords1, valid_mask = pops.projective_transform(Gs, disps, intrinsics, ii, jj) + residual = (target - coords1) + + Gs_list.append(Gs) + disp_list.append(upsample_disp(disps, upmask)) + residual_list.append(valid_mask * residual) + + + return Gs_list, disp_list, residual_list diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/factor_graph.py b/slahmr/third-party/DROID-SLAM/droid_slam/factor_graph.py new file mode 100644 index 0000000000000000000000000000000000000000..eb605d63abde35e7cc1a47ad8e195a8ff59ab848 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/factor_graph.py @@ -0,0 +1,375 @@ +import torch +import lietorch +import numpy as np + +import matplotlib.pyplot as plt +from lietorch import SE3 +from modules.corr import CorrBlock, AltCorrBlock +import geom.projective_ops as pops + + +class FactorGraph: + def __init__(self, video, update_op, device="cuda:0", corr_impl="volume", max_factors=-1, upsample=False): + self.video = video + self.update_op = update_op + self.device = device + self.max_factors = max_factors + self.corr_impl = corr_impl + self.upsample = upsample + + # operator at 1/8 resolution + self.ht = ht = video.ht // 8 + self.wd = wd = video.wd // 8 + + self.coords0 = pops.coords_grid(ht, wd, device=device) + self.ii = torch.as_tensor([], dtype=torch.long, device=device) + self.jj = torch.as_tensor([], dtype=torch.long, device=device) + self.age = torch.as_tensor([], dtype=torch.long, device=device) + + self.corr, self.net, self.inp = None, None, None + self.damping = 1e-6 * torch.ones_like(self.video.disps) + + self.target = torch.zeros([1, 0, ht, wd, 2], device=device, dtype=torch.float) + self.weight = torch.zeros([1, 0, ht, wd, 2], device=device, dtype=torch.float) + + # inactive factors + self.ii_inac = torch.as_tensor([], dtype=torch.long, device=device) + self.jj_inac = torch.as_tensor([], dtype=torch.long, device=device) + self.ii_bad = torch.as_tensor([], dtype=torch.long, device=device) + self.jj_bad = torch.as_tensor([], dtype=torch.long, device=device) + + self.target_inac = torch.zeros([1, 0, ht, wd, 2], device=device, dtype=torch.float) + self.weight_inac = torch.zeros([1, 0, ht, wd, 2], device=device, dtype=torch.float) + + def __filter_repeated_edges(self, ii, jj): + """ remove duplicate edges """ + + keep = torch.zeros(ii.shape[0], dtype=torch.bool, device=ii.device) + eset = set( + [(i.item(), j.item()) for i, j in zip(self.ii, self.jj)] + + [(i.item(), j.item()) for i, j in zip(self.ii_inac, self.jj_inac)]) + + for k, (i, j) in enumerate(zip(ii, jj)): + keep[k] = (i.item(), j.item()) not in eset + + return ii[keep], jj[keep] + + def print_edges(self): + ii = self.ii.cpu().numpy() + jj = self.jj.cpu().numpy() + + ix = np.argsort(ii) + ii = ii[ix] + jj = jj[ix] + + w = torch.mean(self.weight, dim=[0,2,3,4]).cpu().numpy() + w = w[ix] + for e in zip(ii, jj, w): + print(e) + print() + + def filter_edges(self): + """ remove bad edges """ + conf = torch.mean(self.weight, dim=[0,2,3,4]) + mask = (torch.abs(self.ii-self.jj) > 2) & (conf < 0.001) + + self.ii_bad = torch.cat([self.ii_bad, self.ii[mask]]) + self.jj_bad = torch.cat([self.jj_bad, self.jj[mask]]) + self.rm_factors(mask, store=False) + + def clear_edges(self): + self.rm_factors(self.ii >= 0) + self.net = None + self.inp = None + + @torch.cuda.amp.autocast(enabled=True) + def add_factors(self, ii, jj, remove=False): + """ add edges to factor graph """ + + if not isinstance(ii, torch.Tensor): + ii = torch.as_tensor(ii, dtype=torch.long, device=self.device) + + if not isinstance(jj, torch.Tensor): + jj = torch.as_tensor(jj, dtype=torch.long, device=self.device) + + # remove duplicate edges + ii, jj = self.__filter_repeated_edges(ii, jj) + + + if ii.shape[0] == 0: + return + + # place limit on number of factors + if self.max_factors > 0 and self.ii.shape[0] + ii.shape[0] > self.max_factors \ + and self.corr is not None and remove: + + ix = torch.arange(len(self.age))[torch.argsort(self.age).cpu()] + self.rm_factors(ix >= self.max_factors - ii.shape[0], store=True) + + net = self.video.nets[ii].to(self.device).unsqueeze(0) + + # correlation volume for new edges + if self.corr_impl == "volume": + c = (ii == jj).long() + fmap1 = self.video.fmaps[ii,0].to(self.device).unsqueeze(0) + fmap2 = self.video.fmaps[jj,c].to(self.device).unsqueeze(0) + corr = CorrBlock(fmap1, fmap2) + self.corr = corr if self.corr is None else self.corr.cat(corr) + + inp = self.video.inps[ii].to(self.device).unsqueeze(0) + self.inp = inp if self.inp is None else torch.cat([self.inp, inp], 1) + + with torch.cuda.amp.autocast(enabled=False): + target, _ = self.video.reproject(ii, jj) + weight = torch.zeros_like(target) + + self.ii = torch.cat([self.ii, ii], 0) + self.jj = torch.cat([self.jj, jj], 0) + self.age = torch.cat([self.age, torch.zeros_like(ii)], 0) + + # reprojection factors + self.net = net if self.net is None else torch.cat([self.net, net], 1) + + self.target = torch.cat([self.target, target], 1) + self.weight = torch.cat([self.weight, weight], 1) + + @torch.cuda.amp.autocast(enabled=True) + def rm_factors(self, mask, store=False): + """ drop edges from factor graph """ + + # store estimated factors + if store: + self.ii_inac = torch.cat([self.ii_inac, self.ii[mask]], 0) + self.jj_inac = torch.cat([self.jj_inac, self.jj[mask]], 0) + self.target_inac = torch.cat([self.target_inac, self.target[:,mask]], 1) + self.weight_inac = torch.cat([self.weight_inac, self.weight[:,mask]], 1) + + self.ii = self.ii[~mask] + self.jj = self.jj[~mask] + self.age = self.age[~mask] + + if self.corr_impl == "volume": + self.corr = self.corr[~mask] + + if self.net is not None: + self.net = self.net[:,~mask] + + if self.inp is not None: + self.inp = self.inp[:,~mask] + + self.target = self.target[:,~mask] + self.weight = self.weight[:,~mask] + + + @torch.cuda.amp.autocast(enabled=True) + def rm_keyframe(self, ix): + """ drop edges from factor graph """ + + + with self.video.get_lock(): + self.video.images[ix] = self.video.images[ix+1] + self.video.poses[ix] = self.video.poses[ix+1] + self.video.disps[ix] = self.video.disps[ix+1] + self.video.disps_sens[ix] = self.video.disps_sens[ix+1] + self.video.intrinsics[ix] = self.video.intrinsics[ix+1] + + self.video.nets[ix] = self.video.nets[ix+1] + self.video.inps[ix] = self.video.inps[ix+1] + self.video.fmaps[ix] = self.video.fmaps[ix+1] + + m = (self.ii_inac == ix) | (self.jj_inac == ix) + self.ii_inac[self.ii_inac >= ix] -= 1 + self.jj_inac[self.jj_inac >= ix] -= 1 + + if torch.any(m): + self.ii_inac = self.ii_inac[~m] + self.jj_inac = self.jj_inac[~m] + self.target_inac = self.target_inac[:,~m] + self.weight_inac = self.weight_inac[:,~m] + + m = (self.ii == ix) | (self.jj == ix) + + self.ii[self.ii >= ix] -= 1 + self.jj[self.jj >= ix] -= 1 + self.rm_factors(m, store=False) + + + @torch.cuda.amp.autocast(enabled=True) + def update(self, t0=None, t1=None, itrs=2, use_inactive=False, EP=1e-7, motion_only=False): + """ run update operator on factor graph """ + + # motion features + with torch.cuda.amp.autocast(enabled=False): + coords1, mask = self.video.reproject(self.ii, self.jj) + motn = torch.cat([coords1 - self.coords0, self.target - coords1], dim=-1) + motn = motn.permute(0,1,4,2,3).clamp(-64.0, 64.0) + + # correlation features + corr = self.corr(coords1) + + self.net, delta, weight, damping, upmask = \ + self.update_op(self.net, self.inp, corr, motn, self.ii, self.jj) + + if t0 is None: + t0 = max(1, self.ii.min().item()+1) + + with torch.cuda.amp.autocast(enabled=False): + self.target = coords1 + delta.to(dtype=torch.float) + self.weight = weight.to(dtype=torch.float) + + ht, wd = self.coords0.shape[0:2] + self.damping[torch.unique(self.ii)] = damping + + if use_inactive: + m = (self.ii_inac >= t0 - 3) & (self.jj_inac >= t0 - 3) + ii = torch.cat([self.ii_inac[m], self.ii], 0) + jj = torch.cat([self.jj_inac[m], self.jj], 0) + target = torch.cat([self.target_inac[:,m], self.target], 1) + weight = torch.cat([self.weight_inac[:,m], self.weight], 1) + + else: + ii, jj, target, weight = self.ii, self.jj, self.target, self.weight + + + damping = .2 * self.damping[torch.unique(ii)].contiguous() + EP + + target = target.view(-1, ht, wd, 2).permute(0,3,1,2).contiguous() + weight = weight.view(-1, ht, wd, 2).permute(0,3,1,2).contiguous() + + # dense bundle adjustment + self.video.ba(target, weight, damping, ii, jj, t0, t1, + itrs=itrs, lm=1e-4, ep=0.1, motion_only=motion_only) + + if self.upsample: + self.video.upsample(torch.unique(self.ii), upmask) + + self.age += 1 + + + @torch.cuda.amp.autocast(enabled=False) + def update_lowmem(self, t0=None, t1=None, itrs=2, use_inactive=False, EP=1e-7, steps=8): + """ run update operator on factor graph - reduced memory implementation """ + + # alternate corr implementation + t = self.video.counter.value + + num, rig, ch, ht, wd = self.video.fmaps.shape + corr_op = AltCorrBlock(self.video.fmaps.view(1, num*rig, ch, ht, wd)) + + for step in range(steps): + print("Global BA Iteration #{}".format(step+1)) + with torch.cuda.amp.autocast(enabled=False): + coords1, mask = self.video.reproject(self.ii, self.jj) + motn = torch.cat([coords1 - self.coords0, self.target - coords1], dim=-1) + motn = motn.permute(0,1,4,2,3).clamp(-64.0, 64.0) + + s = 8 + for i in range(0, self.jj.max()+1, s): + v = (self.ii >= i) & (self.ii < i + s) + iis = self.ii[v] + jjs = self.jj[v] + + ht, wd = self.coords0.shape[0:2] + corr1 = corr_op(coords1[:,v], rig * iis, rig * jjs + (iis == jjs).long()) + + with torch.cuda.amp.autocast(enabled=True): + + net, delta, weight, damping, upmask = \ + self.update_op(self.net[:,v], self.video.inps[None,iis], corr1, motn[:,v], iis, jjs) + + if self.upsample: + self.video.upsample(torch.unique(iis), upmask) + + self.net[:,v] = net + self.target[:,v] = coords1[:,v] + delta.float() + self.weight[:,v] = weight.float() + self.damping[torch.unique(iis)] = damping + + damping = .2 * self.damping[torch.unique(self.ii)].contiguous() + EP + target = self.target.view(-1, ht, wd, 2).permute(0,3,1,2).contiguous() + weight = self.weight.view(-1, ht, wd, 2).permute(0,3,1,2).contiguous() + + # dense bundle adjustment + self.video.ba(target, weight, damping, self.ii, self.jj, 1, t, + itrs=itrs, lm=1e-5, ep=1e-2, motion_only=False) + + self.video.dirty[:t] = True + + def add_neighborhood_factors(self, t0, t1, r=3): + """ add edges between neighboring frames within radius r """ + + ii, jj = torch.meshgrid(torch.arange(t0,t1), torch.arange(t0,t1)) + ii = ii.reshape(-1).to(dtype=torch.long, device=self.device) + jj = jj.reshape(-1).to(dtype=torch.long, device=self.device) + + c = 1 if self.video.stereo else 0 + + keep = ((ii - jj).abs() > c) & ((ii - jj).abs() <= r) + self.add_factors(ii[keep], jj[keep]) + + + def add_proximity_factors(self, t0=0, t1=0, rad=2, nms=2, beta=0.25, thresh=16.0, remove=False): + """ add edges to the factor graph based on distance """ + + t = self.video.counter.value + ix = torch.arange(t0, t) + jx = torch.arange(t1, t) + + ii, jj = torch.meshgrid(ix, jx) + ii = ii.reshape(-1) + jj = jj.reshape(-1) + + d = self.video.distance(ii, jj, beta=beta) + d[ii - rad < jj] = np.inf + d[d > 100] = np.inf + + ii1 = torch.cat([self.ii, self.ii_bad, self.ii_inac], 0) + jj1 = torch.cat([self.jj, self.jj_bad, self.jj_inac], 0) + for i, j in zip(ii1.cpu().numpy(), jj1.cpu().numpy()): + for di in range(-nms, nms+1): + for dj in range(-nms, nms+1): + if abs(di) + abs(dj) <= max(min(abs(i-j)-2, nms), 0): + i1 = i + di + j1 = j + dj + + if (t0 <= i1 < t) and (t1 <= j1 < t): + d[(i1-t0)*(t-t1) + (j1-t1)] = np.inf + + + es = [] + for i in range(t0, t): + if self.video.stereo: + es.append((i, i)) + d[(i-t0)*(t-t1) + (i-t1)] = np.inf + + for j in range(max(i-rad-1,0), i): + es.append((i,j)) + es.append((j,i)) + d[(i-t0)*(t-t1) + (j-t1)] = np.inf + + ix = torch.argsort(d) + for k in ix: + if d[k].item() > thresh: + continue + + if len(es) > self.max_factors: + break + + i = ii[k] + j = jj[k] + + # bidirectional + es.append((i, j)) + es.append((j, i)) + + for di in range(-nms, nms+1): + for dj in range(-nms, nms+1): + if abs(di) + abs(dj) <= max(min(abs(i-j)-2, nms), 0): + i1 = i + di + j1 = j + dj + + if (t0 <= i1 < t) and (t1 <= j1 < t): + d[(i1-t0)*(t-t1) + (j1-t1)] = np.inf + + ii, jj = torch.as_tensor(es, device=self.device).unbind(dim=-1) + self.add_factors(ii, jj, remove) diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/__init__.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/ba.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/ba.py new file mode 100644 index 0000000000000000000000000000000000000000..34c95c8a7910d5cbe288aeca2533f199580ab04c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/geom/ba.py @@ -0,0 +1,158 @@ +import lietorch +import torch +import torch.nn.functional as F + +from .chol import block_solve, schur_solve +import geom.projective_ops as pops + +from torch_scatter import scatter_sum + + +# utility functions for scattering ops +def safe_scatter_add_mat(A, ii, jj, n, m): + v = (ii >= 0) & (jj >= 0) & (ii < n) & (jj < m) + return scatter_sum(A[:,v], ii[v]*m + jj[v], dim=1, dim_size=n*m) + +def safe_scatter_add_vec(b, ii, n): + v = (ii >= 0) & (ii < n) + return scatter_sum(b[:,v], ii[v], dim=1, dim_size=n) + +# apply retraction operator to inv-depth maps +def disp_retr(disps, dz, ii): + ii = ii.to(device=dz.device) + return disps + scatter_sum(dz, ii, dim=1, dim_size=disps.shape[1]) + +# apply retraction operator to poses +def pose_retr(poses, dx, ii): + ii = ii.to(device=dx.device) + return poses.retr(scatter_sum(dx, ii, dim=1, dim_size=poses.shape[1])) + + +def BA(target, weight, eta, poses, disps, intrinsics, ii, jj, fixedp=1, rig=1): + """ Full Bundle Adjustment """ + + B, P, ht, wd = disps.shape + N = ii.shape[0] + D = poses.manifold_dim + + ### 1: commpute jacobians and residuals ### + coords, valid, (Ji, Jj, Jz) = pops.projective_transform( + poses, disps, intrinsics, ii, jj, jacobian=True) + + r = (target - coords).view(B, N, -1, 1) + w = .001 * (valid * weight).view(B, N, -1, 1) + + ### 2: construct linear system ### + Ji = Ji.reshape(B, N, -1, D) + Jj = Jj.reshape(B, N, -1, D) + wJiT = (w * Ji).transpose(2,3) + wJjT = (w * Jj).transpose(2,3) + + Jz = Jz.reshape(B, N, ht*wd, -1) + + Hii = torch.matmul(wJiT, Ji) + Hij = torch.matmul(wJiT, Jj) + Hji = torch.matmul(wJjT, Ji) + Hjj = torch.matmul(wJjT, Jj) + + vi = torch.matmul(wJiT, r).squeeze(-1) + vj = torch.matmul(wJjT, r).squeeze(-1) + + Ei = (wJiT.view(B,N,D,ht*wd,-1) * Jz[:,:,None]).sum(dim=-1) + Ej = (wJjT.view(B,N,D,ht*wd,-1) * Jz[:,:,None]).sum(dim=-1) + + w = w.view(B, N, ht*wd, -1) + r = r.view(B, N, ht*wd, -1) + wk = torch.sum(w*r*Jz, dim=-1) + Ck = torch.sum(w*Jz*Jz, dim=-1) + + kx, kk = torch.unique(ii, return_inverse=True) + M = kx.shape[0] + + # only optimize keyframe poses + P = P // rig - fixedp + ii = ii // rig - fixedp + jj = jj // rig - fixedp + + H = safe_scatter_add_mat(Hii, ii, ii, P, P) + \ + safe_scatter_add_mat(Hij, ii, jj, P, P) + \ + safe_scatter_add_mat(Hji, jj, ii, P, P) + \ + safe_scatter_add_mat(Hjj, jj, jj, P, P) + + E = safe_scatter_add_mat(Ei, ii, kk, P, M) + \ + safe_scatter_add_mat(Ej, jj, kk, P, M) + + v = safe_scatter_add_vec(vi, ii, P) + \ + safe_scatter_add_vec(vj, jj, P) + + C = safe_scatter_add_vec(Ck, kk, M) + w = safe_scatter_add_vec(wk, kk, M) + + C = C + eta.view(*C.shape) + 1e-7 + + H = H.view(B, P, P, D, D) + E = E.view(B, P, M, D, ht*wd) + + ### 3: solve the system ### + dx, dz = schur_solve(H, E, C, v, w) + + ### 4: apply retraction ### + poses = pose_retr(poses, dx, torch.arange(P) + fixedp) + disps = disp_retr(disps, dz.view(B,-1,ht,wd), kx) + + disps = torch.where(disps > 10, torch.zeros_like(disps), disps) + disps = disps.clamp(min=0.0) + + return poses, disps + + +def MoBA(target, weight, eta, poses, disps, intrinsics, ii, jj, fixedp=1, rig=1): + """ Motion only bundle adjustment """ + + B, P, ht, wd = disps.shape + N = ii.shape[0] + D = poses.manifold_dim + + ### 1: commpute jacobians and residuals ### + coords, valid, (Ji, Jj, Jz) = pops.projective_transform( + poses, disps, intrinsics, ii, jj, jacobian=True) + + r = (target - coords).view(B, N, -1, 1) + w = .001 * (valid * weight).view(B, N, -1, 1) + + ### 2: construct linear system ### + Ji = Ji.reshape(B, N, -1, D) + Jj = Jj.reshape(B, N, -1, D) + wJiT = (w * Ji).transpose(2,3) + wJjT = (w * Jj).transpose(2,3) + + Hii = torch.matmul(wJiT, Ji) + Hij = torch.matmul(wJiT, Jj) + Hji = torch.matmul(wJjT, Ji) + Hjj = torch.matmul(wJjT, Jj) + + vi = torch.matmul(wJiT, r).squeeze(-1) + vj = torch.matmul(wJjT, r).squeeze(-1) + + # only optimize keyframe poses + P = P // rig - fixedp + ii = ii // rig - fixedp + jj = jj // rig - fixedp + + H = safe_scatter_add_mat(Hii, ii, ii, P, P) + \ + safe_scatter_add_mat(Hij, ii, jj, P, P) + \ + safe_scatter_add_mat(Hji, jj, ii, P, P) + \ + safe_scatter_add_mat(Hjj, jj, jj, P, P) + + v = safe_scatter_add_vec(vi, ii, P) + \ + safe_scatter_add_vec(vj, jj, P) + + H = H.view(B, P, P, D, D) + + ### 3: solve the system ### + dx = block_solve(H, v) + + ### 4: apply retraction ### + poses = pose_retr(poses, dx, torch.arange(P) + fixedp) + return poses + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/chol.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/chol.py new file mode 100644 index 0000000000000000000000000000000000000000..86bc8f9b61f16d4faccab8a8d210065e2437f968 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/geom/chol.py @@ -0,0 +1,73 @@ +import torch +import torch.nn.functional as F +import geom.projective_ops as pops + +class CholeskySolver(torch.autograd.Function): + @staticmethod + def forward(ctx, H, b): + # don't crash training if cholesky decomp fails + try: + U = torch.linalg.cholesky(H) + xs = torch.cholesky_solve(b, U) + ctx.save_for_backward(U, xs) + ctx.failed = False + except Exception as e: + print(e) + ctx.failed = True + xs = torch.zeros_like(b) + + return xs + + @staticmethod + def backward(ctx, grad_x): + if ctx.failed: + return None, None + + U, xs = ctx.saved_tensors + dz = torch.cholesky_solve(grad_x, U) + dH = -torch.matmul(xs, dz.transpose(-1,-2)) + + return dH, dz + +def block_solve(H, b, ep=0.1, lm=0.0001): + """ solve normal equations """ + B, N, _, D, _ = H.shape + I = torch.eye(D).to(H.device) + H = H + (ep + lm*H) * I + + H = H.permute(0,1,3,2,4) + H = H.reshape(B, N*D, N*D) + b = b.reshape(B, N*D, 1) + + x = CholeskySolver.apply(H,b) + return x.reshape(B, N, D) + + +def schur_solve(H, E, C, v, w, ep=0.1, lm=0.0001, sless=False): + """ solve using shur complement """ + + B, P, M, D, HW = E.shape + H = H.permute(0,1,3,2,4).reshape(B, P*D, P*D) + E = E.permute(0,1,3,2,4).reshape(B, P*D, M*HW) + Q = (1.0 / C).view(B, M*HW, 1) + + # damping + I = torch.eye(P*D).to(H.device) + H = H + (ep + lm*H) * I + + v = v.reshape(B, P*D, 1) + w = w.reshape(B, M*HW, 1) + + Et = E.transpose(1,2) + S = H - torch.matmul(E, Q*Et) + v = v - torch.matmul(E, Q*w) + + dx = CholeskySolver.apply(S, v) + if sless: + return dx.reshape(B, P, D) + + dz = Q * (w - Et @ dx) + dx = dx.reshape(B, P, D) + dz = dz.reshape(B, M, HW) + + return dx, dz \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/graph_utils.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/graph_utils.py new file mode 100644 index 0000000000000000000000000000000000000000..b06b7de9757b8918881dd84f1654635d7ab4124b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/geom/graph_utils.py @@ -0,0 +1,113 @@ + +import torch +import numpy as np +from collections import OrderedDict + +import lietorch +from data_readers.rgbd_utils import compute_distance_matrix_flow, compute_distance_matrix_flow2 + + +def graph_to_edge_list(graph): + ii, jj, kk = [], [], [] + for s, u in enumerate(graph): + for v in graph[u]: + ii.append(u) + jj.append(v) + kk.append(s) + + ii = torch.as_tensor(ii) + jj = torch.as_tensor(jj) + kk = torch.as_tensor(kk) + return ii, jj, kk + +def keyframe_indicies(graph): + return torch.as_tensor([u for u in graph]) + +def meshgrid(m, n, device='cuda'): + ii, jj = torch.meshgrid(torch.arange(m), torch.arange(n)) + return ii.reshape(-1).to(device), jj.reshape(-1).to(device) + +def neighbourhood_graph(n, r): + ii, jj = meshgrid(n, n) + d = (ii - jj).abs() + keep = (d >= 1) & (d <= r) + return ii[keep], jj[keep] + + +def build_frame_graph(poses, disps, intrinsics, num=16, thresh=24.0, r=2): + """ construct a frame graph between co-visible frames """ + N = poses.shape[1] + poses = poses[0].cpu().numpy() + disps = disps[0][:,3::8,3::8].cpu().numpy() + intrinsics = intrinsics[0].cpu().numpy() / 8.0 + d = compute_distance_matrix_flow(poses, disps, intrinsics) + + count = 0 + graph = OrderedDict() + + for i in range(N): + graph[i] = [] + d[i,i] = np.inf + for j in range(i-r, i+r+1): + if 0 <= j < N and i != j: + graph[i].append(j) + d[i,j] = np.inf + count += 1 + + while count < num: + ix = np.argmin(d) + i, j = ix // N, ix % N + + if d[i,j] < thresh: + graph[i].append(j) + d[i,j] = np.inf + count += 1 + else: + break + + return graph + + + +def build_frame_graph_v2(poses, disps, intrinsics, num=16, thresh=24.0, r=2): + """ construct a frame graph between co-visible frames """ + N = poses.shape[1] + # poses = poses[0].cpu().numpy() + # disps = disps[0].cpu().numpy() + # intrinsics = intrinsics[0].cpu().numpy() + d = compute_distance_matrix_flow2(poses, disps, intrinsics) + + # import matplotlib.pyplot as plt + # plt.imshow(d) + # plt.show() + + count = 0 + graph = OrderedDict() + + for i in range(N): + graph[i] = [] + d[i,i] = np.inf + for j in range(i-r, i+r+1): + if 0 <= j < N and i != j: + graph[i].append(j) + d[i,j] = np.inf + count += 1 + + while 1: + ix = np.argmin(d) + i, j = ix // N, ix % N + + if d[i,j] < thresh: + graph[i].append(j) + + for i1 in range(i-1, i+2): + for j1 in range(j-1, j+2): + if 0 <= i1 < N and 0 <= j1 < N: + d[i1, j1] = np.inf + + count += 1 + else: + break + + return graph + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/losses.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/losses.py new file mode 100644 index 0000000000000000000000000000000000000000..7fa91cf3939beabd4894dc3184cc7a6f32ff662c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/geom/losses.py @@ -0,0 +1,118 @@ +from collections import OrderedDict +import numpy as np +import torch +from lietorch import SO3, SE3, Sim3 +from .graph_utils import graph_to_edge_list +from .projective_ops import projective_transform + + +def pose_metrics(dE): + """ Translation/Rotation/Scaling metrics from Sim3 """ + t, q, s = dE.data.split([3, 4, 1], -1) + ang = SO3(q).log().norm(dim=-1) + + # convert radians to degrees + r_err = (180 / np.pi) * ang + t_err = t.norm(dim=-1) + s_err = (s - 1.0).abs() + return r_err, t_err, s_err + + +def fit_scale(Ps, Gs): + b = Ps.shape[0] + t1 = Ps.data[...,:3].detach().reshape(b, -1) + t2 = Gs.data[...,:3].detach().reshape(b, -1) + + s = (t1*t2).sum(-1) / ((t2*t2).sum(-1) + 1e-8) + return s + + +def geodesic_loss(Ps, Gs, graph, gamma=0.9, do_scale=True): + """ Loss function for training network """ + + # relative pose + ii, jj, kk = graph_to_edge_list(graph) + dP = Ps[:,jj] * Ps[:,ii].inv() + + n = len(Gs) + geodesic_loss = 0.0 + + for i in range(n): + w = gamma ** (n - i - 1) + dG = Gs[i][:,jj] * Gs[i][:,ii].inv() + + if do_scale: + s = fit_scale(dP, dG) + dG = dG.scale(s[:,None]) + + # pose error + d = (dG * dP.inv()).log() + + if isinstance(dG, SE3): + tau, phi = d.split([3,3], dim=-1) + geodesic_loss += w * ( + tau.norm(dim=-1).mean() + + phi.norm(dim=-1).mean()) + + elif isinstance(dG, Sim3): + tau, phi, sig = d.split([3,3,1], dim=-1) + geodesic_loss += w * ( + tau.norm(dim=-1).mean() + + phi.norm(dim=-1).mean() + + 0.05 * sig.norm(dim=-1).mean()) + + dE = Sim3(dG * dP.inv()).detach() + r_err, t_err, s_err = pose_metrics(dE) + + metrics = { + 'rot_error': r_err.mean().item(), + 'tr_error': t_err.mean().item(), + 'bad_rot': (r_err < .1).float().mean().item(), + 'bad_tr': (t_err < .01).float().mean().item(), + } + + return geodesic_loss, metrics + + +def residual_loss(residuals, gamma=0.9): + """ loss on system residuals """ + residual_loss = 0.0 + n = len(residuals) + + for i in range(n): + w = gamma ** (n - i - 1) + residual_loss += w * residuals[i].abs().mean() + + return residual_loss, {'residual': residual_loss.item()} + + +def flow_loss(Ps, disps, poses_est, disps_est, intrinsics, graph, gamma=0.9): + """ optical flow loss """ + + N = Ps.shape[1] + graph = OrderedDict() + for i in range(N): + graph[i] = [j for j in range(N) if abs(i-j)==1] + + ii, jj, kk = graph_to_edge_list(graph) + coords0, val0 = projective_transform(Ps, disps, intrinsics, ii, jj) + val0 = val0 * (disps[:,ii] > 0).float().unsqueeze(dim=-1) + + n = len(poses_est) + flow_loss = 0.0 + + for i in range(n): + w = gamma ** (n - i - 1) + coords1, val1 = projective_transform(poses_est[i], disps_est[i], intrinsics, ii, jj) + + v = (val0 * val1).squeeze(dim=-1) + epe = v * (coords1 - coords0).norm(dim=-1) + flow_loss += w * epe.mean() + + epe = epe.reshape(-1)[v.reshape(-1) > 0.5] + metrics = { + 'f_error': epe.mean().item(), + '1px': (epe<1.0).float().mean().item(), + } + + return flow_loss, metrics diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/geom/projective_ops.py b/slahmr/third-party/DROID-SLAM/droid_slam/geom/projective_ops.py new file mode 100644 index 0000000000000000000000000000000000000000..ad31ffdefc9623fa1a8afb27aaf44163f9e32e42 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/geom/projective_ops.py @@ -0,0 +1,139 @@ +import torch +import torch.nn.functional as F + +from lietorch import SE3, Sim3 + +MIN_DEPTH = 0.2 + +def extract_intrinsics(intrinsics): + return intrinsics[...,None,None,:].unbind(dim=-1) + +def coords_grid(ht, wd, **kwargs): + y, x = torch.meshgrid( + torch.arange(ht).to(**kwargs).float(), + torch.arange(wd).to(**kwargs).float()) + + return torch.stack([x, y], dim=-1) + +def iproj(disps, intrinsics, jacobian=False): + """ pinhole camera inverse projection """ + ht, wd = disps.shape[2:] + fx, fy, cx, cy = extract_intrinsics(intrinsics) + + y, x = torch.meshgrid( + torch.arange(ht).to(disps.device).float(), + torch.arange(wd).to(disps.device).float()) + + i = torch.ones_like(disps) + X = (x - cx) / fx + Y = (y - cy) / fy + pts = torch.stack([X, Y, i, disps], dim=-1) + + if jacobian: + J = torch.zeros_like(pts) + J[...,-1] = 1.0 + return pts, J + + return pts, None + +def proj(Xs, intrinsics, jacobian=False, return_depth=False): + """ pinhole camera projection """ + fx, fy, cx, cy = extract_intrinsics(intrinsics) + X, Y, Z, D = Xs.unbind(dim=-1) + + Z = torch.where(Z < 0.5*MIN_DEPTH, torch.ones_like(Z), Z) + d = 1.0 / Z + + x = fx * (X * d) + cx + y = fy * (Y * d) + cy + if return_depth: + coords = torch.stack([x, y, D*d], dim=-1) + else: + coords = torch.stack([x, y], dim=-1) + + if jacobian: + B, N, H, W = d.shape + o = torch.zeros_like(d) + proj_jac = torch.stack([ + fx*d, o, -fx*X*d*d, o, + o, fy*d, -fy*Y*d*d, o, + # o, o, -D*d*d, d, + ], dim=-1).view(B, N, H, W, 2, 4) + + return coords, proj_jac + + return coords, None + +def actp(Gij, X0, jacobian=False): + """ action on point cloud """ + X1 = Gij[:,:,None,None] * X0 + + if jacobian: + X, Y, Z, d = X1.unbind(dim=-1) + o = torch.zeros_like(d) + B, N, H, W = d.shape + + if isinstance(Gij, SE3): + Ja = torch.stack([ + d, o, o, o, Z, -Y, + o, d, o, -Z, o, X, + o, o, d, Y, -X, o, + o, o, o, o, o, o, + ], dim=-1).view(B, N, H, W, 4, 6) + + elif isinstance(Gij, Sim3): + Ja = torch.stack([ + d, o, o, o, Z, -Y, X, + o, d, o, -Z, o, X, Y, + o, o, d, Y, -X, o, Z, + o, o, o, o, o, o, o + ], dim=-1).view(B, N, H, W, 4, 7) + + return X1, Ja + + return X1, None + +def projective_transform(poses, depths, intrinsics, ii, jj, jacobian=False, return_depth=False): + """ map points from ii->jj """ + + # inverse project (pinhole) + X0, Jz = iproj(depths[:,ii], intrinsics[:,ii], jacobian=jacobian) + + # transform + Gij = poses[:,jj] * poses[:,ii].inv() + + Gij.data[:,ii==jj] = torch.as_tensor([-0.1, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], device="cuda") + X1, Ja = actp(Gij, X0, jacobian=jacobian) + + # project (pinhole) + x1, Jp = proj(X1, intrinsics[:,jj], jacobian=jacobian, return_depth=return_depth) + + # exclude points too close to camera + valid = ((X1[...,2] > MIN_DEPTH) & (X0[...,2] > MIN_DEPTH)).float() + valid = valid.unsqueeze(-1) + + if jacobian: + # Ji transforms according to dual adjoint + Jj = torch.matmul(Jp, Ja) + Ji = -Gij[:,:,None,None,None].adjT(Jj) + + Jz = Gij[:,:,None,None] * Jz + Jz = torch.matmul(Jp, Jz.unsqueeze(-1)) + + return x1, valid, (Ji, Jj, Jz) + + return x1, valid + +def induced_flow(poses, disps, intrinsics, ii, jj): + """ optical flow induced by camera motion """ + + ht, wd = disps.shape[2:] + y, x = torch.meshgrid( + torch.arange(ht).to(disps.device).float(), + torch.arange(wd).to(disps.device).float()) + + coords0 = torch.stack([x, y], dim=-1) + coords1, valid = projective_transform(poses, disps, intrinsics, ii, jj, False) + + return coords1[...,:2] - coords0, valid + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/logger.py b/slahmr/third-party/DROID-SLAM/droid_slam/logger.py new file mode 100644 index 0000000000000000000000000000000000000000..3af7a2cb8f648dbb29abed182aa5eb99ceba015c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/logger.py @@ -0,0 +1,54 @@ + +import torch +from torch.utils.tensorboard import SummaryWriter + + +SUM_FREQ = 100 + +class Logger: + def __init__(self, name, scheduler): + self.total_steps = 0 + self.running_loss = {} + self.writer = None + self.name = name + self.scheduler = scheduler + + def _print_training_status(self): + if self.writer is None: + self.writer = SummaryWriter('runs/%s' % self.name) + print([k for k in self.running_loss]) + + lr = self.scheduler.get_lr().pop() + metrics_data = [self.running_loss[k]/SUM_FREQ for k in self.running_loss.keys()] + training_str = "[{:6d}, {:10.7f}] ".format(self.total_steps+1, lr) + metrics_str = ("{:10.4f}, "*len(metrics_data)).format(*metrics_data) + + # print the training status + print(training_str + metrics_str) + + for key in self.running_loss: + val = self.running_loss[key] / SUM_FREQ + self.writer.add_scalar(key, val, self.total_steps) + self.running_loss[key] = 0.0 + + def push(self, metrics): + + for key in metrics: + if key not in self.running_loss: + self.running_loss[key] = 0.0 + + self.running_loss[key] += metrics[key] + + if self.total_steps % SUM_FREQ == SUM_FREQ-1: + self._print_training_status() + self.running_loss = {} + + self.total_steps += 1 + + def write_dict(self, results): + for key in results: + self.writer.add_scalar(key, results[key], self.total_steps) + + def close(self): + self.writer.close() + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/modules/__init__.py b/slahmr/third-party/DROID-SLAM/droid_slam/modules/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/modules/clipping.py b/slahmr/third-party/DROID-SLAM/droid_slam/modules/clipping.py new file mode 100644 index 0000000000000000000000000000000000000000..e59307f533f7612920ef9eca10cc7ea0e871c928 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/modules/clipping.py @@ -0,0 +1,24 @@ +import torch +import torch.nn as nn +import torch.nn.functional as F + +GRAD_CLIP = .01 + +class GradClip(torch.autograd.Function): + @staticmethod + def forward(ctx, x): + return x + + @staticmethod + def backward(ctx, grad_x): + o = torch.zeros_like(grad_x) + grad_x = torch.where(grad_x.abs()>GRAD_CLIP, o, grad_x) + grad_x = torch.where(torch.isnan(grad_x), o, grad_x) + return grad_x + +class GradientClip(nn.Module): + def __init__(self): + super(GradientClip, self).__init__() + + def forward(self, x): + return GradClip.apply(x) \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/modules/corr.py b/slahmr/third-party/DROID-SLAM/droid_slam/modules/corr.py new file mode 100644 index 0000000000000000000000000000000000000000..6a1e32ad58fd18fa367a5c4897feb16aad7485c4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/modules/corr.py @@ -0,0 +1,140 @@ +import torch +import torch.nn.functional as F + +import droid_backends + +class CorrSampler(torch.autograd.Function): + + @staticmethod + def forward(ctx, volume, coords, radius): + ctx.save_for_backward(volume,coords) + ctx.radius = radius + corr, = droid_backends.corr_index_forward(volume, coords, radius) + return corr + + @staticmethod + def backward(ctx, grad_output): + volume, coords = ctx.saved_tensors + grad_output = grad_output.contiguous() + grad_volume, = droid_backends.corr_index_backward(volume, coords, grad_output, ctx.radius) + return grad_volume, None, None + + +class CorrBlock: + def __init__(self, fmap1, fmap2, num_levels=4, radius=3): + self.num_levels = num_levels + self.radius = radius + self.corr_pyramid = [] + + # all pairs correlation + corr = CorrBlock.corr(fmap1, fmap2) + + batch, num, h1, w1, h2, w2 = corr.shape + corr = corr.reshape(batch*num*h1*w1, 1, h2, w2) + + for i in range(self.num_levels): + self.corr_pyramid.append( + corr.view(batch*num, h1, w1, h2//2**i, w2//2**i)) + corr = F.avg_pool2d(corr, 2, stride=2) + + def __call__(self, coords): + out_pyramid = [] + batch, num, ht, wd, _ = coords.shape + coords = coords.permute(0,1,4,2,3) + coords = coords.contiguous().view(batch*num, 2, ht, wd) + + for i in range(self.num_levels): + corr = CorrSampler.apply(self.corr_pyramid[i], coords/2**i, self.radius) + out_pyramid.append(corr.view(batch, num, -1, ht, wd)) + + return torch.cat(out_pyramid, dim=2) + + def cat(self, other): + for i in range(self.num_levels): + self.corr_pyramid[i] = torch.cat([self.corr_pyramid[i], other.corr_pyramid[i]], 0) + return self + + def __getitem__(self, index): + for i in range(self.num_levels): + self.corr_pyramid[i] = self.corr_pyramid[i][index] + return self + + + @staticmethod + def corr(fmap1, fmap2): + """ all-pairs correlation """ + batch, num, dim, ht, wd = fmap1.shape + fmap1 = fmap1.reshape(batch*num, dim, ht*wd) / 4.0 + fmap2 = fmap2.reshape(batch*num, dim, ht*wd) / 4.0 + + corr = torch.matmul(fmap1.transpose(1,2), fmap2) + return corr.view(batch, num, ht, wd, ht, wd) + + +class CorrLayer(torch.autograd.Function): + @staticmethod + def forward(ctx, fmap1, fmap2, coords, r): + ctx.r = r + ctx.save_for_backward(fmap1, fmap2, coords) + corr, = droid_backends.altcorr_forward(fmap1, fmap2, coords, ctx.r) + return corr + + @staticmethod + def backward(ctx, grad_corr): + fmap1, fmap2, coords = ctx.saved_tensors + grad_corr = grad_corr.contiguous() + fmap1_grad, fmap2_grad, coords_grad = \ + droid_backends.altcorr_backward(fmap1, fmap2, coords, grad_corr, ctx.r) + return fmap1_grad, fmap2_grad, coords_grad, None + + +class AltCorrBlock: + def __init__(self, fmaps, num_levels=4, radius=3): + self.num_levels = num_levels + self.radius = radius + + B, N, C, H, W = fmaps.shape + fmaps = fmaps.view(B*N, C, H, W) / 4.0 + + self.pyramid = [] + for i in range(self.num_levels): + sz = (B, N, H//2**i, W//2**i, C) + fmap_lvl = fmaps.permute(0, 2, 3, 1).contiguous() + self.pyramid.append(fmap_lvl.view(*sz)) + fmaps = F.avg_pool2d(fmaps, 2, stride=2) + + def corr_fn(self, coords, ii, jj): + B, N, H, W, S, _ = coords.shape + coords = coords.permute(0, 1, 4, 2, 3, 5) + + corr_list = [] + for i in range(self.num_levels): + r = self.radius + fmap1_i = self.pyramid[0][:, ii] + fmap2_i = self.pyramid[i][:, jj] + + coords_i = (coords / 2**i).reshape(B*N, S, H, W, 2).contiguous() + fmap1_i = fmap1_i.reshape((B*N,) + fmap1_i.shape[2:]) + fmap2_i = fmap2_i.reshape((B*N,) + fmap2_i.shape[2:]) + + corr = CorrLayer.apply(fmap1_i.float(), fmap2_i.float(), coords_i, self.radius) + corr = corr.view(B, N, S, -1, H, W).permute(0, 1, 3, 4, 5, 2) + corr_list.append(corr) + + corr = torch.cat(corr_list, dim=2) + return corr + + + def __call__(self, coords, ii, jj): + squeeze_output = False + if len(coords.shape) == 5: + coords = coords.unsqueeze(dim=-2) + squeeze_output = True + + corr = self.corr_fn(coords, ii, jj) + + if squeeze_output: + corr = corr.squeeze(dim=-1) + + return corr.contiguous() + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/modules/extractor.py b/slahmr/third-party/DROID-SLAM/droid_slam/modules/extractor.py new file mode 100644 index 0000000000000000000000000000000000000000..5807d45f7494033a54ec06acb651d46a86afb3dc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/modules/extractor.py @@ -0,0 +1,198 @@ +import torch +import torch.nn as nn +import torch.nn.functional as F + + +class ResidualBlock(nn.Module): + def __init__(self, in_planes, planes, norm_fn='group', stride=1): + super(ResidualBlock, self).__init__() + + self.conv1 = nn.Conv2d(in_planes, planes, kernel_size=3, padding=1, stride=stride) + self.conv2 = nn.Conv2d(planes, planes, kernel_size=3, padding=1) + self.relu = nn.ReLU(inplace=True) + + num_groups = planes // 8 + + if norm_fn == 'group': + self.norm1 = nn.GroupNorm(num_groups=num_groups, num_channels=planes) + self.norm2 = nn.GroupNorm(num_groups=num_groups, num_channels=planes) + if not stride == 1: + self.norm3 = nn.GroupNorm(num_groups=num_groups, num_channels=planes) + + elif norm_fn == 'batch': + self.norm1 = nn.BatchNorm2d(planes) + self.norm2 = nn.BatchNorm2d(planes) + if not stride == 1: + self.norm3 = nn.BatchNorm2d(planes) + + elif norm_fn == 'instance': + self.norm1 = nn.InstanceNorm2d(planes) + self.norm2 = nn.InstanceNorm2d(planes) + if not stride == 1: + self.norm3 = nn.InstanceNorm2d(planes) + + elif norm_fn == 'none': + self.norm1 = nn.Sequential() + self.norm2 = nn.Sequential() + if not stride == 1: + self.norm3 = nn.Sequential() + + if stride == 1: + self.downsample = None + + else: + self.downsample = nn.Sequential( + nn.Conv2d(in_planes, planes, kernel_size=1, stride=stride), self.norm3) + + def forward(self, x): + y = x + y = self.relu(self.norm1(self.conv1(y))) + y = self.relu(self.norm2(self.conv2(y))) + + if self.downsample is not None: + x = self.downsample(x) + + return self.relu(x+y) + + +class BottleneckBlock(nn.Module): + def __init__(self, in_planes, planes, norm_fn='group', stride=1): + super(BottleneckBlock, self).__init__() + + self.conv1 = nn.Conv2d(in_planes, planes//4, kernel_size=1, padding=0) + self.conv2 = nn.Conv2d(planes//4, planes//4, kernel_size=3, padding=1, stride=stride) + self.conv3 = nn.Conv2d(planes//4, planes, kernel_size=1, padding=0) + self.relu = nn.ReLU(inplace=True) + + num_groups = planes // 8 + + if norm_fn == 'group': + self.norm1 = nn.GroupNorm(num_groups=num_groups, num_channels=planes//4) + self.norm2 = nn.GroupNorm(num_groups=num_groups, num_channels=planes//4) + self.norm3 = nn.GroupNorm(num_groups=num_groups, num_channels=planes) + if not stride == 1: + self.norm4 = nn.GroupNorm(num_groups=num_groups, num_channels=planes) + + elif norm_fn == 'batch': + self.norm1 = nn.BatchNorm2d(planes//4) + self.norm2 = nn.BatchNorm2d(planes//4) + self.norm3 = nn.BatchNorm2d(planes) + if not stride == 1: + self.norm4 = nn.BatchNorm2d(planes) + + elif norm_fn == 'instance': + self.norm1 = nn.InstanceNorm2d(planes//4) + self.norm2 = nn.InstanceNorm2d(planes//4) + self.norm3 = nn.InstanceNorm2d(planes) + if not stride == 1: + self.norm4 = nn.InstanceNorm2d(planes) + + elif norm_fn == 'none': + self.norm1 = nn.Sequential() + self.norm2 = nn.Sequential() + self.norm3 = nn.Sequential() + if not stride == 1: + self.norm4 = nn.Sequential() + + if stride == 1: + self.downsample = None + + else: + self.downsample = nn.Sequential( + nn.Conv2d(in_planes, planes, kernel_size=1, stride=stride), self.norm4) + + def forward(self, x): + y = x + y = self.relu(self.norm1(self.conv1(y))) + y = self.relu(self.norm2(self.conv2(y))) + y = self.relu(self.norm3(self.conv3(y))) + + if self.downsample is not None: + x = self.downsample(x) + + return self.relu(x+y) + + +DIM=32 + +class BasicEncoder(nn.Module): + def __init__(self, output_dim=128, norm_fn='batch', dropout=0.0, multidim=False): + super(BasicEncoder, self).__init__() + self.norm_fn = norm_fn + self.multidim = multidim + + if self.norm_fn == 'group': + self.norm1 = nn.GroupNorm(num_groups=8, num_channels=DIM) + + elif self.norm_fn == 'batch': + self.norm1 = nn.BatchNorm2d(DIM) + + elif self.norm_fn == 'instance': + self.norm1 = nn.InstanceNorm2d(DIM) + + elif self.norm_fn == 'none': + self.norm1 = nn.Sequential() + + self.conv1 = nn.Conv2d(3, DIM, kernel_size=7, stride=2, padding=3) + self.relu1 = nn.ReLU(inplace=True) + + self.in_planes = DIM + self.layer1 = self._make_layer(DIM, stride=1) + self.layer2 = self._make_layer(2*DIM, stride=2) + self.layer3 = self._make_layer(4*DIM, stride=2) + + # output convolution + self.conv2 = nn.Conv2d(4*DIM, output_dim, kernel_size=1) + + if self.multidim: + self.layer4 = self._make_layer(256, stride=2) + self.layer5 = self._make_layer(512, stride=2) + + self.in_planes = 256 + self.layer6 = self._make_layer(256, stride=1) + + self.in_planes = 128 + self.layer7 = self._make_layer(128, stride=1) + + self.up1 = nn.Conv2d(512, 256, 1) + self.up2 = nn.Conv2d(256, 128, 1) + self.conv3 = nn.Conv2d(128, output_dim, kernel_size=1) + + if dropout > 0: + self.dropout = nn.Dropout2d(p=dropout) + else: + self.dropout = None + + for m in self.modules(): + if isinstance(m, nn.Conv2d): + nn.init.kaiming_normal_(m.weight, mode='fan_out', nonlinearity='relu') + elif isinstance(m, (nn.BatchNorm2d, nn.InstanceNorm2d, nn.GroupNorm)): + if m.weight is not None: + nn.init.constant_(m.weight, 1) + if m.bias is not None: + nn.init.constant_(m.bias, 0) + + def _make_layer(self, dim, stride=1): + layer1 = ResidualBlock(self.in_planes, dim, self.norm_fn, stride=stride) + layer2 = ResidualBlock(dim, dim, self.norm_fn, stride=1) + layers = (layer1, layer2) + + self.in_planes = dim + return nn.Sequential(*layers) + + def forward(self, x): + b, n, c1, h1, w1 = x.shape + x = x.view(b*n, c1, h1, w1) + + x = self.conv1(x) + x = self.norm1(x) + x = self.relu1(x) + + x = self.layer1(x) + x = self.layer2(x) + x = self.layer3(x) + + x = self.conv2(x) + + _, c2, h2, w2 = x.shape + return x.view(b, n, c2, h2, w2) diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/modules/gru.py b/slahmr/third-party/DROID-SLAM/droid_slam/modules/gru.py new file mode 100644 index 0000000000000000000000000000000000000000..84ea5038fb45bbe8cfd92428d04ce5612d74d43a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/modules/gru.py @@ -0,0 +1,34 @@ +import torch +import torch.nn as nn + + +class ConvGRU(nn.Module): + def __init__(self, h_planes=128, i_planes=128): + super(ConvGRU, self).__init__() + self.do_checkpoint = False + self.convz = nn.Conv2d(h_planes+i_planes, h_planes, 3, padding=1) + self.convr = nn.Conv2d(h_planes+i_planes, h_planes, 3, padding=1) + self.convq = nn.Conv2d(h_planes+i_planes, h_planes, 3, padding=1) + + self.w = nn.Conv2d(h_planes, h_planes, 1, padding=0) + + self.convz_glo = nn.Conv2d(h_planes, h_planes, 1, padding=0) + self.convr_glo = nn.Conv2d(h_planes, h_planes, 1, padding=0) + self.convq_glo = nn.Conv2d(h_planes, h_planes, 1, padding=0) + + def forward(self, net, *inputs): + inp = torch.cat(inputs, dim=1) + net_inp = torch.cat([net, inp], dim=1) + + b, c, h, w = net.shape + glo = torch.sigmoid(self.w(net)) * net + glo = glo.view(b, c, h*w).mean(-1).view(b, c, 1, 1) + + z = torch.sigmoid(self.convz(net_inp) + self.convz_glo(glo)) + r = torch.sigmoid(self.convr(net_inp) + self.convr_glo(glo)) + q = torch.tanh(self.convq(torch.cat([r*net, inp], dim=1)) + self.convq_glo(glo)) + + net = (1-z) * net + z * q + return net + + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/motion_filter.py b/slahmr/third-party/DROID-SLAM/droid_slam/motion_filter.py new file mode 100644 index 0000000000000000000000000000000000000000..5cb18d9d12da9fca9d9d6a04bdae65e5181e8a59 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/motion_filter.py @@ -0,0 +1,159 @@ +import cv2 +import torch +import lietorch + +from collections import OrderedDict +from droid_net import DroidNet + +import geom.projective_ops as pops +from modules.corr import CorrBlock + + +class MotionFilter: + """ This class is used to filter incoming frames and extract features """ + + def __init__(self, net, video, thresh=2.5, device="cuda:0"): + + # split net modules + self.cnet = net.cnet + self.fnet = net.fnet + self.update = net.update + + self.video = video + self.thresh = thresh + self.device = device + + self.count = 0 + + # mean, std for image normalization + self.MEAN = torch.as_tensor([0.485, 0.456, 0.406], device=self.device)[:, None, None] + self.STDV = torch.as_tensor([0.229, 0.224, 0.225], device=self.device)[:, None, None] + + @torch.cuda.amp.autocast(enabled=True) + def __context_encoder(self, image): + """ context features """ + net, inp = self.cnet(image).split([128,128], dim=2) + return net.tanh().squeeze(0), inp.relu().squeeze(0) + + @torch.cuda.amp.autocast(enabled=True) + def __feature_encoder(self, image): + """ features for correlation volume """ + return self.fnet(image).squeeze(0) + + @torch.cuda.amp.autocast(enabled=True) + @torch.no_grad() + def track(self, tstamp, image, depth=None, intrinsics=None): + """ main update operation - run on every frame in video """ + + Id = lietorch.SE3.Identity(1,).data.squeeze() + ht = image.shape[-2] // 8 + wd = image.shape[-1] // 8 + + # normalize images + inputs = image[None, :, [2,1,0]].to(self.device) / 255.0 + inputs = inputs.sub_(self.MEAN).div_(self.STDV) + + # extract features + gmap = self.__feature_encoder(inputs) + + ### always add first frame to the depth video ### + if self.video.counter.value == 0: + net, inp = self.__context_encoder(inputs[:,[0]]) + self.net, self.inp, self.fmap = net, inp, gmap + self.video.append(tstamp, image[0], Id, 1.0, depth, intrinsics / 8.0, gmap, net[0,0], inp[0,0]) + + ### only add new frame if there is enough motion ### + else: + # index correlation volume + coords0 = pops.coords_grid(ht, wd, device=self.device)[None,None] + corr = CorrBlock(self.fmap[None,[0]], gmap[None,[0]])(coords0) + + # approximate flow magnitude using 1 update iteration + _, delta, weight = self.update(self.net[None], self.inp[None], corr) + + # check motion magnitue / add new frame to video + if delta.norm(dim=-1).mean().item() > self.thresh: + self.count = 0 + net, inp = self.__context_encoder(inputs[:,[0]]) + self.net, self.inp, self.fmap = net, inp, gmap + self.video.append(tstamp, image[0], None, None, depth, intrinsics / 8.0, gmap, net[0], inp[0]) + + else: + self.count += 1 + + + + +# class MotionFilter: +# """ This class is used to filter incoming frames and extract features """ + +# def __init__(self, net, video, thresh=2.5, device="cuda:0"): + +# # split net modules +# self.cnet = net.cnet +# self.fnet = net.fnet +# self.update = net.update + +# self.video = video +# self.thresh = thresh +# self.device = device + +# self.count = 0 + +# # mean, std for image normalization +# self.MEAN = torch.as_tensor([0.485, 0.456, 0.406], device=self.device)[:, None, None] +# self.STDV = torch.as_tensor([0.229, 0.224, 0.225], device=self.device)[:, None, None] + +# @torch.cuda.amp.autocast(enabled=True) +# def __context_encoder(self, image): +# """ context features """ +# x = self.cnet(image) +# net, inp = self.cnet(image).split([128,128], dim=2) +# return net.tanh().squeeze(0), inp.relu().squeeze(0) + +# @torch.cuda.amp.autocast(enabled=True) +# def __feature_encoder(self, image): +# """ features for correlation volume """ +# return self.fnet(image).squeeze(0) + +# @torch.cuda.amp.autocast(enabled=True) +# @torch.no_grad() +# def track(self, tstamp, image, depth=None, intrinsics=None): +# """ main update operation - run on every frame in video """ + +# Id = lietorch.SE3.Identity(1,).data.squeeze() +# ht = image.shape[-2] // 8 +# wd = image.shape[-1] // 8 + +# # normalize images +# inputs = image[None, None, [2,1,0]].to(self.device) / 255.0 +# inputs = inputs.sub_(self.MEAN).div_(self.STDV) + +# # extract features +# gmap = self.__feature_encoder(inputs) + +# ### always add first frame to the depth video ### +# if self.video.counter.value == 0: +# net, inp = self.__context_encoder(inputs) +# self.net, self.inp, self.fmap = net, inp, gmap +# self.video.append(tstamp, image, Id, 1.0, intrinsics / 8.0, gmap[0], net[0], inp[0]) + +# ### only add new frame if there is enough motion ### +# else: +# # index correlation volume +# coords0 = pops.coords_grid(ht, wd, device=self.device)[None,None] +# corr = CorrBlock(self.fmap[None], gmap[None])(coords0) + +# # approximate flow magnitude using 1 update iteration +# _, delta, weight = self.update(self.net[None], self.inp[None], corr) + +# # check motion magnitue / add new frame to video +# if delta.norm(dim=-1).mean().item() > self.thresh: +# self.count = 0 +# net, inp = self.__context_encoder(inputs) +# self.net, self.inp, self.fmap = net, inp, gmap +# self.video.append(tstamp, image, None, None, intrinsics / 8.0, gmap[0], net[0], inp[0]) + +# else: +# self.count += 1 + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/trajectory_filler.py b/slahmr/third-party/DROID-SLAM/droid_slam/trajectory_filler.py new file mode 100644 index 0000000000000000000000000000000000000000..efa6269bc3734f40760316a83489bec5bba1faa8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/trajectory_filler.py @@ -0,0 +1,104 @@ +import cv2 +import torch +import lietorch + +from lietorch import SE3 +from collections import OrderedDict +from factor_graph import FactorGraph +from droid_net import DroidNet +import geom.projective_ops as pops + + +class PoseTrajectoryFiller: + """ This class is used to fill in non-keyframe poses """ + + def __init__(self, net, video, device="cuda:0"): + + # split net modules + self.cnet = net.cnet + self.fnet = net.fnet + self.update = net.update + + self.count = 0 + self.video = video + self.device = device + + # mean, std for image normalization + self.MEAN = torch.as_tensor([0.485, 0.456, 0.406], device=self.device)[:, None, None] + self.STDV = torch.as_tensor([0.229, 0.224, 0.225], device=self.device)[:, None, None] + + @torch.cuda.amp.autocast(enabled=True) + def __feature_encoder(self, image): + """ features for correlation volume """ + return self.fnet(image) + + def __fill(self, tstamps, images, intrinsics): + """ fill operator """ + + tt = torch.as_tensor(tstamps, device="cuda") + images = torch.stack(images, 0) + intrinsics = torch.stack(intrinsics, 0) + inputs = images[:,:,[2,1,0]].to(self.device) / 255.0 + + ### linear pose interpolation ### + N = self.video.counter.value + M = len(tstamps) + + ts = self.video.tstamp[:N] + Ps = SE3(self.video.poses[:N]) + + t0 = torch.as_tensor([ts[ts<=t].shape[0] - 1 for t in tstamps]) + t1 = torch.where(t0 0: + pose_list += self.__fill(tstamps, images, intrinsics) + + # stitch pose segments together + return lietorch.cat(pose_list, 0) + diff --git a/slahmr/third-party/DROID-SLAM/droid_slam/visualization.py b/slahmr/third-party/DROID-SLAM/droid_slam/visualization.py new file mode 100644 index 0000000000000000000000000000000000000000..b28cc755dba98045dbf360f6403e05927ab06bfe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/droid_slam/visualization.py @@ -0,0 +1,154 @@ +import torch +import cv2 +import lietorch +import droid_backends +import time +import argparse +import numpy as np +import open3d as o3d + +from lietorch import SE3 +import geom.projective_ops as pops + +CAM_POINTS = np.array([ + [ 0, 0, 0], + [-1, -1, 1.5], + [ 1, -1, 1.5], + [ 1, 1, 1.5], + [-1, 1, 1.5], + [-0.5, 1, 1.5], + [ 0.5, 1, 1.5], + [ 0, 1.2, 1.5]]) + +CAM_LINES = np.array([ + [1,2], [2,3], [3,4], [4,1], [1,0], [0,2], [3,0], [0,4], [5,7], [7,6]]) + +def white_balance(img): + # from https://stackoverflow.com/questions/46390779/automatic-white-balancing-with-grayworld-assumption + result = cv2.cvtColor(img, cv2.COLOR_BGR2LAB) + avg_a = np.average(result[:, :, 1]) + avg_b = np.average(result[:, :, 2]) + result[:, :, 1] = result[:, :, 1] - ((avg_a - 128) * (result[:, :, 0] / 255.0) * 1.1) + result[:, :, 2] = result[:, :, 2] - ((avg_b - 128) * (result[:, :, 0] / 255.0) * 1.1) + result = cv2.cvtColor(result, cv2.COLOR_LAB2BGR) + return result + +def create_camera_actor(g, scale=0.05): + """ build open3d camera polydata """ + camera_actor = o3d.geometry.LineSet( + points=o3d.utility.Vector3dVector(scale * CAM_POINTS), + lines=o3d.utility.Vector2iVector(CAM_LINES)) + + color = (g * 1.0, 0.5 * (1-g), 0.9 * (1-g)) + camera_actor.paint_uniform_color(color) + return camera_actor + +def create_point_actor(points, colors): + """ open3d point cloud from numpy array """ + point_cloud = o3d.geometry.PointCloud() + point_cloud.points = o3d.utility.Vector3dVector(points) + point_cloud.colors = o3d.utility.Vector3dVector(colors) + return point_cloud + +def droid_visualization(video, device="cuda:0"): + """ DROID visualization frontend """ + + torch.cuda.set_device(device) + droid_visualization.video = video + droid_visualization.cameras = {} + droid_visualization.points = {} + droid_visualization.warmup = 8 + droid_visualization.scale = 1.0 + droid_visualization.ix = 0 + + droid_visualization.filter_thresh = 0.005 + + def increase_filter(vis): + droid_visualization.filter_thresh *= 2 + with droid_visualization.video.get_lock(): + droid_visualization.video.dirty[:droid_visualization.video.counter.value] = True + + def decrease_filter(vis): + droid_visualization.filter_thresh *= 0.5 + with droid_visualization.video.get_lock(): + droid_visualization.video.dirty[:droid_visualization.video.counter.value] = True + + def animation_callback(vis): + cam = vis.get_view_control().convert_to_pinhole_camera_parameters() + + with torch.no_grad(): + + with video.get_lock(): + t = video.counter.value + dirty_index, = torch.where(video.dirty.clone()) + dirty_index = dirty_index + + if len(dirty_index) == 0: + return + + video.dirty[dirty_index] = False + + # convert poses to 4x4 matrix + poses = torch.index_select(video.poses, 0, dirty_index) + disps = torch.index_select(video.disps, 0, dirty_index) + Ps = SE3(poses).inv().matrix().cpu().numpy() + + images = torch.index_select(video.images, 0, dirty_index) + images = images.cpu()[:,[2,1,0],3::8,3::8].permute(0,2,3,1) / 255.0 + points = droid_backends.iproj(SE3(poses).inv().data, disps, video.intrinsics[0]).cpu() + + thresh = droid_visualization.filter_thresh * torch.ones_like(disps.mean(dim=[1,2])) + + count = droid_backends.depth_filter( + video.poses, video.disps, video.intrinsics[0], dirty_index, thresh) + + count = count.cpu() + disps = disps.cpu() + masks = ((count >= 2) & (disps > .5*disps.mean(dim=[1,2], keepdim=True))) + + for i in range(len(dirty_index)): + pose = Ps[i] + ix = dirty_index[i].item() + + if ix in droid_visualization.cameras: + vis.remove_geometry(droid_visualization.cameras[ix]) + del droid_visualization.cameras[ix] + + if ix in droid_visualization.points: + vis.remove_geometry(droid_visualization.points[ix]) + del droid_visualization.points[ix] + + ### add camera actor ### + cam_actor = create_camera_actor(True) + cam_actor.transform(pose) + vis.add_geometry(cam_actor) + droid_visualization.cameras[ix] = cam_actor + + mask = masks[i].reshape(-1) + pts = points[i].reshape(-1, 3)[mask].cpu().numpy() + clr = images[i].reshape(-1, 3)[mask].cpu().numpy() + + ## add point actor ### + point_actor = create_point_actor(pts, clr) + vis.add_geometry(point_actor) + droid_visualization.points[ix] = point_actor + + # hack to allow interacting with vizualization during inference + if len(droid_visualization.cameras) >= droid_visualization.warmup: + cam = vis.get_view_control().convert_from_pinhole_camera_parameters(cam) + + droid_visualization.ix += 1 + vis.poll_events() + vis.update_renderer() + + ### create Open3D visualization ### + vis = o3d.visualization.VisualizerWithKeyCallback() + vis.register_animation_callback(animation_callback) + vis.register_key_callback(ord("S"), increase_filter) + vis.register_key_callback(ord("A"), decrease_filter) + + vis.create_window(height=540, width=960) + vis.get_render_option().load_from_json("misc/renderoption.json") + + vis.run() + vis.destroy_window() diff --git a/slahmr/third-party/DROID-SLAM/environment.yaml b/slahmr/third-party/DROID-SLAM/environment.yaml new file mode 100644 index 0000000000000000000000000000000000000000..f92153acc588328bd9784dc329febe863cf68b88 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/environment.yaml @@ -0,0 +1,22 @@ +name: droidenv +channels: + - rusty1s + - pytorch + - open3d-admin + - nvidia + - conda-forge + - defaults +dependencies: + - pytorch-scatter + - torchaudio + - torchvision + - open3d + - pytorch=1.10 + - cudatoolkit=11.3 + - tensorboard + - scipy + - opencv + - tqdm + - suitesparse + - matplotlib + - pyyaml diff --git a/slahmr/third-party/DROID-SLAM/environment_novis.yaml b/slahmr/third-party/DROID-SLAM/environment_novis.yaml new file mode 100644 index 0000000000000000000000000000000000000000..e6653f5eccc005894f3c29f35c28f085b9b05d68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/environment_novis.yaml @@ -0,0 +1,20 @@ +name: droidenv +channels: + - rusty1s + - pytorch + - nvidia + - conda-forge + - defaults +dependencies: + - pytorch-scatter + - torchaudio + - torchvision + - pytorch=1.10 + - cudatoolkit=11.3 + - tensorboard + - scipy + - opencv + - tqdm + - suitesparse + - matplotlib + - pyyaml diff --git a/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_eth3d.py b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_eth3d.py new file mode 100644 index 0000000000000000000000000000000000000000..3e9e3186a8c583bdaf8e98b1f49ecb9a0bf67fa8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_eth3d.py @@ -0,0 +1,134 @@ +import sys +sys.path.append('droid_slam') + +from tqdm import tqdm +import numpy as np +import torch +import lietorch +import cv2 +import os +import glob +import time +import argparse + +import torch.nn.functional as F +from droid import Droid + +import matplotlib.pyplot as plt + + +def show_image(image): + image = image.permute(1, 2, 0).cpu().numpy() + cv2.imshow('image', image / 255.0) + cv2.waitKey(1) + +def image_stream(datapath, use_depth=False, stride=1): + """ image generator """ + + fx, fy, cx, cy = np.loadtxt(os.path.join(datapath, 'calibration.txt')).tolist() + image_list = sorted(glob.glob(os.path.join(datapath, 'rgb', '*.png')))[::stride] + depth_list = sorted(glob.glob(os.path.join(datapath, 'depth', '*.png')))[::stride] + + for t, (image_file, depth_file) in enumerate(zip(image_list, depth_list)): + image = cv2.imread(image_file) + depth = cv2.imread(depth_file, cv2.IMREAD_ANYDEPTH) / 5000.0 + + h0, w0, _ = image.shape + h1 = int(h0 * np.sqrt((384 * 512) / (h0 * w0))) + w1 = int(w0 * np.sqrt((384 * 512) / (h0 * w0))) + + image = cv2.resize(image, (w1, h1)) + image = image[:h1-h1%8, :w1-w1%8] + image = torch.as_tensor(image).permute(2, 0, 1) + + depth = torch.as_tensor(depth) + depth = F.interpolate(depth[None,None], (h1, w1)).squeeze() + depth = depth[:h1-h1%8, :w1-w1%8] + + intrinsics = torch.as_tensor([fx, fy, cx, cy]) + intrinsics[0::2] *= (w1 / w0) + intrinsics[1::2] *= (h1 / h0) + + if use_depth: + yield t, image[None], depth, intrinsics + + else: + yield t, image[None], intrinsics + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument("--datapath") + parser.add_argument("--weights", default="droid.pth") + parser.add_argument("--buffer", type=int, default=1024) + parser.add_argument("--image_size", default=[240, 320]) + parser.add_argument("--disable_vis", action="store_true") + + parser.add_argument("--beta", type=float, default=0.5) + parser.add_argument("--filter_thresh", type=float, default=2.0) + parser.add_argument("--warmup", type=int, default=8) + parser.add_argument("--keyframe_thresh", type=float, default=3.5) + parser.add_argument("--frontend_thresh", type=float, default=16.0) + parser.add_argument("--frontend_window", type=int, default=16) + parser.add_argument("--frontend_radius", type=int, default=1) + parser.add_argument("--frontend_nms", type=int, default=0) + + parser.add_argument("--stereo", action="store_true") + parser.add_argument("--depth", action="store_true") + + parser.add_argument("--backend_thresh", type=float, default=22.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=3) + args = parser.parse_args() + + torch.multiprocessing.set_start_method('spawn') + + print("Running evaluation on {}".format(args.datapath)) + print(args) + + # this can usually be set to 2-3 except for "camera_shake" scenes + # set to 2 for test scenes + stride = 1 + + tstamps = [] + for (t, image, depth, intrinsics) in tqdm(image_stream(args.datapath, use_depth=True, stride=stride)): + if not args.disable_vis: + show_image(image[0]) + + if t == 0: + args.image_size = [image.shape[2], image.shape[3]] + droid = Droid(args) + + droid.track(t, image, depth, intrinsics=intrinsics) + + traj_est = droid.terminate(image_stream(args.datapath, use_depth=False, stride=stride)) + + ### run evaluation ### + + print("#"*20 + " Results...") + + import evo + from evo.core.trajectory import PoseTrajectory3D + from evo.tools import file_interface + from evo.core import sync + import evo.main_ape as main_ape + from evo.core.metrics import PoseRelation + + image_path = os.path.join(args.datapath, 'rgb') + images_list = sorted(glob.glob(os.path.join(image_path, '*.png')))[::stride] + tstamps = [float(x.split('/')[-1][:-4]) for x in images_list] + + traj_est = PoseTrajectory3D( + positions_xyz=traj_est[:,:3], + orientations_quat_wxyz=traj_est[:,3:], + timestamps=np.array(tstamps)) + + gt_file = os.path.join(args.datapath, 'groundtruth.txt') + traj_ref = file_interface.read_tum_trajectory_file(gt_file) + + traj_ref, traj_est = sync.associate_trajectories(traj_ref, traj_est) + + result = main_ape.ape(traj_ref, traj_est, est_name='traj', + pose_relation=PoseRelation.translation_part, align=True, correct_scale=False) + + print(result.stats) + diff --git a/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_euroc.py b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_euroc.py new file mode 100644 index 0000000000000000000000000000000000000000..d0214f5f209a5c103732114ea2f012e0454f5775 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_euroc.py @@ -0,0 +1,142 @@ +import sys +sys.path.append('droid_slam') + +from tqdm import tqdm +import numpy as np +import torch +import lietorch +import cv2 +import os +import glob +import time +import argparse + +from torch.multiprocessing import Process +from droid import Droid + +import torch.nn.functional as F + + + +def show_image(image): + image = image.permute(1, 2, 0).cpu().numpy() + cv2.imshow('image', image / 255.0) + cv2.waitKey(1) + +def image_stream(datapath, image_size=[320, 512], stereo=False, stride=1): + """ image generator """ + + K_l = np.array([458.654, 0.0, 367.215, 0.0, 457.296, 248.375, 0.0, 0.0, 1.0]).reshape(3,3) + d_l = np.array([-0.28340811, 0.07395907, 0.00019359, 1.76187114e-05, 0.0]) + R_l = np.array([ + 0.999966347530033, -0.001422739138722922, 0.008079580483432283, + 0.001365741834644127, 0.9999741760894847, 0.007055629199258132, + -0.008089410156878961, -0.007044357138835809, 0.9999424675829176 + ]).reshape(3,3) + + P_l = np.array([435.2046959714599, 0, 367.4517211914062, 0, 0, 435.2046959714599, 252.2008514404297, 0, 0, 0, 1, 0]).reshape(3,4) + map_l = cv2.initUndistortRectifyMap(K_l, d_l, R_l, P_l[:3,:3], (752, 480), cv2.CV_32F) + + K_r = np.array([457.587, 0.0, 379.999, 0.0, 456.134, 255.238, 0.0, 0.0, 1]).reshape(3,3) + d_r = np.array([-0.28368365, 0.07451284, -0.00010473, -3.555907e-05, 0.0]).reshape(5) + R_r = np.array([ + 0.9999633526194376, -0.003625811871560086, 0.007755443660172947, + 0.003680398547259526, 0.9999684752771629, -0.007035845251224894, + -0.007729688520722713, 0.007064130529506649, 0.999945173484644 + ]).reshape(3,3) + + P_r = np.array([435.2046959714599, 0, 367.4517211914062, -47.90639384423901, 0, 435.2046959714599, 252.2008514404297, 0, 0, 0, 1, 0]).reshape(3,4) + map_r = cv2.initUndistortRectifyMap(K_r, d_r, R_r, P_r[:3,:3], (752, 480), cv2.CV_32F) + + intrinsics_vec = [435.2046959714599, 435.2046959714599, 367.4517211914062, 252.2008514404297] + ht0, wd0 = [480, 752] + + # read all png images in folder + images_left = sorted(glob.glob(os.path.join(datapath, 'mav0/cam0/data/*.png')))[::stride] + images_right = [x.replace('cam0', 'cam1') for x in images_left] + + for t, (imgL, imgR) in enumerate(zip(images_left, images_right)): + if stereo and not os.path.isfile(imgR): + continue + tstamp = float(imgL.split('/')[-1][:-4]) + images = [cv2.remap(cv2.imread(imgL), map_l[0], map_l[1], interpolation=cv2.INTER_LINEAR)] + if stereo: + images += [cv2.remap(cv2.imread(imgR), map_r[0], map_r[1], interpolation=cv2.INTER_LINEAR)] + + images = torch.from_numpy(np.stack(images, 0)) + images = images.permute(0, 3, 1, 2).to("cuda:0", dtype=torch.float32) + images = F.interpolate(images, image_size, mode="bilinear", align_corners=False) + + intrinsics = torch.as_tensor(intrinsics_vec).cuda() + intrinsics[0] *= image_size[1] / wd0 + intrinsics[1] *= image_size[0] / ht0 + intrinsics[2] *= image_size[1] / wd0 + intrinsics[3] *= image_size[0] / ht0 + + yield stride*t, images, intrinsics + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument("--datapath", help="path to euroc sequence") + parser.add_argument("--gt", help="path to gt file") + parser.add_argument("--weights", default="droid.pth") + parser.add_argument("--buffer", type=int, default=512) + parser.add_argument("--image_size", default=[320,512]) + parser.add_argument("--disable_vis", action="store_true") + parser.add_argument("--stereo", action="store_true") + + parser.add_argument("--beta", type=float, default=0.3) + parser.add_argument("--filter_thresh", type=float, default=2.4) + parser.add_argument("--warmup", type=int, default=15) + parser.add_argument("--keyframe_thresh", type=float, default=3.5) + parser.add_argument("--frontend_thresh", type=float, default=17.5) + parser.add_argument("--frontend_window", type=int, default=20) + parser.add_argument("--frontend_radius", type=int, default=2) + parser.add_argument("--frontend_nms", type=int, default=1) + + parser.add_argument("--backend_thresh", type=float, default=24.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=2) + args = parser.parse_args() + + torch.multiprocessing.set_start_method('spawn') + + print("Running evaluation on {}".format(args.datapath)) + print(args) + + droid = Droid(args) + time.sleep(5) + + for (t, image, intrinsics) in tqdm(image_stream(args.datapath, stereo=args.stereo, stride=2)): + droid.track(t, image, intrinsics=intrinsics) + + traj_est = droid.terminate(image_stream(args.datapath, stride=1)) + + ### run evaluation ### + + import evo + from evo.core.trajectory import PoseTrajectory3D + from evo.tools import file_interface + from evo.core import sync + import evo.main_ape as main_ape + from evo.core.metrics import PoseRelation + + images_list = sorted(glob.glob(os.path.join(args.datapath, 'mav0/cam0/data/*.png'))) + tstamps = [float(x.split('/')[-1][:-4]) for x in images_list] + + traj_est = PoseTrajectory3D( + positions_xyz=1.10 * traj_est[:,:3], + orientations_quat_wxyz=traj_est[:,3:], + timestamps=np.array(tstamps)) + + traj_ref = file_interface.read_tum_trajectory_file(args.gt) + + traj_ref, traj_est = sync.associate_trajectories(traj_ref, traj_est) + + result = main_ape.ape(traj_ref, traj_est, est_name='traj', + pose_relation=PoseRelation.translation_part, align=True, correct_scale=True) + + print(result) + + diff --git a/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_tum.py b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_tum.py new file mode 100644 index 0000000000000000000000000000000000000000..6c207afc92ed7b5f66e8c14d2eb1876b505c246d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/evaluation_scripts/test_tum.py @@ -0,0 +1,123 @@ +import sys +sys.path.append('droid_slam') + +from tqdm import tqdm +import numpy as np +import torch +import lietorch +import cv2 +import os +import glob +import time +import argparse + +import torch.nn.functional as F +from droid import Droid + + +def show_image(image): + image = image.permute(1, 2, 0).cpu().numpy() + cv2.imshow('image', image / 255.0) + cv2.waitKey(1) + +def image_stream(datapath, image_size=[320, 512]): + """ image generator """ + + fx, fy, cx, cy = 517.3, 516.5, 318.6, 255.3 + + K_l = np.array([fx, 0.0, cx, 0.0, fy, cy, 0.0, 0.0, 1.0]).reshape(3,3) + d_l = np.array([0.2624, -0.9531, -0.0054, 0.0026, 1.1633]) + + # read all png images in folder + images_list = sorted(glob.glob(os.path.join(datapath, 'rgb', '*.png')))[::2] + + for t, imfile in enumerate(images_list): + image = cv2.imread(imfile) + ht0, wd0, _ = image.shape + image = cv2.undistort(image, K_l, d_l) + image = cv2.resize(image, (320+32, 240+16)) + image = torch.from_numpy(image).permute(2,0,1) + + intrinsics = torch.as_tensor([fx, fy, cx, cy]).cuda() + intrinsics[0] *= image.shape[2] / 640.0 + intrinsics[1] *= image.shape[1] / 480.0 + intrinsics[2] *= image.shape[2] / 640.0 + intrinsics[3] *= image.shape[1] / 480.0 + + # crop image to remove distortion boundary + intrinsics[2] -= 16 + intrinsics[3] -= 8 + image = image[:, 8:-8, 16:-16] + + yield t, image[None], intrinsics + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument("--datapath") + parser.add_argument("--weights", default="droid.pth") + parser.add_argument("--buffer", type=int, default=512) + parser.add_argument("--image_size", default=[240, 320]) + parser.add_argument("--disable_vis", action="store_true") + + parser.add_argument("--beta", type=float, default=0.6) + parser.add_argument("--filter_thresh", type=float, default=1.75) + parser.add_argument("--warmup", type=int, default=12) + parser.add_argument("--keyframe_thresh", type=float, default=2.25) + parser.add_argument("--frontend_thresh", type=float, default=12.0) + parser.add_argument("--frontend_window", type=int, default=25) + parser.add_argument("--frontend_radius", type=int, default=2) + parser.add_argument("--frontend_nms", type=int, default=1) + + parser.add_argument("--backend_thresh", type=float, default=15.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=3) + args = parser.parse_args() + + args.stereo = False + torch.multiprocessing.set_start_method('spawn') + + print("Running evaluation on {}".format(args.datapath)) + print(args) + + droid = Droid(args) + time.sleep(5) + + tstamps = [] + for (t, image, intrinsics) in tqdm(image_stream(args.datapath)): + if not args.disable_vis: + show_image(image) + droid.track(t, image, intrinsics=intrinsics) + + + traj_est = droid.terminate(image_stream(args.datapath)) + + ### run evaluation ### + + print("#"*20 + " Results...") + + import evo + from evo.core.trajectory import PoseTrajectory3D + from evo.tools import file_interface + from evo.core import sync + import evo.main_ape as main_ape + from evo.core.metrics import PoseRelation + + image_path = os.path.join(args.datapath, 'rgb') + images_list = sorted(glob.glob(os.path.join(image_path, '*.png')))[::2] + tstamps = [float(x.split('/')[-1][:-4]) for x in images_list] + + traj_est = PoseTrajectory3D( + positions_xyz=traj_est[:,:3], + orientations_quat_wxyz=traj_est[:,3:], + timestamps=np.array(tstamps)) + + gt_file = os.path.join(args.datapath, 'groundtruth.txt') + traj_ref = file_interface.read_tum_trajectory_file(gt_file) + + traj_ref, traj_est = sync.associate_trajectories(traj_ref, traj_est) + result = main_ape.ape(traj_ref, traj_est, est_name='traj', + pose_relation=PoseRelation.translation_part, align=True, correct_scale=True) + + + print(result) + diff --git a/slahmr/third-party/DROID-SLAM/evaluation_scripts/validate_tartanair.py b/slahmr/third-party/DROID-SLAM/evaluation_scripts/validate_tartanair.py new file mode 100644 index 0000000000000000000000000000000000000000..3424bdf368a2b131f2a8dc15c839e0e69482517d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/evaluation_scripts/validate_tartanair.py @@ -0,0 +1,115 @@ +import sys +sys.path.append('droid_slam') +sys.path.append('thirdparty/tartanair_tools') + +from tqdm import tqdm +import numpy as np +import torch +import lietorch +import cv2 +import os +import glob +import time +import yaml +import argparse + +from droid import Droid + +def image_stream(datapath, image_size=[384, 512], intrinsics_vec=[320.0, 320.0, 320.0, 240.0], stereo=False): + """ image generator """ + + # read all png images in folder + ht0, wd0 = [480, 640] + images_left = sorted(glob.glob(os.path.join(datapath, 'image_left/*.png'))) + images_right = sorted(glob.glob(os.path.join(datapath, 'image_right/*.png'))) + + data = [] + for t in range(len(images_left)): + images = [ cv2.resize(cv2.imread(images_left[t]), (image_size[1], image_size[0])) ] + if stereo: + images += [ cv2.resize(cv2.imread(images_right[t]), (image_size[1], image_size[0])) ] + + images = torch.from_numpy(np.stack(images, 0)).permute(0,3,1,2) + intrinsics = .8 * torch.as_tensor(intrinsics_vec) + + data.append((t, images, intrinsics)) + + return data + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument("--datapath", default="datasets/TartanAir") + parser.add_argument("--weights", default="droid.pth") + parser.add_argument("--buffer", type=int, default=1000) + parser.add_argument("--image_size", default=[384,512]) + parser.add_argument("--stereo", action="store_true") + parser.add_argument("--disable_vis", action="store_true") + parser.add_argument("--plot_curve", action="store_true") + parser.add_argument("--id", type=int, default=-1) + + parser.add_argument("--beta", type=float, default=0.3) + parser.add_argument("--filter_thresh", type=float, default=2.4) + parser.add_argument("--warmup", type=int, default=12) + parser.add_argument("--keyframe_thresh", type=float, default=3.5) + parser.add_argument("--frontend_thresh", type=float, default=15) + parser.add_argument("--frontend_window", type=int, default=20) + parser.add_argument("--frontend_radius", type=int, default=1) + parser.add_argument("--frontend_nms", type=int, default=1) + + parser.add_argument("--backend_thresh", type=float, default=20.0) + parser.add_argument("--backend_radius", type=int, default=2) + parser.add_argument("--backend_nms", type=int, default=3) + + args = parser.parse_args() + torch.multiprocessing.set_start_method('spawn') + + from data_readers.tartan import test_split + from evaluation.tartanair_evaluator import TartanAirEvaluator + + if not os.path.isdir("figures"): + os.mkdir("figures") + + if args.id >= 0: + test_split = [ test_split[args.id] ] + + ate_list = [] + for scene in test_split: + print("Performing evaluation on {}".format(scene)) + torch.cuda.empty_cache() + droid = Droid(args) + + scenedir = os.path.join(args.datapath, scene) + + for (tstamp, image, intrinsics) in tqdm(image_stream(scenedir, stereo=args.stereo)): + droid.track(tstamp, image, intrinsics=intrinsics) + + # fill in non-keyframe poses + global BA + traj_est = droid.terminate(image_stream(scenedir)) + + ### do evaluation ### + evaluator = TartanAirEvaluator() + gt_file = os.path.join(scenedir, "pose_left.txt") + traj_ref = np.loadtxt(gt_file, delimiter=' ')[:, [1, 2, 0, 4, 5, 3, 6]] # ned -> xyz + + # usually stereo should not be scale corrected, but we are comparing monocular and stereo here + results = evaluator.evaluate_one_trajectory( + traj_ref, traj_est, scale=True, title=scenedir[-20:].replace('/', '_')) + + print(results) + ate_list.append(results["ate_score"]) + + print("Results") + print(ate_list) + + if args.plot_curve: + import matplotlib.pyplot as plt + ate = np.array(ate_list) + xs = np.linspace(0.0, 1.0, 512) + ys = [np.count_nonzero(ate < t) / ate.shape[0] for t in xs] + + plt.plot(xs, ys) + plt.xlabel("ATE [m]") + plt.ylabel("% runs") + plt.show() + diff --git a/slahmr/third-party/DROID-SLAM/misc/DROID.png b/slahmr/third-party/DROID-SLAM/misc/DROID.png new file mode 100644 index 0000000000000000000000000000000000000000..d7a8f1f83bafa89c576bdd1cda52b3102c753003 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/misc/DROID.png differ diff --git a/slahmr/third-party/DROID-SLAM/misc/renderoption.json b/slahmr/third-party/DROID-SLAM/misc/renderoption.json new file mode 100644 index 0000000000000000000000000000000000000000..80d35c4b1ab67bae5197159fa3f0e1f8a72a3be8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/misc/renderoption.json @@ -0,0 +1,40 @@ +{ + "background_color" : [ 1, 1, 1 ], + "class_name" : "RenderOption", + "default_mesh_color" : [ 0.69999999999999996, 0.69999999999999996, 0.69999999999999996 ], + "image_max_depth" : 3000, + "image_stretch_option" : 0, + "interpolation_option" : 0, + "light0_color" : [ 1, 1, 1 ], + "light0_diffuse_power" : 20, + "light0_position" : [ 0, 0, 20 ], + "light0_specular_power" : 2.20000000000000001, + "light0_specular_shininess" : 100, + "light1_color" : [ 1, 1, 1 ], + "light1_diffuse_power" : 0.66000000000000003, + "light1_position" : [ 0, 0, 2 ], + "light1_specular_power" : 2.20000000000000001, + "light1_specular_shininess" : 100, + "light2_color" : [ 1, 1, 1 ], + "light2_diffuse_power" : 20, + "light2_position" : [ 0, 0, -20 ], + "light2_specular_power" : 2.20000000000000001, + "light2_specular_shininess" : 100, + "light3_color" : [ 1, 1, 1 ], + "light3_diffuse_power" : 20, + "light3_position" : [ 0, 0, -20 ], + "light3_specular_power" : 2.20000000000000001, + "light3_specular_shininess" : 100, + "light_ambient_color" : [ 0, 0, 0 ], + "light_on" : true, + "mesh_color_option" : 1, + "mesh_shade_option" : 0, + "mesh_show_back_face" : false, + "mesh_show_wireframe" : false, + "point_color_option" : 7, + "point_show_normal" : false, + "point_size" : 2, + "show_coordinate_frame" : false, + "version_major" : 1, + "version_minor" : 0 +} diff --git a/slahmr/third-party/DROID-SLAM/misc/screenshot.png b/slahmr/third-party/DROID-SLAM/misc/screenshot.png new file mode 100644 index 0000000000000000000000000000000000000000..88a9aaa55dac9234f66fbbb618216071a54d6cc6 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/misc/screenshot.png differ diff --git a/slahmr/third-party/DROID-SLAM/setup.py b/slahmr/third-party/DROID-SLAM/setup.py new file mode 100644 index 0000000000000000000000000000000000000000..9af97d49c65bd17ce42f19acd3819ee0e8f33834 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/setup.py @@ -0,0 +1,61 @@ +from setuptools import setup +from torch.utils.cpp_extension import BuildExtension, CUDAExtension + +import os.path as osp +ROOT = osp.dirname(osp.abspath(__file__)) + +setup( + name='droid_backends', + ext_modules=[ + CUDAExtension('droid_backends', + include_dirs=[osp.join(ROOT, 'thirdparty/eigen')], + sources=[ + 'src/droid.cpp', + 'src/droid_kernels.cu', + 'src/correlation_kernels.cu', + 'src/altcorr_kernel.cu', + ], + extra_compile_args={ + 'cxx': ['-O3'], + 'nvcc': ['-O3', + '-gencode=arch=compute_60,code=sm_60', + '-gencode=arch=compute_61,code=sm_61', + '-gencode=arch=compute_70,code=sm_70', + '-gencode=arch=compute_75,code=sm_75', + '-gencode=arch=compute_80,code=sm_80', + '-gencode=arch=compute_86,code=sm_86', + ] + }), + ], + cmdclass={ 'build_ext' : BuildExtension } +) + +setup( + name='lietorch', + version='0.2', + description='Lie Groups for PyTorch', + packages=['lietorch'], + package_dir={'': 'thirdparty/lietorch'}, + ext_modules=[ + CUDAExtension('lietorch_backends', + include_dirs=[ + osp.join(ROOT, 'thirdparty/lietorch/lietorch/include'), + osp.join(ROOT, 'thirdparty/eigen')], + sources=[ + 'thirdparty/lietorch/lietorch/src/lietorch.cpp', + 'thirdparty/lietorch/lietorch/src/lietorch_gpu.cu', + 'thirdparty/lietorch/lietorch/src/lietorch_cpu.cpp'], + extra_compile_args={ + 'cxx': ['-O2'], + 'nvcc': ['-O2', + '-gencode=arch=compute_60,code=sm_60', + '-gencode=arch=compute_61,code=sm_61', + '-gencode=arch=compute_70,code=sm_70', + '-gencode=arch=compute_75,code=sm_75', + '-gencode=arch=compute_80,code=sm_80', + '-gencode=arch=compute_86,code=sm_86', + ] + }), + ], + cmdclass={ 'build_ext' : BuildExtension } +) diff --git a/slahmr/third-party/DROID-SLAM/src/altcorr_kernel.cu b/slahmr/third-party/DROID-SLAM/src/altcorr_kernel.cu new file mode 100644 index 0000000000000000000000000000000000000000..f418f5cddd488bb16ab023f2c76cb9d09f721aef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/src/altcorr_kernel.cu @@ -0,0 +1,356 @@ +#include +#include +#include +#include +#include +#include + + +#include +#include +#include +#include + + + +#define BLOCK_H 4 +#define BLOCK_W 8 +#define BLOCK_HW BLOCK_H * BLOCK_W +#define CHANNEL_STRIDE 32 + + +__forceinline__ __device__ +bool within_bounds(int h, int w, int H, int W) { + return h >= 0 && h < H && w >= 0 && w < W; +} + +template +__global__ void altcorr_forward_kernel( + const torch::PackedTensorAccessor32 fmap1, + const torch::PackedTensorAccessor32 fmap2, + const torch::PackedTensorAccessor32 coords, + torch::PackedTensorAccessor32 corr, + int r) +{ + const int b = blockIdx.x; + const int h0 = blockIdx.y * blockDim.x; + const int w0 = blockIdx.z * blockDim.y; + const int tid = threadIdx.x * blockDim.y + threadIdx.y; + + const int H1 = fmap1.size(1); + const int W1 = fmap1.size(2); + const int H2 = fmap2.size(1); + const int W2 = fmap2.size(2); + const int N = coords.size(1); + const int C = fmap1.size(3); + + __shared__ scalar_t f1[CHANNEL_STRIDE][BLOCK_HW]; + __shared__ scalar_t f2[CHANNEL_STRIDE][BLOCK_HW]; + + __shared__ float x2s[BLOCK_HW]; + __shared__ float y2s[BLOCK_HW]; + + for (int c=0; c(floor(y2s[k1])) - r + iy; + int w2 = static_cast(floor(x2s[k1])) - r + ix; + int c2 = tid % CHANNEL_STRIDE; + + if (within_bounds(h2, w2, H2, W2)) + f2[c2][k1] = fmap2[b][h2][w2][c+c2]; + + else + f2[c2][k1] = static_cast(0.0); + } + + __syncthreads(); + + scalar_t s = 0.0; + for (int k=0; k((dy) * (dx)); + scalar_t ne = s * static_cast((dy) * (1-dx)); + scalar_t sw = s * static_cast((1-dy) * (dx)); + scalar_t se = s * static_cast((1-dy) * (1-dx)); + + // if (iy > 0 && ix > 0 && within_bounds(h1, w1, H1, W1)) + // corr[b][n][ix_nw][h1][w1] += nw; + + // if (iy > 0 && ix < rd && within_bounds(h1, w1, H1, W1)) + // corr[b][n][ix_ne][h1][w1] += ne; + + // if (iy < rd && ix > 0 && within_bounds(h1, w1, H1, W1)) + // corr[b][n][ix_sw][h1][w1] += sw; + + // if (iy < rd && ix < rd && within_bounds(h1, w1, H1, W1)) + // corr[b][n][ix_se][h1][w1] += se; + + + scalar_t* corr_ptr = &corr[b][n][0][h1][w1]; + + if (iy > 0 && ix > 0 && within_bounds(h1, w1, H1, W1)) + *(corr_ptr + ix_nw) += nw; + + if (iy > 0 && ix < rd && within_bounds(h1, w1, H1, W1)) + *(corr_ptr + ix_ne) += ne; + + if (iy < rd && ix > 0 && within_bounds(h1, w1, H1, W1)) + *(corr_ptr + ix_sw) += sw; + + if (iy < rd && ix < rd && within_bounds(h1, w1, H1, W1)) + *(corr_ptr + ix_se) += se; + + + } + } + } + } +} + + +template +__global__ void altcorr_backward_kernel( + const torch::PackedTensorAccessor32 fmap1, + const torch::PackedTensorAccessor32 fmap2, + const torch::PackedTensorAccessor32 coords, + const torch::PackedTensorAccessor32 corr_grad, + torch::PackedTensorAccessor32 fmap1_grad, + torch::PackedTensorAccessor32 fmap2_grad, + torch::PackedTensorAccessor32 coords_grad, + int r) +{ + + const int b = blockIdx.x; + const int h0 = blockIdx.y * blockDim.x; + const int w0 = blockIdx.z * blockDim.y; + const int tid = threadIdx.x * blockDim.y + threadIdx.y; + + const int H1 = fmap1.size(1); + const int W1 = fmap1.size(2); + const int H2 = fmap2.size(1); + const int W2 = fmap2.size(2); + const int N = coords.size(1); + const int C = fmap1.size(3); + + __shared__ scalar_t f1[CHANNEL_STRIDE][BLOCK_HW+1]; + __shared__ scalar_t f2[CHANNEL_STRIDE][BLOCK_HW+1]; + + __shared__ scalar_t f1_grad[CHANNEL_STRIDE][BLOCK_HW+1]; + __shared__ scalar_t f2_grad[CHANNEL_STRIDE][BLOCK_HW+1]; + + __shared__ scalar_t x2s[BLOCK_HW]; + __shared__ scalar_t y2s[BLOCK_HW]; + + for (int c=0; c(floor(y2s[k1]))-r+iy; + int w2 = static_cast(floor(x2s[k1]))-r+ix; + int c2 = tid % CHANNEL_STRIDE; + + auto fptr = fmap2[b][h2][w2]; + if (within_bounds(h2, w2, H2, W2)) + f2[c2][k1] = fptr[c+c2]; + else + f2[c2][k1] = 0.0; + + f2_grad[c2][k1] = 0.0; + } + + __syncthreads(); + + const scalar_t* grad_ptr = &corr_grad[b][n][0][h1][w1]; + scalar_t g = 0.0; + + int ix_nw = H1*W1*((iy-1) + rd*(ix-1)); + int ix_ne = H1*W1*((iy-1) + rd*ix); + int ix_sw = H1*W1*(iy + rd*(ix-1)); + int ix_se = H1*W1*(iy + rd*ix); + + if (iy > 0 && ix > 0 && within_bounds(h1, w1, H1, W1)) + g += *(grad_ptr + ix_nw) * dy * dx; + + if (iy > 0 && ix < rd && within_bounds(h1, w1, H1, W1)) + g += *(grad_ptr + ix_ne) * dy * (1-dx); + + if (iy < rd && ix > 0 && within_bounds(h1, w1, H1, W1)) + g += *(grad_ptr + ix_sw) * (1-dy) * dx; + + if (iy < rd && ix < rd && within_bounds(h1, w1, H1, W1)) + g += *(grad_ptr + ix_se) * (1-dy) * (1-dx); + + for (int k=0; k(floor(y2s[k1]))-r+iy; + int w2 = static_cast(floor(x2s[k1]))-r+ix; + int c2 = tid % CHANNEL_STRIDE; + + scalar_t* fptr = &fmap2_grad[b][h2][w2][0]; + if (within_bounds(h2, w2, H2, W2)) + atomicAdd(fptr+c+c2, f2_grad[c2][k1]); + } + } + } + } + __syncthreads(); + + + for (int k=0; k altcorr_cuda_forward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + int radius) +{ + const auto B = coords.size(0); + const auto N = coords.size(1); + const auto H = coords.size(2); + const auto W = coords.size(3); + + const auto rd = 2 * radius + 1; + auto opts = fmap1.options(); + auto corr = torch::zeros({B, N, rd*rd, H, W}, opts); + + const dim3 blocks(B, (H+BLOCK_H-1)/BLOCK_H, (W+BLOCK_W-1)/BLOCK_W); + const dim3 threads(BLOCK_H, BLOCK_W); + + + AT_DISPATCH_FLOATING_TYPES_AND_HALF(fmap1.type(), "altcorr_forward_kernel", ([&] { + altcorr_forward_kernel<<>>( + fmap1.packed_accessor32(), + fmap2.packed_accessor32(), + coords.packed_accessor32(), + corr.packed_accessor32(), + radius); + })); + + return {corr}; +} + +std::vector altcorr_cuda_backward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius) +{ + const auto B = coords.size(0); + const auto N = coords.size(1); + + const auto H1 = fmap1.size(1); + const auto W1 = fmap1.size(2); + const auto H2 = fmap2.size(1); + const auto W2 = fmap2.size(2); + const auto C = fmap1.size(3); + + auto opts = fmap1.options(); + auto fmap1_grad = torch::zeros({B, H1, W1, C}, opts); + auto fmap2_grad = torch::zeros({B, H2, W2, C}, opts); + auto coords_grad = torch::zeros({B, N, H1, W1, 2}, opts); + + const dim3 blocks(B, (H1+BLOCK_H-1)/BLOCK_H, (W1+BLOCK_W-1)/BLOCK_W); + const dim3 threads(BLOCK_H, BLOCK_W); + + altcorr_backward_kernel<<>>( + fmap1.packed_accessor32(), + fmap2.packed_accessor32(), + coords.packed_accessor32(), + corr_grad.packed_accessor32(), + fmap1_grad.packed_accessor32(), + fmap2_grad.packed_accessor32(), + coords_grad.packed_accessor32(), + radius); + + return {fmap1_grad, fmap2_grad, coords_grad}; +} \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/src/correlation_kernels.cu b/slahmr/third-party/DROID-SLAM/src/correlation_kernels.cu new file mode 100644 index 0000000000000000000000000000000000000000..2812067b9d548c7ec1e25d1298e4356878afd365 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/src/correlation_kernels.cu @@ -0,0 +1,185 @@ +#include +#include +#include +#include +#include +#include + + +#include +#include +#include + +#define BLOCK 16 + +__forceinline__ __device__ bool within_bounds(int h, int w, int H, int W) { + return h >= 0 && h < H && w >= 0 && w < W; +} + +template +__global__ void corr_index_forward_kernel( + const torch::PackedTensorAccessor32 volume, + const torch::PackedTensorAccessor32 coords, + torch::PackedTensorAccessor32 corr, + int r) +{ + // batch index + const int x = blockIdx.x * blockDim.x + threadIdx.x; + const int y = blockIdx.y * blockDim.y + threadIdx.y; + const int n = blockIdx.z; + + const int h1 = volume.size(1); + const int w1 = volume.size(2); + const int h2 = volume.size(3); + const int w2 = volume.size(4); + + if (!within_bounds(y, x, h1, w1)) { + return; + } + + float x0 = coords[n][0][y][x]; + float y0 = coords[n][1][y][x]; + + float dx = x0 - floor(x0); + float dy = y0 - floor(y0); + + int rd = 2*r + 1; + for (int i=0; i(floor(x0)) - r + i; + int y1 = static_cast(floor(y0)) - r + j; + + if (within_bounds(y1, x1, h2, w2)) { + scalar_t s = volume[n][y][x][y1][x1]; + + if (i > 0 && j > 0) + corr[n][i-1][j-1][y][x] += s * scalar_t(dx * dy); + + if (i > 0 && j < rd) + corr[n][i-1][j][y][x] += s * scalar_t(dx * (1.0f-dy)); + + if (i < rd && j > 0) + corr[n][i][j-1][y][x] += s * scalar_t((1.0f-dx) * dy); + + if (i < rd && j < rd) + corr[n][i][j][y][x] += s * scalar_t((1.0f-dx) * (1.0f-dy)); + + } + } + } +} + + +template +__global__ void corr_index_backward_kernel( + const torch::PackedTensorAccessor32 coords, + const torch::PackedTensorAccessor32 corr_grad, + torch::PackedTensorAccessor32 volume_grad, + int r) +{ + // batch index + const int x = blockIdx.x * blockDim.x + threadIdx.x; + const int y = blockIdx.y * blockDim.y + threadIdx.y; + const int n = blockIdx.z; + + const int h1 = volume_grad.size(1); + const int w1 = volume_grad.size(2); + const int h2 = volume_grad.size(3); + const int w2 = volume_grad.size(4); + + if (!within_bounds(y, x, h1, w1)) { + return; + } + + float x0 = coords[n][0][y][x]; + float y0 = coords[n][1][y][x]; + + float dx = x0 - floor(x0); + float dy = y0 - floor(y0); + + int rd = 2*r + 1; + for (int i=0; i(floor(x0)) - r + i; + int y1 = static_cast(floor(y0)) - r + j; + + if (within_bounds(y1, x1, h2, w2)) { + scalar_t g = 0.0; + if (i > 0 && j > 0) + g += corr_grad[n][i-1][j-1][y][x] * scalar_t(dx * dy); + + if (i > 0 && j < rd) + g += corr_grad[n][i-1][j][y][x] * scalar_t(dx * (1.0f-dy)); + + if (i < rd && j > 0) + g += corr_grad[n][i][j-1][y][x] * scalar_t((1.0f-dx) * dy); + + if (i < rd && j < rd) + g += corr_grad[n][i][j][y][x] * scalar_t((1.0f-dx) * (1.0f-dy)); + + volume_grad[n][y][x][y1][x1] += g; + } + } + } +} + +std::vector corr_index_cuda_forward( + torch::Tensor volume, + torch::Tensor coords, + int radius) +{ + const auto batch_size = volume.size(0); + const auto ht = volume.size(1); + const auto wd = volume.size(2); + + const dim3 blocks((wd + BLOCK - 1) / BLOCK, + (ht + BLOCK - 1) / BLOCK, + batch_size); + + const dim3 threads(BLOCK, BLOCK); + + auto opts = volume.options(); + torch::Tensor corr = torch::zeros( + {batch_size, 2*radius+1, 2*radius+1, ht, wd}, opts); + + AT_DISPATCH_FLOATING_TYPES_AND_HALF(volume.type(), "sampler_forward_kernel", ([&] { + corr_index_forward_kernel<<>>( + volume.packed_accessor32(), + coords.packed_accessor32(), + corr.packed_accessor32(), + radius); + })); + + return {corr}; + +} + +std::vector corr_index_cuda_backward( + torch::Tensor volume, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius) +{ + const auto batch_size = volume.size(0); + const auto ht = volume.size(1); + const auto wd = volume.size(2); + + auto volume_grad = torch::zeros_like(volume); + + const dim3 blocks((wd + BLOCK - 1) / BLOCK, + (ht + BLOCK - 1) / BLOCK, + batch_size); + + const dim3 threads(BLOCK, BLOCK); + + + AT_DISPATCH_FLOATING_TYPES_AND_HALF(volume.type(), "sampler_backward_kernel", ([&] { + corr_index_backward_kernel<<>>( + coords.packed_accessor32(), + corr_grad.packed_accessor32(), + volume_grad.packed_accessor32(), + radius); + })); + + return {volume_grad}; +} \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/src/droid.cpp b/slahmr/third-party/DROID-SLAM/src/droid.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c38c1faecc783719fd0355449a82993c5fc78901 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/src/droid.cpp @@ -0,0 +1,250 @@ +#include +#include + +// CUDA forward declarations +std::vector projective_transform_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj); + + + +torch::Tensor depth_filter_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ix, + torch::Tensor thresh); + + +torch::Tensor frame_distance_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj, + const float beta); + +std::vector projmap_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj); + +torch::Tensor iproj_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics); + +std::vector ba_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor disps_sens, + torch::Tensor targets, + torch::Tensor weights, + torch::Tensor eta, + torch::Tensor ii, + torch::Tensor jj, + const int t0, + const int t1, + const int iterations, + const float lm, + const float ep, + const bool motion_only); + +std::vector corr_index_cuda_forward( + torch::Tensor volume, + torch::Tensor coords, + int radius); + +std::vector corr_index_cuda_backward( + torch::Tensor volume, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius); + +std::vector altcorr_cuda_forward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + int radius); + +std::vector altcorr_cuda_backward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius); + + +#define CHECK_CONTIGUOUS(x) TORCH_CHECK(x.is_contiguous(), #x " must be contiguous") +#define CHECK_INPUT(x) CHECK_CONTIGUOUS(x) + + +std::vector ba( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor disps_sens, + torch::Tensor targets, + torch::Tensor weights, + torch::Tensor eta, + torch::Tensor ii, + torch::Tensor jj, + const int t0, + const int t1, + const int iterations, + const float lm, + const float ep, + const bool motion_only) { + + CHECK_INPUT(targets); + CHECK_INPUT(weights); + CHECK_INPUT(poses); + CHECK_INPUT(disps); + CHECK_INPUT(intrinsics); + CHECK_INPUT(disps_sens); + CHECK_INPUT(ii); + CHECK_INPUT(jj); + + return ba_cuda(poses, disps, intrinsics, disps_sens, targets, weights, + eta, ii, jj, t0, t1, iterations, lm, ep, motion_only); + +} + + +torch::Tensor frame_distance( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj, + const float beta) { + + CHECK_INPUT(poses); + CHECK_INPUT(disps); + CHECK_INPUT(intrinsics); + CHECK_INPUT(ii); + CHECK_INPUT(jj); + + return frame_distance_cuda(poses, disps, intrinsics, ii, jj, beta); + +} + + +std::vector projmap( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj) { + + CHECK_INPUT(poses); + CHECK_INPUT(disps); + CHECK_INPUT(intrinsics); + CHECK_INPUT(ii); + CHECK_INPUT(jj); + + return projmap_cuda(poses, disps, intrinsics, ii, jj); + +} + + +torch::Tensor iproj( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics) { + CHECK_INPUT(poses); + CHECK_INPUT(disps); + CHECK_INPUT(intrinsics); + + return iproj_cuda(poses, disps, intrinsics); +} + + +// c++ python binding +std::vector corr_index_forward( + torch::Tensor volume, + torch::Tensor coords, + int radius) { + CHECK_INPUT(volume); + CHECK_INPUT(coords); + + return corr_index_cuda_forward(volume, coords, radius); +} + +std::vector corr_index_backward( + torch::Tensor volume, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius) { + CHECK_INPUT(volume); + CHECK_INPUT(coords); + CHECK_INPUT(corr_grad); + + auto volume_grad = corr_index_cuda_backward(volume, coords, corr_grad, radius); + return {volume_grad}; +} + +std::vector altcorr_forward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + int radius) { + CHECK_INPUT(fmap1); + CHECK_INPUT(fmap2); + CHECK_INPUT(coords); + + return altcorr_cuda_forward(fmap1, fmap2, coords, radius); +} + +std::vector altcorr_backward( + torch::Tensor fmap1, + torch::Tensor fmap2, + torch::Tensor coords, + torch::Tensor corr_grad, + int radius) { + CHECK_INPUT(fmap1); + CHECK_INPUT(fmap2); + CHECK_INPUT(coords); + CHECK_INPUT(corr_grad); + + return altcorr_cuda_backward(fmap1, fmap2, coords, corr_grad, radius); +} + + +torch::Tensor depth_filter( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ix, + torch::Tensor thresh) { + + CHECK_INPUT(poses); + CHECK_INPUT(disps); + CHECK_INPUT(intrinsics); + CHECK_INPUT(ix); + CHECK_INPUT(thresh); + + return depth_filter_cuda(poses, disps, intrinsics, ix, thresh); +} + + +PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) { + // bundle adjustment kernels + m.def("ba", &ba, "bundle adjustment"); + m.def("frame_distance", &frame_distance, "frame_distance"); + m.def("projmap", &projmap, "projmap"); + m.def("depth_filter", &depth_filter, "depth_filter"); + m.def("iproj", &iproj, "back projection"); + + // correlation volume kernels + m.def("altcorr_forward", &altcorr_forward, "ALTCORR forward"); + m.def("altcorr_backward", &altcorr_backward, "ALTCORR backward"); + m.def("corr_index_forward", &corr_index_forward, "INDEX forward"); + m.def("corr_index_backward", &corr_index_backward, "INDEX backward"); +} \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/src/droid_kernels.cu b/slahmr/third-party/DROID-SLAM/src/droid_kernels.cu new file mode 100644 index 0000000000000000000000000000000000000000..16ac697f64eefdfc5d1d123af3de933822395cf9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/src/droid_kernels.cu @@ -0,0 +1,1541 @@ +#include +#include +#include +#include + +#include +#include + +#include +#include +#include + +// #include "utils.cuh" + +#include +#include +#include + +typedef Eigen::SparseMatrix SpMat; +typedef Eigen::Triplet T; +typedef std::vector> graph_t; +typedef std::vector tensor_list_t; + + + +#define MIN_DEPTH 0.25 + +#define THREADS 256 +#define NUM_BLOCKS(batch_size) ((batch_size + THREADS - 1) / THREADS) + + +#define GPU_1D_KERNEL_LOOP(k, n) \ + for (size_t k = threadIdx.x; k 1e-4) { + float a = (1 - cosf(theta)) / theta_sq; + crossInplace(phi, tau); + t[0] += a * tau[0]; + t[1] += a * tau[1]; + t[2] += a * tau[2]; + + float b = (theta - sinf(theta)) / (theta * theta_sq); + crossInplace(phi, tau); + t[0] += b * tau[0]; + t[1] += b * tau[1]; + t[2] += b * tau[2]; + } +} +__global__ void projective_transform_kernel( + const torch::PackedTensorAccessor32 target, + const torch::PackedTensorAccessor32 weight, + const torch::PackedTensorAccessor32 poses, + const torch::PackedTensorAccessor32 disps, + const torch::PackedTensorAccessor32 intrinsics, + const torch::PackedTensorAccessor32 ii, + const torch::PackedTensorAccessor32 jj, + torch::PackedTensorAccessor32 Hs, + torch::PackedTensorAccessor32 vs, + torch::PackedTensorAccessor32 Eii, + torch::PackedTensorAccessor32 Eij, + torch::PackedTensorAccessor32 Cii, + torch::PackedTensorAccessor32 bz) +{ + const int block_id = blockIdx.x; + const int thread_id = threadIdx.x; + + const int ht = disps.size(1); + const int wd = disps.size(2); + + int ix = static_cast(ii[block_id]); + int jx = static_cast(jj[block_id]); + + __shared__ float fx; + __shared__ float fy; + __shared__ float cx; + __shared__ float cy; + + __shared__ float ti[3], tj[3], tij[3]; + __shared__ float qi[4], qj[4], qij[4]; + + // load intrinsics from global memory + if (thread_id == 0) { + fx = intrinsics[0]; + fy = intrinsics[1]; + cx = intrinsics[2]; + cy = intrinsics[3]; + } + + __syncthreads(); + + // stereo frames + if (ix == jx) { + if (thread_id == 0) { + tij[0] = -0.1; + tij[1] = 0; + tij[2] = 0; + qij[0] = 0; + qij[1] = 0; + qij[2] = 0; + qij[3] = 1; + } + } + + else { + + // load poses from global memory + if (thread_id < 3) { + ti[thread_id] = poses[ix][thread_id]; + tj[thread_id] = poses[jx][thread_id]; + } + + if (thread_id < 4) { + qi[thread_id] = poses[ix][thread_id+3]; + qj[thread_id] = poses[jx][thread_id+3]; + } + + __syncthreads(); + + if (thread_id == 0) { + relSE3(ti, qi, tj, qj, tij, qij); + } + } + + __syncthreads(); + + //points + float Xi[4]; + float Xj[4]; + + // jacobians + float Jx[12]; + float Jz; + + float* Ji = &Jx[0]; + float* Jj = &Jx[6]; + + // hessians + float hij[12*(12+1)/2]; + + float vi[6], vj[6]; + + int l; + for (l=0; l<12*(12+1)/2; l++) { + hij[l] = 0; + } + + for (int n=0; n<6; n++) { + vi[n] = 0; + vj[n] = 0; + } + + __syncthreads(); + + GPU_1D_KERNEL_LOOP(k, ht*wd) { + + const int i = k / wd; + const int j = k % wd; + + const float u = static_cast(j); + const float v = static_cast(i); + + // homogenous coordinates + Xi[0] = (u - cx) / fx; + Xi[1] = (v - cy) / fy; + Xi[2] = 1; + Xi[3] = disps[ix][i][j]; + + // transform homogenous point + actSE3(tij, qij, Xi, Xj); + + const float x = Xj[0]; + const float y = Xj[1]; + const float h = Xj[3]; + + const float d = (Xj[2] < MIN_DEPTH) ? 0.0 : 1.0 / Xj[2]; + const float d2 = d * d; + + float wu = (Xj[2] < MIN_DEPTH) ? 0.0 : .001 * weight[block_id][0][i][j]; + float wv = (Xj[2] < MIN_DEPTH) ? 0.0 : .001 * weight[block_id][1][i][j]; + const float ru = target[block_id][0][i][j] - (fx * d * x + cx); + const float rv = target[block_id][1][i][j] - (fy * d * y + cy); + + // x - coordinate + + Jj[0] = fx * (h*d); + Jj[1] = fx * 0; + Jj[2] = fx * (-x*h*d2); + Jj[3] = fx * (-x*y*d2); + Jj[4] = fx * (1 + x*x*d2); + Jj[5] = fx * (-y*d); + + Jz = fx * (tij[0] * d - tij[2] * (x * d2)); + Cii[block_id][k] = wu * Jz * Jz; + bz[block_id][k] = wu * ru * Jz; + + if (ix == jx) wu = 0; + + adjSE3(tij, qij, Jj, Ji); + for (int n=0; n<6; n++) Ji[n] *= -1; + + l=0; + for (int n=0; n<12; n++) { + for (int m=0; m<=n; m++) { + hij[l] += wu * Jx[n] * Jx[m]; + l++; + } + } + + for (int n=0; n<6; n++) { + vi[n] += wu * ru * Ji[n]; + vj[n] += wu * ru * Jj[n]; + + Eii[block_id][n][k] = wu * Jz * Ji[n]; + Eij[block_id][n][k] = wu * Jz * Jj[n]; + } + + + Jj[0] = fy * 0; + Jj[1] = fy * (h*d); + Jj[2] = fy * (-y*h*d2); + Jj[3] = fy * (-1 - y*y*d2); + Jj[4] = fy * (x*y*d2); + Jj[5] = fy * (x*d); + + Jz = fy * (tij[1] * d - tij[2] * (y * d2)); + Cii[block_id][k] += wv * Jz * Jz; + bz[block_id][k] += wv * rv * Jz; + + if (ix == jx) wv = 0; + + adjSE3(tij, qij, Jj, Ji); + for (int n=0; n<6; n++) Ji[n] *= -1; + + l=0; + for (int n=0; n<12; n++) { + for (int m=0; m<=n; m++) { + hij[l] += wv * Jx[n] * Jx[m]; + l++; + } + } + + for (int n=0; n<6; n++) { + vi[n] += wv * rv * Ji[n]; + vj[n] += wv * rv * Jj[n]; + + Eii[block_id][n][k] += wv * Jz * Ji[n]; + Eij[block_id][n][k] += wv * Jz * Jj[n]; + } + + + } + + __syncthreads(); + + __shared__ float sdata[THREADS]; + for (int n=0; n<6; n++) { + sdata[threadIdx.x] = vi[n]; + blockReduce(sdata); + if (threadIdx.x == 0) { + vs[0][block_id][n] = sdata[0]; + } + + __syncthreads(); + + sdata[threadIdx.x] = vj[n]; + blockReduce(sdata); + if (threadIdx.x == 0) { + vs[1][block_id][n] = sdata[0]; + } + + } + + l=0; + for (int n=0; n<12; n++) { + for (int m=0; m<=n; m++) { + sdata[threadIdx.x] = hij[l]; + blockReduce(sdata); + + if (threadIdx.x == 0) { + if (n<6 && m<6) { + Hs[0][block_id][n][m] = sdata[0]; + Hs[0][block_id][m][n] = sdata[0]; + } + else if (n >=6 && m<6) { + Hs[1][block_id][m][n-6] = sdata[0]; + Hs[2][block_id][n-6][m] = sdata[0]; + } + else { + Hs[3][block_id][n-6][m-6] = sdata[0]; + Hs[3][block_id][m-6][n-6] = sdata[0]; + } + } + + l++; + } + } +} + + +__global__ void projmap_kernel( + const torch::PackedTensorAccessor32 poses, + const torch::PackedTensorAccessor32 disps, + const torch::PackedTensorAccessor32 intrinsics, + const torch::PackedTensorAccessor32 ii, + const torch::PackedTensorAccessor32 jj, + torch::PackedTensorAccessor32 coords, + torch::PackedTensorAccessor32 valid) +{ + + const int block_id = blockIdx.x; + const int thread_id = threadIdx.x; + + const int ht = disps.size(1); + const int wd = disps.size(2); + + __shared__ int ix; + __shared__ int jx; + + __shared__ float fx; + __shared__ float fy; + __shared__ float cx; + __shared__ float cy; + + __shared__ float ti[3], tj[3], tij[3]; + __shared__ float qi[4], qj[4], qij[4]; + + // load intrinsics from global memory + if (thread_id == 0) { + ix = static_cast(ii[block_id]); + jx = static_cast(jj[block_id]); + fx = intrinsics[0]; + fy = intrinsics[1]; + cx = intrinsics[2]; + cy = intrinsics[3]; + } + + __syncthreads(); + + // load poses from global memory + if (thread_id < 3) { + ti[thread_id] = poses[ix][thread_id]; + tj[thread_id] = poses[jx][thread_id]; + } + + if (thread_id < 4) { + qi[thread_id] = poses[ix][thread_id+3]; + qj[thread_id] = poses[jx][thread_id+3]; + } + + __syncthreads(); + + if (thread_id == 0) { + relSE3(ti, qi, tj, qj, tij, qij); + } + + //points + float Xi[4]; + float Xj[4]; + + __syncthreads(); + + GPU_1D_KERNEL_LOOP(k, ht*wd) { + const int i = k / wd; + const int j = k % wd; + + const float u = static_cast(j); + const float v = static_cast(i); + + // homogenous coordinates + Xi[0] = (u - cx) / fx; + Xi[1] = (v - cy) / fy; + Xi[2] = 1; + Xi[3] = disps[ix][i][j]; + + // transform homogenous point + actSE3(tij, qij, Xi, Xj); + + coords[block_id][i][j][0] = u; + coords[block_id][i][j][1] = v; + + if (Xj[2] > 0.01) { + coords[block_id][i][j][0] = fx * (Xj[0] / Xj[2]) + cx; + coords[block_id][i][j][1] = fy * (Xj[1] / Xj[2]) + cy; + } + + valid[block_id][i][j][0] = (Xj[2] > MIN_DEPTH) ? 1.0 : 0.0; + + } +} + +__global__ void frame_distance_kernel( + const torch::PackedTensorAccessor32 poses, + const torch::PackedTensorAccessor32 disps, + const torch::PackedTensorAccessor32 intrinsics, + const torch::PackedTensorAccessor32 ii, + const torch::PackedTensorAccessor32 jj, + torch::PackedTensorAccessor32 dist, + const float beta) { + + const int block_id = blockIdx.x; + const int thread_id = threadIdx.x; + + const int ht = disps.size(1); + const int wd = disps.size(2); + + __shared__ int ix; + __shared__ int jx; + + __shared__ float fx; + __shared__ float fy; + __shared__ float cx; + __shared__ float cy; + + __shared__ float ti[3], tj[3], tij[3]; + __shared__ float qi[4], qj[4], qij[4]; + + // load intrinsics from global memory + if (thread_id == 0) { + ix = static_cast(ii[block_id]); + jx = static_cast(jj[block_id]); + fx = intrinsics[0]; + fy = intrinsics[1]; + cx = intrinsics[2]; + cy = intrinsics[3]; + } + + __syncthreads(); + + + //points + float Xi[4]; + float Xj[4]; + + __shared__ float accum[THREADS]; accum[thread_id] = 0; + __shared__ float valid[THREADS]; valid[thread_id] = 0; + __shared__ float total[THREADS]; total[thread_id] = 0; + + __syncthreads(); + + for (int n=0; n<1; n++) { + + if (thread_id < 3) { + ti[thread_id] = poses[ix][thread_id]; + tj[thread_id] = poses[jx][thread_id]; + } + + if (thread_id < 4) { + qi[thread_id] = poses[ix][thread_id+3]; + qj[thread_id] = poses[jx][thread_id+3]; + } + + __syncthreads(); + + + relSE3(ti, qi, tj, qj, tij, qij); + + float d, du, dv; + + GPU_1D_KERNEL_LOOP(k, ht*wd) { + const int i = k / wd; + const int j = k % wd; + + const float u = static_cast(j); + const float v = static_cast(i); + + + // if (disps[ix][i][j] < 0.01) { + // continue; + // } + + // homogenous coordinates + Xi[0] = (u - cx) / fx; + Xi[1] = (v - cy) / fy; + Xi[2] = 1; + Xi[3] = disps[ix][i][j]; + + // transform homogenous point + actSE3(tij, qij, Xi, Xj); + + du = fx * (Xj[0] / Xj[2]) + cx - u; + dv = fy * (Xj[1] / Xj[2]) + cy - v; + d = sqrtf(du*du + dv*dv); + + total[threadIdx.x] += beta; + + if (Xj[2] > MIN_DEPTH) { + accum[threadIdx.x] += beta * d; + valid[threadIdx.x] += beta; + } + + Xi[0] = (u - cx) / fx; + Xi[1] = (v - cy) / fy; + Xi[2] = 1; + Xi[3] = disps[ix][i][j]; + + Xj[0] = Xi[0] + Xi[3] * tij[0]; + Xj[1] = Xi[1] + Xi[3] * tij[1]; + Xj[2] = Xi[2] + Xi[3] * tij[2]; + + du = fx * (Xj[0] / Xj[2]) + cx - u; + dv = fy * (Xj[1] / Xj[2]) + cy - v; + d = sqrtf(du*du + dv*dv); + + total[threadIdx.x] += (1 - beta); + + if (Xj[2] > MIN_DEPTH) { + accum[threadIdx.x] += (1 - beta) * d; + valid[threadIdx.x] += (1 - beta); + } + } + + if (threadIdx.x == 0) { + int tmp = ix; + ix = jx; + jx = tmp; + } + + __syncthreads(); + + } + __syncthreads(); blockReduce(accum); + __syncthreads(); blockReduce(total); + __syncthreads(); blockReduce(valid); + + __syncthreads(); + + if (thread_id == 0) { + dist[block_id] = (valid[0] / (total[0] + 1e-8) < 0.75) ? 1000.0 : accum[0] / valid[0]; + } +} + + + +__global__ void depth_filter_kernel( + const torch::PackedTensorAccessor32 poses, + const torch::PackedTensorAccessor32 disps, + const torch::PackedTensorAccessor32 intrinsics, + const torch::PackedTensorAccessor32 inds, + const torch::PackedTensorAccessor32 thresh, + torch::PackedTensorAccessor32 counter) +{ + + const int block_id = blockIdx.x; + const int neigh_id = blockIdx.y; + const int index = blockIdx.z * blockDim.x + threadIdx.x; + + // if (threadIdx.x == 0) { + // printf("%d %d %d %d\n", blockIdx.x, blockIdx.y, blockDim.x, threadIdx.x); + // } + + const int num = disps.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + __shared__ int ix; + __shared__ int jx; + + __shared__ float fx; + __shared__ float fy; + __shared__ float cx; + __shared__ float cy; + + __shared__ float ti[3], tj[3], tij[3]; + __shared__ float qi[4], qj[4], qij[4]; + + if (threadIdx.x == 0) { + ix = static_cast(inds[block_id]); + jx = (neigh_id < 3) ? ix - neigh_id - 1 : ix + neigh_id; + fx = intrinsics[0]; + fy = intrinsics[1]; + cx = intrinsics[2]; + cy = intrinsics[3]; + } + + __syncthreads(); + + if (jx < 0 || jx >= num) { + return; + } + + const float t = thresh[block_id]; + + // load poses from global memory + if (threadIdx.x < 3) { + ti[threadIdx.x] = poses[ix][threadIdx.x]; + tj[threadIdx.x] = poses[jx][threadIdx.x]; + } + + if (threadIdx.x < 4) { + qi[threadIdx.x] = poses[ix][threadIdx.x+3]; + qj[threadIdx.x] = poses[jx][threadIdx.x+3]; + } + + __syncthreads(); + + if (threadIdx.x == 0) { + relSE3(ti, qi, tj, qj, tij, qij); + } + + //points + float Xi[4]; + float Xj[4]; + + __syncthreads(); + + if (index < ht*wd) { + const int i = index / wd; + const int j = index % wd; + + const float ui = static_cast(j); + const float vi = static_cast(i); + const float di = disps[ix][i][j]; + + // homogenous coordinates + Xi[0] = (ui - cx) / fx; + Xi[1] = (vi - cy) / fy; + Xi[2] = 1; + Xi[3] = di; + + // transform homogenous point + actSE3(tij, qij, Xi, Xj); + + const float uj = fx * (Xj[0] / Xj[2]) + cx; + const float vj = fy * (Xj[1] / Xj[2]) + cy; + const float dj = Xj[3] / Xj[2]; + + const int u0 = static_cast(floor(uj)); + const int v0 = static_cast(floor(vj)); + + if (u0 >= 0 && v0 >= 0 && u0 < wd-1 && v0 < ht-1) { + const float wx = ceil(uj) - uj; + const float wy = ceil(vj) - vj; + + const float d00 = disps[jx][v0+0][u0+0]; + const float d01 = disps[jx][v0+0][u0+1]; + const float d10 = disps[jx][v0+1][u0+0]; + const float d11 = disps[jx][v0+1][u0+1]; + + const float dj_hat = wy*wx*d00 + wy*(1-wx)*d01 + (1-wy)*wx*d10 + (1-wy)*(1-wx)*d11; + + const float err = abs(1.0/dj - 1.0/dj_hat); + if (abs(1.0/dj - 1.0/d00) < t) atomicAdd(&counter[block_id][i][j], 1.0f); + else if (abs(1.0/dj - 1.0/d01) < t) atomicAdd(&counter[block_id][i][j], 1.0f); + else if (abs(1.0/dj - 1.0/d10) < t) atomicAdd(&counter[block_id][i][j], 1.0f); + else if (abs(1.0/dj - 1.0/d11) < t) atomicAdd(&counter[block_id][i][j], 1.0f); + } + } +} + + + +__global__ void iproj_kernel( + const torch::PackedTensorAccessor32 poses, + const torch::PackedTensorAccessor32 disps, + const torch::PackedTensorAccessor32 intrinsics, + torch::PackedTensorAccessor32 points) + +{ + + const int block_id = blockIdx.x; + const int index = blockIdx.y * blockDim.x + threadIdx.x; + + + const int num = disps.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + __shared__ float fx; + __shared__ float fy; + __shared__ float cx; + __shared__ float cy; + + __shared__ float t[3]; + __shared__ float q[4]; + + if (threadIdx.x == 0) { + fx = intrinsics[0]; + fy = intrinsics[1]; + cx = intrinsics[2]; + cy = intrinsics[3]; + } + + __syncthreads(); + + + // load poses from global memory + if (threadIdx.x < 3) { + t[threadIdx.x] = poses[block_id][threadIdx.x]; + } + + if (threadIdx.x < 4) { + q[threadIdx.x] = poses[block_id][threadIdx.x+3]; + } + + __syncthreads(); + + //points + float Xi[4]; + float Xj[4]; + + if (index < ht*wd) { + const int i = index / wd; + const int j = index % wd; + + const float ui = static_cast(j); + const float vi = static_cast(i); + const float di = disps[block_id][i][j]; + + // homogenous coordinates + Xi[0] = (ui - cx) / fx; + Xi[1] = (vi - cy) / fy; + Xi[2] = 1; + Xi[3] = di; + + // transform homogenous point + actSE3(t, q, Xi, Xj); + + points[block_id][i][j][0] = Xj[0] / Xj[3]; + points[block_id][i][j][1] = Xj[1] / Xj[3]; + points[block_id][i][j][2] = Xj[2] / Xj[3]; + + } +} + + + +__global__ void accum_kernel( + const torch::PackedTensorAccessor32 inps, + const torch::PackedTensorAccessor32 ptrs, + const torch::PackedTensorAccessor32 idxs, + torch::PackedTensorAccessor32 outs) +{ + + const int block_id = blockIdx.x; + const int D = inps.size(2); + + const int start = ptrs[block_id]; + const int end = ptrs[block_id+1]; + + for (int k=threadIdx.x; k poses, + const torch::PackedTensorAccessor32 dx, + const int t0, const int t1) +{ + + for (int k=t0+threadIdx.x; k disps, + const torch::PackedTensorAccessor32 dz, + const torch::PackedTensorAccessor32 inds) +{ + const int i = inds[blockIdx.x]; + const int ht = disps.size(1); + const int wd = disps.size(2); + + for (int k=threadIdx.x; k(); + long* jx_data = jx_cpu.data_ptr(); + long* kx_data = inds.data_ptr(); + + int count = jx.size(0); + std::vector cols; + + torch::Tensor ptrs_cpu = torch::zeros({count+1}, + torch::TensorOptions().dtype(torch::kInt64)); + + long* ptrs_data = ptrs_cpu.data_ptr(); + ptrs_data[0] = 0; + + int i = 0; + for (int j=0; j(); + + for (int i=0; i>>( + data.packed_accessor32(), + ptrs.packed_accessor32(), + idxs.packed_accessor32(), + out.packed_accessor32()); + + return out; +} + + +__global__ void EEt6x6_kernel( + const torch::PackedTensorAccessor32 E, + const torch::PackedTensorAccessor32 Q, + const torch::PackedTensorAccessor32 idx, + torch::PackedTensorAccessor32 S) +{ + + // indicices + const int ix = idx[blockIdx.x][0]; + const int jx = idx[blockIdx.x][1]; + const int kx = idx[blockIdx.x][2]; + + const int D = E.size(2); + + float dS[6][6]; + float ei[6]; + float ej[6]; + + for (int i=0; i<6; i++) { + for (int j=0; j<6; j++) { + dS[i][j] = 0; + } + } + + for (int k=threadIdx.x; k E, + const torch::PackedTensorAccessor32 Q, + const torch::PackedTensorAccessor32 w, + const torch::PackedTensorAccessor32 idx, + torch::PackedTensorAccessor32 v) +{ + const int D = E.size(2); + const int kx = idx[blockIdx.x][0]; + + float b[6]; + for (int n=0; n<6; n++) { + b[n] = 0.0; + } + + for (int k=threadIdx.x; k E, + const torch::PackedTensorAccessor32 x, + const torch::PackedTensorAccessor32 idx, + torch::PackedTensorAccessor32 w) +{ + + const int D = E.size(2); + const int ix = idx[blockIdx.x]; + + if (idx[blockIdx.x] <= 0 || idx[blockIdx.x] >= x.size(0)) + return; + + for (int k=threadIdx.x; k A; + Eigen::VectorX b; + + SparseBlock(int N, int M) : N(N), M(M) { + A = Eigen::SparseMatrix(N*M, N*M); + b = Eigen::VectorXd::Zero(N*M); + } + + SparseBlock(Eigen::SparseMatrix const& A, Eigen::VectorX const& b, + int N, int M) : A(A), b(b), N(N), M(M) {} + + void update_lhs(torch::Tensor As, torch::Tensor ii, torch::Tensor jj) { + + auto As_cpu = As.to(torch::kCPU).to(torch::kFloat64); + auto ii_cpu = ii.to(torch::kCPU).to(torch::kInt64); + auto jj_cpu = jj.to(torch::kCPU).to(torch::kInt64); + + auto As_acc = As_cpu.accessor(); + auto ii_acc = ii_cpu.accessor(); + auto jj_acc = jj_cpu.accessor(); + + std::vector tripletList; + for (int n=0; n= 0 && j >= 0) { + for (int k=0; k(); + auto ii_acc = ii_cpu.accessor(); + + for (int n=0; n= 0) { + for (int j=0; j get_dense() { + Eigen::MatrixXd Ad = Eigen::MatrixXd(A); + + torch::Tensor H = torch::from_blob(Ad.data(), {N*M, N*M}, torch::TensorOptions() + .dtype(torch::kFloat64)).to(torch::kCUDA).to(torch::kFloat32); + + torch::Tensor v = torch::from_blob(b.data(), {N*M, 1}, torch::TensorOptions() + .dtype(torch::kFloat64)).to(torch::kCUDA).to(torch::kFloat32); + + return std::make_tuple(H, v); + + } + + torch::Tensor solve(const float lm=0.0001, const float ep=0.1) { + + torch::Tensor dx; + + Eigen::SparseMatrix L(A); + L.diagonal().array() += ep + lm * L.diagonal().array(); + + Eigen::SimplicialLLT> solver; + solver.compute(L); + + if (solver.info() == Eigen::Success) { + Eigen::VectorXd x = solver.solve(b); + dx = torch::from_blob(x.data(), {N, M}, torch::TensorOptions() + .dtype(torch::kFloat64)).to(torch::kCUDA).to(torch::kFloat32); + } + else { + dx = torch::zeros({N, M}, torch::TensorOptions() + .device(torch::kCUDA).dtype(torch::kFloat32)); + } + + return dx; + } + + private: + const int N; + const int M; + +}; + + +SparseBlock schur_block(torch::Tensor E, + torch::Tensor Q, + torch::Tensor w, + torch::Tensor ii, + torch::Tensor jj, + torch::Tensor kk, + const int t0, + const int t1) +{ + + torch::Tensor ii_cpu = ii.to(torch::kCPU); + torch::Tensor jj_cpu = jj.to(torch::kCPU); + torch::Tensor kk_cpu = kk.to(torch::kCPU); + + const int P = t1 - t0; + const long* ii_data = ii_cpu.data_ptr(); + const long* jj_data = jj_cpu.data_ptr(); + const long* kk_data = kk_cpu.data_ptr(); + + std::vector> graph(P); + std::vector> index(P); + + for (int n=0; n= t0 && j <= t1) { + const int t = j - t0; + graph[t].push_back(k); + index[t].push_back(n); + } + } + + std::vector ii_list, jj_list, idx, jdx; + + for (int i=0; i>>( + E.packed_accessor32(), + Q.packed_accessor32(), + ix_cuda.packed_accessor32(), + S.packed_accessor32()); + + Ev6x1_kernel<<>>( + E.packed_accessor32(), + Q.packed_accessor32(), + w.packed_accessor32(), + jx_cuda.packed_accessor32(), + v.packed_accessor32()); + + // schur block + SparseBlock A(P, 6); + A.update_lhs(S, ii2_cpu, jj2_cpu); + A.update_rhs(v, jj_cpu - t0); + + return A; +} + + +std::vector ba_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor disps_sens, + torch::Tensor targets, + torch::Tensor weights, + torch::Tensor eta, + torch::Tensor ii, + torch::Tensor jj, + const int t0, + const int t1, + const int iterations, + const float lm, + const float ep, + const bool motion_only) +{ + auto opts = poses.options(); + const int num = ii.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + torch::Tensor ts = torch::arange(t0, t1).to(torch::kCUDA); + torch::Tensor ii_exp = torch::cat({ts, ii}, 0); + torch::Tensor jj_exp = torch::cat({ts, jj}, 0); + + std::tuple kuniq = + torch::_unique(ii_exp, true, true); + + torch::Tensor kx = std::get<0>(kuniq); + torch::Tensor kk_exp = std::get<1>(kuniq); + + torch::Tensor dx; + torch::Tensor dz; + + // initialize buffers + torch::Tensor Hs = torch::zeros({4, num, 6, 6}, opts); + torch::Tensor vs = torch::zeros({2, num, 6}, opts); + torch::Tensor Eii = torch::zeros({num, 6, ht*wd}, opts); + torch::Tensor Eij = torch::zeros({num, 6, ht*wd}, opts); + torch::Tensor Cii = torch::zeros({num, ht*wd}, opts); + torch::Tensor wi = torch::zeros({num, ht*wd}, opts); + + for (int itr=0; itr>>( + targets.packed_accessor32(), + weights.packed_accessor32(), + poses.packed_accessor32(), + disps.packed_accessor32(), + intrinsics.packed_accessor32(), + ii.packed_accessor32(), + jj.packed_accessor32(), + Hs.packed_accessor32(), + vs.packed_accessor32(), + Eii.packed_accessor32(), + Eij.packed_accessor32(), + Cii.packed_accessor32(), + wi.packed_accessor32()); + + + // pose x pose block + SparseBlock A(t1 - t0, 6); + + A.update_lhs(Hs.reshape({-1, 6, 6}), + torch::cat({ii, ii, jj, jj}) - t0, + torch::cat({ii, jj, ii, jj}) - t0); + + A.update_rhs(vs.reshape({-1, 6}), + torch::cat({ii, jj}) - t0); + + if (motion_only) { + dx = A.solve(lm, ep); + + // update poses + pose_retr_kernel<<<1, THREADS>>>( + poses.packed_accessor32(), + dx.packed_accessor32(), t0, t1); + } + + else { + // add depth residual if there are depth sensor measurements + const float alpha = 0.05; + torch::Tensor m = (disps_sens.index({kx, "..."}) > 0).to(torch::TensorOptions().dtype(torch::kFloat32)).view({-1, ht*wd}); + torch::Tensor C = accum_cuda(Cii, ii, kx) + m * alpha + (1 - m) * eta.view({-1, ht*wd}); + torch::Tensor w = accum_cuda(wi, ii, kx) - m * alpha * (disps.index({kx, "..."}) - disps_sens.index({kx, "..."})).view({-1, ht*wd}); + torch::Tensor Q = 1.0 / C; + + torch::Tensor Ei = accum_cuda(Eii.view({num, 6*ht*wd}), ii, ts).view({t1-t0, 6, ht*wd}); + torch::Tensor E = torch::cat({Ei, Eij}, 0); + + SparseBlock S = schur_block(E, Q, w, ii_exp, jj_exp, kk_exp, t0, t1); + dx = (A - S).solve(lm, ep); + + torch::Tensor ix = jj_exp - t0; + torch::Tensor dw = torch::zeros({ix.size(0), ht*wd}, opts); + + EvT6x1_kernel<<>>( + E.packed_accessor32(), + dx.packed_accessor32(), + ix.packed_accessor32(), + dw.packed_accessor32()); + + dz = Q * (w - accum_cuda(dw, ii_exp, kx)); + + // update poses + pose_retr_kernel<<<1, THREADS>>>( + poses.packed_accessor32(), + dx.packed_accessor32(), t0, t1); + + // update disparity maps + disp_retr_kernel<<>>( + disps.packed_accessor32(), + dz.packed_accessor32(), + kx.packed_accessor32()); + } + + } + + return {dx, dz}; +} + + + +torch::Tensor frame_distance_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj, + const float beta) +{ + auto opts = poses.options(); + const int num = ii.size(0); + + torch::Tensor dist = torch::zeros({num}, opts); + + frame_distance_kernel<<>>( + poses.packed_accessor32(), + disps.packed_accessor32(), + intrinsics.packed_accessor32(), + ii.packed_accessor32(), + jj.packed_accessor32(), + dist.packed_accessor32(), beta); + + return dist; +} + + +std::vector projmap_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ii, + torch::Tensor jj) +{ + auto opts = poses.options(); + const int num = ii.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + torch::Tensor coords = torch::zeros({num, ht, wd, 3}, opts); + torch::Tensor valid = torch::zeros({num, ht, wd, 1}, opts); + + projmap_kernel<<>>( + poses.packed_accessor32(), + disps.packed_accessor32(), + intrinsics.packed_accessor32(), + ii.packed_accessor32(), + jj.packed_accessor32(), + coords.packed_accessor32(), + valid.packed_accessor32()); + + return {coords, valid}; +} + + +torch::Tensor depth_filter_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics, + torch::Tensor ix, + torch::Tensor thresh) +{ + const int num = ix.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + torch::Tensor counter = torch::zeros({num, ht, wd}, disps.options()); + + dim3 blocks(num, 6, NUM_BLOCKS(ht * wd)); + + depth_filter_kernel<<>>( + poses.packed_accessor32(), + disps.packed_accessor32(), + intrinsics.packed_accessor32(), + ix.packed_accessor32(), + thresh.packed_accessor32(), + counter.packed_accessor32()); + + return counter; +} + + +torch::Tensor iproj_cuda( + torch::Tensor poses, + torch::Tensor disps, + torch::Tensor intrinsics) +{ + + const int nm = disps.size(0); + const int ht = disps.size(1); + const int wd = disps.size(2); + + auto opts = disps.options(); + torch::Tensor points = torch::zeros({nm, ht, wd, 3}, opts); + + dim3 blocks(nm, NUM_BLOCKS(ht * wd)); + + iproj_kernel<<>>( + poses.packed_accessor32(), + disps.packed_accessor32(), + intrinsics.packed_accessor32(), + points.packed_accessor32()); + + return points; + +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitignore b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..f6ab76fdadf4d5f19c6b124909175d3f509b4c33 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitignore @@ -0,0 +1,38 @@ +qrc_*cxx +*.orig +*.pyc +*.diff +diff +*.save +save +*.old +*.gmo +*.qm +core +core.* +*.bak +*~ +*build* +*.moc.* +*.moc +ui_* +CMakeCache.txt +tags +.*.swp +activity.png +*.out +*.php* +*.log +*.orig +*.rej +log +patch +*.patch +a +a.* +lapack/testing +lapack/reference +.*project +.settings +Makefile +!ci/build.gitlab-ci.yml diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab-ci.yml b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab-ci.yml new file mode 100644 index 0000000000000000000000000000000000000000..e5a3c00af94389f19d96d5ea2712c74477955e79 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab-ci.yml @@ -0,0 +1,23 @@ +# This file is part of Eigen, a lightweight C++ template library +# for linear algebra. +# +# Copyright (C) 2020 Arm Ltd. and Contributors +# +# This Source Code Form is subject to the terms of the Mozilla +# Public License v. 2.0. If a copy of the MPL was not distributed +# with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +stages: + - buildsmoketests + - smoketests + - build + - test + +variables: + BUILDDIR: builddir + EIGEN_CI_CMAKE_GENEATOR: "Ninja" + +include: + - "/ci/smoketests.gitlab-ci.yml" + - "/ci/build.gitlab-ci.yml" + - "/ci/test.gitlab-ci.yml" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Bug Report.md b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Bug Report.md new file mode 100644 index 0000000000000000000000000000000000000000..0c49b0fe38d4a21c32fb4da83d073e992a0fa6a9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Bug Report.md @@ -0,0 +1,69 @@ + + +### Summary + + +### Environment + +- **Operating System** : Windows/Linux +- **Architecture** : x64/Arm64/PowerPC ... +- **Eigen Version** : 3.3.9 +- **Compiler Version** : Gcc7.0 +- **Compile Flags** : -O3 -march=native +- **Vector Extension** : SSE/AVX/NEON ... + +### Minimal Example + + +```cpp +//show your code here +``` + +### Steps to reproduce + + +1. first step +2. second step +3. ... + +### What is the current *bug* behavior? + + +### What is the expected *correct* behavior? + + +### Relevant logs + + + +### Warning Messages + + + +### Benchmark scripts and results + + +### Anything else that might help + + +- [ ] Have a plan to fix this issue. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Feature Request.md b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Feature Request.md new file mode 100644 index 0000000000000000000000000000000000000000..2c6f908af4f9ba0c056d980c89cbe1f6414db295 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/issue_templates/Feature Request.md @@ -0,0 +1,7 @@ +### Describe the feature you would like to be implemented. + +### Would such a feature be useful for other users? Why? + +### Any hints on how to implement the requested feature? + +### Additional resources diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/merge_request_templates/Merge Request Template.md b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/merge_request_templates/Merge Request Template.md new file mode 100644 index 0000000000000000000000000000000000000000..3fe963afa104b0c70bc9fcbe9e7824c8c839a99f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.gitlab/merge_request_templates/Merge Request Template.md @@ -0,0 +1,26 @@ + + +### Reference issue + + +### What does this implement/fix? + + +### Additional information + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.hgeol b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.hgeol new file mode 100644 index 0000000000000000000000000000000000000000..5327df161536cc2b12f8884e9935daaca82690b1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/.hgeol @@ -0,0 +1,11 @@ +[patterns] +*.sh = LF +*.MINPACK = CRLF +scripts/*.in = LF +debug/msvc/*.dat = CRLF +debug/msvc/*.natvis = CRLF +unsupported/test/mpreal/*.* = CRLF +** = native + +[repository] +native = LF diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1ec914b5b1c9bcc4ad749ec68fe4a9b654540fe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CMakeLists.txt @@ -0,0 +1,626 @@ +# cmake_minimum_require must be the first command of the file +cmake_minimum_required(VERSION 3.5.0) + +project(Eigen3) + +set(CMAKE_CXX_STANDARD 11 CACHE STRING "Default C++ standard") +set(CMAKE_CXX_STANDARD_REQUIRED ON CACHE BOOL "Require C++ standard") +set(CMAKE_CXX_EXTENSIONS OFF CACHE BOOL "Allow C++ extensions") + +# guard against in-source builds + +if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR}) + message(FATAL_ERROR "In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. ") +endif() + + +# Alias Eigen_*_DIR to Eigen3_*_DIR: + +set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR}) +set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR}) + +# guard against bad build-type strings + +if (NOT CMAKE_BUILD_TYPE) + set(CMAKE_BUILD_TYPE "Release") +endif() + + +############################################################################# +# retrieve version information # +############################################################################# + +# automatically parse the version number +file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header) +string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}") +set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}") +string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}") +set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}") +string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}") +set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}") +set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION}) + +# if we are not in a git clone +if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.git) + # if the git program is absent or this will leave the EIGEN_GIT_REVNUM string empty, + # but won't stop CMake. + execute_process(COMMAND git ls-remote --refs -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT) +endif() + +# extract the git rev number from the git output... +if(EIGEN_GIT_OUTPUT) +string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}") +set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}") +endif() +#...and show it next to the version number +if(EIGEN_GIT_REVNUM) + set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (git rev ${EIGEN_GIT_REVNUM})") +else() + set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}") +endif() + +include(CheckCXXCompilerFlag) +include(GNUInstallDirs) +include(CMakeDependentOption) + +set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake) + + +option(EIGEN_TEST_CXX11 "Enable testing of unsupported CXX11 tests (i.e. those starting with cxx11_)." OFF) + +macro(ei_add_cxx_compiler_flag FLAG) + string(REGEX REPLACE "-" "" SFLAG1 ${FLAG}) + string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1}) + check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG}) + if(COMPILER_SUPPORT_${SFLAG}) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}") + endif() +endmacro() + +# Determine if we should build shared libraries on this platform. +get_cmake_property(EIGEN_BUILD_SHARED_LIBS TARGET_SUPPORTS_SHARED_LIBS) + +############################################################################# +# find how to link to the standard libraries # +############################################################################# + +find_package(StandardMathLibrary) + + +set(EIGEN_TEST_CUSTOM_LINKER_FLAGS "" CACHE STRING "Additional linker flags when linking unit tests.") +set(EIGEN_TEST_CUSTOM_CXX_FLAGS "" CACHE STRING "Additional compiler flags when compiling unit tests.") + +set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "") + +if(NOT STANDARD_MATH_LIBRARY_FOUND) + + message(FATAL_ERROR + "Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.") + +else() + + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}") + else() + set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}") + endif() + +endif() + +if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}") +else() + message(STATUS "Standard libraries to link to explicitly: none") +endif() + +option(EIGEN_BUILD_BTL "Build benchmark suite" OFF) + +# Disable pkgconfig only for native Windows builds +if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows) + option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON) +endif() + +set(CMAKE_INCLUDE_CURRENT_DIR OFF) + +option(EIGEN_SPLIT_LARGE_TESTS "Split large tests into smaller executables" ON) + +option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF) +if(EIGEN_DEFAULT_TO_ROW_MAJOR) + add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR") +endif() + +set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320") + +if(NOT MSVC) + # We assume that other compilers are partly compatible with GNUCC + + # clang outputs some warnings for unknown flags that are not caught by check_cxx_compiler_flag + # adding -Werror turns such warnings into errors + check_cxx_compiler_flag("-Werror" COMPILER_SUPPORT_WERROR) + if(COMPILER_SUPPORT_WERROR) + set(CMAKE_REQUIRED_FLAGS "-Werror") + endif() + ei_add_cxx_compiler_flag("-pedantic") + ei_add_cxx_compiler_flag("-Wall") + ei_add_cxx_compiler_flag("-Wextra") + #ei_add_cxx_compiler_flag("-Weverything") # clang + + ei_add_cxx_compiler_flag("-Wundef") + ei_add_cxx_compiler_flag("-Wcast-align") + ei_add_cxx_compiler_flag("-Wchar-subscripts") + ei_add_cxx_compiler_flag("-Wnon-virtual-dtor") + ei_add_cxx_compiler_flag("-Wunused-local-typedefs") + ei_add_cxx_compiler_flag("-Wpointer-arith") + ei_add_cxx_compiler_flag("-Wwrite-strings") + ei_add_cxx_compiler_flag("-Wformat-security") + ei_add_cxx_compiler_flag("-Wshorten-64-to-32") + ei_add_cxx_compiler_flag("-Wlogical-op") + ei_add_cxx_compiler_flag("-Wenum-conversion") + ei_add_cxx_compiler_flag("-Wc++11-extensions") + ei_add_cxx_compiler_flag("-Wdouble-promotion") +# ei_add_cxx_compiler_flag("-Wconversion") + + ei_add_cxx_compiler_flag("-Wshadow") + + ei_add_cxx_compiler_flag("-Wno-psabi") + ei_add_cxx_compiler_flag("-Wno-variadic-macros") + ei_add_cxx_compiler_flag("-Wno-long-long") + + ei_add_cxx_compiler_flag("-fno-check-new") + ei_add_cxx_compiler_flag("-fno-common") + ei_add_cxx_compiler_flag("-fstrict-aliasing") + ei_add_cxx_compiler_flag("-wd981") # disable ICC's "operands are evaluated in unspecified order" remark + ei_add_cxx_compiler_flag("-wd2304") # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor + + if(ANDROID_NDK) + ei_add_cxx_compiler_flag("-pie") + ei_add_cxx_compiler_flag("-fPIE") + endif() + + set(CMAKE_REQUIRED_FLAGS "") + + option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF) + if(EIGEN_TEST_SSE2) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2") + message(STATUS "Enabling SSE2 in tests/examples") + endif() + + option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF) + if(EIGEN_TEST_SSE3) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3") + message(STATUS "Enabling SSE3 in tests/examples") + endif() + + option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF) + if(EIGEN_TEST_SSSE3) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3") + message(STATUS "Enabling SSSE3 in tests/examples") + endif() + + option(EIGEN_TEST_SSE4_1 "Enable/Disable SSE4.1 in tests/examples" OFF) + if(EIGEN_TEST_SSE4_1) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.1") + message(STATUS "Enabling SSE4.1 in tests/examples") + endif() + + option(EIGEN_TEST_SSE4_2 "Enable/Disable SSE4.2 in tests/examples" OFF) + if(EIGEN_TEST_SSE4_2) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.2") + message(STATUS "Enabling SSE4.2 in tests/examples") + endif() + + option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF) + if(EIGEN_TEST_AVX) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx") + message(STATUS "Enabling AVX in tests/examples") + endif() + + option(EIGEN_TEST_FMA "Enable/Disable FMA in tests/examples" OFF) + if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfma") + message(STATUS "Enabling FMA in tests/examples") + endif() + + option(EIGEN_TEST_AVX2 "Enable/Disable AVX2 in tests/examples" OFF) + if(EIGEN_TEST_AVX2) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx2 -mfma") + message(STATUS "Enabling AVX2 in tests/examples") + endif() + + option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF) + if(EIGEN_TEST_AVX512) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -mfma") + if (NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang") + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fabi-version=6") + endif() + message(STATUS "Enabling AVX512 in tests/examples") + endif() + + option(EIGEN_TEST_AVX512DQ "Enable/Disable AVX512DQ in tests/examples" OFF) + if(EIGEN_TEST_AVX512DQ) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512dq") + if (NOT "${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang") + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fabi-version=6") + endif() + message(STATUS "Enabling AVX512DQ in tests/examples") + endif() + + option(EIGEN_TEST_F16C "Enable/Disable F16C in tests/examples" OFF) + if(EIGEN_TEST_F16C) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mf16c") + message(STATUS "Enabling F16C in tests/examples") + endif() + + option(EIGEN_TEST_ALTIVEC "Enable/Disable AltiVec in tests/examples" OFF) + if(EIGEN_TEST_ALTIVEC) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec") + message(STATUS "Enabling AltiVec in tests/examples") + endif() + + option(EIGEN_TEST_VSX "Enable/Disable VSX in tests/examples" OFF) + if(EIGEN_TEST_VSX) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m64 -mvsx") + message(STATUS "Enabling VSX in tests/examples") + endif() + + option(EIGEN_TEST_MSA "Enable/Disable MSA in tests/examples" OFF) + if(EIGEN_TEST_MSA) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mmsa") + message(STATUS "Enabling MSA in tests/examples") + endif() + + option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF) + if(EIGEN_TEST_NEON) + if(EIGEN_TEST_FMA) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon-vfpv4") + else() + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon") + endif() + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=hard") + message(STATUS "Enabling NEON in tests/examples") + endif() + + option(EIGEN_TEST_NEON64 "Enable/Disable Neon in tests/examples" OFF) + if(EIGEN_TEST_NEON64) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") + message(STATUS "Enabling NEON in tests/examples") + endif() + + option(EIGEN_TEST_Z13 "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF) + if(EIGEN_TEST_Z13) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector") + message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples") + endif() + + option(EIGEN_TEST_Z14 "Enable/Disable S390X(zEC14) ZVECTOR in tests/examples" OFF) + if(EIGEN_TEST_Z14) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z14 -mzvector") + message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples") + endif() + + check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP) + if(COMPILER_SUPPORT_OPENMP) + option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF) + if(EIGEN_TEST_OPENMP) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp") + message(STATUS "Enabling OpenMP in tests/examples") + endif() + endif() + +else() + + # C4127 - conditional expression is constant + # C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively) + # We can disable this warning in the unit tests since it is clear that it occurs + # because we are oftentimes returning objects that have a destructor or may + # throw exceptions - in particular in the unit tests we are throwing extra many + # exceptions to cover indexing errors. + # C4505 - unreferenced local function has been removed (impossible to deactivate selectively) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714") + + # replace all /Wx by /W4 + string(REGEX REPLACE "/W[0-9]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}") + + check_cxx_compiler_flag("/openmp" COMPILER_SUPPORT_OPENMP) + if(COMPILER_SUPPORT_OPENMP) + option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF) + if(EIGEN_TEST_OPENMP) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /openmp") + message(STATUS "Enabling OpenMP in tests/examples") + endif() + endif() + + option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF) + if(EIGEN_TEST_SSE2) + if(NOT CMAKE_CL_64) + # arch is not supported on 64 bit systems, SSE is enabled automatically. + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2") + endif() + message(STATUS "Enabling SSE2 in tests/examples") + endif() + + option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF) + if(EIGEN_TEST_AVX) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX") + message(STATUS "Enabling AVX in tests/examples") + endif() + + option(EIGEN_TEST_FMA "Enable/Disable FMA/AVX2 in tests/examples" OFF) + if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:AVX2") + message(STATUS "Enabling FMA/AVX2 in tests/examples") + endif() + +endif() + +option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF) +option(EIGEN_TEST_X87 "Force using X87 instructions. Implies no vectorization." OFF) +option(EIGEN_TEST_32BIT "Force generating 32bit code." OFF) + +if(EIGEN_TEST_X87) + set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON) + if(CMAKE_COMPILER_IS_GNUCXX) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpmath=387") + message(STATUS "Forcing use of x87 instructions in tests/examples") + else() + message(STATUS "EIGEN_TEST_X87 ignored on your compiler") + endif() +endif() + +if(EIGEN_TEST_32BIT) + if(CMAKE_COMPILER_IS_GNUCXX) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m32") + message(STATUS "Forcing generation of 32-bit code in tests/examples") + else() + message(STATUS "EIGEN_TEST_32BIT ignored on your compiler") + endif() +endif() + +if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION) + add_definitions(-DEIGEN_DONT_VECTORIZE=1) + message(STATUS "Disabling vectorization in tests/examples") +endif() + +option(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT "Disable explicit alignment (hence vectorization) in tests/examples" OFF) +if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT) + add_definitions(-DEIGEN_DONT_ALIGN=1) + message(STATUS "Disabling alignment in tests/examples") +endif() + +option(EIGEN_TEST_NO_EXCEPTIONS "Disables C++ exceptions" OFF) +if(EIGEN_TEST_NO_EXCEPTIONS) + ei_add_cxx_compiler_flag("-fno-exceptions") + message(STATUS "Disabling exceptions in tests/examples") +endif() + +set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture level to target when compiling CUDA code") + +include_directories(${CMAKE_CURRENT_SOURCE_DIR}) + +# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR +if(EIGEN_INCLUDE_INSTALL_DIR) + message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.") +endif() + +if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR) + set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR} + CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed") +else() + set(INCLUDE_INSTALL_DIR + "${CMAKE_INSTALL_INCLUDEDIR}/eigen3" + CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen header files are installed" + ) +endif() +set(CMAKEPACKAGE_INSTALL_DIR + "${CMAKE_INSTALL_DATADIR}/eigen3/cmake" + CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where Eigen3Config.cmake is installed" + ) +set(PKGCONFIG_INSTALL_DIR + "${CMAKE_INSTALL_DATADIR}/pkgconfig" + CACHE PATH "The directory relative to CMAKE_INSTALL_PREFIX where eigen3.pc is installed" + ) + +foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR) + # If an absolute path is specified, make it relative to "{CMAKE_INSTALL_PREFIX}". + if(IS_ABSOLUTE "${${var}}") + file(RELATIVE_PATH "${var}" "${CMAKE_INSTALL_PREFIX}" "${${var}}") + endif() +endforeach() + +# similar to set_target_properties but append the property instead of overwriting it +macro(ei_add_target_property target prop value) + + get_target_property(previous ${target} ${prop}) + # if the property wasn't previously set, ${previous} is now "previous-NOTFOUND" which cmake allows catching with plain if() + if(NOT previous) + set(previous "") + endif() + set_target_properties(${target} PROPERTIES ${prop} "${previous} ${value}") +endmacro() + +install(FILES + signature_of_eigen3_matrix_library + DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel + ) + +if(EIGEN_BUILD_PKGCONFIG) + configure_file(eigen3.pc.in eigen3.pc @ONLY) + install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc + DESTINATION ${PKGCONFIG_INSTALL_DIR} + ) +endif() + +install(DIRECTORY Eigen DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel) + + +option(EIGEN_BUILD_DOC "Enable creation of Eigen documentation" ON) +if(EIGEN_BUILD_DOC) + add_subdirectory(doc EXCLUDE_FROM_ALL) +endif() + + +option(BUILD_TESTING "Enable creation of Eigen tests." ON) +if(BUILD_TESTING) + include(EigenConfigureTesting) + + if(EIGEN_LEAVE_TEST_IN_ALL_TARGET) + add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest + else() + add_subdirectory(test EXCLUDE_FROM_ALL) + endif() + + add_subdirectory(failtest) +endif() + +if(EIGEN_LEAVE_TEST_IN_ALL_TARGET) + add_subdirectory(blas) + add_subdirectory(lapack) +else() + add_subdirectory(blas EXCLUDE_FROM_ALL) + add_subdirectory(lapack EXCLUDE_FROM_ALL) +endif() + +# add SYCL +option(EIGEN_TEST_SYCL "Add Sycl support." OFF) +option(EIGEN_SYCL_TRISYCL "Use the triSYCL Sycl implementation (ComputeCPP by default)." OFF) +if(EIGEN_TEST_SYCL) + set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}") + find_package(Threads REQUIRED) + if(EIGEN_SYCL_TRISYCL) + message(STATUS "Using triSYCL") + include(FindTriSYCL) + else() + message(STATUS "Using ComputeCPP SYCL") + include(FindComputeCpp) + set(COMPUTECPP_DRIVER_DEFAULT_VALUE OFF) + if (NOT MSVC) + set(COMPUTECPP_DRIVER_DEFAULT_VALUE ON) + endif() + option(COMPUTECPP_USE_COMPILER_DRIVER + "Use ComputeCpp driver instead of a 2 steps compilation" + ${COMPUTECPP_DRIVER_DEFAULT_VALUE} + ) + endif(EIGEN_SYCL_TRISYCL) + option(EIGEN_DONT_VECTORIZE_SYCL "Don't use vectorisation in the SYCL tests." OFF) + if(EIGEN_DONT_VECTORIZE_SYCL) + message(STATUS "Disabling SYCL vectorization in tests/examples") + # When disabling SYCL vectorization, also disable Eigen default vectorization + add_definitions(-DEIGEN_DONT_VECTORIZE=1) + add_definitions(-DEIGEN_DONT_VECTORIZE_SYCL=1) + endif() +endif() + +add_subdirectory(unsupported) + +add_subdirectory(demos EXCLUDE_FROM_ALL) + +# must be after test and unsupported, for configuring buildtests.in +add_subdirectory(scripts EXCLUDE_FROM_ALL) + +# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target "make btl"? +if(EIGEN_BUILD_BTL) + add_subdirectory(bench/btl EXCLUDE_FROM_ALL) +endif() + +if(NOT WIN32) + add_subdirectory(bench/spbench EXCLUDE_FROM_ALL) +endif() + +configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY) + +if(BUILD_TESTING) + ei_testing_print_summary() +endif() + +message(STATUS "") +message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}") +message(STATUS "") + +string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower) +if(cmake_generator_tolower MATCHES "makefile") + message(STATUS "Available targets (use: make TARGET):") +else() + message(STATUS "Available targets (use: cmake --build . --target TARGET):") +endif() +message(STATUS "---------+--------------------------------------------------------------") +message(STATUS "Target | Description") +message(STATUS "---------+--------------------------------------------------------------") +message(STATUS "install | Install Eigen. Headers will be installed to:") +message(STATUS " | /") +message(STATUS " | Using the following values:") +message(STATUS " | CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}") +message(STATUS " | INCLUDE_INSTALL_DIR: ${INCLUDE_INSTALL_DIR}") +message(STATUS " | Change the install location of Eigen headers using:") +message(STATUS " | cmake . -DCMAKE_INSTALL_PREFIX=yourprefix") +message(STATUS " | Or:") +message(STATUS " | cmake . -DINCLUDE_INSTALL_DIR=yourdir") +message(STATUS "doc | Generate the API documentation, requires Doxygen & LaTeX") +if(BUILD_TESTING) + message(STATUS "check | Build and run the unit-tests. Read this page:") + message(STATUS " | http://eigen.tuxfamily.org/index.php?title=Tests") +endif() +message(STATUS "blas | Build BLAS library (not the same thing as Eigen)") +message(STATUS "uninstall| Remove files installed by the install target") +message(STATUS "---------+--------------------------------------------------------------") +message(STATUS "") + + +set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} ) +set ( EIGEN_VERSION_MAJOR ${EIGEN_WORLD_VERSION} ) +set ( EIGEN_VERSION_MINOR ${EIGEN_MAJOR_VERSION} ) +set ( EIGEN_VERSION_PATCH ${EIGEN_MINOR_VERSION} ) + +include (CMakePackageConfigHelpers) + +# Imported target support +add_library (eigen INTERFACE) +add_library (Eigen3::Eigen ALIAS eigen) +target_compile_definitions (eigen INTERFACE ${EIGEN_DEFINITIONS}) +target_include_directories (eigen INTERFACE + $ + $ +) + +# Export as title case Eigen +set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen) + +install (TARGETS eigen EXPORT Eigen3Targets) + +configure_package_config_file ( + ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in + ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake + INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR} + NO_SET_AND_CHECK_MACRO # Eigen does not provide legacy style defines + NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components +) +# Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does +# not depend on architecture specific settings or libraries. More +# specifically, an Eigen3Config.cmake generated from a 64 bit target can be +# used for 32 bit targets as well (and vice versa). +set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P}) +unset (CMAKE_SIZEOF_VOID_P) +write_basic_package_version_file (Eigen3ConfigVersion.cmake + VERSION ${EIGEN_VERSION_NUMBER} + COMPATIBILITY SameMajorVersion) +set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P}) + +# The Eigen target will be located in the Eigen3 namespace. Other CMake +# targets can refer to it using Eigen3::Eigen. +export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake) +# Export Eigen3 package to CMake registry such that it can be easily found by +# CMake even if it has not been installed to a standard directory. +export (PACKAGE Eigen3) + +install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}) + +install (FILES ${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake + ${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake + DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}) + +# Add uninstall target +add_custom_target ( uninstall + COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake) + +if (EIGEN_SPLIT_TESTSUITE) + ei_split_testsuite("${EIGEN_SPLIT_TESTSUITE}") +endif() diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.APACHE b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.APACHE new file mode 100644 index 0000000000000000000000000000000000000000..61e948d2aaa3f7cd1db246b874d3b8ad1e8204fb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.APACHE @@ -0,0 +1,203 @@ +/* + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. For the purposes of this definition, + "control" means (i) the power, direct or indirect, to cause the + direction or management of such entity, whether by contract or + otherwise, or (ii) ownership of fifty percent (50%) or more of the + outstanding shares, or (iii) beneficial ownership of such entity. + + "You" (or "Your") shall mean an individual or Legal Entity + exercising permissions granted by this License. + + "Source" form shall mean the preferred form for making modifications, + including but not limited to software source code, documentation + source, and configuration files. + + "Object" form shall mean any form resulting from mechanical + transformation or translation of a Source form, including but + not limited to compiled object code, generated documentation, + and conversions to other media types. + + "Work" shall mean the work of authorship, whether in Source or + Object form, made available under the License, as indicated by a + copyright notice that is included in or attached to the work + (an example is provided in the Appendix below). + + "Derivative Works" shall mean any work, whether in Source or Object + form, that is based on (or derived from) the Work and for which the + editorial revisions, annotations, elaborations, or other modifications + represent, as a whole, an original work of authorship. For the purposes + of this License, Derivative Works shall not include works that remain + separable from, or merely link (or bind by name) to the interfaces of, + the Work and Derivative Works thereof. + + "Contribution" shall mean any work of authorship, including + the original version of the Work and any modifications or additions + to that Work or Derivative Works thereof, that is intentionally + submitted to Licensor for inclusion in the Work by the copyright owner + or by an individual or Legal Entity authorized to submit on behalf of + the copyright owner. For the purposes of this definition, "submitted" + means any form of electronic, verbal, or written communication sent + to the Licensor or its representatives, including but not limited to + communication on electronic mailing lists, source code control systems, + and issue tracking systems that are managed by, or on behalf of, the + Licensor for the purpose of discussing and improving the Work, but + excluding communication that is conspicuously marked or otherwise + designated in writing by the copyright owner as "Not a Contribution." + + "Contributor" shall mean Licensor and any individual or Legal Entity + on behalf of whom a Contribution has been received by Licensor and + subsequently incorporated within the Work. + + 2. Grant of Copyright License. Subject to the terms and conditions of + this License, each Contributor hereby grants to You a perpetual, + worldwide, non-exclusive, no-charge, royalty-free, irrevocable + copyright license to reproduce, prepare Derivative Works of, + publicly display, publicly perform, sublicense, and distribute the + Work and such Derivative Works in Source or Object form. + + 3. Grant of Patent License. Subject to the terms and conditions of + this License, each Contributor hereby grants to You a perpetual, + worldwide, non-exclusive, no-charge, royalty-free, irrevocable + (except as stated in this section) patent license to make, have made, + use, offer to sell, sell, import, and otherwise transfer the Work, + where such license applies only to those patent claims licensable + by such Contributor that are necessarily infringed by their + Contribution(s) alone or by combination of their Contribution(s) + with the Work to which such Contribution(s) was submitted. If You + institute patent litigation against any entity (including a + cross-claim or counterclaim in a lawsuit) alleging that the Work + or a Contribution incorporated within the Work constitutes direct + or contributory patent infringement, then any patent licenses + granted to You under this License for that Work shall terminate + as of the date such litigation is filed. + + 4. Redistribution. You may reproduce and distribute copies of the + Work or Derivative Works thereof in any medium, with or without + modifications, and in Source or Object form, provided that You + meet the following conditions: + + (a) You must give any other recipients of the Work or + Derivative Works a copy of this License; and + + (b) You must cause any modified files to carry prominent notices + stating that You changed the files; and + + (c) You must retain, in the Source form of any Derivative Works + that You distribute, all copyright, patent, trademark, and + attribution notices from the Source form of the Work, + excluding those notices that do not pertain to any part of + the Derivative Works; and + + (d) If the Work includes a "NOTICE" text file as part of its + distribution, then any Derivative Works that You distribute must + include a readable copy of the attribution notices contained + within such NOTICE file, excluding those notices that do not + pertain to any part of the Derivative Works, in at least one + of the following places: within a NOTICE text file distributed + as part of the Derivative Works; within the Source form or + documentation, if provided along with the Derivative Works; or, + within a display generated by the Derivative Works, if and + wherever such third-party notices normally appear. The contents + of the NOTICE file are for informational purposes only and + do not modify the License. You may add Your own attribution + notices within Derivative Works that You distribute, alongside + or as an addendum to the NOTICE text from the Work, provided + that such additional attribution notices cannot be construed + as modifying the License. + + You may add Your own copyright statement to Your modifications and + may provide additional or different license terms and conditions + for use, reproduction, or distribution of Your modifications, or + for any such Derivative Works as a whole, provided Your use, + reproduction, and distribution of the Work otherwise complies with + the conditions stated in this License. + + 5. Submission of Contributions. Unless You explicitly state otherwise, + any Contribution intentionally submitted for inclusion in the Work + by You to the Licensor shall be under the terms and conditions of + this License, without any additional terms or conditions. + Notwithstanding the above, nothing herein shall supersede or modify + the terms of any separate license agreement you may have executed + with Licensor regarding such Contributions. + + 6. Trademarks. This License does not grant permission to use the trade + names, trademarks, service marks, or product names of the Licensor, + except as required for reasonable and customary use in describing the + origin of the Work and reproducing the content of the NOTICE file. + + 7. Disclaimer of Warranty. Unless required by applicable law or + agreed to in writing, Licensor provides the Work (and each + Contributor provides its Contributions) on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or + implied, including, without limitation, any warranties or conditions + of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A + PARTICULAR PURPOSE. You are solely responsible for determining the + appropriateness of using or redistributing the Work and assume any + risks associated with Your exercise of permissions under this License. + + 8. Limitation of Liability. In no event and under no legal theory, + whether in tort (including negligence), contract, or otherwise, + unless required by applicable law (such as deliberate and grossly + negligent acts) or agreed to in writing, shall any Contributor be + liable to You for damages, including any direct, indirect, special, + incidental, or consequential damages of any character arising as a + result of this License or out of the use or inability to use the + Work (including but not limited to damages for loss of goodwill, + work stoppage, computer failure or malfunction, or any and all + other commercial damages or losses), even if such Contributor + has been advised of the possibility of such damages. + + 9. Accepting Warranty or Additional Liability. While redistributing + the Work or Derivative Works thereof, You may choose to offer, + and charge a fee for, acceptance of support, warranty, indemnity, + or other liability obligations and/or rights consistent with this + License. However, in accepting such obligations, You may act only + on Your own behalf and on Your sole responsibility, not on behalf + of any other Contributor, and only if You agree to indemnify, + defend, and hold each Contributor harmless for any liability + incurred by, or claims asserted against, such Contributor by reason + of your accepting any such warranty or additional liability. + + END OF TERMS AND CONDITIONS + + APPENDIX: How to apply the Apache License to your work. + + To apply the Apache License to your work, attach the following + boilerplate notice, with the fields enclosed by brackets "[]" + replaced with your own identifying information. (Don't include + the brackets!) The text should be enclosed in the appropriate + comment syntax for the file format. We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. +*/ \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.BSD b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.BSD new file mode 100644 index 0000000000000000000000000000000000000000..8964ddfdd0effc65e8dd90ea1d8c411efb30e5fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.BSD @@ -0,0 +1,26 @@ +/* + Copyright (c) 2011, Intel Corporation. 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 Intel Corporation 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. +*/ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.GPL b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.GPL new file mode 100644 index 0000000000000000000000000000000000000000..94a9ed024d3859793618152ea559a168bbcbb5e2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.GPL @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. You can apply it to +your programs, too. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +them if you wish), that you receive source code or can get it if you +want it, that you can change the software or use pieces of it in new +free programs, and that you know you can do these things. + + To protect your rights, we need to prevent others from denying you +these rights or asking you to surrender the rights. Therefore, you have +certain responsibilities if you distribute copies of the software, or if +you modify it: responsibilities to respect the freedom of others. + + For example, if you distribute copies of such a program, whether +gratis or for a fee, you must pass on to the recipients the same +freedoms that you received. You must make sure that they, too, receive +or can get the source code. And you must show them these terms so they +know their rights. + + Developers that use the GNU GPL protect your rights with two steps: +(1) assert copyright on the software, and (2) offer you this License +giving you legal permission to copy, distribute and/or modify it. + + For the developers' and authors' protection, the GPL clearly explains +that there is no warranty for this free software. For both users' and +authors' sake, the GPL requires that modified versions be marked as +changed, so that their problems will not be attributed erroneously to +authors of previous versions. + + Some devices are designed to deny users access to install or run +modified versions of the software inside them, although the manufacturer +can do so. This is fundamentally incompatible with the aim of +protecting users' freedom to change the software. The systematic +pattern of such abuse occurs in the area of products for individuals to +use, which is precisely where it is most unacceptable. Therefore, we +have designed this version of the GPL to prohibit the practice for those +products. If such problems arise substantially in other domains, we +stand ready to extend this provision to those domains in future versions +of the GPL, as needed to protect the freedom of users. + + Finally, every program is threatened constantly by software patents. +States should not allow patents to restrict development and use of +software on general-purpose computers, but in those that do, we wish to +avoid the special danger that patents applied to a free program could +make it effectively proprietary. To prevent this, the GPL assures that +patents cannot be used to render the program non-free. + + The precise terms and conditions for copying, distribution and +modification follow. + + TERMS AND CONDITIONS + + 0. Definitions. + + "This License" refers to version 3 of the GNU General Public License. + + "Copyright" also means copyright-like laws that apply to other kinds of +works, such as semiconductor masks. + + "The Program" refers to any copyrightable work licensed under this +License. Each licensee is addressed as "you". "Licensees" and +"recipients" may be individuals or organizations. + + To "modify" a work means to copy from or adapt all or part of the work +in a fashion requiring copyright permission, other than the making of an +exact copy. The resulting work is called a "modified version" of the +earlier work or a work "based on" the earlier work. + + A "covered work" means either the unmodified Program or a work based +on the Program. + + To "propagate" a work means to do anything with it that, without +permission, would make you directly or secondarily liable for +infringement under applicable copyright law, except executing it on a +computer or modifying a private copy. Propagation includes copying, +distribution (with or without modification), making available to the +public, and in some countries other activities as well. + + To "convey" a work means any kind of propagation that enables other +parties to make or receive copies. Mere interaction with a user through +a computer network, with no transfer of a copy, is not conveying. + + An interactive user interface displays "Appropriate Legal Notices" +to the extent that it includes a convenient and prominently visible +feature that (1) displays an appropriate copyright notice, and (2) +tells the user that there is no warranty for the work (except to the +extent that warranties are provided), that licensees may convey the +work under this License, and how to view a copy of this License. If +the interface presents a list of user commands or options, such as a +menu, a prominent item in the list meets this criterion. + + 1. Source Code. + + The "source code" for a work means the preferred form of the work +for making modifications to it. "Object code" means any non-source +form of a work. + + A "Standard Interface" means an interface that either is an official +standard defined by a recognized standards body, or, in the case of +interfaces specified for a particular programming language, one that +is widely used among developers working in that language. + + The "System Libraries" of an executable work include anything, other +than the work as a whole, that (a) is included in the normal form of +packaging a Major Component, but which is not part of that Major +Component, and (b) serves only to enable use of the work with that +Major Component, or to implement a Standard Interface for which an +implementation is available to the public in source code form. A +"Major Component", in this context, means a major essential component +(kernel, window system, and so on) of the specific operating system +(if any) on which the executable work runs, or a compiler used to +produce the work, or an object code interpreter used to run it. + + The "Corresponding Source" for a work in object code form means all +the source code needed to generate, install, and (for an executable +work) run the object code and to modify the work, including scripts to +control those activities. However, it does not include the work's +System Libraries, or general-purpose tools or generally available free +programs which are used unmodified in performing those activities but +which are not part of the work. For example, Corresponding Source +includes interface definition files associated with source files for +the work, and the source code for shared libraries and dynamically +linked subprograms that the work is specifically designed to require, +such as by intimate data communication or control flow between those +subprograms and other parts of the work. + + The Corresponding Source need not include anything that users +can regenerate automatically from other parts of the Corresponding +Source. + + The Corresponding Source for a work in source code form is that +same work. + + 2. Basic Permissions. + + All rights granted under this License are granted for the term of +copyright on the Program, and are irrevocable provided the stated +conditions are met. This License explicitly affirms your unlimited +permission to run the unmodified Program. The output from running a +covered work is covered by this License only if the output, given its +content, constitutes a covered work. This License acknowledges your +rights of fair use or other equivalent, as provided by copyright law. + + You may make, run and propagate covered works that you do not +convey, without conditions so long as your license otherwise remains +in force. You may convey covered works to others for the sole purpose +of having them make modifications exclusively for you, or provide you +with facilities for running those works, provided that you comply with +the terms of this License in conveying all material for which you do +not control copyright. Those thus making or running the covered works +for you must do so exclusively on your behalf, under your direction +and control, on terms that prohibit them from making any copies of +your copyrighted material outside their relationship with you. + + Conveying under any other circumstances is permitted solely under +the conditions stated below. Sublicensing is not allowed; section 10 +makes it unnecessary. + + 3. Protecting Users' Legal Rights From Anti-Circumvention Law. + + No covered work shall be deemed part of an effective technological +measure under any applicable law fulfilling obligations under article +11 of the WIPO copyright treaty adopted on 20 December 1996, or +similar laws prohibiting or restricting circumvention of such +measures. + + When you convey a covered work, you waive any legal power to forbid +circumvention of technological measures to the extent such circumvention +is effected by exercising rights under this License with respect to +the covered work, and you disclaim any intention to limit operation or +modification of the work as a means of enforcing, against the work's +users, your or third parties' legal rights to forbid circumvention of +technological measures. + + 4. Conveying Verbatim Copies. + + You may convey verbatim copies of the Program's source code as you +receive it, in any medium, provided that you conspicuously and +appropriately publish on each copy an appropriate copyright notice; +keep intact all notices stating that this License and any +non-permissive terms added in accord with section 7 apply to the code; +keep intact all notices of the absence of any warranty; and give all +recipients a copy of this License along with the Program. + + You may charge any price or no price for each copy that you convey, +and you may offer support or warranty protection for a fee. + + 5. Conveying Modified Source Versions. + + You may convey a work based on the Program, or the modifications to +produce it from the Program, in the form of source code under the +terms of section 4, provided that you also meet all of these conditions: + + a) The work must carry prominent notices stating that you modified + it, and giving a relevant date. + + b) The work must carry prominent notices stating that it is + released under this License and any conditions added under section + 7. This requirement modifies the requirement in section 4 to + "keep intact all notices". + + c) You must license the entire work, as a whole, under this + License to anyone who comes into possession of a copy. This + License will therefore apply, along with any applicable section 7 + additional terms, to the whole of the work, and all its parts, + regardless of how they are packaged. This License gives no + permission to license the work in any other way, but it does not + invalidate such permission if you have separately received it. + + d) If the work has interactive user interfaces, each must display + Appropriate Legal Notices; however, if the Program has interactive + interfaces that do not display Appropriate Legal Notices, your + work need not make them do so. + + A compilation of a covered work with other separate and independent +works, which are not by their nature extensions of the covered work, +and which are not combined with it such as to form a larger program, +in or on a volume of a storage or distribution medium, is called an +"aggregate" if the compilation and its resulting copyright are not +used to limit the access or legal rights of the compilation's users +beyond what the individual works permit. Inclusion of a covered work +in an aggregate does not cause this License to apply to the other +parts of the aggregate. + + 6. Conveying Non-Source Forms. + + You may convey a covered work in object code form under the terms +of sections 4 and 5, provided that you also convey the +machine-readable Corresponding Source under the terms of this License, +in one of these ways: + + a) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by the + Corresponding Source fixed on a durable physical medium + customarily used for software interchange. + + b) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by a + written offer, valid for at least three years and valid for as + long as you offer spare parts or customer support for that product + model, to give anyone who possesses the object code either (1) a + copy of the Corresponding Source for all the software in the + product that is covered by this License, on a durable physical + medium customarily used for software interchange, for a price no + more than your reasonable cost of physically performing this + conveying of source, or (2) access to copy the + Corresponding Source from a network server at no charge. + + c) Convey individual copies of the object code with a copy of the + written offer to provide the Corresponding Source. This + alternative is allowed only occasionally and noncommercially, and + only if you received the object code with such an offer, in accord + with subsection 6b. + + d) Convey the object code by offering access from a designated + place (gratis or for a charge), and offer equivalent access to the + Corresponding Source in the same way through the same place at no + further charge. You need not require recipients to copy the + Corresponding Source along with the object code. If the place to + copy the object code is a network server, the Corresponding Source + may be on a different server (operated by you or a third party) + that supports equivalent copying facilities, provided you maintain + clear directions next to the object code saying where to find the + Corresponding Source. Regardless of what server hosts the + Corresponding Source, you remain obligated to ensure that it is + available for as long as needed to satisfy these requirements. + + e) Convey the object code using peer-to-peer transmission, provided + you inform other peers where the object code and Corresponding + Source of the work are being offered to the general public at no + charge under subsection 6d. + + A separable portion of the object code, whose source code is excluded +from the Corresponding Source as a System Library, need not be +included in conveying the object code work. + + A "User Product" is either (1) a "consumer product", which means any +tangible personal property which is normally used for personal, family, +or household purposes, or (2) anything designed or sold for incorporation +into a dwelling. In determining whether a product is a consumer product, +doubtful cases shall be resolved in favor of coverage. For a particular +product received by a particular user, "normally used" refers to a +typical or common use of that class of product, regardless of the status +of the particular user or of the way in which the particular user +actually uses, or expects or is expected to use, the product. A product +is a consumer product regardless of whether the product has substantial +commercial, industrial or non-consumer uses, unless such uses represent +the only significant mode of use of the product. + + "Installation Information" for a User Product means any methods, +procedures, authorization keys, or other information required to install +and execute modified versions of a covered work in that User Product from +a modified version of its Corresponding Source. The information must +suffice to ensure that the continued functioning of the modified object +code is in no case prevented or interfered with solely because +modification has been made. + + If you convey an object code work under this section in, or with, or +specifically for use in, a User Product, and the conveying occurs as +part of a transaction in which the right of possession and use of the +User Product is transferred to the recipient in perpetuity or for a +fixed term (regardless of how the transaction is characterized), the +Corresponding Source conveyed under this section must be accompanied +by the Installation Information. But this requirement does not apply +if neither you nor any third party retains the ability to install +modified object code on the User Product (for example, the work has +been installed in ROM). + + The requirement to provide Installation Information does not include a +requirement to continue to provide support service, warranty, or updates +for a work that has been modified or installed by the recipient, or for +the User Product in which it has been modified or installed. Access to a +network may be denied when the modification itself materially and +adversely affects the operation of the network or violates the rules and +protocols for communication across the network. + + Corresponding Source conveyed, and Installation Information provided, +in accord with this section must be in a format that is publicly +documented (and with an implementation available to the public in +source code form), and must require no special password or key for +unpacking, reading or copying. + + 7. Additional Terms. + + "Additional permissions" are terms that supplement the terms of this +License by making exceptions from one or more of its conditions. +Additional permissions that are applicable to the entire Program shall +be treated as though they were included in this License, to the extent +that they are valid under applicable law. If additional permissions +apply only to part of the Program, that part may be used separately +under those permissions, but the entire Program remains governed by +this License without regard to the additional permissions. + + When you convey a copy of a covered work, you may at your option +remove any additional permissions from that copy, or from any part of +it. (Additional permissions may be written to require their own +removal in certain cases when you modify the work.) You may place +additional permissions on material, added by you to a covered work, +for which you have or can give appropriate copyright permission. + + Notwithstanding any other provision of this License, for material you +add to a covered work, you may (if authorized by the copyright holders of +that material) supplement the terms of this License with terms: + + a) Disclaiming warranty or limiting liability differently from the + terms of sections 15 and 16 of this License; or + + b) Requiring preservation of specified reasonable legal notices or + author attributions in that material or in the Appropriate Legal + Notices displayed by works containing it; or + + c) Prohibiting misrepresentation of the origin of that material, or + requiring that modified versions of such material be marked in + reasonable ways as different from the original version; or + + d) Limiting the use for publicity purposes of names of licensors or + authors of the material; or + + e) Declining to grant rights under trademark law for use of some + trade names, trademarks, or service marks; or + + f) Requiring indemnification of licensors and authors of that + material by anyone who conveys the material (or modified versions of + it) with contractual assumptions of liability to the recipient, for + any liability that these contractual assumptions directly impose on + those licensors and authors. + + All other non-permissive additional terms are considered "further +restrictions" within the meaning of section 10. If the Program as you +received it, or any part of it, contains a notice stating that it is +governed by this License along with a term that is a further +restriction, you may remove that term. If a license document contains +a further restriction but permits relicensing or conveying under this +License, you may add to a covered work material governed by the terms +of that license document, provided that the further restriction does +not survive such relicensing or conveying. + + If you add terms to a covered work in accord with this section, you +must place, in the relevant source files, a statement of the +additional terms that apply to those files, or a notice indicating +where to find the applicable terms. + + Additional terms, permissive or non-permissive, may be stated in the +form of a separately written license, or stated as exceptions; +the above requirements apply either way. + + 8. Termination. + + You may not propagate or modify a covered work except as expressly +provided under this License. Any attempt otherwise to propagate or +modify it is void, and will automatically terminate your rights under +this License (including any patent licenses granted under the third +paragraph of section 11). + + However, if you cease all violation of this License, then your +license from a particular copyright holder is reinstated (a) +provisionally, unless and until the copyright holder explicitly and +finally terminates your license, and (b) permanently, if the copyright +holder fails to notify you of the violation by some reasonable means +prior to 60 days after the cessation. + + Moreover, your license from a particular copyright holder is +reinstated permanently if the copyright holder notifies you of the +violation by some reasonable means, this is the first time you have +received notice of violation of this License (for any work) from that +copyright holder, and you cure the violation prior to 30 days after +your receipt of the notice. + + Termination of your rights under this section does not terminate the +licenses of parties who have received copies or rights from you under +this License. If your rights have been terminated and not permanently +reinstated, you do not qualify to receive new licenses for the same +material under section 10. + + 9. Acceptance Not Required for Having Copies. + + You are not required to accept this License in order to receive or +run a copy of the Program. Ancillary propagation of a covered work +occurring solely as a consequence of using peer-to-peer transmission +to receive a copy likewise does not require acceptance. However, +nothing other than this License grants you permission to propagate or +modify any covered work. These actions infringe copyright if you do +not accept this License. Therefore, by modifying or propagating a +covered work, you indicate your acceptance of this License to do so. + + 10. Automatic Licensing of Downstream Recipients. + + Each time you convey a covered work, the recipient automatically +receives a license from the original licensors, to run, modify and +propagate that work, subject to this License. You are not responsible +for enforcing compliance by third parties with this License. + + An "entity transaction" is a transaction transferring control of an +organization, or substantially all assets of one, or subdividing an +organization, or merging organizations. If propagation of a covered +work results from an entity transaction, each party to that +transaction who receives a copy of the work also receives whatever +licenses to the work the party's predecessor in interest had or could +give under the previous paragraph, plus a right to possession of the +Corresponding Source of the work from the predecessor in interest, if +the predecessor has it or can get it with reasonable efforts. + + You may not impose any further restrictions on the exercise of the +rights granted or affirmed under this License. For example, you may +not impose a license fee, royalty, or other charge for exercise of +rights granted under this License, and you may not initiate litigation +(including a cross-claim or counterclaim in a lawsuit) alleging that +any patent claim is infringed by making, using, selling, offering for +sale, or importing the Program or any portion of it. + + 11. Patents. + + A "contributor" is a copyright holder who authorizes use under this +License of the Program or a work on which the Program is based. The +work thus licensed is called the contributor's "contributor version". + + A contributor's "essential patent claims" are all patent claims +owned or controlled by the contributor, whether already acquired or +hereafter acquired, that would be infringed by some manner, permitted +by this License, of making, using, or selling its contributor version, +but do not include claims that would be infringed only as a +consequence of further modification of the contributor version. For +purposes of this definition, "control" includes the right to grant +patent sublicenses in a manner consistent with the requirements of +this License. + + Each contributor grants you a non-exclusive, worldwide, royalty-free +patent license under the contributor's essential patent claims, to +make, use, sell, offer for sale, import and otherwise run, modify and +propagate the contents of its contributor version. + + In the following three paragraphs, a "patent license" is any express +agreement or commitment, however denominated, not to enforce a patent +(such as an express permission to practice a patent or covenant not to +sue for patent infringement). To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.LGPL b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.LGPL new file mode 100644 index 0000000000000000000000000000000000000000..4362b49151d7b34ef83b3067a8f9c9f877d72a0e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.LGPL @@ -0,0 +1,502 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 2.1, February 1999 + + Copyright (C) 1991, 1999 Free Software Foundation, Inc. + 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + +[This is the first released version of the Lesser GPL. It also counts + as the successor of the GNU Library Public License, version 2, hence + the version number 2.1.] + + Preamble + + The licenses for most software are designed to take away your +freedom to share and change it. By contrast, the GNU General Public +Licenses are intended to guarantee your freedom to share and change +free software--to make sure the software is free for all its users. + + This license, the Lesser General Public License, applies to some +specially designated software packages--typically libraries--of the +Free Software Foundation and other authors who decide to use it. You +can use it too, but we suggest you first think carefully about whether +this license or the ordinary General Public License is the better +strategy to use in any particular case, based on the explanations below. + + When we speak of free software, we are referring to freedom of use, +not price. Our General Public Licenses are designed to make sure that +you have the freedom to distribute copies of free software (and charge +for this service if you wish); that you receive source code or can get +it if you want it; that you can change the software and use pieces of +it in new free programs; and that you are informed that you can do +these things. + + To protect your rights, we need to make restrictions that forbid +distributors to deny you these rights or to ask you to surrender these +rights. These restrictions translate to certain responsibilities for +you if you distribute copies of the library or if you modify it. + + For example, if you distribute copies of the library, whether gratis +or for a fee, you must give the recipients all the rights that we gave +you. You must make sure that they, too, receive or can get the source +code. If you link other code with the library, you must provide +complete object files to the recipients, so that they can relink them +with the library after making changes to the library and recompiling +it. And you must show them these terms so they know their rights. + + We protect your rights with a two-step method: (1) we copyright the +library, and (2) we offer you this license, which gives you legal +permission to copy, distribute and/or modify the library. + + To protect each distributor, we want to make it very clear that +there is no warranty for the free library. Also, if the library is +modified by someone else and passed on, the recipients should know +that what they have is not the original version, so that the original +author's reputation will not be affected by problems that might be +introduced by others. + + Finally, software patents pose a constant threat to the existence of +any free program. We wish to make sure that a company cannot +effectively restrict the users of a free program by obtaining a +restrictive license from a patent holder. Therefore, we insist that +any patent license obtained for a version of the library must be +consistent with the full freedom of use specified in this license. + + Most GNU software, including some libraries, is covered by the +ordinary GNU General Public License. This license, the GNU Lesser +General Public License, applies to certain designated libraries, and +is quite different from the ordinary General Public License. We use +this license for certain libraries in order to permit linking those +libraries into non-free programs. + + When a program is linked with a library, whether statically or using +a shared library, the combination of the two is legally speaking a +combined work, a derivative of the original library. The ordinary +General Public License therefore permits such linking only if the +entire combination fits its criteria of freedom. The Lesser General +Public License permits more lax criteria for linking other code with +the library. + + We call this license the "Lesser" General Public License because it +does Less to protect the user's freedom than the ordinary General +Public License. It also provides other free software developers Less +of an advantage over competing non-free programs. These disadvantages +are the reason we use the ordinary General Public License for many +libraries. However, the Lesser license provides advantages in certain +special circumstances. + + For example, on rare occasions, there may be a special need to +encourage the widest possible use of a certain library, so that it becomes +a de-facto standard. To achieve this, non-free programs must be +allowed to use the library. A more frequent case is that a free +library does the same job as widely used non-free libraries. In this +case, there is little to gain by limiting the free library to free +software only, so we use the Lesser General Public License. + + In other cases, permission to use a particular library in non-free +programs enables a greater number of people to use a large body of +free software. For example, permission to use the GNU C Library in +non-free programs enables many more people to use the whole GNU +operating system, as well as its variant, the GNU/Linux operating +system. + + Although the Lesser General Public License is Less protective of the +users' freedom, it does ensure that the user of a program that is +linked with the Library has the freedom and the wherewithal to run +that program using a modified version of the Library. + + The precise terms and conditions for copying, distribution and +modification follow. Pay close attention to the difference between a +"work based on the library" and a "work that uses the library". The +former contains code derived from the library, whereas the latter must +be combined with the library in order to run. + + GNU LESSER GENERAL PUBLIC LICENSE + TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION + + 0. This License Agreement applies to any software library or other +program which contains a notice placed by the copyright holder or +other authorized party saying it may be distributed under the terms of +this Lesser General Public License (also called "this License"). +Each licensee is addressed as "you". + + A "library" means a collection of software functions and/or data +prepared so as to be conveniently linked with application programs +(which use some of those functions and data) to form executables. + + The "Library", below, refers to any such software library or work +which has been distributed under these terms. A "work based on the +Library" means either the Library or any derivative work under +copyright law: that is to say, a work containing the Library or a +portion of it, either verbatim or with modifications and/or translated +straightforwardly into another language. (Hereinafter, translation is +included without limitation in the term "modification".) + + "Source code" for a work means the preferred form of the work for +making modifications to it. For a library, complete source code means +all the source code for all modules it contains, plus any associated +interface definition files, plus the scripts used to control compilation +and installation of the library. + + Activities other than copying, distribution and modification are not +covered by this License; they are outside its scope. The act of +running a program using the Library is not restricted, and output from +such a program is covered only if its contents constitute a work based +on the Library (independent of the use of the Library in a tool for +writing it). Whether that is true depends on what the Library does +and what the program that uses the Library does. + + 1. You may copy and distribute verbatim copies of the Library's +complete source code as you receive it, in any medium, provided that +you conspicuously and appropriately publish on each copy an +appropriate copyright notice and disclaimer of warranty; keep intact +all the notices that refer to this License and to the absence of any +warranty; and distribute a copy of this License along with the +Library. + + You may charge a fee for the physical act of transferring a copy, +and you may at your option offer warranty protection in exchange for a +fee. + + 2. You may modify your copy or copies of the Library or any portion +of it, thus forming a work based on the Library, and copy and +distribute such modifications or work under the terms of Section 1 +above, provided that you also meet all of these conditions: + + a) The modified work must itself be a software library. + + b) You must cause the files modified to carry prominent notices + stating that you changed the files and the date of any change. + + c) You must cause the whole of the work to be licensed at no + charge to all third parties under the terms of this License. + + d) If a facility in the modified Library refers to a function or a + table of data to be supplied by an application program that uses + the facility, other than as an argument passed when the facility + is invoked, then you must make a good faith effort to ensure that, + in the event an application does not supply such function or + table, the facility still operates, and performs whatever part of + its purpose remains meaningful. + + (For example, a function in a library to compute square roots has + a purpose that is entirely well-defined independent of the + application. Therefore, Subsection 2d requires that any + application-supplied function or table used by this function must + be optional: if the application does not supply it, the square + root function must still compute square roots.) + +These requirements apply to the modified work as a whole. If +identifiable sections of that work are not derived from the Library, +and can be reasonably considered independent and separate works in +themselves, then this License, and its terms, do not apply to those +sections when you distribute them as separate works. But when you +distribute the same sections as part of a whole which is a work based +on the Library, the distribution of the whole must be on the terms of +this License, whose permissions for other licensees extend to the +entire whole, and thus to each and every part regardless of who wrote +it. + +Thus, it is not the intent of this section to claim rights or contest +your rights to work written entirely by you; rather, the intent is to +exercise the right to control the distribution of derivative or +collective works based on the Library. + +In addition, mere aggregation of another work not based on the Library +with the Library (or with a work based on the Library) on a volume of +a storage or distribution medium does not bring the other work under +the scope of this License. + + 3. You may opt to apply the terms of the ordinary GNU General Public +License instead of this License to a given copy of the Library. To do +this, you must alter all the notices that refer to this License, so +that they refer to the ordinary GNU General Public License, version 2, +instead of to this License. (If a newer version than version 2 of the +ordinary GNU General Public License has appeared, then you can specify +that version instead if you wish.) Do not make any other change in +these notices. + + Once this change is made in a given copy, it is irreversible for +that copy, so the ordinary GNU General Public License applies to all +subsequent copies and derivative works made from that copy. + + This option is useful when you wish to copy part of the code of +the Library into a program that is not a library. + + 4. You may copy and distribute the Library (or a portion or +derivative of it, under Section 2) in object code or executable form +under the terms of Sections 1 and 2 above provided that you accompany +it with the complete corresponding machine-readable source code, which +must be distributed under the terms of Sections 1 and 2 above on a +medium customarily used for software interchange. + + If distribution of object code is made by offering access to copy +from a designated place, then offering equivalent access to copy the +source code from the same place satisfies the requirement to +distribute the source code, even though third parties are not +compelled to copy the source along with the object code. + + 5. A program that contains no derivative of any portion of the +Library, but is designed to work with the Library by being compiled or +linked with it, is called a "work that uses the Library". Such a +work, in isolation, is not a derivative work of the Library, and +therefore falls outside the scope of this License. + + However, linking a "work that uses the Library" with the Library +creates an executable that is a derivative of the Library (because it +contains portions of the Library), rather than a "work that uses the +library". The executable is therefore covered by this License. +Section 6 states terms for distribution of such executables. + + When a "work that uses the Library" uses material from a header file +that is part of the Library, the object code for the work may be a +derivative work of the Library even though the source code is not. +Whether this is true is especially significant if the work can be +linked without the Library, or if the work is itself a library. The +threshold for this to be true is not precisely defined by law. + + If such an object file uses only numerical parameters, data +structure layouts and accessors, and small macros and small inline +functions (ten lines or less in length), then the use of the object +file is unrestricted, regardless of whether it is legally a derivative +work. (Executables containing this object code plus portions of the +Library will still fall under Section 6.) + + Otherwise, if the work is a derivative of the Library, you may +distribute the object code for the work under the terms of Section 6. +Any executables containing that work also fall under Section 6, +whether or not they are linked directly with the Library itself. + + 6. As an exception to the Sections above, you may also combine or +link a "work that uses the Library" with the Library to produce a +work containing portions of the Library, and distribute that work +under terms of your choice, provided that the terms permit +modification of the work for the customer's own use and reverse +engineering for debugging such modifications. + + You must give prominent notice with each copy of the work that the +Library is used in it and that the Library and its use are covered by +this License. You must supply a copy of this License. If the work +during execution displays copyright notices, you must include the +copyright notice for the Library among them, as well as a reference +directing the user to the copy of this License. Also, you must do one +of these things: + + a) Accompany the work with the complete corresponding + machine-readable source code for the Library including whatever + changes were used in the work (which must be distributed under + Sections 1 and 2 above); and, if the work is an executable linked + with the Library, with the complete machine-readable "work that + uses the Library", as object code and/or source code, so that the + user can modify the Library and then relink to produce a modified + executable containing the modified Library. (It is understood + that the user who changes the contents of definitions files in the + Library will not necessarily be able to recompile the application + to use the modified definitions.) + + b) Use a suitable shared library mechanism for linking with the + Library. A suitable mechanism is one that (1) uses at run time a + copy of the library already present on the user's computer system, + rather than copying library functions into the executable, and (2) + will operate properly with a modified version of the library, if + the user installs one, as long as the modified version is + interface-compatible with the version that the work was made with. + + c) Accompany the work with a written offer, valid for at + least three years, to give the same user the materials + specified in Subsection 6a, above, for a charge no more + than the cost of performing this distribution. + + d) If distribution of the work is made by offering access to copy + from a designated place, offer equivalent access to copy the above + specified materials from the same place. + + e) Verify that the user has already received a copy of these + materials or that you have already sent this user a copy. + + For an executable, the required form of the "work that uses the +Library" must include any data and utility programs needed for +reproducing the executable from it. However, as a special exception, +the materials to be distributed need not include anything that is +normally distributed (in either source or binary form) with the major +components (compiler, kernel, and so on) of the operating system on +which the executable runs, unless that component itself accompanies +the executable. + + It may happen that this requirement contradicts the license +restrictions of other proprietary libraries that do not normally +accompany the operating system. Such a contradiction means you cannot +use both them and the Library together in an executable that you +distribute. + + 7. You may place library facilities that are a work based on the +Library side-by-side in a single library together with other library +facilities not covered by this License, and distribute such a combined +library, provided that the separate distribution of the work based on +the Library and of the other library facilities is otherwise +permitted, and provided that you do these two things: + + a) Accompany the combined library with a copy of the same work + based on the Library, uncombined with any other library + facilities. This must be distributed under the terms of the + Sections above. + + b) Give prominent notice with the combined library of the fact + that part of it is a work based on the Library, and explaining + where to find the accompanying uncombined form of the same work. + + 8. You may not copy, modify, sublicense, link with, or distribute +the Library except as expressly provided under this License. Any +attempt otherwise to copy, modify, sublicense, link with, or +distribute the Library is void, and will automatically terminate your +rights under this License. However, parties who have received copies, +or rights, from you under this License will not have their licenses +terminated so long as such parties remain in full compliance. + + 9. You are not required to accept this License, since you have not +signed it. However, nothing else grants you permission to modify or +distribute the Library or its derivative works. These actions are +prohibited by law if you do not accept this License. Therefore, by +modifying or distributing the Library (or any work based on the +Library), you indicate your acceptance of this License to do so, and +all its terms and conditions for copying, distributing or modifying +the Library or works based on it. + + 10. Each time you redistribute the Library (or any work based on the +Library), the recipient automatically receives a license from the +original licensor to copy, distribute, link with or modify the Library +subject to these terms and conditions. You may not impose any further +restrictions on the recipients' exercise of the rights granted herein. +You are not responsible for enforcing compliance by third parties with +this License. + + 11. If, as a consequence of a court judgment or allegation of patent +infringement or for any other reason (not limited to patent issues), +conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot +distribute so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you +may not distribute the Library at all. For example, if a patent +license would not permit royalty-free redistribution of the Library by +all those who receive copies directly or indirectly through you, then +the only way you could satisfy both it and this License would be to +refrain entirely from distribution of the Library. + +If any portion of this section is held invalid or unenforceable under any +particular circumstance, the balance of the section is intended to apply, +and the section as a whole is intended to apply in other circumstances. + +It is not the purpose of this section to induce you to infringe any +patents or other property right claims or to contest validity of any +such claims; this section has the sole purpose of protecting the +integrity of the free software distribution system which is +implemented by public license practices. Many people have made +generous contributions to the wide range of software distributed +through that system in reliance on consistent application of that +system; it is up to the author/donor to decide if he or she is willing +to distribute software through any other system and a licensee cannot +impose that choice. + +This section is intended to make thoroughly clear what is believed to +be a consequence of the rest of this License. + + 12. If the distribution and/or use of the Library is restricted in +certain countries either by patents or by copyrighted interfaces, the +original copyright holder who places the Library under this License may add +an explicit geographical distribution limitation excluding those countries, +so that distribution is permitted only in or among countries not thus +excluded. In such case, this License incorporates the limitation as if +written in the body of this License. + + 13. The Free Software Foundation may publish revised and/or new +versions of the Lesser General Public License from time to time. +Such new versions will be similar in spirit to the present version, +but may differ in detail to address new problems or concerns. + +Each version is given a distinguishing version number. If the Library +specifies a version number of this License which applies to it and +"any later version", you have the option of following the terms and +conditions either of that version or of any later version published by +the Free Software Foundation. If the Library does not specify a +license version number, you may choose any version ever published by +the Free Software Foundation. + + 14. If you wish to incorporate parts of the Library into other free +programs whose distribution conditions are incompatible with these, +write to the author to ask for permission. For software which is +copyrighted by the Free Software Foundation, write to the Free +Software Foundation; we sometimes make exceptions for this. Our +decision will be guided by the two goals of preserving the free status +of all derivatives of our free software and of promoting the sharing +and reuse of software generally. + + NO WARRANTY + + 15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO +WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW. +EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR +OTHER PARTIES PROVIDE THE LIBRARY "AS IS" WITHOUT WARRANTY OF ANY +KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE +LIBRARY IS WITH YOU. SHOULD THE LIBRARY PROVE DEFECTIVE, YOU ASSUME +THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN +WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY +AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU +FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR +CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE +LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING +RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A +FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF +SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH +DAMAGES. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Libraries + + If you develop a new library, and you want it to be of the greatest +possible use to the public, we recommend making it free software that +everyone can redistribute and change. You can do so by permitting +redistribution under these terms (or, alternatively, under the terms of the +ordinary General Public License). + + To apply these terms, attach the following notices to the library. It is +safest to attach them to the start of each source file to most effectively +convey the exclusion of warranty; and each file should have at least the +"copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + This library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, write to the Free Software + Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + +Also add information on how to contact you by electronic and paper mail. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the library, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the + library `Frob' (a library for tweaking knobs) written by James Random Hacker. + + , 1 April 1990 + Ty Coon, President of Vice + +That's all there is to it! diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MINPACK b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MINPACK new file mode 100644 index 0000000000000000000000000000000000000000..132cc3f33fa7fd4169a92b05241db59c8428a7ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MINPACK @@ -0,0 +1,51 @@ +Minpack Copyright Notice (1999) University of Chicago. 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. + +3. The end-user documentation included with the +redistribution, if any, must include the following +acknowledgment: + + "This product includes software developed by the + University of Chicago, as Operator of Argonne National + Laboratory. + +Alternately, this acknowledgment may appear in the software +itself, if and wherever such third-party acknowledgments +normally appear. + +4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" +WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE +UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND +THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES +OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE +OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY +OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR +USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF +THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) +DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION +UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL +BE CORRECTED. + +5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT +HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF +ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, +INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF +ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF +PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER +SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT +(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, +EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE +POSSIBILITY OF SUCH LOSS OR DAMAGES. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MPL2 b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MPL2 new file mode 100644 index 0000000000000000000000000000000000000000..14e2f777f6c395e7e04ab4aa306bbcc4b0c1120e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.MPL2 @@ -0,0 +1,373 @@ +Mozilla Public License Version 2.0 +================================== + +1. Definitions +-------------- + +1.1. "Contributor" + means each individual or legal entity that creates, contributes to + the creation of, or owns Covered Software. + +1.2. "Contributor Version" + means the combination of the Contributions of others (if any) used + by a Contributor and that particular Contributor's Contribution. + +1.3. "Contribution" + means Covered Software of a particular Contributor. + +1.4. "Covered Software" + means Source Code Form to which the initial Contributor has attached + the notice in Exhibit A, the Executable Form of such Source Code + Form, and Modifications of such Source Code Form, in each case + including portions thereof. + +1.5. "Incompatible With Secondary Licenses" + means + + (a) that the initial Contributor has attached the notice described + in Exhibit B to the Covered Software; or + + (b) that the Covered Software was made available under the terms of + version 1.1 or earlier of the License, but not also under the + terms of a Secondary License. + +1.6. "Executable Form" + means any form of the work other than Source Code Form. + +1.7. "Larger Work" + means a work that combines Covered Software with other material, in + a separate file or files, that is not Covered Software. + +1.8. "License" + means this document. + +1.9. "Licensable" + means having the right to grant, to the maximum extent possible, + whether at the time of the initial grant or subsequently, any and + all of the rights conveyed by this License. + +1.10. "Modifications" + means any of the following: + + (a) any file in Source Code Form that results from an addition to, + deletion from, or modification of the contents of Covered + Software; or + + (b) any new file in Source Code Form that contains any Covered + Software. + +1.11. "Patent Claims" of a Contributor + means any patent claim(s), including without limitation, method, + process, and apparatus claims, in any patent Licensable by such + Contributor that would be infringed, but for the grant of the + License, by the making, using, selling, offering for sale, having + made, import, or transfer of either its Contributions or its + Contributor Version. + +1.12. "Secondary License" + means either the GNU General Public License, Version 2.0, the GNU + Lesser General Public License, Version 2.1, the GNU Affero General + Public License, Version 3.0, or any later versions of those + licenses. + +1.13. "Source Code Form" + means the form of the work preferred for making modifications. + +1.14. "You" (or "Your") + means an individual or a legal entity exercising rights under this + License. For legal entities, "You" includes any entity that + controls, is controlled by, or is under common control with You. For + purposes of this definition, "control" means (a) the power, direct + or indirect, to cause the direction or management of such entity, + whether by contract or otherwise, or (b) ownership of more than + fifty percent (50%) of the outstanding shares or beneficial + ownership of such entity. + +2. License Grants and Conditions +-------------------------------- + +2.1. Grants + +Each Contributor hereby grants You a world-wide, royalty-free, +non-exclusive license: + +(a) under intellectual property rights (other than patent or trademark) + Licensable by such Contributor to use, reproduce, make available, + modify, display, perform, distribute, and otherwise exploit its + Contributions, either on an unmodified basis, with Modifications, or + as part of a Larger Work; and + +(b) under Patent Claims of such Contributor to make, use, sell, offer + for sale, have made, import, and otherwise transfer either its + Contributions or its Contributor Version. + +2.2. Effective Date + +The licenses granted in Section 2.1 with respect to any Contribution +become effective for each Contribution on the date the Contributor first +distributes such Contribution. + +2.3. Limitations on Grant Scope + +The licenses granted in this Section 2 are the only rights granted under +this License. No additional rights or licenses will be implied from the +distribution or licensing of Covered Software under this License. +Notwithstanding Section 2.1(b) above, no patent license is granted by a +Contributor: + +(a) for any code that a Contributor has removed from Covered Software; + or + +(b) for infringements caused by: (i) Your and any other third party's + modifications of Covered Software, or (ii) the combination of its + Contributions with other software (except as part of its Contributor + Version); or + +(c) under Patent Claims infringed by Covered Software in the absence of + its Contributions. + +This License does not grant any rights in the trademarks, service marks, +or logos of any Contributor (except as may be necessary to comply with +the notice requirements in Section 3.4). + +2.4. Subsequent Licenses + +No Contributor makes additional grants as a result of Your choice to +distribute the Covered Software under a subsequent version of this +License (see Section 10.2) or under the terms of a Secondary License (if +permitted under the terms of Section 3.3). + +2.5. Representation + +Each Contributor represents that the Contributor believes its +Contributions are its original creation(s) or it has sufficient rights +to grant the rights to its Contributions conveyed by this License. + +2.6. Fair Use + +This License is not intended to limit any rights You have under +applicable copyright doctrines of fair use, fair dealing, or other +equivalents. + +2.7. Conditions + +Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted +in Section 2.1. + +3. Responsibilities +------------------- + +3.1. Distribution of Source Form + +All distribution of Covered Software in Source Code Form, including any +Modifications that You create or to which You contribute, must be under +the terms of this License. You must inform recipients that the Source +Code Form of the Covered Software is governed by the terms of this +License, and how they can obtain a copy of this License. You may not +attempt to alter or restrict the recipients' rights in the Source Code +Form. + +3.2. Distribution of Executable Form + +If You distribute Covered Software in Executable Form then: + +(a) such Covered Software must also be made available in Source Code + Form, as described in Section 3.1, and You must inform recipients of + the Executable Form how they can obtain a copy of such Source Code + Form by reasonable means in a timely manner, at a charge no more + than the cost of distribution to the recipient; and + +(b) You may distribute such Executable Form under the terms of this + License, or sublicense it under different terms, provided that the + license for the Executable Form does not attempt to limit or alter + the recipients' rights in the Source Code Form under this License. + +3.3. Distribution of a Larger Work + +You may create and distribute a Larger Work under terms of Your choice, +provided that You also comply with the requirements of this License for +the Covered Software. If the Larger Work is a combination of Covered +Software with a work governed by one or more Secondary Licenses, and the +Covered Software is not Incompatible With Secondary Licenses, this +License permits You to additionally distribute such Covered Software +under the terms of such Secondary License(s), so that the recipient of +the Larger Work may, at their option, further distribute the Covered +Software under the terms of either this License or such Secondary +License(s). + +3.4. Notices + +You may not remove or alter the substance of any license notices +(including copyright notices, patent notices, disclaimers of warranty, +or limitations of liability) contained within the Source Code Form of +the Covered Software, except that You may alter any license notices to +the extent required to remedy known factual inaccuracies. + +3.5. Application of Additional Terms + +You may choose to offer, and to charge a fee for, warranty, support, +indemnity or liability obligations to one or more recipients of Covered +Software. However, You may do so only on Your own behalf, and not on +behalf of any Contributor. You must make it absolutely clear that any +such warranty, support, indemnity, or liability obligation is offered by +You alone, and You hereby agree to indemnify every Contributor for any +liability incurred by such Contributor as a result of warranty, support, +indemnity or liability terms You offer. You may include additional +disclaimers of warranty and limitations of liability specific to any +jurisdiction. + +4. Inability to Comply Due to Statute or Regulation +--------------------------------------------------- + +If it is impossible for You to comply with any of the terms of this +License with respect to some or all of the Covered Software due to +statute, judicial order, or regulation then You must: (a) comply with +the terms of this License to the maximum extent possible; and (b) +describe the limitations and the code they affect. Such description must +be placed in a text file included with all distributions of the Covered +Software under this License. Except to the extent prohibited by statute +or regulation, such description must be sufficiently detailed for a +recipient of ordinary skill to be able to understand it. + +5. Termination +-------------- + +5.1. The rights granted under this License will terminate automatically +if You fail to comply with any of its terms. However, if You become +compliant, then the rights granted under this License from a particular +Contributor are reinstated (a) provisionally, unless and until such +Contributor explicitly and finally terminates Your grants, and (b) on an +ongoing basis, if such Contributor fails to notify You of the +non-compliance by some reasonable means prior to 60 days after You have +come back into compliance. Moreover, Your grants from a particular +Contributor are reinstated on an ongoing basis if such Contributor +notifies You of the non-compliance by some reasonable means, this is the +first time You have received notice of non-compliance with this License +from such Contributor, and You become compliant prior to 30 days after +Your receipt of the notice. + +5.2. If You initiate litigation against any entity by asserting a patent +infringement claim (excluding declaratory judgment actions, +counter-claims, and cross-claims) alleging that a Contributor Version +directly or indirectly infringes any patent, then the rights granted to +You by any and all Contributors for the Covered Software under Section +2.1 of this License shall terminate. + +5.3. In the event of termination under Sections 5.1 or 5.2 above, all +end user license agreements (excluding distributors and resellers) which +have been validly granted by You or Your distributors under this License +prior to termination shall survive termination. + +************************************************************************ +* * +* 6. Disclaimer of Warranty * +* ------------------------- * +* * +* Covered Software is provided under this License on an "as is" * +* basis, without warranty of any kind, either expressed, implied, or * +* statutory, including, without limitation, warranties that the * +* Covered Software is free of defects, merchantable, fit for a * +* particular purpose or non-infringing. The entire risk as to the * +* quality and performance of the Covered Software is with You. * +* Should any Covered Software prove defective in any respect, You * +* (not any Contributor) assume the cost of any necessary servicing, * +* repair, or correction. This disclaimer of warranty constitutes an * +* essential part of this License. No use of any Covered Software is * +* authorized under this License except under this disclaimer. * +* * +************************************************************************ + +************************************************************************ +* * +* 7. Limitation of Liability * +* -------------------------- * +* * +* Under no circumstances and under no legal theory, whether tort * +* (including negligence), contract, or otherwise, shall any * +* Contributor, or anyone who distributes Covered Software as * +* permitted above, be liable to You for any direct, indirect, * +* special, incidental, or consequential damages of any character * +* including, without limitation, damages for lost profits, loss of * +* goodwill, work stoppage, computer failure or malfunction, or any * +* and all other commercial damages or losses, even if such party * +* shall have been informed of the possibility of such damages. This * +* limitation of liability shall not apply to liability for death or * +* personal injury resulting from such party's negligence to the * +* extent applicable law prohibits such limitation. Some * +* jurisdictions do not allow the exclusion or limitation of * +* incidental or consequential damages, so this exclusion and * +* limitation may not apply to You. * +* * +************************************************************************ + +8. Litigation +------------- + +Any litigation relating to this License may be brought only in the +courts of a jurisdiction where the defendant maintains its principal +place of business and such litigation shall be governed by laws of that +jurisdiction, without reference to its conflict-of-law provisions. +Nothing in this Section shall prevent a party's ability to bring +cross-claims or counter-claims. + +9. Miscellaneous +---------------- + +This License represents the complete agreement concerning the subject +matter hereof. If any provision of this License is held to be +unenforceable, such provision shall be reformed only to the extent +necessary to make it enforceable. Any law or regulation which provides +that the language of a contract shall be construed against the drafter +shall not be used to construe this License against a Contributor. + +10. Versions of the License +--------------------------- + +10.1. New Versions + +Mozilla Foundation is the license steward. Except as provided in Section +10.3, no one other than the license steward has the right to modify or +publish new versions of this License. Each version will be given a +distinguishing version number. + +10.2. Effect of New Versions + +You may distribute the Covered Software under the terms of the version +of the License under which You originally received the Covered Software, +or under the terms of any subsequent version published by the license +steward. + +10.3. Modified Versions + +If you create software not governed by this License, and you want to +create a new license for such software, you may create and use a +modified version of this License if you rename the license and remove +any references to the name of the license steward (except to note that +such modified license differs from this License). + +10.4. Distributing Source Code Form that is Incompatible With Secondary +Licenses + +If You choose to distribute Source Code Form that is Incompatible With +Secondary Licenses under the terms of this version of the License, the +notice described in Exhibit B of this License must be attached. + +Exhibit A - Source Code Form License Notice +------------------------------------------- + + This Source Code Form is subject to the terms of the Mozilla Public + License, v. 2.0. If a copy of the MPL was not distributed with this + file, You can obtain one at http://mozilla.org/MPL/2.0/. + +If it is not possible or desirable to put the notice in a particular +file, then You may include the notice in a location (such as a LICENSE +file in a relevant directory) where a recipient would be likely to look +for such a notice. + +You may add additional accurate notices of copyright ownership. + +Exhibit B - "Incompatible With Secondary Licenses" Notice +--------------------------------------------------------- + + This Source Code Form is "Incompatible With Secondary Licenses", as + defined by the Mozilla Public License, v. 2.0. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.README b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.README new file mode 100644 index 0000000000000000000000000000000000000000..de5b6321582327d85c88749388edf2576cd242c8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/COPYING.README @@ -0,0 +1,18 @@ +Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links: + http://www.mozilla.org/MPL/2.0/ + http://www.mozilla.org/MPL/2.0/FAQ.html + +Some files contain third-party code under BSD or LGPL licenses, whence the other +COPYING.* files here. + +All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later. +For this reason, the COPYING.LGPL file contains the LGPL 2.1 text. + +If you want to guarantee that the Eigen code that you are #including is licensed +under the MPL2 and possibly more permissive licenses (like BSD), #define this +preprocessor symbol: + EIGEN_MPL2_ONLY +For example, with most compilers, you could add this to your project CXXFLAGS: + -DEIGEN_MPL2_ONLY +This will cause a compilation error to be generated if you #include any code that is +LGPL licensed. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestConfig.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestConfig.cmake new file mode 100644 index 0000000000000000000000000000000000000000..0ea24b8e3447872d8bbb08e574678af7ef4f937f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestConfig.cmake @@ -0,0 +1,17 @@ +## This file should be placed in the root directory of your project. +## Then modify the CMakeLists.txt file in the root directory of your +## project to incorporate the testing dashboard. +## # The following are required to uses Dart and the Cdash dashboard +## enable_testing() +## include(CTest) +set(CTEST_PROJECT_NAME "Eigen") +set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC") + +set(CTEST_DROP_METHOD "http") +set(CTEST_DROP_SITE "my.cdash.org") +set(CTEST_DROP_LOCATION "/submit.php?project=Eigen") +set(CTEST_DROP_SITE_CDASH TRUE) +#set(CTEST_PROJECT_SUBPROJECTS +#Official +#Unsupported +#) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestCustom.cmake.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestCustom.cmake.in new file mode 100644 index 0000000000000000000000000000000000000000..89e487f05a0d19e336302e09747f6b94df43db03 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/CTestCustom.cmake.in @@ -0,0 +1,4 @@ + +set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "2000") +set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "2000") +list(APPEND CTEST_CUSTOM_ERROR_EXCEPTION @EIGEN_CTEST_ERROR_EXCEPTION@) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Cholesky b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Cholesky new file mode 100644 index 0000000000000000000000000000000000000000..a318ceb797dbaa10b2e1185583eb4803d7a83f8f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Cholesky @@ -0,0 +1,45 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CHOLESKY_MODULE_H +#define EIGEN_CHOLESKY_MODULE_H + +#include "Core" +#include "Jacobi" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup Cholesky_Module Cholesky module + * + * + * + * This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices. + * Those decompositions are also accessible via the following methods: + * - MatrixBase::llt() + * - MatrixBase::ldlt() + * - SelfAdjointView::llt() + * - SelfAdjointView::ldlt() + * + * \code + * #include + * \endcode + */ + +#include "src/Cholesky/LLT.h" +#include "src/Cholesky/LDLT.h" +#ifdef EIGEN_USE_LAPACKE +#ifdef EIGEN_USE_MKL +#include "mkl_lapacke.h" +#else +#include "src/misc/lapacke.h" +#endif +#include "src/Cholesky/LLT_LAPACKE.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_CHOLESKY_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/CholmodSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/CholmodSupport new file mode 100644 index 0000000000000000000000000000000000000000..bed8924d31e0b3f46713cf74ba3deb6a63f9f590 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/CholmodSupport @@ -0,0 +1,48 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H +#define EIGEN_CHOLMODSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +extern "C" { + #include +} + +/** \ingroup Support_modules + * \defgroup CholmodSupport_Module CholmodSupport module + * + * This module provides an interface to the Cholmod library which is part of the suitesparse package. + * It provides the two following main factorization classes: + * - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization. + * - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial). + * + * For the sake of completeness, this module also propose the two following classes: + * - class CholmodSimplicialLLT + * - class CholmodSimplicialLDLT + * Note that these classes does not bring any particular advantage compared to the built-in + * SimplicialLLT and SimplicialLDLT factorization classes. + * + * \code + * #include + * \endcode + * + * In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies. + * The dependencies depend on how cholmod has been compiled. + * For a cmake based project, you can use our FindCholmod.cmake module to help you in this task. + * + */ + +#include "src/CholmodSupport/CholmodSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_CHOLMODSUPPORT_MODULE_H + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Core b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Core new file mode 100644 index 0000000000000000000000000000000000000000..3c03519fe92a36883530496e80674c14aa1e40d2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Core @@ -0,0 +1,385 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2007-2011 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CORE_H +#define EIGEN_CORE_H + +// first thing Eigen does: stop the compiler from reporting useless warnings. +#include "src/Core/util/DisableStupidWarnings.h" + +// then include this file where all our macros are defined. It's really important to do it first because +// it's where we do all the compiler/OS/arch detections and define most defaults. +#include "src/Core/util/Macros.h" + +// This detects SSE/AVX/NEON/etc. and configure alignment settings +#include "src/Core/util/ConfigureVectorization.h" + +// We need cuda_runtime.h/hip_runtime.h to ensure that +// the EIGEN_USING_STD macro works properly on the device side +#if defined(EIGEN_CUDACC) + #include +#elif defined(EIGEN_HIPCC) + #include +#endif + + +#ifdef EIGEN_EXCEPTIONS + #include +#endif + +// Disable the ipa-cp-clone optimization flag with MinGW 6.x or newer (enabled by default with -O3) +// See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=556 for details. +#if EIGEN_COMP_MINGW && EIGEN_GNUC_AT_LEAST(4,6) && EIGEN_GNUC_AT_MOST(5,5) + #pragma GCC optimize ("-fno-ipa-cp-clone") +#endif + +// Prevent ICC from specializing std::complex operators that silently fail +// on device. This allows us to use our own device-compatible specializations +// instead. +#if defined(EIGEN_COMP_ICC) && defined(EIGEN_GPU_COMPILE_PHASE) \ + && !defined(_OVERRIDE_COMPLEX_SPECIALIZATION_) +#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1 +#endif +#include + +// this include file manages BLAS and MKL related macros +// and inclusion of their respective header files +#include "src/Core/util/MKL_support.h" + + +#if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16) + #define EIGEN_HAS_GPU_FP16 +#endif + +#if defined(EIGEN_HAS_CUDA_BF16) || defined(EIGEN_HAS_HIP_BF16) + #define EIGEN_HAS_GPU_BF16 +#endif + +#if (defined _OPENMP) && (!defined EIGEN_DONT_PARALLELIZE) + #define EIGEN_HAS_OPENMP +#endif + +#ifdef EIGEN_HAS_OPENMP +#include +#endif + +// MSVC for windows mobile does not have the errno.h file +#if !(EIGEN_COMP_MSVC && EIGEN_OS_WINCE) && !EIGEN_COMP_ARM +#define EIGEN_HAS_ERRNO +#endif + +#ifdef EIGEN_HAS_ERRNO +#include +#endif +#include +#include +#include +#include +#include +#include +#ifndef EIGEN_NO_IO + #include +#endif +#include +#include +#include +#include // for CHAR_BIT +// for min/max: +#include + +#if EIGEN_HAS_CXX11 +#include +#endif + +// for std::is_nothrow_move_assignable +#ifdef EIGEN_INCLUDE_TYPE_TRAITS +#include +#endif + +// for outputting debug info +#ifdef EIGEN_DEBUG_ASSIGN +#include +#endif + +// required for __cpuid, needs to be included after cmath +// also required for _BitScanReverse on Windows on ARM +#if EIGEN_COMP_MSVC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM64) && !EIGEN_OS_WINCE + #include +#endif + +#if defined(EIGEN_USE_SYCL) + #undef min + #undef max + #undef isnan + #undef isinf + #undef isfinite + #include + #include + #include + #include + #include + #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0 + #define EIGEN_SYCL_LOCAL_THREAD_DIM0 16 + #endif + #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM1 + #define EIGEN_SYCL_LOCAL_THREAD_DIM1 16 + #endif +#endif + + +#if defined EIGEN2_SUPPORT_STAGE40_FULL_EIGEN3_STRICTNESS || defined EIGEN2_SUPPORT_STAGE30_FULL_EIGEN3_API || defined EIGEN2_SUPPORT_STAGE20_RESOLVE_API_CONFLICTS || defined EIGEN2_SUPPORT_STAGE10_FULL_EIGEN2_API || defined EIGEN2_SUPPORT +// This will generate an error message: +#error Eigen2-support is only available up to version 3.2. Please go to "http://eigen.tuxfamily.org/index.php?title=Eigen2" for further information +#endif + +namespace Eigen { + +// we use size_t frequently and we'll never remember to prepend it with std:: every time just to +// ensure QNX/QCC support +using std::size_t; +// gcc 4.6.0 wants std:: for ptrdiff_t +using std::ptrdiff_t; + +} + +/** \defgroup Core_Module Core module + * This is the main module of Eigen providing dense matrix and vector support + * (both fixed and dynamic size) with all the features corresponding to a BLAS library + * and much more... + * + * \code + * #include + * \endcode + */ + +#include "src/Core/util/Constants.h" +#include "src/Core/util/Meta.h" +#include "src/Core/util/ForwardDeclarations.h" +#include "src/Core/util/StaticAssert.h" +#include "src/Core/util/XprHelper.h" +#include "src/Core/util/Memory.h" +#include "src/Core/util/IntegralConstant.h" +#include "src/Core/util/SymbolicIndex.h" + +#include "src/Core/NumTraits.h" +#include "src/Core/MathFunctions.h" +#include "src/Core/GenericPacketMath.h" +#include "src/Core/MathFunctionsImpl.h" +#include "src/Core/arch/Default/ConjHelper.h" +// Generic half float support +#include "src/Core/arch/Default/Half.h" +#include "src/Core/arch/Default/BFloat16.h" +#include "src/Core/arch/Default/TypeCasting.h" +#include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h" + +#if defined EIGEN_VECTORIZE_AVX512 + #include "src/Core/arch/SSE/PacketMath.h" + #include "src/Core/arch/SSE/TypeCasting.h" + #include "src/Core/arch/SSE/Complex.h" + #include "src/Core/arch/AVX/PacketMath.h" + #include "src/Core/arch/AVX/TypeCasting.h" + #include "src/Core/arch/AVX/Complex.h" + #include "src/Core/arch/AVX512/PacketMath.h" + #include "src/Core/arch/AVX512/TypeCasting.h" + #include "src/Core/arch/AVX512/Complex.h" + #include "src/Core/arch/SSE/MathFunctions.h" + #include "src/Core/arch/AVX/MathFunctions.h" + #include "src/Core/arch/AVX512/MathFunctions.h" +#elif defined EIGEN_VECTORIZE_AVX + // Use AVX for floats and doubles, SSE for integers + #include "src/Core/arch/SSE/PacketMath.h" + #include "src/Core/arch/SSE/TypeCasting.h" + #include "src/Core/arch/SSE/Complex.h" + #include "src/Core/arch/AVX/PacketMath.h" + #include "src/Core/arch/AVX/TypeCasting.h" + #include "src/Core/arch/AVX/Complex.h" + #include "src/Core/arch/SSE/MathFunctions.h" + #include "src/Core/arch/AVX/MathFunctions.h" +#elif defined EIGEN_VECTORIZE_SSE + #include "src/Core/arch/SSE/PacketMath.h" + #include "src/Core/arch/SSE/TypeCasting.h" + #include "src/Core/arch/SSE/MathFunctions.h" + #include "src/Core/arch/SSE/Complex.h" +#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX) + #include "src/Core/arch/AltiVec/PacketMath.h" + #include "src/Core/arch/AltiVec/MathFunctions.h" + #include "src/Core/arch/AltiVec/Complex.h" +#elif defined EIGEN_VECTORIZE_NEON + #include "src/Core/arch/NEON/PacketMath.h" + #include "src/Core/arch/NEON/TypeCasting.h" + #include "src/Core/arch/NEON/MathFunctions.h" + #include "src/Core/arch/NEON/Complex.h" +#elif defined EIGEN_VECTORIZE_SVE + #include "src/Core/arch/SVE/PacketMath.h" + #include "src/Core/arch/SVE/TypeCasting.h" + #include "src/Core/arch/SVE/MathFunctions.h" +#elif defined EIGEN_VECTORIZE_ZVECTOR + #include "src/Core/arch/ZVector/PacketMath.h" + #include "src/Core/arch/ZVector/MathFunctions.h" + #include "src/Core/arch/ZVector/Complex.h" +#elif defined EIGEN_VECTORIZE_MSA + #include "src/Core/arch/MSA/PacketMath.h" + #include "src/Core/arch/MSA/MathFunctions.h" + #include "src/Core/arch/MSA/Complex.h" +#endif + +#if defined EIGEN_VECTORIZE_GPU + #include "src/Core/arch/GPU/PacketMath.h" + #include "src/Core/arch/GPU/MathFunctions.h" + #include "src/Core/arch/GPU/TypeCasting.h" +#endif + +#if defined(EIGEN_USE_SYCL) + #include "src/Core/arch/SYCL/SyclMemoryModel.h" + #include "src/Core/arch/SYCL/InteropHeaders.h" +#if !defined(EIGEN_DONT_VECTORIZE_SYCL) + #include "src/Core/arch/SYCL/PacketMath.h" + #include "src/Core/arch/SYCL/MathFunctions.h" + #include "src/Core/arch/SYCL/TypeCasting.h" +#endif +#endif + +#include "src/Core/arch/Default/Settings.h" +// This file provides generic implementations valid for scalar as well +#include "src/Core/arch/Default/GenericPacketMathFunctions.h" + +#include "src/Core/functors/TernaryFunctors.h" +#include "src/Core/functors/BinaryFunctors.h" +#include "src/Core/functors/UnaryFunctors.h" +#include "src/Core/functors/NullaryFunctors.h" +#include "src/Core/functors/StlFunctors.h" +#include "src/Core/functors/AssignmentFunctors.h" + +// Specialized functors to enable the processing of complex numbers +// on CUDA devices +#ifdef EIGEN_CUDACC +#include "src/Core/arch/CUDA/Complex.h" +#endif + +#include "src/Core/util/IndexedViewHelper.h" +#include "src/Core/util/ReshapedHelper.h" +#include "src/Core/ArithmeticSequence.h" +#ifndef EIGEN_NO_IO + #include "src/Core/IO.h" +#endif +#include "src/Core/DenseCoeffsBase.h" +#include "src/Core/DenseBase.h" +#include "src/Core/MatrixBase.h" +#include "src/Core/EigenBase.h" + +#include "src/Core/Product.h" +#include "src/Core/CoreEvaluators.h" +#include "src/Core/AssignEvaluator.h" + +#ifndef EIGEN_PARSED_BY_DOXYGEN // work around Doxygen bug triggered by Assign.h r814874 + // at least confirmed with Doxygen 1.5.5 and 1.5.6 + #include "src/Core/Assign.h" +#endif + +#include "src/Core/ArrayBase.h" +#include "src/Core/util/BlasUtil.h" +#include "src/Core/DenseStorage.h" +#include "src/Core/NestByValue.h" + +// #include "src/Core/ForceAlignedAccess.h" + +#include "src/Core/ReturnByValue.h" +#include "src/Core/NoAlias.h" +#include "src/Core/PlainObjectBase.h" +#include "src/Core/Matrix.h" +#include "src/Core/Array.h" +#include "src/Core/CwiseTernaryOp.h" +#include "src/Core/CwiseBinaryOp.h" +#include "src/Core/CwiseUnaryOp.h" +#include "src/Core/CwiseNullaryOp.h" +#include "src/Core/CwiseUnaryView.h" +#include "src/Core/SelfCwiseBinaryOp.h" +#include "src/Core/Dot.h" +#include "src/Core/StableNorm.h" +#include "src/Core/Stride.h" +#include "src/Core/MapBase.h" +#include "src/Core/Map.h" +#include "src/Core/Ref.h" +#include "src/Core/Block.h" +#include "src/Core/VectorBlock.h" +#include "src/Core/IndexedView.h" +#include "src/Core/Reshaped.h" +#include "src/Core/Transpose.h" +#include "src/Core/DiagonalMatrix.h" +#include "src/Core/Diagonal.h" +#include "src/Core/DiagonalProduct.h" +#include "src/Core/Redux.h" +#include "src/Core/Visitor.h" +#include "src/Core/Fuzzy.h" +#include "src/Core/Swap.h" +#include "src/Core/CommaInitializer.h" +#include "src/Core/GeneralProduct.h" +#include "src/Core/Solve.h" +#include "src/Core/Inverse.h" +#include "src/Core/SolverBase.h" +#include "src/Core/PermutationMatrix.h" +#include "src/Core/Transpositions.h" +#include "src/Core/TriangularMatrix.h" +#include "src/Core/SelfAdjointView.h" +#include "src/Core/products/GeneralBlockPanelKernel.h" +#include "src/Core/products/Parallelizer.h" +#include "src/Core/ProductEvaluators.h" +#include "src/Core/products/GeneralMatrixVector.h" +#include "src/Core/products/GeneralMatrixMatrix.h" +#include "src/Core/SolveTriangular.h" +#include "src/Core/products/GeneralMatrixMatrixTriangular.h" +#include "src/Core/products/SelfadjointMatrixVector.h" +#include "src/Core/products/SelfadjointMatrixMatrix.h" +#include "src/Core/products/SelfadjointProduct.h" +#include "src/Core/products/SelfadjointRank2Update.h" +#include "src/Core/products/TriangularMatrixVector.h" +#include "src/Core/products/TriangularMatrixMatrix.h" +#include "src/Core/products/TriangularSolverMatrix.h" +#include "src/Core/products/TriangularSolverVector.h" +#include "src/Core/BandMatrix.h" +#include "src/Core/CoreIterators.h" +#include "src/Core/ConditionEstimator.h" + +#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX) + #include "src/Core/arch/AltiVec/MatrixProduct.h" +#elif defined EIGEN_VECTORIZE_NEON + #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h" +#endif + +#include "src/Core/BooleanRedux.h" +#include "src/Core/Select.h" +#include "src/Core/VectorwiseOp.h" +#include "src/Core/PartialReduxEvaluator.h" +#include "src/Core/Random.h" +#include "src/Core/Replicate.h" +#include "src/Core/Reverse.h" +#include "src/Core/ArrayWrapper.h" +#include "src/Core/StlIterators.h" + +#ifdef EIGEN_USE_BLAS +#include "src/Core/products/GeneralMatrixMatrix_BLAS.h" +#include "src/Core/products/GeneralMatrixVector_BLAS.h" +#include "src/Core/products/GeneralMatrixMatrixTriangular_BLAS.h" +#include "src/Core/products/SelfadjointMatrixMatrix_BLAS.h" +#include "src/Core/products/SelfadjointMatrixVector_BLAS.h" +#include "src/Core/products/TriangularMatrixMatrix_BLAS.h" +#include "src/Core/products/TriangularMatrixVector_BLAS.h" +#include "src/Core/products/TriangularSolverMatrix_BLAS.h" +#endif // EIGEN_USE_BLAS + +#ifdef EIGEN_USE_MKL_VML +#include "src/Core/Assign_MKL.h" +#endif + +#include "src/Core/GlobalFunctions.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_CORE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Dense b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Dense new file mode 100644 index 0000000000000000000000000000000000000000..5768910bd88c43f0761f2f345c6f0e3b46a4d8ec --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Dense @@ -0,0 +1,7 @@ +#include "Core" +#include "LU" +#include "Cholesky" +#include "QR" +#include "SVD" +#include "Geometry" +#include "Eigenvalues" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigen b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigen new file mode 100644 index 0000000000000000000000000000000000000000..654c8dc6380f7bb21d3ba1a9ce916006043552aa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigen @@ -0,0 +1,2 @@ +#include "Dense" +#include "Sparse" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigenvalues b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigenvalues new file mode 100644 index 0000000000000000000000000000000000000000..5467a2e7b3ecf40c3e544bb29717a66c83f7eaa1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Eigenvalues @@ -0,0 +1,60 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_EIGENVALUES_MODULE_H +#define EIGEN_EIGENVALUES_MODULE_H + +#include "Core" + +#include "Cholesky" +#include "Jacobi" +#include "Householder" +#include "LU" +#include "Geometry" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup Eigenvalues_Module Eigenvalues module + * + * + * + * This module mainly provides various eigenvalue solvers. + * This module also provides some MatrixBase methods, including: + * - MatrixBase::eigenvalues(), + * - MatrixBase::operatorNorm() + * + * \code + * #include + * \endcode + */ + +#include "src/misc/RealSvd2x2.h" +#include "src/Eigenvalues/Tridiagonalization.h" +#include "src/Eigenvalues/RealSchur.h" +#include "src/Eigenvalues/EigenSolver.h" +#include "src/Eigenvalues/SelfAdjointEigenSolver.h" +#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h" +#include "src/Eigenvalues/HessenbergDecomposition.h" +#include "src/Eigenvalues/ComplexSchur.h" +#include "src/Eigenvalues/ComplexEigenSolver.h" +#include "src/Eigenvalues/RealQZ.h" +#include "src/Eigenvalues/GeneralizedEigenSolver.h" +#include "src/Eigenvalues/MatrixBaseEigenvalues.h" +#ifdef EIGEN_USE_LAPACKE +#ifdef EIGEN_USE_MKL +#include "mkl_lapacke.h" +#else +#include "src/misc/lapacke.h" +#endif +#include "src/Eigenvalues/RealSchur_LAPACKE.h" +#include "src/Eigenvalues/ComplexSchur_LAPACKE.h" +#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_EIGENVALUES_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Geometry b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Geometry new file mode 100644 index 0000000000000000000000000000000000000000..bc78110a846693fa45caa0780cf29d7285695f08 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Geometry @@ -0,0 +1,59 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_GEOMETRY_MODULE_H +#define EIGEN_GEOMETRY_MODULE_H + +#include "Core" + +#include "SVD" +#include "LU" +#include + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup Geometry_Module Geometry module + * + * This module provides support for: + * - fixed-size homogeneous transformations + * - translation, scaling, 2D and 3D rotations + * - \link Quaternion quaternions \endlink + * - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3) + * - orthognal vector generation (\ref MatrixBase::unitOrthogonal) + * - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink + * - \link AlignedBox axis aligned bounding boxes \endlink + * - \link umeyama least-square transformation fitting \endlink + * + * \code + * #include + * \endcode + */ + +#include "src/Geometry/OrthoMethods.h" +#include "src/Geometry/EulerAngles.h" + +#include "src/Geometry/Homogeneous.h" +#include "src/Geometry/RotationBase.h" +#include "src/Geometry/Rotation2D.h" +#include "src/Geometry/Quaternion.h" +#include "src/Geometry/AngleAxis.h" +#include "src/Geometry/Transform.h" +#include "src/Geometry/Translation.h" +#include "src/Geometry/Scaling.h" +#include "src/Geometry/Hyperplane.h" +#include "src/Geometry/ParametrizedLine.h" +#include "src/Geometry/AlignedBox.h" +#include "src/Geometry/Umeyama.h" + +// Use the SSE optimized version whenever possible. +#if (defined EIGEN_VECTORIZE_SSE) || (defined EIGEN_VECTORIZE_NEON) +#include "src/Geometry/arch/Geometry_SIMD.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_GEOMETRY_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Householder b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Householder new file mode 100644 index 0000000000000000000000000000000000000000..f2fa79969c96339bd317d157a37c72ec71b4024b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Householder @@ -0,0 +1,29 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_HOUSEHOLDER_MODULE_H +#define EIGEN_HOUSEHOLDER_MODULE_H + +#include "Core" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup Householder_Module Householder module + * This module provides Householder transformations. + * + * \code + * #include + * \endcode + */ + +#include "src/Householder/Householder.h" +#include "src/Householder/HouseholderSequence.h" +#include "src/Householder/BlockHouseholder.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_HOUSEHOLDER_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/IterativeLinearSolvers b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/IterativeLinearSolvers new file mode 100644 index 0000000000000000000000000000000000000000..957d5750b2cd6f9a429c7140335487a4d8b87b25 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/IterativeLinearSolvers @@ -0,0 +1,48 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H +#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H + +#include "SparseCore" +#include "OrderingMethods" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** + * \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module + * + * This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse. + * Those solvers are accessible via the following classes: + * - ConjugateGradient for selfadjoint (hermitian) matrices, + * - LeastSquaresConjugateGradient for rectangular least-square problems, + * - BiCGSTAB for general square matrices. + * + * These iterative solvers are associated with some preconditioners: + * - IdentityPreconditioner - not really useful + * - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices. + * - IncompleteLUT - incomplete LU factorization with dual thresholding + * + * Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport. + * + \code + #include + \endcode + */ + +#include "src/IterativeLinearSolvers/SolveWithGuess.h" +#include "src/IterativeLinearSolvers/IterativeSolverBase.h" +#include "src/IterativeLinearSolvers/BasicPreconditioners.h" +#include "src/IterativeLinearSolvers/ConjugateGradient.h" +#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h" +#include "src/IterativeLinearSolvers/BiCGSTAB.h" +#include "src/IterativeLinearSolvers/IncompleteLUT.h" +#include "src/IterativeLinearSolvers/IncompleteCholesky.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Jacobi b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Jacobi new file mode 100644 index 0000000000000000000000000000000000000000..43edc7a1946edaa8c30c8715c50ebcf8d817fa3a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Jacobi @@ -0,0 +1,32 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_JACOBI_MODULE_H +#define EIGEN_JACOBI_MODULE_H + +#include "Core" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup Jacobi_Module Jacobi module + * This module provides Jacobi and Givens rotations. + * + * \code + * #include + * \endcode + * + * In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation: + * - MatrixBase::applyOnTheLeft() + * - MatrixBase::applyOnTheRight(). + */ + +#include "src/Jacobi/Jacobi.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_JACOBI_MODULE_H + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/KLUSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/KLUSupport new file mode 100644 index 0000000000000000000000000000000000000000..b23d905351566cb425a803cba5868ea43338f9a6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/KLUSupport @@ -0,0 +1,41 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_KLUSUPPORT_MODULE_H +#define EIGEN_KLUSUPPORT_MODULE_H + +#include + +#include + +extern "C" { +#include +#include + } + +/** \ingroup Support_modules + * \defgroup KLUSupport_Module KLUSupport module + * + * This module provides an interface to the KLU library which is part of the suitesparse package. + * It provides the following factorization class: + * - class KLU: a sparse LU factorization, well-suited for circuit simulation. + * + * \code + * #include + * \endcode + * + * In order to use this module, the klu and btf headers must be accessible from the include paths, and your binary must be linked to the klu library and its dependencies. + * The dependencies depend on how umfpack has been compiled. + * For a cmake based project, you can use our FindKLU.cmake module to help you in this task. + * + */ + +#include "src/KLUSupport/KLUSupport.h" + +#include + +#endif // EIGEN_KLUSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/LU b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/LU new file mode 100644 index 0000000000000000000000000000000000000000..1236ceb04676f5e180b589f8ca70c3d9362710cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/LU @@ -0,0 +1,47 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_LU_MODULE_H +#define EIGEN_LU_MODULE_H + +#include "Core" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup LU_Module LU module + * This module includes %LU decomposition and related notions such as matrix inversion and determinant. + * This module defines the following MatrixBase methods: + * - MatrixBase::inverse() + * - MatrixBase::determinant() + * + * \code + * #include + * \endcode + */ + +#include "src/misc/Kernel.h" +#include "src/misc/Image.h" +#include "src/LU/FullPivLU.h" +#include "src/LU/PartialPivLU.h" +#ifdef EIGEN_USE_LAPACKE +#ifdef EIGEN_USE_MKL +#include "mkl_lapacke.h" +#else +#include "src/misc/lapacke.h" +#endif +#include "src/LU/PartialPivLU_LAPACKE.h" +#endif +#include "src/LU/Determinant.h" +#include "src/LU/InverseImpl.h" + +#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_NEON + #include "src/LU/arch/InverseSize4.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_LU_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/MetisSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/MetisSupport new file mode 100644 index 0000000000000000000000000000000000000000..85c41bf340013e4583e505c496dfb567dc6ae80a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/MetisSupport @@ -0,0 +1,35 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_METISSUPPORT_MODULE_H +#define EIGEN_METISSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +extern "C" { +#include +} + + +/** \ingroup Support_modules + * \defgroup MetisSupport_Module MetisSupport module + * + * \code + * #include + * \endcode + * This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis). + * It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink + */ + + +#include "src/MetisSupport/MetisSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_METISSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/OrderingMethods b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/OrderingMethods new file mode 100644 index 0000000000000000000000000000000000000000..29691a62b44d4956a660a677233c7bce3fd05dce --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/OrderingMethods @@ -0,0 +1,70 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ORDERINGMETHODS_MODULE_H +#define EIGEN_ORDERINGMETHODS_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** + * \defgroup OrderingMethods_Module OrderingMethods module + * + * This module is currently for internal use only + * + * It defines various built-in and external ordering methods for sparse matrices. + * They are typically used to reduce the number of elements during + * the sparse matrix decomposition (LLT, LU, QR). + * Precisely, in a preprocessing step, a permutation matrix P is computed using + * those ordering methods and applied to the columns of the matrix. + * Using for instance the sparse Cholesky decomposition, it is expected that + * the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A). + * + * + * Usage : + * \code + * #include + * \endcode + * + * A simple usage is as a template parameter in the sparse decomposition classes : + * + * \code + * SparseLU > solver; + * \endcode + * + * \code + * SparseQR > solver; + * \endcode + * + * It is possible as well to call directly a particular ordering method for your own purpose, + * \code + * AMDOrdering ordering; + * PermutationMatrix perm; + * SparseMatrix A; + * //Fill the matrix ... + * + * ordering(A, perm); // Call AMD + * \endcode + * + * \note Some of these methods (like AMD or METIS), need the sparsity pattern + * of the input matrix to be symmetric. When the matrix is structurally unsymmetric, + * Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method. + * If your matrix is already symmetric (at leat in structure), you can avoid that + * by calling the method with a SelfAdjointView type. + * + * \code + * // Call the ordering on the pattern of the lower triangular matrix A + * ordering(A.selfadjointView(), perm); + * \endcode + */ + +#include "src/OrderingMethods/Amd.h" +#include "src/OrderingMethods/Ordering.h" +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_ORDERINGMETHODS_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PaStiXSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PaStiXSupport new file mode 100644 index 0000000000000000000000000000000000000000..234619accee0e875a418eda983f870b25255c17e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PaStiXSupport @@ -0,0 +1,49 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_PASTIXSUPPORT_MODULE_H +#define EIGEN_PASTIXSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +extern "C" { +#include +#include +} + +#ifdef complex +#undef complex +#endif + +/** \ingroup Support_modules + * \defgroup PaStiXSupport_Module PaStiXSupport module + * + * This module provides an interface to the PaSTiX library. + * PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver. + * It provides the two following main factorization classes: + * - class PastixLLT : a supernodal, parallel LLt Cholesky factorization. + * - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization. + * - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern). + * + * \code + * #include + * \endcode + * + * In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies. + * This wrapper resuires PaStiX version 5.x compiled without MPI support. + * The dependencies depend on how PaSTiX has been compiled. + * For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task. + * + */ + +#include "src/PaStiXSupport/PaStiXSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_PASTIXSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PardisoSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PardisoSupport new file mode 100644 index 0000000000000000000000000000000000000000..340edf51fe2d678294bef93f4cc413a95af0075d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/PardisoSupport @@ -0,0 +1,35 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_PARDISOSUPPORT_MODULE_H +#define EIGEN_PARDISOSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +#include + +/** \ingroup Support_modules + * \defgroup PardisoSupport_Module PardisoSupport module + * + * This module brings support for the Intel(R) MKL PARDISO direct sparse solvers. + * + * \code + * #include + * \endcode + * + * In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies. + * See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration. + * + */ + +#include "src/PardisoSupport/PardisoSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_PARDISOSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QR b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QR new file mode 100644 index 0000000000000000000000000000000000000000..8465b62ceee1aadf915660451142fa2d800db550 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QR @@ -0,0 +1,50 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_QR_MODULE_H +#define EIGEN_QR_MODULE_H + +#include "Core" + +#include "Cholesky" +#include "Jacobi" +#include "Householder" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup QR_Module QR module + * + * + * + * This module provides various QR decompositions + * This module also provides some MatrixBase methods, including: + * - MatrixBase::householderQr() + * - MatrixBase::colPivHouseholderQr() + * - MatrixBase::fullPivHouseholderQr() + * + * \code + * #include + * \endcode + */ + +#include "src/QR/HouseholderQR.h" +#include "src/QR/FullPivHouseholderQR.h" +#include "src/QR/ColPivHouseholderQR.h" +#include "src/QR/CompleteOrthogonalDecomposition.h" +#ifdef EIGEN_USE_LAPACKE +#ifdef EIGEN_USE_MKL +#include "mkl_lapacke.h" +#else +#include "src/misc/lapacke.h" +#endif +#include "src/QR/HouseholderQR_LAPACKE.h" +#include "src/QR/ColPivHouseholderQR_LAPACKE.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_QR_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QtAlignedMalloc b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QtAlignedMalloc new file mode 100644 index 0000000000000000000000000000000000000000..6fe82374a5ebdb0dbc17fa6e0119b1a399f126e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/QtAlignedMalloc @@ -0,0 +1,39 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_QTMALLOC_MODULE_H +#define EIGEN_QTMALLOC_MODULE_H + +#include "Core" + +#if (!EIGEN_MALLOC_ALREADY_ALIGNED) + +#include "src/Core/util/DisableStupidWarnings.h" + +void *qMalloc(std::size_t size) +{ + return Eigen::internal::aligned_malloc(size); +} + +void qFree(void *ptr) +{ + Eigen::internal::aligned_free(ptr); +} + +void *qRealloc(void *ptr, std::size_t size) +{ + void* newPtr = Eigen::internal::aligned_malloc(size); + std::memcpy(newPtr, ptr, size); + Eigen::internal::aligned_free(ptr); + return newPtr; +} + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif + +#endif // EIGEN_QTMALLOC_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SPQRSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SPQRSupport new file mode 100644 index 0000000000000000000000000000000000000000..f70390c17661f10d87eafd69784af67368247dae --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SPQRSupport @@ -0,0 +1,34 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPQRSUPPORT_MODULE_H +#define EIGEN_SPQRSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +#include "SuiteSparseQR.hpp" + +/** \ingroup Support_modules + * \defgroup SPQRSupport_Module SuiteSparseQR module + * + * This module provides an interface to the SPQR library, which is part of the suitesparse package. + * + * \code + * #include + * \endcode + * + * In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...). + * For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules + * + */ + +#include "src/CholmodSupport/CholmodSupport.h" +#include "src/SPQRSupport/SuiteSparseQRSupport.h" + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SVD b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SVD new file mode 100644 index 0000000000000000000000000000000000000000..34517949632099aea944db49f84c4eb8f630ac5c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SVD @@ -0,0 +1,50 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SVD_MODULE_H +#define EIGEN_SVD_MODULE_H + +#include "QR" +#include "Householder" +#include "Jacobi" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup SVD_Module SVD module + * + * + * + * This module provides SVD decomposition for matrices (both real and complex). + * Two decomposition algorithms are provided: + * - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones. + * - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems. + * These decompositions are accessible via the respective classes and following MatrixBase methods: + * - MatrixBase::jacobiSvd() + * - MatrixBase::bdcSvd() + * + * \code + * #include + * \endcode + */ + +#include "src/misc/RealSvd2x2.h" +#include "src/SVD/UpperBidiagonalization.h" +#include "src/SVD/SVDBase.h" +#include "src/SVD/JacobiSVD.h" +#include "src/SVD/BDCSVD.h" +#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT) +#ifdef EIGEN_USE_MKL +#include "mkl_lapacke.h" +#else +#include "src/misc/lapacke.h" +#endif +#include "src/SVD/JacobiSVD_LAPACKE.h" +#endif + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SVD_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Sparse b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Sparse new file mode 100644 index 0000000000000000000000000000000000000000..a2ef7a66526812617c782f76dea260f04593ea58 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/Sparse @@ -0,0 +1,34 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSE_MODULE_H +#define EIGEN_SPARSE_MODULE_H + +/** \defgroup Sparse_Module Sparse meta-module + * + * Meta-module including all related modules: + * - \ref SparseCore_Module + * - \ref OrderingMethods_Module + * - \ref SparseCholesky_Module + * - \ref SparseLU_Module + * - \ref SparseQR_Module + * - \ref IterativeLinearSolvers_Module + * + \code + #include + \endcode + */ + +#include "SparseCore" +#include "OrderingMethods" +#include "SparseCholesky" +#include "SparseLU" +#include "SparseQR" +#include "IterativeLinearSolvers" + +#endif // EIGEN_SPARSE_MODULE_H + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCholesky b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCholesky new file mode 100644 index 0000000000000000000000000000000000000000..d2b1f1276da5192664ba0ba39bbb9a00c18dc225 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCholesky @@ -0,0 +1,37 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2013 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSECHOLESKY_MODULE_H +#define EIGEN_SPARSECHOLESKY_MODULE_H + +#include "SparseCore" +#include "OrderingMethods" + +#include "src/Core/util/DisableStupidWarnings.h" + +/** + * \defgroup SparseCholesky_Module SparseCholesky module + * + * This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices. + * Those decompositions are accessible via the following classes: + * - SimplicialLLt, + * - SimplicialLDLt + * + * Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module. + * + * \code + * #include + * \endcode + */ + +#include "src/SparseCholesky/SimplicialCholesky.h" +#include "src/SparseCholesky/SimplicialCholesky_impl.h" +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SPARSECHOLESKY_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCore b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCore new file mode 100644 index 0000000000000000000000000000000000000000..76966c4c4cb12da2ad59e0fdd7672b052baab6e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseCore @@ -0,0 +1,69 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSECORE_MODULE_H +#define EIGEN_SPARSECORE_MODULE_H + +#include "Core" + +#include "src/Core/util/DisableStupidWarnings.h" + +#include +#include +#include +#include +#include + +/** + * \defgroup SparseCore_Module SparseCore module + * + * This module provides a sparse matrix representation, and basic associated matrix manipulations + * and operations. + * + * See the \ref TutorialSparse "Sparse tutorial" + * + * \code + * #include + * \endcode + * + * This module depends on: Core. + */ + +#include "src/SparseCore/SparseUtil.h" +#include "src/SparseCore/SparseMatrixBase.h" +#include "src/SparseCore/SparseAssign.h" +#include "src/SparseCore/CompressedStorage.h" +#include "src/SparseCore/AmbiVector.h" +#include "src/SparseCore/SparseCompressedBase.h" +#include "src/SparseCore/SparseMatrix.h" +#include "src/SparseCore/SparseMap.h" +#include "src/SparseCore/MappedSparseMatrix.h" +#include "src/SparseCore/SparseVector.h" +#include "src/SparseCore/SparseRef.h" +#include "src/SparseCore/SparseCwiseUnaryOp.h" +#include "src/SparseCore/SparseCwiseBinaryOp.h" +#include "src/SparseCore/SparseTranspose.h" +#include "src/SparseCore/SparseBlock.h" +#include "src/SparseCore/SparseDot.h" +#include "src/SparseCore/SparseRedux.h" +#include "src/SparseCore/SparseView.h" +#include "src/SparseCore/SparseDiagonalProduct.h" +#include "src/SparseCore/ConservativeSparseSparseProduct.h" +#include "src/SparseCore/SparseSparseProductWithPruning.h" +#include "src/SparseCore/SparseProduct.h" +#include "src/SparseCore/SparseDenseProduct.h" +#include "src/SparseCore/SparseSelfAdjointView.h" +#include "src/SparseCore/SparseTriangularView.h" +#include "src/SparseCore/TriangularSolver.h" +#include "src/SparseCore/SparsePermutation.h" +#include "src/SparseCore/SparseFuzzy.h" +#include "src/SparseCore/SparseSolverBase.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SPARSECORE_MODULE_H + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseLU b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseLU new file mode 100644 index 0000000000000000000000000000000000000000..37c4a5c5a8b305add93e2aae0eb7eac624f3ce68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseLU @@ -0,0 +1,50 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSELU_MODULE_H +#define EIGEN_SPARSELU_MODULE_H + +#include "SparseCore" + +/** + * \defgroup SparseLU_Module SparseLU module + * This module defines a supernodal factorization of general sparse matrices. + * The code is fully optimized for supernode-panel updates with specialized kernels. + * Please, see the documentation of the SparseLU class for more details. + */ + +// Ordering interface +#include "OrderingMethods" + +#include "src/Core/util/DisableStupidWarnings.h" + +#include "src/SparseLU/SparseLU_gemm_kernel.h" + +#include "src/SparseLU/SparseLU_Structs.h" +#include "src/SparseLU/SparseLU_SupernodalMatrix.h" +#include "src/SparseLU/SparseLUImpl.h" +#include "src/SparseCore/SparseColEtree.h" +#include "src/SparseLU/SparseLU_Memory.h" +#include "src/SparseLU/SparseLU_heap_relax_snode.h" +#include "src/SparseLU/SparseLU_relax_snode.h" +#include "src/SparseLU/SparseLU_pivotL.h" +#include "src/SparseLU/SparseLU_panel_dfs.h" +#include "src/SparseLU/SparseLU_kernel_bmod.h" +#include "src/SparseLU/SparseLU_panel_bmod.h" +#include "src/SparseLU/SparseLU_column_dfs.h" +#include "src/SparseLU/SparseLU_column_bmod.h" +#include "src/SparseLU/SparseLU_copy_to_ucol.h" +#include "src/SparseLU/SparseLU_pruneL.h" +#include "src/SparseLU/SparseLU_Utils.h" +#include "src/SparseLU/SparseLU.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SPARSELU_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseQR b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseQR new file mode 100644 index 0000000000000000000000000000000000000000..f5fc5fa7feea7350788513081232d764ed32541b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SparseQR @@ -0,0 +1,36 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSEQR_MODULE_H +#define EIGEN_SPARSEQR_MODULE_H + +#include "SparseCore" +#include "OrderingMethods" +#include "src/Core/util/DisableStupidWarnings.h" + +/** \defgroup SparseQR_Module SparseQR module + * \brief Provides QR decomposition for sparse matrices + * + * This module provides a simplicial version of the left-looking Sparse QR decomposition. + * The columns of the input matrix should be reordered to limit the fill-in during the + * decomposition. Built-in methods (COLAMD, AMD) or external methods (METIS) can be used to this end. + * See the \link OrderingMethods_Module OrderingMethods\endlink module for the list + * of built-in and external ordering methods. + * + * \code + * #include + * \endcode + * + * + */ + +#include "src/SparseCore/SparseColEtree.h" +#include "src/SparseQR/SparseQR.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdDeque b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdDeque new file mode 100644 index 0000000000000000000000000000000000000000..bc68397be259fa9666c2a59f4bdb1b9dd8ab0ce6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdDeque @@ -0,0 +1,27 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// Copyright (C) 2009 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_STDDEQUE_MODULE_H +#define EIGEN_STDDEQUE_MODULE_H + +#include "Core" +#include + +#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */ + +#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...) + +#else + +#include "src/StlSupport/StdDeque.h" + +#endif + +#endif // EIGEN_STDDEQUE_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdList b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdList new file mode 100644 index 0000000000000000000000000000000000000000..4c6262c08cc26bcc70d4e21e83027b9533a7e36c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdList @@ -0,0 +1,26 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_STDLIST_MODULE_H +#define EIGEN_STDLIST_MODULE_H + +#include "Core" +#include + +#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */ + +#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...) + +#else + +#include "src/StlSupport/StdList.h" + +#endif + +#endif // EIGEN_STDLIST_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdVector b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdVector new file mode 100644 index 0000000000000000000000000000000000000000..0c4697ad5bed5868d793ba7d94bb9dc3fb9bed4c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/StdVector @@ -0,0 +1,27 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// Copyright (C) 2009 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_STDVECTOR_MODULE_H +#define EIGEN_STDVECTOR_MODULE_H + +#include "Core" +#include + +#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */ + +#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...) + +#else + +#include "src/StlSupport/StdVector.h" + +#endif + +#endif // EIGEN_STDVECTOR_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SuperLUSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SuperLUSupport new file mode 100644 index 0000000000000000000000000000000000000000..59312a82db0703389e21ae6e1b703b261802eadf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/SuperLUSupport @@ -0,0 +1,64 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H +#define EIGEN_SUPERLUSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +#ifdef EMPTY +#define EIGEN_EMPTY_WAS_ALREADY_DEFINED +#endif + +typedef int int_t; +#include +#include +#include + +// slu_util.h defines a preprocessor token named EMPTY which is really polluting, +// so we remove it in favor of a SUPERLU_EMPTY token. +// If EMPTY was already defined then we don't undef it. + +#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED) +# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED +#elif defined(EMPTY) +# undef EMPTY +#endif + +#define SUPERLU_EMPTY (-1) + +namespace Eigen { struct SluMatrix; } + +/** \ingroup Support_modules + * \defgroup SuperLUSupport_Module SuperLUSupport module + * + * This module provides an interface to the SuperLU library. + * It provides the following factorization class: + * - class SuperLU: a supernodal sequential LU factorization. + * - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods). + * + * \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported. + * + * \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting. + * + * \code + * #include + * \endcode + * + * In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies. + * The dependencies depend on how superlu has been compiled. + * For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task. + * + */ + +#include "src/SuperLUSupport/SuperLUSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SUPERLUSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/UmfPackSupport b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/UmfPackSupport new file mode 100644 index 0000000000000000000000000000000000000000..00eec80875fcb209de0f6f746d0f4d299cd2ce8e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/UmfPackSupport @@ -0,0 +1,40 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H +#define EIGEN_UMFPACKSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +extern "C" { +#include +} + +/** \ingroup Support_modules + * \defgroup UmfPackSupport_Module UmfPackSupport module + * + * This module provides an interface to the UmfPack library which is part of the suitesparse package. + * It provides the following factorization class: + * - class UmfPackLU: a multifrontal sequential LU factorization. + * + * \code + * #include + * \endcode + * + * In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies. + * The dependencies depend on how umfpack has been compiled. + * For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task. + * + */ + +#include "src/UmfPackSupport/UmfPackSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_UMFPACKSUPPORT_MODULE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LDLT.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LDLT.h new file mode 100644 index 0000000000000000000000000000000000000000..1dffbb6f6169b31c6bf4d9888251380d4e92774f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LDLT.h @@ -0,0 +1,688 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2011 Gael Guennebaud +// Copyright (C) 2009 Keir Mierle +// Copyright (C) 2009 Benoit Jacob +// Copyright (C) 2011 Timothy E. Holy +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_LDLT_H +#define EIGEN_LDLT_H + +namespace Eigen { + +namespace internal { + template struct traits > + : traits + { + typedef MatrixXpr XprKind; + typedef SolverStorage StorageKind; + typedef int StorageIndex; + enum { Flags = 0 }; + }; + + template struct LDLT_Traits; + + // PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef + enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite }; +} + +/** \ingroup Cholesky_Module + * + * \class LDLT + * + * \brief Robust Cholesky decomposition of a matrix with pivoting + * + * \tparam MatrixType_ the type of the matrix of which to compute the LDL^T Cholesky decomposition + * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper. + * The other triangular part won't be read. + * + * Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite + * matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L + * is lower triangular with a unit diagonal and D is a diagonal matrix. + * + * The decomposition uses pivoting to ensure stability, so that D will have + * zeros in the bottom right rank(A) - n submatrix. Avoiding the square root + * on D also stabilizes the computation. + * + * Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky + * decomposition to determine whether a system of equations has a solution. + * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * + * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT + */ +template class LDLT + : public SolverBase > +{ + public: + typedef MatrixType_ MatrixType; + typedef SolverBase Base; + friend class SolverBase; + + EIGEN_GENERIC_PUBLIC_INTERFACE(LDLT) + enum { + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + UpLo = UpLo_ + }; + typedef Matrix TmpMatrixType; + + typedef Transpositions TranspositionType; + typedef PermutationMatrix PermutationType; + + typedef internal::LDLT_Traits Traits; + + /** \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via LDLT::compute(const MatrixType&). + */ + LDLT() + : m_matrix(), + m_transpositions(), + m_sign(internal::ZeroSign), + m_isInitialized(false) + {} + + /** \brief Default Constructor with memory preallocation + * + * Like the default constructor but with preallocation of the internal data + * according to the specified problem \a size. + * \sa LDLT() + */ + explicit LDLT(Index size) + : m_matrix(size, size), + m_transpositions(size), + m_temporary(size), + m_sign(internal::ZeroSign), + m_isInitialized(false) + {} + + /** \brief Constructor with decomposition + * + * This calculates the decomposition for the input \a matrix. + * + * \sa LDLT(Index size) + */ + template + explicit LDLT(const EigenBase& matrix) + : m_matrix(matrix.rows(), matrix.cols()), + m_transpositions(matrix.rows()), + m_temporary(matrix.rows()), + m_sign(internal::ZeroSign), + m_isInitialized(false) + { + compute(matrix.derived()); + } + + /** \brief Constructs a LDLT factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. + * + * \sa LDLT(const EigenBase&) + */ + template + explicit LDLT(EigenBase& matrix) + : m_matrix(matrix.derived()), + m_transpositions(matrix.rows()), + m_temporary(matrix.rows()), + m_sign(internal::ZeroSign), + m_isInitialized(false) + { + compute(matrix.derived()); + } + + /** Clear any existing decomposition + * \sa rankUpdate(w,sigma) + */ + void setZero() + { + m_isInitialized = false; + } + + /** \returns a view of the upper triangular matrix U */ + inline typename Traits::MatrixU matrixU() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return Traits::getU(m_matrix); + } + + /** \returns a view of the lower triangular matrix L */ + inline typename Traits::MatrixL matrixL() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return Traits::getL(m_matrix); + } + + /** \returns the permutation matrix P as a transposition sequence. + */ + inline const TranspositionType& transpositionsP() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_transpositions; + } + + /** \returns the coefficients of the diagonal matrix D */ + inline Diagonal vectorD() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_matrix.diagonal(); + } + + /** \returns true if the matrix is positive (semidefinite) */ + inline bool isPositive() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign; + } + + /** \returns true if the matrix is negative (semidefinite) */ + inline bool isNegative(void) const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign; + } + + #ifdef EIGEN_PARSED_BY_DOXYGEN + /** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A. + * + * This function also supports in-place solves using the syntax x = decompositionObject.solve(x) . + * + * \note_about_checking_solutions + * + * More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$ + * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$, + * \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then + * \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the + * least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function + * computes the least-square solution of \f$ A x = b \f$ if \f$ A \f$ is singular. + * + * \sa MatrixBase::ldlt(), SelfAdjointView::ldlt() + */ + template + inline const Solve + solve(const MatrixBase& b) const; + #endif + + template + bool solveInPlace(MatrixBase &bAndX) const; + + template + LDLT& compute(const EigenBase& matrix); + + /** \returns an estimate of the reciprocal condition number of the matrix of + * which \c *this is the LDLT decomposition. + */ + RealScalar rcond() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return internal::rcond_estimate_helper(m_l1_norm, *this); + } + + template + LDLT& rankUpdate(const MatrixBase& w, const RealScalar& alpha=1); + + /** \returns the internal LDLT decomposition matrix + * + * TODO: document the storage layout + */ + inline const MatrixType& matrixLDLT() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_matrix; + } + + MatrixType reconstructedMatrix() const; + + /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint. + * + * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: + * \code x = decomposition.adjoint().solve(b) \endcode + */ + const LDLT& adjoint() const { return *this; }; + + EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); } + EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); } + + /** \brief Reports whether previous computation was successful. + * + * \returns \c Success if computation was successful, + * \c NumericalIssue if the factorization failed because of a zero pivot. + */ + ComputationInfo info() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return m_info; + } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + void _solve_impl(const RhsType &rhs, DstType &dst) const; + + template + void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const; + #endif + + protected: + + static void check_template_parameters() + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); + } + + /** \internal + * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U. + * The strict upper part is used during the decomposition, the strict lower + * part correspond to the coefficients of L (its diagonal is equal to 1 and + * is not stored), and the diagonal entries correspond to D. + */ + MatrixType m_matrix; + RealScalar m_l1_norm; + TranspositionType m_transpositions; + TmpMatrixType m_temporary; + internal::SignMatrix m_sign; + bool m_isInitialized; + ComputationInfo m_info; +}; + +namespace internal { + +template struct ldlt_inplace; + +template<> struct ldlt_inplace +{ + template + static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign) + { + using std::abs; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename TranspositionType::StorageIndex IndexType; + eigen_assert(mat.rows()==mat.cols()); + const Index size = mat.rows(); + bool found_zero_pivot = false; + bool ret = true; + + if (size <= 1) + { + transpositions.setIdentity(); + if(size==0) sign = ZeroSign; + else if (numext::real(mat.coeff(0,0)) > static_cast(0) ) sign = PositiveSemiDef; + else if (numext::real(mat.coeff(0,0)) < static_cast(0)) sign = NegativeSemiDef; + else sign = ZeroSign; + return true; + } + + for (Index k = 0; k < size; ++k) + { + // Find largest diagonal element + Index index_of_biggest_in_corner; + mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner); + index_of_biggest_in_corner += k; + + transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner); + if(k != index_of_biggest_in_corner) + { + // apply the transposition while taking care to consider only + // the lower triangular part + Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element + mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k)); + mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s)); + std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner)); + for(Index i=k+1;i::IsComplex) + mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k)); + } + + // partition the matrix: + // A00 | - | - + // lu = A10 | A11 | - + // A20 | A21 | A22 + Index rs = size - k - 1; + Block A21(mat,k+1,k,rs,1); + Block A10(mat,k,0,1,k); + Block A20(mat,k+1,0,rs,k); + + if(k>0) + { + temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint(); + mat.coeffRef(k,k) -= (A10 * temp.head(k)).value(); + if(rs>0) + A21.noalias() -= A20 * temp.head(k); + } + + // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot + // was smaller than the cutoff value. However, since LDLT is not rank-revealing + // we should only make sure that we do not introduce INF or NaN values. + // Remark that LAPACK also uses 0 as the cutoff value. + RealScalar realAkk = numext::real(mat.coeffRef(k,k)); + bool pivot_is_valid = (abs(realAkk) > RealScalar(0)); + + if(k==0 && !pivot_is_valid) + { + // The entire diagonal is zero, there is nothing more to do + // except filling the transpositions, and checking whether the matrix is zero. + sign = ZeroSign; + for(Index j = 0; j0) && pivot_is_valid) + A21 /= realAkk; + else if(rs>0) + ret = ret && (A21.array()==Scalar(0)).all(); + + if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed + else if(!pivot_is_valid) found_zero_pivot = true; + + if (sign == PositiveSemiDef) { + if (realAkk < static_cast(0)) sign = Indefinite; + } else if (sign == NegativeSemiDef) { + if (realAkk > static_cast(0)) sign = Indefinite; + } else if (sign == ZeroSign) { + if (realAkk > static_cast(0)) sign = PositiveSemiDef; + else if (realAkk < static_cast(0)) sign = NegativeSemiDef; + } + } + + return ret; + } + + // Reference for the algorithm: Davis and Hager, "Multiple Rank + // Modifications of a Sparse Cholesky Factorization" (Algorithm 1) + // Trivial rearrangements of their computations (Timothy E. Holy) + // allow their algorithm to work for rank-1 updates even if the + // original matrix is not of full rank. + // Here only rank-1 updates are implemented, to reduce the + // requirement for intermediate storage and improve accuracy + template + static bool updateInPlace(MatrixType& mat, MatrixBase& w, const typename MatrixType::RealScalar& sigma=1) + { + using numext::isfinite; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + + const Index size = mat.rows(); + eigen_assert(mat.cols() == size && w.size()==size); + + RealScalar alpha = 1; + + // Apply the update + for (Index j = 0; j < size; j++) + { + // Check for termination due to an original decomposition of low-rank + if (!(isfinite)(alpha)) + break; + + // Update the diagonal terms + RealScalar dj = numext::real(mat.coeff(j,j)); + Scalar wj = w.coeff(j); + RealScalar swj2 = sigma*numext::abs2(wj); + RealScalar gamma = dj*alpha + swj2; + + mat.coeffRef(j,j) += swj2/alpha; + alpha += swj2/dj; + + + // Update the terms of L + Index rs = size-j-1; + w.tail(rs) -= wj * mat.col(j).tail(rs); + if(gamma != 0) + mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs); + } + return true; + } + + template + static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1) + { + // Apply the permutation to the input w + tmp = transpositions * w; + + return ldlt_inplace::updateInPlace(mat,tmp,sigma); + } +}; + +template<> struct ldlt_inplace +{ + template + static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign) + { + Transpose matt(mat); + return ldlt_inplace::unblocked(matt, transpositions, temp, sign); + } + + template + static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1) + { + Transpose matt(mat); + return ldlt_inplace::update(matt, transpositions, tmp, w.conjugate(), sigma); + } +}; + +template struct LDLT_Traits +{ + typedef const TriangularView MatrixL; + typedef const TriangularView MatrixU; + static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); } + static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); } +}; + +template struct LDLT_Traits +{ + typedef const TriangularView MatrixL; + typedef const TriangularView MatrixU; + static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); } + static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); } +}; + +} // end namespace internal + +/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix + */ +template +template +LDLT& LDLT::compute(const EigenBase& a) +{ + check_template_parameters(); + + eigen_assert(a.rows()==a.cols()); + const Index size = a.rows(); + + m_matrix = a.derived(); + + // Compute matrix L1 norm = max abs column sum. + m_l1_norm = RealScalar(0); + // TODO move this code to SelfAdjointView + for (Index col = 0; col < size; ++col) { + RealScalar abs_col_sum; + if (UpLo_ == Lower) + abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>(); + else + abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>(); + if (abs_col_sum > m_l1_norm) + m_l1_norm = abs_col_sum; + } + + m_transpositions.resize(size); + m_isInitialized = false; + m_temporary.resize(size); + m_sign = internal::ZeroSign; + + m_info = internal::ldlt_inplace::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue; + + m_isInitialized = true; + return *this; +} + +/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T. + * \param w a vector to be incorporated into the decomposition. + * \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1. + * \sa setZero() + */ +template +template +LDLT& LDLT::rankUpdate(const MatrixBase& w, const typename LDLT::RealScalar& sigma) +{ + typedef typename TranspositionType::StorageIndex IndexType; + const Index size = w.rows(); + if (m_isInitialized) + { + eigen_assert(m_matrix.rows()==size); + } + else + { + m_matrix.resize(size,size); + m_matrix.setZero(); + m_transpositions.resize(size); + for (Index i = 0; i < size; i++) + m_transpositions.coeffRef(i) = IndexType(i); + m_temporary.resize(size); + m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef; + m_isInitialized = true; + } + + internal::ldlt_inplace::update(m_matrix, m_transpositions, m_temporary, w, sigma); + + return *this; +} + +#ifndef EIGEN_PARSED_BY_DOXYGEN +template +template +void LDLT::_solve_impl(const RhsType &rhs, DstType &dst) const +{ + _solve_impl_transposed(rhs, dst); +} + +template +template +void LDLT::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const +{ + // dst = P b + dst = m_transpositions * rhs; + + // dst = L^-1 (P b) + // dst = L^-*T (P b) + matrixL().template conjugateIf().solveInPlace(dst); + + // dst = D^-* (L^-1 P b) + // dst = D^-1 (L^-*T P b) + // more precisely, use pseudo-inverse of D (see bug 241) + using std::abs; + const typename Diagonal::RealReturnType vecD(vectorD()); + // In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min()) + // and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS: + // RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits::epsilon(),RealScalar(1) / NumTraits::highest()); + // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest + // diagonal element is not well justified and leads to numerical issues in some cases. + // Moreover, Lapack's xSYTRS routines use 0 for the tolerance. + // Using numeric_limits::min() gives us more robustness to denormals. + RealScalar tolerance = (std::numeric_limits::min)(); + for (Index i = 0; i < vecD.size(); ++i) + { + if(abs(vecD(i)) > tolerance) + dst.row(i) /= vecD(i); + else + dst.row(i).setZero(); + } + + // dst = L^-* (D^-* L^-1 P b) + // dst = L^-T (D^-1 L^-*T P b) + matrixL().transpose().template conjugateIf().solveInPlace(dst); + + // dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b + // dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b + dst = m_transpositions.transpose() * dst; +} +#endif + +/** \internal use x = ldlt_object.solve(x); + * + * This is the \em in-place version of solve(). + * + * \param bAndX represents both the right-hand side matrix b and result x. + * + * \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD. + * + * This version avoids a copy when the right hand side matrix b is not + * needed anymore. + * + * \sa LDLT::solve(), MatrixBase::ldlt() + */ +template +template +bool LDLT::solveInPlace(MatrixBase &bAndX) const +{ + eigen_assert(m_isInitialized && "LDLT is not initialized."); + eigen_assert(m_matrix.rows() == bAndX.rows()); + + bAndX = this->solve(bAndX); + + return true; +} + +/** \returns the matrix represented by the decomposition, + * i.e., it returns the product: P^T L D L^* P. + * This function is provided for debug purpose. */ +template +MatrixType LDLT::reconstructedMatrix() const +{ + eigen_assert(m_isInitialized && "LDLT is not initialized."); + const Index size = m_matrix.rows(); + MatrixType res(size,size); + + // P + res.setIdentity(); + res = transpositionsP() * res; + // L^* P + res = matrixU() * res; + // D(L^*P) + res = vectorD().real().asDiagonal() * res; + // L(DL^*P) + res = matrixL() * res; + // P^T (LDL^*P) + res = transpositionsP().transpose() * res; + + return res; +} + +/** \cholesky_module + * \returns the Cholesky decomposition with full pivoting without square root of \c *this + * \sa MatrixBase::ldlt() + */ +template +inline const LDLT::PlainObject, UpLo> +SelfAdjointView::ldlt() const +{ + return LDLT(m_matrix); +} + +/** \cholesky_module + * \returns the Cholesky decomposition with full pivoting without square root of \c *this + * \sa SelfAdjointView::ldlt() + */ +template +inline const LDLT::PlainObject> +MatrixBase::ldlt() const +{ + return LDLT(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_LDLT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT.h new file mode 100644 index 0000000000000000000000000000000000000000..3b7aa4d3fbe5bcc090c8fccbe5a017632f7bd006 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT.h @@ -0,0 +1,558 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_LLT_H +#define EIGEN_LLT_H + +namespace Eigen { + +namespace internal{ + +template struct traits > + : traits +{ + typedef MatrixXpr XprKind; + typedef SolverStorage StorageKind; + typedef int StorageIndex; + enum { Flags = 0 }; +}; + +template struct LLT_Traits; +} + +/** \ingroup Cholesky_Module + * + * \class LLT + * + * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features + * + * \tparam MatrixType_ the type of the matrix of which we are computing the LL^T Cholesky decomposition + * \tparam UpLo_ the triangular part that will be used for the decomposition: Lower (default) or Upper. + * The other triangular part won't be read. + * + * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite + * matrix A such that A = LL^* = U^*U, where L is lower triangular. + * + * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, + * for that purpose, we recommend the Cholesky decomposition without square root which is more stable + * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other + * situations like generalised eigen problems with hermitian matrices. + * + * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, + * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations + * has a solution. + * + * Example: \include LLT_example.cpp + * Output: \verbinclude LLT_example.out + * + * \b Performance: for best performance, it is recommended to use a column-major storage format + * with the Lower triangular part (the default), or, equivalently, a row-major storage format + * with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization + * step, and rank-updates can be up to 3 times slower. + * + * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. + * + * Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is considered. + * Therefore, the strict lower part does not have to store correct values. + * + * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT + */ +template class LLT + : public SolverBase > +{ + public: + typedef MatrixType_ MatrixType; + typedef SolverBase Base; + friend class SolverBase; + + EIGEN_GENERIC_PUBLIC_INTERFACE(LLT) + enum { + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime + }; + + enum { + PacketSize = internal::packet_traits::size, + AlignmentMask = int(PacketSize)-1, + UpLo = UpLo_ + }; + + typedef internal::LLT_Traits Traits; + + /** + * \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via LLT::compute(const MatrixType&). + */ + LLT() : m_matrix(), m_isInitialized(false) {} + + /** \brief Default Constructor with memory preallocation + * + * Like the default constructor but with preallocation of the internal data + * according to the specified problem \a size. + * \sa LLT() + */ + explicit LLT(Index size) : m_matrix(size, size), + m_isInitialized(false) {} + + template + explicit LLT(const EigenBase& matrix) + : m_matrix(matrix.rows(), matrix.cols()), + m_isInitialized(false) + { + compute(matrix.derived()); + } + + /** \brief Constructs a LLT factorization from a given matrix + * + * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when + * \c MatrixType is a Eigen::Ref. + * + * \sa LLT(const EigenBase&) + */ + template + explicit LLT(EigenBase& matrix) + : m_matrix(matrix.derived()), + m_isInitialized(false) + { + compute(matrix.derived()); + } + + /** \returns a view of the upper triangular matrix U */ + inline typename Traits::MatrixU matrixU() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + return Traits::getU(m_matrix); + } + + /** \returns a view of the lower triangular matrix L */ + inline typename Traits::MatrixL matrixL() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + return Traits::getL(m_matrix); + } + + #ifdef EIGEN_PARSED_BY_DOXYGEN + /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. + * + * Since this LLT class assumes anyway that the matrix A is invertible, the solution + * theoretically exists and is unique regardless of b. + * + * Example: \include LLT_solve.cpp + * Output: \verbinclude LLT_solve.out + * + * \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt() + */ + template + inline const Solve + solve(const MatrixBase& b) const; + #endif + + template + void solveInPlace(const MatrixBase &bAndX) const; + + template + LLT& compute(const EigenBase& matrix); + + /** \returns an estimate of the reciprocal condition number of the matrix of + * which \c *this is the Cholesky decomposition. + */ + RealScalar rcond() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative"); + return internal::rcond_estimate_helper(m_l1_norm, *this); + } + + /** \returns the LLT decomposition matrix + * + * TODO: document the storage layout + */ + inline const MatrixType& matrixLLT() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + return m_matrix; + } + + MatrixType reconstructedMatrix() const; + + + /** \brief Reports whether previous computation was successful. + * + * \returns \c Success if computation was successful, + * \c NumericalIssue if the matrix.appears not to be positive definite. + */ + ComputationInfo info() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + return m_info; + } + + /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint. + * + * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: + * \code x = decomposition.adjoint().solve(b) \endcode + */ + const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; }; + + inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); } + inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); } + + template + LLT & rankUpdate(const VectorType& vec, const RealScalar& sigma = 1); + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + void _solve_impl(const RhsType &rhs, DstType &dst) const; + + template + void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const; + #endif + + protected: + + static void check_template_parameters() + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); + } + + /** \internal + * Used to compute and store L + * The strict upper part is not used and even not initialized. + */ + MatrixType m_matrix; + RealScalar m_l1_norm; + bool m_isInitialized; + ComputationInfo m_info; +}; + +namespace internal { + +template struct llt_inplace; + +template +static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) +{ + using std::sqrt; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename MatrixType::ColXpr ColXpr; + typedef typename internal::remove_all::type ColXprCleaned; + typedef typename ColXprCleaned::SegmentReturnType ColXprSegment; + typedef Matrix TempVectorType; + typedef typename TempVectorType::SegmentReturnType TempVecSegment; + + Index n = mat.cols(); + eigen_assert(mat.rows()==n && vec.size()==n); + + TempVectorType temp; + + if(sigma>0) + { + // This version is based on Givens rotations. + // It is faster than the other one below, but only works for updates, + // i.e., for sigma > 0 + temp = sqrt(sigma) * vec; + + for(Index i=0; i g; + g.makeGivens(mat(i,i), -temp(i), &mat(i,i)); + + Index rs = n-i-1; + if(rs>0) + { + ColXprSegment x(mat.col(i).tail(rs)); + TempVecSegment y(temp.tail(rs)); + apply_rotation_in_the_plane(x, y, g); + } + } + } + else + { + temp = vec; + RealScalar beta = 1; + for(Index j=0; j struct llt_inplace +{ + typedef typename NumTraits::Real RealScalar; + template + static Index unblocked(MatrixType& mat) + { + using std::sqrt; + + eigen_assert(mat.rows()==mat.cols()); + const Index size = mat.rows(); + for(Index k = 0; k < size; ++k) + { + Index rs = size-k-1; // remaining size + + Block A21(mat,k+1,k,rs,1); + Block A10(mat,k,0,1,k); + Block A20(mat,k+1,0,rs,k); + + RealScalar x = numext::real(mat.coeff(k,k)); + if (k>0) x -= A10.squaredNorm(); + if (x<=RealScalar(0)) + return k; + mat.coeffRef(k,k) = x = sqrt(x); + if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint(); + if (rs>0) A21 /= x; + } + return -1; + } + + template + static Index blocked(MatrixType& m) + { + eigen_assert(m.rows()==m.cols()); + Index size = m.rows(); + if(size<32) + return unblocked(m); + + Index blockSize = size/8; + blockSize = (blockSize/16)*16; + blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128)); + + for (Index k=0; k A11(m,k, k, bs,bs); + Block A21(m,k+bs,k, rs,bs); + Block A22(m,k+bs,k+bs,rs,rs); + + Index ret; + if((ret=unblocked(A11))>=0) return k+ret; + if(rs>0) A11.adjoint().template triangularView().template solveInPlace(A21); + if(rs>0) A22.template selfadjointView().rankUpdate(A21,typename NumTraits::Literal(-1)); // bottleneck + } + return -1; + } + + template + static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) + { + return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); + } +}; + +template struct llt_inplace +{ + typedef typename NumTraits::Real RealScalar; + + template + static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat) + { + Transpose matt(mat); + return llt_inplace::unblocked(matt); + } + template + static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat) + { + Transpose matt(mat); + return llt_inplace::blocked(matt); + } + template + static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) + { + Transpose matt(mat); + return llt_inplace::rankUpdate(matt, vec.conjugate(), sigma); + } +}; + +template struct LLT_Traits +{ + typedef const TriangularView MatrixL; + typedef const TriangularView MatrixU; + static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); } + static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); } + static bool inplace_decomposition(MatrixType& m) + { return llt_inplace::blocked(m)==-1; } +}; + +template struct LLT_Traits +{ + typedef const TriangularView MatrixL; + typedef const TriangularView MatrixU; + static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); } + static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); } + static bool inplace_decomposition(MatrixType& m) + { return llt_inplace::blocked(m)==-1; } +}; + +} // end namespace internal + +/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix + * + * \returns a reference to *this + * + * Example: \include TutorialLinAlgComputeTwice.cpp + * Output: \verbinclude TutorialLinAlgComputeTwice.out + */ +template +template +LLT& LLT::compute(const EigenBase& a) +{ + check_template_parameters(); + + eigen_assert(a.rows()==a.cols()); + const Index size = a.rows(); + m_matrix.resize(size, size); + if (!internal::is_same_dense(m_matrix, a.derived())) + m_matrix = a.derived(); + + // Compute matrix L1 norm = max abs column sum. + m_l1_norm = RealScalar(0); + // TODO move this code to SelfAdjointView + for (Index col = 0; col < size; ++col) { + RealScalar abs_col_sum; + if (UpLo_ == Lower) + abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>(); + else + abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>(); + if (abs_col_sum > m_l1_norm) + m_l1_norm = abs_col_sum; + } + + m_isInitialized = true; + bool ok = Traits::inplace_decomposition(m_matrix); + m_info = ok ? Success : NumericalIssue; + + return *this; +} + +/** Performs a rank one update (or dowdate) of the current decomposition. + * If A = LL^* before the rank one update, + * then after it we have LL^* = A + sigma * v v^* where \a v must be a vector + * of same dimension. + */ +template +template +LLT & LLT::rankUpdate(const VectorType& v, const RealScalar& sigma) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType); + eigen_assert(v.size()==m_matrix.cols()); + eigen_assert(m_isInitialized); + if(internal::llt_inplace::rankUpdate(m_matrix,v,sigma)>=0) + m_info = NumericalIssue; + else + m_info = Success; + + return *this; +} + +#ifndef EIGEN_PARSED_BY_DOXYGEN +template +template +void LLT::_solve_impl(const RhsType &rhs, DstType &dst) const +{ + _solve_impl_transposed(rhs, dst); +} + +template +template +void LLT::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const +{ + dst = rhs; + + matrixL().template conjugateIf().solveInPlace(dst); + matrixU().template conjugateIf().solveInPlace(dst); +} +#endif + +/** \internal use x = llt_object.solve(x); + * + * This is the \em in-place version of solve(). + * + * \param bAndX represents both the right-hand side matrix b and result x. + * + * This version avoids a copy when the right hand side matrix b is not needed anymore. + * + * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here. + * This function will const_cast it, so constness isn't honored here. + * + * \sa LLT::solve(), MatrixBase::llt() + */ +template +template +void LLT::solveInPlace(const MatrixBase &bAndX) const +{ + eigen_assert(m_isInitialized && "LLT is not initialized."); + eigen_assert(m_matrix.rows()==bAndX.rows()); + matrixL().solveInPlace(bAndX); + matrixU().solveInPlace(bAndX); +} + +/** \returns the matrix represented by the decomposition, + * i.e., it returns the product: L L^*. + * This function is provided for debug purpose. */ +template +MatrixType LLT::reconstructedMatrix() const +{ + eigen_assert(m_isInitialized && "LLT is not initialized."); + return matrixL() * matrixL().adjoint().toDenseMatrix(); +} + +/** \cholesky_module + * \returns the LLT decomposition of \c *this + * \sa SelfAdjointView::llt() + */ +template +inline const LLT::PlainObject> +MatrixBase::llt() const +{ + return LLT(derived()); +} + +/** \cholesky_module + * \returns the LLT decomposition of \c *this + * \sa SelfAdjointView::llt() + */ +template +inline const LLT::PlainObject, UpLo> +SelfAdjointView::llt() const +{ + return LLT(m_matrix); +} + +} // end namespace Eigen + +#endif // EIGEN_LLT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT_LAPACKE.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT_LAPACKE.h new file mode 100644 index 0000000000000000000000000000000000000000..bc6489e69a98328e016d4cc7e0d36a147744d337 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Cholesky/LLT_LAPACKE.h @@ -0,0 +1,99 @@ +/* + Copyright (c) 2011, Intel Corporation. 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 Intel Corporation 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. + + ******************************************************************************** + * Content : Eigen bindings to LAPACKe + * LLt decomposition based on LAPACKE_?potrf function. + ******************************************************************************** +*/ + +#ifndef EIGEN_LLT_LAPACKE_H +#define EIGEN_LLT_LAPACKE_H + +namespace Eigen { + +namespace internal { + +template struct lapacke_llt; + +#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \ +template<> struct lapacke_llt \ +{ \ + template \ + static inline Index potrf(MatrixType& m, char uplo) \ + { \ + lapack_int matrix_order; \ + lapack_int size, lda, info, StorageOrder; \ + EIGTYPE* a; \ + eigen_assert(m.rows()==m.cols()); \ + /* Set up parameters for ?potrf */ \ + size = convert_index(m.rows()); \ + StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \ + matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \ + a = &(m.coeffRef(0,0)); \ + lda = convert_index(m.outerStride()); \ +\ + info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \ + info = (info==0) ? -1 : info>0 ? info-1 : size; \ + return info; \ + } \ +}; \ +template<> struct llt_inplace \ +{ \ + template \ + static Index blocked(MatrixType& m) \ + { \ + return lapacke_llt::potrf(m, 'L'); \ + } \ + template \ + static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \ + { return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \ +}; \ +template<> struct llt_inplace \ +{ \ + template \ + static Index blocked(MatrixType& m) \ + { \ + return lapacke_llt::potrf(m, 'U'); \ + } \ + template \ + static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \ + { \ + Transpose matt(mat); \ + return llt_inplace::rankUpdate(matt, vec.conjugate(), sigma); \ + } \ +}; + +EIGEN_LAPACKE_LLT(double, double, d) +EIGEN_LAPACKE_LLT(float, float, s) +EIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z) +EIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c) + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_LLT_LAPACKE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/CholmodSupport/CholmodSupport.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/CholmodSupport/CholmodSupport.h new file mode 100644 index 0000000000000000000000000000000000000000..817e769444896ecbba70175ce69d0a9cf0b9ac53 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/CholmodSupport/CholmodSupport.h @@ -0,0 +1,682 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CHOLMODSUPPORT_H +#define EIGEN_CHOLMODSUPPORT_H + +namespace Eigen { + +namespace internal { + +template struct cholmod_configure_matrix; + +template<> struct cholmod_configure_matrix { + template + static void run(CholmodType& mat) { + mat.xtype = CHOLMOD_REAL; + mat.dtype = CHOLMOD_DOUBLE; + } +}; + +template<> struct cholmod_configure_matrix > { + template + static void run(CholmodType& mat) { + mat.xtype = CHOLMOD_COMPLEX; + mat.dtype = CHOLMOD_DOUBLE; + } +}; + +// Other scalar types are not yet supported by Cholmod +// template<> struct cholmod_configure_matrix { +// template +// static void run(CholmodType& mat) { +// mat.xtype = CHOLMOD_REAL; +// mat.dtype = CHOLMOD_SINGLE; +// } +// }; +// +// template<> struct cholmod_configure_matrix > { +// template +// static void run(CholmodType& mat) { +// mat.xtype = CHOLMOD_COMPLEX; +// mat.dtype = CHOLMOD_SINGLE; +// } +// }; + +} // namespace internal + +/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object. + * Note that the data are shared. + */ +template +cholmod_sparse viewAsCholmod(Ref > mat) +{ + cholmod_sparse res; + res.nzmax = mat.nonZeros(); + res.nrow = mat.rows(); + res.ncol = mat.cols(); + res.p = mat.outerIndexPtr(); + res.i = mat.innerIndexPtr(); + res.x = mat.valuePtr(); + res.z = 0; + res.sorted = 1; + if(mat.isCompressed()) + { + res.packed = 1; + res.nz = 0; + } + else + { + res.packed = 0; + res.nz = mat.innerNonZeroPtr(); + } + + res.dtype = 0; + res.stype = -1; + + if (internal::is_same::value) + { + res.itype = CHOLMOD_INT; + } + else if (internal::is_same::value) + { + res.itype = CHOLMOD_LONG; + } + else + { + eigen_assert(false && "Index type not supported yet"); + } + + // setup res.xtype + internal::cholmod_configure_matrix::run(res); + + res.stype = 0; + + return res; +} + +template +const cholmod_sparse viewAsCholmod(const SparseMatrix& mat) +{ + cholmod_sparse res = viewAsCholmod(Ref >(mat.const_cast_derived())); + return res; +} + +template +const cholmod_sparse viewAsCholmod(const SparseVector& mat) +{ + cholmod_sparse res = viewAsCholmod(Ref >(mat.const_cast_derived())); + return res; +} + +/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix. + * The data are not copied but shared. */ +template +cholmod_sparse viewAsCholmod(const SparseSelfAdjointView, UpLo>& mat) +{ + cholmod_sparse res = viewAsCholmod(Ref >(mat.matrix().const_cast_derived())); + + if(UpLo==Upper) res.stype = 1; + if(UpLo==Lower) res.stype = -1; + // swap stype for rowmajor matrices (only works for real matrices) + EIGEN_STATIC_ASSERT((Options_ & RowMajorBit) == 0 || NumTraits::IsComplex == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); + if(Options_ & RowMajorBit) res.stype *=-1; + + return res; +} + +/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix. + * The data are not copied but shared. */ +template +cholmod_dense viewAsCholmod(MatrixBase& mat) +{ + EIGEN_STATIC_ASSERT((internal::traits::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); + typedef typename Derived::Scalar Scalar; + + cholmod_dense res; + res.nrow = mat.rows(); + res.ncol = mat.cols(); + res.nzmax = res.nrow * res.ncol; + res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride(); + res.x = (void*)(mat.derived().data()); + res.z = 0; + + internal::cholmod_configure_matrix::run(res); + + return res; +} + +/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix. + * The data are not copied but shared. */ +template +MappedSparseMatrix viewAsEigen(cholmod_sparse& cm) +{ + return MappedSparseMatrix + (cm.nrow, cm.ncol, static_cast(cm.p)[cm.ncol], + static_cast(cm.p), static_cast(cm.i),static_cast(cm.x) ); +} + +namespace internal { + +// template specializations for int and long that call the correct cholmod method + +#define EIGEN_CHOLMOD_SPECIALIZE0(ret, name) \ + template inline ret cm_ ## name (cholmod_common &Common) { return cholmod_ ## name (&Common); } \ + template<> inline ret cm_ ## name (cholmod_common &Common) { return cholmod_l_ ## name (&Common); } + +#define EIGEN_CHOLMOD_SPECIALIZE1(ret, name, t1, a1) \ + template inline ret cm_ ## name (t1& a1, cholmod_common &Common) { return cholmod_ ## name (&a1, &Common); } \ + template<> inline ret cm_ ## name (t1& a1, cholmod_common &Common) { return cholmod_l_ ## name (&a1, &Common); } + +EIGEN_CHOLMOD_SPECIALIZE0(int, start) +EIGEN_CHOLMOD_SPECIALIZE0(int, finish) + +EIGEN_CHOLMOD_SPECIALIZE1(int, free_factor, cholmod_factor*, L) +EIGEN_CHOLMOD_SPECIALIZE1(int, free_dense, cholmod_dense*, X) +EIGEN_CHOLMOD_SPECIALIZE1(int, free_sparse, cholmod_sparse*, A) + +EIGEN_CHOLMOD_SPECIALIZE1(cholmod_factor*, analyze, cholmod_sparse, A) + +template inline cholmod_dense* cm_solve (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_solve (sys, &L, &B, &Common); } +template<> inline cholmod_dense* cm_solve (int sys, cholmod_factor& L, cholmod_dense& B, cholmod_common &Common) { return cholmod_l_solve (sys, &L, &B, &Common); } + +template inline cholmod_sparse* cm_spsolve (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_spsolve (sys, &L, &B, &Common); } +template<> inline cholmod_sparse* cm_spsolve (int sys, cholmod_factor& L, cholmod_sparse& B, cholmod_common &Common) { return cholmod_l_spsolve (sys, &L, &B, &Common); } + +template +inline int cm_factorize_p (cholmod_sparse* A, double beta[2], StorageIndex_* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_factorize_p (A, beta, fset, fsize, L, &Common); } +template<> +inline int cm_factorize_p (cholmod_sparse* A, double beta[2], SuiteSparse_long* fset, std::size_t fsize, cholmod_factor* L, cholmod_common &Common) { return cholmod_l_factorize_p (A, beta, fset, fsize, L, &Common); } + +#undef EIGEN_CHOLMOD_SPECIALIZE0 +#undef EIGEN_CHOLMOD_SPECIALIZE1 + +} // namespace internal + + +enum CholmodMode { + CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt +}; + + +/** \ingroup CholmodSupport_Module + * \class CholmodBase + * \brief The base class for the direct Cholesky factorization of Cholmod + * \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT + */ +template +class CholmodBase : public SparseSolverBase +{ + protected: + typedef SparseSolverBase Base; + using Base::derived; + using Base::m_isInitialized; + public: + typedef MatrixType_ MatrixType; + enum { UpLo = UpLo_ }; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef MatrixType CholMatrixType; + typedef typename MatrixType::StorageIndex StorageIndex; + enum { + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime + }; + + public: + + CholmodBase() + : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) + { + EIGEN_STATIC_ASSERT((internal::is_same::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY); + m_shiftOffset[0] = m_shiftOffset[1] = 0.0; + internal::cm_start(m_cholmod); + } + + explicit CholmodBase(const MatrixType& matrix) + : m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false) + { + EIGEN_STATIC_ASSERT((internal::is_same::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY); + m_shiftOffset[0] = m_shiftOffset[1] = 0.0; + internal::cm_start(m_cholmod); + compute(matrix); + } + + ~CholmodBase() + { + if(m_cholmodFactor) + internal::cm_free_factor(m_cholmodFactor, m_cholmod); + internal::cm_finish(m_cholmod); + } + + inline StorageIndex cols() const { return internal::convert_index(m_cholmodFactor->n); } + inline StorageIndex rows() const { return internal::convert_index(m_cholmodFactor->n); } + + /** \brief Reports whether previous computation was successful. + * + * \returns \c Success if computation was successful, + * \c NumericalIssue if the matrix.appears to be negative. + */ + ComputationInfo info() const + { + eigen_assert(m_isInitialized && "Decomposition is not initialized."); + return m_info; + } + + /** Computes the sparse Cholesky decomposition of \a matrix */ + Derived& compute(const MatrixType& matrix) + { + analyzePattern(matrix); + factorize(matrix); + return derived(); + } + + /** Performs a symbolic decomposition on the sparsity pattern of \a matrix. + * + * This function is particularly useful when solving for several problems having the same structure. + * + * \sa factorize() + */ + void analyzePattern(const MatrixType& matrix) + { + if(m_cholmodFactor) + { + internal::cm_free_factor(m_cholmodFactor, m_cholmod); + m_cholmodFactor = 0; + } + cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView()); + m_cholmodFactor = internal::cm_analyze(A, m_cholmod); + + this->m_isInitialized = true; + this->m_info = Success; + m_analysisIsOk = true; + m_factorizationIsOk = false; + } + + /** Performs a numeric decomposition of \a matrix + * + * The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed. + * + * \sa analyzePattern() + */ + void factorize(const MatrixType& matrix) + { + eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); + cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView()); + internal::cm_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, m_cholmod); + + // If the factorization failed, minor is the column at which it did. On success minor == n. + this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue); + m_factorizationIsOk = true; + } + + /** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations. + * See the Cholmod user guide for details. */ + cholmod_common& cholmod() { return m_cholmod; } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /** \internal */ + template + void _solve_impl(const MatrixBase &b, MatrixBase &dest) const + { + eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); + const Index size = m_cholmodFactor->n; + EIGEN_UNUSED_VARIABLE(size); + eigen_assert(size==b.rows()); + + // Cholmod needs column-major storage without inner-stride, which corresponds to the default behavior of Ref. + Ref > b_ref(b.derived()); + + cholmod_dense b_cd = viewAsCholmod(b_ref); + cholmod_dense* x_cd = internal::cm_solve(CHOLMOD_A, *m_cholmodFactor, b_cd, m_cholmod); + if(!x_cd) + { + this->m_info = NumericalIssue; + return; + } + // TODO optimize this copy by swapping when possible (be careful with alignment, etc.) + // NOTE Actually, the copy can be avoided by calling cholmod_solve2 instead of cholmod_solve + dest = Matrix::Map(reinterpret_cast(x_cd->x),b.rows(),b.cols()); + internal::cm_free_dense(x_cd, m_cholmod); + } + + /** \internal */ + template + void _solve_impl(const SparseMatrixBase &b, SparseMatrixBase &dest) const + { + eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); + const Index size = m_cholmodFactor->n; + EIGEN_UNUSED_VARIABLE(size); + eigen_assert(size==b.rows()); + + // note: cs stands for Cholmod Sparse + Ref > b_ref(b.const_cast_derived()); + cholmod_sparse b_cs = viewAsCholmod(b_ref); + cholmod_sparse* x_cs = internal::cm_spsolve(CHOLMOD_A, *m_cholmodFactor, b_cs, m_cholmod); + if(!x_cs) + { + this->m_info = NumericalIssue; + return; + } + // TODO optimize this copy by swapping when possible (be careful with alignment, etc.) + // NOTE cholmod_spsolve in fact just calls the dense solver for blocks of 4 columns at a time (similar to Eigen's sparse solver) + dest.derived() = viewAsEigen(*x_cs); + internal::cm_free_sparse(x_cs, m_cholmod); + } + #endif // EIGEN_PARSED_BY_DOXYGEN + + + /** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization. + * + * During the numerical factorization, an offset term is added to the diagonal coefficients:\n + * \c d_ii = \a offset + \c d_ii + * + * The default is \a offset=0. + * + * \returns a reference to \c *this. + */ + Derived& setShift(const RealScalar& offset) + { + m_shiftOffset[0] = double(offset); + return derived(); + } + + /** \returns the determinant of the underlying matrix from the current factorization */ + Scalar determinant() const + { + using std::exp; + return exp(logDeterminant()); + } + + /** \returns the log determinant of the underlying matrix from the current factorization */ + Scalar logDeterminant() const + { + using std::log; + using numext::real; + eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()"); + + RealScalar logDet = 0; + Scalar *x = static_cast(m_cholmodFactor->x); + if (m_cholmodFactor->is_super) + { + // Supernodal factorization stored as a packed list of dense column-major blocs, + // as described by the following structure: + + // super[k] == index of the first column of the j-th super node + StorageIndex *super = static_cast(m_cholmodFactor->super); + // pi[k] == offset to the description of row indices + StorageIndex *pi = static_cast(m_cholmodFactor->pi); + // px[k] == offset to the respective dense block + StorageIndex *px = static_cast(m_cholmodFactor->px); + + Index nb_super_nodes = m_cholmodFactor->nsuper; + for (Index k=0; k < nb_super_nodes; ++k) + { + StorageIndex ncols = super[k + 1] - super[k]; + StorageIndex nrows = pi[k + 1] - pi[k]; + + Map, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1)); + logDet += sk.real().log().sum(); + } + } + else + { + // Simplicial factorization stored as standard CSC matrix. + StorageIndex *p = static_cast(m_cholmodFactor->p); + Index size = m_cholmodFactor->n; + for (Index k=0; kis_ll) + logDet *= 2.0; + return logDet; + }; + + template + void dumpMemory(Stream& /*s*/) + {} + + protected: + mutable cholmod_common m_cholmod; + cholmod_factor* m_cholmodFactor; + double m_shiftOffset[2]; + mutable ComputationInfo m_info; + int m_factorizationIsOk; + int m_analysisIsOk; +}; + +/** \ingroup CholmodSupport_Module + * \class CholmodSimplicialLLT + * \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod + * + * This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization + * using the Cholmod library. + * This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest. + * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices + * X and B can be either dense or sparse. + * + * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<> + * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * + * \implsparsesolverconcept + * + * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. + * + * \warning Only double precision real and complex scalar types are supported by Cholmod. + * + * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT + */ +template +class CholmodSimplicialLLT : public CholmodBase > +{ + typedef CholmodBase Base; + using Base::m_cholmod; + + public: + + typedef MatrixType_ MatrixType; + + CholmodSimplicialLLT() : Base() { init(); } + + CholmodSimplicialLLT(const MatrixType& matrix) : Base() + { + init(); + this->compute(matrix); + } + + ~CholmodSimplicialLLT() {} + protected: + void init() + { + m_cholmod.final_asis = 0; + m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; + m_cholmod.final_ll = 1; + } +}; + + +/** \ingroup CholmodSupport_Module + * \class CholmodSimplicialLDLT + * \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod + * + * This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization + * using the Cholmod library. + * This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest. + * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices + * X and B can be either dense or sparse. + * + * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<> + * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * + * \implsparsesolverconcept + * + * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. + * + * \warning Only double precision real and complex scalar types are supported by Cholmod. + * + * \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT + */ +template +class CholmodSimplicialLDLT : public CholmodBase > +{ + typedef CholmodBase Base; + using Base::m_cholmod; + + public: + + typedef MatrixType_ MatrixType; + + CholmodSimplicialLDLT() : Base() { init(); } + + CholmodSimplicialLDLT(const MatrixType& matrix) : Base() + { + init(); + this->compute(matrix); + } + + ~CholmodSimplicialLDLT() {} + protected: + void init() + { + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; + } +}; + +/** \ingroup CholmodSupport_Module + * \class CholmodSupernodalLLT + * \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod + * + * This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization + * using the Cholmod library. + * This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM. + * The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices + * X and B can be either dense or sparse. + * + * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<> + * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * + * \implsparsesolverconcept + * + * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. + * + * \warning Only double precision real and complex scalar types are supported by Cholmod. + * + * \sa \ref TutorialSparseSolverConcept + */ +template +class CholmodSupernodalLLT : public CholmodBase > +{ + typedef CholmodBase Base; + using Base::m_cholmod; + + public: + + typedef MatrixType_ MatrixType; + + CholmodSupernodalLLT() : Base() { init(); } + + CholmodSupernodalLLT(const MatrixType& matrix) : Base() + { + init(); + this->compute(matrix); + } + + ~CholmodSupernodalLLT() {} + protected: + void init() + { + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_SUPERNODAL; + } +}; + +/** \ingroup CholmodSupport_Module + * \class CholmodDecomposition + * \brief A general Cholesky factorization and solver based on Cholmod + * + * This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization + * using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices + * X and B can be either dense or sparse. + * + * This variant permits to change the underlying Cholesky method at runtime. + * On the other hand, it does not provide access to the result of the factorization. + * The default is to let Cholmod automatically choose between a simplicial and supernodal factorization. + * + * \tparam MatrixType_ the type of the sparse matrix A, it must be a SparseMatrix<> + * \tparam UpLo_ the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * + * \implsparsesolverconcept + * + * This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed. + * + * \warning Only double precision real and complex scalar types are supported by Cholmod. + * + * \sa \ref TutorialSparseSolverConcept + */ +template +class CholmodDecomposition : public CholmodBase > +{ + typedef CholmodBase Base; + using Base::m_cholmod; + + public: + + typedef MatrixType_ MatrixType; + + CholmodDecomposition() : Base() { init(); } + + CholmodDecomposition(const MatrixType& matrix) : Base() + { + init(); + this->compute(matrix); + } + + ~CholmodDecomposition() {} + + void setMode(CholmodMode mode) + { + switch(mode) + { + case CholmodAuto: + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_AUTO; + break; + case CholmodSimplicialLLt: + m_cholmod.final_asis = 0; + m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; + m_cholmod.final_ll = 1; + break; + case CholmodSupernodalLLt: + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_SUPERNODAL; + break; + case CholmodLDLt: + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_SIMPLICIAL; + break; + default: + break; + } + } + protected: + void init() + { + m_cholmod.final_asis = 1; + m_cholmod.supernodal = CHOLMOD_AUTO; + } +}; + +} // end namespace Eigen + +#endif // EIGEN_CHOLMODSUPPORT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArithmeticSequence.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArithmeticSequence.h new file mode 100644 index 0000000000000000000000000000000000000000..b6200fac1b0bef2c60a098f69646fec378e5b646 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArithmeticSequence.h @@ -0,0 +1,413 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2017 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ARITHMETIC_SEQUENCE_H +#define EIGEN_ARITHMETIC_SEQUENCE_H + +namespace Eigen { + +namespace internal { + +#if (!EIGEN_HAS_CXX11) || !((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48) +template struct aseq_negate {}; + +template<> struct aseq_negate { + typedef Index type; +}; + +template struct aseq_negate > { + typedef FixedInt<-N> type; +}; + +// Compilation error in the following case: +template<> struct aseq_negate > {}; + +template::value, + bool SizeIsSymbolic =symbolic::is_symbolic::value> +struct aseq_reverse_first_type { + typedef Index type; +}; + +template +struct aseq_reverse_first_type { + typedef symbolic::AddExpr > >, + symbolic::ValueExpr > + > type; +}; + +template +struct aseq_reverse_first_type_aux { + typedef Index type; +}; + +template +struct aseq_reverse_first_type_aux::type> { + typedef FixedInt<(SizeType::value-1)*IncrType::value> type; +}; + +template +struct aseq_reverse_first_type { + typedef typename aseq_reverse_first_type_aux::type Aux; + typedef symbolic::AddExpr > type; +}; + +template +struct aseq_reverse_first_type { + typedef symbolic::AddExpr > >, + symbolic::ValueExpr >, + symbolic::ValueExpr<> > type; +}; +#endif + +// Helper to cleanup the type of the increment: +template struct cleanup_seq_incr { + typedef typename cleanup_index_type::type type; +}; + +} + +//-------------------------------------------------------------------------------- +// seq(first,last,incr) and seqN(first,size,incr) +//-------------------------------------------------------------------------------- + +template > +class ArithmeticSequence; + +template +ArithmeticSequence::type, + typename internal::cleanup_index_type::type, + typename internal::cleanup_seq_incr::type > +seqN(FirstType first, SizeType size, IncrType incr); + +/** \class ArithmeticSequence + * \ingroup Core_Module + * + * This class represents an arithmetic progression \f$ a_0, a_1, a_2, ..., a_{n-1}\f$ defined by + * its \em first value \f$ a_0 \f$, its \em size (aka length) \em n, and the \em increment (aka stride) + * that is equal to \f$ a_{i+1}-a_{i}\f$ for any \em i. + * + * It is internally used as the return type of the Eigen::seq and Eigen::seqN functions, and as the input arguments + * of DenseBase::operator()(const RowIndices&, const ColIndices&), and most of the time this is the + * only way it is used. + * + * \tparam FirstType type of the first element, usually an Index, + * but internally it can be a symbolic expression + * \tparam SizeType type representing the size of the sequence, usually an Index + * or a compile time integral constant. Internally, it can also be a symbolic expression + * \tparam IncrType type of the increment, can be a runtime Index, or a compile time integral constant (default is compile-time 1) + * + * \sa Eigen::seq, Eigen::seqN, DenseBase::operator()(const RowIndices&, const ColIndices&), class IndexedView + */ +template +class ArithmeticSequence +{ +public: + ArithmeticSequence(FirstType first, SizeType size) : m_first(first), m_size(size) {} + ArithmeticSequence(FirstType first, SizeType size, IncrType incr) : m_first(first), m_size(size), m_incr(incr) {} + + enum { + SizeAtCompileTime = internal::get_fixed_value::value, + IncrAtCompileTime = internal::get_fixed_value::value + }; + + /** \returns the size, i.e., number of elements, of the sequence */ + Index size() const { return m_size; } + + /** \returns the first element \f$ a_0 \f$ in the sequence */ + Index first() const { return m_first; } + + /** \returns the value \f$ a_i \f$ at index \a i in the sequence. */ + Index operator[](Index i) const { return m_first + i * m_incr; } + + const FirstType& firstObject() const { return m_first; } + const SizeType& sizeObject() const { return m_size; } + const IncrType& incrObject() const { return m_incr; } + +protected: + FirstType m_first; + SizeType m_size; + IncrType m_incr; + +public: + +#if EIGEN_HAS_CXX11 && ((!EIGEN_COMP_GNUC) || EIGEN_COMP_GNUC>=48) + auto reverse() const -> decltype(Eigen::seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr)) { + return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr); + } +#else +protected: + typedef typename internal::aseq_negate::type ReverseIncrType; + typedef typename internal::aseq_reverse_first_type::type ReverseFirstType; +public: + ArithmeticSequence + reverse() const { + return seqN(m_first+(m_size+fix<-1>())*m_incr,m_size,-m_incr); + } +#endif +}; + +/** \returns an ArithmeticSequence starting at \a first, of length \a size, and increment \a incr + * + * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */ +template +ArithmeticSequence::type,typename internal::cleanup_index_type::type,typename internal::cleanup_seq_incr::type > +seqN(FirstType first, SizeType size, IncrType incr) { + return ArithmeticSequence::type,typename internal::cleanup_index_type::type,typename internal::cleanup_seq_incr::type>(first,size,incr); +} + +/** \returns an ArithmeticSequence starting at \a first, of length \a size, and unit increment + * + * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) */ +template +ArithmeticSequence::type,typename internal::cleanup_index_type::type > +seqN(FirstType first, SizeType size) { + return ArithmeticSequence::type,typename internal::cleanup_index_type::type>(first,size); +} + +#ifdef EIGEN_PARSED_BY_DOXYGEN + +/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and with positive (or negative) increment \a incr + * + * It is essentially an alias to: + * \code + * seqN(f, (l-f+incr)/incr, incr); + * \endcode + * + * \sa seqN(FirstType,SizeType,IncrType), seq(FirstType,LastType) + */ +template +auto seq(FirstType f, LastType l, IncrType incr); + +/** \returns an ArithmeticSequence starting at \a f, up (or down) to \a l, and unit increment + * + * It is essentially an alias to: + * \code + * seqN(f,l-f+1); + * \endcode + * + * \sa seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) + */ +template +auto seq(FirstType f, LastType l); + +#else // EIGEN_PARSED_BY_DOXYGEN + +#if EIGEN_HAS_CXX11 +template +auto seq(FirstType f, LastType l) -> decltype(seqN(typename internal::cleanup_index_type::type(f), + ( typename internal::cleanup_index_type::type(l) + - typename internal::cleanup_index_type::type(f)+fix<1>()))) +{ + return seqN(typename internal::cleanup_index_type::type(f), + (typename internal::cleanup_index_type::type(l) + -typename internal::cleanup_index_type::type(f)+fix<1>())); +} + +template +auto seq(FirstType f, LastType l, IncrType incr) + -> decltype(seqN(typename internal::cleanup_index_type::type(f), + ( typename internal::cleanup_index_type::type(l) + - typename internal::cleanup_index_type::type(f)+typename internal::cleanup_seq_incr::type(incr) + ) / typename internal::cleanup_seq_incr::type(incr), + typename internal::cleanup_seq_incr::type(incr))) +{ + typedef typename internal::cleanup_seq_incr::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type::type(f), + ( typename internal::cleanup_index_type::type(l) + -typename internal::cleanup_index_type::type(f)+CleanedIncrType(incr)) / CleanedIncrType(incr), + CleanedIncrType(incr)); +} + +#else // EIGEN_HAS_CXX11 + +template +typename internal::enable_if::value || symbolic::is_symbolic::value), + ArithmeticSequence::type,Index> >::type +seq(FirstType f, LastType l) +{ + return seqN(typename internal::cleanup_index_type::type(f), + Index((typename internal::cleanup_index_type::type(l)-typename internal::cleanup_index_type::type(f)+fix<1>()))); +} + +template +typename internal::enable_if::value, + ArithmeticSequence,symbolic::ValueExpr<> >, + symbolic::ValueExpr > > > >::type +seq(const symbolic::BaseExpr &f, LastType l) +{ + return seqN(f.derived(),(typename internal::cleanup_index_type::type(l)-f.derived()+fix<1>())); +} + +template +typename internal::enable_if::value, + ArithmeticSequence::type, + symbolic::AddExpr >, + symbolic::ValueExpr > > > >::type +seq(FirstType f, const symbolic::BaseExpr &l) +{ + return seqN(typename internal::cleanup_index_type::type(f),(l.derived()-typename internal::cleanup_index_type::type(f)+fix<1>())); +} + +template +ArithmeticSequence >,symbolic::ValueExpr > > > +seq(const symbolic::BaseExpr &f, const symbolic::BaseExpr &l) +{ + return seqN(f.derived(),(l.derived()-f.derived()+fix<1>())); +} + + +template +typename internal::enable_if::value || symbolic::is_symbolic::value), + ArithmeticSequence::type,Index,typename internal::cleanup_seq_incr::type> >::type +seq(FirstType f, LastType l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type::type(f), + Index((typename internal::cleanup_index_type::type(l)-typename internal::cleanup_index_type::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr)), incr); +} + +template +typename internal::enable_if::value, + ArithmeticSequence, + symbolic::ValueExpr<> >, + symbolic::ValueExpr::type> >, + symbolic::ValueExpr::type> >, + typename internal::cleanup_seq_incr::type> >::type +seq(const symbolic::BaseExpr &f, LastType l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr::type CleanedIncrType; + return seqN(f.derived(),(typename internal::cleanup_index_type::type(l)-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} + +template +typename internal::enable_if::value, + ArithmeticSequence::type, + symbolic::QuotientExpr >, + symbolic::ValueExpr::type> >, + symbolic::ValueExpr::type> >, + typename internal::cleanup_seq_incr::type> >::type +seq(FirstType f, const symbolic::BaseExpr &l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr::type CleanedIncrType; + return seqN(typename internal::cleanup_index_type::type(f), + (l.derived()-typename internal::cleanup_index_type::type(f)+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} + +template +ArithmeticSequence >, + symbolic::ValueExpr::type> >, + symbolic::ValueExpr::type> >, + typename internal::cleanup_seq_incr::type> +seq(const symbolic::BaseExpr &f, const symbolic::BaseExpr &l, IncrType incr) +{ + typedef typename internal::cleanup_seq_incr::type CleanedIncrType; + return seqN(f.derived(),(l.derived()-f.derived()+CleanedIncrType(incr))/CleanedIncrType(incr), incr); +} +#endif // EIGEN_HAS_CXX11 + +#endif // EIGEN_PARSED_BY_DOXYGEN + + +#if EIGEN_HAS_CXX11 || defined(EIGEN_PARSED_BY_DOXYGEN) +/** \cpp11 + * \returns a symbolic ArithmeticSequence representing the last \a size elements with increment \a incr. + * + * It is a shortcut for: \code seqN(last-(size-fix<1>)*incr, size, incr) \endcode + * + * \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */ +template +auto lastN(SizeType size, IncrType incr) +-> decltype(seqN(Eigen::last-(size-fix<1>())*incr, size, incr)) +{ + return seqN(Eigen::last-(size-fix<1>())*incr, size, incr); +} + +/** \cpp11 + * \returns a symbolic ArithmeticSequence representing the last \a size elements with a unit increment. + * + * It is a shortcut for: \code seq(last+fix<1>-size, last) \endcode + * + * \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */ +template +auto lastN(SizeType size) +-> decltype(seqN(Eigen::last+fix<1>()-size, size)) +{ + return seqN(Eigen::last+fix<1>()-size, size); +} +#endif + +namespace internal { + +// Convert a symbolic span into a usable one (i.e., remove last/end "keywords") +template +struct make_size_type { + typedef typename internal::conditional::value, Index, T>::type type; +}; + +template +struct IndexedViewCompatibleType, XprSize> { + typedef ArithmeticSequence::type,IncrType> type; +}; + +template +ArithmeticSequence::type,IncrType> +makeIndexedViewCompatible(const ArithmeticSequence& ids, Index size,SpecializedType) { + return ArithmeticSequence::type,IncrType>( + eval_expr_given_size(ids.firstObject(),size),eval_expr_given_size(ids.sizeObject(),size),ids.incrObject()); +} + +template +struct get_compile_time_incr > { + enum { value = get_fixed_value::value }; +}; + +} // end namespace internal + +/** \namespace Eigen::indexing + * \ingroup Core_Module + * + * The sole purpose of this namespace is to be able to import all functions + * and symbols that are expected to be used within operator() for indexing + * and slicing. If you already imported the whole Eigen namespace: + * \code using namespace Eigen; \endcode + * then you are already all set. Otherwise, if you don't want/cannot import + * the whole Eigen namespace, the following line: + * \code using namespace Eigen::indexing; \endcode + * is equivalent to: + * \code + using Eigen::all; + using Eigen::seq; + using Eigen::seqN; + using Eigen::lastN; // c++11 only + using Eigen::last; + using Eigen::lastp1; + using Eigen::fix; + \endcode + */ +namespace indexing { + using Eigen::all; + using Eigen::seq; + using Eigen::seqN; + #if EIGEN_HAS_CXX11 + using Eigen::lastN; + #endif + using Eigen::last; + using Eigen::lastp1; + using Eigen::fix; +} + +} // end namespace Eigen + +#endif // EIGEN_ARITHMETIC_SEQUENCE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Array.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Array.h new file mode 100644 index 0000000000000000000000000000000000000000..85676ae9267f019423b5e9b570981c66eb69f861 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Array.h @@ -0,0 +1,417 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ARRAY_H +#define EIGEN_ARRAY_H + +namespace Eigen { + +namespace internal { +template +struct traits > : traits > +{ + typedef ArrayXpr XprKind; + typedef ArrayBase > XprBase; +}; +} + +/** \class Array + * \ingroup Core_Module + * + * \brief General-purpose arrays with easy API for coefficient-wise operations + * + * The %Array class is very similar to the Matrix class. It provides + * general-purpose one- and two-dimensional arrays. The difference between the + * %Array and the %Matrix class is primarily in the API: the API for the + * %Array class provides easy access to coefficient-wise operations, while the + * API for the %Matrix class provides easy access to linear-algebra + * operations. + * + * See documentation of class Matrix for detailed information on the template parameters + * storage layout. + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAY_PLUGIN. + * + * \sa \blank \ref TutorialArrayClass, \ref TopicClassHierarchy + */ +template +class Array + : public PlainObjectBase > +{ + public: + + typedef PlainObjectBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Array) + + enum { Options = Options_ }; + typedef typename Base::PlainObject PlainObject; + + protected: + template + friend struct internal::conservative_resize_like_impl; + + using Base::m_storage; + + public: + + using Base::base; + using Base::coeff; + using Base::coeffRef; + + /** + * The usage of + * using Base::operator=; + * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped + * the usage of 'using'. This should be done only for operator=. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array& operator=(const EigenBase &other) + { + return Base::operator=(other); + } + + /** Set all the entries to \a value. + * \sa DenseBase::setConstant(), DenseBase::fill() + */ + /* This overload is needed because the usage of + * using Base::operator=; + * fails on MSVC. Since the code below is working with GCC and MSVC, we skipped + * the usage of 'using'. This should be done only for operator=. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array& operator=(const Scalar &value) + { + Base::setConstant(value); + return *this; + } + + /** Copies the value of the expression \a other into \c *this with automatic resizing. + * + * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized), + * it will be initialized. + * + * Note that copying a row-vector into a vector (and conversely) is allowed. + * The resizing, if any, is then done in the appropriate way so that row-vectors + * remain row-vectors and vectors remain vectors. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array& operator=(const DenseBase& other) + { + return Base::_set(other); + } + + /** This is a special case of the templated operator=. Its purpose is to + * prevent a default operator= from hiding the templated operator=. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array& operator=(const Array& other) + { + return Base::_set(other); + } + + /** Default constructor. + * + * For fixed-size matrices, does nothing. + * + * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix + * is called a null matrix. This constructor is the unique way to create null matrices: resizing + * a matrix to 0 is not supported. + * + * \sa resize(Index,Index) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array() : Base() + { + Base::_check_template_params(); + EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } + +#ifndef EIGEN_PARSED_BY_DOXYGEN + // FIXME is it still needed ?? + /** \internal */ + EIGEN_DEVICE_FUNC + Array(internal::constructor_without_unaligned_array_assert) + : Base(internal::constructor_without_unaligned_array_assert()) + { + Base::_check_template_params(); + EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } +#endif + +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC + Array(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible::value) + : Base(std::move(other)) + { + Base::_check_template_params(); + } + EIGEN_DEVICE_FUNC + Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable::value) + { + Base::operator=(std::move(other)); + return *this; + } +#endif + + #if EIGEN_HAS_CXX11 + /** \copydoc PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + * + * Example: \include Array_variadic_ctor_cxx11.cpp + * Output: \verbinclude Array_variadic_ctor_cxx11.out + * + * \sa Array(const std::initializer_list>&) + * \sa Array(const Scalar&), Array(const Scalar&,const Scalar&) + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + : Base(a0, a1, a2, a3, args...) {} + + /** \brief Constructs an array and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11 + * + * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients: + * + * Example: \include Array_initializer_list_23_cxx11.cpp + * Output: \verbinclude Array_initializer_list_23_cxx11.out + * + * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered. + * + * In the case of a compile-time column 1D array, implicit transposition from a single row is allowed. + * Therefore Array{{1,2,3,4,5}} is legal and the more verbose syntax + * Array{{1},{2},{3},{4},{5}} can be avoided: + * + * Example: \include Array_initializer_list_vector_cxx11.cpp + * Output: \verbinclude Array_initializer_list_vector_cxx11.out + * + * In the case of fixed-sized arrays, the initializer list sizes must exactly match the array sizes, + * and implicit transposition is allowed for compile-time 1D arrays only. + * + * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const std::initializer_list>& list) : Base(list) {} + #endif // end EIGEN_HAS_CXX11 + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE explicit Array(const T& x) + { + Base::_check_template_params(); + Base::template _init1(x); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const T0& val0, const T1& val1) + { + Base::_check_template_params(); + this->template _init2(val0, val1); + } + + #else + /** \brief Constructs a fixed-sized array initialized with coefficients starting at \a data */ + EIGEN_DEVICE_FUNC explicit Array(const Scalar *data); + /** Constructs a vector or row-vector with given dimension. \only_for_vectors + * + * Note that this is only useful for dynamic-size vectors. For fixed-size vectors, + * it is redundant to pass the dimension here, so it makes more sense to use the default + * constructor Array() instead. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE explicit Array(Index dim); + /** constructs an initialized 1x1 Array with the given coefficient + * \sa const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args */ + Array(const Scalar& value); + /** constructs an uninitialized array with \a rows rows and \a cols columns. + * + * This is useful for dynamic-size arrays. For fixed-size arrays, + * it is redundant to pass these parameters, so one should use the default constructor + * Array() instead. */ + Array(Index rows, Index cols); + /** constructs an initialized 2D vector with given coefficients + * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) */ + Array(const Scalar& val0, const Scalar& val1); + #endif // end EIGEN_PARSED_BY_DOXYGEN + + /** constructs an initialized 3D vector with given coefficients + * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2) + { + Base::_check_template_params(); + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 3) + m_storage.data()[0] = val0; + m_storage.data()[1] = val1; + m_storage.data()[2] = val2; + } + /** constructs an initialized 4D vector with given coefficients + * \sa Array(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const Scalar& val0, const Scalar& val1, const Scalar& val2, const Scalar& val3) + { + Base::_check_template_params(); + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Array, 4) + m_storage.data()[0] = val0; + m_storage.data()[1] = val1; + m_storage.data()[2] = val2; + m_storage.data()[3] = val3; + } + + /** Copy constructor */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const Array& other) + : Base(other) + { } + + private: + struct PrivateType {}; + public: + + /** \sa MatrixBase::operator=(const EigenBase&) */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Array(const EigenBase &other, + typename internal::enable_if::value, + PrivateType>::type = PrivateType()) + : Base(other.derived()) + { } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT{ return 1; } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); } + + #ifdef EIGEN_ARRAY_PLUGIN + #include EIGEN_ARRAY_PLUGIN + #endif + + private: + + template + friend struct internal::matrix_swap_impl; +}; + +/** \defgroup arraytypedefs Global array typedefs + * \ingroup Core_Module + * + * %Eigen defines several typedef shortcuts for most common 1D and 2D array types. + * + * The general patterns are the following: + * + * \c ArrayRowsColsType where \c Rows and \c Cols can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size, + * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd + * for complex double. + * + * For example, \c Array33d is a fixed-size 3x3 array type of doubles, and \c ArrayXXf is a dynamic-size matrix of floats. + * + * There are also \c ArraySizeType which are self-explanatory. For example, \c Array4cf is + * a fixed-size 1D array of 4 complex floats. + * + * With \cpp11, template alias are also defined for common sizes. + * They follow the same pattern as above except that the scalar type suffix is replaced by a + * template parameter, i.e.: + * - `ArrayRowsCols` where `Rows` and `Cols` can be \c 2,\c 3,\c 4, or \c X for fixed or dynamic size. + * - `ArraySize` where `Size` can be \c 2,\c 3,\c 4 or \c X for fixed or dynamic size 1D arrays. + * + * \sa class Array + */ + +#define EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ +/** \ingroup arraytypedefs */ \ +typedef Array Array##SizeSuffix##SizeSuffix##TypeSuffix; \ +/** \ingroup arraytypedefs */ \ +typedef Array Array##SizeSuffix##TypeSuffix; + +#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \ +/** \ingroup arraytypedefs */ \ +typedef Array Array##Size##X##TypeSuffix; \ +/** \ingroup arraytypedefs */ \ +typedef Array Array##X##Size##TypeSuffix; + +#define EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ +EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 2, 2) \ +EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 3, 3) \ +EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, 4, 4) \ +EIGEN_MAKE_ARRAY_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \ +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \ +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \ +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Type, TypeSuffix, 4) + +EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(int, i) +EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(float, f) +EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(double, d) +EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex, cf) +EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES(std::complex, cd) + +#undef EIGEN_MAKE_ARRAY_TYPEDEFS_ALL_SIZES +#undef EIGEN_MAKE_ARRAY_TYPEDEFS +#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS + +#if EIGEN_HAS_CXX11 + +#define EIGEN_MAKE_ARRAY_TYPEDEFS(Size, SizeSuffix) \ +/** \ingroup arraytypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Array##SizeSuffix##SizeSuffix = Array; \ +/** \ingroup arraytypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Array##SizeSuffix = Array; + +#define EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(Size) \ +/** \ingroup arraytypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Array##Size##X = Array; \ +/** \ingroup arraytypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Array##X##Size = Array; + +EIGEN_MAKE_ARRAY_TYPEDEFS(2, 2) +EIGEN_MAKE_ARRAY_TYPEDEFS(3, 3) +EIGEN_MAKE_ARRAY_TYPEDEFS(4, 4) +EIGEN_MAKE_ARRAY_TYPEDEFS(Dynamic, X) +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(2) +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(3) +EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS(4) + +#undef EIGEN_MAKE_ARRAY_TYPEDEFS +#undef EIGEN_MAKE_ARRAY_FIXED_TYPEDEFS + +#endif // EIGEN_HAS_CXX11 + +#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, SizeSuffix) \ +using Eigen::Matrix##SizeSuffix##TypeSuffix; \ +using Eigen::Vector##SizeSuffix##TypeSuffix; \ +using Eigen::RowVector##SizeSuffix##TypeSuffix; + +#define EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(TypeSuffix) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 2) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 3) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, 4) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE_AND_SIZE(TypeSuffix, X) \ + +#define EIGEN_USING_ARRAY_TYPEDEFS \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(i) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(f) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(d) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cf) \ +EIGEN_USING_ARRAY_TYPEDEFS_FOR_TYPE(cd) + +} // end namespace Eigen + +#endif // EIGEN_ARRAY_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayBase.h new file mode 100644 index 0000000000000000000000000000000000000000..ea3dd1c3b38c989ee1e1a5fe3a43b10aa8ee9b70 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayBase.h @@ -0,0 +1,226 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ARRAYBASE_H +#define EIGEN_ARRAYBASE_H + +namespace Eigen { + +template class MatrixWrapper; + +/** \class ArrayBase + * \ingroup Core_Module + * + * \brief Base class for all 1D and 2D array, and related expressions + * + * An array is similar to a dense vector or matrix. While matrices are mathematical + * objects with well defined linear algebra operators, an array is just a collection + * of scalar values arranged in a one or two dimensionnal fashion. As the main consequence, + * all operations applied to an array are performed coefficient wise. Furthermore, + * arrays support scalar math functions of the c++ standard library (e.g., std::sin(x)), and convenient + * constructors allowing to easily write generic code working for both scalar values + * and arrays. + * + * This class is the base that is inherited by all array expression types. + * + * \tparam Derived is the derived type, e.g., an array or an expression type. + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_ARRAYBASE_PLUGIN. + * + * \sa class MatrixBase, \ref TopicClassHierarchy + */ +template class ArrayBase + : public DenseBase +{ + public: +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** The base class for a given storage type. */ + typedef ArrayBase StorageBaseType; + + typedef ArrayBase Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl; + + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::packet_traits::type PacketScalar; + typedef typename NumTraits::Real RealScalar; + + typedef DenseBase Base; + using Base::RowsAtCompileTime; + using Base::ColsAtCompileTime; + using Base::SizeAtCompileTime; + using Base::MaxRowsAtCompileTime; + using Base::MaxColsAtCompileTime; + using Base::MaxSizeAtCompileTime; + using Base::IsVectorAtCompileTime; + using Base::Flags; + + using Base::derived; + using Base::const_cast_derived; + using Base::rows; + using Base::cols; + using Base::size; + using Base::coeff; + using Base::coeffRef; + using Base::lazyAssign; + using Base::operator-; + using Base::operator=; + using Base::operator+=; + using Base::operator-=; + using Base::operator*=; + using Base::operator/=; + + typedef typename Base::CoeffReturnType CoeffReturnType; + +#endif // not EIGEN_PARSED_BY_DOXYGEN + +#ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename Base::PlainObject PlainObject; + + /** \internal Represents a matrix with all coefficients equal to one another*/ + typedef CwiseNullaryOp,PlainObject> ConstantReturnType; +#endif // not EIGEN_PARSED_BY_DOXYGEN + +#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::ArrayBase +#define EIGEN_DOC_UNARY_ADDONS(X,Y) +# include "../plugins/MatrixCwiseUnaryOps.h" +# include "../plugins/ArrayCwiseUnaryOps.h" +# include "../plugins/CommonCwiseBinaryOps.h" +# include "../plugins/MatrixCwiseBinaryOps.h" +# include "../plugins/ArrayCwiseBinaryOps.h" +# ifdef EIGEN_ARRAYBASE_PLUGIN +# include EIGEN_ARRAYBASE_PLUGIN +# endif +#undef EIGEN_CURRENT_STORAGE_BASE_CLASS +#undef EIGEN_DOC_UNARY_ADDONS + + /** Special case of the template operator=, in order to prevent the compiler + * from generating a default operator= (issue hit with g++ 4.1) + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const ArrayBase& other) + { + internal::call_assignment(derived(), other.derived()); + return derived(); + } + + /** Set all the entries to \a value. + * \sa DenseBase::setConstant(), DenseBase::fill() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const Scalar &value) + { Base::setConstant(value); return derived(); } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator+=(const Scalar& scalar); + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator-=(const Scalar& scalar); + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator+=(const ArrayBase& other); + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator-=(const ArrayBase& other); + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator*=(const ArrayBase& other); + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator/=(const ArrayBase& other); + + public: + EIGEN_DEVICE_FUNC + ArrayBase& array() { return *this; } + EIGEN_DEVICE_FUNC + const ArrayBase& array() const { return *this; } + + /** \returns an \link Eigen::MatrixBase Matrix \endlink expression of this array + * \sa MatrixBase::array() */ + EIGEN_DEVICE_FUNC + MatrixWrapper matrix() { return MatrixWrapper(derived()); } + EIGEN_DEVICE_FUNC + const MatrixWrapper matrix() const { return MatrixWrapper(derived()); } + +// template +// inline void evalTo(Dest& dst) const { dst = matrix(); } + + protected: + EIGEN_DEFAULT_COPY_CONSTRUCTOR(ArrayBase) + EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(ArrayBase) + + private: + explicit ArrayBase(Index); + ArrayBase(Index,Index); + template explicit ArrayBase(const ArrayBase&); + protected: + // mixing arrays and matrices is not legal + template Derived& operator+=(const MatrixBase& ) + {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;} + // mixing arrays and matrices is not legal + template Derived& operator-=(const MatrixBase& ) + {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;} +}; + +/** replaces \c *this by \c *this - \a other. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +ArrayBase::operator-=(const ArrayBase &other) +{ + call_assignment(derived(), other.derived(), internal::sub_assign_op()); + return derived(); +} + +/** replaces \c *this by \c *this + \a other. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +ArrayBase::operator+=(const ArrayBase& other) +{ + call_assignment(derived(), other.derived(), internal::add_assign_op()); + return derived(); +} + +/** replaces \c *this by \c *this * \a other coefficient wise. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +ArrayBase::operator*=(const ArrayBase& other) +{ + call_assignment(derived(), other.derived(), internal::mul_assign_op()); + return derived(); +} + +/** replaces \c *this by \c *this / \a other coefficient wise. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +ArrayBase::operator/=(const ArrayBase& other) +{ + call_assignment(derived(), other.derived(), internal::div_assign_op()); + return derived(); +} + +} // end namespace Eigen + +#endif // EIGEN_ARRAYBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayWrapper.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayWrapper.h new file mode 100644 index 0000000000000000000000000000000000000000..2e9555b5374dc723aa181d30194056c05bc96e18 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ArrayWrapper.h @@ -0,0 +1,209 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ARRAYWRAPPER_H +#define EIGEN_ARRAYWRAPPER_H + +namespace Eigen { + +/** \class ArrayWrapper + * \ingroup Core_Module + * + * \brief Expression of a mathematical vector or matrix as an array object + * + * This class is the return type of MatrixBase::array(), and most of the time + * this is the only way it is use. + * + * \sa MatrixBase::array(), class MatrixWrapper + */ + +namespace internal { +template +struct traits > + : public traits::type > +{ + typedef ArrayXpr XprKind; + // Let's remove NestByRefBit + enum { + Flags0 = traits::type >::Flags, + LvalueBitFlag = is_lvalue::value ? LvalueBit : 0, + Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag + }; +}; +} + +template +class ArrayWrapper : public ArrayBase > +{ + public: + typedef ArrayBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(ArrayWrapper) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ArrayWrapper) + typedef typename internal::remove_all::type NestedExpression; + + typedef typename internal::conditional< + internal::is_lvalue::value, + Scalar, + const Scalar + >::type ScalarWithConstIfNotLvalue; + + typedef typename internal::ref_selector::non_const_type NestedExpressionType; + + using Base::coeffRef; + + EIGEN_DEVICE_FUNC + explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {} + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); } + + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); } + EIGEN_DEVICE_FUNC + inline const Scalar* data() const { return m_expression.data(); } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index rowId, Index colId) const + { + return m_expression.coeffRef(rowId, colId); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index index) const + { + return m_expression.coeffRef(index); + } + + template + EIGEN_DEVICE_FUNC + inline void evalTo(Dest& dst) const { dst = m_expression; } + + EIGEN_DEVICE_FUNC + const typename internal::remove_all::type& + nestedExpression() const + { + return m_expression; + } + + /** Forwards the resizing request to the nested expression + * \sa DenseBase::resize(Index) */ + EIGEN_DEVICE_FUNC + void resize(Index newSize) { m_expression.resize(newSize); } + /** Forwards the resizing request to the nested expression + * \sa DenseBase::resize(Index,Index)*/ + EIGEN_DEVICE_FUNC + void resize(Index rows, Index cols) { m_expression.resize(rows,cols); } + + protected: + NestedExpressionType m_expression; +}; + +/** \class MatrixWrapper + * \ingroup Core_Module + * + * \brief Expression of an array as a mathematical vector or matrix + * + * This class is the return type of ArrayBase::matrix(), and most of the time + * this is the only way it is use. + * + * \sa MatrixBase::matrix(), class ArrayWrapper + */ + +namespace internal { +template +struct traits > + : public traits::type > +{ + typedef MatrixXpr XprKind; + // Let's remove NestByRefBit + enum { + Flags0 = traits::type >::Flags, + LvalueBitFlag = is_lvalue::value ? LvalueBit : 0, + Flags = (Flags0 & ~(NestByRefBit | LvalueBit)) | LvalueBitFlag + }; +}; +} + +template +class MatrixWrapper : public MatrixBase > +{ + public: + typedef MatrixBase > Base; + EIGEN_DENSE_PUBLIC_INTERFACE(MatrixWrapper) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(MatrixWrapper) + typedef typename internal::remove_all::type NestedExpression; + + typedef typename internal::conditional< + internal::is_lvalue::value, + Scalar, + const Scalar + >::type ScalarWithConstIfNotLvalue; + + typedef typename internal::ref_selector::non_const_type NestedExpressionType; + + using Base::coeffRef; + + EIGEN_DEVICE_FUNC + explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {} + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); } + + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue* data() { return m_expression.data(); } + EIGEN_DEVICE_FUNC + inline const Scalar* data() const { return m_expression.data(); } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index rowId, Index colId) const + { + return m_expression.derived().coeffRef(rowId, colId); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index index) const + { + return m_expression.coeffRef(index); + } + + EIGEN_DEVICE_FUNC + const typename internal::remove_all::type& + nestedExpression() const + { + return m_expression; + } + + /** Forwards the resizing request to the nested expression + * \sa DenseBase::resize(Index) */ + EIGEN_DEVICE_FUNC + void resize(Index newSize) { m_expression.resize(newSize); } + /** Forwards the resizing request to the nested expression + * \sa DenseBase::resize(Index,Index)*/ + EIGEN_DEVICE_FUNC + void resize(Index rows, Index cols) { m_expression.resize(rows,cols); } + + protected: + NestedExpressionType m_expression; +}; + +} // end namespace Eigen + +#endif // EIGEN_ARRAYWRAPPER_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign.h new file mode 100644 index 0000000000000000000000000000000000000000..655412efd7f26d616b002b3d584ec7fc8a5d9ea4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign.h @@ -0,0 +1,90 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007 Michael Olbrich +// Copyright (C) 2006-2010 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ASSIGN_H +#define EIGEN_ASSIGN_H + +namespace Eigen { + +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase + ::lazyAssign(const DenseBase& other) +{ + enum{ + SameType = internal::is_same::value + }; + + EIGEN_STATIC_ASSERT_LVALUE(Derived) + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived) + EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + + eigen_assert(rows() == other.rows() && cols() == other.cols()); + internal::call_assignment_no_alias(derived(),other.derived()); + + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& DenseBase::operator=(const DenseBase& other) +{ + internal::call_assignment(derived(), other.derived()); + return derived(); +} + +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& DenseBase::operator=(const DenseBase& other) +{ + internal::call_assignment(derived(), other.derived()); + return derived(); +} + +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& MatrixBase::operator=(const MatrixBase& other) +{ + internal::call_assignment(derived(), other.derived()); + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& MatrixBase::operator=(const DenseBase& other) +{ + internal::call_assignment(derived(), other.derived()); + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& MatrixBase::operator=(const EigenBase& other) +{ + internal::call_assignment(derived(), other.derived()); + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE Derived& MatrixBase::operator=(const ReturnByValue& other) +{ + other.derived().evalTo(derived()); + return derived(); +} + +} // end namespace Eigen + +#endif // EIGEN_ASSIGN_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/AssignEvaluator.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/AssignEvaluator.h new file mode 100644 index 0000000000000000000000000000000000000000..7d76f0c256fd6207819921680217b30697e81ca3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/AssignEvaluator.h @@ -0,0 +1,1010 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Benoit Jacob +// Copyright (C) 2011-2014 Gael Guennebaud +// Copyright (C) 2011-2012 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ASSIGN_EVALUATOR_H +#define EIGEN_ASSIGN_EVALUATOR_H + +namespace Eigen { + +// This implementation is based on Assign.h + +namespace internal { + +/*************************************************************************** +* Part 1 : the logic deciding a strategy for traversal and unrolling * +***************************************************************************/ + +// copy_using_evaluator_traits is based on assign_traits + +template +struct copy_using_evaluator_traits +{ + typedef typename DstEvaluator::XprType Dst; + typedef typename Dst::Scalar DstScalar; + + enum { + DstFlags = DstEvaluator::Flags, + SrcFlags = SrcEvaluator::Flags + }; + +public: + enum { + DstAlignment = DstEvaluator::Alignment, + SrcAlignment = SrcEvaluator::Alignment, + DstHasDirectAccess = (DstFlags & DirectAccessBit) == DirectAccessBit, + JointAlignment = EIGEN_PLAIN_ENUM_MIN(DstAlignment,SrcAlignment) + }; + +private: + enum { + InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime) + : int(DstFlags)&RowMajorBit ? int(Dst::ColsAtCompileTime) + : int(Dst::RowsAtCompileTime), + InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime) + : int(DstFlags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime) + : int(Dst::MaxRowsAtCompileTime), + RestrictedInnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(InnerSize,MaxPacketSize), + RestrictedLinearSize = EIGEN_SIZE_MIN_PREFER_FIXED(Dst::SizeAtCompileTime,MaxPacketSize), + OuterStride = int(outer_stride_at_compile_time::ret), + MaxSizeAtCompileTime = Dst::SizeAtCompileTime + }; + + // TODO distinguish between linear traversal and inner-traversals + typedef typename find_best_packet::type LinearPacketType; + typedef typename find_best_packet::type InnerPacketType; + + enum { + LinearPacketSize = unpacket_traits::size, + InnerPacketSize = unpacket_traits::size + }; + +public: + enum { + LinearRequiredAlignment = unpacket_traits::alignment, + InnerRequiredAlignment = unpacket_traits::alignment + }; + +private: + enum { + DstIsRowMajor = DstFlags&RowMajorBit, + SrcIsRowMajor = SrcFlags&RowMajorBit, + StorageOrdersAgree = (int(DstIsRowMajor) == int(SrcIsRowMajor)), + MightVectorize = bool(StorageOrdersAgree) + && (int(DstFlags) & int(SrcFlags) & ActualPacketAccessBit) + && bool(functor_traits::PacketAccess), + MayInnerVectorize = MightVectorize + && int(InnerSize)!=Dynamic && int(InnerSize)%int(InnerPacketSize)==0 + && int(OuterStride)!=Dynamic && int(OuterStride)%int(InnerPacketSize)==0 + && (EIGEN_UNALIGNED_VECTORIZE || int(JointAlignment)>=int(InnerRequiredAlignment)), + MayLinearize = bool(StorageOrdersAgree) && (int(DstFlags) & int(SrcFlags) & LinearAccessBit), + MayLinearVectorize = bool(MightVectorize) && bool(MayLinearize) && bool(DstHasDirectAccess) + && (EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment)) || MaxSizeAtCompileTime == Dynamic), + /* If the destination isn't aligned, we have to do runtime checks and we don't unroll, + so it's only good for large enough sizes. */ + MaySliceVectorize = bool(MightVectorize) && bool(DstHasDirectAccess) + && (int(InnerMaxSize)==Dynamic || int(InnerMaxSize)>=(EIGEN_UNALIGNED_VECTORIZE?InnerPacketSize:(3*InnerPacketSize))) + /* slice vectorization can be slow, so we only want it if the slices are big, which is + indicated by InnerMaxSize rather than InnerSize, think of the case of a dynamic block + in a fixed-size matrix + However, with EIGEN_UNALIGNED_VECTORIZE and unrolling, slice vectorization is still worth it */ + }; + +public: + enum { + Traversal = int(Dst::SizeAtCompileTime) == 0 ? int(AllAtOnceTraversal) // If compile-size is zero, traversing will fail at compile-time. + : (int(MayLinearVectorize) && (LinearPacketSize>InnerPacketSize)) ? int(LinearVectorizedTraversal) + : int(MayInnerVectorize) ? int(InnerVectorizedTraversal) + : int(MayLinearVectorize) ? int(LinearVectorizedTraversal) + : int(MaySliceVectorize) ? int(SliceVectorizedTraversal) + : int(MayLinearize) ? int(LinearTraversal) + : int(DefaultTraversal), + Vectorized = int(Traversal) == InnerVectorizedTraversal + || int(Traversal) == LinearVectorizedTraversal + || int(Traversal) == SliceVectorizedTraversal + }; + + typedef typename conditional::type PacketType; + +private: + enum { + ActualPacketSize = int(Traversal)==LinearVectorizedTraversal ? LinearPacketSize + : Vectorized ? InnerPacketSize + : 1, + UnrollingLimit = EIGEN_UNROLLING_LIMIT * ActualPacketSize, + MayUnrollCompletely = int(Dst::SizeAtCompileTime) != Dynamic + && int(Dst::SizeAtCompileTime) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit), + MayUnrollInner = int(InnerSize) != Dynamic + && int(InnerSize) * (int(DstEvaluator::CoeffReadCost)+int(SrcEvaluator::CoeffReadCost)) <= int(UnrollingLimit) + }; + +public: + enum { + Unrolling = (int(Traversal) == int(InnerVectorizedTraversal) || int(Traversal) == int(DefaultTraversal)) + ? ( + int(MayUnrollCompletely) ? int(CompleteUnrolling) + : int(MayUnrollInner) ? int(InnerUnrolling) + : int(NoUnrolling) + ) + : int(Traversal) == int(LinearVectorizedTraversal) + ? ( bool(MayUnrollCompletely) && ( EIGEN_UNALIGNED_VECTORIZE || (int(DstAlignment)>=int(LinearRequiredAlignment))) + ? int(CompleteUnrolling) + : int(NoUnrolling) ) + : int(Traversal) == int(LinearTraversal) + ? ( bool(MayUnrollCompletely) ? int(CompleteUnrolling) + : int(NoUnrolling) ) +#if EIGEN_UNALIGNED_VECTORIZE + : int(Traversal) == int(SliceVectorizedTraversal) + ? ( bool(MayUnrollInner) ? int(InnerUnrolling) + : int(NoUnrolling) ) +#endif + : int(NoUnrolling) + }; + +#ifdef EIGEN_DEBUG_ASSIGN + static void debug() + { + std::cerr << "DstXpr: " << typeid(typename DstEvaluator::XprType).name() << std::endl; + std::cerr << "SrcXpr: " << typeid(typename SrcEvaluator::XprType).name() << std::endl; + std::cerr.setf(std::ios::hex, std::ios::basefield); + std::cerr << "DstFlags" << " = " << DstFlags << " (" << demangle_flags(DstFlags) << " )" << std::endl; + std::cerr << "SrcFlags" << " = " << SrcFlags << " (" << demangle_flags(SrcFlags) << " )" << std::endl; + std::cerr.unsetf(std::ios::hex); + EIGEN_DEBUG_VAR(DstAlignment) + EIGEN_DEBUG_VAR(SrcAlignment) + EIGEN_DEBUG_VAR(LinearRequiredAlignment) + EIGEN_DEBUG_VAR(InnerRequiredAlignment) + EIGEN_DEBUG_VAR(JointAlignment) + EIGEN_DEBUG_VAR(InnerSize) + EIGEN_DEBUG_VAR(InnerMaxSize) + EIGEN_DEBUG_VAR(LinearPacketSize) + EIGEN_DEBUG_VAR(InnerPacketSize) + EIGEN_DEBUG_VAR(ActualPacketSize) + EIGEN_DEBUG_VAR(StorageOrdersAgree) + EIGEN_DEBUG_VAR(MightVectorize) + EIGEN_DEBUG_VAR(MayLinearize) + EIGEN_DEBUG_VAR(MayInnerVectorize) + EIGEN_DEBUG_VAR(MayLinearVectorize) + EIGEN_DEBUG_VAR(MaySliceVectorize) + std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl; + EIGEN_DEBUG_VAR(SrcEvaluator::CoeffReadCost) + EIGEN_DEBUG_VAR(DstEvaluator::CoeffReadCost) + EIGEN_DEBUG_VAR(Dst::SizeAtCompileTime) + EIGEN_DEBUG_VAR(UnrollingLimit) + EIGEN_DEBUG_VAR(MayUnrollCompletely) + EIGEN_DEBUG_VAR(MayUnrollInner) + std::cerr << "Unrolling" << " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl; + std::cerr << std::endl; + } +#endif +}; + +/*************************************************************************** +* Part 2 : meta-unrollers +***************************************************************************/ + +/************************ +*** Default traversal *** +************************/ + +template +struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling +{ + // FIXME: this is not very clean, perhaps this information should be provided by the kernel? + typedef typename Kernel::DstEvaluatorType DstEvaluatorType; + typedef typename DstEvaluatorType::XprType DstXprType; + + enum { + outer = Index / DstXprType::InnerSizeAtCompileTime, + inner = Index % DstXprType::InnerSizeAtCompileTime + }; + + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + kernel.assignCoeffByOuterInner(outer, inner); + copy_using_evaluator_DefaultTraversal_CompleteUnrolling::run(kernel); + } +}; + +template +struct copy_using_evaluator_DefaultTraversal_CompleteUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { } +}; + +template +struct copy_using_evaluator_DefaultTraversal_InnerUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer) + { + kernel.assignCoeffByOuterInner(outer, Index_); + copy_using_evaluator_DefaultTraversal_InnerUnrolling::run(kernel, outer); + } +}; + +template +struct copy_using_evaluator_DefaultTraversal_InnerUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&, Index) { } +}; + +/*********************** +*** Linear traversal *** +***********************/ + +template +struct copy_using_evaluator_LinearTraversal_CompleteUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel& kernel) + { + kernel.assignCoeff(Index); + copy_using_evaluator_LinearTraversal_CompleteUnrolling::run(kernel); + } +}; + +template +struct copy_using_evaluator_LinearTraversal_CompleteUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { } +}; + +/************************** +*** Inner vectorization *** +**************************/ + +template +struct copy_using_evaluator_innervec_CompleteUnrolling +{ + // FIXME: this is not very clean, perhaps this information should be provided by the kernel? + typedef typename Kernel::DstEvaluatorType DstEvaluatorType; + typedef typename DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::PacketType PacketType; + + enum { + outer = Index / DstXprType::InnerSizeAtCompileTime, + inner = Index % DstXprType::InnerSizeAtCompileTime, + SrcAlignment = Kernel::AssignmentTraits::SrcAlignment, + DstAlignment = Kernel::AssignmentTraits::DstAlignment + }; + + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + kernel.template assignPacketByOuterInner(outer, inner); + enum { NextIndex = Index + unpacket_traits::size }; + copy_using_evaluator_innervec_CompleteUnrolling::run(kernel); + } +}; + +template +struct copy_using_evaluator_innervec_CompleteUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&) { } +}; + +template +struct copy_using_evaluator_innervec_InnerUnrolling +{ + typedef typename Kernel::PacketType PacketType; + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, Index outer) + { + kernel.template assignPacketByOuterInner(outer, Index_); + enum { NextIndex = Index_ + unpacket_traits::size }; + copy_using_evaluator_innervec_InnerUnrolling::run(kernel, outer); + } +}; + +template +struct copy_using_evaluator_innervec_InnerUnrolling +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &, Index) { } +}; + +/*************************************************************************** +* Part 3 : implementation of all cases +***************************************************************************/ + +// dense_assignment_loop is based on assign_impl + +template +struct dense_assignment_loop; + +/************************ +***** Special Cases ***** +************************/ + +// Zero-sized assignment is a no-op. +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE run(Kernel& /*kernel*/) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + EIGEN_STATIC_ASSERT(int(DstXprType::SizeAtCompileTime) == 0, + EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT) + } +}; + +/************************ +*** Default traversal *** +************************/ + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static void EIGEN_STRONG_INLINE run(Kernel &kernel) + { + for(Index outer = 0; outer < kernel.outerSize(); ++outer) { + for(Index inner = 0; inner < kernel.innerSize(); ++inner) { + kernel.assignCoeffByOuterInner(outer, inner); + } + } + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + copy_using_evaluator_DefaultTraversal_CompleteUnrolling::run(kernel); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + + const Index outerSize = kernel.outerSize(); + for(Index outer = 0; outer < outerSize; ++outer) + copy_using_evaluator_DefaultTraversal_InnerUnrolling::run(kernel, outer); + } +}; + +/*************************** +*** Linear vectorization *** +***************************/ + + +// The goal of unaligned_dense_assignment_loop is simply to factorize the handling +// of the non vectorizable beginning and ending parts + +template +struct unaligned_dense_assignment_loop +{ + // if IsAligned = true, then do nothing + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel&, Index, Index) {} +}; + +template <> +struct unaligned_dense_assignment_loop +{ + // MSVC must not inline this functions. If it does, it fails to optimize the + // packet access path. + // FIXME check which version exhibits this issue +#if EIGEN_COMP_MSVC + template + static EIGEN_DONT_INLINE void run(Kernel &kernel, + Index start, + Index end) +#else + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel, + Index start, + Index end) +#endif + { + for (Index index = start; index < end; ++index) + kernel.assignCoeff(index); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + const Index size = kernel.size(); + typedef typename Kernel::Scalar Scalar; + typedef typename Kernel::PacketType PacketType; + enum { + requestedAlignment = Kernel::AssignmentTraits::LinearRequiredAlignment, + packetSize = unpacket_traits::size, + dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment), + dstAlignment = packet_traits::AlignedOnScalar ? int(requestedAlignment) + : int(Kernel::AssignmentTraits::DstAlignment), + srcAlignment = Kernel::AssignmentTraits::JointAlignment + }; + const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned(kernel.dstDataPtr(), size); + const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize; + + unaligned_dense_assignment_loop::run(kernel, 0, alignedStart); + + for(Index index = alignedStart; index < alignedEnd; index += packetSize) + kernel.template assignPacket(index); + + unaligned_dense_assignment_loop<>::run(kernel, alignedEnd, size); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::PacketType PacketType; + + enum { size = DstXprType::SizeAtCompileTime, + packetSize =unpacket_traits::size, + alignedSize = (int(size)/packetSize)*packetSize }; + + copy_using_evaluator_innervec_CompleteUnrolling::run(kernel); + copy_using_evaluator_DefaultTraversal_CompleteUnrolling::run(kernel); + } +}; + +/************************** +*** Inner vectorization *** +**************************/ + +template +struct dense_assignment_loop +{ + typedef typename Kernel::PacketType PacketType; + enum { + SrcAlignment = Kernel::AssignmentTraits::SrcAlignment, + DstAlignment = Kernel::AssignmentTraits::DstAlignment + }; + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + const Index innerSize = kernel.innerSize(); + const Index outerSize = kernel.outerSize(); + const Index packetSize = unpacket_traits::size; + for(Index outer = 0; outer < outerSize; ++outer) + for(Index inner = 0; inner < innerSize; inner+=packetSize) + kernel.template assignPacketByOuterInner(outer, inner); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + copy_using_evaluator_innervec_CompleteUnrolling::run(kernel); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::AssignmentTraits Traits; + const Index outerSize = kernel.outerSize(); + for(Index outer = 0; outer < outerSize; ++outer) + copy_using_evaluator_innervec_InnerUnrolling::run(kernel, outer); + } +}; + +/*********************** +*** Linear traversal *** +***********************/ + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + const Index size = kernel.size(); + for(Index i = 0; i < size; ++i) + kernel.assignCoeff(i); + } +}; + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + copy_using_evaluator_LinearTraversal_CompleteUnrolling::run(kernel); + } +}; + +/************************** +*** Slice vectorization *** +***************************/ + +template +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::Scalar Scalar; + typedef typename Kernel::PacketType PacketType; + enum { + packetSize = unpacket_traits::size, + requestedAlignment = int(Kernel::AssignmentTraits::InnerRequiredAlignment), + alignable = packet_traits::AlignedOnScalar || int(Kernel::AssignmentTraits::DstAlignment)>=sizeof(Scalar), + dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment), + dstAlignment = alignable ? int(requestedAlignment) + : int(Kernel::AssignmentTraits::DstAlignment) + }; + const Scalar *dst_ptr = kernel.dstDataPtr(); + if((!bool(dstIsAligned)) && (UIntPtr(dst_ptr) % sizeof(Scalar))>0) + { + // the pointer is not aligned-on scalar, so alignment is not possible + return dense_assignment_loop::run(kernel); + } + const Index packetAlignedMask = packetSize - 1; + const Index innerSize = kernel.innerSize(); + const Index outerSize = kernel.outerSize(); + const Index alignedStep = alignable ? (packetSize - kernel.outerStride() % packetSize) & packetAlignedMask : 0; + Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, innerSize); + + for(Index outer = 0; outer < outerSize; ++outer) + { + const Index alignedEnd = alignedStart + ((innerSize-alignedStart) & ~packetAlignedMask); + // do the non-vectorizable part of the assignment + for(Index inner = 0; inner(outer, inner); + + // do the non-vectorizable part of the assignment + for(Index inner = alignedEnd; inner +struct dense_assignment_loop +{ + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void run(Kernel &kernel) + { + typedef typename Kernel::DstEvaluatorType::XprType DstXprType; + typedef typename Kernel::PacketType PacketType; + + enum { innerSize = DstXprType::InnerSizeAtCompileTime, + packetSize =unpacket_traits::size, + vectorizableSize = (int(innerSize) / int(packetSize)) * int(packetSize), + size = DstXprType::SizeAtCompileTime }; + + for(Index outer = 0; outer < kernel.outerSize(); ++outer) + { + copy_using_evaluator_innervec_InnerUnrolling::run(kernel, outer); + copy_using_evaluator_DefaultTraversal_InnerUnrolling::run(kernel, outer); + } + } +}; +#endif + + +/*************************************************************************** +* Part 4 : Generic dense assignment kernel +***************************************************************************/ + +// This class generalize the assignment of a coefficient (or packet) from one dense evaluator +// to another dense writable evaluator. +// It is parametrized by the two evaluators, and the actual assignment functor. +// This abstraction level permits to keep the evaluation loops as simple and as generic as possible. +// One can customize the assignment using this generic dense_assignment_kernel with different +// functors, or by completely overloading it, by-passing a functor. +template +class generic_dense_assignment_kernel +{ +protected: + typedef typename DstEvaluatorTypeT::XprType DstXprType; + typedef typename SrcEvaluatorTypeT::XprType SrcXprType; +public: + + typedef DstEvaluatorTypeT DstEvaluatorType; + typedef SrcEvaluatorTypeT SrcEvaluatorType; + typedef typename DstEvaluatorType::Scalar Scalar; + typedef copy_using_evaluator_traits AssignmentTraits; + typedef typename AssignmentTraits::PacketType PacketType; + + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + generic_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr) + : m_dst(dst), m_src(src), m_functor(func), m_dstExpr(dstExpr) + { + #ifdef EIGEN_DEBUG_ASSIGN + AssignmentTraits::debug(); + #endif + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_dstExpr.size(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerSize() const EIGEN_NOEXCEPT { return m_dstExpr.innerSize(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerSize() const EIGEN_NOEXCEPT { return m_dstExpr.outerSize(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_dstExpr.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_dstExpr.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerStride() const EIGEN_NOEXCEPT { return m_dstExpr.outerStride(); } + + EIGEN_DEVICE_FUNC DstEvaluatorType& dstEvaluator() EIGEN_NOEXCEPT { return m_dst; } + EIGEN_DEVICE_FUNC const SrcEvaluatorType& srcEvaluator() const EIGEN_NOEXCEPT { return m_src; } + + /// Assign src(row,col) to dst(row,col) through the assignment functor. + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index row, Index col) + { + m_functor.assignCoeff(m_dst.coeffRef(row,col), m_src.coeff(row,col)); + } + + /// \sa assignCoeff(Index,Index) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeff(Index index) + { + m_functor.assignCoeff(m_dst.coeffRef(index), m_src.coeff(index)); + } + + /// \sa assignCoeff(Index,Index) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignCoeffByOuterInner(Index outer, Index inner) + { + Index row = rowIndexByOuterInner(outer, inner); + Index col = colIndexByOuterInner(outer, inner); + assignCoeff(row, col); + } + + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index row, Index col) + { + m_functor.template assignPacket(&m_dst.coeffRef(row,col), m_src.template packet(row,col)); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacket(Index index) + { + m_functor.template assignPacket(&m_dst.coeffRef(index), m_src.template packet(index)); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void assignPacketByOuterInner(Index outer, Index inner) + { + Index row = rowIndexByOuterInner(outer, inner); + Index col = colIndexByOuterInner(outer, inner); + assignPacket(row, col); + } + + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) + { + typedef typename DstEvaluatorType::ExpressionTraits Traits; + return int(Traits::RowsAtCompileTime) == 1 ? 0 + : int(Traits::ColsAtCompileTime) == 1 ? inner + : int(DstEvaluatorType::Flags)&RowMajorBit ? outer + : inner; + } + + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) + { + typedef typename DstEvaluatorType::ExpressionTraits Traits; + return int(Traits::ColsAtCompileTime) == 1 ? 0 + : int(Traits::RowsAtCompileTime) == 1 ? inner + : int(DstEvaluatorType::Flags)&RowMajorBit ? inner + : outer; + } + + EIGEN_DEVICE_FUNC const Scalar* dstDataPtr() const + { + return m_dstExpr.data(); + } + +protected: + DstEvaluatorType& m_dst; + const SrcEvaluatorType& m_src; + const Functor &m_functor; + // TODO find a way to avoid the needs of the original expression + DstXprType& m_dstExpr; +}; + +// Special kernel used when computing small products whose operands have dynamic dimensions. It ensures that the +// PacketSize used is no larger than 4, thereby increasing the chance that vectorized instructions will be used +// when computing the product. + +template +class restricted_packet_dense_assignment_kernel : public generic_dense_assignment_kernel +{ +protected: + typedef generic_dense_assignment_kernel Base; + public: + typedef typename Base::Scalar Scalar; + typedef typename Base::DstXprType DstXprType; + typedef copy_using_evaluator_traits AssignmentTraits; + typedef typename AssignmentTraits::PacketType PacketType; + + EIGEN_DEVICE_FUNC restricted_packet_dense_assignment_kernel(DstEvaluatorTypeT &dst, const SrcEvaluatorTypeT &src, const Functor &func, DstXprType& dstExpr) + : Base(dst, src, func, dstExpr) + { + } + }; + +/*************************************************************************** +* Part 5 : Entry point for dense rectangular assignment +***************************************************************************/ + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void resize_if_allowed(DstXprType &dst, const SrcXprType& src, const Functor &/*func*/) +{ + EIGEN_ONLY_USED_FOR_DEBUG(dst); + EIGEN_ONLY_USED_FOR_DEBUG(src); + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void resize_if_allowed(DstXprType &dst, const SrcXprType& src, const internal::assign_op &/*func*/) +{ + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if(((dst.rows()!=dstRows) || (dst.cols()!=dstCols))) + dst.resize(dstRows, dstCols); + eigen_assert(dst.rows() == dstRows && dst.cols() == dstCols); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src, const Functor &func) +{ + typedef evaluator DstEvaluatorType; + typedef evaluator SrcEvaluatorType; + + SrcEvaluatorType srcEvaluator(src); + + // NOTE To properly handle A = (A*A.transpose())/s with A rectangular, + // we need to resize the destination after the source evaluator has been created. + resize_if_allowed(dst, src, func); + + DstEvaluatorType dstEvaluator(dst); + + typedef generic_dense_assignment_kernel Kernel; + Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived()); + + dense_assignment_loop::run(kernel); +} + +// Specialization for filling the destination with a constant value. +#ifndef EIGEN_GPU_COMPILE_PHASE +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const Eigen::CwiseNullaryOp, DstXprType>& src, const internal::assign_op& func) +{ + resize_if_allowed(dst, src, func); + std::fill_n(dst.data(), dst.size(), src.functor()()); +} +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src) +{ + call_dense_assignment_loop(dst, src, internal::assign_op()); +} + +/*************************************************************************** +* Part 6 : Generic assignment +***************************************************************************/ + +// Based on the respective shapes of the destination and source, +// the class AssignmentKind determine the kind of assignment mechanism. +// AssignmentKind must define a Kind typedef. +template struct AssignmentKind; + +// Assignment kind defined in this file: +struct Dense2Dense {}; +struct EigenBase2EigenBase {}; + +template struct AssignmentKind { typedef EigenBase2EigenBase Kind; }; +template<> struct AssignmentKind { typedef Dense2Dense Kind; }; + +// This is the main assignment class +template< typename DstXprType, typename SrcXprType, typename Functor, + typename Kind = typename AssignmentKind< typename evaluator_traits::Shape , typename evaluator_traits::Shape >::Kind, + typename EnableIf = void> +struct Assignment; + + +// The only purpose of this call_assignment() function is to deal with noalias() / "assume-aliasing" and automatic transposition. +// Indeed, I (Gael) think that this concept of "assume-aliasing" was a mistake, and it makes thing quite complicated. +// So this intermediate function removes everything related to "assume-aliasing" such that Assignment +// does not has to bother about these annoying details. + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment(Dst& dst, const Src& src) +{ + call_assignment(dst, src, internal::assign_op()); +} +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment(const Dst& dst, const Src& src) +{ + call_assignment(dst, src, internal::assign_op()); +} + +// Deal with "assume-aliasing" +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if< evaluator_assume_aliasing::value, void*>::type = 0) +{ + typename plain_matrix_type::type tmp(src); + call_assignment_no_alias(dst, tmp, func); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment(Dst& dst, const Src& src, const Func& func, typename enable_if::value, void*>::type = 0) +{ + call_assignment_no_alias(dst, src, func); +} + +// by-pass "assume-aliasing" +// When there is no aliasing, we require that 'dst' has been properly resized +template class StorageBase, typename Src, typename Func> +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment(NoAlias& dst, const Src& src, const Func& func) +{ + call_assignment_no_alias(dst.expression(), src, func); +} + + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment_no_alias(Dst& dst, const Src& src, const Func& func) +{ + enum { + NeedToTranspose = ( (int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1) + || (int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1) + ) && int(Dst::SizeAtCompileTime) != 1 + }; + + typedef typename internal::conditional, Dst>::type ActualDstTypeCleaned; + typedef typename internal::conditional, Dst&>::type ActualDstType; + ActualDstType actualDst(dst); + + // TODO check whether this is the right place to perform these checks: + EIGEN_STATIC_ASSERT_LVALUE(Dst) + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(ActualDstTypeCleaned,Src) + EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename ActualDstTypeCleaned::Scalar,typename Src::Scalar); + + Assignment::run(actualDst, src, func); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_restricted_packet_assignment_no_alias(Dst& dst, const Src& src, const Func& func) +{ + typedef evaluator DstEvaluatorType; + typedef evaluator SrcEvaluatorType; + typedef restricted_packet_dense_assignment_kernel Kernel; + + EIGEN_STATIC_ASSERT_LVALUE(Dst) + EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename Dst::Scalar,typename Src::Scalar); + + SrcEvaluatorType srcEvaluator(src); + resize_if_allowed(dst, src, func); + + DstEvaluatorType dstEvaluator(dst); + Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived()); + + dense_assignment_loop::run(kernel); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment_no_alias(Dst& dst, const Src& src) +{ + call_assignment_no_alias(dst, src, internal::assign_op()); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src, const Func& func) +{ + // TODO check whether this is the right place to perform these checks: + EIGEN_STATIC_ASSERT_LVALUE(Dst) + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Dst,Src) + EIGEN_CHECK_BINARY_COMPATIBILIY(Func,typename Dst::Scalar,typename Src::Scalar); + + Assignment::run(dst, src, func); +} +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +void call_assignment_no_alias_no_transpose(Dst& dst, const Src& src) +{ + call_assignment_no_alias_no_transpose(dst, src, internal::assign_op()); +} + +// forward declaration +template void check_for_aliasing(const Dst &dst, const Src &src); + +// Generic Dense to Dense assignment +// Note that the last template argument "Weak" is needed to make it possible to perform +// both partial specialization+SFINAE without ambiguous specialization +template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak> +struct Assignment +{ + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const Functor &func) + { +#ifndef EIGEN_NO_DEBUG + internal::check_for_aliasing(dst, src); +#endif + + call_dense_assignment_loop(dst, src, func); + } +}; + +// Generic assignment through evalTo. +// TODO: not sure we have to keep that one, but it helps porting current code to new evaluator mechanism. +// Note that the last template argument "Weak" is needed to make it possible to perform +// both partial specialization+SFINAE without ambiguous specialization +template< typename DstXprType, typename SrcXprType, typename Functor, typename Weak> +struct Assignment +{ + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op &/*func*/) + { + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) + dst.resize(dstRows, dstCols); + + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + src.evalTo(dst); + } + + // NOTE The following two functions are templated to avoid their instantiation if not needed + // This is needed because some expressions supports evalTo only and/or have 'void' as scalar type. + template + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op &/*func*/) + { + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) + dst.resize(dstRows, dstCols); + + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + src.addTo(dst); + } + + template + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op &/*func*/) + { + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) + dst.resize(dstRows, dstCols); + + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + src.subTo(dst); + } +}; + +} // namespace internal + +} // end namespace Eigen + +#endif // EIGEN_ASSIGN_EVALUATOR_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign_MKL.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign_MKL.h new file mode 100644 index 0000000000000000000000000000000000000000..c6140d185ba07aabfc930cb76f0834ce6231a710 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Assign_MKL.h @@ -0,0 +1,178 @@ +/* + Copyright (c) 2011, Intel Corporation. All rights reserved. + Copyright (C) 2015 Gael Guennebaud + + 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 Intel Corporation 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. + + ******************************************************************************** + * Content : Eigen bindings to Intel(R) MKL + * MKL VML support for coefficient-wise unary Eigen expressions like a=b.sin() + ******************************************************************************** +*/ + +#ifndef EIGEN_ASSIGN_VML_H +#define EIGEN_ASSIGN_VML_H + +namespace Eigen { + +namespace internal { + +template +class vml_assign_traits +{ + private: + enum { + DstHasDirectAccess = Dst::Flags & DirectAccessBit, + SrcHasDirectAccess = Src::Flags & DirectAccessBit, + StorageOrdersAgree = (int(Dst::IsRowMajor) == int(Src::IsRowMajor)), + InnerSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::SizeAtCompileTime) + : int(Dst::Flags)&RowMajorBit ? int(Dst::ColsAtCompileTime) + : int(Dst::RowsAtCompileTime), + InnerMaxSize = int(Dst::IsVectorAtCompileTime) ? int(Dst::MaxSizeAtCompileTime) + : int(Dst::Flags)&RowMajorBit ? int(Dst::MaxColsAtCompileTime) + : int(Dst::MaxRowsAtCompileTime), + MaxSizeAtCompileTime = Dst::SizeAtCompileTime, + + MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess && Src::InnerStrideAtCompileTime==1 && Dst::InnerStrideAtCompileTime==1, + MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit), + VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize, + LargeEnough = VmlSize==Dynamic || VmlSize>=EIGEN_MKL_VML_THRESHOLD + }; + public: + enum { + EnableVml = MightEnableVml && LargeEnough, + Traversal = MightLinearize ? LinearTraversal : DefaultTraversal + }; +}; + +#define EIGEN_PP_EXPAND(ARG) ARG +#if !defined (EIGEN_FAST_MATH) || (EIGEN_FAST_MATH != 1) +#define EIGEN_VMLMODE_EXPAND_xLA , VML_HA +#else +#define EIGEN_VMLMODE_EXPAND_xLA , VML_LA +#endif + +#define EIGEN_VMLMODE_EXPAND_x_ + +#define EIGEN_VMLMODE_PREFIX_xLA vm +#define EIGEN_VMLMODE_PREFIX_x_ v +#define EIGEN_VMLMODE_PREFIX(VMLMODE) EIGEN_CAT(EIGEN_VMLMODE_PREFIX_x,VMLMODE) + +#define EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \ + template< typename DstXprType, typename SrcXprNested> \ + struct Assignment, SrcXprNested>, assign_op, \ + Dense2Dense, typename enable_if::EnableVml>::type> { \ + typedef CwiseUnaryOp, SrcXprNested> SrcXprType; \ + static void run(DstXprType &dst, const SrcXprType &src, const assign_op &func) { \ + resize_if_allowed(dst, src, func); \ + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \ + if(vml_assign_traits::Traversal==LinearTraversal) { \ + VMLOP(dst.size(), (const VMLTYPE*)src.nestedExpression().data(), \ + (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \ + } else { \ + const Index outerSize = dst.outerSize(); \ + for(Index outer = 0; outer < outerSize; ++outer) { \ + const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.nestedExpression().coeffRef(outer,0)) : \ + &(src.nestedExpression().coeffRef(0, outer)); \ + EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \ + VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, \ + (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \ + } \ + } \ + } \ + }; \ + + +#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),s##VMLOP), float, float, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),d##VMLOP), double, double, VMLMODE) + +#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),c##VMLOP), scomplex, MKL_Complex8, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALL(EIGENOP, EIGEN_CAT(EIGEN_VMLMODE_PREFIX(VMLMODE),z##VMLOP), dcomplex, MKL_Complex16, VMLMODE) + +#define EIGEN_MKL_VML_DECLARE_UNARY_CALLS(EIGENOP, VMLOP, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(EIGENOP, VMLOP, VMLMODE) \ + EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(EIGENOP, VMLOP, VMLMODE) + + +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sin, Sin, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(asin, Asin, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sinh, Sinh, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cos, Cos, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(acos, Acos, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(cosh, Cosh, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tan, Tan, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(atan, Atan, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(tanh, Tanh, LA) +// EIGEN_MKL_VML_DECLARE_UNARY_CALLS(abs, Abs, _) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(exp, Exp, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log, Ln, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(log10, Log10, LA) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS(sqrt, Sqrt, _) + +EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(square, Sqr, _) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS_CPLX(arg, Arg, _) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(round, Round, _) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(floor, Floor, _) +EIGEN_MKL_VML_DECLARE_UNARY_CALLS_REAL(ceil, Ceil, _) + +#define EIGEN_MKL_VML_DECLARE_POW_CALL(EIGENOP, VMLOP, EIGENTYPE, VMLTYPE, VMLMODE) \ + template< typename DstXprType, typename SrcXprNested, typename Plain> \ + struct Assignment, SrcXprNested, \ + const CwiseNullaryOp,Plain> >, assign_op, \ + Dense2Dense, typename enable_if::EnableVml>::type> { \ + typedef CwiseBinaryOp, SrcXprNested, \ + const CwiseNullaryOp,Plain> > SrcXprType; \ + static void run(DstXprType &dst, const SrcXprType &src, const assign_op &func) { \ + resize_if_allowed(dst, src, func); \ + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); \ + VMLTYPE exponent = reinterpret_cast(src.rhs().functor().m_other); \ + if(vml_assign_traits::Traversal==LinearTraversal) \ + { \ + VMLOP( dst.size(), (const VMLTYPE*)src.lhs().data(), exponent, \ + (VMLTYPE*)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE) ); \ + } else { \ + const Index outerSize = dst.outerSize(); \ + for(Index outer = 0; outer < outerSize; ++outer) { \ + const EIGENTYPE *src_ptr = src.IsRowMajor ? &(src.lhs().coeffRef(outer,0)) : \ + &(src.lhs().coeffRef(0, outer)); \ + EIGENTYPE *dst_ptr = dst.IsRowMajor ? &(dst.coeffRef(outer,0)) : &(dst.coeffRef(0, outer)); \ + VMLOP( dst.innerSize(), (const VMLTYPE*)src_ptr, exponent, \ + (VMLTYPE*)dst_ptr EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE)); \ + } \ + } \ + } \ + }; + +EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmsPowx, float, float, LA) +EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmdPowx, double, double, LA) +EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmcPowx, scomplex, MKL_Complex8, LA) +EIGEN_MKL_VML_DECLARE_POW_CALL(pow, vmzPowx, dcomplex, MKL_Complex16, LA) + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_ASSIGN_VML_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BandMatrix.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BandMatrix.h new file mode 100644 index 0000000000000000000000000000000000000000..590573bb86b2e04a85357f9cc4e703372de39f1a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BandMatrix.h @@ -0,0 +1,353 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BANDMATRIX_H +#define EIGEN_BANDMATRIX_H + +namespace Eigen { + +namespace internal { + +template +class BandMatrixBase : public EigenBase +{ + public: + + enum { + Flags = internal::traits::Flags, + CoeffReadCost = internal::traits::CoeffReadCost, + RowsAtCompileTime = internal::traits::RowsAtCompileTime, + ColsAtCompileTime = internal::traits::ColsAtCompileTime, + MaxRowsAtCompileTime = internal::traits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = internal::traits::MaxColsAtCompileTime, + Supers = internal::traits::Supers, + Subs = internal::traits::Subs, + Options = internal::traits::Options + }; + typedef typename internal::traits::Scalar Scalar; + typedef Matrix DenseMatrixType; + typedef typename DenseMatrixType::StorageIndex StorageIndex; + typedef typename internal::traits::CoefficientsType CoefficientsType; + typedef EigenBase Base; + + protected: + enum { + DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) + ? 1 + Supers + Subs + : Dynamic, + SizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime) + }; + + public: + + using Base::derived; + using Base::rows; + using Base::cols; + + /** \returns the number of super diagonals */ + inline Index supers() const { return derived().supers(); } + + /** \returns the number of sub diagonals */ + inline Index subs() const { return derived().subs(); } + + /** \returns an expression of the underlying coefficient matrix */ + inline const CoefficientsType& coeffs() const { return derived().coeffs(); } + + /** \returns an expression of the underlying coefficient matrix */ + inline CoefficientsType& coeffs() { return derived().coeffs(); } + + /** \returns a vector expression of the \a i -th column, + * only the meaningful part is returned. + * \warning the internal storage must be column major. */ + inline Block col(Index i) + { + EIGEN_STATIC_ASSERT((int(Options) & int(RowMajor)) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); + Index start = 0; + Index len = coeffs().rows(); + if (i<=supers()) + { + start = supers()-i; + len = (std::min)(rows(),std::max(0,coeffs().rows() - (supers()-i))); + } + else if (i>=rows()-subs()) + len = std::max(0,coeffs().rows() - (i + 1 - rows() + subs())); + return Block(coeffs(), start, i, len, 1); + } + + /** \returns a vector expression of the main diagonal */ + inline Block diagonal() + { return Block(coeffs(),supers(),0,1,(std::min)(rows(),cols())); } + + /** \returns a vector expression of the main diagonal (const version) */ + inline const Block diagonal() const + { return Block(coeffs(),supers(),0,1,(std::min)(rows(),cols())); } + + template struct DiagonalIntReturnType { + enum { + ReturnOpposite = (int(Options) & int(SelfAdjoint)) && (((Index) > 0 && Supers == 0) || ((Index) < 0 && Subs == 0)), + Conjugate = ReturnOpposite && NumTraits::IsComplex, + ActualIndex = ReturnOpposite ? -Index : Index, + DiagonalSize = (RowsAtCompileTime==Dynamic || ColsAtCompileTime==Dynamic) + ? Dynamic + : (ActualIndex<0 + ? EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime + ActualIndex) + : EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime - ActualIndex)) + }; + typedef Block BuildType; + typedef typename internal::conditional,BuildType >, + BuildType>::type Type; + }; + + /** \returns a vector expression of the \a N -th sub or super diagonal */ + template inline typename DiagonalIntReturnType::Type diagonal() + { + return typename DiagonalIntReturnType::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N)); + } + + /** \returns a vector expression of the \a N -th sub or super diagonal */ + template inline const typename DiagonalIntReturnType::Type diagonal() const + { + return typename DiagonalIntReturnType::BuildType(coeffs(), supers()-N, (std::max)(0,N), 1, diagonalLength(N)); + } + + /** \returns a vector expression of the \a i -th sub or super diagonal */ + inline Block diagonal(Index i) + { + eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers())); + return Block(coeffs(), supers()-i, std::max(0,i), 1, diagonalLength(i)); + } + + /** \returns a vector expression of the \a i -th sub or super diagonal */ + inline const Block diagonal(Index i) const + { + eigen_assert((i<0 && -i<=subs()) || (i>=0 && i<=supers())); + return Block(coeffs(), supers()-i, std::max(0,i), 1, diagonalLength(i)); + } + + template inline void evalTo(Dest& dst) const + { + dst.resize(rows(),cols()); + dst.setZero(); + dst.diagonal() = diagonal(); + for (Index i=1; i<=supers();++i) + dst.diagonal(i) = diagonal(i); + for (Index i=1; i<=subs();++i) + dst.diagonal(-i) = diagonal(-i); + } + + DenseMatrixType toDenseMatrix() const + { + DenseMatrixType res(rows(),cols()); + evalTo(res); + return res; + } + + protected: + + inline Index diagonalLength(Index i) const + { return i<0 ? (std::min)(cols(),rows()+i) : (std::min)(rows(),cols()-i); } +}; + +/** + * \class BandMatrix + * \ingroup Core_Module + * + * \brief Represents a rectangular matrix with a banded storage + * + * \tparam Scalar_ Numeric type, i.e. float, double, int + * \tparam Rows_ Number of rows, or \b Dynamic + * \tparam Cols_ Number of columns, or \b Dynamic + * \tparam Supers_ Number of super diagonal + * \tparam Subs_ Number of sub diagonal + * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of \b #SelfAdjoint + * The former controls \ref TopicStorageOrders "storage order", and defaults to + * column-major. The latter controls whether the matrix represents a selfadjoint + * matrix in which case either Supers of Subs have to be null. + * + * \sa class TridiagonalMatrix + */ + +template +struct traits > +{ + typedef Scalar_ Scalar; + typedef Dense StorageKind; + typedef Eigen::Index StorageIndex; + enum { + CoeffReadCost = NumTraits::ReadCost, + RowsAtCompileTime = Rows_, + ColsAtCompileTime = Cols_, + MaxRowsAtCompileTime = Rows_, + MaxColsAtCompileTime = Cols_, + Flags = LvalueBit, + Supers = Supers_, + Subs = Subs_, + Options = Options_, + DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic + }; + typedef Matrix CoefficientsType; +}; + +template +class BandMatrix : public BandMatrixBase > +{ + public: + + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::traits::StorageIndex StorageIndex; + typedef typename internal::traits::CoefficientsType CoefficientsType; + + explicit inline BandMatrix(Index rows=Rows, Index cols=Cols, Index supers=Supers, Index subs=Subs) + : m_coeffs(1+supers+subs,cols), + m_rows(rows), m_supers(supers), m_subs(subs) + { + } + + /** \returns the number of columns */ + inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); } + + /** \returns the number of rows */ + inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); } + + /** \returns the number of super diagonals */ + inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); } + + /** \returns the number of sub diagonals */ + inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); } + + inline const CoefficientsType& coeffs() const { return m_coeffs; } + inline CoefficientsType& coeffs() { return m_coeffs; } + + protected: + + CoefficientsType m_coeffs; + internal::variable_if_dynamic m_rows; + internal::variable_if_dynamic m_supers; + internal::variable_if_dynamic m_subs; +}; + +template +class BandMatrixWrapper; + +template +struct traits > +{ + typedef typename _CoefficientsType::Scalar Scalar; + typedef typename _CoefficientsType::StorageKind StorageKind; + typedef typename _CoefficientsType::StorageIndex StorageIndex; + enum { + CoeffReadCost = internal::traits<_CoefficientsType>::CoeffReadCost, + RowsAtCompileTime = Rows_, + ColsAtCompileTime = Cols_, + MaxRowsAtCompileTime = Rows_, + MaxColsAtCompileTime = Cols_, + Flags = LvalueBit, + Supers = Supers_, + Subs = Subs_, + Options = Options_, + DataRowsAtCompileTime = ((Supers!=Dynamic) && (Subs!=Dynamic)) ? 1 + Supers + Subs : Dynamic + }; + typedef _CoefficientsType CoefficientsType; +}; + +template +class BandMatrixWrapper : public BandMatrixBase > +{ + public: + + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::traits::CoefficientsType CoefficientsType; + typedef typename internal::traits::StorageIndex StorageIndex; + + explicit inline BandMatrixWrapper(const CoefficientsType& coeffs, Index rows=Rows_, Index cols=Cols_, Index supers=Supers_, Index subs=Subs_) + : m_coeffs(coeffs), + m_rows(rows), m_supers(supers), m_subs(subs) + { + EIGEN_UNUSED_VARIABLE(cols); + //internal::assert(coeffs.cols()==cols() && (supers()+subs()+1)==coeffs.rows()); + } + + /** \returns the number of columns */ + inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); } + + /** \returns the number of rows */ + inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); } + + /** \returns the number of super diagonals */ + inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); } + + /** \returns the number of sub diagonals */ + inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); } + + inline const CoefficientsType& coeffs() const { return m_coeffs; } + + protected: + + const CoefficientsType& m_coeffs; + internal::variable_if_dynamic m_rows; + internal::variable_if_dynamic m_supers; + internal::variable_if_dynamic m_subs; +}; + +/** + * \class TridiagonalMatrix + * \ingroup Core_Module + * + * \brief Represents a tridiagonal matrix with a compact banded storage + * + * \tparam Scalar Numeric type, i.e. float, double, int + * \tparam Size Number of rows and cols, or \b Dynamic + * \tparam Options Can be 0 or \b SelfAdjoint + * + * \sa class BandMatrix + */ +template +class TridiagonalMatrix : public BandMatrix +{ + typedef BandMatrix Base; + typedef typename Base::StorageIndex StorageIndex; + public: + explicit TridiagonalMatrix(Index size = Size) : Base(size,size,Options&SelfAdjoint?0:1,1) {} + + inline typename Base::template DiagonalIntReturnType<1>::Type super() + { return Base::template diagonal<1>(); } + inline const typename Base::template DiagonalIntReturnType<1>::Type super() const + { return Base::template diagonal<1>(); } + inline typename Base::template DiagonalIntReturnType<-1>::Type sub() + { return Base::template diagonal<-1>(); } + inline const typename Base::template DiagonalIntReturnType<-1>::Type sub() const + { return Base::template diagonal<-1>(); } + protected: +}; + + +struct BandShape {}; + +template +struct evaluator_traits > + : public evaluator_traits_base > +{ + typedef BandShape Shape; +}; + +template +struct evaluator_traits > + : public evaluator_traits_base > +{ + typedef BandShape Shape; +}; + +template<> struct AssignmentKind { typedef EigenBase2EigenBase Kind; }; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_BANDMATRIX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Block.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Block.h new file mode 100644 index 0000000000000000000000000000000000000000..3206d6633e62c29f4466155f47725511a34ba640 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Block.h @@ -0,0 +1,448 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BLOCK_H +#define EIGEN_BLOCK_H + +namespace Eigen { + +namespace internal { +template +struct traits > : traits +{ + typedef typename traits::Scalar Scalar; + typedef typename traits::StorageKind StorageKind; + typedef typename traits::XprKind XprKind; + typedef typename ref_selector::type XprTypeNested; + typedef typename remove_reference::type _XprTypeNested; + enum{ + MatrixRows = traits::RowsAtCompileTime, + MatrixCols = traits::ColsAtCompileTime, + RowsAtCompileTime = MatrixRows == 0 ? 0 : BlockRows, + ColsAtCompileTime = MatrixCols == 0 ? 0 : BlockCols, + MaxRowsAtCompileTime = BlockRows==0 ? 0 + : RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime) + : int(traits::MaxRowsAtCompileTime), + MaxColsAtCompileTime = BlockCols==0 ? 0 + : ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime) + : int(traits::MaxColsAtCompileTime), + + XprTypeIsRowMajor = (int(traits::Flags)&RowMajorBit) != 0, + IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1 + : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0 + : XprTypeIsRowMajor, + HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor), + InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime), + InnerStrideAtCompileTime = HasSameStorageOrderAsXprType + ? int(inner_stride_at_compile_time::ret) + : int(outer_stride_at_compile_time::ret), + OuterStrideAtCompileTime = HasSameStorageOrderAsXprType + ? int(outer_stride_at_compile_time::ret) + : int(inner_stride_at_compile_time::ret), + + // FIXME, this traits is rather specialized for dense object and it needs to be cleaned further + FlagsLvalueBit = is_lvalue::value ? LvalueBit : 0, + FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0, + Flags = (traits::Flags & (DirectAccessBit | (InnerPanel?CompressedAccessBit:0))) | FlagsLvalueBit | FlagsRowMajorBit, + // FIXME DirectAccessBit should not be handled by expressions + // + // Alignment is needed by MapBase's assertions + // We can sefely set it to false here. Internal alignment errors will be detected by an eigen_internal_assert in the respective evaluator + Alignment = 0 + }; +}; + +template::ret> class BlockImpl_dense; + +} // end namespace internal + +template class BlockImpl; + +/** \class Block + * \ingroup Core_Module + * + * \brief Expression of a fixed-size or dynamic-size block + * + * \tparam XprType the type of the expression in which we are taking a block + * \tparam BlockRows the number of rows of the block we are taking at compile time (optional) + * \tparam BlockCols the number of columns of the block we are taking at compile time (optional) + * \tparam InnerPanel is true, if the block maps to a set of rows of a row major matrix or + * to set of columns of a column major matrix (optional). The parameter allows to determine + * at compile time whether aligned access is possible on the block expression. + * + * This class represents an expression of either a fixed-size or dynamic-size block. It is the return + * type of DenseBase::block(Index,Index,Index,Index) and DenseBase::block(Index,Index) and + * most of the time this is the only way it is used. + * + * However, if you want to directly maniputate block expressions, + * for instance if you want to write a function returning such an expression, you + * will need to use this class. + * + * Here is an example illustrating the dynamic case: + * \include class_Block.cpp + * Output: \verbinclude class_Block.out + * + * \note Even though this expression has dynamic size, in the case where \a XprType + * has fixed size, this expression inherits a fixed maximal size which means that evaluating + * it does not cause a dynamic memory allocation. + * + * Here is an example illustrating the fixed-size case: + * \include class_FixedBlock.cpp + * Output: \verbinclude class_FixedBlock.out + * + * \sa DenseBase::block(Index,Index,Index,Index), DenseBase::block(Index,Index), class VectorBlock + */ +template class Block + : public BlockImpl::StorageKind> +{ + typedef BlockImpl::StorageKind> Impl; + public: + //typedef typename Impl::Base Base; + typedef Impl Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(Block) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block) + + typedef typename internal::remove_all::type NestedExpression; + + /** Column or Row constructor + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Block(XprType& xpr, Index i) : Impl(xpr,i) + { + eigen_assert( (i>=0) && ( + ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && i= 0 && BlockRows >= 0 && startRow + BlockRows <= xpr.rows() + && startCol >= 0 && BlockCols >= 0 && startCol + BlockCols <= xpr.cols()); + } + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Block(XprType& xpr, + Index startRow, Index startCol, + Index blockRows, Index blockCols) + : Impl(xpr, startRow, startCol, blockRows, blockCols) + { + eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==blockRows) + && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==blockCols)); + eigen_assert(startRow >= 0 && blockRows >= 0 && startRow <= xpr.rows() - blockRows + && startCol >= 0 && blockCols >= 0 && startCol <= xpr.cols() - blockCols); + } +}; + +// The generic default implementation for dense block simplu forward to the internal::BlockImpl_dense +// that must be specialized for direct and non-direct access... +template +class BlockImpl + : public internal::BlockImpl_dense +{ + typedef internal::BlockImpl_dense Impl; + typedef typename XprType::StorageIndex StorageIndex; + public: + typedef Impl Base; + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl) + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index i) : Impl(xpr,i) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol) : Impl(xpr, startRow, startCol) {} + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE BlockImpl(XprType& xpr, Index startRow, Index startCol, Index blockRows, Index blockCols) + : Impl(xpr, startRow, startCol, blockRows, blockCols) {} +}; + +namespace internal { + +/** \internal Internal implementation of dense Blocks in the general case. */ +template class BlockImpl_dense + : public internal::dense_xpr_base >::type +{ + typedef Block BlockType; + typedef typename internal::ref_selector::non_const_type XprTypeNested; + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(BlockType) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense) + + // class InnerIterator; // FIXME apparently never used + + /** Column or Row constructor + */ + EIGEN_DEVICE_FUNC + inline BlockImpl_dense(XprType& xpr, Index i) + : m_xpr(xpr), + // It is a row if and only if BlockRows==1 and BlockCols==XprType::ColsAtCompileTime, + // and it is a column if and only if BlockRows==XprType::RowsAtCompileTime and BlockCols==1, + // all other cases are invalid. + // The case a 1x1 matrix seems ambiguous, but the result is the same anyway. + m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0), + m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0), + m_blockRows(BlockRows==1 ? 1 : xpr.rows()), + m_blockCols(BlockCols==1 ? 1 : xpr.cols()) + {} + + /** Fixed-size constructor + */ + EIGEN_DEVICE_FUNC + inline BlockImpl_dense(XprType& xpr, Index startRow, Index startCol) + : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), + m_blockRows(BlockRows), m_blockCols(BlockCols) + {} + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC + inline BlockImpl_dense(XprType& xpr, + Index startRow, Index startCol, + Index blockRows, Index blockCols) + : m_xpr(xpr), m_startRow(startRow), m_startCol(startCol), + m_blockRows(blockRows), m_blockCols(blockCols) + {} + + EIGEN_DEVICE_FUNC inline Index rows() const { return m_blockRows.value(); } + EIGEN_DEVICE_FUNC inline Index cols() const { return m_blockCols.value(); } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index rowId, Index colId) + { + EIGEN_STATIC_ASSERT_LVALUE(XprType) + return m_xpr.coeffRef(rowId + m_startRow.value(), colId + m_startCol.value()); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index rowId, Index colId) const + { + return m_xpr.derived().coeffRef(rowId + m_startRow.value(), colId + m_startCol.value()); + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const + { + return m_xpr.coeff(rowId + m_startRow.value(), colId + m_startCol.value()); + } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index index) + { + EIGEN_STATIC_ASSERT_LVALUE(XprType) + return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index), + m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0)); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index index) const + { + return m_xpr.coeffRef(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index), + m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0)); + } + + EIGEN_DEVICE_FUNC + inline const CoeffReturnType coeff(Index index) const + { + return m_xpr.coeff(m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index), + m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0)); + } + + template + inline PacketScalar packet(Index rowId, Index colId) const + { + return m_xpr.template packet(rowId + m_startRow.value(), colId + m_startCol.value()); + } + + template + inline void writePacket(Index rowId, Index colId, const PacketScalar& val) + { + m_xpr.template writePacket(rowId + m_startRow.value(), colId + m_startCol.value(), val); + } + + template + inline PacketScalar packet(Index index) const + { + return m_xpr.template packet + (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index), + m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0)); + } + + template + inline void writePacket(Index index, const PacketScalar& val) + { + m_xpr.template writePacket + (m_startRow.value() + (RowsAtCompileTime == 1 ? 0 : index), + m_startCol.value() + (RowsAtCompileTime == 1 ? index : 0), val); + } + + #ifdef EIGEN_PARSED_BY_DOXYGEN + /** \sa MapBase::data() */ + EIGEN_DEVICE_FUNC inline const Scalar* data() const; + EIGEN_DEVICE_FUNC inline Index innerStride() const; + EIGEN_DEVICE_FUNC inline Index outerStride() const; + #endif + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const typename internal::remove_all::type& nestedExpression() const + { + return m_xpr; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + XprType& nestedExpression() { return m_xpr; } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + StorageIndex startRow() const EIGEN_NOEXCEPT + { + return m_startRow.value(); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + StorageIndex startCol() const EIGEN_NOEXCEPT + { + return m_startCol.value(); + } + + protected: + + XprTypeNested m_xpr; + const internal::variable_if_dynamic m_startRow; + const internal::variable_if_dynamic m_startCol; + const internal::variable_if_dynamic m_blockRows; + const internal::variable_if_dynamic m_blockCols; +}; + +/** \internal Internal implementation of dense Blocks in the direct access case.*/ +template +class BlockImpl_dense + : public MapBase > +{ + typedef Block BlockType; + typedef typename internal::ref_selector::non_const_type XprTypeNested; + enum { + XprTypeIsRowMajor = (int(traits::Flags)&RowMajorBit) != 0 + }; + public: + + typedef MapBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(BlockType) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(BlockImpl_dense) + + /** Column or Row constructor + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + BlockImpl_dense(XprType& xpr, Index i) + : Base(xpr.data() + i * ( ((BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) && (!XprTypeIsRowMajor)) + || ((BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) && ( XprTypeIsRowMajor)) ? xpr.innerStride() : xpr.outerStride()), + BlockRows==1 ? 1 : xpr.rows(), + BlockCols==1 ? 1 : xpr.cols()), + m_xpr(xpr), + m_startRow( (BlockRows==1) && (BlockCols==XprType::ColsAtCompileTime) ? i : 0), + m_startCol( (BlockRows==XprType::RowsAtCompileTime) && (BlockCols==1) ? i : 0) + { + init(); + } + + /** Fixed-size constructor + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + BlockImpl_dense(XprType& xpr, Index startRow, Index startCol) + : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol)), + m_xpr(xpr), m_startRow(startRow), m_startCol(startCol) + { + init(); + } + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + BlockImpl_dense(XprType& xpr, + Index startRow, Index startCol, + Index blockRows, Index blockCols) + : Base(xpr.data()+xpr.innerStride()*(XprTypeIsRowMajor?startCol:startRow) + xpr.outerStride()*(XprTypeIsRowMajor?startRow:startCol), blockRows, blockCols), + m_xpr(xpr), m_startRow(startRow), m_startCol(startCol) + { + init(); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const typename internal::remove_all::type& nestedExpression() const EIGEN_NOEXCEPT + { + return m_xpr; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + XprType& nestedExpression() { return m_xpr; } + + /** \sa MapBase::innerStride() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index innerStride() const EIGEN_NOEXCEPT + { + return internal::traits::HasSameStorageOrderAsXprType + ? m_xpr.innerStride() + : m_xpr.outerStride(); + } + + /** \sa MapBase::outerStride() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index outerStride() const EIGEN_NOEXCEPT + { + return internal::traits::HasSameStorageOrderAsXprType + ? m_xpr.outerStride() + : m_xpr.innerStride(); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + StorageIndex startRow() const EIGEN_NOEXCEPT { return m_startRow.value(); } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + StorageIndex startCol() const EIGEN_NOEXCEPT { return m_startCol.value(); } + + #ifndef __SUNPRO_CC + // FIXME sunstudio is not friendly with the above friend... + // META-FIXME there is no 'friend' keyword around here. Is this obsolete? + protected: + #endif + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /** \internal used by allowAligned() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + BlockImpl_dense(XprType& xpr, const Scalar* data, Index blockRows, Index blockCols) + : Base(data, blockRows, blockCols), m_xpr(xpr) + { + init(); + } + #endif + + protected: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void init() + { + m_outerStride = internal::traits::HasSameStorageOrderAsXprType + ? m_xpr.outerStride() + : m_xpr.innerStride(); + } + + XprTypeNested m_xpr; + const internal::variable_if_dynamic m_startRow; + const internal::variable_if_dynamic m_startCol; + Index m_outerStride; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_BLOCK_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BooleanRedux.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BooleanRedux.h new file mode 100644 index 0000000000000000000000000000000000000000..852de8b90a565b534a70ff61493ca2684a9d1638 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/BooleanRedux.h @@ -0,0 +1,162 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_ALLANDANY_H +#define EIGEN_ALLANDANY_H + +namespace Eigen { + +namespace internal { + +template +struct all_unroller +{ + enum { + col = (UnrollCount-1) / Rows, + row = (UnrollCount-1) % Rows + }; + + EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat) + { + return all_unroller::run(mat) && mat.coeff(row, col); + } +}; + +template +struct all_unroller +{ + EIGEN_DEVICE_FUNC static inline bool run(const Derived &/*mat*/) { return true; } +}; + +template +struct all_unroller +{ + EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; } +}; + +template +struct any_unroller +{ + enum { + col = (UnrollCount-1) / Rows, + row = (UnrollCount-1) % Rows + }; + + EIGEN_DEVICE_FUNC static inline bool run(const Derived &mat) + { + return any_unroller::run(mat) || mat.coeff(row, col); + } +}; + +template +struct any_unroller +{ + EIGEN_DEVICE_FUNC static inline bool run(const Derived & /*mat*/) { return false; } +}; + +template +struct any_unroller +{ + EIGEN_DEVICE_FUNC static inline bool run(const Derived &) { return false; } +}; + +} // end namespace internal + +/** \returns true if all coefficients are true + * + * Example: \include MatrixBase_all.cpp + * Output: \verbinclude MatrixBase_all.out + * + * \sa any(), Cwise::operator<() + */ +template +EIGEN_DEVICE_FUNC inline bool DenseBase::all() const +{ + typedef internal::evaluator Evaluator; + enum { + unroll = SizeAtCompileTime != Dynamic + && SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits::AddCost)) <= EIGEN_UNROLLING_LIMIT + }; + Evaluator evaluator(derived()); + if(unroll) + return internal::all_unroller::RowsAtCompileTime>::run(evaluator); + else + { + for(Index j = 0; j < cols(); ++j) + for(Index i = 0; i < rows(); ++i) + if (!evaluator.coeff(i, j)) return false; + return true; + } +} + +/** \returns true if at least one coefficient is true + * + * \sa all() + */ +template +EIGEN_DEVICE_FUNC inline bool DenseBase::any() const +{ + typedef internal::evaluator Evaluator; + enum { + unroll = SizeAtCompileTime != Dynamic + && SizeAtCompileTime * (int(Evaluator::CoeffReadCost) + int(NumTraits::AddCost)) <= EIGEN_UNROLLING_LIMIT + }; + Evaluator evaluator(derived()); + if(unroll) + return internal::any_unroller::RowsAtCompileTime>::run(evaluator); + else + { + for(Index j = 0; j < cols(); ++j) + for(Index i = 0; i < rows(); ++i) + if (evaluator.coeff(i, j)) return true; + return false; + } +} + +/** \returns the number of coefficients which evaluate to true + * + * \sa all(), any() + */ +template +EIGEN_DEVICE_FUNC inline Eigen::Index DenseBase::count() const +{ + return derived().template cast().template cast().sum(); +} + +/** \returns true is \c *this contains at least one Not A Number (NaN). + * + * \sa allFinite() + */ +template +inline bool DenseBase::hasNaN() const +{ +#if EIGEN_COMP_MSVC || (defined __FAST_MATH__) + return derived().array().isNaN().any(); +#else + return !((derived().array()==derived().array()).all()); +#endif +} + +/** \returns true if \c *this contains only finite numbers, i.e., no NaN and no +/-INF values. + * + * \sa hasNaN() + */ +template +inline bool DenseBase::allFinite() const +{ +#if EIGEN_COMP_MSVC || (defined __FAST_MATH__) + return derived().array().isFinite().all(); +#else + return !((derived()-derived()).hasNaN()); +#endif +} + +} // end namespace Eigen + +#endif // EIGEN_ALLANDANY_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CommaInitializer.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CommaInitializer.h new file mode 100644 index 0000000000000000000000000000000000000000..c0e29c75c223666d37e6bb25f03af09b8ba65e01 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CommaInitializer.h @@ -0,0 +1,164 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_COMMAINITIALIZER_H +#define EIGEN_COMMAINITIALIZER_H + +namespace Eigen { + +/** \class CommaInitializer + * \ingroup Core_Module + * + * \brief Helper class used by the comma initializer operator + * + * This class is internally used to implement the comma initializer feature. It is + * the return type of MatrixBase::operator<<, and most of the time this is the only + * way it is used. + * + * \sa \blank \ref MatrixBaseCommaInitRef "MatrixBase::operator<<", CommaInitializer::finished() + */ +template +struct CommaInitializer +{ + typedef typename XprType::Scalar Scalar; + + EIGEN_DEVICE_FUNC + inline CommaInitializer(XprType& xpr, const Scalar& s) + : m_xpr(xpr), m_row(0), m_col(1), m_currentBlockRows(1) + { + eigen_assert(m_xpr.rows() > 0 && m_xpr.cols() > 0 + && "Cannot comma-initialize a 0x0 matrix (operator<<)"); + m_xpr.coeffRef(0,0) = s; + } + + template + EIGEN_DEVICE_FUNC + inline CommaInitializer(XprType& xpr, const DenseBase& other) + : m_xpr(xpr), m_row(0), m_col(other.cols()), m_currentBlockRows(other.rows()) + { + eigen_assert(m_xpr.rows() >= other.rows() && m_xpr.cols() >= other.cols() + && "Cannot comma-initialize a 0x0 matrix (operator<<)"); + m_xpr.block(0, 0, other.rows(), other.cols()) = other; + } + + /* Copy/Move constructor which transfers ownership. This is crucial in + * absence of return value optimization to avoid assertions during destruction. */ + // FIXME in C++11 mode this could be replaced by a proper RValue constructor + EIGEN_DEVICE_FUNC + inline CommaInitializer(const CommaInitializer& o) + : m_xpr(o.m_xpr), m_row(o.m_row), m_col(o.m_col), m_currentBlockRows(o.m_currentBlockRows) { + // Mark original object as finished. In absence of R-value references we need to const_cast: + const_cast(o).m_row = m_xpr.rows(); + const_cast(o).m_col = m_xpr.cols(); + const_cast(o).m_currentBlockRows = 0; + } + + /* inserts a scalar value in the target matrix */ + EIGEN_DEVICE_FUNC + CommaInitializer& operator,(const Scalar& s) + { + if (m_col==m_xpr.cols()) + { + m_row+=m_currentBlockRows; + m_col = 0; + m_currentBlockRows = 1; + eigen_assert(m_row + EIGEN_DEVICE_FUNC + CommaInitializer& operator,(const DenseBase& other) + { + if (m_col==m_xpr.cols() && (other.cols()!=0 || other.rows()!=m_currentBlockRows)) + { + m_row+=m_currentBlockRows; + m_col = 0; + m_currentBlockRows = other.rows(); + eigen_assert(m_row+m_currentBlockRows<=m_xpr.rows() + && "Too many rows passed to comma initializer (operator<<)"); + } + eigen_assert((m_col + other.cols() <= m_xpr.cols()) + && "Too many coefficients passed to comma initializer (operator<<)"); + eigen_assert(m_currentBlockRows==other.rows()); + m_xpr.template block + (m_row, m_col, other.rows(), other.cols()) = other; + m_col += other.cols(); + return *this; + } + + EIGEN_DEVICE_FUNC + inline ~CommaInitializer() +#if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS + EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception) +#endif + { + finished(); + } + + /** \returns the built matrix once all its coefficients have been set. + * Calling finished is 100% optional. Its purpose is to write expressions + * like this: + * \code + * quaternion.fromRotationMatrix((Matrix3f() << axis0, axis1, axis2).finished()); + * \endcode + */ + EIGEN_DEVICE_FUNC + inline XprType& finished() { + eigen_assert(((m_row+m_currentBlockRows) == m_xpr.rows() || m_xpr.cols() == 0) + && m_col == m_xpr.cols() + && "Too few coefficients passed to comma initializer (operator<<)"); + return m_xpr; + } + + XprType& m_xpr; // target expression + Index m_row; // current row id + Index m_col; // current col id + Index m_currentBlockRows; // current block height +}; + +/** \anchor MatrixBaseCommaInitRef + * Convenient operator to set the coefficients of a matrix. + * + * The coefficients must be provided in a row major order and exactly match + * the size of the matrix. Otherwise an assertion is raised. + * + * Example: \include MatrixBase_set.cpp + * Output: \verbinclude MatrixBase_set.out + * + * \note According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order. + * + * \sa CommaInitializer::finished(), class CommaInitializer + */ +template +EIGEN_DEVICE_FUNC inline CommaInitializer DenseBase::operator<< (const Scalar& s) +{ + return CommaInitializer(*static_cast(this), s); +} + +/** \sa operator<<(const Scalar&) */ +template +template +EIGEN_DEVICE_FUNC inline CommaInitializer +DenseBase::operator<<(const DenseBase& other) +{ + return CommaInitializer(*static_cast(this), other); +} + +} // end namespace Eigen + +#endif // EIGEN_COMMAINITIALIZER_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ConditionEstimator.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ConditionEstimator.h new file mode 100644 index 0000000000000000000000000000000000000000..51a2e5f1b6f9587ad54fbc889e03c1d11e02d4f4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ConditionEstimator.h @@ -0,0 +1,175 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com) +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CONDITIONESTIMATOR_H +#define EIGEN_CONDITIONESTIMATOR_H + +namespace Eigen { + +namespace internal { + +template +struct rcond_compute_sign { + static inline Vector run(const Vector& v) { + const RealVector v_abs = v.cwiseAbs(); + return (v_abs.array() == static_cast(0)) + .select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs)); + } +}; + +// Partial specialization to avoid elementwise division for real vectors. +template +struct rcond_compute_sign { + static inline Vector run(const Vector& v) { + return (v.array() < static_cast(0)) + .select(-Vector::Ones(v.size()), Vector::Ones(v.size())); + } +}; + +/** + * \returns an estimate of ||inv(matrix)||_1 given a decomposition of + * \a matrix that implements .solve() and .adjoint().solve() methods. + * + * This function implements Algorithms 4.1 and 5.1 from + * http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf + * which also forms the basis for the condition number estimators in + * LAPACK. Since at most 10 calls to the solve method of dec are + * performed, the total cost is O(dims^2), as opposed to O(dims^3) + * needed to compute the inverse matrix explicitly. + * + * The most common usage is in estimating the condition number + * ||matrix||_1 * ||inv(matrix)||_1. The first term ||matrix||_1 can be + * computed directly in O(n^2) operations. + * + * Supports the following decompositions: FullPivLU, PartialPivLU, LDLT, and + * LLT. + * + * \sa FullPivLU, PartialPivLU, LDLT, LLT. + */ +template +typename Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(const Decomposition& dec) +{ + typedef typename Decomposition::MatrixType MatrixType; + typedef typename Decomposition::Scalar Scalar; + typedef typename Decomposition::RealScalar RealScalar; + typedef typename internal::plain_col_type::type Vector; + typedef typename internal::plain_col_type::type RealVector; + const bool is_complex = (NumTraits::IsComplex != 0); + + eigen_assert(dec.rows() == dec.cols()); + const Index n = dec.rows(); + if (n == 0) + return 0; + + // Disable Index to float conversion warning +#ifdef __INTEL_COMPILER + #pragma warning push + #pragma warning ( disable : 2259 ) +#endif + Vector v = dec.solve(Vector::Ones(n) / Scalar(n)); +#ifdef __INTEL_COMPILER + #pragma warning pop +#endif + + // lower_bound is a lower bound on + // ||inv(matrix)||_1 = sup_v ||inv(matrix) v||_1 / ||v||_1 + // and is the objective maximized by the ("super-") gradient ascent + // algorithm below. + RealScalar lower_bound = v.template lpNorm<1>(); + if (n == 1) + return lower_bound; + + // Gradient ascent algorithm follows: We know that the optimum is achieved at + // one of the simplices v = e_i, so in each iteration we follow a + // super-gradient to move towards the optimal one. + RealScalar old_lower_bound = lower_bound; + Vector sign_vector(n); + Vector old_sign_vector; + Index v_max_abs_index = -1; + Index old_v_max_abs_index = v_max_abs_index; + for (int k = 0; k < 4; ++k) + { + sign_vector = internal::rcond_compute_sign::run(v); + if (k > 0 && !is_complex && sign_vector == old_sign_vector) { + // Break if the solution stagnated. + break; + } + // v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )| + v = dec.adjoint().solve(sign_vector); + v.real().cwiseAbs().maxCoeff(&v_max_abs_index); + if (v_max_abs_index == old_v_max_abs_index) { + // Break if the solution stagnated. + break; + } + // Move to the new simplex e_j, where j = v_max_abs_index. + v = dec.solve(Vector::Unit(n, v_max_abs_index)); // v = inv(matrix) * e_j. + lower_bound = v.template lpNorm<1>(); + if (lower_bound <= old_lower_bound) { + // Break if the gradient step did not increase the lower_bound. + break; + } + if (!is_complex) { + old_sign_vector = sign_vector; + } + old_v_max_abs_index = v_max_abs_index; + old_lower_bound = lower_bound; + } + // The following calculates an independent estimate of ||matrix||_1 by + // multiplying matrix by a vector with entries of slowly increasing + // magnitude and alternating sign: + // v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1. + // This improvement to Hager's algorithm above is due to Higham. It was + // added to make the algorithm more robust in certain corner cases where + // large elements in the matrix might otherwise escape detection due to + // exact cancellation (especially when op and op_adjoint correspond to a + // sequence of backsubstitutions and permutations), which could cause + // Hager's algorithm to vastly underestimate ||matrix||_1. + Scalar alternating_sign(RealScalar(1)); + for (Index i = 0; i < n; ++i) { + // The static_cast is needed when Scalar is a complex and RealScalar implements expression templates + v[i] = alternating_sign * static_cast(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1)))); + alternating_sign = -alternating_sign; + } + v = dec.solve(v); + const RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n)); + return numext::maxi(lower_bound, alternate_lower_bound); +} + +/** \brief Reciprocal condition number estimator. + * + * Computing a decomposition of a dense matrix takes O(n^3) operations, while + * this method estimates the condition number quickly and reliably in O(n^2) + * operations. + * + * \returns an estimate of the reciprocal condition number + * (1 / (||matrix||_1 * ||inv(matrix)||_1)) of matrix, given ||matrix||_1 and + * its decomposition. Supports the following decompositions: FullPivLU, + * PartialPivLU, LDLT, and LLT. + * + * \sa FullPivLU, PartialPivLU, LDLT, LLT. + */ +template +typename Decomposition::RealScalar +rcond_estimate_helper(typename Decomposition::RealScalar matrix_norm, const Decomposition& dec) +{ + typedef typename Decomposition::RealScalar RealScalar; + eigen_assert(dec.rows() == dec.cols()); + if (dec.rows() == 0) return NumTraits::infinity(); + if (matrix_norm == RealScalar(0)) return RealScalar(0); + if (dec.rows() == 1) return RealScalar(1); + const RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec); + return (inverse_matrix_norm == RealScalar(0) ? RealScalar(0) + : (RealScalar(1) / inverse_matrix_norm) / matrix_norm); +} + +} // namespace internal + +} // namespace Eigen + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreEvaluators.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreEvaluators.h new file mode 100644 index 0000000000000000000000000000000000000000..0ff8c8deb820deb7bbaa2f762afc5e4366f29616 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreEvaluators.h @@ -0,0 +1,1741 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Benoit Jacob +// Copyright (C) 2011-2014 Gael Guennebaud +// Copyright (C) 2011-2012 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_COREEVALUATORS_H +#define EIGEN_COREEVALUATORS_H + +namespace Eigen { + +namespace internal { + +// This class returns the evaluator kind from the expression storage kind. +// Default assumes index based accessors +template +struct storage_kind_to_evaluator_kind { + typedef IndexBased Kind; +}; + +// This class returns the evaluator shape from the expression storage kind. +// It can be Dense, Sparse, Triangular, Diagonal, SelfAdjoint, Band, etc. +template struct storage_kind_to_shape; + +template<> struct storage_kind_to_shape { typedef DenseShape Shape; }; +template<> struct storage_kind_to_shape { typedef SolverShape Shape; }; +template<> struct storage_kind_to_shape { typedef PermutationShape Shape; }; +template<> struct storage_kind_to_shape { typedef TranspositionsShape Shape; }; + +// Evaluators have to be specialized with respect to various criteria such as: +// - storage/structure/shape +// - scalar type +// - etc. +// Therefore, we need specialization of evaluator providing additional template arguments for each kind of evaluators. +// We currently distinguish the following kind of evaluators: +// - unary_evaluator for expressions taking only one arguments (CwiseUnaryOp, CwiseUnaryView, Transpose, MatrixWrapper, ArrayWrapper, Reverse, Replicate) +// - binary_evaluator for expression taking two arguments (CwiseBinaryOp) +// - ternary_evaluator for expression taking three arguments (CwiseTernaryOp) +// - product_evaluator for linear algebra products (Product); special case of binary_evaluator because it requires additional tags for dispatching. +// - mapbase_evaluator for Map, Block, Ref +// - block_evaluator for Block (special dispatching to a mapbase_evaluator or unary_evaluator) + +template< typename T, + typename Arg1Kind = typename evaluator_traits::Kind, + typename Arg2Kind = typename evaluator_traits::Kind, + typename Arg3Kind = typename evaluator_traits::Kind, + typename Arg1Scalar = typename traits::Scalar, + typename Arg2Scalar = typename traits::Scalar, + typename Arg3Scalar = typename traits::Scalar> struct ternary_evaluator; + +template< typename T, + typename LhsKind = typename evaluator_traits::Kind, + typename RhsKind = typename evaluator_traits::Kind, + typename LhsScalar = typename traits::Scalar, + typename RhsScalar = typename traits::Scalar> struct binary_evaluator; + +template< typename T, + typename Kind = typename evaluator_traits::Kind, + typename Scalar = typename T::Scalar> struct unary_evaluator; + +// evaluator_traits contains traits for evaluator + +template +struct evaluator_traits_base +{ + // by default, get evaluator kind and shape from storage + typedef typename storage_kind_to_evaluator_kind::StorageKind>::Kind Kind; + typedef typename storage_kind_to_shape::StorageKind>::Shape Shape; +}; + +// Default evaluator traits +template +struct evaluator_traits : public evaluator_traits_base +{ +}; + +template::Shape > +struct evaluator_assume_aliasing { + static const bool value = false; +}; + +// By default, we assume a unary expression: +template +struct evaluator : public unary_evaluator +{ + typedef unary_evaluator Base; + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const T& xpr) : Base(xpr) {} +}; + + +// TODO: Think about const-correctness +template +struct evaluator + : evaluator +{ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const T& xpr) : evaluator(xpr) {} +}; + +// ---------- base class for all evaluators ---------- + +template +struct evaluator_base +{ + // TODO that's not very nice to have to propagate all these traits. They are currently only needed to handle outer,inner indices. + typedef traits ExpressionTraits; + + enum { + Alignment = 0 + }; + // noncopyable: + // Don't make this class inherit noncopyable as this kills EBO (Empty Base Optimization) + // and make complex evaluator much larger than then should do. + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE evaluator_base() {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ~evaluator_base() {} +private: + EIGEN_DEVICE_FUNC evaluator_base(const evaluator_base&); + EIGEN_DEVICE_FUNC const evaluator_base& operator=(const evaluator_base&); +}; + +// -------------------- Matrix and Array -------------------- +// +// evaluator is a common base class for the +// Matrix and Array evaluators. +// Here we directly specialize evaluator. This is not really a unary expression, and it is, by definition, dense, +// so no need for more sophisticated dispatching. + +// this helper permits to completely eliminate m_outerStride if it is known at compiletime. +template class plainobjectbase_evaluator_data { +public: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride) : data(ptr) + { +#ifndef EIGEN_INTERNAL_DEBUGGING + EIGEN_UNUSED_VARIABLE(outerStride); +#endif + eigen_internal_assert(outerStride==OuterStride); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index outerStride() const EIGEN_NOEXCEPT { return OuterStride; } + const Scalar *data; +}; + +template class plainobjectbase_evaluator_data { +public: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride) : data(ptr), m_outerStride(outerStride) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Index outerStride() const { return m_outerStride; } + const Scalar *data; +protected: + Index m_outerStride; +}; + +template +struct evaluator > + : evaluator_base +{ + typedef PlainObjectBase PlainObjectType; + typedef typename PlainObjectType::Scalar Scalar; + typedef typename PlainObjectType::CoeffReturnType CoeffReturnType; + + enum { + IsRowMajor = PlainObjectType::IsRowMajor, + IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime, + RowsAtCompileTime = PlainObjectType::RowsAtCompileTime, + ColsAtCompileTime = PlainObjectType::ColsAtCompileTime, + + CoeffReadCost = NumTraits::ReadCost, + Flags = traits::EvaluatorFlags, + Alignment = traits::Alignment + }; + enum { + // We do not need to know the outer stride for vectors + OuterStrideAtCompileTime = IsVectorAtCompileTime ? 0 + : int(IsRowMajor) ? ColsAtCompileTime + : RowsAtCompileTime + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + evaluator() + : m_d(0,OuterStrideAtCompileTime) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const PlainObjectType& m) + : m_d(m.data(),IsVectorAtCompileTime ? 0 : m.outerStride()) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + if (IsRowMajor) + return m_d.data[row * m_d.outerStride() + col]; + else + return m_d.data[row + col * m_d.outerStride()]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_d.data[index]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + if (IsRowMajor) + return const_cast(m_d.data)[row * m_d.outerStride() + col]; + else + return const_cast(m_d.data)[row + col * m_d.outerStride()]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return const_cast(m_d.data)[index]; + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + if (IsRowMajor) + return ploadt(m_d.data + row * m_d.outerStride() + col); + else + return ploadt(m_d.data + row + col * m_d.outerStride()); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return ploadt(m_d.data + index); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + if (IsRowMajor) + return pstoret + (const_cast(m_d.data) + row * m_d.outerStride() + col, x); + else + return pstoret + (const_cast(m_d.data) + row + col * m_d.outerStride(), x); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + return pstoret(const_cast(m_d.data) + index, x); + } + +protected: + + plainobjectbase_evaluator_data m_d; +}; + +template +struct evaluator > + : evaluator > > +{ + typedef Matrix XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + evaluator() {} + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& m) + : evaluator >(m) + { } +}; + +template +struct evaluator > + : evaluator > > +{ + typedef Array XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + evaluator() {} + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& m) + : evaluator >(m) + { } +}; + +// -------------------- Transpose -------------------- + +template +struct unary_evaluator, IndexBased> + : evaluator_base > +{ + typedef Transpose XprType; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + Flags = evaluator::Flags ^ RowMajorBit, + Alignment = evaluator::Alignment + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& t) : m_argImpl(t.nestedExpression()) {} + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_argImpl.coeff(col, row); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_argImpl.coeff(index); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_argImpl.coeffRef(col, row); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + typename XprType::Scalar& coeffRef(Index index) + { + return m_argImpl.coeffRef(index); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_argImpl.template packet(col, row); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return m_argImpl.template packet(index); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + m_argImpl.template writePacket(col, row, x); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + m_argImpl.template writePacket(index, x); + } + +protected: + evaluator m_argImpl; +}; + +// -------------------- CwiseNullaryOp -------------------- +// Like Matrix and Array, this is not really a unary expression, so we directly specialize evaluator. +// Likewise, there is not need to more sophisticated dispatching here. + +template::value, + bool has_unary = has_unary_operator::value, + bool has_binary = has_binary_operator::value> +struct nullary_wrapper +{ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const { return op(i,j); } + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); } + + template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const { return op.template packetOp(i,j); } + template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp(i); } +}; + +template +struct nullary_wrapper +{ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType=0, IndexType=0) const { return op(); } + template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType=0, IndexType=0) const { return op.template packetOp(); } +}; + +template +struct nullary_wrapper +{ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j=0) const { return op(i,j); } + template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j=0) const { return op.template packetOp(i,j); } +}; + +// We need the following specialization for vector-only functors assigned to a runtime vector, +// for instance, using linspace and assigning a RowVectorXd to a MatrixXd or even a row of a MatrixXd. +// In this case, i==0 and j is used for the actual iteration. +template +struct nullary_wrapper +{ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const { + eigen_assert(i==0 || j==0); + return op(i+j); + } + template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const { + eigen_assert(i==0 || j==0); + return op.template packetOp(i+j); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { return op(i); } + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { return op.template packetOp(i); } +}; + +template +struct nullary_wrapper {}; + +#if 0 && EIGEN_COMP_MSVC>0 +// Disable this ugly workaround. This is now handled in traits::match, +// but this piece of code might still become handly if some other weird compilation +// erros pop up again. + +// MSVC exhibits a weird compilation error when +// compiling: +// Eigen::MatrixXf A = MatrixXf::Random(3,3); +// Ref R = 2.f*A; +// and that has_*ary_operator> have not been instantiated yet. +// The "problem" is that evaluator<2.f*A> is instantiated by traits::match<2.f*A> +// and at that time has_*ary_operator returns true regardless of T. +// Then nullary_wrapper is badly instantiated as nullary_wrapper<.,.,true,true,true>. +// The trick is thus to defer the proper instantiation of nullary_wrapper when coeff(), +// and packet() are really instantiated as implemented below: + +// This is a simple wrapper around Index to enforce the re-instantiation of +// has_*ary_operator when needed. +template struct nullary_wrapper_workaround_msvc { + nullary_wrapper_workaround_msvc(const T&); + operator T()const; +}; + +template +struct nullary_wrapper +{ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const { + return nullary_wrapper >::value, + has_unary_operator >::value, + has_binary_operator >::value>().operator()(op,i,j); + } + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const { + return nullary_wrapper >::value, + has_unary_operator >::value, + has_binary_operator >::value>().operator()(op,i); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const { + return nullary_wrapper >::value, + has_unary_operator >::value, + has_binary_operator >::value>().template packetOp(op,i,j); + } + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const { + return nullary_wrapper >::value, + has_unary_operator >::value, + has_binary_operator >::value>().template packetOp(op,i); + } +}; +#endif // MSVC workaround + +template +struct evaluator > + : evaluator_base > +{ + typedef CwiseNullaryOp XprType; + typedef typename internal::remove_all::type PlainObjectTypeCleaned; + + enum { + CoeffReadCost = internal::functor_traits::Cost, + + Flags = (evaluator::Flags + & ( HereditaryBits + | (functor_has_linear_access::ret ? LinearAccessBit : 0) + | (functor_traits::PacketAccess ? PacketAccessBit : 0))) + | (functor_traits::IsRepeatable ? 0 : EvalBeforeNestingBit), + Alignment = AlignedMax + }; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& n) + : m_functor(n.functor()), m_wrapper() + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(IndexType row, IndexType col) const + { + return m_wrapper(m_functor, row, col); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(IndexType index) const + { + return m_wrapper(m_functor,index); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(IndexType row, IndexType col) const + { + return m_wrapper.template packetOp(m_functor, row, col); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(IndexType index) const + { + return m_wrapper.template packetOp(m_functor, index); + } + +protected: + const NullaryOp m_functor; + const internal::nullary_wrapper m_wrapper; +}; + +// -------------------- CwiseUnaryOp -------------------- + +template +struct unary_evaluator, IndexBased > + : evaluator_base > +{ + typedef CwiseUnaryOp XprType; + + enum { + CoeffReadCost = int(evaluator::CoeffReadCost) + int(functor_traits::Cost), + + Flags = evaluator::Flags + & (HereditaryBits | LinearAccessBit | (functor_traits::PacketAccess ? PacketAccessBit : 0)), + Alignment = evaluator::Alignment + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& op) : m_d(op) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits::Cost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_d.func()(m_d.argImpl.coeff(row, col)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_d.func()(m_d.argImpl.coeff(index)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_d.func().packetOp(m_d.argImpl.template packet(row, col)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return m_d.func().packetOp(m_d.argImpl.template packet(index)); + } + +protected: + + // this helper permits to completely eliminate the functor if it is empty + struct Data + { + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Data(const XprType& xpr) : op(xpr.functor()), argImpl(xpr.nestedExpression()) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const UnaryOp& func() const { return op; } + UnaryOp op; + evaluator argImpl; + }; + + Data m_d; +}; + +// -------------------- CwiseTernaryOp -------------------- + +// this is a ternary expression +template +struct evaluator > + : public ternary_evaluator > +{ + typedef CwiseTernaryOp XprType; + typedef ternary_evaluator > Base; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {} +}; + +template +struct ternary_evaluator, IndexBased, IndexBased> + : evaluator_base > +{ + typedef CwiseTernaryOp XprType; + + enum { + CoeffReadCost = int(evaluator::CoeffReadCost) + int(evaluator::CoeffReadCost) + int(evaluator::CoeffReadCost) + int(functor_traits::Cost), + + Arg1Flags = evaluator::Flags, + Arg2Flags = evaluator::Flags, + Arg3Flags = evaluator::Flags, + SameType = is_same::value && is_same::value, + StorageOrdersAgree = (int(Arg1Flags)&RowMajorBit)==(int(Arg2Flags)&RowMajorBit) && (int(Arg1Flags)&RowMajorBit)==(int(Arg3Flags)&RowMajorBit), + Flags0 = (int(Arg1Flags) | int(Arg2Flags) | int(Arg3Flags)) & ( + HereditaryBits + | (int(Arg1Flags) & int(Arg2Flags) & int(Arg3Flags) & + ( (StorageOrdersAgree ? LinearAccessBit : 0) + | (functor_traits::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0) + ) + ) + ), + Flags = (Flags0 & ~RowMajorBit) | (Arg1Flags & RowMajorBit), + Alignment = EIGEN_PLAIN_ENUM_MIN( + EIGEN_PLAIN_ENUM_MIN(evaluator::Alignment, evaluator::Alignment), + evaluator::Alignment) + }; + + EIGEN_DEVICE_FUNC explicit ternary_evaluator(const XprType& xpr) : m_d(xpr) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits::Cost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_d.func()(m_d.arg1Impl.coeff(row, col), m_d.arg2Impl.coeff(row, col), m_d.arg3Impl.coeff(row, col)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_d.func()(m_d.arg1Impl.coeff(index), m_d.arg2Impl.coeff(index), m_d.arg3Impl.coeff(index)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_d.func().packetOp(m_d.arg1Impl.template packet(row, col), + m_d.arg2Impl.template packet(row, col), + m_d.arg3Impl.template packet(row, col)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return m_d.func().packetOp(m_d.arg1Impl.template packet(index), + m_d.arg2Impl.template packet(index), + m_d.arg3Impl.template packet(index)); + } + +protected: + // this helper permits to completely eliminate the functor if it is empty + struct Data + { + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Data(const XprType& xpr) : op(xpr.functor()), arg1Impl(xpr.arg1()), arg2Impl(xpr.arg2()), arg3Impl(xpr.arg3()) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const TernaryOp& func() const { return op; } + TernaryOp op; + evaluator arg1Impl; + evaluator arg2Impl; + evaluator arg3Impl; + }; + + Data m_d; +}; + +// -------------------- CwiseBinaryOp -------------------- + +// this is a binary expression +template +struct evaluator > + : public binary_evaluator > +{ + typedef CwiseBinaryOp XprType; + typedef binary_evaluator > Base; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& xpr) : Base(xpr) {} +}; + +template +struct binary_evaluator, IndexBased, IndexBased> + : evaluator_base > +{ + typedef CwiseBinaryOp XprType; + + enum { + CoeffReadCost = int(evaluator::CoeffReadCost) + int(evaluator::CoeffReadCost) + int(functor_traits::Cost), + + LhsFlags = evaluator::Flags, + RhsFlags = evaluator::Flags, + SameType = is_same::value, + StorageOrdersAgree = (int(LhsFlags)&RowMajorBit)==(int(RhsFlags)&RowMajorBit), + Flags0 = (int(LhsFlags) | int(RhsFlags)) & ( + HereditaryBits + | (int(LhsFlags) & int(RhsFlags) & + ( (StorageOrdersAgree ? LinearAccessBit : 0) + | (functor_traits::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0) + ) + ) + ), + Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit), + Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator::Alignment,evaluator::Alignment) + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit binary_evaluator(const XprType& xpr) : m_d(xpr) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits::Cost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_d.func()(m_d.lhsImpl.coeff(row, col), m_d.rhsImpl.coeff(row, col)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_d.func()(m_d.lhsImpl.coeff(index), m_d.rhsImpl.coeff(index)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_d.func().packetOp(m_d.lhsImpl.template packet(row, col), + m_d.rhsImpl.template packet(row, col)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return m_d.func().packetOp(m_d.lhsImpl.template packet(index), + m_d.rhsImpl.template packet(index)); + } + +protected: + + // this helper permits to completely eliminate the functor if it is empty + struct Data + { + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Data(const XprType& xpr) : op(xpr.functor()), lhsImpl(xpr.lhs()), rhsImpl(xpr.rhs()) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const BinaryOp& func() const { return op; } + BinaryOp op; + evaluator lhsImpl; + evaluator rhsImpl; + }; + + Data m_d; +}; + +// -------------------- CwiseUnaryView -------------------- + +template +struct unary_evaluator, IndexBased> + : evaluator_base > +{ + typedef CwiseUnaryView XprType; + + enum { + CoeffReadCost = int(evaluator::CoeffReadCost) + int(functor_traits::Cost), + + Flags = (evaluator::Flags & (HereditaryBits | LinearAccessBit | DirectAccessBit)), + + Alignment = 0 // FIXME it is not very clear why alignment is necessarily lost... + }; + + EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op) : m_d(op) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits::Cost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_d.func()(m_d.argImpl.coeff(row, col)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_d.func()(m_d.argImpl.coeff(index)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_d.func()(m_d.argImpl.coeffRef(row, col)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return m_d.func()(m_d.argImpl.coeffRef(index)); + } + +protected: + + // this helper permits to completely eliminate the functor if it is empty + struct Data + { + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Data(const XprType& xpr) : op(xpr.functor()), argImpl(xpr.nestedExpression()) {} + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const UnaryOp& func() const { return op; } + UnaryOp op; + evaluator argImpl; + }; + + Data m_d; +}; + +// -------------------- Map -------------------- + +// FIXME perhaps the PlainObjectType could be provided by Derived::PlainObject ? +// but that might complicate template specialization +template +struct mapbase_evaluator; + +template +struct mapbase_evaluator : evaluator_base +{ + typedef Derived XprType; + typedef typename XprType::PointerType PointerType; + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + enum { + IsRowMajor = XprType::RowsAtCompileTime, + ColsAtCompileTime = XprType::ColsAtCompileTime, + CoeffReadCost = NumTraits::ReadCost + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit mapbase_evaluator(const XprType& map) + : m_data(const_cast(map.data())), + m_innerStride(map.innerStride()), + m_outerStride(map.outerStride()) + { + EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(evaluator::Flags&PacketAccessBit, internal::inner_stride_at_compile_time::ret==1), + PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_data[col * colStride() + row * rowStride()]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_data[index * m_innerStride.value()]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_data[col * colStride() + row * rowStride()]; + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return m_data[index * m_innerStride.value()]; + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + PointerType ptr = m_data + row * rowStride() + col * colStride(); + return internal::ploadt(ptr); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return internal::ploadt(m_data + index * m_innerStride.value()); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + PointerType ptr = m_data + row * rowStride() + col * colStride(); + return internal::pstoret(ptr, x); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + internal::pstoret(m_data + index * m_innerStride.value(), x); + } +protected: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rowStride() const EIGEN_NOEXCEPT { + return XprType::IsRowMajor ? m_outerStride.value() : m_innerStride.value(); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index colStride() const EIGEN_NOEXCEPT { + return XprType::IsRowMajor ? m_innerStride.value() : m_outerStride.value(); + } + + PointerType m_data; + const internal::variable_if_dynamic m_innerStride; + const internal::variable_if_dynamic m_outerStride; +}; + +template +struct evaluator > + : public mapbase_evaluator, PlainObjectType> +{ + typedef Map XprType; + typedef typename XprType::Scalar Scalar; + // TODO: should check for smaller packet types once we can handle multi-sized packet types + typedef typename packet_traits::type PacketScalar; + + enum { + InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0 + ? int(PlainObjectType::InnerStrideAtCompileTime) + : int(StrideType::InnerStrideAtCompileTime), + OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0 + ? int(PlainObjectType::OuterStrideAtCompileTime) + : int(StrideType::OuterStrideAtCompileTime), + HasNoInnerStride = InnerStrideAtCompileTime == 1, + HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0, + HasNoStride = HasNoInnerStride && HasNoOuterStride, + IsDynamicSize = PlainObjectType::SizeAtCompileTime==Dynamic, + + PacketAccessMask = bool(HasNoInnerStride) ? ~int(0) : ~int(PacketAccessBit), + LinearAccessMask = bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime) ? ~int(0) : ~int(LinearAccessBit), + Flags = int( evaluator::Flags) & (LinearAccessMask&PacketAccessMask), + + Alignment = int(MapOptions)&int(AlignedMask) + }; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& map) + : mapbase_evaluator(map) + { } +}; + +// -------------------- Ref -------------------- + +template +struct evaluator > + : public mapbase_evaluator, PlainObjectType> +{ + typedef Ref XprType; + + enum { + Flags = evaluator >::Flags, + Alignment = evaluator >::Alignment + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& ref) + : mapbase_evaluator(ref) + { } +}; + +// -------------------- Block -------------------- + +template::ret> struct block_evaluator; + +template +struct evaluator > + : block_evaluator +{ + typedef Block XprType; + typedef typename XprType::Scalar Scalar; + // TODO: should check for smaller packet types once we can handle multi-sized packet types + typedef typename packet_traits::type PacketScalar; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + + RowsAtCompileTime = traits::RowsAtCompileTime, + ColsAtCompileTime = traits::ColsAtCompileTime, + MaxRowsAtCompileTime = traits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = traits::MaxColsAtCompileTime, + + ArgTypeIsRowMajor = (int(evaluator::Flags)&RowMajorBit) != 0, + IsRowMajor = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? 1 + : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0 + : ArgTypeIsRowMajor, + HasSameStorageOrderAsArgType = (IsRowMajor == ArgTypeIsRowMajor), + InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime), + InnerStrideAtCompileTime = HasSameStorageOrderAsArgType + ? int(inner_stride_at_compile_time::ret) + : int(outer_stride_at_compile_time::ret), + OuterStrideAtCompileTime = HasSameStorageOrderAsArgType + ? int(outer_stride_at_compile_time::ret) + : int(inner_stride_at_compile_time::ret), + MaskPacketAccessBit = (InnerStrideAtCompileTime == 1 || HasSameStorageOrderAsArgType) ? PacketAccessBit : 0, + + FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 || (InnerPanel && (evaluator::Flags&LinearAccessBit))) ? LinearAccessBit : 0, + FlagsRowMajorBit = XprType::Flags&RowMajorBit, + Flags0 = evaluator::Flags & ( (HereditaryBits & ~RowMajorBit) | + DirectAccessBit | + MaskPacketAccessBit), + Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit, + + PacketAlignment = unpacket_traits::alignment, + Alignment0 = (InnerPanel && (OuterStrideAtCompileTime!=Dynamic) + && (OuterStrideAtCompileTime!=0) + && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % int(PacketAlignment)) == 0)) ? int(PacketAlignment) : 0, + Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator::Alignment, Alignment0) + }; + typedef block_evaluator block_evaluator_type; + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& block) : block_evaluator_type(block) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } +}; + +// no direct-access => dispatch to a unary evaluator +template +struct block_evaluator + : unary_evaluator > +{ + typedef Block XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit block_evaluator(const XprType& block) + : unary_evaluator(block) + {} +}; + +template +struct unary_evaluator, IndexBased> + : evaluator_base > +{ + typedef Block XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& block) + : m_argImpl(block.nestedExpression()), + m_startRow(block.startRow()), + m_startCol(block.startCol()), + m_linear_offset(ForwardLinearAccess?(ArgType::IsRowMajor ? block.startRow()*block.nestedExpression().cols() + block.startCol() : block.startCol()*block.nestedExpression().rows() + block.startRow()):0) + { } + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + enum { + RowsAtCompileTime = XprType::RowsAtCompileTime, + ForwardLinearAccess = (InnerPanel || int(XprType::IsRowMajor)==int(ArgType::IsRowMajor)) && bool(evaluator::Flags&LinearAccessBit) + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_argImpl.coeff(m_startRow.value() + row, m_startCol.value() + col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return linear_coeff_impl(index, bool_constant()); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_argImpl.coeffRef(m_startRow.value() + row, m_startCol.value() + col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return linear_coeffRef_impl(index, bool_constant()); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_argImpl.template packet(m_startRow.value() + row, m_startCol.value() + col); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + if (ForwardLinearAccess) + return m_argImpl.template packet(m_linear_offset.value() + index); + else + return packet(RowsAtCompileTime == 1 ? 0 : index, + RowsAtCompileTime == 1 ? index : 0); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + return m_argImpl.template writePacket(m_startRow.value() + row, m_startCol.value() + col, x); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + if (ForwardLinearAccess) + return m_argImpl.template writePacket(m_linear_offset.value() + index, x); + else + return writePacket(RowsAtCompileTime == 1 ? 0 : index, + RowsAtCompileTime == 1 ? index : 0, + x); + } + +protected: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType linear_coeff_impl(Index index, internal::true_type /* ForwardLinearAccess */) const + { + return m_argImpl.coeff(m_linear_offset.value() + index); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType linear_coeff_impl(Index index, internal::false_type /* not ForwardLinearAccess */) const + { + return coeff(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& linear_coeffRef_impl(Index index, internal::true_type /* ForwardLinearAccess */) + { + return m_argImpl.coeffRef(m_linear_offset.value() + index); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& linear_coeffRef_impl(Index index, internal::false_type /* not ForwardLinearAccess */) + { + return coeffRef(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0); + } + + evaluator m_argImpl; + const variable_if_dynamic m_startRow; + const variable_if_dynamic m_startCol; + const variable_if_dynamic m_linear_offset; +}; + +// TODO: This evaluator does not actually use the child evaluator; +// all action is via the data() as returned by the Block expression. + +template +struct block_evaluator + : mapbase_evaluator, + typename Block::PlainObject> +{ + typedef Block XprType; + typedef typename XprType::Scalar Scalar; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit block_evaluator(const XprType& block) + : mapbase_evaluator(block) + { + // TODO: for the 3.3 release, this should be turned to an internal assertion, but let's keep it as is for the beta lifetime + eigen_assert(((internal::UIntPtr(block.data()) % EIGEN_PLAIN_ENUM_MAX(1,evaluator::Alignment)) == 0) && "data is not aligned"); + } +}; + + +// -------------------- Select -------------------- +// NOTE shall we introduce a ternary_evaluator? + +// TODO enable vectorization for Select +template +struct evaluator > + : evaluator_base > +{ + typedef Select XprType; + enum { + CoeffReadCost = evaluator::CoeffReadCost + + EIGEN_PLAIN_ENUM_MAX(evaluator::CoeffReadCost, + evaluator::CoeffReadCost), + + Flags = (unsigned int)evaluator::Flags & evaluator::Flags & HereditaryBits, + + Alignment = EIGEN_PLAIN_ENUM_MIN(evaluator::Alignment, evaluator::Alignment) + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& select) + : m_conditionImpl(select.conditionMatrix()), + m_thenImpl(select.thenMatrix()), + m_elseImpl(select.elseMatrix()) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + if (m_conditionImpl.coeff(row, col)) + return m_thenImpl.coeff(row, col); + else + return m_elseImpl.coeff(row, col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + if (m_conditionImpl.coeff(index)) + return m_thenImpl.coeff(index); + else + return m_elseImpl.coeff(index); + } + +protected: + evaluator m_conditionImpl; + evaluator m_thenImpl; + evaluator m_elseImpl; +}; + + +// -------------------- Replicate -------------------- + +template +struct unary_evaluator > + : evaluator_base > +{ + typedef Replicate XprType; + typedef typename XprType::CoeffReturnType CoeffReturnType; + enum { + Factor = (RowFactor==Dynamic || ColFactor==Dynamic) ? Dynamic : RowFactor*ColFactor + }; + typedef typename internal::nested_eval::type ArgTypeNested; + typedef typename internal::remove_all::type ArgTypeNestedCleaned; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + LinearAccessMask = XprType::IsVectorAtCompileTime ? LinearAccessBit : 0, + Flags = (evaluator::Flags & (HereditaryBits|LinearAccessMask) & ~RowMajorBit) | (traits::Flags & RowMajorBit), + + Alignment = evaluator::Alignment + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& replicate) + : m_arg(replicate.nestedExpression()), + m_argImpl(m_arg), + m_rows(replicate.nestedExpression().rows()), + m_cols(replicate.nestedExpression().cols()) + {} + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + // try to avoid using modulo; this is a pure optimization strategy + const Index actual_row = internal::traits::RowsAtCompileTime==1 ? 0 + : RowFactor==1 ? row + : row % m_rows.value(); + const Index actual_col = internal::traits::ColsAtCompileTime==1 ? 0 + : ColFactor==1 ? col + : col % m_cols.value(); + + return m_argImpl.coeff(actual_row, actual_col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + // try to avoid using modulo; this is a pure optimization strategy + const Index actual_index = internal::traits::RowsAtCompileTime==1 + ? (ColFactor==1 ? index : index%m_cols.value()) + : (RowFactor==1 ? index : index%m_rows.value()); + + return m_argImpl.coeff(actual_index); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + const Index actual_row = internal::traits::RowsAtCompileTime==1 ? 0 + : RowFactor==1 ? row + : row % m_rows.value(); + const Index actual_col = internal::traits::ColsAtCompileTime==1 ? 0 + : ColFactor==1 ? col + : col % m_cols.value(); + + return m_argImpl.template packet(actual_row, actual_col); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + const Index actual_index = internal::traits::RowsAtCompileTime==1 + ? (ColFactor==1 ? index : index%m_cols.value()) + : (RowFactor==1 ? index : index%m_rows.value()); + + return m_argImpl.template packet(actual_index); + } + +protected: + const ArgTypeNested m_arg; + evaluator m_argImpl; + const variable_if_dynamic m_rows; + const variable_if_dynamic m_cols; +}; + +// -------------------- MatrixWrapper and ArrayWrapper -------------------- +// +// evaluator_wrapper_base is a common base class for the +// MatrixWrapper and ArrayWrapper evaluators. + +template +struct evaluator_wrapper_base + : evaluator_base +{ + typedef typename remove_all::type ArgType; + enum { + CoeffReadCost = evaluator::CoeffReadCost, + Flags = evaluator::Flags, + Alignment = evaluator::Alignment + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator_wrapper_base(const ArgType& arg) : m_argImpl(arg) {} + + typedef typename ArgType::Scalar Scalar; + typedef typename ArgType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_argImpl.coeff(row, col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_argImpl.coeff(index); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_argImpl.coeffRef(row, col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return m_argImpl.coeffRef(index); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + return m_argImpl.template packet(row, col); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + return m_argImpl.template packet(index); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + m_argImpl.template writePacket(row, col, x); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + m_argImpl.template writePacket(index, x); + } + +protected: + evaluator m_argImpl; +}; + +template +struct unary_evaluator > + : evaluator_wrapper_base > +{ + typedef MatrixWrapper XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& wrapper) + : evaluator_wrapper_base >(wrapper.nestedExpression()) + { } +}; + +template +struct unary_evaluator > + : evaluator_wrapper_base > +{ + typedef ArrayWrapper XprType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& wrapper) + : evaluator_wrapper_base >(wrapper.nestedExpression()) + { } +}; + + +// -------------------- Reverse -------------------- + +// defined in Reverse.h: +template struct reverse_packet_cond; + +template +struct unary_evaluator > + : evaluator_base > +{ + typedef Reverse XprType; + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + enum { + IsRowMajor = XprType::IsRowMajor, + IsColMajor = !IsRowMajor, + ReverseRow = (Direction == Vertical) || (Direction == BothDirections), + ReverseCol = (Direction == Horizontal) || (Direction == BothDirections), + ReversePacket = (Direction == BothDirections) + || ((Direction == Vertical) && IsColMajor) + || ((Direction == Horizontal) && IsRowMajor), + + CoeffReadCost = evaluator::CoeffReadCost, + + // let's enable LinearAccess only with vectorization because of the product overhead + // FIXME enable DirectAccess with negative strides? + Flags0 = evaluator::Flags, + LinearAccess = ( (Direction==BothDirections) && (int(Flags0)&PacketAccessBit) ) + || ((ReverseRow && XprType::ColsAtCompileTime==1) || (ReverseCol && XprType::RowsAtCompileTime==1)) + ? LinearAccessBit : 0, + + Flags = int(Flags0) & (HereditaryBits | PacketAccessBit | LinearAccess), + + Alignment = 0 // FIXME in some rare cases, Alignment could be preserved, like a Vector4f. + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit unary_evaluator(const XprType& reverse) + : m_argImpl(reverse.nestedExpression()), + m_rows(ReverseRow ? reverse.nestedExpression().rows() : 1), + m_cols(ReverseCol ? reverse.nestedExpression().cols() : 1) + { } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_argImpl.coeff(ReverseRow ? m_rows.value() - row - 1 : row, + ReverseCol ? m_cols.value() - col - 1 : col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_argImpl.coeff(m_rows.value() * m_cols.value() - index - 1); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_argImpl.coeffRef(ReverseRow ? m_rows.value() - row - 1 : row, + ReverseCol ? m_cols.value() - col - 1 : col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return m_argImpl.coeffRef(m_rows.value() * m_cols.value() - index - 1); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index row, Index col) const + { + enum { + PacketSize = unpacket_traits::size, + OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1, + OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1 + }; + typedef internal::reverse_packet_cond reverse_packet; + return reverse_packet::run(m_argImpl.template packet( + ReverseRow ? m_rows.value() - row - OffsetRow : row, + ReverseCol ? m_cols.value() - col - OffsetCol : col)); + } + + template + EIGEN_STRONG_INLINE + PacketType packet(Index index) const + { + enum { PacketSize = unpacket_traits::size }; + return preverse(m_argImpl.template packet(m_rows.value() * m_cols.value() - index - PacketSize)); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index row, Index col, const PacketType& x) + { + // FIXME we could factorize some code with packet(i,j) + enum { + PacketSize = unpacket_traits::size, + OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1, + OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1 + }; + typedef internal::reverse_packet_cond reverse_packet; + m_argImpl.template writePacket( + ReverseRow ? m_rows.value() - row - OffsetRow : row, + ReverseCol ? m_cols.value() - col - OffsetCol : col, + reverse_packet::run(x)); + } + + template + EIGEN_STRONG_INLINE + void writePacket(Index index, const PacketType& x) + { + enum { PacketSize = unpacket_traits::size }; + m_argImpl.template writePacket + (m_rows.value() * m_cols.value() - index - PacketSize, preverse(x)); + } + +protected: + evaluator m_argImpl; + + // If we do not reverse rows, then we do not need to know the number of rows; same for columns + // Nonetheless, in this case it is important to set to 1 such that the coeff(index) method works fine for vectors. + const variable_if_dynamic m_rows; + const variable_if_dynamic m_cols; +}; + + +// -------------------- Diagonal -------------------- + +template +struct evaluator > + : evaluator_base > +{ + typedef Diagonal XprType; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + + Flags = (unsigned int)(evaluator::Flags & (HereditaryBits | DirectAccessBit) & ~RowMajorBit) | LinearAccessBit, + + Alignment = 0 + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit evaluator(const XprType& diagonal) + : m_argImpl(diagonal.nestedExpression()), + m_index(diagonal.index()) + { } + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index) const + { + return m_argImpl.coeff(row + rowOffset(), row + colOffset()); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index index) const + { + return m_argImpl.coeff(index + rowOffset(), index + colOffset()); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index) + { + return m_argImpl.coeffRef(row + rowOffset(), row + colOffset()); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + return m_argImpl.coeffRef(index + rowOffset(), index + colOffset()); + } + +protected: + evaluator m_argImpl; + const internal::variable_if_dynamicindex m_index; + +private: + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rowOffset() const { return m_index.value() > 0 ? 0 : -m_index.value(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index colOffset() const { return m_index.value() > 0 ? m_index.value() : 0; } +}; + + +//---------------------------------------------------------------------- +// deprecated code +//---------------------------------------------------------------------- + +// -------------------- EvalToTemp -------------------- + +// expression class for evaluating nested expression to a temporary + +template class EvalToTemp; + +template +struct traits > + : public traits +{ }; + +template +class EvalToTemp + : public dense_xpr_base >::type +{ + public: + + typedef typename dense_xpr_base::type Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(EvalToTemp) + + explicit EvalToTemp(const ArgType& arg) + : m_arg(arg) + { } + + const ArgType& arg() const + { + return m_arg; + } + + EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT + { + return m_arg.rows(); + } + + EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT + { + return m_arg.cols(); + } + + private: + const ArgType& m_arg; +}; + +template +struct evaluator > + : public evaluator +{ + typedef EvalToTemp XprType; + typedef typename ArgType::PlainObject PlainObject; + typedef evaluator Base; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) + : m_result(xpr.arg()) + { + ::new (static_cast(this)) Base(m_result); + } + + // This constructor is used when nesting an EvalTo evaluator in another evaluator + EIGEN_DEVICE_FUNC evaluator(const ArgType& arg) + : m_result(arg) + { + ::new (static_cast(this)) Base(m_result); + } + +protected: + PlainObject m_result; +}; + +} // namespace internal + +} // end namespace Eigen + +#endif // EIGEN_COREEVALUATORS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreIterators.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreIterators.h new file mode 100644 index 0000000000000000000000000000000000000000..b967196813b21194a0119ecf2eb721fa32ce07e8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CoreIterators.h @@ -0,0 +1,132 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_COREITERATORS_H +#define EIGEN_COREITERATORS_H + +namespace Eigen { + +/* This file contains the respective InnerIterator definition of the expressions defined in Eigen/Core + */ + +namespace internal { + +template +class inner_iterator_selector; + +} + +/** \class InnerIterator + * \brief An InnerIterator allows to loop over the element of any matrix expression. + * + * \warning To be used with care because an evaluator is constructed every time an InnerIterator iterator is constructed. + * + * TODO: add a usage example + */ +template +class InnerIterator +{ +protected: + typedef internal::inner_iterator_selector::Kind> IteratorType; + typedef internal::evaluator EvaluatorType; + typedef typename internal::traits::Scalar Scalar; +public: + /** Construct an iterator over the \a outerId -th row or column of \a xpr */ + InnerIterator(const XprType &xpr, const Index &outerId) + : m_eval(xpr), m_iter(m_eval, outerId, xpr.innerSize()) + {} + + /// \returns the value of the current coefficient. + EIGEN_STRONG_INLINE Scalar value() const { return m_iter.value(); } + /** Increment the iterator \c *this to the next non-zero coefficient. + * Explicit zeros are not skipped over. To skip explicit zeros, see class SparseView + */ + EIGEN_STRONG_INLINE InnerIterator& operator++() { m_iter.operator++(); return *this; } + EIGEN_STRONG_INLINE InnerIterator& operator+=(Index i) { m_iter.operator+=(i); return *this; } + EIGEN_STRONG_INLINE InnerIterator operator+(Index i) + { InnerIterator result(*this); result+=i; return result; } + + + /// \returns the column or row index of the current coefficient. + EIGEN_STRONG_INLINE Index index() const { return m_iter.index(); } + /// \returns the row index of the current coefficient. + EIGEN_STRONG_INLINE Index row() const { return m_iter.row(); } + /// \returns the column index of the current coefficient. + EIGEN_STRONG_INLINE Index col() const { return m_iter.col(); } + /// \returns \c true if the iterator \c *this still references a valid coefficient. + EIGEN_STRONG_INLINE operator bool() const { return m_iter; } + +protected: + EvaluatorType m_eval; + IteratorType m_iter; +private: + // If you get here, then you're not using the right InnerIterator type, e.g.: + // SparseMatrix A; + // SparseMatrix::InnerIterator it(A,0); + template InnerIterator(const EigenBase&,Index outer); +}; + +namespace internal { + +// Generic inner iterator implementation for dense objects +template +class inner_iterator_selector +{ +protected: + typedef evaluator EvaluatorType; + typedef typename traits::Scalar Scalar; + enum { IsRowMajor = (XprType::Flags&RowMajorBit)==RowMajorBit }; + +public: + EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &innerSize) + : m_eval(eval), m_inner(0), m_outer(outerId), m_end(innerSize) + {} + + EIGEN_STRONG_INLINE Scalar value() const + { + return (IsRowMajor) ? m_eval.coeff(m_outer, m_inner) + : m_eval.coeff(m_inner, m_outer); + } + + EIGEN_STRONG_INLINE inner_iterator_selector& operator++() { m_inner++; return *this; } + + EIGEN_STRONG_INLINE Index index() const { return m_inner; } + inline Index row() const { return IsRowMajor ? m_outer : index(); } + inline Index col() const { return IsRowMajor ? index() : m_outer; } + + EIGEN_STRONG_INLINE operator bool() const { return m_inner < m_end && m_inner>=0; } + +protected: + const EvaluatorType& m_eval; + Index m_inner; + const Index m_outer; + const Index m_end; +}; + +// For iterator-based evaluator, inner-iterator is already implemented as +// evaluator<>::InnerIterator +template +class inner_iterator_selector + : public evaluator::InnerIterator +{ +protected: + typedef typename evaluator::InnerIterator Base; + typedef evaluator EvaluatorType; + +public: + EIGEN_STRONG_INLINE inner_iterator_selector(const EvaluatorType &eval, const Index &outerId, const Index &/*innerSize*/) + : Base(eval, outerId) + {} +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_COREITERATORS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseBinaryOp.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseBinaryOp.h new file mode 100644 index 0000000000000000000000000000000000000000..2202b1cc6b78c19de49e23ab81fd6e0982372996 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseBinaryOp.h @@ -0,0 +1,183 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2014 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CWISE_BINARY_OP_H +#define EIGEN_CWISE_BINARY_OP_H + +namespace Eigen { + +namespace internal { +template +struct traits > +{ + // we must not inherit from traits since it has + // the potential to cause problems with MSVC + typedef typename remove_all::type Ancestor; + typedef typename traits::XprKind XprKind; + enum { + RowsAtCompileTime = traits::RowsAtCompileTime, + ColsAtCompileTime = traits::ColsAtCompileTime, + MaxRowsAtCompileTime = traits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = traits::MaxColsAtCompileTime + }; + + // even though we require Lhs and Rhs to have the same scalar type (see CwiseBinaryOp constructor), + // we still want to handle the case when the result type is different. + typedef typename result_of< + BinaryOp( + const typename Lhs::Scalar&, + const typename Rhs::Scalar& + ) + >::type Scalar; + typedef typename cwise_promote_storage_type::StorageKind, + typename traits::StorageKind, + BinaryOp>::ret StorageKind; + typedef typename promote_index_type::StorageIndex, + typename traits::StorageIndex>::type StorageIndex; + typedef typename Lhs::Nested LhsNested; + typedef typename Rhs::Nested RhsNested; + typedef typename remove_reference::type _LhsNested; + typedef typename remove_reference::type _RhsNested; + enum { + Flags = cwise_promote_storage_order::StorageKind,typename traits::StorageKind,_LhsNested::Flags & RowMajorBit,_RhsNested::Flags & RowMajorBit>::value + }; +}; +} // end namespace internal + +template +class CwiseBinaryOpImpl; + +/** \class CwiseBinaryOp + * \ingroup Core_Module + * + * \brief Generic expression where a coefficient-wise binary operator is applied to two expressions + * + * \tparam BinaryOp template functor implementing the operator + * \tparam LhsType the type of the left-hand side + * \tparam RhsType the type of the right-hand side + * + * This class represents an expression where a coefficient-wise binary operator is applied to two expressions. + * It is the return type of binary operators, by which we mean only those binary operators where + * both the left-hand side and the right-hand side are Eigen expressions. + * For example, the return type of matrix1+matrix2 is a CwiseBinaryOp. + * + * Most of the time, this is the only way that it is used, so you typically don't have to name + * CwiseBinaryOp types explicitly. + * + * \sa MatrixBase::binaryExpr(const MatrixBase &,const CustomBinaryOp &) const, class CwiseUnaryOp, class CwiseNullaryOp + */ +template +class CwiseBinaryOp : + public CwiseBinaryOpImpl< + BinaryOp, LhsType, RhsType, + typename internal::cwise_promote_storage_type::StorageKind, + typename internal::traits::StorageKind, + BinaryOp>::ret>, + internal::no_assignment_operator +{ + public: + + typedef typename internal::remove_all::type Functor; + typedef typename internal::remove_all::type Lhs; + typedef typename internal::remove_all::type Rhs; + + typedef typename CwiseBinaryOpImpl< + BinaryOp, LhsType, RhsType, + typename internal::cwise_promote_storage_type::StorageKind, + typename internal::traits::StorageKind, + BinaryOp>::ret>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseBinaryOp) + + typedef typename internal::ref_selector::type LhsNested; + typedef typename internal::ref_selector::type RhsNested; + typedef typename internal::remove_reference::type _LhsNested; + typedef typename internal::remove_reference::type _RhsNested; + +#if EIGEN_COMP_MSVC && EIGEN_HAS_CXX11 + //Required for Visual Studio or the Copy constructor will probably not get inlined! + EIGEN_STRONG_INLINE + CwiseBinaryOp(const CwiseBinaryOp&) = default; +#endif + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CwiseBinaryOp(const Lhs& aLhs, const Rhs& aRhs, const BinaryOp& func = BinaryOp()) + : m_lhs(aLhs), m_rhs(aRhs), m_functor(func) + { + EIGEN_CHECK_BINARY_COMPATIBILIY(BinaryOp,typename Lhs::Scalar,typename Rhs::Scalar); + // require the sizes to match + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Lhs, Rhs) + eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols()); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { + // return the fixed size type if available to enable compile time optimizations + return internal::traits::type>::RowsAtCompileTime==Dynamic ? m_rhs.rows() : m_lhs.rows(); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { + // return the fixed size type if available to enable compile time optimizations + return internal::traits::type>::ColsAtCompileTime==Dynamic ? m_rhs.cols() : m_lhs.cols(); + } + + /** \returns the left hand side nested expression */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const _LhsNested& lhs() const { return m_lhs; } + /** \returns the right hand side nested expression */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const _RhsNested& rhs() const { return m_rhs; } + /** \returns the functor representing the binary operation */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const BinaryOp& functor() const { return m_functor; } + + protected: + LhsNested m_lhs; + RhsNested m_rhs; + const BinaryOp m_functor; +}; + +// Generic API dispatcher +template +class CwiseBinaryOpImpl + : public internal::generic_xpr_base >::type +{ +public: + typedef typename internal::generic_xpr_base >::type Base; +}; + +/** replaces \c *this by \c *this - \a other. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +MatrixBase::operator-=(const MatrixBase &other) +{ + call_assignment(derived(), other.derived(), internal::sub_assign_op()); + return derived(); +} + +/** replaces \c *this by \c *this + \a other. + * + * \returns a reference to \c *this + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & +MatrixBase::operator+=(const MatrixBase& other) +{ + call_assignment(derived(), other.derived(), internal::add_assign_op()); + return derived(); +} + +} // end namespace Eigen + +#endif // EIGEN_CWISE_BINARY_OP_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseNullaryOp.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseNullaryOp.h new file mode 100644 index 0000000000000000000000000000000000000000..289ec510a8ac733646e6f5915fd35fb8812ef559 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseNullaryOp.h @@ -0,0 +1,1001 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CWISE_NULLARY_OP_H +#define EIGEN_CWISE_NULLARY_OP_H + +namespace Eigen { + +namespace internal { +template +struct traits > : traits +{ + enum { + Flags = traits::Flags & RowMajorBit + }; +}; + +} // namespace internal + +/** \class CwiseNullaryOp + * \ingroup Core_Module + * + * \brief Generic expression of a matrix where all coefficients are defined by a functor + * + * \tparam NullaryOp template functor implementing the operator + * \tparam PlainObjectType the underlying plain matrix/array type + * + * This class represents an expression of a generic nullary operator. + * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods, + * and most of the time this is the only way it is used. + * + * However, if you want to write a function returning such an expression, you + * will need to use this class. + * + * The functor NullaryOp must expose one of the following method: + + + + +
\c operator()() if the procedural generation does not depend on the coefficient entries (e.g., random numbers)
\c operator()(Index i)if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace)
\c operator()(Index i,Index j)if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)
+ * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors. + * + * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding + * C++11 random number generators. + * + * A nullary expression can also be used to implement custom sophisticated matrix manipulations + * that cannot be covered by the existing set of natively supported matrix manipulations. + * See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations + * on the behavior of CwiseNullaryOp. + * + * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr + */ +template +class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp >::type, internal::no_assignment_operator +{ + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp) + + EIGEN_DEVICE_FUNC + CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp()) + : m_rows(rows), m_cols(cols), m_functor(func) + { + eigen_assert(rows >= 0 + && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) + && cols >= 0 + && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const { return m_rows.value(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const { return m_cols.value(); } + + /** \returns the functor representing the nullary operation */ + EIGEN_DEVICE_FUNC + const NullaryOp& functor() const { return m_functor; } + + protected: + const internal::variable_if_dynamic m_rows; + const internal::variable_if_dynamic m_cols; + const NullaryOp m_functor; +}; + + +/** \returns an expression of a matrix defined by a custom functor \a func + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this MatrixBase type. + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used + * instead. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * \sa class CwiseNullaryOp + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +#ifndef EIGEN_PARSED_BY_DOXYGEN +const CwiseNullaryOp::PlainObject> +#else +const CwiseNullaryOp +#endif +DenseBase::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func) +{ + return CwiseNullaryOp(rows, cols, func); +} + +/** \returns an expression of a matrix defined by a custom functor \a func + * + * The parameter \a size is the size of the returned vector. + * Must be compatible with this MatrixBase type. + * + * \only_for_vectors + * + * This variant is meant to be used for dynamic-size vector types. For fixed-size types, + * it is redundant to pass \a size as argument, so Zero() should be used + * instead. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * Here is an example with C++11 random generators: \include random_cpp11.cpp + * Output: \verbinclude random_cpp11.out + * + * \sa class CwiseNullaryOp + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +#ifndef EIGEN_PARSED_BY_DOXYGEN +const CwiseNullaryOp::PlainObject> +#else +const CwiseNullaryOp +#endif +DenseBase::NullaryExpr(Index size, const CustomNullaryOp& func) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + if(RowsAtCompileTime == 1) return CwiseNullaryOp(1, size, func); + else return CwiseNullaryOp(size, 1, func); +} + +/** \returns an expression of a matrix defined by a custom functor \a func + * + * This variant is only for fixed-size DenseBase types. For dynamic-size types, you + * need to use the variants taking size arguments. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * \sa class CwiseNullaryOp + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +#ifndef EIGEN_PARSED_BY_DOXYGEN +const CwiseNullaryOp::PlainObject> +#else +const CwiseNullaryOp +#endif +DenseBase::NullaryExpr(const CustomNullaryOp& func) +{ + return CwiseNullaryOp(RowsAtCompileTime, ColsAtCompileTime, func); +} + +/** \returns an expression of a constant matrix of value \a value + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this DenseBase type. + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used + * instead. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * \sa class CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Constant(Index rows, Index cols, const Scalar& value) +{ + return DenseBase::NullaryExpr(rows, cols, internal::scalar_constant_op(value)); +} + +/** \returns an expression of a constant matrix of value \a value + * + * The parameter \a size is the size of the returned vector. + * Must be compatible with this DenseBase type. + * + * \only_for_vectors + * + * This variant is meant to be used for dynamic-size vector types. For fixed-size types, + * it is redundant to pass \a size as argument, so Zero() should be used + * instead. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * \sa class CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Constant(Index size, const Scalar& value) +{ + return DenseBase::NullaryExpr(size, internal::scalar_constant_op(value)); +} + +/** \returns an expression of a constant matrix of value \a value + * + * This variant is only for fixed-size DenseBase types. For dynamic-size types, you + * need to use the variants taking size arguments. + * + * The template parameter \a CustomNullaryOp is the type of the functor. + * + * \sa class CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Constant(const Scalar& value) +{ + EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) + return DenseBase::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op(value)); +} + +/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&) + * + * \only_for_vectors + * + * Example: \include DenseBase_LinSpaced_seq_deprecated.cpp + * Output: \verbinclude DenseBase_LinSpaced_seq_deprecated.out + * + * \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&) + */ +template +EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::RandomAccessLinSpacedReturnType +DenseBase::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return DenseBase::NullaryExpr(size, internal::linspaced_op(low,high,size)); +} + +/** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&) + * + * \sa LinSpaced(const Scalar&, const Scalar&) + */ +template +EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::RandomAccessLinSpacedReturnType +DenseBase::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) + return DenseBase::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op(low,high,Derived::SizeAtCompileTime)); +} + +/** + * \brief Sets a linearly spaced vector. + * + * The function generates 'size' equally spaced values in the closed interval [low,high]. + * When size is set to 1, a vector of length 1 containing 'high' is returned. + * + * \only_for_vectors + * + * Example: \include DenseBase_LinSpaced.cpp + * Output: \verbinclude DenseBase_LinSpaced.out + * + * For integer scalar types, an even spacing is possible if and only if the length of the range, + * i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the + * number of values \c high-low+1 (meaning each value can be repeated the same number of time). + * If one of these two considions is not satisfied, then \c high is lowered to the largest value + * satisfying one of this constraint. + * Here are some examples: + * + * Example: \include DenseBase_LinSpacedInt.cpp + * Output: \verbinclude DenseBase_LinSpacedInt.out + * + * \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::RandomAccessLinSpacedReturnType +DenseBase::LinSpaced(Index size, const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return DenseBase::NullaryExpr(size, internal::linspaced_op(low,high,size)); +} + +/** + * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&) + * Special version for fixed size types which does not require the size parameter. + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::RandomAccessLinSpacedReturnType +DenseBase::LinSpaced(const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) + return DenseBase::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op(low,high,Derived::SizeAtCompileTime)); +} + +/** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */ +template +EIGEN_DEVICE_FUNC bool DenseBase::isApproxToConstant +(const Scalar& val, const RealScalar& prec) const +{ + typename internal::nested_eval::type self(derived()); + for(Index j = 0; j < cols(); ++j) + for(Index i = 0; i < rows(); ++i) + if(!internal::isApprox(self.coeff(i, j), val, prec)) + return false; + return true; +} + +/** This is just an alias for isApproxToConstant(). + * + * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */ +template +EIGEN_DEVICE_FUNC bool DenseBase::isConstant +(const Scalar& val, const RealScalar& prec) const +{ + return isApproxToConstant(val, prec); +} + +/** Alias for setConstant(): sets all coefficients in this expression to \a val. + * + * \sa setConstant(), Constant(), class CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase::fill(const Scalar& val) +{ + setConstant(val); +} + +/** Sets all coefficients in this expression to value \a val. + * + * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase::setConstant(const Scalar& val) +{ + return derived() = Constant(rows(), cols(), val); +} + +/** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val. + * + * \only_for_vectors + * + * Example: \include Matrix_setConstant_int.cpp + * Output: \verbinclude Matrix_setConstant_int.out + * + * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setConstant(Index size, const Scalar& val) +{ + resize(size); + return setConstant(val); +} + +/** Resizes to the given size, and sets all coefficients in this expression to the given value \a val. + * + * \param rows the new number of rows + * \param cols the new number of columns + * \param val the value to which all coefficients are set + * + * Example: \include Matrix_setConstant_int_int.cpp + * Output: \verbinclude Matrix_setConstant_int_int.out + * + * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setConstant(Index rows, Index cols, const Scalar& val) +{ + resize(rows, cols); + return setConstant(val); +} + +/** Resizes to the given size, changing only the number of columns, and sets all + * coefficients in this expression to the given value \a val. For the parameter + * of type NoChange_t, just pass the special value \c NoChange. + * + * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setConstant(NoChange_t, Index cols, const Scalar& val) +{ + return setConstant(rows(), cols, val); +} + +/** Resizes to the given size, changing only the number of rows, and sets all + * coefficients in this expression to the given value \a val. For the parameter + * of type NoChange_t, just pass the special value \c NoChange. + * + * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setConstant(Index rows, NoChange_t, const Scalar& val) +{ + return setConstant(rows, cols(), val); +} + + +/** + * \brief Sets a linearly spaced vector. + * + * The function generates 'size' equally spaced values in the closed interval [low,high]. + * When size is set to 1, a vector of length 1 containing 'high' is returned. + * + * \only_for_vectors + * + * Example: \include DenseBase_setLinSpaced.cpp + * Output: \verbinclude DenseBase_setLinSpaced.out + * + * For integer scalar types, do not miss the explanations on the definition + * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. + * + * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op(low,high,newSize)); +} + +/** + * \brief Sets a linearly spaced vector. + * + * The function fills \c *this with equally spaced values in the closed interval [low,high]. + * When size is set to 1, a vector of length 1 containing 'high' is returned. + * + * \only_for_vectors + * + * For integer scalar types, do not miss the explanations on the definition + * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. + * + * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase::setLinSpaced(const Scalar& low, const Scalar& high) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return setLinSpaced(size(), low, high); +} + +// zero: + +/** \returns an expression of a zero matrix. + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this MatrixBase type. + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used + * instead. + * + * Example: \include MatrixBase_zero_int_int.cpp + * Output: \verbinclude MatrixBase_zero_int_int.out + * + * \sa Zero(), Zero(Index) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Zero(Index rows, Index cols) +{ + return Constant(rows, cols, Scalar(0)); +} + +/** \returns an expression of a zero vector. + * + * The parameter \a size is the size of the returned vector. + * Must be compatible with this MatrixBase type. + * + * \only_for_vectors + * + * This variant is meant to be used for dynamic-size vector types. For fixed-size types, + * it is redundant to pass \a size as argument, so Zero() should be used + * instead. + * + * Example: \include MatrixBase_zero_int.cpp + * Output: \verbinclude MatrixBase_zero_int.out + * + * \sa Zero(), Zero(Index,Index) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Zero(Index size) +{ + return Constant(size, Scalar(0)); +} + +/** \returns an expression of a fixed-size zero matrix or vector. + * + * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you + * need to use the variants taking size arguments. + * + * Example: \include MatrixBase_zero.cpp + * Output: \verbinclude MatrixBase_zero.out + * + * \sa Zero(Index), Zero(Index,Index) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Zero() +{ + return Constant(Scalar(0)); +} + +/** \returns true if *this is approximately equal to the zero matrix, + * within the precision given by \a prec. + * + * Example: \include MatrixBase_isZero.cpp + * Output: \verbinclude MatrixBase_isZero.out + * + * \sa class CwiseNullaryOp, Zero() + */ +template +EIGEN_DEVICE_FUNC bool DenseBase::isZero(const RealScalar& prec) const +{ + typename internal::nested_eval::type self(derived()); + for(Index j = 0; j < cols(); ++j) + for(Index i = 0; i < rows(); ++i) + if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast(1), prec)) + return false; + return true; +} + +/** Sets all coefficients in this expression to zero. + * + * Example: \include MatrixBase_setZero.cpp + * Output: \verbinclude MatrixBase_setZero.out + * + * \sa class CwiseNullaryOp, Zero() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase::setZero() +{ + return setConstant(Scalar(0)); +} + +/** Resizes to the given \a size, and sets all coefficients in this expression to zero. + * + * \only_for_vectors + * + * Example: \include Matrix_setZero_int.cpp + * Output: \verbinclude Matrix_setZero_int.out + * + * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setZero(Index newSize) +{ + resize(newSize); + return setConstant(Scalar(0)); +} + +/** Resizes to the given size, and sets all coefficients in this expression to zero. + * + * \param rows the new number of rows + * \param cols the new number of columns + * + * Example: \include Matrix_setZero_int_int.cpp + * Output: \verbinclude Matrix_setZero_int_int.out + * + * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setZero(Index rows, Index cols) +{ + resize(rows, cols); + return setConstant(Scalar(0)); +} + +/** Resizes to the given size, changing only the number of columns, and sets all + * coefficients in this expression to zero. For the parameter of type NoChange_t, + * just pass the special value \c NoChange. + * + * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Zero() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setZero(NoChange_t, Index cols) +{ + return setZero(rows(), cols); +} + +/** Resizes to the given size, changing only the number of rows, and sets all + * coefficients in this expression to zero. For the parameter of type NoChange_t, + * just pass the special value \c NoChange. + * + * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Zero() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setZero(Index rows, NoChange_t) +{ + return setZero(rows, cols()); +} + +// ones: + +/** \returns an expression of a matrix where all coefficients equal one. + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this MatrixBase type. + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used + * instead. + * + * Example: \include MatrixBase_ones_int_int.cpp + * Output: \verbinclude MatrixBase_ones_int_int.out + * + * \sa Ones(), Ones(Index), isOnes(), class Ones + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Ones(Index rows, Index cols) +{ + return Constant(rows, cols, Scalar(1)); +} + +/** \returns an expression of a vector where all coefficients equal one. + * + * The parameter \a newSize is the size of the returned vector. + * Must be compatible with this MatrixBase type. + * + * \only_for_vectors + * + * This variant is meant to be used for dynamic-size vector types. For fixed-size types, + * it is redundant to pass \a size as argument, so Ones() should be used + * instead. + * + * Example: \include MatrixBase_ones_int.cpp + * Output: \verbinclude MatrixBase_ones_int.out + * + * \sa Ones(), Ones(Index,Index), isOnes(), class Ones + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Ones(Index newSize) +{ + return Constant(newSize, Scalar(1)); +} + +/** \returns an expression of a fixed-size matrix or vector where all coefficients equal one. + * + * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you + * need to use the variants taking size arguments. + * + * Example: \include MatrixBase_ones.cpp + * Output: \verbinclude MatrixBase_ones.out + * + * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase::ConstantReturnType +DenseBase::Ones() +{ + return Constant(Scalar(1)); +} + +/** \returns true if *this is approximately equal to the matrix where all coefficients + * are equal to 1, within the precision given by \a prec. + * + * Example: \include MatrixBase_isOnes.cpp + * Output: \verbinclude MatrixBase_isOnes.out + * + * \sa class CwiseNullaryOp, Ones() + */ +template +EIGEN_DEVICE_FUNC bool DenseBase::isOnes +(const RealScalar& prec) const +{ + return isApproxToConstant(Scalar(1), prec); +} + +/** Sets all coefficients in this expression to one. + * + * Example: \include MatrixBase_setOnes.cpp + * Output: \verbinclude MatrixBase_setOnes.out + * + * \sa class CwiseNullaryOp, Ones() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase::setOnes() +{ + return setConstant(Scalar(1)); +} + +/** Resizes to the given \a newSize, and sets all coefficients in this expression to one. + * + * \only_for_vectors + * + * Example: \include Matrix_setOnes_int.cpp + * Output: \verbinclude Matrix_setOnes_int.out + * + * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setOnes(Index newSize) +{ + resize(newSize); + return setConstant(Scalar(1)); +} + +/** Resizes to the given size, and sets all coefficients in this expression to one. + * + * \param rows the new number of rows + * \param cols the new number of columns + * + * Example: \include Matrix_setOnes_int_int.cpp + * Output: \verbinclude Matrix_setOnes_int_int.out + * + * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setOnes(Index rows, Index cols) +{ + resize(rows, cols); + return setConstant(Scalar(1)); +} + +/** Resizes to the given size, changing only the number of rows, and sets all + * coefficients in this expression to one. For the parameter of type NoChange_t, + * just pass the special value \c NoChange. + * + * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(NoChange_t, Index), class CwiseNullaryOp, MatrixBase::Ones() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setOnes(Index rows, NoChange_t) +{ + return setOnes(rows, cols()); +} + +/** Resizes to the given size, changing only the number of columns, and sets all + * coefficients in this expression to one. For the parameter of type NoChange_t, + * just pass the special value \c NoChange. + * + * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(Index, NoChange_t) class CwiseNullaryOp, MatrixBase::Ones() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setOnes(NoChange_t, Index cols) +{ + return setOnes(rows(), cols); +} + +// Identity: + +/** \returns an expression of the identity matrix (not necessarily square). + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this MatrixBase type. + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used + * instead. + * + * Example: \include MatrixBase_identity_int_int.cpp + * Output: \verbinclude MatrixBase_identity_int_int.out + * + * \sa Identity(), setIdentity(), isIdentity() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::IdentityReturnType +MatrixBase::Identity(Index rows, Index cols) +{ + return DenseBase::NullaryExpr(rows, cols, internal::scalar_identity_op()); +} + +/** \returns an expression of the identity matrix (not necessarily square). + * + * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you + * need to use the variant taking size arguments. + * + * Example: \include MatrixBase_identity.cpp + * Output: \verbinclude MatrixBase_identity.out + * + * \sa Identity(Index,Index), setIdentity(), isIdentity() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::IdentityReturnType +MatrixBase::Identity() +{ + EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) + return MatrixBase::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op()); +} + +/** \returns true if *this is approximately equal to the identity matrix + * (not necessarily square), + * within the precision given by \a prec. + * + * Example: \include MatrixBase_isIdentity.cpp + * Output: \verbinclude MatrixBase_isIdentity.out + * + * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity() + */ +template +bool MatrixBase::isIdentity +(const RealScalar& prec) const +{ + typename internal::nested_eval::type self(derived()); + for(Index j = 0; j < cols(); ++j) + { + for(Index i = 0; i < rows(); ++i) + { + if(i == j) + { + if(!internal::isApprox(self.coeff(i, j), static_cast(1), prec)) + return false; + } + else + { + if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast(1), prec)) + return false; + } + } + } + return true; +} + +namespace internal { + +template=16)> +struct setIdentity_impl +{ + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE Derived& run(Derived& m) + { + return m = Derived::Identity(m.rows(), m.cols()); + } +}; + +template +struct setIdentity_impl +{ + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE Derived& run(Derived& m) + { + m.setZero(); + const Index size = numext::mini(m.rows(), m.cols()); + for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1); + return m; + } +}; + +} // end namespace internal + +/** Writes the identity expression (not necessarily square) into *this. + * + * Example: \include MatrixBase_setIdentity.cpp + * Output: \verbinclude MatrixBase_setIdentity.out + * + * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase::setIdentity() +{ + return internal::setIdentity_impl::run(derived()); +} + +/** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this. + * + * \param rows the new number of rows + * \param cols the new number of columns + * + * Example: \include Matrix_setIdentity_int_int.cpp + * Output: \verbinclude Matrix_setIdentity_int_int.out + * + * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase::setIdentity(Index rows, Index cols) +{ + derived().resize(rows, cols); + return setIdentity(); +} + +/** \returns an expression of the i-th unit (basis) vector. + * + * \only_for_vectors + * + * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::Unit(Index newSize, Index i) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i); +} + +/** \returns an expression of the i-th unit (basis) vector. + * + * \only_for_vectors + * + * This variant is for fixed-size vector only. + * + * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::Unit(Index i) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + return BasisReturnType(SquareMatrixType::Identity(),i); +} + +/** \returns an expression of the X axis unit vector (1{,0}^*) + * + * \only_for_vectors + * + * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::UnitX() +{ return Derived::Unit(0); } + +/** \returns an expression of the Y axis unit vector (0,1{,0}^*) + * + * \only_for_vectors + * + * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::UnitY() +{ return Derived::Unit(1); } + +/** \returns an expression of the Z axis unit vector (0,0,1{,0}^*) + * + * \only_for_vectors + * + * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::UnitZ() +{ return Derived::Unit(2); } + +/** \returns an expression of the W axis unit vector (0,0,0,1) + * + * \only_for_vectors + * + * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::BasisReturnType MatrixBase::UnitW() +{ return Derived::Unit(3); } + +/** \brief Set the coefficients of \c *this to the i-th unit (basis) vector + * + * \param i index of the unique coefficient to be set to 1 + * + * \only_for_vectors + * + * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index) + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase::setUnit(Index i) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived); + eigen_assert(i +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase::setUnit(Index newSize, Index i) +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived); + eigen_assert(i +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2016 Eugene Brevdo +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CWISE_TERNARY_OP_H +#define EIGEN_CWISE_TERNARY_OP_H + +namespace Eigen { + +namespace internal { +template +struct traits > { + // we must not inherit from traits since it has + // the potential to cause problems with MSVC + typedef typename remove_all::type Ancestor; + typedef typename traits::XprKind XprKind; + enum { + RowsAtCompileTime = traits::RowsAtCompileTime, + ColsAtCompileTime = traits::ColsAtCompileTime, + MaxRowsAtCompileTime = traits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = traits::MaxColsAtCompileTime + }; + + // even though we require Arg1, Arg2, and Arg3 to have the same scalar type + // (see CwiseTernaryOp constructor), + // we still want to handle the case when the result type is different. + typedef typename result_of::type Scalar; + + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::StorageIndex StorageIndex; + + typedef typename Arg1::Nested Arg1Nested; + typedef typename Arg2::Nested Arg2Nested; + typedef typename Arg3::Nested Arg3Nested; + typedef typename remove_reference::type _Arg1Nested; + typedef typename remove_reference::type _Arg2Nested; + typedef typename remove_reference::type _Arg3Nested; + enum { Flags = _Arg1Nested::Flags & RowMajorBit }; +}; +} // end namespace internal + +template +class CwiseTernaryOpImpl; + +/** \class CwiseTernaryOp + * \ingroup Core_Module + * + * \brief Generic expression where a coefficient-wise ternary operator is + * applied to two expressions + * + * \tparam TernaryOp template functor implementing the operator + * \tparam Arg1Type the type of the first argument + * \tparam Arg2Type the type of the second argument + * \tparam Arg3Type the type of the third argument + * + * This class represents an expression where a coefficient-wise ternary + * operator is applied to three expressions. + * It is the return type of ternary operators, by which we mean only those + * ternary operators where + * all three arguments are Eigen expressions. + * For example, the return type of betainc(matrix1, matrix2, matrix3) is a + * CwiseTernaryOp. + * + * Most of the time, this is the only way that it is used, so you typically + * don't have to name + * CwiseTernaryOp types explicitly. + * + * \sa MatrixBase::ternaryExpr(const MatrixBase &, const + * MatrixBase &, const CustomTernaryOp &) const, class CwiseBinaryOp, + * class CwiseUnaryOp, class CwiseNullaryOp + */ +template +class CwiseTernaryOp : public CwiseTernaryOpImpl< + TernaryOp, Arg1Type, Arg2Type, Arg3Type, + typename internal::traits::StorageKind>, + internal::no_assignment_operator +{ + public: + typedef typename internal::remove_all::type Arg1; + typedef typename internal::remove_all::type Arg2; + typedef typename internal::remove_all::type Arg3; + + typedef typename CwiseTernaryOpImpl< + TernaryOp, Arg1Type, Arg2Type, Arg3Type, + typename internal::traits::StorageKind>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseTernaryOp) + + typedef typename internal::ref_selector::type Arg1Nested; + typedef typename internal::ref_selector::type Arg2Nested; + typedef typename internal::ref_selector::type Arg3Nested; + typedef typename internal::remove_reference::type _Arg1Nested; + typedef typename internal::remove_reference::type _Arg2Nested; + typedef typename internal::remove_reference::type _Arg3Nested; + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CwiseTernaryOp(const Arg1& a1, const Arg2& a2, + const Arg3& a3, + const TernaryOp& func = TernaryOp()) + : m_arg1(a1), m_arg2(a2), m_arg3(a3), m_functor(func) { + // require the sizes to match + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg2) + EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Arg1, Arg3) + + // The index types should match + EIGEN_STATIC_ASSERT((internal::is_same< + typename internal::traits::StorageKind, + typename internal::traits::StorageKind>::value), + STORAGE_KIND_MUST_MATCH) + EIGEN_STATIC_ASSERT((internal::is_same< + typename internal::traits::StorageKind, + typename internal::traits::StorageKind>::value), + STORAGE_KIND_MUST_MATCH) + + eigen_assert(a1.rows() == a2.rows() && a1.cols() == a2.cols() && + a1.rows() == a3.rows() && a1.cols() == a3.cols()); + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Index rows() const { + // return the fixed size type if available to enable compile time + // optimizations + if (internal::traits::type>:: + RowsAtCompileTime == Dynamic && + internal::traits::type>:: + RowsAtCompileTime == Dynamic) + return m_arg3.rows(); + else if (internal::traits::type>:: + RowsAtCompileTime == Dynamic && + internal::traits::type>:: + RowsAtCompileTime == Dynamic) + return m_arg2.rows(); + else + return m_arg1.rows(); + } + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Index cols() const { + // return the fixed size type if available to enable compile time + // optimizations + if (internal::traits::type>:: + ColsAtCompileTime == Dynamic && + internal::traits::type>:: + ColsAtCompileTime == Dynamic) + return m_arg3.cols(); + else if (internal::traits::type>:: + ColsAtCompileTime == Dynamic && + internal::traits::type>:: + ColsAtCompileTime == Dynamic) + return m_arg2.cols(); + else + return m_arg1.cols(); + } + + /** \returns the first argument nested expression */ + EIGEN_DEVICE_FUNC + const _Arg1Nested& arg1() const { return m_arg1; } + /** \returns the first argument nested expression */ + EIGEN_DEVICE_FUNC + const _Arg2Nested& arg2() const { return m_arg2; } + /** \returns the third argument nested expression */ + EIGEN_DEVICE_FUNC + const _Arg3Nested& arg3() const { return m_arg3; } + /** \returns the functor representing the ternary operation */ + EIGEN_DEVICE_FUNC + const TernaryOp& functor() const { return m_functor; } + + protected: + Arg1Nested m_arg1; + Arg2Nested m_arg2; + Arg3Nested m_arg3; + const TernaryOp m_functor; +}; + +// Generic API dispatcher +template +class CwiseTernaryOpImpl + : public internal::generic_xpr_base< + CwiseTernaryOp >::type { + public: + typedef typename internal::generic_xpr_base< + CwiseTernaryOp >::type Base; +}; + +} // end namespace Eigen + +#endif // EIGEN_CWISE_TERNARY_OP_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryOp.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryOp.h new file mode 100644 index 0000000000000000000000000000000000000000..e68c4f7480824e51d0ab360a393b520af6665199 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryOp.h @@ -0,0 +1,103 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2014 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CWISE_UNARY_OP_H +#define EIGEN_CWISE_UNARY_OP_H + +namespace Eigen { + +namespace internal { +template +struct traits > + : traits +{ + typedef typename result_of< + UnaryOp(const typename XprType::Scalar&) + >::type Scalar; + typedef typename XprType::Nested XprTypeNested; + typedef typename remove_reference::type _XprTypeNested; + enum { + Flags = _XprTypeNested::Flags & RowMajorBit + }; +}; +} + +template +class CwiseUnaryOpImpl; + +/** \class CwiseUnaryOp + * \ingroup Core_Module + * + * \brief Generic expression where a coefficient-wise unary operator is applied to an expression + * + * \tparam UnaryOp template functor implementing the operator + * \tparam XprType the type of the expression to which we are applying the unary operator + * + * This class represents an expression where a unary operator is applied to an expression. + * It is the return type of all operations taking exactly 1 input expression, regardless of the + * presence of other inputs such as scalars. For example, the operator* in the expression 3*matrix + * is considered unary, because only the right-hand side is an expression, and its + * return type is a specialization of CwiseUnaryOp. + * + * Most of the time, this is the only way that it is used, so you typically don't have to name + * CwiseUnaryOp types explicitly. + * + * \sa MatrixBase::unaryExpr(const CustomUnaryOp &) const, class CwiseBinaryOp, class CwiseNullaryOp + */ +template +class CwiseUnaryOp : public CwiseUnaryOpImpl::StorageKind>, internal::no_assignment_operator +{ + public: + + typedef typename CwiseUnaryOpImpl::StorageKind>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryOp) + typedef typename internal::ref_selector::type XprTypeNested; + typedef typename internal::remove_all::type NestedExpression; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp()) + : m_xpr(xpr), m_functor(func) {} + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); } + + /** \returns the functor representing the unary operation */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const UnaryOp& functor() const { return m_functor; } + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const typename internal::remove_all::type& + nestedExpression() const { return m_xpr; } + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + typename internal::remove_all::type& + nestedExpression() { return m_xpr; } + + protected: + XprTypeNested m_xpr; + const UnaryOp m_functor; +}; + +// Generic API dispatcher +template +class CwiseUnaryOpImpl + : public internal::generic_xpr_base >::type +{ +public: + typedef typename internal::generic_xpr_base >::type Base; +}; + +} // end namespace Eigen + +#endif // EIGEN_CWISE_UNARY_OP_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryView.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryView.h new file mode 100644 index 0000000000000000000000000000000000000000..a06d7621ec143a3c3354bf4079ae7bd25c6f03b4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/CwiseUnaryView.h @@ -0,0 +1,132 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_CWISE_UNARY_VIEW_H +#define EIGEN_CWISE_UNARY_VIEW_H + +namespace Eigen { + +namespace internal { +template +struct traits > + : traits +{ + typedef typename result_of< + ViewOp(const typename traits::Scalar&) + >::type Scalar; + typedef typename MatrixType::Nested MatrixTypeNested; + typedef typename remove_all::type _MatrixTypeNested; + enum { + FlagsLvalueBit = is_lvalue::value ? LvalueBit : 0, + Flags = traits<_MatrixTypeNested>::Flags & (RowMajorBit | FlagsLvalueBit | DirectAccessBit), // FIXME DirectAccessBit should not be handled by expressions + MatrixTypeInnerStride = inner_stride_at_compile_time::ret, + // need to cast the sizeof's from size_t to int explicitly, otherwise: + // "error: no integral type can represent all of the enumerator values + InnerStrideAtCompileTime = MatrixTypeInnerStride == Dynamic + ? int(Dynamic) + : int(MatrixTypeInnerStride) * int(sizeof(typename traits::Scalar) / sizeof(Scalar)), + OuterStrideAtCompileTime = outer_stride_at_compile_time::ret == Dynamic + ? int(Dynamic) + : outer_stride_at_compile_time::ret * int(sizeof(typename traits::Scalar) / sizeof(Scalar)) + }; +}; +} + +template +class CwiseUnaryViewImpl; + +/** \class CwiseUnaryView + * \ingroup Core_Module + * + * \brief Generic lvalue expression of a coefficient-wise unary operator of a matrix or a vector + * + * \tparam ViewOp template functor implementing the view + * \tparam MatrixType the type of the matrix we are applying the unary operator + * + * This class represents a lvalue expression of a generic unary view operator of a matrix or a vector. + * It is the return type of real() and imag(), and most of the time this is the only way it is used. + * + * \sa MatrixBase::unaryViewExpr(const CustomUnaryOp &) const, class CwiseUnaryOp + */ +template +class CwiseUnaryView : public CwiseUnaryViewImpl::StorageKind> +{ + public: + + typedef typename CwiseUnaryViewImpl::StorageKind>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(CwiseUnaryView) + typedef typename internal::ref_selector::non_const_type MatrixTypeNested; + typedef typename internal::remove_all::type NestedExpression; + + explicit EIGEN_DEVICE_FUNC inline CwiseUnaryView(MatrixType& mat, const ViewOp& func = ViewOp()) + : m_matrix(mat), m_functor(func) {} + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView) + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); } + + /** \returns the functor representing unary operation */ + EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; } + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC const typename internal::remove_all::type& + nestedExpression() const { return m_matrix; } + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC typename internal::remove_reference::type& + nestedExpression() { return m_matrix; } + + protected: + MatrixTypeNested m_matrix; + ViewOp m_functor; +}; + +// Generic API dispatcher +template +class CwiseUnaryViewImpl + : public internal::generic_xpr_base >::type +{ +public: + typedef typename internal::generic_xpr_base >::type Base; +}; + +template +class CwiseUnaryViewImpl + : public internal::dense_xpr_base< CwiseUnaryView >::type +{ + public: + + typedef CwiseUnaryView Derived; + typedef typename internal::dense_xpr_base< CwiseUnaryView >::type Base; + + EIGEN_DENSE_PUBLIC_INTERFACE(Derived) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryViewImpl) + + EIGEN_DEVICE_FUNC inline Scalar* data() { return &(this->coeffRef(0)); } + EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeff(0)); } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const + { + return derived().nestedExpression().innerStride() * sizeof(typename internal::traits::Scalar) / sizeof(Scalar); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const + { + return derived().nestedExpression().outerStride() * sizeof(typename internal::traits::Scalar) / sizeof(Scalar); + } + protected: + EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(CwiseUnaryViewImpl) +}; + +} // end namespace Eigen + +#endif // EIGEN_CWISE_UNARY_VIEW_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseBase.h new file mode 100644 index 0000000000000000000000000000000000000000..9b16db68d48d2bfbf7e5c076ef2ba1504074f3f3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseBase.h @@ -0,0 +1,701 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007-2010 Benoit Jacob +// Copyright (C) 2008-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DENSEBASE_H +#define EIGEN_DENSEBASE_H + +namespace Eigen { + +namespace internal { + +// The index type defined by EIGEN_DEFAULT_DENSE_INDEX_TYPE must be a signed type. +// This dummy function simply aims at checking that at compile time. +static inline void check_DenseIndex_is_signed() { + EIGEN_STATIC_ASSERT(NumTraits::IsSigned,THE_INDEX_TYPE_MUST_BE_A_SIGNED_TYPE) +} + +} // end namespace internal + +/** \class DenseBase + * \ingroup Core_Module + * + * \brief Base class for all dense matrices, vectors, and arrays + * + * This class is the base that is inherited by all dense objects (matrix, vector, arrays, + * and related expression types). The common Eigen API for dense objects is contained in this class. + * + * \tparam Derived is the derived type, e.g., a matrix type or an expression. + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_DENSEBASE_PLUGIN. + * + * \sa \blank \ref TopicClassHierarchy + */ +template class DenseBase +#ifndef EIGEN_PARSED_BY_DOXYGEN + : public DenseCoeffsBase::value> +#else + : public DenseCoeffsBase +#endif // not EIGEN_PARSED_BY_DOXYGEN +{ + public: + + /** Inner iterator type to iterate over the coefficients of a row or column. + * \sa class InnerIterator + */ + typedef Eigen::InnerIterator InnerIterator; + + typedef typename internal::traits::StorageKind StorageKind; + + /** + * \brief The type used to store indices + * \details This typedef is relevant for types that store multiple indices such as + * PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index + * \sa \blank \ref TopicPreprocessorDirectives, Eigen::Index, SparseMatrixBase. + */ + typedef typename internal::traits::StorageIndex StorageIndex; + + /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex, etc. */ + typedef typename internal::traits::Scalar Scalar; + + /** The numeric type of the expression' coefficients, e.g. float, double, int or std::complex, etc. + * + * It is an alias for the Scalar type */ + typedef Scalar value_type; + + typedef typename NumTraits::Real RealScalar; + typedef DenseCoeffsBase::value> Base; + + using Base::derived; + using Base::const_cast_derived; + using Base::rows; + using Base::cols; + using Base::size; + using Base::rowIndexByOuterInner; + using Base::colIndexByOuterInner; + using Base::coeff; + using Base::coeffByOuterInner; + using Base::operator(); + using Base::operator[]; + using Base::x; + using Base::y; + using Base::z; + using Base::w; + using Base::stride; + using Base::innerStride; + using Base::outerStride; + using Base::rowStride; + using Base::colStride; + typedef typename Base::CoeffReturnType CoeffReturnType; + + enum { + + RowsAtCompileTime = internal::traits::RowsAtCompileTime, + /**< The number of rows at compile-time. This is just a copy of the value provided + * by the \a Derived type. If a value is not known at compile-time, + * it is set to the \a Dynamic constant. + * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */ + + ColsAtCompileTime = internal::traits::ColsAtCompileTime, + /**< The number of columns at compile-time. This is just a copy of the value provided + * by the \a Derived type. If a value is not known at compile-time, + * it is set to the \a Dynamic constant. + * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */ + + + SizeAtCompileTime = (internal::size_at_compile_time::RowsAtCompileTime, + internal::traits::ColsAtCompileTime>::ret), + /**< This is equal to the number of coefficients, i.e. the number of + * rows times the number of columns, or to \a Dynamic if this is not + * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */ + + MaxRowsAtCompileTime = internal::traits::MaxRowsAtCompileTime, + /**< This value is equal to the maximum possible number of rows that this expression + * might have. If this expression might have an arbitrarily high number of rows, + * this value is set to \a Dynamic. + * + * This value is useful to know when evaluating an expression, in order to determine + * whether it is possible to avoid doing a dynamic memory allocation. + * + * \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime + */ + + MaxColsAtCompileTime = internal::traits::MaxColsAtCompileTime, + /**< This value is equal to the maximum possible number of columns that this expression + * might have. If this expression might have an arbitrarily high number of columns, + * this value is set to \a Dynamic. + * + * This value is useful to know when evaluating an expression, in order to determine + * whether it is possible to avoid doing a dynamic memory allocation. + * + * \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime + */ + + MaxSizeAtCompileTime = (internal::size_at_compile_time::MaxRowsAtCompileTime, + internal::traits::MaxColsAtCompileTime>::ret), + /**< This value is equal to the maximum possible number of coefficients that this expression + * might have. If this expression might have an arbitrarily high number of coefficients, + * this value is set to \a Dynamic. + * + * This value is useful to know when evaluating an expression, in order to determine + * whether it is possible to avoid doing a dynamic memory allocation. + * + * \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime + */ + + IsVectorAtCompileTime = internal::traits::RowsAtCompileTime == 1 + || internal::traits::ColsAtCompileTime == 1, + /**< This is set to true if either the number of rows or the number of + * columns is known at compile-time to be equal to 1. Indeed, in that case, + * we are dealing with a column-vector (if there is only one column) or with + * a row-vector (if there is only one row). */ + + NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2, + /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors, + * and 2 for matrices. + */ + + Flags = internal::traits::Flags, + /**< This stores expression \ref flags flags which may or may not be inherited by new expressions + * constructed from this one. See the \ref flags "list of flags". + */ + + IsRowMajor = int(Flags) & RowMajorBit, /**< True if this expression has row-major storage order. */ + + InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime) + : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime), + + InnerStrideAtCompileTime = internal::inner_stride_at_compile_time::ret, + OuterStrideAtCompileTime = internal::outer_stride_at_compile_time::ret + }; + + typedef typename internal::find_best_packet::type PacketScalar; + + enum { IsPlainObjectBase = 0 }; + + /** The plain matrix type corresponding to this expression. + * \sa PlainObject */ + typedef Matrix::Scalar, + internal::traits::RowsAtCompileTime, + internal::traits::ColsAtCompileTime, + AutoAlign | (internal::traits::Flags&RowMajorBit ? RowMajor : ColMajor), + internal::traits::MaxRowsAtCompileTime, + internal::traits::MaxColsAtCompileTime + > PlainMatrix; + + /** The plain array type corresponding to this expression. + * \sa PlainObject */ + typedef Array::Scalar, + internal::traits::RowsAtCompileTime, + internal::traits::ColsAtCompileTime, + AutoAlign | (internal::traits::Flags&RowMajorBit ? RowMajor : ColMajor), + internal::traits::MaxRowsAtCompileTime, + internal::traits::MaxColsAtCompileTime + > PlainArray; + + /** \brief The plain matrix or array type corresponding to this expression. + * + * This is not necessarily exactly the return type of eval(). In the case of plain matrices, + * the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed + * that the return type of eval() is either PlainObject or const PlainObject&. + */ + typedef typename internal::conditional::XprKind,MatrixXpr >::value, + PlainMatrix, PlainArray>::type PlainObject; + + /** \returns the number of nonzero coefficients which is in practice the number + * of stored coefficients. */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index nonZeros() const { return size(); } + + /** \returns the outer size. + * + * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension + * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a + * column-major matrix, and the number of rows for a row-major matrix. */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + Index outerSize() const + { + return IsVectorAtCompileTime ? 1 + : int(IsRowMajor) ? this->rows() : this->cols(); + } + + /** \returns the inner size. + * + * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension + * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a + * column-major matrix, and the number of columns for a row-major matrix. */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + Index innerSize() const + { + return IsVectorAtCompileTime ? this->size() + : int(IsRowMajor) ? this->cols() : this->rows(); + } + + /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are + * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does + * nothing else. + */ + EIGEN_DEVICE_FUNC + void resize(Index newSize) + { + EIGEN_ONLY_USED_FOR_DEBUG(newSize); + eigen_assert(newSize == this->size() + && "DenseBase::resize() does not actually allow to resize."); + } + /** Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are + * Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does + * nothing else. + */ + EIGEN_DEVICE_FUNC + void resize(Index rows, Index cols) + { + EIGEN_ONLY_USED_FOR_DEBUG(rows); + EIGEN_ONLY_USED_FOR_DEBUG(cols); + eigen_assert(rows == this->rows() && cols == this->cols() + && "DenseBase::resize() does not actually allow to resize."); + } + +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** \internal Represents a matrix with all coefficients equal to one another*/ + typedef CwiseNullaryOp,PlainObject> ConstantReturnType; + /** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */ + EIGEN_DEPRECATED typedef CwiseNullaryOp,PlainObject> SequentialLinSpacedReturnType; + /** \internal Represents a vector with linearly spaced coefficients that allows random access. */ + typedef CwiseNullaryOp,PlainObject> RandomAccessLinSpacedReturnType; + /** \internal the return type of MatrixBase::eigenvalues() */ + typedef Matrix::Scalar>::Real, internal::traits::ColsAtCompileTime, 1> EigenvaluesReturnType; + +#endif // not EIGEN_PARSED_BY_DOXYGEN + + /** Copies \a other into *this. \returns a reference to *this. */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const DenseBase& other); + + /** Special case of the template operator=, in order to prevent the compiler + * from generating a default operator= (issue hit with g++ 4.1) + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const DenseBase& other); + + template + EIGEN_DEVICE_FUNC + Derived& operator=(const EigenBase &other); + + template + EIGEN_DEVICE_FUNC + Derived& operator+=(const EigenBase &other); + + template + EIGEN_DEVICE_FUNC + Derived& operator-=(const EigenBase &other); + + template + EIGEN_DEVICE_FUNC + Derived& operator=(const ReturnByValue& func); + + /** \internal + * Copies \a other into *this without evaluating other. \returns a reference to *this. */ + template + /** \deprecated */ + EIGEN_DEPRECATED EIGEN_DEVICE_FUNC + Derived& lazyAssign(const DenseBase& other); + + EIGEN_DEVICE_FUNC + CommaInitializer operator<< (const Scalar& s); + + template + /** \deprecated it now returns \c *this */ + EIGEN_DEPRECATED + const Derived& flagged() const + { return derived(); } + + template + EIGEN_DEVICE_FUNC + CommaInitializer operator<< (const DenseBase& other); + + typedef Transpose TransposeReturnType; + EIGEN_DEVICE_FUNC + TransposeReturnType transpose(); + typedef typename internal::add_const >::type ConstTransposeReturnType; + EIGEN_DEVICE_FUNC + ConstTransposeReturnType transpose() const; + EIGEN_DEVICE_FUNC + void transposeInPlace(); + + EIGEN_DEVICE_FUNC static const ConstantReturnType + Constant(Index rows, Index cols, const Scalar& value); + EIGEN_DEVICE_FUNC static const ConstantReturnType + Constant(Index size, const Scalar& value); + EIGEN_DEVICE_FUNC static const ConstantReturnType + Constant(const Scalar& value); + + EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType + LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high); + EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType + LinSpaced(Sequential_t, const Scalar& low, const Scalar& high); + + EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType + LinSpaced(Index size, const Scalar& low, const Scalar& high); + EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType + LinSpaced(const Scalar& low, const Scalar& high); + + template EIGEN_DEVICE_FUNC + static const CwiseNullaryOp + NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func); + template EIGEN_DEVICE_FUNC + static const CwiseNullaryOp + NullaryExpr(Index size, const CustomNullaryOp& func); + template EIGEN_DEVICE_FUNC + static const CwiseNullaryOp + NullaryExpr(const CustomNullaryOp& func); + + EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols); + EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size); + EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(); + EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols); + EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size); + EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(); + + EIGEN_DEVICE_FUNC void fill(const Scalar& value); + EIGEN_DEVICE_FUNC Derived& setConstant(const Scalar& value); + EIGEN_DEVICE_FUNC Derived& setLinSpaced(Index size, const Scalar& low, const Scalar& high); + EIGEN_DEVICE_FUNC Derived& setLinSpaced(const Scalar& low, const Scalar& high); + EIGEN_DEVICE_FUNC Derived& setZero(); + EIGEN_DEVICE_FUNC Derived& setOnes(); + EIGEN_DEVICE_FUNC Derived& setRandom(); + + template EIGEN_DEVICE_FUNC + bool isApprox(const DenseBase& other, + const RealScalar& prec = NumTraits::dummy_precision()) const; + EIGEN_DEVICE_FUNC + bool isMuchSmallerThan(const RealScalar& other, + const RealScalar& prec = NumTraits::dummy_precision()) const; + template EIGEN_DEVICE_FUNC + bool isMuchSmallerThan(const DenseBase& other, + const RealScalar& prec = NumTraits::dummy_precision()) const; + + EIGEN_DEVICE_FUNC bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits::dummy_precision()) const; + EIGEN_DEVICE_FUNC bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits::dummy_precision()) const; + EIGEN_DEVICE_FUNC bool isZero(const RealScalar& prec = NumTraits::dummy_precision()) const; + EIGEN_DEVICE_FUNC bool isOnes(const RealScalar& prec = NumTraits::dummy_precision()) const; + + inline bool hasNaN() const; + inline bool allFinite() const; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator*=(const Scalar& other); + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator/=(const Scalar& other); + + typedef typename internal::add_const_on_value_type::type>::type EvalReturnType; + /** \returns the matrix or vector obtained by evaluating this expression. + * + * Notice that in the case of a plain matrix or vector (not an expression) this function just returns + * a const reference, in order to avoid a useless copy. + * + * \warning Be careful with eval() and the auto C++ keyword, as detailed in this \link TopicPitfalls_auto_keyword page \endlink. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE EvalReturnType eval() const + { + // Even though MSVC does not honor strong inlining when the return type + // is a dynamic matrix, we desperately need strong inlining for fixed + // size types on MSVC. + return typename internal::eval::type(derived()); + } + + /** swaps *this with the expression \a other. + * + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void swap(const DenseBase& other) + { + EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY); + eigen_assert(rows()==other.rows() && cols()==other.cols()); + call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op()); + } + + /** swaps *this with the matrix or array \a other. + * + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void swap(PlainObjectBase& other) + { + eigen_assert(rows()==other.rows() && cols()==other.cols()); + call_assignment(derived(), other.derived(), internal::swap_assign_op()); + } + + EIGEN_DEVICE_FUNC inline const NestByValue nestByValue() const; + EIGEN_DEVICE_FUNC inline const ForceAlignedAccess forceAlignedAccess() const; + EIGEN_DEVICE_FUNC inline ForceAlignedAccess forceAlignedAccess(); + template EIGEN_DEVICE_FUNC + inline const typename internal::conditional,Derived&>::type forceAlignedAccessIf() const; + template EIGEN_DEVICE_FUNC + inline typename internal::conditional,Derived&>::type forceAlignedAccessIf(); + + EIGEN_DEVICE_FUNC Scalar sum() const; + EIGEN_DEVICE_FUNC Scalar mean() const; + EIGEN_DEVICE_FUNC Scalar trace() const; + + EIGEN_DEVICE_FUNC Scalar prod() const; + + template + EIGEN_DEVICE_FUNC typename internal::traits::Scalar minCoeff() const; + template + EIGEN_DEVICE_FUNC typename internal::traits::Scalar maxCoeff() const; + + + // By default, the fastest version with undefined NaN propagation semantics is + // used. + // TODO(rmlarsen): Replace with default template argument when we move to + // c++11 or beyond. + EIGEN_DEVICE_FUNC inline typename internal::traits::Scalar minCoeff() const { + return minCoeff(); + } + EIGEN_DEVICE_FUNC inline typename internal::traits::Scalar maxCoeff() const { + return maxCoeff(); + } + + template + EIGEN_DEVICE_FUNC + typename internal::traits::Scalar minCoeff(IndexType* row, IndexType* col) const; + template + EIGEN_DEVICE_FUNC + typename internal::traits::Scalar maxCoeff(IndexType* row, IndexType* col) const; + template + EIGEN_DEVICE_FUNC + typename internal::traits::Scalar minCoeff(IndexType* index) const; + template + EIGEN_DEVICE_FUNC + typename internal::traits::Scalar maxCoeff(IndexType* index) const; + + // TODO(rmlarsen): Replace these methods with a default template argument. + template + EIGEN_DEVICE_FUNC inline + typename internal::traits::Scalar minCoeff(IndexType* row, IndexType* col) const { + return minCoeff(row, col); + } + template + EIGEN_DEVICE_FUNC inline + typename internal::traits::Scalar maxCoeff(IndexType* row, IndexType* col) const { + return maxCoeff(row, col); + } + template + EIGEN_DEVICE_FUNC inline + typename internal::traits::Scalar minCoeff(IndexType* index) const { + return minCoeff(index); + } + template + EIGEN_DEVICE_FUNC inline + typename internal::traits::Scalar maxCoeff(IndexType* index) const { + return maxCoeff(index); + } + + template + EIGEN_DEVICE_FUNC + Scalar redux(const BinaryOp& func) const; + + template + EIGEN_DEVICE_FUNC + void visit(Visitor& func) const; + + /** \returns a WithFormat proxy object allowing to print a matrix the with given + * format \a fmt. + * + * See class IOFormat for some examples. + * + * \sa class IOFormat, class WithFormat + */ + inline const WithFormat format(const IOFormat& fmt) const + { + return WithFormat(derived(), fmt); + } + + /** \returns the unique coefficient of a 1x1 expression */ + EIGEN_DEVICE_FUNC + CoeffReturnType value() const + { + EIGEN_STATIC_ASSERT_SIZE_1x1(Derived) + eigen_assert(this->rows() == 1 && this->cols() == 1); + return derived().coeff(0,0); + } + + EIGEN_DEVICE_FUNC bool all() const; + EIGEN_DEVICE_FUNC bool any() const; + EIGEN_DEVICE_FUNC Index count() const; + + typedef VectorwiseOp RowwiseReturnType; + typedef const VectorwiseOp ConstRowwiseReturnType; + typedef VectorwiseOp ColwiseReturnType; + typedef const VectorwiseOp ConstColwiseReturnType; + + /** \returns a VectorwiseOp wrapper of *this for broadcasting and partial reductions + * + * Example: \include MatrixBase_rowwise.cpp + * Output: \verbinclude MatrixBase_rowwise.out + * + * \sa colwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting + */ + //Code moved here due to a CUDA compiler bug + EIGEN_DEVICE_FUNC inline ConstRowwiseReturnType rowwise() const { + return ConstRowwiseReturnType(derived()); + } + EIGEN_DEVICE_FUNC RowwiseReturnType rowwise(); + + /** \returns a VectorwiseOp wrapper of *this broadcasting and partial reductions + * + * Example: \include MatrixBase_colwise.cpp + * Output: \verbinclude MatrixBase_colwise.out + * + * \sa rowwise(), class VectorwiseOp, \ref TutorialReductionsVisitorsBroadcasting + */ + EIGEN_DEVICE_FUNC inline ConstColwiseReturnType colwise() const { + return ConstColwiseReturnType(derived()); + } + EIGEN_DEVICE_FUNC ColwiseReturnType colwise(); + + typedef CwiseNullaryOp,PlainObject> RandomReturnType; + static const RandomReturnType Random(Index rows, Index cols); + static const RandomReturnType Random(Index size); + static const RandomReturnType Random(); + + template + inline EIGEN_DEVICE_FUNC const Select + select(const DenseBase& thenMatrix, + const DenseBase& elseMatrix) const; + + template + inline EIGEN_DEVICE_FUNC const Select + select(const DenseBase& thenMatrix, const typename ThenDerived::Scalar& elseScalar) const; + + template + inline EIGEN_DEVICE_FUNC const Select + select(const typename ElseDerived::Scalar& thenScalar, const DenseBase& elseMatrix) const; + + template RealScalar lpNorm() const; + + template + EIGEN_DEVICE_FUNC + const Replicate replicate() const; + /** + * \return an expression of the replication of \c *this + * + * Example: \include MatrixBase_replicate_int_int.cpp + * Output: \verbinclude MatrixBase_replicate_int_int.out + * + * \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate + */ + //Code moved here due to a CUDA compiler bug + EIGEN_DEVICE_FUNC + const Replicate replicate(Index rowFactor, Index colFactor) const + { + return Replicate(derived(), rowFactor, colFactor); + } + + typedef Reverse ReverseReturnType; + typedef const Reverse ConstReverseReturnType; + EIGEN_DEVICE_FUNC ReverseReturnType reverse(); + /** This is the const version of reverse(). */ + //Code moved here due to a CUDA compiler bug + EIGEN_DEVICE_FUNC ConstReverseReturnType reverse() const + { + return ConstReverseReturnType(derived()); + } + EIGEN_DEVICE_FUNC void reverseInPlace(); + + #ifdef EIGEN_PARSED_BY_DOXYGEN + /** STL-like RandomAccessIterator + * iterator type as returned by the begin() and end() methods. + */ + typedef random_access_iterator_type iterator; + /** This is the const version of iterator (aka read-only) */ + typedef random_access_iterator_type const_iterator; + #else + typedef typename internal::conditional< (Flags&DirectAccessBit)==DirectAccessBit, + internal::pointer_based_stl_iterator, + internal::generic_randaccess_stl_iterator + >::type iterator_type; + + typedef typename internal::conditional< (Flags&DirectAccessBit)==DirectAccessBit, + internal::pointer_based_stl_iterator, + internal::generic_randaccess_stl_iterator + >::type const_iterator_type; + + // Stl-style iterators are supported only for vectors. + + typedef typename internal::conditional< IsVectorAtCompileTime, + iterator_type, + void + >::type iterator; + + typedef typename internal::conditional< IsVectorAtCompileTime, + const_iterator_type, + void + >::type const_iterator; + #endif + + inline iterator begin(); + inline const_iterator begin() const; + inline const_iterator cbegin() const; + inline iterator end(); + inline const_iterator end() const; + inline const_iterator cend() const; + +#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase +#define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL +#define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND) +#define EIGEN_DOC_UNARY_ADDONS(X,Y) +# include "../plugins/CommonCwiseUnaryOps.h" +# include "../plugins/BlockMethods.h" +# include "../plugins/IndexedViewMethods.h" +# include "../plugins/ReshapedMethods.h" +# ifdef EIGEN_DENSEBASE_PLUGIN +# include EIGEN_DENSEBASE_PLUGIN +# endif +#undef EIGEN_CURRENT_STORAGE_BASE_CLASS +#undef EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL +#undef EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF +#undef EIGEN_DOC_UNARY_ADDONS + + // disable the use of evalTo for dense objects with a nice compilation error + template + EIGEN_DEVICE_FUNC + inline void evalTo(Dest& ) const + { + EIGEN_STATIC_ASSERT((internal::is_same::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS); + } + + protected: + EIGEN_DEFAULT_COPY_CONSTRUCTOR(DenseBase) + /** Default constructor. Do nothing. */ + EIGEN_DEVICE_FUNC DenseBase() + { + /* Just checks for self-consistency of the flags. + * Only do it when debugging Eigen, as this borders on paranoia and could slow compilation down + */ +#ifdef EIGEN_INTERNAL_DEBUGGING + EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, int(IsRowMajor)) + && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, int(!IsRowMajor))), + INVALID_STORAGE_ORDER_FOR_THIS_VECTOR_EXPRESSION) +#endif + } + + private: + EIGEN_DEVICE_FUNC explicit DenseBase(int); + EIGEN_DEVICE_FUNC DenseBase(int,int); + template EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase&); +}; + +} // end namespace Eigen + +#endif // EIGEN_DENSEBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseCoeffsBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseCoeffsBase.h new file mode 100644 index 0000000000000000000000000000000000000000..37fcdb59119ff83758ce004d7526b69a73dbb275 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseCoeffsBase.h @@ -0,0 +1,685 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DENSECOEFFSBASE_H +#define EIGEN_DENSECOEFFSBASE_H + +namespace Eigen { + +namespace internal { +template struct add_const_on_value_type_if_arithmetic +{ + typedef typename conditional::value, T, typename add_const_on_value_type::type>::type type; +}; +} + +/** \brief Base class providing read-only coefficient access to matrices and arrays. + * \ingroup Core_Module + * \tparam Derived Type of the derived class + * + * \note #ReadOnlyAccessors Constant indicating read-only access + * + * This class defines the \c operator() \c const function and friends, which can be used to read specific + * entries of a matrix or array. + * + * \sa DenseCoeffsBase, DenseCoeffsBase, + * \ref TopicClassHierarchy + */ +template +class DenseCoeffsBase : public EigenBase +{ + public: + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::packet_traits::type PacketScalar; + + // Explanation for this CoeffReturnType typedef. + // - This is the return type of the coeff() method. + // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references + // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value). + // - The is_artihmetic check is required since "const int", "const double", etc. will cause warnings on some systems + // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is + // not possible, since the underlying expressions might not offer a valid address the reference could be referring to. + typedef typename internal::conditional::Flags&LvalueBit), + const Scalar&, + typename internal::conditional::value, Scalar, const Scalar>::type + >::type CoeffReturnType; + + typedef typename internal::add_const_on_value_type_if_arithmetic< + typename internal::packet_traits::type + >::type PacketReturnType; + + typedef EigenBase Base; + using Base::rows; + using Base::cols; + using Base::size; + using Base::derived; + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Index rowIndexByOuterInner(Index outer, Index inner) const + { + return int(Derived::RowsAtCompileTime) == 1 ? 0 + : int(Derived::ColsAtCompileTime) == 1 ? inner + : int(Derived::Flags)&RowMajorBit ? outer + : inner; + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Index colIndexByOuterInner(Index outer, Index inner) const + { + return int(Derived::ColsAtCompileTime) == 1 ? 0 + : int(Derived::RowsAtCompileTime) == 1 ? inner + : int(Derived::Flags)&RowMajorBit ? inner + : outer; + } + + /** Short version: don't use this function, use + * \link operator()(Index,Index) const \endlink instead. + * + * Long version: this function is similar to + * \link operator()(Index,Index) const \endlink, but without the assertion. + * Use this for limiting the performance cost of debugging code when doing + * repeated coefficient access. Only use this when it is guaranteed that the + * parameters \a row and \a col are in range. + * + * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this + * function equivalent to \link operator()(Index,Index) const \endlink. + * + * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const + { + eigen_internal_assert(row >= 0 && row < rows() + && col >= 0 && col < cols()); + return internal::evaluator(derived()).coeff(row,col); + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType coeffByOuterInner(Index outer, Index inner) const + { + return coeff(rowIndexByOuterInner(outer, inner), + colIndexByOuterInner(outer, inner)); + } + + /** \returns the coefficient at given the given row and column. + * + * \sa operator()(Index,Index), operator[](Index) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType operator()(Index row, Index col) const + { + eigen_assert(row >= 0 && row < rows() + && col >= 0 && col < cols()); + return coeff(row, col); + } + + /** Short version: don't use this function, use + * \link operator[](Index) const \endlink instead. + * + * Long version: this function is similar to + * \link operator[](Index) const \endlink, but without the assertion. + * Use this for limiting the performance cost of debugging code when doing + * repeated coefficient access. Only use this when it is guaranteed that the + * parameter \a index is in range. + * + * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this + * function equivalent to \link operator[](Index) const \endlink. + * + * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + coeff(Index index) const + { + EIGEN_STATIC_ASSERT(internal::evaluator::Flags & LinearAccessBit, + THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS) + eigen_internal_assert(index >= 0 && index < size()); + return internal::evaluator(derived()).coeff(index); + } + + + /** \returns the coefficient at given index. + * + * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit. + * + * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const, + * z() const, w() const + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + operator[](Index index) const + { + EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime, + THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD) + eigen_assert(index >= 0 && index < size()); + return coeff(index); + } + + /** \returns the coefficient at given index. + * + * This is synonymous to operator[](Index) const. + * + * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit. + * + * \sa operator[](Index), operator()(Index,Index) const, x() const, y() const, + * z() const, w() const + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + operator()(Index index) const + { + eigen_assert(index >= 0 && index < size()); + return coeff(index); + } + + /** equivalent to operator[](0). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + x() const { return (*this)[0]; } + + /** equivalent to operator[](1). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + y() const + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS); + return (*this)[1]; + } + + /** equivalent to operator[](2). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + z() const + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS); + return (*this)[2]; + } + + /** equivalent to operator[](3). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE CoeffReturnType + w() const + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS); + return (*this)[3]; + } + + /** \internal + * \returns the packet of coefficients starting at the given row and column. It is your responsibility + * to ensure that a packet really starts there. This method is only available on expressions having the + * PacketAccessBit. + * + * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select + * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets + * starting at an address which is a multiple of the packet size. + */ + + template + EIGEN_STRONG_INLINE PacketReturnType packet(Index row, Index col) const + { + typedef typename internal::packet_traits::type DefaultPacketType; + eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols()); + return internal::evaluator(derived()).template packet(row,col); + } + + + /** \internal */ + template + EIGEN_STRONG_INLINE PacketReturnType packetByOuterInner(Index outer, Index inner) const + { + return packet(rowIndexByOuterInner(outer, inner), + colIndexByOuterInner(outer, inner)); + } + + /** \internal + * \returns the packet of coefficients starting at the given index. It is your responsibility + * to ensure that a packet really starts there. This method is only available on expressions having the + * PacketAccessBit and the LinearAccessBit. + * + * The \a LoadMode parameter may have the value \a #Aligned or \a #Unaligned. Its effect is to select + * the appropriate vectorization instruction. Aligned access is faster, but is only possible for packets + * starting at an address which is a multiple of the packet size. + */ + + template + EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const + { + EIGEN_STATIC_ASSERT(internal::evaluator::Flags & LinearAccessBit, + THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS) + typedef typename internal::packet_traits::type DefaultPacketType; + eigen_internal_assert(index >= 0 && index < size()); + return internal::evaluator(derived()).template packet(index); + } + + protected: + // explanation: DenseBase is doing "using ..." on the methods from DenseCoeffsBase. + // But some methods are only available in the DirectAccess case. + // So we add dummy methods here with these names, so that "using... " doesn't fail. + // It's not private so that the child class DenseBase can access them, and it's not public + // either since it's an implementation detail, so has to be protected. + void coeffRef(); + void coeffRefByOuterInner(); + void writePacket(); + void writePacketByOuterInner(); + void copyCoeff(); + void copyCoeffByOuterInner(); + void copyPacket(); + void copyPacketByOuterInner(); + void stride(); + void innerStride(); + void outerStride(); + void rowStride(); + void colStride(); +}; + +/** \brief Base class providing read/write coefficient access to matrices and arrays. + * \ingroup Core_Module + * \tparam Derived Type of the derived class + * + * \note #WriteAccessors Constant indicating read/write access + * + * This class defines the non-const \c operator() function and friends, which can be used to write specific + * entries of a matrix or array. This class inherits DenseCoeffsBase which + * defines the const variant for reading specific entries. + * + * \sa DenseCoeffsBase, \ref TopicClassHierarchy + */ +template +class DenseCoeffsBase : public DenseCoeffsBase +{ + public: + + typedef DenseCoeffsBase Base; + + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::packet_traits::type PacketScalar; + typedef typename NumTraits::Real RealScalar; + + using Base::coeff; + using Base::rows; + using Base::cols; + using Base::size; + using Base::derived; + using Base::rowIndexByOuterInner; + using Base::colIndexByOuterInner; + using Base::operator[]; + using Base::operator(); + using Base::x; + using Base::y; + using Base::z; + using Base::w; + + /** Short version: don't use this function, use + * \link operator()(Index,Index) \endlink instead. + * + * Long version: this function is similar to + * \link operator()(Index,Index) \endlink, but without the assertion. + * Use this for limiting the performance cost of debugging code when doing + * repeated coefficient access. Only use this when it is guaranteed that the + * parameters \a row and \a col are in range. + * + * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this + * function equivalent to \link operator()(Index,Index) \endlink. + * + * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) + { + eigen_internal_assert(row >= 0 && row < rows() + && col >= 0 && col < cols()); + return internal::evaluator(derived()).coeffRef(row,col); + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + coeffRefByOuterInner(Index outer, Index inner) + { + return coeffRef(rowIndexByOuterInner(outer, inner), + colIndexByOuterInner(outer, inner)); + } + + /** \returns a reference to the coefficient at given the given row and column. + * + * \sa operator[](Index) + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + operator()(Index row, Index col) + { + eigen_assert(row >= 0 && row < rows() + && col >= 0 && col < cols()); + return coeffRef(row, col); + } + + + /** Short version: don't use this function, use + * \link operator[](Index) \endlink instead. + * + * Long version: this function is similar to + * \link operator[](Index) \endlink, but without the assertion. + * Use this for limiting the performance cost of debugging code when doing + * repeated coefficient access. Only use this when it is guaranteed that the + * parameters \a row and \a col are in range. + * + * If EIGEN_INTERNAL_DEBUGGING is defined, an assertion will be made, making this + * function equivalent to \link operator[](Index) \endlink. + * + * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index) + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + coeffRef(Index index) + { + EIGEN_STATIC_ASSERT(internal::evaluator::Flags & LinearAccessBit, + THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS) + eigen_internal_assert(index >= 0 && index < size()); + return internal::evaluator(derived()).coeffRef(index); + } + + /** \returns a reference to the coefficient at given index. + * + * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit. + * + * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w() + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + operator[](Index index) + { + EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime, + THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD) + eigen_assert(index >= 0 && index < size()); + return coeffRef(index); + } + + /** \returns a reference to the coefficient at given index. + * + * This is synonymous to operator[](Index). + * + * This method is allowed only for vector expressions, and for matrix expressions having the LinearAccessBit. + * + * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w() + */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + operator()(Index index) + { + eigen_assert(index >= 0 && index < size()); + return coeffRef(index); + } + + /** equivalent to operator[](0). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + x() { return (*this)[0]; } + + /** equivalent to operator[](1). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + y() + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=2, OUT_OF_RANGE_ACCESS); + return (*this)[1]; + } + + /** equivalent to operator[](2). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + z() + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=3, OUT_OF_RANGE_ACCESS); + return (*this)[2]; + } + + /** equivalent to operator[](3). */ + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& + w() + { + EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime==-1 || Derived::SizeAtCompileTime>=4, OUT_OF_RANGE_ACCESS); + return (*this)[3]; + } +}; + +/** \brief Base class providing direct read-only coefficient access to matrices and arrays. + * \ingroup Core_Module + * \tparam Derived Type of the derived class + * + * \note #DirectAccessors Constant indicating direct access + * + * This class defines functions to work with strides which can be used to access entries directly. This class + * inherits DenseCoeffsBase which defines functions to access entries read-only using + * \c operator() . + * + * \sa \blank \ref TopicClassHierarchy + */ +template +class DenseCoeffsBase : public DenseCoeffsBase +{ + public: + + typedef DenseCoeffsBase Base; + typedef typename internal::traits::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + using Base::rows; + using Base::cols; + using Base::size; + using Base::derived; + + /** \returns the pointer increment between two consecutive elements within a slice in the inner direction. + * + * \sa outerStride(), rowStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const + { + return derived().innerStride(); + } + + /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns + * in a column-major matrix). + * + * \sa innerStride(), rowStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const + { + return derived().outerStride(); + } + + // FIXME shall we remove it ? + EIGEN_CONSTEXPR inline Index stride() const + { + return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); + } + + /** \returns the pointer increment between two consecutive rows. + * + * \sa innerStride(), outerStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rowStride() const + { + return Derived::IsRowMajor ? outerStride() : innerStride(); + } + + /** \returns the pointer increment between two consecutive columns. + * + * \sa innerStride(), outerStride(), rowStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index colStride() const + { + return Derived::IsRowMajor ? innerStride() : outerStride(); + } +}; + +/** \brief Base class providing direct read/write coefficient access to matrices and arrays. + * \ingroup Core_Module + * \tparam Derived Type of the derived class + * + * \note #DirectWriteAccessors Constant indicating direct access + * + * This class defines functions to work with strides which can be used to access entries directly. This class + * inherits DenseCoeffsBase which defines functions to access entries read/write using + * \c operator(). + * + * \sa \blank \ref TopicClassHierarchy + */ +template +class DenseCoeffsBase + : public DenseCoeffsBase +{ + public: + + typedef DenseCoeffsBase Base; + typedef typename internal::traits::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + using Base::rows; + using Base::cols; + using Base::size; + using Base::derived; + + /** \returns the pointer increment between two consecutive elements within a slice in the inner direction. + * + * \sa outerStride(), rowStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT + { + return derived().innerStride(); + } + + /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns + * in a column-major matrix). + * + * \sa innerStride(), rowStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT + { + return derived().outerStride(); + } + + // FIXME shall we remove it ? + EIGEN_CONSTEXPR inline Index stride() const EIGEN_NOEXCEPT + { + return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); + } + + /** \returns the pointer increment between two consecutive rows. + * + * \sa innerStride(), outerStride(), colStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rowStride() const EIGEN_NOEXCEPT + { + return Derived::IsRowMajor ? outerStride() : innerStride(); + } + + /** \returns the pointer increment between two consecutive columns. + * + * \sa innerStride(), outerStride(), rowStride() + */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index colStride() const EIGEN_NOEXCEPT + { + return Derived::IsRowMajor ? innerStride() : outerStride(); + } +}; + +namespace internal { + +template +struct first_aligned_impl +{ + static EIGEN_CONSTEXPR inline Index run(const Derived&) EIGEN_NOEXCEPT + { return 0; } +}; + +template +struct first_aligned_impl +{ + static inline Index run(const Derived& m) + { + return internal::first_aligned(m.data(), m.size()); + } +}; + +/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization. + * + * \tparam Alignment requested alignment in Bytes. + * + * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more + * documentation. + */ +template +static inline Index first_aligned(const DenseBase& m) +{ + enum { ReturnZero = (int(evaluator::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) }; + return first_aligned_impl::run(m.derived()); +} + +template +static inline Index first_default_aligned(const DenseBase& m) +{ + typedef typename Derived::Scalar Scalar; + typedef typename packet_traits::type DefaultPacketType; + return internal::first_aligned::alignment),Derived>(m); +} + +template::ret> +struct inner_stride_at_compile_time +{ + enum { ret = traits::InnerStrideAtCompileTime }; +}; + +template +struct inner_stride_at_compile_time +{ + enum { ret = 0 }; +}; + +template::ret> +struct outer_stride_at_compile_time +{ + enum { ret = traits::OuterStrideAtCompileTime }; +}; + +template +struct outer_stride_at_compile_time +{ + enum { ret = 0 }; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_DENSECOEFFSBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseStorage.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseStorage.h new file mode 100644 index 0000000000000000000000000000000000000000..38050845745fc415a55c058eaa7cffbb74eeb7cd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DenseStorage.h @@ -0,0 +1,652 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2009 Benoit Jacob +// Copyright (C) 2010-2013 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIXSTORAGE_H +#define EIGEN_MATRIXSTORAGE_H + +#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN + #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) X; EIGEN_DENSE_STORAGE_CTOR_PLUGIN; +#else + #define EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(X) +#endif + +namespace Eigen { + +namespace internal { + +struct constructor_without_unaligned_array_assert {}; + +template +EIGEN_DEVICE_FUNC +void check_static_allocation_size() +{ + // if EIGEN_STACK_ALLOCATION_LIMIT is defined to 0, then no limit + #if EIGEN_STACK_ALLOCATION_LIMIT + EIGEN_STATIC_ASSERT(Size * sizeof(T) <= EIGEN_STACK_ALLOCATION_LIMIT, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG); + #endif +} + +/** \internal + * Static array. If the MatrixOrArrayOptions require auto-alignment, the array will be automatically aligned: + * to 16 bytes boundary if the total size is a multiple of 16 bytes. + */ +template ::value > +struct plain_array +{ + T array[Size]; + + EIGEN_DEVICE_FUNC + plain_array() + { + check_static_allocation_size(); + } + + EIGEN_DEVICE_FUNC + plain_array(constructor_without_unaligned_array_assert) + { + check_static_allocation_size(); + } +}; + +#if defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT) + #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) +#elif EIGEN_GNUC_AT_LEAST(4,7) + // GCC 4.7 is too aggressive in its optimizations and remove the alignment test based on the fact the array is declared to be aligned. + // See this bug report: http://gcc.gnu.org/bugzilla/show_bug.cgi?id=53900 + // Hiding the origin of the array pointer behind a function argument seems to do the trick even if the function is inlined: + template + EIGEN_ALWAYS_INLINE PtrType eigen_unaligned_array_assert_workaround_gcc47(PtrType array) { return array; } + #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \ + eigen_assert((internal::UIntPtr(eigen_unaligned_array_assert_workaround_gcc47(array)) & (sizemask)) == 0 \ + && "this assertion is explained here: " \ + "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \ + " **** READ THIS WEB PAGE !!! ****"); +#else + #define EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(sizemask) \ + eigen_assert((internal::UIntPtr(array) & (sizemask)) == 0 \ + && "this assertion is explained here: " \ + "http://eigen.tuxfamily.org/dox-devel/group__TopicUnalignedArrayAssert.html" \ + " **** READ THIS WEB PAGE !!! ****"); +#endif + +template +struct plain_array +{ + EIGEN_ALIGN_TO_BOUNDARY(8) T array[Size]; + + EIGEN_DEVICE_FUNC + plain_array() + { + EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(7); + check_static_allocation_size(); + } + + EIGEN_DEVICE_FUNC + plain_array(constructor_without_unaligned_array_assert) + { + check_static_allocation_size(); + } +}; + +template +struct plain_array +{ + EIGEN_ALIGN_TO_BOUNDARY(16) T array[Size]; + + EIGEN_DEVICE_FUNC + plain_array() + { + EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(15); + check_static_allocation_size(); + } + + EIGEN_DEVICE_FUNC + plain_array(constructor_without_unaligned_array_assert) + { + check_static_allocation_size(); + } +}; + +template +struct plain_array +{ + EIGEN_ALIGN_TO_BOUNDARY(32) T array[Size]; + + EIGEN_DEVICE_FUNC + plain_array() + { + EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(31); + check_static_allocation_size(); + } + + EIGEN_DEVICE_FUNC + plain_array(constructor_without_unaligned_array_assert) + { + check_static_allocation_size(); + } +}; + +template +struct plain_array +{ + EIGEN_ALIGN_TO_BOUNDARY(64) T array[Size]; + + EIGEN_DEVICE_FUNC + plain_array() + { + EIGEN_MAKE_UNALIGNED_ARRAY_ASSERT(63); + check_static_allocation_size(); + } + + EIGEN_DEVICE_FUNC + plain_array(constructor_without_unaligned_array_assert) + { + check_static_allocation_size(); + } +}; + +template +struct plain_array +{ + T array[1]; + EIGEN_DEVICE_FUNC plain_array() {} + EIGEN_DEVICE_FUNC plain_array(constructor_without_unaligned_array_assert) {} +}; + +struct plain_array_helper { + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + static void copy(const plain_array& src, const Eigen::Index size, + plain_array& dst) { + smart_copy(src.array, src.array + size, dst.array); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + static void swap(plain_array& a, const Eigen::Index a_size, + plain_array& b, const Eigen::Index b_size) { + if (a_size < b_size) { + std::swap_ranges(b.array, b.array + a_size, a.array); + smart_move(b.array + a_size, b.array + b_size, a.array + a_size); + } else if (a_size > b_size) { + std::swap_ranges(a.array, a.array + b_size, b.array); + smart_move(a.array + b_size, a.array + a_size, b.array + b_size); + } else { + std::swap_ranges(a.array, a.array + a_size, b.array); + } + } +}; + +} // end namespace internal + +/** \internal + * + * \class DenseStorage + * \ingroup Core_Module + * + * \brief Stores the data of a matrix + * + * This class stores the data of fixed-size, dynamic-size or mixed matrices + * in a way as compact as possible. + * + * \sa Matrix + */ +template class DenseStorage; + +// purely fixed-size matrix +template class DenseStorage +{ + internal::plain_array m_data; + public: + EIGEN_DEVICE_FUNC DenseStorage() { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size) + } + EIGEN_DEVICE_FUNC + explicit DenseStorage(internal::constructor_without_unaligned_array_assert) + : m_data(internal::constructor_without_unaligned_array_assert()) {} +#if !EIGEN_HAS_CXX11 || defined(EIGEN_DENSE_STORAGE_CTOR_PLUGIN) + EIGEN_DEVICE_FUNC + DenseStorage(const DenseStorage& other) : m_data(other.m_data) { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = Size) + } +#else + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) = default; +#endif +#if !EIGEN_HAS_CXX11 + EIGEN_DEVICE_FUNC + DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) m_data = other.m_data; + return *this; + } +#else + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) = default; +#endif +#if EIGEN_HAS_RVALUE_REFERENCES +#if !EIGEN_HAS_CXX11 + EIGEN_DEVICE_FUNC DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT + : m_data(std::move(other.m_data)) + { + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT + { + if (this != &other) + m_data = std::move(other.m_data); + return *this; + } +#else + EIGEN_DEVICE_FUNC DenseStorage(DenseStorage&&) = default; + EIGEN_DEVICE_FUNC DenseStorage& operator=(DenseStorage&&) = default; +#endif +#endif + EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + eigen_internal_assert(size==rows*cols && rows==Rows_ && cols==Cols_); + EIGEN_UNUSED_VARIABLE(size); + EIGEN_UNUSED_VARIABLE(rows); + EIGEN_UNUSED_VARIABLE(cols); + } + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { + numext::swap(m_data, other.m_data); + } + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;} + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return Cols_;} + EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {} + EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {} + EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; } + EIGEN_DEVICE_FUNC T *data() { return m_data.array; } +}; + +// null matrix +template class DenseStorage +{ + public: + EIGEN_DEVICE_FUNC DenseStorage() {} + EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) {} + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage&) {} + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage&) { return *this; } + EIGEN_DEVICE_FUNC DenseStorage(Index,Index,Index) {} + EIGEN_DEVICE_FUNC void swap(DenseStorage& ) {} + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;} + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) EIGEN_NOEXCEPT {return Cols_;} + EIGEN_DEVICE_FUNC void conservativeResize(Index,Index,Index) {} + EIGEN_DEVICE_FUNC void resize(Index,Index,Index) {} + EIGEN_DEVICE_FUNC const T *data() const { return 0; } + EIGEN_DEVICE_FUNC T *data() { return 0; } +}; + +// more specializations for null matrices; these are necessary to resolve ambiguities +template class DenseStorage +: public DenseStorage { }; + +template class DenseStorage +: public DenseStorage { }; + +template class DenseStorage +: public DenseStorage { }; + +// dynamic-size matrix with fixed-size storage +template class DenseStorage +{ + internal::plain_array m_data; + Index m_rows; + Index m_cols; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0), m_cols(0) {} + EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) + : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0), m_cols(0) {} + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows), m_cols(other.m_cols) + { + internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data); + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + m_rows = other.m_rows; + m_cols = other.m_cols; + internal::plain_array_helper::copy(other.m_data, m_rows * m_cols, m_data); + } + return *this; + } + EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index cols) : m_rows(rows), m_cols(cols) {} + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) + { + internal::plain_array_helper::swap(m_data, m_rows * m_cols, other.m_data, other.m_rows * other.m_cols); + numext::swap(m_rows,other.m_rows); + numext::swap(m_cols,other.m_cols); + } + EIGEN_DEVICE_FUNC Index rows() const {return m_rows;} + EIGEN_DEVICE_FUNC Index cols() const {return m_cols;} + EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; } + EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index cols) { m_rows = rows; m_cols = cols; } + EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; } + EIGEN_DEVICE_FUNC T *data() { return m_data.array; } +}; + +// dynamic-size matrix with fixed-size storage and fixed width +template class DenseStorage +{ + internal::plain_array m_data; + Index m_rows; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_rows(0) {} + EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) + : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(0) {} + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::constructor_without_unaligned_array_assert()), m_rows(other.m_rows) + { + internal::plain_array_helper::copy(other.m_data, m_rows * Cols_, m_data); + } + + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + m_rows = other.m_rows; + internal::plain_array_helper::copy(other.m_data, m_rows * Cols_, m_data); + } + return *this; + } + EIGEN_DEVICE_FUNC DenseStorage(Index, Index rows, Index) : m_rows(rows) {} + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) + { + internal::plain_array_helper::swap(m_data, m_rows * Cols_, other.m_data, other.m_rows * Cols_); + numext::swap(m_rows, other.m_rows); + } + EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;} + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols(void) const EIGEN_NOEXCEPT {return Cols_;} + EIGEN_DEVICE_FUNC void conservativeResize(Index, Index rows, Index) { m_rows = rows; } + EIGEN_DEVICE_FUNC void resize(Index, Index rows, Index) { m_rows = rows; } + EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; } + EIGEN_DEVICE_FUNC T *data() { return m_data.array; } +}; + +// dynamic-size matrix with fixed-size storage and fixed height +template class DenseStorage +{ + internal::plain_array m_data; + Index m_cols; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_cols(0) {} + EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) + : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(0) {} + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::constructor_without_unaligned_array_assert()), m_cols(other.m_cols) + { + internal::plain_array_helper::copy(other.m_data, Rows_ * m_cols, m_data); + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + m_cols = other.m_cols; + internal::plain_array_helper::copy(other.m_data, Rows_ * m_cols, m_data); + } + return *this; + } + EIGEN_DEVICE_FUNC DenseStorage(Index, Index, Index cols) : m_cols(cols) {} + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { + internal::plain_array_helper::swap(m_data, Rows_ * m_cols, other.m_data, Rows_ * other.m_cols); + numext::swap(m_cols, other.m_cols); + } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows(void) const EIGEN_NOEXCEPT {return Rows_;} + EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;} + EIGEN_DEVICE_FUNC void conservativeResize(Index, Index, Index cols) { m_cols = cols; } + EIGEN_DEVICE_FUNC void resize(Index, Index, Index cols) { m_cols = cols; } + EIGEN_DEVICE_FUNC const T *data() const { return m_data.array; } + EIGEN_DEVICE_FUNC T *data() { return m_data.array; } +}; + +// purely dynamic matrix. +template class DenseStorage +{ + T *m_data; + Index m_rows; + Index m_cols; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0), m_cols(0) {} + EIGEN_DEVICE_FUNC explicit DenseStorage(internal::constructor_without_unaligned_array_assert) + : m_data(0), m_rows(0), m_cols(0) {} + EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) + : m_data(internal::conditional_aligned_new_auto(size)), m_rows(rows), m_cols(cols) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + eigen_internal_assert(size==rows*cols && rows>=0 && cols >=0); + } + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::conditional_aligned_new_auto(other.m_rows*other.m_cols)) + , m_rows(other.m_rows) + , m_cols(other.m_cols) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*m_cols) + internal::smart_copy(other.m_data, other.m_data+other.m_rows*other.m_cols, m_data); + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + DenseStorage tmp(other); + this->swap(tmp); + } + return *this; + } +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC + DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT + : m_data(std::move(other.m_data)) + , m_rows(std::move(other.m_rows)) + , m_cols(std::move(other.m_cols)) + { + other.m_data = nullptr; + other.m_rows = 0; + other.m_cols = 0; + } + EIGEN_DEVICE_FUNC + DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT + { + numext::swap(m_data, other.m_data); + numext::swap(m_rows, other.m_rows); + numext::swap(m_cols, other.m_cols); + return *this; + } +#endif + EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto(m_data, m_rows*m_cols); } + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) + { + numext::swap(m_data,other.m_data); + numext::swap(m_rows,other.m_rows); + numext::swap(m_cols,other.m_cols); + } + EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;} + EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;} + void conservativeResize(Index size, Index rows, Index cols) + { + m_data = internal::conditional_aligned_realloc_new_auto(m_data, size, m_rows*m_cols); + m_rows = rows; + m_cols = cols; + } + EIGEN_DEVICE_FUNC void resize(Index size, Index rows, Index cols) + { + if(size != m_rows*m_cols) + { + internal::conditional_aligned_delete_auto(m_data, m_rows*m_cols); + if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative + m_data = internal::conditional_aligned_new_auto(size); + else + m_data = 0; + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + } + m_rows = rows; + m_cols = cols; + } + EIGEN_DEVICE_FUNC const T *data() const { return m_data; } + EIGEN_DEVICE_FUNC T *data() { return m_data; } +}; + +// matrix with dynamic width and fixed height (so that matrix has dynamic size). +template class DenseStorage +{ + T *m_data; + Index m_cols; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_cols(0) {} + explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_cols(0) {} + EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto(size)), m_cols(cols) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + eigen_internal_assert(size==rows*cols && rows==Rows_ && cols >=0); + EIGEN_UNUSED_VARIABLE(rows); + } + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::conditional_aligned_new_auto(Rows_*other.m_cols)) + , m_cols(other.m_cols) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_cols*Rows_) + internal::smart_copy(other.m_data, other.m_data+Rows_*m_cols, m_data); + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + DenseStorage tmp(other); + this->swap(tmp); + } + return *this; + } +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC + DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT + : m_data(std::move(other.m_data)) + , m_cols(std::move(other.m_cols)) + { + other.m_data = nullptr; + other.m_cols = 0; + } + EIGEN_DEVICE_FUNC + DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT + { + numext::swap(m_data, other.m_data); + numext::swap(m_cols, other.m_cols); + return *this; + } +#endif + EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto(m_data, Rows_*m_cols); } + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { + numext::swap(m_data,other.m_data); + numext::swap(m_cols,other.m_cols); + } + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index rows(void) EIGEN_NOEXCEPT {return Rows_;} + EIGEN_DEVICE_FUNC Index cols(void) const EIGEN_NOEXCEPT {return m_cols;} + EIGEN_DEVICE_FUNC void conservativeResize(Index size, Index, Index cols) + { + m_data = internal::conditional_aligned_realloc_new_auto(m_data, size, Rows_*m_cols); + m_cols = cols; + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index, Index cols) + { + if(size != Rows_*m_cols) + { + internal::conditional_aligned_delete_auto(m_data, Rows_*m_cols); + if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative + m_data = internal::conditional_aligned_new_auto(size); + else + m_data = 0; + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + } + m_cols = cols; + } + EIGEN_DEVICE_FUNC const T *data() const { return m_data; } + EIGEN_DEVICE_FUNC T *data() { return m_data; } +}; + +// matrix with dynamic height and fixed width (so that matrix has dynamic size). +template class DenseStorage +{ + T *m_data; + Index m_rows; + public: + EIGEN_DEVICE_FUNC DenseStorage() : m_data(0), m_rows(0) {} + explicit DenseStorage(internal::constructor_without_unaligned_array_assert) : m_data(0), m_rows(0) {} + EIGEN_DEVICE_FUNC DenseStorage(Index size, Index rows, Index cols) : m_data(internal::conditional_aligned_new_auto(size)), m_rows(rows) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + eigen_internal_assert(size==rows*cols && rows>=0 && cols == Cols_); + EIGEN_UNUSED_VARIABLE(cols); + } + EIGEN_DEVICE_FUNC DenseStorage(const DenseStorage& other) + : m_data(internal::conditional_aligned_new_auto(other.m_rows*Cols_)) + , m_rows(other.m_rows) + { + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN(Index size = m_rows*Cols_) + internal::smart_copy(other.m_data, other.m_data+other.m_rows*Cols_, m_data); + } + EIGEN_DEVICE_FUNC DenseStorage& operator=(const DenseStorage& other) + { + if (this != &other) + { + DenseStorage tmp(other); + this->swap(tmp); + } + return *this; + } +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC + DenseStorage(DenseStorage&& other) EIGEN_NOEXCEPT + : m_data(std::move(other.m_data)) + , m_rows(std::move(other.m_rows)) + { + other.m_data = nullptr; + other.m_rows = 0; + } + EIGEN_DEVICE_FUNC + DenseStorage& operator=(DenseStorage&& other) EIGEN_NOEXCEPT + { + numext::swap(m_data, other.m_data); + numext::swap(m_rows, other.m_rows); + return *this; + } +#endif + EIGEN_DEVICE_FUNC ~DenseStorage() { internal::conditional_aligned_delete_auto(m_data, Cols_*m_rows); } + EIGEN_DEVICE_FUNC void swap(DenseStorage& other) { + numext::swap(m_data,other.m_data); + numext::swap(m_rows,other.m_rows); + } + EIGEN_DEVICE_FUNC Index rows(void) const EIGEN_NOEXCEPT {return m_rows;} + EIGEN_DEVICE_FUNC static EIGEN_CONSTEXPR Index cols(void) {return Cols_;} + void conservativeResize(Index size, Index rows, Index) + { + m_data = internal::conditional_aligned_realloc_new_auto(m_data, size, m_rows*Cols_); + m_rows = rows; + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void resize(Index size, Index rows, Index) + { + if(size != m_rows*Cols_) + { + internal::conditional_aligned_delete_auto(m_data, Cols_*m_rows); + if (size>0) // >0 and not simply !=0 to let the compiler knows that size cannot be negative + m_data = internal::conditional_aligned_new_auto(size); + else + m_data = 0; + EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN({}) + } + m_rows = rows; + } + EIGEN_DEVICE_FUNC const T *data() const { return m_data; } + EIGEN_DEVICE_FUNC T *data() { return m_data; } +}; + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Diagonal.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Diagonal.h new file mode 100644 index 0000000000000000000000000000000000000000..d15f0af8e3235aae6dbed7a1e19c8be9f1c18bea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Diagonal.h @@ -0,0 +1,258 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007-2009 Benoit Jacob +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DIAGONAL_H +#define EIGEN_DIAGONAL_H + +namespace Eigen { + +/** \class Diagonal + * \ingroup Core_Module + * + * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix + * + * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal + * \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal. + * A positive value means a superdiagonal, a negative value means a subdiagonal. + * You can also use DynamicIndex so the index can be set at runtime. + * + * The matrix is not required to be square. + * + * This class represents an expression of the main diagonal, or any sub/super diagonal + * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the + * time this is the only way it is used. + * + * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index) + */ + +namespace internal { +template +struct traits > + : traits +{ + typedef typename ref_selector::type MatrixTypeNested; + typedef typename remove_reference::type _MatrixTypeNested; + typedef typename MatrixType::StorageKind StorageKind; + enum { + RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic + : (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0), + MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))), + ColsAtCompileTime = 1, + MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic + : DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime, + MatrixType::MaxColsAtCompileTime) + : (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0), + MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))), + MaxColsAtCompileTime = 1, + MaskLvalueBit = is_lvalue::value ? LvalueBit : 0, + Flags = (unsigned int)_MatrixTypeNested::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions + MatrixTypeOuterStride = outer_stride_at_compile_time::ret, + InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1, + OuterStrideAtCompileTime = 0 + }; +}; +} + +template class Diagonal + : public internal::dense_xpr_base< Diagonal >::type +{ + public: + + enum { DiagIndex = DiagIndex_ }; + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal) + + EIGEN_DEVICE_FUNC + explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index) + { + eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() ); + } + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal) + + EIGEN_DEVICE_FUNC + inline Index rows() const + { + return m_index.value()<0 ? numext::mini(m_matrix.cols(),m_matrix.rows()+m_index.value()) + : numext::mini(m_matrix.rows(),m_matrix.cols()-m_index.value()); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return 1; } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT { + return m_matrix.outerStride() + 1; + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return 0; } + + typedef typename internal::conditional< + internal::is_lvalue::value, + Scalar, + const Scalar + >::type ScalarWithConstIfNotLvalue; + + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); } + EIGEN_DEVICE_FUNC + inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index row, Index) + { + EIGEN_STATIC_ASSERT_LVALUE(MatrixType) + return m_matrix.coeffRef(row+rowOffset(), row+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index row, Index) const + { + return m_matrix.coeffRef(row+rowOffset(), row+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline CoeffReturnType coeff(Index row, Index) const + { + return m_matrix.coeff(row+rowOffset(), row+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index idx) + { + EIGEN_STATIC_ASSERT_LVALUE(MatrixType) + return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index idx) const + { + return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline CoeffReturnType coeff(Index idx) const + { + return m_matrix.coeff(idx+rowOffset(), idx+colOffset()); + } + + EIGEN_DEVICE_FUNC + inline const typename internal::remove_all::type& + nestedExpression() const + { + return m_matrix; + } + + EIGEN_DEVICE_FUNC + inline Index index() const + { + return m_index.value(); + } + + protected: + typename internal::ref_selector::non_const_type m_matrix; + const internal::variable_if_dynamicindex m_index; + + private: + // some compilers may fail to optimize std::max etc in case of compile-time constants... + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index absDiagIndex() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : -m_index.value(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rowOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? 0 : -m_index.value(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index colOffset() const EIGEN_NOEXCEPT { return m_index.value()>0 ? m_index.value() : 0; } + // trigger a compile-time error if someone try to call packet + template typename MatrixType::PacketReturnType packet(Index) const; + template typename MatrixType::PacketReturnType packet(Index,Index) const; +}; + +/** \returns an expression of the main diagonal of the matrix \c *this + * + * \c *this is not required to be square. + * + * Example: \include MatrixBase_diagonal.cpp + * Output: \verbinclude MatrixBase_diagonal.out + * + * \sa class Diagonal */ +template +EIGEN_DEVICE_FUNC inline typename MatrixBase::DiagonalReturnType +MatrixBase::diagonal() +{ + return DiagonalReturnType(derived()); +} + +/** This is the const version of diagonal(). */ +template +EIGEN_DEVICE_FUNC inline typename MatrixBase::ConstDiagonalReturnType +MatrixBase::diagonal() const +{ + return ConstDiagonalReturnType(derived()); +} + +/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this + * + * \c *this is not required to be square. + * + * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0 + * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal. + * + * Example: \include MatrixBase_diagonal_int.cpp + * Output: \verbinclude MatrixBase_diagonal_int.out + * + * \sa MatrixBase::diagonal(), class Diagonal */ +template +EIGEN_DEVICE_FUNC inline typename MatrixBase::DiagonalDynamicIndexReturnType +MatrixBase::diagonal(Index index) +{ + return DiagonalDynamicIndexReturnType(derived(), index); +} + +/** This is the const version of diagonal(Index). */ +template +EIGEN_DEVICE_FUNC inline typename MatrixBase::ConstDiagonalDynamicIndexReturnType +MatrixBase::diagonal(Index index) const +{ + return ConstDiagonalDynamicIndexReturnType(derived(), index); +} + +/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this + * + * \c *this is not required to be square. + * + * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0 + * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal. + * + * Example: \include MatrixBase_diagonal_template_int.cpp + * Output: \verbinclude MatrixBase_diagonal_template_int.out + * + * \sa MatrixBase::diagonal(), class Diagonal */ +template +template +EIGEN_DEVICE_FUNC +inline typename MatrixBase::template DiagonalIndexReturnType::Type +MatrixBase::diagonal() +{ + return typename DiagonalIndexReturnType::Type(derived()); +} + +/** This is the const version of diagonal(). */ +template +template +EIGEN_DEVICE_FUNC +inline typename MatrixBase::template ConstDiagonalIndexReturnType::Type +MatrixBase::diagonal() const +{ + return typename ConstDiagonalIndexReturnType::Type(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_DIAGONAL_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalMatrix.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalMatrix.h new file mode 100644 index 0000000000000000000000000000000000000000..474dcfae276d2a7495786e6f6c11fbc470256d08 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalMatrix.h @@ -0,0 +1,391 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// Copyright (C) 2007-2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DIAGONALMATRIX_H +#define EIGEN_DIAGONALMATRIX_H + +namespace Eigen { + +#ifndef EIGEN_PARSED_BY_DOXYGEN +template +class DiagonalBase : public EigenBase +{ + public: + typedef typename internal::traits::DiagonalVectorType DiagonalVectorType; + typedef typename DiagonalVectorType::Scalar Scalar; + typedef typename DiagonalVectorType::RealScalar RealScalar; + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::StorageIndex StorageIndex; + + enum { + RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime, + ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime, + MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime, + MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime, + IsVectorAtCompileTime = 0, + Flags = NoPreferredStorageOrderBit + }; + + typedef Matrix DenseMatrixType; + typedef DenseMatrixType DenseType; + typedef DiagonalMatrix PlainObject; + + EIGEN_DEVICE_FUNC + inline const Derived& derived() const { return *static_cast(this); } + EIGEN_DEVICE_FUNC + inline Derived& derived() { return *static_cast(this); } + + EIGEN_DEVICE_FUNC + DenseMatrixType toDenseMatrix() const { return derived(); } + + EIGEN_DEVICE_FUNC + inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); } + EIGEN_DEVICE_FUNC + inline DiagonalVectorType& diagonal() { return derived().diagonal(); } + + EIGEN_DEVICE_FUNC + inline Index rows() const { return diagonal().size(); } + EIGEN_DEVICE_FUNC + inline Index cols() const { return diagonal().size(); } + + template + EIGEN_DEVICE_FUNC + const Product + operator*(const MatrixBase &matrix) const + { + return Product(derived(),matrix.derived()); + } + + typedef DiagonalWrapper, const DiagonalVectorType> > InverseReturnType; + EIGEN_DEVICE_FUNC + inline const InverseReturnType + inverse() const + { + return InverseReturnType(diagonal().cwiseInverse()); + } + + EIGEN_DEVICE_FUNC + inline const DiagonalWrapper + operator*(const Scalar& scalar) const + { + return DiagonalWrapper(diagonal() * scalar); + } + EIGEN_DEVICE_FUNC + friend inline const DiagonalWrapper + operator*(const Scalar& scalar, const DiagonalBase& other) + { + return DiagonalWrapper(scalar * other.diagonal()); + } + + template + EIGEN_DEVICE_FUNC + #ifdef EIGEN_PARSED_BY_DOXYGEN + inline unspecified_expression_type + #else + inline const DiagonalWrapper + #endif + operator+(const DiagonalBase& other) const + { + return (diagonal() + other.diagonal()).asDiagonal(); + } + + template + EIGEN_DEVICE_FUNC + #ifdef EIGEN_PARSED_BY_DOXYGEN + inline unspecified_expression_type + #else + inline const DiagonalWrapper + #endif + operator-(const DiagonalBase& other) const + { + return (diagonal() - other.diagonal()).asDiagonal(); + } +}; + +#endif + +/** \class DiagonalMatrix + * \ingroup Core_Module + * + * \brief Represents a diagonal matrix with its storage + * + * \param Scalar_ the type of coefficients + * \param SizeAtCompileTime the dimension of the matrix, or Dynamic + * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults + * to SizeAtCompileTime. Most of the time, you do not need to specify it. + * + * \sa class DiagonalWrapper + */ + +namespace internal { +template +struct traits > + : traits > +{ + typedef Matrix DiagonalVectorType; + typedef DiagonalShape StorageKind; + enum { + Flags = LvalueBit | NoPreferredStorageOrderBit + }; +}; +} +template +class DiagonalMatrix + : public DiagonalBase > +{ + public: + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename internal::traits::DiagonalVectorType DiagonalVectorType; + typedef const DiagonalMatrix& Nested; + typedef Scalar_ Scalar; + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::StorageIndex StorageIndex; + #endif + + protected: + + DiagonalVectorType m_diagonal; + + public: + + /** const version of diagonal(). */ + EIGEN_DEVICE_FUNC + inline const DiagonalVectorType& diagonal() const { return m_diagonal; } + /** \returns a reference to the stored vector of diagonal coefficients. */ + EIGEN_DEVICE_FUNC + inline DiagonalVectorType& diagonal() { return m_diagonal; } + + /** Default constructor without initialization */ + EIGEN_DEVICE_FUNC + inline DiagonalMatrix() {} + + /** Constructs a diagonal matrix with given dimension */ + EIGEN_DEVICE_FUNC + explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {} + + /** 2D constructor. */ + EIGEN_DEVICE_FUNC + inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {} + + /** 3D constructor. */ + EIGEN_DEVICE_FUNC + inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {} + + #if EIGEN_HAS_CXX11 + /** \brief Construct a diagonal matrix with fixed size from an arbitrary number of coefficients. \cpp11 + * + * There exists C++98 anologue constructors for fixed-size diagonal matrices having 2 or 3 coefficients. + * + * \warning To construct a diagonal matrix of fixed size, the number of values passed to this + * constructor must match the fixed dimension of \c *this. + * + * \sa DiagonalMatrix(const Scalar&, const Scalar&) + * \sa DiagonalMatrix(const Scalar&, const Scalar&, const Scalar&) + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + DiagonalMatrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const ArgTypes&... args) + : m_diagonal(a0, a1, a2, args...) {} + + /** \brief Constructs a DiagonalMatrix and initializes it by elements given by an initializer list of initializer + * lists \cpp11 + */ + EIGEN_DEVICE_FUNC + explicit EIGEN_STRONG_INLINE DiagonalMatrix(const std::initializer_list>& list) + : m_diagonal(list) {} + #endif // EIGEN_HAS_CXX11 + + /** Copy constructor. */ + template + EIGEN_DEVICE_FUNC + inline DiagonalMatrix(const DiagonalBase& other) : m_diagonal(other.diagonal()) {} + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */ + inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {} + #endif + + /** generic constructor from expression of the diagonal coefficients */ + template + EIGEN_DEVICE_FUNC + explicit inline DiagonalMatrix(const MatrixBase& other) : m_diagonal(other) + {} + + /** Copy operator. */ + template + EIGEN_DEVICE_FUNC + DiagonalMatrix& operator=(const DiagonalBase& other) + { + m_diagonal = other.diagonal(); + return *this; + } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /** This is a special case of the templated operator=. Its purpose is to + * prevent a default operator= from hiding the templated operator=. + */ + EIGEN_DEVICE_FUNC + DiagonalMatrix& operator=(const DiagonalMatrix& other) + { + m_diagonal = other.diagonal(); + return *this; + } + #endif + + /** Resizes to given size. */ + EIGEN_DEVICE_FUNC + inline void resize(Index size) { m_diagonal.resize(size); } + /** Sets all coefficients to zero. */ + EIGEN_DEVICE_FUNC + inline void setZero() { m_diagonal.setZero(); } + /** Resizes and sets all coefficients to zero. */ + EIGEN_DEVICE_FUNC + inline void setZero(Index size) { m_diagonal.setZero(size); } + /** Sets this matrix to be the identity matrix of the current size. */ + EIGEN_DEVICE_FUNC + inline void setIdentity() { m_diagonal.setOnes(); } + /** Sets this matrix to be the identity matrix of the given size. */ + EIGEN_DEVICE_FUNC + inline void setIdentity(Index size) { m_diagonal.setOnes(size); } +}; + +/** \class DiagonalWrapper + * \ingroup Core_Module + * + * \brief Expression of a diagonal matrix + * + * \param DiagonalVectorType_ the type of the vector of diagonal coefficients + * + * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients, + * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal() + * and most of the time this is the only way that it is used. + * + * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal() + */ + +namespace internal { +template +struct traits > +{ + typedef DiagonalVectorType_ DiagonalVectorType; + typedef typename DiagonalVectorType::Scalar Scalar; + typedef typename DiagonalVectorType::StorageIndex StorageIndex; + typedef DiagonalShape StorageKind; + typedef typename traits::XprKind XprKind; + enum { + RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime, + ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime, + MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime, + MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime, + Flags = (traits::Flags & LvalueBit) | NoPreferredStorageOrderBit + }; +}; +} + +template +class DiagonalWrapper + : public DiagonalBase >, internal::no_assignment_operator +{ + public: + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef DiagonalVectorType_ DiagonalVectorType; + typedef DiagonalWrapper Nested; + #endif + + /** Constructor from expression of diagonal coefficients to wrap. */ + EIGEN_DEVICE_FUNC + explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {} + + /** \returns a const reference to the wrapped expression of diagonal coefficients. */ + EIGEN_DEVICE_FUNC + const DiagonalVectorType& diagonal() const { return m_diagonal; } + + protected: + typename DiagonalVectorType::Nested m_diagonal; +}; + +/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients + * + * \only_for_vectors + * + * Example: \include MatrixBase_asDiagonal.cpp + * Output: \verbinclude MatrixBase_asDiagonal.out + * + * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal() + **/ +template +EIGEN_DEVICE_FUNC inline const DiagonalWrapper +MatrixBase::asDiagonal() const +{ + return DiagonalWrapper(derived()); +} + +/** \returns true if *this is approximately equal to a diagonal matrix, + * within the precision given by \a prec. + * + * Example: \include MatrixBase_isDiagonal.cpp + * Output: \verbinclude MatrixBase_isDiagonal.out + * + * \sa asDiagonal() + */ +template +bool MatrixBase::isDiagonal(const RealScalar& prec) const +{ + if(cols() != rows()) return false; + RealScalar maxAbsOnDiagonal = static_cast(-1); + for(Index j = 0; j < cols(); ++j) + { + RealScalar absOnDiagonal = numext::abs(coeff(j,j)); + if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal; + } + for(Index j = 0; j < cols(); ++j) + for(Index i = 0; i < j; ++i) + { + if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false; + if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false; + } + return true; +} + +namespace internal { + +template<> struct storage_kind_to_shape { typedef DiagonalShape Shape; }; + +struct Diagonal2Dense {}; + +template<> struct AssignmentKind { typedef Diagonal2Dense Kind; }; + +// Diagonal matrix to Dense assignment +template< typename DstXprType, typename SrcXprType, typename Functor> +struct Assignment +{ + static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op &/*func*/) + { + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) + dst.resize(dstRows, dstCols); + + dst.setZero(); + dst.diagonal() = src.diagonal(); + } + + static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op &/*func*/) + { dst.diagonal() += src.diagonal(); } + + static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op &/*func*/) + { dst.diagonal() -= src.diagonal(); } +}; + +} // namespace internal + +} // end namespace Eigen + +#endif // EIGEN_DIAGONALMATRIX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalProduct.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalProduct.h new file mode 100644 index 0000000000000000000000000000000000000000..7911d1cd174a3b59195b81169ed7ec9546342464 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/DiagonalProduct.h @@ -0,0 +1,28 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2007-2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DIAGONALPRODUCT_H +#define EIGEN_DIAGONALPRODUCT_H + +namespace Eigen { + +/** \returns the diagonal matrix product of \c *this by the diagonal matrix \a diagonal. + */ +template +template +EIGEN_DEVICE_FUNC inline const Product +MatrixBase::operator*(const DiagonalBase &a_diagonal) const +{ + return Product(derived(),a_diagonal.derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_DIAGONALPRODUCT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Dot.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Dot.h new file mode 100644 index 0000000000000000000000000000000000000000..5c3441b9266a4e1929a29f373e5c509f77c5e0ef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Dot.h @@ -0,0 +1,318 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008, 2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DOT_H +#define EIGEN_DOT_H + +namespace Eigen { + +namespace internal { + +// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot +// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE +// looking at the static assertions. Thus this is a trick to get better compile errors. +template +struct dot_nocheck +{ + typedef scalar_conj_product_op::Scalar,typename traits::Scalar> conj_prod; + typedef typename conj_prod::result_type ResScalar; + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE + static ResScalar run(const MatrixBase& a, const MatrixBase& b) + { + return a.template binaryExpr(b).sum(); + } +}; + +template +struct dot_nocheck +{ + typedef scalar_conj_product_op::Scalar,typename traits::Scalar> conj_prod; + typedef typename conj_prod::result_type ResScalar; + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE + static ResScalar run(const MatrixBase& a, const MatrixBase& b) + { + return a.transpose().template binaryExpr(b).sum(); + } +}; + +} // end namespace internal + +/** \fn MatrixBase::dot + * \returns the dot product of *this with other. + * + * \only_for_vectors + * + * \note If the scalar type is complex numbers, then this function returns the hermitian + * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the + * second variable. + * + * \sa squaredNorm(), norm() + */ +template +template +EIGEN_DEVICE_FUNC +EIGEN_STRONG_INLINE +typename ScalarBinaryOpTraits::Scalar,typename internal::traits::Scalar>::ReturnType +MatrixBase::dot(const MatrixBase& other) const +{ + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived) + EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived) +#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG)) + typedef internal::scalar_conj_product_op func; + EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar); +#endif + + eigen_assert(size() == other.size()); + + return internal::dot_nocheck::run(*this, other); +} + +//---------- implementation of L2 norm and related functions ---------- + +/** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the squared Frobenius norm. + * In both cases, it consists in the sum of the square of all the matrix entries. + * For vectors, this is also equals to the dot product of \c *this with itself. + * + * \sa dot(), norm(), lpNorm() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits::Scalar>::Real MatrixBase::squaredNorm() const +{ + return numext::real((*this).cwiseAbs2().sum()); +} + +/** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm. + * In both cases, it consists in the square root of the sum of the square of all the matrix entries. + * For vectors, this is also equals to the square root of the dot product of \c *this with itself. + * + * \sa lpNorm(), dot(), squaredNorm() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename NumTraits::Scalar>::Real MatrixBase::norm() const +{ + return numext::sqrt(squaredNorm()); +} + +/** \returns an expression of the quotient of \c *this by its own norm. + * + * \warning If the input vector is too small (i.e., this->norm()==0), + * then this function returns a copy of the input. + * + * \only_for_vectors + * + * \sa norm(), normalize() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::PlainObject +MatrixBase::normalized() const +{ + typedef typename internal::nested_eval::type _Nested; + _Nested n(derived()); + RealScalar z = n.squaredNorm(); + // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU + if(z>RealScalar(0)) + return n / numext::sqrt(z); + else + return n; +} + +/** Normalizes the vector, i.e. divides it by its own norm. + * + * \only_for_vectors + * + * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged. + * + * \sa norm(), normalized() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase::normalize() +{ + RealScalar z = squaredNorm(); + // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU + if(z>RealScalar(0)) + derived() /= numext::sqrt(z); +} + +/** \returns an expression of the quotient of \c *this by its own norm while avoiding underflow and overflow. + * + * \only_for_vectors + * + * This method is analogue to the normalized() method, but it reduces the risk of + * underflow and overflow when computing the norm. + * + * \warning If the input vector is too small (i.e., this->norm()==0), + * then this function returns a copy of the input. + * + * \sa stableNorm(), stableNormalize(), normalized() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase::PlainObject +MatrixBase::stableNormalized() const +{ + typedef typename internal::nested_eval::type _Nested; + _Nested n(derived()); + RealScalar w = n.cwiseAbs().maxCoeff(); + RealScalar z = (n/w).squaredNorm(); + if(z>RealScalar(0)) + return n / (numext::sqrt(z)*w); + else + return n; +} + +/** Normalizes the vector while avoid underflow and overflow + * + * \only_for_vectors + * + * This method is analogue to the normalize() method, but it reduces the risk of + * underflow and overflow when computing the norm. + * + * \warning If the input vector is too small (i.e., this->norm()==0), then \c *this is left unchanged. + * + * \sa stableNorm(), stableNormalized(), normalize() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void MatrixBase::stableNormalize() +{ + RealScalar w = cwiseAbs().maxCoeff(); + RealScalar z = (derived()/w).squaredNorm(); + if(z>RealScalar(0)) + derived() /= numext::sqrt(z)*w; +} + +//---------- implementation of other norms ---------- + +namespace internal { + +template +struct lpNorm_selector +{ + typedef typename NumTraits::Scalar>::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const MatrixBase& m) + { + EIGEN_USING_STD(pow) + return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p); + } +}; + +template +struct lpNorm_selector +{ + EIGEN_DEVICE_FUNC + static inline typename NumTraits::Scalar>::Real run(const MatrixBase& m) + { + return m.cwiseAbs().sum(); + } +}; + +template +struct lpNorm_selector +{ + EIGEN_DEVICE_FUNC + static inline typename NumTraits::Scalar>::Real run(const MatrixBase& m) + { + return m.norm(); + } +}; + +template +struct lpNorm_selector +{ + typedef typename NumTraits::Scalar>::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const MatrixBase& m) + { + if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==Dynamic && m.size()==0)) + return RealScalar(0); + return m.cwiseAbs().maxCoeff(); + } +}; + +} // end namespace internal + +/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values + * of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$ + * norm, that is the maximum of the absolute values of the coefficients of \c *this. + * + * In all cases, if \c *this is empty, then the value 0 is returned. + * + * \note For matrices, this function does not compute the operator-norm. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink. + * + * \sa norm() + */ +template +template +#ifndef EIGEN_PARSED_BY_DOXYGEN +EIGEN_DEVICE_FUNC inline typename NumTraits::Scalar>::Real +#else +EIGEN_DEVICE_FUNC MatrixBase::RealScalar +#endif +MatrixBase::lpNorm() const +{ + return internal::lpNorm_selector::run(*this); +} + +//---------- implementation of isOrthogonal / isUnitary ---------- + +/** \returns true if *this is approximately orthogonal to \a other, + * within the precision given by \a prec. + * + * Example: \include MatrixBase_isOrthogonal.cpp + * Output: \verbinclude MatrixBase_isOrthogonal.out + */ +template +template +bool MatrixBase::isOrthogonal +(const MatrixBase& other, const RealScalar& prec) const +{ + typename internal::nested_eval::type nested(derived()); + typename internal::nested_eval::type otherNested(other.derived()); + return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm(); +} + +/** \returns true if *this is approximately an unitary matrix, + * within the precision given by \a prec. In the case where the \a Scalar + * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name. + * + * \note This can be used to check whether a family of vectors forms an orthonormal basis. + * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an + * orthonormal basis. + * + * Example: \include MatrixBase_isUnitary.cpp + * Output: \verbinclude MatrixBase_isUnitary.out + */ +template +bool MatrixBase::isUnitary(const RealScalar& prec) const +{ + typename internal::nested_eval::type self(derived()); + for(Index i = 0; i < cols(); ++i) + { + if(!internal::isApprox(self.col(i).squaredNorm(), static_cast(1), prec)) + return false; + for(Index j = 0; j < i; ++j) + if(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast(1), prec)) + return false; + } + return true; +} + +} // end namespace Eigen + +#endif // EIGEN_DOT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/EigenBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/EigenBase.h new file mode 100644 index 0000000000000000000000000000000000000000..6b3c7d3745e2ae96233789208c8dd2d586a3baa3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/EigenBase.h @@ -0,0 +1,160 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Benoit Jacob +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_EIGENBASE_H +#define EIGEN_EIGENBASE_H + +namespace Eigen { + +/** \class EigenBase + * \ingroup Core_Module + * + * Common base class for all classes T such that MatrixBase has an operator=(T) and a constructor MatrixBase(T). + * + * In other words, an EigenBase object is an object that can be copied into a MatrixBase. + * + * Besides MatrixBase-derived classes, this also includes special matrix classes such as diagonal matrices, etc. + * + * Notice that this class is trivial, it is only used to disambiguate overloaded functions. + * + * \sa \blank \ref TopicClassHierarchy + */ +template struct EigenBase +{ +// typedef typename internal::plain_matrix_type::type PlainObject; + + /** \brief The interface type of indices + * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE. + * \sa StorageIndex, \ref TopicPreprocessorDirectives. + * DEPRECATED: Since Eigen 3.3, its usage is deprecated. Use Eigen::Index instead. + * Deprecation is not marked with a doxygen comment because there are too many existing usages to add the deprecation attribute. + */ + typedef Eigen::Index Index; + + // FIXME is it needed? + typedef typename internal::traits::StorageKind StorageKind; + + /** \returns a reference to the derived object */ + EIGEN_DEVICE_FUNC + Derived& derived() { return *static_cast(this); } + /** \returns a const reference to the derived object */ + EIGEN_DEVICE_FUNC + const Derived& derived() const { return *static_cast(this); } + + EIGEN_DEVICE_FUNC + inline Derived& const_cast_derived() const + { return *static_cast(const_cast(this)); } + EIGEN_DEVICE_FUNC + inline const Derived& const_derived() const + { return *static_cast(this); } + + /** \returns the number of rows. \sa cols(), RowsAtCompileTime */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); } + /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); } + /** \returns the number of coefficients, which is rows()*cols(). + * \sa rows(), cols(), SizeAtCompileTime. */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index size() const EIGEN_NOEXCEPT { return rows() * cols(); } + + /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */ + template + EIGEN_DEVICE_FUNC + inline void evalTo(Dest& dst) const + { derived().evalTo(dst); } + + /** \internal Don't use it, but do the equivalent: \code dst += *this; \endcode */ + template + EIGEN_DEVICE_FUNC + inline void addTo(Dest& dst) const + { + // This is the default implementation, + // derived class can reimplement it in a more optimized way. + typename Dest::PlainObject res(rows(),cols()); + evalTo(res); + dst += res; + } + + /** \internal Don't use it, but do the equivalent: \code dst -= *this; \endcode */ + template + EIGEN_DEVICE_FUNC + inline void subTo(Dest& dst) const + { + // This is the default implementation, + // derived class can reimplement it in a more optimized way. + typename Dest::PlainObject res(rows(),cols()); + evalTo(res); + dst -= res; + } + + /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheRight(*this); \endcode */ + template + EIGEN_DEVICE_FUNC inline void applyThisOnTheRight(Dest& dst) const + { + // This is the default implementation, + // derived class can reimplement it in a more optimized way. + dst = dst * this->derived(); + } + + /** \internal Don't use it, but do the equivalent: \code dst.applyOnTheLeft(*this); \endcode */ + template + EIGEN_DEVICE_FUNC inline void applyThisOnTheLeft(Dest& dst) const + { + // This is the default implementation, + // derived class can reimplement it in a more optimized way. + dst = this->derived() * dst; + } + +}; + +/*************************************************************************** +* Implementation of matrix base methods +***************************************************************************/ + +/** \brief Copies the generic expression \a other into *this. + * + * \details The expression must provide a (templated) evalTo(Derived& dst) const + * function which does the actual job. In practice, this allows any user to write + * its own special matrix without having to modify MatrixBase + * + * \returns a reference to *this. + */ +template +template +EIGEN_DEVICE_FUNC +Derived& DenseBase::operator=(const EigenBase &other) +{ + call_assignment(derived(), other.derived()); + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +Derived& DenseBase::operator+=(const EigenBase &other) +{ + call_assignment(derived(), other.derived(), internal::add_assign_op()); + return derived(); +} + +template +template +EIGEN_DEVICE_FUNC +Derived& DenseBase::operator-=(const EigenBase &other) +{ + call_assignment(derived(), other.derived(), internal::sub_assign_op()); + return derived(); +} + +} // end namespace Eigen + +#endif // EIGEN_EIGENBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ForceAlignedAccess.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ForceAlignedAccess.h new file mode 100644 index 0000000000000000000000000000000000000000..817a43afced3a74477485099d821dc2bcf4f4e79 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ForceAlignedAccess.h @@ -0,0 +1,150 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_FORCEALIGNEDACCESS_H +#define EIGEN_FORCEALIGNEDACCESS_H + +namespace Eigen { + +/** \class ForceAlignedAccess + * \ingroup Core_Module + * + * \brief Enforce aligned packet loads and stores regardless of what is requested + * + * \param ExpressionType the type of the object of which we are forcing aligned packet access + * + * This class is the return type of MatrixBase::forceAlignedAccess() + * and most of the time this is the only way it is used. + * + * \sa MatrixBase::forceAlignedAccess() + */ + +namespace internal { +template +struct traits > : public traits +{}; +} + +template class ForceAlignedAccess + : public internal::dense_xpr_base< ForceAlignedAccess >::type +{ + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(ForceAlignedAccess) + + EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {} + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return m_expression.outerStride(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT { return m_expression.innerStride(); } + + EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const + { + return m_expression.coeff(row, col); + } + + EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index row, Index col) + { + return m_expression.const_cast_derived().coeffRef(row, col); + } + + EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index index) const + { + return m_expression.coeff(index); + } + + EIGEN_DEVICE_FUNC inline Scalar& coeffRef(Index index) + { + return m_expression.const_cast_derived().coeffRef(index); + } + + template + inline const PacketScalar packet(Index row, Index col) const + { + return m_expression.template packet(row, col); + } + + template + inline void writePacket(Index row, Index col, const PacketScalar& x) + { + m_expression.const_cast_derived().template writePacket(row, col, x); + } + + template + inline const PacketScalar packet(Index index) const + { + return m_expression.template packet(index); + } + + template + inline void writePacket(Index index, const PacketScalar& x) + { + m_expression.const_cast_derived().template writePacket(index, x); + } + + EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; } + + protected: + const ExpressionType& m_expression; + + private: + ForceAlignedAccess& operator=(const ForceAlignedAccess&); +}; + +/** \returns an expression of *this with forced aligned access + * \sa forceAlignedAccessIf(),class ForceAlignedAccess + */ +template +inline const ForceAlignedAccess +MatrixBase::forceAlignedAccess() const +{ + return ForceAlignedAccess(derived()); +} + +/** \returns an expression of *this with forced aligned access + * \sa forceAlignedAccessIf(), class ForceAlignedAccess + */ +template +inline ForceAlignedAccess +MatrixBase::forceAlignedAccess() +{ + return ForceAlignedAccess(derived()); +} + +/** \returns an expression of *this with forced aligned access if \a Enable is true. + * \sa forceAlignedAccess(), class ForceAlignedAccess + */ +template +template +inline typename internal::add_const_on_value_type,Derived&>::type>::type +MatrixBase::forceAlignedAccessIf() const +{ + return derived(); // FIXME This should not work but apparently is never used +} + +/** \returns an expression of *this with forced aligned access if \a Enable is true. + * \sa forceAlignedAccess(), class ForceAlignedAccess + */ +template +template +inline typename internal::conditional,Derived&>::type +MatrixBase::forceAlignedAccessIf() +{ + return derived(); // FIXME This should not work but apparently is never used +} + +} // end namespace Eigen + +#endif // EIGEN_FORCEALIGNEDACCESS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Fuzzy.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Fuzzy.h new file mode 100644 index 0000000000000000000000000000000000000000..43aa49b2bc2f4636b08ecac59d3d2bf3217815b5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Fuzzy.h @@ -0,0 +1,155 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_FUZZY_H +#define EIGEN_FUZZY_H + +namespace Eigen { + +namespace internal +{ + +template::IsInteger> +struct isApprox_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) + { + typename internal::nested_eval::type nested(x); + typename internal::nested_eval::type otherNested(y); + return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * numext::mini(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum()); + } +}; + +template +struct isApprox_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&) + { + return x.matrix() == y.matrix(); + } +}; + +template::IsInteger> +struct isMuchSmallerThan_object_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec) + { + return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum(); + } +}; + +template +struct isMuchSmallerThan_object_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&) + { + return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); + } +}; + +template::IsInteger> +struct isMuchSmallerThan_scalar_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec) + { + return x.cwiseAbs2().sum() <= numext::abs2(prec * y); + } +}; + +template +struct isMuchSmallerThan_scalar_selector +{ + EIGEN_DEVICE_FUNC + static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&) + { + return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix(); + } +}; + +} // end namespace internal + + +/** \returns \c true if \c *this is approximately equal to \a other, within the precision + * determined by \a prec. + * + * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$ + * are considered to be approximately equal within precision \f$ p \f$ if + * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f] + * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm + * L2 norm). + * + * \note Because of the multiplicativeness of this comparison, one can't use this function + * to check whether \c *this is approximately equal to the zero matrix or vector. + * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix + * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const + * RealScalar&, RealScalar) instead. + * + * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const + */ +template +template +EIGEN_DEVICE_FUNC bool DenseBase::isApprox( + const DenseBase& other, + const RealScalar& prec +) const +{ + return internal::isApprox_selector::run(derived(), other.derived(), prec); +} + +/** \returns \c true if the norm of \c *this is much smaller than \a other, + * within the precision determined by \a prec. + * + * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is + * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if + * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f] + * + * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, + * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm + * of a reference matrix of same dimensions. + * + * \sa isApprox(), isMuchSmallerThan(const DenseBase&, RealScalar) const + */ +template +EIGEN_DEVICE_FUNC bool DenseBase::isMuchSmallerThan( + const typename NumTraits::Real& other, + const RealScalar& prec +) const +{ + return internal::isMuchSmallerThan_scalar_selector::run(derived(), other, prec); +} + +/** \returns \c true if the norm of \c *this is much smaller than the norm of \a other, + * within the precision determined by \a prec. + * + * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is + * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if + * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f] + * For matrices, the comparison is done using the Hilbert-Schmidt norm. + * + * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const + */ +template +template +EIGEN_DEVICE_FUNC bool DenseBase::isMuchSmallerThan( + const DenseBase& other, + const RealScalar& prec +) const +{ + return internal::isMuchSmallerThan_object_selector::run(derived(), other.derived(), prec); +} + +} // end namespace Eigen + +#endif // EIGEN_FUZZY_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GeneralProduct.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GeneralProduct.h new file mode 100644 index 0000000000000000000000000000000000000000..6906aa75d106c4b2ccb12e0848d4d42b5ecc9e9f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GeneralProduct.h @@ -0,0 +1,465 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2008-2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_GENERAL_PRODUCT_H +#define EIGEN_GENERAL_PRODUCT_H + +namespace Eigen { + +enum { + Large = 2, + Small = 3 +}; + +// Define the threshold value to fallback from the generic matrix-matrix product +// implementation (heavy) to the lightweight coeff-based product one. +// See generic_product_impl +// in products/GeneralMatrixMatrix.h for more details. +// TODO This threshold should also be used in the compile-time selector below. +#ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD +// This default value has been obtained on a Haswell architecture. +#define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20 +#endif + +namespace internal { + +template struct product_type_selector; + +template struct product_size_category +{ + enum { + #ifndef EIGEN_GPU_COMPILE_PHASE + is_large = MaxSize == Dynamic || + Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD || + (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD), + #else + is_large = 0, + #endif + value = is_large ? Large + : Size == 1 ? 1 + : Small + }; +}; + +template struct product_type +{ + typedef typename remove_all::type _Lhs; + typedef typename remove_all::type _Rhs; + enum { + MaxRows = traits<_Lhs>::MaxRowsAtCompileTime, + Rows = traits<_Lhs>::RowsAtCompileTime, + MaxCols = traits<_Rhs>::MaxColsAtCompileTime, + Cols = traits<_Rhs>::ColsAtCompileTime, + MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime, + traits<_Rhs>::MaxRowsAtCompileTime), + Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime, + traits<_Rhs>::RowsAtCompileTime) + }; + + // the splitting into different lines of code here, introducing the _select enums and the typedef below, + // is to work around an internal compiler error with gcc 4.1 and 4.2. +private: + enum { + rows_select = product_size_category::value, + cols_select = product_size_category::value, + depth_select = product_size_category::value + }; + typedef product_type_selector selector; + +public: + enum { + value = selector::ret, + ret = selector::ret + }; +#ifdef EIGEN_DEBUG_PRODUCT + static void debug() + { + EIGEN_DEBUG_VAR(Rows); + EIGEN_DEBUG_VAR(Cols); + EIGEN_DEBUG_VAR(Depth); + EIGEN_DEBUG_VAR(rows_select); + EIGEN_DEBUG_VAR(cols_select); + EIGEN_DEBUG_VAR(depth_select); + EIGEN_DEBUG_VAR(value); + } +#endif +}; + +/* The following allows to select the kind of product at compile time + * based on the three dimensions of the product. + * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */ +// FIXME I'm not sure the current mapping is the ideal one. +template struct product_type_selector { enum { ret = OuterProduct }; }; +template struct product_type_selector { enum { ret = LazyCoeffBasedProductMode }; }; +template struct product_type_selector<1, N, 1> { enum { ret = LazyCoeffBasedProductMode }; }; +template struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; }; +template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = LazyCoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = LazyCoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = LazyCoeffBasedProductMode }; }; +template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; }; +template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = GemvProduct }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = GemmProduct }; }; +template<> struct product_type_selector { enum { ret = GemmProduct }; }; +template<> struct product_type_selector { enum { ret = GemmProduct }; }; +template<> struct product_type_selector { enum { ret = GemmProduct }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = CoeffBasedProductMode }; }; +template<> struct product_type_selector { enum { ret = GemmProduct }; }; + +} // end namespace internal + +/*********************************************************************** +* Implementation of Inner Vector Vector Product +***********************************************************************/ + +// FIXME : maybe the "inner product" could return a Scalar +// instead of a 1x1 matrix ?? +// Pro: more natural for the user +// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix +// product ends up to a row-vector times col-vector product... To tackle this use +// case, we could have a specialization for Block with: operator=(Scalar x); + +/*********************************************************************** +* Implementation of Outer Vector Vector Product +***********************************************************************/ + +/*********************************************************************** +* Implementation of General Matrix Vector Product +***********************************************************************/ + +/* According to the shape/flags of the matrix we have to distinghish 3 different cases: + * 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine + * 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine + * 3 - all other cases are handled using a simple loop along the outer-storage direction. + * Therefore we need a lower level meta selector. + * Furthermore, if the matrix is the rhs, then the product has to be transposed. + */ +namespace internal { + +template +struct gemv_dense_selector; + +} // end namespace internal + +namespace internal { + +template struct gemv_static_vector_if; + +template +struct gemv_static_vector_if +{ + EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; } +}; + +template +struct gemv_static_vector_if +{ + EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { return 0; } +}; + +template +struct gemv_static_vector_if +{ + enum { + ForceAlignment = internal::packet_traits::Vectorizable, + PacketSize = internal::packet_traits::size + }; + #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0 + internal::plain_array m_data; + EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; } + #else + // Some architectures cannot align on the stack, + // => let's manually enforce alignment by allocating more data and return the address of the first aligned element. + internal::plain_array m_data; + EIGEN_STRONG_INLINE Scalar* data() { + return ForceAlignment + ? reinterpret_cast((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES) + : m_data.array; + } + #endif +}; + +// The vector is on the left => transposition +template +struct gemv_dense_selector +{ + template + static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha) + { + Transpose destT(dest); + enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor }; + gemv_dense_selector + ::run(rhs.transpose(), lhs.transpose(), destT, alpha); + } +}; + +template<> struct gemv_dense_selector +{ + template + static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha) + { + typedef typename Lhs::Scalar LhsScalar; + typedef typename Rhs::Scalar RhsScalar; + typedef typename Dest::Scalar ResScalar; + typedef typename Dest::RealScalar RealScalar; + + typedef internal::blas_traits LhsBlasTraits; + typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType; + typedef internal::blas_traits RhsBlasTraits; + typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType; + + typedef Map, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits::size)> MappedDest; + + ActualLhsType actualLhs = LhsBlasTraits::extract(lhs); + ActualRhsType actualRhs = RhsBlasTraits::extract(rhs); + + ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs); + + // make sure Dest is a compile-time vector type (bug 1166) + typedef typename conditional::type ActualDest; + + enum { + // FIXME find a way to allow an inner stride on the result if packet_traits::size==1 + // on, the other hand it is good for the cache to pack the vector anyways... + EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1), + ComplexByReal = (NumTraits::IsComplex) && (!NumTraits::IsComplex), + MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime!=0) + }; + + typedef const_blas_data_mapper LhsMapper; + typedef const_blas_data_mapper RhsMapper; + RhsScalar compatibleAlpha = get_factor::run(actualAlpha); + + if(!MightCannotUseDest) + { + // shortcut if we are sure to be able to use dest directly, + // this ease the compiler to generate cleaner and more optimzized code for most common cases + general_matrix_vector_product + ::run( + actualLhs.rows(), actualLhs.cols(), + LhsMapper(actualLhs.data(), actualLhs.outerStride()), + RhsMapper(actualRhs.data(), actualRhs.innerStride()), + dest.data(), 1, + compatibleAlpha); + } + else + { + gemv_static_vector_if static_dest; + + const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0)); + const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible; + + ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(), + evalToDest ? dest.data() : static_dest.data()); + + if(!evalToDest) + { + #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN + Index size = dest.size(); + EIGEN_DENSE_STORAGE_CTOR_PLUGIN + #endif + if(!alphaIsCompatible) + { + MappedDest(actualDestPtr, dest.size()).setZero(); + compatibleAlpha = RhsScalar(1); + } + else + MappedDest(actualDestPtr, dest.size()) = dest; + } + + general_matrix_vector_product + ::run( + actualLhs.rows(), actualLhs.cols(), + LhsMapper(actualLhs.data(), actualLhs.outerStride()), + RhsMapper(actualRhs.data(), actualRhs.innerStride()), + actualDestPtr, 1, + compatibleAlpha); + + if (!evalToDest) + { + if(!alphaIsCompatible) + dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size()); + else + dest = MappedDest(actualDestPtr, dest.size()); + } + } + } +}; + +template<> struct gemv_dense_selector +{ + template + static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha) + { + typedef typename Lhs::Scalar LhsScalar; + typedef typename Rhs::Scalar RhsScalar; + typedef typename Dest::Scalar ResScalar; + + typedef internal::blas_traits LhsBlasTraits; + typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType; + typedef internal::blas_traits RhsBlasTraits; + typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType; + typedef typename internal::remove_all::type ActualRhsTypeCleaned; + + typename add_const::type actualLhs = LhsBlasTraits::extract(lhs); + typename add_const::type actualRhs = RhsBlasTraits::extract(rhs); + + ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs); + + enum { + // FIXME find a way to allow an inner stride on the result if packet_traits::size==1 + // on, the other hand it is good for the cache to pack the vector anyways... + DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime==0 + }; + + gemv_static_vector_if static_rhs; + + ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(), + DirectlyUseRhs ? const_cast(actualRhs.data()) : static_rhs.data()); + + if(!DirectlyUseRhs) + { + #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN + Index size = actualRhs.size(); + EIGEN_DENSE_STORAGE_CTOR_PLUGIN + #endif + Map(actualRhsPtr, actualRhs.size()) = actualRhs; + } + + typedef const_blas_data_mapper LhsMapper; + typedef const_blas_data_mapper RhsMapper; + general_matrix_vector_product + ::run( + actualLhs.rows(), actualLhs.cols(), + LhsMapper(actualLhs.data(), actualLhs.outerStride()), + RhsMapper(actualRhsPtr, 1), + dest.data(), dest.col(0).innerStride(), //NOTE if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166) + actualAlpha); + } +}; + +template<> struct gemv_dense_selector +{ + template + static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha) + { + EIGEN_STATIC_ASSERT((!nested_eval::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE); + // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp + typename nested_eval::type actual_rhs(rhs); + const Index size = rhs.rows(); + for(Index k=0; k struct gemv_dense_selector +{ + template + static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha) + { + EIGEN_STATIC_ASSERT((!nested_eval::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE); + typename nested_eval::type actual_rhs(rhs); + const Index rows = dest.rows(); + for(Index i=0; i +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +const Product +MatrixBase::operator*(const MatrixBase &other) const +{ + // A note regarding the function declaration: In MSVC, this function will sometimes + // not be inlined since DenseStorage is an unwindable object for dynamic + // matrices and product types are holding a member to store the result. + // Thus it does not help tagging this function with EIGEN_STRONG_INLINE. + enum { + ProductIsValid = Derived::ColsAtCompileTime==Dynamic + || OtherDerived::RowsAtCompileTime==Dynamic + || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime), + AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime, + SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived) + }; + // note to the lost user: + // * for a dot product use: v1.dot(v2) + // * for a coeff-wise product use: v1.cwiseProduct(v2) + EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes), + INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS) + EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors), + INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION) + EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT) +#ifdef EIGEN_DEBUG_PRODUCT + internal::product_type::debug(); +#endif + + return Product(derived(), other.derived()); +} + +/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation. + * + * The returned product will behave like any other expressions: the coefficients of the product will be + * computed once at a time as requested. This might be useful in some extremely rare cases when only + * a small and no coherent fraction of the result's coefficients have to be computed. + * + * \warning This version of the matrix product can be much much slower. So use it only if you know + * what you are doing and that you measured a true speed improvement. + * + * \sa operator*(const MatrixBase&) + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +const Product +MatrixBase::lazyProduct(const MatrixBase &other) const +{ + enum { + ProductIsValid = Derived::ColsAtCompileTime==Dynamic + || OtherDerived::RowsAtCompileTime==Dynamic + || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime), + AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime, + SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived) + }; + // note to the lost user: + // * for a dot product use: v1.dot(v2) + // * for a coeff-wise product use: v1.cwiseProduct(v2) + EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes), + INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS) + EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors), + INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION) + EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT) + + return Product(derived(), other.derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_PRODUCT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GenericPacketMath.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GenericPacketMath.h new file mode 100644 index 0000000000000000000000000000000000000000..cf677a1905f1e80697eb6c0daccb48f745c605e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GenericPacketMath.h @@ -0,0 +1,1040 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_GENERIC_PACKET_MATH_H +#define EIGEN_GENERIC_PACKET_MATH_H + +namespace Eigen { + +namespace internal { + +/** \internal + * \file GenericPacketMath.h + * + * Default implementation for types not supported by the vectorization. + * In practice these functions are provided to make easier the writing + * of generic vectorized code. + */ + +#ifndef EIGEN_DEBUG_ALIGNED_LOAD +#define EIGEN_DEBUG_ALIGNED_LOAD +#endif + +#ifndef EIGEN_DEBUG_UNALIGNED_LOAD +#define EIGEN_DEBUG_UNALIGNED_LOAD +#endif + +#ifndef EIGEN_DEBUG_ALIGNED_STORE +#define EIGEN_DEBUG_ALIGNED_STORE +#endif + +#ifndef EIGEN_DEBUG_UNALIGNED_STORE +#define EIGEN_DEBUG_UNALIGNED_STORE +#endif + +struct default_packet_traits +{ + enum { + HasHalfPacket = 0, + + HasAdd = 1, + HasSub = 1, + HasShift = 1, + HasMul = 1, + HasNegate = 1, + HasAbs = 1, + HasArg = 0, + HasAbs2 = 1, + HasAbsDiff = 0, + HasMin = 1, + HasMax = 1, + HasConj = 1, + HasSetLinear = 1, + HasBlend = 0, + // This flag is used to indicate whether packet comparison is supported. + // pcmp_eq, pcmp_lt and pcmp_le should be defined for it to be true. + HasCmp = 0, + + HasDiv = 0, + HasSqrt = 0, + HasRsqrt = 0, + HasExp = 0, + HasExpm1 = 0, + HasLog = 0, + HasLog1p = 0, + HasLog10 = 0, + HasPow = 0, + + HasSin = 0, + HasCos = 0, + HasTan = 0, + HasASin = 0, + HasACos = 0, + HasATan = 0, + HasSinh = 0, + HasCosh = 0, + HasTanh = 0, + HasLGamma = 0, + HasDiGamma = 0, + HasZeta = 0, + HasPolygamma = 0, + HasErf = 0, + HasErfc = 0, + HasNdtri = 0, + HasBessel = 0, + HasIGamma = 0, + HasIGammaDerA = 0, + HasGammaSampleDerAlpha = 0, + HasIGammac = 0, + HasBetaInc = 0, + + HasRound = 0, + HasRint = 0, + HasFloor = 0, + HasCeil = 0, + HasSign = 0 + }; +}; + +template struct packet_traits : default_packet_traits +{ + typedef T type; + typedef T half; + enum { + Vectorizable = 0, + size = 1, + AlignedOnScalar = 0, + HasHalfPacket = 0 + }; + enum { + HasAdd = 0, + HasSub = 0, + HasMul = 0, + HasNegate = 0, + HasAbs = 0, + HasAbs2 = 0, + HasMin = 0, + HasMax = 0, + HasConj = 0, + HasSetLinear = 0 + }; +}; + +template struct packet_traits : packet_traits { }; + +template struct unpacket_traits +{ + typedef T type; + typedef T half; + enum + { + size = 1, + alignment = 1, + vectorizable = false, + masked_load_available=false, + masked_store_available=false + }; +}; + +template struct unpacket_traits : unpacket_traits { }; + +template struct type_casting_traits { + enum { + VectorizedCast = 0, + SrcCoeffRatio = 1, + TgtCoeffRatio = 1 + }; +}; + +/** \internal Wrapper to ensure that multiple packet types can map to the same + same underlying vector type. */ +template +struct eigen_packet_wrapper +{ + EIGEN_ALWAYS_INLINE operator T&() { return m_val; } + EIGEN_ALWAYS_INLINE operator const T&() const { return m_val; } + EIGEN_ALWAYS_INLINE eigen_packet_wrapper() {} + EIGEN_ALWAYS_INLINE eigen_packet_wrapper(const T &v) : m_val(v) {} + EIGEN_ALWAYS_INLINE eigen_packet_wrapper& operator=(const T &v) { + m_val = v; + return *this; + } + + T m_val; +}; + + +/** \internal A convenience utility for determining if the type is a scalar. + * This is used to enable some generic packet implementations. + */ +template +struct is_scalar { + typedef typename unpacket_traits::type Scalar; + enum { + value = internal::is_same::value + }; +}; + +/** \internal \returns static_cast(a) (coeff-wise) */ +template +EIGEN_DEVICE_FUNC inline TgtPacket +pcast(const SrcPacket& a) { + return static_cast(a); +} +template +EIGEN_DEVICE_FUNC inline TgtPacket +pcast(const SrcPacket& a, const SrcPacket& /*b*/) { + return static_cast(a); +} +template +EIGEN_DEVICE_FUNC inline TgtPacket +pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) { + return static_cast(a); +} +template +EIGEN_DEVICE_FUNC inline TgtPacket +pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/, + const SrcPacket& /*e*/, const SrcPacket& /*f*/, const SrcPacket& /*g*/, const SrcPacket& /*h*/) { + return static_cast(a); +} + +/** \internal \returns reinterpret_cast(a) */ +template +EIGEN_DEVICE_FUNC inline Target +preinterpret(const Packet& a); /* { return reinterpret_cast(a); } */ + +/** \internal \returns a + b (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +padd(const Packet& a, const Packet& b) { return a+b; } +// Avoid compiler warning for boolean algebra. +template<> EIGEN_DEVICE_FUNC inline bool +padd(const bool& a, const bool& b) { return a || b; } + +/** \internal \returns a - b (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +psub(const Packet& a, const Packet& b) { return a-b; } + +/** \internal \returns -a (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pnegate(const Packet& a) { return -a; } + +template<> EIGEN_DEVICE_FUNC inline bool +pnegate(const bool& a) { return !a; } + +/** \internal \returns conj(a) (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pconj(const Packet& a) { return numext::conj(a); } + +/** \internal \returns a * b (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pmul(const Packet& a, const Packet& b) { return a*b; } +// Avoid compiler warning for boolean algebra. +template<> EIGEN_DEVICE_FUNC inline bool +pmul(const bool& a, const bool& b) { return a && b; } + +/** \internal \returns a / b (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pdiv(const Packet& a, const Packet& b) { return a/b; } + +// In the generic case, memset to all one bits. +template +struct ptrue_impl { + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/){ + Packet b; + memset(static_cast(&b), 0xff, sizeof(Packet)); + return b; + } +}; + +// For non-trivial scalars, set to Scalar(1) (i.e. a non-zero value). +// Although this is technically not a valid bitmask, the scalar path for pselect +// uses a comparison to zero, so this should still work in most cases. We don't +// have another option, since the scalar type requires initialization. +template +struct ptrue_impl::value && NumTraits::RequireInitialization>::type > { + static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/){ + return T(1); + } +}; + +/** \internal \returns one bits. */ +template EIGEN_DEVICE_FUNC inline Packet +ptrue(const Packet& a) { + return ptrue_impl::run(a); +} + +// In the general case, memset to zero. +template +struct pzero_impl { + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/) { + Packet b; + memset(static_cast(&b), 0x00, sizeof(Packet)); + return b; + } +}; + +// For scalars, explicitly set to Scalar(0), since the underlying representation +// for zero may not consist of all-zero bits. +template +struct pzero_impl::value>::type> { + static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/) { + return T(0); + } +}; + +/** \internal \returns packet of zeros */ +template EIGEN_DEVICE_FUNC inline Packet +pzero(const Packet& a) { + return pzero_impl::run(a); +} + +/** \internal \returns a <= b as a bit mask */ +template EIGEN_DEVICE_FUNC inline Packet +pcmp_le(const Packet& a, const Packet& b) { return a<=b ? ptrue(a) : pzero(a); } + +/** \internal \returns a < b as a bit mask */ +template EIGEN_DEVICE_FUNC inline Packet +pcmp_lt(const Packet& a, const Packet& b) { return a EIGEN_DEVICE_FUNC inline Packet +pcmp_eq(const Packet& a, const Packet& b) { return a==b ? ptrue(a) : pzero(a); } + +/** \internal \returns a < b or a==NaN or b==NaN as a bit mask */ +template EIGEN_DEVICE_FUNC inline Packet +pcmp_lt_or_nan(const Packet& a, const Packet& b) { return a>=b ? pzero(a) : ptrue(a); } + +template +struct bit_and { + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { + return a & b; + } +}; + +template +struct bit_or { + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { + return a | b; + } +}; + +template +struct bit_xor { + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { + return a ^ b; + } +}; + +template +struct bit_not { + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a) const { + return ~a; + } +}; + +// Use operators &, |, ^, ~. +template +struct operator_bitwise_helper { + EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b) { return bit_and()(a, b); } + EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b) { return bit_or()(a, b); } + EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b) { return bit_xor()(a, b); } + EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) { return bit_not()(a); } +}; + +// Apply binary operations byte-by-byte +template +struct bytewise_bitwise_helper { + EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b) { + return binary(a, b, bit_and()); + } + EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b) { + return binary(a, b, bit_or()); + } + EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b) { + return binary(a, b, bit_xor()); + } + EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) { + return unary(a,bit_not()); + } + + private: + template + EIGEN_DEVICE_FUNC static inline T unary(const T& a, Op op) { + const unsigned char* a_ptr = reinterpret_cast(&a); + T c; + unsigned char* c_ptr = reinterpret_cast(&c); + for (size_t i = 0; i < sizeof(T); ++i) { + *c_ptr++ = op(*a_ptr++); + } + return c; + } + + template + EIGEN_DEVICE_FUNC static inline T binary(const T& a, const T& b, Op op) { + const unsigned char* a_ptr = reinterpret_cast(&a); + const unsigned char* b_ptr = reinterpret_cast(&b); + T c; + unsigned char* c_ptr = reinterpret_cast(&c); + for (size_t i = 0; i < sizeof(T); ++i) { + *c_ptr++ = op(*a_ptr++, *b_ptr++); + } + return c; + } +}; + +// In the general case, use byte-by-byte manipulation. +template +struct bitwise_helper : public bytewise_bitwise_helper {}; + +// For integers or non-trivial scalars, use binary operators. +template +struct bitwise_helper::value && (NumTraits::IsInteger || NumTraits::RequireInitialization)>::type + > : public operator_bitwise_helper {}; + +/** \internal \returns the bitwise and of \a a and \a b */ +template EIGEN_DEVICE_FUNC inline Packet +pand(const Packet& a, const Packet& b) { + return bitwise_helper::bitwise_and(a, b); +} + +/** \internal \returns the bitwise or of \a a and \a b */ +template EIGEN_DEVICE_FUNC inline Packet +por(const Packet& a, const Packet& b) { + return bitwise_helper::bitwise_or(a, b); +} + +/** \internal \returns the bitwise xor of \a a and \a b */ +template EIGEN_DEVICE_FUNC inline Packet +pxor(const Packet& a, const Packet& b) { + return bitwise_helper::bitwise_xor(a, b); +} + +/** \internal \returns the bitwise not of \a a */ +template EIGEN_DEVICE_FUNC inline Packet +pnot(const Packet& a) { + return bitwise_helper::bitwise_not(a); +} + +/** \internal \returns the bitwise and of \a a and not \a b */ +template EIGEN_DEVICE_FUNC inline Packet +pandnot(const Packet& a, const Packet& b) { return pand(a, pnot(b)); } + +// In the general case, use bitwise select. +template +struct pselect_impl { + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) { + return por(pand(a,mask),pandnot(b,mask)); + } +}; + +// For scalars, use ternary select. +template +struct pselect_impl::value>::type > { + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) { + return numext::equal_strict(mask, Packet(0)) ? b : a; + } +}; + +/** \internal \returns \a or \b for each field in packet according to \mask */ +template EIGEN_DEVICE_FUNC inline Packet +pselect(const Packet& mask, const Packet& a, const Packet& b) { + return pselect_impl::run(mask, a, b); +} + +template<> EIGEN_DEVICE_FUNC inline bool pselect( + const bool& cond, const bool& a, const bool& b) { + return cond ? a : b; +} + +/** \internal \returns the min or of \a a and \a b (coeff-wise) + If either \a a or \a b are NaN, the result is implementation defined. */ +template +struct pminmax_impl { + template + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) { + return op(a,b); + } +}; + +/** \internal \returns the min or max of \a a and \a b (coeff-wise) + If either \a a or \a b are NaN, NaN is returned. */ +template<> +struct pminmax_impl { + template + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) { + Packet not_nan_mask_a = pcmp_eq(a, a); + Packet not_nan_mask_b = pcmp_eq(b, b); + return pselect(not_nan_mask_a, + pselect(not_nan_mask_b, op(a, b), b), + a); + } +}; + +/** \internal \returns the min or max of \a a and \a b (coeff-wise) + If both \a a and \a b are NaN, NaN is returned. + Equivalent to std::fmin(a, b). */ +template<> +struct pminmax_impl { + template + static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) { + Packet not_nan_mask_a = pcmp_eq(a, a); + Packet not_nan_mask_b = pcmp_eq(b, b); + return pselect(not_nan_mask_a, + pselect(not_nan_mask_b, op(a, b), a), + b); + } +}; + + +#ifndef SYCL_DEVICE_ONLY +#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) Func +#else +#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) \ +[](const Type& a, const Type& b) { \ + return Func(a, b);} +#endif + +/** \internal \returns the min of \a a and \a b (coeff-wise). + If \a a or \b b is NaN, the return value is implementation defined. */ +template EIGEN_DEVICE_FUNC inline Packet +pmin(const Packet& a, const Packet& b) { return numext::mini(a,b); } + +/** \internal \returns the min of \a a and \a b (coeff-wise). + NaNPropagation determines the NaN propagation semantics. */ +template +EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) { + return pminmax_impl::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmin))); +} + +/** \internal \returns the max of \a a and \a b (coeff-wise) + If \a a or \b b is NaN, the return value is implementation defined. */ +template EIGEN_DEVICE_FUNC inline Packet +pmax(const Packet& a, const Packet& b) { return numext::maxi(a, b); } + +/** \internal \returns the max of \a a and \a b (coeff-wise). + NaNPropagation determines the NaN propagation semantics. */ +template +EIGEN_DEVICE_FUNC inline Packet pmax(const Packet& a, const Packet& b) { + return pminmax_impl::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet,(pmax))); +} + +/** \internal \returns the absolute value of \a a */ +template EIGEN_DEVICE_FUNC inline Packet +pabs(const Packet& a) { return numext::abs(a); } +template<> EIGEN_DEVICE_FUNC inline unsigned int +pabs(const unsigned int& a) { return a; } +template<> EIGEN_DEVICE_FUNC inline unsigned long +pabs(const unsigned long& a) { return a; } +template<> EIGEN_DEVICE_FUNC inline unsigned long long +pabs(const unsigned long long& a) { return a; } + +/** \internal \returns the addsub value of \a a,b */ +template EIGEN_DEVICE_FUNC inline Packet +paddsub(const Packet& a, const Packet& b) { + return pselect(peven_mask(a), padd(a, b), psub(a, b)); + } + +/** \internal \returns the phase angle of \a a */ +template EIGEN_DEVICE_FUNC inline Packet +parg(const Packet& a) { using numext::arg; return arg(a); } + + +/** \internal \returns \a a logically shifted by N bits to the right */ +template EIGEN_DEVICE_FUNC inline int +parithmetic_shift_right(const int& a) { return a >> N; } +template EIGEN_DEVICE_FUNC inline long int +parithmetic_shift_right(const long int& a) { return a >> N; } + +/** \internal \returns \a a arithmetically shifted by N bits to the right */ +template EIGEN_DEVICE_FUNC inline int +plogical_shift_right(const int& a) { return static_cast(static_cast(a) >> N); } +template EIGEN_DEVICE_FUNC inline long int +plogical_shift_right(const long int& a) { return static_cast(static_cast(a) >> N); } + +/** \internal \returns \a a shifted by N bits to the left */ +template EIGEN_DEVICE_FUNC inline int +plogical_shift_left(const int& a) { return a << N; } +template EIGEN_DEVICE_FUNC inline long int +plogical_shift_left(const long int& a) { return a << N; } + +/** \internal \returns the significant and exponent of the underlying floating point numbers + * See https://en.cppreference.com/w/cpp/numeric/math/frexp + */ +template +EIGEN_DEVICE_FUNC inline Packet pfrexp(const Packet& a, Packet& exponent) { + int exp; + EIGEN_USING_STD(frexp); + Packet result = static_cast(frexp(a, &exp)); + exponent = static_cast(exp); + return result; +} + +/** \internal \returns a * 2^((int)exponent) + * See https://en.cppreference.com/w/cpp/numeric/math/ldexp + */ +template EIGEN_DEVICE_FUNC inline Packet +pldexp(const Packet &a, const Packet &exponent) { + EIGEN_USING_STD(ldexp) + return static_cast(ldexp(a, static_cast(exponent))); +} + +/** \internal \returns the min of \a a and \a b (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pabsdiff(const Packet& a, const Packet& b) { return pselect(pcmp_lt(a, b), psub(b, a), psub(a, b)); } + +/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */ +template EIGEN_DEVICE_FUNC inline Packet +pload(const typename unpacket_traits::type* from) { return *from; } + +/** \internal \returns a packet version of \a *from, (un-aligned load) */ +template EIGEN_DEVICE_FUNC inline Packet +ploadu(const typename unpacket_traits::type* from) { return *from; } + +/** \internal \returns a packet version of \a *from, (un-aligned masked load) + * There is no generic implementation. We only have implementations for specialized + * cases. Generic case should not be called. + */ +template EIGEN_DEVICE_FUNC inline +typename enable_if::masked_load_available, Packet>::type +ploadu(const typename unpacket_traits::type* from, typename unpacket_traits::mask_t umask); + +/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */ +template EIGEN_DEVICE_FUNC inline Packet +pset1(const typename unpacket_traits::type& a) { return a; } + +/** \internal \returns a packet with constant coefficients set from bits */ +template EIGEN_DEVICE_FUNC inline Packet +pset1frombits(BitsType a); + +/** \internal \returns a packet with constant coefficients \a a[0], e.g.: (a[0],a[0],a[0],a[0]) */ +template EIGEN_DEVICE_FUNC inline Packet +pload1(const typename unpacket_traits::type *a) { return pset1(*a); } + +/** \internal \returns a packet with elements of \a *from duplicated. + * For instance, for a packet of 8 elements, 4 scalars will be read from \a *from and + * duplicated to form: {from[0],from[0],from[1],from[1],from[2],from[2],from[3],from[3]} + * Currently, this function is only used for scalar * complex products. + */ +template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet +ploaddup(const typename unpacket_traits::type* from) { return *from; } + +/** \internal \returns a packet with elements of \a *from quadrupled. + * For instance, for a packet of 8 elements, 2 scalars will be read from \a *from and + * replicated to form: {from[0],from[0],from[0],from[0],from[1],from[1],from[1],from[1]} + * Currently, this function is only used in matrix products. + * For packet-size smaller or equal to 4, this function is equivalent to pload1 + */ +template EIGEN_DEVICE_FUNC inline Packet +ploadquad(const typename unpacket_traits::type* from) +{ return pload1(from); } + +/** \internal equivalent to + * \code + * a0 = pload1(a+0); + * a1 = pload1(a+1); + * a2 = pload1(a+2); + * a3 = pload1(a+3); + * \endcode + * \sa pset1, pload1, ploaddup, pbroadcast2 + */ +template EIGEN_DEVICE_FUNC +inline void pbroadcast4(const typename unpacket_traits::type *a, + Packet& a0, Packet& a1, Packet& a2, Packet& a3) +{ + a0 = pload1(a+0); + a1 = pload1(a+1); + a2 = pload1(a+2); + a3 = pload1(a+3); +} + +/** \internal equivalent to + * \code + * a0 = pload1(a+0); + * a1 = pload1(a+1); + * \endcode + * \sa pset1, pload1, ploaddup, pbroadcast4 + */ +template EIGEN_DEVICE_FUNC +inline void pbroadcast2(const typename unpacket_traits::type *a, + Packet& a0, Packet& a1) +{ + a0 = pload1(a+0); + a1 = pload1(a+1); +} + +/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */ +template EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet +plset(const typename unpacket_traits::type& a) { return a; } + +/** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0), + where x is the value of all 1-bits. */ +template EIGEN_DEVICE_FUNC inline Packet +peven_mask(const Packet& /*a*/) { + typedef typename unpacket_traits::type Scalar; + const size_t n = unpacket_traits::size; + EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n]; + for(size_t i = 0; i < n; ++i) { + memset(elements+i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar)); + } + return ploadu(elements); +} + + +/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */ +template EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from) +{ (*to) = from; } + +/** \internal copy the packet \a from to \a *to, (un-aligned store) */ +template EIGEN_DEVICE_FUNC inline void pstoreu(Scalar* to, const Packet& from) +{ (*to) = from; } + +/** \internal copy the packet \a from to \a *to, (un-aligned store with a mask) + * There is no generic implementation. We only have implementations for specialized + * cases. Generic case should not be called. + */ +template +EIGEN_DEVICE_FUNC inline +typename enable_if::masked_store_available, void>::type +pstoreu(Scalar* to, const Packet& from, typename unpacket_traits::mask_t umask); + + template EIGEN_DEVICE_FUNC inline Packet pgather(const Scalar* from, Index /*stride*/) + { return ploadu(from); } + + template EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from, Index /*stride*/) + { pstore(to, from); } + +/** \internal tries to do cache prefetching of \a addr */ +template EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr) +{ +#if defined(EIGEN_HIP_DEVICE_COMPILE) + // do nothing +#elif defined(EIGEN_CUDA_ARCH) +#if defined(__LP64__) || EIGEN_OS_WIN64 + // 64-bit pointer operand constraint for inlined asm + asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr)); +#else + // 32-bit pointer operand constraint for inlined asm + asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr)); +#endif +#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC) + __builtin_prefetch(addr); +#endif +} + +/** \internal \returns the reversed elements of \a a*/ +template EIGEN_DEVICE_FUNC inline Packet preverse(const Packet& a) +{ return a; } + +/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */ +template EIGEN_DEVICE_FUNC inline Packet pcplxflip(const Packet& a) +{ + return Packet(numext::imag(a),numext::real(a)); +} + +/************************** +* Special math functions +***************************/ + +/** \internal \returns the sine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet psin(const Packet& a) { EIGEN_USING_STD(sin); return sin(a); } + +/** \internal \returns the cosine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pcos(const Packet& a) { EIGEN_USING_STD(cos); return cos(a); } + +/** \internal \returns the tan of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet ptan(const Packet& a) { EIGEN_USING_STD(tan); return tan(a); } + +/** \internal \returns the arc sine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pasin(const Packet& a) { EIGEN_USING_STD(asin); return asin(a); } + +/** \internal \returns the arc cosine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pacos(const Packet& a) { EIGEN_USING_STD(acos); return acos(a); } + +/** \internal \returns the arc tangent of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet patan(const Packet& a) { EIGEN_USING_STD(atan); return atan(a); } + +/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet psinh(const Packet& a) { EIGEN_USING_STD(sinh); return sinh(a); } + +/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pcosh(const Packet& a) { EIGEN_USING_STD(cosh); return cosh(a); } + +/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet ptanh(const Packet& a) { EIGEN_USING_STD(tanh); return tanh(a); } + +/** \internal \returns the exp of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pexp(const Packet& a) { EIGEN_USING_STD(exp); return exp(a); } + +/** \internal \returns the expm1 of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pexpm1(const Packet& a) { return numext::expm1(a); } + +/** \internal \returns the log of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet plog(const Packet& a) { EIGEN_USING_STD(log); return log(a); } + +/** \internal \returns the log1p of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet plog1p(const Packet& a) { return numext::log1p(a); } + +/** \internal \returns the log10 of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet plog10(const Packet& a) { EIGEN_USING_STD(log10); return log10(a); } + +/** \internal \returns the log10 of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet plog2(const Packet& a) { + typedef typename internal::unpacket_traits::type Scalar; + return pmul(pset1(Scalar(EIGEN_LOG2E)), plog(a)); +} + +/** \internal \returns the square-root of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet psqrt(const Packet& a) { return numext::sqrt(a); } + +/** \internal \returns the reciprocal square-root of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet prsqrt(const Packet& a) { + typedef typename internal::unpacket_traits::type Scalar; + return pdiv(pset1(Scalar(1)), psqrt(a)); +} + +/** \internal \returns the rounded value of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pround(const Packet& a) { using numext::round; return round(a); } + +/** \internal \returns the floor of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pfloor(const Packet& a) { using numext::floor; return floor(a); } + +/** \internal \returns the rounded value of \a a (coeff-wise) with current + * rounding mode */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet print(const Packet& a) { using numext::rint; return rint(a); } + +/** \internal \returns the ceil of \a a (coeff-wise) */ +template EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS +Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); } + +/** \internal \returns the first element of a packet */ +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type +pfirst(const Packet& a) +{ return a; } + +/** \internal \returns the sum of the elements of upper and lower half of \a a if \a a is larger than 4. + * For a packet {a0, a1, a2, a3, a4, a5, a6, a7}, it returns a half packet {a0+a4, a1+a5, a2+a6, a3+a7} + * For packet-size smaller or equal to 4, this boils down to a noop. + */ +template +EIGEN_DEVICE_FUNC inline typename conditional<(unpacket_traits::size%8)==0,typename unpacket_traits::half,Packet>::type +predux_half_dowto4(const Packet& a) +{ return a; } + +// Slow generic implementation of Packet reduction. +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type +predux_helper(const Packet& a, Op op) { + typedef typename unpacket_traits::type Scalar; + const size_t n = unpacket_traits::size; + EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n]; + pstoreu(elements, a); + for(size_t k = n / 2; k > 0; k /= 2) { + for(size_t i = 0; i < k; ++i) { + elements[i] = op(elements[i], elements[i + k]); + } + } + return elements[0]; +} + +/** \internal \returns the sum of the elements of \a a*/ +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type +predux(const Packet& a) +{ + return a; +} + +/** \internal \returns the product of the elements of \a a */ +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type predux_mul( + const Packet& a) { + typedef typename unpacket_traits::type Scalar; + return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmul))); +} + +/** \internal \returns the min of the elements of \a a */ +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type predux_min( + const Packet &a) { + typedef typename unpacket_traits::type Scalar; + return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin))); +} + +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type predux_min( + const Packet& a) { + typedef typename unpacket_traits::type Scalar; + return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin))); +} + +/** \internal \returns the min of the elements of \a a */ +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type predux_max( + const Packet &a) { + typedef typename unpacket_traits::type Scalar; + return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax))); +} + +template +EIGEN_DEVICE_FUNC inline typename unpacket_traits::type predux_max( + const Packet& a) { + typedef typename unpacket_traits::type Scalar; + return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax))); +} + +#undef EIGEN_BINARY_OP_NAN_PROPAGATION + +/** \internal \returns true if all coeffs of \a a means "true" + * It is supposed to be called on values returned by pcmp_*. + */ +// not needed yet +// template EIGEN_DEVICE_FUNC inline bool predux_all(const Packet& a) +// { return bool(a); } + +/** \internal \returns true if any coeffs of \a a means "true" + * It is supposed to be called on values returned by pcmp_*. + */ +template EIGEN_DEVICE_FUNC inline bool predux_any(const Packet& a) +{ + // Dirty but generic implementation where "true" is assumed to be non 0 and all the sames. + // It is expected that "true" is either: + // - Scalar(1) + // - bits full of ones (NaN for floats), + // - or first bit equals to 1 (1 for ints, smallest denormal for floats). + // For all these cases, taking the sum is just fine, and this boils down to a no-op for scalars. + typedef typename unpacket_traits::type Scalar; + return numext::not_equal_strict(predux(a), Scalar(0)); +} + +/*************************************************************************** +* The following functions might not have to be overwritten for vectorized types +***************************************************************************/ + +/** \internal copy a packet with constant coefficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */ +// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type) +template +inline void pstore1(typename unpacket_traits::type* to, const typename unpacket_traits::type& a) +{ + pstore(to, pset1(a)); +} + +/** \internal \returns a * b + c (coeff-wise) */ +template EIGEN_DEVICE_FUNC inline Packet +pmadd(const Packet& a, + const Packet& b, + const Packet& c) +{ return padd(pmul(a, b),c); } + +/** \internal \returns a packet version of \a *from. + * The pointer \a from must be aligned on a \a Alignment bytes boundary. */ +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt(const typename unpacket_traits::type* from) +{ + if(Alignment >= unpacket_traits::alignment) + return pload(from); + else + return ploadu(from); +} + +/** \internal copy the packet \a from to \a *to. + * The pointer \a from must be aligned on a \a Alignment bytes boundary. */ +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(Scalar* to, const Packet& from) +{ + if(Alignment >= unpacket_traits::alignment) + pstore(to, from); + else + pstoreu(to, from); +} + +/** \internal \returns a packet version of \a *from. + * Unlike ploadt, ploadt_ro takes advantage of the read-only memory path on the + * hardware if available to speedup the loading of data that won't be modified + * by the current computation. + */ +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_ro(const typename unpacket_traits::type* from) +{ + return ploadt(from); +} + +/*************************************************************************** +* Fast complex products (GCC generates a function call which is very slow) +***************************************************************************/ + +// Eigen+CUDA does not support complexes. +#if !defined(EIGEN_GPUCC) + +template<> inline std::complex pmul(const std::complex& a, const std::complex& b) +{ return std::complex(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); } + +template<> inline std::complex pmul(const std::complex& a, const std::complex& b) +{ return std::complex(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); } + +#endif + + +/*************************************************************************** + * PacketBlock, that is a collection of N packets where the number of words + * in the packet is a multiple of N. +***************************************************************************/ +template ::size> struct PacketBlock { + Packet packet[N]; +}; + +template EIGEN_DEVICE_FUNC inline void +ptranspose(PacketBlock& /*kernel*/) { + // Nothing to do in the scalar case, i.e. a 1x1 matrix. +} + +/*************************************************************************** + * Selector, i.e. vector of N boolean values used to select (i.e. blend) + * words from 2 packets. +***************************************************************************/ +template struct Selector { + bool select[N]; +}; + +template EIGEN_DEVICE_FUNC inline Packet +pblend(const Selector::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) { + return ifPacket.select[0] ? thenPacket : elsePacket; +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_GENERIC_PACKET_MATH_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GlobalFunctions.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GlobalFunctions.h new file mode 100644 index 0000000000000000000000000000000000000000..629af94b9940f3b474b399dd6646cb2b1f1ad29a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/GlobalFunctions.h @@ -0,0 +1,194 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2016 Gael Guennebaud +// Copyright (C) 2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_GLOBAL_FUNCTIONS_H +#define EIGEN_GLOBAL_FUNCTIONS_H + +#ifdef EIGEN_PARSED_BY_DOXYGEN + +#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \ + /** \returns an expression of the coefficient-wise DOC_OP of \a x + + DOC_DETAILS + + \sa Math functions, class CwiseUnaryOp + */ \ + template \ + inline const Eigen::CwiseUnaryOp, const Derived> \ + NAME(const Eigen::ArrayBase& x); + +#else + +#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR,DOC_OP,DOC_DETAILS) \ + template \ + inline const Eigen::CwiseUnaryOp, const Derived> \ + (NAME)(const Eigen::ArrayBase& x) { \ + return Eigen::CwiseUnaryOp, const Derived>(x.derived()); \ + } + +#endif // EIGEN_PARSED_BY_DOXYGEN + +#define EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(NAME,FUNCTOR) \ + \ + template \ + struct NAME##_retval > \ + { \ + typedef const Eigen::CwiseUnaryOp, const Derived> type; \ + }; \ + template \ + struct NAME##_impl > \ + { \ + static inline typename NAME##_retval >::type run(const Eigen::ArrayBase& x) \ + { \ + return typename NAME##_retval >::type(x.derived()); \ + } \ + }; + +namespace Eigen +{ + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op,real part,\sa ArrayBase::real) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op,imaginary part,\sa ArrayBase::imag) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(conj,scalar_conjugate_op,complex conjugate,\sa ArrayBase::conjugate) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(inverse,scalar_inverse_op,inverse,\sa ArrayBase::inverse) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op,sine,\sa ArrayBase::sin) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op,cosine,\sa ArrayBase::cos) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op,tangent,\sa ArrayBase::tan) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atan,scalar_atan_op,arc-tangent,\sa ArrayBase::atan) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op,arc-sine,\sa ArrayBase::asin) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op,arc-consine,\sa ArrayBase::acos) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op,hyperbolic sine,\sa ArrayBase::sinh) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op,hyperbolic cosine,\sa ArrayBase::cosh) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op,hyperbolic tangent,\sa ArrayBase::tanh) +#if EIGEN_HAS_CXX11_MATH + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asinh,scalar_asinh_op,inverse hyperbolic sine,\sa ArrayBase::asinh) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acosh,scalar_acosh_op,inverse hyperbolic cosine,\sa ArrayBase::acosh) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(atanh,scalar_atanh_op,inverse hyperbolic tangent,\sa ArrayBase::atanh) +#endif + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(logistic,scalar_logistic_op,logistic function,\sa ArrayBase::logistic) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op,natural logarithm of the gamma function,\sa ArrayBase::lgamma) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(digamma,scalar_digamma_op,derivative of lgamma,\sa ArrayBase::digamma) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op,error function,\sa ArrayBase::erf) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op,complement error function,\sa ArrayBase::erfc) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri,scalar_ndtri_op,inverse normal distribution function,\sa ArrayBase::ndtri) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op,exponential,\sa ArrayBase::exp) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1,scalar_expm1_op,exponential of a value minus 1,\sa ArrayBase::expm1) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op,natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p,scalar_log1p_op,natural logarithm of 1 plus the value,\sa ArrayBase::log1p) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op,base 10 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log10) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log2,scalar_log2_op,base 2 logarithm,\sa Eigen::log DOXCOMMA ArrayBase::log2) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op,absolute value,\sa ArrayBase::abs DOXCOMMA MatrixBase::cwiseAbs) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs2,scalar_abs2_op,squared absolute value,\sa ArrayBase::abs2 DOXCOMMA MatrixBase::cwiseAbs2) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(arg,scalar_arg_op,complex argument,\sa ArrayBase::arg DOXCOMMA MatrixBase::cwiseArg) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op,square root,\sa ArrayBase::sqrt DOXCOMMA MatrixBase::cwiseSqrt) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rsqrt,scalar_rsqrt_op,reciprocal square root,\sa ArrayBase::rsqrt) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(square,scalar_square_op,square (power 2),\sa Eigen::abs2 DOXCOMMA Eigen::pow DOXCOMMA ArrayBase::square) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cube,scalar_cube_op,cube (power 3),\sa Eigen::pow DOXCOMMA ArrayBase::cube) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(rint,scalar_rint_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(round,scalar_round_op,nearest integer,\sa Eigen::floor DOXCOMMA Eigen::ceil DOXCOMMA ArrayBase::round) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(floor,scalar_floor_op,nearest integer not greater than the giben value,\sa Eigen::ceil DOXCOMMA ArrayBase::floor) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ceil,scalar_ceil_op,nearest integer not less than the giben value,\sa Eigen::floor DOXCOMMA ArrayBase::ceil) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isnan,scalar_isnan_op,not-a-number test,\sa Eigen::isinf DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isnan) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isinf,scalar_isinf_op,infinite value test,\sa Eigen::isnan DOXCOMMA Eigen::isfinite DOXCOMMA ArrayBase::isinf) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(isfinite,scalar_isfinite_op,finite value test,\sa Eigen::isinf DOXCOMMA Eigen::isnan DOXCOMMA ArrayBase::isfinite) + EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sign,scalar_sign_op,sign (or 0),\sa ArrayBase::sign) + + /** \returns an expression of the coefficient-wise power of \a x to the given constant \a exponent. + * + * \tparam ScalarExponent is the scalar type of \a exponent. It must be compatible with the scalar type of the given expression (\c Derived::Scalar). + * + * \sa ArrayBase::pow() + * + * \relates ArrayBase + */ +#ifdef EIGEN_PARSED_BY_DOXYGEN + template + inline const CwiseBinaryOp,Derived,Constant > + pow(const Eigen::ArrayBase& x, const ScalarExponent& exponent); +#else + template + EIGEN_DEVICE_FUNC inline + EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE( + const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg::type,pow)) + pow(const Eigen::ArrayBase& x, const ScalarExponent& exponent) + { + typedef typename internal::promote_scalar_arg::type PromotedExponent; + return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedExponent,pow)(x.derived(), + typename internal::plain_constant_type::type(x.derived().rows(), x.derived().cols(), internal::scalar_constant_op(exponent))); + } +#endif + + /** \returns an expression of the coefficient-wise power of \a x to the given array of \a exponents. + * + * This function computes the coefficient-wise power. + * + * Example: \include Cwise_array_power_array.cpp + * Output: \verbinclude Cwise_array_power_array.out + * + * \sa ArrayBase::pow() + * + * \relates ArrayBase + */ + template + inline const Eigen::CwiseBinaryOp, const Derived, const ExponentDerived> + pow(const Eigen::ArrayBase& x, const Eigen::ArrayBase& exponents) + { + return Eigen::CwiseBinaryOp, const Derived, const ExponentDerived>( + x.derived(), + exponents.derived() + ); + } + + /** \returns an expression of the coefficient-wise power of the scalar \a x to the given array of \a exponents. + * + * This function computes the coefficient-wise power between a scalar and an array of exponents. + * + * \tparam Scalar is the scalar type of \a x. It must be compatible with the scalar type of the given array expression (\c Derived::Scalar). + * + * Example: \include Cwise_scalar_power_array.cpp + * Output: \verbinclude Cwise_scalar_power_array.out + * + * \sa ArrayBase::pow() + * + * \relates ArrayBase + */ +#ifdef EIGEN_PARSED_BY_DOXYGEN + template + inline const CwiseBinaryOp,Constant,Derived> + pow(const Scalar& x,const Eigen::ArrayBase& x); +#else + template + EIGEN_DEVICE_FUNC inline + EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE( + const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg::type,Derived,pow)) + pow(const Scalar& x, const Eigen::ArrayBase& exponents) { + typedef typename internal::promote_scalar_arg::type PromotedScalar; + return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedScalar,Derived,pow)( + typename internal::plain_constant_type::type(exponents.derived().rows(), exponents.derived().cols(), internal::scalar_constant_op(x)), exponents.derived()); + } +#endif + + + namespace internal + { + EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op) + EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op) + EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op) + } +} + +// TODO: cleanly disable those functions that are not supported on Array (numext::real_ref, internal::random, internal::isApprox...) + +#endif // EIGEN_GLOBAL_FUNCTIONS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IO.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IO.h new file mode 100644 index 0000000000000000000000000000000000000000..e81c3152168ba3a3e806ca262a0d2046d729f9d4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IO.h @@ -0,0 +1,258 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_IO_H +#define EIGEN_IO_H + +namespace Eigen { + +enum { DontAlignCols = 1 }; +enum { StreamPrecision = -1, + FullPrecision = -2 }; + +namespace internal { +template +std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt); +} + +/** \class IOFormat + * \ingroup Core_Module + * + * \brief Stores a set of parameters controlling the way matrices are printed + * + * List of available parameters: + * - \b precision number of digits for floating point values, or one of the special constants \c StreamPrecision and \c FullPrecision. + * The default is the special value \c StreamPrecision which means to use the + * stream's own precision setting, as set for instance using \c cout.precision(3). The other special value + * \c FullPrecision means that the number of digits will be computed to match the full precision of each floating-point + * type. + * - \b flags an OR-ed combination of flags, the default value is 0, the only currently available flag is \c DontAlignCols which + * allows to disable the alignment of columns, resulting in faster code. + * - \b coeffSeparator string printed between two coefficients of the same row + * - \b rowSeparator string printed between two rows + * - \b rowPrefix string printed at the beginning of each row + * - \b rowSuffix string printed at the end of each row + * - \b matPrefix string printed at the beginning of the matrix + * - \b matSuffix string printed at the end of the matrix + * - \b fill character printed to fill the empty space in aligned columns + * + * Example: \include IOFormat.cpp + * Output: \verbinclude IOFormat.out + * + * \sa DenseBase::format(), class WithFormat + */ +struct IOFormat +{ + /** Default constructor, see class IOFormat for the meaning of the parameters */ + IOFormat(int _precision = StreamPrecision, int _flags = 0, + const std::string& _coeffSeparator = " ", + const std::string& _rowSeparator = "\n", const std::string& _rowPrefix="", const std::string& _rowSuffix="", + const std::string& _matPrefix="", const std::string& _matSuffix="", const char _fill=' ') + : matPrefix(_matPrefix), matSuffix(_matSuffix), rowPrefix(_rowPrefix), rowSuffix(_rowSuffix), rowSeparator(_rowSeparator), + rowSpacer(""), coeffSeparator(_coeffSeparator), fill(_fill), precision(_precision), flags(_flags) + { + // TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline + // don't add rowSpacer if columns are not to be aligned + if((flags & DontAlignCols)) + return; + int i = int(matSuffix.length())-1; + while (i>=0 && matSuffix[i]!='\n') + { + rowSpacer += ' '; + i--; + } + } + std::string matPrefix, matSuffix; + std::string rowPrefix, rowSuffix, rowSeparator, rowSpacer; + std::string coeffSeparator; + char fill; + int precision; + int flags; +}; + +/** \class WithFormat + * \ingroup Core_Module + * + * \brief Pseudo expression providing matrix output with given format + * + * \tparam ExpressionType the type of the object on which IO stream operations are performed + * + * This class represents an expression with stream operators controlled by a given IOFormat. + * It is the return type of DenseBase::format() + * and most of the time this is the only way it is used. + * + * See class IOFormat for some examples. + * + * \sa DenseBase::format(), class IOFormat + */ +template +class WithFormat +{ + public: + + WithFormat(const ExpressionType& matrix, const IOFormat& format) + : m_matrix(matrix), m_format(format) + {} + + friend std::ostream & operator << (std::ostream & s, const WithFormat& wf) + { + return internal::print_matrix(s, wf.m_matrix.eval(), wf.m_format); + } + + protected: + typename ExpressionType::Nested m_matrix; + IOFormat m_format; +}; + +namespace internal { + +// NOTE: This helper is kept for backward compatibility with previous code specializing +// this internal::significant_decimals_impl structure. In the future we should directly +// call digits10() which has been introduced in July 2016 in 3.3. +template +struct significant_decimals_impl +{ + static inline int run() + { + return NumTraits::digits10(); + } +}; + +/** \internal + * print the matrix \a _m to the output stream \a s using the output format \a fmt */ +template +std::ostream & print_matrix(std::ostream & s, const Derived& _m, const IOFormat& fmt) +{ + using internal::is_same; + using internal::conditional; + + if(_m.size() == 0) + { + s << fmt.matPrefix << fmt.matSuffix; + return s; + } + + typename Derived::Nested m = _m; + typedef typename Derived::Scalar Scalar; + typedef typename + conditional< + is_same::value || + is_same::value || + is_same::value || + is_same::value, + int, + typename conditional< + is_same >::value || + is_same >::value || + is_same >::value || + is_same >::value, + std::complex, + const Scalar& + >::type + >::type PrintType; + + Index width = 0; + + std::streamsize explicit_precision; + if(fmt.precision == StreamPrecision) + { + explicit_precision = 0; + } + else if(fmt.precision == FullPrecision) + { + if (NumTraits::IsInteger) + { + explicit_precision = 0; + } + else + { + explicit_precision = significant_decimals_impl::run(); + } + } + else + { + explicit_precision = fmt.precision; + } + + std::streamsize old_precision = 0; + if(explicit_precision) old_precision = s.precision(explicit_precision); + + bool align_cols = !(fmt.flags & DontAlignCols); + if(align_cols) + { + // compute the largest width + for(Index j = 0; j < m.cols(); ++j) + for(Index i = 0; i < m.rows(); ++i) + { + std::stringstream sstr; + sstr.copyfmt(s); + sstr << static_cast(m.coeff(i,j)); + width = std::max(width, Index(sstr.str().length())); + } + } + std::streamsize old_width = s.width(); + char old_fill_character = s.fill(); + s << fmt.matPrefix; + for(Index i = 0; i < m.rows(); ++i) + { + if (i) + s << fmt.rowSpacer; + s << fmt.rowPrefix; + if(width) { + s.fill(fmt.fill); + s.width(width); + } + s << static_cast(m.coeff(i, 0)); + for(Index j = 1; j < m.cols(); ++j) + { + s << fmt.coeffSeparator; + if(width) { + s.fill(fmt.fill); + s.width(width); + } + s << static_cast(m.coeff(i, j)); + } + s << fmt.rowSuffix; + if( i < m.rows() - 1) + s << fmt.rowSeparator; + } + s << fmt.matSuffix; + if(explicit_precision) s.precision(old_precision); + if(width) { + s.fill(old_fill_character); + s.width(old_width); + } + return s; +} + +} // end namespace internal + +/** \relates DenseBase + * + * Outputs the matrix, to the given stream. + * + * If you wish to print the matrix with a format different than the default, use DenseBase::format(). + * + * It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. + * If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters. + * + * \sa DenseBase::format() + */ +template +std::ostream & operator << +(std::ostream & s, + const DenseBase & m) +{ + return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT); +} + +} // end namespace Eigen + +#endif // EIGEN_IO_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IndexedView.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IndexedView.h new file mode 100644 index 0000000000000000000000000000000000000000..08476251d32234dfdd2e9b0cba788c58484bc458 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/IndexedView.h @@ -0,0 +1,237 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2017 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_INDEXED_VIEW_H +#define EIGEN_INDEXED_VIEW_H + +namespace Eigen { + +namespace internal { + +template +struct traits > + : traits +{ + enum { + RowsAtCompileTime = int(array_size::value), + ColsAtCompileTime = int(array_size::value), + MaxRowsAtCompileTime = RowsAtCompileTime != Dynamic ? int(RowsAtCompileTime) : Dynamic, + MaxColsAtCompileTime = ColsAtCompileTime != Dynamic ? int(ColsAtCompileTime) : Dynamic, + + XprTypeIsRowMajor = (int(traits::Flags)&RowMajorBit) != 0, + IsRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1 + : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0 + : XprTypeIsRowMajor, + + RowIncr = int(get_compile_time_incr::value), + ColIncr = int(get_compile_time_incr::value), + InnerIncr = IsRowMajor ? ColIncr : RowIncr, + OuterIncr = IsRowMajor ? RowIncr : ColIncr, + + HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor), + XprInnerStride = HasSameStorageOrderAsXprType ? int(inner_stride_at_compile_time::ret) : int(outer_stride_at_compile_time::ret), + XprOuterstride = HasSameStorageOrderAsXprType ? int(outer_stride_at_compile_time::ret) : int(inner_stride_at_compile_time::ret), + + InnerSize = XprTypeIsRowMajor ? ColsAtCompileTime : RowsAtCompileTime, + IsBlockAlike = InnerIncr==1 && OuterIncr==1, + IsInnerPannel = HasSameStorageOrderAsXprType && is_same,typename conditional::type>::value, + + InnerStrideAtCompileTime = InnerIncr<0 || InnerIncr==DynamicIndex || XprInnerStride==Dynamic ? Dynamic : XprInnerStride * InnerIncr, + OuterStrideAtCompileTime = OuterIncr<0 || OuterIncr==DynamicIndex || XprOuterstride==Dynamic ? Dynamic : XprOuterstride * OuterIncr, + + ReturnAsScalar = is_same::value && is_same::value, + ReturnAsBlock = (!ReturnAsScalar) && IsBlockAlike, + ReturnAsIndexedView = (!ReturnAsScalar) && (!ReturnAsBlock), + + // FIXME we deal with compile-time strides if and only if we have DirectAccessBit flag, + // but this is too strict regarding negative strides... + DirectAccessMask = (int(InnerIncr)!=UndefinedIncr && int(OuterIncr)!=UndefinedIncr && InnerIncr>=0 && OuterIncr>=0) ? DirectAccessBit : 0, + FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0, + FlagsLvalueBit = is_lvalue::value ? LvalueBit : 0, + FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0, + Flags = (traits::Flags & (HereditaryBits | DirectAccessMask )) | FlagsLvalueBit | FlagsRowMajorBit | FlagsLinearAccessBit + }; + + typedef Block BlockType; +}; + +} + +template +class IndexedViewImpl; + + +/** \class IndexedView + * \ingroup Core_Module + * + * \brief Expression of a non-sequential sub-matrix defined by arbitrary sequences of row and column indices + * + * \tparam XprType the type of the expression in which we are taking the intersections of sub-rows and sub-columns + * \tparam RowIndices the type of the object defining the sequence of row indices + * \tparam ColIndices the type of the object defining the sequence of column indices + * + * This class represents an expression of a sub-matrix (or sub-vector) defined as the intersection + * of sub-sets of rows and columns, that are themself defined by generic sequences of row indices \f$ \{r_0,r_1,..r_{m-1}\} \f$ + * and column indices \f$ \{c_0,c_1,..c_{n-1} \}\f$. Let \f$ A \f$ be the nested matrix, then the resulting matrix \f$ B \f$ has \c m + * rows and \c n columns, and its entries are given by: \f$ B(i,j) = A(r_i,c_j) \f$. + * + * The \c RowIndices and \c ColIndices types must be compatible with the following API: + * \code + * operator[](Index) const; + * Index size() const; + * \endcode + * + * Typical supported types thus include: + * - std::vector + * - std::valarray + * - std::array + * - Plain C arrays: int[N] + * - Eigen::ArrayXi + * - decltype(ArrayXi::LinSpaced(...)) + * - Any view/expressions of the previous types + * - Eigen::ArithmeticSequence + * - Eigen::internal::AllRange (helper for Eigen::all) + * - Eigen::internal::SingleRange (helper for single index) + * - etc. + * + * In typical usages of %Eigen, this class should never be used directly. It is the return type of + * DenseBase::operator()(const RowIndices&, const ColIndices&). + * + * \sa class Block + */ +template +class IndexedView : public IndexedViewImpl::StorageKind> +{ +public: + typedef typename IndexedViewImpl::StorageKind>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(IndexedView) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(IndexedView) + + typedef typename internal::ref_selector::non_const_type MatrixTypeNested; + typedef typename internal::remove_all::type NestedExpression; + + template + IndexedView(XprType& xpr, const T0& rowIndices, const T1& colIndices) + : m_xpr(xpr), m_rowIndices(rowIndices), m_colIndices(colIndices) + {} + + /** \returns number of rows */ + Index rows() const { return internal::size(m_rowIndices); } + + /** \returns number of columns */ + Index cols() const { return internal::size(m_colIndices); } + + /** \returns the nested expression */ + const typename internal::remove_all::type& + nestedExpression() const { return m_xpr; } + + /** \returns the nested expression */ + typename internal::remove_reference::type& + nestedExpression() { return m_xpr; } + + /** \returns a const reference to the object storing/generating the row indices */ + const RowIndices& rowIndices() const { return m_rowIndices; } + + /** \returns a const reference to the object storing/generating the column indices */ + const ColIndices& colIndices() const { return m_colIndices; } + +protected: + MatrixTypeNested m_xpr; + RowIndices m_rowIndices; + ColIndices m_colIndices; +}; + + +// Generic API dispatcher +template +class IndexedViewImpl + : public internal::generic_xpr_base >::type +{ +public: + typedef typename internal::generic_xpr_base >::type Base; +}; + +namespace internal { + + +template +struct unary_evaluator, IndexBased> + : evaluator_base > +{ + typedef IndexedView XprType; + + enum { + CoeffReadCost = evaluator::CoeffReadCost /* TODO + cost of row/col index */, + + FlagsLinearAccessBit = (traits::RowsAtCompileTime == 1 || traits::ColsAtCompileTime == 1) ? LinearAccessBit : 0, + + FlagsRowMajorBit = traits::FlagsRowMajorBit, + + Flags = (evaluator::Flags & (HereditaryBits & ~RowMajorBit /*| LinearAccessBit | DirectAccessBit*/)) | FlagsLinearAccessBit | FlagsRowMajorBit, + + Alignment = 0 + }; + + EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeff(Index row, Index col) const + { + return m_argImpl.coeff(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index row, Index col) + { + return m_argImpl.coeffRef(m_xpr.rowIndices()[row], m_xpr.colIndices()[col]); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Scalar& coeffRef(Index index) + { + EIGEN_STATIC_ASSERT_LVALUE(XprType) + Index row = XprType::RowsAtCompileTime == 1 ? 0 : index; + Index col = XprType::RowsAtCompileTime == 1 ? index : 0; + return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const Scalar& coeffRef(Index index) const + { + Index row = XprType::RowsAtCompileTime == 1 ? 0 : index; + Index col = XprType::RowsAtCompileTime == 1 ? index : 0; + return m_argImpl.coeffRef( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const CoeffReturnType coeff(Index index) const + { + Index row = XprType::RowsAtCompileTime == 1 ? 0 : index; + Index col = XprType::RowsAtCompileTime == 1 ? index : 0; + return m_argImpl.coeff( m_xpr.rowIndices()[row], m_xpr.colIndices()[col]); + } + +protected: + + evaluator m_argImpl; + const XprType& m_xpr; + +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_INDEXED_VIEW_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Inverse.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Inverse.h new file mode 100644 index 0000000000000000000000000000000000000000..c514438c45e64863e1eb93071c4374d0d29ef969 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Inverse.h @@ -0,0 +1,117 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014-2019 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_INVERSE_H +#define EIGEN_INVERSE_H + +namespace Eigen { + +template class InverseImpl; + +namespace internal { + +template +struct traits > + : traits +{ + typedef typename XprType::PlainObject PlainObject; + typedef traits BaseTraits; + enum { + Flags = BaseTraits::Flags & RowMajorBit + }; +}; + +} // end namespace internal + +/** \class Inverse + * + * \brief Expression of the inverse of another expression + * + * \tparam XprType the type of the expression we are taking the inverse + * + * This class represents an abstract expression of A.inverse() + * and most of the time this is the only way it is used. + * + */ +template +class Inverse : public InverseImpl::StorageKind> +{ +public: + typedef typename XprType::StorageIndex StorageIndex; + typedef typename XprType::Scalar Scalar; + typedef typename internal::ref_selector::type XprTypeNested; + typedef typename internal::remove_all::type XprTypeNestedCleaned; + typedef typename internal::ref_selector::type Nested; + typedef typename internal::remove_all::type NestedExpression; + + explicit EIGEN_DEVICE_FUNC Inverse(const XprType &xpr) + : m_xpr(xpr) + {} + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.cols(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.rows(); } + + EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; } + +protected: + XprTypeNested m_xpr; +}; + +// Generic API dispatcher +template +class InverseImpl + : public internal::generic_xpr_base >::type +{ +public: + typedef typename internal::generic_xpr_base >::type Base; + typedef typename XprType::Scalar Scalar; +private: + + Scalar coeff(Index row, Index col) const; + Scalar coeff(Index i) const; +}; + +namespace internal { + +/** \internal + * \brief Default evaluator for Inverse expression. + * + * This default evaluator for Inverse expression simply evaluate the inverse into a temporary + * by a call to internal::call_assignment_no_alias. + * Therefore, inverse implementers only have to specialize Assignment, ...> for + * there own nested expression. + * + * \sa class Inverse + */ +template +struct unary_evaluator > + : public evaluator::PlainObject> +{ + typedef Inverse InverseType; + typedef typename InverseType::PlainObject PlainObject; + typedef evaluator Base; + + enum { Flags = Base::Flags | EvalBeforeNestingBit }; + + unary_evaluator(const InverseType& inv_xpr) + : m_result(inv_xpr.rows(), inv_xpr.cols()) + { + ::new (static_cast(this)) Base(m_result); + internal::call_assignment_no_alias(m_result, inv_xpr); + } + +protected: + PlainObject m_result; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_INVERSE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Map.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Map.h new file mode 100644 index 0000000000000000000000000000000000000000..218cc157f386924cae44ca6741d6aaba9fc96f74 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Map.h @@ -0,0 +1,171 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007-2010 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MAP_H +#define EIGEN_MAP_H + +namespace Eigen { + +namespace internal { +template +struct traits > + : public traits +{ + typedef traits TraitsBase; + enum { + PlainObjectTypeInnerSize = ((traits::Flags&RowMajorBit)==RowMajorBit) + ? PlainObjectType::ColsAtCompileTime + : PlainObjectType::RowsAtCompileTime, + + InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0 + ? int(PlainObjectType::InnerStrideAtCompileTime) + : int(StrideType::InnerStrideAtCompileTime), + OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0 + ? (InnerStrideAtCompileTime==Dynamic || PlainObjectTypeInnerSize==Dynamic + ? Dynamic + : int(InnerStrideAtCompileTime) * int(PlainObjectTypeInnerSize)) + : int(StrideType::OuterStrideAtCompileTime), + Alignment = int(MapOptions)&int(AlignedMask), + Flags0 = TraitsBase::Flags & (~NestByRefBit), + Flags = is_lvalue::value ? int(Flags0) : (int(Flags0) & ~LvalueBit) + }; +private: + enum { Options }; // Expressions don't have Options +}; +} + +/** \class Map + * \ingroup Core_Module + * + * \brief A matrix or vector expression mapping an existing array of data. + * + * \tparam PlainObjectType the equivalent matrix type of the mapped data + * \tparam MapOptions specifies the pointer alignment in bytes. It can be: \c #Aligned128, \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned. + * The default is \c #Unaligned. + * \tparam StrideType optionally specifies strides. By default, Map assumes the memory layout + * of an ordinary, contiguous array. This can be overridden by specifying strides. + * The type passed here must be a specialization of the Stride template, see examples below. + * + * This class represents a matrix or vector expression mapping an existing array of data. + * It can be used to let Eigen interface without any overhead with non-Eigen data structures, + * such as plain C arrays or structures from other libraries. By default, it assumes that the + * data is laid out contiguously in memory. You can however override this by explicitly specifying + * inner and outer strides. + * + * Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix: + * \include Map_simple.cpp + * Output: \verbinclude Map_simple.out + * + * If you need to map non-contiguous arrays, you can do so by specifying strides: + * + * Here's an example of mapping an array as a vector, specifying an inner stride, that is, the pointer + * increment between two consecutive coefficients. Here, we're specifying the inner stride as a compile-time + * fixed value. + * \include Map_inner_stride.cpp + * Output: \verbinclude Map_inner_stride.out + * + * Here's an example of mapping an array while specifying an outer stride. Here, since we're mapping + * as a column-major matrix, 'outer stride' means the pointer increment between two consecutive columns. + * Here, we're specifying the outer stride as a runtime parameter. Note that here \c OuterStride<> is + * a short version of \c OuterStride because the default template parameter of OuterStride + * is \c Dynamic + * \include Map_outer_stride.cpp + * Output: \verbinclude Map_outer_stride.out + * + * For more details and for an example of specifying both an inner and an outer stride, see class Stride. + * + * \b Tip: to change the array of data mapped by a Map object, you can use the C++ + * placement new syntax: + * + * Example: \include Map_placement_new.cpp + * Output: \verbinclude Map_placement_new.out + * + * This class is the return type of PlainObjectBase::Map() but can also be used directly. + * + * \sa PlainObjectBase::Map(), \ref TopicStorageOrders + */ +template class Map + : public MapBase > +{ + public: + + typedef MapBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Map) + + typedef typename Base::PointerType PointerType; + typedef PointerType PointerArgType; + EIGEN_DEVICE_FUNC + inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const + { + return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1; + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const + { + return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer() + : internal::traits::OuterStrideAtCompileTime != Dynamic ? Index(internal::traits::OuterStrideAtCompileTime) + : IsVectorAtCompileTime ? (this->size() * innerStride()) + : int(Flags)&RowMajorBit ? (this->cols() * innerStride()) + : (this->rows() * innerStride()); + } + + /** Constructor in the fixed-size case. + * + * \param dataPtr pointer to the array to map + * \param stride optional Stride object, passing the strides. + */ + EIGEN_DEVICE_FUNC + explicit inline Map(PointerArgType dataPtr, const StrideType& stride = StrideType()) + : Base(cast_to_pointer_type(dataPtr)), m_stride(stride) + { + PlainObjectType::Base::_check_template_params(); + } + + /** Constructor in the dynamic-size vector case. + * + * \param dataPtr pointer to the array to map + * \param size the size of the vector expression + * \param stride optional Stride object, passing the strides. + */ + EIGEN_DEVICE_FUNC + inline Map(PointerArgType dataPtr, Index size, const StrideType& stride = StrideType()) + : Base(cast_to_pointer_type(dataPtr), size), m_stride(stride) + { + PlainObjectType::Base::_check_template_params(); + } + + /** Constructor in the dynamic-size matrix case. + * + * \param dataPtr pointer to the array to map + * \param rows the number of rows of the matrix expression + * \param cols the number of columns of the matrix expression + * \param stride optional Stride object, passing the strides. + */ + EIGEN_DEVICE_FUNC + inline Map(PointerArgType dataPtr, Index rows, Index cols, const StrideType& stride = StrideType()) + : Base(cast_to_pointer_type(dataPtr), rows, cols), m_stride(stride) + { + PlainObjectType::Base::_check_template_params(); + } + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map) + + protected: + StrideType m_stride; +}; + + +} // end namespace Eigen + +#endif // EIGEN_MAP_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MapBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MapBase.h new file mode 100644 index 0000000000000000000000000000000000000000..d856447f03e57a749ec250456c0e00e539d7e700 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MapBase.h @@ -0,0 +1,310 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007-2010 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MAPBASE_H +#define EIGEN_MAPBASE_H + +#define EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) \ + EIGEN_STATIC_ASSERT((int(internal::evaluator::Flags) & LinearAccessBit) || Derived::IsVectorAtCompileTime, \ + YOU_ARE_TRYING_TO_USE_AN_INDEX_BASED_ACCESSOR_ON_AN_EXPRESSION_THAT_DOES_NOT_SUPPORT_THAT) + +namespace Eigen { + +/** \ingroup Core_Module + * + * \brief Base class for dense Map and Block expression with direct access + * + * This base class provides the const low-level accessors (e.g. coeff, coeffRef) of dense + * Map and Block objects with direct access. + * Typical users do not have to directly deal with this class. + * + * This class can be extended by through the macro plugin \c EIGEN_MAPBASE_PLUGIN. + * See \link TopicCustomizing_Plugins customizing Eigen \endlink for details. + * + * The \c Derived class has to provide the following two methods describing the memory layout: + * \code Index innerStride() const; \endcode + * \code Index outerStride() const; \endcode + * + * \sa class Map, class Block + */ +template class MapBase + : public internal::dense_xpr_base::type +{ + public: + + typedef typename internal::dense_xpr_base::type Base; + enum { + RowsAtCompileTime = internal::traits::RowsAtCompileTime, + ColsAtCompileTime = internal::traits::ColsAtCompileTime, + InnerStrideAtCompileTime = internal::traits::InnerStrideAtCompileTime, + SizeAtCompileTime = Base::SizeAtCompileTime + }; + + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::packet_traits::type PacketScalar; + typedef typename NumTraits::Real RealScalar; + typedef typename internal::conditional< + bool(internal::is_lvalue::value), + Scalar *, + const Scalar *>::type + PointerType; + + using Base::derived; +// using Base::RowsAtCompileTime; +// using Base::ColsAtCompileTime; +// using Base::SizeAtCompileTime; + using Base::MaxRowsAtCompileTime; + using Base::MaxColsAtCompileTime; + using Base::MaxSizeAtCompileTime; + using Base::IsVectorAtCompileTime; + using Base::Flags; + using Base::IsRowMajor; + + using Base::rows; + using Base::cols; + using Base::size; + using Base::coeff; + using Base::coeffRef; + using Base::lazyAssign; + using Base::eval; + + using Base::innerStride; + using Base::outerStride; + using Base::rowStride; + using Base::colStride; + + // bug 217 - compile error on ICC 11.1 + using Base::operator=; + + typedef typename Base::CoeffReturnType CoeffReturnType; + + /** \copydoc DenseBase::rows() */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return m_rows.value(); } + /** \copydoc DenseBase::cols() */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return m_cols.value(); } + + /** Returns a pointer to the first coefficient of the matrix or vector. + * + * \note When addressing this data, make sure to honor the strides returned by innerStride() and outerStride(). + * + * \sa innerStride(), outerStride() + */ + EIGEN_DEVICE_FUNC inline const Scalar* data() const { return m_data; } + + /** \copydoc PlainObjectBase::coeff(Index,Index) const */ + EIGEN_DEVICE_FUNC + inline const Scalar& coeff(Index rowId, Index colId) const + { + return m_data[colId * colStride() + rowId * rowStride()]; + } + + /** \copydoc PlainObjectBase::coeff(Index) const */ + EIGEN_DEVICE_FUNC + inline const Scalar& coeff(Index index) const + { + EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) + return m_data[index * innerStride()]; + } + + /** \copydoc PlainObjectBase::coeffRef(Index,Index) const */ + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index rowId, Index colId) const + { + return this->m_data[colId * colStride() + rowId * rowStride()]; + } + + /** \copydoc PlainObjectBase::coeffRef(Index) const */ + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index index) const + { + EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) + return this->m_data[index * innerStride()]; + } + + /** \internal */ + template + inline PacketScalar packet(Index rowId, Index colId) const + { + return internal::ploadt + (m_data + (colId * colStride() + rowId * rowStride())); + } + + /** \internal */ + template + inline PacketScalar packet(Index index) const + { + EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) + return internal::ploadt(m_data + index * innerStride()); + } + + /** \internal Constructor for fixed size matrices or vectors */ + EIGEN_DEVICE_FUNC + explicit inline MapBase(PointerType dataPtr) : m_data(dataPtr), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime) + { + EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) + checkSanity(); + } + + /** \internal Constructor for dynamically sized vectors */ + EIGEN_DEVICE_FUNC + inline MapBase(PointerType dataPtr, Index vecSize) + : m_data(dataPtr), + m_rows(RowsAtCompileTime == Dynamic ? vecSize : Index(RowsAtCompileTime)), + m_cols(ColsAtCompileTime == Dynamic ? vecSize : Index(ColsAtCompileTime)) + { + EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) + eigen_assert(vecSize >= 0); + eigen_assert(dataPtr == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == vecSize); + checkSanity(); + } + + /** \internal Constructor for dynamically sized matrices */ + EIGEN_DEVICE_FUNC + inline MapBase(PointerType dataPtr, Index rows, Index cols) + : m_data(dataPtr), m_rows(rows), m_cols(cols) + { + eigen_assert( (dataPtr == 0) + || ( rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) + && cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols))); + checkSanity(); + } + + #ifdef EIGEN_MAPBASE_PLUGIN + #include EIGEN_MAPBASE_PLUGIN + #endif + + protected: + EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase) + EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase) + + template + EIGEN_DEVICE_FUNC + void checkSanity(typename internal::enable_if<(internal::traits::Alignment>0),void*>::type = 0) const + { +#if EIGEN_MAX_ALIGN_BYTES>0 + // innerStride() is not set yet when this function is called, so we optimistically assume the lowest plausible value: + const Index minInnerStride = InnerStrideAtCompileTime == Dynamic ? 1 : Index(InnerStrideAtCompileTime); + EIGEN_ONLY_USED_FOR_DEBUG(minInnerStride); + eigen_assert(( ((internal::UIntPtr(m_data) % internal::traits::Alignment) == 0) + || (cols() * rows() * minInnerStride * sizeof(Scalar)) < internal::traits::Alignment ) && "data is not aligned"); +#endif + } + + template + EIGEN_DEVICE_FUNC + void checkSanity(typename internal::enable_if::Alignment==0,void*>::type = 0) const + {} + + PointerType m_data; + const internal::variable_if_dynamic m_rows; + const internal::variable_if_dynamic m_cols; +}; + +/** \ingroup Core_Module + * + * \brief Base class for non-const dense Map and Block expression with direct access + * + * This base class provides the non-const low-level accessors (e.g. coeff and coeffRef) of + * dense Map and Block objects with direct access. + * It inherits MapBase which defines the const variant for reading specific entries. + * + * \sa class Map, class Block + */ +template class MapBase + : public MapBase +{ + typedef MapBase ReadOnlyMapBase; + public: + + typedef MapBase Base; + + typedef typename Base::Scalar Scalar; + typedef typename Base::PacketScalar PacketScalar; + typedef typename Base::StorageIndex StorageIndex; + typedef typename Base::PointerType PointerType; + + using Base::derived; + using Base::rows; + using Base::cols; + using Base::size; + using Base::coeff; + using Base::coeffRef; + + using Base::innerStride; + using Base::outerStride; + using Base::rowStride; + using Base::colStride; + + typedef typename internal::conditional< + internal::is_lvalue::value, + Scalar, + const Scalar + >::type ScalarWithConstIfNotLvalue; + + EIGEN_DEVICE_FUNC + inline const Scalar* data() const { return this->m_data; } + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue* data() { return this->m_data; } // no const-cast here so non-const-correct code will give a compile error + + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue& coeffRef(Index row, Index col) + { + return this->m_data[col * colStride() + row * rowStride()]; + } + + EIGEN_DEVICE_FUNC + inline ScalarWithConstIfNotLvalue& coeffRef(Index index) + { + EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) + return this->m_data[index * innerStride()]; + } + + template + inline void writePacket(Index row, Index col, const PacketScalar& val) + { + internal::pstoret + (this->m_data + (col * colStride() + row * rowStride()), val); + } + + template + inline void writePacket(Index index, const PacketScalar& val) + { + EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS(Derived) + internal::pstoret + (this->m_data + index * innerStride(), val); + } + + EIGEN_DEVICE_FUNC explicit inline MapBase(PointerType dataPtr) : Base(dataPtr) {} + EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index vecSize) : Base(dataPtr, vecSize) {} + EIGEN_DEVICE_FUNC inline MapBase(PointerType dataPtr, Index rows, Index cols) : Base(dataPtr, rows, cols) {} + + EIGEN_DEVICE_FUNC + Derived& operator=(const MapBase& other) + { + ReadOnlyMapBase::Base::operator=(other); + return derived(); + } + + // In theory we could simply refer to Base:Base::operator=, but MSVC does not like Base::Base, + // see bugs 821 and 920. + using ReadOnlyMapBase::Base::operator=; + protected: + EIGEN_DEFAULT_COPY_CONSTRUCTOR(MapBase) + EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MapBase) +}; + +#undef EIGEN_STATIC_ASSERT_INDEX_BASED_ACCESS + +} // end namespace Eigen + +#endif // EIGEN_MAPBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctions.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctions.h new file mode 100644 index 0000000000000000000000000000000000000000..61b78f4f20a6a3820b168796db9aeb79d712bb11 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctions.h @@ -0,0 +1,2057 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATHFUNCTIONS_H +#define EIGEN_MATHFUNCTIONS_H + +// TODO this should better be moved to NumTraits +// Source: WolframAlpha +#define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L +#define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L +#define EIGEN_LN2 0.693147180559945309417232121458176568075500134360255254120680009493393621L + +namespace Eigen { + +// On WINCE, std::abs is defined for int only, so let's defined our own overloads: +// This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too. +#if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500 +long abs(long x) { return (labs(x)); } +double abs(double x) { return (fabs(x)); } +float abs(float x) { return (fabsf(x)); } +long double abs(long double x) { return (fabsl(x)); } +#endif + +namespace internal { + +/** \internal \class global_math_functions_filtering_base + * + * What it does: + * Defines a typedef 'type' as follows: + * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then + * global_math_functions_filtering_base::type is a typedef for it. + * - otherwise, global_math_functions_filtering_base::type is a typedef for T. + * + * How it's used: + * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions. + * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know + * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase. + * So we must make sure to use sin_impl > and not sin_impl, otherwise our partial specialization + * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it. + * + * How it's implemented: + * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace + * the typename dummy by an integer template parameter, it doesn't work anymore! + */ + +template +struct global_math_functions_filtering_base +{ + typedef T type; +}; + +template struct always_void { typedef void type; }; + +template +struct global_math_functions_filtering_base + ::type + > +{ + typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type; +}; + +#define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl::type> +#define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval::type>::type + +/**************************************************************************** +* Implementation of real * +****************************************************************************/ + +template::IsComplex> +struct real_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return x; + } +}; + +template +struct real_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + using std::real; + return real(x); + } +}; + +template struct real_impl : real_default_impl {}; + +#if defined(EIGEN_GPU_COMPILE_PHASE) +template +struct real_impl > +{ + typedef T RealScalar; + EIGEN_DEVICE_FUNC + static inline T run(const std::complex& x) + { + return x.real(); + } +}; +#endif + +template +struct real_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of imag * +****************************************************************************/ + +template::IsComplex> +struct imag_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar&) + { + return RealScalar(0); + } +}; + +template +struct imag_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + using std::imag; + return imag(x); + } +}; + +template struct imag_impl : imag_default_impl {}; + +#if defined(EIGEN_GPU_COMPILE_PHASE) +template +struct imag_impl > +{ + typedef T RealScalar; + EIGEN_DEVICE_FUNC + static inline T run(const std::complex& x) + { + return x.imag(); + } +}; +#endif + +template +struct imag_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of real_ref * +****************************************************************************/ + +template +struct real_ref_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar& run(Scalar& x) + { + return reinterpret_cast(&x)[0]; + } + EIGEN_DEVICE_FUNC + static inline const RealScalar& run(const Scalar& x) + { + return reinterpret_cast(&x)[0]; + } +}; + +template +struct real_ref_retval +{ + typedef typename NumTraits::Real & type; +}; + +/**************************************************************************** +* Implementation of imag_ref * +****************************************************************************/ + +template +struct imag_ref_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar& run(Scalar& x) + { + return reinterpret_cast(&x)[1]; + } + EIGEN_DEVICE_FUNC + static inline const RealScalar& run(const Scalar& x) + { + return reinterpret_cast(&x)[1]; + } +}; + +template +struct imag_ref_default_impl +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline Scalar run(Scalar&) + { + return Scalar(0); + } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline const Scalar run(const Scalar&) + { + return Scalar(0); + } +}; + +template +struct imag_ref_impl : imag_ref_default_impl::IsComplex> {}; + +template +struct imag_ref_retval +{ + typedef typename NumTraits::Real & type; +}; + +/**************************************************************************** +* Implementation of conj * +****************************************************************************/ + +template::IsComplex> +struct conj_default_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + return x; + } +}; + +template +struct conj_default_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + using std::conj; + return conj(x); + } +}; + +template::IsComplex> +struct conj_impl : conj_default_impl {}; + +template +struct conj_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of abs2 * +****************************************************************************/ + +template +struct abs2_impl_default +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return x*x; + } +}; + +template +struct abs2_impl_default // IsComplex +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return x.real()*x.real() + x.imag()*x.imag(); + } +}; + +template +struct abs2_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return abs2_impl_default::IsComplex>::run(x); + } +}; + +template +struct abs2_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of sqrt/rsqrt * +****************************************************************************/ + +template +struct sqrt_impl +{ + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE Scalar run(const Scalar& x) + { + EIGEN_USING_STD(sqrt); + return sqrt(x); + } +}; + +// Complex sqrt defined in MathFunctionsImpl.h. +template EIGEN_DEVICE_FUNC std::complex complex_sqrt(const std::complex& a_x); + +// Custom implementation is faster than `std::sqrt`, works on +// GPU, and correctly handles special cases (unlike MSVC). +template +struct sqrt_impl > +{ + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE std::complex run(const std::complex& x) + { + return complex_sqrt(x); + } +}; + +template +struct sqrt_retval +{ + typedef Scalar type; +}; + +// Default implementation relies on numext::sqrt, at bottom of file. +template +struct rsqrt_impl; + +// Complex rsqrt defined in MathFunctionsImpl.h. +template EIGEN_DEVICE_FUNC std::complex complex_rsqrt(const std::complex& a_x); + +template +struct rsqrt_impl > +{ + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE std::complex run(const std::complex& x) + { + return complex_rsqrt(x); + } +}; + +template +struct rsqrt_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of norm1 * +****************************************************************************/ + +template +struct norm1_default_impl; + +template +struct norm1_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + EIGEN_USING_STD(abs); + return abs(x.real()) + abs(x.imag()); + } +}; + +template +struct norm1_default_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + EIGEN_USING_STD(abs); + return abs(x); + } +}; + +template +struct norm1_impl : norm1_default_impl::IsComplex> {}; + +template +struct norm1_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of hypot * +****************************************************************************/ + +template struct hypot_impl; + +template +struct hypot_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of cast * +****************************************************************************/ + +template +struct cast_impl +{ + EIGEN_DEVICE_FUNC + static inline NewType run(const OldType& x) + { + return static_cast(x); + } +}; + +// Casting from S -> Complex leads to an implicit conversion from S to T, +// generating warnings on clang. Here we explicitly cast the real component. +template +struct cast_impl::IsComplex && NumTraits::IsComplex + >::type> +{ + EIGEN_DEVICE_FUNC + static inline NewType run(const OldType& x) + { + typedef typename NumTraits::Real NewReal; + return static_cast(static_cast(x)); + } +}; + +// here, for once, we're plainly returning NewType: we don't want cast to do weird things. + +template +EIGEN_DEVICE_FUNC +inline NewType cast(const OldType& x) +{ + return cast_impl::run(x); +} + +/**************************************************************************** +* Implementation of round * +****************************************************************************/ + +template +struct round_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT((!NumTraits::IsComplex), NUMERIC_TYPE_MUST_BE_REAL) +#if EIGEN_HAS_CXX11_MATH + EIGEN_USING_STD(round); +#endif + return Scalar(round(x)); + } +}; + +#if !EIGEN_HAS_CXX11_MATH +#if EIGEN_HAS_C99_MATH +// Use ::roundf for float. +template<> +struct round_impl { + EIGEN_DEVICE_FUNC + static inline float run(const float& x) + { + return ::roundf(x); + } +}; +#else +template +struct round_using_floor_ceil_impl +{ + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT((!NumTraits::IsComplex), NUMERIC_TYPE_MUST_BE_REAL) + // Without C99 round/roundf, resort to floor/ceil. + EIGEN_USING_STD(floor); + EIGEN_USING_STD(ceil); + // If not enough precision to resolve a decimal at all, return the input. + // Otherwise, adding 0.5 can trigger an increment by 1. + const Scalar limit = Scalar(1ull << (NumTraits::digits() - 1)); + if (x >= limit || x <= -limit) { + return x; + } + return (x > Scalar(0)) ? Scalar(floor(x + Scalar(0.5))) : Scalar(ceil(x - Scalar(0.5))); + } +}; + +template<> +struct round_impl : round_using_floor_ceil_impl {}; + +template<> +struct round_impl : round_using_floor_ceil_impl {}; +#endif // EIGEN_HAS_C99_MATH +#endif // !EIGEN_HAS_CXX11_MATH + +template +struct round_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of rint * +****************************************************************************/ + +template +struct rint_impl { + EIGEN_DEVICE_FUNC + static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT((!NumTraits::IsComplex), NUMERIC_TYPE_MUST_BE_REAL) +#if EIGEN_HAS_CXX11_MATH + EIGEN_USING_STD(rint); +#endif + return rint(x); + } +}; + +#if !EIGEN_HAS_CXX11_MATH +template<> +struct rint_impl { + EIGEN_DEVICE_FUNC + static inline double run(const double& x) + { + return ::rint(x); + } +}; +template<> +struct rint_impl { + EIGEN_DEVICE_FUNC + static inline float run(const float& x) + { + return ::rintf(x); + } +}; +#endif + +template +struct rint_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of arg * +****************************************************************************/ + +// Visual Studio 2017 has a bug where arg(float) returns 0 for negative inputs. +// This seems to be fixed in VS 2019. +#if EIGEN_HAS_CXX11_MATH && (!EIGEN_COMP_MSVC || EIGEN_COMP_MSVC >= 1920) +// std::arg is only defined for types of std::complex, or integer types or float/double/long double +template::IsComplex || is_integral::value + || is_same::value || is_same::value + || is_same::value > +struct arg_default_impl; + +template +struct arg_default_impl { + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + #if defined(EIGEN_HIP_DEVICE_COMPILE) + // HIP does not seem to have a native device side implementation for the math routine "arg" + using std::arg; + #else + EIGEN_USING_STD(arg); + #endif + return static_cast(arg(x)); + } +}; + +// Must be non-complex floating-point type (e.g. half/bfloat16). +template +struct arg_default_impl { + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return (x < Scalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0); + } +}; +#else +template::IsComplex> +struct arg_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + return (x < RealScalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0); + } +}; + +template +struct arg_default_impl +{ + typedef typename NumTraits::Real RealScalar; + EIGEN_DEVICE_FUNC + static inline RealScalar run(const Scalar& x) + { + EIGEN_USING_STD(arg); + return arg(x); + } +}; +#endif +template struct arg_impl : arg_default_impl {}; + +template +struct arg_retval +{ + typedef typename NumTraits::Real type; +}; + +/**************************************************************************** +* Implementation of expm1 * +****************************************************************************/ + +// This implementation is based on GSL Math's expm1. +namespace std_fallback { + // fallback expm1 implementation in case there is no expm1(Scalar) function in namespace of Scalar, + // or that there is no suitable std::expm1 function available. Implementation + // attributed to Kahan. See: http://www.plunk.org/~hatch/rightway.php. + template + EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) + typedef typename NumTraits::Real RealScalar; + + EIGEN_USING_STD(exp); + Scalar u = exp(x); + if (numext::equal_strict(u, Scalar(1))) { + return x; + } + Scalar um1 = u - RealScalar(1); + if (numext::equal_strict(um1, Scalar(-1))) { + return RealScalar(-1); + } + + EIGEN_USING_STD(log); + Scalar logu = log(u); + return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu; + } +} + +template +struct expm1_impl { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) + #if EIGEN_HAS_CXX11_MATH + using std::expm1; + #else + using std_fallback::expm1; + #endif + return expm1(x); + } +}; + +template +struct expm1_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of log * +****************************************************************************/ + +// Complex log defined in MathFunctionsImpl.h. +template EIGEN_DEVICE_FUNC std::complex complex_log(const std::complex& z); + +template +struct log_impl { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) + { + EIGEN_USING_STD(log); + return static_cast(log(x)); + } +}; + +template +struct log_impl > { + EIGEN_DEVICE_FUNC static inline std::complex run(const std::complex& z) + { + return complex_log(z); + } +}; + +/**************************************************************************** +* Implementation of log1p * +****************************************************************************/ + +namespace std_fallback { + // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar, + // or that there is no suitable std::log1p function available + template + EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) + typedef typename NumTraits::Real RealScalar; + EIGEN_USING_STD(log); + Scalar x1p = RealScalar(1) + x; + Scalar log_1p = log_impl::run(x1p); + const bool is_small = numext::equal_strict(x1p, Scalar(1)); + const bool is_inf = numext::equal_strict(x1p, log_1p); + return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1))); + } +} + +template +struct log1p_impl { + EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x) + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) + #if EIGEN_HAS_CXX11_MATH + using std::log1p; + #else + using std_fallback::log1p; + #endif + return log1p(x); + } +}; + +// Specialization for complex types that are not supported by std::log1p. +template +struct log1p_impl > { + EIGEN_DEVICE_FUNC static inline std::complex run( + const std::complex& x) { + EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar) + return std_fallback::log1p(x); + } +}; + +template +struct log1p_retval +{ + typedef Scalar type; +}; + +/**************************************************************************** +* Implementation of pow * +****************************************************************************/ + +template::IsInteger&&NumTraits::IsInteger> +struct pow_impl +{ + //typedef Scalar retval; + typedef typename ScalarBinaryOpTraits >::ReturnType result_type; + static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y) + { + EIGEN_USING_STD(pow); + return pow(x, y); + } +}; + +template +struct pow_impl +{ + typedef ScalarX result_type; + static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y) + { + ScalarX res(1); + eigen_assert(!NumTraits::IsSigned || y >= 0); + if(y & 1) res *= x; + y >>= 1; + while(y) + { + x *= x; + if(y&1) res *= x; + y >>= 1; + } + return res; + } +}; + +/**************************************************************************** +* Implementation of random * +****************************************************************************/ + +template +struct random_default_impl {}; + +template +struct random_impl : random_default_impl::IsComplex, NumTraits::IsInteger> {}; + +template +struct random_retval +{ + typedef Scalar type; +}; + +template inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y); +template inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(); + +template +struct random_default_impl +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX); + } + static inline Scalar run() + { + return run(Scalar(NumTraits::IsSigned ? -1 : 0), Scalar(1)); + } +}; + +enum { + meta_floor_log2_terminate, + meta_floor_log2_move_up, + meta_floor_log2_move_down, + meta_floor_log2_bogus +}; + +template struct meta_floor_log2_selector +{ + enum { middle = (lower + upper) / 2, + value = (upper <= lower + 1) ? int(meta_floor_log2_terminate) + : (n < (1 << middle)) ? int(meta_floor_log2_move_down) + : (n==0) ? int(meta_floor_log2_bogus) + : int(meta_floor_log2_move_up) + }; +}; + +template::value> +struct meta_floor_log2 {}; + +template +struct meta_floor_log2 +{ + enum { value = meta_floor_log2::middle>::value }; +}; + +template +struct meta_floor_log2 +{ + enum { value = meta_floor_log2::middle, upper>::value }; +}; + +template +struct meta_floor_log2 +{ + enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower }; +}; + +template +struct meta_floor_log2 +{ + // no value, error at compile time +}; + +template +struct random_default_impl +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + if (y <= x) + return x; + // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself. + typedef typename make_unsigned::type ScalarU; + // ScalarX is the widest of ScalarU and unsigned int. + // We'll deal only with ScalarX and unsigned int below thus avoiding signed + // types and arithmetic and signed overflows (which are undefined behavior). + typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned>::type ScalarX; + // The following difference doesn't overflow, provided our integer types are two's + // complement and have the same number of padding bits in signed and unsigned variants. + // This is the case in most modern implementations of C++. + ScalarX range = ScalarX(y) - ScalarX(x); + ScalarX offset = 0; + ScalarX divisor = 1; + ScalarX multiplier = 1; + const unsigned rand_max = RAND_MAX; + if (range <= rand_max) divisor = (rand_max + 1) / (range + 1); + else multiplier = 1 + range / (rand_max + 1); + // Rejection sampling. + do { + offset = (unsigned(std::rand()) * multiplier) / divisor; + } while (offset > range); + return Scalar(ScalarX(x) + offset); + } + + static inline Scalar run() + { +#ifdef EIGEN_MAKING_DOCS + return run(Scalar(NumTraits::IsSigned ? -10 : 0), Scalar(10)); +#else + enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value, + scalar_bits = sizeof(Scalar) * CHAR_BIT, + shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)), + offset = NumTraits::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0 + }; + return Scalar((std::rand() >> shift) - offset); +#endif + } +}; + +template +struct random_default_impl +{ + static inline Scalar run(const Scalar& x, const Scalar& y) + { + return Scalar(random(x.real(), y.real()), + random(x.imag(), y.imag())); + } + static inline Scalar run() + { + typedef typename NumTraits::Real RealScalar; + return Scalar(random(), random()); + } +}; + +template +inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y) +{ + return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y); +} + +template +inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random() +{ + return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(); +} + +// Implementation of is* functions + +// std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang. +#if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG) +#define EIGEN_USE_STD_FPCLASSIFY 1 +#else +#define EIGEN_USE_STD_FPCLASSIFY 0 +#endif + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if::value,bool>::type +isnan_impl(const T&) { return false; } + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if::value,bool>::type +isinf_impl(const T&) { return false; } + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if::value,bool>::type +isfinite_impl(const T&) { return true; } + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral::value)&&(!NumTraits::IsComplex),bool>::type +isfinite_impl(const T& x) +{ + #if defined(EIGEN_GPU_COMPILE_PHASE) + return (::isfinite)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isfinite; + return isfinite EIGEN_NOT_A_MACRO (x); + #else + return x<=NumTraits::highest() && x>=NumTraits::lowest(); + #endif +} + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral::value)&&(!NumTraits::IsComplex),bool>::type +isinf_impl(const T& x) +{ + #if defined(EIGEN_GPU_COMPILE_PHASE) + return (::isinf)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isinf; + return isinf EIGEN_NOT_A_MACRO (x); + #else + return x>NumTraits::highest() || x::lowest(); + #endif +} + +template +EIGEN_DEVICE_FUNC +typename internal::enable_if<(!internal::is_integral::value)&&(!NumTraits::IsComplex),bool>::type +isnan_impl(const T& x) +{ + #if defined(EIGEN_GPU_COMPILE_PHASE) + return (::isnan)(x); + #elif EIGEN_USE_STD_FPCLASSIFY + using std::isnan; + return isnan EIGEN_NOT_A_MACRO (x); + #else + return x != x; + #endif +} + +#if (!EIGEN_USE_STD_FPCLASSIFY) + +#if EIGEN_COMP_MSVC + +template EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x) +{ + return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF; +} + +//MSVC defines a _isnan builtin function, but for double only +EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; } +EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; } +EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; } + +EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); } +EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); } +EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); } + +#elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC) + +#if EIGEN_GNUC_AT_LEAST(5,0) + #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only"))) +#else + // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol), + // while the second prevent too aggressive optimizations in fast-math mode: + #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only"))) +#endif + +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); } +template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); } + +#undef EIGEN_TMP_NOOPT_ATTRIB + +#endif + +#endif + +// The following overload are defined at the end of this file +template EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex& x); +template EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex& x); +template EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex& x); + +template T generic_fast_tanh_float(const T& a_x); +} // end namespace internal + +/**************************************************************************** +* Generic math functions * +****************************************************************************/ + +namespace numext { + +#if (!defined(EIGEN_GPUCC) || defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC)) +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) +{ + EIGEN_USING_STD(min) + return min EIGEN_NOT_A_MACRO (x,y); +} + +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) +{ + EIGEN_USING_STD(max) + return max EIGEN_NOT_A_MACRO (x,y); +} +#else +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y) +{ + return y < x ? y : x; +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y) +{ + return fminf(x, y); +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE double mini(const double& x, const double& y) +{ + return fmin(x, y); +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y) +{ +#if defined(EIGEN_HIPCC) + // no "fminl" on HIP yet + return (x < y) ? x : y; +#else + return fminl(x, y); +#endif +} + +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y) +{ + return x < y ? y : x; +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y) +{ + return fmaxf(x, y); +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE double maxi(const double& x, const double& y) +{ + return fmax(x, y); +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y) +{ +#if defined(EIGEN_HIPCC) + // no "fmaxl" on HIP yet + return (x > y) ? x : y; +#else + return fmaxl(x, y); +#endif +} +#endif + +#if defined(SYCL_DEVICE_ONLY) + + +#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_long) +#define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_long) +#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong) +#define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong) +#define SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(NAME, FUNC) \ + SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \ + SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) +#define SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(NAME, FUNC) \ + SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \ + SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) +#define SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(NAME, FUNC) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \ + SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC,cl::sycl::cl_double) +#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(NAME, FUNC) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \ + SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC,cl::sycl::cl_double) +#define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(NAME, FUNC, RET_TYPE) \ + SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_float) \ + SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_double) + +#define SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \ +template<> \ + EIGEN_DEVICE_FUNC \ + EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE& x) { \ + return cl::sycl::FUNC(x); \ + } + +#define SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, TYPE) \ + SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, TYPE, TYPE) + +#define SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE1, ARG_TYPE2) \ + template<> \ + EIGEN_DEVICE_FUNC \ + EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE1& x, const ARG_TYPE2& y) { \ + return cl::sycl::FUNC(x, y); \ + } + +#define SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \ + SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE, ARG_TYPE) + +#define SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, TYPE) \ + SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, TYPE, TYPE) + +SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(mini, min) +SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(mini, fmin) +SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(maxi, max) +SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(maxi, fmax) + +#endif + + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x) +{ + return internal::real_ref_impl::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x) +{ + return internal::imag_ref_impl::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x); +} + +EIGEN_DEVICE_FUNC +inline bool abs2(bool x) { return x; } + +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE T absdiff(const T& x, const T& y) +{ + return x > y ? x - y : y - x; +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE float absdiff(const float& x, const float& y) +{ + return fabsf(x - y); +} +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE double absdiff(const double& x, const double& y) +{ + return fabs(x - y); +} + +#if !defined(EIGEN_GPUCC) +// HIP and CUDA do not support long double. +template<> +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE long double absdiff(const long double& x, const long double& y) { + return fabsl(x - y); +} +#endif + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y) +{ + return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y); +} + +#if defined(SYCL_DEVICE_ONLY) + SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(hypot, hypot) +#endif + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log1p, log1p) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float log1p(const float &x) { return ::log1pf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double log1p(const double &x) { return ::log1p(x); } +#endif + +template +EIGEN_DEVICE_FUNC +inline typename internal::pow_impl::result_type pow(const ScalarX& x, const ScalarY& y) +{ + return internal::pow_impl::run(x, y); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(pow, pow) +#endif + +template EIGEN_DEVICE_FUNC bool (isnan) (const T &x) { return internal::isnan_impl(x); } +template EIGEN_DEVICE_FUNC bool (isinf) (const T &x) { return internal::isinf_impl(x); } +template EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); } + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isnan, isnan, bool) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isinf, isinf, bool) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isfinite, isfinite, bool) +#endif + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(rint, Scalar) rint(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(rint, Scalar)::run(x); +} + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(round, round) +#endif + +template +EIGEN_DEVICE_FUNC +T (floor)(const T& x) +{ + EIGEN_USING_STD(floor) + return floor(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(floor, floor) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float floor(const float &x) { return ::floorf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double floor(const double &x) { return ::floor(x); } +#endif + +template +EIGEN_DEVICE_FUNC +T (ceil)(const T& x) +{ + EIGEN_USING_STD(ceil); + return ceil(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(ceil, ceil) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float ceil(const float &x) { return ::ceilf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double ceil(const double &x) { return ::ceil(x); } +#endif + + +/** Log base 2 for 32 bits positive integers. + * Conveniently returns 0 for x==0. */ +inline int log2(int x) +{ + eigen_assert(x>=0); + unsigned int v(x); + static const int table[32] = { 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31 }; + v |= v >> 1; + v |= v >> 2; + v |= v >> 4; + v |= v >> 8; + v |= v >> 16; + return table[(v * 0x07C4ACDDU) >> 27]; +} + +/** \returns the square root of \a x. + * + * It is essentially equivalent to + * \code using std::sqrt; return sqrt(x); \endcode + * but slightly faster for float/double and some compilers (e.g., gcc), thanks to + * specializations when SSE is enabled. + * + * It's usage is justified in performance critical functions, like norm/normalize. + */ +template +EIGEN_DEVICE_FUNC +EIGEN_ALWAYS_INLINE EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x); +} + +// Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool). +template<> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC +bool sqrt(const bool &x) { return x; } + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt) +#endif + +/** \returns the reciprocal square root of \a x. **/ +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T rsqrt(const T& x) +{ + return internal::rsqrt_impl::run(x); +} + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T log(const T &x) { + return internal::log_impl::run(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log, log) +#endif + + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float log(const float &x) { return ::logf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double log(const double &x) { return ::log(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +typename internal::enable_if::IsSigned || NumTraits::IsComplex,typename NumTraits::Real>::type +abs(const T &x) { + EIGEN_USING_STD(abs); + return abs(x); +} + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +typename internal::enable_if::IsSigned || NumTraits::IsComplex),typename NumTraits::Real>::type +abs(const T &x) { + return x; +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(abs, abs) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(abs, fabs) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float abs(const float &x) { return ::fabsf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double abs(const double &x) { return ::fabs(x); } + +template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float abs(const std::complex& x) { + return ::hypotf(x.real(), x.imag()); +} + +template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double abs(const std::complex& x) { + return ::hypot(x.real(), x.imag()); +} +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T exp(const T &x) { + EIGEN_USING_STD(exp); + return exp(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp, exp) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float exp(const float &x) { return ::expf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double exp(const double &x) { return ::exp(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +std::complex exp(const std::complex& x) { + float com = ::expf(x.real()); + float res_real = com * ::cosf(x.imag()); + float res_imag = com * ::sinf(x.imag()); + return std::complex(res_real, res_imag); +} + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +std::complex exp(const std::complex& x) { + double com = ::exp(x.real()); + double res_real = com * ::cos(x.imag()); + double res_imag = com * ::sin(x.imag()); + return std::complex(res_real, res_imag); +} +#endif + +template +EIGEN_DEVICE_FUNC +inline EIGEN_MATHFUNC_RETVAL(expm1, Scalar) expm1(const Scalar& x) +{ + return EIGEN_MATHFUNC_IMPL(expm1, Scalar)::run(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(expm1, expm1) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float expm1(const float &x) { return ::expm1f(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double expm1(const double &x) { return ::expm1(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T cos(const T &x) { + EIGEN_USING_STD(cos); + return cos(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cos,cos) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float cos(const float &x) { return ::cosf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double cos(const double &x) { return ::cos(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T sin(const T &x) { + EIGEN_USING_STD(sin); + return sin(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sin, sin) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float sin(const float &x) { return ::sinf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double sin(const double &x) { return ::sin(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T tan(const T &x) { + EIGEN_USING_STD(tan); + return tan(x); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tan, tan) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float tan(const float &x) { return ::tanf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double tan(const double &x) { return ::tan(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T acos(const T &x) { + EIGEN_USING_STD(acos); + return acos(x); +} + +#if EIGEN_HAS_CXX11_MATH +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T acosh(const T &x) { + EIGEN_USING_STD(acosh); + return static_cast(acosh(x)); +} +#endif + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acos, acos) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acosh, acosh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float acos(const float &x) { return ::acosf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double acos(const double &x) { return ::acos(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T asin(const T &x) { + EIGEN_USING_STD(asin); + return asin(x); +} + +#if EIGEN_HAS_CXX11_MATH +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T asinh(const T &x) { + EIGEN_USING_STD(asinh); + return static_cast(asinh(x)); +} +#endif + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asin, asin) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asinh, asinh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float asin(const float &x) { return ::asinf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double asin(const double &x) { return ::asin(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T atan(const T &x) { + EIGEN_USING_STD(atan); + return static_cast(atan(x)); +} + +#if EIGEN_HAS_CXX11_MATH +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T atanh(const T &x) { + EIGEN_USING_STD(atanh); + return static_cast(atanh(x)); +} +#endif + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atan, atan) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atanh, atanh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float atan(const float &x) { return ::atanf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double atan(const double &x) { return ::atan(x); } +#endif + + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T cosh(const T &x) { + EIGEN_USING_STD(cosh); + return static_cast(cosh(x)); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cosh, cosh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float cosh(const float &x) { return ::coshf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double cosh(const double &x) { return ::cosh(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T sinh(const T &x) { + EIGEN_USING_STD(sinh); + return static_cast(sinh(x)); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sinh, sinh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float sinh(const float &x) { return ::sinhf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double sinh(const double &x) { return ::sinh(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T tanh(const T &x) { + EIGEN_USING_STD(tanh); + return tanh(x); +} + +#if (!defined(EIGEN_GPUCC)) && EIGEN_FAST_MATH && !defined(SYCL_DEVICE_ONLY) +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float tanh(float x) { return internal::generic_fast_tanh_float(x); } +#endif + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tanh, tanh) +#endif + +#if defined(EIGEN_GPUCC) +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float tanh(const float &x) { return ::tanhf(x); } + +template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double tanh(const double &x) { return ::tanh(x); } +#endif + +template +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +T fmod(const T& a, const T& b) { + EIGEN_USING_STD(fmod); + return fmod(a, b); +} + +#if defined(SYCL_DEVICE_ONLY) +SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(fmod, fmod) +#endif + +#if defined(EIGEN_GPUCC) +template <> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +float fmod(const float& a, const float& b) { + return ::fmodf(a, b); +} + +template <> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +double fmod(const double& a, const double& b) { + return ::fmod(a, b); +} +#endif + +#if defined(SYCL_DEVICE_ONLY) +#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY +#undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY +#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY +#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY +#undef SYCL_SPECIALIZE_INTEGER_TYPES_BINARY +#undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY +#undef SYCL_SPECIALIZE_FLOATING_TYPES_BINARY +#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY +#undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE +#undef SYCL_SPECIALIZE_GEN_UNARY_FUNC +#undef SYCL_SPECIALIZE_UNARY_FUNC +#undef SYCL_SPECIALIZE_GEN1_BINARY_FUNC +#undef SYCL_SPECIALIZE_GEN2_BINARY_FUNC +#undef SYCL_SPECIALIZE_BINARY_FUNC +#endif + +} // end namespace numext + +namespace internal { + +template +EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex& x) +{ + return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x)); +} + +template +EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex& x) +{ + return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x)); +} + +template +EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex& x) +{ + return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x)); +} + +/**************************************************************************** +* Implementation of fuzzy comparisons * +****************************************************************************/ + +template +struct scalar_fuzzy_default_impl {}; + +template +struct scalar_fuzzy_default_impl +{ + typedef typename NumTraits::Real RealScalar; + template EIGEN_DEVICE_FUNC + static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec) + { + return numext::abs(x) <= numext::abs(y) * prec; + } + EIGEN_DEVICE_FUNC + static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec) + { + return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec; + } + EIGEN_DEVICE_FUNC + static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec) + { + return x <= y || isApprox(x, y, prec); + } +}; + +template +struct scalar_fuzzy_default_impl +{ + typedef typename NumTraits::Real RealScalar; + template EIGEN_DEVICE_FUNC + static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&) + { + return x == Scalar(0); + } + EIGEN_DEVICE_FUNC + static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&) + { + return x == y; + } + EIGEN_DEVICE_FUNC + static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&) + { + return x <= y; + } +}; + +template +struct scalar_fuzzy_default_impl +{ + typedef typename NumTraits::Real RealScalar; + template EIGEN_DEVICE_FUNC + static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec) + { + return numext::abs2(x) <= numext::abs2(y) * prec * prec; + } + EIGEN_DEVICE_FUNC + static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec) + { + return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec; + } +}; + +template +struct scalar_fuzzy_impl : scalar_fuzzy_default_impl::IsComplex, NumTraits::IsInteger> {}; + +template EIGEN_DEVICE_FUNC +inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, + const typename NumTraits::Real &precision = NumTraits::dummy_precision()) +{ + return scalar_fuzzy_impl::template isMuchSmallerThan(x, y, precision); +} + +template EIGEN_DEVICE_FUNC +inline bool isApprox(const Scalar& x, const Scalar& y, + const typename NumTraits::Real &precision = NumTraits::dummy_precision()) +{ + return scalar_fuzzy_impl::isApprox(x, y, precision); +} + +template EIGEN_DEVICE_FUNC +inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, + const typename NumTraits::Real &precision = NumTraits::dummy_precision()) +{ + return scalar_fuzzy_impl::isApproxOrLessThan(x, y, precision); +} + +/****************************************** +*** The special case of the bool type *** +******************************************/ + +template<> struct random_impl +{ + static inline bool run() + { + return random(0,1)==0 ? false : true; + } + + static inline bool run(const bool& a, const bool& b) + { + return random(a, b)==0 ? false : true; + } +}; + +template<> struct scalar_fuzzy_impl +{ + typedef bool RealScalar; + + template EIGEN_DEVICE_FUNC + static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&) + { + return !x; + } + + EIGEN_DEVICE_FUNC + static inline bool isApprox(bool x, bool y, bool) + { + return x == y; + } + + EIGEN_DEVICE_FUNC + static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&) + { + return (!x) || y; + } + +}; + +} // end namespace internal + +// Default implementations that rely on other numext implementations +namespace internal { + +// Specialization for complex types that are not supported by std::expm1. +template +struct expm1_impl > { + EIGEN_DEVICE_FUNC static inline std::complex run( + const std::complex& x) { + EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar) + RealScalar xr = x.real(); + RealScalar xi = x.imag(); + // expm1(z) = exp(z) - 1 + // = exp(x + i * y) - 1 + // = exp(x) * (cos(y) + i * sin(y)) - 1 + // = exp(x) * cos(y) - 1 + i * exp(x) * sin(y) + // Imag(expm1(z)) = exp(x) * sin(y) + // Real(expm1(z)) = exp(x) * cos(y) - 1 + // = exp(x) * cos(y) - 1. + // = expm1(x) + exp(x) * (cos(y) - 1) + // = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2) + RealScalar erm1 = numext::expm1(xr); + RealScalar er = erm1 + RealScalar(1.); + RealScalar sin2 = numext::sin(xi / RealScalar(2.)); + sin2 = sin2 * sin2; + RealScalar s = numext::sin(xi); + RealScalar real_part = erm1 - RealScalar(2.) * er * sin2; + return std::complex(real_part, er * s); + } +}; + +template +struct rsqrt_impl { + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE T run(const T& x) { + return T(1)/numext::sqrt(x); + } +}; + +#if defined(EIGEN_GPU_COMPILE_PHASE) +template +struct conj_impl, true> +{ + EIGEN_DEVICE_FUNC + static inline std::complex run(const std::complex& x) + { + return std::complex(numext::real(x), -numext::imag(x)); + } +}; +#endif + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATHFUNCTIONS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctionsImpl.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctionsImpl.h new file mode 100644 index 0000000000000000000000000000000000000000..4eaaaa78449031830cea7446210226afcd2467d0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MathFunctionsImpl.h @@ -0,0 +1,200 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) +// Copyright (C) 2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATHFUNCTIONSIMPL_H +#define EIGEN_MATHFUNCTIONSIMPL_H + +namespace Eigen { + +namespace internal { + +/** \internal \returns the hyperbolic tan of \a a (coeff-wise) + Doesn't do anything fancy, just a 13/6-degree rational interpolant which + is accurate up to a couple of ulps in the (approximate) range [-8, 8], + outside of which tanh(x) = +/-1 in single precision. The input is clamped + to the range [-c, c]. The value c is chosen as the smallest value where + the approximation evaluates to exactly 1. In the reange [-0.0004, 0.0004] + the approxmation tanh(x) ~= x is used for better accuracy as x tends to zero. + + This implementation works on both scalars and packets. +*/ +template +T generic_fast_tanh_float(const T& a_x) +{ + // Clamp the inputs to the range [-c, c] +#ifdef EIGEN_VECTORIZE_FMA + const T plus_clamp = pset1(7.99881172180175781f); + const T minus_clamp = pset1(-7.99881172180175781f); +#else + const T plus_clamp = pset1(7.90531110763549805f); + const T minus_clamp = pset1(-7.90531110763549805f); +#endif + const T tiny = pset1(0.0004f); + const T x = pmax(pmin(a_x, plus_clamp), minus_clamp); + const T tiny_mask = pcmp_lt(pabs(a_x), tiny); + // The monomial coefficients of the numerator polynomial (odd). + const T alpha_1 = pset1(4.89352455891786e-03f); + const T alpha_3 = pset1(6.37261928875436e-04f); + const T alpha_5 = pset1(1.48572235717979e-05f); + const T alpha_7 = pset1(5.12229709037114e-08f); + const T alpha_9 = pset1(-8.60467152213735e-11f); + const T alpha_11 = pset1(2.00018790482477e-13f); + const T alpha_13 = pset1(-2.76076847742355e-16f); + + // The monomial coefficients of the denominator polynomial (even). + const T beta_0 = pset1(4.89352518554385e-03f); + const T beta_2 = pset1(2.26843463243900e-03f); + const T beta_4 = pset1(1.18534705686654e-04f); + const T beta_6 = pset1(1.19825839466702e-06f); + + // Since the polynomials are odd/even, we need x^2. + const T x2 = pmul(x, x); + + // Evaluate the numerator polynomial p. + T p = pmadd(x2, alpha_13, alpha_11); + p = pmadd(x2, p, alpha_9); + p = pmadd(x2, p, alpha_7); + p = pmadd(x2, p, alpha_5); + p = pmadd(x2, p, alpha_3); + p = pmadd(x2, p, alpha_1); + p = pmul(x, p); + + // Evaluate the denominator polynomial q. + T q = pmadd(x2, beta_6, beta_4); + q = pmadd(x2, q, beta_2); + q = pmadd(x2, q, beta_0); + + // Divide the numerator by the denominator. + return pselect(tiny_mask, x, pdiv(p, q)); +} + +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE +RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y) +{ + // IEEE IEC 6059 special cases. + if ((numext::isinf)(x) || (numext::isinf)(y)) + return NumTraits::infinity(); + if ((numext::isnan)(x) || (numext::isnan)(y)) + return NumTraits::quiet_NaN(); + + EIGEN_USING_STD(sqrt); + RealScalar p, qp; + p = numext::maxi(x,y); + if(p==RealScalar(0)) return RealScalar(0); + qp = numext::mini(y,x) / p; + return p * sqrt(RealScalar(1) + qp*qp); +} + +template +struct hypot_impl +{ + typedef typename NumTraits::Real RealScalar; + static EIGEN_DEVICE_FUNC + inline RealScalar run(const Scalar& x, const Scalar& y) + { + EIGEN_USING_STD(abs); + return positive_real_hypot(abs(x), abs(y)); + } +}; + +// Generic complex sqrt implementation that correctly handles corner cases +// according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt +template +EIGEN_DEVICE_FUNC std::complex complex_sqrt(const std::complex& z) { + // Computes the principal sqrt of the input. + // + // For a complex square root of the number x + i*y. We want to find real + // numbers u and v such that + // (u + i*v)^2 = x + i*y <=> + // u^2 - v^2 + i*2*u*v = x + i*v. + // By equating the real and imaginary parts we get: + // u^2 - v^2 = x + // 2*u*v = y. + // + // For x >= 0, this has the numerically stable solution + // u = sqrt(0.5 * (x + sqrt(x^2 + y^2))) + // v = y / (2 * u) + // and for x < 0, + // v = sign(y) * sqrt(0.5 * (-x + sqrt(x^2 + y^2))) + // u = y / (2 * v) + // + // Letting w = sqrt(0.5 * (|x| + |z|)), + // if x == 0: u = w, v = sign(y) * w + // if x > 0: u = w, v = y / (2 * w) + // if x < 0: u = |y| / (2 * w), v = sign(y) * w + + const T x = numext::real(z); + const T y = numext::imag(z); + const T zero = T(0); + const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y))); + + return + (numext::isinf)(y) ? std::complex(NumTraits::infinity(), y) + : x == zero ? std::complex(w, y < zero ? -w : w) + : x > zero ? std::complex(w, y / (2 * w)) + : std::complex(numext::abs(y) / (2 * w), y < zero ? -w : w ); +} + +// Generic complex rsqrt implementation. +template +EIGEN_DEVICE_FUNC std::complex complex_rsqrt(const std::complex& z) { + // Computes the principal reciprocal sqrt of the input. + // + // For a complex reciprocal square root of the number z = x + i*y. We want to + // find real numbers u and v such that + // (u + i*v)^2 = 1 / (x + i*y) <=> + // u^2 - v^2 + i*2*u*v = x/|z|^2 - i*v/|z|^2. + // By equating the real and imaginary parts we get: + // u^2 - v^2 = x/|z|^2 + // 2*u*v = y/|z|^2. + // + // For x >= 0, this has the numerically stable solution + // u = sqrt(0.5 * (x + |z|)) / |z| + // v = -y / (2 * u * |z|) + // and for x < 0, + // v = -sign(y) * sqrt(0.5 * (-x + |z|)) / |z| + // u = -y / (2 * v * |z|) + // + // Letting w = sqrt(0.5 * (|x| + |z|)), + // if x == 0: u = w / |z|, v = -sign(y) * w / |z| + // if x > 0: u = w / |z|, v = -y / (2 * w * |z|) + // if x < 0: u = |y| / (2 * w * |z|), v = -sign(y) * w / |z| + + const T x = numext::real(z); + const T y = numext::imag(z); + const T zero = T(0); + + const T abs_z = numext::hypot(x, y); + const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z)); + const T woz = w / abs_z; + // Corner cases consistent with 1/sqrt(z) on gcc/clang. + return + abs_z == zero ? std::complex(NumTraits::infinity(), NumTraits::quiet_NaN()) + : ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex(zero, zero) + : x == zero ? std::complex(woz, y < zero ? woz : -woz) + : x > zero ? std::complex(woz, -y / (2 * w * abs_z)) + : std::complex(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz ); +} + +template +EIGEN_DEVICE_FUNC std::complex complex_log(const std::complex& z) { + // Computes complex log. + T a = numext::abs(z); + EIGEN_USING_STD(atan2); + T b = atan2(z.imag(), z.real()); + return std::complex(numext::log(a), b); +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATHFUNCTIONSIMPL_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Matrix.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Matrix.h new file mode 100644 index 0000000000000000000000000000000000000000..de54824ce22f801f62242ab65e1ada021cd8f214 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Matrix.h @@ -0,0 +1,565 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIX_H +#define EIGEN_MATRIX_H + +namespace Eigen { + +namespace internal { +template +struct traits > +{ +private: + enum { size = internal::size_at_compile_time::ret }; + typedef typename find_best_packet::type PacketScalar; + enum { + row_major_bit = Options_&RowMajor ? RowMajorBit : 0, + is_dynamic_size_storage = MaxRows_==Dynamic || MaxCols_==Dynamic, + max_size = is_dynamic_size_storage ? Dynamic : MaxRows_*MaxCols_, + default_alignment = compute_default_alignment::value, + actual_alignment = ((Options_&DontAlign)==0) ? default_alignment : 0, + required_alignment = unpacket_traits::alignment, + packet_access_bit = (packet_traits::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=required_alignment))) ? PacketAccessBit : 0 + }; + +public: + typedef Scalar_ Scalar; + typedef Dense StorageKind; + typedef Eigen::Index StorageIndex; + typedef MatrixXpr XprKind; + enum { + RowsAtCompileTime = Rows_, + ColsAtCompileTime = Cols_, + MaxRowsAtCompileTime = MaxRows_, + MaxColsAtCompileTime = MaxCols_, + Flags = compute_matrix_flags::ret, + Options = Options_, + InnerStrideAtCompileTime = 1, + OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime, + + // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase + EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit, + Alignment = actual_alignment + }; +}; +} + +/** \class Matrix + * \ingroup Core_Module + * + * \brief The matrix class, also used for vectors and row-vectors + * + * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen. + * Vectors are matrices with one column, and row-vectors are matrices with one row. + * + * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note"). + * + * The first three template parameters are required: + * \tparam Scalar_ Numeric type, e.g. float, double, int or std::complex. + * User defined scalar types are supported as well (see \ref user_defined_scalars "here"). + * \tparam Rows_ Number of rows, or \b Dynamic + * \tparam Cols_ Number of columns, or \b Dynamic + * + * The remaining template parameters are optional -- in most cases you don't have to worry about them. + * \tparam Options_ A combination of either \b #RowMajor or \b #ColMajor, and of either + * \b #AutoAlign or \b #DontAlign. + * The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required + * for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size. + * \tparam MaxRows_ Maximum number of rows. Defaults to \a Rows_ (\ref maxrows "note"). + * \tparam MaxCols_ Maximum number of columns. Defaults to \a Cols_ (\ref maxrows "note"). + * + * Eigen provides a number of typedefs covering the usual cases. Here are some examples: + * + * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix) + * \li \c Vector4f is a vector of 4 floats (\c Matrix) + * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix) + * + * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix) + * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix) + * + * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix) + * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix) + * + * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs. + * + * You can access elements of vectors and matrices using normal subscripting: + * + * \code + * Eigen::VectorXd v(10); + * v[0] = 0.1; + * v[1] = 0.2; + * v(0) = 0.3; + * v(1) = 0.4; + * + * Eigen::MatrixXi m(10, 10); + * m(0, 1) = 1; + * m(0, 2) = 2; + * m(0, 3) = 3; + * \endcode + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN. + * + * Some notes: + * + *
+ *
\anchor dense Dense versus sparse:
+ *
This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module. + * + * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array. + * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.
+ * + *
\anchor fixedsize Fixed-size versus dynamic-size:
+ *
Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array + * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up + * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time. + * + * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime + * variables, and the array of coefficients is allocated dynamically on the heap. + * + * Note that \em dense matrices, be they Fixed-size or Dynamic-size, do not expand dynamically in the sense of a std::map. + * If you want this behavior, see the Sparse module.
+ * + *
\anchor maxrows MaxRows_ and MaxCols_:
+ *
In most cases, one just leaves these parameters to the default values. + * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases + * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot + * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case MaxRows_ and MaxCols_ + * are the dimensions of the original matrix, while Rows_ and Cols_ are Dynamic.
+ *
+ * + * ABI and storage layout + * + * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3. + * + * + * + * + * + * + *
Matrix typeEquivalent C structure
\code Matrix \endcode\code + * struct { + * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 + * Eigen::Index rows, cols; + * }; + * \endcode
\code + * Matrix + * Matrix \endcode\code + * struct { + * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0 + * Eigen::Index size; + * }; + * \endcode
\code Matrix \endcode\code + * struct { + * T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0 + * }; + * \endcode
\code Matrix \endcode\code + * struct { + * T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0 + * Eigen::Index rows, cols; + * }; + * \endcode
+ * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two + * smaller to EIGEN_MAX_STATIC_ALIGN_BYTES. + * + * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, + * \ref TopicStorageOrders + */ + +template +class Matrix + : public PlainObjectBase > +{ + public: + + /** \brief Base class typedef. + * \sa PlainObjectBase + */ + typedef PlainObjectBase Base; + + enum { Options = Options_ }; + + EIGEN_DENSE_PUBLIC_INTERFACE(Matrix) + + typedef typename Base::PlainObject PlainObject; + + using Base::base; + using Base::coeffRef; + + /** + * \brief Assigns matrices to each other. + * + * \note This is a special case of the templated operator=. Its purpose is + * to prevent a default operator= from hiding the templated operator=. + * + * \callgraph + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other) + { + return Base::_set(other); + } + + /** \internal + * \brief Copies the value of the expression \a other into \c *this with automatic resizing. + * + * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized), + * it will be initialized. + * + * Note that copying a row-vector into a vector (and conversely) is allowed. + * The resizing, if any, is then done in the appropriate way so that row-vectors + * remain row-vectors and vectors remain vectors. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase& other) + { + return Base::_set(other); + } + + /* Here, doxygen failed to copy the brief information when using \copydoc */ + + /** + * \brief Copies the generic expression \a other into *this. + * \copydetails DenseBase::operator=(const EigenBase &other) + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase &other) + { + return Base::operator=(other); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue& func) + { + return Base::operator=(func); + } + + /** \brief Default constructor. + * + * For fixed-size matrices, does nothing. + * + * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix + * is called a null matrix. This constructor is the unique way to create null matrices: resizing + * a matrix to 0 is not supported. + * + * \sa resize(Index,Index) + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Matrix() : Base() + { + Base::_check_template_params(); + EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } + + // FIXME is it still needed + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit Matrix(internal::constructor_without_unaligned_array_assert) + : Base(internal::constructor_without_unaligned_array_assert()) + { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED } + +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible::value) + : Base(std::move(other)) + { + Base::_check_template_params(); + } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable::value) + { + Base::operator=(std::move(other)); + return *this; + } +#endif + +#if EIGEN_HAS_CXX11 + /** \copydoc PlainObjectBase(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&... args) + * + * Example: \include Matrix_variadic_ctor_cxx11.cpp + * Output: \verbinclude Matrix_variadic_ctor_cxx11.out + * + * \sa Matrix(const std::initializer_list>&) + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + : Base(a0, a1, a2, a3, args...) {} + + /** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. \cpp11 + * + * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients: + * + * Example: \include Matrix_initializer_list_23_cxx11.cpp + * Output: \verbinclude Matrix_initializer_list_23_cxx11.out + * + * Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered. + * + * In the case of a compile-time column vector, implicit transposition from a single row is allowed. + * Therefore VectorXd{{1,2,3,4,5}} is legal and the more verbose syntax + * RowVectorXd{{1},{2},{3},{4},{5}} can be avoided: + * + * Example: \include Matrix_initializer_list_vector_cxx11.cpp + * Output: \verbinclude Matrix_initializer_list_vector_cxx11.out + * + * In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes, + * and implicit transposition is allowed for compile-time vectors only. + * + * \sa Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + */ + EIGEN_DEVICE_FUNC + explicit EIGEN_STRONG_INLINE Matrix(const std::initializer_list>& list) : Base(list) {} +#endif // end EIGEN_HAS_CXX11 + +#ifndef EIGEN_PARSED_BY_DOXYGEN + + // This constructor is for both 1x1 matrices and dynamic vectors + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit Matrix(const T& x) + { + Base::_check_template_params(); + Base::template _init1(x); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Matrix(const T0& x, const T1& y) + { + Base::_check_template_params(); + Base::template _init2(x, y); + } + + +#else + /** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */ + EIGEN_DEVICE_FUNC + explicit Matrix(const Scalar *data); + + /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors + * + * This is useful for dynamic-size vectors. For fixed-size vectors, + * it is redundant to pass these parameters, so one should use the default constructor + * Matrix() instead. + * + * \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance, + * calling Matrix(1) will call the initialization constructor: Matrix(const Scalar&). + * For fixed-size \c 1x1 matrices it is therefore recommended to use the default + * constructor Matrix() instead, especially when using one of the non standard + * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives). + */ + EIGEN_STRONG_INLINE explicit Matrix(Index dim); + /** \brief Constructs an initialized 1x1 matrix with the given coefficient + * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */ + Matrix(const Scalar& x); + /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns. + * + * This is useful for dynamic-size matrices. For fixed-size matrices, + * it is redundant to pass these parameters, so one should use the default constructor + * Matrix() instead. + * + * \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance, + * calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y). + * For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default + * constructor Matrix() instead, especially when using one of the non standard + * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives). + */ + EIGEN_DEVICE_FUNC + Matrix(Index rows, Index cols); + + /** \brief Constructs an initialized 2D vector with given coefficients + * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) */ + Matrix(const Scalar& x, const Scalar& y); + #endif // end EIGEN_PARSED_BY_DOXYGEN + + /** \brief Constructs an initialized 3D vector with given coefficients + * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z) + { + Base::_check_template_params(); + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3) + m_storage.data()[0] = x; + m_storage.data()[1] = y; + m_storage.data()[2] = z; + } + /** \brief Constructs an initialized 4D vector with given coefficients + * \sa Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w) + { + Base::_check_template_params(); + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4) + m_storage.data()[0] = x; + m_storage.data()[1] = y; + m_storage.data()[2] = z; + m_storage.data()[3] = w; + } + + + /** \brief Copy constructor */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other) + { } + + /** \brief Copy constructor for generic expressions. + * \sa MatrixBase::operator=(const EigenBase&) + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Matrix(const EigenBase &other) + : Base(other.derived()) + { } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const EIGEN_NOEXCEPT { return 1; } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); } + + /////////// Geometry module /////////// + + template + EIGEN_DEVICE_FUNC + explicit Matrix(const RotationBase& r); + template + EIGEN_DEVICE_FUNC + Matrix& operator=(const RotationBase& r); + + // allow to extend Matrix outside Eigen + #ifdef EIGEN_MATRIX_PLUGIN + #include EIGEN_MATRIX_PLUGIN + #endif + + protected: + template + friend struct internal::conservative_resize_like_impl; + + using Base::m_storage; +}; + +/** \defgroup matrixtypedefs Global matrix typedefs + * + * \ingroup Core_Module + * + * %Eigen defines several typedef shortcuts for most common matrix and vector types. + * + * The general patterns are the following: + * + * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size, + * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd + * for complex double. + * + * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats. + * + * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is + * a fixed-size vector of 4 complex floats. + * + * With \cpp11, template alias are also defined for common sizes. + * They follow the same pattern as above except that the scalar type suffix is replaced by a + * template parameter, i.e.: + * - `MatrixSize` where `Size` can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size. + * - `MatrixXSize` and `MatrixSizeX` where `Size` can be \c 2,\c 3,\c 4 for hybrid dynamic/fixed matrices. + * - `VectorSize` and `RowVectorSize` for column and row vectors. + * + * With \cpp11, you can also use fully generic column and row vector types: `Vector` and `RowVector`. + * + * \sa class Matrix + */ + +#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ +/** \ingroup matrixtypedefs */ \ +typedef Matrix Matrix##SizeSuffix##TypeSuffix; \ +/** \ingroup matrixtypedefs */ \ +typedef Matrix Vector##SizeSuffix##TypeSuffix; \ +/** \ingroup matrixtypedefs */ \ +typedef Matrix RowVector##SizeSuffix##TypeSuffix; + +#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \ +/** \ingroup matrixtypedefs */ \ +typedef Matrix Matrix##Size##X##TypeSuffix; \ +/** \ingroup matrixtypedefs */ \ +typedef Matrix Matrix##X##Size##TypeSuffix; + +#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ +EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ +EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ +EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ +EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \ +EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \ +EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \ +EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4) + +EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) +EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) +EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) +EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex, cf) +EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex, cd) + +#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES +#undef EIGEN_MAKE_TYPEDEFS +#undef EIGEN_MAKE_FIXED_TYPEDEFS + +#if EIGEN_HAS_CXX11 + +#define EIGEN_MAKE_TYPEDEFS(Size, SizeSuffix) \ +/** \ingroup matrixtypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Matrix##SizeSuffix = Matrix; \ +/** \ingroup matrixtypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Vector##SizeSuffix = Matrix; \ +/** \ingroup matrixtypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using RowVector##SizeSuffix = Matrix; + +#define EIGEN_MAKE_FIXED_TYPEDEFS(Size) \ +/** \ingroup matrixtypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Matrix##Size##X = Matrix; \ +/** \ingroup matrixtypedefs */ \ +/** \brief \cpp11 */ \ +template \ +using Matrix##X##Size = Matrix; + +EIGEN_MAKE_TYPEDEFS(2, 2) +EIGEN_MAKE_TYPEDEFS(3, 3) +EIGEN_MAKE_TYPEDEFS(4, 4) +EIGEN_MAKE_TYPEDEFS(Dynamic, X) +EIGEN_MAKE_FIXED_TYPEDEFS(2) +EIGEN_MAKE_FIXED_TYPEDEFS(3) +EIGEN_MAKE_FIXED_TYPEDEFS(4) + +/** \ingroup matrixtypedefs + * \brief \cpp11 */ +template +using Vector = Matrix; + +/** \ingroup matrixtypedefs + * \brief \cpp11 */ +template +using RowVector = Matrix; + +#undef EIGEN_MAKE_TYPEDEFS +#undef EIGEN_MAKE_FIXED_TYPEDEFS + +#endif // EIGEN_HAS_CXX11 + +} // end namespace Eigen + +#endif // EIGEN_MATRIX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MatrixBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MatrixBase.h new file mode 100644 index 0000000000000000000000000000000000000000..45c3a596ecb09d5e55f4eaf3c742d0badb624373 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/MatrixBase.h @@ -0,0 +1,547 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2009 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATRIXBASE_H +#define EIGEN_MATRIXBASE_H + +namespace Eigen { + +/** \class MatrixBase + * \ingroup Core_Module + * + * \brief Base class for all dense matrices, vectors, and expressions + * + * This class is the base that is inherited by all matrix, vector, and related expression + * types. Most of the Eigen API is contained in this class, and its base classes. Other important + * classes for the Eigen API are Matrix, and VectorwiseOp. + * + * Note that some methods are defined in other modules such as the \ref LU_Module LU module + * for all functions related to matrix inversions. + * + * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc. + * + * When writing a function taking Eigen objects as argument, if you want your function + * to take as argument any matrix, vector, or expression, just let it take a + * MatrixBase argument. As an example, here is a function printFirstRow which, given + * a matrix, vector, or expression \a x, prints the first row of \a x. + * + * \code + template + void printFirstRow(const Eigen::MatrixBase& x) + { + cout << x.row(0) << endl; + } + * \endcode + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN. + * + * \sa \blank \ref TopicClassHierarchy + */ +template class MatrixBase + : public DenseBase +{ + public: +#ifndef EIGEN_PARSED_BY_DOXYGEN + typedef MatrixBase StorageBaseType; + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::StorageIndex StorageIndex; + typedef typename internal::traits::Scalar Scalar; + typedef typename internal::packet_traits::type PacketScalar; + typedef typename NumTraits::Real RealScalar; + + typedef DenseBase Base; + using Base::RowsAtCompileTime; + using Base::ColsAtCompileTime; + using Base::SizeAtCompileTime; + using Base::MaxRowsAtCompileTime; + using Base::MaxColsAtCompileTime; + using Base::MaxSizeAtCompileTime; + using Base::IsVectorAtCompileTime; + using Base::Flags; + + using Base::derived; + using Base::const_cast_derived; + using Base::rows; + using Base::cols; + using Base::size; + using Base::coeff; + using Base::coeffRef; + using Base::lazyAssign; + using Base::eval; + using Base::operator-; + using Base::operator+=; + using Base::operator-=; + using Base::operator*=; + using Base::operator/=; + + typedef typename Base::CoeffReturnType CoeffReturnType; + typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType; + typedef typename Base::RowXpr RowXpr; + typedef typename Base::ColXpr ColXpr; +#endif // not EIGEN_PARSED_BY_DOXYGEN + + + +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** type of the equivalent square matrix */ + typedef Matrix SquareMatrixType; +#endif // not EIGEN_PARSED_BY_DOXYGEN + + /** \returns the size of the main diagonal, which is min(rows(),cols()). + * \sa rows(), cols(), SizeAtCompileTime. */ + EIGEN_DEVICE_FUNC + inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); } + + typedef typename Base::PlainObject PlainObject; + +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** \internal Represents a matrix with all coefficients equal to one another*/ + typedef CwiseNullaryOp,PlainObject> ConstantReturnType; + /** \internal the return type of MatrixBase::adjoint() */ + typedef typename internal::conditional::IsComplex, + CwiseUnaryOp, ConstTransposeReturnType>, + ConstTransposeReturnType + >::type AdjointReturnType; + /** \internal Return type of eigenvalues() */ + typedef Matrix, internal::traits::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType; + /** \internal the return type of identity */ + typedef CwiseNullaryOp,PlainObject> IdentityReturnType; + /** \internal the return type of unit vectors */ + typedef Block, SquareMatrixType>, + internal::traits::RowsAtCompileTime, + internal::traits::ColsAtCompileTime> BasisReturnType; +#endif // not EIGEN_PARSED_BY_DOXYGEN + +#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase +#define EIGEN_DOC_UNARY_ADDONS(X,Y) +# include "../plugins/CommonCwiseBinaryOps.h" +# include "../plugins/MatrixCwiseUnaryOps.h" +# include "../plugins/MatrixCwiseBinaryOps.h" +# ifdef EIGEN_MATRIXBASE_PLUGIN +# include EIGEN_MATRIXBASE_PLUGIN +# endif +#undef EIGEN_CURRENT_STORAGE_BASE_CLASS +#undef EIGEN_DOC_UNARY_ADDONS + + /** Special case of the template operator=, in order to prevent the compiler + * from generating a default operator= (issue hit with g++ 4.1) + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const MatrixBase& other); + + // We cannot inherit here via Base::operator= since it is causing + // trouble with MSVC. + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator=(const DenseBase& other); + + template + EIGEN_DEVICE_FUNC + Derived& operator=(const EigenBase& other); + + template + EIGEN_DEVICE_FUNC + Derived& operator=(const ReturnByValue& other); + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator+=(const MatrixBase& other); + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Derived& operator-=(const MatrixBase& other); + + template + EIGEN_DEVICE_FUNC + const Product + operator*(const MatrixBase &other) const; + + template + EIGEN_DEVICE_FUNC + const Product + lazyProduct(const MatrixBase &other) const; + + template + Derived& operator*=(const EigenBase& other); + + template + void applyOnTheLeft(const EigenBase& other); + + template + void applyOnTheRight(const EigenBase& other); + + template + EIGEN_DEVICE_FUNC + const Product + operator*(const DiagonalBase &diagonal) const; + + template + EIGEN_DEVICE_FUNC + typename ScalarBinaryOpTraits::Scalar,typename internal::traits::Scalar>::ReturnType + dot(const MatrixBase& other) const; + + EIGEN_DEVICE_FUNC RealScalar squaredNorm() const; + EIGEN_DEVICE_FUNC RealScalar norm() const; + RealScalar stableNorm() const; + RealScalar blueNorm() const; + RealScalar hypotNorm() const; + EIGEN_DEVICE_FUNC const PlainObject normalized() const; + EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const; + EIGEN_DEVICE_FUNC void normalize(); + EIGEN_DEVICE_FUNC void stableNormalize(); + + EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const; + EIGEN_DEVICE_FUNC void adjointInPlace(); + + typedef Diagonal DiagonalReturnType; + EIGEN_DEVICE_FUNC + DiagonalReturnType diagonal(); + + typedef typename internal::add_const >::type ConstDiagonalReturnType; + EIGEN_DEVICE_FUNC + ConstDiagonalReturnType diagonal() const; + + template struct DiagonalIndexReturnType { typedef Diagonal Type; }; + template struct ConstDiagonalIndexReturnType { typedef const Diagonal Type; }; + + template + EIGEN_DEVICE_FUNC + typename DiagonalIndexReturnType::Type diagonal(); + + template + EIGEN_DEVICE_FUNC + typename ConstDiagonalIndexReturnType::Type diagonal() const; + + typedef Diagonal DiagonalDynamicIndexReturnType; + typedef typename internal::add_const >::type ConstDiagonalDynamicIndexReturnType; + + EIGEN_DEVICE_FUNC + DiagonalDynamicIndexReturnType diagonal(Index index); + EIGEN_DEVICE_FUNC + ConstDiagonalDynamicIndexReturnType diagonal(Index index) const; + + template struct TriangularViewReturnType { typedef TriangularView Type; }; + template struct ConstTriangularViewReturnType { typedef const TriangularView Type; }; + + template + EIGEN_DEVICE_FUNC + typename TriangularViewReturnType::Type triangularView(); + template + EIGEN_DEVICE_FUNC + typename ConstTriangularViewReturnType::Type triangularView() const; + + template struct SelfAdjointViewReturnType { typedef SelfAdjointView Type; }; + template struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView Type; }; + + template + EIGEN_DEVICE_FUNC + typename SelfAdjointViewReturnType::Type selfadjointView(); + template + EIGEN_DEVICE_FUNC + typename ConstSelfAdjointViewReturnType::Type selfadjointView() const; + + const SparseView sparseView(const Scalar& m_reference = Scalar(0), + const typename NumTraits::Real& m_epsilon = NumTraits::dummy_precision()) const; + EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(); + EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols); + EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i); + EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i); + EIGEN_DEVICE_FUNC static const BasisReturnType UnitX(); + EIGEN_DEVICE_FUNC static const BasisReturnType UnitY(); + EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ(); + EIGEN_DEVICE_FUNC static const BasisReturnType UnitW(); + + EIGEN_DEVICE_FUNC + const DiagonalWrapper asDiagonal() const; + const PermutationWrapper asPermutation() const; + + EIGEN_DEVICE_FUNC + Derived& setIdentity(); + EIGEN_DEVICE_FUNC + Derived& setIdentity(Index rows, Index cols); + EIGEN_DEVICE_FUNC Derived& setUnit(Index i); + EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i); + + bool isIdentity(const RealScalar& prec = NumTraits::dummy_precision()) const; + bool isDiagonal(const RealScalar& prec = NumTraits::dummy_precision()) const; + + bool isUpperTriangular(const RealScalar& prec = NumTraits::dummy_precision()) const; + bool isLowerTriangular(const RealScalar& prec = NumTraits::dummy_precision()) const; + + template + bool isOrthogonal(const MatrixBase& other, + const RealScalar& prec = NumTraits::dummy_precision()) const; + bool isUnitary(const RealScalar& prec = NumTraits::dummy_precision()) const; + + /** \returns true if each coefficients of \c *this and \a other are all exactly equal. + * \warning When using floating point scalar values you probably should rather use a + * fuzzy comparison such as isApprox() + * \sa isApprox(), operator!= */ + template + EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase& other) const + { return cwiseEqual(other).all(); } + + /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other. + * \warning When using floating point scalar values you probably should rather use a + * fuzzy comparison such as isApprox() + * \sa isApprox(), operator== */ + template + EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase& other) const + { return cwiseNotEqual(other).any(); } + + NoAlias EIGEN_DEVICE_FUNC noalias(); + + // TODO forceAlignedAccess is temporarily disabled + // Need to find a nicer workaround. + inline const Derived& forceAlignedAccess() const { return derived(); } + inline Derived& forceAlignedAccess() { return derived(); } + template inline const Derived& forceAlignedAccessIf() const { return derived(); } + template inline Derived& forceAlignedAccessIf() { return derived(); } + + EIGEN_DEVICE_FUNC Scalar trace() const; + + template EIGEN_DEVICE_FUNC RealScalar lpNorm() const; + + EIGEN_DEVICE_FUNC MatrixBase& matrix() { return *this; } + EIGEN_DEVICE_FUNC const MatrixBase& matrix() const { return *this; } + + /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix + * \sa ArrayBase::matrix() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper array() { return ArrayWrapper(derived()); } + /** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix + * \sa ArrayBase::matrix() */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper array() const { return ArrayWrapper(derived()); } + +/////////// LU module /////////// + + inline const FullPivLU fullPivLu() const; + inline const PartialPivLU partialPivLu() const; + + inline const PartialPivLU lu() const; + + EIGEN_DEVICE_FUNC + inline const Inverse inverse() const; + + template + inline void computeInverseAndDetWithCheck( + ResultType& inverse, + typename ResultType::Scalar& determinant, + bool& invertible, + const RealScalar& absDeterminantThreshold = NumTraits::dummy_precision() + ) const; + + template + inline void computeInverseWithCheck( + ResultType& inverse, + bool& invertible, + const RealScalar& absDeterminantThreshold = NumTraits::dummy_precision() + ) const; + + EIGEN_DEVICE_FUNC + Scalar determinant() const; + +/////////// Cholesky module /////////// + + inline const LLT llt() const; + inline const LDLT ldlt() const; + +/////////// QR module /////////// + + inline const HouseholderQR householderQr() const; + inline const ColPivHouseholderQR colPivHouseholderQr() const; + inline const FullPivHouseholderQR fullPivHouseholderQr() const; + inline const CompleteOrthogonalDecomposition completeOrthogonalDecomposition() const; + +/////////// Eigenvalues module /////////// + + inline EigenvaluesReturnType eigenvalues() const; + inline RealScalar operatorNorm() const; + +/////////// SVD module /////////// + + inline JacobiSVD jacobiSvd(unsigned int computationOptions = 0) const; + inline BDCSVD bdcSvd(unsigned int computationOptions = 0) const; + +/////////// Geometry module /////////// + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /// \internal helper struct to form the return type of the cross product + template struct cross_product_return_type { + typedef typename ScalarBinaryOpTraits::Scalar,typename internal::traits::Scalar>::ReturnType Scalar; + typedef Matrix type; + }; + #endif // EIGEN_PARSED_BY_DOXYGEN + template + EIGEN_DEVICE_FUNC +#ifndef EIGEN_PARSED_BY_DOXYGEN + inline typename cross_product_return_type::type +#else + inline PlainObject +#endif + cross(const MatrixBase& other) const; + + template + EIGEN_DEVICE_FUNC + inline PlainObject cross3(const MatrixBase& other) const; + + EIGEN_DEVICE_FUNC + inline PlainObject unitOrthogonal(void) const; + + EIGEN_DEVICE_FUNC + inline Matrix eulerAngles(Index a0, Index a1, Index a2) const; + + // put this as separate enum value to work around possible GCC 4.3 bug (?) + enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical) + : ColsAtCompileTime==1 ? Vertical : Horizontal }; + typedef Homogeneous HomogeneousReturnType; + EIGEN_DEVICE_FUNC + inline HomogeneousReturnType homogeneous() const; + + enum { + SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1 + }; + typedef Block::ColsAtCompileTime==1 ? SizeMinusOne : 1, + internal::traits::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne; + typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType; + EIGEN_DEVICE_FUNC + inline const HNormalizedReturnType hnormalized() const; + +////////// Householder module /////////// + + EIGEN_DEVICE_FUNC + void makeHouseholderInPlace(Scalar& tau, RealScalar& beta); + template + EIGEN_DEVICE_FUNC + void makeHouseholder(EssentialPart& essential, + Scalar& tau, RealScalar& beta) const; + template + EIGEN_DEVICE_FUNC + void applyHouseholderOnTheLeft(const EssentialPart& essential, + const Scalar& tau, + Scalar* workspace); + template + EIGEN_DEVICE_FUNC + void applyHouseholderOnTheRight(const EssentialPart& essential, + const Scalar& tau, + Scalar* workspace); + +///////// Jacobi module ///////// + + template + EIGEN_DEVICE_FUNC + void applyOnTheLeft(Index p, Index q, const JacobiRotation& j); + template + EIGEN_DEVICE_FUNC + void applyOnTheRight(Index p, Index q, const JacobiRotation& j); + +///////// SparseCore module ///////// + + template + EIGEN_STRONG_INLINE const typename SparseMatrixBase::template CwiseProductDenseReturnType::Type + cwiseProduct(const SparseMatrixBase &other) const + { + return other.cwiseProduct(derived()); + } + +///////// MatrixFunctions module ///////// + + typedef typename internal::stem_function::type StemFunction; +#define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \ + /** \returns an expression of the matrix Description of \c *this. \brief This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise Description use ArrayBase::##Name . */ \ + const ReturnType Name() const; +#define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \ + /** \returns an expression of the matrix Description of \c *this. \brief This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise Description use ArrayBase::##Name . */ \ + const ReturnType Name(Argument) const; + + EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential) + /** \brief Helper function for the unsupported MatrixFunctions module.*/ + const MatrixFunctionReturnValue matrixFunction(StemFunction f) const; + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine) + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine) +#if EIGEN_HAS_CXX11_MATH + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine) + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine) + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine) +#endif + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine) + EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine) + EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root) + EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm) + EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p) + EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex& p) + + protected: + EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase) + EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase) + + private: + EIGEN_DEVICE_FUNC explicit MatrixBase(int); + EIGEN_DEVICE_FUNC MatrixBase(int,int); + template EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase&); + protected: + // mixing arrays and matrices is not legal + template Derived& operator+=(const ArrayBase& ) + {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;} + // mixing arrays and matrices is not legal + template Derived& operator-=(const ArrayBase& ) + {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;} +}; + + +/*************************************************************************** +* Implementation of matrix base methods +***************************************************************************/ + +/** replaces \c *this by \c *this * \a other. + * + * \returns a reference to \c *this + * + * Example: \include MatrixBase_applyOnTheRight.cpp + * Output: \verbinclude MatrixBase_applyOnTheRight.out + */ +template +template +inline Derived& +MatrixBase::operator*=(const EigenBase &other) +{ + other.derived().applyThisOnTheRight(derived()); + return derived(); +} + +/** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=(). + * + * Example: \include MatrixBase_applyOnTheRight.cpp + * Output: \verbinclude MatrixBase_applyOnTheRight.out + */ +template +template +inline void MatrixBase::applyOnTheRight(const EigenBase &other) +{ + other.derived().applyThisOnTheRight(derived()); +} + +/** replaces \c *this by \a other * \c *this. + * + * Example: \include MatrixBase_applyOnTheLeft.cpp + * Output: \verbinclude MatrixBase_applyOnTheLeft.out + */ +template +template +inline void MatrixBase::applyOnTheLeft(const EigenBase &other) +{ + other.derived().applyThisOnTheLeft(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_MATRIXBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NestByValue.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NestByValue.h new file mode 100644 index 0000000000000000000000000000000000000000..b4275768a01df3b8e2a06424010bd8d33cffea30 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NestByValue.h @@ -0,0 +1,85 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NESTBYVALUE_H +#define EIGEN_NESTBYVALUE_H + +namespace Eigen { + +namespace internal { +template +struct traits > : public traits +{ + enum { + Flags = traits::Flags & ~NestByRefBit + }; +}; +} + +/** \class NestByValue + * \ingroup Core_Module + * + * \brief Expression which must be nested by value + * + * \tparam ExpressionType the type of the object of which we are requiring nesting-by-value + * + * This class is the return type of MatrixBase::nestByValue() + * and most of the time this is the only way it is used. + * + * \sa MatrixBase::nestByValue() + */ +template class NestByValue + : public internal::dense_xpr_base< NestByValue >::type +{ + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(NestByValue) + + EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {} + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); } + + EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; } + + EIGEN_DEVICE_FUNC const ExpressionType& nestedExpression() const { return m_expression; } + + protected: + const ExpressionType m_expression; +}; + +/** \returns an expression of the temporary version of *this. + */ +template +EIGEN_DEVICE_FUNC inline const NestByValue +DenseBase::nestByValue() const +{ + return NestByValue(derived()); +} + +namespace internal { + +// Evaluator of Solve -> eval into a temporary +template +struct evaluator > + : public evaluator +{ + typedef evaluator Base; + + EIGEN_DEVICE_FUNC explicit evaluator(const NestByValue& xpr) + : Base(xpr.nestedExpression()) + {} +}; +} + +} // end namespace Eigen + +#endif // EIGEN_NESTBYVALUE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NoAlias.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NoAlias.h new file mode 100644 index 0000000000000000000000000000000000000000..570283d90f1c5fba2b3cae629421b624128283c2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NoAlias.h @@ -0,0 +1,109 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NOALIAS_H +#define EIGEN_NOALIAS_H + +namespace Eigen { + +/** \class NoAlias + * \ingroup Core_Module + * + * \brief Pseudo expression providing an operator = assuming no aliasing + * + * \tparam ExpressionType the type of the object on which to do the lazy assignment + * + * This class represents an expression with special assignment operators + * assuming no aliasing between the target expression and the source expression. + * More precisely it alloas to bypass the EvalBeforeAssignBit flag of the source expression. + * It is the return type of MatrixBase::noalias() + * and most of the time this is the only way it is used. + * + * \sa MatrixBase::noalias() + */ +template class StorageBase> +class NoAlias +{ + public: + typedef typename ExpressionType::Scalar Scalar; + + EIGEN_DEVICE_FUNC + explicit NoAlias(ExpressionType& expression) : m_expression(expression) {} + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE ExpressionType& operator=(const StorageBase& other) + { + call_assignment_no_alias(m_expression, other.derived(), internal::assign_op()); + return m_expression; + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE ExpressionType& operator+=(const StorageBase& other) + { + call_assignment_no_alias(m_expression, other.derived(), internal::add_assign_op()); + return m_expression; + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE ExpressionType& operator-=(const StorageBase& other) + { + call_assignment_no_alias(m_expression, other.derived(), internal::sub_assign_op()); + return m_expression; + } + + EIGEN_DEVICE_FUNC + ExpressionType& expression() const + { + return m_expression; + } + + protected: + ExpressionType& m_expression; +}; + +/** \returns a pseudo expression of \c *this with an operator= assuming + * no aliasing between \c *this and the source expression. + * + * More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. + * Currently, even though several expressions may alias, only product + * expressions have this flag. Therefore, noalias() is only useful when + * the source expression contains a matrix product. + * + * Here are some examples where noalias is useful: + * \code + * D.noalias() = A * B; + * D.noalias() += A.transpose() * B; + * D.noalias() -= 2 * A * B.adjoint(); + * \endcode + * + * On the other hand the following example will lead to a \b wrong result: + * \code + * A.noalias() = A * B; + * \endcode + * because the result matrix A is also an operand of the matrix product. Therefore, + * there is no alternative than evaluating A * B in a temporary, that is the default + * behavior when you write: + * \code + * A = A * B; + * \endcode + * + * \sa class NoAlias + */ +template +NoAlias EIGEN_DEVICE_FUNC MatrixBase::noalias() +{ + return NoAlias(derived()); +} + +} // end namespace Eigen + +#endif // EIGEN_NOALIAS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NumTraits.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NumTraits.h new file mode 100644 index 0000000000000000000000000000000000000000..608a4e7474aec092f7e3cd21e7792453c3b94386 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/NumTraits.h @@ -0,0 +1,335 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NUMTRAITS_H +#define EIGEN_NUMTRAITS_H + +namespace Eigen { + +namespace internal { + +// default implementation of digits10(), based on numeric_limits if specialized, +// 0 for integer types, and log10(epsilon()) otherwise. +template< typename T, + bool use_numeric_limits = std::numeric_limits::is_specialized, + bool is_integer = NumTraits::IsInteger> +struct default_digits10_impl +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { return std::numeric_limits::digits10; } +}; + +template +struct default_digits10_impl // Floating point +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { + using std::log10; + using std::ceil; + typedef typename NumTraits::Real Real; + return int(ceil(-log10(NumTraits::epsilon()))); + } +}; + +template +struct default_digits10_impl // Integer +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { return 0; } +}; + + +// default implementation of digits(), based on numeric_limits if specialized, +// 0 for integer types, and log2(epsilon()) otherwise. +template< typename T, + bool use_numeric_limits = std::numeric_limits::is_specialized, + bool is_integer = NumTraits::IsInteger> +struct default_digits_impl +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { return std::numeric_limits::digits; } +}; + +template +struct default_digits_impl // Floating point +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { + using std::log; + using std::ceil; + typedef typename NumTraits::Real Real; + return int(ceil(-log(NumTraits::epsilon())/log(static_cast(2)))); + } +}; + +template +struct default_digits_impl // Integer +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static int run() { return 0; } +}; + +} // end namespace internal + +namespace numext { +/** \internal bit-wise cast without changing the underlying bit representation. */ + +// TODO: Replace by std::bit_cast (available in C++20) +template +EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) { +#if EIGEN_HAS_TYPE_TRAITS + // The behaviour of memcpy is not specified for non-trivially copyable types + EIGEN_STATIC_ASSERT(std::is_trivially_copyable::value, THIS_TYPE_IS_NOT_SUPPORTED); + EIGEN_STATIC_ASSERT(std::is_trivially_copyable::value && std::is_default_constructible::value, + THIS_TYPE_IS_NOT_SUPPORTED); +#endif + + EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED); + Tgt tgt; + EIGEN_USING_STD(memcpy) + memcpy(&tgt, &src, sizeof(Tgt)); + return tgt; +} +} // namespace numext + +/** \class NumTraits + * \ingroup Core_Module + * + * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen. + * + * \tparam T the numeric type at hand + * + * This class stores enums, typedefs and static methods giving information about a numeric type. + * + * The provided data consists of: + * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real, + * then \c Real is just a typedef to \a T. If \a T is \c std::complex then \c Real + * is a typedef to \a U. + * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values, + * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives + * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to + * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is + * only intended as a helper for code that needs to explicitly promote types. + * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex, Literal is defined as \c U. + * Of course, this type must be fully compatible with \a T. In doubt, just use \a T here. + * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what + * this means, just use \a T here. + * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex + * type, and to 0 otherwise. + * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, + * and to \c 0 otherwise. + * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed + * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers. + * Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost. + * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned. + * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must + * be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise. + * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), + * it returns a \a Real instead of a \a T. + * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default + * value by the fuzzy comparison operators. + * \li highest() and lowest() functions returning the highest and lowest possible values respectively. + * \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point). This is + * the analogue of std::numeric_limits::digits + * which is used as the default implementation if specialized. + * \li digits10() function returning the number of decimal digits that can be represented without change. This is + * the analogue of std::numeric_limits::digits10 + * which is used as the default implementation if specialized. + * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively, + * such that the radix raised to the power exponent-1 is a normalized floating-point number. These are equivalent to + * std::numeric_limits::min_exponent/ + * std::numeric_limits::max_exponent. + * \li infinity() function returning a representation of positive infinity, if available. + * \li quiet_NaN function returning a non-signaling "not-a-number", if available. + */ + +template struct GenericNumTraits +{ + enum { + IsInteger = std::numeric_limits::is_integer, + IsSigned = std::numeric_limits::is_signed, + IsComplex = 0, + RequireInitialization = internal::is_arithmetic::value ? 0 : 1, + ReadCost = 1, + AddCost = 1, + MulCost = 1 + }; + + typedef T Real; + typedef typename internal::conditional< + IsInteger, + typename internal::conditional::type, + T + >::type NonInteger; + typedef T Nested; + typedef T Literal; + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline Real epsilon() + { + return numext::numeric_limits::epsilon(); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline int digits10() + { + return internal::default_digits10_impl::run(); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline int digits() + { + return internal::default_digits_impl::run(); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline int min_exponent() + { + return numext::numeric_limits::min_exponent; + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline int max_exponent() + { + return numext::numeric_limits::max_exponent; + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline Real dummy_precision() + { + // make sure to override this for floating-point types + return Real(0); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline T highest() { + return (numext::numeric_limits::max)(); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline T lowest() { + return IsInteger ? (numext::numeric_limits::min)() + : static_cast(-(numext::numeric_limits::max)()); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline T infinity() { + return numext::numeric_limits::infinity(); + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline T quiet_NaN() { + return numext::numeric_limits::quiet_NaN(); + } +}; + +template struct NumTraits : GenericNumTraits +{}; + +template<> struct NumTraits + : GenericNumTraits +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline float dummy_precision() { return 1e-5f; } +}; + +template<> struct NumTraits : GenericNumTraits +{ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline double dummy_precision() { return 1e-12; } +}; + +template<> struct NumTraits + : GenericNumTraits +{ + EIGEN_CONSTEXPR + static inline long double dummy_precision() { return 1e-15l; } +}; + +template struct NumTraits > + : GenericNumTraits > +{ + typedef Real_ Real; + typedef typename NumTraits::Literal Literal; + enum { + IsComplex = 1, + RequireInitialization = NumTraits::RequireInitialization, + ReadCost = 2 * NumTraits::ReadCost, + AddCost = 2 * NumTraits::AddCost, + MulCost = 4 * NumTraits::MulCost + 2 * NumTraits::AddCost + }; + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline Real epsilon() { return NumTraits::epsilon(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline Real dummy_precision() { return NumTraits::dummy_precision(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline int digits10() { return NumTraits::digits10(); } +}; + +template +struct NumTraits > +{ + typedef Array ArrayType; + typedef typename NumTraits::Real RealScalar; + typedef Array Real; + typedef typename NumTraits::NonInteger NonIntegerScalar; + typedef Array NonInteger; + typedef ArrayType & Nested; + typedef typename NumTraits::Literal Literal; + + enum { + IsComplex = NumTraits::IsComplex, + IsInteger = NumTraits::IsInteger, + IsSigned = NumTraits::IsSigned, + RequireInitialization = 1, + ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits::ReadCost), + AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits::AddCost), + MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * int(NumTraits::MulCost) + }; + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline RealScalar epsilon() { return NumTraits::epsilon(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + static inline RealScalar dummy_precision() { return NumTraits::dummy_precision(); } + + EIGEN_CONSTEXPR + static inline int digits10() { return NumTraits::digits10(); } +}; + +template<> struct NumTraits + : GenericNumTraits +{ + enum { + RequireInitialization = 1, + ReadCost = HugeCost, + AddCost = HugeCost, + MulCost = HugeCost + }; + + EIGEN_CONSTEXPR + static inline int digits10() { return 0; } + +private: + static inline std::string epsilon(); + static inline std::string dummy_precision(); + static inline std::string lowest(); + static inline std::string highest(); + static inline std::string infinity(); + static inline std::string quiet_NaN(); +}; + +// Empty specialization for void to allow template specialization based on NumTraits::Real with T==void and SFINAE. +template<> struct NumTraits {}; + +template<> struct NumTraits : GenericNumTraits {}; + +} // end namespace Eigen + +#endif // EIGEN_NUMTRAITS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PartialReduxEvaluator.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PartialReduxEvaluator.h new file mode 100644 index 0000000000000000000000000000000000000000..29abf35b99b06032c35b5366f003d415026e35aa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PartialReduxEvaluator.h @@ -0,0 +1,232 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011-2018 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_PARTIALREDUX_H +#define EIGEN_PARTIALREDUX_H + +namespace Eigen { + +namespace internal { + + +/*************************************************************************** +* +* This file provides evaluators for partial reductions. +* There are two modes: +* +* - scalar path: simply calls the respective function on the column or row. +* -> nothing special here, all the tricky part is handled by the return +* types of VectorwiseOp's members. They embed the functor calling the +* respective DenseBase's member function. +* +* - vectorized path: implements a packet-wise reductions followed by +* some (optional) processing of the outcome, e.g., division by n for mean. +* +* For the vectorized path let's observe that the packet-size and outer-unrolling +* are both decided by the assignement logic. So all we have to do is to decide +* on the inner unrolling. +* +* For the unrolling, we can reuse "internal::redux_vec_unroller" from Redux.h, +* but be need to be careful to specify correct increment. +* +***************************************************************************/ + + +/* logic deciding a strategy for unrolling of vectorized paths */ +template +struct packetwise_redux_traits +{ + enum { + OuterSize = int(Evaluator::IsRowMajor) ? Evaluator::RowsAtCompileTime : Evaluator::ColsAtCompileTime, + Cost = OuterSize == Dynamic ? HugeCost + : OuterSize * Evaluator::CoeffReadCost + (OuterSize-1) * functor_traits::Cost, + Unrolling = Cost <= EIGEN_UNROLLING_LIMIT ? CompleteUnrolling : NoUnrolling + }; + +}; + +/* Value to be returned when size==0 , by default let's return 0 */ +template +EIGEN_DEVICE_FUNC +PacketType packetwise_redux_empty_value(const Func& ) { return pset1(0); } + +/* For products the default is 1 */ +template +EIGEN_DEVICE_FUNC +PacketType packetwise_redux_empty_value(const scalar_product_op& ) { return pset1(1); } + +/* Perform the actual reduction */ +template::Unrolling +> +struct packetwise_redux_impl; + +/* Perform the actual reduction with unrolling */ +template +struct packetwise_redux_impl +{ + typedef redux_novec_unroller Base; + typedef typename Evaluator::Scalar Scalar; + + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE + PacketType run(const Evaluator &eval, const Func& func, Index /*size*/) + { + return redux_vec_unroller::OuterSize>::template run(eval,func); + } +}; + +/* Add a specialization of redux_vec_unroller for size==0 at compiletime. + * This specialization is not required for general reductions, which is + * why it is defined here. + */ +template +struct redux_vec_unroller +{ + template + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE PacketType run(const Evaluator &, const Func& f) + { + return packetwise_redux_empty_value(f); + } +}; + +/* Perform the actual reduction for dynamic sizes */ +template +struct packetwise_redux_impl +{ + typedef typename Evaluator::Scalar Scalar; + typedef typename redux_traits::PacketType PacketScalar; + + template + EIGEN_DEVICE_FUNC + static PacketType run(const Evaluator &eval, const Func& func, Index size) + { + if(size==0) + return packetwise_redux_empty_value(func); + + const Index size4 = (size-1)&(~3); + PacketType p = eval.template packetByOuterInner(0,0); + Index i = 1; + // This loop is optimized for instruction pipelining: + // - each iteration generates two independent instructions + // - thanks to branch prediction and out-of-order execution we have independent instructions across loops + for(; i(i+0,0),eval.template packetByOuterInner(i+1,0)), + func.packetOp(eval.template packetByOuterInner(i+2,0),eval.template packetByOuterInner(i+3,0)))); + for(; i(i,0)); + return p; + } +}; + +template< typename ArgType, typename MemberOp, int Direction> +struct evaluator > + : evaluator_base > +{ + typedef PartialReduxExpr XprType; + typedef typename internal::nested_eval::type ArgTypeNested; + typedef typename internal::add_const_on_value_type::type ConstArgTypeNested; + typedef typename internal::remove_all::type ArgTypeNestedCleaned; + typedef typename ArgType::Scalar InputScalar; + typedef typename XprType::Scalar Scalar; + enum { + TraversalSize = Direction==int(Vertical) ? int(ArgType::RowsAtCompileTime) : int(ArgType::ColsAtCompileTime) + }; + typedef typename MemberOp::template Cost CostOpType; + enum { + CoeffReadCost = TraversalSize==Dynamic ? HugeCost + : TraversalSize==0 ? 1 + : int(TraversalSize) * int(evaluator::CoeffReadCost) + int(CostOpType::value), + + _ArgFlags = evaluator::Flags, + + _Vectorizable = bool(int(_ArgFlags)&PacketAccessBit) + && bool(MemberOp::Vectorizable) + && (Direction==int(Vertical) ? bool(_ArgFlags&RowMajorBit) : (_ArgFlags&RowMajorBit)==0) + && (TraversalSize!=0), + + Flags = (traits::Flags&RowMajorBit) + | (evaluator::Flags&(HereditaryBits&(~RowMajorBit))) + | (_Vectorizable ? PacketAccessBit : 0) + | LinearAccessBit, + + Alignment = 0 // FIXME this will need to be improved once PartialReduxExpr is vectorized + }; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType xpr) + : m_arg(xpr.nestedExpression()), m_functor(xpr.functor()) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(TraversalSize==Dynamic ? HugeCost : (TraversalSize==0 ? 1 : int(CostOpType::value))); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const Scalar coeff(Index i, Index j) const + { + return coeff(Direction==Vertical ? j : i); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const Scalar coeff(Index index) const + { + return m_functor(m_arg.template subVector(index)); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + PacketType packet(Index i, Index j) const + { + return packet(Direction==Vertical ? j : i); + } + + template + EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC + PacketType packet(Index idx) const + { + enum { PacketSize = internal::unpacket_traits::size }; + typedef Block PanelType; + + PanelType panel(m_arg, + Direction==Vertical ? 0 : idx, + Direction==Vertical ? idx : 0, + Direction==Vertical ? m_arg.rows() : Index(PacketSize), + Direction==Vertical ? Index(PacketSize) : m_arg.cols()); + + // FIXME + // See bug 1612, currently if PacketSize==1 (i.e. complex with 128bits registers) then the storage-order of panel get reversed + // and methods like packetByOuterInner do not make sense anymore in this context. + // So let's just by pass "vectorization" in this case: + if(PacketSize==1) + return internal::pset1(coeff(idx)); + + typedef typename internal::redux_evaluator PanelEvaluator; + PanelEvaluator panel_eval(panel); + typedef typename MemberOp::BinaryOp BinaryOp; + PacketType p = internal::packetwise_redux_impl::template run(panel_eval,m_functor.binaryFunc(),m_arg.outerSize()); + return p; + } + +protected: + ConstArgTypeNested m_arg; + const MemberOp m_functor; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_PARTIALREDUX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PermutationMatrix.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PermutationMatrix.h new file mode 100644 index 0000000000000000000000000000000000000000..24fe660bea922d21101f7c2a50a0068a41b20beb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PermutationMatrix.h @@ -0,0 +1,605 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Benoit Jacob +// Copyright (C) 2009-2015 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_PERMUTATIONMATRIX_H +#define EIGEN_PERMUTATIONMATRIX_H + +namespace Eigen { + +namespace internal { + +enum PermPermProduct_t {PermPermProduct}; + +} // end namespace internal + +/** \class PermutationBase + * \ingroup Core_Module + * + * \brief Base class for permutations + * + * \tparam Derived the derived class + * + * This class is the base class for all expressions representing a permutation matrix, + * internally stored as a vector of integers. + * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix + * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have: + * \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f] + * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have: + * \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f] + * + * Permutation matrices are square and invertible. + * + * Notice that in addition to the member functions and operators listed here, there also are non-member + * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase) + * on either side. + * + * \sa class PermutationMatrix, class PermutationWrapper + */ +template +class PermutationBase : public EigenBase +{ + typedef internal::traits Traits; + typedef EigenBase Base; + public: + + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename Traits::IndicesType IndicesType; + enum { + Flags = Traits::Flags, + RowsAtCompileTime = Traits::RowsAtCompileTime, + ColsAtCompileTime = Traits::ColsAtCompileTime, + MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = Traits::MaxColsAtCompileTime + }; + typedef typename Traits::StorageIndex StorageIndex; + typedef Matrix + DenseMatrixType; + typedef PermutationMatrix + PlainPermutationType; + typedef PlainPermutationType PlainObject; + using Base::derived; + typedef Inverse InverseReturnType; + typedef void Scalar; + #endif + + /** Copies the other permutation into *this */ + template + Derived& operator=(const PermutationBase& other) + { + indices() = other.indices(); + return derived(); + } + + /** Assignment from the Transpositions \a tr */ + template + Derived& operator=(const TranspositionsBase& tr) + { + setIdentity(tr.size()); + for(Index k=size()-1; k>=0; --k) + applyTranspositionOnTheRight(k,tr.coeff(k)); + return derived(); + } + + /** \returns the number of rows */ + inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); } + + /** \returns the number of columns */ + inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); } + + /** \returns the size of a side of the respective square matrix, i.e., the number of indices */ + inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + void evalTo(MatrixBase& other) const + { + other.setZero(); + for (Index i=0; i=0 && j>=0 && i=0 && j>=0 && i + void assignTranspose(const PermutationBase& other) + { + for (Index i=0; i + void assignProduct(const Lhs& lhs, const Rhs& rhs) + { + eigen_assert(lhs.cols() == rhs.rows()); + for (Index i=0; i + inline PlainPermutationType operator*(const PermutationBase& other) const + { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); } + + /** \returns the product of a permutation with another inverse permutation. + * + * \note \blank \note_try_to_help_rvo + */ + template + inline PlainPermutationType operator*(const InverseImpl& other) const + { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); } + + /** \returns the product of an inverse permutation with another permutation. + * + * \note \blank \note_try_to_help_rvo + */ + template friend + inline PlainPermutationType operator*(const InverseImpl& other, const PermutationBase& perm) + { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); } + + /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation. + * + * This function is O(\c n) procedure allocating a buffer of \c n booleans. + */ + Index determinant() const + { + Index res = 1; + Index n = size(); + Matrix mask(n); + mask.fill(false); + Index r = 0; + while(r < n) + { + // search for the next seed + while(r=n) + break; + // we got one, let's follow it until we are back to the seed + Index k0 = r++; + mask.coeffRef(k0) = true; + for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k)) + { + mask.coeffRef(k) = true; + res = -res; + } + } + return res; + } + + protected: + +}; + +namespace internal { +template +struct traits > + : traits > +{ + typedef PermutationStorage StorageKind; + typedef Matrix IndicesType; + typedef StorageIndex_ StorageIndex; + typedef void Scalar; +}; +} + +/** \class PermutationMatrix + * \ingroup Core_Module + * + * \brief Permutation matrix + * + * \tparam SizeAtCompileTime the number of rows/cols, or Dynamic + * \tparam MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it. + * \tparam StorageIndex_ the integer type of the indices + * + * This class represents a permutation matrix, internally stored as a vector of integers. + * + * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix + */ +template +class PermutationMatrix : public PermutationBase > +{ + typedef PermutationBase Base; + typedef internal::traits Traits; + public: + + typedef const PermutationMatrix& Nested; + + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename Traits::IndicesType IndicesType; + typedef typename Traits::StorageIndex StorageIndex; + #endif + + inline PermutationMatrix() + {} + + /** Constructs an uninitialized permutation matrix of given size. + */ + explicit inline PermutationMatrix(Index size) : m_indices(size) + { + eigen_internal_assert(size <= NumTraits::highest()); + } + + /** Copy constructor. */ + template + inline PermutationMatrix(const PermutationBase& other) + : m_indices(other.indices()) {} + + /** Generic constructor from expression of the indices. The indices + * array has the meaning that the permutations sends each integer i to indices[i]. + * + * \warning It is your responsibility to check that the indices array that you passes actually + * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the + * array's size. + */ + template + explicit inline PermutationMatrix(const MatrixBase& indices) : m_indices(indices) + {} + + /** Convert the Transpositions \a tr to a permutation matrix */ + template + explicit PermutationMatrix(const TranspositionsBase& tr) + : m_indices(tr.size()) + { + *this = tr; + } + + /** Copies the other permutation into *this */ + template + PermutationMatrix& operator=(const PermutationBase& other) + { + m_indices = other.indices(); + return *this; + } + + /** Assignment from the Transpositions \a tr */ + template + PermutationMatrix& operator=(const TranspositionsBase& tr) + { + return Base::operator=(tr.derived()); + } + + /** const version of indices(). */ + const IndicesType& indices() const { return m_indices; } + /** \returns a reference to the stored array representing the permutation. */ + IndicesType& indices() { return m_indices; } + + + /**** multiplication helpers to hopefully get RVO ****/ + +#ifndef EIGEN_PARSED_BY_DOXYGEN + template + PermutationMatrix(const InverseImpl& other) + : m_indices(other.derived().nestedExpression().size()) + { + eigen_internal_assert(m_indices.size() <= NumTraits::highest()); + StorageIndex end = StorageIndex(m_indices.size()); + for (StorageIndex i=0; i + PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs) + : m_indices(lhs.indices().size()) + { + Base::assignProduct(lhs,rhs); + } +#endif + + protected: + + IndicesType m_indices; +}; + + +namespace internal { +template +struct traits,_PacketAccess> > + : traits > +{ + typedef PermutationStorage StorageKind; + typedef Map, _PacketAccess> IndicesType; + typedef StorageIndex_ StorageIndex; + typedef void Scalar; +}; +} + +template +class Map,_PacketAccess> + : public PermutationBase,_PacketAccess> > +{ + typedef PermutationBase Base; + typedef internal::traits Traits; + public: + + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename Traits::IndicesType IndicesType; + typedef typename IndicesType::Scalar StorageIndex; + #endif + + inline Map(const StorageIndex* indicesPtr) + : m_indices(indicesPtr) + {} + + inline Map(const StorageIndex* indicesPtr, Index size) + : m_indices(indicesPtr,size) + {} + + /** Copies the other permutation into *this */ + template + Map& operator=(const PermutationBase& other) + { return Base::operator=(other.derived()); } + + /** Assignment from the Transpositions \a tr */ + template + Map& operator=(const TranspositionsBase& tr) + { return Base::operator=(tr.derived()); } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + /** This is a special case of the templated operator=. Its purpose is to + * prevent a default operator= from hiding the templated operator=. + */ + Map& operator=(const Map& other) + { + m_indices = other.m_indices; + return *this; + } + #endif + + /** const version of indices(). */ + const IndicesType& indices() const { return m_indices; } + /** \returns a reference to the stored array representing the permutation. */ + IndicesType& indices() { return m_indices; } + + protected: + + IndicesType m_indices; +}; + +template class TranspositionsWrapper; +namespace internal { +template +struct traits > +{ + typedef PermutationStorage StorageKind; + typedef void Scalar; + typedef typename IndicesType_::Scalar StorageIndex; + typedef IndicesType_ IndicesType; + enum { + RowsAtCompileTime = IndicesType_::SizeAtCompileTime, + ColsAtCompileTime = IndicesType_::SizeAtCompileTime, + MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime, + MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime, + Flags = 0 + }; +}; +} + +/** \class PermutationWrapper + * \ingroup Core_Module + * + * \brief Class to view a vector of integers as a permutation matrix + * + * \tparam IndicesType_ the type of the vector of integer (can be any compatible expression) + * + * This class allows to view any vector expression of integers as a permutation matrix. + * + * \sa class PermutationBase, class PermutationMatrix + */ +template +class PermutationWrapper : public PermutationBase > +{ + typedef PermutationBase Base; + typedef internal::traits Traits; + public: + + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename Traits::IndicesType IndicesType; + #endif + + inline PermutationWrapper(const IndicesType& indices) + : m_indices(indices) + {} + + /** const version of indices(). */ + const typename internal::remove_all::type& + indices() const { return m_indices; } + + protected: + + typename IndicesType::Nested m_indices; +}; + + +/** \returns the matrix with the permutation applied to the columns. + */ +template +EIGEN_DEVICE_FUNC +const Product +operator*(const MatrixBase &matrix, + const PermutationBase& permutation) +{ + return Product + (matrix.derived(), permutation.derived()); +} + +/** \returns the matrix with the permutation applied to the rows. + */ +template +EIGEN_DEVICE_FUNC +const Product +operator*(const PermutationBase &permutation, + const MatrixBase& matrix) +{ + return Product + (permutation.derived(), matrix.derived()); +} + + +template +class InverseImpl + : public EigenBase > +{ + typedef typename PermutationType::PlainPermutationType PlainPermutationType; + typedef internal::traits PermTraits; + protected: + InverseImpl() {} + public: + typedef Inverse InverseType; + using EigenBase >::derived; + + #ifndef EIGEN_PARSED_BY_DOXYGEN + typedef typename PermutationType::DenseMatrixType DenseMatrixType; + enum { + RowsAtCompileTime = PermTraits::RowsAtCompileTime, + ColsAtCompileTime = PermTraits::ColsAtCompileTime, + MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime + }; + #endif + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + void evalTo(MatrixBase& other) const + { + other.setZero(); + for (Index i=0; i friend + const Product + operator*(const MatrixBase& matrix, const InverseType& trPerm) + { + return Product(matrix.derived(), trPerm.derived()); + } + + /** \returns the matrix with the inverse permutation applied to the rows. + */ + template + const Product + operator*(const MatrixBase& matrix) const + { + return Product(derived(), matrix.derived()); + } +}; + +template +const PermutationWrapper MatrixBase::asPermutation() const +{ + return derived(); +} + +namespace internal { + +template<> struct AssignmentKind { typedef EigenBase2EigenBase Kind; }; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_PERMUTATIONMATRIX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PlainObjectBase.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PlainObjectBase.h new file mode 100644 index 0000000000000000000000000000000000000000..00cdc55f2dc26742a8aa0942b56c1b3d2ece57ff --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/PlainObjectBase.h @@ -0,0 +1,1128 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_DENSESTORAGEBASE_H +#define EIGEN_DENSESTORAGEBASE_H + +#if defined(EIGEN_INITIALIZE_MATRICES_BY_ZERO) +# define EIGEN_INITIALIZE_COEFFS +# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED for(Index i=0;i::quiet_NaN(); +#else +# undef EIGEN_INITIALIZE_COEFFS +# define EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED +#endif + +namespace Eigen { + +namespace internal { + +template struct check_rows_cols_for_overflow { + template + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE void run(Index, Index) + { + } +}; + +template<> struct check_rows_cols_for_overflow { + template + EIGEN_DEVICE_FUNC + static EIGEN_ALWAYS_INLINE void run(Index rows, Index cols) + { + // http://hg.mozilla.org/mozilla-central/file/6c8a909977d3/xpcom/ds/CheckedInt.h#l242 + // we assume Index is signed + Index max_index = (std::size_t(1) << (8 * sizeof(Index) - 1)) - 1; // assume Index is signed + bool error = (rows == 0 || cols == 0) ? false + : (rows > max_index / cols); + if (error) + throw_std_bad_alloc(); + } +}; + +template +struct conservative_resize_like_impl; + +template struct matrix_swap_impl; + +} // end namespace internal + +#ifdef EIGEN_PARSED_BY_DOXYGEN +namespace doxygen { + +// This is a workaround to doxygen not being able to understand the inheritance logic +// when it is hidden by the dense_xpr_base helper struct. +// Moreover, doxygen fails to include members that are not documented in the declaration body of +// MatrixBase if we inherits MatrixBase >, +// this is why we simply inherits MatrixBase, though this does not make sense. + +/** This class is just a workaround for Doxygen and it does not not actually exist. */ +template struct dense_xpr_base_dispatcher; +/** This class is just a workaround for Doxygen and it does not not actually exist. */ +template +struct dense_xpr_base_dispatcher > + : public MatrixBase {}; +/** This class is just a workaround for Doxygen and it does not not actually exist. */ +template +struct dense_xpr_base_dispatcher > + : public ArrayBase {}; + +} // namespace doxygen + +/** \class PlainObjectBase + * \ingroup Core_Module + * \brief %Dense storage base class for matrices and arrays. + * + * This class can be extended with the help of the plugin mechanism described on the page + * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_PLAINOBJECTBASE_PLUGIN. + * + * \tparam Derived is the derived type, e.g., a Matrix or Array + * + * \sa \ref TopicClassHierarchy + */ +template +class PlainObjectBase : public doxygen::dense_xpr_base_dispatcher +#else +template +class PlainObjectBase : public internal::dense_xpr_base::type +#endif +{ + public: + enum { Options = internal::traits::Options }; + typedef typename internal::dense_xpr_base::type Base; + + typedef typename internal::traits::StorageKind StorageKind; + typedef typename internal::traits::Scalar Scalar; + + typedef typename internal::packet_traits::type PacketScalar; + typedef typename NumTraits::Real RealScalar; + typedef Derived DenseType; + + using Base::RowsAtCompileTime; + using Base::ColsAtCompileTime; + using Base::SizeAtCompileTime; + using Base::MaxRowsAtCompileTime; + using Base::MaxColsAtCompileTime; + using Base::MaxSizeAtCompileTime; + using Base::IsVectorAtCompileTime; + using Base::Flags; + + typedef Eigen::Map MapType; + typedef const Eigen::Map ConstMapType; + typedef Eigen::Map AlignedMapType; + typedef const Eigen::Map ConstAlignedMapType; + template struct StridedMapType { typedef Eigen::Map type; }; + template struct StridedConstMapType { typedef Eigen::Map type; }; + template struct StridedAlignedMapType { typedef Eigen::Map type; }; + template struct StridedConstAlignedMapType { typedef Eigen::Map type; }; + + protected: + DenseStorage m_storage; + + public: + enum { NeedsToAlign = (SizeAtCompileTime != Dynamic) && (internal::traits::Alignment>0) }; + EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign) + + EIGEN_DEVICE_FUNC + Base& base() { return *static_cast(this); } + EIGEN_DEVICE_FUNC + const Base& base() const { return *static_cast(this); } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { return m_storage.rows(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { return m_storage.cols(); } + + /** This is an overloaded version of DenseCoeffsBase::coeff(Index,Index) const + * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts. + * + * See DenseCoeffsBase::coeff(Index) const for details. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const Scalar& coeff(Index rowId, Index colId) const + { + if(Flags & RowMajorBit) + return m_storage.data()[colId + rowId * m_storage.cols()]; + else // column-major + return m_storage.data()[rowId + colId * m_storage.rows()]; + } + + /** This is an overloaded version of DenseCoeffsBase::coeff(Index) const + * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts. + * + * See DenseCoeffsBase::coeff(Index) const for details. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const + { + return m_storage.data()[index]; + } + + /** This is an overloaded version of DenseCoeffsBase::coeffRef(Index,Index) const + * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts. + * + * See DenseCoeffsBase::coeffRef(Index,Index) const for details. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& coeffRef(Index rowId, Index colId) + { + if(Flags & RowMajorBit) + return m_storage.data()[colId + rowId * m_storage.cols()]; + else // column-major + return m_storage.data()[rowId + colId * m_storage.rows()]; + } + + /** This is an overloaded version of DenseCoeffsBase::coeffRef(Index) const + * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts. + * + * See DenseCoeffsBase::coeffRef(Index) const for details. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) + { + return m_storage.data()[index]; + } + + /** This is the const version of coeffRef(Index,Index) which is thus synonym of coeff(Index,Index). + * It is provided for convenience. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const Scalar& coeffRef(Index rowId, Index colId) const + { + if(Flags & RowMajorBit) + return m_storage.data()[colId + rowId * m_storage.cols()]; + else // column-major + return m_storage.data()[rowId + colId * m_storage.rows()]; + } + + /** This is the const version of coeffRef(Index) which is thus synonym of coeff(Index). + * It is provided for convenience. */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const Scalar& coeffRef(Index index) const + { + return m_storage.data()[index]; + } + + /** \internal */ + template + EIGEN_STRONG_INLINE PacketScalar packet(Index rowId, Index colId) const + { + return internal::ploadt + (m_storage.data() + (Flags & RowMajorBit + ? colId + rowId * m_storage.cols() + : rowId + colId * m_storage.rows())); + } + + /** \internal */ + template + EIGEN_STRONG_INLINE PacketScalar packet(Index index) const + { + return internal::ploadt(m_storage.data() + index); + } + + /** \internal */ + template + EIGEN_STRONG_INLINE void writePacket(Index rowId, Index colId, const PacketScalar& val) + { + internal::pstoret + (m_storage.data() + (Flags & RowMajorBit + ? colId + rowId * m_storage.cols() + : rowId + colId * m_storage.rows()), val); + } + + /** \internal */ + template + EIGEN_STRONG_INLINE void writePacket(Index index, const PacketScalar& val) + { + internal::pstoret(m_storage.data() + index, val); + } + + /** \returns a const pointer to the data array of this matrix */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar *data() const + { return m_storage.data(); } + + /** \returns a pointer to the data array of this matrix */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar *data() + { return m_storage.data(); } + + /** Resizes \c *this to a \a rows x \a cols matrix. + * + * This method is intended for dynamic-size matrices, although it is legal to call it on any + * matrix as long as fixed dimensions are left unchanged. If you only want to change the number + * of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t). + * + * If the current number of coefficients of \c *this exactly matches the + * product \a rows * \a cols, then no memory allocation is performed and + * the current values are left unchanged. In all other cases, including + * shrinking, the data is reallocated and all previous values are lost. + * + * Example: \include Matrix_resize_int_int.cpp + * Output: \verbinclude Matrix_resize_int_int.out + * + * \sa resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t) + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void resize(Index rows, Index cols) + { + eigen_assert( EIGEN_IMPLIES(RowsAtCompileTime!=Dynamic,rows==RowsAtCompileTime) + && EIGEN_IMPLIES(ColsAtCompileTime!=Dynamic,cols==ColsAtCompileTime) + && EIGEN_IMPLIES(RowsAtCompileTime==Dynamic && MaxRowsAtCompileTime!=Dynamic,rows<=MaxRowsAtCompileTime) + && EIGEN_IMPLIES(ColsAtCompileTime==Dynamic && MaxColsAtCompileTime!=Dynamic,cols<=MaxColsAtCompileTime) + && rows>=0 && cols>=0 && "Invalid sizes when resizing a matrix or array."); + internal::check_rows_cols_for_overflow::run(rows, cols); + #ifdef EIGEN_INITIALIZE_COEFFS + Index size = rows*cols; + bool size_changed = size != this->size(); + m_storage.resize(size, rows, cols); + if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + #else + m_storage.resize(rows*cols, rows, cols); + #endif + } + + /** Resizes \c *this to a vector of length \a size + * + * \only_for_vectors. This method does not work for + * partially dynamic matrices when the static dimension is anything other + * than 1. For example it will not work with Matrix. + * + * Example: \include Matrix_resize_int.cpp + * Output: \verbinclude Matrix_resize_int.out + * + * \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t) + */ + EIGEN_DEVICE_FUNC + inline void resize(Index size) + { + EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase) + eigen_assert(((SizeAtCompileTime == Dynamic && (MaxSizeAtCompileTime==Dynamic || size<=MaxSizeAtCompileTime)) || SizeAtCompileTime == size) && size>=0); + #ifdef EIGEN_INITIALIZE_COEFFS + bool size_changed = size != this->size(); + #endif + if(RowsAtCompileTime == 1) + m_storage.resize(size, 1, size); + else + m_storage.resize(size, size, 1); + #ifdef EIGEN_INITIALIZE_COEFFS + if(size_changed) EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + #endif + } + + /** Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value \c NoChange + * as in the example below. + * + * Example: \include Matrix_resize_NoChange_int.cpp + * Output: \verbinclude Matrix_resize_NoChange_int.out + * + * \sa resize(Index,Index) + */ + EIGEN_DEVICE_FUNC + inline void resize(NoChange_t, Index cols) + { + resize(rows(), cols); + } + + /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value \c NoChange + * as in the example below. + * + * Example: \include Matrix_resize_int_NoChange.cpp + * Output: \verbinclude Matrix_resize_int_NoChange.out + * + * \sa resize(Index,Index) + */ + EIGEN_DEVICE_FUNC + inline void resize(Index rows, NoChange_t) + { + resize(rows, cols()); + } + + /** Resizes \c *this to have the same dimensions as \a other. + * Takes care of doing all the checking that's needed. + * + * Note that copying a row-vector into a vector (and conversely) is allowed. + * The resizing, if any, is then done in the appropriate way so that row-vectors + * remain row-vectors and vectors remain vectors. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void resizeLike(const EigenBase& _other) + { + const OtherDerived& other = _other.derived(); + internal::check_rows_cols_for_overflow::run(other.rows(), other.cols()); + const Index othersize = other.rows()*other.cols(); + if(RowsAtCompileTime == 1) + { + eigen_assert(other.rows() == 1 || other.cols() == 1); + resize(1, othersize); + } + else if(ColsAtCompileTime == 1) + { + eigen_assert(other.rows() == 1 || other.cols() == 1); + resize(othersize, 1); + } + else resize(other.rows(), other.cols()); + } + + /** Resizes the matrix to \a rows x \a cols while leaving old values untouched. + * + * The method is intended for matrices of dynamic size. If you only want to change the number + * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or + * conservativeResize(Index, NoChange_t). + * + * Matrices are resized relative to the top-left element. In case values need to be + * appended to the matrix they will be uninitialized. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void conservativeResize(Index rows, Index cols) + { + internal::conservative_resize_like_impl::run(*this, rows, cols); + } + + /** Resizes the matrix to \a rows x \a cols while leaving old values untouched. + * + * As opposed to conservativeResize(Index rows, Index cols), this version leaves + * the number of columns unchanged. + * + * In case the matrix is growing, new rows will be uninitialized. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void conservativeResize(Index rows, NoChange_t) + { + // Note: see the comment in conservativeResize(Index,Index) + conservativeResize(rows, cols()); + } + + /** Resizes the matrix to \a rows x \a cols while leaving old values untouched. + * + * As opposed to conservativeResize(Index rows, Index cols), this version leaves + * the number of rows unchanged. + * + * In case the matrix is growing, new columns will be uninitialized. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void conservativeResize(NoChange_t, Index cols) + { + // Note: see the comment in conservativeResize(Index,Index) + conservativeResize(rows(), cols); + } + + /** Resizes the vector to \a size while retaining old values. + * + * \only_for_vectors. This method does not work for + * partially dynamic matrices when the static dimension is anything other + * than 1. For example it will not work with Matrix. + * + * When values are appended, they will be uninitialized. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void conservativeResize(Index size) + { + internal::conservative_resize_like_impl::run(*this, size); + } + + /** Resizes the matrix to \a rows x \a cols of \c other, while leaving old values untouched. + * + * The method is intended for matrices of dynamic size. If you only want to change the number + * of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or + * conservativeResize(Index, NoChange_t). + * + * Matrices are resized relative to the top-left element. In case values need to be + * appended to the matrix they will copied from \c other. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void conservativeResizeLike(const DenseBase& other) + { + internal::conservative_resize_like_impl::run(*this, other); + } + + /** This is a special case of the templated operator=. Its purpose is to + * prevent a default operator= from hiding the templated operator=. + */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& operator=(const PlainObjectBase& other) + { + return _set(other); + } + + /** \sa MatrixBase::lazyAssign() */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& lazyAssign(const DenseBase& other) + { + _resize_to_match(other); + return Base::lazyAssign(other.derived()); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& operator=(const ReturnByValue& func) + { + resize(func.rows(), func.cols()); + return Base::operator=(func); + } + + // Prevent user from trying to instantiate PlainObjectBase objects + // by making all its constructor protected. See bug 1074. + protected: + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase() : m_storage() + { +// _check_template_params(); +// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } + +#ifndef EIGEN_PARSED_BY_DOXYGEN + // FIXME is it still needed ? + /** \internal */ + EIGEN_DEVICE_FUNC + explicit PlainObjectBase(internal::constructor_without_unaligned_array_assert) + : m_storage(internal::constructor_without_unaligned_array_assert()) + { +// _check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } +#endif + +#if EIGEN_HAS_RVALUE_REFERENCES + EIGEN_DEVICE_FUNC + PlainObjectBase(PlainObjectBase&& other) EIGEN_NOEXCEPT + : m_storage( std::move(other.m_storage) ) + { + } + + EIGEN_DEVICE_FUNC + PlainObjectBase& operator=(PlainObjectBase&& other) EIGEN_NOEXCEPT + { + _check_template_params(); + m_storage = std::move(other.m_storage); + return *this; + } +#endif + + /** Copy constructor */ + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase(const PlainObjectBase& other) + : Base(), m_storage(other.m_storage) { } + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols) + : m_storage(size, rows, cols) + { +// _check_template_params(); +// EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED + } + + #if EIGEN_HAS_CXX11 + /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients. \cpp11 + * + * \only_for_vectors + * + * This constructor is for 1D array or vectors with more than 4 coefficients. + * There exists C++98 analogue constructors for fixed-size array/vector having 1, 2, 3, or 4 coefficients. + * + * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this + * constructor must match the the fixed number of rows (resp. columns) of \c *this. + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args) + : m_storage() + { + _check_template_params(); + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, sizeof...(args) + 4); + m_storage.data()[0] = a0; + m_storage.data()[1] = a1; + m_storage.data()[2] = a2; + m_storage.data()[3] = a3; + Index i = 4; + auto x = {(m_storage.data()[i++] = args, 0)...}; + static_cast(x); + } + + /** \brief Constructs a Matrix or Array and initializes it by elements given by an initializer list of initializer + * lists \cpp11 + */ + EIGEN_DEVICE_FUNC + explicit EIGEN_STRONG_INLINE PlainObjectBase(const std::initializer_list>& list) + : m_storage() + { + _check_template_params(); + + size_t list_size = 0; + if (list.begin() != list.end()) { + list_size = list.begin()->size(); + } + + // This is to allow syntax like VectorXi {{1, 2, 3, 4}} + if (ColsAtCompileTime == 1 && list.size() == 1) { + eigen_assert(list_size == static_cast(RowsAtCompileTime) || RowsAtCompileTime == Dynamic); + resize(list_size, ColsAtCompileTime); + std::copy(list.begin()->begin(), list.begin()->end(), m_storage.data()); + } else { + eigen_assert(list.size() == static_cast(RowsAtCompileTime) || RowsAtCompileTime == Dynamic); + eigen_assert(list_size == static_cast(ColsAtCompileTime) || ColsAtCompileTime == Dynamic); + resize(list.size(), list_size); + + Index row_index = 0; + for (const std::initializer_list& row : list) { + eigen_assert(list_size == row.size()); + Index col_index = 0; + for (const Scalar& e : row) { + coeffRef(row_index, col_index) = e; + ++col_index; + } + ++row_index; + } + } + } + #endif // end EIGEN_HAS_CXX11 + + /** \sa PlainObjectBase::operator=(const EigenBase&) */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase(const DenseBase &other) + : m_storage() + { + _check_template_params(); + resizeLike(other); + _set_noalias(other); + } + + /** \sa PlainObjectBase::operator=(const EigenBase&) */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase(const EigenBase &other) + : m_storage() + { + _check_template_params(); + resizeLike(other); + *this = other.derived(); + } + /** \brief Copy constructor with in-place evaluation */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE PlainObjectBase(const ReturnByValue& other) + { + _check_template_params(); + // FIXME this does not automatically transpose vectors if necessary + resize(other.rows(), other.cols()); + other.evalTo(this->derived()); + } + + public: + + /** \brief Copies the generic expression \a other into *this. + * \copydetails DenseBase::operator=(const EigenBase &other) + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& operator=(const EigenBase &other) + { + _resize_to_match(other); + Base::operator=(other.derived()); + return this->derived(); + } + + /** \name Map + * These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects, + * while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned + * \a data pointers. + * + * Here is an example using strides: + * \include Matrix_Map_stride.cpp + * Output: \verbinclude Matrix_Map_stride.out + * + * \see class Map + */ + //@{ + static inline ConstMapType Map(const Scalar* data) + { return ConstMapType(data); } + static inline MapType Map(Scalar* data) + { return MapType(data); } + static inline ConstMapType Map(const Scalar* data, Index size) + { return ConstMapType(data, size); } + static inline MapType Map(Scalar* data, Index size) + { return MapType(data, size); } + static inline ConstMapType Map(const Scalar* data, Index rows, Index cols) + { return ConstMapType(data, rows, cols); } + static inline MapType Map(Scalar* data, Index rows, Index cols) + { return MapType(data, rows, cols); } + + static inline ConstAlignedMapType MapAligned(const Scalar* data) + { return ConstAlignedMapType(data); } + static inline AlignedMapType MapAligned(Scalar* data) + { return AlignedMapType(data); } + static inline ConstAlignedMapType MapAligned(const Scalar* data, Index size) + { return ConstAlignedMapType(data, size); } + static inline AlignedMapType MapAligned(Scalar* data, Index size) + { return AlignedMapType(data, size); } + static inline ConstAlignedMapType MapAligned(const Scalar* data, Index rows, Index cols) + { return ConstAlignedMapType(data, rows, cols); } + static inline AlignedMapType MapAligned(Scalar* data, Index rows, Index cols) + { return AlignedMapType(data, rows, cols); } + + template + static inline typename StridedConstMapType >::type Map(const Scalar* data, const Stride& stride) + { return typename StridedConstMapType >::type(data, stride); } + template + static inline typename StridedMapType >::type Map(Scalar* data, const Stride& stride) + { return typename StridedMapType >::type(data, stride); } + template + static inline typename StridedConstMapType >::type Map(const Scalar* data, Index size, const Stride& stride) + { return typename StridedConstMapType >::type(data, size, stride); } + template + static inline typename StridedMapType >::type Map(Scalar* data, Index size, const Stride& stride) + { return typename StridedMapType >::type(data, size, stride); } + template + static inline typename StridedConstMapType >::type Map(const Scalar* data, Index rows, Index cols, const Stride& stride) + { return typename StridedConstMapType >::type(data, rows, cols, stride); } + template + static inline typename StridedMapType >::type Map(Scalar* data, Index rows, Index cols, const Stride& stride) + { return typename StridedMapType >::type(data, rows, cols, stride); } + + template + static inline typename StridedConstAlignedMapType >::type MapAligned(const Scalar* data, const Stride& stride) + { return typename StridedConstAlignedMapType >::type(data, stride); } + template + static inline typename StridedAlignedMapType >::type MapAligned(Scalar* data, const Stride& stride) + { return typename StridedAlignedMapType >::type(data, stride); } + template + static inline typename StridedConstAlignedMapType >::type MapAligned(const Scalar* data, Index size, const Stride& stride) + { return typename StridedConstAlignedMapType >::type(data, size, stride); } + template + static inline typename StridedAlignedMapType >::type MapAligned(Scalar* data, Index size, const Stride& stride) + { return typename StridedAlignedMapType >::type(data, size, stride); } + template + static inline typename StridedConstAlignedMapType >::type MapAligned(const Scalar* data, Index rows, Index cols, const Stride& stride) + { return typename StridedConstAlignedMapType >::type(data, rows, cols, stride); } + template + static inline typename StridedAlignedMapType >::type MapAligned(Scalar* data, Index rows, Index cols, const Stride& stride) + { return typename StridedAlignedMapType >::type(data, rows, cols, stride); } + //@} + + using Base::setConstant; + EIGEN_DEVICE_FUNC Derived& setConstant(Index size, const Scalar& val); + EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, Index cols, const Scalar& val); + EIGEN_DEVICE_FUNC Derived& setConstant(NoChange_t, Index cols, const Scalar& val); + EIGEN_DEVICE_FUNC Derived& setConstant(Index rows, NoChange_t, const Scalar& val); + + using Base::setZero; + EIGEN_DEVICE_FUNC Derived& setZero(Index size); + EIGEN_DEVICE_FUNC Derived& setZero(Index rows, Index cols); + EIGEN_DEVICE_FUNC Derived& setZero(NoChange_t, Index cols); + EIGEN_DEVICE_FUNC Derived& setZero(Index rows, NoChange_t); + + using Base::setOnes; + EIGEN_DEVICE_FUNC Derived& setOnes(Index size); + EIGEN_DEVICE_FUNC Derived& setOnes(Index rows, Index cols); + EIGEN_DEVICE_FUNC Derived& setOnes(NoChange_t, Index cols); + EIGEN_DEVICE_FUNC Derived& setOnes(Index rows, NoChange_t); + + using Base::setRandom; + Derived& setRandom(Index size); + Derived& setRandom(Index rows, Index cols); + Derived& setRandom(NoChange_t, Index cols); + Derived& setRandom(Index rows, NoChange_t); + + #ifdef EIGEN_PLAINOBJECTBASE_PLUGIN + #include EIGEN_PLAINOBJECTBASE_PLUGIN + #endif + + protected: + /** \internal Resizes *this in preparation for assigning \a other to it. + * Takes care of doing all the checking that's needed. + * + * Note that copying a row-vector into a vector (and conversely) is allowed. + * The resizing, if any, is then done in the appropriate way so that row-vectors + * remain row-vectors and vectors remain vectors. + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _resize_to_match(const EigenBase& other) + { + #ifdef EIGEN_NO_AUTOMATIC_RESIZING + eigen_assert((this->size()==0 || (IsVectorAtCompileTime ? (this->size() == other.size()) + : (rows() == other.rows() && cols() == other.cols()))) + && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined"); + EIGEN_ONLY_USED_FOR_DEBUG(other); + #else + resizeLike(other); + #endif + } + + /** + * \brief Copies the value of the expression \a other into \c *this with automatic resizing. + * + * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized), + * it will be initialized. + * + * Note that copying a row-vector into a vector (and conversely) is allowed. + * The resizing, if any, is then done in the appropriate way so that row-vectors + * remain row-vectors and vectors remain vectors. + * + * \sa operator=(const MatrixBase&), _set_noalias() + * + * \internal + */ + // aliasing is dealt once in internal::call_assignment + // so at this stage we have to assume aliasing... and resising has to be done later. + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& _set(const DenseBase& other) + { + internal::call_assignment(this->derived(), other.derived()); + return this->derived(); + } + + /** \internal Like _set() but additionally makes the assumption that no aliasing effect can happen (which + * is the case when creating a new matrix) so one can enforce lazy evaluation. + * + * \sa operator=(const MatrixBase&), _set() + */ + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE Derived& _set_noalias(const DenseBase& other) + { + // I don't think we need this resize call since the lazyAssign will anyways resize + // and lazyAssign will be called by the assign selector. + //_resize_to_match(other); + // the 'false' below means to enforce lazy evaluation. We don't use lazyAssign() because + // it wouldn't allow to copy a row-vector into a column-vector. + internal::call_assignment_no_alias(this->derived(), other.derived(), internal::assign_op()); + return this->derived(); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init2(Index rows, Index cols, typename internal::enable_if::type* = 0) + { + const bool t0_is_integer_alike = internal::is_valid_index_type::value; + const bool t1_is_integer_alike = internal::is_valid_index_type::value; + EIGEN_STATIC_ASSERT(t0_is_integer_alike && + t1_is_integer_alike, + FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED) + resize(rows,cols); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init2(const T0& val0, const T1& val1, typename internal::enable_if::type* = 0) + { + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2) + m_storage.data()[0] = Scalar(val0); + m_storage.data()[1] = Scalar(val1); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init2(const Index& val0, const Index& val1, + typename internal::enable_if< (!internal::is_same::value) + && (internal::is_same::value) + && (internal::is_same::value) + && Base::SizeAtCompileTime==2,T1>::type* = 0) + { + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 2) + m_storage.data()[0] = Scalar(val0); + m_storage.data()[1] = Scalar(val1); + } + + // The argument is convertible to the Index type and we either have a non 1x1 Matrix, or a dynamic-sized Array, + // then the argument is meant to be the size of the object. + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(Index size, typename internal::enable_if< (Base::SizeAtCompileTime!=1 || !internal::is_convertible::value) + && ((!internal::is_same::XprKind,ArrayXpr>::value || Base::SizeAtCompileTime==Dynamic)),T>::type* = 0) + { + // NOTE MSVC 2008 complains if we directly put bool(NumTraits::IsInteger) as the EIGEN_STATIC_ASSERT argument. + const bool is_integer_alike = internal::is_valid_index_type::value; + EIGEN_UNUSED_VARIABLE(is_integer_alike); + EIGEN_STATIC_ASSERT(is_integer_alike, + FLOATING_POINT_ARGUMENT_PASSED__INTEGER_WAS_EXPECTED) + resize(size); + } + + // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type can be implicitly converted) + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Scalar& val0, typename internal::enable_if::value,T>::type* = 0) + { + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1) + m_storage.data()[0] = val0; + } + + // We have a 1x1 matrix/array => the argument is interpreted as the value of the unique coefficient (case where scalar type match the index type) + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Index& val0, + typename internal::enable_if< (!internal::is_same::value) + && (internal::is_same::value) + && Base::SizeAtCompileTime==1 + && internal::is_convertible::value,T*>::type* = 0) + { + EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(PlainObjectBase, 1) + m_storage.data()[0] = Scalar(val0); + } + + // Initialize a fixed size matrix from a pointer to raw data + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Scalar* data){ + this->_set_noalias(ConstMapType(data)); + } + + // Initialize an arbitrary matrix from a dense expression + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const DenseBase& other){ + this->_set_noalias(other); + } + + // Initialize an arbitrary matrix from an object convertible to the Derived type. + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Derived& other){ + this->_set_noalias(other); + } + + // Initialize an arbitrary matrix from a generic Eigen expression + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const EigenBase& other){ + this->derived() = other; + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const ReturnByValue& other) + { + resize(other.rows(), other.cols()); + other.evalTo(this->derived()); + } + + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const RotationBase& r) + { + this->derived() = r; + } + + // For fixed-size Array + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Scalar& val0, + typename internal::enable_if< Base::SizeAtCompileTime!=Dynamic + && Base::SizeAtCompileTime!=1 + && internal::is_convertible::value + && internal::is_same::XprKind,ArrayXpr>::value,T>::type* = 0) + { + Base::setConstant(val0); + } + + // For fixed-size Array + template + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE void _init1(const Index& val0, + typename internal::enable_if< (!internal::is_same::value) + && (internal::is_same::value) + && Base::SizeAtCompileTime!=Dynamic + && Base::SizeAtCompileTime!=1 + && internal::is_convertible::value + && internal::is_same::XprKind,ArrayXpr>::value,T*>::type* = 0) + { + Base::setConstant(val0); + } + + template + friend struct internal::matrix_swap_impl; + + public: + +#ifndef EIGEN_PARSED_BY_DOXYGEN + /** \internal + * \brief Override DenseBase::swap() since for dynamic-sized matrices + * of same type it is enough to swap the data pointers. + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void swap(DenseBase & other) + { + enum { SwapPointers = internal::is_same::value && Base::SizeAtCompileTime==Dynamic }; + internal::matrix_swap_impl::run(this->derived(), other.derived()); + } + + /** \internal + * \brief const version forwarded to DenseBase::swap + */ + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void swap(DenseBase const & other) + { Base::swap(other.derived()); } + + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void _check_template_params() + { + EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (int(Options)&RowMajor)==RowMajor) + && EIGEN_IMPLIES(MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1, (int(Options)&RowMajor)==0) + && ((RowsAtCompileTime == Dynamic) || (RowsAtCompileTime >= 0)) + && ((ColsAtCompileTime == Dynamic) || (ColsAtCompileTime >= 0)) + && ((MaxRowsAtCompileTime == Dynamic) || (MaxRowsAtCompileTime >= 0)) + && ((MaxColsAtCompileTime == Dynamic) || (MaxColsAtCompileTime >= 0)) + && (MaxRowsAtCompileTime == RowsAtCompileTime || RowsAtCompileTime==Dynamic) + && (MaxColsAtCompileTime == ColsAtCompileTime || ColsAtCompileTime==Dynamic) + && (Options & (DontAlign|RowMajor)) == Options), + INVALID_MATRIX_TEMPLATE_PARAMETERS) + } + + enum { IsPlainObjectBase = 1 }; +#endif + public: + // These apparently need to be down here for nvcc+icc to prevent duplicate + // Map symbol. + template friend class Eigen::Map; + friend class Eigen::Map; + friend class Eigen::Map; +#if EIGEN_MAX_ALIGN_BYTES>0 + // for EIGEN_MAX_ALIGN_BYTES==0, AlignedMax==Unaligned, and many compilers generate warnings for friend-ing a class twice. + friend class Eigen::Map; + friend class Eigen::Map; +#endif +}; + +namespace internal { + +template +struct conservative_resize_like_impl +{ + #if EIGEN_HAS_TYPE_TRAITS + static const bool IsRelocatable = std::is_trivially_copyable::value; + #else + static const bool IsRelocatable = !NumTraits::RequireInitialization; + #endif + static void run(DenseBase& _this, Index rows, Index cols) + { + if (_this.rows() == rows && _this.cols() == cols) return; + EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived) + + if ( IsRelocatable + && (( Derived::IsRowMajor && _this.cols() == cols) || // row-major and we change only the number of rows + (!Derived::IsRowMajor && _this.rows() == rows) )) // column-major and we change only the number of columns + { + internal::check_rows_cols_for_overflow::run(rows, cols); + _this.derived().m_storage.conservativeResize(rows*cols,rows,cols); + } + else + { + // The storage order does not allow us to use reallocation. + Derived tmp(rows,cols); + const Index common_rows = numext::mini(rows, _this.rows()); + const Index common_cols = numext::mini(cols, _this.cols()); + tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols); + _this.derived().swap(tmp); + } + } + + static void run(DenseBase& _this, const DenseBase& other) + { + if (_this.rows() == other.rows() && _this.cols() == other.cols()) return; + + // Note: Here is space for improvement. Basically, for conservativeResize(Index,Index), + // neither RowsAtCompileTime or ColsAtCompileTime must be Dynamic. If only one of the + // dimensions is dynamic, one could use either conservativeResize(Index rows, NoChange_t) or + // conservativeResize(NoChange_t, Index cols). For these methods new static asserts like + // EIGEN_STATIC_ASSERT_DYNAMIC_ROWS and EIGEN_STATIC_ASSERT_DYNAMIC_COLS would be good. + EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(Derived) + EIGEN_STATIC_ASSERT_DYNAMIC_SIZE(OtherDerived) + + if ( IsRelocatable && + (( Derived::IsRowMajor && _this.cols() == other.cols()) || // row-major and we change only the number of rows + (!Derived::IsRowMajor && _this.rows() == other.rows()) )) // column-major and we change only the number of columns + { + const Index new_rows = other.rows() - _this.rows(); + const Index new_cols = other.cols() - _this.cols(); + _this.derived().m_storage.conservativeResize(other.size(),other.rows(),other.cols()); + if (new_rows>0) + _this.bottomRightCorner(new_rows, other.cols()) = other.bottomRows(new_rows); + else if (new_cols>0) + _this.bottomRightCorner(other.rows(), new_cols) = other.rightCols(new_cols); + } + else + { + // The storage order does not allow us to use reallocation. + Derived tmp(other); + const Index common_rows = numext::mini(tmp.rows(), _this.rows()); + const Index common_cols = numext::mini(tmp.cols(), _this.cols()); + tmp.block(0,0,common_rows,common_cols) = _this.block(0,0,common_rows,common_cols); + _this.derived().swap(tmp); + } + } +}; + +// Here, the specialization for vectors inherits from the general matrix case +// to allow calling .conservativeResize(rows,cols) on vectors. +template +struct conservative_resize_like_impl + : conservative_resize_like_impl +{ + typedef conservative_resize_like_impl Base; + using Base::run; + using Base::IsRelocatable; + + static void run(DenseBase& _this, Index size) + { + const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : size; + const Index new_cols = Derived::RowsAtCompileTime==1 ? size : 1; + if(IsRelocatable) + _this.derived().m_storage.conservativeResize(size,new_rows,new_cols); + else + Base::run(_this.derived(), new_rows, new_cols); + } + + static void run(DenseBase& _this, const DenseBase& other) + { + if (_this.rows() == other.rows() && _this.cols() == other.cols()) return; + + const Index num_new_elements = other.size() - _this.size(); + + const Index new_rows = Derived::RowsAtCompileTime==1 ? 1 : other.rows(); + const Index new_cols = Derived::RowsAtCompileTime==1 ? other.cols() : 1; + if(IsRelocatable) + _this.derived().m_storage.conservativeResize(other.size(),new_rows,new_cols); + else + Base::run(_this.derived(), new_rows, new_cols); + + if (num_new_elements > 0) + _this.tail(num_new_elements) = other.tail(num_new_elements); + } +}; + +template +struct matrix_swap_impl +{ + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE void run(MatrixTypeA& a, MatrixTypeB& b) + { + a.base().swap(b); + } +}; + +template +struct matrix_swap_impl +{ + EIGEN_DEVICE_FUNC + static inline void run(MatrixTypeA& a, MatrixTypeB& b) + { + static_cast(a).m_storage.swap(static_cast(b).m_storage); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_DENSESTORAGEBASE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Product.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Product.h new file mode 100644 index 0000000000000000000000000000000000000000..19417493e7a3e2727eeaf7c0c5c764be0e3716a8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Product.h @@ -0,0 +1,191 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_PRODUCT_H +#define EIGEN_PRODUCT_H + +namespace Eigen { + +template class ProductImpl; + +namespace internal { + +template +struct traits > +{ + typedef typename remove_all::type LhsCleaned; + typedef typename remove_all::type RhsCleaned; + typedef traits LhsTraits; + typedef traits RhsTraits; + + typedef MatrixXpr XprKind; + + typedef typename ScalarBinaryOpTraits::Scalar, typename traits::Scalar>::ReturnType Scalar; + typedef typename product_promote_storage_type::ret>::ret StorageKind; + typedef typename promote_index_type::type StorageIndex; + + enum { + RowsAtCompileTime = LhsTraits::RowsAtCompileTime, + ColsAtCompileTime = RhsTraits::ColsAtCompileTime, + MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime, + MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime, + + // FIXME: only needed by GeneralMatrixMatrixTriangular + InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime), + + // The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator. + Flags = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? RowMajorBit + : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0 + : ( ((LhsTraits::Flags&NoPreferredStorageOrderBit) && (RhsTraits::Flags&RowMajorBit)) + || ((RhsTraits::Flags&NoPreferredStorageOrderBit) && (LhsTraits::Flags&RowMajorBit)) ) ? RowMajorBit + : NoPreferredStorageOrderBit + }; +}; + +} // end namespace internal + +/** \class Product + * \ingroup Core_Module + * + * \brief Expression of the product of two arbitrary matrices or vectors + * + * \tparam Lhs_ the type of the left-hand side expression + * \tparam Rhs_ the type of the right-hand side expression + * + * This class represents an expression of the product of two arbitrary matrices. + * + * The other template parameters are: + * \tparam Option can be DefaultProduct, AliasFreeProduct, or LazyProduct + * + */ +template +class Product : public ProductImpl::StorageKind, + typename internal::traits::StorageKind, + internal::product_type::ret>::ret> +{ + public: + + typedef Lhs_ Lhs; + typedef Rhs_ Rhs; + + typedef typename ProductImpl< + Lhs, Rhs, Option, + typename internal::product_promote_storage_type::StorageKind, + typename internal::traits::StorageKind, + internal::product_type::ret>::ret>::Base Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(Product) + + typedef typename internal::ref_selector::type LhsNested; + typedef typename internal::ref_selector::type RhsNested; + typedef typename internal::remove_all::type LhsNestedCleaned; + typedef typename internal::remove_all::type RhsNestedCleaned; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs) + { + eigen_assert(lhs.cols() == rhs.rows() + && "invalid matrix product" + && "if you wanted a coeff-wise or a dot product use the respective explicit functions"); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR + Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const LhsNestedCleaned& lhs() const { return m_lhs; } + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const RhsNestedCleaned& rhs() const { return m_rhs; } + + protected: + + LhsNested m_lhs; + RhsNested m_rhs; +}; + +namespace internal { + +template::ret> +class dense_product_base + : public internal::dense_xpr_base >::type +{}; + +/** Conversion to scalar for inner-products */ +template +class dense_product_base + : public internal::dense_xpr_base >::type +{ + typedef Product ProductXpr; + typedef typename internal::dense_xpr_base::type Base; +public: + using Base::derived; + typedef typename Base::Scalar Scalar; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator const Scalar() const + { + return internal::evaluator(derived()).coeff(0,0); + } +}; + +} // namespace internal + +// Generic API dispatcher +template +class ProductImpl : public internal::generic_xpr_base, MatrixXpr, StorageKind>::type +{ + public: + typedef typename internal::generic_xpr_base, MatrixXpr, StorageKind>::type Base; +}; + +template +class ProductImpl + : public internal::dense_product_base +{ + typedef Product Derived; + + public: + + typedef typename internal::dense_product_base Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Derived) + protected: + enum { + IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) && + (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic), + EnableCoeff = IsOneByOne || Option==LazyProduct + }; + + public: + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const + { + EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS); + eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) ); + + return internal::evaluator(derived()).coeff(row,col); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const + { + EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS); + eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) ); + + return internal::evaluator(derived()).coeff(i); + } + + +}; + +} // end namespace Eigen + +#endif // EIGEN_PRODUCT_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ProductEvaluators.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ProductEvaluators.h new file mode 100644 index 0000000000000000000000000000000000000000..b9eab97f95b0c6508d5c11dd37b02c06d950b279 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ProductEvaluators.h @@ -0,0 +1,1179 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2008-2010 Gael Guennebaud +// Copyright (C) 2011 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_PRODUCTEVALUATORS_H +#define EIGEN_PRODUCTEVALUATORS_H + +namespace Eigen { + +namespace internal { + +/** \internal + * Evaluator of a product expression. + * Since products require special treatments to handle all possible cases, + * we simply defer the evaluation logic to a product_evaluator class + * which offers more partial specialization possibilities. + * + * \sa class product_evaluator + */ +template +struct evaluator > + : public product_evaluator > +{ + typedef Product XprType; + typedef product_evaluator Base; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {} +}; + +// Catch "scalar * ( A * B )" and transform it to "(A*scalar) * B" +// TODO we should apply that rule only if that's really helpful +template +struct evaluator_assume_aliasing, + const CwiseNullaryOp, Plain1>, + const Product > > +{ + static const bool value = true; +}; +template +struct evaluator, + const CwiseNullaryOp, Plain1>, + const Product > > + : public evaluator > +{ + typedef CwiseBinaryOp, + const CwiseNullaryOp, Plain1>, + const Product > XprType; + typedef evaluator > Base; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) + : Base(xpr.lhs().functor().m_other * xpr.rhs().lhs() * xpr.rhs().rhs()) + {} +}; + + +template +struct evaluator, DiagIndex> > + : public evaluator, DiagIndex> > +{ + typedef Diagonal, DiagIndex> XprType; + typedef evaluator, DiagIndex> > Base; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) + : Base(Diagonal, DiagIndex>( + Product(xpr.nestedExpression().lhs(), xpr.nestedExpression().rhs()), + xpr.index() )) + {} +}; + + +// Helper class to perform a matrix product with the destination at hand. +// Depending on the sizes of the factors, there are different evaluation strategies +// as controlled by internal::product_type. +template< typename Lhs, typename Rhs, + typename LhsShape = typename evaluator_traits::Shape, + typename RhsShape = typename evaluator_traits::Shape, + int ProductType = internal::product_type::value> +struct generic_product_impl; + +template +struct evaluator_assume_aliasing > { + static const bool value = true; +}; + +// This is the default evaluator implementation for products: +// It creates a temporary and call generic_product_impl +template +struct product_evaluator, ProductTag, LhsShape, RhsShape> + : public evaluator::PlainObject> +{ + typedef Product XprType; + typedef typename XprType::PlainObject PlainObject; + typedef evaluator Base; + enum { + Flags = Base::Flags | EvalBeforeNestingBit + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit product_evaluator(const XprType& xpr) + : m_result(xpr.rows(), xpr.cols()) + { + ::new (static_cast(this)) Base(m_result); + +// FIXME shall we handle nested_eval here?, +// if so, then we must take care at removing the call to nested_eval in the specializations (e.g., in permutation_matrix_product, transposition_matrix_product, etc.) +// typedef typename internal::nested_eval::type LhsNested; +// typedef typename internal::nested_eval::type RhsNested; +// typedef typename internal::remove_all::type LhsNestedCleaned; +// typedef typename internal::remove_all::type RhsNestedCleaned; +// +// const LhsNested lhs(xpr.lhs()); +// const RhsNested rhs(xpr.rhs()); +// +// generic_product_impl::evalTo(m_result, lhs, rhs); + + generic_product_impl::evalTo(m_result, xpr.lhs(), xpr.rhs()); + } + +protected: + PlainObject m_result; +}; + +// The following three shortcuts are enabled only if the scalar types match exactly. +// TODO: we could enable them for different scalar types when the product is not vectorized. + +// Dense = Product +template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> +struct Assignment, internal::assign_op, Dense2Dense, + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> +{ + typedef Product SrcXprType; + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op &) + { + Index dstRows = src.rows(); + Index dstCols = src.cols(); + if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) + dst.resize(dstRows, dstCols); + // FIXME shall we handle nested_eval here? + generic_product_impl::evalTo(dst, src.lhs(), src.rhs()); + } +}; + +// Dense += Product +template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> +struct Assignment, internal::add_assign_op, Dense2Dense, + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> +{ + typedef Product SrcXprType; + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op &) + { + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + // FIXME shall we handle nested_eval here? + generic_product_impl::addTo(dst, src.lhs(), src.rhs()); + } +}; + +// Dense -= Product +template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar> +struct Assignment, internal::sub_assign_op, Dense2Dense, + typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type> +{ + typedef Product SrcXprType; + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op &) + { + eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols()); + // FIXME shall we handle nested_eval here? + generic_product_impl::subTo(dst, src.lhs(), src.rhs()); + } +}; + + +// Dense ?= scalar * Product +// TODO we should apply that rule if that's really helpful +// for instance, this is not good for inner products +template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain> +struct Assignment, const CwiseNullaryOp,Plain>, + const Product >, AssignFunc, Dense2Dense> +{ + typedef CwiseBinaryOp, + const CwiseNullaryOp,Plain>, + const Product > SrcXprType; + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func) + { + call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func); + } +}; + +//---------------------------------------- +// Catch "Dense ?= xpr + Product<>" expression to save one temporary +// FIXME we could probably enable these rules for any product, i.e., not only Dense and DefaultProduct + +template +struct evaluator_assume_aliasing::Scalar>, const OtherXpr, + const Product >, DenseShape > { + static const bool value = true; +}; + +template +struct evaluator_assume_aliasing::Scalar>, const OtherXpr, + const Product >, DenseShape > { + static const bool value = true; +}; + +template +struct assignment_from_xpr_op_product +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/) + { + call_assignment_no_alias(dst, src.lhs(), Func1()); + call_assignment_no_alias(dst, src.rhs(), Func2()); + } +}; + +#define EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(ASSIGN_OP,BINOP,ASSIGN_OP2) \ + template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar> \ + struct Assignment, const OtherXpr, \ + const Product >, internal::ASSIGN_OP, Dense2Dense> \ + : assignment_from_xpr_op_product, internal::ASSIGN_OP, internal::ASSIGN_OP2 > \ + {} + +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op, scalar_sum_op,add_assign_op); +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_sum_op,add_assign_op); +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_sum_op,sub_assign_op); + +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op, scalar_difference_op,sub_assign_op); +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_difference_op,sub_assign_op); +EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_difference_op,add_assign_op); + +//---------------------------------------- + +template +struct generic_product_impl +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum(); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + dst.coeffRef(0,0) += (lhs.transpose().cwiseProduct(rhs)).sum(); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { dst.coeffRef(0,0) -= (lhs.transpose().cwiseProduct(rhs)).sum(); } +}; + + +/*********************************************************************** +* Implementation of outer dense * dense vector product +***********************************************************************/ + +// Column major result +template +void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&) +{ + evaluator rhsEval(rhs); + ei_declare_local_nested_eval(Lhs,lhs,Rhs::SizeAtCompileTime,actual_lhs); + // FIXME if cols is large enough, then it might be useful to make sure that lhs is sequentially stored + // FIXME not very good if rhs is real and lhs complex while alpha is real too + const Index cols = dst.cols(); + for (Index j=0; j +void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&) +{ + evaluator lhsEval(lhs); + ei_declare_local_nested_eval(Rhs,rhs,Lhs::SizeAtCompileTime,actual_rhs); + // FIXME if rows is large enough, then it might be useful to make sure that rhs is sequentially stored + // FIXME not very good if lhs is real and rhs complex while alpha is real too + const Index rows = dst.rows(); + for (Index i=0; i +struct generic_product_impl +{ + template struct is_row_major : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {}; + typedef typename Product::Scalar Scalar; + + // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose + struct set { template EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() = src; } }; + struct add { template EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } }; + struct sub { template EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } }; + struct adds { + Scalar m_scale; + explicit adds(const Scalar& s) : m_scale(s) {} + template void EIGEN_DEVICE_FUNC operator()(const Dst& dst, const Src& src) const { + dst.const_cast_derived() += m_scale * src; + } + }; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major()); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major()); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major()); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major()); + } + +}; + + +// This base class provides default implementations for evalTo, addTo, subTo, in terms of scaleAndAddTo +template +struct generic_product_impl_base +{ + typedef typename Product::Scalar Scalar; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { scaleAndAddTo(dst,lhs, rhs, Scalar(1)); } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); } + +}; + +template +struct generic_product_impl + : generic_product_impl_base > +{ + typedef typename nested_eval::type LhsNested; + typedef typename nested_eval::type RhsNested; + typedef typename Product::Scalar Scalar; + enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight }; + typedef typename internal::remove_all::type>::type MatrixType; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + // Fallback to inner product if both the lhs and rhs is a runtime vector. + if (lhs.rows() == 1 && rhs.cols() == 1) { + dst.coeffRef(0,0) += alpha * lhs.row(0).conjugate().dot(rhs.col(0)); + return; + } + LhsNested actual_lhs(lhs); + RhsNested actual_rhs(rhs); + internal::gemv_dense_selector::HasUsableDirectAccess) + >::run(actual_lhs, actual_rhs, dst, alpha); + } +}; + +template +struct generic_product_impl +{ + typedef typename Product::Scalar Scalar; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + // Same as: dst.noalias() = lhs.lazyProduct(rhs); + // but easier on the compiler side + call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op()); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + // dst.noalias() += lhs.lazyProduct(rhs); + call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op()); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs) + { + // dst.noalias() -= lhs.lazyProduct(rhs); + call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op()); + } + + // This is a special evaluation path called from generic_product_impl<...,GemmProduct> in file GeneralMatrixMatrix.h + // This variant tries to extract scalar multiples from both the LHS and RHS and factor them out. For instance: + // dst {,+,-}= (s1*A)*(B*s2) + // will be rewritten as: + // dst {,+,-}= (s1*s2) * (A.lazyProduct(B)) + // There are at least four benefits of doing so: + // 1 - huge performance gain for heap-allocated matrix types as it save costly allocations. + // 2 - it is faster than simply by-passing the heap allocation through stack allocation. + // 3 - it makes this fallback consistent with the heavy GEMM routine. + // 4 - it fully by-passes huge stack allocation attempts when multiplying huge fixed-size matrices. + // (see https://stackoverflow.com/questions/54738495) + // For small fixed sizes matrices, howver, the gains are less obvious, it is sometimes x2 faster, but sometimes x3 slower, + // and the behavior depends also a lot on the compiler... This is why this re-writting strategy is currently + // enabled only when falling back from the main GEMM. + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void eval_dynamic(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Func &func) + { + enum { + HasScalarFactor = blas_traits::HasScalarFactor || blas_traits::HasScalarFactor, + ConjLhs = blas_traits::NeedToConjugate, + ConjRhs = blas_traits::NeedToConjugate + }; + // FIXME: in c++11 this should be auto, and extractScalarFactor should also return auto + // this is important for real*complex_mat + Scalar actualAlpha = combine_scalar_factors(lhs, rhs); + + eval_dynamic_impl(dst, + blas_traits::extract(lhs).template conjugateIf(), + blas_traits::extract(rhs).template conjugateIf(), + func, + actualAlpha, + typename conditional::type()); + } + +protected: + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s /* == 1 */, false_type) + { + EIGEN_UNUSED_VARIABLE(s); + eigen_internal_assert(s==Scalar(1)); + call_restricted_packet_assignment_no_alias(dst, lhs.lazyProduct(rhs), func); + } + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s, true_type) + { + call_restricted_packet_assignment_no_alias(dst, s * lhs.lazyProduct(rhs), func); + } +}; + +// This specialization enforces the use of a coefficient-based evaluation strategy +template +struct generic_product_impl + : generic_product_impl {}; + +// Case 2: Evaluate coeff by coeff +// +// This is mostly taken from CoeffBasedProduct.h +// The main difference is that we add an extra argument to the etor_product_*_impl::run() function +// for the inner dimension of the product, because evaluator object do not know their size. + +template +struct etor_product_coeff_impl; + +template +struct etor_product_packet_impl; + +template +struct product_evaluator, ProductTag, DenseShape, DenseShape> + : evaluator_base > +{ + typedef Product XprType; + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit product_evaluator(const XprType& xpr) + : m_lhs(xpr.lhs()), + m_rhs(xpr.rhs()), + m_lhsImpl(m_lhs), // FIXME the creation of the evaluator objects should result in a no-op, but check that! + m_rhsImpl(m_rhs), // Moreover, they are only useful for the packet path, so we could completely disable them when not needed, + // or perhaps declare them on the fly on the packet method... We have experiment to check what's best. + m_innerDim(xpr.lhs().cols()) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits::MulCost); + EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits::AddCost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); +#if 0 + std::cerr << "LhsOuterStrideBytes= " << LhsOuterStrideBytes << "\n"; + std::cerr << "RhsOuterStrideBytes= " << RhsOuterStrideBytes << "\n"; + std::cerr << "LhsAlignment= " << LhsAlignment << "\n"; + std::cerr << "RhsAlignment= " << RhsAlignment << "\n"; + std::cerr << "CanVectorizeLhs= " << CanVectorizeLhs << "\n"; + std::cerr << "CanVectorizeRhs= " << CanVectorizeRhs << "\n"; + std::cerr << "CanVectorizeInner= " << CanVectorizeInner << "\n"; + std::cerr << "EvalToRowMajor= " << EvalToRowMajor << "\n"; + std::cerr << "Alignment= " << Alignment << "\n"; + std::cerr << "Flags= " << Flags << "\n"; +#endif + } + + // Everything below here is taken from CoeffBasedProduct.h + + typedef typename internal::nested_eval::type LhsNested; + typedef typename internal::nested_eval::type RhsNested; + + typedef typename internal::remove_all::type LhsNestedCleaned; + typedef typename internal::remove_all::type RhsNestedCleaned; + + typedef evaluator LhsEtorType; + typedef evaluator RhsEtorType; + + enum { + RowsAtCompileTime = LhsNestedCleaned::RowsAtCompileTime, + ColsAtCompileTime = RhsNestedCleaned::ColsAtCompileTime, + InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsNestedCleaned::ColsAtCompileTime, RhsNestedCleaned::RowsAtCompileTime), + MaxRowsAtCompileTime = LhsNestedCleaned::MaxRowsAtCompileTime, + MaxColsAtCompileTime = RhsNestedCleaned::MaxColsAtCompileTime + }; + + typedef typename find_best_packet::type LhsVecPacketType; + typedef typename find_best_packet::type RhsVecPacketType; + + enum { + + LhsCoeffReadCost = LhsEtorType::CoeffReadCost, + RhsCoeffReadCost = RhsEtorType::CoeffReadCost, + CoeffReadCost = InnerSize==0 ? NumTraits::ReadCost + : InnerSize == Dynamic ? HugeCost + : InnerSize * (NumTraits::MulCost + int(LhsCoeffReadCost) + int(RhsCoeffReadCost)) + + (InnerSize - 1) * NumTraits::AddCost, + + Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT, + + LhsFlags = LhsEtorType::Flags, + RhsFlags = RhsEtorType::Flags, + + LhsRowMajor = LhsFlags & RowMajorBit, + RhsRowMajor = RhsFlags & RowMajorBit, + + LhsVecPacketSize = unpacket_traits::size, + RhsVecPacketSize = unpacket_traits::size, + + // Here, we don't care about alignment larger than the usable packet size. + LhsAlignment = EIGEN_PLAIN_ENUM_MIN(LhsEtorType::Alignment,LhsVecPacketSize*int(sizeof(typename LhsNestedCleaned::Scalar))), + RhsAlignment = EIGEN_PLAIN_ENUM_MIN(RhsEtorType::Alignment,RhsVecPacketSize*int(sizeof(typename RhsNestedCleaned::Scalar))), + + SameType = is_same::value, + + CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1), + CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime!=1), + + EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1 + : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0 + : (bool(RhsRowMajor) && !CanVectorizeLhs), + + Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & ~RowMajorBit) + | (EvalToRowMajor ? RowMajorBit : 0) + // TODO enable vectorization for mixed types + | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0) + | (XprType::IsVectorAtCompileTime ? LinearAccessBit : 0), + + LhsOuterStrideBytes = int(LhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename LhsNestedCleaned::Scalar)), + RhsOuterStrideBytes = int(RhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename RhsNestedCleaned::Scalar)), + + Alignment = bool(CanVectorizeLhs) ? (LhsOuterStrideBytes<=0 || (int(LhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,LhsAlignment))!=0 ? 0 : LhsAlignment) + : bool(CanVectorizeRhs) ? (RhsOuterStrideBytes<=0 || (int(RhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,RhsAlignment))!=0 ? 0 : RhsAlignment) + : 0, + + /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside + * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner + * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect + * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI. + */ + CanVectorizeInner = SameType + && LhsRowMajor + && (!RhsRowMajor) + && (int(LhsFlags) & int(RhsFlags) & ActualPacketAccessBit) + && (int(InnerSize) % packet_traits::size == 0) + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const + { + return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum(); + } + + /* Allow index-based non-packet access. It is impossible though to allow index-based packed access, + * which is why we don't set the LinearAccessBit. + * TODO: this seems possible when the result is a vector + */ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const CoeffReturnType coeff(Index index) const + { + const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index; + const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0; + return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum(); + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const PacketType packet(Index row, Index col) const + { + PacketType res; + typedef etor_product_packet_impl PacketImpl; + PacketImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res); + return res; + } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + const PacketType packet(Index index) const + { + const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index; + const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0; + return packet(row,col); + } + +protected: + typename internal::add_const_on_value_type::type m_lhs; + typename internal::add_const_on_value_type::type m_rhs; + + LhsEtorType m_lhsImpl; + RhsEtorType m_rhsImpl; + + // TODO: Get rid of m_innerDim if known at compile time + Index m_innerDim; +}; + +template +struct product_evaluator, LazyCoeffBasedProductMode, DenseShape, DenseShape> + : product_evaluator, CoeffBasedProductMode, DenseShape, DenseShape> +{ + typedef Product XprType; + typedef Product BaseProduct; + typedef product_evaluator Base; + enum { + Flags = Base::Flags | EvalBeforeNestingBit + }; + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit product_evaluator(const XprType& xpr) + : Base(BaseProduct(xpr.lhs(),xpr.rhs())) + {} +}; + +/**************************************** +*** Coeff based product, Packet path *** +****************************************/ + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res) + { + etor_product_packet_impl::run(row, col, lhs, rhs, innerDim, res); + res = pmadd(pset1(lhs.coeff(row, Index(UnrollingIndex-1))), rhs.template packet(Index(UnrollingIndex-1), col), res); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res) + { + etor_product_packet_impl::run(row, col, lhs, rhs, innerDim, res); + res = pmadd(lhs.template packet(row, Index(UnrollingIndex-1)), pset1(rhs.coeff(Index(UnrollingIndex-1), col)), res); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res) + { + res = pmul(pset1(lhs.coeff(row, Index(0))),rhs.template packet(Index(0), col)); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res) + { + res = pmul(lhs.template packet(row, Index(0)), pset1(rhs.coeff(Index(0), col))); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res) + { + res = pset1(typename unpacket_traits::type(0)); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res) + { + res = pset1(typename unpacket_traits::type(0)); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res) + { + res = pset1(typename unpacket_traits::type(0)); + for(Index i = 0; i < innerDim; ++i) + res = pmadd(pset1(lhs.coeff(row, i)), rhs.template packet(i, col), res); + } +}; + +template +struct etor_product_packet_impl +{ + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res) + { + res = pset1(typename unpacket_traits::type(0)); + for(Index i = 0; i < innerDim; ++i) + res = pmadd(lhs.template packet(row, i), pset1(rhs.coeff(i, col)), res); + } +}; + + +/*************************************************************************** +* Triangular products +***************************************************************************/ +template +struct triangular_product_impl; + +template +struct generic_product_impl + : generic_product_impl_base > +{ + typedef typename Product::Scalar Scalar; + + template + static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + triangular_product_impl + ::run(dst, lhs.nestedExpression(), rhs, alpha); + } +}; + +template +struct generic_product_impl +: generic_product_impl_base > +{ + typedef typename Product::Scalar Scalar; + + template + static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + triangular_product_impl::run(dst, lhs, rhs.nestedExpression(), alpha); + } +}; + + +/*************************************************************************** +* SelfAdjoint products +***************************************************************************/ +template +struct selfadjoint_product_impl; + +template +struct generic_product_impl + : generic_product_impl_base > +{ + typedef typename Product::Scalar Scalar; + + template + static EIGEN_DEVICE_FUNC + void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + selfadjoint_product_impl::run(dst, lhs.nestedExpression(), rhs, alpha); + } +}; + +template +struct generic_product_impl +: generic_product_impl_base > +{ + typedef typename Product::Scalar Scalar; + + template + static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) + { + selfadjoint_product_impl::run(dst, lhs, rhs.nestedExpression(), alpha); + } +}; + + +/*************************************************************************** +* Diagonal products +***************************************************************************/ + +template +struct diagonal_product_evaluator_base + : evaluator_base +{ + typedef typename ScalarBinaryOpTraits::ReturnType Scalar; +public: + enum { + CoeffReadCost = int(NumTraits::MulCost) + int(evaluator::CoeffReadCost) + int(evaluator::CoeffReadCost), + + MatrixFlags = evaluator::Flags, + DiagFlags = evaluator::Flags, + + StorageOrder_ = (Derived::MaxRowsAtCompileTime==1 && Derived::MaxColsAtCompileTime!=1) ? RowMajor + : (Derived::MaxColsAtCompileTime==1 && Derived::MaxRowsAtCompileTime!=1) ? ColMajor + : MatrixFlags & RowMajorBit ? RowMajor : ColMajor, + _SameStorageOrder = StorageOrder_ == (MatrixFlags & RowMajorBit ? RowMajor : ColMajor), + + _ScalarAccessOnDiag = !((int(StorageOrder_) == ColMajor && int(ProductOrder) == OnTheLeft) + ||(int(StorageOrder_) == RowMajor && int(ProductOrder) == OnTheRight)), + _SameTypes = is_same::value, + // FIXME currently we need same types, but in the future the next rule should be the one + //_Vectorizable = bool(int(MatrixFlags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagFlags)&PacketAccessBit))), + _Vectorizable = bool(int(MatrixFlags)&PacketAccessBit) + && _SameTypes + && (_SameStorageOrder || (MatrixFlags&LinearAccessBit)==LinearAccessBit) + && (_ScalarAccessOnDiag || (bool(int(DiagFlags)&PacketAccessBit))), + _LinearAccessMask = (MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1) ? LinearAccessBit : 0, + Flags = ((HereditaryBits|_LinearAccessMask) & (unsigned int)(MatrixFlags)) | (_Vectorizable ? PacketAccessBit : 0), + Alignment = evaluator::Alignment, + + AsScalarProduct = (DiagonalType::SizeAtCompileTime==1) + || (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::RowsAtCompileTime==1 && ProductOrder==OnTheLeft) + || (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==1 && ProductOrder==OnTheRight) + }; + + EIGEN_DEVICE_FUNC diagonal_product_evaluator_base(const MatrixType &mat, const DiagonalType &diag) + : m_diagImpl(diag), m_matImpl(mat) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits::MulCost); + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const + { + if(AsScalarProduct) + return m_diagImpl.coeff(0) * m_matImpl.coeff(idx); + else + return m_diagImpl.coeff(idx) * m_matImpl.coeff(idx); + } + +protected: + template + EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::true_type) const + { + return internal::pmul(m_matImpl.template packet(row, col), + internal::pset1(m_diagImpl.coeff(id))); + } + + template + EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::false_type) const + { + enum { + InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime, + DiagonalPacketLoadMode = EIGEN_PLAIN_ENUM_MIN(LoadMode,((InnerSize%16) == 0) ? int(Aligned16) : int(evaluator::Alignment)) // FIXME hardcoded 16!! + }; + return internal::pmul(m_matImpl.template packet(row, col), + m_diagImpl.template packet(id)); + } + + evaluator m_diagImpl; + evaluator m_matImpl; +}; + +// diagonal * dense +template +struct product_evaluator, ProductTag, DiagonalShape, DenseShape> + : diagonal_product_evaluator_base, OnTheLeft> +{ + typedef diagonal_product_evaluator_base, OnTheLeft> Base; + using Base::m_diagImpl; + using Base::m_matImpl; + using Base::coeff; + typedef typename Base::Scalar Scalar; + + typedef Product XprType; + typedef typename XprType::PlainObject PlainObject; + typedef typename Lhs::DiagonalVectorType DiagonalType; + + + enum { StorageOrder = Base::StorageOrder_ }; + + EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr) + : Base(xpr.rhs(), xpr.lhs().diagonal()) + { + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const + { + return m_diagImpl.coeff(row) * m_matImpl.coeff(row, col); + } + +#ifndef EIGEN_GPUCC + template + EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const + { + // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case. + // See also similar calls below. + return this->template packet_impl(row,col, row, + typename internal::conditional::type()); + } + + template + EIGEN_STRONG_INLINE PacketType packet(Index idx) const + { + return packet(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx); + } +#endif +}; + +// dense * diagonal +template +struct product_evaluator, ProductTag, DenseShape, DiagonalShape> + : diagonal_product_evaluator_base, OnTheRight> +{ + typedef diagonal_product_evaluator_base, OnTheRight> Base; + using Base::m_diagImpl; + using Base::m_matImpl; + using Base::coeff; + typedef typename Base::Scalar Scalar; + + typedef Product XprType; + typedef typename XprType::PlainObject PlainObject; + + enum { StorageOrder = Base::StorageOrder_ }; + + EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr) + : Base(xpr.lhs(), xpr.rhs().diagonal()) + { + } + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const + { + return m_matImpl.coeff(row, col) * m_diagImpl.coeff(col); + } + +#ifndef EIGEN_GPUCC + template + EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const + { + return this->template packet_impl(row,col, col, + typename internal::conditional::type()); + } + + template + EIGEN_STRONG_INLINE PacketType packet(Index idx) const + { + return packet(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx); + } +#endif +}; + +/*************************************************************************** +* Products with permutation matrices +***************************************************************************/ + +/** \internal + * \class permutation_matrix_product + * Internal helper class implementing the product between a permutation matrix and a matrix. + * This class is specialized for DenseShape below and for SparseShape in SparseCore/SparsePermutation.h + */ +template +struct permutation_matrix_product; + +template +struct permutation_matrix_product +{ + typedef typename nested_eval::type MatrixType; + typedef typename remove_all::type MatrixTypeCleaned; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr) + { + MatrixType mat(xpr); + const Index n = Side==OnTheLeft ? mat.rows() : mat.cols(); + // FIXME we need an is_same for expression that is not sensitive to constness. For instance + // is_same_xpr, Block >::value should be true. + //if(is_same::value && extract_data(dst) == extract_data(mat)) + if(is_same_dense(dst, mat)) + { + // apply the permutation inplace + Matrix mask(perm.size()); + mask.fill(false); + Index r = 0; + while(r < perm.size()) + { + // search for the next seed + while(r=perm.size()) + break; + // we got one, let's follow it until we are back to the seed + Index k0 = r++; + Index kPrev = k0; + mask.coeffRef(k0) = true; + for(Index k=perm.indices().coeff(k0); k!=k0; k=perm.indices().coeff(k)) + { + Block(dst, k) + .swap(Block + (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev)); + + mask.coeffRef(k) = true; + kPrev = k; + } + } + } + else + { + for(Index i = 0; i < n; ++i) + { + Block + (dst, ((Side==OnTheLeft) ^ Transposed) ? perm.indices().coeff(i) : i) + + = + + Block + (mat, ((Side==OnTheRight) ^ Transposed) ? perm.indices().coeff(i) : i); + } + } + } +}; + +template +struct generic_product_impl +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs) + { + permutation_matrix_product::run(dst, lhs, rhs); + } +}; + +template +struct generic_product_impl +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs) + { + permutation_matrix_product::run(dst, rhs, lhs); + } +}; + +template +struct generic_product_impl, Rhs, PermutationShape, MatrixShape, ProductTag> +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Inverse& lhs, const Rhs& rhs) + { + permutation_matrix_product::run(dst, lhs.nestedExpression(), rhs); + } +}; + +template +struct generic_product_impl, MatrixShape, PermutationShape, ProductTag> +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Inverse& rhs) + { + permutation_matrix_product::run(dst, rhs.nestedExpression(), lhs); + } +}; + + +/*************************************************************************** +* Products with transpositions matrices +***************************************************************************/ + +// FIXME could we unify Transpositions and Permutation into a single "shape"?? + +/** \internal + * \class transposition_matrix_product + * Internal helper class implementing the product between a permutation matrix and a matrix. + */ +template +struct transposition_matrix_product +{ + typedef typename nested_eval::type MatrixType; + typedef typename remove_all::type MatrixTypeCleaned; + + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr) + { + MatrixType mat(xpr); + typedef typename TranspositionType::StorageIndex StorageIndex; + const Index size = tr.size(); + StorageIndex j = 0; + + if(!is_same_dense(dst,mat)) + dst = mat; + + for(Index k=(Transposed?size-1:0) ; Transposed?k>=0:k +struct generic_product_impl +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs) + { + transposition_matrix_product::run(dst, lhs, rhs); + } +}; + +template +struct generic_product_impl +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs) + { + transposition_matrix_product::run(dst, rhs, lhs); + } +}; + + +template +struct generic_product_impl, Rhs, TranspositionsShape, MatrixShape, ProductTag> +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Transpose& lhs, const Rhs& rhs) + { + transposition_matrix_product::run(dst, lhs.nestedExpression(), rhs); + } +}; + +template +struct generic_product_impl, MatrixShape, TranspositionsShape, ProductTag> +{ + template + static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Transpose& rhs) + { + transposition_matrix_product::run(dst, rhs.nestedExpression(), lhs); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_PRODUCT_EVALUATORS_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Random.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Random.h new file mode 100644 index 0000000000000000000000000000000000000000..dab2ac8e9e84e564aa90465089d15188be8cda1c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Random.h @@ -0,0 +1,218 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_RANDOM_H +#define EIGEN_RANDOM_H + +namespace Eigen { + +namespace internal { + +template struct scalar_random_op { + EIGEN_EMPTY_STRUCT_CTOR(scalar_random_op) + inline const Scalar operator() () const { return random(); } +}; + +template +struct functor_traits > +{ enum { Cost = 5 * NumTraits::MulCost, PacketAccess = false, IsRepeatable = false }; }; + +} // end namespace internal + +/** \returns a random matrix expression + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * The parameters \a rows and \a cols are the number of rows and of columns of + * the returned matrix. Must be compatible with this MatrixBase type. + * + * \not_reentrant + * + * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, + * it is redundant to pass \a rows and \a cols as arguments, so Random() should be used + * instead. + * + * + * Example: \include MatrixBase_random_int_int.cpp + * Output: \verbinclude MatrixBase_random_int_int.out + * + * This expression has the "evaluate before nesting" flag so that it will be evaluated into + * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected + * behavior with expressions involving random matrices. + * + * See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators. + * + * \sa DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random() + */ +template +inline const typename DenseBase::RandomReturnType +DenseBase::Random(Index rows, Index cols) +{ + return NullaryExpr(rows, cols, internal::scalar_random_op()); +} + +/** \returns a random vector expression + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * The parameter \a size is the size of the returned vector. + * Must be compatible with this MatrixBase type. + * + * \only_for_vectors + * \not_reentrant + * + * This variant is meant to be used for dynamic-size vector types. For fixed-size types, + * it is redundant to pass \a size as argument, so Random() should be used + * instead. + * + * Example: \include MatrixBase_random_int.cpp + * Output: \verbinclude MatrixBase_random_int.out + * + * This expression has the "evaluate before nesting" flag so that it will be evaluated into + * a temporary vector whenever it is nested in a larger expression. This prevents unexpected + * behavior with expressions involving random matrices. + * + * \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random() + */ +template +inline const typename DenseBase::RandomReturnType +DenseBase::Random(Index size) +{ + return NullaryExpr(size, internal::scalar_random_op()); +} + +/** \returns a fixed-size random matrix or vector expression + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you + * need to use the variants taking size arguments. + * + * Example: \include MatrixBase_random.cpp + * Output: \verbinclude MatrixBase_random.out + * + * This expression has the "evaluate before nesting" flag so that it will be evaluated into + * a temporary matrix whenever it is nested in a larger expression. This prevents unexpected + * behavior with expressions involving random matrices. + * + * \not_reentrant + * + * \sa DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index) + */ +template +inline const typename DenseBase::RandomReturnType +DenseBase::Random() +{ + return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op()); +} + +/** Sets all coefficients in this expression to random values. + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * \not_reentrant + * + * Example: \include MatrixBase_setRandom.cpp + * Output: \verbinclude MatrixBase_setRandom.out + * + * \sa class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index) + */ +template +EIGEN_DEVICE_FUNC inline Derived& DenseBase::setRandom() +{ + return *this = Random(rows(), cols()); +} + +/** Resizes to the given \a newSize, and sets all coefficients in this expression to random values. + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * \only_for_vectors + * \not_reentrant + * + * Example: \include Matrix_setRandom_int.cpp + * Output: \verbinclude Matrix_setRandom_int.out + * + * \sa DenseBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, DenseBase::Random() + */ +template +EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setRandom(Index newSize) +{ + resize(newSize); + return setRandom(); +} + +/** Resizes to the given size, and sets all coefficients in this expression to random values. + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * \not_reentrant + * + * \param rows the new number of rows + * \param cols the new number of columns + * + * Example: \include Matrix_setRandom_int_int.cpp + * Output: \verbinclude Matrix_setRandom_int_int.out + * + * \sa DenseBase::setRandom(), setRandom(Index), class CwiseNullaryOp, DenseBase::Random() + */ +template +EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setRandom(Index rows, Index cols) +{ + resize(rows, cols); + return setRandom(); +} + +/** Resizes to the given size, changing only the number of columns, and sets all + * coefficients in this expression to random values. For the parameter of type + * NoChange_t, just pass the special value \c NoChange. + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * \not_reentrant + * + * \sa DenseBase::setRandom(), setRandom(Index), setRandom(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Random() + */ +template +EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setRandom(NoChange_t, Index cols) +{ + return setRandom(rows(), cols); +} + +/** Resizes to the given size, changing only the number of rows, and sets all + * coefficients in this expression to random values. For the parameter of type + * NoChange_t, just pass the special value \c NoChange. + * + * Numbers are uniformly spread through their whole definition range for integer types, + * and in the [-1:1] range for floating point scalar types. + * + * \not_reentrant + * + * \sa DenseBase::setRandom(), setRandom(Index), setRandom(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Random() + */ +template +EIGEN_STRONG_INLINE Derived& +PlainObjectBase::setRandom(Index rows, NoChange_t) +{ + return setRandom(rows, cols()); +} + +} // end namespace Eigen + +#endif // EIGEN_RANDOM_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Redux.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Redux.h new file mode 100644 index 0000000000000000000000000000000000000000..5732ba8c66241d9c955b2ada9a0dcd39e95cb1bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Redux.h @@ -0,0 +1,515 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_REDUX_H +#define EIGEN_REDUX_H + +namespace Eigen { + +namespace internal { + +// TODO +// * implement other kind of vectorization +// * factorize code + +/*************************************************************************** +* Part 1 : the logic deciding a strategy for vectorization and unrolling +***************************************************************************/ + +template +struct redux_traits +{ +public: + typedef typename find_best_packet::type PacketType; + enum { + PacketSize = unpacket_traits::size, + InnerMaxSize = int(Evaluator::IsRowMajor) + ? Evaluator::MaxColsAtCompileTime + : Evaluator::MaxRowsAtCompileTime, + OuterMaxSize = int(Evaluator::IsRowMajor) + ? Evaluator::MaxRowsAtCompileTime + : Evaluator::MaxColsAtCompileTime, + SliceVectorizedWork = int(InnerMaxSize)==Dynamic ? Dynamic + : int(OuterMaxSize)==Dynamic ? (int(InnerMaxSize)>=int(PacketSize) ? Dynamic : 0) + : (int(InnerMaxSize)/int(PacketSize)) * int(OuterMaxSize) + }; + + enum { + MightVectorize = (int(Evaluator::Flags)&ActualPacketAccessBit) + && (functor_traits::PacketAccess), + MayLinearVectorize = bool(MightVectorize) && (int(Evaluator::Flags)&LinearAccessBit), + MaySliceVectorize = bool(MightVectorize) && (int(SliceVectorizedWork)==Dynamic || int(SliceVectorizedWork)>=3) + }; + +public: + enum { + Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal) + : int(MaySliceVectorize) ? int(SliceVectorizedTraversal) + : int(DefaultTraversal) + }; + +public: + enum { + Cost = Evaluator::SizeAtCompileTime == Dynamic ? HugeCost + : int(Evaluator::SizeAtCompileTime) * int(Evaluator::CoeffReadCost) + (Evaluator::SizeAtCompileTime-1) * functor_traits::Cost, + UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize)) + }; + +public: + enum { + Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling + }; + +#ifdef EIGEN_DEBUG_ASSIGN + static void debug() + { + std::cerr << "Xpr: " << typeid(typename Evaluator::XprType).name() << std::endl; + std::cerr.setf(std::ios::hex, std::ios::basefield); + EIGEN_DEBUG_VAR(Evaluator::Flags) + std::cerr.unsetf(std::ios::hex); + EIGEN_DEBUG_VAR(InnerMaxSize) + EIGEN_DEBUG_VAR(OuterMaxSize) + EIGEN_DEBUG_VAR(SliceVectorizedWork) + EIGEN_DEBUG_VAR(PacketSize) + EIGEN_DEBUG_VAR(MightVectorize) + EIGEN_DEBUG_VAR(MayLinearVectorize) + EIGEN_DEBUG_VAR(MaySliceVectorize) + std::cerr << "Traversal" << " = " << Traversal << " (" << demangle_traversal(Traversal) << ")" << std::endl; + EIGEN_DEBUG_VAR(UnrollingLimit) + std::cerr << "Unrolling" << " = " << Unrolling << " (" << demangle_unrolling(Unrolling) << ")" << std::endl; + std::cerr << std::endl; + } +#endif +}; + +/*************************************************************************** +* Part 2 : unrollers +***************************************************************************/ + +/*** no vectorization ***/ + +template +struct redux_novec_unroller +{ + enum { + HalfLength = Length/2 + }; + + typedef typename Evaluator::Scalar Scalar; + + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func& func) + { + return func(redux_novec_unroller::run(eval,func), + redux_novec_unroller::run(eval,func)); + } +}; + +template +struct redux_novec_unroller +{ + enum { + outer = Start / Evaluator::InnerSizeAtCompileTime, + inner = Start % Evaluator::InnerSizeAtCompileTime + }; + + typedef typename Evaluator::Scalar Scalar; + + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE Scalar run(const Evaluator &eval, const Func&) + { + return eval.coeffByOuterInner(outer, inner); + } +}; + +// This is actually dead code and will never be called. It is required +// to prevent false warnings regarding failed inlining though +// for 0 length run() will never be called at all. +template +struct redux_novec_unroller +{ + typedef typename Evaluator::Scalar Scalar; + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE Scalar run(const Evaluator&, const Func&) { return Scalar(); } +}; + +/*** vectorization ***/ + +template +struct redux_vec_unroller +{ + template + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func& func) + { + enum { + PacketSize = unpacket_traits::size, + HalfLength = Length/2 + }; + + return func.packetOp( + redux_vec_unroller::template run(eval,func), + redux_vec_unroller::template run(eval,func) ); + } +}; + +template +struct redux_vec_unroller +{ + template + EIGEN_DEVICE_FUNC + static EIGEN_STRONG_INLINE PacketType run(const Evaluator &eval, const Func&) + { + enum { + PacketSize = unpacket_traits::size, + index = Start * PacketSize, + outer = index / int(Evaluator::InnerSizeAtCompileTime), + inner = index % int(Evaluator::InnerSizeAtCompileTime), + alignment = Evaluator::Alignment + }; + return eval.template packetByOuterInner(outer, inner); + } +}; + +/*************************************************************************** +* Part 3 : implementation of all cases +***************************************************************************/ + +template::Traversal, + int Unrolling = redux_traits::Unrolling +> +struct redux_impl; + +template +struct redux_impl +{ + typedef typename Evaluator::Scalar Scalar; + + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE + Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr) + { + eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix"); + Scalar res; + res = eval.coeffByOuterInner(0, 0); + for(Index i = 1; i < xpr.innerSize(); ++i) + res = func(res, eval.coeffByOuterInner(0, i)); + for(Index i = 1; i < xpr.outerSize(); ++i) + for(Index j = 0; j < xpr.innerSize(); ++j) + res = func(res, eval.coeffByOuterInner(i, j)); + return res; + } +}; + +template +struct redux_impl + : redux_novec_unroller +{ + typedef redux_novec_unroller Base; + typedef typename Evaluator::Scalar Scalar; + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE + Scalar run(const Evaluator &eval, const Func& func, const XprType& /*xpr*/) + { + return Base::run(eval,func); + } +}; + +template +struct redux_impl +{ + typedef typename Evaluator::Scalar Scalar; + typedef typename redux_traits::PacketType PacketScalar; + + template + static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr) + { + const Index size = xpr.size(); + + const Index packetSize = redux_traits::PacketSize; + const int packetAlignment = unpacket_traits::alignment; + enum { + alignment0 = (bool(Evaluator::Flags & DirectAccessBit) && bool(packet_traits::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned), + alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Evaluator::Alignment) + }; + const Index alignedStart = internal::first_default_aligned(xpr); + const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize); + const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize); + const Index alignedEnd2 = alignedStart + alignedSize2; + const Index alignedEnd = alignedStart + alignedSize; + Scalar res; + if(alignedSize) + { + PacketScalar packet_res0 = eval.template packet(alignedStart); + if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop + { + PacketScalar packet_res1 = eval.template packet(alignedStart+packetSize); + for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize) + { + packet_res0 = func.packetOp(packet_res0, eval.template packet(index)); + packet_res1 = func.packetOp(packet_res1, eval.template packet(index+packetSize)); + } + + packet_res0 = func.packetOp(packet_res0,packet_res1); + if(alignedEnd>alignedEnd2) + packet_res0 = func.packetOp(packet_res0, eval.template packet(alignedEnd2)); + } + res = func.predux(packet_res0); + + for(Index index = 0; index < alignedStart; ++index) + res = func(res,eval.coeff(index)); + + for(Index index = alignedEnd; index < size; ++index) + res = func(res,eval.coeff(index)); + } + else // too small to vectorize anything. + // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize. + { + res = eval.coeff(0); + for(Index index = 1; index < size; ++index) + res = func(res,eval.coeff(index)); + } + + return res; + } +}; + +// NOTE: for SliceVectorizedTraversal we simply bypass unrolling +template +struct redux_impl +{ + typedef typename Evaluator::Scalar Scalar; + typedef typename redux_traits::PacketType PacketType; + + template + EIGEN_DEVICE_FUNC static Scalar run(const Evaluator &eval, const Func& func, const XprType& xpr) + { + eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix"); + const Index innerSize = xpr.innerSize(); + const Index outerSize = xpr.outerSize(); + enum { + packetSize = redux_traits::PacketSize + }; + const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize; + Scalar res; + if(packetedInnerSize) + { + PacketType packet_res = eval.template packet(0,0); + for(Index j=0; j(j,i)); + + res = func.predux(packet_res); + for(Index j=0; j::run(eval, func, xpr); + } + + return res; + } +}; + +template +struct redux_impl +{ + typedef typename Evaluator::Scalar Scalar; + + typedef typename redux_traits::PacketType PacketType; + enum { + PacketSize = redux_traits::PacketSize, + Size = Evaluator::SizeAtCompileTime, + VectorizedSize = (int(Size) / int(PacketSize)) * int(PacketSize) + }; + + template + EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE + Scalar run(const Evaluator &eval, const Func& func, const XprType &xpr) + { + EIGEN_ONLY_USED_FOR_DEBUG(xpr) + eigen_assert(xpr.rows()>0 && xpr.cols()>0 && "you are using an empty matrix"); + if (VectorizedSize > 0) { + Scalar res = func.predux(redux_vec_unroller::template run(eval,func)); + if (VectorizedSize != Size) + res = func(res,redux_novec_unroller::run(eval,func)); + return res; + } + else { + return redux_novec_unroller::run(eval,func); + } + } +}; + +// evaluator adaptor +template +class redux_evaluator : public internal::evaluator +{ + typedef internal::evaluator Base; +public: + typedef XprType_ XprType; + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + explicit redux_evaluator(const XprType &xpr) : Base(xpr) {} + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + typedef typename XprType::PacketScalar PacketScalar; + + enum { + MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = XprType::MaxColsAtCompileTime, + // TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime from the evaluator + Flags = Base::Flags & ~DirectAccessBit, + IsRowMajor = XprType::IsRowMajor, + SizeAtCompileTime = XprType::SizeAtCompileTime, + InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime + }; + + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + CoeffReturnType coeffByOuterInner(Index outer, Index inner) const + { return Base::coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); } + + template + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE + PacketType packetByOuterInner(Index outer, Index inner) const + { return Base::template packet(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); } + +}; + +} // end namespace internal + +/*************************************************************************** +* Part 4 : public API +***************************************************************************/ + + +/** \returns the result of a full redux operation on the whole matrix or vector using \a func + * + * The template parameter \a BinaryOp is the type of the functor \a func which must be + * an associative operator. Both current C++98 and C++11 functor styles are handled. + * + * \warning the matrix must be not empty, otherwise an assertion is triggered. + * + * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise() + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::redux(const Func& func) const +{ + eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix"); + + typedef typename internal::redux_evaluator ThisEvaluator; + ThisEvaluator thisEval(derived()); + + // The initial expression is passed to the reducer as an additional argument instead of + // passing it as a member of redux_evaluator to help + return internal::redux_impl::run(thisEval, func, derived()); +} + +/** \returns the minimum of all coefficients of \c *this. + * In case \c *this contains NaN, NaNPropagation determines the behavior: + * NaNPropagation == PropagateFast : undefined + * NaNPropagation == PropagateNaN : result is NaN + * NaNPropagation == PropagateNumbers : result is minimum of elements that are not NaN + * \warning the matrix must be not empty, otherwise an assertion is triggered. + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::minCoeff() const +{ + return derived().redux(Eigen::internal::scalar_min_op()); +} + +/** \returns the maximum of all coefficients of \c *this. + * In case \c *this contains NaN, NaNPropagation determines the behavior: + * NaNPropagation == PropagateFast : undefined + * NaNPropagation == PropagateNaN : result is NaN + * NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN + * \warning the matrix must be not empty, otherwise an assertion is triggered. + */ +template +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::maxCoeff() const +{ + return derived().redux(Eigen::internal::scalar_max_op()); +} + +/** \returns the sum of all coefficients of \c *this + * + * If \c *this is empty, then the value 0 is returned. + * + * \sa trace(), prod(), mean() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::sum() const +{ + if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0)) + return Scalar(0); + return derived().redux(Eigen::internal::scalar_sum_op()); +} + +/** \returns the mean of all coefficients of *this +* +* \sa trace(), prod(), sum() +*/ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::mean() const +{ +#ifdef __INTEL_COMPILER + #pragma warning push + #pragma warning ( disable : 2259 ) +#endif + return Scalar(derived().redux(Eigen::internal::scalar_sum_op())) / Scalar(this->size()); +#ifdef __INTEL_COMPILER + #pragma warning pop +#endif +} + +/** \returns the product of all coefficients of *this + * + * Example: \include MatrixBase_prod.cpp + * Output: \verbinclude MatrixBase_prod.out + * + * \sa sum(), mean(), trace() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +DenseBase::prod() const +{ + if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0)) + return Scalar(1); + return derived().redux(Eigen::internal::scalar_product_op()); +} + +/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal. + * + * \c *this can be any matrix, not necessarily square. + * + * \sa diagonal(), sum() + */ +template +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::traits::Scalar +MatrixBase::trace() const +{ + return derived().diagonal().sum(); +} + +} // end namespace Eigen + +#endif // EIGEN_REDUX_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Ref.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Ref.h new file mode 100644 index 0000000000000000000000000000000000000000..716552a70a3b581fb3b377285f622cf7c2ba21ff --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Ref.h @@ -0,0 +1,381 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_REF_H +#define EIGEN_REF_H + +namespace Eigen { + +namespace internal { + +template +struct traits > + : public traits > +{ + typedef _PlainObjectType PlainObjectType; + typedef _StrideType StrideType; + enum { + Options = Options_, + Flags = traits >::Flags | NestByRefBit, + Alignment = traits >::Alignment + }; + + template struct match { + enum { + IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime || Derived::IsVectorAtCompileTime, + HasDirectAccess = internal::has_direct_access::ret, + StorageOrderMatch = IsVectorAtCompileTime || ((PlainObjectType::Flags&RowMajorBit)==(Derived::Flags&RowMajorBit)), + InnerStrideMatch = int(StrideType::InnerStrideAtCompileTime)==int(Dynamic) + || int(StrideType::InnerStrideAtCompileTime)==int(Derived::InnerStrideAtCompileTime) + || (int(StrideType::InnerStrideAtCompileTime)==0 && int(Derived::InnerStrideAtCompileTime)==1), + OuterStrideMatch = IsVectorAtCompileTime + || int(StrideType::OuterStrideAtCompileTime)==int(Dynamic) || int(StrideType::OuterStrideAtCompileTime)==int(Derived::OuterStrideAtCompileTime), + // NOTE, this indirection of evaluator::Alignment is needed + // to workaround a very strange bug in MSVC related to the instantiation + // of has_*ary_operator in evaluator. + // This line is surprisingly very sensitive. For instance, simply adding parenthesis + // as "DerivedAlignment = (int(evaluator::Alignment))," will make MSVC fail... + DerivedAlignment = int(evaluator::Alignment), + AlignmentMatch = (int(traits::Alignment)==int(Unaligned)) || (DerivedAlignment >= int(Alignment)), // FIXME the first condition is not very clear, it should be replaced by the required alignment + ScalarTypeMatch = internal::is_same::value, + MatchAtCompileTime = HasDirectAccess && StorageOrderMatch && InnerStrideMatch && OuterStrideMatch && AlignmentMatch && ScalarTypeMatch + }; + typedef typename internal::conditional::type type; + }; + +}; + +template +struct traits > : public traits {}; + +} + +template class RefBase + : public MapBase +{ + typedef typename internal::traits::PlainObjectType PlainObjectType; + typedef typename internal::traits::StrideType StrideType; + +public: + + typedef MapBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(RefBase) + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const + { + return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1; + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const + { + return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer() + : IsVectorAtCompileTime ? this->size() + : int(Flags)&RowMajorBit ? this->cols() + : this->rows(); + } + + EIGEN_DEVICE_FUNC RefBase() + : Base(0,RowsAtCompileTime==Dynamic?0:RowsAtCompileTime,ColsAtCompileTime==Dynamic?0:ColsAtCompileTime), + // Stride<> does not allow default ctor for Dynamic strides, so let' initialize it with dummy values: + m_stride(StrideType::OuterStrideAtCompileTime==Dynamic?0:StrideType::OuterStrideAtCompileTime, + StrideType::InnerStrideAtCompileTime==Dynamic?0:StrideType::InnerStrideAtCompileTime) + {} + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(RefBase) + +protected: + + typedef Stride StrideBase; + + // Resolves inner stride if default 0. + static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveInnerStride(Index inner) { + return inner == 0 ? 1 : inner; + } + + // Resolves outer stride if default 0. + static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveOuterStride(Index inner, Index outer, Index rows, Index cols, bool isVectorAtCompileTime, bool isRowMajor) { + return outer == 0 ? isVectorAtCompileTime ? inner * rows * cols : isRowMajor ? inner * cols : inner * rows : outer; + } + + // Returns true if construction is valid, false if there is a stride mismatch, + // and fails if there is a size mismatch. + template + EIGEN_DEVICE_FUNC bool construct(Expression& expr) + { + // Check matrix sizes. If this is a compile-time vector, we do allow + // implicitly transposing. + EIGEN_STATIC_ASSERT( + EIGEN_PREDICATE_SAME_MATRIX_SIZE(PlainObjectType, Expression) + // If it is a vector, the transpose sizes might match. + || ( PlainObjectType::IsVectorAtCompileTime + && ((int(PlainObjectType::RowsAtCompileTime)==Eigen::Dynamic + || int(Expression::ColsAtCompileTime)==Eigen::Dynamic + || int(PlainObjectType::RowsAtCompileTime)==int(Expression::ColsAtCompileTime)) + && (int(PlainObjectType::ColsAtCompileTime)==Eigen::Dynamic + || int(Expression::RowsAtCompileTime)==Eigen::Dynamic + || int(PlainObjectType::ColsAtCompileTime)==int(Expression::RowsAtCompileTime)))), + YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES + ) + + // Determine runtime rows and columns. + Index rows = expr.rows(); + Index cols = expr.cols(); + if(PlainObjectType::RowsAtCompileTime==1) + { + eigen_assert(expr.rows()==1 || expr.cols()==1); + rows = 1; + cols = expr.size(); + } + else if(PlainObjectType::ColsAtCompileTime==1) + { + eigen_assert(expr.rows()==1 || expr.cols()==1); + rows = expr.size(); + cols = 1; + } + // Verify that the sizes are valid. + eigen_assert( + (PlainObjectType::RowsAtCompileTime == Dynamic) || (PlainObjectType::RowsAtCompileTime == rows)); + eigen_assert( + (PlainObjectType::ColsAtCompileTime == Dynamic) || (PlainObjectType::ColsAtCompileTime == cols)); + + + // If this is a vector, we might be transposing, which means that stride should swap. + const bool transpose = PlainObjectType::IsVectorAtCompileTime && (rows != expr.rows()); + // If the storage format differs, we also need to swap the stride. + const bool row_major = ((PlainObjectType::Flags)&RowMajorBit) != 0; + const bool expr_row_major = (Expression::Flags&RowMajorBit) != 0; + const bool storage_differs = (row_major != expr_row_major); + + const bool swap_stride = (transpose != storage_differs); + + // Determine expr's actual strides, resolving any defaults if zero. + const Index expr_inner_actual = resolveInnerStride(expr.innerStride()); + const Index expr_outer_actual = resolveOuterStride(expr_inner_actual, + expr.outerStride(), + expr.rows(), + expr.cols(), + Expression::IsVectorAtCompileTime != 0, + expr_row_major); + + // If this is a column-major row vector or row-major column vector, the inner-stride + // is arbitrary, so set it to either the compile-time inner stride or 1. + const bool row_vector = (rows == 1); + const bool col_vector = (cols == 1); + const Index inner_stride = + ( (!row_major && row_vector) || (row_major && col_vector) ) ? + ( StrideType::InnerStrideAtCompileTime > 0 ? Index(StrideType::InnerStrideAtCompileTime) : 1) + : swap_stride ? expr_outer_actual : expr_inner_actual; + + // If this is a column-major column vector or row-major row vector, the outer-stride + // is arbitrary, so set it to either the compile-time outer stride or vector size. + const Index outer_stride = + ( (!row_major && col_vector) || (row_major && row_vector) ) ? + ( StrideType::OuterStrideAtCompileTime > 0 ? Index(StrideType::OuterStrideAtCompileTime) : rows * cols * inner_stride) + : swap_stride ? expr_inner_actual : expr_outer_actual; + + // Check if given inner/outer strides are compatible with compile-time strides. + const bool inner_valid = (StrideType::InnerStrideAtCompileTime == Dynamic) + || (resolveInnerStride(Index(StrideType::InnerStrideAtCompileTime)) == inner_stride); + if (!inner_valid) { + return false; + } + + const bool outer_valid = (StrideType::OuterStrideAtCompileTime == Dynamic) + || (resolveOuterStride( + inner_stride, + Index(StrideType::OuterStrideAtCompileTime), + rows, cols, PlainObjectType::IsVectorAtCompileTime != 0, + row_major) + == outer_stride); + if (!outer_valid) { + return false; + } + + ::new (static_cast(this)) Base(expr.data(), rows, cols); + ::new (&m_stride) StrideBase( + (StrideType::OuterStrideAtCompileTime == 0) ? 0 : outer_stride, + (StrideType::InnerStrideAtCompileTime == 0) ? 0 : inner_stride ); + return true; + } + + StrideBase m_stride; +}; + +/** \class Ref + * \ingroup Core_Module + * + * \brief A matrix or vector expression mapping an existing expression + * + * \tparam PlainObjectType the equivalent matrix type of the mapped data + * \tparam Options specifies the pointer alignment in bytes. It can be: \c #Aligned128, , \c #Aligned64, \c #Aligned32, \c #Aligned16, \c #Aligned8 or \c #Unaligned. + * The default is \c #Unaligned. + * \tparam StrideType optionally specifies strides. By default, Ref implies a contiguous storage along the inner dimension (inner stride==1), + * but accepts a variable outer stride (leading dimension). + * This can be overridden by specifying strides. + * The type passed here must be a specialization of the Stride template, see examples below. + * + * This class provides a way to write non-template functions taking Eigen objects as parameters while limiting the number of copies. + * A Ref<> object can represent either a const expression or a l-value: + * \code + * // in-out argument: + * void foo1(Ref x); + * + * // read-only const argument: + * void foo2(const Ref& x); + * \endcode + * + * In the in-out case, the input argument must satisfy the constraints of the actual Ref<> type, otherwise a compilation issue will be triggered. + * By default, a Ref can reference any dense vector expression of float having a contiguous memory layout. + * Likewise, a Ref can reference any column-major dense matrix expression of float whose column's elements are contiguously stored with + * the possibility to have a constant space in-between each column, i.e. the inner stride must be equal to 1, but the outer stride (or leading dimension) + * can be greater than the number of rows. + * + * In the const case, if the input expression does not match the above requirement, then it is evaluated into a temporary before being passed to the function. + * Here are some examples: + * \code + * MatrixXf A; + * VectorXf a; + * foo1(a.head()); // OK + * foo1(A.col()); // OK + * foo1(A.row()); // Compilation error because here innerstride!=1 + * foo2(A.row()); // Compilation error because A.row() is a 1xN object while foo2 is expecting a Nx1 object + * foo2(A.row().transpose()); // The row is copied into a contiguous temporary + * foo2(2*a); // The expression is evaluated into a temporary + * foo2(A.col().segment(2,4)); // No temporary + * \endcode + * + * The range of inputs that can be referenced without temporary can be enlarged using the last two template parameters. + * Here is an example accepting an innerstride!=1: + * \code + * // in-out argument: + * void foo3(Ref > x); + * foo3(A.row()); // OK + * \endcode + * The downside here is that the function foo3 might be significantly slower than foo1 because it won't be able to exploit vectorization, and will involve more + * expensive address computations even if the input is contiguously stored in memory. To overcome this issue, one might propose to overload internally calling a + * template function, e.g.: + * \code + * // in the .h: + * void foo(const Ref& A); + * void foo(const Ref >& A); + * + * // in the .cpp: + * template void foo_impl(const TypeOfA& A) { + * ... // crazy code goes here + * } + * void foo(const Ref& A) { foo_impl(A); } + * void foo(const Ref >& A) { foo_impl(A); } + * \endcode + * + * See also the following stackoverflow questions for further references: + * - Correct usage of the Eigen::Ref<> class + * + * \sa PlainObjectBase::Map(), \ref TopicStorageOrders + */ +template class Ref + : public RefBase > +{ + private: + typedef internal::traits Traits; + template + EIGEN_DEVICE_FUNC inline Ref(const PlainObjectBase& expr, + typename internal::enable_if::MatchAtCompileTime),Derived>::type* = 0); + public: + + typedef RefBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Ref) + + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template + EIGEN_DEVICE_FUNC inline Ref(PlainObjectBase& expr, + typename internal::enable_if::MatchAtCompileTime),Derived>::type* = 0) + { + EIGEN_STATIC_ASSERT(bool(Traits::template match::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH); + // Construction must pass since we will not create temprary storage in the non-const case. + const bool success = Base::construct(expr.derived()); + EIGEN_UNUSED_VARIABLE(success) + eigen_assert(success); + } + template + EIGEN_DEVICE_FUNC inline Ref(const DenseBase& expr, + typename internal::enable_if::MatchAtCompileTime),Derived>::type* = 0) + #else + /** Implicit constructor from any dense expression */ + template + inline Ref(DenseBase& expr) + #endif + { + EIGEN_STATIC_ASSERT(bool(internal::is_lvalue::value), THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY); + EIGEN_STATIC_ASSERT(bool(Traits::template match::MatchAtCompileTime), STORAGE_LAYOUT_DOES_NOT_MATCH); + EIGEN_STATIC_ASSERT(!Derived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY); + // Construction must pass since we will not create temporary storage in the non-const case. + const bool success = Base::construct(expr.const_cast_derived()); + EIGEN_UNUSED_VARIABLE(success) + eigen_assert(success); + } + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Ref) + +}; + +// this is the const ref version +template class Ref + : public RefBase > +{ + typedef internal::traits Traits; + public: + + typedef RefBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Ref) + + template + EIGEN_DEVICE_FUNC inline Ref(const DenseBase& expr, + typename internal::enable_if::ScalarTypeMatch),Derived>::type* = 0) + { +// std::cout << match_helper::HasDirectAccess << "," << match_helper::OuterStrideMatch << "," << match_helper::InnerStrideMatch << "\n"; +// std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n"; +// std::cout << int(StrideType::InnerStrideAtCompileTime) << " - " << int(Derived::InnerStrideAtCompileTime) << "\n"; + construct(expr.derived(), typename Traits::template match::type()); + } + + EIGEN_DEVICE_FUNC inline Ref(const Ref& other) : Base(other) { + // copy constructor shall not copy the m_object, to avoid unnecessary malloc and copy + } + + template + EIGEN_DEVICE_FUNC inline Ref(const RefBase& other) { + construct(other.derived(), typename Traits::template match::type()); + } + + protected: + + template + EIGEN_DEVICE_FUNC void construct(const Expression& expr,internal::true_type) + { + // Check if we can use the underlying expr's storage directly, otherwise call the copy version. + if (!Base::construct(expr)) { + construct(expr, internal::false_type()); + } + } + + template + EIGEN_DEVICE_FUNC void construct(const Expression& expr, internal::false_type) + { + internal::call_assignment_no_alias(m_object,expr,internal::assign_op()); + Base::construct(m_object); + } + + protected: + TPlainObjectType m_object; +}; + +} // end namespace Eigen + +#endif // EIGEN_REF_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Replicate.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Replicate.h new file mode 100644 index 0000000000000000000000000000000000000000..ab5be7e64bc2b464760d1f6b9e2998b18fa416cb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Replicate.h @@ -0,0 +1,142 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_REPLICATE_H +#define EIGEN_REPLICATE_H + +namespace Eigen { + +namespace internal { +template +struct traits > + : traits +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename traits::StorageKind StorageKind; + typedef typename traits::XprKind XprKind; + typedef typename ref_selector::type MatrixTypeNested; + typedef typename remove_reference::type _MatrixTypeNested; + enum { + RowsAtCompileTime = RowFactor==Dynamic || int(MatrixType::RowsAtCompileTime)==Dynamic + ? Dynamic + : RowFactor * MatrixType::RowsAtCompileTime, + ColsAtCompileTime = ColFactor==Dynamic || int(MatrixType::ColsAtCompileTime)==Dynamic + ? Dynamic + : ColFactor * MatrixType::ColsAtCompileTime, + //FIXME we don't propagate the max sizes !!! + MaxRowsAtCompileTime = RowsAtCompileTime, + MaxColsAtCompileTime = ColsAtCompileTime, + IsRowMajor = MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1 ? 1 + : MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1 ? 0 + : (MatrixType::Flags & RowMajorBit) ? 1 : 0, + + // FIXME enable DirectAccess with negative strides? + Flags = IsRowMajor ? RowMajorBit : 0 + }; +}; +} + +/** + * \class Replicate + * \ingroup Core_Module + * + * \brief Expression of the multiple replication of a matrix or vector + * + * \tparam MatrixType the type of the object we are replicating + * \tparam RowFactor number of repetitions at compile time along the vertical direction, can be Dynamic. + * \tparam ColFactor number of repetitions at compile time along the horizontal direction, can be Dynamic. + * + * This class represents an expression of the multiple replication of a matrix or vector. + * It is the return type of DenseBase::replicate() and most of the time + * this is the only way it is used. + * + * \sa DenseBase::replicate() + */ +template class Replicate + : public internal::dense_xpr_base< Replicate >::type +{ + typedef typename internal::traits::MatrixTypeNested MatrixTypeNested; + typedef typename internal::traits::_MatrixTypeNested _MatrixTypeNested; + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Replicate) + typedef typename internal::remove_all::type NestedExpression; + + template + EIGEN_DEVICE_FUNC + inline explicit Replicate(const OriginalMatrixType& matrix) + : m_matrix(matrix), m_rowFactor(RowFactor), m_colFactor(ColFactor) + { + EIGEN_STATIC_ASSERT((internal::is_same::type,OriginalMatrixType>::value), + THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE) + eigen_assert(RowFactor!=Dynamic && ColFactor!=Dynamic); + } + + template + EIGEN_DEVICE_FUNC + inline Replicate(const OriginalMatrixType& matrix, Index rowFactor, Index colFactor) + : m_matrix(matrix), m_rowFactor(rowFactor), m_colFactor(colFactor) + { + EIGEN_STATIC_ASSERT((internal::is_same::type,OriginalMatrixType>::value), + THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE) + } + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); } + + EIGEN_DEVICE_FUNC + const _MatrixTypeNested& nestedExpression() const + { + return m_matrix; + } + + protected: + MatrixTypeNested m_matrix; + const internal::variable_if_dynamic m_rowFactor; + const internal::variable_if_dynamic m_colFactor; +}; + +/** + * \return an expression of the replication of \c *this + * + * Example: \include MatrixBase_replicate.cpp + * Output: \verbinclude MatrixBase_replicate.out + * + * \sa VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate + */ +template +template +EIGEN_DEVICE_FUNC const Replicate +DenseBase::replicate() const +{ + return Replicate(derived()); +} + +/** + * \return an expression of the replication of each column (or row) of \c *this + * + * Example: \include DirectionWise_replicate_int.cpp + * Output: \verbinclude DirectionWise_replicate_int.out + * + * \sa VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate + */ +template +EIGEN_DEVICE_FUNC const typename VectorwiseOp::ReplicateReturnType +VectorwiseOp::replicate(Index factor) const +{ + return typename VectorwiseOp::ReplicateReturnType + (_expression(),Direction==Vertical?factor:1,Direction==Horizontal?factor:1); +} + +} // end namespace Eigen + +#endif // EIGEN_REPLICATE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reshaped.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reshaped.h new file mode 100644 index 0000000000000000000000000000000000000000..52de73b6fc371b8cbd45e13599d7c49b790903f7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reshaped.h @@ -0,0 +1,454 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2017 Gael Guennebaud +// Copyright (C) 2014 yoco +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_RESHAPED_H +#define EIGEN_RESHAPED_H + +namespace Eigen { + +/** \class Reshaped + * \ingroup Core_Module + * + * \brief Expression of a fixed-size or dynamic-size reshape + * + * \tparam XprType the type of the expression in which we are taking a reshape + * \tparam Rows the number of rows of the reshape we are taking at compile time (optional) + * \tparam Cols the number of columns of the reshape we are taking at compile time (optional) + * \tparam Order can be ColMajor or RowMajor, default is ColMajor. + * + * This class represents an expression of either a fixed-size or dynamic-size reshape. + * It is the return type of DenseBase::reshaped(NRowsType,NColsType) and + * most of the time this is the only way it is used. + * + * However, in C++98, if you want to directly maniputate reshaped expressions, + * for instance if you want to write a function returning such an expression, you + * will need to use this class. In C++11, it is advised to use the \em auto + * keyword for such use cases. + * + * Here is an example illustrating the dynamic case: + * \include class_Reshaped.cpp + * Output: \verbinclude class_Reshaped.out + * + * Here is an example illustrating the fixed-size case: + * \include class_FixedReshaped.cpp + * Output: \verbinclude class_FixedReshaped.out + * + * \sa DenseBase::reshaped(NRowsType,NColsType) + */ + +namespace internal { + +template +struct traits > : traits +{ + typedef typename traits::Scalar Scalar; + typedef typename traits::StorageKind StorageKind; + typedef typename traits::XprKind XprKind; + enum{ + MatrixRows = traits::RowsAtCompileTime, + MatrixCols = traits::ColsAtCompileTime, + RowsAtCompileTime = Rows, + ColsAtCompileTime = Cols, + MaxRowsAtCompileTime = Rows, + MaxColsAtCompileTime = Cols, + XpxStorageOrder = ((int(traits::Flags) & RowMajorBit) == RowMajorBit) ? RowMajor : ColMajor, + ReshapedStorageOrder = (RowsAtCompileTime == 1 && ColsAtCompileTime != 1) ? RowMajor + : (ColsAtCompileTime == 1 && RowsAtCompileTime != 1) ? ColMajor + : XpxStorageOrder, + HasSameStorageOrderAsXprType = (ReshapedStorageOrder == XpxStorageOrder), + InnerSize = (ReshapedStorageOrder==int(RowMajor)) ? int(ColsAtCompileTime) : int(RowsAtCompileTime), + InnerStrideAtCompileTime = HasSameStorageOrderAsXprType + ? int(inner_stride_at_compile_time::ret) + : Dynamic, + OuterStrideAtCompileTime = Dynamic, + + HasDirectAccess = internal::has_direct_access::ret + && (Order==int(XpxStorageOrder)) + && ((evaluator::Flags&LinearAccessBit)==LinearAccessBit), + + MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits::size) == 0) + && (InnerStrideAtCompileTime == 1) + ? PacketAccessBit : 0, + //MaskAlignedBit = ((OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0, + FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0, + FlagsLvalueBit = is_lvalue::value ? LvalueBit : 0, + FlagsRowMajorBit = (ReshapedStorageOrder==int(RowMajor)) ? RowMajorBit : 0, + FlagsDirectAccessBit = HasDirectAccess ? DirectAccessBit : 0, + Flags0 = traits::Flags & ( (HereditaryBits & ~RowMajorBit) | MaskPacketAccessBit), + + Flags = (Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit | FlagsDirectAccessBit) + }; +}; + +template class ReshapedImpl_dense; + +} // end namespace internal + +template class ReshapedImpl; + +template class Reshaped + : public ReshapedImpl::StorageKind> +{ + typedef ReshapedImpl::StorageKind> Impl; + public: + //typedef typename Impl::Base Base; + typedef Impl Base; + EIGEN_GENERIC_PUBLIC_INTERFACE(Reshaped) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reshaped) + + /** Fixed-size constructor + */ + EIGEN_DEVICE_FUNC + inline Reshaped(XprType& xpr) + : Impl(xpr) + { + EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE) + eigen_assert(Rows * Cols == xpr.rows() * xpr.cols()); + } + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC + inline Reshaped(XprType& xpr, + Index reshapeRows, Index reshapeCols) + : Impl(xpr, reshapeRows, reshapeCols) + { + eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==reshapeRows) + && (ColsAtCompileTime==Dynamic || ColsAtCompileTime==reshapeCols)); + eigen_assert(reshapeRows * reshapeCols == xpr.rows() * xpr.cols()); + } +}; + +// The generic default implementation for dense reshape simply forward to the internal::ReshapedImpl_dense +// that must be specialized for direct and non-direct access... +template +class ReshapedImpl + : public internal::ReshapedImpl_dense >::HasDirectAccess> +{ + typedef internal::ReshapedImpl_dense >::HasDirectAccess> Impl; + public: + typedef Impl Base; + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl) + EIGEN_DEVICE_FUNC inline ReshapedImpl(XprType& xpr) : Impl(xpr) {} + EIGEN_DEVICE_FUNC inline ReshapedImpl(XprType& xpr, Index reshapeRows, Index reshapeCols) + : Impl(xpr, reshapeRows, reshapeCols) {} +}; + +namespace internal { + +/** \internal Internal implementation of dense Reshaped in the general case. */ +template +class ReshapedImpl_dense + : public internal::dense_xpr_base >::type +{ + typedef Reshaped ReshapedType; + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(ReshapedType) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl_dense) + + typedef typename internal::ref_selector::non_const_type MatrixTypeNested; + typedef typename internal::remove_all::type NestedExpression; + + class InnerIterator; + + /** Fixed-size constructor + */ + EIGEN_DEVICE_FUNC + inline ReshapedImpl_dense(XprType& xpr) + : m_xpr(xpr), m_rows(Rows), m_cols(Cols) + {} + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC + inline ReshapedImpl_dense(XprType& xpr, Index nRows, Index nCols) + : m_xpr(xpr), m_rows(nRows), m_cols(nCols) + {} + + EIGEN_DEVICE_FUNC Index rows() const { return m_rows; } + EIGEN_DEVICE_FUNC Index cols() const { return m_cols; } + + #ifdef EIGEN_PARSED_BY_DOXYGEN + /** \sa MapBase::data() */ + EIGEN_DEVICE_FUNC inline const Scalar* data() const; + EIGEN_DEVICE_FUNC inline Index innerStride() const; + EIGEN_DEVICE_FUNC inline Index outerStride() const; + #endif + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC + const typename internal::remove_all::type& + nestedExpression() const { return m_xpr; } + + /** \returns the nested expression */ + EIGEN_DEVICE_FUNC + typename internal::remove_reference::type& + nestedExpression() { return m_xpr; } + + protected: + + MatrixTypeNested m_xpr; + const internal::variable_if_dynamic m_rows; + const internal::variable_if_dynamic m_cols; +}; + + +/** \internal Internal implementation of dense Reshaped in the direct access case. */ +template +class ReshapedImpl_dense + : public MapBase > +{ + typedef Reshaped ReshapedType; + typedef typename internal::ref_selector::non_const_type XprTypeNested; + public: + + typedef MapBase Base; + EIGEN_DENSE_PUBLIC_INTERFACE(ReshapedType) + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapedImpl_dense) + + /** Fixed-size constructor + */ + EIGEN_DEVICE_FUNC + inline ReshapedImpl_dense(XprType& xpr) + : Base(xpr.data()), m_xpr(xpr) + {} + + /** Dynamic-size constructor + */ + EIGEN_DEVICE_FUNC + inline ReshapedImpl_dense(XprType& xpr, Index nRows, Index nCols) + : Base(xpr.data(), nRows, nCols), + m_xpr(xpr) + {} + + EIGEN_DEVICE_FUNC + const typename internal::remove_all::type& nestedExpression() const + { + return m_xpr; + } + + EIGEN_DEVICE_FUNC + XprType& nestedExpression() { return m_xpr; } + + /** \sa MapBase::innerStride() */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index innerStride() const + { + return m_xpr.innerStride(); + } + + /** \sa MapBase::outerStride() */ + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index outerStride() const + { + return ((Flags&RowMajorBit)==RowMajorBit) ? this->cols() : this->rows(); + } + + protected: + + XprTypeNested m_xpr; +}; + +// Evaluators +template struct reshaped_evaluator; + +template +struct evaluator > + : reshaped_evaluator >::HasDirectAccess> +{ + typedef Reshaped XprType; + typedef typename XprType::Scalar Scalar; + // TODO: should check for smaller packet types + typedef typename packet_traits::type PacketScalar; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + HasDirectAccess = traits::HasDirectAccess, + +// RowsAtCompileTime = traits::RowsAtCompileTime, +// ColsAtCompileTime = traits::ColsAtCompileTime, +// MaxRowsAtCompileTime = traits::MaxRowsAtCompileTime, +// MaxColsAtCompileTime = traits::MaxColsAtCompileTime, +// +// InnerStrideAtCompileTime = traits::HasSameStorageOrderAsXprType +// ? int(inner_stride_at_compile_time::ret) +// : Dynamic, +// OuterStrideAtCompileTime = Dynamic, + + FlagsLinearAccessBit = (traits::RowsAtCompileTime == 1 || traits::ColsAtCompileTime == 1 || HasDirectAccess) ? LinearAccessBit : 0, + FlagsRowMajorBit = (traits::ReshapedStorageOrder==int(RowMajor)) ? RowMajorBit : 0, + FlagsDirectAccessBit = HasDirectAccess ? DirectAccessBit : 0, + Flags0 = evaluator::Flags & (HereditaryBits & ~RowMajorBit), + Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit | FlagsDirectAccessBit, + + PacketAlignment = unpacket_traits::alignment, + Alignment = evaluator::Alignment + }; + typedef reshaped_evaluator reshaped_evaluator_type; + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : reshaped_evaluator_type(xpr) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } +}; + +template +struct reshaped_evaluator + : evaluator_base > +{ + typedef Reshaped XprType; + + enum { + CoeffReadCost = evaluator::CoeffReadCost /* TODO + cost of index computations */, + + Flags = (evaluator::Flags & (HereditaryBits /*| LinearAccessBit | DirectAccessBit*/)), + + Alignment = 0 + }; + + EIGEN_DEVICE_FUNC explicit reshaped_evaluator(const XprType& xpr) : m_argImpl(xpr.nestedExpression()), m_xpr(xpr) + { + EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost); + } + + typedef typename XprType::Scalar Scalar; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + typedef std::pair RowCol; + + inline RowCol index_remap(Index rowId, Index colId) const + { + if(Order==ColMajor) + { + const Index nth_elem_idx = colId * m_xpr.rows() + rowId; + return RowCol(nth_elem_idx % m_xpr.nestedExpression().rows(), + nth_elem_idx / m_xpr.nestedExpression().rows()); + } + else + { + const Index nth_elem_idx = colId + rowId * m_xpr.cols(); + return RowCol(nth_elem_idx / m_xpr.nestedExpression().cols(), + nth_elem_idx % m_xpr.nestedExpression().cols()); + } + } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index rowId, Index colId) + { + EIGEN_STATIC_ASSERT_LVALUE(XprType) + const RowCol row_col = index_remap(rowId, colId); + return m_argImpl.coeffRef(row_col.first, row_col.second); + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index rowId, Index colId) const + { + const RowCol row_col = index_remap(rowId, colId); + return m_argImpl.coeffRef(row_col.first, row_col.second); + } + + EIGEN_DEVICE_FUNC + EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const + { + const RowCol row_col = index_remap(rowId, colId); + return m_argImpl.coeff(row_col.first, row_col.second); + } + + EIGEN_DEVICE_FUNC + inline Scalar& coeffRef(Index index) + { + EIGEN_STATIC_ASSERT_LVALUE(XprType) + const RowCol row_col = index_remap(Rows == 1 ? 0 : index, + Rows == 1 ? index : 0); + return m_argImpl.coeffRef(row_col.first, row_col.second); + + } + + EIGEN_DEVICE_FUNC + inline const Scalar& coeffRef(Index index) const + { + const RowCol row_col = index_remap(Rows == 1 ? 0 : index, + Rows == 1 ? index : 0); + return m_argImpl.coeffRef(row_col.first, row_col.second); + } + + EIGEN_DEVICE_FUNC + inline const CoeffReturnType coeff(Index index) const + { + const RowCol row_col = index_remap(Rows == 1 ? 0 : index, + Rows == 1 ? index : 0); + return m_argImpl.coeff(row_col.first, row_col.second); + } +#if 0 + EIGEN_DEVICE_FUNC + template + inline PacketScalar packet(Index rowId, Index colId) const + { + const RowCol row_col = index_remap(rowId, colId); + return m_argImpl.template packet(row_col.first, row_col.second); + + } + + template + EIGEN_DEVICE_FUNC + inline void writePacket(Index rowId, Index colId, const PacketScalar& val) + { + const RowCol row_col = index_remap(rowId, colId); + m_argImpl.const_cast_derived().template writePacket + (row_col.first, row_col.second, val); + } + + template + EIGEN_DEVICE_FUNC + inline PacketScalar packet(Index index) const + { + const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index, + RowsAtCompileTime == 1 ? index : 0); + return m_argImpl.template packet(row_col.first, row_col.second); + } + + template + EIGEN_DEVICE_FUNC + inline void writePacket(Index index, const PacketScalar& val) + { + const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index, + RowsAtCompileTime == 1 ? index : 0); + return m_argImpl.template packet(row_col.first, row_col.second, val); + } +#endif +protected: + + evaluator m_argImpl; + const XprType& m_xpr; + +}; + +template +struct reshaped_evaluator +: mapbase_evaluator, + typename Reshaped::PlainObject> +{ + typedef Reshaped XprType; + typedef typename XprType::Scalar Scalar; + + EIGEN_DEVICE_FUNC explicit reshaped_evaluator(const XprType& xpr) + : mapbase_evaluator(xpr) + { + // TODO: for the 3.4 release, this should be turned to an internal assertion, but let's keep it as is for the beta lifetime + eigen_assert(((internal::UIntPtr(xpr.data()) % EIGEN_PLAIN_ENUM_MAX(1,evaluator::Alignment)) == 0) && "data is not aligned"); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_RESHAPED_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ReturnByValue.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ReturnByValue.h new file mode 100644 index 0000000000000000000000000000000000000000..4dad13ea11872682099c8d41438a87a5ef9726ec --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/ReturnByValue.h @@ -0,0 +1,119 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Gael Guennebaud +// Copyright (C) 2009-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_RETURNBYVALUE_H +#define EIGEN_RETURNBYVALUE_H + +namespace Eigen { + +namespace internal { + +template +struct traits > + : public traits::ReturnType> +{ + enum { + // We're disabling the DirectAccess because e.g. the constructor of + // the Block-with-DirectAccess expression requires to have a coeffRef method. + // Also, we don't want to have to implement the stride stuff. + Flags = (traits::ReturnType>::Flags + | EvalBeforeNestingBit) & ~DirectAccessBit + }; +}; + +/* The ReturnByValue object doesn't even have a coeff() method. + * So the only way that nesting it in an expression can work, is by evaluating it into a plain matrix. + * So internal::nested always gives the plain return matrix type. + * + * FIXME: I don't understand why we need this specialization: isn't this taken care of by the EvalBeforeNestingBit ?? + * Answer: EvalBeforeNestingBit should be deprecated since we have the evaluators + */ +template +struct nested_eval, n, PlainObject> +{ + typedef typename traits::ReturnType type; +}; + +} // end namespace internal + +/** \class ReturnByValue + * \ingroup Core_Module + * + */ +template class ReturnByValue + : public internal::dense_xpr_base< ReturnByValue >::type, internal::no_assignment_operator +{ + public: + typedef typename internal::traits::ReturnType ReturnType; + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(ReturnByValue) + + template + EIGEN_DEVICE_FUNC + inline void evalTo(Dest& dst) const + { static_cast(this)->evalTo(dst); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return static_cast(this)->rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return static_cast(this)->cols(); } + +#ifndef EIGEN_PARSED_BY_DOXYGEN +#define Unusable YOU_ARE_TRYING_TO_ACCESS_A_SINGLE_COEFFICIENT_IN_A_SPECIAL_EXPRESSION_WHERE_THAT_IS_NOT_ALLOWED_BECAUSE_THAT_WOULD_BE_INEFFICIENT + class Unusable{ + Unusable(const Unusable&) {} + Unusable& operator=(const Unusable&) {return *this;} + }; + const Unusable& coeff(Index) const { return *reinterpret_cast(this); } + const Unusable& coeff(Index,Index) const { return *reinterpret_cast(this); } + Unusable& coeffRef(Index) { return *reinterpret_cast(this); } + Unusable& coeffRef(Index,Index) { return *reinterpret_cast(this); } +#undef Unusable +#endif +}; + +template +template +EIGEN_DEVICE_FUNC Derived& DenseBase::operator=(const ReturnByValue& other) +{ + other.evalTo(derived()); + return derived(); +} + +namespace internal { + +// Expression is evaluated in a temporary; default implementation of Assignment is bypassed so that +// when a ReturnByValue expression is assigned, the evaluator is not constructed. +// TODO: Finalize port to new regime; ReturnByValue should not exist in the expression world + +template +struct evaluator > + : public evaluator::ReturnType> +{ + typedef ReturnByValue XprType; + typedef typename internal::traits::ReturnType PlainObject; + typedef evaluator Base; + + EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) + : m_result(xpr.rows(), xpr.cols()) + { + ::new (static_cast(this)) Base(m_result); + xpr.evalTo(m_result); + } + +protected: + PlainObject m_result; +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_RETURNBYVALUE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reverse.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reverse.h new file mode 100644 index 0000000000000000000000000000000000000000..28cdd76acaa83e93e2d9775e3e3fc1c851c2279a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Reverse.h @@ -0,0 +1,217 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2009 Ricard Marxer +// Copyright (C) 2009-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_REVERSE_H +#define EIGEN_REVERSE_H + +namespace Eigen { + +namespace internal { + +template +struct traits > + : traits +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename traits::StorageKind StorageKind; + typedef typename traits::XprKind XprKind; + typedef typename ref_selector::type MatrixTypeNested; + typedef typename remove_reference::type _MatrixTypeNested; + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + Flags = _MatrixTypeNested::Flags & (RowMajorBit | LvalueBit) + }; +}; + +template struct reverse_packet_cond +{ + static inline PacketType run(const PacketType& x) { return preverse(x); } +}; + +template struct reverse_packet_cond +{ + static inline PacketType run(const PacketType& x) { return x; } +}; + +} // end namespace internal + +/** \class Reverse + * \ingroup Core_Module + * + * \brief Expression of the reverse of a vector or matrix + * + * \tparam MatrixType the type of the object of which we are taking the reverse + * \tparam Direction defines the direction of the reverse operation, can be Vertical, Horizontal, or BothDirections + * + * This class represents an expression of the reverse of a vector. + * It is the return type of MatrixBase::reverse() and VectorwiseOp::reverse() + * and most of the time this is the only way it is used. + * + * \sa MatrixBase::reverse(), VectorwiseOp::reverse() + */ +template class Reverse + : public internal::dense_xpr_base< Reverse >::type +{ + public: + + typedef typename internal::dense_xpr_base::type Base; + EIGEN_DENSE_PUBLIC_INTERFACE(Reverse) + typedef typename internal::remove_all::type NestedExpression; + using Base::IsRowMajor; + + protected: + enum { + PacketSize = internal::packet_traits::size, + IsColMajor = !IsRowMajor, + ReverseRow = (Direction == Vertical) || (Direction == BothDirections), + ReverseCol = (Direction == Horizontal) || (Direction == BothDirections), + OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1, + OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1, + ReversePacket = (Direction == BothDirections) + || ((Direction == Vertical) && IsColMajor) + || ((Direction == Horizontal) && IsRowMajor) + }; + typedef internal::reverse_packet_cond reverse_packet; + public: + + EIGEN_DEVICE_FUNC explicit inline Reverse(const MatrixType& matrix) : m_matrix(matrix) { } + + EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse) + + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); } + EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR + inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); } + + EIGEN_DEVICE_FUNC inline Index innerStride() const + { + return -m_matrix.innerStride(); + } + + EIGEN_DEVICE_FUNC const typename internal::remove_all::type& + nestedExpression() const + { + return m_matrix; + } + + protected: + typename MatrixType::Nested m_matrix; +}; + +/** \returns an expression of the reverse of *this. + * + * Example: \include MatrixBase_reverse.cpp + * Output: \verbinclude MatrixBase_reverse.out + * + */ +template +EIGEN_DEVICE_FUNC inline typename DenseBase::ReverseReturnType +DenseBase::reverse() +{ + return ReverseReturnType(derived()); +} + + +//reverse const overload moved DenseBase.h due to a CUDA compiler bug + +/** This is the "in place" version of reverse: it reverses \c *this. + * + * In most cases it is probably better to simply use the reversed expression + * of a matrix. However, when reversing the matrix data itself is really needed, + * then this "in-place" version is probably the right choice because it provides + * the following additional benefits: + * - less error prone: doing the same operation with .reverse() requires special care: + * \code m = m.reverse().eval(); \endcode + * - this API enables reverse operations without the need for a temporary + * - it allows future optimizations (cache friendliness, etc.) + * + * \sa VectorwiseOp::reverseInPlace(), reverse() */ +template +EIGEN_DEVICE_FUNC inline void DenseBase::reverseInPlace() +{ + if(cols()>rows()) + { + Index half = cols()/2; + leftCols(half).swap(rightCols(half).reverse()); + if((cols()%2)==1) + { + Index half2 = rows()/2; + col(half).head(half2).swap(col(half).tail(half2).reverse()); + } + } + else + { + Index half = rows()/2; + topRows(half).swap(bottomRows(half).reverse()); + if((rows()%2)==1) + { + Index half2 = cols()/2; + row(half).head(half2).swap(row(half).tail(half2).reverse()); + } + } +} + +namespace internal { + +template +struct vectorwise_reverse_inplace_impl; + +template<> +struct vectorwise_reverse_inplace_impl +{ + template + static void run(ExpressionType &xpr) + { + const int HalfAtCompileTime = ExpressionType::RowsAtCompileTime==Dynamic?Dynamic:ExpressionType::RowsAtCompileTime/2; + Index half = xpr.rows()/2; + xpr.topRows(fix(half)) + .swap(xpr.bottomRows(fix(half)).colwise().reverse()); + } +}; + +template<> +struct vectorwise_reverse_inplace_impl +{ + template + static void run(ExpressionType &xpr) + { + const int HalfAtCompileTime = ExpressionType::ColsAtCompileTime==Dynamic?Dynamic:ExpressionType::ColsAtCompileTime/2; + Index half = xpr.cols()/2; + xpr.leftCols(fix(half)) + .swap(xpr.rightCols(fix(half)).rowwise().reverse()); + } +}; + +} // end namespace internal + +/** This is the "in place" version of VectorwiseOp::reverse: it reverses each column or row of \c *this. + * + * In most cases it is probably better to simply use the reversed expression + * of a matrix. However, when reversing the matrix data itself is really needed, + * then this "in-place" version is probably the right choice because it provides + * the following additional benefits: + * - less error prone: doing the same operation with .reverse() requires special care: + * \code m = m.reverse().eval(); \endcode + * - this API enables reverse operations without the need for a temporary + * + * \sa DenseBase::reverseInPlace(), reverse() */ +template +EIGEN_DEVICE_FUNC void VectorwiseOp::reverseInPlace() +{ + internal::vectorwise_reverse_inplace_impl::run(m_matrix); +} + +} // end namespace Eigen + +#endif // EIGEN_REVERSE_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Select.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Select.h new file mode 100644 index 0000000000000000000000000000000000000000..7c86bf87c170163f04b4fda8a4210526b16e3bbd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/Eigen/src/Core/Select.h @@ -0,0 +1,164 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SELECT_H +#define EIGEN_SELECT_H + +namespace Eigen { + +/** \class Select + * \ingroup Core_Module + * + * \brief Expression of a coefficient wise version of the C++ ternary operator ?: + * + * \param ConditionMatrixType the type of the \em condition expression which must be a boolean matrix + * \param ThenMatrixType the type of the \em then expression + * \param ElseMatrixType the type of the \em else expression + * + * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:. + * It is the return type of DenseBase::select() and most of the time this is the only way it is used. + * + * \sa DenseBase::select(const DenseBase&, const DenseBase&) const + */ + +namespace internal { +template +struct traits > + : traits +{ + typedef typename traits::Scalar Scalar; + typedef Dense StorageKind; + typedef typename traits::XprKind XprKind; + typedef typename ConditionMatrixType::Nested ConditionMatrixNested; + typedef typename ThenMatrixType::Nested ThenMatrixNested; + typedef typename ElseMatrixType::Nested ElseMatrixNested; + enum { + RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime, + ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime, + MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime, + Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & RowMajorBit + }; +}; +} + +template +class Select : public internal::dense_xpr_base< Select >::type, + internal::no_assignment_operator +{ + public: + + typedef typename internal::dense_xpr_base" << endl; + cerr << "available actions:" << endl; + for (auto it = available_actions.begin(); it != available_actions.end(); ++it) { + cerr << " " << (*it)->invokation_name() << endl; + } + cerr << "the input files should each contain an output of benchmark-blocking-sizes" << endl; + exit(1); +} + +int main(int argc, char* argv[]) +{ + cout.precision(default_precision); + cerr.precision(default_precision); + + vector> available_actions; + available_actions.emplace_back(new partition_action_t); + available_actions.emplace_back(new evaluate_defaults_action_t); + + vector input_filenames; + + action_t* action = nullptr; + + if (argc < 2) { + show_usage_and_exit(argc, argv, available_actions); + } + for (int i = 1; i < argc; i++) { + bool arg_handled = false; + // Step 1. Try to match action invocation names. + for (auto it = available_actions.begin(); it != available_actions.end(); ++it) { + if (!strcmp(argv[i], (*it)->invokation_name())) { + if (!action) { + action = it->get(); + arg_handled = true; + break; + } else { + cerr << "can't specify more than one action!" << endl; + show_usage_and_exit(argc, argv, available_actions); + } + } + } + if (arg_handled) { + continue; + } + // Step 2. Try to match option names. + if (argv[i][0] == '-') { + if (!strcmp(argv[i], "--only-cubic-sizes")) { + only_cubic_sizes = true; + arg_handled = true; + } + if (!strcmp(argv[i], "--dump-tables")) { + dump_tables = true; + arg_handled = true; + } + if (!arg_handled) { + cerr << "Unrecognized option: " << argv[i] << endl; + show_usage_and_exit(argc, argv, available_actions); + } + } + if (arg_handled) { + continue; + } + // Step 3. Default to interpreting args as input filenames. + input_filenames.emplace_back(argv[i]); + } + + if (dump_tables && only_cubic_sizes) { + cerr << "Incompatible options: --only-cubic-sizes and --dump-tables." << endl; + show_usage_and_exit(argc, argv, available_actions); + } + + if (!action) { + show_usage_and_exit(argc, argv, available_actions); + } + + action->run(input_filenames); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbench.cxxlist b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbench.cxxlist new file mode 100644 index 0000000000000000000000000000000000000000..a8ab34e0df72f2a172885d98472910d1c035c3d1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbench.cxxlist @@ -0,0 +1,28 @@ +#!/bin/bash + +# CLIST[((g++))]="g++-3.4 -O3 -DNDEBUG" +# CLIST[((g++))]="g++-3.4 -O3 -DNDEBUG -finline-limit=20000" + +# CLIST[((g++))]="g++-4.1 -O3 -DNDEBUG" +#CLIST[((g++))]="g++-4.1 -O3 -DNDEBUG -finline-limit=20000" + +# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG" +#CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000" +# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate" +# CLIST[((g++))]="g++-4.2 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use" + +# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG" +#CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000" +# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-generate" +# CLIST[((g++))]="g++-4.3 -O3 -DNDEBUG -finline-limit=20000 -fprofile-use" + +# CLIST[((g++))]="icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-genx" +# CLIST[((g++))]="icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -prof-use" + +#CLIST[((g++))]="/opt/intel/Compiler/11.1/072/bin/intel64/icpc -fast -DNDEBUG -fno-exceptions -no-inline-max-size -lrt" +CLIST[((g++))]="/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt" +CLIST[((g++))]="/home/orzel/svn/llvm/Release/bin/clang++ -O3 -DNDEBUG -lrt" +CLIST[((g++))]="g++-4.4.4 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt" +CLIST[((g++))]="g++-4.4.4 -O3 -DNDEBUG -lrt" +CLIST[((g++))]="g++-4.5.0 -O3 -DNDEBUG -DEIGEN_DONT_VECTORIZE -lrt" +CLIST[((g++))]="g++-4.5.0 -O3 -DNDEBUG -lrt" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a26ea853fc753d9b0caf35d5ea9c90b829b48c98 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.cpp @@ -0,0 +1,35 @@ + +#include +#include "BenchUtil.h" +#include "basicbenchmark.h" + +int main(int argc, char *argv[]) +{ + DISABLE_SSE_EXCEPTIONS(); + + // this is the list of matrix type and size we want to bench: + // ((suffix) (matrix size) (number of iterations)) + #define MODES ((3d)(3)(4000000)) ((4d)(4)(1000000)) ((Xd)(4)(1000000)) ((Xd)(20)(10000)) +// #define MODES ((Xd)(20)(10000)) + + #define _GENERATE_HEADER(R,ARG,EL) << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_HEAD(EL)) << "-" \ + << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << "x" \ + << BOOST_PP_STRINGIZE(BOOST_PP_SEQ_ELEM(1,EL)) << " / " + + std::cout BOOST_PP_SEQ_FOR_EACH(_GENERATE_HEADER, ~, MODES ) << endl; + + const int tries = 10; + + #define _RUN_BENCH(R,ARG,EL) \ + std::cout << ARG( \ + BOOST_PP_CAT(Matrix, BOOST_PP_SEQ_HEAD(EL)) (\ + BOOST_PP_SEQ_ELEM(1,EL),BOOST_PP_SEQ_ELEM(1,EL)), BOOST_PP_SEQ_ELEM(2,EL), tries) \ + << " "; + + BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic, MODES ); + std::cout << endl; + BOOST_PP_SEQ_FOR_EACH(_RUN_BENCH, benchBasic, MODES ); + std::cout << endl; + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.h new file mode 100644 index 0000000000000000000000000000000000000000..8059375b5e1fde71a28583b2c62f667f5cb84154 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/basicbenchmark.h @@ -0,0 +1,63 @@ + +#ifndef EIGEN_BENCH_BASICBENCH_H +#define EIGEN_BENCH_BASICBENCH_H + +enum {LazyEval, EarlyEval, OmpEval}; + +template +void benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations) __attribute__((noinline)); + +template +void benchBasic_loop(const MatrixType& I, MatrixType& m, int iterations) +{ + for(int a = 0; a < iterations; a++) + { + if (Mode==LazyEval) + { + asm("#begin_bench_loop LazyEval"); + if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize"); + m = (I + 0.00005 * (m + m.lazyProduct(m))).eval(); + } + else if (Mode==OmpEval) + { + asm("#begin_bench_loop OmpEval"); + if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize"); + m = (I + 0.00005 * (m + m.lazyProduct(m))).eval(); + } + else + { + asm("#begin_bench_loop EarlyEval"); + if (MatrixType::SizeAtCompileTime!=Eigen::Dynamic) asm("#fixedsize"); + m = I + 0.00005 * (m + m * m); + } + asm("#end_bench_loop"); + } +} + +template +double benchBasic(const MatrixType& mat, int size, int tries) __attribute__((noinline)); + +template +double benchBasic(const MatrixType& mat, int iterations, int tries) +{ + const int rows = mat.rows(); + const int cols = mat.cols(); + + MatrixType I(rows,cols); + MatrixType m(rows,cols); + + initMatrix_identity(I); + + Eigen::BenchTimer timer; + for(uint t=0; t(I, m, iterations); + timer.stop(); + cerr << m; + } + return timer.value(); +}; + +#endif // EIGEN_BENCH_BASICBENCH_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchBlasGemm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchBlasGemm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb086a555a3678b2854ecf9959e8dcbd63b17904 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchBlasGemm.cpp @@ -0,0 +1,219 @@ +// g++ -O3 -DNDEBUG -I.. -L /usr/lib64/atlas/ benchBlasGemm.cpp -o benchBlasGemm -lrt -lcblas +// possible options: +// -DEIGEN_DONT_VECTORIZE +// -msse2 + +// #define EIGEN_DEFAULT_TO_ROW_MAJOR +#define _FLOAT + +#include + +#include +#include "BenchTimer.h" + +// include the BLAS headers +extern "C" { +#include +} +#include + +#ifdef _FLOAT +typedef float Scalar; +#define CBLAS_GEMM cblas_sgemm +#else +typedef double Scalar; +#define CBLAS_GEMM cblas_dgemm +#endif + + +typedef Eigen::Matrix MyMatrix; +void bench_eigengemm(MyMatrix& mc, const MyMatrix& ma, const MyMatrix& mb, int nbloops); +void check_product(int M, int N, int K); +void check_product(void); + +int main(int argc, char *argv[]) +{ + // disable SSE exceptions + #ifdef __GNUC__ + { + int aux; + asm( + "stmxcsr %[aux] \n\t" + "orl $32832, %[aux] \n\t" + "ldmxcsr %[aux] \n\t" + : : [aux] "m" (aux)); + } + #endif + + int nbtries=1, nbloops=1, M, N, K; + + if (argc==2) + { + if (std::string(argv[1])=="check") + check_product(); + else + M = N = K = atoi(argv[1]); + } + else if ((argc==3) && (std::string(argv[1])=="auto")) + { + M = N = K = atoi(argv[2]); + nbloops = 1000000000/(M*M*M); + if (nbloops<1) + nbloops = 1; + nbtries = 6; + } + else if (argc==4) + { + M = N = K = atoi(argv[1]); + nbloops = atoi(argv[2]); + nbtries = atoi(argv[3]); + } + else if (argc==6) + { + M = atoi(argv[1]); + N = atoi(argv[2]); + K = atoi(argv[3]); + nbloops = atoi(argv[4]); + nbtries = atoi(argv[5]); + } + else + { + std::cout << "Usage: " << argv[0] << " size \n"; + std::cout << "Usage: " << argv[0] << " auto size\n"; + std::cout << "Usage: " << argv[0] << " size nbloops nbtries\n"; + std::cout << "Usage: " << argv[0] << " M N K nbloops nbtries\n"; + std::cout << "Usage: " << argv[0] << " check\n"; + std::cout << "Options:\n"; + std::cout << " size unique size of the 2 matrices (integer)\n"; + std::cout << " auto automatically set the number of repetitions and tries\n"; + std::cout << " nbloops number of times the GEMM routines is executed\n"; + std::cout << " nbtries number of times the loop is benched (return the best try)\n"; + std::cout << " M N K sizes of the matrices: MxN = MxK * KxN (integers)\n"; + std::cout << " check check eigen product using cblas as a reference\n"; + exit(1); + } + + double nbmad = double(M) * double(N) * double(K) * double(nbloops); + + if (!(std::string(argv[1])=="auto")) + std::cout << M << " x " << N << " x " << K << "\n"; + + Scalar alpha, beta; + MyMatrix ma(M,K), mb(K,N), mc(M,N); + ma = MyMatrix::Random(M,K); + mb = MyMatrix::Random(K,N); + mc = MyMatrix::Random(M,N); + + Eigen::BenchTimer timer; + + // we simply compute c += a*b, so: + alpha = 1; + beta = 1; + + // bench cblas + // ROWS_A, COLS_B, COLS_A, 1.0, A, COLS_A, B, COLS_B, 0.0, C, COLS_B); + if (!(std::string(argv[1])=="auto")) + { + timer.reset(); + for (uint k=0 ; k(1,64); + N = internal::random(1,768); + K = internal::random(1,768); + M = (0 + M) * 1; + std::cout << M << " x " << N << " x " << K << "\n"; + check_product(M, N, K); + } +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchCholesky.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchCholesky.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0dc94e5b4983974a379c012808e54d7cc701778e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchCholesky.cpp @@ -0,0 +1,141 @@ +// g++ -DNDEBUG -O3 -I.. benchCholesky.cpp -o benchCholesky && ./benchCholesky +// options: +// -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3 +// -DEIGEN_DONT_VECTORIZE +// -msse2 +// -DREPEAT=100 +// -DTRIES=10 +// -DSCALAR=double + +#include + +#include +#include +#include +using namespace Eigen; + +#ifndef REPEAT +#define REPEAT 10000 +#endif + +#ifndef TRIES +#define TRIES 10 +#endif + +typedef float Scalar; + +template +__attribute__ ((noinline)) void benchLLT(const MatrixType& m) +{ + int rows = m.rows(); + int cols = m.cols(); + + double cost = 0; + for (int j=0; j SquareMatrixType; + + MatrixType a = MatrixType::Random(rows,cols); + SquareMatrixType covMat = a * a.adjoint(); + + BenchTimer timerNoSqrt, timerSqrt; + + Scalar acc = 0; + int r = internal::random(0,covMat.rows()-1); + int c = internal::random(0,covMat.cols()-1); + for (int t=0; t cholnosqrt(covMat); + acc += cholnosqrt.matrixL().coeff(r,c); + } + timerNoSqrt.stop(); + } + + for (int t=0; t chol(covMat); + acc += chol.matrixL().coeff(r,c); + } + timerSqrt.stop(); + } + + if (MatrixType::RowsAtCompileTime==Dynamic) + std::cout << "dyn "; + else + std::cout << "fixed "; + std::cout << covMat.rows() << " \t" + << (timerNoSqrt.best()) / repeats << "s " + << "(" << 1e-9 * cost*repeats/timerNoSqrt.best() << " GFLOPS)\t" + << (timerSqrt.best()) / repeats << "s " + << "(" << 1e-9 * cost*repeats/timerSqrt.best() << " GFLOPS)\n"; + + + #ifdef BENCH_GSL + if (MatrixType::RowsAtCompileTime==Dynamic) + { + timerSqrt.reset(); + + gsl_matrix* gslCovMat = gsl_matrix_alloc(covMat.rows(),covMat.cols()); + gsl_matrix* gslCopy = gsl_matrix_alloc(covMat.rows(),covMat.cols()); + + eiToGsl(covMat, &gslCovMat); + for (int t=0; t0; ++i) + benchLLT(Matrix(dynsizes[i],dynsizes[i])); + + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + benchLLT(Matrix()); + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchEigenSolver.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchEigenSolver.cpp new file mode 100644 index 0000000000000000000000000000000000000000..dd78c7e016fac442179349b13e807ade01fcb9bd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchEigenSolver.cpp @@ -0,0 +1,212 @@ + +// g++ -DNDEBUG -O3 -I.. benchEigenSolver.cpp -o benchEigenSolver && ./benchEigenSolver +// options: +// -DBENCH_GMM +// -DBENCH_GSL -lgsl /usr/lib/libcblas.so.3 +// -DEIGEN_DONT_VECTORIZE +// -msse2 +// -DREPEAT=100 +// -DTRIES=10 +// -DSCALAR=double + +#include + +#include +#include +#include +using namespace Eigen; + +#ifndef REPEAT +#define REPEAT 1000 +#endif + +#ifndef TRIES +#define TRIES 4 +#endif + +#ifndef SCALAR +#define SCALAR float +#endif + +typedef SCALAR Scalar; + +template +__attribute__ ((noinline)) void benchEigenSolver(const MatrixType& m) +{ + int rows = m.rows(); + int cols = m.cols(); + + int stdRepeats = std::max(1,int((REPEAT*1000)/(rows*rows*sqrt(rows)))); + int saRepeats = stdRepeats * 4; + + typedef typename MatrixType::Scalar Scalar; + typedef Matrix SquareMatrixType; + + MatrixType a = MatrixType::Random(rows,cols); + SquareMatrixType covMat = a * a.adjoint(); + + BenchTimer timerSa, timerStd; + + Scalar acc = 0; + int r = internal::random(0,covMat.rows()-1); + int c = internal::random(0,covMat.cols()-1); + { + SelfAdjointEigenSolver ei(covMat); + for (int t=0; t ei(covMat); + for (int t=0; t gmmCovMat(covMat.rows(),covMat.cols()); + gmm::dense_matrix eigvect(covMat.rows(),covMat.cols()); + std::vector eigval(covMat.rows()); + eiToGmm(covMat, gmmCovMat); + for (int t=0; t0; ++i) + benchEigenSolver(Matrix(dynsizes[i],dynsizes[i])); + + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + benchEigenSolver(Matrix()); + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchFFT.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchFFT.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3eb1a1ac01bd267021bab0ee8167ab3d2c95477d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchFFT.cpp @@ -0,0 +1,115 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Mark Borgerding mark a borgerding net +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include + +#include +#include +#include +#include + +#include + +using namespace Eigen; +using namespace std; + + +template +string nameof(); + +template <> string nameof() {return "float";} +template <> string nameof() {return "double";} +template <> string nameof() {return "long double";} + +#ifndef TYPE +#define TYPE float +#endif + +#ifndef NFFT +#define NFFT 1024 +#endif +#ifndef NDATA +#define NDATA 1000000 +#endif + +using namespace Eigen; + +template +void bench(int nfft,bool fwd,bool unscaled=false, bool halfspec=false) +{ + typedef typename NumTraits::Real Scalar; + typedef typename std::complex Complex; + int nits = NDATA/nfft; + vector inbuf(nfft); + vector outbuf(nfft); + FFT< Scalar > fft; + + if (unscaled) { + fft.SetFlag(fft.Unscaled); + cout << "unscaled "; + } + if (halfspec) { + fft.SetFlag(fft.HalfSpectrum); + cout << "halfspec "; + } + + + std::fill(inbuf.begin(),inbuf.end(),0); + fft.fwd( outbuf , inbuf); + + BenchTimer timer; + timer.reset(); + for (int k=0;k<8;++k) { + timer.start(); + if (fwd) + for(int i = 0; i < nits; i++) + fft.fwd( outbuf , inbuf); + else + for(int i = 0; i < nits; i++) + fft.inv(inbuf,outbuf); + timer.stop(); + } + + cout << nameof() << " "; + double mflops = 5.*nfft*log2((double)nfft) / (1e6 * timer.value() / (double)nits ); + if ( NumTraits::IsComplex ) { + cout << "complex"; + }else{ + cout << "real "; + mflops /= 2; + } + + + if (fwd) + cout << " fwd"; + else + cout << " inv"; + + cout << " NFFT=" << nfft << " " << (double(1e-6*nfft*nits)/timer.value()) << " MS/s " << mflops << "MFLOPS\n"; +} + +int main(int argc,char ** argv) +{ + bench >(NFFT,true); + bench >(NFFT,false); + bench(NFFT,true); + bench(NFFT,false); + bench(NFFT,false,true); + bench(NFFT,false,true,true); + + bench >(NFFT,true); + bench >(NFFT,false); + bench(NFFT,true); + bench(NFFT,false); + bench >(NFFT,true); + bench >(NFFT,false); + bench(NFFT,true); + bench(NFFT,false); + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchGeometry.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchGeometry.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6e16c0331d84829cb1042837fbb8f3c1e8f10c4e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchGeometry.cpp @@ -0,0 +1,134 @@ +#include +#include +#include +#include +#include + +using namespace Eigen; +using namespace std; + +#ifndef REPEAT +#define REPEAT 1000000 +#endif + +enum func_opt +{ + TV, + TMATV, + TMATVMAT, +}; + + +template +struct func; + +template +struct func +{ + static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 ) + { + asm (""); + return a1 * a2; + } +}; + +template +struct func +{ + static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 ) + { + asm (""); + return a1.matrix() * a2; + } +}; + +template +struct func +{ + static EIGEN_DONT_INLINE res run( arg1& a1, arg2& a2 ) + { + asm (""); + return res(a1.matrix() * a2.matrix()); + } +}; + +template +struct test_transform +{ + static void run() + { + arg1 a1; + a1.setIdentity(); + arg2 a2; + a2.setIdentity(); + + BenchTimer timer; + timer.reset(); + for (int k=0; k<10; ++k) + { + timer.start(); + for (int k=0; k Trans;\ + typedef Matrix Vec;\ + typedef func Func;\ + test_transform< Func, Trans, Vec >::run();\ + } + +#define run_trans( op, scalar, mode, option ) \ + std::cout << #scalar << "\t " << #mode << "\t " << #option << " "; \ + {\ + typedef Transform Trans;\ + typedef func Func;\ + test_transform< Func, Trans, Trans >::run();\ + } + +int main(int argc, char* argv[]) +{ + cout << "vec = trans * vec" << endl; + run_vec(TV, float, Isometry, AutoAlign, 3); + run_vec(TV, float, Isometry, DontAlign, 3); + run_vec(TV, float, Isometry, AutoAlign, 4); + run_vec(TV, float, Isometry, DontAlign, 4); + run_vec(TV, float, Projective, AutoAlign, 4); + run_vec(TV, float, Projective, DontAlign, 4); + run_vec(TV, double, Isometry, AutoAlign, 3); + run_vec(TV, double, Isometry, DontAlign, 3); + run_vec(TV, double, Isometry, AutoAlign, 4); + run_vec(TV, double, Isometry, DontAlign, 4); + run_vec(TV, double, Projective, AutoAlign, 4); + run_vec(TV, double, Projective, DontAlign, 4); + + cout << "vec = trans.matrix() * vec" << endl; + run_vec(TMATV, float, Isometry, AutoAlign, 4); + run_vec(TMATV, float, Isometry, DontAlign, 4); + run_vec(TMATV, double, Isometry, AutoAlign, 4); + run_vec(TMATV, double, Isometry, DontAlign, 4); + + cout << "trans = trans1 * trans" << endl; + run_trans(TV, float, Isometry, AutoAlign); + run_trans(TV, float, Isometry, DontAlign); + run_trans(TV, double, Isometry, AutoAlign); + run_trans(TV, double, Isometry, DontAlign); + run_trans(TV, float, Projective, AutoAlign); + run_trans(TV, float, Projective, DontAlign); + run_trans(TV, double, Projective, AutoAlign); + run_trans(TV, double, Projective, DontAlign); + + cout << "trans = trans1.matrix() * trans.matrix()" << endl; + run_trans(TMATVMAT, float, Isometry, AutoAlign); + run_trans(TMATVMAT, float, Isometry, DontAlign); + run_trans(TMATVMAT, double, Isometry, AutoAlign); + run_trans(TMATVMAT, double, Isometry, DontAlign); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchVecAdd.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchVecAdd.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ce8e1e91103e6388b021dadf2abf3bb4e706bce4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchVecAdd.cpp @@ -0,0 +1,135 @@ + +#include +#include +#include +using namespace Eigen; + +#ifndef SIZE +#define SIZE 50 +#endif + +#ifndef REPEAT +#define REPEAT 10000 +#endif + +typedef float Scalar; + +__attribute__ ((noinline)) void benchVec(Scalar* a, Scalar* b, Scalar* c, int size); +__attribute__ ((noinline)) void benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c); +__attribute__ ((noinline)) void benchVec(VectorXf& a, VectorXf& b, VectorXf& c); + +int main(int argc, char* argv[]) +{ + int size = SIZE * 8; + int size2 = size * size; + Scalar* a = internal::aligned_new(size2); + Scalar* b = internal::aligned_new(size2+4)+1; + Scalar* c = internal::aligned_new(size2); + + for (int i=0; i2 ; --innersize) + { + if (size2%innersize==0) + { + int outersize = size2/innersize; + MatrixXf ma = Map(a, innersize, outersize ); + MatrixXf mb = Map(b, innersize, outersize ); + MatrixXf mc = Map(c, innersize, outersize ); + timer.reset(); + for (int k=0; k<3; ++k) + { + timer.start(); + benchVec(ma, mb, mc); + timer.stop(); + } + std::cout << innersize << " x " << outersize << " " << timer.value() << "s " << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << " GFlops\n"; + } + } + + VectorXf va = Map(a, size2); + VectorXf vb = Map(b, size2); + VectorXf vc = Map(c, size2); + timer.reset(); + for (int k=0; k<3; ++k) + { + timer.start(); + benchVec(va, vb, vc); + timer.stop(); + } + std::cout << timer.value() << "s " << (double(size2*REPEAT)/timer.value())/(1024.*1024.*1024.) << " GFlops\n"; + + return 0; +} + +void benchVec(MatrixXf& a, MatrixXf& b, MatrixXf& c) +{ + for (int k=0; k::type PacketScalar; + const int PacketSize = internal::packet_traits::size; + PacketScalar a0, a1, a2, a3, b0, b1, b2, b3; + for (int k=0; k +// -DSCALARA=double or -DSCALARB=double +// -DHAVE_BLAS +// -DDECOUPLED +// + +#include +#include +#include + + +using namespace std; +using namespace Eigen; + +#ifndef SCALAR +// #define SCALAR std::complex +#define SCALAR float +#endif + +#ifndef SCALARA +#define SCALARA SCALAR +#endif + +#ifndef SCALARB +#define SCALARB SCALAR +#endif + +#ifdef ROWMAJ_A +const int opt_A = RowMajor; +#else +const int opt_A = ColMajor; +#endif + +#ifdef ROWMAJ_B +const int opt_B = RowMajor; +#else +const int opt_B = ColMajor; +#endif + +typedef SCALAR Scalar; +typedef NumTraits::Real RealScalar; +typedef Matrix A; +typedef Matrix B; +typedef Matrix C; +typedef Matrix M; + +#ifdef HAVE_BLAS + +extern "C" { + #include +} + +static float fone = 1; +static float fzero = 0; +static double done = 1; +static double szero = 0; +static std::complex cfone = 1; +static std::complex cfzero = 0; +static std::complex cdone = 1; +static std::complex cdzero = 0; +static char notrans = 'N'; +static char trans = 'T'; +static char nonunit = 'N'; +static char lower = 'L'; +static char right = 'R'; +static int intone = 1; + +#ifdef ROWMAJ_A +const char transA = trans; +#else +const char transA = notrans; +#endif + +#ifdef ROWMAJ_B +const char transB = trans; +#else +const char transB = notrans; +#endif + +template +void blas_gemm(const A& a, const B& b, MatrixXf& c) +{ + int M = c.rows(); int N = c.cols(); int K = a.cols(); + int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows(); + + sgemm_(&transA,&transB,&M,&N,&K,&fone, + const_cast(a.data()),&lda, + const_cast(b.data()),&ldb,&fone, + c.data(),&ldc); +} + +template +void blas_gemm(const A& a, const B& b, MatrixXd& c) +{ + int M = c.rows(); int N = c.cols(); int K = a.cols(); + int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows(); + + dgemm_(&transA,&transB,&M,&N,&K,&done, + const_cast(a.data()),&lda, + const_cast(b.data()),&ldb,&done, + c.data(),&ldc); +} + +template +void blas_gemm(const A& a, const B& b, MatrixXcf& c) +{ + int M = c.rows(); int N = c.cols(); int K = a.cols(); + int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows(); + + cgemm_(&transA,&transB,&M,&N,&K,(float*)&cfone, + const_cast((const float*)a.data()),&lda, + const_cast((const float*)b.data()),&ldb,(float*)&cfone, + (float*)c.data(),&ldc); +} + +template +void blas_gemm(const A& a, const B& b, MatrixXcd& c) +{ + int M = c.rows(); int N = c.cols(); int K = a.cols(); + int lda = a.outerStride(); int ldb = b.outerStride(); int ldc = c.rows(); + + zgemm_(&transA,&transB,&M,&N,&K,(double*)&cdone, + const_cast((const double*)a.data()),&lda, + const_cast((const double*)b.data()),&ldb,(double*)&cdone, + (double*)c.data(),&ldc); +} + + + +#endif + +void matlab_cplx_cplx(const M& ar, const M& ai, const M& br, const M& bi, M& cr, M& ci) +{ + cr.noalias() += ar * br; + cr.noalias() -= ai * bi; + ci.noalias() += ar * bi; + ci.noalias() += ai * br; + // [cr ci] += [ar ai] * br + [-ai ar] * bi +} + +void matlab_real_cplx(const M& a, const M& br, const M& bi, M& cr, M& ci) +{ + cr.noalias() += a * br; + ci.noalias() += a * bi; +} + +void matlab_cplx_real(const M& ar, const M& ai, const M& b, M& cr, M& ci) +{ + cr.noalias() += ar * b; + ci.noalias() += ai * b; +} + + + +template +EIGEN_DONT_INLINE void gemm(const A& a, const B& b, C& c) +{ + c.noalias() += a * b; +} + +int main(int argc, char ** argv) +{ + std::ptrdiff_t l1 = internal::queryL1CacheSize(); + std::ptrdiff_t l2 = internal::queryTopLevelCacheSize(); + std::cout << "L1 cache size = " << (l1>0 ? l1/1024 : -1) << " KB\n"; + std::cout << "L2/L3 cache size = " << (l2>0 ? l2/1024 : -1) << " KB\n"; + typedef internal::gebp_traits Traits; + std::cout << "Register blocking = " << Traits::mr << " x " << Traits::nr << "\n"; + + int rep = 1; // number of repetitions per try + int tries = 2; // number of tries, we keep the best + + int s = 2048; + int m = s; + int n = s; + int p = s; + int cache_size1=-1, cache_size2=l2, cache_size3 = 0; + + bool need_help = false; + for (int i=1; i -c -t -p \n"; + std::cout << " : size\n"; + std::cout << " : rows columns depth\n"; + return 1; + } + +#if EIGEN_VERSION_AT_LEAST(3,2,90) + if(cache_size1>0) + setCpuCacheSizes(cache_size1,cache_size2,cache_size3); +#endif + + A a(m,p); a.setRandom(); + B b(p,n); b.setRandom(); + C c(m,n); c.setOnes(); + C rc = c; + + std::cout << "Matrix sizes = " << m << "x" << p << " * " << p << "x" << n << "\n"; + std::ptrdiff_t mc(m), nc(n), kc(p); + internal::computeProductBlockingSizes(kc, mc, nc); + std::cout << "blocking size (mc x kc) = " << mc << " x " << kc << " x " << nc << "\n"; + + C r = c; + + // check the parallel product is correct + #if defined EIGEN_HAS_OPENMP + Eigen::initParallel(); + int procs = omp_get_max_threads(); + if(procs>1) + { + #ifdef HAVE_BLAS + blas_gemm(a,b,r); + #else + omp_set_num_threads(1); + r.noalias() += a * b; + omp_set_num_threads(procs); + #endif + c.noalias() += a * b; + if(!r.isApprox(c)) std::cerr << "Warning, your parallel product is crap!\n\n"; + } + #elif defined HAVE_BLAS + blas_gemm(a,b,r); + c.noalias() += a * b; + if(!r.isApprox(c)) { + std::cout << (r - c).norm()/r.norm() << "\n"; + std::cerr << "Warning, your product is crap!\n\n"; + } + #else + if(1.*m*n*p<2000.*2000*2000) + { + gemm(a,b,c); + r.noalias() += a.cast() .lazyProduct( b.cast() ); + if(!r.isApprox(c)) { + std::cout << (r - c).norm()/r.norm() << "\n"; + std::cerr << "Warning, your product is crap!\n\n"; + } + } + #endif + + #ifdef HAVE_BLAS + BenchTimer tblas; + c = rc; + BENCH(tblas, tries, rep, blas_gemm(a,b,c)); + std::cout << "blas cpu " << tblas.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tblas.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tblas.total(CPU_TIMER) << "s)\n"; + std::cout << "blas real " << tblas.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tblas.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tblas.total(REAL_TIMER) << "s)\n"; + #endif + + // warm start + if(b.norm()+a.norm()==123.554) std::cout << "\n"; + + BenchTimer tmt; + c = rc; + BENCH(tmt, tries, rep, gemm(a,b,c)); + std::cout << "eigen cpu " << tmt.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER) << "s)\n"; + std::cout << "eigen real " << tmt.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER) << "s)\n"; + + #ifdef EIGEN_HAS_OPENMP + if(procs>1) + { + BenchTimer tmono; + omp_set_num_threads(1); + Eigen::setNbThreads(1); + c = rc; + BENCH(tmono, tries, rep, gemm(a,b,c)); + std::cout << "eigen mono cpu " << tmono.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmono.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmono.total(CPU_TIMER) << "s)\n"; + std::cout << "eigen mono real " << tmono.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmono.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmono.total(REAL_TIMER) << "s)\n"; + std::cout << "mt speed up x" << tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER) << " => " << (100.0*tmono.best(CPU_TIMER) / tmt.best(REAL_TIMER))/procs << "%\n"; + } + #endif + + if(1.*m*n*p<30*30*30) + { + BenchTimer tmt; + c = rc; + BENCH(tmt, tries, rep, c.noalias()+=a.lazyProduct(b)); + std::cout << "lazy cpu " << tmt.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(CPU_TIMER) << "s)\n"; + std::cout << "lazy real " << tmt.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/tmt.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << tmt.total(REAL_TIMER) << "s)\n"; + } + + #ifdef DECOUPLED + if((NumTraits::IsComplex) && (NumTraits::IsComplex)) + { + M ar(m,p); ar.setRandom(); + M ai(m,p); ai.setRandom(); + M br(p,n); br.setRandom(); + M bi(p,n); bi.setRandom(); + M cr(m,n); cr.setRandom(); + M ci(m,n); ci.setRandom(); + + BenchTimer t; + BENCH(t, tries, rep, matlab_cplx_cplx(ar,ai,br,bi,cr,ci)); + std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n"; + std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n"; + } + if((!NumTraits::IsComplex) && (NumTraits::IsComplex)) + { + M a(m,p); a.setRandom(); + M br(p,n); br.setRandom(); + M bi(p,n); bi.setRandom(); + M cr(m,n); cr.setRandom(); + M ci(m,n); ci.setRandom(); + + BenchTimer t; + BENCH(t, tries, rep, matlab_real_cplx(a,br,bi,cr,ci)); + std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n"; + std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n"; + } + if((NumTraits::IsComplex) && (!NumTraits::IsComplex)) + { + M ar(m,p); ar.setRandom(); + M ai(m,p); ai.setRandom(); + M b(p,n); b.setRandom(); + M cr(m,n); cr.setRandom(); + M ci(m,n); ci.setRandom(); + + BenchTimer t; + BENCH(t, tries, rep, matlab_cplx_real(ar,ai,b,cr,ci)); + std::cout << "\"matlab\" cpu " << t.best(CPU_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(CPU_TIMER))*1e-9 << " GFLOPS \t(" << t.total(CPU_TIMER) << "s)\n"; + std::cout << "\"matlab\" real " << t.best(REAL_TIMER)/rep << "s \t" << (double(m)*n*p*rep*2/t.best(REAL_TIMER))*1e-9 << " GFLOPS \t(" << t.total(REAL_TIMER) << "s)\n"; + } + #endif + + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_move_semantics.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_move_semantics.cpp new file mode 100644 index 0000000000000000000000000000000000000000..323d80417c0c87316c6f616ba031c4dfa01b8a6b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_move_semantics.cpp @@ -0,0 +1,57 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2020 Sebastien Boisvert +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "BenchTimer.h" +#include "../test/MovableScalar.h" + +#include + +#include +#include + +template +void copy_matrix(MatrixType& m) +{ + MatrixType tmp(m); + m = tmp; +} + +template +void move_matrix(MatrixType&& m) +{ + MatrixType tmp(std::move(m)); + m = std::move(tmp); +} + +template +void bench(const std::string& label) +{ + using MatrixType = Eigen::Matrix,1,10>; + Eigen::BenchTimer t; + + int tries = 10; + int rep = 1000000; + + MatrixType data = MatrixType::Random().eval(); + MatrixType dest; + + BENCH(t, tries, rep, copy_matrix(data)); + std::cout << label << " copy semantics: " << 1e3*t.best(Eigen::CPU_TIMER) << " ms" << std::endl; + + BENCH(t, tries, rep, move_matrix(std::move(data))); + std::cout << label << " move semantics: " << 1e3*t.best(Eigen::CPU_TIMER) << " ms" << std::endl; +} + +int main() +{ + bench("float"); + bench("double"); + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_multi_compilers.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_multi_compilers.sh new file mode 100644 index 0000000000000000000000000000000000000000..27e91f1d5ebfa8ccbd47c9073f68ed0b86641ac3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_multi_compilers.sh @@ -0,0 +1,28 @@ +#!/bin/bash + +if (($# < 2)); then + echo "Usage: $0 compilerlist.txt benchfile.cpp" +else + +compilerlist=$1 +benchfile=$2 + +g=0 +source $compilerlist + +# for each compiler, compile benchfile and run the benchmark +for (( i=0 ; i /dev/null + echo "" + else + echo "compiler not found: $compiler" + fi +done + +fi diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_norm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_norm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..592f25d66e0744dac7581d30669d5cade3cc8d5f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_norm.cpp @@ -0,0 +1,360 @@ +#include +#include +#include +#include "BenchTimer.h" +using namespace Eigen; +using namespace std; + +template +EIGEN_DONT_INLINE typename T::Scalar sqsumNorm(T& v) +{ + return v.norm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar stableNorm(T& v) +{ + return v.stableNorm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar hypotNorm(T& v) +{ + return v.hypotNorm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar blueNorm(T& v) +{ + return v.blueNorm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar lapackNorm(T& v) +{ + typedef typename T::Scalar Scalar; + int n = v.size(); + Scalar scale = 0; + Scalar ssq = 1; + for (int i=0;i= ax) + { + ssq += numext::abs2(ax/scale); + } + else + { + ssq = Scalar(1) + ssq * numext::abs2(scale/ax); + scale = ax; + } + } + return scale * std::sqrt(ssq); +} + +template +EIGEN_DONT_INLINE typename T::Scalar twopassNorm(T& v) +{ + typedef typename T::Scalar Scalar; + Scalar s = v.array().abs().maxCoeff(); + return s*(v/s).norm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar bl2passNorm(T& v) +{ + return v.stableNorm(); +} + +template +EIGEN_DONT_INLINE typename T::Scalar divacNorm(T& v) +{ + int n =v.size() / 2; + for (int i=0;i0) + { + for (int i=0;i +EIGEN_DONT_INLINE typename T::Scalar pblueNorm(const T& v) +{ + #ifndef EIGEN_VECTORIZE + return v.blueNorm(); + #else + typedef typename T::Scalar Scalar; + + static int nmax = 0; + static Scalar b1, b2, s1m, s2m, overfl, rbig, relerr; + int n; + + if(nmax <= 0) + { + int nbig, ibeta, it, iemin, iemax, iexp; + Scalar abig, eps; + + nbig = NumTraits::highest(); // largest integer + ibeta = std::numeric_limits::radix; // NumTraits::Base; // base for floating-point numbers + it = NumTraits::digits(); // NumTraits::Mantissa; // number of base-beta digits in mantissa + iemin = NumTraits::min_exponent(); // minimum exponent + iemax = NumTraits::max_exponent(); // maximum exponent + rbig = NumTraits::highest(); // largest floating-point number + + // Check the basic machine-dependent constants. + if(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) + || (it<=4 && ibeta <= 3 ) || it<2) + { + eigen_assert(false && "the algorithm cannot be guaranteed on this computer"); + } + iexp = -((1-iemin)/2); + b1 = std::pow(ibeta, iexp); // lower boundary of midrange + iexp = (iemax + 1 - it)/2; + b2 = std::pow(ibeta,iexp); // upper boundary of midrange + + iexp = (2-iemin)/2; + s1m = std::pow(ibeta,iexp); // scaling factor for lower range + iexp = - ((iemax+it)/2); + s2m = std::pow(ibeta,iexp); // scaling factor for upper range + + overfl = rbig*s2m; // overflow boundary for abig + eps = std::pow(ibeta, 1-it); + relerr = std::sqrt(eps); // tolerance for neglecting asml + abig = 1.0/eps - 1.0; + if (Scalar(nbig)>abig) nmax = abig; // largest safe n + else nmax = nbig; + } + + typedef typename internal::packet_traits::type Packet; + const int ps = internal::packet_traits::size; + Packet pasml = internal::pset1(Scalar(0)); + Packet pamed = internal::pset1(Scalar(0)); + Packet pabig = internal::pset1(Scalar(0)); + Packet ps2m = internal::pset1(s2m); + Packet ps1m = internal::pset1(s1m); + Packet pb2 = internal::pset1(b2); + Packet pb1 = internal::pset1(b1); + for(int j=0; j(j)); + Packet ax_s2m = internal::pmul(ax,ps2m); + Packet ax_s1m = internal::pmul(ax,ps1m); + Packet maskBig = internal::plt(pb2,ax); + Packet maskSml = internal::plt(ax,pb1); + +// Packet maskMed = internal::pand(maskSml,maskBig); +// Packet scale = internal::pset1(Scalar(0)); +// scale = internal::por(scale, internal::pand(maskBig,ps2m)); +// scale = internal::por(scale, internal::pand(maskSml,ps1m)); +// scale = internal::por(scale, internal::pandnot(internal::pset1(Scalar(1)),maskMed)); +// ax = internal::pmul(ax,scale); +// ax = internal::pmul(ax,ax); +// pabig = internal::padd(pabig, internal::pand(maskBig, ax)); +// pasml = internal::padd(pasml, internal::pand(maskSml, ax)); +// pamed = internal::padd(pamed, internal::pandnot(ax,maskMed)); + + + pabig = internal::padd(pabig, internal::pand(maskBig, internal::pmul(ax_s2m,ax_s2m))); + pasml = internal::padd(pasml, internal::pand(maskSml, internal::pmul(ax_s1m,ax_s1m))); + pamed = internal::padd(pamed, internal::pandnot(internal::pmul(ax,ax),internal::pand(maskSml,maskBig))); + } + Scalar abig = internal::predux(pabig); + Scalar asml = internal::predux(pasml); + Scalar amed = internal::predux(pamed); + if(abig > Scalar(0)) + { + abig = std::sqrt(abig); + if(abig > overfl) + { + eigen_assert(false && "overflow"); + return rbig; + } + if(amed > Scalar(0)) + { + abig = abig/s2m; + amed = std::sqrt(amed); + } + else + { + return abig/s2m; + } + + } + else if(asml > Scalar(0)) + { + if (amed > Scalar(0)) + { + abig = std::sqrt(amed); + amed = std::sqrt(asml) / s1m; + } + else + { + return std::sqrt(asml)/s1m; + } + } + else + { + return std::sqrt(amed); + } + asml = std::min(abig, amed); + abig = std::max(abig, amed); + if(asml <= abig*relerr) + return abig; + else + return abig * std::sqrt(Scalar(1) + numext::abs2(asml/abig)); + #endif +} + +#define BENCH_PERF(NRM) { \ + float af = 0; double ad = 0; std::complex ac = 0; \ + Eigen::BenchTimer tf, td, tcf; tf.reset(); td.reset(); tcf.reset();\ + for (int k=0; k()); + double yd = based * std::abs(internal::random()); + VectorXf vf = VectorXf::Ones(s) * yf; + VectorXd vd = VectorXd::Ones(s) * yd; + + std::cout << "reference\t" << std::sqrt(double(s))*yf << "\t" << std::sqrt(double(s))*yd << "\n"; + std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\n"; + std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\n"; + std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\n"; + std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\n"; + std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\n"; + std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\n"; + std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\n"; +} + +void check_accuracy_var(int ef0, int ef1, int ed0, int ed1, int s) +{ + VectorXf vf(s); + VectorXd vd(s); + for (int i=0; i()) * std::pow(double(10), internal::random(ef0,ef1)); + vd[i] = std::abs(internal::random()) * std::pow(double(10), internal::random(ed0,ed1)); + } + + //std::cout << "reference\t" << internal::sqrt(double(s))*yf << "\t" << internal::sqrt(double(s))*yd << "\n"; + std::cout << "sqsumNorm\t" << sqsumNorm(vf) << "\t" << sqsumNorm(vd) << "\t" << sqsumNorm(vf.cast()) << "\t" << sqsumNorm(vd.cast()) << "\n"; + std::cout << "hypotNorm\t" << hypotNorm(vf) << "\t" << hypotNorm(vd) << "\t" << hypotNorm(vf.cast()) << "\t" << hypotNorm(vd.cast()) << "\n"; + std::cout << "blueNorm\t" << blueNorm(vf) << "\t" << blueNorm(vd) << "\t" << blueNorm(vf.cast()) << "\t" << blueNorm(vd.cast()) << "\n"; + std::cout << "pblueNorm\t" << pblueNorm(vf) << "\t" << pblueNorm(vd) << "\t" << blueNorm(vf.cast()) << "\t" << blueNorm(vd.cast()) << "\n"; + std::cout << "lapackNorm\t" << lapackNorm(vf) << "\t" << lapackNorm(vd) << "\t" << lapackNorm(vf.cast()) << "\t" << lapackNorm(vd.cast()) << "\n"; + std::cout << "twopassNorm\t" << twopassNorm(vf) << "\t" << twopassNorm(vd) << "\t" << twopassNorm(vf.cast()) << "\t" << twopassNorm(vd.cast()) << "\n"; +// std::cout << "bl2passNorm\t" << bl2passNorm(vf) << "\t" << bl2passNorm(vd) << "\t" << bl2passNorm(vf.cast()) << "\t" << bl2passNorm(vd.cast()) << "\n"; +} + +int main(int argc, char** argv) +{ + int tries = 10; + int iters = 100000; + double y = 1.1345743233455785456788e12 * internal::random(); + VectorXf v = VectorXf::Ones(1024) * y; + +// return 0; + int s = 10000; + double basef_ok = 1.1345743233455785456788e15; + double based_ok = 1.1345743233455785456788e95; + + double basef_under = 1.1345743233455785456788e-27; + double based_under = 1.1345743233455785456788e-303; + + double basef_over = 1.1345743233455785456788e+27; + double based_over = 1.1345743233455785456788e+302; + + std::cout.precision(20); + + std::cerr << "\nNo under/overflow:\n"; + check_accuracy(basef_ok, based_ok, s); + + std::cerr << "\nUnderflow:\n"; + check_accuracy(basef_under, based_under, s); + + std::cerr << "\nOverflow:\n"; + check_accuracy(basef_over, based_over, s); + + std::cerr << "\nVarying (over):\n"; + for (int k=0; k<1; ++k) + { + check_accuracy_var(20,27,190,302,s); + std::cout << "\n"; + } + + std::cerr << "\nVarying (under):\n"; + for (int k=0; k<1; ++k) + { + check_accuracy_var(-27,20,-302,-190,s); + std::cout << "\n"; + } + + y = 1; + std::cout.precision(4); + int s1 = 1024*1024*32; + std::cerr << "Performance (out of cache, " << s1 << "):\n"; + { + int iters = 1; + VectorXf vf = VectorXf::Random(s1) * y; + VectorXd vd = VectorXd::Random(s1) * y; + VectorXcf vcf = VectorXcf::Random(s1) * y; + BENCH_PERF(sqsumNorm); + BENCH_PERF(stableNorm); + BENCH_PERF(blueNorm); + BENCH_PERF(pblueNorm); + BENCH_PERF(lapackNorm); + BENCH_PERF(hypotNorm); + BENCH_PERF(twopassNorm); + BENCH_PERF(bl2passNorm); + } + + std::cerr << "\nPerformance (in cache, " << 512 << "):\n"; + { + int iters = 100000; + VectorXf vf = VectorXf::Random(512) * y; + VectorXd vd = VectorXd::Random(512) * y; + VectorXcf vcf = VectorXcf::Random(512) * y; + BENCH_PERF(sqsumNorm); + BENCH_PERF(stableNorm); + BENCH_PERF(blueNorm); + BENCH_PERF(pblueNorm); + BENCH_PERF(lapackNorm); + BENCH_PERF(hypotNorm); + BENCH_PERF(twopassNorm); + BENCH_PERF(bl2passNorm); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_reverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_reverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1e69ca1b29c89ad291119da5878cbcebd983216b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_reverse.cpp @@ -0,0 +1,84 @@ + +#include +#include +#include +using namespace Eigen; + +#ifndef REPEAT +#define REPEAT 100000 +#endif + +#ifndef TRIES +#define TRIES 20 +#endif + +typedef double Scalar; + +template +__attribute__ ((noinline)) void bench_reverse(const MatrixType& m) +{ + int rows = m.rows(); + int cols = m.cols(); + int size = m.size(); + + int repeats = (REPEAT*1000)/size; + MatrixType a = MatrixType::Random(rows,cols); + MatrixType b = MatrixType::Random(rows,cols); + + BenchTimer timerB, timerH, timerV; + + Scalar acc = 0; + int r = internal::random(0,rows-1); + int c = internal::random(0,cols-1); + for (int t=0; t0; ++i) + { + bench_reverse(Matrix(dynsizes[i],dynsizes[i])); + bench_reverse(Matrix(dynsizes[i]*dynsizes[i])); + } +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); +// bench_reverse(Matrix()); + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_sum.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_sum.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a3d925e4fc7f78b16996d7025fefc72cc75869ed --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_sum.cpp @@ -0,0 +1,18 @@ +#include +#include +using namespace Eigen; +using namespace std; + +int main() +{ + typedef Matrix Vec; + Vec v(SIZE); + v.setZero(); + v[0] = 1; + v[1] = 2; + for(int i = 0; i < 1000000; i++) + { + v.coeffRef(0) += v.sum() * SCALAR(1e-20); + } + cout << v.sum() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_unrolling b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_unrolling new file mode 100644 index 0000000000000000000000000000000000000000..826443845b7be258f8931b5a63cc1f9dd98354b7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/bench_unrolling @@ -0,0 +1,12 @@ +#!/bin/bash + +# gcc : CXX="g++ -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000" +# icc : CXX="icpc -fast -no-inline-max-size -fno-exceptions" +CXX=${CXX-g++ -finline-limit=10000 -ftemplate-depth-2000 --param max-inline-recursive-depth=2000} # default value + +for ((i=1; i<16; ++i)); do + echo "Matrix size: $i x $i :" + $CXX -O3 -I.. -DNDEBUG benchmark.cpp -DMATSIZE=$i -DEIGEN_UNROLLING_LIMIT=400 -o benchmark && time ./benchmark >/dev/null + $CXX -O3 -I.. -DNDEBUG -finline-limit=10000 benchmark.cpp -DMATSIZE=$i -DEIGEN_DONT_USE_UNROLLED_LOOPS=1 -o benchmark && time ./benchmark >/dev/null + echo " " +done diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark-blocking-sizes.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark-blocking-sizes.cpp new file mode 100644 index 0000000000000000000000000000000000000000..827be2880294bfa395a20b51f151d0d8387655eb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark-blocking-sizes.cpp @@ -0,0 +1,677 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include +#include +#include +#include +#include +#include +#include + +bool eigen_use_specific_block_size; +int eigen_block_size_k, eigen_block_size_m, eigen_block_size_n; +#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZES eigen_use_specific_block_size +#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_K eigen_block_size_k +#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_M eigen_block_size_m +#define EIGEN_TEST_SPECIFIC_BLOCKING_SIZE_N eigen_block_size_n +#include + +#include + +using namespace Eigen; +using namespace std; + +static BenchTimer timer; + +// how many times we repeat each measurement. +// measurements are randomly shuffled - we're not doing +// all N identical measurements in a row. +const int measurement_repetitions = 3; + +// Timings below this value are too short to be accurate, +// we'll repeat measurements with more iterations until +// we get a timing above that threshold. +const float min_accurate_time = 1e-2f; + +// See --min-working-set-size command line parameter. +size_t min_working_set_size = 0; + +float max_clock_speed = 0.0f; + +// range of sizes that we will benchmark (in all 3 K,M,N dimensions) +const size_t maxsize = 2048; +const size_t minsize = 16; + +typedef MatrixXf MatrixType; +typedef MatrixType::Scalar Scalar; +typedef internal::packet_traits::type Packet; + +static_assert((maxsize & (maxsize - 1)) == 0, "maxsize must be a power of two"); +static_assert((minsize & (minsize - 1)) == 0, "minsize must be a power of two"); +static_assert(maxsize > minsize, "maxsize must be larger than minsize"); +static_assert(maxsize < (minsize << 16), "maxsize must be less than (minsize<<16)"); + +// just a helper to store a triple of K,M,N sizes for matrix product +struct size_triple_t +{ + size_t k, m, n; + size_triple_t() : k(0), m(0), n(0) {} + size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {} + size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {} + size_triple_t(uint16_t compact) + { + k = 1 << ((compact & 0xf00) >> 8); + m = 1 << ((compact & 0x0f0) >> 4); + n = 1 << ((compact & 0x00f) >> 0); + } +}; + +uint8_t log2_pot(size_t x) { + size_t l = 0; + while (x >>= 1) l++; + return l; +} + +// Convert between size tripes and a compact form fitting in 12 bits +// where each size, which must be a POT, is encoded as its log2, on 4 bits +// so the largest representable size is 2^15 == 32k ... big enough. +uint16_t compact_size_triple(size_t k, size_t m, size_t n) +{ + return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n); +} + +uint16_t compact_size_triple(const size_triple_t& t) +{ + return compact_size_triple(t.k, t.m, t.n); +} + +// A single benchmark. Initially only contains benchmark params. +// Then call run(), which stores the result in the gflops field. +struct benchmark_t +{ + uint16_t compact_product_size; + uint16_t compact_block_size; + bool use_default_block_size; + float gflops; + benchmark_t() + : compact_product_size(0) + , compact_block_size(0) + , use_default_block_size(false) + , gflops(0) + { + } + benchmark_t(size_t pk, size_t pm, size_t pn, + size_t bk, size_t bm, size_t bn) + : compact_product_size(compact_size_triple(pk, pm, pn)) + , compact_block_size(compact_size_triple(bk, bm, bn)) + , use_default_block_size(false) + , gflops(0) + {} + benchmark_t(size_t pk, size_t pm, size_t pn) + : compact_product_size(compact_size_triple(pk, pm, pn)) + , compact_block_size(0) + , use_default_block_size(true) + , gflops(0) + {} + + void run(); +}; + +ostream& operator<<(ostream& s, const benchmark_t& b) +{ + s << hex << b.compact_product_size << dec; + if (b.use_default_block_size) { + size_triple_t t(b.compact_product_size); + Index k = t.k, m = t.m, n = t.n; + internal::computeProductBlockingSizes(k, m, n); + s << " default(" << k << ", " << m << ", " << n << ")"; + } else { + s << " " << hex << b.compact_block_size << dec; + } + s << " " << b.gflops; + return s; +} + +// We sort first by increasing benchmark parameters, +// then by decreasing performance. +bool operator<(const benchmark_t& b1, const benchmark_t& b2) +{ + return b1.compact_product_size < b2.compact_product_size || + (b1.compact_product_size == b2.compact_product_size && ( + (b1.compact_block_size < b2.compact_block_size || ( + b1.compact_block_size == b2.compact_block_size && + b1.gflops > b2.gflops)))); +} + +void benchmark_t::run() +{ + size_triple_t productsizes(compact_product_size); + + if (use_default_block_size) { + eigen_use_specific_block_size = false; + } else { + // feed eigen with our custom blocking params + eigen_use_specific_block_size = true; + size_triple_t blocksizes(compact_block_size); + eigen_block_size_k = blocksizes.k; + eigen_block_size_m = blocksizes.m; + eigen_block_size_n = blocksizes.n; + } + + // set up the matrix pool + + const size_t combined_three_matrices_sizes = + sizeof(Scalar) * + (productsizes.k * productsizes.m + + productsizes.k * productsizes.n + + productsizes.m * productsizes.n); + + // 64 M is large enough that nobody has a cache bigger than that, + // while still being small enough that everybody has this much RAM, + // so conveniently we don't need to special-case platforms here. + const size_t unlikely_large_cache_size = 64 << 20; + + const size_t working_set_size = + min_working_set_size ? min_working_set_size : unlikely_large_cache_size; + + const size_t matrix_pool_size = + 1 + working_set_size / combined_three_matrices_sizes; + + MatrixType *lhs = new MatrixType[matrix_pool_size]; + MatrixType *rhs = new MatrixType[matrix_pool_size]; + MatrixType *dst = new MatrixType[matrix_pool_size]; + + for (size_t i = 0; i < matrix_pool_size; i++) { + lhs[i] = MatrixType::Zero(productsizes.m, productsizes.k); + rhs[i] = MatrixType::Zero(productsizes.k, productsizes.n); + dst[i] = MatrixType::Zero(productsizes.m, productsizes.n); + } + + // main benchmark loop + + int iters_at_a_time = 1; + float time_per_iter = 0.0f; + size_t matrix_index = 0; + while (true) { + + double starttime = timer.getCpuTime(); + for (int i = 0; i < iters_at_a_time; i++) { + dst[matrix_index].noalias() = lhs[matrix_index] * rhs[matrix_index]; + matrix_index++; + if (matrix_index == matrix_pool_size) { + matrix_index = 0; + } + } + double endtime = timer.getCpuTime(); + + const float timing = float(endtime - starttime); + + if (timing >= min_accurate_time) { + time_per_iter = timing / iters_at_a_time; + break; + } + + iters_at_a_time *= 2; + } + + delete[] lhs; + delete[] rhs; + delete[] dst; + + gflops = 2e-9 * productsizes.k * productsizes.m * productsizes.n / time_per_iter; +} + +void print_cpuinfo() +{ +#ifdef __linux__ + cout << "contents of /proc/cpuinfo:" << endl; + string line; + ifstream cpuinfo("/proc/cpuinfo"); + if (cpuinfo.is_open()) { + while (getline(cpuinfo, line)) { + cout << line << endl; + } + cpuinfo.close(); + } + cout << endl; +#elif defined __APPLE__ + cout << "output of sysctl hw:" << endl; + system("sysctl hw"); + cout << endl; +#endif +} + +template +string type_name() +{ + return "unknown"; +} + +template<> +string type_name() +{ + return "float"; +} + +template<> +string type_name() +{ + return "double"; +} + +struct action_t +{ + virtual const char* invokation_name() const { abort(); return nullptr; } + virtual void run() const { abort(); } + virtual ~action_t() {} +}; + +void show_usage_and_exit(int /*argc*/, char* argv[], + const vector>& available_actions) +{ + cerr << "usage: " << argv[0] << " [options...]" << endl << endl; + cerr << "available actions:" << endl << endl; + for (auto it = available_actions.begin(); it != available_actions.end(); ++it) { + cerr << " " << (*it)->invokation_name() << endl; + } + cerr << endl; + cerr << "options:" << endl << endl; + cerr << " --min-working-set-size=N:" << endl; + cerr << " Set the minimum working set size to N bytes." << endl; + cerr << " This is rounded up as needed to a multiple of matrix size." << endl; + cerr << " A larger working set lowers the chance of a warm cache." << endl; + cerr << " The default value 0 means use a large enough working" << endl; + cerr << " set to likely outsize caches." << endl; + cerr << " A value of 1 (that is, 1 byte) would mean don't do anything to" << endl; + cerr << " avoid warm caches." << endl; + exit(1); +} + +float measure_clock_speed() +{ + cerr << "Measuring clock speed... \r" << flush; + + vector all_gflops; + for (int i = 0; i < 8; i++) { + benchmark_t b(1024, 1024, 1024); + b.run(); + all_gflops.push_back(b.gflops); + } + + sort(all_gflops.begin(), all_gflops.end()); + float stable_estimate = all_gflops[2] + all_gflops[3] + all_gflops[4] + all_gflops[5]; + + // multiply by an arbitrary constant to discourage trying doing anything with the + // returned values besides just comparing them with each other. + float result = stable_estimate * 123.456f; + + return result; +} + +struct human_duration_t +{ + int seconds; + human_duration_t(int s) : seconds(s) {} +}; + +ostream& operator<<(ostream& s, const human_duration_t& d) +{ + int remainder = d.seconds; + if (remainder > 3600) { + int hours = remainder / 3600; + s << hours << " h "; + remainder -= hours * 3600; + } + if (remainder > 60) { + int minutes = remainder / 60; + s << minutes << " min "; + remainder -= minutes * 60; + } + if (d.seconds < 600) { + s << remainder << " s"; + } + return s; +} + +const char session_filename[] = "/data/local/tmp/benchmark-blocking-sizes-session.data"; + +void serialize_benchmarks(const char* filename, const vector& benchmarks, size_t first_benchmark_to_run) +{ + FILE* file = fopen(filename, "w"); + if (!file) { + cerr << "Could not open file " << filename << " for writing." << endl; + cerr << "Do you have write permissions on the current working directory?" << endl; + exit(1); + } + size_t benchmarks_vector_size = benchmarks.size(); + fwrite(&max_clock_speed, sizeof(max_clock_speed), 1, file); + fwrite(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file); + fwrite(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file); + fwrite(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file); + fclose(file); +} + +bool deserialize_benchmarks(const char* filename, vector& benchmarks, size_t& first_benchmark_to_run) +{ + FILE* file = fopen(filename, "r"); + if (!file) { + return false; + } + if (1 != fread(&max_clock_speed, sizeof(max_clock_speed), 1, file)) { + return false; + } + size_t benchmarks_vector_size = 0; + if (1 != fread(&benchmarks_vector_size, sizeof(benchmarks_vector_size), 1, file)) { + return false; + } + if (1 != fread(&first_benchmark_to_run, sizeof(first_benchmark_to_run), 1, file)) { + return false; + } + benchmarks.resize(benchmarks_vector_size); + if (benchmarks.size() != fread(benchmarks.data(), sizeof(benchmark_t), benchmarks.size(), file)) { + return false; + } + unlink(filename); + return true; +} + +void try_run_some_benchmarks( + vector& benchmarks, + double time_start, + size_t& first_benchmark_to_run) +{ + if (first_benchmark_to_run == benchmarks.size()) { + return; + } + + double time_last_progress_update = 0; + double time_last_clock_speed_measurement = 0; + double time_now = 0; + + size_t benchmark_index = first_benchmark_to_run; + + while (true) { + float ratio_done = float(benchmark_index) / benchmarks.size(); + time_now = timer.getRealTime(); + + // We check clock speed every minute and at the end. + if (benchmark_index == benchmarks.size() || + time_now > time_last_clock_speed_measurement + 60.0f) + { + time_last_clock_speed_measurement = time_now; + + // Ensure that clock speed is as expected + float current_clock_speed = measure_clock_speed(); + + // The tolerance needs to be smaller than the relative difference between + // clock speeds that a device could operate under. + // It seems unlikely that a device would be throttling clock speeds by + // amounts smaller than 2%. + // With a value of 1%, I was getting within noise on a Sandy Bridge. + const float clock_speed_tolerance = 0.02f; + + if (current_clock_speed > (1 + clock_speed_tolerance) * max_clock_speed) { + // Clock speed is now higher than we previously measured. + // Either our initial measurement was inaccurate, which won't happen + // too many times as we are keeping the best clock speed value and + // and allowing some tolerance; or something really weird happened, + // which invalidates all benchmark results collected so far. + // Either way, we better restart all over again now. + if (benchmark_index) { + cerr << "Restarting at " << 100.0f * ratio_done + << " % because clock speed increased. " << endl; + } + max_clock_speed = current_clock_speed; + first_benchmark_to_run = 0; + return; + } + + bool rerun_last_tests = false; + + if (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) { + cerr << "Measurements completed so far: " + << 100.0f * ratio_done + << " % " << endl; + cerr << "Clock speed seems to be only " + << current_clock_speed/max_clock_speed + << " times what it used to be." << endl; + + unsigned int seconds_to_sleep_if_lower_clock_speed = 1; + + while (current_clock_speed < (1 - clock_speed_tolerance) * max_clock_speed) { + if (seconds_to_sleep_if_lower_clock_speed > 32) { + cerr << "Sleeping longer probably won't make a difference." << endl; + cerr << "Serializing benchmarks to " << session_filename << endl; + serialize_benchmarks(session_filename, benchmarks, first_benchmark_to_run); + cerr << "Now restart this benchmark, and it should pick up where we left." << endl; + exit(2); + } + rerun_last_tests = true; + cerr << "Sleeping " + << seconds_to_sleep_if_lower_clock_speed + << " s... \r" << endl; + sleep(seconds_to_sleep_if_lower_clock_speed); + current_clock_speed = measure_clock_speed(); + seconds_to_sleep_if_lower_clock_speed *= 2; + } + } + + if (rerun_last_tests) { + cerr << "Redoing the last " + << 100.0f * float(benchmark_index - first_benchmark_to_run) / benchmarks.size() + << " % because clock speed had been low. " << endl; + return; + } + + // nothing wrong with the clock speed so far, so there won't be a need to rerun + // benchmarks run so far in case we later encounter a lower clock speed. + first_benchmark_to_run = benchmark_index; + } + + if (benchmark_index == benchmarks.size()) { + // We're done! + first_benchmark_to_run = benchmarks.size(); + // Erase progress info + cerr << " " << endl; + return; + } + + // Display progress info on stderr + if (time_now > time_last_progress_update + 1.0f) { + time_last_progress_update = time_now; + cerr << "Measurements... " << 100.0f * ratio_done + << " %, ETA " + << human_duration_t(float(time_now - time_start) * (1.0f - ratio_done) / ratio_done) + << " \r" << flush; + } + + // This is where we actually run a benchmark! + benchmarks[benchmark_index].run(); + benchmark_index++; + } +} + +void run_benchmarks(vector& benchmarks) +{ + size_t first_benchmark_to_run; + vector deserialized_benchmarks; + bool use_deserialized_benchmarks = false; + if (deserialize_benchmarks(session_filename, deserialized_benchmarks, first_benchmark_to_run)) { + cerr << "Found serialized session with " + << 100.0f * first_benchmark_to_run / deserialized_benchmarks.size() + << " % already done" << endl; + if (deserialized_benchmarks.size() == benchmarks.size() && + first_benchmark_to_run > 0 && + first_benchmark_to_run < benchmarks.size()) + { + use_deserialized_benchmarks = true; + } + } + + if (use_deserialized_benchmarks) { + benchmarks = deserialized_benchmarks; + } else { + // not using deserialized benchmarks, starting from scratch + first_benchmark_to_run = 0; + + // Randomly shuffling benchmarks allows us to get accurate enough progress info, + // as now the cheap/expensive benchmarks are randomly mixed so they average out. + // It also means that if data is corrupted for some time span, the odds are that + // not all repetitions of a given benchmark will be corrupted. + random_shuffle(benchmarks.begin(), benchmarks.end()); + } + + for (int i = 0; i < 4; i++) { + max_clock_speed = max(max_clock_speed, measure_clock_speed()); + } + + double time_start = 0.0; + while (first_benchmark_to_run < benchmarks.size()) { + if (first_benchmark_to_run == 0) { + time_start = timer.getRealTime(); + } + try_run_some_benchmarks(benchmarks, + time_start, + first_benchmark_to_run); + } + + // Sort timings by increasing benchmark parameters, and decreasing gflops. + // The latter is very important. It means that we can ignore all but the first + // benchmark with given parameters. + sort(benchmarks.begin(), benchmarks.end()); + + // Collect best (i.e. now first) results for each parameter values. + vector best_benchmarks; + for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) { + if (best_benchmarks.empty() || + best_benchmarks.back().compact_product_size != it->compact_product_size || + best_benchmarks.back().compact_block_size != it->compact_block_size) + { + best_benchmarks.push_back(*it); + } + } + + // keep and return only the best benchmarks + benchmarks = best_benchmarks; +} + +struct measure_all_pot_sizes_action_t : action_t +{ + virtual const char* invokation_name() const { return "all-pot-sizes"; } + virtual void run() const + { + vector benchmarks; + for (int repetition = 0; repetition < measurement_repetitions; repetition++) { + for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) { + for (size_t msize = minsize; msize <= maxsize; msize *= 2) { + for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) { + for (size_t kblock = minsize; kblock <= ksize; kblock *= 2) { + for (size_t mblock = minsize; mblock <= msize; mblock *= 2) { + for (size_t nblock = minsize; nblock <= nsize; nblock *= 2) { + benchmarks.emplace_back(ksize, msize, nsize, kblock, mblock, nblock); + } + } + } + } + } + } + } + + run_benchmarks(benchmarks); + + cout << "BEGIN MEASUREMENTS ALL POT SIZES" << endl; + for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) { + cout << *it << endl; + } + } +}; + +struct measure_default_sizes_action_t : action_t +{ + virtual const char* invokation_name() const { return "default-sizes"; } + virtual void run() const + { + vector benchmarks; + for (int repetition = 0; repetition < measurement_repetitions; repetition++) { + for (size_t ksize = minsize; ksize <= maxsize; ksize *= 2) { + for (size_t msize = minsize; msize <= maxsize; msize *= 2) { + for (size_t nsize = minsize; nsize <= maxsize; nsize *= 2) { + benchmarks.emplace_back(ksize, msize, nsize); + } + } + } + } + + run_benchmarks(benchmarks); + + cout << "BEGIN MEASUREMENTS DEFAULT SIZES" << endl; + for (auto it = benchmarks.begin(); it != benchmarks.end(); ++it) { + cout << *it << endl; + } + } +}; + +int main(int argc, char* argv[]) +{ + double time_start = timer.getRealTime(); + cout.precision(4); + cerr.precision(4); + + vector> available_actions; + available_actions.emplace_back(new measure_all_pot_sizes_action_t); + available_actions.emplace_back(new measure_default_sizes_action_t); + + auto action = available_actions.end(); + + if (argc <= 1) { + show_usage_and_exit(argc, argv, available_actions); + } + for (auto it = available_actions.begin(); it != available_actions.end(); ++it) { + if (!strcmp(argv[1], (*it)->invokation_name())) { + action = it; + break; + } + } + + if (action == available_actions.end()) { + show_usage_and_exit(argc, argv, available_actions); + } + + for (int i = 2; i < argc; i++) { + if (argv[i] == strstr(argv[i], "--min-working-set-size=")) { + const char* equals_sign = strchr(argv[i], '='); + min_working_set_size = strtoul(equals_sign+1, nullptr, 10); + } else { + cerr << "unrecognized option: " << argv[i] << endl << endl; + show_usage_and_exit(argc, argv, available_actions); + } + } + + print_cpuinfo(); + + cout << "benchmark parameters:" << endl; + cout << "pointer size: " << 8*sizeof(void*) << " bits" << endl; + cout << "scalar type: " << type_name() << endl; + cout << "packet size: " << internal::packet_traits::size << endl; + cout << "minsize = " << minsize << endl; + cout << "maxsize = " << maxsize << endl; + cout << "measurement_repetitions = " << measurement_repetitions << endl; + cout << "min_accurate_time = " << min_accurate_time << endl; + cout << "min_working_set_size = " << min_working_set_size; + if (min_working_set_size == 0) { + cout << " (try to outsize caches)"; + } + cout << endl << endl; + + (*action)->run(); + + double time_end = timer.getRealTime(); + cerr << "Finished in " << human_duration_t(time_end - time_start) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c721b908179ede86f57c56563b5dfb252aff4d2a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark.cpp @@ -0,0 +1,39 @@ +// g++ -O3 -DNDEBUG -DMATSIZE= benchmark.cpp -o benchmark && time ./benchmark + +#include + +#include + +#ifndef MATSIZE +#define MATSIZE 3 +#endif + +using namespace std; +using namespace Eigen; + +#ifndef REPEAT +#define REPEAT 40000000 +#endif + +#ifndef SCALAR +#define SCALAR double +#endif + +int main(int argc, char *argv[]) +{ + Matrix I = Matrix::Ones(); + Matrix m; + for(int i = 0; i < MATSIZE; i++) + for(int j = 0; j < MATSIZE; j++) + { + m(i,j) = (i+MATSIZE*j); + } + asm("#begin"); + for(int a = 0; a < REPEAT; a++) + { + m = Matrix::Ones() + 0.00005 * (m + (m*m)); + } + asm("#end"); + cout << m << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkSlice.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkSlice.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c5b89c545572c77e285e30231fed1c5f4330b693 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkSlice.cpp @@ -0,0 +1,38 @@ +// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX + +#include + +#include + +using namespace std; +using namespace Eigen; + +#ifndef REPEAT +#define REPEAT 10000 +#endif + +#ifndef SCALAR +#define SCALAR float +#endif + +int main(int argc, char *argv[]) +{ + typedef Matrix Mat; + Mat m(100, 100); + m.setRandom(); + + for(int a = 0; a < REPEAT; a++) + { + int r, c, nr, nc; + r = Eigen::internal::random(0,10); + c = Eigen::internal::random(0,10); + nr = Eigen::internal::random(50,80); + nc = Eigen::internal::random(50,80); + m.block(r,c,nr,nc) += Mat::Ones(nr,nc); + m.block(r,c,nr,nc) *= SCALAR(10); + m.block(r,c,nr,nc) -= Mat::constant(nr,nc,10); + m.block(r,c,nr,nc) /= SCALAR(10); + } + cout << m[0] << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkX.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkX.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8e4b60c2b7dd5718655a00317c3edba30014fd29 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkX.cpp @@ -0,0 +1,36 @@ +// g++ -fopenmp -I .. -O3 -DNDEBUG -finline-limit=1000 benchmarkX.cpp -o b && time ./b + +#include + +#include + +using namespace std; +using namespace Eigen; + +#ifndef MATTYPE +#define MATTYPE MatrixXLd +#endif + +#ifndef MATSIZE +#define MATSIZE 400 +#endif + +#ifndef REPEAT +#define REPEAT 100 +#endif + +int main(int argc, char *argv[]) +{ + MATTYPE I = MATTYPE::Ones(MATSIZE,MATSIZE); + MATTYPE m(MATSIZE,MATSIZE); + for(int i = 0; i < MATSIZE; i++) for(int j = 0; j < MATSIZE; j++) + { + m(i,j) = (i+j+1)/(MATSIZE*MATSIZE); + } + for(int a = 0; a < REPEAT; a++) + { + m = I + 0.0001 * (m + m*m); + } + cout << m(0,0) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkXcwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkXcwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..62437435efc25a090809b3caeb147e51aa0080ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmarkXcwise.cpp @@ -0,0 +1,35 @@ +// g++ -O3 -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX + +#include +#include + +using namespace std; +using namespace Eigen; + +#ifndef VECTYPE +#define VECTYPE VectorXLd +#endif + +#ifndef VECSIZE +#define VECSIZE 1000000 +#endif + +#ifndef REPEAT +#define REPEAT 1000 +#endif + +int main(int argc, char *argv[]) +{ + VECTYPE I = VECTYPE::Ones(VECSIZE); + VECTYPE m(VECSIZE,1); + for(int i = 0; i < VECSIZE; i++) + { + m[i] = 0.1 * i/VECSIZE; + } + for(int a = 0; a < REPEAT; a++) + { + m = VECTYPE::Ones(VECSIZE) + 0.00005 * (m.cwise().square() + m/4); + } + cout << m[0] << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark_suite b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark_suite new file mode 100644 index 0000000000000000000000000000000000000000..3f21d366178817a790340049dd3fcdab0f42b5a5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/benchmark_suite @@ -0,0 +1,18 @@ +#!/bin/bash +CXX=${CXX-g++} # default value unless caller has defined CXX +echo "Fixed size 3x3, column-major, -DNDEBUG" +$CXX -O3 -I .. -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null +echo "Fixed size 3x3, column-major, with asserts" +$CXX -O3 -I .. benchmark.cpp -o benchmark && time ./benchmark >/dev/null +echo "Fixed size 3x3, row-major, -DNDEBUG" +$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmark.cpp -o benchmark && time ./benchmark >/dev/null +echo "Fixed size 3x3, row-major, with asserts" +$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmark.cpp -o benchmark && time ./benchmark >/dev/null +echo "Dynamic size 20x20, column-major, -DNDEBUG" +$CXX -O3 -I .. -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null +echo "Dynamic size 20x20, column-major, with asserts" +$CXX -O3 -I .. benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null +echo "Dynamic size 20x20, row-major, -DNDEBUG" +$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR -DNDEBUG benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null +echo "Dynamic size 20x20, row-major, with asserts" +$CXX -O3 -I .. -DEIGEN_DEFAULT_TO_ROW_MAJOR benchmarkX.cpp -o benchmarkX && time ./benchmarkX >/dev/null diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..42094e867d29b4063419d30b58c1355c5e18cdf7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/CMakeLists.txt @@ -0,0 +1,107 @@ +project(BTL) + +cmake_minimum_required(VERSION 2.6.2) + +set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake ${Eigen_SOURCE_DIR}/cmake) +include(MacroOptionalAddSubdirectory) + +option(BTL_NOVEC "Disable SSE/Altivec optimizations when possible" OFF) + +set(CMAKE_INCLUDE_CURRENT_DIR ON) + +string(REGEX MATCH icpc IS_ICPC ${CMAKE_CXX_COMPILER}) +if(CMAKE_COMPILER_IS_GNUCXX OR IS_ICPC) + set(CMAKE_CXX_FLAGS "-g0 -O3 -DNDEBUG ${CMAKE_CXX_FLAGS}") + set(CMAKE_Fortran_FLAGS "-g0 -O3 -DNDEBUG ${CMAKE_Fortran_FLAGS}") + if(BTL_NOVEC) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -DEIGEN_DONT_VECTORIZE") + endif(BTL_NOVEC) +endif(CMAKE_COMPILER_IS_GNUCXX OR IS_ICPC) + +if(MSVC) + set(CMAKE_CXX_FLAGS " /O2 /Ot /GL /fp:fast -DNDEBUG") +# set(CMAKE_Fortran_FLAGS "-g0 -O3 -DNDEBUG") + if(BTL_NOVEC) + set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -DEIGEN_DONT_VECTORIZE") + endif(BTL_NOVEC) +endif(MSVC) + +if(IS_ICPC) + set(CMAKE_CXX_FLAGS "-fast ${CMAKE_CXX_FLAGS}") + set(CMAKE_Fortran_FLAGS "-fast ${CMAKE_Fortran_FLAGS}") +endif() + +include_directories( + ${PROJECT_SOURCE_DIR}/actions + ${PROJECT_SOURCE_DIR}/generic_bench + ${PROJECT_SOURCE_DIR}/generic_bench/utils + ${PROJECT_SOURCE_DIR}/libs/STL) + +# find_package(MKL) +# if (MKL_FOUND) +# add_definitions(-DHAVE_MKL) +# set(DEFAULT_LIBRARIES ${MKL_LIBRARIES}) +# endif () + +find_library(EIGEN_BTL_RT_LIBRARY rt) +# if we cannot find it easily, then we don't need it! +if(NOT EIGEN_BTL_RT_LIBRARY) + set(EIGEN_BTL_RT_LIBRARY "") +endif() + +macro(BTL_ADD_BENCH targetname) + + foreach(_current_var ${ARGN}) + set(_last_var ${_current_var}) + endforeach() + + set(_sources ${ARGN}) + list(LENGTH _sources _argn_length) + + list(REMOVE_ITEM _sources ON OFF TRUE FALSE) + + list(LENGTH _sources _src_length) + + if (${_argn_length} EQUAL ${_src_length}) + set(_last_var ON) + endif () + + option(BUILD_${targetname} "Build benchmark ${targetname}" ${_last_var}) + + if(BUILD_${targetname}) + add_executable(${targetname} ${_sources}) + add_test(${targetname} "${targetname}") + target_link_libraries(${targetname} ${DEFAULT_LIBRARIES} ${EIGEN_BTL_RT_LIBRARY}) + endif(BUILD_${targetname}) + +endmacro(BTL_ADD_BENCH) + +macro(btl_add_target_property target prop value) + + if(BUILD_${target}) + get_target_property(previous ${target} ${prop}) + if(NOT previous) + set(previous "") + endif() + set_target_properties(${target} PROPERTIES ${prop} "${previous} ${value}") + endif() + +endmacro() + +enable_testing() + +add_subdirectory(libs/eigen3) +add_subdirectory(libs/eigen2) +add_subdirectory(libs/tensors) +add_subdirectory(libs/BLAS) +add_subdirectory(libs/ublas) +add_subdirectory(libs/gmm) +add_subdirectory(libs/mtl4) +add_subdirectory(libs/blitz) +add_subdirectory(libs/tvmet) +add_subdirectory(libs/STL) +add_subdirectory(libs/blaze) + +add_subdirectory(data) + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/COPYING b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/COPYING new file mode 100644 index 0000000000000000000000000000000000000000..486449cc3a4ea92893622b41c5a24ee0b6c96499 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/COPYING @@ -0,0 +1,340 @@ + GNU GENERAL PUBLIC LICENSE + Version 2, June 1991 + + Copyright (C) 1989, 1991 Free Software Foundation, Inc. + 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The licenses for most software are designed to take away your +freedom to share and change it. By contrast, the GNU General Public +License is intended to guarantee your freedom to share and change free +software--to make sure the software is free for all its users. This +General Public License applies to most of the Free Software +Foundation's software and to any other program whose authors commit to +using it. (Some other Free Software Foundation software is covered by +the GNU Library General Public License instead.) You can apply it to +your programs, too. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +this service if you wish), that you receive source code or can get it +if you want it, that you can change the software or use pieces of it +in new free programs; and that you know you can do these things. + + To protect your rights, we need to make restrictions that forbid +anyone to deny you these rights or to ask you to surrender the rights. +These restrictions translate to certain responsibilities for you if you +distribute copies of the software, or if you modify it. + + For example, if you distribute copies of such a program, whether +gratis or for a fee, you must give the recipients all the rights that +you have. You must make sure that they, too, receive or can get the +source code. And you must show them these terms so they know their +rights. + + We protect your rights with two steps: (1) copyright the software, and +(2) offer you this license which gives you legal permission to copy, +distribute and/or modify the software. + + Also, for each author's protection and ours, we want to make certain +that everyone understands that there is no warranty for this free +software. If the software is modified by someone else and passed on, we +want its recipients to know that what they have is not the original, so +that any problems introduced by others will not reflect on the original +authors' reputations. + + Finally, any free program is threatened constantly by software +patents. We wish to avoid the danger that redistributors of a free +program will individually obtain patent licenses, in effect making the +program proprietary. To prevent this, we have made it clear that any +patent must be licensed for everyone's free use or not licensed at all. + + The precise terms and conditions for copying, distribution and +modification follow. + + GNU GENERAL PUBLIC LICENSE + TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION + + 0. This License applies to any program or other work which contains +a notice placed by the copyright holder saying it may be distributed +under the terms of this General Public License. The "Program", below, +refers to any such program or work, and a "work based on the Program" +means either the Program or any derivative work under copyright law: +that is to say, a work containing the Program or a portion of it, +either verbatim or with modifications and/or translated into another +language. (Hereinafter, translation is included without limitation in +the term "modification".) Each licensee is addressed as "you". + +Activities other than copying, distribution and modification are not +covered by this License; they are outside its scope. The act of +running the Program is not restricted, and the output from the Program +is covered only if its contents constitute a work based on the +Program (independent of having been made by running the Program). +Whether that is true depends on what the Program does. + + 1. You may copy and distribute verbatim copies of the Program's +source code as you receive it, in any medium, provided that you +conspicuously and appropriately publish on each copy an appropriate +copyright notice and disclaimer of warranty; keep intact all the +notices that refer to this License and to the absence of any warranty; +and give any other recipients of the Program a copy of this License +along with the Program. + +You may charge a fee for the physical act of transferring a copy, and +you may at your option offer warranty protection in exchange for a fee. + + 2. You may modify your copy or copies of the Program or any portion +of it, thus forming a work based on the Program, and copy and +distribute such modifications or work under the terms of Section 1 +above, provided that you also meet all of these conditions: + + a) You must cause the modified files to carry prominent notices + stating that you changed the files and the date of any change. + + b) You must cause any work that you distribute or publish, that in + whole or in part contains or is derived from the Program or any + part thereof, to be licensed as a whole at no charge to all third + parties under the terms of this License. + + c) If the modified program normally reads commands interactively + when run, you must cause it, when started running for such + interactive use in the most ordinary way, to print or display an + announcement including an appropriate copyright notice and a + notice that there is no warranty (or else, saying that you provide + a warranty) and that users may redistribute the program under + these conditions, and telling the user how to view a copy of this + License. (Exception: if the Program itself is interactive but + does not normally print such an announcement, your work based on + the Program is not required to print an announcement.) + +These requirements apply to the modified work as a whole. If +identifiable sections of that work are not derived from the Program, +and can be reasonably considered independent and separate works in +themselves, then this License, and its terms, do not apply to those +sections when you distribute them as separate works. But when you +distribute the same sections as part of a whole which is a work based +on the Program, the distribution of the whole must be on the terms of +this License, whose permissions for other licensees extend to the +entire whole, and thus to each and every part regardless of who wrote it. + +Thus, it is not the intent of this section to claim rights or contest +your rights to work written entirely by you; rather, the intent is to +exercise the right to control the distribution of derivative or +collective works based on the Program. + +In addition, mere aggregation of another work not based on the Program +with the Program (or with a work based on the Program) on a volume of +a storage or distribution medium does not bring the other work under +the scope of this License. + + 3. You may copy and distribute the Program (or a work based on it, +under Section 2) in object code or executable form under the terms of +Sections 1 and 2 above provided that you also do one of the following: + + a) Accompany it with the complete corresponding machine-readable + source code, which must be distributed under the terms of Sections + 1 and 2 above on a medium customarily used for software interchange; or, + + b) Accompany it with a written offer, valid for at least three + years, to give any third party, for a charge no more than your + cost of physically performing source distribution, a complete + machine-readable copy of the corresponding source code, to be + distributed under the terms of Sections 1 and 2 above on a medium + customarily used for software interchange; or, + + c) Accompany it with the information you received as to the offer + to distribute corresponding source code. (This alternative is + allowed only for noncommercial distribution and only if you + received the program in object code or executable form with such + an offer, in accord with Subsection b above.) + +The source code for a work means the preferred form of the work for +making modifications to it. For an executable work, complete source +code means all the source code for all modules it contains, plus any +associated interface definition files, plus the scripts used to +control compilation and installation of the executable. However, as a +special exception, the source code distributed need not include +anything that is normally distributed (in either source or binary +form) with the major components (compiler, kernel, and so on) of the +operating system on which the executable runs, unless that component +itself accompanies the executable. + +If distribution of executable or object code is made by offering +access to copy from a designated place, then offering equivalent +access to copy the source code from the same place counts as +distribution of the source code, even though third parties are not +compelled to copy the source along with the object code. + + 4. You may not copy, modify, sublicense, or distribute the Program +except as expressly provided under this License. Any attempt +otherwise to copy, modify, sublicense or distribute the Program is +void, and will automatically terminate your rights under this License. +However, parties who have received copies, or rights, from you under +this License will not have their licenses terminated so long as such +parties remain in full compliance. + + 5. You are not required to accept this License, since you have not +signed it. However, nothing else grants you permission to modify or +distribute the Program or its derivative works. These actions are +prohibited by law if you do not accept this License. Therefore, by +modifying or distributing the Program (or any work based on the +Program), you indicate your acceptance of this License to do so, and +all its terms and conditions for copying, distributing or modifying +the Program or works based on it. + + 6. Each time you redistribute the Program (or any work based on the +Program), the recipient automatically receives a license from the +original licensor to copy, distribute or modify the Program subject to +these terms and conditions. You may not impose any further +restrictions on the recipients' exercise of the rights granted herein. +You are not responsible for enforcing compliance by third parties to +this License. + + 7. If, as a consequence of a court judgment or allegation of patent +infringement or for any other reason (not limited to patent issues), +conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot +distribute so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you +may not distribute the Program at all. For example, if a patent +license would not permit royalty-free redistribution of the Program by +all those who receive copies directly or indirectly through you, then +the only way you could satisfy both it and this License would be to +refrain entirely from distribution of the Program. + +If any portion of this section is held invalid or unenforceable under +any particular circumstance, the balance of the section is intended to +apply and the section as a whole is intended to apply in other +circumstances. + +It is not the purpose of this section to induce you to infringe any +patents or other property right claims or to contest validity of any +such claims; this section has the sole purpose of protecting the +integrity of the free software distribution system, which is +implemented by public license practices. Many people have made +generous contributions to the wide range of software distributed +through that system in reliance on consistent application of that +system; it is up to the author/donor to decide if he or she is willing +to distribute software through any other system and a licensee cannot +impose that choice. + +This section is intended to make thoroughly clear what is believed to +be a consequence of the rest of this License. + + 8. If the distribution and/or use of the Program is restricted in +certain countries either by patents or by copyrighted interfaces, the +original copyright holder who places the Program under this License +may add an explicit geographical distribution limitation excluding +those countries, so that distribution is permitted only in or among +countries not thus excluded. In such case, this License incorporates +the limitation as if written in the body of this License. + + 9. The Free Software Foundation may publish revised and/or new versions +of the General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + +Each version is given a distinguishing version number. If the Program +specifies a version number of this License which applies to it and "any +later version", you have the option of following the terms and conditions +either of that version or of any later version published by the Free +Software Foundation. If the Program does not specify a version number of +this License, you may choose any version ever published by the Free Software +Foundation. + + 10. If you wish to incorporate parts of the Program into other free +programs whose distribution conditions are different, write to the author +to ask for permission. For software which is copyrighted by the Free +Software Foundation, write to the Free Software Foundation; we sometimes +make exceptions for this. Our decision will be guided by the two goals +of preserving the free status of all derivatives of our free software and +of promoting the sharing and reuse of software generally. + + NO WARRANTY + + 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY +FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN +OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES +PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED +OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF +MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS +TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE +PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, +REPAIR OR CORRECTION. + + 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR +REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, +INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING +OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED +TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY +YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER +PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE +POSSIBILITY OF SUCH DAMAGES. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +convey the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software; you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 2 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program; if not, write to the Free Software + Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + + +Also add information on how to contact you by electronic and paper mail. + +If the program is interactive, make it output a short notice like this +when it starts in an interactive mode: + + Gnomovision version 69, Copyright (C) year name of author + Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, the commands you use may +be called something other than `show w' and `show c'; they could even be +mouse-clicks or menu items--whatever suits your program. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the program, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the program + `Gnomovision' (which makes passes at compilers) written by James Hacker. + + , 1 April 1989 + Ty Coon, President of Vice + +This General Public License does not permit incorporating your program into +proprietary programs. If your program is a subroutine library, you may +consider it more useful to permit linking proprietary applications with the +library. If this is what you want to do, use the GNU Library General +Public License instead of this License. diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/README b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/README new file mode 100644 index 0000000000000000000000000000000000000000..ebed8896078fe7050e647266acc04af0e112e3cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/README @@ -0,0 +1,154 @@ +Bench Template Library + +**************************************** +Introduction : + +The aim of this project is to compare the performance +of available numerical libraries. The code is designed +as generic and modular as possible. Thus, adding new +numerical libraries or new numerical tests should +require minimal effort. + + +***************************************** + +Installation : + +BTL uses cmake / ctest: + +1 - create a build directory: + + $ mkdir build + $ cd build + +2 - configure: + + $ ccmake .. + +3 - run the bench using ctest: + + $ ctest -V + +You can run the benchmarks only on libraries matching a given regular expression: + ctest -V -R +For instance: + ctest -V -R eigen2 + +You can also select a given set of actions defining the environment variable BTL_CONFIG this way: + BTL_CONFIG="-a action1{:action2}*" ctest -V +An example: + BTL_CONFIG="-a axpy:vector_matrix:trisolve:ata" ctest -V -R eigen2 + +Finally, if bench results already exist (the bench*.dat files) then they merges by keeping the best for each matrix size. If you want to overwrite the previous ones you can simply add the "--overwrite" option: + BTL_CONFIG="-a axpy:vector_matrix:trisolve:ata --overwrite" ctest -V -R eigen2 + +4 : Analyze the result. different data files (.dat) are produced in each libs directories. + If gnuplot is available, choose a directory name in the data directory to store the results and type: + $ cd data + $ mkdir my_directory + $ cp ../libs/*/*.dat my_directory + Build the data utilities in this (data) directory + make + Then you can look the raw data, + go_mean my_directory + or smooth the data first : + smooth_all.sh my_directory + go_mean my_directory_smooth + + +************************************************* + +Files and directories : + + generic_bench : all the bench sources common to all libraries + + actions : sources for different action wrappers (axpy, matrix-matrix product) to be tested. + + libs/* : bench sources specific to each tested libraries. + + machine_dep : directory used to store machine specific Makefile.in + + data : directory used to store gnuplot scripts and data analysis utilities + +************************************************** + +Principles : the code modularity is achieved by defining two concepts : + + ****** Action concept : This is a class defining which kind + of test must be performed (e.g. a matrix_vector_product). + An Action should define the following methods : + + *** Ctor using the size of the problem (matrix or vector size) as an argument + Action action(size); + *** initialize : this method initialize the calculation (e.g. initialize the matrices and vectors arguments) + action.initialize(); + *** calculate : this method actually launch the calculation to be benchmarked + action.calculate; + *** nb_op_base() : this method returns the complexity of the calculate method (allowing the mflops evaluation) + *** name() : this method returns the name of the action (std::string) + + ****** Interface concept : This is a class or namespace defining how to use a given library and + its specific containers (matrix and vector). Up to now an interface should following types + + *** real_type : kind of float to be used (float or double) + *** stl_vector : must correspond to std::vector + *** stl_matrix : must correspond to std::vector + *** gene_vector : the vector type for this interface --> e.g. (real_type *) for the C_interface + *** gene_matrix : the matrix type for this interface --> e.g. (gene_vector *) for the C_interface + + + the following common methods + + *** free_matrix(gene_matrix & A, int N) dealocation of a N sized gene_matrix A + *** free_vector(gene_vector & B) dealocation of a N sized gene_vector B + *** matrix_from_stl(gene_matrix & A, stl_matrix & A_stl) copy the content of an stl_matrix A_stl into a gene_matrix A. + The allocation of A is done in this function. + *** vector_to_stl(gene_vector & B, stl_vector & B_stl) copy the content of an stl_vector B_stl into a gene_vector B. + The allocation of B is done in this function. + *** matrix_to_stl(gene_matrix & A, stl_matrix & A_stl) copy the content of an gene_matrix A into an stl_matrix A_stl. + The size of A_STL must corresponds to the size of A. + *** vector_to_stl(gene_vector & A, stl_vector & A_stl) copy the content of an gene_vector A into an stl_vector A_stl. + The size of B_STL must corresponds to the size of B. + *** copy_matrix(gene_matrix & source, gene_matrix & cible, int N) : copy the content of source in cible. Both source + and cible must be sized NxN. + *** copy_vector(gene_vector & source, gene_vector & cible, int N) : copy the content of source in cible. Both source + and cible must be sized N. + + and the following method corresponding to the action one wants to be benchmarked : + + *** matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int N) + *** matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N) + *** ata_product(const gene_matrix & A, gene_matrix & X, int N) + *** aat_product(const gene_matrix & A, gene_matrix & X, int N) + *** axpy(real coef, const gene_vector & X, gene_vector & Y, int N) + + The bench algorithm (generic_bench/bench.hh) is templated with an action itself templated with + an interface. A typical main.cpp source stored in a given library directory libs/A_LIB + looks like : + + bench< AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ; + + this function will produce XY data file containing measured mflops as a function of the size for 50 + sizes between 10 and 10000. + + This algorithm can be adapted by providing a given Perf_Analyzer object which determines how the time + measurements must be done. For example, the X86_Perf_Analyzer use the asm rdtsc function and provides + a very fast and accurate (but less portable) timing method. The default is the Portable_Perf_Analyzer + so + + bench< AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ; + + is equivalent to + + bench< Portable_Perf_Analyzer,AN_ACTION < AN_INTERFACE > >( 10 , 1000 , 50 ) ; + + If your system supports it we suggest to use a mixed implementation (X86_perf_Analyzer+Portable_Perf_Analyzer). + replace + bench(size_min,size_max,nb_point); + with + bench(size_min,size_max,nb_point); + in generic/bench.hh + +. + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_aat_product.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_aat_product.hh new file mode 100644 index 0000000000000000000000000000000000000000..aa5b35c94f298eb7775f49ddf93836135e6829ce --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_aat_product.hh @@ -0,0 +1,145 @@ +//===================================================== +// File : action_aat_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_AAT_PRODUCT +#define ACTION_AAT_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_aat_product { + +public : + + // Ctor + + Action_aat_product( int size ):_size(size) + { + MESSAGE("Action_aat_product Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_matrix(X_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(X_ref,X_stl); + + Interface::matrix_from_stl(A,A_stl); + Interface::matrix_from_stl(X,X_stl); + + } + + // invalidate copy ctor + + Action_aat_product( const Action_aat_product & ) + { + INFOS("illegal call to Action_aat_product Copy Ctor"); + exit(0); + } + + // Dtor + + ~Action_aat_product( void ){ + + MESSAGE("Action_aat_product Dtor"); + + // deallocation + + Interface::free_matrix(A,_size); + Interface::free_matrix(X,_size); + + Interface::free_matrix(A_ref,_size); + Interface::free_matrix(X_ref,_size); + + } + + // action name + + static inline std::string name( void ) + { + return "aat_"+Interface::name(); + } + + double nb_op_base( void ){ + return double(_size)*double(_size)*double(_size); + } + + inline void initialize( void ){ + + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_matrix(X_ref,X,_size); + + } + + inline void calculate( void ) { + + Interface::aat_product(A,X,_size); + + } + + void check_result( void ){ + if (_size>128) return; + // calculation check + + Interface::matrix_to_stl(X,resu_stl); + + STL_interface::aat_product(A_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(1); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix X; + + + int _size; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ata_product.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ata_product.hh new file mode 100644 index 0000000000000000000000000000000000000000..04364fe6756e071477f8dd19d975168ad5a904a2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ata_product.hh @@ -0,0 +1,145 @@ +//===================================================== +// File : action_ata_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_ATA_PRODUCT +#define ACTION_ATA_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_ata_product { + +public : + + // Ctor + + Action_ata_product( int size ):_size(size) + { + MESSAGE("Action_ata_product Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_matrix(X_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(X_ref,X_stl); + + Interface::matrix_from_stl(A,A_stl); + Interface::matrix_from_stl(X,X_stl); + + } + + // invalidate copy ctor + + Action_ata_product( const Action_ata_product & ) + { + INFOS("illegal call to Action_ata_product Copy Ctor"); + exit(0); + } + + // Dtor + + ~Action_ata_product( void ){ + + MESSAGE("Action_ata_product Dtor"); + + // deallocation + + Interface::free_matrix(A,_size); + Interface::free_matrix(X,_size); + + Interface::free_matrix(A_ref,_size); + Interface::free_matrix(X_ref,_size); + + } + + // action name + + static inline std::string name( void ) + { + return "ata_"+Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size*_size; + } + + inline void initialize( void ){ + + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_matrix(X_ref,X,_size); + + } + + inline void calculate( void ) { + + Interface::ata_product(A,X,_size); + + } + + void check_result( void ){ + if (_size>128) return; + // calculation check + + Interface::matrix_to_stl(X,resu_stl); + + STL_interface::ata_product(A_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(1); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix X; + + + int _size; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_atv_product.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_atv_product.hh new file mode 100644 index 0000000000000000000000000000000000000000..a8234514bff380873d82f181e866db67b42918b2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_atv_product.hh @@ -0,0 +1,134 @@ +//===================================================== +// File : action_atv_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_ATV_PRODUCT +#define ACTION_ATV_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_atv_product { + +public : + + Action_atv_product( int size ) : _size(size) + { + MESSAGE("Action_atv_product Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(X_ref,X_stl); + + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X,X_stl); + } + + // invalidate copy ctor + Action_atv_product( const Action_atv_product & ) + { + INFOS("illegal call to Action_atv_product Copy Ctor"); + exit(1); + } + + ~Action_atv_product( void ) + { + MESSAGE("Action_atv_product Dtor"); + + Interface::free_matrix(A,_size); + Interface::free_vector(B); + Interface::free_vector(X); + + Interface::free_matrix(A_ref,_size); + Interface::free_vector(B_ref); + Interface::free_vector(X_ref); + } + + static inline std::string name() { return "atv_" + Interface::name(); } + + double nb_op_base( void ) { return 2.0*_size*_size; } + + inline void initialize( void ){ + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + Interface::copy_vector(X_ref,X,_size); + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("begin atv"); + Interface::atv_product(A,B,X,_size); + BTL_ASM_COMMENT("end atv"); + } + + void check_result( void ) + { + if (_size>128) return; + Interface::vector_to_stl(X,resu_stl); + + STL_interface::atv_product(A_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(1); + } + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_vector B_ref; + typename Interface::gene_vector X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + + int _size; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpby.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpby.hh new file mode 100644 index 0000000000000000000000000000000000000000..dadd0ccf3ca0340f8643a7d373d689245b9c819c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpby.hh @@ -0,0 +1,127 @@ +//===================================================== +// File : action_axpby.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_AXPBY +#define ACTION_AXPBY +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_axpby { + +public : + + // Ctor + Action_axpby( int size ):_alpha(0.5),_beta(0.95),_size(size) + { + MESSAGE("Action_axpby Ctor"); + + // STL vector initialization + init_vector(X_stl,_size); + init_vector(Y_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(Y_ref,Y_stl); + + Interface::vector_from_stl(X,X_stl); + Interface::vector_from_stl(Y,Y_stl); + } + + // invalidate copy ctor + Action_axpby( const Action_axpby & ) + { + INFOS("illegal call to Action_axpby Copy Ctor"); + exit(1); + } + + // Dtor + ~Action_axpby( void ){ + MESSAGE("Action_axpby Dtor"); + + // deallocation + Interface::free_vector(X_ref); + Interface::free_vector(Y_ref); + + Interface::free_vector(X); + Interface::free_vector(Y); + } + + // action name + static inline std::string name( void ) + { + return "axpby_"+Interface::name(); + } + + double nb_op_base( void ){ + return 3.0*_size; + } + + inline void initialize( void ){ + Interface::copy_vector(X_ref,X,_size); + Interface::copy_vector(Y_ref,Y,_size); + } + + inline void calculate( void ) { + BTL_ASM_COMMENT("mybegin axpby"); + Interface::axpby(_alpha,X,_beta,Y,_size); + BTL_ASM_COMMENT("myend axpby"); + } + + void check_result( void ){ + if (_size>128) return; + // calculation check + Interface::vector_to_stl(Y,resu_stl); + + STL_interface::axpby(_alpha,X_stl,_beta,Y_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(Y_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(2); + } + } + +private : + + typename Interface::stl_vector X_stl; + typename Interface::stl_vector Y_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_vector X_ref; + typename Interface::gene_vector Y_ref; + + typename Interface::gene_vector X; + typename Interface::gene_vector Y; + + typename Interface::real_type _alpha; + typename Interface::real_type _beta; + + int _size; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpy.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpy.hh new file mode 100644 index 0000000000000000000000000000000000000000..261be4cb8eb9dca0b673852330ab40291ee07d29 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_axpy.hh @@ -0,0 +1,139 @@ +//===================================================== +// File : action_axpy.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_AXPY +#define ACTION_AXPY +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_axpy { + +public : + + // Ctor + + Action_axpy( int size ):_coef(1.0),_size(size) + { + MESSAGE("Action_axpy Ctor"); + + // STL vector initialization + + init_vector(X_stl,_size); + init_vector(Y_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(Y_ref,Y_stl); + + Interface::vector_from_stl(X,X_stl); + Interface::vector_from_stl(Y,Y_stl); + + + } + + // invalidate copy ctor + + Action_axpy( const Action_axpy & ) + { + INFOS("illegal call to Action_axpy Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_axpy( void ){ + + MESSAGE("Action_axpy Dtor"); + + // deallocation + + Interface::free_vector(X_ref); + Interface::free_vector(Y_ref); + + Interface::free_vector(X); + Interface::free_vector(Y); + } + + // action name + + static inline std::string name( void ) + { + return "axpy_"+Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size; + } + + inline void initialize( void ){ + Interface::copy_vector(X_ref,X,_size); + Interface::copy_vector(Y_ref,Y,_size); + } + + inline void calculate( void ) { + BTL_ASM_COMMENT("mybegin axpy"); + Interface::axpy(_coef,X,Y,_size); + BTL_ASM_COMMENT("myend axpy"); + } + + void check_result( void ){ + if (_size>128) return; + // calculation check + + Interface::vector_to_stl(Y,resu_stl); + + STL_interface::axpy(_coef,X_stl,Y_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(Y_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(0); + } + + } + +private : + + typename Interface::stl_vector X_stl; + typename Interface::stl_vector Y_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_vector X_ref; + typename Interface::gene_vector Y_ref; + + typename Interface::gene_vector X; + typename Interface::gene_vector Y; + + typename Interface::real_type _coef; + + int _size; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_cholesky.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_cholesky.hh new file mode 100644 index 0000000000000000000000000000000000000000..5f66d113afe0d721a9a3d048db5c3f27275fed64 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_cholesky.hh @@ -0,0 +1,128 @@ +//===================================================== +// File : action_cholesky.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_CHOLESKY +#define ACTION_CHOLESKY +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_cholesky { + +public : + + // Ctor + + Action_cholesky( int size ):_size(size) + { + MESSAGE("Action_cholesky Ctor"); + + // STL mat/vec initialization + init_matrix_symm(X_stl,_size); + init_matrix(C_stl,_size); + + // make sure X is invertible + for (int i=0; i<_size; ++i) + X_stl[i][i] = std::abs(X_stl[i][i]) * 1e2 + 100; + + // generic matrix and vector initialization + Interface::matrix_from_stl(X_ref,X_stl); + Interface::matrix_from_stl(X,X_stl); + Interface::matrix_from_stl(C,C_stl); + + _cost = 0; + for (int j=0; j<_size; ++j) + { + double r = std::max(_size - j -1,0); + _cost += 2*(r*j+r+j); + } + } + + // invalidate copy ctor + + Action_cholesky( const Action_cholesky & ) + { + INFOS("illegal call to Action_cholesky Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_cholesky( void ){ + + MESSAGE("Action_cholesky Dtor"); + + // deallocation + Interface::free_matrix(X_ref,_size); + Interface::free_matrix(X,_size); + Interface::free_matrix(C,_size); + } + + // action name + + static inline std::string name( void ) + { + return "cholesky_"+Interface::name(); + } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + Interface::copy_matrix(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::cholesky(X,C,_size); + } + + void check_result( void ){ + // calculation check +// STL_interface::cholesky(X_stl,C_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(C_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix C_stl; + + typename Interface::gene_matrix X_ref; + typename Interface::gene_matrix X; + typename Interface::gene_matrix C; + + int _size; + double _cost; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ger.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ger.hh new file mode 100644 index 0000000000000000000000000000000000000000..dc766efc597ff184a46672c09157a12b10d57d03 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_ger.hh @@ -0,0 +1,128 @@ + +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_GER +#define ACTION_GER +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_ger { + +public : + + // Ctor + BTL_DONT_INLINE Action_ger( int size ):_size(size) + { + MESSAGE("Action_ger Ctor"); + + // STL matrix and vector initialization + typename Interface::stl_matrix tmp; + init_matrix(A_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(X,X_stl); + } + + // invalidate copy ctor + Action_ger( const Action_ger & ) + { + INFOS("illegal call to Action_ger Copy Ctor"); + exit(1); + } + + // Dtor + BTL_DONT_INLINE ~Action_ger( void ){ + MESSAGE("Action_ger Dtor"); + Interface::free_matrix(A,_size); + Interface::free_vector(B); + Interface::free_vector(X); + Interface::free_matrix(A_ref,_size); + Interface::free_vector(B_ref); + Interface::free_vector(X_ref); + + } + + // action name + static inline std::string name( void ) + { + return "ger_" + Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size; + } + + BTL_DONT_INLINE void initialize( void ){ + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + Interface::copy_vector(X_ref,X,_size); + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("#begin ger"); + Interface::ger(A,B,X,_size); + BTL_ASM_COMMENT("end ger"); + } + + BTL_DONT_INLINE void check_result( void ){ + // calculation check + Interface::vector_to_stl(X,resu_stl); + + STL_interface::ger(A_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-3){ + INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_vector B_ref; + typename Interface::gene_vector X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + int _size; +}; + + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_hessenberg.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_hessenberg.hh new file mode 100644 index 0000000000000000000000000000000000000000..2100ebd89053072ffc9341ffa49d0c875cdb9138 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_hessenberg.hh @@ -0,0 +1,233 @@ +//===================================================== +// File : action_hessenberg.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_HESSENBERG +#define ACTION_HESSENBERG +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_hessenberg { + +public : + + // Ctor + + Action_hessenberg( int size ):_size(size) + { + MESSAGE("Action_hessenberg Ctor"); + + // STL vector initialization + init_matrix(X_stl,_size); + + init_matrix(C_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(X_ref,X_stl); + Interface::matrix_from_stl(X,X_stl); + Interface::matrix_from_stl(C,C_stl); + + _cost = 0; + for (int j=0; j<_size-2; ++j) + { + double r = std::max(0,_size-j-1); + double b = std::max(0,_size-j-2); + _cost += 6 + 3*b + r*r*4 + r*_size*4; + } + } + + // invalidate copy ctor + + Action_hessenberg( const Action_hessenberg & ) + { + INFOS("illegal call to Action_hessenberg Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_hessenberg( void ){ + + MESSAGE("Action_hessenberg Dtor"); + + // deallocation + Interface::free_matrix(X_ref,_size); + Interface::free_matrix(X,_size); + Interface::free_matrix(C,_size); + } + + // action name + + static inline std::string name( void ) + { + return "hessenberg_"+Interface::name(); + } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + Interface::copy_matrix(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::hessenberg(X,C,_size); + } + + void check_result( void ){ + // calculation check + Interface::matrix_to_stl(C,resu_stl); + +// STL_interface::hessenberg(X_stl,C_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(C_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix C_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix X_ref; + typename Interface::gene_matrix X; + typename Interface::gene_matrix C; + + int _size; + double _cost; +}; + +template +class Action_tridiagonalization { + +public : + + // Ctor + + Action_tridiagonalization( int size ):_size(size) + { + MESSAGE("Action_tridiagonalization Ctor"); + + // STL vector initialization + init_matrix(X_stl,_size); + + for(int i=0; i<_size; ++i) + { + for(int j=0; j(C_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(X_ref,X_stl); + Interface::matrix_from_stl(X,X_stl); + Interface::matrix_from_stl(C,C_stl); + + _cost = 0; + for (int j=0; j<_size-2; ++j) + { + double r = std::max(0,_size-j-1); + double b = std::max(0,_size-j-2); + _cost += 6. + 3.*b + r*r*8.; + } + } + + // invalidate copy ctor + + Action_tridiagonalization( const Action_tridiagonalization & ) + { + INFOS("illegal call to Action_tridiagonalization Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_tridiagonalization( void ){ + + MESSAGE("Action_tridiagonalization Dtor"); + + // deallocation + Interface::free_matrix(X_ref,_size); + Interface::free_matrix(X,_size); + Interface::free_matrix(C,_size); + } + + // action name + + static inline std::string name( void ) { return "tridiagonalization_"+Interface::name(); } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + Interface::copy_matrix(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::tridiagonalization(X,C,_size); + } + + void check_result( void ){ + // calculation check + Interface::matrix_to_stl(C,resu_stl); + +// STL_interface::tridiagonalization(X_stl,C_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(C_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix C_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix X_ref; + typename Interface::gene_matrix X; + typename Interface::gene_matrix C; + + int _size; + double _cost; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_decomp.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_decomp.hh new file mode 100644 index 0000000000000000000000000000000000000000..2448e82c42bddfecbe25d070c0c5df061bf70579 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_decomp.hh @@ -0,0 +1,124 @@ +//===================================================== +// File : action_lu_decomp.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_LU_DECOMP +#define ACTION_LU_DECOMP +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_lu_decomp { + +public : + + // Ctor + + Action_lu_decomp( int size ):_size(size) + { + MESSAGE("Action_lu_decomp Ctor"); + + // STL vector initialization + init_matrix(X_stl,_size); + + init_matrix(C_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(X_ref,X_stl); + Interface::matrix_from_stl(X,X_stl); + Interface::matrix_from_stl(C,C_stl); + + _cost = 2.0*size*size*size/3.0 + size*size; + } + + // invalidate copy ctor + + Action_lu_decomp( const Action_lu_decomp & ) + { + INFOS("illegal call to Action_lu_decomp Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_lu_decomp( void ){ + + MESSAGE("Action_lu_decomp Dtor"); + + // deallocation + Interface::free_matrix(X_ref,_size); + Interface::free_matrix(X,_size); + Interface::free_matrix(C,_size); + } + + // action name + + static inline std::string name( void ) + { + return "complete_lu_decomp_"+Interface::name(); + } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + Interface::copy_matrix(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::lu_decomp(X,C,_size); + } + + void check_result( void ){ + // calculation check + Interface::matrix_to_stl(C,resu_stl); + +// STL_interface::lu_decomp(X_stl,C_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(C_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix C_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix X_ref; + typename Interface::gene_matrix X; + typename Interface::gene_matrix C; + + int _size; + double _cost; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_solve.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_solve.hh new file mode 100644 index 0000000000000000000000000000000000000000..5a81e6341ea4e4247cd91228b365b63033944139 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_lu_solve.hh @@ -0,0 +1,136 @@ +//===================================================== +// File : action_lu_solve.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_LU_SOLVE +#define ACTION_LU_SOLVE +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_lu_solve +{ + +public : + + static inline std::string name( void ) + { + return "lu_solve_"+Interface::name(); + } + + static double nb_op_base(int size){ + return 2.0*size*size*size/3.0; // questionable but not really important + } + + + static double calculate( int nb_calc, int size ) { + + // STL matrix and vector initialization + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + + init_matrix(A_stl,size); + init_vector(B_stl,size); + init_vector(X_stl,size); + + // generic matrix and vector initialization + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + typename Interface::gene_matrix LU; + + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X,X_stl); + Interface::matrix_from_stl(LU,A_stl); + + // local variable : + + typename Interface::Pivot_Vector pivot; // pivot vector + Interface::new_Pivot_Vector(pivot,size); + + // timer utilities + + Portable_Timer chronos; + + // time measurement + + chronos.start(); + + for (int ii=0;ii::matrix_vector_product(A_stl,X_stl,B_new_stl,size); + + typename Interface::real_type error= + STL_interface::norm_diff(B_stl,B_new_stl); + + if (error>1.e-5){ + INFOS("WRONG CALCULATION...residual=" << error); + STL_interface::display_vector(B_stl); + STL_interface::display_vector(B_new_stl); + exit(0); + } + + // deallocation and return time + + Interface::free_matrix(A,size); + Interface::free_vector(B); + Interface::free_vector(X); + Interface::free_Pivot_Vector(pivot); + + return time; + } + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product.hh new file mode 100644 index 0000000000000000000000000000000000000000..f65ee0529090b77efe326bb2c6b13d8a0b913dd2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product.hh @@ -0,0 +1,150 @@ +//===================================================== +// File : action_matrix_matrix_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_MATRIX_MATRIX_PRODUCT +#define ACTION_MATRIX_MATRIX_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_matrix_matrix_product { + +public : + + // Ctor + + Action_matrix_matrix_product( int size ):_size(size) + { + MESSAGE("Action_matrix_matrix_product Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_matrix(B_stl,_size); + init_matrix(X_stl,_size); + init_matrix(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(B_ref,B_stl); + Interface::matrix_from_stl(X_ref,X_stl); + + Interface::matrix_from_stl(A,A_stl); + Interface::matrix_from_stl(B,B_stl); + Interface::matrix_from_stl(X,X_stl); + + } + + // invalidate copy ctor + + Action_matrix_matrix_product( const Action_matrix_matrix_product & ) + { + INFOS("illegal call to Action_matrix_matrix_product Copy Ctor"); + exit(0); + } + + // Dtor + + ~Action_matrix_matrix_product( void ){ + + MESSAGE("Action_matrix_matrix_product Dtor"); + + // deallocation + + Interface::free_matrix(A,_size); + Interface::free_matrix(B,_size); + Interface::free_matrix(X,_size); + + Interface::free_matrix(A_ref,_size); + Interface::free_matrix(B_ref,_size); + Interface::free_matrix(X_ref,_size); + + } + + // action name + + static inline std::string name( void ) + { + return "matrix_matrix_"+Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size*_size; + } + + inline void initialize( void ){ + + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_matrix(B_ref,B,_size); + Interface::copy_matrix(X_ref,X,_size); + + } + + inline void calculate( void ) { + Interface::matrix_matrix_product(A,B,X,_size); + } + + void check_result( void ){ + + // calculation check + if (_size<200) + { + Interface::matrix_to_stl(X,resu_stl); + STL_interface::matrix_matrix_product(A_stl,B_stl,X_stl,_size); + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(1); + } + } + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix B_stl; + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix B_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix B; + typename Interface::gene_matrix X; + + + int _size; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product_bis.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product_bis.hh new file mode 100644 index 0000000000000000000000000000000000000000..29c10a6e2742d278fb6384d59832f0fc297f1b81 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_matrix_product_bis.hh @@ -0,0 +1,152 @@ +//===================================================== +// File : action_matrix_matrix_product_bis.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_MATRIX_MATRIX_PRODUCT_BIS +#define ACTION_MATRIX_MATRIX_PRODUCT_BIS +#include "utilities.h" +#include "STL_interface.hh" +#include "STL_timer.hh" +#include +#include "init_function.hh" +#include "init_vector.hh" +#include "init_matrix.hh" + +using namespace std; + +template +class Action_matrix_matrix_product_bis { + +public : + + static inline std::string name( void ) + { + return "matrix_matrix_"+Interface::name(); + } + + static double nb_op_base(int size){ + return 2.0*size*size*size; + } + + static double calculate( int nb_calc, int size ) { + + // STL matrix and vector initialization + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix B_stl; + typename Interface::stl_matrix X_stl; + + init_matrix(A_stl,size); + init_matrix(B_stl,size); + init_matrix(X_stl,size); + + // generic matrix and vector initialization + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix B_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix B; + typename Interface::gene_matrix X; + + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(B_ref,B_stl); + Interface::matrix_from_stl(X_ref,X_stl); + + Interface::matrix_from_stl(A,A_stl); + Interface::matrix_from_stl(B,B_stl); + Interface::matrix_from_stl(X,X_stl); + + + // STL_timer utilities + + STL_timer chronos; + + // Baseline evaluation + + chronos.start_baseline(nb_calc); + + do { + + Interface::copy_matrix(A_ref,A,size); + Interface::copy_matrix(B_ref,B,size); + Interface::copy_matrix(X_ref,X,size); + + + // Interface::matrix_matrix_product(A,B,X,size); This line must be commented !!!! + } + while(chronos.check()); + + chronos.report(true); + + // Time measurement + + chronos.start(nb_calc); + + do { + + Interface::copy_matrix(A_ref,A,size); + Interface::copy_matrix(B_ref,B,size); + Interface::copy_matrix(X_ref,X,size); + + Interface::matrix_matrix_product(A,B,X,size); // here it is not commented !!!! + } + while(chronos.check()); + + chronos.report(true); + + double time=chronos.calculated_time/2000.0; + + // calculation check + + typename Interface::stl_matrix resu_stl(size); + + Interface::matrix_to_stl(X,resu_stl); + + STL_interface::matrix_matrix_product(A_stl,B_stl,X_stl,size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-6){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(1); + } + + // deallocation and return time + + Interface::free_matrix(A,size); + Interface::free_matrix(B,size); + Interface::free_matrix(X,size); + + Interface::free_matrix(A_ref,size); + Interface::free_matrix(B_ref,size); + Interface::free_matrix(X_ref,size); + + return time; + } + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_vector_product.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_vector_product.hh new file mode 100644 index 0000000000000000000000000000000000000000..8bab79d18b4e614a56fb8f389658ca7e318121e1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_matrix_vector_product.hh @@ -0,0 +1,153 @@ +//===================================================== +// File : action_matrix_vector_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_MATRIX_VECTOR_PRODUCT +#define ACTION_MATRIX_VECTOR_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_matrix_vector_product { + +public : + + // Ctor + + BTL_DONT_INLINE Action_matrix_vector_product( int size ):_size(size) + { + MESSAGE("Action_matrix_vector_product Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(X,X_stl); + + } + + // invalidate copy ctor + + Action_matrix_vector_product( const Action_matrix_vector_product & ) + { + INFOS("illegal call to Action_matrix_vector_product Copy Ctor"); + exit(1); + } + + // Dtor + + BTL_DONT_INLINE ~Action_matrix_vector_product( void ){ + + MESSAGE("Action_matrix_vector_product Dtor"); + + // deallocation + + Interface::free_matrix(A,_size); + Interface::free_vector(B); + Interface::free_vector(X); + + Interface::free_matrix(A_ref,_size); + Interface::free_vector(B_ref); + Interface::free_vector(X_ref); + + } + + // action name + + static inline std::string name( void ) + { + return "matrix_vector_" + Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size; + } + + BTL_DONT_INLINE void initialize( void ){ + + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + Interface::copy_vector(X_ref,X,_size); + + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("#begin matrix_vector_product"); + Interface::matrix_vector_product(A,B,X,_size); + BTL_ASM_COMMENT("end matrix_vector_product"); + } + + BTL_DONT_INLINE void check_result( void ){ + + // calculation check + + Interface::vector_to_stl(X,resu_stl); + + STL_interface::matrix_vector_product(A_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-5){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(0); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_vector B_ref; + typename Interface::gene_vector X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + + int _size; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_partial_lu.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_partial_lu.hh new file mode 100644 index 0000000000000000000000000000000000000000..770ea1d1e74331748fbd605269c320f6c195057f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_partial_lu.hh @@ -0,0 +1,125 @@ +//===================================================== +// File : action_lu_decomp.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_PARTIAL_LU +#define ACTION_PARTIAL_LU +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_partial_lu { + +public : + + // Ctor + + Action_partial_lu( int size ):_size(size) + { + MESSAGE("Action_partial_lu Ctor"); + + // STL vector initialization + init_matrix(X_stl,_size); + init_matrix(C_stl,_size); + + // make sure X is invertible + for (int i=0; i<_size; ++i) + X_stl[i][i] = X_stl[i][i] * 1e2 + 1; + + // generic matrix and vector initialization + Interface::matrix_from_stl(X_ref,X_stl); + Interface::matrix_from_stl(X,X_stl); + Interface::matrix_from_stl(C,C_stl); + + _cost = 2.0*size*size*size/3.0 + size*size; + } + + // invalidate copy ctor + + Action_partial_lu( const Action_partial_lu & ) + { + INFOS("illegal call to Action_partial_lu Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_partial_lu( void ){ + + MESSAGE("Action_partial_lu Dtor"); + + // deallocation + Interface::free_matrix(X_ref,_size); + Interface::free_matrix(X,_size); + Interface::free_matrix(C,_size); + } + + // action name + + static inline std::string name( void ) + { + return "partial_lu_decomp_"+Interface::name(); + } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + Interface::copy_matrix(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::partial_lu_decomp(X,C,_size); + } + + void check_result( void ){ + // calculation check +// Interface::matrix_to_stl(C,resu_stl); + +// STL_interface::lu_decomp(X_stl,C_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(C_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix C_stl; + + typename Interface::gene_matrix X_ref; + typename Interface::gene_matrix X; + typename Interface::gene_matrix C; + + int _size; + double _cost; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_rot.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_rot.hh new file mode 100644 index 0000000000000000000000000000000000000000..df822a6d610f8d0bcd20e8528b7670e256b433b6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_rot.hh @@ -0,0 +1,116 @@ + +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_ROT +#define ACTION_ROT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_rot { + +public : + + // Ctor + BTL_DONT_INLINE Action_rot( int size ):_size(size) + { + MESSAGE("Action_rot Ctor"); + + // STL matrix and vector initialization + typename Interface::stl_matrix tmp; + init_vector(A_stl,_size); + init_vector(B_stl,_size); + + // generic matrix and vector initialization + Interface::vector_from_stl(A_ref,A_stl); + Interface::vector_from_stl(A,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(B,B_stl); + } + + // invalidate copy ctor + Action_rot( const Action_rot & ) + { + INFOS("illegal call to Action_rot Copy Ctor"); + exit(1); + } + + // Dtor + BTL_DONT_INLINE ~Action_rot( void ){ + MESSAGE("Action_rot Dtor"); + Interface::free_vector(A); + Interface::free_vector(B); + Interface::free_vector(A_ref); + Interface::free_vector(B_ref); + } + + // action name + static inline std::string name( void ) + { + return "rot_" + Interface::name(); + } + + double nb_op_base( void ){ + return 6.0*_size; + } + + BTL_DONT_INLINE void initialize( void ){ + Interface::copy_vector(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("#begin rot"); + Interface::rot(A,B,0.5,0.6,_size); + BTL_ASM_COMMENT("end rot"); + } + + BTL_DONT_INLINE void check_result( void ){ + // calculation check +// Interface::vector_to_stl(X,resu_stl); + +// STL_interface::rot(A_stl,B_stl,X_stl,_size); + +// typename Interface::real_type error= +// STL_interface::norm_diff(X_stl,resu_stl); + +// if (error>1.e-3){ +// INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); +// } + + } + +private : + + typename Interface::stl_vector A_stl; + typename Interface::stl_vector B_stl; + + typename Interface::gene_vector A_ref; + typename Interface::gene_vector B_ref; + + typename Interface::gene_vector A; + typename Interface::gene_vector B; + + int _size; +}; + + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_symv.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_symv.hh new file mode 100644 index 0000000000000000000000000000000000000000..a32b9dfa0648a75856717b1b4433b948c15c0f57 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_symv.hh @@ -0,0 +1,139 @@ +//===================================================== +// File : action_symv.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_SYMV +#define ACTION_SYMV +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_symv { + +public : + + // Ctor + + BTL_DONT_INLINE Action_symv( int size ):_size(size) + { + MESSAGE("Action_symv Ctor"); + + // STL matrix and vector initialization + init_matrix_symm(A_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(X,X_stl); + + } + + // invalidate copy ctor + + Action_symv( const Action_symv & ) + { + INFOS("illegal call to Action_symv Copy Ctor"); + exit(1); + } + + // Dtor + BTL_DONT_INLINE ~Action_symv( void ){ + Interface::free_matrix(A,_size); + Interface::free_vector(B); + Interface::free_vector(X); + Interface::free_matrix(A_ref,_size); + Interface::free_vector(B_ref); + Interface::free_vector(X_ref); + } + + // action name + + static inline std::string name( void ) + { + return "symv_" + Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size; + } + + BTL_DONT_INLINE void initialize( void ){ + + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + Interface::copy_vector(X_ref,X,_size); + + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("#begin symv"); + Interface::symv(A,B,X,_size); + BTL_ASM_COMMENT("end symv"); + } + + BTL_DONT_INLINE void check_result( void ){ + if (_size>128) return; + // calculation check + Interface::vector_to_stl(X,resu_stl); + + STL_interface::symv(A_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-5){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(0); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_vector B_ref; + typename Interface::gene_vector X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + + int _size; + +}; + + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_syr2.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_syr2.hh new file mode 100644 index 0000000000000000000000000000000000000000..7c6712b131f57089ad3d97c4c4eb09a43f2a45af --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_syr2.hh @@ -0,0 +1,133 @@ +//===================================================== +// File : action_syr2.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_SYR2 +#define ACTION_SYR2 +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_syr2 { + +public : + + // Ctor + + BTL_DONT_INLINE Action_syr2( int size ):_size(size) + { + // STL matrix and vector initialization + typename Interface::stl_matrix tmp; + init_matrix(A_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + init_vector(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(A_ref,A_stl); + Interface::matrix_from_stl(A,A_stl); + Interface::vector_from_stl(B_ref,B_stl); + Interface::vector_from_stl(B,B_stl); + Interface::vector_from_stl(X_ref,X_stl); + Interface::vector_from_stl(X,X_stl); + } + + // invalidate copy ctor + Action_syr2( const Action_syr2 & ) + { + INFOS("illegal call to Action_syr2 Copy Ctor"); + exit(1); + } + + // Dtor + BTL_DONT_INLINE ~Action_syr2( void ){ + Interface::free_matrix(A,_size); + Interface::free_vector(B); + Interface::free_vector(X); + Interface::free_matrix(A_ref,_size); + Interface::free_vector(B_ref); + Interface::free_vector(X_ref); + } + + // action name + + static inline std::string name( void ) + { + return "syr2_" + Interface::name(); + } + + double nb_op_base( void ){ + return 2.0*_size*_size; + } + + BTL_DONT_INLINE void initialize( void ){ + Interface::copy_matrix(A_ref,A,_size); + Interface::copy_vector(B_ref,B,_size); + Interface::copy_vector(X_ref,X,_size); + } + + BTL_DONT_INLINE void calculate( void ) { + BTL_ASM_COMMENT("#begin syr2"); + Interface::syr2(A,B,X,_size); + BTL_ASM_COMMENT("end syr2"); + } + + BTL_DONT_INLINE void check_result( void ){ + // calculation check + Interface::vector_to_stl(X,resu_stl); + + STL_interface::syr2(A_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-3){ + INFOS("WRONG CALCULATION...residual=" << error); +// exit(0); + } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_vector B_ref; + typename Interface::gene_vector X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_vector B; + typename Interface::gene_vector X; + + + int _size; + +}; + + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve.hh new file mode 100644 index 0000000000000000000000000000000000000000..d6f0b477eec0f11a671fdea6cfb37f753b395059 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve.hh @@ -0,0 +1,137 @@ +//===================================================== +// File : action_trisolve.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_TRISOLVE +#define ACTION_TRISOLVE +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_trisolve { + +public : + + // Ctor + + Action_trisolve( int size ):_size(size) + { + MESSAGE("Action_trisolve Ctor"); + + // STL vector initialization + init_matrix(L_stl,_size); + init_vector(B_stl,_size); + init_vector(X_stl,_size); + for (int j=0; j<_size; ++j) + { + for (int i=0; i(resu_stl,_size); + + // generic matrix and vector initialization + Interface::matrix_from_stl(L,L_stl); + Interface::vector_from_stl(X,X_stl); + Interface::vector_from_stl(B,B_stl); + + _cost = 0; + for (int j=0; j<_size; ++j) + { + _cost += 2*j + 1; + } + } + + // invalidate copy ctor + + Action_trisolve( const Action_trisolve & ) + { + INFOS("illegal call to Action_trisolve Copy Ctor"); + exit(1); + } + + // Dtor + + ~Action_trisolve( void ){ + + MESSAGE("Action_trisolve Dtor"); + + // deallocation + Interface::free_matrix(L,_size); + Interface::free_vector(B); + Interface::free_vector(X); + } + + // action name + + static inline std::string name( void ) + { + return "trisolve_vector_"+Interface::name(); + } + + double nb_op_base( void ){ + return _cost; + } + + inline void initialize( void ){ + //Interface::copy_vector(X_ref,X,_size); + } + + inline void calculate( void ) { + Interface::trisolve_lower(L,B,X,_size); + } + + void check_result(){ + if (_size>128) return; + // calculation check + Interface::vector_to_stl(X,resu_stl); + + STL_interface::trisolve_lower(L_stl,B_stl,X_stl,_size); + + typename Interface::real_type error= + STL_interface::norm_diff(X_stl,resu_stl); + + if (error>1.e-4){ + INFOS("WRONG CALCULATION...residual=" << error); + exit(2); + } //else INFOS("CALCULATION OK...residual=" << error); + + } + +private : + + typename Interface::stl_matrix L_stl; + typename Interface::stl_vector X_stl; + typename Interface::stl_vector B_stl; + typename Interface::stl_vector resu_stl; + + typename Interface::gene_matrix L; + typename Interface::gene_vector X; + typename Interface::gene_vector B; + + int _size; + double _cost; +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve_matrix.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve_matrix.hh new file mode 100644 index 0000000000000000000000000000000000000000..0fc2bb9effb6625af165d9b774cce809e3ed19d5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trisolve_matrix.hh @@ -0,0 +1,165 @@ +//===================================================== +// File : action_matrix_matrix_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_TRISOLVE_MATRIX_PRODUCT +#define ACTION_TRISOLVE_MATRIX_PRODUCT +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_trisolve_matrix { + +public : + + // Ctor + + Action_trisolve_matrix( int size ):_size(size) + { + MESSAGE("Action_trisolve_matrix Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_matrix(B_stl,_size); + init_matrix(X_stl,_size); + init_matrix(resu_stl,_size); + + for (int j=0; j<_size; ++j) + { + for (int i=0; i::matrix_matrix_product(A_stl,B_stl,X_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(X_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// // exit(1); +// } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix B_stl; + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix B_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix B; + typename Interface::gene_matrix X; + + int _size; + double _cost; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trmm.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trmm.hh new file mode 100644 index 0000000000000000000000000000000000000000..8f7813818424216f71027235a7255efe20e7d2b4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/action_trmm.hh @@ -0,0 +1,165 @@ +//===================================================== +// File : action_matrix_matrix_product.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef ACTION_TRMM +#define ACTION_TRMM +#include "utilities.h" +#include "STL_interface.hh" +#include +#include "init/init_function.hh" +#include "init/init_vector.hh" +#include "init/init_matrix.hh" + +using namespace std; + +template +class Action_trmm { + +public : + + // Ctor + + Action_trmm( int size ):_size(size) + { + MESSAGE("Action_trmm Ctor"); + + // STL matrix and vector initialization + + init_matrix(A_stl,_size); + init_matrix(B_stl,_size); + init_matrix(X_stl,_size); + init_matrix(resu_stl,_size); + + for (int j=0; j<_size; ++j) + { + for (int i=0; i::matrix_matrix_product(A_stl,B_stl,X_stl,_size); +// +// typename Interface::real_type error= +// STL_interface::norm_diff(X_stl,resu_stl); +// +// if (error>1.e-6){ +// INFOS("WRONG CALCULATION...residual=" << error); +// // exit(1); +// } + + } + +private : + + typename Interface::stl_matrix A_stl; + typename Interface::stl_matrix B_stl; + typename Interface::stl_matrix X_stl; + typename Interface::stl_matrix resu_stl; + + typename Interface::gene_matrix A_ref; + typename Interface::gene_matrix B_ref; + typename Interface::gene_matrix X_ref; + + typename Interface::gene_matrix A; + typename Interface::gene_matrix B; + typename Interface::gene_matrix X; + + int _size; + double _cost; + +}; + + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/basic_actions.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/basic_actions.hh new file mode 100644 index 0000000000000000000000000000000000000000..62442f01fb42d51eeb486651e8616663de6beb00 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/actions/basic_actions.hh @@ -0,0 +1,21 @@ + +#include "action_axpy.hh" +#include "action_axpby.hh" + +#include "action_matrix_vector_product.hh" +#include "action_atv_product.hh" + +#include "action_matrix_matrix_product.hh" +#include "action_ata_product.hh" +#include "action_aat_product.hh" + +#include "action_trisolve.hh" +#include "action_trmm.hh" +#include "action_symv.hh" +// #include "action_symm.hh" +#include "action_syr2.hh" +#include "action_ger.hh" +#include "action_rot.hh" + +// #include "action_lu_solve.hh" + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindACML.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindACML.cmake new file mode 100644 index 0000000000000000000000000000000000000000..daeeb535da721cee1b3ae87c95900894ec19a4bb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindACML.cmake @@ -0,0 +1,51 @@ + +if (ACML_LIBRARIES) + set(ACML_FIND_QUIETLY TRUE) +endif () + +find_library(ACML_LIBRARIES + NAMES + acml_mp acml_mv + PATHS + $ENV{ACMLDIR}/lib + $ENV{ACML_DIR}/lib + ${LIB_INSTALL_DIR} +) + +find_file(ACML_LIBRARIES + NAMES + libacml_mp.so + PATHS + /usr/lib + /usr/lib64 + $ENV{ACMLDIR}/lib + ${LIB_INSTALL_DIR} +) + +if(NOT ACML_LIBRARIES) + message(STATUS "Multi-threaded library not found, looking for single-threaded") + find_library(ACML_LIBRARIES + NAMES + acml acml_mv + PATHS + $ENV{ACMLDIR}/lib + $ENV{ACML_DIR}/lib + ${LIB_INSTALL_DIR} + ) + find_file(ACML_LIBRARIES + libacml.so libacml_mv.so + PATHS + /usr/lib + /usr/lib64 + $ENV{ACMLDIR}/lib + ${LIB_INSTALL_DIR} + ) +endif() + + + + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(ACML DEFAULT_MSG ACML_LIBRARIES) + +mark_as_advanced(ACML_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindATLAS.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindATLAS.cmake new file mode 100644 index 0000000000000000000000000000000000000000..572a4c0b212c06f3ce1277bc41f62ca67354d0db --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindATLAS.cmake @@ -0,0 +1,31 @@ + +if (ATLAS_LIBRARIES) + set(ATLAS_FIND_QUIETLY TRUE) +endif () + +find_file(ATLAS_LIB libatlas.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) +find_library(ATLAS_LIB satlas PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) + +find_file(ATLAS_LAPACK NAMES liblapack_atlas.so.3 liblapack.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) +find_library(ATLAS_LAPACK NAMES lapack_atlas lapack PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) + +find_file(ATLAS_F77BLAS libf77blas.so.3 PATHS /usr/lib /usr/lib/atlas /usr/lib64 /usr/lib64/atlas $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) +find_library(ATLAS_F77BLAS f77blas PATHS $ENV{ATLASDIR} ${LIB_INSTALL_DIR}) + +if(ATLAS_LIB AND ATLAS_CBLAS AND ATLAS_LAPACK AND ATLAS_F77BLAS) + + set(ATLAS_LIBRARIES ${ATLAS_LAPACK} ${ATLAS_LIB}) + + # search the default lapack lib link to it + find_file(ATLAS_REFERENCE_LAPACK liblapack.so.3 PATHS /usr/lib /usr/lib64) + find_library(ATLAS_REFERENCE_LAPACK NAMES lapack) +# if(ATLAS_REFERENCE_LAPACK) +# set(ATLAS_LIBRARIES ${ATLAS_LIBRARIES} ${ATLAS_REFERENCE_LAPACK}) +# endif() + +endif() + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(ATLAS DEFAULT_MSG ATLAS_LIBRARIES) + +mark_as_advanced(ATLAS_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBLAZE.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBLAZE.cmake new file mode 100644 index 0000000000000000000000000000000000000000..18a878ff9aeb8e4262dff6abe9efcef9a82d9422 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBLAZE.cmake @@ -0,0 +1,31 @@ +# - Try to find eigen2 headers +# Once done this will define +# +# BLAZE_FOUND - system has blaze lib +# BLAZE_INCLUDE_DIR - the blaze include directory +# +# Copyright (C) 2008 Gael Guennebaud +# Adapted from FindEigen.cmake: +# Copyright (c) 2006, 2007 Montel Laurent, +# Redistribution and use is allowed according to the terms of the BSD license. +# For details see the accompanying COPYING-CMAKE-SCRIPTS file. + +if (BLAZE_INCLUDE_DIR) + + # in cache already + set(BLAZE_FOUND TRUE) + +else () + +find_path(BLAZE_INCLUDE_DIR NAMES blaze/Blaze.h + PATHS + ${INCLUDE_INSTALL_DIR} + ) + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(BLAZE DEFAULT_MSG BLAZE_INCLUDE_DIR) + +mark_as_advanced(BLAZE_INCLUDE_DIR) + +endif() + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBlitz.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBlitz.cmake new file mode 100644 index 0000000000000000000000000000000000000000..7ab375fd87b626d08b4ac6d2e1c7cc582903efeb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindBlitz.cmake @@ -0,0 +1,40 @@ +# - Try to find blitz lib +# Once done this will define +# +# BLITZ_FOUND - system has blitz lib +# BLITZ_INCLUDES - the blitz include directory +# BLITZ_LIBRARIES - The libraries needed to use blitz + +# Copyright (c) 2006, Montel Laurent, +# Copyright (c) 2007, Allen Winter, +# Copyright (C) 2008 Gael Guennebaud +# Redistribution and use is allowed according to the terms of the BSD license. +# For details see the accompanying COPYING-CMAKE-SCRIPTS file. + +# include(FindLibraryWithDebug) + +if (BLITZ_INCLUDES AND BLITZ_LIBRARIES) + set(Blitz_FIND_QUIETLY TRUE) +endif () + +find_path(BLITZ_INCLUDES + NAMES + blitz/array.h + PATH_SUFFIXES blitz* + PATHS + $ENV{BLITZDIR}/include + ${INCLUDE_INSTALL_DIR} +) + +find_library(BLITZ_LIBRARIES + blitz + PATHS + $ENV{BLITZDIR}/lib + ${LIB_INSTALL_DIR} +) + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(Blitz DEFAULT_MSG + BLITZ_INCLUDES BLITZ_LIBRARIES) + +mark_as_advanced(BLITZ_INCLUDES BLITZ_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindCBLAS.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindCBLAS.cmake new file mode 100644 index 0000000000000000000000000000000000000000..43a90f7f656e4060ebfdd46af4b10c033facdbbd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindCBLAS.cmake @@ -0,0 +1,35 @@ +# include(FindLibraryWithDebug) + +if (CBLAS_INCLUDES AND CBLAS_LIBRARIES) + set(CBLAS_FIND_QUIETLY TRUE) +endif () + +find_path(CBLAS_INCLUDES + NAMES + cblas.h + PATHS + $ENV{CBLASDIR}/include + ${INCLUDE_INSTALL_DIR} +) + +find_library(CBLAS_LIBRARIES + cblas + PATHS + $ENV{CBLASDIR}/lib + ${LIB_INSTALL_DIR} +) + +find_file(CBLAS_LIBRARIES + libcblas.so.3 + PATHS + /usr/lib + /usr/lib64 + $ENV{CBLASDIR}/lib + ${LIB_INSTALL_DIR} +) + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(CBLAS DEFAULT_MSG + CBLAS_INCLUDES CBLAS_LIBRARIES) + +mark_as_advanced(CBLAS_INCLUDES CBLAS_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindGMM.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindGMM.cmake new file mode 100644 index 0000000000000000000000000000000000000000..ff45e6a0cfaacb4882190ecc408b60b587350c8b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindGMM.cmake @@ -0,0 +1,17 @@ +if (GMM_INCLUDE_DIR) + # in cache already + set(GMM_FOUND TRUE) +else () + +find_path(GMM_INCLUDE_DIR NAMES gmm/gmm.h + PATHS + ${INCLUDE_INSTALL_DIR} + ${GMM_INCLUDE_PATH} + ) + +include(FindPackageHandleStandardArgs) +FIND_PACKAGE_HANDLE_STANDARD_ARGS(GMM DEFAULT_MSG GMM_INCLUDE_DIR ) + +mark_as_advanced(GMM_INCLUDE_DIR) + +endif() diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMKL.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMKL.cmake new file mode 100644 index 0000000000000000000000000000000000000000..23e77279ab97ffa26264ef2a6584fd4a57d044f1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMKL.cmake @@ -0,0 +1,65 @@ + +if (MKL_LIBRARIES) + set(MKL_FIND_QUIETLY TRUE) +endif () + +if(CMAKE_MINOR_VERSION GREATER 4) + +if(${CMAKE_HOST_SYSTEM_PROCESSOR} STREQUAL "x86_64") + +find_library(MKL_LIBRARIES + mkl_core + PATHS + $ENV{MKLLIB} + /opt/intel/mkl/*/lib/em64t + /opt/intel/Compiler/*/*/mkl/lib/em64t + ${LIB_INSTALL_DIR} +) + +find_library(MKL_GUIDE + guide + PATHS + $ENV{MKLLIB} + /opt/intel/mkl/*/lib/em64t + /opt/intel/Compiler/*/*/mkl/lib/em64t + /opt/intel/Compiler/*/*/lib/intel64 + ${LIB_INSTALL_DIR} +) + +if(MKL_LIBRARIES AND MKL_GUIDE) + set(MKL_LIBRARIES ${MKL_LIBRARIES} mkl_intel_lp64 mkl_sequential ${MKL_GUIDE} pthread) +endif() + +else() + +find_library(MKL_LIBRARIES + mkl_core + PATHS + $ENV{MKLLIB} + /opt/intel/mkl/*/lib/32 + /opt/intel/Compiler/*/*/mkl/lib/32 + ${LIB_INSTALL_DIR} +) + +find_library(MKL_GUIDE + guide + PATHS + $ENV{MKLLIB} + /opt/intel/mkl/*/lib/32 + /opt/intel/Compiler/*/*/mkl/lib/32 + /opt/intel/Compiler/*/*/lib/intel32 + ${LIB_INSTALL_DIR} +) + +if(MKL_LIBRARIES AND MKL_GUIDE) + set(MKL_LIBRARIES ${MKL_LIBRARIES} mkl_intel mkl_sequential ${MKL_GUIDE} pthread) +endif() + +endif() + +endif() + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(MKL DEFAULT_MSG MKL_LIBRARIES) + +mark_as_advanced(MKL_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMTL4.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMTL4.cmake new file mode 100644 index 0000000000000000000000000000000000000000..1bafc93a6b43c9a851205ddb98aac61c488d4b14 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindMTL4.cmake @@ -0,0 +1,31 @@ +# - Try to find eigen2 headers +# Once done this will define +# +# MTL4_FOUND - system has eigen2 lib +# MTL4_INCLUDE_DIR - the eigen2 include directory +# +# Copyright (C) 2008 Gael Guennebaud +# Adapted from FindEigen.cmake: +# Copyright (c) 2006, 2007 Montel Laurent, +# Redistribution and use is allowed according to the terms of the BSD license. +# For details see the accompanying COPYING-CMAKE-SCRIPTS file. + +if (MTL4_INCLUDE_DIR) + + # in cache already + set(MTL4_FOUND TRUE) + +else () + +find_path(MTL4_INCLUDE_DIR NAMES boost/numeric/mtl/mtl.hpp + PATHS + ${INCLUDE_INSTALL_DIR} + ) + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(MTL4 DEFAULT_MSG MTL4_INCLUDE_DIR) + +mark_as_advanced(MTL4_INCLUDE_DIR) + +endif() + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindOPENBLAS.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindOPENBLAS.cmake new file mode 100644 index 0000000000000000000000000000000000000000..5c0762306d65532e040adba0fd2899238a8134d1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindOPENBLAS.cmake @@ -0,0 +1,17 @@ + +if (OPENBLAS_LIBRARIES) + set(OPENBLAS_FIND_QUIETLY TRUE) +endif () + +find_file(OPENBLAS_LIBRARIES NAMES libopenblas.so libopenblas.so.0 PATHS /usr/lib /usr/lib64 $ENV{OPENBLASDIR} ${LIB_INSTALL_DIR}) +find_library(OPENBLAS_LIBRARIES openblas PATHS $ENV{OPENBLASDIR} ${LIB_INSTALL_DIR}) + +if(OPENBLAS_LIBRARIES AND CMAKE_COMPILER_IS_GNUCXX) + set(OPENBLAS_LIBRARIES ${OPENBLAS_LIBRARIES} "-lpthread -lgfortran") +endif() + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(OPENBLAS DEFAULT_MSG + OPENBLAS_LIBRARIES) + +mark_as_advanced(OPENBLAS_LIBRARIES) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindPackageHandleStandardArgs.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindPackageHandleStandardArgs.cmake new file mode 100644 index 0000000000000000000000000000000000000000..05d7e65bd2e06a34bf1f58073075ee45d9a223ba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindPackageHandleStandardArgs.cmake @@ -0,0 +1,60 @@ +# FIND_PACKAGE_HANDLE_STANDARD_ARGS(NAME (DEFAULT_MSG|"Custom failure message") VAR1 ... ) +# +# This macro is intended to be used in FindXXX.cmake modules files. +# It handles the REQUIRED and QUIET argument to find_package() and +# it also sets the _FOUND variable. +# The package is found if all variables listed are TRUE. +# Example: +# +# FIND_PACKAGE_HANDLE_STANDARD_ARGS(LibXml2 DEFAULT_MSG LIBXML2_LIBRARIES LIBXML2_INCLUDE_DIR) +# +# LibXml2 is considered to be found, if both LIBXML2_LIBRARIES and +# LIBXML2_INCLUDE_DIR are valid. Then also LIBXML2_FOUND is set to TRUE. +# If it is not found and REQUIRED was used, it fails with FATAL_ERROR, +# independent whether QUIET was used or not. +# +# If it is found, the location is reported using the VAR1 argument, so +# here a message "Found LibXml2: /usr/lib/libxml2.so" will be printed out. +# If the second argument is DEFAULT_MSG, the message in the failure case will +# be "Could NOT find LibXml2", if you don't like this message you can specify +# your own custom failure message there. + +macro(FIND_PACKAGE_HANDLE_STANDARD_ARGS _NAME _FAIL_MSG _VAR1 ) + + if("${_FAIL_MSG}" STREQUAL "DEFAULT_MSG") + if (${_NAME}_FIND_REQUIRED) + set(_FAIL_MESSAGE "Could not find REQUIRED package ${_NAME}") + else (${_NAME}_FIND_REQUIRED) + set(_FAIL_MESSAGE "Could not find OPTIONAL package ${_NAME}") + endif (${_NAME}_FIND_REQUIRED) + else("${_FAIL_MSG}" STREQUAL "DEFAULT_MSG") + set(_FAIL_MESSAGE "${_FAIL_MSG}") + endif("${_FAIL_MSG}" STREQUAL "DEFAULT_MSG") + + string(TOUPPER ${_NAME} _NAME_UPPER) + + set(${_NAME_UPPER}_FOUND TRUE) + if(NOT ${_VAR1}) + set(${_NAME_UPPER}_FOUND FALSE) + endif(NOT ${_VAR1}) + + foreach(_CURRENT_VAR ${ARGN}) + if(NOT ${_CURRENT_VAR}) + set(${_NAME_UPPER}_FOUND FALSE) + endif(NOT ${_CURRENT_VAR}) + endforeach(_CURRENT_VAR) + + if (${_NAME_UPPER}_FOUND) + if (NOT ${_NAME}_FIND_QUIETLY) + message(STATUS "Found ${_NAME}: ${${_VAR1}}") + endif (NOT ${_NAME}_FIND_QUIETLY) + else (${_NAME_UPPER}_FOUND) + if (${_NAME}_FIND_REQUIRED) + message(FATAL_ERROR "${_FAIL_MESSAGE}") + else (${_NAME}_FIND_REQUIRED) + if (NOT ${_NAME}_FIND_QUIETLY) + message(STATUS "${_FAIL_MESSAGE}") + endif (NOT ${_NAME}_FIND_QUIETLY) + endif (${_NAME}_FIND_REQUIRED) + endif (${_NAME_UPPER}_FOUND) +endmacro(FIND_PACKAGE_HANDLE_STANDARD_ARGS) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindTvmet.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindTvmet.cmake new file mode 100644 index 0000000000000000000000000000000000000000..8ccae271b99f1552da0b07534078a31563ce25bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/FindTvmet.cmake @@ -0,0 +1,32 @@ +# - Try to find tvmet headers +# Once done this will define +# +# TVMET_FOUND - system has tvmet lib +# TVMET_INCLUDE_DIR - the tvmet include directory +# +# Copyright (C) 2008 Gael Guennebaud +# Adapted from FindEigen.cmake: +# Copyright (c) 2006, 2007 Montel Laurent, +# Redistribution and use is allowed according to the terms of the BSD license. +# For details see the accompanying COPYING-CMAKE-SCRIPTS file. + +if (TVMET_INCLUDE_DIR) + + # in cache already + set(TVMET_FOUND TRUE) + +else () + +find_path(TVMET_INCLUDE_DIR NAMES tvmet/tvmet.h + PATHS + ${TVMETDIR}/ + ${INCLUDE_INSTALL_DIR} + ) + +include(FindPackageHandleStandardArgs) +find_package_handle_standard_args(Tvmet DEFAULT_MSG TVMET_INCLUDE_DIR) + +mark_as_advanced(TVMET_INCLUDE_DIR) + +endif() + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/MacroOptionalAddSubdirectory.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/MacroOptionalAddSubdirectory.cmake new file mode 100644 index 0000000000000000000000000000000000000000..8d46fcea2ab90d8149c380c010e348bcec28d2e6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/cmake/MacroOptionalAddSubdirectory.cmake @@ -0,0 +1,31 @@ +# - MACRO_OPTIONAL_ADD_SUBDIRECTORY() combines add_subdirectory() with an option() +# MACRO_OPTIONAL_ADD_SUBDIRECTORY( ) +# If you use MACRO_OPTIONAL_ADD_SUBDIRECTORY() instead of add_subdirectory(), +# this will have two effects +# 1 - CMake will not complain if the directory doesn't exist +# This makes sense if you want to distribute just one of the subdirs +# in a source package, e.g. just one of the subdirs in kdeextragear. +# 2 - If the directory exists, it will offer an option to skip the +# subdirectory. +# This is useful if you want to compile only a subset of all +# directories. + +# Copyright (c) 2007, Alexander Neundorf, +# +# Redistribution and use is allowed according to the terms of the BSD license. +# For details see the accompanying COPYING-CMAKE-SCRIPTS file. + + +macro (MACRO_OPTIONAL_ADD_SUBDIRECTORY _dir ) + get_filename_component(_fullPath ${_dir} ABSOLUTE) + if(EXISTS ${_fullPath}) + if(${ARGC} EQUAL 2) + option(BUILD_${_dir} "Build directory ${_dir}" ${ARGV1}) + else(${ARGC} EQUAL 2) + option(BUILD_${_dir} "Build directory ${_dir}" TRUE) + endif(${ARGC} EQUAL 2) + if(BUILD_${_dir}) + add_subdirectory(${_dir}) + endif(BUILD_${_dir}) + endif(EXISTS ${_fullPath}) +endmacro (MACRO_OPTIONAL_ADD_SUBDIRECTORY) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..580c1ced0fb438971fabcbb023607ef087552da5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/CMakeLists.txt @@ -0,0 +1,32 @@ + +add_custom_target(copy_scripts) + +set(script_files go_mean mk_mean_script.sh mk_new_gnuplot.sh + perlib_plot_settings.txt action_settings.txt gnuplot_common_settings.hh ) + +foreach(script_file ${script_files}) +add_custom_command( + TARGET copy_scripts + POST_BUILD + COMMAND ${CMAKE_COMMAND} -E copy ${CMAKE_CURRENT_SOURCE_DIR}/${script_file} ${CMAKE_CURRENT_BINARY_DIR}/ + ARGS +) +endforeach(script_file) + +add_custom_command( + TARGET copy_scripts + POST_BUILD + COMMAND ${CMAKE_CXX_COMPILER} --version | head -n 1 > ${CMAKE_CURRENT_BINARY_DIR}/compiler_version.txt + ARGS +) +add_custom_command( + TARGET copy_scripts + POST_BUILD + COMMAND echo "${Eigen_SOURCE_DIR}" > ${CMAKE_CURRENT_BINARY_DIR}/eigen_root_dir.txt + ARGS +) + +add_executable(smooth smooth.cxx) +add_executable(regularize regularize.cxx) +add_executable(main mean.cxx) +add_dependencies(main copy_scripts) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/action_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/action_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..39d2b5dc48d9965c1f504d468f85be69ccaa492c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/action_settings.txt @@ -0,0 +1,19 @@ +aat ; "{/*1.5 A x A^T}" ; "matrix size" ; 4:5000 +ata ; "{/*1.5 A^T x A}" ; "matrix size" ; 4:5000 +atv ; "{/*1.5 matrix^T x vector}" ; "matrix size" ; 4:5000 +axpby ; "{/*1.5 Y = alpha X + beta Y}" ; "vector size" ; 5:1000000 +axpy ; "{/*1.5 Y += alpha X}" ; "vector size" ; 5:1000000 +matrix_matrix ; "{/*1.5 matrix matrix product}" ; "matrix size" ; 4:5000 +matrix_vector ; "{/*1.5 matrix vector product}" ; "matrix size" ; 4:5000 +trmm ; "{/*1.5 triangular matrix matrix product}" ; "matrix size" ; 4:5000 +trisolve_vector ; "{/*1.5 triangular solver - vector (X = inv(L) X)}" ; "size" ; 4:5000 +trisolve_matrix ; "{/*1.5 triangular solver - matrix (M = inv(L) M)}" ; "size" ; 4:5000 +cholesky ; "{/*1.5 Cholesky decomposition}" ; "matrix size" ; 4:5000 +complete_lu_decomp ; "{/*1.5 Complete LU decomposition}" ; "matrix size" ; 4:5000 +partial_lu_decomp ; "{/*1.5 Partial LU decomposition}" ; "matrix size" ; 4:5000 +tridiagonalization ; "{/*1.5 Tridiagonalization}" ; "matrix size" ; 4:5000 +hessenberg ; "{/*1.5 Hessenberg decomposition}" ; "matrix size" ; 4:5000 +symv ; "{/*1.5 symmetric matrix vector product}" ; "matrix size" ; 4:5000 +syr2 ; "{/*1.5 symmretric rank-2 update (A += u^T v + u v^T)}" ; "matrix size" ; 4:5000 +ger ; "{/*1.5 general rank-1 update (A += u v^T)}" ; "matrix size" ; 4:5000 +rot ; "{/*1.5 apply rotation in the plane}" ; "vector size" ; 4:1000000 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/gnuplot_common_settings.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/gnuplot_common_settings.hh new file mode 100644 index 0000000000000000000000000000000000000000..6f677df60a33a62150055e7ae84282a69a12e254 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/gnuplot_common_settings.hh @@ -0,0 +1,87 @@ +set noclip points +set clip one +set noclip two +set bar 1.000000 +set border 31 lt -1 lw 1.000 +set xdata +set ydata +set zdata +set x2data +set y2data +set boxwidth +set dummy x,y +set format x "%g" +set format y "%g" +set format x2 "%g" +set format y2 "%g" +set format z "%g" +set angles radians +set nogrid +set key title "" +set key left top Right noreverse box linetype -2 linewidth 1.000 samplen 4 spacing 1 width 0 +set nolabel +set noarrow +# set nolinestyle # deprecated +set nologscale +set logscale x 10 +set offsets 0, 0, 0, 0 +set pointsize 1 +set encoding default +set nopolar +set noparametric +set view 60, 30, 1, 1 +set samples 100, 100 +set isosamples 10, 10 +set surface +set nocontour +set clabel '%8.3g' +set mapping cartesian +set nohidden3d +set cntrparam order 4 +set cntrparam linear +set cntrparam levels auto 5 +set cntrparam points 5 +set size ratio 0 1,1 +set origin 0,0 +# set data style lines +# set function style lines +set xzeroaxis lt -2 lw 1.000 +set x2zeroaxis lt -2 lw 1.000 +set yzeroaxis lt -2 lw 1.000 +set y2zeroaxis lt -2 lw 1.000 +set tics in +set ticslevel 0.5 +set tics scale 1, 0.5 +set mxtics default +set mytics default +set mx2tics default +set my2tics default +set xtics border mirror norotate autofreq +set ytics border mirror norotate autofreq +set ztics border nomirror norotate autofreq +set nox2tics +set noy2tics +set timestamp "" bottom norotate offset 0,0 +set rrange [ * : * ] noreverse nowriteback # (currently [-0:10] ) +set trange [ * : * ] noreverse nowriteback # (currently [-5:5] ) +set urange [ * : * ] noreverse nowriteback # (currently [-5:5] ) +set vrange [ * : * ] noreverse nowriteback # (currently [-5:5] ) +set xlabel "matrix size" offset 0,0 +set x2label "" offset 0,0 +set timefmt "%d/%m/%y\n%H:%M" +set xrange [ 10 : 1000 ] noreverse nowriteback +set x2range [ * : * ] noreverse nowriteback # (currently [-10:10] ) +set ylabel "MFLOPS" offset 0,0 +set y2label "" offset 0,0 +set yrange [ * : * ] noreverse nowriteback # (currently [-10:10] ) +set y2range [ * : * ] noreverse nowriteback # (currently [-10:10] ) +set zlabel "" offset 0,0 +set zrange [ * : * ] noreverse nowriteback # (currently [-10:10] ) +set zero 1e-08 +set lmargin -1 +set bmargin -1 +set rmargin -1 +set tmargin -1 +set locale "C" +set xrange [4:1024] + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/go_mean b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/go_mean new file mode 100644 index 0000000000000000000000000000000000000000..d014269099534ca88020d2a29bd966a51bb8efb9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/go_mean @@ -0,0 +1,58 @@ +#!/bin/bash + +if [ $# < 1 ]; then + echo "Usage: $0 working_directory [tiny|large [prefix]]" +else + +mkdir -p $1 +##cp ../libs/*/*.dat $1 + +mode=large +if [ $# > 2 ]; then + mode=$2 +fi +if [ $# > 3 ]; then + prefix=$3 +fi + +EIGENDIR=`cat eigen_root_dir.txt` + +webpagefilename=$1/index.html +meanstatsfilename=$1/mean.html + +echo '' > $meanstatsfilename +echo '' > $webpagefilename +echo '

Configuration' >> $webpagefilename +echo '

    '\ + '
  • ' `cat /proc/cpuinfo | grep "model name" | head -n 1`\ + ' (' `uname -m` ')
  • '\ + '
  • compiler: ' `cat compiler_version.txt` '
  • '\ + '
  • eigen3: ' `git ls-remote --refs -q $EIGENDIR HEAD | cut -f 1` '
  • '\ + '
' \ + '

' >> $webpagefilename + +source mk_mean_script.sh axpy $1 11 2500 100000 250000 $mode $prefix +source mk_mean_script.sh axpby $1 11 2500 100000 250000 $mode $prefix +source mk_mean_script.sh matrix_vector $1 11 50 300 1000 $mode $prefix +source mk_mean_script.sh atv $1 11 50 300 1000 $mode $prefix +source mk_mean_script.sh matrix_matrix $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh aat $1 11 100 300 1000 $mode $prefix +# source mk_mean_script.sh ata $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh trmm $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh trisolve_vector $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh trisolve_matrix $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh cholesky $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh partial_lu_decomp $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh tridiagonalization $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh hessenberg $1 11 100 300 1000 $mode $prefix +source mk_mean_script.sh symv $1 11 50 300 1000 $mode $prefix +source mk_mean_script.sh syr2 $1 11 50 300 1000 $mode $prefix +source mk_mean_script.sh ger $1 11 50 300 1000 $mode $prefix +source mk_mean_script.sh rot $1 11 2500 100000 250000 $mode $prefix +source mk_mean_script.sh complete_lu_decomp $1 11 100 300 1000 $mode $prefix + +fi + +## compile the web page ## + +#echo `cat footer.html` >> $webpagefilename \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mean.cxx b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mean.cxx new file mode 100644 index 0000000000000000000000000000000000000000..c567ef33e7c81406b15001d4b5462cd85cc0f0e7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mean.cxx @@ -0,0 +1,182 @@ +//===================================================== +// File : mean.cxx +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:15 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include +#include +#include +#include +#include "bench_parameter.hh" +#include "utils/xy_file.hh" +#include + +using namespace std; + +double mean_calc(const vector & tab_sizes, const vector & tab_mflops, const int size_min, const int size_max); + +class Lib_Mean{ + +public: + Lib_Mean( void ):_lib_name(),_mean_in_cache(),_mean_out_of_cache(){ + MESSAGE("Lib_mean Default Ctor"); + MESSAGE("!!! should not be used"); + exit(0); + } + Lib_Mean(const string & name, const double & mic, const double & moc):_lib_name(name),_mean_in_cache(mic),_mean_out_of_cache(moc){ + MESSAGE("Lib_mean Ctor"); + } + Lib_Mean(const Lib_Mean & lm):_lib_name(lm._lib_name),_mean_in_cache(lm._mean_in_cache),_mean_out_of_cache(lm._mean_out_of_cache){ + MESSAGE("Lib_mean Copy Ctor"); + } + ~Lib_Mean( void ){ + MESSAGE("Lib_mean Dtor"); + } + + double _mean_in_cache; + double _mean_out_of_cache; + string _lib_name; + + bool operator < ( const Lib_Mean &right) const + { + //return ( this->_mean_out_of_cache > right._mean_out_of_cache) ; + return ( this->_mean_in_cache > right._mean_in_cache) ; + } + +}; + + +int main( int argc , char *argv[] ) +{ + + if (argc<6){ + INFOS("!!! Error ... usage : main what mic Mic moc Moc filename1 finename2..."); + exit(0); + } + INFOS(argc); + + int min_in_cache=atoi(argv[2]); + int max_in_cache=atoi(argv[3]); + int min_out_of_cache=atoi(argv[4]); + int max_out_of_cache=atoi(argv[5]); + + + multiset s_lib_mean ; + + for (int i=6;i tab_sizes; + vector tab_mflops; + + read_xy_file(filename,tab_sizes,tab_mflops); + + mic=mean_calc(tab_sizes,tab_mflops,min_in_cache,max_in_cache); + moc=mean_calc(tab_sizes,tab_mflops,min_out_of_cache,max_out_of_cache); + + Lib_Mean cur_lib_mean(filename,mic,moc); + + s_lib_mean.insert(cur_lib_mean); + + } + + } + + + cout << "" << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + + multiset::iterator is = s_lib_mean.begin(); + Lib_Mean best(*is); + + + for (is=s_lib_mean.begin(); is!=s_lib_mean.end() ; is++){ + + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + cout << " " << endl ; + + } + + cout << "
" << argv[1] << " in cache
mean perf
Mflops
in cache
% best
out of cache
mean perf
Mflops
out of cache
% best
details comments
" << is->_lib_name << " " << is->_mean_in_cache << " " << 100*(is->_mean_in_cache/best._mean_in_cache) << " " << is->_mean_out_of_cache << " " << 100*(is->_mean_out_of_cache/best._mean_out_of_cache) << " " << + "_lib_name<<"_"<snippet/" + "_lib_name<<"_flags\">flags " << + "_lib_name<<"_comments\">click here
" << endl ; + + ofstream output_file ("../order_lib",ios::out) ; + + for (is=s_lib_mean.begin(); is!=s_lib_mean.end() ; is++){ + output_file << is->_lib_name << endl ; + } + + output_file.close(); + +} + +double mean_calc(const vector & tab_sizes, const vector & tab_mflops, const int size_min, const int size_max){ + + int size=tab_sizes.size(); + int nb_sample=0; + double mean=0.0; + + for (int i=0;i=size_min)&&(tab_sizes[i]<=size_max)){ + + nb_sample++; + mean+=tab_mflops[i]; + + } + + + } + + if (nb_sample==0){ + INFOS("no data for mean calculation"); + return 0.0; + } + + return mean/nb_sample; +} + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_gnuplot_script.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_gnuplot_script.sh new file mode 100644 index 0000000000000000000000000000000000000000..2ca7b5cb5e1684aa79dc1a483ac96922e8c6293d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_gnuplot_script.sh @@ -0,0 +1,68 @@ +#! /bin/bash +WHAT=$1 +DIR=$2 +echo $WHAT script generation +cat $WHAT.hh > $WHAT.gnuplot + +DATA_FILE=`find $DIR -name "*.dat" | grep $WHAT` + +echo plot \\ >> $WHAT.gnuplot + +for FILE in $DATA_FILE +do + LAST=$FILE +done + +echo LAST=$LAST + +for FILE in $DATA_FILE +do + if [ $FILE != $LAST ] + then + BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} + echo "'"$FILE"'" title "'"$TITLE"'" ",\\" >> $WHAT.gnuplot + fi +done +BASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} +echo "'"$LAST"'" title "'"$TITLE"'" >> $WHAT.gnuplot + +#echo set term postscript color >> $WHAT.gnuplot +#echo set output "'"$WHAT.ps"'" >> $WHAT.gnuplot +echo set term pbm small color >> $WHAT.gnuplot +echo set output "'"$WHAT.ppm"'" >> $WHAT.gnuplot +echo plot \\ >> $WHAT.gnuplot + +for FILE in $DATA_FILE +do + if [ $FILE != $LAST ] + then + BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} + echo "'"$FILE"'" title "'"$TITLE"'" ",\\" >> $WHAT.gnuplot + fi +done +BASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} +echo "'"$LAST"'" title "'"$TITLE"'" >> $WHAT.gnuplot + +echo set term jpeg large >> $WHAT.gnuplot +echo set output "'"$WHAT.jpg"'" >> $WHAT.gnuplot +echo plot \\ >> $WHAT.gnuplot + +for FILE in $DATA_FILE +do + if [ $FILE != $LAST ] + then + BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} + echo "'"$FILE"'" title "'"$TITLE"'" ",\\" >> $WHAT.gnuplot + fi +done +BASE=${LAST##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} +echo "'"$LAST"'" title "'"$TITLE"'" >> $WHAT.gnuplot + + +gnuplot -persist < $WHAT.gnuplot + +rm $WHAT.gnuplot + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_mean_script.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_mean_script.sh new file mode 100644 index 0000000000000000000000000000000000000000..b10df0240a524e5f600cf03330a260c455a96fc8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_mean_script.sh @@ -0,0 +1,52 @@ +#! /bin/bash +WHAT=$1 +DIR=$2 +MINIC=$3 +MAXIC=$4 +MINOC=$5 +MAXOC=$6 +prefix=$8 + +meanstatsfilename=$2/mean.html + +WORK_DIR=tmp +mkdir $WORK_DIR + +DATA_FILE=`find $DIR -name "*.dat" | grep _${WHAT}` + +if [ -n "$DATA_FILE" ]; then + + echo "" + echo "$1..." + for FILE in $DATA_FILE + do + ##echo hello world + ##echo "mk_mean_script1" ${FILE} + BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} + + ##echo "mk_mean_script1" ${TITLE} + cp $FILE ${WORK_DIR}/${TITLE} + + done + + cd $WORK_DIR + ../main $1 $3 $4 $5 $6 * >> ../$meanstatsfilename + ../mk_new_gnuplot.sh $1 $2 $7 + rm -f *.gnuplot + cd .. + + echo '
' >> $meanstatsfilename + + webpagefilename=$2/index.html + # echo '

'${WHAT}'

' >> $webpagefilename + echo '
'${WHAT}'
' >> $webpagefilename + +fi + +rm -R $WORK_DIR + + + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_new_gnuplot.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_new_gnuplot.sh new file mode 100644 index 0000000000000000000000000000000000000000..fad3b23a46dc0e6d6a24f78dff7a9d5785c3e1d2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/mk_new_gnuplot.sh @@ -0,0 +1,54 @@ +#!/bin/bash +WHAT=$1 +DIR=$2 + +cat ../gnuplot_common_settings.hh > ${WHAT}.gnuplot + +echo "set title " `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d ";" -f 2` >> $WHAT.gnuplot +echo "set xlabel " `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d ";" -f 3` " offset 0,0" >> $WHAT.gnuplot +echo "set xrange [" `grep ${WHAT} ../action_settings.txt | head -n 1 | cut -d ";" -f 4` "]" >> $WHAT.gnuplot + +if [ $# > 3 ]; then + if [ "$3" == "tiny" ]; then + echo "set xrange [2:16]" >> $WHAT.gnuplot + echo "set nologscale" >> $WHAT.gnuplot + fi +fi + + + +DATA_FILE=`cat ../order_lib` +echo set term postscript color rounded enhanced >> $WHAT.gnuplot +echo set output "'"../${DIR}/$WHAT.ps"'" >> $WHAT.gnuplot + +# echo set term svg color rounded enhanced >> $WHAT.gnuplot +# echo "set terminal svg enhanced size 1000 1000 fname \"Times\" fsize 36" >> $WHAT.gnuplot +# echo set output "'"../${DIR}/$WHAT.svg"'" >> $WHAT.gnuplot + +echo plot \\ >> $WHAT.gnuplot + +for FILE in $DATA_FILE +do + LAST=$FILE +done + +for FILE in $DATA_FILE +do + BASE=${FILE##*/} ; BASE=${FILE##*/} ; AVANT=bench_${WHAT}_ ; REDUC=${BASE##*$AVANT} ; TITLE=${REDUC%.dat} + + echo "'"$FILE"'" `grep $TITLE ../perlib_plot_settings.txt | head -n 1 | cut -d ";" -f 2` "\\" >> $WHAT.gnuplot + if [ $FILE != $LAST ] + then + echo ", \\" >> $WHAT.gnuplot + fi +done +echo " " >> $WHAT.gnuplot + +gnuplot -persist < $WHAT.gnuplot + +rm $WHAT.gnuplot + +ps2pdf ../${DIR}/$WHAT.ps ../${DIR}/$WHAT.pdf +convert -background white -density 120 -rotate 90 -resize 800 +dither -colors 256 -quality 0 ../${DIR}/$WHAT.ps -background white -flatten ../${DIR}/$WHAT.png + +# pstoedit -rotate -90 -xscale 0.8 -yscale 0.8 -centered -yshift -50 -xshift -100 -f plot-svg aat.ps aat2.svg diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/perlib_plot_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/perlib_plot_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..f023cfe02f82ef2d3bd5fb68884df03907691205 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/perlib_plot_settings.txt @@ -0,0 +1,16 @@ +eigen3 ; with lines lw 4 lt 1 lc rgbcolor "black" +eigen2 ; with lines lw 3 lt 1 lc rgbcolor "#999999" +EigenBLAS ; with lines lw 3 lt 3 lc rgbcolor "#999999" +eigen3_novec ; with lines lw 2 lt 1 lc rgbcolor "#999999" +eigen3_nogccvec ; with lines lw 2 lt 2 lc rgbcolor "#991010" +INTEL_MKL ; with lines lw 3 lt 1 lc rgbcolor "#ff0000" +ATLAS ; with lines lw 3 lt 1 lc rgbcolor "#008000" +gmm ; with lines lw 3 lt 1 lc rgbcolor "#0000ff" +ublas ; with lines lw 3 lt 1 lc rgbcolor "#00b7ff" +mtl4 ; with lines lw 3 lt 1 lc rgbcolor "#d18847" +blitz ; with lines lw 3 lt 1 lc rgbcolor "#ff00ff" +F77 ; with lines lw 3 lt 3 lc rgbcolor "#e6e64c" +OPENBLAS ; with lines lw 3 lt 1 lc rgbcolor "#C05600" +C ; with lines lw 3 lt 3 lc rgbcolor "#e6bd96" +ACML ; with lines lw 2 lt 3 lc rgbcolor "#e6e64c" +blaze ; with lines lw 3 lt 1 lc rgbcolor "#ff00ff" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/regularize.cxx b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/regularize.cxx new file mode 100644 index 0000000000000000000000000000000000000000..eea2b8b85f2f50863dd1e1d53d00cf45c34cc49b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/regularize.cxx @@ -0,0 +1,131 @@ +//===================================================== +// File : regularize.cxx +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:15 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include +#include +#include +#include +#include "bench_parameter.hh" +#include + +using namespace std; + +void read_xy_file(const string & filename, vector & tab_sizes, vector & tab_mflops); +void regularize_curve(const string & filename, + const vector & tab_mflops, + const vector & tab_sizes, + int start_cut_size, int stop_cut_size); +///////////////////////////////////////////////////////////////////////////////////////////////// + +int main( int argc , char *argv[] ) +{ + + // input data + + if (argc<4){ + INFOS("!!! Error ... usage : main filename start_cut_size stop_cut_size regularize_filename"); + exit(0); + } + INFOS(argc); + + int start_cut_size=atoi(argv[2]); + int stop_cut_size=atoi(argv[3]); + + string filename=argv[1]; + string regularize_filename=argv[4]; + + INFOS(filename); + INFOS("start_cut_size="< tab_sizes; + vector tab_mflops; + + read_xy_file(filename,tab_sizes,tab_mflops); + + // regularizeing + + regularize_curve(regularize_filename,tab_mflops,tab_sizes,start_cut_size,stop_cut_size); + + +} + +////////////////////////////////////////////////////////////////////////////////////// + +void regularize_curve(const string & filename, + const vector & tab_mflops, + const vector & tab_sizes, + int start_cut_size, int stop_cut_size) +{ + int size=tab_mflops.size(); + ofstream output_file (filename.c_str(),ios::out) ; + + int i=0; + + while(tab_sizes[i] & tab_sizes, vector & tab_mflops){ + + ifstream input_file (filename.c_str(),ios::in) ; + + if (!input_file){ + INFOS("!!! Error opening "<> size >> mflops ){ + nb_point++; + tab_sizes.push_back(size); + tab_mflops.push_back(mflops); + } + SCRUTE(nb_point); + + input_file.close(); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth.cxx b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth.cxx new file mode 100644 index 0000000000000000000000000000000000000000..e5270cc3295a4e43d7d1cf6ed30bfb4dac874c0a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth.cxx @@ -0,0 +1,198 @@ +//===================================================== +// File : smooth.cxx +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:15 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include +#include +#include +#include +#include +#include "bench_parameter.hh" +#include + +using namespace std; + +void read_xy_file(const string & filename, vector & tab_sizes, vector & tab_mflops); +void write_xy_file(const string & filename, vector & tab_sizes, vector & tab_mflops); +void smooth_curve(const vector & tab_mflops, vector & smooth_tab_mflops,int window_half_width); +void centered_smooth_curve(const vector & tab_mflops, vector & smooth_tab_mflops,int window_half_width); + +///////////////////////////////////////////////////////////////////////////////////////////////// + +int main( int argc , char *argv[] ) +{ + + // input data + + if (argc<3){ + INFOS("!!! Error ... usage : main filename window_half_width smooth_filename"); + exit(0); + } + INFOS(argc); + + int window_half_width=atoi(argv[2]); + + string filename=argv[1]; + string smooth_filename=argv[3]; + + INFOS(filename); + INFOS("window_half_width="< tab_sizes; + vector tab_mflops; + + read_xy_file(filename,tab_sizes,tab_mflops); + + // smoothing + + vector smooth_tab_mflops; + + //smooth_curve(tab_mflops,smooth_tab_mflops,window_half_width); + centered_smooth_curve(tab_mflops,smooth_tab_mflops,window_half_width); + + // output result + + write_xy_file(smooth_filename,tab_sizes,smooth_tab_mflops); + + +} + +/////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + +template +double weighted_mean(const VECTOR & data) +{ + + double mean=0.0; + + for (int i=0 ; i & tab_mflops, vector & smooth_tab_mflops,int window_half_width){ + + int window_width=2*window_half_width+1; + + int size=tab_mflops.size(); + + vector sample(window_width); + + for (int i=0 ; i < size ; i++){ + + for ( int j=0 ; j < window_width ; j++ ){ + + int shifted_index=i+j-window_half_width; + if (shifted_index<0) shifted_index=0; + if (shifted_index>size-1) shifted_index=size-1; + sample[j]=tab_mflops[shifted_index]; + + } + + smooth_tab_mflops.push_back(weighted_mean(sample)); + + } + +} + +void centered_smooth_curve(const vector & tab_mflops, vector & smooth_tab_mflops,int window_half_width){ + + int max_window_width=2*window_half_width+1; + + int size=tab_mflops.size(); + + + for (int i=0 ; i < size ; i++){ + + deque sample; + + + sample.push_back(tab_mflops[i]); + + for ( int j=1 ; j <= window_half_width ; j++ ){ + + int before=i-j; + int after=i+j; + + if ((before>=0)&&(after & tab_sizes, vector & tab_mflops){ + + ofstream output_file (filename.c_str(),ios::out) ; + + for (int i=0 ; i < tab_sizes.size() ; i++) + { + output_file << tab_sizes[i] << " " << tab_mflops[i] << endl ; + } + + output_file.close(); + +} + + +/////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + +void read_xy_file(const string & filename, vector & tab_sizes, vector & tab_mflops){ + + ifstream input_file (filename.c_str(),ios::in) ; + + if (!input_file){ + INFOS("!!! Error opening "<> size >> mflops ){ + nb_point++; + tab_sizes.push_back(size); + tab_mflops.push_back(mflops); + } + SCRUTE(nb_point); + + input_file.close(); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth_all.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth_all.sh new file mode 100644 index 0000000000000000000000000000000000000000..3e5bfdf47f6b6ecce273307f126d3fb75e97eb5a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/data/smooth_all.sh @@ -0,0 +1,68 @@ +#! /bin/bash +ORIG_DIR=$1 +SMOOTH_DIR=${ORIG_DIR}_smooth +mkdir ${SMOOTH_DIR} + +AXPY_FILE=`find ${ORIG_DIR} -name "*.dat" | grep axpy` +for FILE in ${AXPY_FILE} +do + echo $FILE + BASE=${FILE##*/} + ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}_tmp + ./regularize ${SMOOTH_DIR}/${BASE}_tmp 2500 15000 ${SMOOTH_DIR}/${BASE} + rm -f ${SMOOTH_DIR}/${BASE}_tmp +done + + +MATRIX_VECTOR_FILE=`find ${ORIG_DIR} -name "*.dat" | grep matrix_vector` +for FILE in ${MATRIX_VECTOR_FILE} +do + echo $FILE + BASE=${FILE##*/} + ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE}_tmp + ./regularize ${SMOOTH_DIR}/${BASE}_tmp 50 180 ${SMOOTH_DIR}/${BASE} + rm -f ${SMOOTH_DIR}/${BASE}_tmp +done + +MATRIX_MATRIX_FILE=`find ${ORIG_DIR} -name "*.dat" | grep matrix_matrix` +for FILE in ${MATRIX_MATRIX_FILE} +do + echo $FILE + BASE=${FILE##*/} + ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE} +done + +AAT_FILE=`find ${ORIG_DIR} -name "*.dat" | grep _aat` +for FILE in ${AAT_FILE} +do + echo $FILE + BASE=${FILE##*/} + ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE} +done + + +ATA_FILE=`find ${ORIG_DIR} -name "*.dat" | grep _ata` +for FILE in ${ATA_FILE} +do + echo $FILE + BASE=${FILE##*/} + ./smooth ${ORIG_DIR}/${BASE} 4 ${SMOOTH_DIR}/${BASE} +done + +### no smoothing for tinyvector and matrices libs + +TINY_BLITZ_FILE=`find ${ORIG_DIR} -name "*.dat" | grep tiny_blitz` +for FILE in ${TINY_BLITZ_FILE} +do + echo $FILE + BASE=${FILE##*/} + cp ${ORIG_DIR}/${BASE} ${SMOOTH_DIR}/${BASE} +done + +TVMET_FILE=`find ${ORIG_DIR} -name "*.dat" | grep tvmet` +for FILE in ${TVMET_FILE} +do + echo $FILE + BASE=${FILE##*/} + cp ${ORIG_DIR}/${BASE} ${SMOOTH_DIR}/${BASE} +done diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench.hh new file mode 100644 index 0000000000000000000000000000000000000000..0732940d532679af3345b836e52dfeefcb887548 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench.hh @@ -0,0 +1,168 @@ +//===================================================== +// File : bench.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:16 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BENCH_HH +#define BENCH_HH + +#include "btl.hh" +#include "bench_parameter.hh" +#include +#include "utilities.h" +#include "size_lin_log.hh" +#include "xy_file.hh" +#include +#include +#include "timers/portable_perf_analyzer.hh" +// #include "timers/mixed_perf_analyzer.hh" +// #include "timers/x86_perf_analyzer.hh" +// #include "timers/STL_perf_analyzer.hh" +#ifdef HAVE_MKL +extern "C" void cblas_saxpy(const int, const float, const float*, const int, float *, const int); +#endif +using namespace std; + +template class Perf_Analyzer, class Action> +BTL_DONT_INLINE void bench( int size_min, int size_max, int nb_point ) +{ + if (BtlConfig::skipAction(Action::name())) + return; + + string filename="bench_"+Action::name()+".dat"; + + INFOS("starting " < tab_mflops(nb_point); + std::vector tab_sizes(nb_point); + + // matrices and vector size calculations + size_lin_log(nb_point,size_min,size_max,tab_sizes); + + std::vector oldSizes; + std::vector oldFlops; + bool hasOldResults = read_xy_file(filename, oldSizes, oldFlops, true); + int oldi = oldSizes.size() - 1; + + // loop on matrix size + Perf_Analyzer perf_action; + for (int i=nb_point-1;i>=0;i--) + { + //INFOS("size=" <=0 && oldSizes[oldi]>tab_sizes[i]) + --oldi; + if (oldi>=0 && oldSizes[oldi]==tab_sizes[i]) + { + if (oldFlops[oldi] "; + else + std::cout << "\t < "; + std::cout << oldFlops[oldi]; + } + --oldi; + } + std::cout << " MFlops (" << nb_point-i << "/" << nb_point << ")" << std::endl; + } + + if (!BtlConfig::Instance.overwriteResults) + { + if (hasOldResults) + { + // merge the two data + std::vector newSizes; + std::vector newFlops; + unsigned int i=0; + unsigned int j=0; + while (i +BTL_DONT_INLINE void bench( int size_min, int size_max, int nb_point ){ + + // if the rdtsc is not available : + bench(size_min,size_max,nb_point); + // if the rdtsc is available : +// bench(size_min,size_max,nb_point); + + + // Only for small problem size. Otherwise it will be too long +// bench(size_min,size_max,nb_point); +// bench(size_min,size_max,nb_point); + +} + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench_parameter.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench_parameter.hh new file mode 100644 index 0000000000000000000000000000000000000000..2b01149f914433f2f4cf79e3080409badf734037 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/bench_parameter.hh @@ -0,0 +1,53 @@ +//===================================================== +// File : bench_parameter.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:16 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BENCH_PARAMETER_HH +#define BENCH_PARAMETER_HH + +// minimal time for each measurement +#define REAL_TYPE float +// minimal time for each measurement +#define MIN_TIME 0.2 +// nb of point on bench curves +#define NB_POINT 100 +// min vector size for axpy bench +#define MIN_AXPY 5 +// max vector size for axpy bench +#define MAX_AXPY 3000000 +// min matrix size for matrix vector product bench +#define MIN_MV 5 +// max matrix size for matrix vector product bench +#define MAX_MV 5000 +// min matrix size for matrix matrix product bench +#define MIN_MM 5 +// max matrix size for matrix matrix product bench +#define MAX_MM MAX_MV +// min matrix size for LU bench +#define MIN_LU 5 +// max matrix size for LU bench +#define MAX_LU 3000 +// max size for tiny vector and matrix +#define TINY_MV_MAX_SIZE 16 +// default nb_sample for x86 timer +#define DEFAULT_NB_SAMPLE 1000 + +// how many times we run a single bench (keep the best perf) +#define DEFAULT_NB_TRIES 3 + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/btl.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/btl.hh new file mode 100644 index 0000000000000000000000000000000000000000..706b00fb05f1109852a8537f01618031ab792de7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/btl.hh @@ -0,0 +1,242 @@ +//===================================================== +// File : btl.hh +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BTL_HH +#define BTL_HH + +#include "bench_parameter.hh" +#include +#include +#include +#include +#include "utilities.h" + +#if (defined __GNUC__) +#define BTL_ALWAYS_INLINE __attribute__((always_inline)) inline +#else +#define BTL_ALWAYS_INLINE inline +#endif + +#if (defined __GNUC__) +#define BTL_DONT_INLINE __attribute__((noinline)) +#else +#define BTL_DONT_INLINE +#endif + +#if (defined __GNUC__) +#define BTL_ASM_COMMENT(X) asm("#" X) +#else +#define BTL_ASM_COMMENT(X) +#endif + +#ifdef __SSE__ +#include "xmmintrin.h" +// This enables flush to zero (FTZ) and denormals are zero (DAZ) modes: +#define BTL_DISABLE_SSE_EXCEPTIONS() { _mm_setcsr(_mm_getcsr() | 0x8040); } +#else +#define BTL_DISABLE_SSE_EXCEPTIONS() +#endif + +/** Enhanced std::string +*/ +class BtlString : public std::string +{ +public: + BtlString() : std::string() {} + BtlString(const BtlString& str) : std::string(static_cast(str)) {} + BtlString(const std::string& str) : std::string(str) {} + BtlString(const char* str) : std::string(str) {} + + operator const char* () const { return c_str(); } + + void trim( bool left = true, bool right = true ) + { + int lspaces, rspaces, len = length(), i; + lspaces = rspaces = 0; + + if ( left ) + for (i=0; i=0 && (at(i)==' '||at(i)=='\t'||at(i)=='\r'||at(i)=='\n'); rspaces++,i--); + + *this = substr(lspaces, len-lspaces-rspaces); + } + + std::vector split( const BtlString& delims = "\t\n ") const + { + std::vector ret; + unsigned int numSplits = 0; + size_t start, pos; + start = 0; + do + { + pos = find_first_of(delims, start); + if (pos == start) + { + ret.push_back(""); + start = pos + 1; + } + else if (pos == npos) + ret.push_back( substr(start) ); + else + { + ret.push_back( substr(start, pos - start) ); + start = pos + 1; + } + //start = find_first_not_of(delims, start); + ++numSplits; + } while (pos != npos); + return ret; + } + + bool endsWith(const BtlString& str) const + { + if(str.size()>this->size()) + return false; + return this->substr(this->size()-str.size(),str.size()) == str; + } + bool contains(const BtlString& str) const + { + return this->find(str)size(); + } + bool beginsWith(const BtlString& str) const + { + if(str.size()>this->size()) + return false; + return this->substr(0,str.size()) == str; + } + + BtlString toLowerCase( void ) + { + std::transform(begin(), end(), begin(), static_cast(::tolower) ); + return *this; + } + BtlString toUpperCase( void ) + { + std::transform(begin(), end(), begin(), static_cast(::toupper) ); + return *this; + } + + /** Case insensitive comparison. + */ + bool isEquiv(const BtlString& str) const + { + BtlString str0 = *this; + str0.toLowerCase(); + BtlString str1 = str; + str1.toLowerCase(); + return str0 == str1; + } + + /** Decompose the current string as a path and a file. + For instance: "dir1/dir2/file.ext" leads to path="dir1/dir2/" and filename="file.ext" + */ + void decomposePathAndFile(BtlString& path, BtlString& filename) const + { + std::vector elements = this->split("/\\"); + path = ""; + filename = elements.back(); + elements.pop_back(); + if (this->at(0)=='/') + path = "/"; + for (unsigned int i=0 ; i config = BtlString(_config).split(" \t\n"); + for (unsigned int i = 0; i m_selectedActionNames; +}; + +#define BTL_MAIN \ + BtlConfig BtlConfig::Instance + +#endif // BTL_HH diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_function.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_function.hh new file mode 100644 index 0000000000000000000000000000000000000000..e467cb64845c64b13b418c7873eef2f8b056ee4f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_function.hh @@ -0,0 +1,54 @@ +//===================================================== +// File : init_function.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:18 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef INIT_FUNCTION_HH +#define INIT_FUNCTION_HH + +double simple_function(int index) +{ + return index; +} + +double simple_function(int index_i, int index_j) +{ + return index_i+index_j; +} + +double pseudo_random(int /*index*/) +{ + return std::rand()/double(RAND_MAX); +} + +double pseudo_random(int /*index_i*/, int /*index_j*/) +{ + return std::rand()/double(RAND_MAX); +} + + +double null_function(int /*index*/) +{ + return 0.0; +} + +double null_function(int /*index_i*/, int /*index_j*/) +{ + return 0.0; +} + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_matrix.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_matrix.hh new file mode 100644 index 0000000000000000000000000000000000000000..6382d30c830caa346fd17f88be35c3d2470544fb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/init/init_matrix.hh @@ -0,0 +1,64 @@ +//===================================================== +// File : init_matrix.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:19 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef INIT_MATRIX_HH +#define INIT_MATRIX_HH + +// The Vector class must satisfy the following part of STL vector concept : +// resize() method +// [] operator for setting element +// value_type defined +template +BTL_DONT_INLINE void init_row(Vector & X, int size, int row){ + + X.resize(size); + + for (unsigned int j=0;j +BTL_DONT_INLINE void init_matrix(Vector & A, int size){ + A.resize(size); + for (unsigned int row=0; row(A[row],size,row); + } +} + +template +BTL_DONT_INLINE void init_matrix_symm(Matrix& A, int size){ + A.resize(size); + for (unsigned int row=0; row +// Copyright (C) EDF R&D, lun sep 30 14:23:18 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef INIT_VECTOR_HH +#define INIT_VECTOR_HH + +// The Vector class must satisfy the following part of STL vector concept : +// resize() method +// [] operator for setting element +// value_type defined +template +void init_vector(Vector & X, int size){ + + X.resize(size); + + for (unsigned int i=0;i +// Copyright (C) EDF R&D, lun sep 30 14:23:16 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BENCH_STATIC_HH +#define BENCH_STATIC_HH + +#include "btl.hh" +#include "bench_parameter.hh" +#include +#include "utilities.h" +#include "xy_file.hh" +#include "static/static_size_generator.hh" +#include "timers/portable_perf_analyzer.hh" +// #include "timers/mixed_perf_analyzer.hh" +// #include "timers/x86_perf_analyzer.hh" + +using namespace std; + + +template class Perf_Analyzer, template class Action, template class Interface> +BTL_DONT_INLINE void bench_static(void) +{ + if (BtlConfig::skipAction(Action >::name())) + return; + + string filename = "bench_" + Action >::name() + ".dat"; + + INFOS("starting " << filename); + + const int max_size = TINY_MV_MAX_SIZE; + + std::vector tab_mflops; + std::vector tab_sizes; + + static_size_generator::go(tab_sizes,tab_mflops); + + dump_xy_file(tab_sizes,tab_mflops,filename); +} + +// default Perf Analyzer +template class Action, template class Interface> +BTL_DONT_INLINE void bench_static(void) +{ + bench_static(); + //bench_static(); + //bench_static(); +} + +#endif + + + + + + + + + + + + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/static/intel_bench_fixed_size.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/static/intel_bench_fixed_size.hh new file mode 100644 index 0000000000000000000000000000000000000000..b4edcbc46b88b41885becf1d9761201d744f120b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/static/intel_bench_fixed_size.hh @@ -0,0 +1,66 @@ +//===================================================== +// File : intel_bench_fixed_size.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar déc 3 18:59:37 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _BENCH_FIXED_SIZE_HH_ +#define _BENCH_FIXED_SIZE_HH_ + +#include "utilities.h" +#include "function_time.hh" + +template +double bench_fixed_size(int size, unsigned long long & nb_calc,unsigned long long & nb_init) +{ + + Action action(size); + + double time_baseline=time_init(nb_init,action); + + while (time_baseline < MIN_TIME) { + + //INFOS("nb_init="< > > perf_action; + tab_mflops.push_back(perf_action.eval_mflops(SIZE)); + std::cout << tab_mflops.back() << " MFlops" << std::endl; + static_size_generator::go(tab_sizes,tab_mflops); + }; +}; + +//recursion end + +template class Perf_Analyzer, template class Action, template class Interface> +struct static_size_generator<1,Perf_Analyzer,Action,Interface>{ + static void go(vector & tab_sizes, vector & tab_mflops) + { + tab_sizes.push_back(1); + Perf_Analyzer > > perf_action; + tab_mflops.push_back(perf_action.eval_mflops(1)); + }; +}; + +#endif + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/STL_perf_analyzer.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/STL_perf_analyzer.hh new file mode 100644 index 0000000000000000000000000000000000000000..c9f894b1ffed96e630f1c54eb7972a51a77bf3cc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/STL_perf_analyzer.hh @@ -0,0 +1,82 @@ +//===================================================== +// File : STL_perf_analyzer.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar déc 3 18:59:35 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _STL_PERF_ANALYSER_HH +#define _STL_PERF_ANALYSER_HH + +#include "STL_timer.hh" +#include "bench_parameter.hh" + +template +class STL_Perf_Analyzer{ +public: + STL_Perf_Analyzer(unsigned long long nb_sample=DEFAULT_NB_SAMPLE):_nb_sample(nb_sample),_chronos() + { + MESSAGE("STL_Perf_Analyzer Ctor"); + }; + STL_Perf_Analyzer( const STL_Perf_Analyzer & ){ + INFOS("Copy Ctor not implemented"); + exit(0); + }; + ~STL_Perf_Analyzer( void ){ + MESSAGE("STL_Perf_Analyzer Dtor"); + }; + + + inline double eval_mflops(int size) + { + + ACTION action(size); + + _chronos.start_baseline(_nb_sample); + + do { + + action.initialize(); + } while (_chronos.check()); + + double baseline_time=_chronos.get_time(); + + _chronos.start(_nb_sample); + do { + action.initialize(); + action.calculate(); + } while (_chronos.check()); + + double calculate_time=_chronos.get_time(); + + double corrected_time=calculate_time-baseline_time; + + // cout << size <<" "< +// Copyright (C) EDF R&D, mar déc 3 18:59:35 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +// STL Timer Class. Adapted (L.P.) from the timer class by Musser et Al +// described int the Book : STL Tutorial and reference guide. +// Define a timer class for analyzing algorithm performance. +#include +#include +#include +#include +#include +using namespace std; + +class STL_Timer { +public: + STL_Timer(){ baseline = false; }; // Default constructor + // Start a series of r trials: + void start(unsigned int r){ + reps = r; + count = 0; + iterations.clear(); + iterations.reserve(reps); + initial = time(0); + }; + // Start a series of r trials to determine baseline time: + void start_baseline(unsigned int r) + { + baseline = true; + start(r); + } + // Returns true if the trials have been completed, else false + bool check() + { + ++count; + final = time(0); + if (initial < final) { + iterations.push_back(count); + initial = final; + count = 0; + } + return (iterations.size() < reps); + }; + // Returns the results for external use + double get_time( void ) + { + sort(iterations.begin(), iterations.end()); + return 1.0/iterations[reps/2]; + }; +private: + unsigned int reps; // Number of trials + // For storing loop iterations of a trial + vector iterations; + // For saving initial and final times of a trial + time_t initial, final; + // For counting loop iterations of a trial + unsigned long count; + // true if this is a baseline computation, false otherwise + bool baseline; + // For recording the baseline time + double baseline_time; +}; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/mixed_perf_analyzer.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/mixed_perf_analyzer.hh new file mode 100644 index 0000000000000000000000000000000000000000..e190236e0a6b7208c18698170bd234a5fd63c9c8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/mixed_perf_analyzer.hh @@ -0,0 +1,73 @@ +//===================================================== +// File : mixed_perf_analyzer.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar déc 3 18:59:36 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _MIXED_PERF_ANALYSER_HH +#define _MIXED_PERF_ANALYSER_HH + +#include "x86_perf_analyzer.hh" +#include "portable_perf_analyzer.hh" + +// choose portable perf analyzer for long calculations and x86 analyser for short ones + + +template +class Mixed_Perf_Analyzer{ + +public: + Mixed_Perf_Analyzer( void ):_x86pa(),_ppa(),_use_ppa(true) + { + MESSAGE("Mixed_Perf_Analyzer Ctor"); + }; + Mixed_Perf_Analyzer( const Mixed_Perf_Analyzer & ){ + INFOS("Copy Ctor not implemented"); + exit(0); + }; + ~Mixed_Perf_Analyzer( void ){ + MESSAGE("Mixed_Perf_Analyzer Dtor"); + }; + + + inline double eval_mflops(int size) + { + + double result=0.0; + if (_use_ppa){ + result=_ppa.eval_mflops(size); + if (_ppa.get_nb_calc()>DEFAULT_NB_SAMPLE){_use_ppa=false;} + } + else{ + result=_x86pa.eval_mflops(size); + } + + return result; + } + +private: + + Portable_Perf_Analyzer _ppa; + X86_Perf_Analyzer _x86pa; + bool _use_ppa; + +}; + +#endif + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/portable_perf_analyzer.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/portable_perf_analyzer.hh new file mode 100644 index 0000000000000000000000000000000000000000..5e579fb49afe063ff18874aa52f54fcbacda3bb9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/portable_perf_analyzer.hh @@ -0,0 +1,103 @@ +//===================================================== +// File : portable_perf_analyzer.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar d�c 3 18:59:35 CET 2002 +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _PORTABLE_PERF_ANALYZER_HH +#define _PORTABLE_PERF_ANALYZER_HH + +#include "utilities.h" +#include "timers/portable_timer.hh" + +template +class Portable_Perf_Analyzer{ +public: + Portable_Perf_Analyzer( ):_nb_calc(0), m_time_action(0), _chronos(){ + MESSAGE("Portable_Perf_Analyzer Ctor"); + }; + Portable_Perf_Analyzer( const Portable_Perf_Analyzer & ){ + INFOS("Copy Ctor not implemented"); + exit(0); + }; + ~Portable_Perf_Analyzer(){ + MESSAGE("Portable_Perf_Analyzer Dtor"); + }; + + BTL_DONT_INLINE double eval_mflops(int size) + { + Action action(size); + +// action.initialize(); +// time_action = time_calculate(action); + while (m_time_action < MIN_TIME) + { + if(_nb_calc==0) _nb_calc = 1; + else _nb_calc *= 2; + action.initialize(); + m_time_action = time_calculate(action); + } + + // optimize + for (int i=1; i +// Copyright (C) EDF R&D, mar d�c 3 18:59:35 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _PORTABLE_PERF_ANALYZER_HH +#define _PORTABLE_PERF_ANALYZER_HH + +#include "utilities.h" +#include "timers/portable_timer.hh" + +template +class Portable_Perf_Analyzer{ +public: + Portable_Perf_Analyzer( void ):_nb_calc(1),_nb_init(1),_chronos(){ + MESSAGE("Portable_Perf_Analyzer Ctor"); + }; + Portable_Perf_Analyzer( const Portable_Perf_Analyzer & ){ + INFOS("Copy Ctor not implemented"); + exit(0); + }; + ~Portable_Perf_Analyzer( void ){ + MESSAGE("Portable_Perf_Analyzer Dtor"); + }; + + + + inline double eval_mflops(int size) + { + + Action action(size); + +// double time_baseline = time_init(action); +// while (time_baseline < MIN_TIME_INIT) +// { +// _nb_init *= 2; +// time_baseline = time_init(action); +// } +// +// // optimize +// for (int i=1; i +#include + + +class Portable_Timer +{ + public: + + Portable_Timer() + { + } + + void start() + { + m_start_time = double(mach_absolute_time())*1e-9;; + + } + + void stop() + { + m_stop_time = double(mach_absolute_time())*1e-9;; + + } + + double elapsed() + { + return user_time(); + } + + double user_time() + { + return m_stop_time - m_start_time; + } + + +private: + + double m_stop_time, m_start_time; + +}; // Portable_Timer (Apple) + +#else + +#include +#include +#include +#include + +class Portable_Timer +{ + public: + + Portable_Timer() + { + m_clkid = BtlConfig::Instance.realclock ? CLOCK_REALTIME : CLOCK_PROCESS_CPUTIME_ID; + } + + Portable_Timer(int clkid) : m_clkid(clkid) + {} + + void start() + { + timespec ts; + clock_gettime(m_clkid, &ts); + m_start_time = double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec); + + } + + void stop() + { + timespec ts; + clock_gettime(m_clkid, &ts); + m_stop_time = double(ts.tv_sec) + 1e-9 * double(ts.tv_nsec); + + } + + double elapsed() + { + return user_time(); + } + + double user_time() + { + return m_stop_time - m_start_time; + } + + +private: + + int m_clkid; + double m_stop_time, m_start_time; + +}; // Portable_Timer (Linux) + +#endif + +#endif // PORTABLE_TIMER_HPP diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/x86_perf_analyzer.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/x86_perf_analyzer.hh new file mode 100644 index 0000000000000000000000000000000000000000..37ea21dcc81750813a059af0addc4a5eaaaee750 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/timers/x86_perf_analyzer.hh @@ -0,0 +1,108 @@ +//===================================================== +// File : x86_perf_analyzer.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar d�c 3 18:59:35 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _X86_PERF_ANALYSER_HH +#define _X86_PERF_ANALYSER_HH + +#include "x86_timer.hh" +#include "bench_parameter.hh" + +template +class X86_Perf_Analyzer{ +public: + X86_Perf_Analyzer( unsigned long long nb_sample=DEFAULT_NB_SAMPLE):_nb_sample(nb_sample),_chronos() + { + MESSAGE("X86_Perf_Analyzer Ctor"); + _chronos.find_frequency(); + }; + X86_Perf_Analyzer( const X86_Perf_Analyzer & ){ + INFOS("Copy Ctor not implemented"); + exit(0); + }; + ~X86_Perf_Analyzer( void ){ + MESSAGE("X86_Perf_Analyzer Dtor"); + }; + + + inline double eval_mflops(int size) + { + + ACTION action(size); + + int nb_loop=5; + double calculate_time=0.0; + double baseline_time=0.0; + + for (int j=0 ; j < nb_loop ; j++){ + + _chronos.clear(); + + for(int i=0 ; i < _nb_sample ; i++) + { + _chronos.start(); + action.initialize(); + action.calculate(); + _chronos.stop(); + _chronos.add_get_click(); + } + + calculate_time += double(_chronos.get_shortest_clicks())/_chronos.frequency(); + + if (j==0) action.check_result(); + + _chronos.clear(); + + for(int i=0 ; i < _nb_sample ; i++) + { + _chronos.start(); + action.initialize(); + _chronos.stop(); + _chronos.add_get_click(); + + } + + baseline_time+=double(_chronos.get_shortest_clicks())/_chronos.frequency(); + + } + + double corrected_time = (calculate_time-baseline_time)/double(nb_loop); + + +// INFOS("_nb_sample="<<_nb_sample); +// INFOS("baseline_time="< +// Copyright (C) EDF R&D, mar d�c 3 18:59:35 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef _X86_TIMER_HH +#define _X86_TIMER_HH + +#include +#include +#include +#include +//#include "system_time.h" +#define u32 unsigned int +#include +#include "utilities.h" +#include +#include +#include +#include + +// frequence de la becanne en Hz +//#define FREQUENCY 648000000 +//#define FREQUENCY 1400000000 +#define FREQUENCY 1695000000 + +using namespace std; + + +class X86_Timer { + +public : + + X86_Timer( void ):_frequency(FREQUENCY),_nb_sample(0) + { + MESSAGE("X86_Timer Default Ctor"); + } + + inline void start( void ){ + + rdtsc(_click_start.n32[0],_click_start.n32[1]); + + } + + + inline void stop( void ){ + + rdtsc(_click_stop.n32[0],_click_stop.n32[1]); + + } + + + inline double frequency( void ){ + return _frequency; + } + + double get_elapsed_time_in_second( void ){ + + return (_click_stop.n64-_click_start.n64)/double(FREQUENCY); + + + } + + unsigned long long get_click( void ){ + + return (_click_stop.n64-_click_start.n64); + + } + + inline void find_frequency( void ){ + + time_t initial, final; + int dummy=2; + + initial = time(0); + start(); + do { + dummy+=2; + } + while(time(0)==initial); + // On est au debut d'un cycle d'une seconde !!! + initial = time(0); + start(); + do { + dummy+=2; + } + while(time(0)==initial); + final=time(0); + stop(); + // INFOS("fine grained time : "<< get_elapsed_time_in_second()); + // INFOS("coarse grained time : "<< final-initial); + _frequency=_frequency*get_elapsed_time_in_second()/double(final-initial); + /// INFOS("CPU frequency : "<< _frequency); + + } + + void add_get_click( void ){ + + _nb_sample++; + _counted_clicks[get_click()]++; + fill_history_clicks(); + + } + + void dump_statistics(string filemane){ + + ofstream outfile (filemane.c_str(),ios::out) ; + + std::map::iterator itr; + for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end() ; itr++) + { + outfile << (*itr).first << " " << (*itr).second << endl ; + } + + outfile.close(); + + } + + void dump_history(string filemane){ + + ofstream outfile (filemane.c_str(),ios::out) ; + + + + for(int i=0 ; i<_history_mean_clicks.size() ; i++) + { + outfile << i << " " + << _history_mean_clicks[i] << " " + << _history_shortest_clicks[i] << " " + << _history_most_occured_clicks[i] << endl ; + } + + outfile.close(); + + } + + + + double get_mean_clicks( void ){ + + std::map::iterator itr; + + unsigned long long mean_clicks=0; + + for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end() ; itr++) + { + + mean_clicks+=(*itr).second*(*itr).first; + } + + return mean_clicks/double(_nb_sample); + + } + + double get_shortest_clicks( void ){ + + return double((*_counted_clicks.begin()).first); + + } + + void fill_history_clicks( void ){ + + _history_mean_clicks.push_back(get_mean_clicks()); + _history_shortest_clicks.push_back(get_shortest_clicks()); + _history_most_occured_clicks.push_back(get_most_occured_clicks()); + + } + + + double get_most_occured_clicks( void ){ + + unsigned long long moc=0; + unsigned long long max_occurence=0; + + std::map::iterator itr; + + for(itr=_counted_clicks.begin() ; itr!=_counted_clicks.end() ; itr++) + { + + if (max_occurence<=(*itr).second){ + max_occurence=(*itr).second; + moc=(*itr).first; + } + } + + return double(moc); + + } + + void clear( void ) + { + _counted_clicks.clear(); + + _history_mean_clicks.clear(); + _history_shortest_clicks.clear(); + _history_most_occured_clicks.clear(); + + _nb_sample=0; + } + + + +private : + + union + { + unsigned long int n32[2] ; + unsigned long long n64 ; + } _click_start; + + union + { + unsigned long int n32[2] ; + unsigned long long n64 ; + } _click_stop; + + double _frequency ; + + map _counted_clicks; + + vector _history_mean_clicks; + vector _history_shortest_clicks; + vector _history_most_occured_clicks; + + unsigned long long _nb_sample; + + + +}; + + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/utils/size_lin_log.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/utils/size_lin_log.hh new file mode 100644 index 0000000000000000000000000000000000000000..bbc9f543df14630d30295a505fe473e04a5a4506 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/generic_bench/utils/size_lin_log.hh @@ -0,0 +1,70 @@ +//===================================================== +// File : size_lin_log.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, mar déc 3 18:59:37 CET 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef SIZE_LIN_LOG +#define SIZE_LIN_LOG + +#include "size_log.hh" + +template +void size_lin_log(const int nb_point, const int /*size_min*/, const int size_max, Vector & X) +{ + int ten=10; + int nine=9; + + X.resize(nb_point); + + if (nb_point>ten){ + + for (int i=0;i +void size_log(const int nb_point, const int size_min, const int size_max, Vector & X) +{ + X.resize(nb_point); + + float ls_min=log(float(size_min)); + float ls_max=log(float(size_max)); + + float ls=0.0; + + float delta_ls=(ls_max-ls_min)/(float(nb_point-1)); + + int size=0; + + for (int i=0;i +//# include ok for gcc3.01 +# include + +/* --- INFOS is always defined (without _DEBUG_): to be used for warnings, with release version --- */ + +# define HEREWEARE cout< +// Copyright (C) EDF R&D, lun sep 30 14:23:20 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef XY_FILE_HH +#define XY_FILE_HH +#include +#include +#include +#include +using namespace std; + +bool read_xy_file(const std::string & filename, std::vector & tab_sizes, + std::vector & tab_mflops, bool quiet = false) +{ + + std::ifstream input_file (filename.c_str(),std::ios::in); + + if (!input_file){ + if (!quiet) { + INFOS("!!! Error opening "<> size >> mflops ){ + nb_point++; + tab_sizes.push_back(size); + tab_mflops.push_back(mflops); + } + SCRUTE(nb_point); + + input_file.close(); + return true; +} + +// The Vector class must satisfy the following part of STL vector concept : +// resize() method +// [] operator for setting element +// the vector element must have the << operator define + +using namespace std; + +template +void dump_xy_file(const Vector_A & X, const Vector_B & Y, const std::string & filename){ + + ofstream outfile (filename.c_str(),ios::out) ; + int size=X.size(); + + for (int i=0;i BLASFUNC(cdotu) (int *, float *, int *, float *, int *); +std::complex BLASFUNC(cdotc) (int *, float *, int *, float *, int *); +std::complex BLASFUNC(zdotu) (int *, double *, int *, double *, int *); +std::complex BLASFUNC(zdotc) (int *, double *, int *, double *, int *); +double BLASFUNC(xdotu) (int *, double *, int *, double *, int *); +double BLASFUNC(xdotc) (int *, double *, int *, double *, int *); +#endif + +int BLASFUNC(cdotuw) (int *, float *, int *, float *, int *, float*); +int BLASFUNC(cdotcw) (int *, float *, int *, float *, int *, float*); +int BLASFUNC(zdotuw) (int *, double *, int *, double *, int *, double*); +int BLASFUNC(zdotcw) (int *, double *, int *, double *, int *, double*); + +int BLASFUNC(saxpy) (int *, float *, float *, int *, float *, int *); +int BLASFUNC(daxpy) (int *, double *, double *, int *, double *, int *); +int BLASFUNC(qaxpy) (int *, double *, double *, int *, double *, int *); +int BLASFUNC(caxpy) (int *, float *, float *, int *, float *, int *); +int BLASFUNC(zaxpy) (int *, double *, double *, int *, double *, int *); +int BLASFUNC(xaxpy) (int *, double *, double *, int *, double *, int *); +int BLASFUNC(caxpyc)(int *, float *, float *, int *, float *, int *); +int BLASFUNC(zaxpyc)(int *, double *, double *, int *, double *, int *); +int BLASFUNC(xaxpyc)(int *, double *, double *, int *, double *, int *); + +int BLASFUNC(scopy) (int *, float *, int *, float *, int *); +int BLASFUNC(dcopy) (int *, double *, int *, double *, int *); +int BLASFUNC(qcopy) (int *, double *, int *, double *, int *); +int BLASFUNC(ccopy) (int *, float *, int *, float *, int *); +int BLASFUNC(zcopy) (int *, double *, int *, double *, int *); +int BLASFUNC(xcopy) (int *, double *, int *, double *, int *); + +int BLASFUNC(sswap) (int *, float *, int *, float *, int *); +int BLASFUNC(dswap) (int *, double *, int *, double *, int *); +int BLASFUNC(qswap) (int *, double *, int *, double *, int *); +int BLASFUNC(cswap) (int *, float *, int *, float *, int *); +int BLASFUNC(zswap) (int *, double *, int *, double *, int *); +int BLASFUNC(xswap) (int *, double *, int *, double *, int *); + +float BLASFUNC(sasum) (int *, float *, int *); +float BLASFUNC(scasum)(int *, float *, int *); +double BLASFUNC(dasum) (int *, double *, int *); +double BLASFUNC(qasum) (int *, double *, int *); +double BLASFUNC(dzasum)(int *, double *, int *); +double BLASFUNC(qxasum)(int *, double *, int *); + +int BLASFUNC(isamax)(int *, float *, int *); +int BLASFUNC(idamax)(int *, double *, int *); +int BLASFUNC(iqamax)(int *, double *, int *); +int BLASFUNC(icamax)(int *, float *, int *); +int BLASFUNC(izamax)(int *, double *, int *); +int BLASFUNC(ixamax)(int *, double *, int *); + +int BLASFUNC(ismax) (int *, float *, int *); +int BLASFUNC(idmax) (int *, double *, int *); +int BLASFUNC(iqmax) (int *, double *, int *); +int BLASFUNC(icmax) (int *, float *, int *); +int BLASFUNC(izmax) (int *, double *, int *); +int BLASFUNC(ixmax) (int *, double *, int *); + +int BLASFUNC(isamin)(int *, float *, int *); +int BLASFUNC(idamin)(int *, double *, int *); +int BLASFUNC(iqamin)(int *, double *, int *); +int BLASFUNC(icamin)(int *, float *, int *); +int BLASFUNC(izamin)(int *, double *, int *); +int BLASFUNC(ixamin)(int *, double *, int *); + +int BLASFUNC(ismin)(int *, float *, int *); +int BLASFUNC(idmin)(int *, double *, int *); +int BLASFUNC(iqmin)(int *, double *, int *); +int BLASFUNC(icmin)(int *, float *, int *); +int BLASFUNC(izmin)(int *, double *, int *); +int BLASFUNC(ixmin)(int *, double *, int *); + +float BLASFUNC(samax) (int *, float *, int *); +double BLASFUNC(damax) (int *, double *, int *); +double BLASFUNC(qamax) (int *, double *, int *); +float BLASFUNC(scamax)(int *, float *, int *); +double BLASFUNC(dzamax)(int *, double *, int *); +double BLASFUNC(qxamax)(int *, double *, int *); + +float BLASFUNC(samin) (int *, float *, int *); +double BLASFUNC(damin) (int *, double *, int *); +double BLASFUNC(qamin) (int *, double *, int *); +float BLASFUNC(scamin)(int *, float *, int *); +double BLASFUNC(dzamin)(int *, double *, int *); +double BLASFUNC(qxamin)(int *, double *, int *); + +float BLASFUNC(smax) (int *, float *, int *); +double BLASFUNC(dmax) (int *, double *, int *); +double BLASFUNC(qmax) (int *, double *, int *); +float BLASFUNC(scmax) (int *, float *, int *); +double BLASFUNC(dzmax) (int *, double *, int *); +double BLASFUNC(qxmax) (int *, double *, int *); + +float BLASFUNC(smin) (int *, float *, int *); +double BLASFUNC(dmin) (int *, double *, int *); +double BLASFUNC(qmin) (int *, double *, int *); +float BLASFUNC(scmin) (int *, float *, int *); +double BLASFUNC(dzmin) (int *, double *, int *); +double BLASFUNC(qxmin) (int *, double *, int *); + +int BLASFUNC(sscal) (int *, float *, float *, int *); +int BLASFUNC(dscal) (int *, double *, double *, int *); +int BLASFUNC(qscal) (int *, double *, double *, int *); +int BLASFUNC(cscal) (int *, float *, float *, int *); +int BLASFUNC(zscal) (int *, double *, double *, int *); +int BLASFUNC(xscal) (int *, double *, double *, int *); +int BLASFUNC(csscal)(int *, float *, float *, int *); +int BLASFUNC(zdscal)(int *, double *, double *, int *); +int BLASFUNC(xqscal)(int *, double *, double *, int *); + +float BLASFUNC(snrm2) (int *, float *, int *); +float BLASFUNC(scnrm2)(int *, float *, int *); + +double BLASFUNC(dnrm2) (int *, double *, int *); +double BLASFUNC(qnrm2) (int *, double *, int *); +double BLASFUNC(dznrm2)(int *, double *, int *); +double BLASFUNC(qxnrm2)(int *, double *, int *); + +int BLASFUNC(srot) (int *, float *, int *, float *, int *, float *, float *); +int BLASFUNC(drot) (int *, double *, int *, double *, int *, double *, double *); +int BLASFUNC(qrot) (int *, double *, int *, double *, int *, double *, double *); +int BLASFUNC(csrot) (int *, float *, int *, float *, int *, float *, float *); +int BLASFUNC(zdrot) (int *, double *, int *, double *, int *, double *, double *); +int BLASFUNC(xqrot) (int *, double *, int *, double *, int *, double *, double *); + +int BLASFUNC(srotg) (float *, float *, float *, float *); +int BLASFUNC(drotg) (double *, double *, double *, double *); +int BLASFUNC(qrotg) (double *, double *, double *, double *); +int BLASFUNC(crotg) (float *, float *, float *, float *); +int BLASFUNC(zrotg) (double *, double *, double *, double *); +int BLASFUNC(xrotg) (double *, double *, double *, double *); + +int BLASFUNC(srotmg)(float *, float *, float *, float *, float *); +int BLASFUNC(drotmg)(double *, double *, double *, double *, double *); + +int BLASFUNC(srotm) (int *, float *, int *, float *, int *, float *); +int BLASFUNC(drotm) (int *, double *, int *, double *, int *, double *); +int BLASFUNC(qrotm) (int *, double *, int *, double *, int *, double *); + +/* Level 2 routines */ + +int BLASFUNC(sger)(int *, int *, float *, float *, int *, + float *, int *, float *, int *); +int BLASFUNC(dger)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); +int BLASFUNC(qger)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); +int BLASFUNC(cgeru)(int *, int *, float *, float *, int *, + float *, int *, float *, int *); +int BLASFUNC(cgerc)(int *, int *, float *, float *, int *, + float *, int *, float *, int *); +int BLASFUNC(zgeru)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); +int BLASFUNC(zgerc)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); +int BLASFUNC(xgeru)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); +int BLASFUNC(xgerc)(int *, int *, double *, double *, int *, + double *, int *, double *, int *); + +int BLASFUNC(sgemv)(char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dgemv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(qgemv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(cgemv)(char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zgemv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xgemv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(strsv) (char *, char *, char *, int *, float *, int *, + float *, int *); +int BLASFUNC(dtrsv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(qtrsv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(ctrsv) (char *, char *, char *, int *, float *, int *, + float *, int *); +int BLASFUNC(ztrsv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(xtrsv) (char *, char *, char *, int *, double *, int *, + double *, int *); + +int BLASFUNC(stpsv) (char *, char *, char *, int *, float *, float *, int *); +int BLASFUNC(dtpsv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(qtpsv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(ctpsv) (char *, char *, char *, int *, float *, float *, int *); +int BLASFUNC(ztpsv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(xtpsv) (char *, char *, char *, int *, double *, double *, int *); + +int BLASFUNC(strmv) (char *, char *, char *, int *, float *, int *, + float *, int *); +int BLASFUNC(dtrmv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(qtrmv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(ctrmv) (char *, char *, char *, int *, float *, int *, + float *, int *); +int BLASFUNC(ztrmv) (char *, char *, char *, int *, double *, int *, + double *, int *); +int BLASFUNC(xtrmv) (char *, char *, char *, int *, double *, int *, + double *, int *); + +int BLASFUNC(stpmv) (char *, char *, char *, int *, float *, float *, int *); +int BLASFUNC(dtpmv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(qtpmv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(ctpmv) (char *, char *, char *, int *, float *, float *, int *); +int BLASFUNC(ztpmv) (char *, char *, char *, int *, double *, double *, int *); +int BLASFUNC(xtpmv) (char *, char *, char *, int *, double *, double *, int *); + +int BLASFUNC(stbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *); +int BLASFUNC(dtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(qtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(ctbmv) (char *, char *, char *, int *, int *, float *, int *, float *, int *); +int BLASFUNC(ztbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(xtbmv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); + +int BLASFUNC(stbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *); +int BLASFUNC(dtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(qtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(ctbsv) (char *, char *, char *, int *, int *, float *, int *, float *, int *); +int BLASFUNC(ztbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); +int BLASFUNC(xtbsv) (char *, char *, char *, int *, int *, double *, int *, double *, int *); + +int BLASFUNC(ssymv) (char *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dsymv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(qsymv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(csymv) (char *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zsymv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xsymv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(sspmv) (char *, int *, float *, float *, + float *, int *, float *, float *, int *); +int BLASFUNC(dspmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); +int BLASFUNC(qspmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); +int BLASFUNC(cspmv) (char *, int *, float *, float *, + float *, int *, float *, float *, int *); +int BLASFUNC(zspmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); +int BLASFUNC(xspmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); + +int BLASFUNC(ssyr) (char *, int *, float *, float *, int *, + float *, int *); +int BLASFUNC(dsyr) (char *, int *, double *, double *, int *, + double *, int *); +int BLASFUNC(qsyr) (char *, int *, double *, double *, int *, + double *, int *); +int BLASFUNC(csyr) (char *, int *, float *, float *, int *, + float *, int *); +int BLASFUNC(zsyr) (char *, int *, double *, double *, int *, + double *, int *); +int BLASFUNC(xsyr) (char *, int *, double *, double *, int *, + double *, int *); + +int BLASFUNC(ssyr2) (char *, int *, float *, + float *, int *, float *, int *, float *, int *); +int BLASFUNC(dsyr2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); +int BLASFUNC(qsyr2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); +int BLASFUNC(csyr2) (char *, int *, float *, + float *, int *, float *, int *, float *, int *); +int BLASFUNC(zsyr2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); +int BLASFUNC(xsyr2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); + +int BLASFUNC(sspr) (char *, int *, float *, float *, int *, + float *); +int BLASFUNC(dspr) (char *, int *, double *, double *, int *, + double *); +int BLASFUNC(qspr) (char *, int *, double *, double *, int *, + double *); +int BLASFUNC(cspr) (char *, int *, float *, float *, int *, + float *); +int BLASFUNC(zspr) (char *, int *, double *, double *, int *, + double *); +int BLASFUNC(xspr) (char *, int *, double *, double *, int *, + double *); + +int BLASFUNC(sspr2) (char *, int *, float *, + float *, int *, float *, int *, float *); +int BLASFUNC(dspr2) (char *, int *, double *, + double *, int *, double *, int *, double *); +int BLASFUNC(qspr2) (char *, int *, double *, + double *, int *, double *, int *, double *); +int BLASFUNC(cspr2) (char *, int *, float *, + float *, int *, float *, int *, float *); +int BLASFUNC(zspr2) (char *, int *, double *, + double *, int *, double *, int *, double *); +int BLASFUNC(xspr2) (char *, int *, double *, + double *, int *, double *, int *, double *); + +int BLASFUNC(cher) (char *, int *, float *, float *, int *, + float *, int *); +int BLASFUNC(zher) (char *, int *, double *, double *, int *, + double *, int *); +int BLASFUNC(xher) (char *, int *, double *, double *, int *, + double *, int *); + +int BLASFUNC(chpr) (char *, int *, float *, float *, int *, float *); +int BLASFUNC(zhpr) (char *, int *, double *, double *, int *, double *); +int BLASFUNC(xhpr) (char *, int *, double *, double *, int *, double *); + +int BLASFUNC(cher2) (char *, int *, float *, + float *, int *, float *, int *, float *, int *); +int BLASFUNC(zher2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); +int BLASFUNC(xher2) (char *, int *, double *, + double *, int *, double *, int *, double *, int *); + +int BLASFUNC(chpr2) (char *, int *, float *, + float *, int *, float *, int *, float *); +int BLASFUNC(zhpr2) (char *, int *, double *, + double *, int *, double *, int *, double *); +int BLASFUNC(xhpr2) (char *, int *, double *, + double *, int *, double *, int *, double *); + +int BLASFUNC(chemv) (char *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zhemv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xhemv) (char *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(chpmv) (char *, int *, float *, float *, + float *, int *, float *, float *, int *); +int BLASFUNC(zhpmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); +int BLASFUNC(xhpmv) (char *, int *, double *, double *, + double *, int *, double *, double *, int *); + +int BLASFUNC(snorm)(char *, int *, int *, float *, int *); +int BLASFUNC(dnorm)(char *, int *, int *, double *, int *); +int BLASFUNC(cnorm)(char *, int *, int *, float *, int *); +int BLASFUNC(znorm)(char *, int *, int *, double *, int *); + +int BLASFUNC(sgbmv)(char *, int *, int *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dgbmv)(char *, int *, int *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(qgbmv)(char *, int *, int *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(cgbmv)(char *, int *, int *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zgbmv)(char *, int *, int *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xgbmv)(char *, int *, int *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(ssbmv)(char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dsbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(qsbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(csbmv)(char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zsbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xsbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(chbmv)(char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zhbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xhbmv)(char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +/* Level 3 routines */ + +int BLASFUNC(sgemm)(char *, char *, int *, int *, int *, float *, + float *, int *, float *, int *, float *, float *, int *); +int BLASFUNC(dgemm)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); +int BLASFUNC(qgemm)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); +int BLASFUNC(cgemm)(char *, char *, int *, int *, int *, float *, + float *, int *, float *, int *, float *, float *, int *); +int BLASFUNC(zgemm)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); +int BLASFUNC(xgemm)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); + +int BLASFUNC(cgemm3m)(char *, char *, int *, int *, int *, float *, + float *, int *, float *, int *, float *, float *, int *); +int BLASFUNC(zgemm3m)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); +int BLASFUNC(xgemm3m)(char *, char *, int *, int *, int *, double *, + double *, int *, double *, int *, double *, double *, int *); + +int BLASFUNC(sge2mm)(char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *, + float *, float *, int *); +int BLASFUNC(dge2mm)(char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *, + double *, double *, int *); +int BLASFUNC(cge2mm)(char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *, + float *, float *, int *); +int BLASFUNC(zge2mm)(char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *, + double *, double *, int *); + +int BLASFUNC(strsm)(char *, char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *); +int BLASFUNC(dtrsm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(qtrsm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(ctrsm)(char *, char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *); +int BLASFUNC(ztrsm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(xtrsm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); + +int BLASFUNC(strmm)(char *, char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *); +int BLASFUNC(dtrmm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(qtrmm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(ctrmm)(char *, char *, char *, char *, int *, int *, + float *, float *, int *, float *, int *); +int BLASFUNC(ztrmm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); +int BLASFUNC(xtrmm)(char *, char *, char *, char *, int *, int *, + double *, double *, int *, double *, int *); + +int BLASFUNC(ssymm)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dsymm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(qsymm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(csymm)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zsymm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xsymm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(csymm3m)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zsymm3m)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xsymm3m)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(ssyrk)(char *, char *, int *, int *, float *, float *, int *, + float *, float *, int *); +int BLASFUNC(dsyrk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); +int BLASFUNC(qsyrk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); +int BLASFUNC(csyrk)(char *, char *, int *, int *, float *, float *, int *, + float *, float *, int *); +int BLASFUNC(zsyrk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); +int BLASFUNC(xsyrk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); + +int BLASFUNC(ssyr2k)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(dsyr2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(qsyr2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(csyr2k)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zsyr2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(xsyr2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); + +int BLASFUNC(chemm)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zhemm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xhemm)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(chemm3m)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zhemm3m)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); +int BLASFUNC(xhemm3m)(char *, char *, int *, int *, double *, double *, int *, + double *, int *, double *, double *, int *); + +int BLASFUNC(cherk)(char *, char *, int *, int *, float *, float *, int *, + float *, float *, int *); +int BLASFUNC(zherk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); +int BLASFUNC(xherk)(char *, char *, int *, int *, double *, double *, int *, + double *, double *, int *); + +int BLASFUNC(cher2k)(char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zher2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(xher2k)(char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(cher2m)(char *, char *, char *, int *, int *, float *, float *, int *, + float *, int *, float *, float *, int *); +int BLASFUNC(zher2m)(char *, char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); +int BLASFUNC(xher2m)(char *, char *, char *, int *, int *, double *, double *, int *, + double*, int *, double *, double *, int *); + +int BLASFUNC(sgemt)(char *, int *, int *, float *, float *, int *, + float *, int *); +int BLASFUNC(dgemt)(char *, int *, int *, double *, double *, int *, + double *, int *); +int BLASFUNC(cgemt)(char *, int *, int *, float *, float *, int *, + float *, int *); +int BLASFUNC(zgemt)(char *, int *, int *, double *, double *, int *, + double *, int *); + +int BLASFUNC(sgema)(char *, char *, int *, int *, float *, + float *, int *, float *, float *, int *, float *, int *); +int BLASFUNC(dgema)(char *, char *, int *, int *, double *, + double *, int *, double*, double *, int *, double*, int *); +int BLASFUNC(cgema)(char *, char *, int *, int *, float *, + float *, int *, float *, float *, int *, float *, int *); +int BLASFUNC(zgema)(char *, char *, int *, int *, double *, + double *, int *, double*, double *, int *, double*, int *); + +int BLASFUNC(sgems)(char *, char *, int *, int *, float *, + float *, int *, float *, float *, int *, float *, int *); +int BLASFUNC(dgems)(char *, char *, int *, int *, double *, + double *, int *, double*, double *, int *, double*, int *); +int BLASFUNC(cgems)(char *, char *, int *, int *, float *, + float *, int *, float *, float *, int *, float *, int *); +int BLASFUNC(zgems)(char *, char *, int *, int *, double *, + double *, int *, double*, double *, int *, double*, int *); + +int BLASFUNC(sgetf2)(int *, int *, float *, int *, int *, int *); +int BLASFUNC(dgetf2)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(qgetf2)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(cgetf2)(int *, int *, float *, int *, int *, int *); +int BLASFUNC(zgetf2)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(xgetf2)(int *, int *, double *, int *, int *, int *); + +int BLASFUNC(sgetrf)(int *, int *, float *, int *, int *, int *); +int BLASFUNC(dgetrf)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(qgetrf)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(cgetrf)(int *, int *, float *, int *, int *, int *); +int BLASFUNC(zgetrf)(int *, int *, double *, int *, int *, int *); +int BLASFUNC(xgetrf)(int *, int *, double *, int *, int *, int *); + +int BLASFUNC(slaswp)(int *, float *, int *, int *, int *, int *, int *); +int BLASFUNC(dlaswp)(int *, double *, int *, int *, int *, int *, int *); +int BLASFUNC(qlaswp)(int *, double *, int *, int *, int *, int *, int *); +int BLASFUNC(claswp)(int *, float *, int *, int *, int *, int *, int *); +int BLASFUNC(zlaswp)(int *, double *, int *, int *, int *, int *, int *); +int BLASFUNC(xlaswp)(int *, double *, int *, int *, int *, int *, int *); + +int BLASFUNC(sgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *); +int BLASFUNC(dgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *); +int BLASFUNC(qgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *); +int BLASFUNC(cgetrs)(char *, int *, int *, float *, int *, int *, float *, int *, int *); +int BLASFUNC(zgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *); +int BLASFUNC(xgetrs)(char *, int *, int *, double *, int *, int *, double *, int *, int *); + +int BLASFUNC(sgesv)(int *, int *, float *, int *, int *, float *, int *, int *); +int BLASFUNC(dgesv)(int *, int *, double *, int *, int *, double*, int *, int *); +int BLASFUNC(qgesv)(int *, int *, double *, int *, int *, double*, int *, int *); +int BLASFUNC(cgesv)(int *, int *, float *, int *, int *, float *, int *, int *); +int BLASFUNC(zgesv)(int *, int *, double *, int *, int *, double*, int *, int *); +int BLASFUNC(xgesv)(int *, int *, double *, int *, int *, double*, int *, int *); + +int BLASFUNC(spotf2)(char *, int *, float *, int *, int *); +int BLASFUNC(dpotf2)(char *, int *, double *, int *, int *); +int BLASFUNC(qpotf2)(char *, int *, double *, int *, int *); +int BLASFUNC(cpotf2)(char *, int *, float *, int *, int *); +int BLASFUNC(zpotf2)(char *, int *, double *, int *, int *); +int BLASFUNC(xpotf2)(char *, int *, double *, int *, int *); + +int BLASFUNC(spotrf)(char *, int *, float *, int *, int *); +int BLASFUNC(dpotrf)(char *, int *, double *, int *, int *); +int BLASFUNC(qpotrf)(char *, int *, double *, int *, int *); +int BLASFUNC(cpotrf)(char *, int *, float *, int *, int *); +int BLASFUNC(zpotrf)(char *, int *, double *, int *, int *); +int BLASFUNC(xpotrf)(char *, int *, double *, int *, int *); + +int BLASFUNC(slauu2)(char *, int *, float *, int *, int *); +int BLASFUNC(dlauu2)(char *, int *, double *, int *, int *); +int BLASFUNC(qlauu2)(char *, int *, double *, int *, int *); +int BLASFUNC(clauu2)(char *, int *, float *, int *, int *); +int BLASFUNC(zlauu2)(char *, int *, double *, int *, int *); +int BLASFUNC(xlauu2)(char *, int *, double *, int *, int *); + +int BLASFUNC(slauum)(char *, int *, float *, int *, int *); +int BLASFUNC(dlauum)(char *, int *, double *, int *, int *); +int BLASFUNC(qlauum)(char *, int *, double *, int *, int *); +int BLASFUNC(clauum)(char *, int *, float *, int *, int *); +int BLASFUNC(zlauum)(char *, int *, double *, int *, int *); +int BLASFUNC(xlauum)(char *, int *, double *, int *, int *); + +int BLASFUNC(strti2)(char *, char *, int *, float *, int *, int *); +int BLASFUNC(dtrti2)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(qtrti2)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(ctrti2)(char *, char *, int *, float *, int *, int *); +int BLASFUNC(ztrti2)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(xtrti2)(char *, char *, int *, double *, int *, int *); + +int BLASFUNC(strtri)(char *, char *, int *, float *, int *, int *); +int BLASFUNC(dtrtri)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(qtrtri)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(ctrtri)(char *, char *, int *, float *, int *, int *); +int BLASFUNC(ztrtri)(char *, char *, int *, double *, int *, int *); +int BLASFUNC(xtrtri)(char *, char *, int *, double *, int *, int *); + +int BLASFUNC(spotri)(char *, int *, float *, int *, int *); +int BLASFUNC(dpotri)(char *, int *, double *, int *, int *); +int BLASFUNC(qpotri)(char *, int *, double *, int *, int *); +int BLASFUNC(cpotri)(char *, int *, float *, int *, int *); +int BLASFUNC(zpotri)(char *, int *, double *, int *, int *); +int BLASFUNC(xpotri)(char *, int *, double *, int *, int *); + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..6510546323266634e9302f2419e40fece91be908 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface.hh @@ -0,0 +1,83 @@ +//===================================================== +// File : blas_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:28 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef blas_PRODUIT_MATRICE_VECTEUR_HH +#define blas_PRODUIT_MATRICE_VECTEUR_HH + +#include +#include +extern "C" +{ +#include "blas.h" + + // Cholesky Factorization +// void spotrf_(const char* uplo, const int* n, float *a, const int* ld, int* info); +// void dpotrf_(const char* uplo, const int* n, double *a, const int* ld, int* info); + void ssytrd_(char *uplo, const int *n, float *a, const int *lda, float *d, float *e, float *tau, float *work, int *lwork, int *info ); + void dsytrd_(char *uplo, const int *n, double *a, const int *lda, double *d, double *e, double *tau, double *work, int *lwork, int *info ); + void sgehrd_( const int *n, int *ilo, int *ihi, float *a, const int *lda, float *tau, float *work, int *lwork, int *info ); + void dgehrd_( const int *n, int *ilo, int *ihi, double *a, const int *lda, double *tau, double *work, int *lwork, int *info ); + + // LU row pivoting +// void dgetrf_( int *m, int *n, double *a, int *lda, int *ipiv, int *info ); +// void sgetrf_(const int* m, const int* n, float *a, const int* ld, int* ipivot, int* info); + // LU full pivoting + void sgetc2_(const int* n, float *a, const int *lda, int *ipiv, int *jpiv, int*info ); + void dgetc2_(const int* n, double *a, const int *lda, int *ipiv, int *jpiv, int*info ); +#ifdef HAS_LAPACK +#endif +} + +#define MAKE_STRING2(S) #S +#define MAKE_STRING(S) MAKE_STRING2(S) + +#define CAT2(A,B) A##B +#define CAT(A,B) CAT2(A,B) + + +template class blas_interface; + + +static char notrans = 'N'; +static char trans = 'T'; +static char nonunit = 'N'; +static char lower = 'L'; +static char right = 'R'; +static char left = 'L'; +static int intone = 1; + + + +#define SCALAR float +#define SCALAR_PREFIX s +#include "blas_interface_impl.hh" +#undef SCALAR +#undef SCALAR_PREFIX + + +#define SCALAR double +#define SCALAR_PREFIX d +#include "blas_interface_impl.hh" +#undef SCALAR +#undef SCALAR_PREFIX + +#endif + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface_impl.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface_impl.hh new file mode 100644 index 0000000000000000000000000000000000000000..9e0a649052847102a752542c3e6d786d969ad031 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/blas_interface_impl.hh @@ -0,0 +1,147 @@ + +#define BLAS_FUNC(NAME) CAT(CAT(SCALAR_PREFIX,NAME),_) + +template<> class blas_interface : public c_interface_base +{ + +public : + + static SCALAR fone; + static SCALAR fzero; + + static inline std::string name() + { + return MAKE_STRING(CBLASNAME); + } + + static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + BLAS_FUNC(gemv)(¬rans,&N,&N,&fone,A,&N,B,&intone,&fzero,X,&intone); + } + + static inline void symv(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + BLAS_FUNC(symv)(&lower, &N,&fone,A,&N,B,&intone,&fzero,X,&intone); + } + + static inline void syr2(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + BLAS_FUNC(syr2)(&lower,&N,&fone,B,&intone,X,&intone,A,&N); + } + + static inline void ger(gene_matrix & A, gene_vector & X, gene_vector & Y, int N){ + BLAS_FUNC(ger)(&N,&N,&fone,X,&intone,Y,&intone,A,&N); + } + + static inline void rot(gene_vector & A, gene_vector & B, SCALAR c, SCALAR s, int N){ + BLAS_FUNC(rot)(&N,A,&intone,B,&intone,&c,&s); + } + + static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + BLAS_FUNC(gemv)(&trans,&N,&N,&fone,A,&N,B,&intone,&fzero,X,&intone); + } + + static inline void matrix_matrix_product(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){ + BLAS_FUNC(gemm)(¬rans,¬rans,&N,&N,&N,&fone,A,&N,B,&N,&fzero,X,&N); + } + + static inline void transposed_matrix_matrix_product(gene_matrix & A, gene_matrix & B, gene_matrix & X, int N){ + BLAS_FUNC(gemm)(¬rans,¬rans,&N,&N,&N,&fone,A,&N,B,&N,&fzero,X,&N); + } + + static inline void ata_product(gene_matrix & A, gene_matrix & X, int N){ + BLAS_FUNC(syrk)(&lower,&trans,&N,&N,&fone,A,&N,&fzero,X,&N); + } + + static inline void aat_product(gene_matrix & A, gene_matrix & X, int N){ + BLAS_FUNC(syrk)(&lower,¬rans,&N,&N,&fone,A,&N,&fzero,X,&N); + } + + static inline void axpy(SCALAR coef, const gene_vector & X, gene_vector & Y, int N){ + BLAS_FUNC(axpy)(&N,&coef,X,&intone,Y,&intone); + } + + static inline void axpby(SCALAR a, const gene_vector & X, SCALAR b, gene_vector & Y, int N){ + BLAS_FUNC(scal)(&N,&b,Y,&intone); + BLAS_FUNC(axpy)(&N,&a,X,&intone,Y,&intone); + } + + static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){ + int N2 = N*N; + BLAS_FUNC(copy)(&N2, X, &intone, C, &intone); + char uplo = 'L'; + int info = 0; + BLAS_FUNC(potrf)(&uplo, &N, C, &N, &info); + if(info!=0) std::cerr << "potrf_ error " << info << "\n"; + } + + static inline void partial_lu_decomp(const gene_matrix & X, gene_matrix & C, int N){ + int N2 = N*N; + BLAS_FUNC(copy)(&N2, X, &intone, C, &intone); + int info = 0; + int * ipiv = (int*)alloca(sizeof(int)*N); + BLAS_FUNC(getrf)(&N, &N, C, &N, ipiv, &info); + if(info!=0) std::cerr << "getrf_ error " << info << "\n"; + } + + static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){ + BLAS_FUNC(copy)(&N, B, &intone, X, &intone); + BLAS_FUNC(trsv)(&lower, ¬rans, &nonunit, &N, L, &N, X, &intone); + } + + static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix & X, int N){ + BLAS_FUNC(copy)(&N, B, &intone, X, &intone); + BLAS_FUNC(trsm)(&right, &lower, ¬rans, &nonunit, &N, &N, &fone, L, &N, X, &N); + } + + static inline void trmm(gene_matrix & A, gene_matrix & B, gene_matrix & /*X*/, int N){ + BLAS_FUNC(trmm)(&left, &lower, ¬rans,&nonunit, &N,&N,&fone,A,&N,B,&N); + } + + #ifdef HAS_LAPACK + + static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int N){ + int N2 = N*N; + BLAS_FUNC(copy)(&N2, X, &intone, C, &intone); + int info = 0; + int * ipiv = (int*)alloca(sizeof(int)*N); + int * jpiv = (int*)alloca(sizeof(int)*N); + BLAS_FUNC(getc2)(&N, C, &N, ipiv, jpiv, &info); + } + + + + static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int N){ + { + int N2 = N*N; + int inc = 1; + BLAS_FUNC(copy)(&N2, X, &inc, C, &inc); + } + int info = 0; + int ilo = 1; + int ihi = N; + int bsize = 64; + int worksize = N*bsize; + SCALAR* d = new SCALAR[N+worksize]; + BLAS_FUNC(gehrd)(&N, &ilo, &ihi, C, &N, d, d+N, &worksize, &info); + delete[] d; + } + + static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int N){ + { + int N2 = N*N; + int inc = 1; + BLAS_FUNC(copy)(&N2, X, &inc, C, &inc); + } + char uplo = 'U'; + int info = 0; + int bsize = 64; + int worksize = N*bsize; + SCALAR* d = new SCALAR[3*N+worksize]; + BLAS_FUNC(sytrd)(&uplo, &N, C, &N, d, d+N, d+2*N, d+3*N, &worksize, &info); + delete[] d; + } + + #endif // HAS_LAPACK + +}; + +SCALAR blas_interface::fone = SCALAR(1); +SCALAR blas_interface::fzero = SCALAR(0); diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/c_interface_base.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/c_interface_base.h new file mode 100644 index 0000000000000000000000000000000000000000..de613803b7a55beb6635768219d1125dadcefd87 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/BLAS/c_interface_base.h @@ -0,0 +1,73 @@ + +#ifndef BTL_C_INTERFACE_BASE_H +#define BTL_C_INTERFACE_BASE_H + +#include "utilities.h" +#include + +template class c_interface_base +{ + +public: + + typedef real real_type; + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef real* gene_matrix; + typedef real* gene_vector; + + static void free_matrix(gene_matrix & A, int /*N*/){ + delete[] A; + } + + static void free_vector(gene_vector & B){ + delete[] B; + } + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + int N = A_stl.size(); + A = new real[N*N]; + for (int j=0;j +// Copyright (C) EDF R&D, lun sep 30 14:23:28 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "blas_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +#include "action_cholesky.hh" +#include "action_lu_decomp.hh" +#include "action_partial_lu.hh" +#include "action_trisolve_matrix.hh" + +#ifdef HAS_LAPACK +#include "action_hessenberg.hh" +#endif + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + + #ifdef HAS_LAPACK +// bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + #endif + + //bench > >(MIN_LU,MAX_LU,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..4cfc2dcf298fbd1baba1fb0202f3b9d48bae2bd1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/CMakeLists.txt @@ -0,0 +1,2 @@ + +btl_add_bench(btl_STL main.cpp OFF) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/STL_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/STL_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..16658c4baa1768e6de86513dde0badaf102e3b9c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/STL/STL_interface.hh @@ -0,0 +1,244 @@ +//===================================================== +// File : STL_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:24 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef STL_INTERFACE_HH +#define STL_INTERFACE_HH +#include +#include +#include "utilities.h" + +using namespace std; + +template +class STL_interface{ + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef stl_matrix gene_matrix; + + typedef stl_vector gene_vector; + + static inline std::string name( void ) + { + return "STL"; + } + + static void free_matrix(gene_matrix & /*A*/, int /*N*/){} + + static void free_vector(gene_vector & /*B*/){} + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A = A_stl; + } + + static inline void vector_from_stl(gene_vector & B, stl_vector & B_stl){ + B = B_stl; + } + + static inline void vector_to_stl(gene_vector & B, stl_vector & B_stl){ + B_stl = B ; + } + + + static inline void matrix_to_stl(gene_matrix & A, stl_matrix & A_stl){ + A_stl = A ; + } + + static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){ + for (int i=0;i=j) + { + for (int k=0;k > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..e99a0855c997e908ecab1044adef58eb587ec263 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/CMakeLists.txt @@ -0,0 +1,13 @@ + +find_package(BLAZE) +find_package(Boost COMPONENTS system) +if (BLAZE_FOUND AND Boost_FOUND) + include_directories(${BLAZE_INCLUDE_DIR} ${Boost_INCLUDE_DIRS}) + btl_add_bench(btl_blaze main.cpp) + # Note: The newest blaze version requires C++14. + # Ideally, we should set this depending on the version of Blaze we found + set_property(TARGET btl_blaze PROPERTY CXX_STANDARD 14) + if(BUILD_btl_blaze) + target_link_libraries(btl_blaze ${Boost_LIBRARIES}) + endif() +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/blaze_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/blaze_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..7b418f6da067b1d15c0d77cdfa90f057c0f3976b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/blaze_interface.hh @@ -0,0 +1,141 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BLAZE_INTERFACE_HH +#define BLAZE_INTERFACE_HH + +#include +#include +#include +// using namespace blaze; + +#include + +template +class blaze_interface { + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef blaze::DynamicMatrix gene_matrix; + typedef blaze::DynamicVector gene_vector; + + static inline std::string name() { return "blaze"; } + + static void free_matrix(gene_matrix & A, int N){ + return ; + } + + static void free_vector(gene_vector & B){ + return ; + } + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl[0].size(), A_stl.size()); + + for (int j=0; j ipvt(N); +// lu_factor(R, ipvt); +// } + +// static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){ +// X = lower_trisolve(L, B); +// } + + static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){ + cible = source; + } + + static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){ + cible = source; + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/main.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/main.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ccae0cbd57f92b6a7739e4f65452a4a655df5e15 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blaze/main.cpp @@ -0,0 +1,40 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "blaze_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..e203c81522e0b7bdc5f1c0e65fb944d0e8d69049 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/CMakeLists.txt @@ -0,0 +1,17 @@ + +find_package(Blitz) + +if (BLITZ_FOUND) + include_directories(${BLITZ_INCLUDES}) + + btl_add_bench(btl_blitz btl_blitz.cpp) + if (BUILD_btl_blitz) + target_link_libraries(btl_blitz ${BLITZ_LIBRARIES}) + endif () + + btl_add_bench(btl_tiny_blitz btl_tiny_blitz.cpp OFF) + if (BUILD_btl_tiny_blitz) + target_link_libraries(btl_tiny_blitz ${BLITZ_LIBRARIES}) + endif () + +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_LU_solve_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_LU_solve_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..dcb9f567feb098552c8090722769ffafee67d32d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_LU_solve_interface.hh @@ -0,0 +1,192 @@ +//===================================================== +// File : blitz_LU_solve_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BLITZ_LU_SOLVE_INTERFACE_HH +#define BLITZ_LU_SOLVE_INTERFACE_HH + +#include "blitz/array.h" +#include + +BZ_USING_NAMESPACE(blitz) + +template +class blitz_LU_solve_interface : public blitz_interface +{ + +public : + + typedef typename blitz_interface::gene_matrix gene_matrix; + typedef typename blitz_interface::gene_vector gene_vector; + + typedef blitz::Array Pivot_Vector; + + inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N) + { + + pivot.resize(N); + + } + + inline static void free_Pivot_Vector(Pivot_Vector & pivot) + { + + return; + + } + + + static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end) + { + + real somme=0.; + + for (int j=col_start ; j=big ) big = abs( LU( i, j ) ) ; + } + if( big==0. ) { + INFOS( "blitz_LU_factor::Singular matrix" ) ; + exit( 0 ) ; + } + ImplicitScaling( i ) = 1./big ; + } + // Loop over columns of Crout's method : + for( int j=0; j=big ) { + dum = ImplicitScaling( i )*abs( theSum ) ; + big = dum ; + index_max = i ; + } + } + // Interchanging rows and the scale factor : + if( j!=index_max ) { + for( int k=0; k=0; i-- ) { + theSum = X( i ) ; + // theSum = B( i ) ; + theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ; + // Store a component of the solution vector : + X( i ) = theSum/LU( i, i ) ; + // B( i ) = theSum/LU( i, i ) ; + } + + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..a67c47c759df51a89f1f041d65c41f55cd87378d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/blitz_interface.hh @@ -0,0 +1,147 @@ +//===================================================== +// File : blitz_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BLITZ_INTERFACE_HH +#define BLITZ_INTERFACE_HH + +#include +#include +#include +#include +#include +#include + +BZ_USING_NAMESPACE(blitz) + +template +class blitz_interface{ + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef blitz::Array gene_matrix; + typedef blitz::Array gene_vector; +// typedef blitz::Matrix gene_matrix; +// typedef blitz::Vector gene_vector; + + static inline std::string name() { return "blitz"; } + + static void free_matrix(gene_matrix & A, int N){} + + static void free_vector(gene_vector & B){} + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl[0].size(),A_stl.size()); + for (int j=0; j(source); +// for (int i=0;i(source); + cible = source; + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_blitz.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_blitz.cpp new file mode 100644 index 0000000000000000000000000000000000000000..16d2b59517cccceeb228df4f8b9cbb91c578462a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_blitz.cpp @@ -0,0 +1,51 @@ +//===================================================== +// File : main.cpp +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "blitz_interface.hh" +#include "blitz_LU_solve_interface.hh" +#include "bench.hh" +#include "action_matrix_vector_product.hh" +#include "action_matrix_matrix_product.hh" +#include "action_axpy.hh" +#include "action_lu_solve.hh" +#include "action_ata_product.hh" +#include "action_aat_product.hh" +#include "action_atv_product.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + //bench > >(MIN_LU,MAX_LU,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_tiny_blitz.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_tiny_blitz.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9fddde75233704ca04a0e1f253c70293d780de80 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/btl_tiny_blitz.cpp @@ -0,0 +1,38 @@ +//===================================================== +// File : main.cpp +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "tiny_blitz_interface.hh" +#include "static/bench_static.hh" +#include "action_matrix_vector_product.hh" +#include "action_matrix_matrix_product.hh" +#include "action_axpy.hh" + +BTL_MAIN; + +int main() +{ + bench_static(); + bench_static(); + bench_static(); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/tiny_blitz_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/tiny_blitz_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..6b26db72df99443d830887b6a4979582eaefdf24 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/blitz/tiny_blitz_interface.hh @@ -0,0 +1,106 @@ +//===================================================== +// File : tiny_blitz_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef TINY_BLITZ_INTERFACE_HH +#define TINY_BLITZ_INTERFACE_HH + +#include "blitz/array.h" +#include "blitz/tiny.h" +#include "blitz/tinymat.h" +#include "blitz/tinyvec.h" +#include + +#include + +BZ_USING_NAMESPACE(blitz) + +template +class tiny_blitz_interface +{ + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef TinyVector gene_vector; + typedef TinyMatrix gene_matrix; + + static inline std::string name() { return "tiny_blitz"; } + + static void free_matrix(gene_matrix & A, int N){} + + static void free_vector(gene_vector & B){} + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + for (int j=0; j +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "static/bench_static.hh" +#include "action_matrix_vector_product.hh" +#include "action_matrix_matrix_product.hh" +#include "action_axpy.hh" +#include "action_lu_solve.hh" +#include "action_ata_product.hh" +#include "action_aat_product.hh" +#include "action_atv_product.hh" +#include "action_cholesky.hh" +#include "action_trisolve.hh" + +BTL_MAIN; + +int main() +{ + + bench_static(); + bench_static(); + bench_static(); + bench_static(); + bench_static(); + bench_static(); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/eigen2_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/eigen2_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..1deabdae2177fe865aade19ae3dd14594033e336 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/eigen2_interface.hh @@ -0,0 +1,168 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef EIGEN2_INTERFACE_HH +#define EIGEN2_INTERFACE_HH +// #include +#include +#include +#include +#include +#include +#include "btl.hh" + +using namespace Eigen; + +template +class eigen2_interface +{ + +public : + + enum {IsFixedSize = (SIZE!=Dynamic)}; + + typedef real real_type; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef Eigen::Matrix gene_matrix; + typedef Eigen::Matrix gene_vector; + + static inline std::string name( void ) + { + #if defined(EIGEN_VECTORIZE_SSE) + if (SIZE==Dynamic) return "eigen2"; else return "tiny_eigen2"; + #elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX) + if (SIZE==Dynamic) return "eigen2"; else return "tiny_eigen2"; + #else + if (SIZE==Dynamic) return "eigen2_novec"; else return "tiny_eigen2_novec"; + #endif + } + + static void free_matrix(gene_matrix & A, int N) {} + + static void free_vector(gene_vector & B) {} + + static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl[0].size(), A_stl.size()); + + for (int j=0; j().solveTriangular(B); + } + + static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int N){ + X = L.template marked().solveTriangular(B); + } + + static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){ + C = X.llt().matrixL(); +// C = X; +// Cholesky::computeInPlace(C); +// Cholesky::computeInPlaceBlock(C); + } + + static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int N){ + C = X.lu().matrixLU(); +// C = X.inverse(); + } + + static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int N){ + C = Tridiagonalization(X).packedMatrix(); + } + + static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int N){ + C = HessenbergDecomposition(X).packedMatrix(); + } + + + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_adv.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_adv.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fe336892534aa0e1a4106925eaaf74a19a265f09 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_adv.cpp @@ -0,0 +1,44 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen2_interface.hh" +#include "bench.hh" +#include "action_trisolve.hh" +#include "action_trisolve_matrix.hh" +#include "action_cholesky.hh" +#include "action_hessenberg.hh" +#include "action_lu_decomp.hh" +// #include "action_partial_lu.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_linear.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_linear.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c17d16c08c4b3666e99e6012fd4ef08728f12585 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_linear.cpp @@ -0,0 +1,34 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen2_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_matmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_matmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cd9dc9cb0bbd2cbb4043ebbbb74205573163d5fa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_matmat.cpp @@ -0,0 +1,35 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen2_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_vecmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_vecmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8b66cd2d9b5088cb62f416e93bd3033b07b5c07f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen2/main_vecmat.cpp @@ -0,0 +1,36 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen2_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); +// bench > >(MIN_MV,MAX_MV,NB_POINT); +// bench > >(MIN_MV,MAX_MV,NB_POINT); +// bench > >(MIN_MV,MAX_MV,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..06a72b4fb993ff1fb36fe4cc4d8b199da6590802 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/CMakeLists.txt @@ -0,0 +1,65 @@ + + +if((NOT EIGEN3_INCLUDE_DIR) AND Eigen_SOURCE_DIR) + # unless EIGEN3_INCLUDE_DIR is defined, let's use current Eigen version + set(EIGEN3_INCLUDE_DIR ${Eigen_SOURCE_DIR}) + set(EIGEN3_FOUND TRUE) +else() + find_package(Eigen3) +endif() + +if (EIGEN3_FOUND) + + include_directories(${EIGEN3_INCLUDE_DIR}) + btl_add_bench(btl_eigen3_linear main_linear.cpp) + btl_add_bench(btl_eigen3_vecmat main_vecmat.cpp) + btl_add_bench(btl_eigen3_matmat main_matmat.cpp) + btl_add_bench(btl_eigen3_adv main_adv.cpp ) + + btl_add_target_property(btl_eigen3_linear COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=eigen3") + btl_add_target_property(btl_eigen3_vecmat COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=eigen3") + btl_add_target_property(btl_eigen3_matmat COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=eigen3") + btl_add_target_property(btl_eigen3_adv COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=eigen3") + + option(BTL_BENCH_NOGCCVEC "also bench Eigen explicit vec without GCC's auto vec" OFF) + if(CMAKE_COMPILER_IS_GNUCXX AND BTL_BENCH_NOGCCVEC) + btl_add_bench(btl_eigen3_nogccvec_linear main_linear.cpp) + btl_add_bench(btl_eigen3_nogccvec_vecmat main_vecmat.cpp) + btl_add_bench(btl_eigen3_nogccvec_matmat main_matmat.cpp) + btl_add_bench(btl_eigen3_nogccvec_adv main_adv.cpp ) + + btl_add_target_property(btl_eigen3_nogccvec_linear COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec") + btl_add_target_property(btl_eigen3_nogccvec_vecmat COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec") + btl_add_target_property(btl_eigen3_nogccvec_matmat COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec") + btl_add_target_property(btl_eigen3_nogccvec_adv COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=eigen3_nogccvec") + endif() + + + if(NOT BTL_NOVEC) + btl_add_bench(btl_eigen3_novec_linear main_linear.cpp OFF) + btl_add_bench(btl_eigen3_novec_vecmat main_vecmat.cpp OFF) + btl_add_bench(btl_eigen3_novec_matmat main_matmat.cpp OFF) + btl_add_bench(btl_eigen3_novec_adv main_adv.cpp OFF) + btl_add_target_property(btl_eigen3_novec_linear COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec") + btl_add_target_property(btl_eigen3_novec_vecmat COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec") + btl_add_target_property(btl_eigen3_novec_matmat COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec") + btl_add_target_property(btl_eigen3_novec_adv COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_novec") + +# if(BUILD_btl_eigen3_adv) +# target_link_libraries(btl_eigen3_adv ${MKL_LIBRARIES}) +# endif() + + endif() + + btl_add_bench(btl_tiny_eigen3 btl_tiny_eigen3.cpp OFF) + + if(NOT BTL_NOVEC) + btl_add_bench(btl_tiny_eigen3_novec btl_tiny_eigen3.cpp OFF) + btl_add_target_property(btl_tiny_eigen3_novec COMPILE_FLAGS "-DBTL_PREFIX=eigen3_tiny") + + if(BUILD_btl_tiny_eigen3_novec) + btl_add_target_property(btl_tiny_eigen3_novec COMPILE_FLAGS "-DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=eigen3_tiny_novec") + endif() + endif() + +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/btl_tiny_eigen3.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/btl_tiny_eigen3.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d1515be846232c8d0a23b150d870c90df25cc32e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/btl_tiny_eigen3.cpp @@ -0,0 +1,46 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "static/bench_static.hh" +#include "action_matrix_vector_product.hh" +#include "action_matrix_matrix_product.hh" +#include "action_axpy.hh" +#include "action_lu_solve.hh" +#include "action_ata_product.hh" +#include "action_aat_product.hh" +#include "action_atv_product.hh" +#include "action_cholesky.hh" +#include "action_trisolve.hh" + +BTL_MAIN; + +int main() +{ + + bench_static(); + bench_static(); + bench_static(); + bench_static(); + bench_static(); + bench_static(); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/eigen3_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/eigen3_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..2e302d0729306515cfca1975ca6c1689e212d361 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/eigen3_interface.hh @@ -0,0 +1,242 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef EIGEN3_INTERFACE_HH +#define EIGEN3_INTERFACE_HH + +#include +#include +#include "btl.hh" + +using namespace Eigen; + +template +class eigen3_interface +{ + +public : + + enum {IsFixedSize = (SIZE!=Dynamic)}; + + typedef real real_type; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef Eigen::Matrix gene_matrix; + typedef Eigen::Matrix gene_vector; + + static inline std::string name( void ) + { + return EIGEN_MAKESTRING(BTL_PREFIX); + } + + static void free_matrix(gene_matrix & /*A*/, int /*N*/) {} + + static void free_vector(gene_vector & /*B*/) {} + + static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl[0].size(), A_stl.size()); + + for (unsigned int j=0; j().setZero(); + X.template selfadjointView().rankUpdate(A.transpose()); + } + + static inline void aat_product(const gene_matrix & A, gene_matrix & X, int /*N*/){ + X.template triangularView().setZero(); + X.template selfadjointView().rankUpdate(A); + } + + static inline void matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int /*N*/){ + X.noalias() = A*B; + } + + static inline void symv(const gene_matrix & A, const gene_vector & B, gene_vector & X, int /*N*/){ + X.noalias() = (A.template selfadjointView() * B); +// internal::product_selfadjoint_vector(N,A.data(),N, B.data(), 1, X.data(), 1); + } + + template static void triassign(Dest& dst, const Src& src) + { + typedef typename Dest::Scalar Scalar; + typedef typename internal::packet_traits::type Packet; + const int PacketSize = sizeof(Packet)/sizeof(Scalar); + int size = dst.cols(); + for(int j=0; j(j, index, src); + else + dst.template copyPacket(index, j, src); + } + + // do the non-vectorizable part of the assignment + for (int index = alignedEnd; index(N,A.data(),N, X.data(), 1, Y.data(), 1, -1); + for(int j=0; j(c,s)); + } + + static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int /*N*/){ + X.noalias() = (A.transpose()*B); + } + + static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int /*N*/){ + Y += coef * X; + } + + static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int /*N*/){ + Y = a*X + b*Y; + } + + static EIGEN_DONT_INLINE void copy_matrix(const gene_matrix & source, gene_matrix & cible, int /*N*/){ + cible = source; + } + + static EIGEN_DONT_INLINE void copy_vector(const gene_vector & source, gene_vector & cible, int /*N*/){ + cible = source; + } + + static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector& X, int /*N*/){ + X = L.template triangularView().solve(B); + } + + static inline void trisolve_lower_matrix(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int /*N*/){ + X = L.template triangularView().solve(B); + } + + static inline void trmm(const gene_matrix & L, const gene_matrix& B, gene_matrix& X, int /*N*/){ + X.noalias() = L.template triangularView() * B; + } + + static inline void cholesky(const gene_matrix & X, gene_matrix & C, int /*N*/){ + C = X; + internal::llt_inplace::blocked(C); + //C = X.llt().matrixL(); +// C = X; +// Cholesky::computeInPlace(C); +// Cholesky::computeInPlaceBlock(C); + } + + static inline void lu_decomp(const gene_matrix & X, gene_matrix & C, int /*N*/){ + C = X.fullPivLu().matrixLU(); + } + + static inline void partial_lu_decomp(const gene_matrix & X, gene_matrix & C, int N){ + Matrix piv(N); + DenseIndex nb; + C = X; + internal::partial_lu_inplace(C,piv,nb); +// C = X.partialPivLu().matrixLU(); + } + + static inline void tridiagonalization(const gene_matrix & X, gene_matrix & C, int N){ + typename Tridiagonalization::CoeffVectorType aux(N-1); + C = X; + internal::tridiagonalization_inplace(C, aux); + } + + static inline void hessenberg(const gene_matrix & X, gene_matrix & C, int /*N*/){ + C = HessenbergDecomposition(X).packedMatrix(); + } + + + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_adv.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_adv.cpp new file mode 100644 index 0000000000000000000000000000000000000000..95865357e0ec1bea9e0bb2f9928ff5f202d8e68e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_adv.cpp @@ -0,0 +1,44 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "bench.hh" +#include "action_trisolve.hh" +#include "action_trisolve_matrix.hh" +#include "action_cholesky.hh" +#include "action_hessenberg.hh" +#include "action_lu_decomp.hh" +#include "action_partial_lu.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); +// bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + +// bench > >(MIN_LU,MAX_LU,NB_POINT); + bench > >(MIN_LU,MAX_LU,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_linear.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_linear.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e8538b7d0fb746bc14d665709750568f2c755749 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_linear.cpp @@ -0,0 +1,35 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_matmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_matmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..052810a16b7836333d6d989e506614e8a05bc0fb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_matmat.cpp @@ -0,0 +1,35 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_vecmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_vecmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0dda444cfad0f0ca774e85197336190fb3e98066 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/eigen3/main_vecmat.cpp @@ -0,0 +1,36 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "eigen3_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..0bcb0465935f9c40b7f36debb5c7f9309ff20b75 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/CMakeLists.txt @@ -0,0 +1,6 @@ + +find_package(GMM) +if (GMM_FOUND) + include_directories(${GMM_INCLUDES}) + btl_add_bench(btl_gmm main.cpp) +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_LU_solve_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_LU_solve_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..dcb9f567feb098552c8090722769ffafee67d32d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_LU_solve_interface.hh @@ -0,0 +1,192 @@ +//===================================================== +// File : blitz_LU_solve_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BLITZ_LU_SOLVE_INTERFACE_HH +#define BLITZ_LU_SOLVE_INTERFACE_HH + +#include "blitz/array.h" +#include + +BZ_USING_NAMESPACE(blitz) + +template +class blitz_LU_solve_interface : public blitz_interface +{ + +public : + + typedef typename blitz_interface::gene_matrix gene_matrix; + typedef typename blitz_interface::gene_vector gene_vector; + + typedef blitz::Array Pivot_Vector; + + inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N) + { + + pivot.resize(N); + + } + + inline static void free_Pivot_Vector(Pivot_Vector & pivot) + { + + return; + + } + + + static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end) + { + + real somme=0.; + + for (int j=col_start ; j=big ) big = abs( LU( i, j ) ) ; + } + if( big==0. ) { + INFOS( "blitz_LU_factor::Singular matrix" ) ; + exit( 0 ) ; + } + ImplicitScaling( i ) = 1./big ; + } + // Loop over columns of Crout's method : + for( int j=0; j=big ) { + dum = ImplicitScaling( i )*abs( theSum ) ; + big = dum ; + index_max = i ; + } + } + // Interchanging rows and the scale factor : + if( j!=index_max ) { + for( int k=0; k=0; i-- ) { + theSum = X( i ) ; + // theSum = B( i ) ; + theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ; + // Store a component of the solution vector : + X( i ) = theSum/LU( i, i ) ; + // B( i ) = theSum/LU( i, i ) ; + } + + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..3ea303c1bb5b70f520433f168c299a61d06a8e36 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/gmm_interface.hh @@ -0,0 +1,144 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef GMM_INTERFACE_HH +#define GMM_INTERFACE_HH + +#include +#include + +using namespace gmm; + +template +class gmm_interface { + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef gmm::dense_matrix gene_matrix; + typedef stl_vector gene_vector; + + static inline std::string name( void ) + { + return "gmm"; + } + + static void free_matrix(gene_matrix & A, int N){ + return ; + } + + static void free_vector(gene_vector & B){ + return ; + } + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl[0].size(),A_stl.size()); + + for (int j=0; j ipvt(N); + gmm::lu_factor(R, ipvt); + } + + static inline void hessenberg(const gene_matrix & X, gene_matrix & R, int N){ + gmm::copy(X,R); + gmm::Hessenberg_reduction(R,X,false); + } + + static inline void tridiagonalization(const gene_matrix & X, gene_matrix & R, int N){ + gmm::copy(X,R); + gmm::Householder_tridiagonalization(R,X,false); + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/main.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/main.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1f0c051eb997cbedcfab817d2bd0316be0328838 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/gmm/main.cpp @@ -0,0 +1,51 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "gmm_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" +#include "action_hessenberg.hh" +#include "action_partial_lu.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + //bench > >(MIN_LU,MAX_LU,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/.kdbgrc.main b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/.kdbgrc.main new file mode 100644 index 0000000000000000000000000000000000000000..fed082f7f58239a598b2f69344e74744a8567200 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/.kdbgrc.main @@ -0,0 +1,12 @@ +[General] +DebuggerCmdStr= +DriverName=GDB +FileVersion=1 +OptionsSelected= +ProgramArgs= +TTYLevel=7 +WorkingDirectory= + +[Memory] +ColumnWidths=80,0 +NumExprs=0 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..132a501bea47545f6d663db75fc5a0a685bc5b53 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/CMakeLists.txt @@ -0,0 +1,6 @@ + +find_package(MTL4) +if (MTL4_FOUND) + include_directories(${MTL4_INCLUDE_DIR}) + btl_add_bench(btl_mtl4 main.cpp) +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/main.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/main.cpp new file mode 100644 index 0000000000000000000000000000000000000000..96fcfb9c9d06ab40afcc39015c580bef54d6adbe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/main.cpp @@ -0,0 +1,46 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "mtl4_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" +#include "action_cholesky.hh" +// #include "action_lu_decomp.hh" + +BTL_MAIN; + +int main() +{ + + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_LU_solve_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_LU_solve_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..dcb9f567feb098552c8090722769ffafee67d32d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_LU_solve_interface.hh @@ -0,0 +1,192 @@ +//===================================================== +// File : blitz_LU_solve_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:31 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef BLITZ_LU_SOLVE_INTERFACE_HH +#define BLITZ_LU_SOLVE_INTERFACE_HH + +#include "blitz/array.h" +#include + +BZ_USING_NAMESPACE(blitz) + +template +class blitz_LU_solve_interface : public blitz_interface +{ + +public : + + typedef typename blitz_interface::gene_matrix gene_matrix; + typedef typename blitz_interface::gene_vector gene_vector; + + typedef blitz::Array Pivot_Vector; + + inline static void new_Pivot_Vector(Pivot_Vector & pivot,int N) + { + + pivot.resize(N); + + } + + inline static void free_Pivot_Vector(Pivot_Vector & pivot) + { + + return; + + } + + + static inline real matrix_vector_product_sliced(const gene_matrix & A, gene_vector B, int row, int col_start, int col_end) + { + + real somme=0.; + + for (int j=col_start ; j=big ) big = abs( LU( i, j ) ) ; + } + if( big==0. ) { + INFOS( "blitz_LU_factor::Singular matrix" ) ; + exit( 0 ) ; + } + ImplicitScaling( i ) = 1./big ; + } + // Loop over columns of Crout's method : + for( int j=0; j=big ) { + dum = ImplicitScaling( i )*abs( theSum ) ; + big = dum ; + index_max = i ; + } + } + // Interchanging rows and the scale factor : + if( j!=index_max ) { + for( int k=0; k=0; i-- ) { + theSum = X( i ) ; + // theSum = B( i ) ; + theSum -= matrix_vector_product_sliced(LU, X, i, i+1, N) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*X( Range( i+1, toEnd ) ) ) ; + // theSum -= sum( LU( i, Range( i+1, toEnd ) )*B( Range( i+1, toEnd ) ) ) ; + // Store a component of the solution vector : + X( i ) = theSum/LU( i, i ) ; + // B( i ) = theSum/LU( i, i ) ; + } + + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..3795ac61ec02f23dab639d1f4d9814bf67da10cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/mtl4/mtl4_interface.hh @@ -0,0 +1,144 @@ +//===================================================== +// Copyright (C) 2008 Gael Guennebaud +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef MTL4_INTERFACE_HH +#define MTL4_INTERFACE_HH + +#include +#include +// #include +#include + +using namespace mtl; + +template +class mtl4_interface { + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef mtl::dense2D > gene_matrix; + typedef mtl::dense_vector gene_vector; + + static inline std::string name() { return "mtl4"; } + + static void free_matrix(gene_matrix & A, int N){ + return ; + } + + static void free_vector(gene_vector & B){ + return ; + } + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.change_dim(A_stl[0].size(), A_stl.size()); + + for (int j=0; j C(N,N); +// C = B; +// X = (A*C); + } + + static inline void transposed_matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int N){ + X = (trans(A)*trans(B)); + } + +// static inline void ata_product(const gene_matrix & A, gene_matrix & X, int N){ +// X = (trans(A)*A); +// } + + static inline void aat_product(const gene_matrix & A, gene_matrix & X, int N){ + X = (A*trans(A)); + } + + static inline void matrix_vector_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + X = (A*B); + } + + static inline void atv_product(gene_matrix & A, gene_vector & B, gene_vector & X, int N){ + X = (trans(A)*B); + } + + static inline void axpy(const real coef, const gene_vector & X, gene_vector & Y, int N){ + Y += coef * X; + } + + static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int N){ + Y = a*X + b*Y; + } + +// static inline void cholesky(const gene_matrix & X, gene_matrix & C, int N){ +// C = X; +// recursive_cholesky(C); +// } + +// static inline void lu_decomp(const gene_matrix & X, gene_matrix & R, int N){ +// R = X; +// std::vector ipvt(N); +// lu_factor(R, ipvt); +// } + + static inline void trisolve_lower(const gene_matrix & L, const gene_vector& B, gene_vector & X, int N){ + X = lower_trisolve(L, B); + } + + static inline void copy_matrix(const gene_matrix & source, gene_matrix & cible, int N){ + cible = source; + } + + static inline void copy_vector(const gene_vector & source, gene_vector & cible, int N){ + cible = source; + } + +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..e10a736f575db9864be39d1e1e1e53807e22febe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/CMakeLists.txt @@ -0,0 +1,44 @@ + + +if((NOT TENSOR_INCLUDE_DIR) AND Eigen_SOURCE_DIR) + # unless TENSOR_INCLUDE_DIR is defined, let's use current Eigen version + set(TENSOR_INCLUDE_DIR ${Eigen_SOURCE_DIR}) + set(TENSOR_FOUND TRUE) +else() + find_package(Tensor) +endif() + +if (TENSOR_FOUND) + + include_directories(${TENSOR_INCLUDE_DIR}) + btl_add_bench(btl_tensor_linear main_linear.cpp) + btl_add_bench(btl_tensor_vecmat main_vecmat.cpp) + btl_add_bench(btl_tensor_matmat main_matmat.cpp) + + btl_add_target_property(btl_tensor_linear COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=tensor") + btl_add_target_property(btl_tensor_vecmat COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=tensor") + btl_add_target_property(btl_tensor_matmat COMPILE_FLAGS "-fno-exceptions -DBTL_PREFIX=tensor") + + option(BTL_BENCH_NOGCCVEC "also bench Eigen explicit vec without GCC's auto vec" OFF) + if(CMAKE_COMPILER_IS_GNUCXX AND BTL_BENCH_NOGCCVEC) + btl_add_bench(btl_tensor_nogccvec_linear main_linear.cpp) + btl_add_bench(btl_tensor_nogccvec_vecmat main_vecmat.cpp) + btl_add_bench(btl_tensor_nogccvec_matmat main_matmat.cpp) + + btl_add_target_property(btl_tensor_nogccvec_linear COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec") + btl_add_target_property(btl_tensor_nogccvec_vecmat COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec") + btl_add_target_property(btl_tensor_nogccvec_matmat COMPILE_FLAGS "-fno-exceptions -fno-tree-vectorize -DBTL_PREFIX=tensor_nogccvec") + endif() + + + if(NOT BTL_NOVEC) + btl_add_bench(btl_tensor_novec_linear main_linear.cpp OFF) + btl_add_bench(btl_tensor_novec_vecmat main_vecmat.cpp OFF) + btl_add_bench(btl_tensor_novec_matmat main_matmat.cpp OFF) + btl_add_target_property(btl_tensor_novec_linear COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec") + btl_add_target_property(btl_tensor_novec_vecmat COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec") + btl_add_target_property(btl_tensor_novec_matmat COMPILE_FLAGS "-fno-exceptions -DEIGEN_DONT_VECTORIZE -DBTL_PREFIX=tensor_novec") + + endif() + +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_linear.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_linear.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e257f1e72e0b4249a7a2d74869a353f14d912002 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_linear.cpp @@ -0,0 +1,23 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Benoit Steiner +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "utilities.h" +#include "tensor_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_matmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_matmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..675fcfc6d573edfe806c3b0e211f4e58bbe75bf9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_matmat.cpp @@ -0,0 +1,21 @@ +//===================================================== +// Copyright (C) 2014 Benoit Steiner +//===================================================== +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +// +#include "utilities.h" +#include "tensor_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_vecmat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_vecmat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1af00c81b42fcc2438e5471f397bafa2381244ea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/main_vecmat.cpp @@ -0,0 +1,21 @@ +//===================================================== +// Copyright (C) 2014 Benoit Steiner +//===================================================== +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +// +#include "utilities.h" +#include "tensor_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_MV,MAX_MV,NB_POINT); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/tensor_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/tensor_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..97b8e0f0b30a7dcc33d9f973ae865e294400ece0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tensors/tensor_interface.hh @@ -0,0 +1,105 @@ +//===================================================== +// Copyright (C) 2014 Benoit Steiner +//===================================================== +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +// +#ifndef TENSOR_INTERFACE_HH +#define TENSOR_INTERFACE_HH + +#include +#include +#include "btl.hh" + +using namespace Eigen; + +template +class tensor_interface +{ +public : + typedef real real_type; + typedef typename Eigen::Tensor::Index Index; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef Eigen::Tensor gene_matrix; + typedef Eigen::Tensor gene_vector; + + + static inline std::string name( void ) + { + return EIGEN_MAKESTRING(BTL_PREFIX); + } + + static void free_matrix(gene_matrix & /*A*/, int /*N*/) {} + + static void free_vector(gene_vector & /*B*/) {} + + static BTL_DONT_INLINE void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(Eigen::array(A_stl[0].size(), A_stl.size())); + + for (unsigned int j=0; j(i,j)) = A_stl[j][i]; + } + } + } + + static BTL_DONT_INLINE void vector_from_stl(gene_vector & B, stl_vector & B_stl){ + B.resize(B_stl.size()); + + for (unsigned int i=0; i(i,j)); + } + } + } + + static inline void matrix_matrix_product(const gene_matrix & A, const gene_matrix & B, gene_matrix & X, int /*N*/){ + typedef typename Eigen::Tensor::DimensionPair DimPair; + const Eigen::array dims(DimPair(1, 0)); + X/*.noalias()*/ = A.contract(B, dims); + } + + static inline void matrix_vector_product(const gene_matrix & A, const gene_vector & B, gene_vector & X, int /*N*/){ + typedef typename Eigen::Tensor::DimensionPair DimPair; + const Eigen::array dims(DimPair(1, 0)); + X/*.noalias()*/ = A.contract(B, dims); + } + + static inline void axpy(real coef, const gene_vector & X, gene_vector & Y, int /*N*/){ + Y += X.constant(coef) * X; + } + + static inline void axpby(real a, const gene_vector & X, real b, gene_vector & Y, int /*N*/){ + Y = X.constant(a)*X + Y.constant(b)*Y; + } + + static EIGEN_DONT_INLINE void copy_matrix(const gene_matrix & source, gene_matrix & cible, int /*N*/){ + cible = source; + } + + static EIGEN_DONT_INLINE void copy_vector(const gene_vector & source, gene_vector & cible, int /*N*/){ + cible = source; + } +}; + +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7376972cb53dde76ae29f08e8d39cb27437d05b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/CMakeLists.txt @@ -0,0 +1,6 @@ + +find_package(Tvmet) +if (TVMET_FOUND) + include_directories(${TVMET_INCLUDE_DIR}) + btl_add_bench(btl_tvmet main.cpp OFF) +endif () diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/main.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/main.cpp new file mode 100644 index 0000000000000000000000000000000000000000..633215c43626fc179fe8d16ca0c1ff8e35f8cf54 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/main.cpp @@ -0,0 +1,40 @@ +//===================================================== +// File : main.cpp +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "tvmet_interface.hh" +#include "static/bench_static.hh" +#include "action_matrix_vector_product.hh" +#include "action_matrix_matrix_product.hh" +#include "action_atv_product.hh" +#include "action_axpy.hh" + +BTL_MAIN; + +int main() +{ + bench_static(); + bench_static(); + bench_static(); + bench_static(); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/tvmet_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/tvmet_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..b441ada2125bb4236e29eea4dc7c6ddfa570f162 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/tvmet/tvmet_interface.hh @@ -0,0 +1,104 @@ +//===================================================== +// File : tvmet_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:30 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef TVMET_INTERFACE_HH +#define TVMET_INTERFACE_HH + +#include +#include +#include + +#include + +using namespace tvmet; + +template +class tvmet_interface{ + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef Vector gene_vector; + typedef Matrix gene_matrix; + + static inline std::string name() { return "tiny_tvmet"; } + + static void free_matrix(gene_matrix & A, int N){} + + static void free_vector(gene_vector & B){} + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + for (int j=0; j +// Copyright (C) EDF R&D, lun sep 30 14:23:27 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#include "utilities.h" +#include "ublas_interface.hh" +#include "bench.hh" +#include "basic_actions.hh" + +BTL_MAIN; + +int main() +{ + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + bench > >(MIN_AXPY,MAX_AXPY,NB_POINT); + + bench > >(MIN_MV,MAX_MV,NB_POINT); + bench > >(MIN_MV,MAX_MV,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); +// bench > >(MIN_MM,MAX_MM,NB_POINT); + + bench > >(MIN_MM,MAX_MM,NB_POINT); + + return 0; +} + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/ublas/ublas_interface.hh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/ublas/ublas_interface.hh new file mode 100644 index 0000000000000000000000000000000000000000..f59b7cf2f537802329a2f39c76063f7a039cd362 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/btl/libs/ublas/ublas_interface.hh @@ -0,0 +1,141 @@ +//===================================================== +// File : ublas_interface.hh +// Author : L. Plagne +// Copyright (C) EDF R&D, lun sep 30 14:23:27 CEST 2002 +//===================================================== +// +// This program is free software; you can redistribute it and/or +// modify it under the terms of the GNU General Public License +// as published by the Free Software Foundation; either version 2 +// of the License, or (at your option) any later version. +// +// This program is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. +// You should have received a copy of the GNU General Public License +// along with this program; if not, write to the Free Software +// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +// +#ifndef UBLAS_INTERFACE_HH +#define UBLAS_INTERFACE_HH + +#include +#include +#include +#include + +using namespace boost::numeric; + +template +class ublas_interface{ + +public : + + typedef real real_type ; + + typedef std::vector stl_vector; + typedef std::vector stl_matrix; + + typedef typename boost::numeric::ublas::matrix gene_matrix; + typedef typename boost::numeric::ublas::vector gene_vector; + + static inline std::string name( void ) { return "ublas"; } + + static void free_matrix(gene_matrix & A, int N) {} + + static void free_vector(gene_vector & B) {} + + static inline void matrix_from_stl(gene_matrix & A, stl_matrix & A_stl){ + A.resize(A_stl.size(),A_stl[0].size()); + for (int j=0; j +#include "../Eigen/Core" + +using namespace Eigen; +using namespace std; + +#define DUMP_CPUID(CODE) {\ + int abcd[4]; \ + abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;\ + EIGEN_CPUID(abcd, CODE, 0); \ + std::cout << "The code " << CODE << " gives " \ + << (int*)(abcd[0]) << " " << (int*)(abcd[1]) << " " \ + << (int*)(abcd[2]) << " " << (int*)(abcd[3]) << " " << std::endl; \ + } + +int main() +{ + cout << "Eigen's L1 = " << internal::queryL1CacheSize() << endl; + cout << "Eigen's L2/L3 = " << internal::queryTopLevelCacheSize() << endl; + int l1, l2, l3; + internal::queryCacheSizes(l1, l2, l3); + cout << "Eigen's L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl; + + #ifdef EIGEN_CPUID + + int abcd[4]; + int string[8]; + char* string_char = (char*)(string); + + // vendor ID + EIGEN_CPUID(abcd,0x0,0); + string[0] = abcd[1]; + string[1] = abcd[3]; + string[2] = abcd[2]; + string[3] = 0; + cout << endl; + cout << "vendor id = " << string_char << endl; + cout << endl; + int max_funcs = abcd[0]; + + internal::queryCacheSizes_intel_codes(l1, l2, l3); + cout << "Eigen's intel codes L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl; + if(max_funcs>=4) + { + internal::queryCacheSizes_intel_direct(l1, l2, l3); + cout << "Eigen's intel direct L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl; + } + internal::queryCacheSizes_amd(l1, l2, l3); + cout << "Eigen's amd L1, L2, L3 = " << l1 << " " << l2 << " " << l3 << endl; + cout << endl; + + // dump Intel direct method + if(max_funcs>=4) + { + l1 = l2 = l3 = 0; + int cache_id = 0; + int cache_type = 0; + do { + abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0; + EIGEN_CPUID(abcd,0x4,cache_id); + cache_type = (abcd[0] & 0x0F) >> 0; + int cache_level = (abcd[0] & 0xE0) >> 5; // A[7:5] + int ways = (abcd[1] & 0xFFC00000) >> 22; // B[31:22] + int partitions = (abcd[1] & 0x003FF000) >> 12; // B[21:12] + int line_size = (abcd[1] & 0x00000FFF) >> 0; // B[11:0] + int sets = (abcd[2]); // C[31:0] + int cache_size = (ways+1) * (partitions+1) * (line_size+1) * (sets+1); + + cout << "cache[" << cache_id << "].type = " << cache_type << "\n"; + cout << "cache[" << cache_id << "].level = " << cache_level << "\n"; + cout << "cache[" << cache_id << "].ways = " << ways << "\n"; + cout << "cache[" << cache_id << "].partitions = " << partitions << "\n"; + cout << "cache[" << cache_id << "].line_size = " << line_size << "\n"; + cout << "cache[" << cache_id << "].sets = " << sets << "\n"; + cout << "cache[" << cache_id << "].size = " << cache_size << "\n"; + + cache_id++; + } while(cache_type>0 && cache_id<16); + } + + // dump everything + std::cout << endl <<"Raw dump:" << endl; + for(int i=0; i +#include "BenchTimer.h" +#include +#include +#include +#include +#include +using namespace Eigen; + +std::map > results; +std::vector labels; +std::vector sizes; + +template +EIGEN_DONT_INLINE +void compute_norm_equation(Solver &solver, const MatrixType &A) { + if(A.rows()!=A.cols()) + solver.compute(A.transpose()*A); + else + solver.compute(A); +} + +template +EIGEN_DONT_INLINE +void compute(Solver &solver, const MatrixType &A) { + solver.compute(A); +} + +template +void bench(int id, int rows, int size = Size) +{ + typedef Matrix Mat; + typedef Matrix MatDyn; + typedef Matrix MatSquare; + Mat A(rows,size); + A.setRandom(); + if(rows==size) + A = A*A.adjoint(); + BenchTimer t_llt, t_ldlt, t_lu, t_fplu, t_qr, t_cpqr, t_cod, t_fpqr, t_jsvd, t_bdcsvd; + + int svd_opt = ComputeThinU|ComputeThinV; + + int tries = 5; + int rep = 1000/size; + if(rep==0) rep = 1; +// rep = rep*rep; + + LLT llt(size); + LDLT ldlt(size); + PartialPivLU lu(size); + FullPivLU fplu(size,size); + HouseholderQR qr(A.rows(),A.cols()); + ColPivHouseholderQR cpqr(A.rows(),A.cols()); + CompleteOrthogonalDecomposition cod(A.rows(),A.cols()); + FullPivHouseholderQR fpqr(A.rows(),A.cols()); + JacobiSVD jsvd(A.rows(),A.cols()); + BDCSVD bdcsvd(A.rows(),A.cols()); + + BENCH(t_llt, tries, rep, compute_norm_equation(llt,A)); + BENCH(t_ldlt, tries, rep, compute_norm_equation(ldlt,A)); + BENCH(t_lu, tries, rep, compute_norm_equation(lu,A)); + if(size<=1000) + BENCH(t_fplu, tries, rep, compute_norm_equation(fplu,A)); + BENCH(t_qr, tries, rep, compute(qr,A)); + BENCH(t_cpqr, tries, rep, compute(cpqr,A)); + BENCH(t_cod, tries, rep, compute(cod,A)); + if(size*rows<=10000000) + BENCH(t_fpqr, tries, rep, compute(fpqr,A)); + if(size<500) // JacobiSVD is really too slow for too large matrices + BENCH(t_jsvd, tries, rep, jsvd.compute(A,svd_opt)); +// if(size*rows<=20000000) + BENCH(t_bdcsvd, tries, rep, bdcsvd.compute(A,svd_opt)); + + results["LLT"][id] = t_llt.best(); + results["LDLT"][id] = t_ldlt.best(); + results["PartialPivLU"][id] = t_lu.best(); + results["FullPivLU"][id] = t_fplu.best(); + results["HouseholderQR"][id] = t_qr.best(); + results["ColPivHouseholderQR"][id] = t_cpqr.best(); + results["CompleteOrthogonalDecomposition"][id] = t_cod.best(); + results["FullPivHouseholderQR"][id] = t_fpqr.best(); + results["JacobiSVD"][id] = t_jsvd.best(); + results["BDCSVD"][id] = t_bdcsvd.best(); +} + + +int main() +{ + labels.push_back("LLT"); + labels.push_back("LDLT"); + labels.push_back("PartialPivLU"); + labels.push_back("FullPivLU"); + labels.push_back("HouseholderQR"); + labels.push_back("ColPivHouseholderQR"); + labels.push_back("CompleteOrthogonalDecomposition"); + labels.push_back("FullPivHouseholderQR"); + labels.push_back("JacobiSVD"); + labels.push_back("BDCSVD"); + + for(int i=0; i(k,sizes[k](0),sizes[k](1)); + } + + cout.width(32); + cout << "solver/size"; + cout << " "; + for(int k=0; k=1e6) cout << "-"; + else cout << r(k); + cout << " "; + } + cout << endl; + } + + // HTML output + cout << "" << endl; + cout << "" << endl; + for(int k=0; k" << sizes[k](0) << "x" << sizes[k](1) << ""; + cout << "" << endl; + for(int i=0; i"; + ArrayXf r = (results[labels[i]]*100000.f).floor()/100.f; + for(int k=0; k=1e6) cout << ""; + else + { + cout << ""; + } + } + cout << "" << endl; + } + cout << "
solver/size
" << labels[i] << "-" << r(k); + if(i>0) + cout << " (x" << numext::round(10.f*results[labels[i]](k)/results["LLT"](k))/10.f << ")"; + if(i<4 && sizes[k](0)!=sizes[k](1)) + cout << " *"; + cout << "
" << endl; + +// cout << "LLT (ms) " << (results["LLT"]*1000.).format(fmt) << "\n"; +// cout << "LDLT (%) " << (results["LDLT"]/results["LLT"]).format(fmt) << "\n"; +// cout << "PartialPivLU (%) " << (results["PartialPivLU"]/results["LLT"]).format(fmt) << "\n"; +// cout << "FullPivLU (%) " << (results["FullPivLU"]/results["LLT"]).format(fmt) << "\n"; +// cout << "HouseholderQR (%) " << (results["HouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "ColPivHouseholderQR (%) " << (results["ColPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "CompleteOrthogonalDecomposition (%) " << (results["CompleteOrthogonalDecomposition"]/results["LLT"]).format(fmt) << "\n"; +// cout << "FullPivHouseholderQR (%) " << (results["FullPivHouseholderQR"]/results["LLT"]).format(fmt) << "\n"; +// cout << "JacobiSVD (%) " << (results["JacobiSVD"]/results["LLT"]).format(fmt) << "\n"; +// cout << "BDCSVD (%) " << (results["BDCSVD"]/results["LLT"]).format(fmt) << "\n"; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/eig33.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/eig33.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f003d8a53aed5b9fbf0322b0097c4f225c4d029c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/eig33.cpp @@ -0,0 +1,195 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// The computeRoots function included in this is based on materials +// covered by the following copyright and license: +// +// Geometric Tools, LLC +// Copyright (c) 1998-2010 +// Distributed under the Boost Software License, Version 1.0. +// +// Permission is hereby granted, free of charge, to any person or organization +// obtaining a copy of the software and accompanying documentation covered by +// this license (the "Software") to use, reproduce, display, distribute, +// execute, and transmit the Software, and to prepare derivative works of the +// Software, and to permit third-parties to whom the Software is furnished to +// do so, all subject to the following: +// +// The copyright notices in the Software and this entire statement, including +// the above license grant, this restriction and the following disclaimer, +// must be included in all copies of the Software, in whole or in part, and +// all derivative works of the Software, unless such copies or derivative +// works are solely in the form of machine-executable object code generated by +// a source language processor. +// +// 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, TITLE AND NON-INFRINGEMENT. IN NO EVENT +// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS IN THE SOFTWARE. + +#include +#include +#include +#include +#include + +using namespace Eigen; +using namespace std; + +template +inline void computeRoots(const Matrix& m, Roots& roots) +{ + typedef typename Matrix::Scalar Scalar; + const Scalar s_inv3 = 1.0/3.0; + const Scalar s_sqrt3 = std::sqrt(Scalar(3.0)); + + // The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The + // eigenvalues are the roots to this equation, all guaranteed to be + // real-valued, because the matrix is symmetric. + Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(0,1)*m(0,2)*m(1,2) - m(0,0)*m(1,2)*m(1,2) - m(1,1)*m(0,2)*m(0,2) - m(2,2)*m(0,1)*m(0,1); + Scalar c1 = m(0,0)*m(1,1) - m(0,1)*m(0,1) + m(0,0)*m(2,2) - m(0,2)*m(0,2) + m(1,1)*m(2,2) - m(1,2)*m(1,2); + Scalar c2 = m(0,0) + m(1,1) + m(2,2); + + // Construct the parameters used in classifying the roots of the equation + // and in solving the equation for the roots in closed form. + Scalar c2_over_3 = c2*s_inv3; + Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3; + if (a_over_3 > Scalar(0)) + a_over_3 = Scalar(0); + + Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1)); + + Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3; + if (q > Scalar(0)) + q = Scalar(0); + + // Compute the eigenvalues by solving for the roots of the polynomial. + Scalar rho = std::sqrt(-a_over_3); + Scalar theta = std::atan2(std::sqrt(-q),half_b)*s_inv3; + Scalar cos_theta = std::cos(theta); + Scalar sin_theta = std::sin(theta); + roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta; + roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); + roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); +} + +template +void eigen33(const Matrix& mat, Matrix& evecs, Vector& evals) +{ + typedef typename Matrix::Scalar Scalar; + // Scale the matrix so its entries are in [-1,1]. The scaling is applied + // only when at least one matrix entry has magnitude larger than 1. + + Scalar shift = mat.trace()/3; + Matrix scaledMat = mat; + scaledMat.diagonal().array() -= shift; + Scalar scale = scaledMat.cwiseAbs()/*.template triangularView()*/.maxCoeff(); + scale = std::max(scale,Scalar(1)); + scaledMat/=scale; + + // Compute the eigenvalues +// scaledMat.setZero(); + computeRoots(scaledMat,evals); + + // compute the eigen vectors + // **here we assume 3 different eigenvalues** + + // "optimized version" which appears to be slower with gcc! +// Vector base; +// Scalar alpha, beta; +// base << scaledMat(1,0) * scaledMat(2,1), +// scaledMat(1,0) * scaledMat(2,0), +// -scaledMat(1,0) * scaledMat(1,0); +// for(int k=0; k<2; ++k) +// { +// alpha = scaledMat(0,0) - evals(k); +// beta = scaledMat(1,1) - evals(k); +// evecs.col(k) = (base + Vector(-beta*scaledMat(2,0), -alpha*scaledMat(2,1), alpha*beta)).normalized(); +// } +// evecs.col(2) = evecs.col(0).cross(evecs.col(1)).normalized(); + +// // naive version +// Matrix tmp; +// tmp = scaledMat; +// tmp.diagonal().array() -= evals(0); +// evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized(); +// +// tmp = scaledMat; +// tmp.diagonal().array() -= evals(1); +// evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized(); +// +// tmp = scaledMat; +// tmp.diagonal().array() -= evals(2); +// evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized(); + + // a more stable version: + if((evals(2)-evals(0))<=Eigen::NumTraits::epsilon()) + { + evecs.setIdentity(); + } + else + { + Matrix tmp; + tmp = scaledMat; + tmp.diagonal ().array () -= evals (2); + evecs.col (2) = tmp.row (0).cross (tmp.row (1)).normalized (); + + tmp = scaledMat; + tmp.diagonal ().array () -= evals (1); + evecs.col(1) = tmp.row (0).cross(tmp.row (1)); + Scalar n1 = evecs.col(1).norm(); + if(n1<=Eigen::NumTraits::epsilon()) + evecs.col(1) = evecs.col(2).unitOrthogonal(); + else + evecs.col(1) /= n1; + + // make sure that evecs[1] is orthogonal to evecs[2] + evecs.col(1) = evecs.col(2).cross(evecs.col(1).cross(evecs.col(2))).normalized(); + evecs.col(0) = evecs.col(2).cross(evecs.col(1)); + } + + // Rescale back to the original size. + evals *= scale; + evals.array()+=shift; +} + +int main() +{ + BenchTimer t; + int tries = 10; + int rep = 400000; + typedef Matrix3d Mat; + typedef Vector3d Vec; + Mat A = Mat::Random(3,3); + A = A.adjoint() * A; +// Mat Q = A.householderQr().householderQ(); +// A = Q * Vec(2.2424567,2.2424566,7.454353).asDiagonal() * Q.transpose(); + + SelfAdjointEigenSolver eig(A); + BENCH(t, tries, rep, eig.compute(A)); + std::cout << "Eigen iterative: " << t.best() << "s\n"; + + BENCH(t, tries, rep, eig.computeDirect(A)); + std::cout << "Eigen direct : " << t.best() << "s\n"; + + Mat evecs; + Vec evals; + BENCH(t, tries, rep, eigen33(A,evecs,evals)); + std::cout << "Direct: " << t.best() << "s\n\n"; + +// std::cerr << "Eigenvalue/eigenvector diffs:\n"; +// std::cerr << (evals - eig.eigenvalues()).transpose() << "\n"; +// for(int k=0;k<3;++k) +// if(evecs.col(k).dot(eig.eigenvectors().col(k))<0) +// evecs.col(k) = -evecs.col(k); +// std::cerr << evecs - eig.eigenvectors() << "\n\n"; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/geometry.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/geometry.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b187a515f58d1f6f64f79a75614a404376016c02 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/geometry.cpp @@ -0,0 +1,126 @@ + +#include +#include +#include + +using namespace std; +using namespace Eigen; + +#ifndef SCALAR +#define SCALAR float +#endif + +#ifndef SIZE +#define SIZE 8 +#endif + +typedef SCALAR Scalar; +typedef NumTraits::Real RealScalar; +typedef Matrix A; +typedef Matrix B; +typedef Matrix C; +typedef Matrix M; + +template +EIGEN_DONT_INLINE void transform(const Transformation& t, Data& data) +{ + EIGEN_ASM_COMMENT("begin"); + data = t * data; + EIGEN_ASM_COMMENT("end"); +} + +template +EIGEN_DONT_INLINE void transform(const Quaternion& t, Data& data) +{ + EIGEN_ASM_COMMENT("begin quat"); + for(int i=0;i struct ToRotationMatrixWrapper +{ + enum {Dim = T::Dim}; + typedef typename T::Scalar Scalar; + ToRotationMatrixWrapper(const T& o) : object(o) {} + T object; +}; + +template +EIGEN_DONT_INLINE void transform(const ToRotationMatrixWrapper& t, Data& data) +{ + EIGEN_ASM_COMMENT("begin quat via mat"); + data = t.object.toRotationMatrix() * data; + EIGEN_ASM_COMMENT("end quat via mat"); +} + +template +EIGEN_DONT_INLINE void transform(const Transform& t, Data& data) +{ + data = (t * data.colwise().homogeneous()).template block(0,0); +} + +template struct get_dim { enum { Dim = T::Dim }; }; +template +struct get_dim > { enum { Dim = R }; }; + +template +struct bench_impl +{ + static EIGEN_DONT_INLINE void run(const Transformation& t) + { + Matrix::Dim,N> data; + data.setRandom(); + bench_impl::run(t); + BenchTimer timer; + BENCH(timer,10,100000,transform(t,data)); + cout.width(9); + cout << timer.best() << " "; + } +}; + + +template +struct bench_impl +{ + static EIGEN_DONT_INLINE void run(const Transformation&) {} +}; + +template +EIGEN_DONT_INLINE void bench(const std::string& msg, const Transformation& t) +{ + cout << msg << " "; + bench_impl::run(t); + std::cout << "\n"; +} + +int main(int argc, char ** argv) +{ + Matrix mat34; mat34.setRandom(); + Transform iso3(mat34); + Transform aff3(mat34); + Transform caff3(mat34); + Transform proj3(mat34); + Quaternion quat;quat.setIdentity(); + ToRotationMatrixWrapper > quatmat(quat); + Matrix mat33; mat33.setRandom(); + + cout.precision(4); + std::cout + << "N "; + for(int i=0;i Also optimized the blocking parameters to take
into account the number of threads used for a computation. +6782dde63499c # generalized gemv +6799f98650d0a # ensured that contractions that can be reduced to a matrix vector product +#6840918c51e60 # merge tensor +684e972b55ec4 # change prefetching in gebp +#68598604576d1 # merge index conversion +68963eb0f6fe6 # clean blocking size computation +689db05f2d01e # rotating kernel for ARM only +#6901b7e12847d # result_of +69226275b250a # fix prefetching change for ARM +692692136350b # prefetching +693a8ad8887bf # blocking size strategy +693bcf9bb5c1f # avoid redundant pack_rhs +6987550107028 # dynamic loop swapping +69858740ce4c6 # rm dynamic loop swapping,
adjust lhs's micro panel height to fully exploit L1 cache +698cd3bbffa73 # blocking heuristic:
block on the rhs in L1 if the lhs fit in L1. +701488c15615a # organize a little our default cache sizes,
and use a saner default L1 outside of x86 (10% faster on Nexus 5) +701e56aabf205 # Refactor computeProductBlockingSizes to make room
for the possibility of using lookup tables +701ca5c12587b # Polish lookup tables generation +7013589a9c115 # actual_panel_rows computation should always be resilient
to parameters not consistent with the known L1 cache size, see comment +70102babb9c0f # Provide a empirical lookup table for blocking sizes measured on a Nexus 5.
Only for float, only for Android on ARM 32bit for now. +7088481dc21ea # Bug 986: add support for coefficient-based
product with 0 depth. +709d7f51feb07 # Bug 992: don't select a 3p GEMM path with non-SIMD scalar types. +759f9303cc7c5 # 3.3-alpha1 +765aba1eda71e # help clang inlining +770fe630c9873 # Improve numerical accuracy in LLT and triangular solve
by using true scalar divisions (instead of x * (1/y)) +#8741d23430628 # Improved the matrix multiplication blocking in the case
where mr is not a power of 2 (e.g on Haswell CPUs) +878f629fe95c8 # Made the index type a template parameter to evaluateProductBlockingSizes.
Use numext::mini and numext::maxi instead of
std::min/std::max to compute blocking sizes. +8975d51a7f12c # Don't optimize the processing of the last rows of
a matrix matrix product in cases that violate
the assumptions made by the optimized code path. +8986136f4fdd4 # Remove the rotating kernel. +898e68e165a23 # Bug 256: enable vectorization with unaligned loads/stores. +91466e99ab6a1 # Relax mixing-type constraints for binary coeff-wise operators +91776236cdea4 # merge +917101ea26f5e # Include the cost of stores in unrolling +921672076db5d # Fix perf regression introduced in changeset e56aabf205 +9210fa9e4a15c # Fix perf regression in dgemm introduced by changeset 5d51a7f12c +936f6b3cf8de9 # 3.3-beta2 +944504a4404f1 # Optimize expression matching 'd?=a-b*c' as 'd?=a; d?=b*c;' +95877e27fbeee # 3.3-rc1 +959779774f98c # Bug 1311: fix alignment logic in some cases
of (scalar*small).lazyProduct(small) +9729f9d8d2f62 # Disabled part of the matrix matrix peeling code
that's incompatible with 512 bit registers +979eeac81b8c0 # 3.3.0 +989c927af60ed # Fix a performance regression in (mat*mat)*vec
for which mat*mat was evaluated multiple times. +994fe696022ec # Operators += and -= do not resize! +99466f65ccc36 # Ease compiler generating clean and efficient code in mat*vec +9946a5fe86098 # Complete rewrite of column-major-matrix * vector product
to deliver higher performance of modern CPU. +99591003f3b86 # Improve performance of row-major-dense-matrix * vector products
for recent CPUs. +997eb621413c1 # Revert vec/y to vec*(1/y) in row-major TRSM +10444bbc320468 # Bug 1435: fix aliasing issue in exressions like: A = C - B*A; +1073624df50945 # Adds missing EIGEN_STRONG_INLINE to support MSVC
properly inlining small vector calculations +1094d428a199ab # Bug 1562: optimize evaluation of small products
of the form s*A*B by rewriting them as: s*(A.lazyProduct(B))
to save a costly temporary.
Measured speedup from 2x to 5x. +1096de9e31a06d # Introduce the macro ei_declare_local_nested_eval to
help allocating on the stack local temporaries via alloca,
and let outer-products makes a good use of it. +11087b91c11207 # Bug 1578: Improve prefetching in matrix multiplication on MIPS. +1153aa110e681b # PR 526: Speed up multiplication of small, dynamically sized matrices +11544ad359237a # Vectorize row-by-row gebp loop iterations on 16 packets as well +1157a476054879 # Bug 1624: improve matrix-matrix product on ARM 64, 20% speedup +1160a4159dba08 # do not read buffers out of bounds +1163c53eececb0 # Implement AVX512 vectorization of std::complex +11644e7746fe22 # Bug 1636: fix gemm performance issue with gcc>=6 and no FMA +1164956678a4ef # Bug 1515: disable gebp's 3pX4 micro kernel
for MSVC<=19.14 because of register spilling. +1165426bce7529 # fix EIGEN_GEBP_2PX4_SPILLING_WORKAROUND
for non vectorized type, and non x86/64 target +11660d90637838 # enable spilling workaround on architectures with SSE/AVX +1166f159cf3d75 # Artificially increase l1-blocking size for AVX512.
+10% speedup with current kernels. +11686dd93f7e3b # Make code compile again for older compilers. +1175dbfcceabf5 # Bug: 1633: refactor gebp kernel and optimize for neon +117670e133333d # Bug 1661: fix regression in GEBP and AVX512 +11760f028f61cb # GEBP: cleanup logic to choose between
a 4 packets of 1 packet (=e118ce86fd+fix) +1180de77bf5d6c # gebp: Add new ½ and ¼ packet rows per (peeling) round on the lhs diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..804139db7a2ffbc27a059ef91693efc7d15c552b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm.cpp @@ -0,0 +1,12 @@ +#include "gemm_common.h" + +EIGEN_DONT_INLINE +void gemm(const Mat &A, const Mat &B, Mat &C) +{ + C.noalias() += A * B; +} + +int main(int argc, char **argv) +{ + return main_gemm(argc, argv, gemm); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_common.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_common.h new file mode 100644 index 0000000000000000000000000000000000000000..30dbc0df68db28831aa4af2a4833a4cf0e6908b4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_common.h @@ -0,0 +1,67 @@ +#include +#include +#include +#include +#include "eigen_src/Eigen/Core" +#include "../BenchTimer.h" +using namespace Eigen; + +#ifndef SCALAR +#error SCALAR must be defined +#endif + +typedef SCALAR Scalar; + +typedef Matrix Mat; + +template +EIGEN_DONT_INLINE +double bench(long m, long n, long k, const Func& f) +{ + Mat A(m,k); + Mat B(k,n); + Mat C(m,n); + A.setRandom(); + B.setRandom(); + C.setZero(); + + BenchTimer t; + + double up = 1e8*4/sizeof(Scalar); + double tm0 = 4, tm1 = 10; + if(NumTraits::IsComplex) + { + up /= 4; + tm0 = 2; + tm1 = 4; + } + + double flops = 2. * m * n * k; + long rep = std::max(1., std::min(100., up/flops) ); + long tries = std::max(tm0, std::min(tm1, up/flops) ); + + BENCH(t, tries, rep, f(A,B,C)); + + return 1e-9 * rep * flops / t.best(); +} + +template +int main_gemm(int argc, char **argv, const Func& f) +{ + std::vector results; + + std::string filename = std::string("gemm_settings.txt"); + if(argc>1) + filename = std::string(argv[1]); + std::ifstream settings(filename); + long m, n, k; + while(settings >> m >> n >> k) + { + //std::cerr << " Testing " << m << " " << n << " " << k << std::endl; + results.push_back( bench(m, n, k, f) ); + } + + std::cout << RowVectorXd::Map(results.data(), results.size()); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c43e1c7d1b33f73d7bc09fbe0e0746d1bd3b55b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_settings.txt @@ -0,0 +1,15 @@ +8 8 8 +9 9 9 +24 24 24 +239 239 239 +240 240 240 +2400 24 24 +24 2400 24 +24 24 2400 +24 2400 2400 +2400 24 2400 +2400 2400 24 +2400 2400 64 +4800 23 160 +23 4800 160 +2400 2400 2400 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_square_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_square_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..98474d1736423175879f75e3bd1d641d4a707ca3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemm_square_settings.txt @@ -0,0 +1,11 @@ +8 8 8 +9 9 9 +12 12 12 +15 15 15 +16 16 16 +24 24 24 +102 102 102 +239 239 239 +240 240 240 +2400 2400 2400 +2463 2463 2463 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv.cpp new file mode 100644 index 0000000000000000000000000000000000000000..82e5ab96031b413a9543b483e80eeaab8048fc98 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv.cpp @@ -0,0 +1,12 @@ +#include "gemv_common.h" + +EIGEN_DONT_INLINE +void gemv(const Mat &A, const Vec &B, Vec &C) +{ + C.noalias() += A * B; +} + +int main(int argc, char **argv) +{ + return main_gemv(argc, argv, gemv); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_common.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_common.h new file mode 100644 index 0000000000000000000000000000000000000000..cc32577291384d208fad4e2dc9763d87bbb40538 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_common.h @@ -0,0 +1,69 @@ +#include +#include +#include +#include +#include +#include "eigen_src/Eigen/Core" +#include "../BenchTimer.h" +using namespace Eigen; + +#ifndef SCALAR +#error SCALAR must be defined +#endif + +typedef SCALAR Scalar; + +typedef Matrix Mat; +typedef Matrix Vec; + +template +EIGEN_DONT_INLINE +double bench(long m, long n, Func &f) +{ + Mat A(m,n); + Vec B(n); + Vec C(m); + A.setRandom(); + B.setRandom(); + C.setRandom(); + + BenchTimer t; + + double up = 1e8/sizeof(Scalar); + double tm0 = 4, tm1 = 10; + if(NumTraits::IsComplex) + { + up /= 4; + tm0 = 2; + tm1 = 4; + } + + double flops = 2. * m * n; + long rep = std::max(1., std::min(100., up/flops) ); + long tries = std::max(tm0, std::min(tm1, up/flops) ); + + BENCH(t, tries, rep, f(A,B,C)); + + return 1e-9 * rep * flops / t.best(); +} + +template +int main_gemv(int argc, char **argv, Func& f) +{ + std::vector results; + + std::string filename = std::string("gemv_settings.txt"); + if(argc>1) + filename = std::string(argv[1]); + std::ifstream settings(filename); + long m, n; + while(settings >> m >> n) + { + //std::cerr << " Testing " << m << " " << n << std::endl; + results.push_back( bench(m, n, f) ); + } + + std::cout << RowVectorXd::Map(results.data(), results.size()); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..21a5ee051984f74da4d5d88ff3508d4fa3f7125c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_settings.txt @@ -0,0 +1,11 @@ +8 8 +9 9 +24 24 +239 239 +240 240 +2400 24 +24 2400 +24 240 +2400 2400 +4800 23 +23 4800 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_square_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_square_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..5165759f494e7a3b520103c62b32cdcc9608064b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemv_square_settings.txt @@ -0,0 +1,13 @@ +8 8 +9 9 +12 12 +15 15 +16 16 +24 24 +53 53 +74 74 +102 102 +239 239 +240 240 +2400 2400 +2463 2463 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemvt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemvt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fe945767ed223ca1df1fa15938b9b4c2b4dd7903 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/gemvt.cpp @@ -0,0 +1,12 @@ +#include "gemv_common.h" + +EIGEN_DONT_INLINE +void gemv(const Mat &A, Vec &B, const Vec &C) +{ + B.noalias() += A.transpose() * C; +} + +int main(int argc, char **argv) +{ + return main_gemv(argc, argv, gemv); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..773306048d8e1bb85baf919585a9dca412890203 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm.cpp @@ -0,0 +1,101 @@ +#include +#include +#include +#include +#include "../../BenchTimer.h" +using namespace Eigen; + +#ifndef SCALAR +#error SCALAR must be defined +#endif + +typedef SCALAR Scalar; + +template +EIGEN_DONT_INLINE +void lazy_gemm(const MatA &A, const MatB &B, MatC &C) +{ +// escape((void*)A.data()); +// escape((void*)B.data()); + C.noalias() += A.lazyProduct(B); +// escape((void*)C.data()); +} + +template +EIGEN_DONT_INLINE +double bench() +{ + typedef Matrix MatA; + typedef Matrix MatB; + typedef Matrix MatC; + + MatA A(m,k); + MatB B(k,n); + MatC C(m,n); + A.setRandom(); + B.setRandom(); + C.setZero(); + + BenchTimer t; + + double up = 1e7*4/sizeof(Scalar); + double tm0 = 10, tm1 = 20; + + double flops = 2. * m * n * k; + long rep = std::max(10., std::min(10000., up/flops) ); + long tries = std::max(tm0, std::min(tm1, up/flops) ); + + BENCH(t, tries, rep, lazy_gemm(A,B,C)); + + return 1e-9 * rep * flops / t.best(); +} + +template +double bench_t(int t) +{ + if(t) + return bench(); + else + return bench(); +} + +EIGEN_DONT_INLINE +double bench_mnk(int m, int n, int k, int t) +{ + int id = m*10000 + n*100 + k; + switch(id) { + case 10101 : return bench_t< 1, 1, 1>(t); break; + case 20202 : return bench_t< 2, 2, 2>(t); break; + case 30303 : return bench_t< 3, 3, 3>(t); break; + case 40404 : return bench_t< 4, 4, 4>(t); break; + case 50505 : return bench_t< 5, 5, 5>(t); break; + case 60606 : return bench_t< 6, 6, 6>(t); break; + case 70707 : return bench_t< 7, 7, 7>(t); break; + case 80808 : return bench_t< 8, 8, 8>(t); break; + case 90909 : return bench_t< 9, 9, 9>(t); break; + case 101010 : return bench_t<10,10,10>(t); break; + case 111111 : return bench_t<11,11,11>(t); break; + case 121212 : return bench_t<12,12,12>(t); break; + } + return 0; +} + +int main(int argc, char **argv) +{ + std::vector results; + + std::string filename = std::string("lazy_gemm_settings.txt"); + if(argc>1) + filename = std::string(argv[1]); + std::ifstream settings(filename); + long m, n, k, t; + while(settings >> m >> n >> k >> t) + { + //std::cerr << " Testing " << m << " " << n << " " << k << std::endl; + results.push_back( bench_mnk(m, n, k, t) ); + } + + std::cout << RowVectorXd::Map(results.data(), results.size()); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm_settings.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm_settings.txt new file mode 100644 index 0000000000000000000000000000000000000000..407d5d4fad773fd419347c5f3ee313fc3b9e7d7b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/lazy_gemm_settings.txt @@ -0,0 +1,15 @@ +1 1 1 0 +2 2 2 0 +3 3 3 0 +4 4 4 0 +4 4 4 1 +5 5 5 0 +6 6 6 0 +7 7 7 0 +7 7 7 1 +8 8 8 0 +9 9 9 0 +10 10 10 0 +11 11 11 0 +12 12 12 0 +12 12 12 1 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/llt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/llt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d55b7d80340a7a07c1090da6f82bb97b515b4842 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/llt.cpp @@ -0,0 +1,15 @@ +#include "gemm_common.h" +#include + +EIGEN_DONT_INLINE +void llt(const Mat &A, const Mat &B, Mat &C) +{ + C = A; + C.diagonal().array() += 1000; + Eigen::internal::llt_inplace::blocked(C); +} + +int main(int argc, char **argv) +{ + return main_gemm(argc, argv, llt); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/make_plot.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/make_plot.sh new file mode 100644 index 0000000000000000000000000000000000000000..65aaf66f9612f3f333cb6dd931af95f81aa5c457 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/make_plot.sh @@ -0,0 +1,112 @@ +#!/bin/bash + +# base name of the bench +# it reads $1.out +# and generates $1.pdf +WHAT=$1 +bench=$2 +settings_file=$3 + +header="rev " +while read line +do + if [ ! -z '$line' ]; then + header="$header \"$line\"" + fi +done < $settings_file + +echo $header > $WHAT.out.header +cat $WHAT.out >> $WHAT.out.header + + +echo "set title '$WHAT'" > $WHAT.gnuplot +echo "set key autotitle columnhead outside " >> $WHAT.gnuplot +echo "set xtics rotate 1" >> $WHAT.gnuplot + +echo "set term pdf color rounded enhanced fontscale 0.35 size 7in,5in" >> $WHAT.gnuplot +echo set output "'"$WHAT.pdf"'" >> $WHAT.gnuplot + +col=`cat $settings_file | wc -l` +echo "plot for [col=2:$col+1] '$WHAT.out.header' using 0:col:xticlabels(1) with lines" >> $WHAT.gnuplot +echo " " >> $WHAT.gnuplot + +gnuplot -persist < $WHAT.gnuplot + +# generate a png file (thumbnail) +convert -colors 256 -background white -density 300 -resize 300 -quality 0 $WHAT.pdf -background white -flatten $WHAT.png + +# clean +rm $WHAT.out.header $WHAT.gnuplot + + +# generate html/svg graph + +echo " " > $WHAT.html +cat resources/chart_header.html > $WHAT.html +echo 'var customSettings = {"TITLE":"","SUBTITLE":"","XLABEL":"","YLABEL":""};' >> $WHAT.html +# 'data' is an array of datasets (i.e. curves), each of which is an object of the form +# { +# key: , +# color: , +# values: [{ +# r: , +# v: +# }] +# } +echo 'var data = [' >> $WHAT.html + +col=2 +while read line +do + if [ ! -z '$line' ]; then + header="$header \"$line\"" + echo '{"key":"'$line'","values":[' >> $WHAT.html + i=0 + while read line2 + do + if [ ! -z "$line2" ]; then + val=`echo $line2 | cut -s -f $col -d ' '` + if [ -n "$val" ]; then # skip build failures + echo '{"r":'$i',"v":'$val'},' >> $WHAT.html + fi + fi + ((i++)) + done < $WHAT.out + echo ']},' >> $WHAT.html + fi + ((col++)) +done < $settings_file +echo '];' >> $WHAT.html + +echo 'var changesets = [' >> $WHAT.html +while read line2 +do + if [ ! -z '$line2' ]; then + echo '"'`echo $line2 | cut -f 1 -d ' '`'",' >> $WHAT.html + fi +done < $WHAT.out +echo '];' >> $WHAT.html + +echo 'var changesets_details = [' >> $WHAT.html +while read line2 +do + if [ ! -z '$line2' ]; then + num=`echo "$line2" | cut -f 1 -d ' '` + comment=`grep ":$num" changesets.txt | cut -f 2 -d '#'` + echo '"'"$comment"'",' >> $WHAT.html + fi +done < $WHAT.out +echo '];' >> $WHAT.html + +echo 'var changesets_count = [' >> $WHAT.html +i=0 +while read line2 +do + if [ ! -z '$line2' ]; then + echo $i ',' >> $WHAT.html + fi + ((i++)) +done < $WHAT.out +echo '];' >> $WHAT.html + +cat resources/chart_footer.html >> $WHAT.html diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_footer.html b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_footer.html new file mode 100644 index 0000000000000000000000000000000000000000..a96cdb898c09220e2dd7064bc69237b21d920d56 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_footer.html @@ -0,0 +1,41 @@ + /* setup the chart and its options */ + var chart = nv.models.lineChart() + .color(d3.scale.category10().range()) + .margin({left: 75, bottom: 100}) + .forceX([0]).forceY([0]); + + chart.x(function(datum){ return datum.r; }) + .xAxis.options({ + axisLabel: customSettings.XLABEL || 'Changeset', + tickFormat: d3.format('.0f') + }); + chart.xAxis + .tickValues(changesets_count) + .tickFormat(function(d){return changesets[d]}) + .rotateLabels(-90); + + chart.y(function(datum){ return datum.v; }) + .yAxis.options({ + axisLabel: customSettings.YLABEL || 'GFlops'/*, + tickFormat: function(val){ return d3.format('.0f')(val) + ' GFlops'; }*/ + }); + + chart.tooltip.headerFormatter(function(d) { return changesets[d] + + '

' + + changesets_details[d] + "

"; }); + + //chart.useInteractiveGuideline(true); + d3.select('#chart').datum(data).call(chart); + var plot = d3.select('#chart > g'); + + /* setup the title */ + plot.append('text') + .style('font-size', '24px') + .attr('text-anchor', 'middle').attr('x', '50%').attr('y', '20px') + .text(customSettings.TITLE || ''); + + /* ensure the chart is responsive */ + nv.utils.windowResize(chart.update); + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_header.html b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_header.html new file mode 100644 index 0000000000000000000000000000000000000000..27eb02e546a8fc4bee5a1e998bee588fda7eaae9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/bench/perf_monitoring/resources/chart_header.html @@ -0,0 +1,45 @@ + + + + + + + + + + + + + + +$treeview +$search +$mathjax + + + + + + + + +
Please, help us to better know about our user community by answering the following short survey: https://forms.gle/wpyrxWi18ox9Z5ae9
+ +
+ + +
+ + + + + + + + + + + + + + + + + + + + + +
+
$projectname +  $projectnumber +
+
$projectbrief
+
+
$projectbrief
+
$searchbox
+
+ + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_layout.xml.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_layout.xml.in new file mode 100644 index 0000000000000000000000000000000000000000..c14b621e5f7f3edcc6830d01753f8c21b94a75a6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_layout.xml.in @@ -0,0 +1,178 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_tabs.css b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_tabs.css new file mode 100644 index 0000000000000000000000000000000000000000..21920562a831f80ad5df7d913b1d3d64db994510 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/eigendoxy_tabs.css @@ -0,0 +1,59 @@ +.tabs, .tabs2, .tabs3 { + background-image: url('tab_b.png'); + width: 100%; + z-index: 101; + font-size: 13px; +} + +.tabs2 { + font-size: 10px; +} +.tabs3 { + font-size: 9px; +} + +.tablist { + margin: 0; + padding: 0; + display: table; +} + +.tablist li { + float: left; + display: table-cell; + background-image: url('tab_b.png'); + line-height: 36px; + list-style: none; +} + +.tablist a { + display: block; + padding: 0 20px; + font-weight: bold; + background-image:url('tab_s.png'); + background-repeat:no-repeat; + background-position:right; + color: #283A5D; + text-shadow: 0px 1px 1px rgba(255, 255, 255, 0.9); + text-decoration: none; + outline: none; +} + +.tabs3 .tablist a { + padding: 0 10px; +} + +.tablist a:hover { + background-image: url('tab_h.png'); + background-repeat:repeat-x; + color: #fff; + text-shadow: 0px 1px 1px rgba(0, 0, 0, 1.0); + text-decoration: none; +} + +.tablist li.current a { + background-image: url('tab_a.png'); + background-repeat:repeat-x; + color: #fff; + text-shadow: 0px 1px 1px rgba(0, 0, 0, 1.0); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/.krazy b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/.krazy new file mode 100644 index 0000000000000000000000000000000000000000..00b99405d28b6a59136871da3569538ff9de5256 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/.krazy @@ -0,0 +1,2 @@ +EXCLUDE copyright +EXCLUDE license diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..dd49e3cec233d1470d8ddb409a49bc9e495c5687 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CMakeLists.txt @@ -0,0 +1,16 @@ +file(GLOB examples_SRCS "*.cpp") + +foreach(example_src ${examples_SRCS}) + get_filename_component(example ${example_src} NAME_WE) + add_executable(${example} ${example_src}) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + target_link_libraries(${example} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) + endif() + add_custom_command( + TARGET ${example} + POST_BUILD + COMMAND ${example} + ARGS >${CMAKE_CURRENT_BINARY_DIR}/${example}.out + ) + add_dependencies(all_examples ${example}) +endforeach() diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CustomizingEigen_Inheritance.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CustomizingEigen_Inheritance.cpp new file mode 100644 index 0000000000000000000000000000000000000000..48df64ee3613c2cc406516a0c3a4e05bfbd933a4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/CustomizingEigen_Inheritance.cpp @@ -0,0 +1,30 @@ +#include +#include + +class MyVectorType : public Eigen::VectorXd +{ +public: + MyVectorType(void):Eigen::VectorXd() {} + + // This constructor allows you to construct MyVectorType from Eigen expressions + template + MyVectorType(const Eigen::MatrixBase& other) + : Eigen::VectorXd(other) + { } + + // This method allows you to assign Eigen expressions to MyVectorType + template + MyVectorType& operator=(const Eigen::MatrixBase & other) + { + this->Eigen::VectorXd::operator=(other); + return *this; + } +}; + +int main() +{ + MyVectorType v = MyVectorType::Ones(4); + v(2) += 10; + v = 2 * v; + std::cout << v.transpose() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erf.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erf.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e7cd2c1c0f7a43e834f10fb0fac6cd54f2ad1a2d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erf.cpp @@ -0,0 +1,9 @@ +#include +#include +#include +using namespace Eigen; +int main() +{ + Array4d v(-0.5,2,0,-7); + std::cout << v.erf() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erfc.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erfc.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d8bb04c307631ef0d5a02d91179dcd2f46bfe07f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_erfc.cpp @@ -0,0 +1,9 @@ +#include +#include +#include +using namespace Eigen; +int main() +{ + Array4d v(-0.5,2,0,-7); + std::cout << v.erfc() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_lgamma.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_lgamma.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6bfaccbce3bd0761907c17a73e07fa1a738bac2f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Cwise_lgamma.cpp @@ -0,0 +1,9 @@ +#include +#include +#include +using namespace Eigen; +int main() +{ + Array4d v(0.5,10,0,-1); + std::cout << v.lgamma() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleCols_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleCols_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0ebd955ec8965e3433d32db7b3d6a7d3027347ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleCols_int.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main(void) +{ + int const N = 5; + MatrixXi A(N,N); + A.setRandom(); + cout << "A =\n" << A << '\n' << endl; + cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleRows_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleRows_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a6fe9e8445775309756f5c34702c98956b400467 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_middleRows_int.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main(void) +{ + int const N = 5; + MatrixXi A(N,N); + A.setRandom(); + cout << "A =\n" << A << '\n' << endl; + cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleCols.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleCols.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6191d79c878eae3b3f8fac0af545a88a33c71d86 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleCols.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main(void) +{ + int const N = 5; + MatrixXi A(N,N); + A.setRandom(); + cout << "A =\n" << A << '\n' << endl; + cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleRows.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleRows.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7e8b6573f0ce6feb38270b2b71bc94f71bb6e1ca --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/DenseBase_template_int_middleRows.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main(void) +{ + int const N = 5; + MatrixXi A(N,N); + A.setRandom(); + cout << "A =\n" << A << '\n' << endl; + cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7238c0c43d653f6d36e4b80b66c4f3ef619a31d0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example.cpp @@ -0,0 +1,14 @@ +#include +#include + +using Eigen::MatrixXd; + +int main() +{ + MatrixXd m(2,2); + m(0,0) = 3; + m(1,0) = 2.5; + m(0,1) = -1; + m(1,1) = m(1,0) + m(0,1); + std::cout << m << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_dynamic.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_dynamic.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ff6746e21861f2e25d590e5865ca4260e73dfcb0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_dynamic.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + MatrixXd m = MatrixXd::Random(3,3); + m = (m + MatrixXd::Constant(3,3,1.2)) * 50; + cout << "m =" << endl << m << endl; + VectorXd v(3); + v << 1, 2, 3; + cout << "m * v =" << endl << m * v << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_fixed.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_fixed.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d9117527391a7e167511513f864f9658432a764d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/QuickStart_example2_fixed.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + Matrix3d m = Matrix3d::Random(); + m = (m + Matrix3d::Constant(1.2)) * 50; + cout << "m =" << endl << m << endl; + Vector3d v(1,2,3); + + cout << "m * v =" << endl << m * v << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_flexible.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_flexible.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9d85292dd5d267fa3fd621c67aec308d796d9b8c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_flexible.cpp @@ -0,0 +1,22 @@ +#include +#include + +using namespace Eigen; + +template +void copyUpperTriangularPart(MatrixBase& dst, const MatrixBase& src) +{ + /* Note the 'template' keywords in the following line! */ + dst.template triangularView() = src.template triangularView(); +} + +int main() +{ + MatrixXi m1 = MatrixXi::Ones(5,5); + MatrixXi m2 = MatrixXi::Random(4,4); + std::cout << "m2 before copy:" << std::endl; + std::cout << m2 << std::endl << std::endl; + copyUpperTriangularPart(m2, m1.topLeftCorner(4,4)); + std::cout << "m2 after copy:" << std::endl; + std::cout << m2 << std::endl << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_simple.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_simple.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6998c17692569a5462c75ecbbdf44d774a5931f4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TemplateKeyword_simple.cpp @@ -0,0 +1,20 @@ +#include +#include + +using namespace Eigen; + +void copyUpperTriangularPart(MatrixXf& dst, const MatrixXf& src) +{ + dst.triangularView() = src.triangularView(); +} + +int main() +{ + MatrixXf m1 = MatrixXf::Ones(4,4); + MatrixXf m2 = MatrixXf::Random(4,4); + std::cout << "m2 before copy:" << std::endl; + std::cout << m2 << std::endl << std::endl; + copyUpperTriangularPart(m2, m1); + std::cout << "m2 after copy:" << std::endl; + std::cout << m2 << std::endl << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialInplaceLU.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialInplaceLU.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb9c59b607a265216da2fc0ff54c040686a697cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialInplaceLU.cpp @@ -0,0 +1,61 @@ +#include +struct init { + init() { std::cout << "[" << "init" << "]" << std::endl; } +}; +init init_obj; +// [init] +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXd A(2,2); + A << 2, -1, 1, 3; + cout << "Here is the input matrix A before decomposition:\n" << A << endl; +cout << "[init]" << endl; + +cout << "[declaration]" << endl; + PartialPivLU > lu(A); + cout << "Here is the input matrix A after decomposition:\n" << A << endl; +cout << "[declaration]" << endl; + +cout << "[matrixLU]" << endl; + cout << "Here is the matrix storing the L and U factors:\n" << lu.matrixLU() << endl; +cout << "[matrixLU]" << endl; + +cout << "[solve]" << endl; + MatrixXd A0(2,2); A0 << 2, -1, 1, 3; + VectorXd b(2); b << 1, 2; + VectorXd x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[solve]" << endl; + +cout << "[modifyA]" << endl; + A << 3, 4, -2, 1; + x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[modifyA]" << endl; + +cout << "[recompute]" << endl; + A0 = A; // save A + lu.compute(A); + x = lu.solve(b); + cout << "Residual: " << (A0 * x - b).norm() << endl; +cout << "[recompute]" << endl; + +cout << "[recompute_bis0]" << endl; + MatrixXd A1(2,2); + A1 << 5,-2,3,4; + lu.compute(A1); + cout << "Here is the input matrix A1 after decomposition:\n" << A1 << endl; +cout << "[recompute_bis0]" << endl; + +cout << "[recompute_bis1]" << endl; + x = lu.solve(b); + cout << "Residual: " << (A1 * x - b).norm() << endl; +cout << "[recompute_bis1]" << endl; + +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgComputeTwice.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgComputeTwice.cpp new file mode 100644 index 0000000000000000000000000000000000000000..06ba6461a9cd039747099a078e79377874836828 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgComputeTwice.cpp @@ -0,0 +1,23 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix2f A, b; + LLT llt; + A << 2, -1, -1, 3; + b << 1, 2, 3, 1; + cout << "Here is the matrix A:\n" << A << endl; + cout << "Here is the right hand side b:\n" << b << endl; + cout << "Computing LLT decomposition..." << endl; + llt.compute(A); + cout << "The solution is:\n" << llt.solve(b) << endl; + A(1,1)++; + cout << "The matrix A is now:\n" << A << endl; + cout << "Computing LLT decomposition..." << endl; + llt.compute(A); + cout << "The solution is now:\n" << llt.solve(b) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExComputeSolveError.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExComputeSolveError.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f362fb71a62b1055a3fd89def1bf657058cec0b9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExComputeSolveError.cpp @@ -0,0 +1,14 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXd A = MatrixXd::Random(100,100); + MatrixXd b = MatrixXd::Random(100,50); + MatrixXd x = A.fullPivLu().solve(b); + double relative_error = (A*x - b).norm() / b.norm(); // norm() is L2 norm + cout << "The relative error is:\n" << relative_error << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3a99a94d75bc938abb4a82134875b928dbbfa32b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveColPivHouseholderQR.cpp @@ -0,0 +1,17 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix3f A; + Vector3f b; + A << 1,2,3, 4,5,6, 7,8,10; + b << 3, 3, 4; + cout << "Here is the matrix A:\n" << A << endl; + cout << "Here is the vector b:\n" << b << endl; + Vector3f x = A.colPivHouseholderQr().solve(b); + cout << "The solution is:\n" << x << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveLDLT.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveLDLT.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f8beacd275287a499e084c5653758cd26edbe1d3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgExSolveLDLT.cpp @@ -0,0 +1,16 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix2f A, b; + A << 2, -1, -1, 3; + b << 1, 2, 3, 1; + cout << "Here is the matrix A:\n" << A << endl; + cout << "Here is the right hand side b:\n" << b << endl; + Matrix2f x = A.ldlt().solve(b); + cout << "The solution is:\n" << x << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgInverseDeterminant.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgInverseDeterminant.cpp new file mode 100644 index 0000000000000000000000000000000000000000..14dde5b357571621c90b8ff29d1bbf20d7d37814 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgInverseDeterminant.cpp @@ -0,0 +1,16 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix3f A; + A << 1, 2, 1, + 2, 1, 0, + -1, 1, 2; + cout << "Here is the matrix A:\n" << A << endl; + cout << "The determinant of A is " << A.determinant() << endl; + cout << "The inverse of A is:\n" << A.inverse() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgRankRevealing.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgRankRevealing.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c5165077fb1170ae640f058d51affca860c5997b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgRankRevealing.cpp @@ -0,0 +1,20 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix3f A; + A << 1, 2, 5, + 2, 1, 4, + 3, 0, 3; + cout << "Here is the matrix A:\n" << A << endl; + FullPivLU lu_decomp(A); + cout << "The rank of A is " << lu_decomp.rank() << endl; + cout << "Here is a matrix whose columns form a basis of the null-space of A:\n" + << lu_decomp.kernel() << endl; + cout << "Here is a matrix whose columns form a basis of the column-space of A:\n" + << lu_decomp.image(A) << endl; // yes, have to pass the original A +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSVDSolve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSVDSolve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f109f04e582398075541f1ca72eee89247f05850 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSVDSolve.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXf A = MatrixXf::Random(3, 2); + cout << "Here is the matrix A:\n" << A << endl; + VectorXf b = VectorXf::Random(3); + cout << "Here is the right hand side b:\n" << b << endl; + cout << "The least-squares solution is:\n" + << A.bdcSvd(ComputeThinU | ComputeThinV).solve(b) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8d1d1ed65a3f0befc8ef0f2ea33312da501c4bfb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp @@ -0,0 +1,18 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix2f A; + A << 1, 2, 2, 3; + cout << "Here is the matrix A:\n" << A << endl; + SelfAdjointEigenSolver eigensolver(A); + if (eigensolver.info() != Success) abort(); + cout << "The eigenvalues of A are:\n" << eigensolver.eigenvalues() << endl; + cout << "Here's a matrix whose columns are eigenvectors of A \n" + << "corresponding to these eigenvalues:\n" + << eigensolver.eigenvectors() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSetThreshold.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSetThreshold.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3956b13a39dfe35031cf3a4b411051604618113e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/TutorialLinAlgSetThreshold.cpp @@ -0,0 +1,16 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix2d A; + A << 2, 1, + 2, 0.9999999999; + FullPivLU lu(A); + cout << "By default, the rank of A is found to be " << lu.rank() << endl; + lu.setThreshold(1e-5); + cout << "With threshold 1e-5, the rank of A is found to be " << lu.rank() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_accessors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_accessors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..dc720ff58769d56116a9e9d5e15e0509be574444 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_accessors.cpp @@ -0,0 +1,24 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + ArrayXXf m(2,2); + + // assign some values coefficient by coefficient + m(0,0) = 1.0; m(0,1) = 2.0; + m(1,0) = 3.0; m(1,1) = m(0,1) + m(1,0); + + // print values to standard output + cout << m << endl << endl; + + // using the comma-initializer is also allowed + m << 1.0,2.0, + 3.0,4.0; + + // print values to standard output + cout << m << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_addition.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_addition.cpp new file mode 100644 index 0000000000000000000000000000000000000000..480ffb00ff86b1f88fa30e010e304d8f89b083f3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_addition.cpp @@ -0,0 +1,23 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + ArrayXXf a(3,3); + ArrayXXf b(3,3); + a << 1,2,3, + 4,5,6, + 7,8,9; + b << 1,2,3, + 1,2,3, + 1,2,3; + + // Adding two arrays + cout << "a + b = " << endl << a + b << endl << endl; + + // Subtracting a scalar from an array + cout << "a - 2 = " << endl << a - 2 << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_cwise_other.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_cwise_other.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d9046c63de0e9e0f53be463cd775d2a9c2781153 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_cwise_other.cpp @@ -0,0 +1,19 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + ArrayXf a = ArrayXf::Random(5); + a *= 2; + cout << "a =" << endl + << a << endl; + cout << "a.abs() =" << endl + << a.abs() << endl; + cout << "a.abs().sqrt() =" << endl + << a.abs().sqrt() << endl; + cout << "a.min(a.abs().sqrt()) =" << endl + << a.min(a.abs().sqrt()) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop.cpp new file mode 100644 index 0000000000000000000000000000000000000000..371f070680c0aa48a8270e4891edd99574a31260 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop.cpp @@ -0,0 +1,22 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + MatrixXf m(2,2); + MatrixXf n(2,2); + MatrixXf result(2,2); + + m << 1,2, + 3,4; + n << 5,6, + 7,8; + + result = (m.array() + 4).matrix() * m; + cout << "-- Combination 1: --" << endl << result << endl << endl; + result = (m.array() * n.array()).matrix() * m; + cout << "-- Combination 2: --" << endl << result << endl << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1014275116afd9366790b7d4cfe64dd8f65c820a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_interop_matrix.cpp @@ -0,0 +1,26 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + MatrixXf m(2,2); + MatrixXf n(2,2); + MatrixXf result(2,2); + + m << 1,2, + 3,4; + n << 5,6, + 7,8; + + result = m * n; + cout << "-- Matrix m*n: --" << endl << result << endl << endl; + result = m.array() * n.array(); + cout << "-- Array m*n: --" << endl << result << endl << endl; + result = m.cwiseProduct(n); + cout << "-- With cwiseProduct: --" << endl << result << endl << endl; + result = m.array() + 4; + cout << "-- Array m + 4: --" << endl << result << endl << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_mult.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_mult.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6cb439ff76e4ef6aca0ce235d3e779b1e7c7f31c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ArrayClass_mult.cpp @@ -0,0 +1,16 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + ArrayXXf a(2,2); + ArrayXXf b(2,2); + a << 1,2, + 3,4; + b << 5,6, + 7,8; + cout << "a * b = " << endl << a * b << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_block_assignment.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_block_assignment.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0b87313a1cf83776df0ce492100358c8f9a7ce9e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_block_assignment.cpp @@ -0,0 +1,18 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Array22f m; + m << 1,2, + 3,4; + Array44f a = Array44f::Constant(0.6); + cout << "Here is the array a:" << endl << a << endl << endl; + a.block<2,2>(1,1) = m; + cout << "Here is now a with m copied into its central 2x2 block:" << endl << a << endl << endl; + a.block(0,0,2,3) = a.block(2,1,2,3); + cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x3 block:" << endl << a << endl << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_colrow.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_colrow.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2e7eb009b77010c5bc3aaf6fe2b0c5dbae143b7a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_colrow.cpp @@ -0,0 +1,17 @@ +#include +#include + +using namespace std; + +int main() +{ + Eigen::MatrixXf m(3,3); + m << 1,2,3, + 4,5,6, + 7,8,9; + cout << "Here is the matrix m:" << endl << m << endl; + cout << "2nd Row: " << m.row(1) << endl; + m.col(2) += 3 * m.col(0); + cout << "After adding 3 times the first column into the third column, the matrix m is:\n"; + cout << m << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_corner.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_corner.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3a31507aa63e01f69d312b3733a338106be5f9b5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_corner.cpp @@ -0,0 +1,17 @@ +#include +#include + +using namespace std; + +int main() +{ + Eigen::Matrix4f m; + m << 1, 2, 3, 4, + 5, 6, 7, 8, + 9, 10,11,12, + 13,14,15,16; + cout << "m.leftCols(2) =" << endl << m.leftCols(2) << endl << endl; + cout << "m.bottomRows<2>() =" << endl << m.bottomRows<2>() << endl << endl; + m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose(); + cout << "After assignment, m = " << endl << m << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_print_block.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_print_block.cpp new file mode 100644 index 0000000000000000000000000000000000000000..edea4aefea0d1123589ec3575352089272c79529 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_print_block.cpp @@ -0,0 +1,20 @@ +#include +#include + +using namespace std; + +int main() +{ + Eigen::MatrixXf m(4,4); + m << 1, 2, 3, 4, + 5, 6, 7, 8, + 9,10,11,12, + 13,14,15,16; + cout << "Block in the middle" << endl; + cout << m.block<2,2>(1,1) << endl << endl; + for (int i = 1; i <= 3; ++i) + { + cout << "Block of size " << i << "x" << i << endl; + cout << m.block(0,0,i,i) << endl << endl; + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_vector.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_vector.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4a0b02342435c4c71094b42cb5e90907d311c483 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_BlockOperations_vector.cpp @@ -0,0 +1,14 @@ +#include +#include + +using namespace std; + +int main() +{ + Eigen::ArrayXf v(6); + v << 1, 2, 3, 4, 5, 6; + cout << "v.head(3) =" << endl << v.head(3) << endl << endl; + cout << "v.tail<3>() = " << endl << v.tail<3>() << endl << endl; + v.segment(1,4) *= 2; + cout << "after 'v.segment(1,4) *= 2', v =" << endl << v << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_PartialLU_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_PartialLU_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a5608792fe5bb12d5a234fd9b5b9d504ff94a0ba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_PartialLU_solve.cpp @@ -0,0 +1,18 @@ +#include +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Matrix3f A; + Vector3f b; + A << 1,2,3, 4,5,6, 7,8,10; + b << 3, 3, 4; + cout << "Here is the matrix A:" << endl << A << endl; + cout << "Here is the vector b:" << endl << b << endl; + Vector3f x = A.lu().solve(b); + cout << "The solution is:" << endl << x << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp new file mode 100644 index 0000000000000000000000000000000000000000..334b4d852b06bf22a0fcaa999fa008120dd8591d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_1nn.cpp @@ -0,0 +1,24 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Eigen::MatrixXf m(2,4); + Eigen::VectorXf v(2); + + m << 1, 23, 6, 9, + 3, 11, 7, 2; + + v << 2, + 3; + + MatrixXf::Index index; + // find nearest neighbour + (m.colwise() - v).colwise().squaredNorm().minCoeff(&index); + + cout << "Nearest neighbour is column " << index << ":" << endl; + cout << m.col(index) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e6c87c6a4524f256e78646945e43e6d2bf845410 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple.cpp @@ -0,0 +1,21 @@ +#include +#include + +using namespace std; +int main() +{ + Eigen::MatrixXf mat(2,4); + Eigen::VectorXf v(2); + + mat << 1, 2, 6, 9, + 3, 1, 7, 2; + + v << 0, + 1; + + //add v to each column of m + mat.colwise() += v; + + std::cout << "Broadcasting result: " << std::endl; + std::cout << mat << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d87c96ab1be657d04b8f8797a860b49c12ff9970 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_broadcast_simple_rowwise.cpp @@ -0,0 +1,20 @@ +#include +#include + +using namespace std; +int main() +{ + Eigen::MatrixXf mat(2,4); + Eigen::VectorXf v(4); + + mat << 1, 2, 6, 9, + 3, 1, 7, 2; + + v << 0,1,2,3; + + //add v to each row of m + mat.rowwise() += v.transpose(); + + std::cout << "Broadcasting result: " << std::endl; + std::cout << mat << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..df6825663a24a2cdc90c5eccd8cc290fdbadfa8f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_colwise.cpp @@ -0,0 +1,13 @@ +#include +#include + +using namespace std; +int main() +{ + Eigen::MatrixXf mat(2,4); + mat << 1, 2, 6, 9, + 3, 1, 7, 2; + + std::cout << "Column's maximum: " << std::endl + << mat.colwise().maxCoeff() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..049c747b08525ad25925474b3687bcf8027a373c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_maxnorm.cpp @@ -0,0 +1,20 @@ +#include +#include + +using namespace std; +using namespace Eigen; +int main() +{ + MatrixXf mat(2,4); + mat << 1, 2, 6, 9, + 3, 1, 7, 2; + + MatrixXf::Index maxIndex; + float maxNorm = mat.colwise().sum().maxCoeff(&maxIndex); + + std::cout << "Maximum sum at position " << maxIndex << std::endl; + + std::cout << "The corresponding vector is: " << std::endl; + std::cout << mat.col( maxIndex ) << std::endl; + std::cout << "And its sum is is: " << maxNorm << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0cca37f3678de45b3596b2113c72f8275c136d68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_bool.cpp @@ -0,0 +1,21 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + ArrayXXf a(2,2); + + a << 1,2, + 3,4; + + cout << "(a > 0).all() = " << (a > 0).all() << endl; + cout << "(a > 0).any() = " << (a > 0).any() << endl; + cout << "(a > 0).count() = " << (a > 0).count() << endl; + cout << endl; + cout << "(a > 2).all() = " << (a > 2).all() << endl; + cout << "(a > 2).any() = " << (a > 2).any() << endl; + cout << "(a > 2).count() = " << (a > 2).count() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..740439fb37c70054144476197ef892e4a40fd00d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_norm.cpp @@ -0,0 +1,28 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + VectorXf v(2); + MatrixXf m(2,2), n(2,2); + + v << -1, + 2; + + m << 1,-2, + -3,4; + + cout << "v.squaredNorm() = " << v.squaredNorm() << endl; + cout << "v.norm() = " << v.norm() << endl; + cout << "v.lpNorm<1>() = " << v.lpNorm<1>() << endl; + cout << "v.lpNorm() = " << v.lpNorm() << endl; + + cout << endl; + cout << "m.squaredNorm() = " << m.squaredNorm() << endl; + cout << "m.norm() = " << m.norm() << endl; + cout << "m.lpNorm<1>() = " << m.lpNorm<1>() << endl; + cout << "m.lpNorm() = " << m.lpNorm() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..62e28fc31666fd1a61d71e33b12d5a07e9085e8d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_reductions_operatornorm.cpp @@ -0,0 +1,18 @@ +#include +#include + +using namespace Eigen; +using namespace std; + +int main() +{ + MatrixXf m(2,2); + m << 1,-2, + -3,4; + + cout << "1-norm(m) = " << m.cwiseAbs().colwise().sum().maxCoeff() + << " == " << m.colwise().lpNorm<1>().maxCoeff() << endl; + + cout << "infty-norm(m) = " << m.cwiseAbs().rowwise().sum().maxCoeff() + << " == " << m.rowwise().lpNorm<1>().maxCoeff() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..80427c9f75e655c1d45bb0e0555aaee05ae2df3a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_rowwise.cpp @@ -0,0 +1,13 @@ +#include +#include + +using namespace std; +int main() +{ + Eigen::MatrixXf mat(2,4); + mat << 1, 2, 6, 9, + 3, 1, 7, 2; + + std::cout << "Row's maximum: " << std::endl + << mat.rowwise().maxCoeff() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b54e9aa3124337437e2c44df0a3b3cb26063382e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_ReductionsVisitorsBroadcasting_visitors.cpp @@ -0,0 +1,26 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + Eigen::MatrixXf m(2,2); + + m << 1, 2, + 3, 4; + + //get location of maximum + MatrixXf::Index maxRow, maxCol; + float max = m.maxCoeff(&maxRow, &maxCol); + + //get location of minimum + MatrixXf::Index minRow, minCol; + float min = m.minCoeff(&minRow, &minCol); + + cout << "Max: " << max << ", at: " << + maxRow << "," << maxCol << endl; + cout << "Min: " << min << ", at: " << + minRow << "," << minCol << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_simple_example_dynamic_size.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_simple_example_dynamic_size.cpp new file mode 100644 index 0000000000000000000000000000000000000000..defcb1ee42ce0d59b35b0e1bea7ef63fe421e5e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/Tutorial_simple_example_dynamic_size.cpp @@ -0,0 +1,22 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + for (int size=1; size<=4; ++size) + { + MatrixXi m(size,size+1); // a (size)x(size+1)-matrix of int's + for (int j=0; j +#include + +using namespace Eigen; + +int main() +{ + Matrix3f m3; + m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9; + Matrix4f m4 = Matrix4f::Identity(); + Vector4i v4(1, 2, 3, 4); + + std::cout << "m3\n" << m3 << "\nm4:\n" + << m4 << "\nv4:\n" << v4 << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Block.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Block.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ace719afc58f1fe7b9cb60a675be21ecfc699c37 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Block.cpp @@ -0,0 +1,27 @@ +#include +#include +using namespace Eigen; +using namespace std; + +template +Eigen::Block +topLeftCorner(MatrixBase& m, int rows, int cols) +{ + return Eigen::Block(m.derived(), 0, 0, rows, cols); +} + +template +const Eigen::Block +topLeftCorner(const MatrixBase& m, int rows, int cols) +{ + return Eigen::Block(m.derived(), 0, 0, rows, cols); +} + +int main(int, char**) +{ + Matrix4d m = Matrix4d::Identity(); + cout << topLeftCorner(4*m, 2, 3) << endl; // calls the const version + topLeftCorner(m, 2, 3) *= 5; // calls the non-const version + cout << "Now the matrix m is:" << endl << m << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseBinaryOp.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseBinaryOp.cpp new file mode 100644 index 0000000000000000000000000000000000000000..682af46de49b95dae4825daf92c8863b65c2a0c1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseBinaryOp.cpp @@ -0,0 +1,18 @@ +#include +#include +using namespace Eigen; +using namespace std; + +// define a custom template binary functor +template struct MakeComplexOp { + EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp) + typedef complex result_type; + complex operator()(const Scalar& a, const Scalar& b) const { return complex(a,b); } +}; + +int main(int, char**) +{ + Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random(); + cout << m1.binaryExpr(m2, MakeComplexOp()) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a5fcc153d070c8f626a7baaf3150db7539afb06d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp.cpp @@ -0,0 +1,19 @@ +#include +#include +using namespace Eigen; +using namespace std; + +// define a custom template unary functor +template +struct CwiseClampOp { + CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} + const Scalar operator()(const Scalar& x) const { return xm_sup ? m_sup : x); } + Scalar m_inf, m_sup; +}; + +int main(int, char**) +{ + Matrix4d m1 = Matrix4d::Random(); + cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp(-0.5,0.5)) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp_ptrfun.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp_ptrfun.cpp new file mode 100644 index 0000000000000000000000000000000000000000..36706d8eddc3d4efaf2839d48107a2de76865ad8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_CwiseUnaryOp_ptrfun.cpp @@ -0,0 +1,20 @@ +#include +#include +using namespace Eigen; +using namespace std; + +// define function to be applied coefficient-wise +double ramp(double x) +{ + if (x > 0) + return x; + else + return 0; +} + +int main(int, char**) +{ + Matrix4d m1 = Matrix4d::Random(); + cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedBlock.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedBlock.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9978b32e8ed9c4a1036f7194709386a3643678d2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedBlock.cpp @@ -0,0 +1,27 @@ +#include +#include +using namespace Eigen; +using namespace std; + +template +Eigen::Block +topLeft2x2Corner(MatrixBase& m) +{ + return Eigen::Block(m.derived(), 0, 0); +} + +template +const Eigen::Block +topLeft2x2Corner(const MatrixBase& m) +{ + return Eigen::Block(m.derived(), 0, 0); +} + +int main(int, char**) +{ + Matrix3d m = Matrix3d::Identity(); + cout << topLeft2x2Corner(4*m) << endl; // calls the const version + topLeft2x2Corner(m) *= 2; // calls the non-const version + cout << "Now the matrix m is:" << endl << m << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedReshaped.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedReshaped.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b6d4085dea39cc0d291ddc4670bf034d2c48ccae --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedReshaped.cpp @@ -0,0 +1,22 @@ +#include +#include +using namespace Eigen; +using namespace std; + +template +Eigen::Reshaped +reshape_helper(MatrixBase& m) +{ + return Eigen::Reshaped(m.derived()); +} + +int main(int, char**) +{ + MatrixXd m(2, 4); + m << 1, 2, 3, 4, + 5, 6, 7, 8; + MatrixXd n = reshape_helper(m); + cout << "matrix m is:" << endl << m << endl; + cout << "matrix n is:" << endl << n << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedVectorBlock.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedVectorBlock.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c88c9fbf1a8ff0c098ee8efdd2ccc43bd6eec73c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_FixedVectorBlock.cpp @@ -0,0 +1,27 @@ +#include +#include +using namespace Eigen; +using namespace std; + +template +Eigen::VectorBlock +firstTwo(MatrixBase& v) +{ + return Eigen::VectorBlock(v.derived(), 0); +} + +template +const Eigen::VectorBlock +firstTwo(const MatrixBase& v) +{ + return Eigen::VectorBlock(v.derived(), 0); +} + +int main(int, char**) +{ + Matrix v; v << 1,2,3,4,5,6; + cout << firstTwo(4*v) << endl; // calls the const version + firstTwo(v) *= 2; // calls the non-const version + cout << "Now the vector v is:" << endl << v << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Reshaped.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Reshaped.cpp new file mode 100644 index 0000000000000000000000000000000000000000..18fb45454de20474dce470f50d83454b2e85c157 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_Reshaped.cpp @@ -0,0 +1,23 @@ +#include +#include +using namespace std; +using namespace Eigen; + +template +const Reshaped +reshape_helper(const MatrixBase& m, int rows, int cols) +{ + return Reshaped(m.derived(), rows, cols); +} + +int main(int, char**) +{ + MatrixXd m(3, 4); + m << 1, 4, 7, 10, + 2, 5, 8, 11, + 3, 6, 9, 12; + cout << m << endl; + Ref n = reshape_helper(m, 2, 6); + cout << "Matrix m is:" << endl << m << endl; + cout << "Matrix n is:" << endl << n << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_VectorBlock.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_VectorBlock.cpp new file mode 100644 index 0000000000000000000000000000000000000000..dc213df20f8c5aaaa81d06a16b43e51168499d34 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/class_VectorBlock.cpp @@ -0,0 +1,27 @@ +#include +#include +using namespace Eigen; +using namespace std; + +template +Eigen::VectorBlock +segmentFromRange(MatrixBase& v, int start, int end) +{ + return Eigen::VectorBlock(v.derived(), start, end-start); +} + +template +const Eigen::VectorBlock +segmentFromRange(const MatrixBase& v, int start, int end) +{ + return Eigen::VectorBlock(v.derived(), start, end-start); +} + +int main(int, char**) +{ + Matrix v; v << 1,2,3,4,5,6; + cout << segmentFromRange(2*v, 2, 4) << endl; // calls the const version + segmentFromRange(v, 1, 3) *= 5; // calls the non-const version + cout << "Now the vector v is:" << endl << v << endl; + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_eigenbase.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_eigenbase.cpp new file mode 100644 index 0000000000000000000000000000000000000000..49d94b3d669de579d06bbe0bb827ef08b64b46ba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_eigenbase.cpp @@ -0,0 +1,18 @@ +#include +#include +using namespace Eigen; + +template +void print_size(const EigenBase& b) +{ + std::cout << "size (rows, cols): " << b.size() << " (" << b.rows() + << ", " << b.cols() << ")" << std::endl; +} + +int main() +{ + Vector3f v; + print_size(v); + // v.asDiagonal() returns a 3x3 diagonal matrix pseudo-expression + print_size(v.asDiagonal()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_ref.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_ref.cpp new file mode 100644 index 0000000000000000000000000000000000000000..162a202e4dc258e07b04438c37416c9fa6db32da --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/function_taking_ref.cpp @@ -0,0 +1,19 @@ +#include +#include +using namespace Eigen; +using namespace std; + +float inv_cond(const Ref& a) +{ + const VectorXf sing_vals = a.jacobiSvd().singularValues(); + return sing_vals(sing_vals.size()-1) / sing_vals(0); +} + +int main() +{ + Matrix4f m = Matrix4f::Random(); + cout << "matrix m:" << endl << m << endl << endl; + cout << "inv_cond(m): " << inv_cond(m) << endl; + cout << "inv_cond(m(1:3,1:3)): " << inv_cond(m.topLeftCorner(3,3)) << endl; + cout << "inv_cond(m+I): " << inv_cond(m+Matrix4f::Identity()) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp new file mode 100644 index 0000000000000000000000000000000000000000..92e6aaa2b2c8a264b5b7f7666bdb46a9d0ce67bd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp @@ -0,0 +1,11 @@ +/* +This program is presented in several fragments in the doc page. +Every fragment is in its own file; this file simply combines them. +*/ + +#include "make_circulant.cpp.preamble" +#include "make_circulant.cpp.traits" +#include "make_circulant.cpp.expression" +#include "make_circulant.cpp.evaluator" +#include "make_circulant.cpp.entry" +#include "make_circulant.cpp.main" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.entry b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.entry new file mode 100644 index 0000000000000000000000000000000000000000..f9d2eb8a9599c06bb96ed1df16c93b2945cf39de --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.entry @@ -0,0 +1,5 @@ +template +Circulant makeCirculant(const Eigen::MatrixBase& arg) +{ + return Circulant(arg.derived()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.evaluator b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.evaluator new file mode 100644 index 0000000000000000000000000000000000000000..2ba79e78369f403ac122fa24f9d2898a74241e68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.evaluator @@ -0,0 +1,32 @@ +namespace Eigen { + namespace internal { + template + struct evaluator > + : evaluator_base > + { + typedef Circulant XprType; + typedef typename nested_eval::type ArgTypeNested; + typedef typename remove_all::type ArgTypeNestedCleaned; + typedef typename XprType::CoeffReturnType CoeffReturnType; + + enum { + CoeffReadCost = evaluator::CoeffReadCost, + Flags = Eigen::ColMajor + }; + + evaluator(const XprType& xpr) + : m_argImpl(xpr.m_arg), m_rows(xpr.rows()) + { } + + CoeffReturnType coeff(Index row, Index col) const + { + Index index = row - col; + if (index < 0) index += m_rows; + return m_argImpl.coeff(index); + } + + evaluator m_argImpl; + const Index m_rows; + }; + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.expression b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.expression new file mode 100644 index 0000000000000000000000000000000000000000..380cd445045df643925a2a4478d50cf738b9369f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.expression @@ -0,0 +1,20 @@ +template +class Circulant : public Eigen::MatrixBase > +{ +public: + Circulant(const ArgType& arg) + : m_arg(arg) + { + EIGEN_STATIC_ASSERT(ArgType::ColsAtCompileTime == 1, + YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX); + } + + typedef typename Eigen::internal::ref_selector::type Nested; + + typedef Eigen::Index Index; + Index rows() const { return m_arg.rows(); } + Index cols() const { return m_arg.rows(); } + + typedef typename Eigen::internal::ref_selector::type ArgTypeNested; + ArgTypeNested m_arg; +}; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.main b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.main new file mode 100644 index 0000000000000000000000000000000000000000..877f97f62abb858821275ac048fe33e7b52c97e8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.main @@ -0,0 +1,8 @@ +int main() +{ + Eigen::VectorXd vec(4); + vec << 1, 2, 4, 8; + Eigen::MatrixXd mat; + mat = makeCirculant(vec); + std::cout << mat << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.preamble b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.preamble new file mode 100644 index 0000000000000000000000000000000000000000..e575cce1467b2a92d1cf918055be2e775e866e2a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.preamble @@ -0,0 +1,4 @@ +#include +#include + +template class Circulant; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.traits b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.traits new file mode 100644 index 0000000000000000000000000000000000000000..4e04535d31f36aaf6b12dfb84ad3014b43b721ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant.cpp.traits @@ -0,0 +1,19 @@ +namespace Eigen { + namespace internal { + template + struct traits > + { + typedef Eigen::Dense StorageKind; + typedef Eigen::MatrixXpr XprKind; + typedef typename ArgType::StorageIndex StorageIndex; + typedef typename ArgType::Scalar Scalar; + enum { + Flags = Eigen::ColMajor, + RowsAtCompileTime = ArgType::RowsAtCompileTime, + ColsAtCompileTime = ArgType::RowsAtCompileTime, + MaxRowsAtCompileTime = ArgType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = ArgType::MaxRowsAtCompileTime + }; + }; + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..95d3dd31a153c8f2cbc3ad4ab85feb7a8b5dd97c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/make_circulant2.cpp @@ -0,0 +1,52 @@ +#include +#include + +using namespace Eigen; + +// [circulant_func] +template +class circulant_functor { + const ArgType &m_vec; +public: + circulant_functor(const ArgType& arg) : m_vec(arg) {} + + const typename ArgType::Scalar& operator() (Index row, Index col) const { + Index index = row - col; + if (index < 0) index += m_vec.size(); + return m_vec(index); + } +}; +// [circulant_func] + +// [square] +template +struct circulant_helper { + typedef Matrix MatrixType; +}; +// [square] + +// [makeCirculant] +template +CwiseNullaryOp, typename circulant_helper::MatrixType> +makeCirculant(const Eigen::MatrixBase& arg) +{ + typedef typename circulant_helper::MatrixType MatrixType; + return MatrixType::NullaryExpr(arg.size(), arg.size(), circulant_functor(arg.derived())); +} +// [makeCirculant] + +// [main] +int main() +{ + Eigen::VectorXd vec(4); + vec << 1, 2, 4, 8; + Eigen::MatrixXd mat; + mat = makeCirculant(vec); + std::cout << mat << std::endl; +} +// [main] diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/matrixfree_cg.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/matrixfree_cg.cpp new file mode 100644 index 0000000000000000000000000000000000000000..74699381c7e834159317c19002165d3ff7f357b2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/matrixfree_cg.cpp @@ -0,0 +1,129 @@ +#include +#include +#include +#include +#include + +class MatrixReplacement; +using Eigen::SparseMatrix; + +namespace Eigen { +namespace internal { + // MatrixReplacement looks-like a SparseMatrix, so let's inherits its traits: + template<> + struct traits : public Eigen::internal::traits > + {}; +} +} + +// Example of a matrix-free wrapper from a user type to Eigen's compatible type +// For the sake of simplicity, this example simply wrap a Eigen::SparseMatrix. +class MatrixReplacement : public Eigen::EigenBase { +public: + // Required typedefs, constants, and method: + typedef double Scalar; + typedef double RealScalar; + typedef int StorageIndex; + enum { + ColsAtCompileTime = Eigen::Dynamic, + MaxColsAtCompileTime = Eigen::Dynamic, + IsRowMajor = false + }; + + Index rows() const { return mp_mat->rows(); } + Index cols() const { return mp_mat->cols(); } + + template + Eigen::Product operator*(const Eigen::MatrixBase& x) const { + return Eigen::Product(*this, x.derived()); + } + + // Custom API: + MatrixReplacement() : mp_mat(0) {} + + void attachMyMatrix(const SparseMatrix &mat) { + mp_mat = &mat; + } + const SparseMatrix my_matrix() const { return *mp_mat; } + +private: + const SparseMatrix *mp_mat; +}; + + +// Implementation of MatrixReplacement * Eigen::DenseVector though a specialization of internal::generic_product_impl: +namespace Eigen { +namespace internal { + + template + struct generic_product_impl // GEMV stands for matrix-vector + : generic_product_impl_base > + { + typedef typename Product::Scalar Scalar; + + template + static void scaleAndAddTo(Dest& dst, const MatrixReplacement& lhs, const Rhs& rhs, const Scalar& alpha) + { + // This method should implement "dst += alpha * lhs * rhs" inplace, + // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it. + assert(alpha==Scalar(1) && "scaling is not implemented"); + EIGEN_ONLY_USED_FOR_DEBUG(alpha); + + // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs, + // but let's do something fancier (and less efficient): + for(Index i=0; i S = Eigen::MatrixXd::Random(n,n).sparseView(0.5,1); + S = S.transpose()*S; + + MatrixReplacement A; + A.attachMyMatrix(S); + + Eigen::VectorXd b(n), x; + b.setRandom(); + + // Solve Ax = b using various iterative solver with matrix-free version: + { + Eigen::ConjugateGradient cg; + cg.compute(A); + x = cg.solve(b); + std::cout << "CG: #iterations: " << cg.iterations() << ", estimated error: " << cg.error() << std::endl; + } + + { + Eigen::BiCGSTAB bicg; + bicg.compute(A); + x = bicg.solve(b); + std::cout << "BiCGSTAB: #iterations: " << bicg.iterations() << ", estimated error: " << bicg.error() << std::endl; + } + + { + Eigen::GMRES gmres; + gmres.compute(A); + x = gmres.solve(b); + std::cout << "GMRES: #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl; + } + + { + Eigen::DGMRES gmres; + gmres.compute(A); + x = gmres.solve(b); + std::cout << "DGMRES: #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl; + } + + { + Eigen::MINRES minres; + minres.compute(A); + x = minres.solve(b); + std::cout << "MINRES: #iterations: " << minres.iterations() << ", estimated error: " << minres.error() << std::endl; + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/nullary_indexing.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/nullary_indexing.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b74db5fd14a6b3071bbb300597ea8901f1c4f77d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/nullary_indexing.cpp @@ -0,0 +1,66 @@ +#include +#include + +using namespace Eigen; + +// [functor] +template +class indexing_functor { + const ArgType &m_arg; + const RowIndexType &m_rowIndices; + const ColIndexType &m_colIndices; +public: + typedef Matrix MatrixType; + + indexing_functor(const ArgType& arg, const RowIndexType& row_indices, const ColIndexType& col_indices) + : m_arg(arg), m_rowIndices(row_indices), m_colIndices(col_indices) + {} + + const typename ArgType::Scalar& operator() (Index row, Index col) const { + return m_arg(m_rowIndices[row], m_colIndices[col]); + } +}; +// [functor] + +// [function] +template +CwiseNullaryOp, typename indexing_functor::MatrixType> +mat_indexing(const Eigen::MatrixBase& arg, const RowIndexType& row_indices, const ColIndexType& col_indices) +{ + typedef indexing_functor Func; + typedef typename Func::MatrixType MatrixType; + return MatrixType::NullaryExpr(row_indices.size(), col_indices.size(), Func(arg.derived(), row_indices, col_indices)); +} +// [function] + + +int main() +{ + std::cout << "[main1]\n"; + Eigen::MatrixXi A = Eigen::MatrixXi::Random(4,4); + Array3i ri(1,2,1); + ArrayXi ci(6); ci << 3,2,1,0,0,2; + Eigen::MatrixXi B = mat_indexing(A, ri, ci); + std::cout << "A =" << std::endl; + std::cout << A << std::endl << std::endl; + std::cout << "A([" << ri.transpose() << "], [" << ci.transpose() << "]) =" << std::endl; + std::cout << B << std::endl; + std::cout << "[main1]\n"; + + std::cout << "[main2]\n"; + B = mat_indexing(A, ri+1, ci); + std::cout << "A(ri+1,ci) =" << std::endl; + std::cout << B << std::endl << std::endl; +#if EIGEN_COMP_CXXVER >= 11 + B = mat_indexing(A, ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), ArrayXi::LinSpaced(4,0,3)); + std::cout << "A(ArrayXi::LinSpaced(13,0,12).unaryExpr([](int x){return x%4;}), ArrayXi::LinSpaced(4,0,3)) =" << std::endl; + std::cout << B << std::endl << std::endl; +#endif + std::cout << "[main2]\n"; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_add_sub.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_add_sub.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e97477b6eb90f5cbe298e0c24a7fbf71bf736ba1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_add_sub.cpp @@ -0,0 +1,22 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + Matrix2d a; + a << 1, 2, + 3, 4; + MatrixXd b(2,2); + b << 2, 3, + 1, 4; + std::cout << "a + b =\n" << a + b << std::endl; + std::cout << "a - b =\n" << a - b << std::endl; + std::cout << "Doing a += b;" << std::endl; + a += b; + std::cout << "Now a =\n" << a << std::endl; + Vector3d v(1,2,3); + Vector3d w(1,0,0); + std::cout << "-v + w - v =\n" << -v + w - v << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_dot_cross.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_dot_cross.cpp new file mode 100644 index 0000000000000000000000000000000000000000..631c9a5e04b009a33007249a2f99ef5e95bfc4aa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_dot_cross.cpp @@ -0,0 +1,15 @@ +#include +#include + +using namespace Eigen; +using namespace std; +int main() +{ + Vector3d v(1,2,3); + Vector3d w(0,1,2); + + cout << "Dot product: " << v.dot(w) << endl; + double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar + cout << "Dot product via a matrix product: " << dp << endl; + cout << "Cross product:\n" << v.cross(w) << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_matrix_mul.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_matrix_mul.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f21390241cf3bee0c6a70cfe8d4991cf1cb99694 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_matrix_mul.cpp @@ -0,0 +1,19 @@ +#include +#include + +using namespace Eigen; +int main() +{ + Matrix2d mat; + mat << 1, 2, + 3, 4; + Vector2d u(-1,1), v(2,0); + std::cout << "Here is mat*mat:\n" << mat*mat << std::endl; + std::cout << "Here is mat*u:\n" << mat*u << std::endl; + std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl; + std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl; + std::cout << "Here is u*v^T:\n" << u*v.transpose() << std::endl; + std::cout << "Let's multiply mat by itself" << std::endl; + mat = mat*mat; + std::cout << "Now mat is mat:\n" << mat << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_redux_basic.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_redux_basic.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5632fb52efe857a3a3d5c5e2b2e5950b609dffb2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_redux_basic.cpp @@ -0,0 +1,16 @@ +#include +#include + +using namespace std; +int main() +{ + Eigen::Matrix2d mat; + mat << 1, 2, + 3, 4; + cout << "Here is mat.sum(): " << mat.sum() << endl; + cout << "Here is mat.prod(): " << mat.prod() << endl; + cout << "Here is mat.mean(): " << mat.mean() << endl; + cout << "Here is mat.minCoeff(): " << mat.minCoeff() << endl; + cout << "Here is mat.maxCoeff(): " << mat.maxCoeff() << endl; + cout << "Here is mat.trace(): " << mat.trace() << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_scalar_mul_div.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_scalar_mul_div.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d5f65b53e454951dc8ea0984b39ef46e800967e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_arithmetic_scalar_mul_div.cpp @@ -0,0 +1,17 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + Matrix2d a; + a << 1, 2, + 3, 4; + Vector3d v(1,2,3); + std::cout << "a * 2.5 =\n" << a * 2.5 << std::endl; + std::cout << "0.1 * v =\n" << 0.1 * v << std::endl; + std::cout << "Doing v *= 2;" << std::endl; + v *= 2; + std::cout << "Now v =\n" << v << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_coefficient_accessors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_coefficient_accessors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c2da17158cf5eb4362dca24a3b9d4e08fe4c4358 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_coefficient_accessors.cpp @@ -0,0 +1,18 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + MatrixXd m(2,2); + m(0,0) = 3; + m(1,0) = 2.5; + m(0,1) = -1; + m(1,1) = m(1,0) + m(0,1); + std::cout << "Here is the matrix m:\n" << m << std::endl; + VectorXd v(2); + v(0) = 4; + v(1) = v(0) - 1; + std::cout << "Here is the vector v:\n" << v << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0392c3aa58a1b4e625e4d39b13e6af6f0f0817c5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize.cpp @@ -0,0 +1,18 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + MatrixXd m(2,5); + m.resize(4,3); + std::cout << "The matrix m is of size " + << m.rows() << "x" << m.cols() << std::endl; + std::cout << "It has " << m.size() << " coefficients" << std::endl; + VectorXd v(2); + v.resize(5); + std::cout << "The vector v is of size " << v.size() << std::endl; + std::cout << "As a matrix, v is of size " + << v.rows() << "x" << v.cols() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize_fixed_size.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize_fixed_size.cpp new file mode 100644 index 0000000000000000000000000000000000000000..dcbdfa783d3693b7c4415d580ace1cdf626c4c1b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/examples/tut_matrix_resize_fixed_size.cpp @@ -0,0 +1,12 @@ +#include +#include + +using namespace Eigen; + +int main() +{ + Matrix4d m; + m.resize(4,4); // no operation + std::cout << "The matrix m is of size " + << m.rows() << "x" << m.cols() << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2node.png b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2node.png new file mode 100644 index 0000000000000000000000000000000000000000..63c605bb4c3d941c921a4b6cfa74951e946bcb48 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2node.png differ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2pnode.png b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2pnode.png new file mode 100644 index 0000000000000000000000000000000000000000..c6ee22f937a07d1dbfc27c669d11f8ed13e2f152 Binary files /dev/null and b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/ftv2pnode.png differ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/.krazy b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/.krazy new file mode 100644 index 0000000000000000000000000000000000000000..00b99405d28b6a59136871da3569538ff9de5256 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/.krazy @@ -0,0 +1,2 @@ +EXCLUDE copyright +EXCLUDE license diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/AngleAxis_mimic_euler.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/AngleAxis_mimic_euler.cpp new file mode 100644 index 0000000000000000000000000000000000000000..456de7f7e98d92930c0e7c149a039c6f63d9506e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/AngleAxis_mimic_euler.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m = AngleAxisf(0.25*M_PI, Vector3f::UnitX()) + * AngleAxisf(0.5*M_PI, Vector3f::UnitY()) + * AngleAxisf(0.33*M_PI, Vector3f::UnitZ()); +cout << m << endl << "is unitary: " << m.isUnitary() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_23_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_23_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2c2166eab1f0fecfa5aab0d3eec6b3beda5d5326 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_23_cxx11.cpp @@ -0,0 +1,5 @@ +ArrayXXi a { + {1, 2, 3}, + {3, 4, 5} +}; +cout << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_vector_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_vector_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a668d84accbd8747fa4fdada7adeac5aa7b712da --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_initializer_list_vector_cxx11.cpp @@ -0,0 +1,2 @@ +Array v {{1, 2, 3, 4, 5}}; +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_variadic_ctor_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_variadic_ctor_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0e4ec4469f9ae08fe8a44d41ec8ab0091d9d5655 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Array_variadic_ctor_cxx11.cpp @@ -0,0 +1,3 @@ +Array a(1, 2, 3, 4, 5, 6); +Array b {1, 2, 3}; +cout << a << "\n\n" << b << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_simple.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_simple.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8c8829fd3a0125f2b2941428ed0e1f8de481cab9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_simple.cpp @@ -0,0 +1,11 @@ + int n = 10000; + VectorXd x(n), b(n); + SparseMatrix A(n,n); + /* ... fill A and b ... */ + BiCGSTAB > solver; + solver.compute(A); + x = solver.solve(b); + std::cout << "#iterations: " << solver.iterations() << std::endl; + std::cout << "estimated error: " << solver.error() << std::endl; + /* ... update b ... */ + x = solver.solve(b); // solve again diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_step_by_step.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_step_by_step.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6c95d5a9caa1cc377a40b7e477b6da4f3dcdd50b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/BiCGSTAB_step_by_step.cpp @@ -0,0 +1,14 @@ + int n = 10000; + VectorXd x(n), b(n); + SparseMatrix A(n,n); + /* ... fill A and b ... */ + BiCGSTAB > solver(A); + // start from a random solution + x = VectorXd::Random(n); + solver.setMaxIterations(1); + int i = 0; + do { + x = solver.solveWithGuess(b,x); + std::cout << i << " : " << solver.error() << std::endl; + ++i; + } while (solver.info()!=Success && i<100); diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..868d669053de84ffb2d6885aa826f1e8d0b5507e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/CMakeLists.txt @@ -0,0 +1,31 @@ +file(GLOB snippets_SRCS "*.cpp") + +add_custom_target(all_snippets) + +foreach(snippet_src ${snippets_SRCS}) + get_filename_component(snippet ${snippet_src} NAME_WE) + set(compile_snippet_target compile_${snippet}) + set(compile_snippet_src ${compile_snippet_target}.cpp) + + file(READ ${snippet_src} snippet_source_code) + configure_file(${CMAKE_CURRENT_SOURCE_DIR}/compile_snippet.cpp.in + ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}) + add_executable(${compile_snippet_target} + ${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src}) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + target_link_libraries(${compile_snippet_target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) + endif() + + if(${snippet_src} MATCHES "deprecated") + set_target_properties(${compile_snippet_target} PROPERTIES COMPILE_FLAGS "-DEIGEN_NO_DEPRECATED_WARNING") + endif() + add_custom_command( + TARGET ${compile_snippet_target} + POST_BUILD + COMMAND ${compile_snippet_target} + ARGS >${CMAKE_CURRENT_BINARY_DIR}/${snippet}.out + ) + add_dependencies(all_snippets ${compile_snippet_target}) + set_source_files_properties(${CMAKE_CURRENT_BINARY_DIR}/${compile_snippet_src} + PROPERTIES OBJECT_DEPENDS ${snippet_src}) +endforeach() diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ColPivHouseholderQR_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ColPivHouseholderQR_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b7b204a18a857a8d5d64fc08bbdca8331b13485f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ColPivHouseholderQR_solve.cpp @@ -0,0 +1,8 @@ +Matrix3f m = Matrix3f::Random(); +Matrix3f y = Matrix3f::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the matrix y:" << endl << y << endl; +Matrix3f x; +x = m.colPivHouseholderQr().solve(y); +assert(y.isApprox(m*x)); +cout << "Here is a solution x to the equation mx=y:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..11d6bd3992ac06922d8899ef79cd1601a0279967 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_compute.cpp @@ -0,0 +1,16 @@ +MatrixXcf A = MatrixXcf::Random(4,4); +cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl; + +ComplexEigenSolver ces; +ces.compute(A); +cout << "The eigenvalues of A are:" << endl << ces.eigenvalues() << endl; +cout << "The matrix of eigenvectors, V, is:" << endl << ces.eigenvectors() << endl << endl; + +complex lambda = ces.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXcf v = ces.eigenvectors().col(0); +cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; +cout << "... and A * v = " << endl << A * v << endl << endl; + +cout << "Finally, V * D * V^(-1) = " << endl + << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5509bd89746365e00d0c865f42829fd3ca51827d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +MatrixXcf ones = MatrixXcf::Ones(3,3); +ComplexEigenSolver ces(ones, /* computeEigenvectors = */ false); +cout << "The eigenvalues of the 3x3 matrix of ones are:" + << endl << ces.eigenvalues() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvectors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvectors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..adeed9af64e43535ae708f7b1c7fb3dbd8655008 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexEigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +MatrixXcf ones = MatrixXcf::Ones(3,3); +ComplexEigenSolver ces(ones); +cout << "The first eigenvector of the 3x3 matrix of ones is:" + << endl << ces.eigenvectors().col(0) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3a51701014f7b35ef87c808a6fb62a1312631e18 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_compute.cpp @@ -0,0 +1,6 @@ +MatrixXcf A = MatrixXcf::Random(4,4); +ComplexSchur schur(4); +schur.compute(A); +cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl; +schur.compute(A.inverse()); +cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixT.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixT.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8380571ac781de661be5b53e510dfd9461567b7f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixT.cpp @@ -0,0 +1,4 @@ +MatrixXcf A = MatrixXcf::Random(4,4); +cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl; +ComplexSchur schurOfA(A, false); // false means do not compute U +cout << "The triangular matrix T is:" << endl << schurOfA.matrixT() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixU.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixU.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ba3d9c22ec7cf31d7ec2cd24c8bd87cb16a5d20b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/ComplexSchur_matrixU.cpp @@ -0,0 +1,4 @@ +MatrixXcf A = MatrixXcf::Random(4,4); +cout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl; +ComplexSchur schurOfA(A); +cout << "The unitary matrix U is:" << endl << schurOfA.matrixU() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0aeec3a40d41eceacf4e695307e0d47e3d97deee --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs.cpp @@ -0,0 +1,2 @@ +Array3d v(1,-2,-3); +cout << v.abs() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2c4f9b3440a4d32e5403bbb0329531766aebd2d2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_abs2.cpp @@ -0,0 +1,2 @@ +Array3d v(1,-2,-3); +cout << v.abs2() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_acos.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_acos.cpp new file mode 100644 index 0000000000000000000000000000000000000000..34432cbacfb9aa120213a85a1f3190392b0629ad --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_acos.cpp @@ -0,0 +1,2 @@ +Array3d v(0, sqrt(2.)/2, 1); +cout << v.acos() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_arg.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_arg.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3f45133b62eabf65e0b0fe7fa558700e62bb1b6d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_arg.cpp @@ -0,0 +1,3 @@ +ArrayXcf v = ArrayXcf::Random(3); +cout << v << endl << endl; +cout << arg(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_array_power_array.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_array_power_array.cpp new file mode 100644 index 0000000000000000000000000000000000000000..432a76ee59c29f045f018fc489ba8fda8cf3152f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_array_power_array.cpp @@ -0,0 +1,4 @@ +Array x(8,25,3), + e(1./3.,0.5,2.); +cout << "[" << x << "]^[" << e << "] = " << x.pow(e) << endl; // using ArrayBase::pow +cout << "[" << x << "]^[" << e << "] = " << pow(x,e) << endl; // using Eigen::pow diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_asin.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_asin.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8dad838fd9f29731cceabf9641953396d2a0ebfd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_asin.cpp @@ -0,0 +1,2 @@ +Array3d v(0, sqrt(2.)/2, 1); +cout << v.asin() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_atan.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_atan.cpp new file mode 100644 index 0000000000000000000000000000000000000000..446844726622a8a9c3bf99c8dd834412985809ef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_atan.cpp @@ -0,0 +1,2 @@ +ArrayXd v = ArrayXd::LinSpaced(5,0,1); +cout << v.atan() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_boolean_and.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_boolean_and.cpp new file mode 100644 index 0000000000000000000000000000000000000000..df6b60d92332d4b571eb11a7a086c7c24b23ce37 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_boolean_and.cpp @@ -0,0 +1,2 @@ +Array3d v(-1,2,1), w(-3,2,3); +cout << ((vw) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_greater_equal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_greater_equal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6a08f894841c17a507c511380dddbbd9db66faea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_greater_equal.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v>=w) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_inverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_inverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3967a7ecf30026d0beafaaaf37b9bfa4d27a0b45 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_inverse.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4); +cout << v.inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isFinite.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isFinite.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1da55fd1602ce21ea6c14b46b79532e63bb5ac3a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isFinite.cpp @@ -0,0 +1,5 @@ +Array3d v(1,2,3); +v(1) *= 0.0/0.0; +v(2) /= 0.0; +cout << v << endl << endl; +cout << isfinite(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isInf.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isInf.cpp new file mode 100644 index 0000000000000000000000000000000000000000..be793081cf27e70af8f89ac2e6c1c56e99298e14 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isInf.cpp @@ -0,0 +1,5 @@ +Array3d v(1,2,3); +v(1) *= 0.0/0.0; +v(2) /= 0.0; +cout << v << endl << endl; +cout << isinf(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isNaN.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isNaN.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7b2a930829c23f30ecbee79de48bcd0b07e27bef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_isNaN.cpp @@ -0,0 +1,5 @@ +Array3d v(1,2,3); +v(1) *= 0.0/0.0; +v(2) /= 0.0; +cout << v << endl << endl; +cout << isnan(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_less.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_less.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cafd3b6e0a08e10509484993f9aca37cd5bcbbcc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_less.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,3), w(3,2,1); +cout << (v e(2,-3,1./3.); +cout << "10^[" << e << "] = " << pow(10,e) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sign.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sign.cpp new file mode 100644 index 0000000000000000000000000000000000000000..49920e4f12c1eeb0e861267bcb310551d90fa372 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sign.cpp @@ -0,0 +1,2 @@ +Array3d v(-3,5,0); +cout << v.sign() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sin.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sin.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46fa908cb8caed7e29f14e0fee9344bef99ba559 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sin.cpp @@ -0,0 +1,2 @@ +Array3d v(M_PI, M_PI/2, M_PI/3); +cout << v.sin() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sinh.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sinh.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fac9b19a854ea2d3a9292ebf57c15609ed14ea9e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sinh.cpp @@ -0,0 +1,2 @@ +ArrayXd v = ArrayXd::LinSpaced(5,0,1); +cout << sinh(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_slash_equal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_slash_equal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2efd32d84ec3f9f40a878f4df8ff0897e5b38bef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_slash_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(3,2,4), w(5,4,2); +v /= w; +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sqrt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sqrt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..97bafe8b3a2ddb64ed95a4385f3014890c13d2a6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_sqrt.cpp @@ -0,0 +1,2 @@ +Array3d v(1,2,4); +cout << v.sqrt() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_square.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_square.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f704c5e0ba533625334528d56d4feb11bd705165 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_square.cpp @@ -0,0 +1,2 @@ +Array3d v(2,3,4); +cout << v.square() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tan.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tan.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b758ef04a109159bdb44be7b3e7c62cee7933a8f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tan.cpp @@ -0,0 +1,2 @@ +Array3d v(M_PI, M_PI/2, M_PI/3); +cout << v.tan() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tanh.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tanh.cpp new file mode 100644 index 0000000000000000000000000000000000000000..30cd0450d9a51f2c706182370af7cbd4fc9d3435 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_tanh.cpp @@ -0,0 +1,2 @@ +ArrayXd v = ArrayXd::LinSpaced(5,0,1); +cout << tanh(v) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_times_equal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_times_equal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..147556c737e3ee8a15f8ebe9bffd0107b7d9e84a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Cwise_times_equal.cpp @@ -0,0 +1,3 @@ +Array3d v(1,2,3), w(2,3,0); +v *= w; +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8e54b17fc4332f65dd132db2e759cc90c303b980 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced.cpp @@ -0,0 +1,2 @@ +cout << VectorXi::LinSpaced(4,7,10).transpose() << endl; +cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpacedInt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpacedInt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0d7ae068e4dddd5d64917672d05af4ce4744349a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpacedInt.cpp @@ -0,0 +1,8 @@ +cout << "Even spacing inputs:" << endl; +cout << VectorXi::LinSpaced(8,1,4).transpose() << endl; +cout << VectorXi::LinSpaced(8,1,8).transpose() << endl; +cout << VectorXi::LinSpaced(8,1,15).transpose() << endl; +cout << "Uneven spacing inputs:" << endl; +cout << VectorXi::LinSpaced(8,1,7).transpose() << endl; +cout << VectorXi::LinSpaced(8,1,9).transpose() << endl; +cout << VectorXi::LinSpaced(8,1,16).transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f55c5085d7e2e503313d2b9c87e999bd6602727a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_LinSpaced_seq_deprecated.cpp @@ -0,0 +1,2 @@ +cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl; +cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_setLinSpaced.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_setLinSpaced.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46054f234ffb7a07a3c40e5d2a08ebd178ccd8ea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DenseBase_setLinSpaced.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setLinSpaced(5,0.5f,1.5f); +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_hnormalized.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_hnormalized.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2451f6e7bbbe754f4ce1e155a8a6157f06441562 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_hnormalized.cpp @@ -0,0 +1,6 @@ +Matrix4Xd M = Matrix4Xd::Random(4,5); +Projective3d P(Matrix4d::Random()); +cout << "The matrix M is:" << endl << M << endl << endl; +cout << "M.colwise().hnormalized():" << endl << M.colwise().hnormalized() << endl << endl; +cout << "P*M:" << endl << P*M << endl << endl; +cout << "(P*M).colwise().hnormalized():" << endl << (P*M).colwise().hnormalized() << endl << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d92d4a3507ac5fce74c5dccfdcf7ba446725f4cd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate.cpp @@ -0,0 +1,4 @@ +MatrixXi m = MatrixXi::Random(2,3); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "m.colwise().replicate<3>() = ..." << endl; +cout << m.colwise().replicate<3>() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f9b1b5355f191f7d372168c3b2929ce9cf1b1ee1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/DirectionWise_replicate_int.cpp @@ -0,0 +1,4 @@ +Vector3i v = Vector3i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "v.rowwise().replicate(5) = ..." << endl; +cout << v.rowwise().replicate(5) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c1d9fa8797e84940d14782ff20bf5c6d2f785aef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_EigenSolver_MatrixType.cpp @@ -0,0 +1,16 @@ +MatrixXd A = MatrixXd::Random(6,6); +cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl; + +EigenSolver es(A); +cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl; +cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; + +complex lambda = es.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXcd v = es.eigenvectors().col(0); +cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; +cout << "... and A * v = " << endl << A.cast >() * v << endl << endl; + +MatrixXcd D = es.eigenvalues().asDiagonal(); +MatrixXcd V = es.eigenvectors(); +cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a5c96e9b46b406541715f2367c4f014c4fe2d929 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_compute.cpp @@ -0,0 +1,6 @@ +EigenSolver es; +MatrixXf A = MatrixXf::Random(4,4); +es.compute(A, /* computeEigenvectors = */ false); +cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl; +es.compute(A + MatrixXf::Identity(4,4), false); // re-use es to compute eigenvalues of A+I +cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ed28869a08d340edb8dd558b92c9cc466600fb96 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +EigenSolver es(ones, false); +cout << "The eigenvalues of the 3x3 matrix of ones are:" + << endl << es.eigenvalues() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvectors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvectors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8355f76c94b66ddb80ad3302ace9f05877054378 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +EigenSolver es(ones); +cout << "The first eigenvector of the 3x3 matrix of ones is:" + << endl << es.eigenvectors().col(0) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_pseudoEigenvectors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_pseudoEigenvectors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..85e2569df37a6c94f3564f131509554152330600 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/EigenSolver_pseudoEigenvectors.cpp @@ -0,0 +1,9 @@ +MatrixXd A = MatrixXd::Random(6,6); +cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl; + +EigenSolver es(A); +MatrixXd D = es.pseudoEigenvalueMatrix(); +MatrixXd V = es.pseudoEigenvectors(); +cout << "The pseudo-eigenvalue matrix D is:" << endl << D << endl; +cout << "The pseudo-eigenvector matrix V is:" << endl << V << endl; +cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivHouseholderQR_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivHouseholderQR_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..23bc0749d5c25beab69a9f421bbaa2414ed64251 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivHouseholderQR_solve.cpp @@ -0,0 +1,8 @@ +Matrix3f m = Matrix3f::Random(); +Matrix3f y = Matrix3f::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the matrix y:" << endl << y << endl; +Matrix3f x; +x = m.fullPivHouseholderQr().solve(y); +assert(y.isApprox(m*x)); +cout << "Here is a solution x to the equation mx=y:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_image.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_image.cpp new file mode 100644 index 0000000000000000000000000000000000000000..817bc1e2dfd9fbb73467bd08929a505c7cfe5e68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_image.cpp @@ -0,0 +1,9 @@ +Matrix3d m; +m << 1,1,0, + 1,3,2, + 0,1,1; +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Notice that the middle column is the sum of the two others, so the " + << "columns are linearly dependent." << endl; +cout << "Here is a matrix whose columns have the same span but are linearly independent:" + << endl << m.fullPivLu().image(m) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_kernel.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_kernel.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7086e01e2ca9852f7db951978c3671e1afc3eee6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_kernel.cpp @@ -0,0 +1,7 @@ +MatrixXf m = MatrixXf::Random(3,5); +cout << "Here is the matrix m:" << endl << m << endl; +MatrixXf ker = m.fullPivLu().kernel(); +cout << "Here is a matrix whose columns form a basis of the kernel of m:" + << endl << ker << endl; +cout << "By definition of the kernel, m*ker is zero:" + << endl << m*ker << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c1f88235e089c5bb894939e727ffc7ea5c3e4535 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/FullPivLU_solve.cpp @@ -0,0 +1,11 @@ +Matrix m = Matrix::Random(); +Matrix2f y = Matrix2f::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the matrix y:" << endl << y << endl; +Matrix x = m.fullPivLu().solve(y); +if((m*x).isApprox(y)) +{ + cout << "Here is a solution x to the equation mx=y:" << endl << x << endl; +} +else + cout << "The equation mx=y does not have any solution." << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/GeneralizedEigenSolver.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/GeneralizedEigenSolver.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2acda45fad9a875d6c4e1fda63b00851ff76f603 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/GeneralizedEigenSolver.cpp @@ -0,0 +1,7 @@ +GeneralizedEigenSolver ges; +MatrixXf A = MatrixXf::Random(4,4); +MatrixXf B = MatrixXf::Random(4,4); +ges.compute(A, B); +cout << "The (complex) numerators of the generalzied eigenvalues are: " << ges.alphas().transpose() << endl; +cout << "The (real) denominatore of the generalzied eigenvalues are: " << ges.betas().transpose() << endl; +cout << "The (complex) generalzied eigenvalues are (alphas./beta): " << ges.eigenvalues().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..50e37833a11b8d4024d7a8ac76d986f3169acbb1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_compute.cpp @@ -0,0 +1,6 @@ +MatrixXcf A = MatrixXcf::Random(4,4); +HessenbergDecomposition hd(4); +hd.compute(A); +cout << "The matrix H in the decomposition of A is:" << endl << hd.matrixH() << endl; +hd.compute(2*A); // re-use hd to compute and store decomposition of 2A +cout << "The matrix H in the decomposition of 2A is:" << endl << hd.matrixH() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_matrixH.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_matrixH.cpp new file mode 100644 index 0000000000000000000000000000000000000000..af01366683fdc3534efcf23a9ffa3bc34f9bf41b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_matrixH.cpp @@ -0,0 +1,8 @@ +Matrix4f A = MatrixXf::Random(4,4); +cout << "Here is a random 4x4 matrix:" << endl << A << endl; +HessenbergDecomposition hessOfA(A); +MatrixXf H = hessOfA.matrixH(); +cout << "The Hessenberg matrix H is:" << endl << H << endl; +MatrixXf Q = hessOfA.matrixQ(); +cout << "The orthogonal matrix Q is:" << endl << Q << endl; +cout << "Q H Q^T is:" << endl << Q * H * Q.transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_packedMatrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_packedMatrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4fa5957e86ed6a9f135ba8dcd8c3c0df88bcb367 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HessenbergDecomposition_packedMatrix.cpp @@ -0,0 +1,9 @@ +Matrix4d A = Matrix4d::Random(4,4); +cout << "Here is a random 4x4 matrix:" << endl << A << endl; +HessenbergDecomposition hessOfA(A); +Matrix4d pm = hessOfA.packedMatrix(); +cout << "The packed matrix M is:" << endl << pm << endl; +cout << "The upper Hessenberg part corresponds to the matrix H, which is:" + << endl << hessOfA.matrixH() << endl; +Vector3d hc = hessOfA.householderCoefficients(); +cout << "The vector of Householder coefficients is:" << endl << hc << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_householderQ.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_householderQ.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e859ce55b72706fe47c486912bc06b0bbc39d99d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_householderQ.cpp @@ -0,0 +1,7 @@ +MatrixXf A(MatrixXf::Random(5,3)), thinQ(MatrixXf::Identity(5,3)), Q; +A.setRandom(); +HouseholderQR qr(A); +Q = qr.householderQ(); +thinQ = qr.householderQ() * thinQ; +std::cout << "The complete unitary matrix Q is:\n" << Q << "\n\n"; +std::cout << "The thin matrix Q is:\n" << thinQ << "\n\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8cce6ce6c1fecf324f0cb8ee327ec8aca468789a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderQR_solve.cpp @@ -0,0 +1,9 @@ +typedef Matrix Matrix3x3; +Matrix3x3 m = Matrix3x3::Random(); +Matrix3f y = Matrix3f::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the matrix y:" << endl << y << endl; +Matrix3f x; +x = m.householderQr().solve(y); +assert(y.isApprox(m*x)); +cout << "Here is a solution x to the equation mx=y:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderSequence_HouseholderSequence.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderSequence_HouseholderSequence.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2632b83b9fa665743d115b996f667adacb87f13d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/HouseholderSequence_HouseholderSequence.cpp @@ -0,0 +1,31 @@ +Matrix3d v = Matrix3d::Random(); +cout << "The matrix v is:" << endl; +cout << v << endl; + +Vector3d v0(1, v(1,0), v(2,0)); +cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl; +Vector3d v1(0, 1, v(2,1)); +cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl; +Vector3d v2(0, 0, 1); +cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl; + +Vector3d h = Vector3d::Random(); +cout << "The Householder coefficients are: h = " << h.transpose() << endl; + +Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint(); +cout << "The first Householder reflection is represented by H_0 = " << endl; +cout << H0 << endl; +Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint(); +cout << "The second Householder reflection is represented by H_1 = " << endl; +cout << H1 << endl; +Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint(); +cout << "The third Householder reflection is represented by H_2 = " << endl; +cout << H2 << endl; +cout << "Their product is H_0 H_1 H_2 = " << endl; +cout << H0 * H1 * H2 << endl; + +HouseholderSequence hhSeq(v, h); +Matrix3d hhSeqAsMatrix(hhSeq); +cout << "If we construct a HouseholderSequence from v and h" << endl; +cout << "and convert it to a matrix, we get:" << endl; +cout << hhSeqAsMatrix << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/IOFormat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/IOFormat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..735f5dd85c001d51d3ed4b5dbdb327152bb5bc85 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/IOFormat.cpp @@ -0,0 +1,14 @@ +std::string sep = "\n----------------------------------------\n"; +Matrix3d m1; +m1 << 1.111111, 2, 3.33333, 4, 5, 6, 7, 8.888888, 9; + +IOFormat CommaInitFmt(StreamPrecision, DontAlignCols, ", ", ", ", "", "", " << ", ";"); +IOFormat CleanFmt(4, 0, ", ", "\n", "[", "]"); +IOFormat OctaveFmt(StreamPrecision, 0, ", ", ";\n", "", "", "[", "]"); +IOFormat HeavyFmt(FullPrecision, 0, ", ", ";\n", "[", "]", "[", "]"); + +std::cout << m1 << sep; +std::cout << m1.format(CommaInitFmt) << sep; +std::cout << m1.format(CleanFmt) << sep; +std::cout << m1.format(OctaveFmt) << sep; +std::cout << m1.format(HeavyFmt) << sep; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/JacobiSVD_basic.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/JacobiSVD_basic.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ab24b9bcaa4df2f8ad482c8ba7a4d92bc015149d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/JacobiSVD_basic.cpp @@ -0,0 +1,9 @@ +MatrixXf m = MatrixXf::Random(3,2); +cout << "Here is the matrix m:" << endl << m << endl; +JacobiSVD svd(m, ComputeThinU | ComputeThinV); +cout << "Its singular values are:" << endl << svd.singularValues() << endl; +cout << "Its left singular vectors are the columns of the thin U matrix:" << endl << svd.matrixU() << endl; +cout << "Its right singular vectors are the columns of the thin V matrix:" << endl << svd.matrixV() << endl; +Vector3f rhs(1, 0, 0); +cout << "Now consider this rhs vector:" << endl << rhs << endl; +cout << "A least-squares solution of m*x = rhs is:" << endl << svd.solve(rhs) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeGivens.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeGivens.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6f8ec054aed538cc2939ce74fd246370fa1c0111 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeGivens.cpp @@ -0,0 +1,6 @@ +Vector2f v = Vector2f::Random(); +JacobiRotation G; +G.makeGivens(v.x(), v.y()); +cout << "Here is the vector v:" << endl << v << endl; +v.applyOnTheLeft(0, 1, G.adjoint()); +cout << "Here is the vector J' * v:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeJacobi.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeJacobi.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a86e80a6297305c8256c968876be579d52990eb3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Jacobi_makeJacobi.cpp @@ -0,0 +1,8 @@ +Matrix2f m = Matrix2f::Random(); +m = (m + m.adjoint()).eval(); +JacobiRotation J; +J.makeJacobi(m, 0, 1); +cout << "Here is the matrix m:" << endl << m << endl; +m.applyOnTheLeft(0, 1, J.adjoint()); +m.applyOnTheRight(0, 1, J); +cout << "Here is the matrix J' * m * J:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_example.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_example.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46fb4070450149dc6e411cc516d4ccaedc2d5284 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_example.cpp @@ -0,0 +1,12 @@ +MatrixXd A(3,3); +A << 4,-1,2, -1,6,0, 2,0,5; +cout << "The matrix A is" << endl << A << endl; + +LLT lltOfA(A); // compute the Cholesky decomposition of A +MatrixXd L = lltOfA.matrixL(); // retrieve factor L in the decomposition +// The previous two lines can also be written as "L = A.llt().matrixL()" + +cout << "The Cholesky factor L is" << endl << L << endl; +cout << "To check this, let us compute L * L.transpose()" << endl; +cout << L * L.transpose() << endl; +cout << "This should equal the matrix A" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7095d2cc39ea1542d7eee78ceeea5e6d6b2b035b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LLT_solve.cpp @@ -0,0 +1,8 @@ +typedef Matrix DataMatrix; +// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise) +DataMatrix samples = DataMatrix::Random(12,2); +VectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1; +// and let's solve samples * [x y]^T = elevations in least square sense: +Matrix xy + = (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations)); +cout << xy << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresNormalEquations.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresNormalEquations.cpp new file mode 100644 index 0000000000000000000000000000000000000000..997cf1715b29f93a66981232486b1b54d9926198 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresNormalEquations.cpp @@ -0,0 +1,4 @@ +MatrixXf A = MatrixXf::Random(3, 2); +VectorXf b = VectorXf::Random(3); +cout << "The solution using normal equations is:\n" + << (A.transpose() * A).ldlt().solve(A.transpose() * b) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresQR.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresQR.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6c97045479ec646a2dbf0992a79a8d2022f9d26f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/LeastSquaresQR.cpp @@ -0,0 +1,4 @@ +MatrixXf A = MatrixXf::Random(3, 2); +VectorXf b = VectorXf::Random(3); +cout << "The solution using the QR decomposition is:\n" + << A.colPivHouseholderQr().solve(b) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_general_stride.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_general_stride.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0657e7f845b5a9568722b8a6720d7f89b22fa7ee --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_general_stride.cpp @@ -0,0 +1,5 @@ +int array[24]; +for(int i = 0; i < 24; ++i) array[i] = i; +cout << Map > + (array, 3, 3, Stride(8, 2)) + << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_inner_stride.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_inner_stride.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d95ae9b3ed82f5d2f1dcf3307f244649d88106c5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_inner_stride.cpp @@ -0,0 +1,5 @@ +int array[12]; +for(int i = 0; i < 12; ++i) array[i] = i; +cout << Map > + (array, 6) // the inner stride has already been passed as template parameter + << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_outer_stride.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_outer_stride.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2f6f052c35b63c8122dbe1c6b63fbebfc152a343 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_outer_stride.cpp @@ -0,0 +1,3 @@ +int array[12]; +for(int i = 0; i < 12; ++i) array[i] = i; +cout << Map >(array, 3, 3, OuterStride<>(4)) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_placement_new.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_placement_new.cpp new file mode 100644 index 0000000000000000000000000000000000000000..83b83a893238facb599a8ce4147f0300849f855b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_placement_new.cpp @@ -0,0 +1,5 @@ +int data[] = {1,2,3,4,5,6,7,8,9}; +Map v(data,4); +cout << "The mapped vector v is: " << v << "\n"; +new (&v) Map(data+4,5); +cout << "Now v is: " << v << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_simple.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_simple.cpp new file mode 100644 index 0000000000000000000000000000000000000000..423bb52ad94d01310582f0681279dcc108a9e231 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Map_simple.cpp @@ -0,0 +1,3 @@ +int array[9]; +for(int i = 0; i < 9; ++i) array[i] = i; +cout << Map(array) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_adjoint.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_adjoint.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4680d5938db43202ab6cfeb2efa87bdb387d4bb0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_adjoint.cpp @@ -0,0 +1,3 @@ +Matrix2cf m = Matrix2cf::Random(); +cout << "Here is the 2x2 complex matrix m:" << endl << m << endl; +cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_all.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_all.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46f26f189bbe74ffffe12af2359ad94a39cab12c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_all.cpp @@ -0,0 +1,7 @@ +Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones()); +Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs(); +// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax: +cout << "Is (" << p0.transpose() << ") inside the box: " + << ((boxMin.array()p0.array()).all()) << endl; +cout << "Is (" << p1.transpose() << ") inside the box: " + << ((boxMin.array()p1.array()).all()) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheLeft.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheLeft.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6398c873ac55d9ae545735bb3f038151f8786ddf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheLeft.cpp @@ -0,0 +1,7 @@ +Matrix3f A = Matrix3f::Random(3,3), B; +B << 0,1,0, + 0,0,1, + 1,0,0; +cout << "At start, A = " << endl << A << endl; +A.applyOnTheLeft(B); +cout << "After applyOnTheLeft, A = " << endl << A << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheRight.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheRight.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e4b71b2d8813d77fdce69bb53146414a8669b899 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_applyOnTheRight.cpp @@ -0,0 +1,9 @@ +Matrix3f A = Matrix3f::Random(3,3), B; +B << 0,1,0, + 0,0,1, + 1,0,0; +cout << "At start, A = " << endl << A << endl; +A *= B; +cout << "After A *= B, A = " << endl << A << endl; +A.applyOnTheRight(B); // equivalent to A *= B +cout << "After applyOnTheRight, A = " << endl << A << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f215086db2cbc1b604dcf5f018e9416091857fd9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array.cpp @@ -0,0 +1,4 @@ +Vector3d v(1,2,3); +v.array() += 3; +v.array() -= 2; +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cd3b26a7cf4c84812bd9e4cca480dd3ff9f204d2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_array_const.cpp @@ -0,0 +1,4 @@ +Vector3d v(-1,2,-3); +cout << "the absolute values:" << endl << v.array().abs() << endl; +cout << "the absolute values plus one:" << endl << v.array().abs()+1 << endl; +cout << "sum of the squares: " << v.array().square().sum() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_asDiagonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_asDiagonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b01082db11e644a81e5be57ed16cc604f93c002d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_asDiagonal.cpp @@ -0,0 +1 @@ +cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f99b6d4ca62175621bed8eb3e5f1256300a2e96a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl; +m.block<2,2>(1,1).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7238cbbeda9d8e7e045c55d1eddb334d0dfe0bee --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_block_int_int_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl; +m.block(1, 1, 2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ebae95e1d5679b3b35b6f324a3125dde5ad9ffaa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomLeftCorner(2, 2):" << endl; +cout << m.bottomLeftCorner(2, 2) << endl; +m.bottomLeftCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..bf05093afdf03794b9219dfb4f765a15d8b2ba52 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomRightCorner(2, 2):" << endl; +cout << m.bottomRightCorner(2, 2) << endl; +m.bottomRightCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRows_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRows_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..47ca92ec3ccc695ba8bea9ff16536e2f81fdfe12 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_bottomRows_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.bottomRows(2):" << endl; +cout << a.bottomRows(2) << endl; +a.bottomRows(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cast.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cast.cpp new file mode 100644 index 0000000000000000000000000000000000000000..016880b40c4e5e0c15ddef2f3c1e58990c60b3fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cast.cpp @@ -0,0 +1,3 @@ +Matrix2d md = Matrix2d::Identity() * 0.45; +Matrix2f mf = Matrix2f::Identity(); +cout << md + mf.cast() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_col.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_col.cpp new file mode 100644 index 0000000000000000000000000000000000000000..87c91b1297739c7899822d7e80b53ad7c4cbba95 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_col.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Identity(); +m.col(1) = Vector3d(4,5,6); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a048beffa9d8bc60be38dd1b7444eced0253ec22 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl; +cout << "Here is the maximum absolute value of each column:" + << endl << m.cwiseAbs().colwise().maxCoeff() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..116063fb15f7d4556f3d3e556de3474388c761f2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_colwise_iterator_cxx11.cpp @@ -0,0 +1,12 @@ +Matrix3i m = Matrix3i::Random(); +cout << "Here is the initial matrix m:" << endl << m << endl; +int i = -1; +for(auto c: m.colwise()) { + c *= i; + ++i; +} +cout << "Here is the matrix m after the for-range-loop:" << endl << m << endl; +auto cols = m.colwise(); +auto it = std::find_if(cols.cbegin(), cols.cend(), + [](Matrix3i::ConstColXpr x) { return x.squaredNorm() == 0; }); +cout << "The first empty column is: " << distance(cols.cbegin(),it) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a7b084fd00e71d6a0d2638d81d1cf79ae927aaa2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseAndDetWithCheck.cpp @@ -0,0 +1,13 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix3d inverse; +bool invertible; +double determinant; +m.computeInverseAndDetWithCheck(inverse,determinant,invertible); +cout << "Its determinant is " << determinant << endl; +if(invertible) { + cout << "It is invertible, and its inverse is:" << endl << inverse << endl; +} +else { + cout << "It is not invertible." << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseWithCheck.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseWithCheck.cpp new file mode 100644 index 0000000000000000000000000000000000000000..873a9f8701f7e7dc7b8e08a5d825495c3db9f854 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_computeInverseWithCheck.cpp @@ -0,0 +1,11 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix3d inverse; +bool invertible; +m.computeInverseWithCheck(inverse,invertible); +if(invertible) { + cout << "It is invertible, and its inverse is:" << endl << inverse << endl; +} +else { + cout << "It is not invertible." << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs.cpp new file mode 100644 index 0000000000000000000000000000000000000000..28a31600f56abfb37fabcb3876a48a04c7e1568e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, -4, 6, + -5, 1, 0; +cout << m.cwiseAbs() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..889a2e2ba0d4bb9726cd0b494659ab4015b6a30c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseAbs2.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, -4, 6, + -5, 1, 0; +cout << m.cwiseAbs2() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseArg.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseArg.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e0857cf97e11c7b2f2cc56a76005538ada587fc0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseArg.cpp @@ -0,0 +1,3 @@ +MatrixXcf v = MatrixXcf::Random(2, 3); +cout << v << endl << endl; +cout << v.cwiseArg() << endl; \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseEqual.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseEqual.cpp new file mode 100644 index 0000000000000000000000000000000000000000..469af642c94c3df60b055b497cf0b9c5ccba31d3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseEqual.cpp @@ -0,0 +1,7 @@ +MatrixXi m(2,2); +m << 1, 0, + 1, 1; +cout << "Comparing m with identity matrix:" << endl; +cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl; +Index count = m.cwiseEqual(MatrixXi::Identity(2,2)).count(); +cout << "Number of coefficients that are equal: " << count << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseInverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseInverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..23e08f7b9f7eca329ef5f0bdafeddded12dffb03 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseInverse.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, 0.5, 1, + 3, 0.25, 1; +cout << m.cwiseInverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMax.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMax.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3c956818bd5f5f162c67c6f9b06f6e7b50aa4693 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMax.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseMax(w) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMin.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMin.cpp new file mode 100644 index 0000000000000000000000000000000000000000..82fc761e28522f9d7e0a0b9d8d0fd35dd8ed1151 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseMin.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseMin(w) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseNotEqual.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseNotEqual.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7f0a105d67baa74f872ba0299c4c71e599180384 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseNotEqual.cpp @@ -0,0 +1,7 @@ +MatrixXi m(2,2); +m << 1, 0, + 1, 1; +cout << "Comparing m with identity matrix:" << endl; +cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl; +Index count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count(); +cout << "Number of coefficients that are not equal: " << count << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseProduct.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseProduct.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1db3a11324b6a3abe53c4d4d049d1f2d2b38166a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseProduct.cpp @@ -0,0 +1,4 @@ +Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random(); +Matrix3i c = a.cwiseProduct(b); +cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseQuotient.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseQuotient.cpp new file mode 100644 index 0000000000000000000000000000000000000000..969121208dacd79b7ba7fec645fe9da5316892af --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseQuotient.cpp @@ -0,0 +1,2 @@ +Vector3d v(2,3,4), w(4,2,3); +cout << v.cwiseQuotient(w) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSign.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSign.cpp new file mode 100644 index 0000000000000000000000000000000000000000..efd717955fdcf50e9b1a235354821da486e91a24 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSign.cpp @@ -0,0 +1,4 @@ +MatrixXd m(2,3); +m << 2, -4, 6, + -5, 1, 0; +cout << m.cwiseSign() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSqrt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSqrt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4bfd75d506567b1b91bcbed9aba611b300d3420f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_cwiseSqrt.cpp @@ -0,0 +1,2 @@ +Vector3d v(1,2,4); +cout << v.cwiseSqrt() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cd63413f37f71b837bccda5508882cc2beefae83 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal.cpp @@ -0,0 +1,4 @@ +Matrix3i m = Matrix3i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the main diagonal of m:" << endl + << m.diagonal() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7b66abf67448ba7e7f3d0e5509125b79114c7644 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl + << m.diagonal(1).transpose() << endl + << m.diagonal(-2).transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_template_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_template_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0e73d1c16d4712212e5cb94778628deadd64d480 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_diagonal_template_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl + << m.diagonal<1>().transpose() << endl + << m.diagonal<-2>().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..039f887018ae9e2da08ad590cdbc68dce1b8f7ce --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eigenvalues.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +VectorXcd eivals = ones.eigenvalues(); +cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_end_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_end_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..03c54a9318c7f9fb3dcaabdedc50e089999deea2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_end_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.tail(2):" << endl << v.tail(2) << endl; +v.tail(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eval.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eval.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1df3aa01dec18ed8042828b80aaf3b5d681cec57 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_eval.cpp @@ -0,0 +1,12 @@ +Matrix2f M = Matrix2f::Random(); +Matrix2f m; +m = M; +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Now we want to copy a column into a row." << endl; +cout << "If we do m.col(1) = m.row(0), then m becomes:" << endl; +m.col(1) = m.row(0); +cout << m << endl << "which is wrong!" << endl; +cout << "Now let us instead do m.col(1) = m.row(0).eval(). Then m becomes" << endl; +m = M; +m.col(1) = m.row(0).eval(); +cout << m << endl << "which is right." << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_fixedBlock_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_fixedBlock_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3201127483c467691597e11d46bde3aa82a35df9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_fixedBlock_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4d m = Vector4d(1,2,3,4).asDiagonal(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.fixed<2, 2>(2, 2):" << endl << m.block<2, 2>(2, 2) << endl; +m.block<2, 2>(2, 0) = m.block<2, 2>(2, 2); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_hnormalized.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_hnormalized.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b714adcc3591d6c8f15c1d8482fb6c4bc0d98c21 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_hnormalized.cpp @@ -0,0 +1,6 @@ +Vector4d v = Vector4d::Random(); +Projective3d P(Matrix4d::Random()); +cout << "v = " << v.transpose() << "]^T" << endl; +cout << "v.hnormalized() = " << v.hnormalized().transpose() << "]^T" << endl; +cout << "P*v = " << (P*v).transpose() << "]^T" << endl; +cout << "(P*v).hnormalized() = " << (P*v).hnormalized().transpose() << "]^T" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_homogeneous.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_homogeneous.cpp new file mode 100644 index 0000000000000000000000000000000000000000..26319609769547d6846b1eeb8b7aace5471bd079 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_homogeneous.cpp @@ -0,0 +1,6 @@ +Vector3d v = Vector3d::Random(), w; +Projective3d P(Matrix4d::Random()); +cout << "v = [" << v.transpose() << "]^T" << endl; +cout << "h.homogeneous() = [" << v.homogeneous().transpose() << "]^T" << endl; +cout << "(P * v.homogeneous()) = [" << (P * v.homogeneous()).transpose() << "]^T" << endl; +cout << "(P * v.homogeneous()).hnormalized() = [" << (P * v.homogeneous()).eval().hnormalized().transpose() << "]^T" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b5c1e59c9d73564f8187048d3b8b821b4bf092d1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity.cpp @@ -0,0 +1 @@ +cout << Matrix::Identity() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..918649d64f0cb57b34519b4b8a431149cd1b4840 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_identity_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXd::Identity(4, 3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_inverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_inverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a56142ee05d01292acf96080c3d8d947c58e79bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_inverse.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Its inverse is:" << endl << m.inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isDiagonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isDiagonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5b1d59977658d19981c171602ace45b7e9829c1f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isDiagonal.cpp @@ -0,0 +1,6 @@ +Matrix3d m = 10000 * Matrix3d::Identity(); +m(0,2) = 1; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl; +cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isIdentity.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isIdentity.cpp new file mode 100644 index 0000000000000000000000000000000000000000..17b756c97de3b8d72a77fe94ced95a2f943e1420 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isIdentity.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Identity(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isIdentity() returns: " << m.isIdentity() << endl; +cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOnes.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOnes.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f82f62809c2c028cd3ef87d10450542d84259115 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOnes.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Ones(); +m(0,2) += 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isOnes() returns: " << m.isOnes() << endl; +cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOrthogonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOrthogonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b22af066cdd7c8a1bf5b724b1a8fd7bc4209838f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isOrthogonal.cpp @@ -0,0 +1,6 @@ +Vector3d v(1,0,0); +Vector3d w(1e-4,0,1); +cout << "Here's the vector v:" << endl << v << endl; +cout << "Here's the vector w:" << endl << w << endl; +cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl; +cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isUnitary.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isUnitary.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3877da3479b93d64702f6ecf32d0255e5f23d291 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isUnitary.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Identity(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isUnitary() returns: " << m.isUnitary() << endl; +cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isZero.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isZero.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c2cfe2201240d96a88bc2baa71880b8c68f13ee9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_isZero.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Zero(); +m(0,2) = 1e-4; +cout << "Here's the matrix m:" << endl << m << endl; +cout << "m.isZero() returns: " << m.isZero() << endl; +cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_leftCols_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_leftCols_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6ea984e4e73b0ab91467b6859100f3e172aeeb5a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_leftCols_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.leftCols(2):" << endl; +cout << a.leftCols(2) << endl; +a.leftCols(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_noalias.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_noalias.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3b54a79a6711e5801c2fa335b84f373309c320de --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_noalias.cpp @@ -0,0 +1,3 @@ +Matrix2d a, b, c; a << 1,2,3,4; b << 5,6,7,8; +c.noalias() = a * b; // this computes the product directly to c +cout << c << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones.cpp new file mode 100644 index 0000000000000000000000000000000000000000..02c767c95c8d3c3b568ba15881d93de04f50f6ac --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones.cpp @@ -0,0 +1,2 @@ +cout << Matrix2d::Ones() << endl; +cout << 6 * RowVector4i::Ones() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2ef188e7d23f538be8be7a157acfbaef67ffe154 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int.cpp @@ -0,0 +1,2 @@ +cout << 6 * RowVectorXi::Ones(4) << endl; +cout << VectorXf::Ones(2) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..60f5a31eb956ec955f835cd6bd9357dcea0f650d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_ones_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Ones(2,3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_operatorNorm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_operatorNorm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..355246f0df4ee38bc1725f9f632dec1b12a95082 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_operatorNorm.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +cout << "The operator norm of the 3x3 matrix of ones is " + << ones.operatorNorm() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_prod.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_prod.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d2f27bdc3279c836d21d1fc2f2a4598724efe5c1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_prod.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random.cpp new file mode 100644 index 0000000000000000000000000000000000000000..65fc524f1f67b5e3c181ed41f42ba502526a0632 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random.cpp @@ -0,0 +1 @@ +cout << 100 * Matrix2i::Random() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f161d03c2d1a24f2131525e80da53796263fbe64 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int.cpp @@ -0,0 +1 @@ +cout << VectorXi::Random(2) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3f0f7dd5d8faf3e84ae06981db20f35191fe2bbd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_random_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Random(2,3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3ce52bcd5dba51c843dc4a0fda5f0a955640271e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate.cpp @@ -0,0 +1,4 @@ +MatrixXi m = MatrixXi::Random(2,3); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "m.replicate<3,2>() = ..." << endl; +cout << m.replicate<3,2>() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b1dbc70bcded3df156f986f1ef4a6826454c65b8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_replicate_int_int.cpp @@ -0,0 +1,4 @@ +Vector3i v = Vector3i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "v.replicate(2,5) = ..." << endl; +cout << v.replicate(2,5) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_auto.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_auto.cpp new file mode 100644 index 0000000000000000000000000000000000000000..59f9d3f60c762c18600ac47e07cbd508bb5d0a54 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_auto.cpp @@ -0,0 +1,4 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped(2, AutoSize):" << endl << m.reshaped(2, AutoSize) << endl; +cout << "Here is m.reshaped(AutoSize, fix<8>):" << endl << m.reshaped(AutoSize, fix<8>) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_fixed.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_fixed.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3e9e2cfb675984d3b0142c30917aa130d588ed42 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_fixed.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped(fix<2>,fix<8>):" << endl << m.reshaped(fix<2>,fix<8>) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..af4ca592f907053664b534c36d585b16da5cc861 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_int_int.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_to_vector.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_to_vector.cpp new file mode 100644 index 0000000000000000000000000000000000000000..37f65f7c6049ba34ad1589c8d8492b207ab2bf56 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reshaped_to_vector.cpp @@ -0,0 +1,4 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped().transpose():" << endl << m.reshaped().transpose() << endl; +cout << "Here is m.reshaped().transpose(): " << endl << m.reshaped().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f545a2837fdbfa92b6a5eec91912e8f1f9f76969 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_reverse.cpp @@ -0,0 +1,8 @@ +MatrixXi m = MatrixXi::Random(3,4); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the reverse of m:" << endl << m.reverse() << endl; +cout << "Here is the coefficient (1,0) in the reverse of m:" << endl + << m.reverse()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 4." << endl; +m.reverse()(1,0) = 4; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rightCols_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rightCols_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb513401b295c9c7c01b5775c1185cf5a835c495 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rightCols_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.rightCols(2):" << endl; +cout << a.rightCols(2) << endl; +a.rightCols(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_row.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_row.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b15e6260c851b80b36f9f7530550b7c45eabde70 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_row.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Identity(); +m.row(1) = Vector3d(4,5,6); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rowwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rowwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ae93964eae3da8d7f9d674f754a4f16ecfaac349 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_rowwise.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; +cout << "Here is the maximum absolute value of each row:" + << endl << m.cwiseAbs().rowwise().maxCoeff() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_segment_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_segment_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..70cd6d2664cacc536917624b659a64716b1ea090 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_segment_int_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl; +v.segment(1, 2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_select.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_select.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ae5477f02774d83368ee5540bcb3a1c6e49c0862 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_select.cpp @@ -0,0 +1,6 @@ +MatrixXi m(3, 3); +m << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +m = (m.array() >= 5).select(-m, m); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_selfadjointView.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_selfadjointView.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4bd3c7eeb2ebaab4d3b9ee7104bd0df0b8e5e174 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_selfadjointView.cpp @@ -0,0 +1,6 @@ +Matrix3i m = Matrix3i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the symmetric matrix extracted from the upper part of m:" << endl + << Matrix3i(m.selfadjointView()) << endl; +cout << "Here is the symmetric matrix extracted from the lower part of m:" << endl + << Matrix3i(m.selfadjointView()) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_set.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_set.cpp new file mode 100644 index 0000000000000000000000000000000000000000..50ecf5fb97f728cc51fc58dd0a12eb9320b5786e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_set.cpp @@ -0,0 +1,13 @@ +Matrix3i m1; +m1 << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +cout << m1 << endl << endl; +Matrix3i m2 = Matrix3i::Identity(); +m2.block(0,0, 2,2) << 10, 11, 12, 13; +cout << m2 << endl << endl; +Vector2i v1; +v1 << 14, 15; +m2 << v1.transpose(), 16, + v1, m1.block(1,1,2,2); +cout << m2 << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setIdentity.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setIdentity.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4fd0aa24acd6fca58719162f47fea50f1bac44d5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setIdentity.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Zero(); +m.block<3,3>(1,0).setIdentity(); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setOnes.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setOnes.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4cef9c1eb52b053e9958ff53ca449edd60dc9c92 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setOnes.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +m.row(1).setOnes(); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setRandom.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setRandom.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e2c257d44fe77f190e2204feca52c60bedb89ce0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setRandom.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Zero(); +m.col(1).setRandom(); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setZero.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setZero.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9b5b9583c2193654c656090e57987e38e0165541 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_setZero.cpp @@ -0,0 +1,3 @@ +Matrix4i m = Matrix4i::Random(); +m.row(1).setZero(); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_start_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_start_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c261d2b4e8f0ee1bc61e2083f296c62788bc15fe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_start_int.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.head(2):" << endl << v.head(2) << endl; +v.head(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_bottomRows.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_bottomRows.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f9ea892da46ed8bd9acc4e93aafdb07e44c0c207 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_bottomRows.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.bottomRows<2>():" << endl; +cout << a.bottomRows<2>() << endl; +a.bottomRows<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_end.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_end.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f5ccb00f6ee316a9733a7ded193b3d943efd1210 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_end.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl; +v.tail<2>().setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4dced03baa48c6804cb75ca1f5cd4776779c7a2f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_block_int_int_int_int.cpp @@ -0,0 +1,5 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl; +m.block<2, Dynamic>(1, 1, 2, 3).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp new file mode 100644 index 0000000000000000000000000000000000000000..847892a2723a298e817941b3ee7c2e1b1de7d366 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomLeftCorner<2,2>():" << endl; +cout << m.bottomLeftCorner<2,2>() << endl; +m.bottomLeftCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a1edcc8088cfd7bc52981363e5ae04c6e41702e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomLeftCorner<2,Dynamic>(2,2):" << endl; +cout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl; +m.bottomLeftCorner<2,Dynamic>(2,2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp new file mode 100644 index 0000000000000000000000000000000000000000..abacb014e7ff36da36d6b390371d837b519f3611 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomRightCorner<2,2>():" << endl; +cout << m.bottomRightCorner<2,2>() << endl; +m.bottomRightCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a65508fd8ee0a9de5867921d404072fd552cffdc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_bottomRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.bottomRightCorner<2,Dynamic>(2,2):" << endl; +cout << m.bottomRightCorner<2,Dynamic>(2,2) << endl; +m.bottomRightCorner<2,Dynamic>(2,2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1899d902d3876be413299c17c862b2b265d826c1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topLeftCorner<2,2>():" << endl; +cout << m.topLeftCorner<2,2>() << endl; +m.topLeftCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fac761f63e2b6ebf501fc451f49b893f16e51b42 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topLeftCorner<2,Dynamic>(2,2):" << endl; +cout << m.topLeftCorner<2,Dynamic>(2,2) << endl; +m.topLeftCorner<2,Dynamic>(2,2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c3a177110dd90fae7e65b7720b8fb2f47489c70f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topRightCorner<2,2>():" << endl; +cout << m.topRightCorner<2,2>() << endl; +m.topRightCorner<2,2>().setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a17acc004ed98ae56011a0ab9f6d4e98decafa5f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_int_topRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topRightCorner<2,Dynamic>(2,2):" << endl; +cout << m.topRightCorner<2,Dynamic>(2,2) << endl; +m.topRightCorner<2,Dynamic>(2,2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_leftCols.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_leftCols.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1c425d917be1d0b0569106d294edca6da9568d65 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_leftCols.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.leftCols<2>():" << endl; +cout << a.leftCols<2>() << endl; +a.leftCols<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_rightCols.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_rightCols.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fc8c0d93c66ea2df5dc5831da18efb65b0d2c3ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_rightCols.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.rightCols<2>():" << endl; +cout << a.rightCols<2>() << endl; +a.rightCols<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_segment.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_segment.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e448b402241ef41263219bfdda6137e3bc0ecb3b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_segment.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl; +v.segment<2>(2).setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_start.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_start.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d336b37160f0ca8e2f06bc6d8585b8191d8ef4a5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_start.cpp @@ -0,0 +1,5 @@ +RowVector4i v = RowVector4i::Random(); +cout << "Here is the vector v:" << endl << v << endl; +cout << "Here is v.head(2):" << endl << v.head<2>() << endl; +v.head<2>().setZero(); +cout << "Now the vector v is:" << endl << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_topRows.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_topRows.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0110251a51cdba81c291b58488937057de1764b1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_template_int_topRows.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.topRows<2>():" << endl; +cout << a.topRows<2>() << endl; +a.topRows<2>().setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e52cb3bdbecc44ae033153a6826c9f09c6950484 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topLeftCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topLeftCorner(2, 2):" << endl; +cout << m.topLeftCorner(2, 2) << endl; +m.topLeftCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRightCorner_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRightCorner_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..811fa563e5ede85557da48f35a10d8d05b086e17 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRightCorner_int_int.cpp @@ -0,0 +1,6 @@ +Matrix4i m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.topRightCorner(2, 2):" << endl; +cout << m.topRightCorner(2, 2) << endl; +m.topRightCorner(2, 2).setZero(); +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRows_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRows_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f2d75f1cb840ca67b41ac87b36552bad13e80519 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_topRows_int.cpp @@ -0,0 +1,6 @@ +Array44i a = Array44i::Random(); +cout << "Here is the array a:" << endl << a << endl; +cout << "Here is a.topRows(2):" << endl; +cout << a.topRows(2) << endl; +a.topRows(2).setZero(); +cout << "Now the array a is:" << endl << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_transpose.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_transpose.cpp new file mode 100644 index 0000000000000000000000000000000000000000..88eea83c4780a969f2ad563f978a92453683ce44 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_transpose.cpp @@ -0,0 +1,8 @@ +Matrix2i m = Matrix2i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the transpose of m:" << endl << m.transpose() << endl; +cout << "Here is the coefficient (1,0) in the transpose of m:" << endl + << m.transpose()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 0." << endl; +m.transpose()(1,0) = 0; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_triangularView.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_triangularView.cpp new file mode 100644 index 0000000000000000000000000000000000000000..03aa303f0dd915c4334dd76e8fdd8a594b3b9ae7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_triangularView.cpp @@ -0,0 +1,9 @@ +Matrix3i m = Matrix3i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the upper-triangular matrix extracted from m:" << endl + << Matrix3i(m.triangularView()) << endl; +cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl + << Matrix3i(m.triangularView()) << endl; +cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl + << Matrix3i(m.triangularView()) << endl; +// FIXME need to implement output for triangularViews (Bug 885) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero.cpp new file mode 100644 index 0000000000000000000000000000000000000000..606493677e2f5674546990e8f1a4fdf7009bb2bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero.cpp @@ -0,0 +1,2 @@ +cout << Matrix2d::Zero() << endl; +cout << RowVector4i::Zero() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..370a9ba0af375de7e5cfa3e7f2d243f1baf8c4fe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int.cpp @@ -0,0 +1,2 @@ +cout << RowVectorXi::Zero(4) << endl; +cout << VectorXf::Zero(2) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4099c5d4dde0623d65193f8f9762596ee1c6a3e6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/MatrixBase_zero_int_int.cpp @@ -0,0 +1 @@ +cout << MatrixXi::Zero(2,3) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_Map_stride.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_Map_stride.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ae42a127af54c6d9c193232987479b6293bb1f78 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_Map_stride.cpp @@ -0,0 +1,7 @@ +Matrix4i A; +A << 1, 2, 3, 4, + 5, 6, 7, 8, + 9, 10, 11, 12, + 13, 14, 15, 16; + +std::cout << Matrix2i::Map(&A(1,1),Stride<8,2>()) << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_23_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_23_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..60280ab58e4b8109b292efda240fafee072cbef0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_23_cxx11.cpp @@ -0,0 +1,5 @@ +MatrixXd m { + {1, 2, 3}, + {4, 5, 6} +}; +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..325257cb0c57b6f30720eb28d5f40eb0155ab4f9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_initializer_list_vector_cxx11.cpp @@ -0,0 +1,2 @@ +VectorXi v {{1, 2}}; +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_NoChange_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_NoChange_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..acdf18c460e166a240fb4c9e01c60dc8d86af998 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_NoChange_int.cpp @@ -0,0 +1,3 @@ +MatrixXd m(3,4); +m.resize(NoChange, 5); +cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..044c78989fd89a4ba20d5b786815ac3e061054b7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int.cpp @@ -0,0 +1,6 @@ +VectorXd v(10); +v.resize(3); +RowVector3d w; +w.resize(3); // this is legal, but has no effect +cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl; +cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_NoChange.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_NoChange.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5c37c9067e12e66d59779d7453b025274ac78981 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_NoChange.cpp @@ -0,0 +1,3 @@ +MatrixXd m(3,4); +m.resize(5, NoChange); +cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..bfd474159657e63dbee97decd55b5c738f8d79bd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_resize_int_int.cpp @@ -0,0 +1,9 @@ +MatrixXd m(2,3); +m << 1,2,3,4,5,6; +cout << "here's the 2x3 matrix m:" << endl << m << endl; +cout << "let's resize m to 3x2. This is a conservative resizing because 2*3==3*2." << endl; +m.resize(3,2); +cout << "here's the 3x2 matrix m:" << endl << m << endl; +cout << "now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:" << endl; +m.resize(2,2); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ff5a86c98e9d0d609b609935848491ca2b60f8ee --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setConstant(3, 5); +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..32b950cfd1e70701a8eea238d5042855b8b88d08 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setConstant_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setConstant(3, 3, 5); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setIdentity_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setIdentity_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a6596719929d1b641227b523515c9f0cb83e664e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setIdentity_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setIdentity(3, 3); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..752cb35b26a647192d70ca444a830fe26479442a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setOnes(3); +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1ffb66bbdda0ffc30b8d0ad81e39d1dd15c36da2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setOnes_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setOnes(3, 3); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e160dd7dfce4c02820b59ffef4bb6b105cb5427f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setRandom(3); +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..80cda11d7b54cbf2f120badb790b1daaa2aa9b07 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setRandom_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setRandom(3, 3); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0fb16c1f33c3e61580e23b7898945407a873c8a4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int.cpp @@ -0,0 +1,3 @@ +VectorXf v; +v.setZero(3); +cout << v << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ad883b916b223112a8d87a68bb418bcf808cd2ea --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_setZero_int_int.cpp @@ -0,0 +1,3 @@ +MatrixXf m; +m.setZero(3, 3); +cout << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_variadic_ctor_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_variadic_ctor_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..06d33f57130048dd867bf29e319b0ed205c95c57 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Matrix_variadic_ctor_cxx11.cpp @@ -0,0 +1,3 @@ +Matrix a(1, 2, 3, 4, 5, 6); +Matrix b {1, 2, 3}; +cout << a << "\n\n" << b << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialPivLU_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialPivLU_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fa3570ab8d247e2b7daa926be090064c7da668e3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialPivLU_solve.cpp @@ -0,0 +1,7 @@ +MatrixXd A = MatrixXd::Random(3,3); +MatrixXd B = MatrixXd::Random(3,2); +cout << "Here is the invertible matrix A:" << endl << A << endl; +cout << "Here is the matrix B:" << endl << B << endl; +MatrixXd X = A.lu().solve(B); +cout << "Here is the (unique) solution X to the equation AX=B:" << endl << X << endl; +cout << "Relative error: " << (A*X-B).norm() / B.norm() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_count.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_count.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1c3b3a28f9b3659ef4c3aa12df49a18eefc0d31c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_count.cpp @@ -0,0 +1,5 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Matrix res = (m.array() >= 0.5).rowwise().count(); +cout << "Here is the count of elements larger or equal than 0.5 of each row:" << endl; +cout << res << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_maxCoeff.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_maxCoeff.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e8fd3820d839cfea6ef70d9b7d61b0bf547ae677 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_maxCoeff.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the maximum of each column:" << endl << m.colwise().maxCoeff() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_minCoeff.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_minCoeff.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d717bc0d18905bebb7809f39ba1cc1be75280bd5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_minCoeff.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the minimum of each column:" << endl << m.colwise().minCoeff() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_norm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_norm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..dbcf290a0eb710abd576867945856223b8f3013a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_norm.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the norm of each column:" << endl << m.colwise().norm() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_prod.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_prod.cpp new file mode 100644 index 0000000000000000000000000000000000000000..aacf09cbb76502067718673de8f526c40dda335a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_prod.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the product of each row:" << endl << m.rowwise().prod() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_squaredNorm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_squaredNorm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9f3293e658c59d61af3c1724beaa3575d9b55bca --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_squaredNorm.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the square norm of each row:" << endl << m.rowwise().squaredNorm() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_sum.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_sum.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ec82d3e41bcd2ccbd07e44d1996a2347f05f20fb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/PartialRedux_sum.cpp @@ -0,0 +1,3 @@ +Matrix3d m = Matrix3d::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealQZ_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealQZ_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a18da42e828cb573f6f100cd032d8611a1cad912 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealQZ_compute.cpp @@ -0,0 +1,17 @@ +MatrixXf A = MatrixXf::Random(4,4); +MatrixXf B = MatrixXf::Random(4,4); +RealQZ qz(4); // preallocate space for 4x4 matrices +qz.compute(A,B); // A = Q S Z, B = Q T Z + +// print original matrices and result of decomposition +cout << "A:\n" << A << "\n" << "B:\n" << B << "\n"; +cout << "S:\n" << qz.matrixS() << "\n" << "T:\n" << qz.matrixT() << "\n"; +cout << "Q:\n" << qz.matrixQ() << "\n" << "Z:\n" << qz.matrixZ() << "\n"; + +// verify precision +cout << "\nErrors:" + << "\n|A-QSZ|: " << (A-qz.matrixQ()*qz.matrixS()*qz.matrixZ()).norm() + << ", |B-QTZ|: " << (B-qz.matrixQ()*qz.matrixT()*qz.matrixZ()).norm() + << "\n|QQ* - I|: " << (qz.matrixQ()*qz.matrixQ().adjoint() - MatrixXf::Identity(4,4)).norm() + << ", |ZZ* - I|: " << (qz.matrixZ()*qz.matrixZ().adjoint() - MatrixXf::Identity(4,4)).norm() + << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_RealSchur_MatrixType.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_RealSchur_MatrixType.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a5530dcc8f786835a8a7d8beb9fe5e16bfa7fa6b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_RealSchur_MatrixType.cpp @@ -0,0 +1,10 @@ +MatrixXd A = MatrixXd::Random(6,6); +cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl; + +RealSchur schur(A); +cout << "The orthogonal matrix U is:" << endl << schur.matrixU() << endl; +cout << "The quasi-triangular matrix T is:" << endl << schur.matrixT() << endl << endl; + +MatrixXd U = schur.matrixU(); +MatrixXd T = schur.matrixT(); +cout << "U * T * U^T = " << endl << U * T * U.transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..20c2611b888babe979a4a25c56a56f0fcfcdfc78 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/RealSchur_compute.cpp @@ -0,0 +1,6 @@ +MatrixXf A = MatrixXf::Random(4,4); +RealSchur schur(4); +schur.compute(A, /* computeU = */ false); +cout << "The matrix T in the decomposition of A is:" << endl << schur.matrixT() << endl; +schur.compute(A.inverse(), /* computeU = */ false); +cout << "The matrix T in the decomposition of A^(-1) is:" << endl << schur.matrixT() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp new file mode 100644 index 0000000000000000000000000000000000000000..73a7f6252cbf915910688b21110616e07b736641 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver.cpp @@ -0,0 +1,7 @@ +SelfAdjointEigenSolver es; +Matrix4f X = Matrix4f::Random(4,4); +Matrix4f A = X + X.transpose(); +es.compute(A); +cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl; +es.compute(A + Matrix4f::Identity(4,4)); // re-use es to compute eigenvalues of A+I +cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3599b17a04e503fa2539ed861411aca3ed8b0459 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp @@ -0,0 +1,17 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver es(A); +cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl; +cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; + +double lambda = es.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXd v = es.eigenvectors().col(0); +cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; +cout << "... and A * v = " << endl << A * v << endl << endl; + +MatrixXd D = es.eigenvalues().asDiagonal(); +MatrixXd V = es.eigenvectors(); +cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..bbb821e02bdcff11dd55ac9d777db0937a53fa1b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp @@ -0,0 +1,16 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric matrix, A:" << endl << A << endl; +X = MatrixXd::Random(5,5); +MatrixXd B = X * X.transpose(); +cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl; + +GeneralizedSelfAdjointEigenSolver es(A,B); +cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; +cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; + +double lambda = es.eigenvalues()[0]; +cout << "Consider the first eigenvalue, lambda = " << lambda << endl; +VectorXd v = es.eigenvectors().col(0); +cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl; +cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2975cc3f290238d2202fcc35f74191d75cbbfbe8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType.cpp @@ -0,0 +1,7 @@ +SelfAdjointEigenSolver es(4); +MatrixXf X = MatrixXf::Random(4,4); +MatrixXf A = X + X.transpose(); +es.compute(A); +cout << "The eigenvalues of A are: " << es.eigenvalues().transpose() << endl; +es.compute(A + MatrixXf::Identity(4,4)); // re-use es to compute eigenvalues of A+I +cout << "The eigenvalues of A+I are: " << es.eigenvalues().transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..07c92a1e4f0366f3998d36fb807cfa2add7b7d1a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X * X.transpose(); +X = MatrixXd::Random(5,5); +MatrixXd B = X * X.transpose(); + +GeneralizedSelfAdjointEigenSolver es(A,B,EigenvaluesOnly); +cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; +es.compute(B,A,false); +cout << "The eigenvalues of the pencil (B,A) are:" << endl << es.eigenvalues() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0ff33c68d50acdf73d5937e45f7fdff28227d312 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvalues.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +SelfAdjointEigenSolver es(ones); +cout << "The eigenvalues of the 3x3 matrix of ones are:" + << endl << es.eigenvalues() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp new file mode 100644 index 0000000000000000000000000000000000000000..94b0d6ebd3c08f1414ae1ae7b5adf87d0da7d0d4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_eigenvectors.cpp @@ -0,0 +1,4 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +SelfAdjointEigenSolver es(ones); +cout << "The first eigenvector of the 3x3 matrix of ones is:" + << endl << es.eigenvectors().col(0) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..114c65fb3e15ccd1797bf844e38b07b1a5ec9576 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorInverseSqrt.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(4,4); +MatrixXd A = X * X.transpose(); +cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver es(A); +cout << "The inverse square root of A is: " << endl; +cout << es.operatorInverseSqrt() << endl; +cout << "We can also compute it with operatorSqrt() and inverse(). That yields: " << endl; +cout << es.operatorSqrt().inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp new file mode 100644 index 0000000000000000000000000000000000000000..eeacca74becdf24c41b5916005e63e88a4e55fe6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointEigenSolver_operatorSqrt.cpp @@ -0,0 +1,8 @@ +MatrixXd X = MatrixXd::Random(4,4); +MatrixXd A = X * X.transpose(); +cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl; + +SelfAdjointEigenSolver es(A); +MatrixXd sqrtA = es.operatorSqrt(); +cout << "The square root of A is: " << endl << sqrtA << endl; +cout << "If we square this, we get: " << endl << sqrtA*sqrtA << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..be198677840c786158f76e010c85b25cdd6ba81f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_eigenvalues.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +VectorXd eivals = ones.selfadjointView().eigenvalues(); +cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_operatorNorm.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_operatorNorm.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f380f559452a8427fbab8285ae90d63617993bd5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SelfAdjointView_operatorNorm.cpp @@ -0,0 +1,3 @@ +MatrixXd ones = MatrixXd::Ones(3,3); +cout << "The operator norm of the 3x3 matrix of ones is " + << ones.selfadjointView().operatorNorm() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_arrayexpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_arrayexpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2df8180981455072097c156cf46b2d5c42dba8a1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_arrayexpr.cpp @@ -0,0 +1,4 @@ +ArrayXi ind(5); ind<<4,2,5,5,3; +MatrixXi A = MatrixXi::Random(4,6); +cout << "Initial matrix A:\n" << A << "\n\n"; +cout << "A(all,ind-1):\n" << A(all,ind-1) << "\n\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_custom_padding_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_custom_padding_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..24db98b7db76c28e4a835a403d62c644eabce1fb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_custom_padding_cxx11.cpp @@ -0,0 +1,12 @@ +struct pad { + Index size() const { return out_size; } + Index operator[] (Index i) const { return std::max(0,i-(out_size-in_size)); } + Index in_size, out_size; +}; + +Matrix3i A; +A.reshaped() = VectorXi::LinSpaced(9,1,9); +cout << "Initial matrix A:\n" << A << "\n\n"; +MatrixXi B(5,5); +B = A(pad{3,5}, pad{3,5}); +cout << "A(pad{3,N}, pad{3,N}):\n" << B << "\n\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_rawarray_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_rawarray_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1087131ab02366110b269402f18e8d64a662bed2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_rawarray_cxx11.cpp @@ -0,0 +1,5 @@ +#if EIGEN_HAS_STATIC_ARRAY_TEMPLATE +MatrixXi A = MatrixXi::Random(4,6); +cout << "Initial matrix A:\n" << A << "\n\n"; +cout << "A(all,{4,2,5,5,3}):\n" << A(all,{4,2,5,5,3}) << "\n\n"; +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_stdvector_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_stdvector_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..555f6625f2306f738074c9a23eaba68b3542b4a2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Slicing_stdvector_cxx11.cpp @@ -0,0 +1,4 @@ +std::vector ind{4,2,5,5,3}; +MatrixXi A = MatrixXi::Random(4,6); +cout << "Initial matrix A:\n" << A << "\n\n"; +cout << "A(all,ind):\n" << A(all,ind) << "\n\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SparseMatrix_coeffs.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SparseMatrix_coeffs.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f71a69b078d0f19a01ba678fe78ee3d32b7f83f1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/SparseMatrix_coeffs.cpp @@ -0,0 +1,9 @@ +SparseMatrix A(3,3); +A.insert(1,2) = 0; +A.insert(0,1) = 1; +A.insert(2,0) = 2; +A.makeCompressed(); +cout << "The matrix A is:" << endl << MatrixXd(A) << endl; +cout << "it has " << A.nonZeros() << " stored non zero coefficients that are: " << A.coeffs().transpose() << endl; +A.coeffs() += 10; +cout << "After adding 10 to every stored non zero coefficient, the matrix A is:" << endl << MatrixXd(A) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block.cpp new file mode 100644 index 0000000000000000000000000000000000000000..03282f4f0e5af52ef8cf391c21a653e662e603c2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block.cpp @@ -0,0 +1,7 @@ +MatrixXi mat(3,3); +mat << 1, 2, 3, 4, 5, 6, 7, 8, 9; +cout << "Here is the matrix mat:\n" << mat << endl; + +// This assignment shows the aliasing problem +mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2); +cout << "After the assignment, mat = \n" << mat << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block_correct.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block_correct.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6fee5801eb86108d3f281cbb03903e1b4d23ed8b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_block_correct.cpp @@ -0,0 +1,7 @@ +MatrixXi mat(3,3); +mat << 1, 2, 3, 4, 5, 6, 7, 8, 9; +cout << "Here is the matrix mat:\n" << mat << endl; + +// The eval() solves the aliasing problem +mat.bottomRightCorner(2,2) = mat.topLeftCorner(2,2).eval(); +cout << "After the assignment, mat = \n" << mat << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_cwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_cwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7049f6c56491c6fef963fd899c1f7cd5a59b1a50 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_cwise.cpp @@ -0,0 +1,20 @@ +MatrixXf mat(2,2); +mat << 1, 2, 4, 7; +cout << "Here is the matrix mat:\n" << mat << endl << endl; + +mat = 2 * mat; +cout << "After 'mat = 2 * mat', mat = \n" << mat << endl << endl; + + +mat = mat - MatrixXf::Identity(2,2); +cout << "After the subtraction, it becomes\n" << mat << endl << endl; + + +ArrayXXf arr = mat; +arr = arr.square(); +cout << "After squaring, it becomes\n" << arr << endl << endl; + +// Combining all operations in one statement: +mat << 1, 2, 4, 7; +mat = (2 * mat - MatrixXf::Identity(2,2)).array().square(); +cout << "Doing everything at once yields\n" << mat << endl << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cd7e9004c92f5b6ea25bbc295d92fcbf541fdc02 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult1.cpp @@ -0,0 +1,4 @@ +MatrixXf matA(2,2); +matA << 2, 0, 0, 2; +matA = matA * matA; +cout << matA; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a3ff56851cf21b355714ebb4cdb05ae27f6ec2a6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult2.cpp @@ -0,0 +1,10 @@ +MatrixXf matA(2,2), matB(2,2); +matA << 2, 0, 0, 2; + +// Simple but not quite as efficient +matB = matA * matA; +cout << matB << endl << endl; + +// More complicated but also more efficient +matB.noalias() = matA * matA; +cout << matB; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult3.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult3.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1d12a6c670e4b9b97bd54c7cf66fdd27c107858a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult3.cpp @@ -0,0 +1,4 @@ +MatrixXf matA(2,2); +matA << 2, 0, 0, 2; +matA.noalias() = matA * matA; +cout << matA; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult4.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult4.cpp new file mode 100644 index 0000000000000000000000000000000000000000..01c1c6d77c5e4d75ab5f63756737367c7c271196 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult4.cpp @@ -0,0 +1,5 @@ +MatrixXf A(2,2), B(3,2); +B << 2, 0, 0, 3, 1, 1; +A << 2, 0, 0, -2; +A = (B * A).cwiseAbs(); +cout << A; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult5.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult5.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1a36defde3b99fab572dae66c1f11d33179945aa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicAliasing_mult5.cpp @@ -0,0 +1,5 @@ +MatrixXf A(2,2), B(3,2); +B << 2, 0, 0, 3, 1, 1; +A << 2, 0, 0, -2; +A = (B * A).eval().cwiseAbs(); +cout << A; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicStorageOrders_example.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicStorageOrders_example.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0623ef0c2aa1ed3f8054bd1dc60073d7c53a70b4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/TopicStorageOrders_example.cpp @@ -0,0 +1,18 @@ +Matrix Acolmajor; +Acolmajor << 8, 2, 2, 9, + 9, 1, 4, 4, + 3, 5, 4, 5; +cout << "The matrix A:" << endl; +cout << Acolmajor << endl << endl; + +cout << "In memory (column-major):" << endl; +for (int i = 0; i < Acolmajor.size(); i++) + cout << *(Acolmajor.data() + i) << " "; +cout << endl << endl; + +Matrix Arowmajor = Acolmajor; +cout << "In memory (row-major):" << endl; +for (int i = 0; i < Arowmajor.size(); i++) + cout << *(Arowmajor.data() + i) << " "; +cout << endl; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Triangular_solve.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Triangular_solve.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5484424673261816628d73454c225092074eed69 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Triangular_solve.cpp @@ -0,0 +1,11 @@ +Matrix3d m = Matrix3d::Zero(); +m.triangularView().setOnes(); +cout << "Here is the matrix m:\n" << m << endl; +Matrix3d n = Matrix3d::Ones(); +n.triangularView() *= 2; +cout << "Here is the matrix n:\n" << n << endl; +cout << "And now here is m.inverse()*n, taking advantage of the fact that" + " m is upper-triangular:\n" + << m.triangularView().solve(n) << endl; +cout << "And this is n*m.inverse():\n" + << m.triangularView().solve(n); diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a260124334c7d117e6ab152b192e825bee15dd60 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_Tridiagonalization_MatrixType.cpp @@ -0,0 +1,9 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl; +Tridiagonalization triOfA(A); +MatrixXd Q = triOfA.matrixQ(); +cout << "The orthogonal matrix Q is:" << endl << Q << endl; +MatrixXd T = triOfA.matrixT(); +cout << "The tridiagonal matrix T is:" << endl << T << endl << endl; +cout << "Q * T * Q^T = " << endl << Q * T * Q.transpose() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_compute.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_compute.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0062a99e8901248e4d37da97a48e3945124913ab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_compute.cpp @@ -0,0 +1,9 @@ +Tridiagonalization tri; +MatrixXf X = MatrixXf::Random(4,4); +MatrixXf A = X + X.transpose(); +tri.compute(A); +cout << "The matrix T in the tridiagonal decomposition of A is: " << endl; +cout << tri.matrixT() << endl; +tri.compute(2*A); // re-use tri to compute eigenvalues of 2A +cout << "The matrix T in the tridiagonal decomposition of 2A is: " << endl; +cout << tri.matrixT() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_decomposeInPlace.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_decomposeInPlace.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3cdce679b2e96b6507f597f5e5575a735bec9e19 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_decomposeInPlace.cpp @@ -0,0 +1,11 @@ +MatrixXd X = MatrixXd::Random(5,5); +MatrixXd A = X + X.transpose(); +cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl; + +VectorXd diag(5); +VectorXd subdiag(4); +VectorXd hcoeffs(4); // Scratch space for householder reflector. +internal::tridiagonalization_inplace(A, diag, subdiag, hcoeffs, true); +cout << "The orthogonal matrix Q is:" << endl << A << endl; +cout << "The diagonal of the tridiagonal matrix T is:" << endl << diag << endl; +cout << "The subdiagonal of the tridiagonal matrix T is:" << endl << subdiag << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_diagonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_diagonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6eec82169608db95b20b64152ffd37acbbfc44cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_diagonal.cpp @@ -0,0 +1,13 @@ +MatrixXcd X = MatrixXcd::Random(4,4); +MatrixXcd A = X + X.adjoint(); +cout << "Here is a random self-adjoint 4x4 matrix:" << endl << A << endl << endl; + +Tridiagonalization triOfA(A); +MatrixXd T = triOfA.matrixT(); +cout << "The tridiagonal matrix T is:" << endl << T << endl << endl; + +cout << "We can also extract the diagonals of T directly ..." << endl; +VectorXd diag = triOfA.diagonal(); +cout << "The diagonal is:" << endl << diag << endl; +VectorXd subdiag = triOfA.subDiagonal(); +cout << "The subdiagonal is:" << endl << subdiag << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_householderCoefficients.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_householderCoefficients.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e5d87288020662ca08bf69a7aaeee358b1748b0f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_householderCoefficients.cpp @@ -0,0 +1,6 @@ +Matrix4d X = Matrix4d::Random(4,4); +Matrix4d A = X + X.transpose(); +cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl; +Tridiagonalization triOfA(A); +Vector3d hc = triOfA.householderCoefficients(); +cout << "The vector of Householder coefficients is:" << endl << hc << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_packedMatrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_packedMatrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0f55d0c281aa25f9e10d0e2d28a66f106d94845e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tridiagonalization_packedMatrix.cpp @@ -0,0 +1,8 @@ +Matrix4d X = Matrix4d::Random(4,4); +Matrix4d A = X + X.transpose(); +cout << "Here is a random symmetric 4x4 matrix:" << endl << A << endl; +Tridiagonalization triOfA(A); +Matrix4d pm = triOfA.packedMatrix(); +cout << "The packed matrix M is:" << endl << pm << endl; +cout << "The diagonal and subdiagonal corresponds to the matrix T, which is:" + << endl << triOfA.matrixT() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp new file mode 100644 index 0000000000000000000000000000000000000000..96e40acfbc4423609f8ddb21fb0249d9fbd8a91d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Block.cpp @@ -0,0 +1,5 @@ +MatrixXf matA(2, 2); +matA << 1, 2, 3, 4; +MatrixXf matB(4, 4); +matB << matA, matA/10, matA/10, matA; +std::cout << matB << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp new file mode 100644 index 0000000000000000000000000000000000000000..50cff4cb6b69555b449e137cf10f4bf7d0b1166f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_CommaTemporary.cpp @@ -0,0 +1,4 @@ +MatrixXf mat = MatrixXf::Random(2, 3); +std::cout << mat << std::endl << std::endl; +mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat; +std::cout << mat << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp new file mode 100644 index 0000000000000000000000000000000000000000..55a21539d6781065c82bef26a0fbdb660e5c3e3c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Join.cpp @@ -0,0 +1,11 @@ +RowVectorXd vec1(3); +vec1 << 1, 2, 3; +std::cout << "vec1 = " << vec1 << std::endl; + +RowVectorXd vec2(4); +vec2 << 1, 4, 9, 16; +std::cout << "vec2 = " << vec2 << std::endl; + +RowVectorXd joined(7); +joined << vec1, vec2; +std::cout << "joined = " << joined << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c6a73ab8cb1048e9f8b702d90bb549de3b834461 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_LinSpaced.cpp @@ -0,0 +1,7 @@ +ArrayXXf table(10, 4); +table.col(0) = ArrayXf::LinSpaced(10, 0, 90); +table.col(1) = M_PI / 180 * table.col(0); +table.col(2) = table.col(1).sin(); +table.col(3) = table.col(1).cos(); +std::cout << " Degrees Radians Sine Cosine\n"; +std::cout << table << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb7457652d00976eeb6d12cdddde4207f16db03c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_ThreeWays.cpp @@ -0,0 +1,20 @@ +const int size = 6; +MatrixXd mat1(size, size); +mat1.topLeftCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2); +mat1.topRightCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2); +mat1.bottomLeftCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2); +mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2); +std::cout << mat1 << std::endl << std::endl; + +MatrixXd mat2(size, size); +mat2.topLeftCorner(size/2, size/2).setZero(); +mat2.topRightCorner(size/2, size/2).setIdentity(); +mat2.bottomLeftCorner(size/2, size/2).setIdentity(); +mat2.bottomRightCorner(size/2, size/2).setZero(); +std::cout << mat2 << std::endl << std::endl; + +MatrixXd mat3(size, size); +mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2), + MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2); +std::cout << mat3 << std::endl; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp new file mode 100644 index 0000000000000000000000000000000000000000..76a36a31917bb457e5383af9ecafa3843d09836d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_AdvancedInitialization_Zero.cpp @@ -0,0 +1,13 @@ +std::cout << "A fixed-size array:\n"; +Array33f a1 = Array33f::Zero(); +std::cout << a1 << "\n\n"; + + +std::cout << "A one-dimensional dynamic-size array:\n"; +ArrayXf a2 = ArrayXf::Zero(3); +std::cout << a2 << "\n\n"; + + +std::cout << "A two-dimensional dynamic-size array:\n"; +ArrayXXf a3 = ArrayXXf::Zero(3, 4); +std::cout << a3 << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_rowmajor.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_rowmajor.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fd45ace03ac86d2d4d7dec7b59dee9cf38095349 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_rowmajor.cpp @@ -0,0 +1,7 @@ +int array[8]; +for(int i = 0; i < 8; ++i) array[i] = i; +cout << "Column-major:\n" << Map >(array) << endl; +cout << "Row-major:\n" << Map >(array) << endl; +cout << "Row-major using stride:\n" << + Map, Unaligned, Stride<1,4> >(array) << endl; + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_using.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_using.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e5e499f1fc06ef89056b0d73704f1229be469f5f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_Map_using.cpp @@ -0,0 +1,21 @@ +typedef Matrix MatrixType; +typedef Map MapType; +typedef Map MapTypeConst; // a read-only map +const int n_dims = 5; + +MatrixType m1(n_dims), m2(n_dims); +m1.setRandom(); +m2.setRandom(); +float *p = &m2(0); // get the address storing the data for m2 +MapType m2map(p,m2.size()); // m2map shares data with m2 +MapTypeConst m2mapconst(p,m2.size()); // a read-only accessor for m2 + +cout << "m1: " << m1 << endl; +cout << "m2: " << m2 << endl; +cout << "Squared euclidean distance: " << (m1-m2).squaredNorm() << endl; +cout << "Squared euclidean distance, using map: " << + (m1-m2map).squaredNorm() << endl; +m2map(3) = 7; // this will change m2, since they share the same array +cout << "Updated m2: " << m2 << endl; +cout << "m2 coefficient 2, constant accessor: " << m2mapconst(2) << endl; +/* m2mapconst(2) = 5; */ // this yields a compile-time error diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Mat.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Mat.cpp new file mode 100644 index 0000000000000000000000000000000000000000..737afecb8078fc998c5b3a16146e5e49d927b23b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Mat.cpp @@ -0,0 +1,6 @@ +MatrixXf M1(2,6); // Column-major storage +M1 << 1, 2, 3, 4, 5, 6, + 7, 8, 9, 10, 11, 12; + +Map M2(M1.data(), 6,2); +cout << "M2:" << endl << M2 << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Vec.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Vec.cpp new file mode 100644 index 0000000000000000000000000000000000000000..32980a790a2eef57d1344f1fbfa13bc942f684db --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_ReshapeMat2Vec.cpp @@ -0,0 +1,11 @@ +MatrixXf M1(3,3); // Column-major storage +M1 << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; + +Map v1(M1.data(), M1.size()); +cout << "v1:" << endl << v1 << endl; + +Matrix M2(M1); +Map v2(M2.data(), M2.size()); +cout << "v2:" << endl << v2 << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingCol.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingCol.cpp new file mode 100644 index 0000000000000000000000000000000000000000..695d130140e14fe0e837e88903a5bf2bdd4b45dc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingCol.cpp @@ -0,0 +1,11 @@ +MatrixXf M1 = MatrixXf::Random(3,8); +cout << "Column major input:" << endl << M1 << "\n"; +Map > M2(M1.data(), M1.rows(), (M1.cols()+2)/3, OuterStride<>(M1.outerStride()*3)); +cout << "1 column over 3:" << endl << M2 << "\n"; + +typedef Matrix RowMajorMatrixXf; +RowMajorMatrixXf M3(M1); +cout << "Row major input:" << endl << M3 << "\n"; +Map > M4(M3.data(), M3.rows(), (M3.cols()+2)/3, + Stride(M3.outerStride(),3)); +cout << "1 column over 3:" << endl << M4 << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingVec.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingVec.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9b822464d6a5b0ea45b6f80798c6d09126f21f71 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_SlicingVec.cpp @@ -0,0 +1,4 @@ +RowVectorXf v = RowVectorXf::LinSpaced(20,0,19); +cout << "Input:" << endl << v << endl; +Map > v2(v.data(), v.size()/2); +cout << "Even:" << v2 << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01.cpp new file mode 100644 index 0000000000000000000000000000000000000000..47ba31dc9f364ba52256eda4817ac38f097f3316 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m << 1, 2, 3, + 4, 5, 6, + 7, 8, 9; +std::cout << m; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01b.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01b.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2adb2e213f25aa6fbd607d37b3379caa9dff062b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_01b.cpp @@ -0,0 +1,5 @@ +Matrix3f m; +m.row(0) << 1, 2, 3; +m.block(1,0,2,2) << 4, 5, 7, 8; +m.col(2).tail(2) << 6, 9; +std::cout << m; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_02.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_02.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c960d6ab5978a3fdd61a3d9b543daa8e71b4a733 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_commainit_02.cpp @@ -0,0 +1,7 @@ +int rows=5, cols=5; +MatrixXf m(rows,cols); +m << (Matrix3f() << 1, 2, 3, 4, 5, 6, 7, 8, 9).finished(), + MatrixXf::Zero(3,cols-3), + MatrixXf::Zero(rows-3,3), + MatrixXf::Identity(rows-3,cols-3); +cout << m; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e72e715d849fa16df6e83bc93aa68a8f712d6c63 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_1d_cxx11.cpp @@ -0,0 +1,4 @@ +VectorXi v = VectorXi::Random(4); +cout << "Here is the vector v:\n"; +for(auto x : v) cout << x << " "; +cout << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4a12d26c71f69721808f6a5a8e86ceaa4f971f80 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_range_for_loop_2d_cxx11.cpp @@ -0,0 +1,5 @@ +Matrix2i A = Matrix2i::Random(); +cout << "Here are the coeffs of the 2x2 matrix A:\n"; +for(auto x : A.reshaped()) + cout << x << " "; +cout << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e520e8e6b3871b3b6b900a6e772ea2e41a4d983f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_1.cpp @@ -0,0 +1,5 @@ +MatrixXi m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl; +m.resize(2,8); +cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..50dc454883041d61c9f660c4764fdd715f7386d4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_reshaped_vs_resize_2.cpp @@ -0,0 +1,6 @@ +Matrix m = Matrix4i::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl; +cout << "Here is m.reshaped(2, 8):" << endl << m.reshaped(2, 8) << endl; +m.resize(2,8); +cout << "Here is the matrix m after m.resize(2,8):" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_matrix_inverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_matrix_inverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fff324446a9e7c81ec2d41ce89b775e1d0ed7cf1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_matrix_inverse.cpp @@ -0,0 +1,6 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 4,5,6, 7,8,10; +b << 3, 3, 4; +Vector3f x = A.inverse() * b; +cout << "The solution is:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_multiple_rhs.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_multiple_rhs.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5411a44abe7e4759fea5d6626d073a2a7b2b7404 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_multiple_rhs.cpp @@ -0,0 +1,10 @@ +Matrix3f A(3,3); +A << 1,2,3, 4,5,6, 7,8,10; +Matrix B; +B << 3,1, 3,1, 4,1; +Matrix X; +X = A.fullPivLu().solve(B); +cout << "The solution with right-hand side (3,3,4) is:" << endl; +cout << X.col(0) << endl; +cout << "The solution with right-hand side (1,1,1) is:" << endl; +cout << X.col(1) << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_reuse_decomposition.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_reuse_decomposition.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3ca06453afd68d1b9fc1bb572e1a1253afbca9a7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_reuse_decomposition.cpp @@ -0,0 +1,13 @@ +Matrix3f A(3,3); +A << 1,2,3, 4,5,6, 7,8,10; +PartialPivLU luOfA(A); // compute LU decomposition of A +Vector3f b; +b << 3,3,4; +Vector3f x; +x = luOfA.solve(b); +cout << "The solution with right-hand side (3,3,4) is:" << endl; +cout << x << endl; +b << 1,1,1; +x = luOfA.solve(b); +cout << "The solution with right-hand side (1,1,1) is:" << endl; +cout << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_singular.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_singular.cpp new file mode 100644 index 0000000000000000000000000000000000000000..abff1ef73893c22fabc55a8a0ab3ad7020320ae3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_singular.cpp @@ -0,0 +1,9 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 4,5,6, 7,8,9; +b << 3, 3, 4; +cout << "Here is the matrix A:" << endl << A << endl; +cout << "Here is the vector b:" << endl << b << endl; +Vector3f x; +x = A.lu().solve(b); +cout << "The solution is:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9d13f22ec11b9be9447a3c913695d999552a09c1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular.cpp @@ -0,0 +1,8 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 0,5,6, 0,0,10; +b << 3, 3, 4; +cout << "Here is the matrix A:" << endl << A << endl; +cout << "Here is the vector b:" << endl << b << endl; +Vector3f x = A.triangularView().solve(b); +cout << "The solution is:" << endl << x << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular_inplace.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular_inplace.cpp new file mode 100644 index 0000000000000000000000000000000000000000..16ae633a30e340fe8163792b109bb1f855c115be --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_solve_triangular_inplace.cpp @@ -0,0 +1,6 @@ +Matrix3f A; +Vector3f b; +A << 1,2,3, 0,5,6, 0,0,10; +b << 3, 3, 4; +A.triangularView().solveInPlace(b); +cout << "The solution is:" << endl << b << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cde2a6f1b4c142dcf71cfe6840190329e27b428e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort.cpp @@ -0,0 +1,4 @@ +Array4i v = Array4i::Random().abs(); +cout << "Here is the initial vector v:\n" << v.transpose() << "\n"; +std::sort(v.begin(), v.end()); +cout << "Here is the sorted vector v:\n" << v.transpose() << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..03641603d86cbd95b4e1b6be0f6de4ba3d9ab842 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Tutorial_std_sort_rows_cxx11.cpp @@ -0,0 +1,5 @@ +ArrayXXi A = ArrayXXi::Random(4,4).abs(); +cout << "Here is the initial matrix A:\n" << A << "\n"; +for(auto row : A.rowwise()) + std::sort(row.begin(), row.end()); +cout << "Here is the sorted matrix A:\n" << A << "\n"; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/VectorwiseOp_homogeneous.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/VectorwiseOp_homogeneous.cpp new file mode 100644 index 0000000000000000000000000000000000000000..67cf5737d12de68b29baa3d196fd5c73e57934a5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/VectorwiseOp_homogeneous.cpp @@ -0,0 +1,6 @@ +Matrix3Xd M = Matrix3Xd::Random(3,5); +Projective3d P(Matrix4d::Random()); +cout << "The matrix M is:" << endl << M << endl << endl; +cout << "M.colwise().homogeneous():" << endl << M.colwise().homogeneous() << endl << endl; +cout << "P * M.colwise().homogeneous():" << endl << P * M.colwise().homogeneous() << endl << endl; +cout << "P * M.colwise().homogeneous().hnormalized(): " << endl << (P * M.colwise().homogeneous()).colwise().hnormalized() << endl << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Vectorwise_reverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Vectorwise_reverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2f6a3508017cdab28a50977840bae8b0d14a1521 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/Vectorwise_reverse.cpp @@ -0,0 +1,10 @@ +MatrixXi m = MatrixXi::Random(3,4); +cout << "Here is the matrix m:" << endl << m << endl; +cout << "Here is the rowwise reverse of m:" << endl << m.rowwise().reverse() << endl; +cout << "Here is the colwise reverse of m:" << endl << m.colwise().reverse() << endl; + +cout << "Here is the coefficient (1,0) in the rowise reverse of m:" << endl +<< m.rowwise().reverse()(1,0) << endl; +cout << "Let us overwrite this coefficient with the value 4." << endl; +//m.colwise().reverse()(1,0) = 4; +cout << "Now the matrix m is:" << endl << m << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/class_FullPivLU.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/class_FullPivLU.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fce7fac0969e06855acd8a12c6cb45b281755e48 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/class_FullPivLU.cpp @@ -0,0 +1,16 @@ +typedef Matrix Matrix5x3; +typedef Matrix Matrix5x5; +Matrix5x3 m = Matrix5x3::Random(); +cout << "Here is the matrix m:" << endl << m << endl; +Eigen::FullPivLU lu(m); +cout << "Here is, up to permutations, its LU decomposition matrix:" + << endl << lu.matrixLU() << endl; +cout << "Here is the L part:" << endl; +Matrix5x5 l = Matrix5x5::Identity(); +l.block<5,3>(0,0).triangularView() = lu.matrixLU(); +cout << l << endl; +cout << "Here is the U part:" << endl; +Matrix5x3 u = lu.matrixLU().triangularView(); +cout << u << endl; +cout << "Let us now reconstruct the original matrix m:" << endl; +cout << lu.permutationP().inverse() * l * u * lu.permutationQ().inverse() << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/compile_snippet.cpp.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/compile_snippet.cpp.in new file mode 100644 index 0000000000000000000000000000000000000000..c11457a3f576df2555fa5d45fbae5a08c29962a5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/compile_snippet.cpp.in @@ -0,0 +1,23 @@ +static bool eigen_did_assert = false; +#define eigen_assert(X) if(!eigen_did_assert && !(X)){ std::cout << "### Assertion raised in " << __FILE__ << ":" << __LINE__ << ":\n" #X << "\n### The following would happen without assertions:\n"; eigen_did_assert = true;} + +#include +#include + +#ifndef M_PI +#define M_PI 3.1415926535897932384626433832795 +#endif + + +using namespace Eigen; +using namespace std; + +int main(int, char**) +{ + cout.precision(3); +// intentionally remove indentation of snippet +{ +${snippet_source_code} +} + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_redux_minmax.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_redux_minmax.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f4ae7f406c8c1753230f20fcdb579a355b1d6d52 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_redux_minmax.cpp @@ -0,0 +1,12 @@ + Matrix3f m = Matrix3f::Random(); + std::ptrdiff_t i, j; + float minOfM = m.minCoeff(&i,&j); + cout << "Here is the matrix m:\n" << m << endl; + cout << "Its minimum coefficient (" << minOfM + << ") is at position (" << i << "," << j << ")\n\n"; + + RowVector4i v = RowVector4i::Random(); + int maxOfV = v.maxCoeff(&i); + cout << "Here is the vector v: " << v << endl; + cout << "Its maximum coefficient (" << maxOfV + << ") is at position " << i << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_aliasing.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_aliasing.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f82e6f2ac98170299112c7185282df2937991c78 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_aliasing.cpp @@ -0,0 +1,5 @@ +Matrix2i a; a << 1, 2, 3, 4; +cout << "Here is the matrix a:\n" << a << endl; + +a = a.transpose(); // !!! do NOT do this !!! +cout << "and the result of the aliasing effect:\n" << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_conjugate.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_conjugate.cpp new file mode 100644 index 0000000000000000000000000000000000000000..88496b22d92d2cfee65114e5ca5e01cc9fe05837 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_conjugate.cpp @@ -0,0 +1,12 @@ +MatrixXcf a = MatrixXcf::Random(2,2); +cout << "Here is the matrix a\n" << a << endl; + +cout << "Here is the matrix a^T\n" << a.transpose() << endl; + + +cout << "Here is the conjugate of a\n" << a.conjugate() << endl; + + +cout << "Here is the matrix a^*\n" << a.adjoint() << endl; + + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_inplace.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_inplace.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5c81c9e02df83f78784c96cec5bb0fb436db99be --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_arithmetic_transpose_inplace.cpp @@ -0,0 +1,6 @@ +MatrixXf a(2,3); a << 1, 2, 3, 4, 5, 6; +cout << "Here is the initial matrix a:\n" << a << endl; + + +a.transposeInPlace(); +cout << "and after being transposed:\n" << a << endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_matrix_assignment_resizing.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_matrix_assignment_resizing.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cf189983fb5fcb30bed3e1285377e35c9689ae69 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/snippets/tut_matrix_assignment_resizing.cpp @@ -0,0 +1,5 @@ +MatrixXf a(2,2); +std::cout << "a is of size " << a.rows() << "x" << a.cols() << std::endl; +MatrixXf b(3,3); +a = b; +std::cout << "a is now of size " << a.rows() << "x" << a.cols() << std::endl; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..e6407aaea60e38384cb65810578f201231171ac0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/CMakeLists.txt @@ -0,0 +1,31 @@ +if(NOT EIGEN_TEST_NOQT) + find_package(Qt4) + if(QT4_FOUND) + include(${QT_USE_FILE}) + endif() +endif() + +if(QT4_FOUND) + add_executable(Tutorial_sparse_example Tutorial_sparse_example.cpp Tutorial_sparse_example_details.cpp) + target_link_libraries(Tutorial_sparse_example ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${QT_QTCORE_LIBRARY} ${QT_QTGUI_LIBRARY}) + + add_custom_command( + TARGET Tutorial_sparse_example + POST_BUILD + COMMAND ${CMAKE_COMMAND} -E make_directory ${CMAKE_CURRENT_BINARY_DIR}/../html/ + COMMAND Tutorial_sparse_example ARGS ${CMAKE_CURRENT_BINARY_DIR}/../html/Tutorial_sparse_example.jpeg + ) + + add_dependencies(all_examples Tutorial_sparse_example) +endif() + +add_executable(random_cpp11 random_cpp11.cpp) +target_link_libraries(random_cpp11 ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) +add_dependencies(all_examples random_cpp11) + +add_custom_command( + TARGET random_cpp11 + POST_BUILD + COMMAND random_cpp11 + ARGS >${CMAKE_CURRENT_BINARY_DIR}/random_cpp11.out +) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8850db052f63d564c80e424334e6017e1f5e9fd9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example.cpp @@ -0,0 +1,38 @@ +#include +#include +#include + +typedef Eigen::SparseMatrix SpMat; // declares a column-major sparse matrix type of double +typedef Eigen::Triplet T; + +void buildProblem(std::vector& coefficients, Eigen::VectorXd& b, int n); +void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename); + +int main(int argc, char** argv) +{ + if(argc!=2) { + std::cerr << "Error: expected one and only one argument.\n"; + return -1; + } + + int n = 300; // size of the image + int m = n*n; // number of unknowns (=number of pixels) + + // Assembly: + std::vector coefficients; // list of non-zeros coefficients + Eigen::VectorXd b(m); // the right hand side-vector resulting from the constraints + buildProblem(coefficients, b, n); + + SpMat A(m,m); + A.setFromTriplets(coefficients.begin(), coefficients.end()); + + // Solving: + Eigen::SimplicialCholesky chol(A); // performs a Cholesky factorization of A + Eigen::VectorXd x = chol.solve(b); // use the factorization to solve for the given right hand side + + // Export the result to a file: + saveAsBitmap(x, n, argv[1]); + + return 0; +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example_details.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example_details.cpp new file mode 100644 index 0000000000000000000000000000000000000000..bc18b0188478002707a8237f74e1e91b39740679 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/Tutorial_sparse_example_details.cpp @@ -0,0 +1,44 @@ +#include +#include +#include + +typedef Eigen::SparseMatrix SpMat; // declares a column-major sparse matrix type of double +typedef Eigen::Triplet T; + +void insertCoefficient(int id, int i, int j, double w, std::vector& coeffs, + Eigen::VectorXd& b, const Eigen::VectorXd& boundary) +{ + int n = int(boundary.size()); + int id1 = i+j*n; + + if(i==-1 || i==n) b(id) -= w * boundary(j); // constrained coefficient + else if(j==-1 || j==n) b(id) -= w * boundary(i); // constrained coefficient + else coeffs.push_back(T(id,id1,w)); // unknown coefficient +} + +void buildProblem(std::vector& coefficients, Eigen::VectorXd& b, int n) +{ + b.setZero(); + Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0,M_PI).sin().pow(2); + for(int j=0; j bits = (x*255).cast(); + QImage img(bits.data(), n,n,QImage::Format_Indexed8); + img.setColorCount(256); + for(int i=0;i<256;i++) img.setColor(i,qRgb(i,i,i)); + img.save(filename); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/random_cpp11.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/random_cpp11.cpp new file mode 100644 index 0000000000000000000000000000000000000000..33744c051662f76299e223305b1aa912d45d4fa2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/special_examples/random_cpp11.cpp @@ -0,0 +1,14 @@ +#include +#include +#include + +using namespace Eigen; + +int main() { + std::default_random_engine generator; + std::poisson_distribution distribution(4.1); + auto poisson = [&] () {return distribution(generator);}; + + RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson ); + std::cout << v << "\n"; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/tutorial.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/tutorial.cpp new file mode 100644 index 0000000000000000000000000000000000000000..62be7c2707b746c71c4df7cdaf419cfcfe1d35fe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/doc/tutorial.cpp @@ -0,0 +1,62 @@ +#include + +int main(int argc, char *argv[]) +{ + std::cout.precision(2); + + // demo static functions + Eigen::Matrix3f m3 = Eigen::Matrix3f::Random(); + Eigen::Matrix4f m4 = Eigen::Matrix4f::Identity(); + + std::cout << "*** Step 1 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl; + + // demo non-static set... functions + m4.setZero(); + m3.diagonal().setOnes(); + + std::cout << "*** Step 2 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl; + + // demo fixed-size block() expression as lvalue and as rvalue + m4.block<3,3>(0,1) = m3; + m3.row(2) = m4.block<1,3>(2,0); + + std::cout << "*** Step 3 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl; + + // demo dynamic-size block() + { + int rows = 3, cols = 3; + m4.block(0,1,3,3).setIdentity(); + std::cout << "*** Step 4 ***\nm4:\n" << m4 << std::endl; + } + + // demo vector blocks + m4.diagonal().block(1,2).setOnes(); + std::cout << "*** Step 5 ***\nm4.diagonal():\n" << m4.diagonal() << std::endl; + std::cout << "m4.diagonal().start(3)\n" << m4.diagonal().start(3) << std::endl; + + // demo coeff-wise operations + m4 = m4.cwise()*m4; + m3 = m3.cwise().cos(); + std::cout << "*** Step 6 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl; + + // sums of coefficients + std::cout << "*** Step 7 ***\n m4.sum(): " << m4.sum() << std::endl; + std::cout << "m4.col(2).sum(): " << m4.col(2).sum() << std::endl; + std::cout << "m4.colwise().sum():\n" << m4.colwise().sum() << std::endl; + std::cout << "m4.rowwise().sum():\n" << m4.rowwise().sum() << std::endl; + + // demo intelligent auto-evaluation + m4 = m4 * m4; // auto-evaluates so no aliasing problem (performance penalty is low) + Eigen::Matrix4f other = (m4 * m4).lazy(); // forces lazy evaluation + m4 = m4 + m4; // here Eigen goes for lazy evaluation, as with most expressions + m4 = -m4 + m4 + 5 * m4; // same here, Eigen chooses lazy evaluation for all that. + m4 = m4 * (m4 + m4); // here Eigen chooses to first evaluate m4 + m4 into a temporary. + // indeed, here it is an optimization to cache this intermediate result. + m3 = m3 * m4.block<3,3>(1,1); // here Eigen chooses NOT to evaluate block() into a temporary + // because accessing coefficients of that block expression is not more costly than accessing + // coefficients of a plain matrix. + m4 = m4 * m4.transpose(); // same here, lazy evaluation of the transpose. + m4 = m4 * m4.transpose().eval(); // forces immediate evaluation of the transpose + + std::cout << "*** Step 8 ***\nm3:\n" << m3 << "\nm4:\n" << m4 << std::endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/eigen3.pc.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/eigen3.pc.in new file mode 100644 index 0000000000000000000000000000000000000000..3368a3aa1d4f6cf647632101d949d88427386a1d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/eigen3.pc.in @@ -0,0 +1,9 @@ +prefix=@CMAKE_INSTALL_PREFIX@ +exec_prefix=${prefix} + +Name: Eigen3 +Description: A C++ template library for linear algebra: vectors, matrices, and related algorithms +Requires: +Version: @EIGEN_VERSION_NUMBER@ +Libs: +Cflags: -I${prefix}/@INCLUDE_INSTALL_DIR@ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..2c5fc33517c474ab8adb5901e0ac0cb21505d076 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/CMakeLists.txt @@ -0,0 +1,66 @@ + +ei_add_failtest("failtest_sanity_check") + +ei_add_failtest("block_nonconst_ctor_on_const_xpr_0") +ei_add_failtest("block_nonconst_ctor_on_const_xpr_1") +ei_add_failtest("block_nonconst_ctor_on_const_xpr_2") +ei_add_failtest("transpose_nonconst_ctor_on_const_xpr") +ei_add_failtest("diagonal_nonconst_ctor_on_const_xpr") +ei_add_failtest("cwiseunaryview_nonconst_ctor_on_const_xpr") +ei_add_failtest("triangularview_nonconst_ctor_on_const_xpr") +ei_add_failtest("selfadjointview_nonconst_ctor_on_const_xpr") + +ei_add_failtest("const_qualified_block_method_retval_0") +ei_add_failtest("const_qualified_block_method_retval_1") +ei_add_failtest("const_qualified_transpose_method_retval") +ei_add_failtest("const_qualified_diagonal_method_retval") + +ei_add_failtest("map_nonconst_ctor_on_const_ptr_0") +ei_add_failtest("map_nonconst_ctor_on_const_ptr_1") +ei_add_failtest("map_nonconst_ctor_on_const_ptr_2") +ei_add_failtest("map_nonconst_ctor_on_const_ptr_3") +ei_add_failtest("map_nonconst_ctor_on_const_ptr_4") + +ei_add_failtest("map_on_const_type_actually_const_0") +ei_add_failtest("map_on_const_type_actually_const_1") +ei_add_failtest("block_on_const_type_actually_const_0") +ei_add_failtest("block_on_const_type_actually_const_1") +ei_add_failtest("transpose_on_const_type_actually_const") +ei_add_failtest("diagonal_on_const_type_actually_const") +ei_add_failtest("cwiseunaryview_on_const_type_actually_const") +ei_add_failtest("triangularview_on_const_type_actually_const") +ei_add_failtest("selfadjointview_on_const_type_actually_const") + +ei_add_failtest("ref_1") +ei_add_failtest("ref_2") +ei_add_failtest("ref_3") +ei_add_failtest("ref_4") +ei_add_failtest("ref_5") + +ei_add_failtest("swap_1") +ei_add_failtest("swap_2") + +ei_add_failtest("ternary_1") +ei_add_failtest("ternary_2") + +ei_add_failtest("sparse_ref_1") +ei_add_failtest("sparse_ref_2") +ei_add_failtest("sparse_ref_3") +ei_add_failtest("sparse_ref_4") +ei_add_failtest("sparse_ref_5") + +ei_add_failtest("sparse_storage_mismatch") + +ei_add_failtest("partialpivlu_int") +ei_add_failtest("fullpivlu_int") +ei_add_failtest("llt_int") +ei_add_failtest("ldlt_int") +ei_add_failtest("qr_int") +ei_add_failtest("colpivqr_int") +ei_add_failtest("fullpivqr_int") +ei_add_failtest("jacobisvd_int") +ei_add_failtest("bdcsvd_int") +ei_add_failtest("eigensolver_int") +ei_add_failtest("eigensolver_cplx") +ei_add_failtest("initializer_list_1") +ei_add_failtest("initializer_list_2") diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/bdcsvd_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/bdcsvd_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..670752cf5928b18ba8a9bf4791d681015ff0d2e5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/bdcsvd_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/SVD" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + BDCSVD > qr(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_0.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_0.cpp new file mode 100644 index 0000000000000000000000000000000000000000..40b82014f9eda66b1da961dd8745196c80a697ec --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_0.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Block b(m,0,0); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ef6d53702aba7810908c858a8ad437887f4e599b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_1.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Block b(m,0,0,3,3); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..43f18aecf0651861ef268382b12b20f62ff9adba --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_nonconst_ctor_on_const_xpr_2.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + // row/column constructor + Block b(m,0); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_0.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_0.cpp new file mode 100644 index 0000000000000000000000000000000000000000..009bebece08e09f94459d1628856ecc42cf4386c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_0.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + Matrix3f m; + Block(m, 0, 0, 3, 3).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4c3e93ffe0134939035a6d87ed5ac403c182d8ee --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/block_on_const_type_actually_const_1.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + Block(m, 0, 0).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/colpivqr_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/colpivqr_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..db11910d42a58066af6bec7ddd1aa26fdb470327 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/colpivqr_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/QR" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + ColPivHouseholderQR > qr(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_0.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_0.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a6bd5fee20ec3bc1c002c881c109dc487b8d64fe --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_0.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Block b(m.block<3,3>(0,0)); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ef40c247cef71113eca1c2f73d8e589fa9eff4f4 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_block_method_retval_1.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Block b(m.block(0,0,3,3)); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_diagonal_method_retval.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_diagonal_method_retval.cpp new file mode 100644 index 0000000000000000000000000000000000000000..809594aabc315f95d0e1117ca0038fd8f916d7ca --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_diagonal_method_retval.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Diagonal b(m.diagonal()); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_transpose_method_retval.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_transpose_method_retval.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2d7f19cabc31b5db4d6503dea2d9e4efb200d65f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/const_qualified_transpose_method_retval.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Transpose b(m.transpose()); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e23cf8fd8d07ab5d3c587a709d5bbd16c3ec2ab9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_nonconst_ctor_on_const_xpr.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + CwiseUnaryView,Matrix3d> t(m); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_on_const_type_actually_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_on_const_type_actually_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fcd41dfdb882fd869ff19fcbb7987114786ca3fa --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/cwiseunaryview_on_const_type_actually_const.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + CwiseUnaryView,CV_QUALIFIER MatrixXf>(m).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..76398a2c26e147c5f11ed534b27418b503c54f4c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_nonconst_ctor_on_const_xpr.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Diagonal d(m); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_on_const_type_actually_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_on_const_type_actually_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d4b2fd9b82f708e8919984d04538f2341e3252ff --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/diagonal_on_const_type_actually_const.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + Diagonal(m).coeffRef(0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_cplx.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_cplx.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c2e21e189bdd261a7d679f000ba3b208ff5da028 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_cplx.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Eigenvalues" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR std::complex +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + EigenSolver > eig(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..eda8dc20b237ae5016f0539167ed7f516d9502c3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/eigensolver_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Eigenvalues" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + EigenSolver > eig(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/failtest_sanity_check.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/failtest_sanity_check.cpp new file mode 100644 index 0000000000000000000000000000000000000000..769fa942d5dc1477070398b8788e1617c7512726 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/failtest_sanity_check.cpp @@ -0,0 +1,5 @@ +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +This is just some text that won't compile as a C++ file, as a basic sanity check for failtest. +#else +int main() {} +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivlu_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivlu_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e9d2c6eb32290507381f8cfc9e339c17f58123b7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivlu_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/LU" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + FullPivLU > lu(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivqr_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivqr_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d182a7b6b327d45ec0ec160928b3a7b5dafdfa0b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/fullpivqr_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/QR" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + FullPivHouseholderQR > qr(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..92dfd1f658aed123c3a6a1125d4f444bc8e270cf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_1.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define ROWS Dynamic +#else +#define ROWS 3 +#endif + +using namespace Eigen; + +int main() +{ + Matrix {1, 2, 3}; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1996050a781b53bfce99685da2ccbc5481766ad3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/initializer_list_2.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define ROWS Dynamic +#define COLS Dynamic +#else +#define ROWS 3 +#define COLS 1 +#endif + +using namespace Eigen; + +int main() +{ + Matrix {1, 2, 3}; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/jacobisvd_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/jacobisvd_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..12790aef1e90ebc1474a31fe078cdf36861b1a6d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/jacobisvd_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/SVD" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + JacobiSVD > qr(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ldlt_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ldlt_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..243e457468cf6e2b50c849a32853b7c6f46b4e72 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ldlt_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Cholesky" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + LDLT > ldlt(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/llt_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/llt_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb020650d4c9900be15a4109230178d13086a0fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/llt_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Cholesky" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + LLT > llt(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_0.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_0.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d75686f5809cd821cecab9d8e0bad9070f7427dd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_0.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER float *ptr){ + Map m(ptr); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..eda134dc8878bf624be1be6200de58b023cad778 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_1.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER float *ptr, DenseIndex size){ + Map m(ptr, size); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..06b4b6275d04e20a49790a4d3f3717b828e3d76f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_2.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){ + Map m(ptr, rows, cols); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_3.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_3.cpp new file mode 100644 index 0000000000000000000000000000000000000000..830f6f0c9453aad0eacb9e62dea8403de1f0ce7f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_3.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER float *ptr, DenseIndex rows, DenseIndex cols){ + Map > m(ptr, rows, cols, InnerStride<2>()); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_4.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_4.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c3e8c952cf11e61af0060c3111354b492ad99550 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_nonconst_ctor_on_const_ptr_4.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER +#else +#define CV_QUALIFIER const +#endif + +using namespace Eigen; + +void foo(const float *ptr, DenseIndex rows, DenseIndex cols){ + Map > m(ptr, rows, cols, OuterStride<>(2)); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_0.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_0.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8cb6aa0cda9d266cf87bac450c7f29764856d23d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_0.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(float *ptr){ + Map(ptr, 1, 1).coeffRef(0,0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..04e067c34085a3b52245a78453082c1e2abc8342 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/map_on_const_type_actually_const_1.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(float *ptr){ + Map(ptr).coeffRef(0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/partialpivlu_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/partialpivlu_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..98ef282eadd45fa17c87f84c9a69c0f7d67eaa18 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/partialpivlu_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/LU" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + PartialPivLU > lu(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/qr_int.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/qr_int.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ce200e818afbaa27dedb838d54e9201ad4d58027 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/qr_int.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/QR" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define SCALAR int +#else +#define SCALAR float +#endif + +using namespace Eigen; + +int main() +{ + HouseholderQR > qr(Matrix::Random(10,10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..8b798d53d41e3205badb7a9746438426dfbaa3eb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_1.cpp @@ -0,0 +1,18 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void call_ref(Ref a) { } + +int main() +{ + VectorXf a(10); + CV_QUALIFIER VectorXf& ac(a); + call_ref(ac); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0b779ccf54c011be49c256a058b331b9ef112efb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_2.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +void call_ref(Ref a) { } + +int main() +{ + MatrixXf A(10,10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(A.row(3)); +#else + call_ref(A.col(3)); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_3.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_3.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f46027d48e073eeafc0a7a1aadf62357becb6264 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_3.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +void call_ref(Ref a) { } +#else +void call_ref(const Ref &a) { } +#endif + +int main() +{ + VectorXf a(10); + call_ref(a+a); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_4.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_4.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6c11fa4cbce41af6021e846d0d743da0c4c7fdb7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_4.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +void call_ref(Ref > a) {} + +int main() +{ + MatrixXf A(10,10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(A.transpose()); +#else + call_ref(A); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_5.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_5.cpp new file mode 100644 index 0000000000000000000000000000000000000000..846d52795721f9739ac1c0a333a727758edb937d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ref_5.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +void call_ref(Ref a) { } + +int main() +{ + VectorXf a(10); + DenseBase &ac(a); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(ac); +#else + call_ref(ac.derived()); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a240f818480d12ed8eeeb1777d6031ad1b503199 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_nonconst_ctor_on_const_xpr.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + SelfAdjointView t(m); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_on_const_type_actually_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_on_const_type_actually_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..19aaad6d098dad7ca691b53edd6a596fefd4f1c7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/selfadjointview_on_const_type_actually_const.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + SelfAdjointView(m).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d78d1f9b1158a759beaa71ee7d7691a379527856 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_1.cpp @@ -0,0 +1,18 @@ +#include "../Eigen/Sparse" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void call_ref(Ref > a) { } + +int main() +{ + SparseMatrix a(10,10); + CV_QUALIFIER SparseMatrix& ac(a); + call_ref(ac); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46c9440c2fa2e42dd953ebebbea06d5a82c3345d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_2.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Sparse" + +using namespace Eigen; + +void call_ref(Ref > a) { } + +int main() +{ + SparseMatrix A(10,10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(A.row(3)); +#else + call_ref(A.col(3)); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_3.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_3.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a9949b552cd2e2d5fe74d93933141032a0aa836b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_3.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Sparse" + +using namespace Eigen; + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +void call_ref(Ref > a) { } +#else +void call_ref(const Ref > &a) { } +#endif + +int main() +{ + SparseMatrix a(10,10); + call_ref(a+a); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_4.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_4.cpp new file mode 100644 index 0000000000000000000000000000000000000000..57bb6a1fcd019128c000d45cac20ce95b053056d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_4.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Sparse" + +using namespace Eigen; + +void call_ref(Ref > a) {} + +int main() +{ + SparseMatrix A(10,10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(A.transpose()); +#else + call_ref(A); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_5.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_5.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4478f6f2f1eca88a4ed3b992e0f681ecb944f30d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_ref_5.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Sparse" + +using namespace Eigen; + +void call_ref(Ref > a) { } + +int main() +{ + SparseMatrix a(10,10); + SparseMatrixBase > &ac(a); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + call_ref(ac); +#else + call_ref(ac.derived()); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_storage_mismatch.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_storage_mismatch.cpp new file mode 100644 index 0000000000000000000000000000000000000000..51840d416a91e2011b67a7ef6a9a92c80b823d14 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/sparse_storage_mismatch.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Sparse" +using namespace Eigen; + +typedef SparseMatrix Mat1; +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +typedef SparseMatrix Mat2; +#else +typedef SparseMatrix Mat2; +#endif + +int main() +{ + Mat1 a(10,10); + Mat2 b(10,10); + a += b; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..106379720a444b81e7c98ea2eb6bfdadccc365bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_1.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +int main() +{ + VectorXf a(10), b(10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + const DenseBase &ac(a); +#else + DenseBase &ac(a); +#endif + b.swap(ac); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b386cf419ff5762479f2a7a9a34d116952d654fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/swap_2.cpp @@ -0,0 +1,14 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +int main() +{ + VectorXf a(10), b(10); + VectorXf const &ac(a); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + b.swap(ac); +#else + b.swap(ac.const_cast_derived()); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_1.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b40bcb0cc2310243d690a32c6e7449d6b7e9d5c8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_1.cpp @@ -0,0 +1,13 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +int main(int argc,char **) +{ + VectorXf a(10), b(10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + b = argc>1 ? 2*a : -a; +#else + b = argc>1 ? 2*a : VectorXf(-a); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_2.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a46b12b2b95506d42fd9873c75b937d8f1f615d8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/ternary_2.cpp @@ -0,0 +1,13 @@ +#include "../Eigen/Core" + +using namespace Eigen; + +int main(int argc,char **) +{ + VectorXf a(10), b(10); +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD + b = argc>1 ? 2*a : a+a; +#else + b = argc>1 ? VectorXf(2*a) : VectorXf(a+a); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_nonconst_ctor_on_const_xpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_nonconst_ctor_on_const_xpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4223e7fd7cb82b2cc058ecfc16db6c1a5a1e3e04 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_nonconst_ctor_on_const_xpr.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + Transpose t(m); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_on_const_type_actually_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_on_const_type_actually_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d0b7d0df67f8dcfff72134c95c2d1bc80b93c55d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/transpose_on_const_type_actually_const.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + Transpose(m).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp new file mode 100644 index 0000000000000000000000000000000000000000..807447e4bf81ca1aefb45ef72afcd7994292967b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_nonconst_ctor_on_const_xpr.cpp @@ -0,0 +1,15 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(CV_QUALIFIER Matrix3d &m){ + TriangularView t(m); +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_on_const_type_actually_const.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_on_const_type_actually_const.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0a381a6126953a17a859c5d0d1c532606373da97 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/failtest/triangularview_on_const_type_actually_const.cpp @@ -0,0 +1,16 @@ +#include "../Eigen/Core" + +#ifdef EIGEN_SHOULD_FAIL_TO_BUILD +#define CV_QUALIFIER const +#else +#define CV_QUALIFIER +#endif + +using namespace Eigen; + +void foo(){ + MatrixXf m; + TriangularView(m).coeffRef(0, 0) = 1.0f; +} + +int main() {} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..c8ca640019e4afa691c1de532042556b5088f899 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/CMakeLists.txt @@ -0,0 +1,459 @@ +project(EigenLapack CXX) + +include(CheckLanguage) +check_language(Fortran) +if(CMAKE_Fortran_COMPILER) + enable_language(Fortran) + if("${CMAKE_Fortran_COMPILER_ID}" STREQUAL "GNU") + if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER_EQUAL 10.0) + # We use an old version of LAPACK with argument type mismatches. + # Allow them to compile anyway with newer GNU versions. + set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} -fallow-argument-mismatch") + endif() + endif() + set(EIGEN_Fortran_COMPILER_WORKS ON) +else() + set(EIGEN_Fortran_COMPILER_WORKS OFF) +endif() + +add_custom_target(lapack) +include_directories(../blas) + +set(EigenLapack_SRCS +single.cpp double.cpp complex_single.cpp complex_double.cpp ../blas/xerbla.cpp +) + +if(EIGEN_Fortran_COMPILER_WORKS) + +set(EigenLapack_SRCS ${EigenLapack_SRCS} + slarft.f dlarft.f clarft.f zlarft.f + slarfb.f dlarfb.f clarfb.f zlarfb.f + slarfg.f dlarfg.f clarfg.f zlarfg.f + slarf.f dlarf.f clarf.f zlarf.f + sladiv.f dladiv.f cladiv.f zladiv.f + ilaslr.f iladlr.f ilaclr.f ilazlr.f + ilaslc.f iladlc.f ilaclc.f ilazlc.f + dlapy2.f dlapy3.f slapy2.f slapy3.f + clacgv.f zlacgv.f + slamch.f dlamch.f + second_NONE.f dsecnd_NONE.f +) + +option(EIGEN_ENABLE_LAPACK_TESTS OFF "Enable the Lapack unit tests") + +if(EIGEN_ENABLE_LAPACK_TESTS) + + get_filename_component(eigen_full_path_to_reference_lapack "./reference/" ABSOLUTE) + if(NOT EXISTS ${eigen_full_path_to_reference_lapack}) + # Download lapack and install sources and testing at the right place + message(STATUS "Download lapack_addons_3.4.1.tgz...") + + file(DOWNLOAD "http://downloads.tuxfamily.org/eigen/lapack_addons_3.4.1.tgz" + "${CMAKE_CURRENT_SOURCE_DIR}/lapack_addons_3.4.1.tgz" + INACTIVITY_TIMEOUT 15 + TIMEOUT 240 + STATUS download_status + EXPECTED_MD5 ab5742640617e3221a873aba44bbdc93 + SHOW_PROGRESS) + + message(STATUS ${download_status}) + list(GET download_status 0 download_status_num) + set(download_status_num 0) + if(download_status_num EQUAL 0) + message(STATUS "Setup lapack reference and lapack unit tests") + execute_process(COMMAND tar xzf "lapack_addons_3.4.1.tgz" WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}) + else() + message(STATUS "Download of lapack_addons_3.4.1.tgz failed, LAPACK unit tests won't be enabled") + set(EIGEN_ENABLE_LAPACK_TESTS false) + endif() + + endif() + + get_filename_component(eigen_full_path_to_reference_lapack "./reference/" ABSOLUTE) + if(EXISTS ${eigen_full_path_to_reference_lapack}) + set(EigenLapack_funcfilenames + ssyev.f dsyev.f csyev.f zsyev.f + spotrf.f dpotrf.f cpotrf.f zpotrf.f + spotrs.f dpotrs.f cpotrs.f zpotrs.f + sgetrf.f dgetrf.f cgetrf.f zgetrf.f + sgetrs.f dgetrs.f cgetrs.f zgetrs.f) + + file(GLOB ReferenceLapack_SRCS0 RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} "reference/*.f") + foreach(filename1 IN LISTS ReferenceLapack_SRCS0) + string(REPLACE "reference/" "" filename ${filename1}) + list(FIND EigenLapack_SRCS ${filename} id1) + list(FIND EigenLapack_funcfilenames ${filename} id2) + if((id1 EQUAL -1) AND (id2 EQUAL -1)) + set(ReferenceLapack_SRCS ${ReferenceLapack_SRCS} reference/${filename}) + endif() + endforeach() + endif() + + +endif() + +endif() + +set(EIGEN_LAPACK_TARGETS "") + +add_library(eigen_lapack_static ${EigenLapack_SRCS} ${ReferenceLapack_SRCS}) +list(APPEND EIGEN_LAPACK_TARGETS eigen_lapack_static) + +if (EIGEN_BUILD_SHARED_LIBS) + add_library(eigen_lapack SHARED ${EigenLapack_SRCS}) + list(APPEND EIGEN_LAPACK_TARGETS eigen_lapack) + target_link_libraries(eigen_lapack eigen_blas) +endif() + +foreach(target IN LISTS EIGEN_LAPACK_TARGETS) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) + target_link_libraries(${target} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) + endif() + add_dependencies(lapack ${target}) + install(TARGETS ${target} + RUNTIME DESTINATION bin + LIBRARY DESTINATION lib + ARCHIVE DESTINATION lib) +endforeach() + + +get_filename_component(eigen_full_path_to_testing_lapack "./testing/" ABSOLUTE) +if(EXISTS ${eigen_full_path_to_testing_lapack}) + + # The following comes from lapack/TESTING/CMakeLists.txt + # Get Python + find_package(PythonInterp) + message(STATUS "Looking for Python found - ${PYTHONINTERP_FOUND}") + if (PYTHONINTERP_FOUND) + message(STATUS "Using Python version ${PYTHON_VERSION_STRING}") + endif() + + set(LAPACK_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR}) + set(LAPACK_BINARY_DIR ${CMAKE_CURRENT_BINARY_DIR}) + set(BUILD_SINGLE true) + set(BUILD_DOUBLE true) + set(BUILD_COMPLEX true) + set(BUILD_COMPLEX16E true) + + if(MSVC_VERSION) +# string(REPLACE "/STACK:10000000" "/STACK:900000000000000000" +# CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS}") + string(REGEX REPLACE "(.*)/STACK:(.*) (.*)" "\\1/STACK:900000000000000000 \\3" + CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS}") + endif() + file(MAKE_DIRECTORY "${LAPACK_BINARY_DIR}/TESTING") + add_subdirectory(testing/MATGEN) + add_subdirectory(testing/LIN) + add_subdirectory(testing/EIG) + macro(add_lapack_test output input target) + set(TEST_INPUT "${LAPACK_SOURCE_DIR}/testing/${input}") + set(TEST_OUTPUT "${LAPACK_BINARY_DIR}/TESTING/${output}") + string(REPLACE "." "_" input_name ${input}) + set(testName "${target}_${input_name}") + if(EXISTS "${TEST_INPUT}") + add_dependencies(buildtests ${target}) + add_test(NAME LAPACK-${testName} + COMMAND "${CMAKE_COMMAND}" + -DTEST=$ + -DINPUT=${TEST_INPUT} + -DOUTPUT=${TEST_OUTPUT} + -DINTDIR=${CMAKE_CFG_INTDIR} + -P "${LAPACK_SOURCE_DIR}/testing/runtest.cmake") + endif() + endmacro() + + if (BUILD_SINGLE) + add_lapack_test(stest.out stest.in xlintsts) + # + # ======== SINGLE RFP LIN TESTS ======================== + add_lapack_test(stest_rfp.out stest_rfp.in xlintstrfs) + # + # + # ======== SINGLE EIG TESTS =========================== + # + + add_lapack_test(snep.out nep.in xeigtsts) + + + add_lapack_test(ssep.out sep.in xeigtsts) + + + add_lapack_test(ssvd.out svd.in xeigtsts) + + + add_lapack_test(sec.out sec.in xeigtsts) + + + add_lapack_test(sed.out sed.in xeigtsts) + + + add_lapack_test(sgg.out sgg.in xeigtsts) + + + add_lapack_test(sgd.out sgd.in xeigtsts) + + + add_lapack_test(ssb.out ssb.in xeigtsts) + + + add_lapack_test(ssg.out ssg.in xeigtsts) + + + add_lapack_test(sbal.out sbal.in xeigtsts) + + + add_lapack_test(sbak.out sbak.in xeigtsts) + + + add_lapack_test(sgbal.out sgbal.in xeigtsts) + + + add_lapack_test(sgbak.out sgbak.in xeigtsts) + + + add_lapack_test(sbb.out sbb.in xeigtsts) + + + add_lapack_test(sglm.out glm.in xeigtsts) + + + add_lapack_test(sgqr.out gqr.in xeigtsts) + + + add_lapack_test(sgsv.out gsv.in xeigtsts) + + + add_lapack_test(scsd.out csd.in xeigtsts) + + + add_lapack_test(slse.out lse.in xeigtsts) + endif() + + if (BUILD_DOUBLE) + # + # ======== DOUBLE LIN TESTS =========================== + add_lapack_test(dtest.out dtest.in xlintstd) + # + # ======== DOUBLE RFP LIN TESTS ======================== + add_lapack_test(dtest_rfp.out dtest_rfp.in xlintstrfd) + # + # ======== DOUBLE EIG TESTS =========================== + + add_lapack_test(dnep.out nep.in xeigtstd) + + + add_lapack_test(dsep.out sep.in xeigtstd) + + + add_lapack_test(dsvd.out svd.in xeigtstd) + + + add_lapack_test(dec.out dec.in xeigtstd) + + + add_lapack_test(ded.out ded.in xeigtstd) + + + add_lapack_test(dgg.out dgg.in xeigtstd) + + + add_lapack_test(dgd.out dgd.in xeigtstd) + + + add_lapack_test(dsb.out dsb.in xeigtstd) + + + add_lapack_test(dsg.out dsg.in xeigtstd) + + + add_lapack_test(dbal.out dbal.in xeigtstd) + + + add_lapack_test(dbak.out dbak.in xeigtstd) + + + add_lapack_test(dgbal.out dgbal.in xeigtstd) + + + add_lapack_test(dgbak.out dgbak.in xeigtstd) + + + add_lapack_test(dbb.out dbb.in xeigtstd) + + + add_lapack_test(dglm.out glm.in xeigtstd) + + + add_lapack_test(dgqr.out gqr.in xeigtstd) + + + add_lapack_test(dgsv.out gsv.in xeigtstd) + + + add_lapack_test(dcsd.out csd.in xeigtstd) + + + add_lapack_test(dlse.out lse.in xeigtstd) + endif() + + if (BUILD_COMPLEX) + add_lapack_test(ctest.out ctest.in xlintstc) + # + # ======== COMPLEX RFP LIN TESTS ======================== + add_lapack_test(ctest_rfp.out ctest_rfp.in xlintstrfc) + # + # ======== COMPLEX EIG TESTS =========================== + + add_lapack_test(cnep.out nep.in xeigtstc) + + + add_lapack_test(csep.out sep.in xeigtstc) + + + add_lapack_test(csvd.out svd.in xeigtstc) + + + add_lapack_test(cec.out cec.in xeigtstc) + + + add_lapack_test(ced.out ced.in xeigtstc) + + + add_lapack_test(cgg.out cgg.in xeigtstc) + + + add_lapack_test(cgd.out cgd.in xeigtstc) + + + add_lapack_test(csb.out csb.in xeigtstc) + + + add_lapack_test(csg.out csg.in xeigtstc) + + + add_lapack_test(cbal.out cbal.in xeigtstc) + + + add_lapack_test(cbak.out cbak.in xeigtstc) + + + add_lapack_test(cgbal.out cgbal.in xeigtstc) + + + add_lapack_test(cgbak.out cgbak.in xeigtstc) + + + add_lapack_test(cbb.out cbb.in xeigtstc) + + + add_lapack_test(cglm.out glm.in xeigtstc) + + + add_lapack_test(cgqr.out gqr.in xeigtstc) + + + add_lapack_test(cgsv.out gsv.in xeigtstc) + + + add_lapack_test(ccsd.out csd.in xeigtstc) + + + add_lapack_test(clse.out lse.in xeigtstc) + endif() + + if (BUILD_COMPLEX16) + # + # ======== COMPLEX16 LIN TESTS ======================== + add_lapack_test(ztest.out ztest.in xlintstz) + # + # ======== COMPLEX16 RFP LIN TESTS ======================== + add_lapack_test(ztest_rfp.out ztest_rfp.in xlintstrfz) + # + # ======== COMPLEX16 EIG TESTS =========================== + + add_lapack_test(znep.out nep.in xeigtstz) + + + add_lapack_test(zsep.out sep.in xeigtstz) + + + add_lapack_test(zsvd.out svd.in xeigtstz) + + + add_lapack_test(zec.out zec.in xeigtstz) + + + add_lapack_test(zed.out zed.in xeigtstz) + + + add_lapack_test(zgg.out zgg.in xeigtstz) + + + add_lapack_test(zgd.out zgd.in xeigtstz) + + + add_lapack_test(zsb.out zsb.in xeigtstz) + + + add_lapack_test(zsg.out zsg.in xeigtstz) + + + add_lapack_test(zbal.out zbal.in xeigtstz) + + + add_lapack_test(zbak.out zbak.in xeigtstz) + + + add_lapack_test(zgbal.out zgbal.in xeigtstz) + + + add_lapack_test(zgbak.out zgbak.in xeigtstz) + + + add_lapack_test(zbb.out zbb.in xeigtstz) + + + add_lapack_test(zglm.out glm.in xeigtstz) + + + add_lapack_test(zgqr.out gqr.in xeigtstz) + + + add_lapack_test(zgsv.out gsv.in xeigtstz) + + + add_lapack_test(zcsd.out csd.in xeigtstz) + + + add_lapack_test(zlse.out lse.in xeigtstz) + endif() + + + if (BUILD_SIMPLE) + if (BUILD_DOUBLE) + # + # ======== SINGLE-DOUBLE PROTO LIN TESTS ============== + add_lapack_test(dstest.out dstest.in xlintstds) + endif() + endif() + + + if (BUILD_COMPLEX) + if (BUILD_COMPLEX16) + # + # ======== COMPLEX-COMPLEX16 LIN TESTS ======================== + add_lapack_test(zctest.out zctest.in xlintstzc) + endif() + endif() + + # ============================================================================== + + execute_process(COMMAND ${CMAKE_COMMAND} -E copy ${LAPACK_SOURCE_DIR}/testing/lapack_testing.py ${LAPACK_BINARY_DIR}) + add_test( + NAME LAPACK_Test_Summary + WORKING_DIRECTORY ${LAPACK_BINARY_DIR} + COMMAND ${PYTHON_EXECUTABLE} "lapack_testing.py" + ) + +endif() + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cholesky.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cholesky.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ea3bc123be605fb6accac8e85fd95fcd86ae2d26 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cholesky.cpp @@ -0,0 +1,72 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "lapack_common.h" +#include + +// POTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. +EIGEN_LAPACK_FUNC(potrf,(char* uplo, int *n, RealScalar *pa, int *lda, int *info)) +{ + *info = 0; + if(UPLO(*uplo)==INVALID) *info = -1; + else if(*n<0) *info = -2; + else if(*lda(pa); + MatrixType A(a,*n,*n,*lda); + int ret; + if(UPLO(*uplo)==UP) ret = int(internal::llt_inplace::blocked(A)); + else ret = int(internal::llt_inplace::blocked(A)); + + if(ret>=0) + *info = ret+1; + + return 0; +} + +// POTRS solves a system of linear equations A*X = B with a symmetric +// positive definite matrix A using the Cholesky factorization +// A = U**T*U or A = L*L**T computed by DPOTRF. +EIGEN_LAPACK_FUNC(potrs,(char* uplo, int *n, int *nrhs, RealScalar *pa, int *lda, RealScalar *pb, int *ldb, int *info)) +{ + *info = 0; + if(UPLO(*uplo)==INVALID) *info = -1; + else if(*n<0) *info = -2; + else if(*nrhs<0) *info = -3; + else if(*lda(pa); + Scalar* b = reinterpret_cast(pb); + MatrixType A(a,*n,*n,*lda); + MatrixType B(b,*n,*nrhs,*ldb); + + if(UPLO(*uplo)==UP) + { + A.triangularView().adjoint().solveInPlace(B); + A.triangularView().solveInPlace(B); + } + else + { + A.triangularView().solveInPlace(B); + A.triangularView().adjoint().solveInPlace(B); + } + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clacgv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clacgv.f new file mode 100644 index 0000000000000000000000000000000000000000..359eb07f36509880a5ee9d12f93a06c516da6101 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clacgv.f @@ -0,0 +1,116 @@ +*> \brief \b CLACGV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLACGV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLACGV( N, X, INCX ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* .. +* .. Array Arguments .. +* COMPLEX X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLACGV conjugates a complex vector of length N. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The length of the vector X. N >= 0. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array, dimension +*> (1+(N-1)*abs(INCX)) +*> On entry, the vector of length N to be conjugated. +*> On exit, X is overwritten with conjg(X). +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The spacing between successive elements of X. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + SUBROUTINE CLACGV( N, X, INCX ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N +* .. +* .. Array Arguments .. + COMPLEX X( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, IOFF +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG +* .. +* .. Executable Statements .. +* + IF( INCX.EQ.1 ) THEN + DO 10 I = 1, N + X( I ) = CONJG( X( I ) ) + 10 CONTINUE + ELSE + IOFF = 1 + IF( INCX.LT.0 ) + $ IOFF = 1 - ( N-1 )*INCX + DO 20 I = 1, N + X( IOFF ) = CONJG( X( IOFF ) ) + IOFF = IOFF + INCX + 20 CONTINUE + END IF + RETURN +* +* End of CLACGV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cladiv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cladiv.f new file mode 100644 index 0000000000000000000000000000000000000000..2807ac5fc1ebb34a3398821445f433e41750dd09 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/cladiv.f @@ -0,0 +1,97 @@ +*> \brief \b CLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* COMPLEX FUNCTION CLADIV( X, Y ) +* +* .. Scalar Arguments .. +* COMPLEX X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLADIV := X / Y, where X and Y are complex. The computation of X / Y +*> will not overflow on an intermediary step unless the results +*> overflows. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is COMPLEX +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX +*> The complex scalars X and Y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + COMPLEX FUNCTION CLADIV( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + COMPLEX X, Y +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + REAL ZI, ZR +* .. +* .. External Subroutines .. + EXTERNAL SLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC AIMAG, CMPLX, REAL +* .. +* .. Executable Statements .. +* + CALL SLADIV( REAL( X ), AIMAG( X ), REAL( Y ), AIMAG( Y ), ZR, + $ ZI ) + CLADIV = CMPLX( ZR, ZI ) +* + RETURN +* +* End of CLADIV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarf.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarf.f new file mode 100644 index 0000000000000000000000000000000000000000..ca0328fb58ef538011d14a3fd88b998afa1df4e6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarf.f @@ -0,0 +1,232 @@ +*> \brief \b CLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLARF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER SIDE +* INTEGER INCV, LDC, M, N +* COMPLEX TAU +* .. +* .. Array Arguments .. +* COMPLEX C( LDC, * ), V( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLARF applies a complex elementary reflector H to a complex M-by-N +*> matrix C, from either the left or the right. H is represented in the +*> form +*> +*> H = I - tau * v * v**H +*> +*> where tau is a complex scalar and v is a complex vector. +*> +*> If tau = 0, then H is taken to be the unit matrix. +*> +*> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead +*> tau. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': form H * C +*> = 'R': form C * H +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX array, dimension +*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' +*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' +*> The vector v in the representation of H. V is not used if +*> TAU = 0. +*> \endverbatim +*> +*> \param[in] INCV +*> \verbatim +*> INCV is INTEGER +*> The increment between elements of v. INCV <> 0. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX +*> The value tau in the representation of H. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array, dimension (LDC,N) +*> On entry, the M-by-N matrix C. +*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', +*> or C * H if SIDE = 'R'. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension +*> (N) if SIDE = 'L' +*> or (M) if SIDE = 'R' +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER SIDE + INTEGER INCV, LDC, M, N + COMPLEX TAU +* .. +* .. Array Arguments .. + COMPLEX C( LDC, * ), V( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE, ZERO + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), + $ ZERO = ( 0.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL APPLYLEFT + INTEGER I, LASTV, LASTC +* .. +* .. External Subroutines .. + EXTERNAL CGEMV, CGERC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILACLR, ILACLC + EXTERNAL LSAME, ILACLR, ILACLC +* .. +* .. Executable Statements .. +* + APPLYLEFT = LSAME( SIDE, 'L' ) + LASTV = 0 + LASTC = 0 + IF( TAU.NE.ZERO ) THEN +! Set up variables for scanning V. LASTV begins pointing to the end +! of V. + IF( APPLYLEFT ) THEN + LASTV = M + ELSE + LASTV = N + END IF + IF( INCV.GT.0 ) THEN + I = 1 + (LASTV-1) * INCV + ELSE + I = 1 + END IF +! Look for the last non-zero row in V. + DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) + LASTV = LASTV - 1 + I = I - INCV + END DO + IF( APPLYLEFT ) THEN +! Scan for the last non-zero column in C(1:lastv,:). + LASTC = ILACLC(LASTV, N, C, LDC) + ELSE +! Scan for the last non-zero row in C(:,1:lastv). + LASTC = ILACLR(M, LASTV, C, LDC) + END IF + END IF +! Note that lastc.eq.0 renders the BLAS operations null; no special +! case is needed at this level. + IF( APPLYLEFT ) THEN +* +* Form H * C +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) +* + CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, + $ C, LDC, V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H +* + CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) + END IF + ELSE +* +* Form C * H +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) +* + CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, + $ V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H +* + CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) + END IF + END IF + RETURN +* +* End of CLARF +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfb.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfb.f new file mode 100644 index 0000000000000000000000000000000000000000..40bbdf48783eaae73a2ca9e744996c264ed006d5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfb.f @@ -0,0 +1,771 @@ +*> \brief \b CLARFB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLARFB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, +* T, LDT, C, LDC, WORK, LDWORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, SIDE, STOREV, TRANS +* INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. +* COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ), +* $ WORK( LDWORK, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLARFB applies a complex block reflector H or its transpose H**H to a +*> complex M-by-N matrix C, from either the left or the right. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': apply H or H**H from the Left +*> = 'R': apply H or H**H from the Right +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': apply H (No transpose) +*> = 'C': apply H**H (Conjugate transpose) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Indicates how H is formed from a product of elementary +*> reflectors +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Indicates how the vectors which define the elementary +*> reflectors are stored: +*> = 'C': Columnwise +*> = 'R': Rowwise +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the matrix T (= the number of elementary +*> reflectors whose product defines the block reflector). +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,M) if STOREV = 'R' and SIDE = 'L' +*> (LDV,N) if STOREV = 'R' and SIDE = 'R' +*> The matrix V. See Further Details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); +*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); +*> if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] T +*> \verbatim +*> T is COMPLEX array, dimension (LDT,K) +*> The triangular K-by-K matrix T in the representation of the +*> block reflector. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX array, dimension (LDC,N) +*> On entry, the M-by-N matrix C. +*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (LDWORK,K) +*> \endverbatim +*> +*> \param[in] LDWORK +*> \verbatim +*> LDWORK is INTEGER +*> The leading dimension of the array WORK. +*> If SIDE = 'L', LDWORK >= max(1,N); +*> if SIDE = 'R', LDWORK >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, + $ T, LDT, C, LDC, WORK, LDWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, SIDE, STOREV, TRANS + INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. + COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ), + $ WORK( LDWORK, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + CHARACTER TRANST + INTEGER I, J, LASTV, LASTC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILACLR, ILACLC + EXTERNAL LSAME, ILACLR, ILACLC +* .. +* .. External Subroutines .. + EXTERNAL CCOPY, CGEMM, CLACGV, CTRMM +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.LE.0 .OR. N.LE.0 ) + $ RETURN +* + IF( LSAME( TRANS, 'N' ) ) THEN + TRANST = 'C' + ELSE + TRANST = 'N' + END IF +* + IF( LSAME( STOREV, 'C' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 ) (first K rows) +* ( V2 ) +* where V1 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILACLR( M, K, V, LDV ) ) + LASTC = ILACLC( LASTV, N, C, LDC ) +* +* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) +* +* W := C1**H +* + DO 10 J = 1, K + CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + CALL CLACGV( LASTC, WORK( 1, J ), 1 ) + 10 CONTINUE +* +* W := W * V1 +* + CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**H *V2 +* + CALL CGEMM( 'Conjugate transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC, + $ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**H +* + IF( M.GT.K ) THEN +* +* C2 := C2 - V2 * W**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTV-K, LASTC, K, -ONE, V( K+1, 1 ), LDV, + $ WORK, LDWORK, ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1**H +* + CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**H +* + DO 30 J = 1, K + DO 20 I = 1, LASTC + C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) ) + 20 CONTINUE + 30 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILACLR( N, K, V, LDV ) ) + LASTC = ILACLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C1 +* + DO 40 J = 1, K + CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 40 CONTINUE +* +* W := W * V1 +* + CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2 +* + CALL CGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**H +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1**H +* + CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 60 J = 1, K + DO 50 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 50 CONTINUE + 60 CONTINUE + END IF +* + ELSE +* +* Let V = ( V1 ) +* ( V2 ) (last K rows) +* where V2 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILACLR( M, K, V, LDV ) ) + LASTC = ILACLC( LASTV, N, C, LDC ) +* +* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) +* +* W := C2**H +* + DO 70 J = 1, K + CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + CALL CLACGV( LASTC, WORK( 1, J ), 1 ) + 70 CONTINUE +* +* W := W * V2 +* + CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**H*V1 +* + CALL CGEMM( 'Conjugate transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1 * W**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**H +* + CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**H +* + DO 90 J = 1, K + DO 80 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - + $ CONJG( WORK( I, J ) ) + 80 CONTINUE + 90 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILACLR( N, K, V, LDV ) ) + LASTC = ILACLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C2 +* + DO 100 J = 1, K + CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 100 CONTINUE +* +* W := W * V2 +* + CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1 +* + CALL CGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**H +* + CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W +* + DO 120 J = 1, K + DO 110 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) + $ - WORK( I, J ) + 110 CONTINUE + 120 CONTINUE + END IF + END IF +* + ELSE IF( LSAME( STOREV, 'R' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 V2 ) (V1: first K columns) +* where V1 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILACLC( K, M, V, LDV ) ) + LASTC = ILACLC( LASTV, N, C, LDC ) +* +* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) +* +* W := C1**H +* + DO 130 J = 1, K + CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + CALL CLACGV( LASTC, WORK( 1, J ), 1 ) + 130 CONTINUE +* +* W := W * V1**H +* + CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**H*V2**H +* + CALL CGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**H * W**H +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2**H * W**H +* + CALL CGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTV-K, LASTC, K, + $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**H +* + DO 150 J = 1, K + DO 140 I = 1, LASTC + C( J, I ) = C( J, I ) - CONJG( WORK( I, J ) ) + 140 CONTINUE + 150 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILACLC( K, N, V, LDV ) ) + LASTC = ILACLR( M, LASTV, C, LDC ) +* +* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) +* +* W := C1 +* + DO 160 J = 1, K + CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 160 CONTINUE +* +* W := W * V1**H +* + CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC, + $ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2 +* + CALL CGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 180 J = 1, K + DO 170 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 170 CONTINUE + 180 CONTINUE +* + END IF +* + ELSE +* +* Let V = ( V1 V2 ) (V2: last K columns) +* where V2 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILACLC( K, M, V, LDV ) ) + LASTC = ILACLC( LASTV, N, C, LDC ) +* +* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) +* +* W := C2**H +* + DO 190 J = 1, K + CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + CALL CLACGV( LASTC, WORK( 1, J ), 1 ) + 190 CONTINUE +* +* W := W * V2**H +* + CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**H * V1**H +* + CALL CGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTC, K, LASTV-K, + $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**H * W**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1**H * W**H +* + CALL CGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTV-K, LASTC, K, + $ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**H +* + DO 210 J = 1, K + DO 200 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - + $ CONJG( WORK( I, J ) ) + 200 CONTINUE + 210 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILACLC( K, N, V, LDV ) ) + LASTC = ILACLR( M, LASTV, C, LDC ) +* +* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) +* +* W := C2 +* + DO 220 J = 1, K + CALL CCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 220 CONTINUE +* +* W := W * V2**H +* + CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1**H +* + CALL CGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE, + $ WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1 +* + CALL CGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL CTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 240 J = 1, K + DO 230 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) + $ - WORK( I, J ) + 230 CONTINUE + 240 CONTINUE +* + END IF +* + END IF + END IF +* + RETURN +* +* End of CLARFB +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfg.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfg.f new file mode 100644 index 0000000000000000000000000000000000000000..d64f396c3d508a6ef0b1e7edd417c44b7a44800a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarfg.f @@ -0,0 +1,203 @@ +*> \brief \b CLARFG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLARFG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* COMPLEX ALPHA, TAU +* .. +* .. Array Arguments .. +* COMPLEX X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLARFG generates a complex elementary reflector H of order n, such +*> that +*> +*> H**H * ( alpha ) = ( beta ), H**H * H = I. +*> ( x ) ( 0 ) +*> +*> where alpha and beta are scalars, with beta real, and x is an +*> (n-1)-element complex vector. H is represented in the form +*> +*> H = I - tau * ( 1 ) * ( 1 v**H ) , +*> ( v ) +*> +*> where tau is a complex scalar and v is a complex (n-1)-element +*> vector. Note that H is not hermitian. +*> +*> If the elements of x are all zero and alpha is real, then tau = 0 +*> and H is taken to be the unit matrix. +*> +*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the elementary reflector. +*> \endverbatim +*> +*> \param[in,out] ALPHA +*> \verbatim +*> ALPHA is COMPLEX +*> On entry, the value alpha. +*> On exit, it is overwritten with the value beta. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array, dimension +*> (1+(N-2)*abs(INCX)) +*> On entry, the vector x. +*> On exit, it is overwritten with the vector v. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between elements of X. INCX > 0. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX +*> The value tau. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + COMPLEX ALPHA, TAU +* .. +* .. Array Arguments .. + COMPLEX X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER J, KNT + REAL ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM +* .. +* .. External Functions .. + REAL SCNRM2, SLAMCH, SLAPY3 + COMPLEX CLADIV + EXTERNAL SCNRM2, SLAMCH, SLAPY3, CLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, AIMAG, CMPLX, REAL, SIGN +* .. +* .. External Subroutines .. + EXTERNAL CSCAL, CSSCAL +* .. +* .. Executable Statements .. +* + IF( N.LE.0 ) THEN + TAU = ZERO + RETURN + END IF +* + XNORM = SCNRM2( N-1, X, INCX ) + ALPHR = REAL( ALPHA ) + ALPHI = AIMAG( ALPHA ) +* + IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN +* +* H = I +* + TAU = ZERO + ELSE +* +* general case +* + BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' ) + RSAFMN = ONE / SAFMIN +* + KNT = 0 + IF( ABS( BETA ).LT.SAFMIN ) THEN +* +* XNORM, BETA may be inaccurate; scale X and recompute them +* + 10 CONTINUE + KNT = KNT + 1 + CALL CSSCAL( N-1, RSAFMN, X, INCX ) + BETA = BETA*RSAFMN + ALPHI = ALPHI*RSAFMN + ALPHR = ALPHR*RSAFMN + IF( ABS( BETA ).LT.SAFMIN ) + $ GO TO 10 +* +* New BETA is at most 1, at least SAFMIN +* + XNORM = SCNRM2( N-1, X, INCX ) + ALPHA = CMPLX( ALPHR, ALPHI ) + BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + END IF + TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) + ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA ) + CALL CSCAL( N-1, ALPHA, X, INCX ) +* +* If ALPHA is subnormal, it may lose relative accuracy +* + DO 20 J = 1, KNT + BETA = BETA*SAFMIN + 20 CONTINUE + ALPHA = BETA + END IF +* + RETURN +* +* End of CLARFG +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarft.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarft.f new file mode 100644 index 0000000000000000000000000000000000000000..981447f7724936cc3056559fcbcbccf27e684481 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/clarft.f @@ -0,0 +1,328 @@ +*> \brief \b CLARFT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLARFT forms the triangular factor T of a complex block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**H +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**H * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complexOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE, ZERO + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), + $ ZERO = ( 0.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL CGEMV, CLACGV, CTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( PREVLASTV, I ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) +* + CALL CGEMV( 'Conjugate transpose', J-I, I-1, + $ -TAU( I ), V( I+1, 1 ), LDV, + $ V( I+1, I ), 1, + $ ONE, T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H +* + CALL CGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), LDT ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL CTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) +* + CALL CGEMV( 'Conjugate transpose', N-K+I-J, K-I, + $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), + $ 1, ONE, T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H +* + CALL CGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), + $ V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), LDT ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL CTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of CLARFT +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_double.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_double.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c9c5752731d01f1d1defedffba7be767f1e2aedc --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_double.cpp @@ -0,0 +1,18 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define SCALAR std::complex +#define SCALAR_SUFFIX z +#define SCALAR_SUFFIX_UP "Z" +#define REAL_SCALAR_SUFFIX d +#define ISCOMPLEX 1 + +#include "cholesky.cpp" +#include "lu.cpp" +#include "svd.cpp" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_single.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_single.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6d11b26cdf88eaf90f005b3f6b47152c6755e67c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/complex_single.cpp @@ -0,0 +1,18 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define SCALAR std::complex +#define SCALAR_SUFFIX c +#define SCALAR_SUFFIX_UP "C" +#define REAL_SCALAR_SUFFIX s +#define ISCOMPLEX 1 + +#include "cholesky.cpp" +#include "lu.cpp" +#include "svd.cpp" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dladiv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dladiv.f new file mode 100644 index 0000000000000000000000000000000000000000..090a90654f1a2e55e08605c79e98504275b5bfc0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dladiv.f @@ -0,0 +1,128 @@ +*> \brief \b DLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLADIV( A, B, C, D, P, Q ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, D, P, Q +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLADIV performs complex division in real arithmetic +*> +*> a + i*b +*> p + i*q = --------- +*> c + i*d +*> +*> The algorithm is due to Robert L. Smith and can be found +*> in D. Knuth, The art of Computer Programming, Vol.2, p.195 +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION +*> The scalars a, b, c, and d in the above expression. +*> \endverbatim +*> +*> \param[out] P +*> \verbatim +*> P is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is DOUBLE PRECISION +*> The scalars p and q in the above expression. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLADIV( A, B, C, D, P, Q ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B, C, D, P, Q +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION E, F +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + IF( ABS( D ).LT.ABS( C ) ) THEN + E = D / C + F = C + D*E + P = ( A+B*E ) / F + Q = ( B-A*E ) / F + ELSE + E = C / D + F = D + C*E + P = ( B+A*E ) / F + Q = ( -A+B*E ) / F + END IF +* + RETURN +* +* End of DLADIV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlamch.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlamch.f new file mode 100644 index 0000000000000000000000000000000000000000..eb307e5e1c74fb769fdc10e6a6d983c22d65a6f2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlamch.f @@ -0,0 +1,189 @@ +*> \brief \b DLAMCH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAMCH determines double precision machine parameters. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CMACH +*> \verbatim +*> Specifies the value to be returned by DLAMCH: +*> = 'E' or 'e', DLAMCH := eps +*> = 'S' or 's , DLAMCH := sfmin +*> = 'B' or 'b', DLAMCH := base +*> = 'P' or 'p', DLAMCH := eps*base +*> = 'N' or 'n', DLAMCH := t +*> = 'R' or 'r', DLAMCH := rnd +*> = 'M' or 'm', DLAMCH := emin +*> = 'U' or 'u', DLAMCH := rmin +*> = 'L' or 'l', DLAMCH := emax +*> = 'O' or 'o', DLAMCH := rmax +*> where +*> eps = relative machine precision +*> sfmin = safe minimum, such that 1/sfmin does not overflow +*> base = base of the machine +*> prec = eps*base +*> t = number of (base) digits in the mantissa +*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise +*> emin = minimum exponent before (gradual) underflow +*> rmin = underflow threshold - base**(emin-1) +*> emax = largest exponent before overflow +*> rmax = overflow threshold - (base**emax)*(1-eps) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CMACH +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION RND, EPS, SFMIN, SMALL, RMACH +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, + $ MINEXPONENT, RADIX, TINY +* .. +* .. Executable Statements .. +* +* +* Assume rounding, not chopping. Always. +* + RND = ONE +* + IF( ONE.EQ.RND ) THEN + EPS = EPSILON(ZERO) * 0.5 + ELSE + EPS = EPSILON(ZERO) + END IF +* + IF( LSAME( CMACH, 'E' ) ) THEN + RMACH = EPS + ELSE IF( LSAME( CMACH, 'S' ) ) THEN + SFMIN = TINY(ZERO) + SMALL = ONE / HUGE(ZERO) + IF( SMALL.GE.SFMIN ) THEN +* +* Use SMALL plus a bit, to avoid the possibility of rounding +* causing overflow when computing 1/sfmin. +* + SFMIN = SMALL*( ONE+EPS ) + END IF + RMACH = SFMIN + ELSE IF( LSAME( CMACH, 'B' ) ) THEN + RMACH = RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'P' ) ) THEN + RMACH = EPS * RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'N' ) ) THEN + RMACH = DIGITS(ZERO) + ELSE IF( LSAME( CMACH, 'R' ) ) THEN + RMACH = RND + ELSE IF( LSAME( CMACH, 'M' ) ) THEN + RMACH = MINEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'U' ) ) THEN + RMACH = tiny(zero) + ELSE IF( LSAME( CMACH, 'L' ) ) THEN + RMACH = MAXEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'O' ) ) THEN + RMACH = HUGE(ZERO) + ELSE + RMACH = ZERO + END IF +* + DLAMCH = RMACH + RETURN +* +* End of DLAMCH +* + END +************************************************************************ +*> \brief \b DLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> DLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date November 2011 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> A is a DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is a DOUBLE PRECISION +*> The values A and B. +*> \endverbatim +*> + DOUBLE PRECISION FUNCTION DLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + DLAMC3 = A + B +* + RETURN +* +* End of DLAMC3 +* + END +* +************************************************************************ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy2.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy2.f new file mode 100644 index 0000000000000000000000000000000000000000..e6a62bf4abf2a1c60680a7502b314d0ee81da4b3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy2.f @@ -0,0 +1,104 @@ +*> \brief \b DLAPY2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAPY2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary +*> overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION +*> X and Y specify the values x and y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION X, Y +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION W, XABS, YABS, Z +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + W = MAX( XABS, YABS ) + Z = MIN( XABS, YABS ) + IF( Z.EQ.ZERO ) THEN + DLAPY2 = W + ELSE + DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) + END IF + RETURN +* +* End of DLAPY2 +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy3.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy3.f new file mode 100644 index 0000000000000000000000000000000000000000..ae9844f80e766874e4fd029ddaecab2039c8dd18 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlapy3.f @@ -0,0 +1,111 @@ +*> \brief \b DLAPY3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAPY3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION X, Y, Z +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause +*> unnecessary overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION +*> X, Y and Z specify the values x, y and z. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION X, Y, Z +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION W, XABS, YABS, ZABS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + ZABS = ABS( Z ) + W = MAX( XABS, YABS, ZABS ) + IF( W.EQ.ZERO ) THEN +* W can be zero for max(0,nan,0) +* adding all three entries together will make sure +* NaN will not disappear. + DLAPY3 = XABS + YABS + ZABS + ELSE + DLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ + $ ( ZABS / W )**2 ) + END IF + RETURN +* +* End of DLAPY3 +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarf.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarf.f new file mode 100644 index 0000000000000000000000000000000000000000..2a82ff4399c2e8675b08fb60c40eec881d1fb7e0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarf.f @@ -0,0 +1,227 @@ +*> \brief \b DLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER SIDE +* INTEGER INCV, LDC, M, N +* DOUBLE PRECISION TAU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARF applies a real elementary reflector H to a real m by n matrix +*> C, from either the left or the right. H is represented in the form +*> +*> H = I - tau * v * v**T +*> +*> where tau is a real scalar and v is a real vector. +*> +*> If tau = 0, then H is taken to be the unit matrix. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': form H * C +*> = 'R': form C * H +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' +*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' +*> The vector v in the representation of H. V is not used if +*> TAU = 0. +*> \endverbatim +*> +*> \param[in] INCV +*> \verbatim +*> INCV is INTEGER +*> The increment between elements of v. INCV <> 0. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION +*> The value tau in the representation of H. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension (LDC,N) +*> On entry, the m by n matrix C. +*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', +*> or C * H if SIDE = 'R'. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension +*> (N) if SIDE = 'L' +*> or (M) if SIDE = 'R' +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER SIDE + INTEGER INCV, LDC, M, N + DOUBLE PRECISION TAU +* .. +* .. Array Arguments .. + DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL APPLYLEFT + INTEGER I, LASTV, LASTC +* .. +* .. External Subroutines .. + EXTERNAL DGEMV, DGER +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILADLR, ILADLC + EXTERNAL LSAME, ILADLR, ILADLC +* .. +* .. Executable Statements .. +* + APPLYLEFT = LSAME( SIDE, 'L' ) + LASTV = 0 + LASTC = 0 + IF( TAU.NE.ZERO ) THEN +! Set up variables for scanning V. LASTV begins pointing to the end +! of V. + IF( APPLYLEFT ) THEN + LASTV = M + ELSE + LASTV = N + END IF + IF( INCV.GT.0 ) THEN + I = 1 + (LASTV-1) * INCV + ELSE + I = 1 + END IF +! Look for the last non-zero row in V. + DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) + LASTV = LASTV - 1 + I = I - INCV + END DO + IF( APPLYLEFT ) THEN +! Scan for the last non-zero column in C(1:lastv,:). + LASTC = ILADLC(LASTV, N, C, LDC) + ELSE +! Scan for the last non-zero row in C(:,1:lastv). + LASTC = ILADLR(M, LASTV, C, LDC) + END IF + END IF +! Note that lastc.eq.0 renders the BLAS operations null; no special +! case is needed at this level. + IF( APPLYLEFT ) THEN +* +* Form H * C +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) +* + CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, + $ ZERO, WORK, 1 ) +* +* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T +* + CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) + END IF + ELSE +* +* Form C * H +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) +* + CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, + $ V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T +* + CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) + END IF + END IF + RETURN +* +* End of DLARF +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfb.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfb.f new file mode 100644 index 0000000000000000000000000000000000000000..206d3b268287b2d5a34dd4e0c72f6aa31288497d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfb.f @@ -0,0 +1,762 @@ +*> \brief \b DLARFB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARFB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, +* T, LDT, C, LDC, WORK, LDWORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, SIDE, STOREV, TRANS +* INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), +* $ WORK( LDWORK, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARFB applies a real block reflector H or its transpose H**T to a +*> real m by n matrix C, from either the left or the right. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': apply H or H**T from the Left +*> = 'R': apply H or H**T from the Right +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': apply H (No transpose) +*> = 'T': apply H**T (Transpose) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Indicates how H is formed from a product of elementary +*> reflectors +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Indicates how the vectors which define the elementary +*> reflectors are stored: +*> = 'C': Columnwise +*> = 'R': Rowwise +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the matrix T (= the number of elementary +*> reflectors whose product defines the block reflector). +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,M) if STOREV = 'R' and SIDE = 'L' +*> (LDV,N) if STOREV = 'R' and SIDE = 'R' +*> The matrix V. See Further Details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); +*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); +*> if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDT,K) +*> The triangular k by k matrix T in the representation of the +*> block reflector. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension (LDC,N) +*> On entry, the m by n matrix C. +*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (LDWORK,K) +*> \endverbatim +*> +*> \param[in] LDWORK +*> \verbatim +*> LDWORK is INTEGER +*> The leading dimension of the array WORK. +*> If SIDE = 'L', LDWORK >= max(1,N); +*> if SIDE = 'R', LDWORK >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, + $ T, LDT, C, LDC, WORK, LDWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, SIDE, STOREV, TRANS + INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), + $ WORK( LDWORK, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + CHARACTER TRANST + INTEGER I, J, LASTV, LASTC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILADLR, ILADLC + EXTERNAL LSAME, ILADLR, ILADLC +* .. +* .. External Subroutines .. + EXTERNAL DCOPY, DGEMM, DTRMM +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.LE.0 .OR. N.LE.0 ) + $ RETURN +* + IF( LSAME( TRANS, 'N' ) ) THEN + TRANST = 'T' + ELSE + TRANST = 'N' + END IF +* + IF( LSAME( STOREV, 'C' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 ) (first K rows) +* ( V2 ) +* where V1 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILADLR( M, K, V, LDV ) ) + LASTC = ILADLC( LASTV, N, C, LDC ) +* +* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) +* +* W := C1**T +* + DO 10 J = 1, K + CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + 10 CONTINUE +* +* W := W * V1 +* + CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**T *V2 +* + CALL DGEMM( 'Transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2 * W**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, + $ C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1**T +* + CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**T +* + DO 30 J = 1, K + DO 20 I = 1, LASTC + C( J, I ) = C( J, I ) - WORK( I, J ) + 20 CONTINUE + 30 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILADLR( N, K, V, LDV ) ) + LASTC = ILADLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C1 +* + DO 40 J = 1, K + CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 40 CONTINUE +* +* W := W * V1 +* + CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2 +* + CALL DGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, + $ C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1**T +* + CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 60 J = 1, K + DO 50 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 50 CONTINUE + 60 CONTINUE + END IF +* + ELSE +* +* Let V = ( V1 ) +* ( V2 ) (last K rows) +* where V2 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILADLR( M, K, V, LDV ) ) + LASTC = ILADLC( LASTV, N, C, LDC ) +* +* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) +* +* W := C2**T +* + DO 70 J = 1, K + CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + 70 CONTINUE +* +* W := W * V2 +* + CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**T*V1 +* + CALL DGEMM( 'Transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1 * W**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**T +* + CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**T +* + DO 90 J = 1, K + DO 80 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) + 80 CONTINUE + 90 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILADLR( N, K, V, LDV ) ) + LASTC = ILADLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C2 +* + DO 100 J = 1, K + CALL DCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) + 100 CONTINUE +* +* W := W * V2 +* + CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1 +* + CALL DGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**T +* + CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W +* + DO 120 J = 1, K + DO 110 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J) + 110 CONTINUE + 120 CONTINUE + END IF + END IF +* + ELSE IF( LSAME( STOREV, 'R' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 V2 ) (V1: first K columns) +* where V1 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILADLC( K, M, V, LDV ) ) + LASTC = ILADLC( LASTV, N, C, LDC ) +* +* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) +* +* W := C1**T +* + DO 130 J = 1, K + CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + 130 CONTINUE +* +* W := W * V1**T +* + CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**T*V2**T +* + CALL DGEMM( 'Transpose', 'Transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**T * W**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2**T * W**T +* + CALL DGEMM( 'Transpose', 'Transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**T +* + DO 150 J = 1, K + DO 140 I = 1, LASTC + C( J, I ) = C( J, I ) - WORK( I, J ) + 140 CONTINUE + 150 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILADLC( K, N, V, LDV ) ) + LASTC = ILADLR( M, LASTV, C, LDC ) +* +* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) +* +* W := C1 +* + DO 160 J = 1, K + CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 160 CONTINUE +* +* W := W * V1**T +* + CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2 +* + CALL DGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 180 J = 1, K + DO 170 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 170 CONTINUE + 180 CONTINUE +* + END IF +* + ELSE +* +* Let V = ( V1 V2 ) (V2: last K columns) +* where V2 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILADLC( K, M, V, LDV ) ) + LASTC = ILADLC( LASTV, N, C, LDC ) +* +* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) +* +* W := C2**T +* + DO 190 J = 1, K + CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + 190 CONTINUE +* +* W := W * V2**T +* + CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**T * V1**T +* + CALL DGEMM( 'Transpose', 'Transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**T * W**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1**T * W**T +* + CALL DGEMM( 'Transpose', 'Transpose', + $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**T +* + DO 210 J = 1, K + DO 200 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) + 200 CONTINUE + 210 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILADLC( K, N, V, LDV ) ) + LASTC = ILADLR( M, LASTV, C, LDC ) +* +* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) +* +* W := C2 +* + DO 220 J = 1, K + CALL DCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 220 CONTINUE +* +* W := W * V2**T +* + CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1**T +* + CALL DGEMM( 'No transpose', 'Transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1 +* + CALL DGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 240 J = 1, K + DO 230 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J) + 230 CONTINUE + 240 CONTINUE +* + END IF +* + END IF + END IF +* + RETURN +* +* End of DLARFB +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfg.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfg.f new file mode 100644 index 0000000000000000000000000000000000000000..458ad2e053f3b34ba38306557987280c8acf1796 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarfg.f @@ -0,0 +1,196 @@ +*> \brief \b DLARFG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARFG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* DOUBLE PRECISION ALPHA, TAU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARFG generates a real elementary reflector H of order n, such +*> that +*> +*> H * ( alpha ) = ( beta ), H**T * H = I. +*> ( x ) ( 0 ) +*> +*> where alpha and beta are scalars, and x is an (n-1)-element real +*> vector. H is represented in the form +*> +*> H = I - tau * ( 1 ) * ( 1 v**T ) , +*> ( v ) +*> +*> where tau is a real scalar and v is a real (n-1)-element +*> vector. +*> +*> If the elements of x are all zero, then tau = 0 and H is taken to be +*> the unit matrix. +*> +*> Otherwise 1 <= tau <= 2. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the elementary reflector. +*> \endverbatim +*> +*> \param[in,out] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION +*> On entry, the value alpha. +*> On exit, it is overwritten with the value beta. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension +*> (1+(N-2)*abs(INCX)) +*> On entry, the vector x. +*> On exit, it is overwritten with the vector v. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between elements of X. INCX > 0. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION +*> The value tau. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + DOUBLE PRECISION ALPHA, TAU +* .. +* .. Array Arguments .. + DOUBLE PRECISION X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER J, KNT + DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 + EXTERNAL DLAMCH, DLAPY2, DNRM2 +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, SIGN +* .. +* .. External Subroutines .. + EXTERNAL DSCAL +* .. +* .. Executable Statements .. +* + IF( N.LE.1 ) THEN + TAU = ZERO + RETURN + END IF +* + XNORM = DNRM2( N-1, X, INCX ) +* + IF( XNORM.EQ.ZERO ) THEN +* +* H = I +* + TAU = ZERO + ELSE +* +* general case +* + BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) + SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) + KNT = 0 + IF( ABS( BETA ).LT.SAFMIN ) THEN +* +* XNORM, BETA may be inaccurate; scale X and recompute them +* + RSAFMN = ONE / SAFMIN + 10 CONTINUE + KNT = KNT + 1 + CALL DSCAL( N-1, RSAFMN, X, INCX ) + BETA = BETA*RSAFMN + ALPHA = ALPHA*RSAFMN + IF( ABS( BETA ).LT.SAFMIN ) + $ GO TO 10 +* +* New BETA is at most 1, at least SAFMIN +* + XNORM = DNRM2( N-1, X, INCX ) + BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) + END IF + TAU = ( BETA-ALPHA ) / BETA + CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) +* +* If ALPHA is subnormal, it may lose relative accuracy +* + DO 20 J = 1, KNT + BETA = BETA*SAFMIN + 20 CONTINUE + ALPHA = BETA + END IF +* + RETURN +* +* End of DLARFG +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarft.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarft.f new file mode 100644 index 0000000000000000000000000000000000000000..4b75504037565aa0594ce3bf6515fda63b948282 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dlarft.f @@ -0,0 +1,326 @@ +*> \brief \b DLARFT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARFT forms the triangular factor T of a real block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL DGEMV, DTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( I, PREVLASTV ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( I , J ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) +* + CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), + $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, + $ T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T +* + CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, + $ T( 1, I ), 1 ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( N-K+I , J ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) +* + CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), + $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, + $ T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T +* + CALL DGEMV( 'No transpose', K-I, N-K+I-J, + $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), 1 ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of DLARFT +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/double.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/double.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ea78bb66218ef28607903b448e05d65f46079375 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/double.cpp @@ -0,0 +1,18 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define SCALAR double +#define SCALAR_SUFFIX d +#define SCALAR_SUFFIX_UP "D" +#define ISCOMPLEX 0 + +#include "cholesky.cpp" +#include "lu.cpp" +#include "eigenvalues.cpp" +#include "svd.cpp" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dsecnd_NONE.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dsecnd_NONE.f new file mode 100644 index 0000000000000000000000000000000000000000..61a8dff1349248ee981155311597cb075098816d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/dsecnd_NONE.f @@ -0,0 +1,52 @@ +*> \brief \b DSECND returns nothing +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DSECND( ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSECND returns nothing instead of returning the user time for a process in seconds. +*> If you are using that routine, it means that neither EXTERNAL ETIME, +*> EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available on +*> your machine. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DSECND( ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* ===================================================================== +* + DSECND = 0.0D+0 + RETURN +* +* End of DSECND +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/eigenvalues.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/eigenvalues.cpp new file mode 100644 index 0000000000000000000000000000000000000000..921c51569708f5a2ca5dede14162c14ce3caf2fd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/eigenvalues.cpp @@ -0,0 +1,62 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "lapack_common.h" +#include + +// computes eigen values and vectors of a general N-by-N matrix A +EIGEN_LAPACK_FUNC(syev,(char *jobz, char *uplo, int* n, Scalar* a, int *lda, Scalar* w, Scalar* /*work*/, int* lwork, int *info)) +{ + // TODO exploit the work buffer + bool query_size = *lwork==-1; + + *info = 0; + if(*jobz!='N' && *jobz!='V') *info = -1; + else if(UPLO(*uplo)==INVALID) *info = -2; + else if(*n<0) *info = -3; + else if(*lda eig(mat,computeVectors?ComputeEigenvectors:EigenvaluesOnly); + + if(eig.info()==NoConvergence) + { + make_vector(w,*n).setZero(); + if(computeVectors) + matrix(a,*n,*n,*lda).setIdentity(); + //*info = 1; + return 0; + } + + make_vector(w,*n) = eig.eigenvalues(); + if(computeVectors) + matrix(a,*n,*n,*lda) = eig.eigenvectors(); + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclc.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclc.f new file mode 100644 index 0000000000000000000000000000000000000000..4ceb61c5279f1d14ce96acb6cb2ea788d5196470 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclc.f @@ -0,0 +1,118 @@ +*> \brief \b ILACLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILACLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILACLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILACLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILACLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILACLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILACLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILACLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILACLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclr.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclr.f new file mode 100644 index 0000000000000000000000000000000000000000..d8ab09c5532660052e50292b8466331e76901a10 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaclr.f @@ -0,0 +1,121 @@ +*> \brief \b ILACLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILACLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILACLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILACLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILACLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILACLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILACLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILACLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILACLR = MAX( ILACLR, I ) + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlc.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlc.f new file mode 100644 index 0000000000000000000000000000000000000000..f84bd833a7c0f90319dff3f00221b21106fe1c31 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlc.f @@ -0,0 +1,118 @@ +*> \brief \b ILADLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILADLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILADLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILADLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILADLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILADLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILADLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILADLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILADLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlr.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlr.f new file mode 100644 index 0000000000000000000000000000000000000000..2114c616418ea5bd040ee95d601107d5f3c2c2c8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/iladlr.f @@ -0,0 +1,121 @@ +*> \brief \b ILADLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILADLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILADLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILADLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILADLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILADLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILADLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILADLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILADLR = MAX( ILADLR, I ) + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslc.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslc.f new file mode 100644 index 0000000000000000000000000000000000000000..e3db0f4ae6040e9cea0d26889ded4329e894e5dd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslc.f @@ -0,0 +1,118 @@ +*> \brief \b ILASLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILASLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILASLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* REAL A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILASLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILASLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + REAL A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILASLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILASLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILASLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILASLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslr.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslr.f new file mode 100644 index 0000000000000000000000000000000000000000..48b73f44df4ca1f7e534cc8cb0b427821750bf3b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilaslr.f @@ -0,0 +1,121 @@ +*> \brief \b ILASLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILASLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILASLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* REAL A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILASLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILASLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + REAL A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILASLR = M + ELSEIF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILASLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILASLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILASLR = MAX( ILASLR, I ) + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlc.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlc.f new file mode 100644 index 0000000000000000000000000000000000000000..15b149022a1a9c01a960504ccea50ab60f97ea79 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlc.f @@ -0,0 +1,118 @@ +*> \brief \b ILAZLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILAZLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILAZLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILAZLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILAZLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ZERO + PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILAZLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILAZLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILAZLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILAZLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlr.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlr.f new file mode 100644 index 0000000000000000000000000000000000000000..b2ab943ca0a2b9b84c0c6a92e46b1569c8b582a9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/ilazlr.f @@ -0,0 +1,121 @@ +*> \brief \b ILAZLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILAZLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILAZLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILAZLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILAZLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ZERO + PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILAZLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILAZLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILAZLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILAZLR = MAX( ILAZLR, I ) + END DO + END IF + RETURN + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lapack_common.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lapack_common.h new file mode 100644 index 0000000000000000000000000000000000000000..c872a813e6f573e32a7f2277fd4c85a1540fb1f2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lapack_common.h @@ -0,0 +1,29 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_LAPACK_COMMON_H +#define EIGEN_LAPACK_COMMON_H + +#include "../blas/common.h" +#include "../Eigen/src/misc/lapack.h" + +#define EIGEN_LAPACK_FUNC(FUNC,ARGLIST) \ + extern "C" { int EIGEN_BLAS_FUNC(FUNC) ARGLIST; } \ + int EIGEN_BLAS_FUNC(FUNC) ARGLIST + +typedef Eigen::Map > PivotsType; + +#if ISCOMPLEX +#define EIGEN_LAPACK_ARG_IF_COMPLEX(X) X, +#else +#define EIGEN_LAPACK_ARG_IF_COMPLEX(X) +#endif + + +#endif // EIGEN_LAPACK_COMMON_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lu.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lu.cpp new file mode 100644 index 0000000000000000000000000000000000000000..90cebe0f4801c40c5b5979b7eb0553952b880951 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/lu.cpp @@ -0,0 +1,89 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "common.h" +#include + +// computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges +EIGEN_LAPACK_FUNC(getrf,(int *m, int *n, RealScalar *pa, int *lda, int *ipiv, int *info)) +{ + *info = 0; + if(*m<0) *info = -1; + else if(*n<0) *info = -2; + else if(*lda(pa); + int nb_transpositions; + int ret = int(Eigen::internal::partial_lu_impl + ::blocked_lu(*m, *n, a, *lda, ipiv, nb_transpositions)); + + for(int i=0; i=0) + *info = ret+1; + + return 0; +} + +//GETRS solves a system of linear equations +// A * X = B or A' * X = B +// with a general N-by-N matrix A using the LU factorization computed by GETRF +EIGEN_LAPACK_FUNC(getrs,(char *trans, int *n, int *nrhs, RealScalar *pa, int *lda, int *ipiv, RealScalar *pb, int *ldb, int *info)) +{ + *info = 0; + if(OP(*trans)==INVALID) *info = -1; + else if(*n<0) *info = -2; + else if(*nrhs<0) *info = -3; + else if(*lda(pa); + Scalar* b = reinterpret_cast(pb); + MatrixType lu(a,*n,*n,*lda); + MatrixType B(b,*n,*nrhs,*ldb); + + for(int i=0; i<*n; ++i) + ipiv[i]--; + if(OP(*trans)==NOTR) + { + B = PivotsType(ipiv,*n) * B; + lu.triangularView().solveInPlace(B); + lu.triangularView().solveInPlace(B); + } + else if(OP(*trans)==TR) + { + lu.triangularView().transpose().solveInPlace(B); + lu.triangularView().transpose().solveInPlace(B); + B = PivotsType(ipiv,*n).transpose() * B; + } + else if(OP(*trans)==ADJ) + { + lu.triangularView().adjoint().solveInPlace(B); + lu.triangularView().adjoint().solveInPlace(B); + B = PivotsType(ipiv,*n).transpose() * B; + } + for(int i=0; i<*n; ++i) + ipiv[i]++; + + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/second_NONE.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/second_NONE.f new file mode 100644 index 0000000000000000000000000000000000000000..d3e6d3319b54f71589468653759f6ef63948029d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/second_NONE.f @@ -0,0 +1,52 @@ +*> \brief \b SECOND returns nothing +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* REAL FUNCTION SECOND( ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SECOND returns nothing instead of returning the user time for a process in seconds. +*> If you are using that routine, it means that neither EXTERNAL ETIME, +*> EXTERNAL ETIME_, INTERNAL ETIME, INTERNAL CPU_TIME is available on +*> your machine. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SECOND( ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* ===================================================================== +* + SECOND = 0.0E+0 + RETURN +* +* End of SECOND +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/single.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/single.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c7da3effad2a095d0c5a279418b6af68eee42897 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/single.cpp @@ -0,0 +1,18 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define SCALAR float +#define SCALAR_SUFFIX s +#define SCALAR_SUFFIX_UP "S" +#define ISCOMPLEX 0 + +#include "cholesky.cpp" +#include "lu.cpp" +#include "eigenvalues.cpp" +#include "svd.cpp" diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/sladiv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/sladiv.f new file mode 100644 index 0000000000000000000000000000000000000000..da3afa36b83d2eef45c409874a8454cd7551a14e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/sladiv.f @@ -0,0 +1,128 @@ +*> \brief \b SLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLADIV( A, B, C, D, P, Q ) +* +* .. Scalar Arguments .. +* REAL A, B, C, D, P, Q +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLADIV performs complex division in real arithmetic +*> +*> a + i*b +*> p + i*q = --------- +*> c + i*d +*> +*> The algorithm is due to Robert L. Smith and can be found +*> in D. Knuth, The art of Computer Programming, Vol.2, p.195 +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is REAL +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is REAL +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL +*> The scalars a, b, c, and d in the above expression. +*> \endverbatim +*> +*> \param[out] P +*> \verbatim +*> P is REAL +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is REAL +*> The scalars p and q in the above expression. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE SLADIV( A, B, C, D, P, Q ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL A, B, C, D, P, Q +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + REAL E, F +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + IF( ABS( D ).LT.ABS( C ) ) THEN + E = D / C + F = C + D*E + P = ( A+B*E ) / F + Q = ( B-A*E ) / F + ELSE + E = C / D + F = D + C*E + P = ( B+A*E ) / F + Q = ( -A+B*E ) / F + END IF +* + RETURN +* +* End of SLADIV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slamch.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slamch.f new file mode 100644 index 0000000000000000000000000000000000000000..4bffad0eb67cf4cc45dacf7302149caea0f19e9c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slamch.f @@ -0,0 +1,192 @@ +*> \brief \b SLAMCH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* REAL FUNCTION SLAMCH( CMACH ) +* +* .. Scalar Arguments .. +* CHARACTER CMACH +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAMCH determines single precision machine parameters. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CMACH +*> \verbatim +*> Specifies the value to be returned by SLAMCH: +*> = 'E' or 'e', SLAMCH := eps +*> = 'S' or 's , SLAMCH := sfmin +*> = 'B' or 'b', SLAMCH := base +*> = 'P' or 'p', SLAMCH := eps*base +*> = 'N' or 'n', SLAMCH := t +*> = 'R' or 'r', SLAMCH := rnd +*> = 'M' or 'm', SLAMCH := emin +*> = 'U' or 'u', SLAMCH := rmin +*> = 'L' or 'l', SLAMCH := emax +*> = 'O' or 'o', SLAMCH := rmax +*> where +*> eps = relative machine precision +*> sfmin = safe minimum, such that 1/sfmin does not overflow +*> base = base of the machine +*> prec = eps*base +*> t = number of (base) digits in the mantissa +*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise +*> emin = minimum exponent before (gradual) underflow +*> rmin = underflow threshold - base**(emin-1) +*> emax = largest exponent before overflow +*> rmax = overflow threshold - (base**emax)*(1-eps) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAMCH( CMACH ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CMACH +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + REAL RND, EPS, SFMIN, SMALL, RMACH +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, + $ MINEXPONENT, RADIX, TINY +* .. +* .. Executable Statements .. +* +* +* Assume rounding, not chopping. Always. +* + RND = ONE +* + IF( ONE.EQ.RND ) THEN + EPS = EPSILON(ZERO) * 0.5 + ELSE + EPS = EPSILON(ZERO) + END IF +* + IF( LSAME( CMACH, 'E' ) ) THEN + RMACH = EPS + ELSE IF( LSAME( CMACH, 'S' ) ) THEN + SFMIN = TINY(ZERO) + SMALL = ONE / HUGE(ZERO) + IF( SMALL.GE.SFMIN ) THEN +* +* Use SMALL plus a bit, to avoid the possibility of rounding +* causing overflow when computing 1/sfmin. +* + SFMIN = SMALL*( ONE+EPS ) + END IF + RMACH = SFMIN + ELSE IF( LSAME( CMACH, 'B' ) ) THEN + RMACH = RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'P' ) ) THEN + RMACH = EPS * RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'N' ) ) THEN + RMACH = DIGITS(ZERO) + ELSE IF( LSAME( CMACH, 'R' ) ) THEN + RMACH = RND + ELSE IF( LSAME( CMACH, 'M' ) ) THEN + RMACH = MINEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'U' ) ) THEN + RMACH = tiny(zero) + ELSE IF( LSAME( CMACH, 'L' ) ) THEN + RMACH = MAXEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'O' ) ) THEN + RMACH = HUGE(ZERO) + ELSE + RMACH = ZERO + END IF +* + SLAMCH = RMACH + RETURN +* +* End of SLAMCH +* + END +************************************************************************ +*> \brief \b SLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> SLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date November 2011 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> The values A and B. +*> \endverbatim +*> +* + REAL FUNCTION SLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + REAL A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + SLAMC3 = A + B +* + RETURN +* +* End of SLAMC3 +* + END +* +************************************************************************ diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy2.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy2.f new file mode 100644 index 0000000000000000000000000000000000000000..1f6b1ca4f39da6bf3c61110244b39f519e981e62 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy2.f @@ -0,0 +1,104 @@ +*> \brief \b SLAPY2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLAPY2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* REAL FUNCTION SLAPY2( X, Y ) +* +* .. Scalar Arguments .. +* REAL X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary +*> overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is REAL +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL +*> X and Y specify the values x and y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAPY2( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL X, Y +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E0 ) + REAL ONE + PARAMETER ( ONE = 1.0E0 ) +* .. +* .. Local Scalars .. + REAL W, XABS, YABS, Z +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + W = MAX( XABS, YABS ) + Z = MIN( XABS, YABS ) + IF( Z.EQ.ZERO ) THEN + SLAPY2 = W + ELSE + SLAPY2 = W*SQRT( ONE+( Z / W )**2 ) + END IF + RETURN +* +* End of SLAPY2 +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy3.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy3.f new file mode 100644 index 0000000000000000000000000000000000000000..aa2f5bfc4d3478e9c1b564cc5ae1b6734d927ad6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slapy3.f @@ -0,0 +1,111 @@ +*> \brief \b SLAPY3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLAPY3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* REAL FUNCTION SLAPY3( X, Y, Z ) +* +* .. Scalar Arguments .. +* REAL X, Y, Z +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause +*> unnecessary overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is REAL +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is REAL +*> X, Y and Z specify the values x, y and z. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAPY3( X, Y, Z ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL X, Y, Z +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E0 ) +* .. +* .. Local Scalars .. + REAL W, XABS, YABS, ZABS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + ZABS = ABS( Z ) + W = MAX( XABS, YABS, ZABS ) + IF( W.EQ.ZERO ) THEN +* W can be zero for max(0,nan,0) +* adding all three entries together will make sure +* NaN will not disappear. + SLAPY3 = XABS + YABS + ZABS + ELSE + SLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ + $ ( ZABS / W )**2 ) + END IF + RETURN +* +* End of SLAPY3 +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarf.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarf.f new file mode 100644 index 0000000000000000000000000000000000000000..8a8ff308ea595a8875225ac44a8fba4b172ff857 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarf.f @@ -0,0 +1,227 @@ +*> \brief \b SLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLARF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER SIDE +* INTEGER INCV, LDC, M, N +* REAL TAU +* .. +* .. Array Arguments .. +* REAL C( LDC, * ), V( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLARF applies a real elementary reflector H to a real m by n matrix +*> C, from either the left or the right. H is represented in the form +*> +*> H = I - tau * v * v**T +*> +*> where tau is a real scalar and v is a real vector. +*> +*> If tau = 0, then H is taken to be the unit matrix. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': form H * C +*> = 'R': form C * H +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is REAL array, dimension +*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' +*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' +*> The vector v in the representation of H. V is not used if +*> TAU = 0. +*> \endverbatim +*> +*> \param[in] INCV +*> \verbatim +*> INCV is INTEGER +*> The increment between elements of v. INCV <> 0. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is REAL +*> The value tau in the representation of H. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array, dimension (LDC,N) +*> On entry, the m by n matrix C. +*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', +*> or C * H if SIDE = 'R'. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension +*> (N) if SIDE = 'L' +*> or (M) if SIDE = 'R' +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER SIDE + INTEGER INCV, LDC, M, N + REAL TAU +* .. +* .. Array Arguments .. + REAL C( LDC, * ), V( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + LOGICAL APPLYLEFT + INTEGER I, LASTV, LASTC +* .. +* .. External Subroutines .. + EXTERNAL SGEMV, SGER +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILASLR, ILASLC + EXTERNAL LSAME, ILASLR, ILASLC +* .. +* .. Executable Statements .. +* + APPLYLEFT = LSAME( SIDE, 'L' ) + LASTV = 0 + LASTC = 0 + IF( TAU.NE.ZERO ) THEN +! Set up variables for scanning V. LASTV begins pointing to the end +! of V. + IF( APPLYLEFT ) THEN + LASTV = M + ELSE + LASTV = N + END IF + IF( INCV.GT.0 ) THEN + I = 1 + (LASTV-1) * INCV + ELSE + I = 1 + END IF +! Look for the last non-zero row in V. + DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) + LASTV = LASTV - 1 + I = I - INCV + END DO + IF( APPLYLEFT ) THEN +! Scan for the last non-zero column in C(1:lastv,:). + LASTC = ILASLC(LASTV, N, C, LDC) + ELSE +! Scan for the last non-zero row in C(:,1:lastv). + LASTC = ILASLR(M, LASTV, C, LDC) + END IF + END IF +! Note that lastc.eq.0 renders the BLAS operations null; no special +! case is needed at this level. + IF( APPLYLEFT ) THEN +* +* Form H * C +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) +* + CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, + $ ZERO, WORK, 1 ) +* +* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T +* + CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) + END IF + ELSE +* +* Form C * H +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) +* + CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, + $ V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T +* + CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) + END IF + END IF + RETURN +* +* End of SLARF +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfb.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfb.f new file mode 100644 index 0000000000000000000000000000000000000000..eb95990b37e5618178e0f2000036383677fbf17f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfb.f @@ -0,0 +1,763 @@ +*> \brief \b SLARFB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLARFB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, +* T, LDT, C, LDC, WORK, LDWORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, SIDE, STOREV, TRANS +* INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. +* REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), +* $ WORK( LDWORK, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLARFB applies a real block reflector H or its transpose H**T to a +*> real m by n matrix C, from either the left or the right. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': apply H or H**T from the Left +*> = 'R': apply H or H**T from the Right +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': apply H (No transpose) +*> = 'T': apply H**T (Transpose) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Indicates how H is formed from a product of elementary +*> reflectors +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Indicates how the vectors which define the elementary +*> reflectors are stored: +*> = 'C': Columnwise +*> = 'R': Rowwise +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the matrix T (= the number of elementary +*> reflectors whose product defines the block reflector). +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is REAL array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,M) if STOREV = 'R' and SIDE = 'L' +*> (LDV,N) if STOREV = 'R' and SIDE = 'R' +*> The matrix V. See Further Details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); +*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); +*> if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] T +*> \verbatim +*> T is REAL array, dimension (LDT,K) +*> The triangular k by k matrix T in the representation of the +*> block reflector. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is REAL array, dimension (LDC,N) +*> On entry, the m by n matrix C. +*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (LDWORK,K) +*> \endverbatim +*> +*> \param[in] LDWORK +*> \verbatim +*> LDWORK is INTEGER +*> The leading dimension of the array WORK. +*> If SIDE = 'L', LDWORK >= max(1,N); +*> if SIDE = 'R', LDWORK >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, + $ T, LDT, C, LDC, WORK, LDWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, SIDE, STOREV, TRANS + INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. + REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), + $ WORK( LDWORK, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE + PARAMETER ( ONE = 1.0E+0 ) +* .. +* .. Local Scalars .. + CHARACTER TRANST + INTEGER I, J, LASTV, LASTC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILASLR, ILASLC + EXTERNAL LSAME, ILASLR, ILASLC +* .. +* .. External Subroutines .. + EXTERNAL SCOPY, SGEMM, STRMM +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.LE.0 .OR. N.LE.0 ) + $ RETURN +* + IF( LSAME( TRANS, 'N' ) ) THEN + TRANST = 'T' + ELSE + TRANST = 'N' + END IF +* + IF( LSAME( STOREV, 'C' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 ) (first K rows) +* ( V2 ) +* where V1 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) + LASTC = ILASLC( LASTV, N, C, LDC ) +* +* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) +* +* W := C1**T +* + DO 10 J = 1, K + CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + 10 CONTINUE +* +* W := W * V1 +* + CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**T *V2 +* + CALL SGEMM( 'Transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2 * W**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, + $ C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1**T +* + CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**T +* + DO 30 J = 1, K + DO 20 I = 1, LASTC + C( J, I ) = C( J, I ) - WORK( I, J ) + 20 CONTINUE + 30 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) + LASTC = ILASLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C1 +* + DO 40 J = 1, K + CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 40 CONTINUE +* +* W := W * V1 +* + CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2 +* + CALL SGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, + $ C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1**T +* + CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 60 J = 1, K + DO 50 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 50 CONTINUE + 60 CONTINUE + END IF +* + ELSE +* +* Let V = ( V1 ) +* ( V2 ) (last K rows) +* where V2 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) + LASTC = ILASLC( LASTV, N, C, LDC ) +* +* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) +* +* W := C2**T +* + DO 70 J = 1, K + CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + 70 CONTINUE +* +* W := W * V2 +* + CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**T*V1 +* + CALL SGEMM( 'Transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1 * W**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**T +* + CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**T +* + DO 90 J = 1, K + DO 80 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) + 80 CONTINUE + 90 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) + LASTC = ILASLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C2 +* + DO 100 J = 1, K + CALL SCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) + 100 CONTINUE +* +* W := W * V2 +* + CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1 +* + CALL SGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**T +* + CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W +* + DO 120 J = 1, K + DO 110 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J) + 110 CONTINUE + 120 CONTINUE + END IF + END IF +* + ELSE IF( LSAME( STOREV, 'R' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 V2 ) (V1: first K columns) +* where V1 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) + LASTC = ILASLC( LASTV, N, C, LDC ) +* +* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) +* +* W := C1**T +* + DO 130 J = 1, K + CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + 130 CONTINUE +* +* W := W * V1**T +* + CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**T*V2**T +* + CALL SGEMM( 'Transpose', 'Transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**T * W**T +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2**T * W**T +* + CALL SGEMM( 'Transpose', 'Transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**T +* + DO 150 J = 1, K + DO 140 I = 1, LASTC + C( J, I ) = C( J, I ) - WORK( I, J ) + 140 CONTINUE + 150 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) + LASTC = ILASLR( M, LASTV, C, LDC ) +* +* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) +* +* W := C1 +* + DO 160 J = 1, K + CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 160 CONTINUE +* +* W := W * V1**T +* + CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2 +* + CALL SGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 180 J = 1, K + DO 170 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 170 CONTINUE + 180 CONTINUE +* + END IF +* + ELSE +* +* Let V = ( V1 V2 ) (V2: last K columns) +* where V2 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**T * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) + LASTC = ILASLC( LASTV, N, C, LDC ) +* +* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) +* +* W := C2**T +* + DO 190 J = 1, K + CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + 190 CONTINUE +* +* W := W * V2**T +* + CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**T * V1**T +* + CALL SGEMM( 'Transpose', 'Transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**T or W * T +* + CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**T * W**T +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1**T * W**T +* + CALL SGEMM( 'Transpose', 'Transpose', + $ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**T +* + DO 210 J = 1, K + DO 200 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) + 200 CONTINUE + 210 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**T where C = ( C1 C2 ) +* + LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) + LASTC = ILASLR( M, LASTV, C, LDC ) +* +* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) +* +* W := C2 +* + DO 220 J = 1, K + CALL SCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 220 CONTINUE +* +* W := W * V2**T +* + CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1**T +* + CALL SGEMM( 'No transpose', 'Transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**T +* + CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1 +* + CALL SGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 240 J = 1, K + DO 230 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) + $ - WORK( I, J ) + 230 CONTINUE + 240 CONTINUE +* + END IF +* + END IF + END IF +* + RETURN +* +* End of SLARFB +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfg.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfg.f new file mode 100644 index 0000000000000000000000000000000000000000..4f10ffcafb1ad8ac830a4e34cf7c0da6a6cfde95 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarfg.f @@ -0,0 +1,196 @@ +*> \brief \b SLARFG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLARFG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* REAL ALPHA, TAU +* .. +* .. Array Arguments .. +* REAL X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLARFG generates a real elementary reflector H of order n, such +*> that +*> +*> H * ( alpha ) = ( beta ), H**T * H = I. +*> ( x ) ( 0 ) +*> +*> where alpha and beta are scalars, and x is an (n-1)-element real +*> vector. H is represented in the form +*> +*> H = I - tau * ( 1 ) * ( 1 v**T ) , +*> ( v ) +*> +*> where tau is a real scalar and v is a real (n-1)-element +*> vector. +*> +*> If the elements of x are all zero, then tau = 0 and H is taken to be +*> the unit matrix. +*> +*> Otherwise 1 <= tau <= 2. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the elementary reflector. +*> \endverbatim +*> +*> \param[in,out] ALPHA +*> \verbatim +*> ALPHA is REAL +*> On entry, the value alpha. +*> On exit, it is overwritten with the value beta. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is REAL array, dimension +*> (1+(N-2)*abs(INCX)) +*> On entry, the vector x. +*> On exit, it is overwritten with the vector v. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between elements of X. INCX > 0. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is REAL +*> The value tau. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + REAL ALPHA, TAU +* .. +* .. Array Arguments .. + REAL X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER J, KNT + REAL BETA, RSAFMN, SAFMIN, XNORM +* .. +* .. External Functions .. + REAL SLAMCH, SLAPY2, SNRM2 + EXTERNAL SLAMCH, SLAPY2, SNRM2 +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, SIGN +* .. +* .. External Subroutines .. + EXTERNAL SSCAL +* .. +* .. Executable Statements .. +* + IF( N.LE.1 ) THEN + TAU = ZERO + RETURN + END IF +* + XNORM = SNRM2( N-1, X, INCX ) +* + IF( XNORM.EQ.ZERO ) THEN +* +* H = I +* + TAU = ZERO + ELSE +* +* general case +* + BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA ) + SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' ) + KNT = 0 + IF( ABS( BETA ).LT.SAFMIN ) THEN +* +* XNORM, BETA may be inaccurate; scale X and recompute them +* + RSAFMN = ONE / SAFMIN + 10 CONTINUE + KNT = KNT + 1 + CALL SSCAL( N-1, RSAFMN, X, INCX ) + BETA = BETA*RSAFMN + ALPHA = ALPHA*RSAFMN + IF( ABS( BETA ).LT.SAFMIN ) + $ GO TO 10 +* +* New BETA is at most 1, at least SAFMIN +* + XNORM = SNRM2( N-1, X, INCX ) + BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA ) + END IF + TAU = ( BETA-ALPHA ) / BETA + CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) +* +* If ALPHA is subnormal, it may lose relative accuracy +* + DO 20 J = 1, KNT + BETA = BETA*SAFMIN + 20 CONTINUE + ALPHA = BETA + END IF +* + RETURN +* +* End of SLARFG +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarft.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarft.f new file mode 100644 index 0000000000000000000000000000000000000000..30b0668e4f7e59fd3fb5015a21fe9529c9666a98 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/slarft.f @@ -0,0 +1,326 @@ +*> \brief \b SLARFT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* REAL T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLARFT forms the triangular factor T of a real block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is REAL array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is REAL array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is REAL array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup realOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + REAL T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL SGEMV, STRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( I, PREVLASTV ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( I , J ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) +* + CALL SGEMV( 'Transpose', J-I, I-1, -TAU( I ), + $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, + $ T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T +* + CALL SGEMV( 'No transpose', I-1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), 1 ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL STRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( N-K+I , J ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) +* + CALL SGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), + $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, + $ T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T +* + CALL SGEMV( 'No transpose', K-I, N-K+I-J, + $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), 1 ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL STRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of SLARFT +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/svd.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/svd.cpp new file mode 100644 index 0000000000000000000000000000000000000000..77b302b6b4bac1c063b77d982f81a1340f6f3d37 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/svd.cpp @@ -0,0 +1,138 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "lapack_common.h" +#include + +// computes the singular values/vectors a general M-by-N matrix A using divide-and-conquer +EIGEN_LAPACK_FUNC(gesdd,(char *jobz, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork, + EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int * /*iwork*/, int *info)) +{ + // TODO exploit the work buffer + bool query_size = *lwork==-1; + int diag_size = (std::min)(*m,*n); + + *info = 0; + if(*jobz!='A' && *jobz!='S' && *jobz!='O' && *jobz!='N') *info = -1; + else if(*m<0) *info = -2; + else if(*n<0) *info = -3; + else if(*lda=*n && *ldvt<*n)) *info = -10; + + if(*info!=0) + { + int e = -*info; + return xerbla_(SCALAR_SUFFIX_UP"GESDD ", &e, 6); + } + + if(query_size) + { + *lwork = 0; + return 0; + } + + if(*n==0 || *m==0) + return 0; + + PlainMatrixType mat(*m,*n); + mat = matrix(a,*m,*n,*lda); + + int option = *jobz=='A' ? ComputeFullU|ComputeFullV + : *jobz=='S' ? ComputeThinU|ComputeThinV + : *jobz=='O' ? ComputeThinU|ComputeThinV + : 0; + + BDCSVD svd(mat,option); + + make_vector(s,diag_size) = svd.singularValues().head(diag_size); + + if(*jobz=='A') + { + matrix(u,*m,*m,*ldu) = svd.matrixU(); + matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint(); + } + else if(*jobz=='S') + { + matrix(u,*m,diag_size,*ldu) = svd.matrixU(); + matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint(); + } + else if(*jobz=='O' && *m>=*n) + { + matrix(a,*m,*n,*lda) = svd.matrixU(); + matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint(); + } + else if(*jobz=='O') + { + matrix(u,*m,*m,*ldu) = svd.matrixU(); + matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint(); + } + + return 0; +} + +// computes the singular values/vectors a general M-by-N matrix A using two sided jacobi algorithm +EIGEN_LAPACK_FUNC(gesvd,(char *jobu, char *jobv, int *m, int* n, Scalar* a, int *lda, RealScalar *s, Scalar *u, int *ldu, Scalar *vt, int *ldvt, Scalar* /*work*/, int* lwork, + EIGEN_LAPACK_ARG_IF_COMPLEX(RealScalar */*rwork*/) int *info)) +{ + // TODO exploit the work buffer + bool query_size = *lwork==-1; + int diag_size = (std::min)(*m,*n); + + *info = 0; + if( *jobu!='A' && *jobu!='S' && *jobu!='O' && *jobu!='N') *info = -1; + else if((*jobv!='A' && *jobv!='S' && *jobv!='O' && *jobv!='N') + || (*jobu=='O' && *jobv=='O')) *info = -2; + else if(*m<0) *info = -3; + else if(*n<0) *info = -4; + else if(*lda svd(mat,option); + + make_vector(s,diag_size) = svd.singularValues().head(diag_size); + { + if(*jobu=='A') matrix(u,*m,*m,*ldu) = svd.matrixU(); + else if(*jobu=='S') matrix(u,*m,diag_size,*ldu) = svd.matrixU(); + else if(*jobu=='O') matrix(a,*m,diag_size,*lda) = svd.matrixU(); + } + { + if(*jobv=='A') matrix(vt,*n,*n,*ldvt) = svd.matrixV().adjoint(); + else if(*jobv=='S') matrix(vt,diag_size,*n,*ldvt) = svd.matrixV().adjoint(); + else if(*jobv=='O') matrix(a,diag_size,*n,*lda) = svd.matrixV().adjoint(); + } + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlacgv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlacgv.f new file mode 100644 index 0000000000000000000000000000000000000000..16c2e2ed949d50fe908c95db8dbfd87eb8872960 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlacgv.f @@ -0,0 +1,116 @@ +*> \brief \b ZLACGV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLACGV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLACGV( N, X, INCX ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* .. +* .. Array Arguments .. +* COMPLEX*16 X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLACGV conjugates a complex vector of length N. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The length of the vector X. N >= 0. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension +*> (1+(N-1)*abs(INCX)) +*> On entry, the vector of length N to be conjugated. +*> On exit, X is overwritten with conjg(X). +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The spacing between successive elements of X. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + SUBROUTINE ZLACGV( N, X, INCX ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N +* .. +* .. Array Arguments .. + COMPLEX*16 X( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, IOFF +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* .. Executable Statements .. +* + IF( INCX.EQ.1 ) THEN + DO 10 I = 1, N + X( I ) = DCONJG( X( I ) ) + 10 CONTINUE + ELSE + IOFF = 1 + IF( INCX.LT.0 ) + $ IOFF = 1 - ( N-1 )*INCX + DO 20 I = 1, N + X( IOFF ) = DCONJG( X( IOFF ) ) + IOFF = IOFF + INCX + 20 CONTINUE + END IF + RETURN +* +* End of ZLACGV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zladiv.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zladiv.f new file mode 100644 index 0000000000000000000000000000000000000000..aa71db14af8bc1f0914b8aba08d17142fb0a01ff --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zladiv.f @@ -0,0 +1,97 @@ +*> \brief \b ZLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* COMPLEX*16 FUNCTION ZLADIV( X, Y ) +* +* .. Scalar Arguments .. +* COMPLEX*16 X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLADIV := X / Y, where X and Y are complex. The computation of X / Y +*> will not overflow on an intermediary step unless the results +*> overflows. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 +*> The complex scalars X and Y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + COMPLEX*16 FUNCTION ZLADIV( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + COMPLEX*16 X, Y +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION ZI, ZR +* .. +* .. External Subroutines .. + EXTERNAL DLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE, DCMPLX, DIMAG +* .. +* .. Executable Statements .. +* + CALL DLADIV( DBLE( X ), DIMAG( X ), DBLE( Y ), DIMAG( Y ), ZR, + $ ZI ) + ZLADIV = DCMPLX( ZR, ZI ) +* + RETURN +* +* End of ZLADIV +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarf.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarf.f new file mode 100644 index 0000000000000000000000000000000000000000..53f314d64531d82df28e078aa5561cc0437ffb28 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarf.f @@ -0,0 +1,232 @@ +*> \brief \b ZLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* .. Scalar Arguments .. +* CHARACTER SIDE +* INTEGER INCV, LDC, M, N +* COMPLEX*16 TAU +* .. +* .. Array Arguments .. +* COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARF applies a complex elementary reflector H to a complex M-by-N +*> matrix C, from either the left or the right. H is represented in the +*> form +*> +*> H = I - tau * v * v**H +*> +*> where tau is a complex scalar and v is a complex vector. +*> +*> If tau = 0, then H is taken to be the unit matrix. +*> +*> To apply H**H, supply conjg(tau) instead +*> tau. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': form H * C +*> = 'R': form C * H +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' +*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' +*> The vector v in the representation of H. V is not used if +*> TAU = 0. +*> \endverbatim +*> +*> \param[in] INCV +*> \verbatim +*> INCV is INTEGER +*> The increment between elements of v. INCV <> 0. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX*16 +*> The value tau in the representation of H. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array, dimension (LDC,N) +*> On entry, the M-by-N matrix C. +*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', +*> or C * H if SIDE = 'R'. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension +*> (N) if SIDE = 'L' +*> or (M) if SIDE = 'R' +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER SIDE + INTEGER INCV, LDC, M, N + COMPLEX*16 TAU +* .. +* .. Array Arguments .. + COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE, ZERO + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), + $ ZERO = ( 0.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL APPLYLEFT + INTEGER I, LASTV, LASTC +* .. +* .. External Subroutines .. + EXTERNAL ZGEMV, ZGERC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAZLR, ILAZLC + EXTERNAL LSAME, ILAZLR, ILAZLC +* .. +* .. Executable Statements .. +* + APPLYLEFT = LSAME( SIDE, 'L' ) + LASTV = 0 + LASTC = 0 + IF( TAU.NE.ZERO ) THEN +* Set up variables for scanning V. LASTV begins pointing to the end +* of V. + IF( APPLYLEFT ) THEN + LASTV = M + ELSE + LASTV = N + END IF + IF( INCV.GT.0 ) THEN + I = 1 + (LASTV-1) * INCV + ELSE + I = 1 + END IF +* Look for the last non-zero row in V. + DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) + LASTV = LASTV - 1 + I = I - INCV + END DO + IF( APPLYLEFT ) THEN +* Scan for the last non-zero column in C(1:lastv,:). + LASTC = ILAZLC(LASTV, N, C, LDC) + ELSE +* Scan for the last non-zero row in C(:,1:lastv). + LASTC = ILAZLR(M, LASTV, C, LDC) + END IF + END IF +* Note that lastc.eq.0 renders the BLAS operations null; no special +* case is needed at this level. + IF( APPLYLEFT ) THEN +* +* Form H * C +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) +* + CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, + $ C, LDC, V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H +* + CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) + END IF + ELSE +* +* Form C * H +* + IF( LASTV.GT.0 ) THEN +* +* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) +* + CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, + $ V, INCV, ZERO, WORK, 1 ) +* +* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H +* + CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) + END IF + END IF + RETURN +* +* End of ZLARF +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfb.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfb.f new file mode 100644 index 0000000000000000000000000000000000000000..30fc4b9407aedb3025a490959b18a5298067f6ed --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfb.f @@ -0,0 +1,774 @@ +*> \brief \b ZLARFB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, +* T, LDT, C, LDC, WORK, LDWORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, SIDE, STOREV, TRANS +* INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. +* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), +* $ WORK( LDWORK, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFB applies a complex block reflector H or its transpose H**H to a +*> complex M-by-N matrix C, from either the left or the right. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': apply H or H**H from the Left +*> = 'R': apply H or H**H from the Right +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': apply H (No transpose) +*> = 'C': apply H**H (Conjugate transpose) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Indicates how H is formed from a product of elementary +*> reflectors +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Indicates how the vectors which define the elementary +*> reflectors are stored: +*> = 'C': Columnwise +*> = 'R': Rowwise +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the matrix T (= the number of elementary +*> reflectors whose product defines the block reflector). +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,M) if STOREV = 'R' and SIDE = 'L' +*> (LDV,N) if STOREV = 'R' and SIDE = 'R' +*> See Further Details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); +*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); +*> if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] T +*> \verbatim +*> T is COMPLEX*16 array, dimension (LDT,K) +*> The triangular K-by-K matrix T in the representation of the +*> block reflector. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array, dimension (LDC,N) +*> On entry, the M-by-N matrix C. +*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (LDWORK,K) +*> \endverbatim +*> +*> \param[in] LDWORK +*> \verbatim +*> LDWORK is INTEGER +*> The leading dimension of the array WORK. +*> If SIDE = 'L', LDWORK >= max(1,N); +*> if SIDE = 'R', LDWORK >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, + $ T, LDT, C, LDC, WORK, LDWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, SIDE, STOREV, TRANS + INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), + $ WORK( LDWORK, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + CHARACTER TRANST + INTEGER I, J, LASTV, LASTC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAZLR, ILAZLC + EXTERNAL LSAME, ILAZLR, ILAZLC +* .. +* .. External Subroutines .. + EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.LE.0 .OR. N.LE.0 ) + $ RETURN +* + IF( LSAME( TRANS, 'N' ) ) THEN + TRANST = 'C' + ELSE + TRANST = 'N' + END IF +* + IF( LSAME( STOREV, 'C' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 ) (first K rows) +* ( V2 ) +* where V1 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILAZLR( M, K, V, LDV ) ) + LASTC = ILAZLC( LASTV, N, C, LDC ) +* +* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) +* +* W := C1**H +* + DO 10 J = 1, K + CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) + 10 CONTINUE +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**H *V2 +* + CALL ZGEMM( 'Conjugate transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC, + $ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**H +* + IF( M.GT.K ) THEN +* +* C2 := C2 - V2 * W**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1**H +* + CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**H +* + DO 30 J = 1, K + DO 20 I = 1, LASTC + C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) + 20 CONTINUE + 30 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILAZLR( N, K, V, LDV ) ) + LASTC = ILAZLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C1 +* + DO 40 J = 1, K + CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 40 CONTINUE +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2 +* + CALL ZGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**H +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1**H +* + CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 60 J = 1, K + DO 50 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 50 CONTINUE + 60 CONTINUE + END IF +* + ELSE +* +* Let V = ( V1 ) +* ( V2 ) (last K rows) +* where V2 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILAZLR( M, K, V, LDV ) ) + LASTC = ILAZLC( LASTV, N, C, LDC ) +* +* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) +* +* W := C2**H +* + DO 70 J = 1, K + CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) + 70 CONTINUE +* +* W := W * V2 +* + CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**H*V1 +* + CALL ZGEMM( 'Conjugate transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C, LDC, V, LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V * W**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1 * W**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V, LDV, WORK, LDWORK, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**H +* + CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**H +* + DO 90 J = 1, K + DO 80 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - + $ DCONJG( WORK( I, J ) ) + 80 CONTINUE + 90 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILAZLR( N, K, V, LDV ) ) + LASTC = ILAZLR( M, LASTV, C, LDC ) +* +* W := C * V = (C1*V1 + C2*V2) (stored in WORK) +* +* W := C2 +* + DO 100 J = 1, K + CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 100 CONTINUE +* +* W := W * V2 +* + CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1 +* + CALL ZGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2**H +* + CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W +* + DO 120 J = 1, K + DO 110 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) + $ - WORK( I, J ) + 110 CONTINUE + 120 CONTINUE + END IF + END IF +* + ELSE IF( LSAME( STOREV, 'R' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 V2 ) (V1: first K columns) +* where V1 is unit upper triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILAZLC( K, M, V, LDV ) ) + LASTC = ILAZLC( LASTV, N, C, LDC ) +* +* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) +* +* W := C1**H +* + DO 130 J = 1, K + CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) + 130 CONTINUE +* +* W := W * V1**H +* + CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**H*V2**H +* + CALL ZGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTC, K, LASTV-K, + $ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, + $ ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**H * W**H +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - V2**H * W**H +* + CALL ZGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTV-K, LASTC, K, + $ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**H +* + DO 150 J = 1, K + DO 140 I = 1, LASTC + C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) + 140 CONTINUE + 150 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILAZLC( K, N, V, LDV ) ) + LASTC = ILAZLR( M, LASTV, C, LDC ) +* +* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) +* +* W := C1 +* + DO 160 J = 1, K + CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 160 CONTINUE +* +* W := W * V1**H +* + CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC, + $ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2 +* + CALL ZGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + END IF +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 180 J = 1, K + DO 170 I = 1, LASTC + C( I, J ) = C( I, J ) - WORK( I, J ) + 170 CONTINUE + 180 CONTINUE +* + END IF +* + ELSE +* +* Let V = ( V1 V2 ) (V2: last K columns) +* where V2 is unit lower triangular. +* + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form H * C or H**H * C where C = ( C1 ) +* ( C2 ) +* + LASTV = MAX( K, ILAZLC( K, M, V, LDV ) ) + LASTC = ILAZLC( LASTV, N, C, LDC ) +* +* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) +* +* W := C2**H +* + DO 190 J = 1, K + CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, + $ WORK( 1, J ), 1 ) + CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) + 190 CONTINUE +* +* W := W * V2**H +* + CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1**H * V1**H +* + CALL ZGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTC, K, LASTV-K, + $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) + END IF +* +* W := W * T**H or W * T +* + CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - V**H * W**H +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - V1**H * W**H +* + CALL ZGEMM( 'Conjugate transpose', + $ 'Conjugate transpose', LASTV-K, LASTC, K, + $ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C2 := C2 - W**H +* + DO 210 J = 1, K + DO 200 I = 1, LASTC + C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - + $ DCONJG( WORK( I, J ) ) + 200 CONTINUE + 210 CONTINUE +* + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form C * H or C * H**H where C = ( C1 C2 ) +* + LASTV = MAX( K, ILAZLC( K, N, V, LDV ) ) + LASTC = ILAZLR( M, LASTV, C, LDC ) +* +* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) +* +* W := C2 +* + DO 220 J = 1, K + CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1, + $ WORK( 1, J ), 1 ) + 220 CONTINUE +* +* W := W * V2**H +* + CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C1 * V1**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE, + $ WORK, LDWORK ) + END IF +* +* W := W * T or W * T**H +* + CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', + $ LASTC, K, ONE, T, LDT, WORK, LDWORK ) +* +* C := C - W * V +* + IF( LASTV.GT.K ) THEN +* +* C1 := C1 - W * V1 +* + CALL ZGEMM( 'No transpose', 'No transpose', + $ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, + $ ONE, C, LDC ) + END IF +* +* W := W * V2 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, + $ WORK, LDWORK ) +* +* C1 := C1 - W +* + DO 240 J = 1, K + DO 230 I = 1, LASTC + C( I, LASTV-K+J ) = C( I, LASTV-K+J ) + $ - WORK( I, J ) + 230 CONTINUE + 240 CONTINUE +* + END IF +* + END IF + END IF +* + RETURN +* +* End of ZLARFB +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfg.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfg.f new file mode 100644 index 0000000000000000000000000000000000000000..a90ae9f745cbb13dff9f16efa0216ab78e4bc090 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarfg.f @@ -0,0 +1,203 @@ +*> \brief \b ZLARFG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* COMPLEX*16 ALPHA, TAU +* .. +* .. Array Arguments .. +* COMPLEX*16 X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFG generates a complex elementary reflector H of order n, such +*> that +*> +*> H**H * ( alpha ) = ( beta ), H**H * H = I. +*> ( x ) ( 0 ) +*> +*> where alpha and beta are scalars, with beta real, and x is an +*> (n-1)-element complex vector. H is represented in the form +*> +*> H = I - tau * ( 1 ) * ( 1 v**H ) , +*> ( v ) +*> +*> where tau is a complex scalar and v is a complex (n-1)-element +*> vector. Note that H is not hermitian. +*> +*> If the elements of x are all zero and alpha is real, then tau = 0 +*> and H is taken to be the unit matrix. +*> +*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the elementary reflector. +*> \endverbatim +*> +*> \param[in,out] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, the value alpha. +*> On exit, it is overwritten with the value beta. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension +*> (1+(N-2)*abs(INCX)) +*> On entry, the vector x. +*> On exit, it is overwritten with the vector v. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between elements of X. INCX > 0. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX*16 +*> The value tau. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + COMPLEX*16 ALPHA, TAU +* .. +* .. Array Arguments .. + COMPLEX*16 X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER J, KNT + DOUBLE PRECISION ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH, DLAPY3, DZNRM2 + COMPLEX*16 ZLADIV + EXTERNAL DLAMCH, DLAPY3, DZNRM2, ZLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DCMPLX, DIMAG, SIGN +* .. +* .. External Subroutines .. + EXTERNAL ZDSCAL, ZSCAL +* .. +* .. Executable Statements .. +* + IF( N.LE.0 ) THEN + TAU = ZERO + RETURN + END IF +* + XNORM = DZNRM2( N-1, X, INCX ) + ALPHR = DBLE( ALPHA ) + ALPHI = DIMAG( ALPHA ) +* + IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN +* +* H = I +* + TAU = ZERO + ELSE +* +* general case +* + BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) + RSAFMN = ONE / SAFMIN +* + KNT = 0 + IF( ABS( BETA ).LT.SAFMIN ) THEN +* +* XNORM, BETA may be inaccurate; scale X and recompute them +* + 10 CONTINUE + KNT = KNT + 1 + CALL ZDSCAL( N-1, RSAFMN, X, INCX ) + BETA = BETA*RSAFMN + ALPHI = ALPHI*RSAFMN + ALPHR = ALPHR*RSAFMN + IF( ABS( BETA ).LT.SAFMIN ) + $ GO TO 10 +* +* New BETA is at most 1, at least SAFMIN +* + XNORM = DZNRM2( N-1, X, INCX ) + ALPHA = DCMPLX( ALPHR, ALPHI ) + BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + END IF + TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) + ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) + CALL ZSCAL( N-1, ALPHA, X, INCX ) +* +* If ALPHA is subnormal, it may lose relative accuracy +* + DO 20 J = 1, KNT + BETA = BETA*SAFMIN + 20 CONTINUE + ALPHA = BETA + END IF +* + RETURN +* +* End of ZLARFG +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarft.f b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarft.f new file mode 100644 index 0000000000000000000000000000000000000000..6a6151fd0325d8bba5cf479c7660cbcc56c91bdb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/lapack/zlarft.f @@ -0,0 +1,327 @@ +*> \brief \b ZLARFT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFT forms the triangular factor T of a complex block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**H +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**H * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX*16 array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complex16OTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE, ZERO + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), + $ ZERO = ( 0.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL ZGEMV, ZLACGV, ZTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( PREVLASTV, I ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) +* + CALL ZGEMV( 'Conjugate transpose', J-I, I-1, + $ -TAU( I ), V( I+1, 1 ), LDV, + $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H +* + CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), LDT ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) +* + CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, + $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), + $ 1, ONE, T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H +* + CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), + $ V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), LDT ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of ZLARFT +* + END diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..0d9a631a9dd0d46b726703af0e51d5f49fddf029 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/CMakeLists.txt @@ -0,0 +1,6 @@ +get_property(EIGEN_TESTS_LIST GLOBAL PROPERTY EIGEN_TESTS_LIST) +configure_file(buildtests.in ${CMAKE_BINARY_DIR}/buildtests.sh @ONLY) + +configure_file(check.in ${CMAKE_BINARY_DIR}/check.sh COPYONLY) +configure_file(debug.in ${CMAKE_BINARY_DIR}/debug.sh COPYONLY) +configure_file(release.in ${CMAKE_BINARY_DIR}/release.sh COPYONLY) diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/buildtests.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/buildtests.in new file mode 100644 index 0000000000000000000000000000000000000000..ab9c18fb1d54c52ecb3f5ee61fffad8767721c83 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/buildtests.in @@ -0,0 +1,22 @@ +#!/bin/bash + +if [[ $# != 1 || $1 == *help ]] +then + echo "usage: $0 regexp" + echo " Builds tests matching the regexp." + echo " The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'." + echo " For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'" + exit 0 +fi + +TESTSLIST="@EIGEN_TESTS_LIST@" +targets_to_make=$(echo "$TESTSLIST" | grep -E "$1" | xargs echo) + +if [ -n "${EIGEN_MAKE_ARGS:+x}" ] +then + @CMAKE_MAKE_PROGRAM@ $targets_to_make ${EIGEN_MAKE_ARGS} +else + @CMAKE_MAKE_PROGRAM@ $targets_to_make @EIGEN_TEST_BUILD_FLAGS@ +fi +exit $? + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/cdashtesting.cmake.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/cdashtesting.cmake.in new file mode 100644 index 0000000000000000000000000000000000000000..0bf0fac2a2e179cd6ce7b4df436ead091cfd0161 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/cdashtesting.cmake.in @@ -0,0 +1,49 @@ + +set(CTEST_SOURCE_DIRECTORY "@CMAKE_SOURCE_DIR@") +set(CTEST_BINARY_DIRECTORY "@CMAKE_BINARY_DIR@") +set(CTEST_CMAKE_GENERATOR "@CMAKE_GENERATOR@") +set(CTEST_BUILD_NAME "@BUILDNAME@") +set(CTEST_SITE "@SITE@") + +set(MODEL Experimental) +if(${CTEST_SCRIPT_ARG} MATCHES Nightly) + set(MODEL Nightly) +elseif(${CTEST_SCRIPT_ARG} MATCHES Continuous) + set(MODEL Continuous) +endif() + +find_program(CTEST_GIT_COMMAND NAMES git) +set(CTEST_UPDATE_COMMAND "${CTEST_GIT_COMMAND}") + +ctest_start(${MODEL} ${CTEST_SOURCE_DIRECTORY} ${CTEST_BINARY_DIRECTORY}) + +ctest_update(SOURCE "${CTEST_SOURCE_DIRECTORY}") +ctest_submit(PARTS Update Notes) + +# to get CTEST_PROJECT_SUBPROJECTS definition: +include("${CTEST_SOURCE_DIRECTORY}/CTestConfig.cmake") + +foreach(subproject ${CTEST_PROJECT_SUBPROJECTS}) + message("") + message("Process ${subproject}") + + set_property(GLOBAL PROPERTY SubProject ${subproject}) + set_property(GLOBAL PROPERTY Label ${subproject}) + + ctest_configure(BUILD ${CTEST_BINARY_DIRECTORY} SOURCE ${CTEST_SOURCE_DIRECTORY} ) + ctest_submit(PARTS Configure) + + set(CTEST_BUILD_TARGET "Build${subproject}") + message("Build ${CTEST_BUILD_TARGET}") + ctest_build(BUILD "${CTEST_BINARY_DIRECTORY}" APPEND) + # builds target ${CTEST_BUILD_TARGET} + ctest_submit(PARTS Build) + + ctest_test(BUILD "${CTEST_BINARY_DIRECTORY}" INCLUDE_LABEL "${subproject}" ) + # runs only tests that have a LABELS property matching "${subproject}" + + ctest_coverage(BUILD "${CTEST_BINARY_DIRECTORY}" LABELS "${subproject}" ) + + ctest_submit(PARTS Test) + +endforeach() diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/check.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/check.in new file mode 100644 index 0000000000000000000000000000000000000000..7717e2d939b9ba33dcf91f855bc14787fdf5383f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/check.in @@ -0,0 +1,21 @@ +#!/bin/bash +# check : shorthand for make and ctest -R + +if [[ $# != 1 || $1 == *help ]] +then + echo "usage: $0 regexp" + echo " Builds and runs tests matching the regexp." + echo " The EIGEN_MAKE_ARGS environment variable allows to pass args to 'make'." + echo " For example, to launch 5 concurrent builds, use EIGEN_MAKE_ARGS='-j5'" + echo " The EIGEN_CTEST_ARGS environment variable allows to pass args to 'ctest'." + echo " For example, with CTest 2.8, you can use EIGEN_CTEST_ARGS='-j5'." + exit 0 +fi + +if [ -n "${EIGEN_CTEST_ARGS:+x}" ] +then + ./buildtests.sh "$1" && ctest -R "$1" ${EIGEN_CTEST_ARGS} +else + ./buildtests.sh "$1" && ctest -R "$1" +fi +exit $? diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/debug.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/debug.in new file mode 100644 index 0000000000000000000000000000000000000000..d339d3d1f9067ad52197ae05062aa36d94371506 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/debug.in @@ -0,0 +1,3 @@ +#!/bin/sh + +cmake -DCMAKE_BUILD_TYPE=Debug . diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_credits.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_credits.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f2e81631dd4b0118fdcb4844cb94e0c3b88538bf --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_credits.cpp @@ -0,0 +1,232 @@ +#include +#include +#include +#include +#include +#include +#include + +using namespace std; + +// this function takes a line that may contain a name and/or email address, +// and returns just the name, while fixing the "bad cases". +std::string contributor_name(const std::string& line) +{ + string result; + + // let's first take care of the case of isolated email addresses, like + // "user@localhost.localdomain" entries + if(line.find("markb@localhost.localdomain") != string::npos) + { + return "Mark Borgerding"; + } + + if(line.find("kayhman@contact.intra.cea.fr") != string::npos) + { + return "Guillaume Saupin"; + } + + // from there on we assume that we have a entry of the form + // either: + // Bla bli Blurp + // or: + // Bla bli Blurp + + size_t position_of_email_address = line.find_first_of('<'); + if(position_of_email_address != string::npos) + { + // there is an e-mail address in <...>. + + // Hauke once committed as "John Smith", fix that. + if(line.find("hauke.heibel") != string::npos) + result = "Hauke Heibel"; + else + { + // just remove the e-mail address + result = line.substr(0, position_of_email_address); + } + } + else + { + // there is no e-mail address in <...>. + + if(line.find("convert-repo") != string::npos) + result = ""; + else + result = line; + } + + // remove trailing spaces + size_t length = result.length(); + while(length >= 1 && result[length-1] == ' ') result.erase(--length); + + return result; +} + +// parses hg churn output to generate a contributors map. +map contributors_map_from_churn_output(const char *filename) +{ + map contributors_map; + + string line; + ifstream churn_out; + churn_out.open(filename, ios::in); + while(!getline(churn_out,line).eof()) + { + // remove the histograms "******" that hg churn may draw at the end of some lines + size_t first_star = line.find_first_of('*'); + if(first_star != string::npos) line.erase(first_star); + + // remove trailing spaces + size_t length = line.length(); + while(length >= 1 && line[length-1] == ' ') line.erase(--length); + + // now the last space indicates where the number starts + size_t last_space = line.find_last_of(' '); + + // get the number (of changesets or of modified lines for each contributor) + int number; + istringstream(line.substr(last_space+1)) >> number; + + // get the name of the contributor + line.erase(last_space); + string name = contributor_name(line); + + map::iterator it = contributors_map.find(name); + // if new contributor, insert + if(it == contributors_map.end()) + contributors_map.insert(pair(name, number)); + // if duplicate, just add the number + else + it->second += number; + } + churn_out.close(); + + return contributors_map; +} + +// find the last name, i.e. the last word. +// for "van den Schbling" types of last names, that's not a problem, that's actually what we want. +string lastname(const string& name) +{ + size_t last_space = name.find_last_of(' '); + if(last_space >= name.length()-1) return name; + else return name.substr(last_space+1); +} + +struct contributor +{ + string name; + int changedlines; + int changesets; + string url; + string misc; + + contributor() : changedlines(0), changesets(0) {} + + bool operator < (const contributor& other) + { + return lastname(name).compare(lastname(other.name)) < 0; + } +}; + +void add_online_info_into_contributors_list(list& contributors_list, const char *filename) +{ + string line; + ifstream online_info; + online_info.open(filename, ios::in); + while(!getline(online_info,line).eof()) + { + string hgname, realname, url, misc; + + size_t last_bar = line.find_last_of('|'); + if(last_bar == string::npos) continue; + if(last_bar < line.length()) + misc = line.substr(last_bar+1); + line.erase(last_bar); + + last_bar = line.find_last_of('|'); + if(last_bar == string::npos) continue; + if(last_bar < line.length()) + url = line.substr(last_bar+1); + line.erase(last_bar); + + last_bar = line.find_last_of('|'); + if(last_bar == string::npos) continue; + if(last_bar < line.length()) + realname = line.substr(last_bar+1); + line.erase(last_bar); + + hgname = line; + + // remove the example line + if(hgname.find("MercurialName") != string::npos) continue; + + list::iterator it; + for(it=contributors_list.begin(); it != contributors_list.end() && it->name != hgname; ++it) + {} + + if(it == contributors_list.end()) + { + contributor c; + c.name = realname; + c.url = url; + c.misc = misc; + contributors_list.push_back(c); + } + else + { + it->name = realname; + it->url = url; + it->misc = misc; + } + } +} + +int main() +{ + // parse the hg churn output files + map contributors_map_for_changedlines = contributors_map_from_churn_output("churn-changedlines.out"); + //map contributors_map_for_changesets = contributors_map_from_churn_output("churn-changesets.out"); + + // merge into the contributors list + list contributors_list; + map::iterator it; + for(it=contributors_map_for_changedlines.begin(); it != contributors_map_for_changedlines.end(); ++it) + { + contributor c; + c.name = it->first; + c.changedlines = it->second; + c.changesets = 0; //contributors_map_for_changesets.find(it->first)->second; + contributors_list.push_back(c); + } + + add_online_info_into_contributors_list(contributors_list, "online-info.out"); + + contributors_list.sort(); + + cout << "{| cellpadding=\"5\"\n"; + cout << "!\n"; + cout << "! Lines changed\n"; + cout << "!\n"; + + list::iterator itc; + int i = 0; + for(itc=contributors_list.begin(); itc != contributors_list.end(); ++itc) + { + if(itc->name.length() == 0) continue; + if(i%2) cout << "|-\n"; + else cout << "|- style=\"background:#FFFFD0\"\n"; + if(itc->url.length()) + cout << "| [" << itc->url << " " << itc->name << "]\n"; + else + cout << "| " << itc->name << "\n"; + if(itc->changedlines) + cout << "| " << itc->changedlines << "\n"; + else + cout << "| (no information)\n"; + cout << "| " << itc->misc << "\n"; + i++; + } + cout << "|}" << endl; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_docs b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_docs new file mode 100644 index 0000000000000000000000000000000000000000..787dcb325faf1e052fc80e0da18f4c213871d3bb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_docs @@ -0,0 +1,24 @@ +#!/bin/sh + +# configuration +# You should call this script with USER set as you want, else some default +# will be used +USER=${USER:-'orzel'} +UPLOAD_DIR=dox-devel + +#ulimit -v 1024000 + +# step 1 : build +rm build/doc/html -Rf +mkdir build -p +(cd build && cmake .. && make doc) || { echo "make failed"; exit 1; } + +#step 2 : upload +# (the '/' at the end of path is very important, see rsync documentation) +rsync -az --no-p --delete build/doc/html/ $USER@ssh.tuxfamily.org:eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR/ || { echo "upload failed"; exit 1; } + +#step 3 : fix the perm +ssh $USER@ssh.tuxfamily.org "chmod -R g+w /home/eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR" || { echo "perm failed"; exit 1; } + +echo "Uploaded successfully" + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_split_test_help.cmake b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_split_test_help.cmake new file mode 100644 index 0000000000000000000000000000000000000000..e43f5aabec38103cf449219b26f0f0c07d4cb461 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_gen_split_test_help.cmake @@ -0,0 +1,11 @@ +#!cmake -P +file(WRITE split_test_helper.h "") +foreach(i RANGE 1 999) + file(APPEND split_test_helper.h + "#if defined(EIGEN_TEST_PART_${i}) || defined(EIGEN_TEST_PART_ALL)\n" + "#define CALL_SUBTEST_${i}(FUNC) CALL_SUBTEST(FUNC)\n" + "#else\n" + "#define CALL_SUBTEST_${i}(FUNC)\n" + "#endif\n\n" + ) +endforeach() \ No newline at end of file diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_monitor_perf.sh b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_monitor_perf.sh new file mode 100644 index 0000000000000000000000000000000000000000..8f3425dafcf077602d48d16023606df05938e7ca --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/eigen_monitor_perf.sh @@ -0,0 +1,25 @@ +#!/bin/bash + +# This is a script example to automatically update and upload performance unit tests. +# The following five variables must be adjusted to match your settings. + +USER='ggael' +UPLOAD_DIR=perf_monitoring/ggaelmacbook26 +EIGEN_SOURCE_PATH=$HOME/Eigen/eigen +export PREFIX="haswell-fma" +export CXX_FLAGS="-mfma -w" + +#### + +BENCH_PATH=$EIGEN_SOURCE_PATH/bench/perf_monitoring/$PREFIX +PREVPATH=$(pwd) +cd $EIGEN_SOURCE_PATH/bench/perf_monitoring && ./runall.sh "Haswell 2.6GHz, FMA, Apple's clang" "$@" +cd $PREVPATH || exit 1 + +ALLFILES="$BENCH_PATH/*.png $BENCH_PATH/*.html $BENCH_PATH/index.html $BENCH_PATH/s1.js $BENCH_PATH/s2.js" + +# (the '/' at the end of path is very important, see rsync documentation) +rsync -az --no-p --delete $ALLFILES $USER@ssh.tuxfamily.org:eigen/eigen.tuxfamily.org-web/htdocs/$UPLOAD_DIR/ || { echo "upload failed"; exit 1; } + +# fix the perm +ssh $USER@ssh.tuxfamily.org "chmod -R g+w /home/eigen/eigen.tuxfamily.org-web/htdocs/perf_monitoring" || { echo "perm failed"; exit 1; } diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/release.in b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/release.in new file mode 100644 index 0000000000000000000000000000000000000000..db2d9d940283f607a103a5ae979f6921d5a8bea1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/release.in @@ -0,0 +1,3 @@ +#!/bin/sh + +cmake -DCMAKE_BUILD_TYPE=Release . diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/relicense.py b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/relicense.py new file mode 100644 index 0000000000000000000000000000000000000000..8a5265f1f171ab8afc7cc7892a773099f7723d84 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/scripts/relicense.py @@ -0,0 +1,69 @@ +# This file is part of Eigen, a lightweight C++ template library +# for linear algebra. +# +# Copyright (C) 2012 Keir Mierle +# +# This Source Code Form is subject to the terms of the Mozilla +# Public License v. 2.0. If a copy of the MPL was not distributed +# with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +# +# Author: mierle@gmail.com (Keir Mierle) +# +# Make the long-awaited conversion to MPL. + +lgpl3_header = ''' +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see . +''' + +mpl2_header = """ +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +""" + +import os +import sys + +exclusions = set(['relicense.py']) + +def update(text): + if text.find(lgpl3_header) == -1: + return text, False + return text.replace(lgpl3_header, mpl2_header), True + +rootdir = sys.argv[1] +for root, sub_folders, files in os.walk(rootdir): + for basename in files: + if basename in exclusions: + print 'SKIPPED', filename + continue + filename = os.path.join(root, basename) + fo = file(filename) + text = fo.read() + fo.close() + + text, updated = update(text) + if updated: + fo = file(filename, "w") + fo.write(text) + fo.close() + print 'UPDATED', filename + else: + print ' ', filename diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/signature_of_eigen3_matrix_library b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/signature_of_eigen3_matrix_library new file mode 100644 index 0000000000000000000000000000000000000000..80aaf4621fef3c9455f91c375926cad1ec62d527 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/signature_of_eigen3_matrix_library @@ -0,0 +1 @@ +This file is just there as a signature to help identify directories containing Eigen3. When writing a script looking for Eigen3, just look for this file. This is especially useful to help disambiguate with Eigen2... diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/AnnoyingScalar.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/AnnoyingScalar.h new file mode 100644 index 0000000000000000000000000000000000000000..7ace083c51e1977fa684588076a11943fc2fc016 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/AnnoyingScalar.h @@ -0,0 +1,165 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011-2018 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_TEST_ANNOYING_SCALAR_H +#define EIGEN_TEST_ANNOYING_SCALAR_H + +#include + +#if EIGEN_COMP_GNUC +#pragma GCC diagnostic ignored "-Wshadow" +#endif + +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW +struct my_exception +{ + my_exception() {} + ~my_exception() {} +}; +#endif + +// An AnnoyingScalar is a pseudo scalar type that: +// - can randomly through an exception in operator + +// - randomly allocate on the heap or initialize a reference to itself making it non trivially copyable, nor movable, nor relocatable. + +class AnnoyingScalar +{ + public: + AnnoyingScalar() { init(); *v = 0; } + AnnoyingScalar(long double _v) { init(); *v = _v; } + AnnoyingScalar(double _v) { init(); *v = _v; } + AnnoyingScalar(float _v) { init(); *v = _v; } + AnnoyingScalar(int _v) { init(); *v = _v; } + AnnoyingScalar(long _v) { init(); *v = _v; } + #if EIGEN_HAS_CXX11 + AnnoyingScalar(long long _v) { init(); *v = _v; } + #endif + AnnoyingScalar(const AnnoyingScalar& other) { init(); *v = *(other.v); } + ~AnnoyingScalar() { + if(v!=&data) + delete v; + instances--; + } + + void init() { + if(internal::random()) + v = new float; + else + v = &data; + instances++; + } + + AnnoyingScalar operator+(const AnnoyingScalar& other) const + { + #ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW + countdown--; + if(countdown<=0 && !dont_throw) + throw my_exception(); + #endif + return AnnoyingScalar(*v+*other.v); + } + + AnnoyingScalar operator-() const + { return AnnoyingScalar(-*v); } + + AnnoyingScalar operator-(const AnnoyingScalar& other) const + { return AnnoyingScalar(*v-*other.v); } + + AnnoyingScalar operator*(const AnnoyingScalar& other) const + { return AnnoyingScalar((*v)*(*other.v)); } + + AnnoyingScalar operator/(const AnnoyingScalar& other) const + { return AnnoyingScalar((*v)/(*other.v)); } + + AnnoyingScalar& operator+=(const AnnoyingScalar& other) { *v += *other.v; return *this; } + AnnoyingScalar& operator-=(const AnnoyingScalar& other) { *v -= *other.v; return *this; } + AnnoyingScalar& operator*=(const AnnoyingScalar& other) { *v *= *other.v; return *this; } + AnnoyingScalar& operator/=(const AnnoyingScalar& other) { *v /= *other.v; return *this; } + AnnoyingScalar& operator= (const AnnoyingScalar& other) { *v = *other.v; return *this; } + + bool operator==(const AnnoyingScalar& other) const { return *v == *other.v; } + bool operator!=(const AnnoyingScalar& other) const { return *v != *other.v; } + bool operator<=(const AnnoyingScalar& other) const { return *v <= *other.v; } + bool operator< (const AnnoyingScalar& other) const { return *v < *other.v; } + bool operator>=(const AnnoyingScalar& other) const { return *v >= *other.v; } + bool operator> (const AnnoyingScalar& other) const { return *v > *other.v; } + + float* v; + float data; + static int instances; +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW + static int countdown; + static bool dont_throw; +#endif +}; + +AnnoyingScalar real(const AnnoyingScalar &x) { return x; } +AnnoyingScalar imag(const AnnoyingScalar & ) { return 0; } +AnnoyingScalar conj(const AnnoyingScalar &x) { return x; } +AnnoyingScalar sqrt(const AnnoyingScalar &x) { return std::sqrt(*x.v); } +AnnoyingScalar abs (const AnnoyingScalar &x) { return std::abs(*x.v); } +AnnoyingScalar cos (const AnnoyingScalar &x) { return std::cos(*x.v); } +AnnoyingScalar sin (const AnnoyingScalar &x) { return std::sin(*x.v); } +AnnoyingScalar acos(const AnnoyingScalar &x) { return std::acos(*x.v); } +AnnoyingScalar atan2(const AnnoyingScalar &y,const AnnoyingScalar &x) { return std::atan2(*y.v,*x.v); } + +std::ostream& operator<<(std::ostream& stream,const AnnoyingScalar& x) { + stream << (*(x.v)); + return stream; +} + +int AnnoyingScalar::instances = 0; + +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW +int AnnoyingScalar::countdown = 0; +bool AnnoyingScalar::dont_throw = false; +#endif + +namespace Eigen { +template<> +struct NumTraits : NumTraits +{ + enum { + RequireInitialization = 1, + }; + typedef AnnoyingScalar Real; + typedef AnnoyingScalar Nested; + typedef AnnoyingScalar Literal; + typedef AnnoyingScalar NonInteger; +}; + +template<> inline AnnoyingScalar test_precision() { return test_precision(); } + +namespace numext { +template<> +EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE +bool (isfinite)(const AnnoyingScalar& x) { + return (numext::isfinite)(*x.v); +} +} + +namespace internal { + template<> EIGEN_STRONG_INLINE double cast(const AnnoyingScalar& x) { return double(*x.v); } + template<> EIGEN_STRONG_INLINE float cast(const AnnoyingScalar& x) { return *x.v; } +} +} // namespace Eigen + +AnnoyingScalar get_test_precision(const AnnoyingScalar&) +{ return Eigen::test_precision(); } + +AnnoyingScalar test_relative_error(const AnnoyingScalar &a, const AnnoyingScalar &b) +{ return test_relative_error(*a.v, *b.v); } + +inline bool test_isApprox(const AnnoyingScalar &a, const AnnoyingScalar &b) +{ return internal::isApprox(*a.v, *b.v, test_precision()); } + +inline bool test_isMuchSmallerThan(const AnnoyingScalar &a, const AnnoyingScalar &b) +{ return test_isMuchSmallerThan(*a.v, *b.v); } + +#endif // EIGEN_TEST_ANNOYING_SCALAR_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/CMakeLists.txt b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/CMakeLists.txt new file mode 100644 index 0000000000000000000000000000000000000000..f0136db349267e4f917f3ed492d7574c449e6350 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/CMakeLists.txt @@ -0,0 +1,463 @@ +# The file split_test_helper.h was generated at first run, +# it is now included in test/ +if(EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h) + file(REMOVE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h) +endif() + +# check if we have a Fortran compiler +include(CheckLanguage) +check_language(Fortran) +if(CMAKE_Fortran_COMPILER) + enable_language(Fortran) + set(EIGEN_Fortran_COMPILER_WORKS ON) +else() + set(EIGEN_Fortran_COMPILER_WORKS OFF) + # search for a default Lapack library to complete Eigen's one + find_package(LAPACK QUIET) +endif() + +# TODO do the same for EXTERNAL_LAPACK +option(EIGEN_TEST_EXTERNAL_BLAS "Use external BLAS library for testsuite" OFF) +if(EIGEN_TEST_EXTERNAL_BLAS) + find_package(BLAS REQUIRED) + message(STATUS "BLAS_COMPILER_FLAGS: ${BLAS_COMPILER_FLAGS}") + add_definitions("-DEIGEN_USE_BLAS") # is adding ${BLAS_COMPILER_FLAGS} necessary? + list(APPEND EXTERNAL_LIBS "${BLAS_LIBRARIES}") +endif() + +# configure blas/lapack (use Eigen's ones) +set(EIGEN_BLAS_LIBRARIES eigen_blas) +set(EIGEN_LAPACK_LIBRARIES eigen_lapack) + +set(EIGEN_TEST_MATRIX_DIR "" CACHE STRING "Enable testing of realword sparse matrices contained in the specified path") +if(EIGEN_TEST_MATRIX_DIR) + if(NOT WIN32) + message(STATUS "Test realworld sparse matrices: ${EIGEN_TEST_MATRIX_DIR}") + add_definitions( -DTEST_REAL_CASES="${EIGEN_TEST_MATRIX_DIR}" ) + else() + message(STATUS "REAL CASES CAN NOT BE CURRENTLY TESTED ON WIN32") + endif() +endif() + +set(SPARSE_LIBS " ") + +find_package(CHOLMOD) +if(CHOLMOD_FOUND) + add_definitions("-DEIGEN_CHOLMOD_SUPPORT") + include_directories(${CHOLMOD_INCLUDES}) + set(SPARSE_LIBS ${SPARSE_LIBS} ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES}) + set(CHOLMOD_ALL_LIBS ${CHOLMOD_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES}) + ei_add_property(EIGEN_TESTED_BACKENDS "CHOLMOD, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "CHOLMOD, ") +endif() + +find_package(UMFPACK) +if(UMFPACK_FOUND) + add_definitions("-DEIGEN_UMFPACK_SUPPORT") + include_directories(${UMFPACK_INCLUDES}) + set(SPARSE_LIBS ${SPARSE_LIBS} ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + set(UMFPACK_ALL_LIBS ${UMFPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + ei_add_property(EIGEN_TESTED_BACKENDS "UMFPACK, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "UMFPACK, ") +endif() + +find_package(KLU) +if(KLU_FOUND) + add_definitions("-DEIGEN_KLU_SUPPORT") + include_directories(${KLU_INCLUDES}) + set(SPARSE_LIBS ${SPARSE_LIBS} ${KLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + set(KLU_ALL_LIBS ${KLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + ei_add_property(EIGEN_TESTED_BACKENDS "KLU, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "KLU, ") +endif() + +find_package(SuperLU 4.0) +if(SuperLU_FOUND) + add_definitions("-DEIGEN_SUPERLU_SUPPORT") + include_directories(${SUPERLU_INCLUDES}) + set(SPARSE_LIBS ${SPARSE_LIBS} ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + set(SUPERLU_ALL_LIBS ${SUPERLU_LIBRARIES} ${EIGEN_BLAS_LIBRARIES}) + ei_add_property(EIGEN_TESTED_BACKENDS "SuperLU, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "SuperLU, ") +endif() + + +find_package(PASTIX QUIET COMPONENTS METIS SEQ) +# check that the PASTIX found is a version without MPI +find_path(PASTIX_pastix_nompi.h_INCLUDE_DIRS + NAMES pastix_nompi.h + HINTS ${PASTIX_INCLUDE_DIRS} +) +if (NOT PASTIX_pastix_nompi.h_INCLUDE_DIRS) + message(STATUS "A version of Pastix has been found but pastix_nompi.h does not exist in the include directory." + " Because Eigen tests require a version without MPI, we disable the Pastix backend.") +endif() +if(PASTIX_FOUND AND PASTIX_pastix_nompi.h_INCLUDE_DIRS) + add_definitions("-DEIGEN_PASTIX_SUPPORT") + include_directories(${PASTIX_INCLUDE_DIRS_DEP}) + if(SCOTCH_FOUND) + include_directories(${SCOTCH_INCLUDE_DIRS}) + set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES}) + elseif(METIS_FOUND) + include_directories(${METIS_INCLUDE_DIRS}) + set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES}) + else() + ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ") + endif() + set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES_DEP} ${ORDERING_LIBRARIES}) + set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES_DEP}) + ei_add_property(EIGEN_TESTED_BACKENDS "PaStiX, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ") +endif() + +if(METIS_FOUND) + add_definitions("-DEIGEN_METIS_SUPPORT") + include_directories(${METIS_INCLUDE_DIRS}) + ei_add_property(EIGEN_TESTED_BACKENDS "METIS, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "METIS, ") +endif() + +find_package(SPQR) +if(SPQR_FOUND AND CHOLMOD_FOUND AND (EIGEN_Fortran_COMPILER_WORKS OR LAPACK_FOUND) ) + add_definitions("-DEIGEN_SPQR_SUPPORT") + include_directories(${SPQR_INCLUDES}) + set(SPQR_ALL_LIBS ${SPQR_LIBRARIES} ${CHOLMOD_LIBRARIES} ${EIGEN_LAPACK_LIBRARIES} ${EIGEN_BLAS_LIBRARIES} ${LAPACK_LIBRARIES}) + set(SPARSE_LIBS ${SPARSE_LIBS} ${SPQR_ALL_LIBS}) + ei_add_property(EIGEN_TESTED_BACKENDS "SPQR, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "SPQR, ") +endif() + +option(EIGEN_TEST_NOQT "Disable Qt support in unit tests" OFF) +if(NOT EIGEN_TEST_NOQT) + find_package(Qt4) + if(QT4_FOUND) + include(${QT_USE_FILE}) + ei_add_property(EIGEN_TESTED_BACKENDS "Qt4 support, ") + else() + ei_add_property(EIGEN_MISSING_BACKENDS "Qt4 support, ") + endif() +endif() + +if(TEST_LIB) + add_definitions("-DEIGEN_EXTERN_INSTANTIATIONS=1") +endif() + +set_property(GLOBAL PROPERTY EIGEN_CURRENT_SUBPROJECT "Official") +add_custom_target(BuildOfficial) + +ei_add_test(rand) +ei_add_test(meta) +ei_add_test(numext) +ei_add_test(sizeof) +ei_add_test(dynalloc) +ei_add_test(nomalloc) +ei_add_test(first_aligned) +ei_add_test(type_alias) +ei_add_test(nullary) +ei_add_test(mixingtypes) +ei_add_test(io) +ei_add_test(packetmath "-DEIGEN_FAST_MATH=1") +ei_add_test(vectorization_logic) +ei_add_test(basicstuff) +ei_add_test(constructor) +ei_add_test(linearstructure) +ei_add_test(integer_types) +ei_add_test(unalignedcount) +if(NOT EIGEN_TEST_NO_EXCEPTIONS AND NOT EIGEN_TEST_OPENMP) + ei_add_test(exceptions) +endif() +ei_add_test(redux) +ei_add_test(visitor) +ei_add_test(block) +ei_add_test(corners) +ei_add_test(symbolic_index) +ei_add_test(indexed_view) +ei_add_test(reshape) +ei_add_test(swap) +ei_add_test(resize) +ei_add_test(conservative_resize) +ei_add_test(product_small) +ei_add_test(product_large) +ei_add_test(product_extra) +ei_add_test(diagonalmatrices) +ei_add_test(adjoint) +ei_add_test(diagonal) +ei_add_test(miscmatrices) +ei_add_test(commainitializer) +ei_add_test(smallvectors) +ei_add_test(mapped_matrix) +ei_add_test(mapstride) +ei_add_test(mapstaticmethods) +ei_add_test(array_cwise) +ei_add_test(array_for_matrix) +ei_add_test(array_replicate) +ei_add_test(array_reverse) +ei_add_test(ref) +ei_add_test(is_same_dense) +ei_add_test(triangular) +ei_add_test(selfadjoint) +ei_add_test(product_selfadjoint) +ei_add_test(product_symm) +ei_add_test(product_syrk) +ei_add_test(product_trmv) +ei_add_test(product_trmm) +ei_add_test(product_trsolve) +ei_add_test(product_mmtr) +ei_add_test(product_notemporary) +ei_add_test(stable_norm) +ei_add_test(permutationmatrices) +ei_add_test(bandmatrix) +ei_add_test(cholesky) +ei_add_test(lu) +ei_add_test(determinant) +ei_add_test(inverse) +ei_add_test(qr) +ei_add_test(qr_colpivoting) +ei_add_test(qr_fullpivoting) +ei_add_test(upperbidiagonalization) +ei_add_test(hessenberg) +ei_add_test(schur_real) +ei_add_test(schur_complex) +ei_add_test(eigensolver_selfadjoint) +ei_add_test(eigensolver_generic) +ei_add_test(eigensolver_complex) +ei_add_test(real_qz) +ei_add_test(eigensolver_generalized_real) +ei_add_test(jacobi) +ei_add_test(jacobisvd) +ei_add_test(bdcsvd) +ei_add_test(householder) +ei_add_test(geo_orthomethods) +ei_add_test(geo_quaternion) +ei_add_test(geo_eulerangles) +ei_add_test(geo_parametrizedline) +ei_add_test(geo_alignedbox) +ei_add_test(geo_hyperplane) +ei_add_test(geo_transformations) +ei_add_test(geo_homogeneous) +ei_add_test(stdvector) +ei_add_test(stdvector_overload) +ei_add_test(stdlist) +ei_add_test(stdlist_overload) +ei_add_test(stddeque) +ei_add_test(stddeque_overload) +ei_add_test(sparse_basic) +ei_add_test(sparse_block) +ei_add_test(sparse_vector) +ei_add_test(sparse_product) +ei_add_test(sparse_ref) +ei_add_test(sparse_solvers) +ei_add_test(sparse_permutations) +ei_add_test(simplicial_cholesky) +ei_add_test(conjugate_gradient) +ei_add_test(incomplete_cholesky) +ei_add_test(bicgstab) +ei_add_test(lscg) +ei_add_test(sparselu) +ei_add_test(sparseqr) +ei_add_test(umeyama) +ei_add_test(nesting_ops "${CMAKE_CXX_FLAGS_DEBUG}") +ei_add_test(nestbyvalue) +ei_add_test(zerosized) +ei_add_test(dontalign) +ei_add_test(evaluators) +if(NOT EIGEN_TEST_NO_EXCEPTIONS) + ei_add_test(sizeoverflow) +endif() +ei_add_test(prec_inverse_4x4) +ei_add_test(vectorwiseop) +ei_add_test(special_numbers) +ei_add_test(rvalue_types) +ei_add_test(dense_storage) +ei_add_test(ctorleak) +ei_add_test(mpl2only) +ei_add_test(inplace_decomposition) +ei_add_test(half_float) +ei_add_test(bfloat16_float) +ei_add_test(array_of_string) +ei_add_test(num_dimensions) +ei_add_test(stl_iterators) +ei_add_test(blasutil) +ei_add_test(random_matrix) +ei_add_test(initializer_list_construction) +ei_add_test(diagonal_matrix_variadic_ctor) + +add_executable(bug1213 bug1213.cpp bug1213_main.cpp) + +check_cxx_compiler_flag("-ffast-math" COMPILER_SUPPORT_FASTMATH) +if(COMPILER_SUPPORT_FASTMATH) + set(EIGEN_FASTMATH_FLAGS "-ffast-math") +else() + check_cxx_compiler_flag("/fp:fast" COMPILER_SUPPORT_FPFAST) + if(COMPILER_SUPPORT_FPFAST) + set(EIGEN_FASTMATH_FLAGS "/fp:fast") + endif() +endif() + +ei_add_test(fastmath " ${EIGEN_FASTMATH_FLAGS} ") + +# # ei_add_test(denseLM) + +if(QT4_FOUND) + ei_add_test(qtvector "" "${QT_QTCORE_LIBRARY}") +endif() + +if(UMFPACK_FOUND) + ei_add_test(umfpack_support "" "${UMFPACK_ALL_LIBS}") +endif() + +if(KLU_FOUND OR SuiteSparse_FOUND) + ei_add_test(klu_support "" "${KLU_ALL_LIBS}") +endif() + +if(SUPERLU_FOUND) + ei_add_test(superlu_support "" "${SUPERLU_ALL_LIBS}") +endif() + +if(CHOLMOD_FOUND) + ei_add_test(cholmod_support "" "${CHOLMOD_ALL_LIBS}") +endif() + +if(PARDISO_FOUND) + ei_add_test(pardiso_support "" "${PARDISO_ALL_LIBS}") +endif() + +if(PASTIX_FOUND AND (SCOTCH_FOUND OR METIS_FOUND)) + ei_add_test(pastix_support "" "${PASTIX_ALL_LIBS}") +endif() + +if(SPQR_FOUND AND CHOLMOD_FOUND) + ei_add_test(spqr_support "" "${SPQR_ALL_LIBS}") +endif() + +if(METIS_FOUND) +ei_add_test(metis_support "" "${METIS_LIBRARIES}") +endif() + +string(TOLOWER "${CMAKE_CXX_COMPILER}" cmake_cxx_compiler_tolower) +if(cmake_cxx_compiler_tolower MATCHES "qcc") + set(CXX_IS_QCC "ON") +endif() + +ei_add_property(EIGEN_TESTING_SUMMARY "CXX: ${CMAKE_CXX_COMPILER}\n") +if(CMAKE_COMPILER_IS_GNUCXX AND NOT CXX_IS_QCC) + execute_process(COMMAND ${CMAKE_CXX_COMPILER} --version COMMAND head -n 1 OUTPUT_VARIABLE EIGEN_CXX_VERSION_STRING OUTPUT_STRIP_TRAILING_WHITESPACE) + ei_add_property(EIGEN_TESTING_SUMMARY "CXX_VERSION: ${EIGEN_CXX_VERSION_STRING}\n") +endif() +ei_add_property(EIGEN_TESTING_SUMMARY "CXX_FLAGS: ${CMAKE_CXX_FLAGS}\n") +if (EIGEN_TEST_CUSTOM_CXX_FLAGS) + ei_add_property(EIGEN_TESTING_SUMMARY "Custom CXX flags: ${EIGEN_TEST_CUSTOM_CXX_FLAGS}\n") +endif() +ei_add_property(EIGEN_TESTING_SUMMARY "Sparse lib flags: ${SPARSE_LIBS}\n") + +option(EIGEN_TEST_EIGEN2 "Run whole Eigen2 test suite against EIGEN2_SUPPORT" OFF) +mark_as_advanced(EIGEN_TEST_EIGEN2) +if(EIGEN_TEST_EIGEN2) + message(WARNING "The Eigen2 test suite has been removed") +endif() + +# boost MP unit test +find_package(Boost 1.53.0) +if(Boost_FOUND) + include_directories(${Boost_INCLUDE_DIRS}) + ei_add_test(boostmultiprec "" "${Boost_LIBRARIES}") + ei_add_property(EIGEN_TESTED_BACKENDS "Boost.Multiprecision, ") +else() + ei_add_property(EIGEN_MISSING_BACKENDS "Boost.Multiprecision, ") +endif() + + +# CUDA unit tests +option(EIGEN_TEST_CUDA "Enable CUDA support in unit tests" OFF) +option(EIGEN_TEST_CUDA_CLANG "Use clang instead of nvcc to compile the CUDA tests" OFF) + +if(EIGEN_TEST_CUDA_CLANG AND NOT CMAKE_CXX_COMPILER MATCHES "clang") + message(WARNING "EIGEN_TEST_CUDA_CLANG is set, but CMAKE_CXX_COMPILER does not appear to be clang.") +endif() + +if(EIGEN_TEST_CUDA) + +find_package(CUDA 5.0) +if(CUDA_FOUND) + + set(CUDA_PROPAGATE_HOST_FLAGS OFF) + + set(EIGEN_CUDA_RELAXED_CONSTEXPR "--expt-relaxed-constexpr") + if (${CUDA_VERSION} STREQUAL "7.0") + set(EIGEN_CUDA_RELAXED_CONSTEXPR "--relaxed-constexpr") + endif() + + if("${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang") + set(CUDA_NVCC_FLAGS "-ccbin ${CMAKE_C_COMPILER}" CACHE STRING "nvcc flags" FORCE) + endif() + if(EIGEN_TEST_CUDA_CLANG) + string(APPEND CMAKE_CXX_FLAGS " --cuda-path=${CUDA_TOOLKIT_ROOT_DIR}") + foreach(GPU IN LISTS EIGEN_CUDA_COMPUTE_ARCH) + string(APPEND CMAKE_CXX_FLAGS " --cuda-gpu-arch=sm_${GPU}") + endforeach() + else() + foreach(GPU IN LISTS EIGEN_CUDA_COMPUTE_ARCH) + string(APPEND CUDA_NVCC_FLAGS " -gencode arch=compute_${GPU},code=sm_${GPU}") + endforeach() + endif() + string(APPEND CUDA_NVCC_FLAGS " ${EIGEN_CUDA_RELAXED_CONSTEXPR}") + set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu") + + ei_add_test(gpu_basic) + + unset(EIGEN_ADD_TEST_FILENAME_EXTENSION) + +endif() + +endif() + + +# HIP unit tests +option(EIGEN_TEST_HIP "Add HIP support." OFF) +if (EIGEN_TEST_HIP) + + set(HIP_PATH "/opt/rocm/hip" CACHE STRING "Path to the HIP installation.") + + if (EXISTS ${HIP_PATH}) + + list(APPEND CMAKE_MODULE_PATH ${HIP_PATH}/cmake) + + find_package(HIP REQUIRED) + if (HIP_FOUND) + + execute_process(COMMAND ${HIP_PATH}/bin/hipconfig --platform OUTPUT_VARIABLE HIP_PLATFORM) + + if ((${HIP_PLATFORM} STREQUAL "hcc") OR (${HIP_PLATFORM} STREQUAL "amd")) + + include_directories(${HIP_PATH}/include) + + set(EIGEN_ADD_TEST_FILENAME_EXTENSION "cu") + ei_add_test(gpu_basic) + unset(EIGEN_ADD_TEST_FILENAME_EXTENSION) + + elseif ((${HIP_PLATFORM} STREQUAL "nvcc") OR (${HIP_PLATFORM} STREQUAL "nvidia")) + message(FATAL_ERROR "HIP_PLATFORM = nvcc is not supported within Eigen") + else () + message(FATAL_ERROR "Unknown HIP_PLATFORM = ${HIP_PLATFORM}") + endif() + endif() + else () + message(FATAL_ERROR "EIGEN_TEST_HIP is ON, but the specified HIP_PATH (${HIP_PATH}) does not exist") + endif() +endif() + +cmake_dependent_option(EIGEN_TEST_BUILD_DOCUMENTATION "Test building the doxygen documentation" OFF "EIGEN_BUILD_DOC" OFF) +if(EIGEN_TEST_BUILD_DOCUMENTATION) + add_dependencies(buildtests doc) +endif() + +# Register all smoke tests +include("EigenSmokeTestList") +ei_add_smoke_tests("${ei_smoke_test_list}") diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/MovableScalar.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/MovableScalar.h new file mode 100644 index 0000000000000000000000000000000000000000..6a90d037a852f6981bf206dd6aaac5baa9e71287 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/MovableScalar.h @@ -0,0 +1,35 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2020 Sebastien Boisvert +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MISC_MOVABLE_SCALAR_H +#define EIGEN_MISC_MOVABLE_SCALAR_H + +#include + +namespace Eigen +{ +template > +struct MovableScalar : public Base +{ + MovableScalar() = default; + ~MovableScalar() = default; + MovableScalar(const MovableScalar&) = default; + MovableScalar(MovableScalar&& other) = default; + MovableScalar& operator=(const MovableScalar&) = default; + MovableScalar& operator=(MovableScalar&& other) = default; + MovableScalar(Scalar scalar) : Base(100, scalar) {} + + operator Scalar() const { return this->size() > 0 ? this->back() : Scalar(); } +}; + +template<> struct NumTraits> : GenericNumTraits {}; +} + +#endif + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/OffByOneScalar.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/OffByOneScalar.h new file mode 100644 index 0000000000000000000000000000000000000000..c0371a6c721b0921d093eea210f647234e2a2643 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/OffByOneScalar.h @@ -0,0 +1,28 @@ + +// A Scalar with internal representation T+1 so that zero is internally +// represented by T(1). This is used to test memory fill. +// +template +class OffByOneScalar { + public: + OffByOneScalar() : val_(1) {} + OffByOneScalar(const OffByOneScalar& other) { + *this = other; + } + OffByOneScalar& operator=(const OffByOneScalar& other) { + val_ = other.val_; + return *this; + } + + OffByOneScalar(T val) : val_(val + 1) {} + OffByOneScalar& operator=(T val) { + val_ = val + 1; + } + + operator T() const { + return val_ - 1; + } + + private: + T val_; +}; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/SafeScalar.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/SafeScalar.h new file mode 100644 index 0000000000000000000000000000000000000000..c5cb75717c7c0131814ee98ceb840ac83b48dd26 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/SafeScalar.h @@ -0,0 +1,30 @@ + +// A Scalar that asserts for uninitialized access. +template +class SafeScalar { + public: + SafeScalar() : initialized_(false) {} + SafeScalar(const SafeScalar& other) { + *this = other; + } + SafeScalar& operator=(const SafeScalar& other) { + val_ = T(other); + initialized_ = true; + return *this; + } + + SafeScalar(T val) : val_(val), initialized_(true) {} + SafeScalar& operator=(T val) { + val_ = val; + initialized_ = true; + } + + operator T() const { + VERIFY(initialized_ && "Uninitialized access."); + return val_; + } + + private: + T val_; + bool initialized_; +}; diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/adjoint.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/adjoint.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4c4f98bb978c0277957089217caf9c21f14f4cad --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/adjoint.cpp @@ -0,0 +1,219 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT + +#include "main.h" + +template struct adjoint_specific; + +template<> struct adjoint_specific { + template + static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) { + VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), 0)); + VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), 0)); + + // check compatibility of dot and adjoint + VERIFY(test_isApproxWithRef(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), 0)); + } +}; + +template<> struct adjoint_specific { + template + static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) { + typedef typename NumTraits::Real RealScalar; + using std::abs; + + RealScalar ref = NumTraits::IsInteger ? RealScalar(0) : (std::max)((s1 * v1 + s2 * v2).norm(),v3.norm()); + VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), ref)); + VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), ref)); + + VERIFY_IS_APPROX(v1.squaredNorm(), v1.norm() * v1.norm()); + // check normalized() and normalize() + VERIFY_IS_APPROX(v1, v1.norm() * v1.normalized()); + v3 = v1; + v3.normalize(); + VERIFY_IS_APPROX(v1, v1.norm() * v3); + VERIFY_IS_APPROX(v3, v1.normalized()); + VERIFY_IS_APPROX(v3.norm(), RealScalar(1)); + + // check null inputs + VERIFY_IS_APPROX((v1*0).normalized(), (v1*0)); +#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE) + RealScalar very_small = (std::numeric_limits::min)(); + VERIFY( (v1*very_small).norm() == 0 ); + VERIFY_IS_APPROX((v1*very_small).normalized(), (v1*very_small)); + v3 = v1*very_small; + v3.normalize(); + VERIFY_IS_APPROX(v3, (v1*very_small)); +#endif + + // check compatibility of dot and adjoint + ref = NumTraits::IsInteger ? 0 : (std::max)((std::max)(v1.norm(),v2.norm()),(std::max)((square * v2).norm(),(square.adjoint() * v1).norm())); + VERIFY(internal::isMuchSmallerThan(abs(v1.dot(square * v2) - (square.adjoint() * v1).dot(v2)), ref, test_precision())); + + // check that Random().normalized() works: tricky as the random xpr must be evaluated by + // normalized() in order to produce a consistent result. + VERIFY_IS_APPROX(Vec::Random(v1.size()).normalized().norm(), RealScalar(1)); + } +}; + +template void adjoint(const MatrixType& m) +{ + /* this test covers the following files: + Transpose.h Conjugate.h Dot.h + */ + using std::abs; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix VectorType; + typedef Matrix SquareMatrixType; + const Index PacketSize = internal::packet_traits::size; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols), + square = SquareMatrixType::Random(rows, rows); + VectorType v1 = VectorType::Random(rows), + v2 = VectorType::Random(rows), + v3 = VectorType::Random(rows), + vzero = VectorType::Zero(rows); + + Scalar s1 = internal::random(), + s2 = internal::random(); + + // check basic compatibility of adjoint, transpose, conjugate + VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1); + VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(), m1); + + // check multiplicative behavior + VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(), m2.adjoint() * m1); + VERIFY_IS_APPROX((s1 * m1).adjoint(), numext::conj(s1) * m1.adjoint()); + + // check basic properties of dot, squaredNorm + VERIFY_IS_APPROX(numext::conj(v1.dot(v2)), v2.dot(v1)); + VERIFY_IS_APPROX(numext::real(v1.dot(v1)), v1.squaredNorm()); + + adjoint_specific::IsInteger>::run(v1, v2, v3, square, s1, s2); + + VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)), static_cast(1)); + + // like in testBasicStuff, test operator() to check const-qualification + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + VERIFY_IS_APPROX(m1.conjugate()(r,c), numext::conj(m1(r,c))); + VERIFY_IS_APPROX(m1.adjoint()(c,r), numext::conj(m1(r,c))); + + // check inplace transpose + m3 = m1; + m3.transposeInPlace(); + VERIFY_IS_APPROX(m3,m1.transpose()); + m3.transposeInPlace(); + VERIFY_IS_APPROX(m3,m1); + + if(PacketSize(0,m3.rows()-PacketSize); + Index j = internal::random(0,m3.cols()-PacketSize); + m3.template block(i,j).transposeInPlace(); + VERIFY_IS_APPROX( (m3.template block(i,j)), (m1.template block(i,j).transpose()) ); + m3.template block(i,j).transposeInPlace(); + VERIFY_IS_APPROX(m3,m1); + } + + // check inplace adjoint + m3 = m1; + m3.adjointInPlace(); + VERIFY_IS_APPROX(m3,m1.adjoint()); + m3.transposeInPlace(); + VERIFY_IS_APPROX(m3,m1.conjugate()); + + // check mixed dot product + typedef Matrix RealVectorType; + RealVectorType rv1 = RealVectorType::Random(rows); + VERIFY_IS_APPROX(v1.dot(rv1.template cast()), v1.dot(rv1)); + VERIFY_IS_APPROX(rv1.template cast().dot(v1), rv1.dot(v1)); + + VERIFY( is_same_type(m1,m1.template conjugateIf()) ); + VERIFY( is_same_type(m1.conjugate(),m1.template conjugateIf()) ); +} + +template +void adjoint_extra() +{ + MatrixXcf a(10,10), b(10,10); + VERIFY_RAISES_ASSERT(a = a.transpose()); + VERIFY_RAISES_ASSERT(a = a.transpose() + b); + VERIFY_RAISES_ASSERT(a = b + a.transpose()); + VERIFY_RAISES_ASSERT(a = a.conjugate().transpose()); + VERIFY_RAISES_ASSERT(a = a.adjoint()); + VERIFY_RAISES_ASSERT(a = a.adjoint() + b); + VERIFY_RAISES_ASSERT(a = b + a.adjoint()); + + // no assertion should be triggered for these cases: + a.transpose() = a.transpose(); + a.transpose() += a.transpose(); + a.transpose() += a.transpose() + b; + a.transpose() = a.adjoint(); + a.transpose() += a.adjoint(); + a.transpose() += a.adjoint() + b; + + // regression tests for check_for_aliasing + MatrixXd c(10,10); + c = 1.0 * MatrixXd::Ones(10,10) + c; + c = MatrixXd::Ones(10,10) * 1.0 + c; + c = c + MatrixXd::Ones(10,10) .cwiseProduct( MatrixXd::Zero(10,10) ); + c = MatrixXd::Ones(10,10) * MatrixXd::Zero(10,10); + + // regression for bug 1646 + for (int j = 0; j < 10; ++j) { + c.col(j).head(j) = c.row(j).head(j); + } + + for (int j = 0; j < 10; ++j) { + c.col(j) = c.row(j); + } + + a.conservativeResize(1,1); + a = a.transpose(); + + a.conservativeResize(0,0); + a = a.transpose(); +} + +EIGEN_DECLARE_TEST(adjoint) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( adjoint(Matrix()) ); + CALL_SUBTEST_2( adjoint(Matrix3d()) ); + CALL_SUBTEST_3( adjoint(Matrix4f()) ); + + CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE/2), internal::random(1,EIGEN_TEST_MAX_SIZE/2))) ); + CALL_SUBTEST_5( adjoint(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( adjoint(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + + // Complement for 128 bits vectorization: + CALL_SUBTEST_8( adjoint(Matrix2d()) ); + CALL_SUBTEST_9( adjoint(Matrix()) ); + + // 256 bits vectorization: + CALL_SUBTEST_10( adjoint(Matrix()) ); + CALL_SUBTEST_11( adjoint(Matrix()) ); + CALL_SUBTEST_12( adjoint(Matrix()) ); + } + // test a large static matrix only once + CALL_SUBTEST_7( adjoint(Matrix()) ); + + CALL_SUBTEST_13( adjoint_extra<0>() ); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_cwise.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_cwise.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0cc438b39ba4249c7f72fbba221f480630ae1aef --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_cwise.cpp @@ -0,0 +1,710 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + + +// Test the corner cases of pow(x, y) for real types. +template +void pow_test() { + const Scalar zero = Scalar(0); + const Scalar eps = Eigen::NumTraits::epsilon(); + const Scalar one = Scalar(1); + const Scalar two = Scalar(2); + const Scalar three = Scalar(3); + const Scalar sqrt_half = Scalar(std::sqrt(0.5)); + const Scalar sqrt2 = Scalar(std::sqrt(2)); + const Scalar inf = Eigen::NumTraits::infinity(); + const Scalar nan = Eigen::NumTraits::quiet_NaN(); + const Scalar denorm_min = std::numeric_limits::denorm_min(); + const Scalar min = (std::numeric_limits::min)(); + const Scalar max = (std::numeric_limits::max)(); + const Scalar max_exp = (static_cast(int(Eigen::NumTraits::max_exponent())) * Scalar(EIGEN_LN2)) / eps; + + const static Scalar abs_vals[] = {zero, + denorm_min, + min, + eps, + sqrt_half, + one, + sqrt2, + two, + three, + max_exp, + max, + inf, + nan}; + const int abs_cases = 13; + const int num_cases = 2*abs_cases * 2*abs_cases; + // Repeat the same value to make sure we hit the vectorized path. + const int num_repeats = 32; + Array x(num_repeats, num_cases); + Array y(num_repeats, num_cases); + int count = 0; + for (int i = 0; i < abs_cases; ++i) { + const Scalar abs_x = abs_vals[i]; + for (int sign_x = 0; sign_x < 2; ++sign_x) { + Scalar x_case = sign_x == 0 ? -abs_x : abs_x; + for (int j = 0; j < abs_cases; ++j) { + const Scalar abs_y = abs_vals[j]; + for (int sign_y = 0; sign_y < 2; ++sign_y) { + Scalar y_case = sign_y == 0 ? -abs_y : abs_y; + for (int repeat = 0; repeat < num_repeats; ++repeat) { + x(repeat, count) = x_case; + y(repeat, count) = y_case; + } + ++count; + } + } + } + } + + Array actual = x.pow(y); + const Scalar tol = test_precision(); + bool all_pass = true; + for (int i = 0; i < 1; ++i) { + for (int j = 0; j < num_cases; ++j) { + Scalar e = static_cast(std::pow(x(i,j), y(i,j))); + Scalar a = actual(i, j); + bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e)); + all_pass &= !fail; + if (fail) { + std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl; + } + } + } + VERIFY(all_pass); +} + +template void array(const ArrayType& m) +{ + typedef typename ArrayType::Scalar Scalar; + typedef typename ArrayType::RealScalar RealScalar; + typedef Array ColVectorType; + typedef Array RowVectorType; + + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2 = ArrayType::Random(rows, cols), + m3(rows, cols); + ArrayType m4 = m1; // copy constructor + VERIFY_IS_APPROX(m1, m4); + + ColVectorType cv1 = ColVectorType::Random(rows); + RowVectorType rv1 = RowVectorType::Random(cols); + + Scalar s1 = internal::random(), + s2 = internal::random(); + + // scalar addition + VERIFY_IS_APPROX(m1 + s1, s1 + m1); + VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1); + VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 ); + VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1)); + VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1); + VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) ); + m3 = m1; + m3 += s2; + VERIFY_IS_APPROX(m3, m1 + s2); + m3 = m1; + m3 -= s1; + VERIFY_IS_APPROX(m3, m1 - s1); + + // scalar operators via Maps + m3 = m1; + ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); + VERIFY_IS_APPROX(m1, m3 - m2); + + m3 = m1; + ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols()); + VERIFY_IS_APPROX(m1, m3 + m2); + + m3 = m1; + ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); + VERIFY_IS_APPROX(m1, m3 * m2); + + m3 = m1; + m2 = ArrayType::Random(rows,cols); + m2 = (m2==0).select(1,m2); + ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols()); + VERIFY_IS_APPROX(m1, m3 / m2); + + // reductions + VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum()); + VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum()); + using std::abs; + VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum()); + VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum()); + if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision())) + VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum()); + VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op())); + + // vector-wise ops + m3 = m1; + VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1); + m3 = m1; + VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1); + m3 = m1; + VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1); + m3 = m1; + VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1); + + // Conversion from scalar + VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1)); + VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1)); + VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1)); + typedef Array FixedArrayType; + { + FixedArrayType f1(s1); + VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1)); + FixedArrayType f2(numext::real(s1)); + VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1))); + FixedArrayType f3((int)100*numext::real(s1)); + VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1))); + f1.setRandom(); + FixedArrayType f4(f1.data()); + VERIFY_IS_APPROX(f4, f1); + } + #if EIGEN_HAS_CXX11 + { + FixedArrayType f1{s1}; + VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1)); + FixedArrayType f2{numext::real(s1)}; + VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1))); + FixedArrayType f3{(int)100*numext::real(s1)}; + VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1))); + f1.setRandom(); + FixedArrayType f4{f1.data()}; + VERIFY_IS_APPROX(f4, f1); + } + #endif + + // pow + VERIFY_IS_APPROX(m1.pow(2), m1.square()); + VERIFY_IS_APPROX(pow(m1,2), m1.square()); + VERIFY_IS_APPROX(m1.pow(3), m1.cube()); + VERIFY_IS_APPROX(pow(m1,3), m1.cube()); + VERIFY_IS_APPROX((-m1).pow(3), -m1.cube()); + VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube()); + ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2)); + VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square()); + VERIFY_IS_APPROX(m1.pow(exponents), m1.square()); + VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square()); + VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square()); + VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square()); + VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square()); + VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0))); + + // Check possible conflicts with 1D ctor + typedef Array OneDArrayType; + { + OneDArrayType o1(rows); + VERIFY(o1.size()==rows); + OneDArrayType o2(static_cast(rows)); + VERIFY(o2.size()==rows); + } + #if EIGEN_HAS_CXX11 + { + OneDArrayType o1{rows}; + VERIFY(o1.size()==rows); + OneDArrayType o4{int(rows)}; + VERIFY(o4.size()==rows); + } + #endif + // Check possible conflicts with 2D ctor + typedef Array TwoDArrayType; + typedef Array ArrayType2; + { + TwoDArrayType o1(rows,cols); + VERIFY(o1.rows()==rows); + VERIFY(o1.cols()==cols); + TwoDArrayType o2(static_cast(rows),static_cast(cols)); + VERIFY(o2.rows()==rows); + VERIFY(o2.cols()==cols); + + ArrayType2 o3(rows,cols); + VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); + ArrayType2 o4(static_cast(rows),static_cast(cols)); + VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); + } + #if EIGEN_HAS_CXX11 + { + TwoDArrayType o1{rows,cols}; + VERIFY(o1.rows()==rows); + VERIFY(o1.cols()==cols); + TwoDArrayType o2{int(rows),int(cols)}; + VERIFY(o2.rows()==rows); + VERIFY(o2.cols()==cols); + + ArrayType2 o3{rows,cols}; + VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); + ArrayType2 o4{int(rows),int(cols)}; + VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); + } + #endif +} + +template void comparisons(const ArrayType& m) +{ + using std::abs; + typedef typename ArrayType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2 = ArrayType::Random(rows, cols), + m3(rows, cols), + m4 = m1; + + m4 = (m4.abs()==Scalar(0)).select(1,m4); + + VERIFY(((m1 + Scalar(1)) > m1).all()); + VERIFY(((m1 - Scalar(1)) < m1).all()); + if (rows*cols>1) + { + m3 = m1; + m3(r,c) += 1; + VERIFY(! (m1 < m3).all() ); + VERIFY(! (m1 > m3).all() ); + } + VERIFY(!(m1 > m2 && m1 < m2).any()); + VERIFY((m1 <= m2 || m1 >= m2).all()); + + // comparisons array to scalar + VERIFY( (m1 != (m1(r,c)+1) ).any() ); + VERIFY( (m1 > (m1(r,c)-1) ).any() ); + VERIFY( (m1 < (m1(r,c)+1) ).any() ); + VERIFY( (m1 == m1(r,c) ).any() ); + + // comparisons scalar to array + VERIFY( ( (m1(r,c)+1) != m1).any() ); + VERIFY( ( (m1(r,c)-1) < m1).any() ); + VERIFY( ( (m1(r,c)+1) > m1).any() ); + VERIFY( ( m1(r,c) == m1).any() ); + + // test Select + VERIFY_IS_APPROX( (m1m2).select(m1,m2), m1.cwiseMax(m2) ); + Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2); + for (int j=0; j=ArrayType::Constant(rows,cols,mid)) + .select(m1,0), m3); + // even shorter version: + VERIFY_IS_APPROX( (m1.abs()RealScalar(0.1)).count() == rows*cols); + + // and/or + VERIFY( (m1RealScalar(0)).count() == 0); + VERIFY( (m1=RealScalar(0)).count() == rows*cols); + RealScalar a = m1.abs().mean(); + VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count()); + + typedef Array ArrayOfIndices; + + // TODO allows colwise/rowwise for array + VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose()); + VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols)); +} + +template void array_real(const ArrayType& m) +{ + using std::abs; + using std::sqrt; + typedef typename ArrayType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2 = ArrayType::Random(rows, cols), + m3(rows, cols), + m4 = m1; + + m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4); + + Scalar s1 = internal::random(); + + // these tests are mostly to check possible compilation issues with free-functions. + VERIFY_IS_APPROX(m1.sin(), sin(m1)); + VERIFY_IS_APPROX(m1.cos(), cos(m1)); + VERIFY_IS_APPROX(m1.tan(), tan(m1)); + VERIFY_IS_APPROX(m1.asin(), asin(m1)); + VERIFY_IS_APPROX(m1.acos(), acos(m1)); + VERIFY_IS_APPROX(m1.atan(), atan(m1)); + VERIFY_IS_APPROX(m1.sinh(), sinh(m1)); + VERIFY_IS_APPROX(m1.cosh(), cosh(m1)); + VERIFY_IS_APPROX(m1.tanh(), tanh(m1)); +#if EIGEN_HAS_CXX11_MATH + VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1))); + VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1))); + VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1))); +#endif + VERIFY_IS_APPROX(m1.logistic(), logistic(m1)); + + VERIFY_IS_APPROX(m1.arg(), arg(m1)); + VERIFY_IS_APPROX(m1.round(), round(m1)); + VERIFY_IS_APPROX(m1.rint(), rint(m1)); + VERIFY_IS_APPROX(m1.floor(), floor(m1)); + VERIFY_IS_APPROX(m1.ceil(), ceil(m1)); + VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all()); + VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all()); + VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all()); + VERIFY_IS_APPROX(m4.inverse(), inverse(m4)); + VERIFY_IS_APPROX(m1.abs(), abs(m1)); + VERIFY_IS_APPROX(m1.abs2(), abs2(m1)); + VERIFY_IS_APPROX(m1.square(), square(m1)); + VERIFY_IS_APPROX(m1.cube(), cube(m1)); + VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval())); + VERIFY_IS_APPROX(m1.sign(), sign(m1)); + VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all()); + + // avoid inf and NaNs so verification doesn't fail + m3 = m4.abs(); + VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3))); + VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3))); + VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3))); + VERIFY_IS_APPROX(m3.log(), log(m3)); + VERIFY_IS_APPROX(m3.log1p(), log1p(m3)); + VERIFY_IS_APPROX(m3.log10(), log10(m3)); + VERIFY_IS_APPROX(m3.log2(), log2(m3)); + + + VERIFY((!(m1>m2) == (m1<=m2)).all()); + + VERIFY_IS_APPROX(sin(m1.asin()), m1); + VERIFY_IS_APPROX(cos(m1.acos()), m1); + VERIFY_IS_APPROX(tan(m1.atan()), m1); + VERIFY_IS_APPROX(sinh(m1), Scalar(0.5)*(exp(m1)-exp(-m1))); + VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1))); + VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1)))); + VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1)))); + VERIFY_IS_APPROX(arg(m1), ((m1())*Scalar(std::acos(Scalar(-1)))); + VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all()); + VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all()); + VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all()); + VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all()); + VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all()); + VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all()); + VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all()); + VERIFY((Eigen::isinf)(m4/Scalar(0)).all()); + VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all()); + VERIFY_IS_APPROX(inverse(inverse(m4)),m4); + VERIFY((abs(m1) == m1 || abs(m1) == -m1).all()); + VERIFY_IS_APPROX(m3, sqrt(abs2(m3))); + VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1)); + VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() ); + VERIFY_IS_APPROX( m1*m1.sign(),m1.abs()); + VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1); + + VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1)); + VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1)); + if(!NumTraits::IsComplex) + VERIFY_IS_APPROX(numext::real(m1), m1); + + // shift argument of logarithm so that it is not zero + Scalar smallNumber = NumTraits::dummy_precision(); + VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m3) + smallNumber)); + VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + smallNumber)); + + VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2)); + VERIFY_IS_APPROX(m1.exp(), exp(m1)); + VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp()); + + VERIFY_IS_APPROX(m1.expm1(), expm1(m1)); + VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber)); + + VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt()); + VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt()); + + VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt()); + VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt()); + + // Avoid inf and NaN. + m3 = (m1.square()::epsilon()).select(Scalar(1),m3); + VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse()); + pow_test(); + + VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10))); + VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2))); + + // scalar by array division + const RealScalar tiny = sqrt(std::numeric_limits::epsilon()); + s1 += Scalar(tiny); + m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); + VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); + + // check inplace transpose + m3 = m1; + m3.transposeInPlace(); + VERIFY_IS_APPROX(m3, m1.transpose()); + m3.transposeInPlace(); + VERIFY_IS_APPROX(m3, m1); +} + +template void array_complex(const ArrayType& m) +{ + typedef typename ArrayType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2(rows, cols), + m4 = m1; + + m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real()); + m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag()); + + Array m3(rows, cols); + + for (Index i = 0; i < m.rows(); ++i) + for (Index j = 0; j < m.cols(); ++j) + m2(i,j) = sqrt(m1(i,j)); + + // these tests are mostly to check possible compilation issues with free-functions. + VERIFY_IS_APPROX(m1.sin(), sin(m1)); + VERIFY_IS_APPROX(m1.cos(), cos(m1)); + VERIFY_IS_APPROX(m1.tan(), tan(m1)); + VERIFY_IS_APPROX(m1.sinh(), sinh(m1)); + VERIFY_IS_APPROX(m1.cosh(), cosh(m1)); + VERIFY_IS_APPROX(m1.tanh(), tanh(m1)); + VERIFY_IS_APPROX(m1.logistic(), logistic(m1)); + VERIFY_IS_APPROX(m1.arg(), arg(m1)); + VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all()); + VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all()); + VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all()); + VERIFY_IS_APPROX(m4.inverse(), inverse(m4)); + VERIFY_IS_APPROX(m1.log(), log(m1)); + VERIFY_IS_APPROX(m1.log10(), log10(m1)); + VERIFY_IS_APPROX(m1.log2(), log2(m1)); + VERIFY_IS_APPROX(m1.abs(), abs(m1)); + VERIFY_IS_APPROX(m1.abs2(), abs2(m1)); + VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1)); + VERIFY_IS_APPROX(m1.square(), square(m1)); + VERIFY_IS_APPROX(m1.cube(), cube(m1)); + VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval())); + VERIFY_IS_APPROX(m1.sign(), sign(m1)); + + + VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2)); + VERIFY_IS_APPROX(m1.exp(), exp(m1)); + VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp()); + + VERIFY_IS_APPROX(m1.expm1(), expm1(m1)); + VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.); + // Check for larger magnitude complex numbers that expm1 matches exp - 1. + VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.); + + VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1))); + VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1))); + VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1)))); + VERIFY_IS_APPROX(logistic(m1), (1.0/(1.0 + exp(-m1)))); + + for (Index i = 0; i < m.rows(); ++i) + for (Index j = 0; j < m.cols(); ++j) + m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real()); + VERIFY_IS_APPROX(arg(m1), m3); + + std::complex zero(0.0,0.0); + VERIFY((Eigen::isnan)(m1*zero/zero).all()); +#if EIGEN_COMP_MSVC + // msvc complex division is not robust + VERIFY((Eigen::isinf)(m4/RealScalar(0)).all()); +#else +#if EIGEN_COMP_CLANG + // clang's complex division is notoriously broken too + if((numext::isinf)(m4(0,0)/RealScalar(0))) { +#endif + VERIFY((Eigen::isinf)(m4/zero).all()); +#if EIGEN_COMP_CLANG + } + else + { + VERIFY((Eigen::isinf)(m4.real()/zero.real()).all()); + } +#endif +#endif // MSVC + + VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all()); + + VERIFY_IS_APPROX(inverse(inverse(m4)),m4); + VERIFY_IS_APPROX(conj(m1.conjugate()), m1); + VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag()))); + VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1))); + VERIFY_IS_APPROX(log10(m1), log(m1)/log(10)); + VERIFY_IS_APPROX(log2(m1), log(m1)/log(2)); + + VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() ); + VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1); + + // scalar by array division + Scalar s1 = internal::random(); + const RealScalar tiny = std::sqrt(std::numeric_limits::epsilon()); + s1 += Scalar(tiny); + m1 += ArrayType::Constant(rows,cols,Scalar(tiny)); + VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse()); + + // check inplace transpose + m2 = m1; + m2.transposeInPlace(); + VERIFY_IS_APPROX(m2, m1.transpose()); + m2.transposeInPlace(); + VERIFY_IS_APPROX(m2, m1); + // Check vectorized inplace transpose. + ArrayType m5 = ArrayType::Random(131, 131); + ArrayType m6 = m5; + m6.transposeInPlace(); + VERIFY_IS_APPROX(m6, m5.transpose()); +} + +template void min_max(const ArrayType& m) +{ + typedef typename ArrayType::Scalar Scalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols); + + // min/max with array + Scalar maxM1 = m1.maxCoeff(); + Scalar minM1 = m1.minCoeff(); + + VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1))); + VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1))); + + VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1))); + VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1))); + + // min/max with scalar input + VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1)); + VERIFY_IS_APPROX(m1, (m1.min)( maxM1)); + + VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1)); + VERIFY_IS_APPROX(m1, (m1.max)( minM1)); + + + // min/max with various NaN propagation options. + if (m1.size() > 1 && !NumTraits::IsInteger) { + m1(0,0) = NumTraits::quiet_NaN(); + maxM1 = m1.template maxCoeff(); + minM1 = m1.template minCoeff(); + VERIFY((numext::isnan)(maxM1)); + VERIFY((numext::isnan)(minM1)); + + maxM1 = m1.template maxCoeff(); + minM1 = m1.template minCoeff(); + VERIFY(!(numext::isnan)(maxM1)); + VERIFY(!(numext::isnan)(minM1)); + } +} + +template +struct shift_left { + template + Scalar operator()(const Scalar& v) const { + return v << N; + } +}; + +template +struct arithmetic_shift_right { + template + Scalar operator()(const Scalar& v) const { + return v >> N; + } +}; + +template void array_integer(const ArrayType& m) +{ + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2(rows, cols); + + m2 = m1.template shiftLeft<2>(); + VERIFY( (m2 == m1.unaryExpr(shift_left<2>())).all() ); + m2 = m1.template shiftLeft<9>(); + VERIFY( (m2 == m1.unaryExpr(shift_left<9>())).all() ); + + m2 = m1.template shiftRight<2>(); + VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all() ); + m2 = m1.template shiftRight<9>(); + VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all() ); +} + +EIGEN_DECLARE_TEST(array_cwise) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( array(Array()) ); + CALL_SUBTEST_2( array(Array22f()) ); + CALL_SUBTEST_3( array(Array44d()) ); + CALL_SUBTEST_4( array(ArrayXXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_5( array(ArrayXXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array(ArrayXXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array(Array(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array_integer(ArrayXXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array_integer(Array(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( comparisons(Array()) ); + CALL_SUBTEST_2( comparisons(Array22f()) ); + CALL_SUBTEST_3( comparisons(Array44d()) ); + CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( min_max(Array()) ); + CALL_SUBTEST_2( min_max(Array22f()) ); + CALL_SUBTEST_3( min_max(Array44d()) ); + CALL_SUBTEST_5( min_max(ArrayXXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( min_max(ArrayXXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( array_real(Array()) ); + CALL_SUBTEST_2( array_real(Array22f()) ); + CALL_SUBTEST_3( array_real(Array44d()) ); + CALL_SUBTEST_5( array_real(ArrayXXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_7( array_real(Array()) ); + CALL_SUBTEST_8( array_real(Array()) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + + VERIFY((internal::is_same< internal::global_math_functions_filtering_base::type, int >::value)); + VERIFY((internal::is_same< internal::global_math_functions_filtering_base::type, float >::value)); + VERIFY((internal::is_same< internal::global_math_functions_filtering_base::type, ArrayBase >::value)); + typedef CwiseUnaryOp, ArrayXd > Xpr; + VERIFY((internal::is_same< internal::global_math_functions_filtering_base::type, + ArrayBase + >::value)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_for_matrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_for_matrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fb6be351e69af963db61c903ea0e9f6e3c6d52da --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_for_matrix.cpp @@ -0,0 +1,307 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void array_for_matrix(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix ColVectorType; + typedef Matrix RowVectorType; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols); + + ColVectorType cv1 = ColVectorType::Random(rows); + RowVectorType rv1 = RowVectorType::Random(cols); + + Scalar s1 = internal::random(), + s2 = internal::random(); + + // scalar addition + VERIFY_IS_APPROX(m1.array() + s1, s1 + m1.array()); + VERIFY_IS_APPROX((m1.array() + s1).matrix(), MatrixType::Constant(rows,cols,s1) + m1); + VERIFY_IS_APPROX(((m1*Scalar(2)).array() - s2).matrix(), (m1+m1) - MatrixType::Constant(rows,cols,s2) ); + m3 = m1; + m3.array() += s2; + VERIFY_IS_APPROX(m3, (m1.array() + s2).matrix()); + m3 = m1; + m3.array() -= s1; + VERIFY_IS_APPROX(m3, (m1.array() - s1).matrix()); + + // reductions + VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum().sum() - m1.sum(), m1.squaredNorm()); + VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum().sum() - m1.sum(), m1.squaredNorm()); + VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum() + m2.colwise().sum() - (m1+m2).colwise().sum(), (m1+m2).squaredNorm()); + VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum() - m2.rowwise().sum() - (m1-m2).rowwise().sum(), (m1-m2).squaredNorm()); + VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op())); + + // vector-wise ops + m3 = m1; + VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1); + m3 = m1; + VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1); + m3 = m1; + VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1); + m3 = m1; + VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1); + + // empty objects + VERIFY_IS_APPROX((m1.template block<0,Dynamic>(0,0,0,cols).colwise().sum()), RowVectorType::Zero(cols)); + VERIFY_IS_APPROX((m1.template block(0,0,rows,0).rowwise().sum()), ColVectorType::Zero(rows)); + VERIFY_IS_APPROX((m1.template block<0,Dynamic>(0,0,0,cols).colwise().prod()), RowVectorType::Ones(cols)); + VERIFY_IS_APPROX((m1.template block(0,0,rows,0).rowwise().prod()), ColVectorType::Ones(rows)); + + VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().sum(), RowVectorType::Zero(cols)); + VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().sum(), ColVectorType::Zero(rows)); + VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().prod(), RowVectorType::Ones(cols)); + VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().prod(), ColVectorType::Ones(rows)); + + // verify the const accessors exist + const Scalar& ref_m1 = m.matrix().array().coeffRef(0); + const Scalar& ref_m2 = m.matrix().array().coeffRef(0,0); + const Scalar& ref_a1 = m.array().matrix().coeffRef(0); + const Scalar& ref_a2 = m.array().matrix().coeffRef(0,0); + VERIFY(&ref_a1 == &ref_m1); + VERIFY(&ref_a2 == &ref_m2); + + // Check write accessors: + m1.array().coeffRef(0,0) = 1; + VERIFY_IS_APPROX(m1(0,0),Scalar(1)); + m1.array()(0,0) = 2; + VERIFY_IS_APPROX(m1(0,0),Scalar(2)); + m1.array().matrix().coeffRef(0,0) = 3; + VERIFY_IS_APPROX(m1(0,0),Scalar(3)); + m1.array().matrix()(0,0) = 4; + VERIFY_IS_APPROX(m1(0,0),Scalar(4)); +} + +template void comparisons(const MatrixType& m) +{ + using std::abs; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols); + + VERIFY(((m1.array() + Scalar(1)) > m1.array()).all()); + VERIFY(((m1.array() - Scalar(1)) < m1.array()).all()); + if (rows*cols>1) + { + m3 = m1; + m3(r,c) += 1; + VERIFY(! (m1.array() < m3.array()).all() ); + VERIFY(! (m1.array() > m3.array()).all() ); + } + + // comparisons to scalar + VERIFY( (m1.array() != (m1(r,c)+1) ).any() ); + VERIFY( (m1.array() > (m1(r,c)-1) ).any() ); + VERIFY( (m1.array() < (m1(r,c)+1) ).any() ); + VERIFY( (m1.array() == m1(r,c) ).any() ); + VERIFY( m1.cwiseEqual(m1(r,c)).any() ); + + // test Select + VERIFY_IS_APPROX( (m1.array()m2.array()).select(m1,m2), m1.cwiseMax(m2) ); + Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2); + for (int j=0; j=MatrixType::Constant(rows,cols,mid).array()) + .select(m1,0), m3); + // even shorter version: + VERIFY_IS_APPROX( (m1.array().abs()RealScalar(0.1)).count() == rows*cols); + + // and/or + VERIFY( ((m1.array()RealScalar(0)).matrix()).count() == 0); + VERIFY( ((m1.array()=RealScalar(0)).matrix()).count() == rows*cols); + RealScalar a = m1.cwiseAbs().mean(); + VERIFY( ((m1.array()<-a).matrix() || (m1.array()>a).matrix()).count() == (m1.cwiseAbs().array()>a).count()); + + typedef Matrix VectorOfIndices; + + // TODO allows colwise/rowwise for array + VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().colwise().count(), VectorOfIndices::Constant(cols,rows).transpose()); + VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().rowwise().count(), VectorOfIndices::Constant(rows, cols)); +} + +template void lpNorm(const VectorType& v) +{ + using std::sqrt; + typedef typename VectorType::RealScalar RealScalar; + VectorType u = VectorType::Random(v.size()); + + if(v.size()==0) + { + VERIFY_IS_APPROX(u.template lpNorm(), RealScalar(0)); + VERIFY_IS_APPROX(u.template lpNorm<1>(), RealScalar(0)); + VERIFY_IS_APPROX(u.template lpNorm<2>(), RealScalar(0)); + VERIFY_IS_APPROX(u.template lpNorm<5>(), RealScalar(0)); + } + else + { + VERIFY_IS_APPROX(u.template lpNorm(), u.cwiseAbs().maxCoeff()); + } + + VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum()); + VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum())); + VERIFY_IS_APPROX(numext::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum()); +} + +template void cwise_min_max(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols); + + // min/max with array + Scalar maxM1 = m1.maxCoeff(); + Scalar minM1 = m1.minCoeff(); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin(MatrixType::Constant(rows,cols, minM1))); + VERIFY_IS_APPROX(m1, m1.cwiseMin(MatrixType::Constant(rows,cols, maxM1))); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax(MatrixType::Constant(rows,cols, maxM1))); + VERIFY_IS_APPROX(m1, m1.cwiseMax(MatrixType::Constant(rows,cols, minM1))); + + // min/max with scalar input + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin( minM1)); + VERIFY_IS_APPROX(m1, m1.cwiseMin(maxM1)); + VERIFY_IS_APPROX(-m1, (-m1).cwiseMin(-minM1)); + VERIFY_IS_APPROX(-m1.array(), ((-m1).array().min)( -minM1)); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax( maxM1)); + VERIFY_IS_APPROX(m1, m1.cwiseMax(minM1)); + VERIFY_IS_APPROX(-m1, (-m1).cwiseMax(-maxM1)); + VERIFY_IS_APPROX(-m1.array(), ((-m1).array().max)(-maxM1)); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1).array(), (m1.array().min)( minM1)); + VERIFY_IS_APPROX(m1.array(), (m1.array().min)( maxM1)); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1).array(), (m1.array().max)( maxM1)); + VERIFY_IS_APPROX(m1.array(), (m1.array().max)( minM1)); + +} + +template void resize(const MatrixTraits& t) +{ + typedef typename MatrixTraits::Scalar Scalar; + typedef Matrix MatrixType; + typedef Array Array2DType; + typedef Matrix VectorType; + typedef Array Array1DType; + + Index rows = t.rows(), cols = t.cols(); + + MatrixType m(rows,cols); + VectorType v(rows); + Array2DType a2(rows,cols); + Array1DType a1(rows); + + m.array().resize(rows+1,cols+1); + VERIFY(m.rows()==rows+1 && m.cols()==cols+1); + a2.matrix().resize(rows+1,cols+1); + VERIFY(a2.rows()==rows+1 && a2.cols()==cols+1); + v.array().resize(cols); + VERIFY(v.size()==cols); + a1.matrix().resize(cols); + VERIFY(a1.size()==cols); +} + +template +void regression_bug_654() +{ + ArrayXf a = RowVectorXf(3); + VectorXf v = Array(3); +} + +// Check propagation of LvalueBit through Array/Matrix-Wrapper +template +void regrrssion_bug_1410() +{ + const Matrix4i M; + const Array4i A; + ArrayWrapper MA = M.array(); + MA.row(0); + MatrixWrapper AM = A.matrix(); + AM.row(0); + + VERIFY((internal::traits >::Flags&LvalueBit)==0); + VERIFY((internal::traits >::Flags&LvalueBit)==0); + + VERIFY((internal::traits >::Flags&LvalueBit)==LvalueBit); + VERIFY((internal::traits >::Flags&LvalueBit)==LvalueBit); +} + +EIGEN_DECLARE_TEST(array_for_matrix) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( array_for_matrix(Matrix()) ); + CALL_SUBTEST_2( array_for_matrix(Matrix2f()) ); + CALL_SUBTEST_3( array_for_matrix(Matrix4d()) ); + CALL_SUBTEST_4( array_for_matrix(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_5( array_for_matrix(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array_for_matrix(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( comparisons(Matrix()) ); + CALL_SUBTEST_2( comparisons(Matrix2f()) ); + CALL_SUBTEST_3( comparisons(Matrix4d()) ); + CALL_SUBTEST_5( comparisons(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( comparisons(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( cwise_min_max(Matrix()) ); + CALL_SUBTEST_2( cwise_min_max(Matrix2f()) ); + CALL_SUBTEST_3( cwise_min_max(Matrix4d()) ); + CALL_SUBTEST_5( cwise_min_max(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( cwise_min_max(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( lpNorm(Matrix()) ); + CALL_SUBTEST_2( lpNorm(Vector2f()) ); + CALL_SUBTEST_7( lpNorm(Vector3d()) ); + CALL_SUBTEST_8( lpNorm(Vector4f()) ); + CALL_SUBTEST_5( lpNorm(VectorXf(internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_4( lpNorm(VectorXcf(internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + CALL_SUBTEST_5( lpNorm(VectorXf(0)) ); + CALL_SUBTEST_4( lpNorm(VectorXcf(0)) ); + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_4( resize(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_5( resize(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( resize(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + CALL_SUBTEST_6( regression_bug_654<0>() ); + CALL_SUBTEST_6( regrrssion_bug_1410<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_of_string.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_of_string.cpp new file mode 100644 index 0000000000000000000000000000000000000000..23e51529b105f2b45b807e8d6bc6fdcf7f2a7058 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_of_string.cpp @@ -0,0 +1,32 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +EIGEN_DECLARE_TEST(array_of_string) +{ + typedef Array ArrayXs; + ArrayXs a1(3), a2(3), a3(3), a3ref(3); + a1 << "one", "two", "three"; + a2 << "1", "2", "3"; + a3ref << "one (1)", "two (2)", "three (3)"; + std::stringstream s1; + s1 << a1; + VERIFY_IS_EQUAL(s1.str(), std::string(" one two three")); + a3 = a1 + std::string(" (") + a2 + std::string(")"); + VERIFY((a3==a3ref).all()); + + a3 = a1; + a3 += std::string(" (") + a2 + std::string(")"); + VERIFY((a3==a3ref).all()); + + a1.swap(a3); + VERIFY((a1==a3ref).all()); + VERIFY((a3!=a3ref).all()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_replicate.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_replicate.cpp new file mode 100644 index 0000000000000000000000000000000000000000..057c3c77b4996fbaf92d2b0fa063ac4caa33ef22 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_replicate.cpp @@ -0,0 +1,81 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void replicate(const MatrixType& m) +{ + /* this test covers the following files: + Replicate.cpp + */ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + typedef Matrix MatrixX; + typedef Matrix VectorX; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols); + + VectorType v1 = VectorType::Random(rows); + + MatrixX x1, x2; + VectorX vx1; + + int f1 = internal::random(1,10), + f2 = internal::random(1,10); + + x1.resize(rows*f1,cols*f2); + for(int j=0; j())); + + x2.resize(rows,3*cols); + x2 << m2, m2, m2; + VERIFY_IS_APPROX(x2, (m2.template replicate<1,3>())); + + vx1.resize(3*rows,cols); + vx1 << m2, m2, m2; + VERIFY_IS_APPROX(vx1+vx1, vx1+(m2.template replicate<3,1>())); + + vx1=m2+(m2.colwise().replicate(1)); + + if(m2.cols()==1) + VERIFY_IS_APPROX(m2.coeff(0), (m2.template replicate<3,1>().coeff(m2.rows()))); + + x2.resize(rows,f1); + for (int j=0; j()) ); + CALL_SUBTEST_2( replicate(Vector2f()) ); + CALL_SUBTEST_3( replicate(Vector3d()) ); + CALL_SUBTEST_4( replicate(Vector4f()) ); + CALL_SUBTEST_5( replicate(VectorXf(16)) ); + CALL_SUBTEST_6( replicate(VectorXcd(10)) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_reverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_reverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c77528a5bba280a30af5fc5c0feff638d1b4762d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/array_reverse.cpp @@ -0,0 +1,204 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2009 Ricard Marxer +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +using namespace std; + +template void reverse(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + + Index rows = m.rows(); + Index cols = m.cols(); + + // this test relies a lot on Random.h, and there's not much more that we can do + // to test it, hence I consider that we will have tested Random.h + MatrixType m1 = MatrixType::Random(rows, cols), m2; + VectorType v1 = VectorType::Random(rows); + + MatrixType m1_r = m1.reverse(); + // Verify that MatrixBase::reverse() works + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_r(i, j), m1(rows - 1 - i, cols - 1 - j)); + } + } + + Reverse m1_rd(m1); + // Verify that a Reverse default (in both directions) of an expression works + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_rd(i, j), m1(rows - 1 - i, cols - 1 - j)); + } + } + + Reverse m1_rb(m1); + // Verify that a Reverse in both directions of an expression works + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_rb(i, j), m1(rows - 1 - i, cols - 1 - j)); + } + } + + Reverse m1_rv(m1); + // Verify that a Reverse in the vertical directions of an expression works + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_rv(i, j), m1(rows - 1 - i, j)); + } + } + + Reverse m1_rh(m1); + // Verify that a Reverse in the horizontal directions of an expression works + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_rh(i, j), m1(i, cols - 1 - j)); + } + } + + VectorType v1_r = v1.reverse(); + // Verify that a VectorType::reverse() of an expression works + for ( int i = 0; i < rows; i++ ) { + VERIFY_IS_APPROX(v1_r(i), v1(rows - 1 - i)); + } + + MatrixType m1_cr = m1.colwise().reverse(); + // Verify that PartialRedux::reverse() works (for colwise()) + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_cr(i, j), m1(rows - 1 - i, j)); + } + } + + MatrixType m1_rr = m1.rowwise().reverse(); + // Verify that PartialRedux::reverse() works (for rowwise()) + for ( int i = 0; i < rows; i++ ) { + for ( int j = 0; j < cols; j++ ) { + VERIFY_IS_APPROX(m1_rr(i, j), m1(i, cols - 1 - j)); + } + } + + Scalar x = internal::random(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + m1.reverse()(r, c) = x; + VERIFY_IS_APPROX(x, m1(rows - 1 - r, cols - 1 - c)); + + m2 = m1; + m2.reverseInPlace(); + VERIFY_IS_APPROX(m2,m1.reverse().eval()); + + m2 = m1; + m2.col(0).reverseInPlace(); + VERIFY_IS_APPROX(m2.col(0),m1.col(0).reverse().eval()); + + m2 = m1; + m2.row(0).reverseInPlace(); + VERIFY_IS_APPROX(m2.row(0),m1.row(0).reverse().eval()); + + m2 = m1; + m2.rowwise().reverseInPlace(); + VERIFY_IS_APPROX(m2,m1.rowwise().reverse().eval()); + + m2 = m1; + m2.colwise().reverseInPlace(); + VERIFY_IS_APPROX(m2,m1.colwise().reverse().eval()); + + m1.colwise().reverse()(r, c) = x; + VERIFY_IS_APPROX(x, m1(rows - 1 - r, c)); + + m1.rowwise().reverse()(r, c) = x; + VERIFY_IS_APPROX(x, m1(r, cols - 1 - c)); +} + +template +void array_reverse_extra() +{ + Vector4f x; x << 1, 2, 3, 4; + Vector4f y; y << 4, 3, 2, 1; + VERIFY(x.reverse()[1] == 3); + VERIFY(x.reverse() == y); +} + +// Simpler version of reverseInPlace leveraging a bug +// in clang 6/7 with -O2 and AVX or AVX512 enabled. +// This simpler version ensure that the clang bug is not simply hidden +// through mis-inlining of reverseInPlace or other minor changes. +template +EIGEN_DONT_INLINE +void bug1684_job1(MatrixType& m1, MatrixType& m2) +{ + m2 = m1; + m2.col(0).swap(m2.col(3)); + m2.col(1).swap(m2.col(2)); +} + +template +EIGEN_DONT_INLINE +void bug1684_job2(MatrixType& m1, MatrixType& m2) +{ + m2 = m1; // load m1/m2 in AVX registers + m1.col(0) = m2.col(3); // perform 128 bits moves + m1.col(1) = m2.col(2); + m1.col(2) = m2.col(1); + m1.col(3) = m2.col(0); +} + +template +EIGEN_DONT_INLINE +void bug1684_job3(MatrixType& m1, MatrixType& m2) +{ + m2 = m1; + Vector4f tmp; + tmp = m2.col(0); + m2.col(0) = m2.col(3); + m2.col(3) = tmp; + tmp = m2.col(1); + m2.col(1) = m2.col(2); + m2.col(2) = tmp; + +} + +template +void bug1684() +{ + Matrix4f m1 = Matrix4f::Random(); + Matrix4f m2 = Matrix4f::Random(); + bug1684_job1(m1,m2); + VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval()); + bug1684_job2(m1,m2); + VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval()); + // This one still fail after our swap's workaround, + // but I expect users not to implement their own swap. + // bug1684_job3(m1,m2); + // VERIFY_IS_APPROX(m2, m1.rowwise().reverse().eval()); +} + +EIGEN_DECLARE_TEST(array_reverse) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( reverse(Matrix()) ); + CALL_SUBTEST_2( reverse(Matrix2f()) ); + CALL_SUBTEST_3( reverse(Matrix4f()) ); + CALL_SUBTEST_4( reverse(Matrix4d()) ); + CALL_SUBTEST_5( reverse(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( reverse(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_7( reverse(MatrixXcd(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_8( reverse(Matrix()) ); + CALL_SUBTEST_9( reverse(Matrix(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_3( bug1684<0>() ); + } + CALL_SUBTEST_3( array_reverse_extra<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bandmatrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bandmatrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..66a1b0db4734e01baf0e4368a9bc2fb7f56c58f7 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bandmatrix.cpp @@ -0,0 +1,71 @@ +// This file is triangularView of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void bandmatrix(const MatrixType& _m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix DenseMatrixType; + + Index rows = _m.rows(); + Index cols = _m.cols(); + Index supers = _m.supers(); + Index subs = _m.subs(); + + MatrixType m(rows,cols,supers,subs); + + DenseMatrixType dm1(rows,cols); + dm1.setZero(); + + m.diagonal().setConstant(123); + dm1.diagonal().setConstant(123); + for (int i=1; i<=m.supers();++i) + { + m.diagonal(i).setConstant(static_cast(i)); + dm1.diagonal(i).setConstant(static_cast(i)); + } + for (int i=1; i<=m.subs();++i) + { + m.diagonal(-i).setConstant(-static_cast(i)); + dm1.diagonal(-i).setConstant(-static_cast(i)); + } + //std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n\n\n"; + VERIFY_IS_APPROX(dm1,m.toDenseMatrix()); + + for (int i=0; i(i+1)); + dm1.col(i).setConstant(static_cast(i+1)); + } + Index d = (std::min)(rows,cols); + Index a = std::max(0,cols-d-supers); + Index b = std::max(0,rows-d-subs); + if(a>0) dm1.block(0,d+supers,rows,a).setZero(); + dm1.block(0,supers+1,cols-supers-1-a,cols-supers-1-a).template triangularView().setZero(); + dm1.block(subs+1,0,rows-subs-1-b,rows-subs-1-b).template triangularView().setZero(); + if(b>0) dm1.block(d+subs,0,b,cols).setZero(); + //std::cerr << m.m_data << "\n\n" << m.toDense() << "\n\n" << dm1 << "\n\n"; + VERIFY_IS_APPROX(dm1,m.toDenseMatrix()); + +} + +using Eigen::internal::BandMatrix; + +EIGEN_DECLARE_TEST(bandmatrix) +{ + for(int i = 0; i < 10*g_repeat ; i++) { + Index rows = internal::random(1,10); + Index cols = internal::random(1,10); + Index sups = internal::random(0,cols-1); + Index subs = internal::random(0,rows-1); + CALL_SUBTEST(bandmatrix(BandMatrix(rows,cols,sups,subs)) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/basicstuff.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/basicstuff.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4ca607c8248d99a32efbfa53cf779177c70d3360 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/basicstuff.cpp @@ -0,0 +1,356 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT + +#include "main.h" +#include "random_without_cast_overflow.h" + +template void basicStuff(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + typedef Matrix SquareMatrixType; + + Index rows = m.rows(); + Index cols = m.cols(); + + // this test relies a lot on Random.h, and there's not much more that we can do + // to test it, hence I consider that we will have tested Random.h + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols), + mzero = MatrixType::Zero(rows, cols), + square = Matrix::Random(rows, rows); + VectorType v1 = VectorType::Random(rows), + vzero = VectorType::Zero(rows); + SquareMatrixType sm1 = SquareMatrixType::Random(rows,rows), sm2(rows,rows); + + Scalar x = 0; + while(x == Scalar(0)) x = internal::random(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + m1.coeffRef(r,c) = x; + VERIFY_IS_APPROX(x, m1.coeff(r,c)); + m1(r,c) = x; + VERIFY_IS_APPROX(x, m1(r,c)); + v1.coeffRef(r) = x; + VERIFY_IS_APPROX(x, v1.coeff(r)); + v1(r) = x; + VERIFY_IS_APPROX(x, v1(r)); + v1[r] = x; + VERIFY_IS_APPROX(x, v1[r]); + + // test fetching with various index types. + Index r1 = internal::random(0, numext::mini(Index(127),rows-1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); +#if EIGEN_HAS_CXX11 + x = v1(static_cast(r1)); + x = v1(static_cast(r1)); +#endif + + VERIFY_IS_APPROX( v1, v1); + VERIFY_IS_NOT_APPROX( v1, 2*v1); + VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1); + VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1.squaredNorm()); + VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1, v1); + VERIFY_IS_APPROX( vzero, v1-v1); + VERIFY_IS_APPROX( m1, m1); + VERIFY_IS_NOT_APPROX( m1, 2*m1); + VERIFY_IS_MUCH_SMALLER_THAN( mzero, m1); + VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1, m1); + VERIFY_IS_APPROX( mzero, m1-m1); + + // always test operator() on each read-only expression class, + // in order to check const-qualifiers. + // indeed, if an expression class (here Zero) is meant to be read-only, + // hence has no _write() method, the corresponding MatrixBase method (here zero()) + // should return a const-qualified object so that it is the const-qualified + // operator() that gets called, which in turn calls _read(). + VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast(1)); + + // now test copying a row-vector into a (column-)vector and conversely. + square.col(r) = square.row(r).eval(); + Matrix rv(rows); + Matrix cv(rows); + rv = square.row(r); + cv = square.col(r); + + VERIFY_IS_APPROX(rv, cv.transpose()); + + if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic) + { + VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1))); + } + + if(cols!=1 && rows!=1) + { + VERIFY_RAISES_ASSERT(m1[0]); + VERIFY_RAISES_ASSERT((m1+m1)[0]); + } + + VERIFY_IS_APPROX(m3 = m1,m1); + MatrixType m4; + VERIFY_IS_APPROX(m4 = m1,m1); + + m3.real() = m1.real(); + VERIFY_IS_APPROX(static_cast(m3).real(), static_cast(m1).real()); + VERIFY_IS_APPROX(static_cast(m3).real(), m1.real()); + + // check == / != operators + VERIFY(m1==m1); + VERIFY(m1!=m2); + VERIFY(!(m1==m2)); + VERIFY(!(m1!=m1)); + m1 = m2; + VERIFY(m1==m2); + VERIFY(!(m1!=m2)); + + // check automatic transposition + sm2.setZero(); + for(Index i=0;i(0,10)>5; + m3 = b ? m1 : m2; + if(b) VERIFY_IS_APPROX(m3,m1); + else VERIFY_IS_APPROX(m3,m2); + m3 = b ? -m1 : m2; + if(b) VERIFY_IS_APPROX(m3,-m1); + else VERIFY_IS_APPROX(m3,m2); + m3 = b ? m1 : -m2; + if(b) VERIFY_IS_APPROX(m3,m1); + else VERIFY_IS_APPROX(m3,-m2); + } +} + +template void basicStuffComplex(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix RealMatrixType; + + Index rows = m.rows(); + Index cols = m.cols(); + + Scalar s1 = internal::random(), + s2 = internal::random(); + + VERIFY(numext::real(s1)==numext::real_ref(s1)); + VERIFY(numext::imag(s1)==numext::imag_ref(s1)); + numext::real_ref(s1) = numext::real(s2); + numext::imag_ref(s1) = numext::imag(s2); + VERIFY(internal::isApprox(s1, s2, NumTraits::epsilon())); + // extended precision in Intel FPUs means that s1 == s2 in the line above is not guaranteed. + + RealMatrixType rm1 = RealMatrixType::Random(rows,cols), + rm2 = RealMatrixType::Random(rows,cols); + MatrixType cm(rows,cols); + cm.real() = rm1; + cm.imag() = rm2; + VERIFY_IS_APPROX(static_cast(cm).real(), rm1); + VERIFY_IS_APPROX(static_cast(cm).imag(), rm2); + rm1.setZero(); + rm2.setZero(); + rm1 = cm.real(); + rm2 = cm.imag(); + VERIFY_IS_APPROX(static_cast(cm).real(), rm1); + VERIFY_IS_APPROX(static_cast(cm).imag(), rm2); + cm.real().setZero(); + VERIFY(static_cast(cm).real().isZero()); + VERIFY(!static_cast(cm).imag().isZero()); +} + +template +struct casting_test { + static void run() { + Matrix m; + for (int i=0; i::value(); + } + } + Matrix n = m.template cast(); + for (int i=0; i(m(i, j)))); + } + } + } +}; + +template +struct casting_test_runner { + static void run() { + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test::run(); +#if EIGEN_HAS_CXX11 + casting_test::run(); + casting_test::run(); +#endif + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test::run(); + casting_test >::run(); + casting_test >::run(); + } +}; + +template +struct casting_test_runner::IsComplex)>::type> +{ + static void run() { + // Only a few casts from std::complex are defined. + casting_test::run(); + casting_test::run(); + casting_test >::run(); + casting_test >::run(); + } +}; + +void casting_all() { + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); +#if EIGEN_HAS_CXX11 + casting_test_runner::run(); + casting_test_runner::run(); +#endif + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner::run(); + casting_test_runner >::run(); + casting_test_runner >::run(); +} + +template +void fixedSizeMatrixConstruction() +{ + Scalar raw[4]; + for(int k=0; k<4; ++k) + raw[k] = internal::random(); + + { + Matrix m(raw); + Array a(raw); + for(int k=0; k<4; ++k) VERIFY(m(k) == raw[k]); + for(int k=0; k<4; ++k) VERIFY(a(k) == raw[k]); + VERIFY_IS_EQUAL(m,(Matrix(raw[0],raw[1],raw[2],raw[3]))); + VERIFY((a==(Array(raw[0],raw[1],raw[2],raw[3]))).all()); + } + { + Matrix m(raw); + Array a(raw); + for(int k=0; k<3; ++k) VERIFY(m(k) == raw[k]); + for(int k=0; k<3; ++k) VERIFY(a(k) == raw[k]); + VERIFY_IS_EQUAL(m,(Matrix(raw[0],raw[1],raw[2]))); + VERIFY((a==Array(raw[0],raw[1],raw[2])).all()); + } + { + Matrix m(raw), m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ); + Array a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ); + for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]); + for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]); + VERIFY_IS_EQUAL(m,(Matrix(raw[0],raw[1]))); + VERIFY((a==Array(raw[0],raw[1])).all()); + for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k])); + for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k])); + } + { + Matrix m(raw), + m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ), + m3( (int(raw[0])), (int(raw[1])) ), + m4( (float(raw[0])), (float(raw[1])) ); + Array a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ); + for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]); + for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]); + VERIFY_IS_EQUAL(m,(Matrix(raw[0],raw[1]))); + VERIFY((a==Array(raw[0],raw[1])).all()); + for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k])); + for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k])); + for(int k=0; k<2; ++k) VERIFY(m3(k) == int(raw[k])); + for(int k=0; k<2; ++k) VERIFY((m4(k)) == Scalar(float(raw[k]))); + } + { + Matrix m(raw), m1(raw[0]), m2( (DenseIndex(raw[0])) ), m3( (int(raw[0])) ); + Array a(raw), a1(raw[0]), a2( (DenseIndex(raw[0])) ); + VERIFY(m(0) == raw[0]); + VERIFY(a(0) == raw[0]); + VERIFY(m1(0) == raw[0]); + VERIFY(a1(0) == raw[0]); + VERIFY(m2(0) == DenseIndex(raw[0])); + VERIFY(a2(0) == DenseIndex(raw[0])); + VERIFY(m3(0) == int(raw[0])); + VERIFY_IS_EQUAL(m,(Matrix(raw[0]))); + VERIFY((a==Array(raw[0])).all()); + } +} + +EIGEN_DECLARE_TEST(basicstuff) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( basicStuff(Matrix()) ); + CALL_SUBTEST_2( basicStuff(Matrix4d()) ); + CALL_SUBTEST_3( basicStuff(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_4( basicStuff(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_5( basicStuff(MatrixXcd(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( basicStuff(Matrix()) ); + CALL_SUBTEST_7( basicStuff(Matrix(internal::random(1,EIGEN_TEST_MAX_SIZE),internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_8( casting_all() ); + + CALL_SUBTEST_3( basicStuffComplex(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_5( basicStuffComplex(MatrixXcd(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); + CALL_SUBTEST_1(fixedSizeMatrixConstruction()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bdcsvd.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bdcsvd.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e92a7dc97d185d7b2e67992b09435f01f1a08d31 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bdcsvd.cpp @@ -0,0 +1,118 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2013 Gauthier Brun +// Copyright (C) 2013 Nicolas Carre +// Copyright (C) 2013 Jean Ceccato +// Copyright (C) 2013 Pierre Zoppitelli +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/ + +// discard stack allocation as that too bypasses malloc +#define EIGEN_STACK_ALLOCATION_LIMIT 0 +#define EIGEN_RUNTIME_NO_MALLOC + +#include "main.h" +#include +#include +#include + + +#define SVD_DEFAULT(M) BDCSVD +#define SVD_FOR_MIN_NORM(M) BDCSVD +#include "svd_common.h" + +// Check all variants of JacobiSVD +template +void bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true) +{ + MatrixType m; + if(pickrandom) { + m.resizeLike(a); + svd_fill_random(m); + } + else + m = a; + + CALL_SUBTEST(( svd_test_all_computation_options >(m, false) )); +} + +template +void bdcsvd_method() +{ + enum { Size = MatrixType::RowsAtCompileTime }; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix RealVecType; + MatrixType m = MatrixType::Identity(); + VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones()); + VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU()); + VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV()); + VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m); + VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).transpose().solve(m), m); + VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).adjoint().solve(m), m); +} + +// compare the Singular values returned with Jacobi and Bdc +template +void compare_bdc_jacobi(const MatrixType& a = MatrixType(), unsigned int computationOptions = 0) +{ + MatrixType m = MatrixType::Random(a.rows(), a.cols()); + BDCSVD bdc_svd(m); + JacobiSVD jacobi_svd(m); + VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues()); + if(computationOptions & ComputeFullU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU()); + if(computationOptions & ComputeThinU) VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU()); + if(computationOptions & ComputeFullV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV()); + if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV()); +} + +EIGEN_DECLARE_TEST(bdcsvd) +{ + CALL_SUBTEST_3(( svd_verify_assert >(Matrix3f()) )); + CALL_SUBTEST_4(( svd_verify_assert >(Matrix4d()) )); + CALL_SUBTEST_7(( svd_verify_assert >(MatrixXf(10,12)) )); + CALL_SUBTEST_8(( svd_verify_assert >(MatrixXcd(7,5)) )); + + CALL_SUBTEST_101(( svd_all_trivial_2x2(bdcsvd) )); + CALL_SUBTEST_102(( svd_all_trivial_2x2(bdcsvd) )); + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_3(( bdcsvd() )); + CALL_SUBTEST_4(( bdcsvd() )); + CALL_SUBTEST_5(( bdcsvd >() )); + + int r = internal::random(1, EIGEN_TEST_MAX_SIZE/2), + c = internal::random(1, EIGEN_TEST_MAX_SIZE/2); + + TEST_SET_BUT_UNUSED_VARIABLE(r) + TEST_SET_BUT_UNUSED_VARIABLE(c) + + CALL_SUBTEST_6(( bdcsvd(Matrix(r,2)) )); + CALL_SUBTEST_7(( bdcsvd(MatrixXf(r,c)) )); + CALL_SUBTEST_7(( compare_bdc_jacobi(MatrixXf(r,c)) )); + CALL_SUBTEST_10(( bdcsvd(MatrixXd(r,c)) )); + CALL_SUBTEST_10(( compare_bdc_jacobi(MatrixXd(r,c)) )); + CALL_SUBTEST_8(( bdcsvd(MatrixXcd(r,c)) )); + CALL_SUBTEST_8(( compare_bdc_jacobi(MatrixXcd(r,c)) )); + + // Test on inf/nan matrix + CALL_SUBTEST_7( (svd_inf_nan, MatrixXf>()) ); + CALL_SUBTEST_10( (svd_inf_nan, MatrixXd>()) ); + } + + // test matrixbase method + CALL_SUBTEST_1(( bdcsvd_method() )); + CALL_SUBTEST_3(( bdcsvd_method() )); + + // Test problem size constructors + CALL_SUBTEST_7( BDCSVD(10,10) ); + + // Check that preallocation avoids subsequent mallocs + // Disabled because not supported by BDCSVD + // CALL_SUBTEST_9( svd_preallocate() ); + + CALL_SUBTEST_2( svd_underoverflow() ); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bfloat16_float.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bfloat16_float.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c3de0b19a0ce6aaa8b65140dd2cebd88e33a1de1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bfloat16_float.cpp @@ -0,0 +1,378 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include +#include +#include + +#include "main.h" + +#include + +#define VERIFY_BFLOAT16_BITS_EQUAL(h, bits) \ + VERIFY_IS_EQUAL((numext::bit_cast(h)), (static_cast(bits))) + +// Make sure it's possible to forward declare Eigen::bfloat16 +namespace Eigen { +struct bfloat16; +} + +using Eigen::bfloat16; + +float BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa, + uint32_t low_mantissa) { + float dest; + uint32_t src = (sign << 31) + (exponent << 23) + (high_mantissa << 16) + low_mantissa; + memcpy(static_cast(&dest), + static_cast(&src), sizeof(dest)); + return dest; +} + +template + void test_roundtrip() { + // Representable T round trip via bfloat16 + VERIFY_IS_EQUAL((internal::cast(internal::cast(-std::numeric_limits::infinity()))), -std::numeric_limits::infinity()); + VERIFY_IS_EQUAL((internal::cast(internal::cast(std::numeric_limits::infinity()))), std::numeric_limits::infinity()); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(-1.0)))), T(-1.0)); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(-0.5)))), T(-0.5)); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(-0.0)))), T(-0.0)); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(1.0)))), T(1.0)); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(0.5)))), T(0.5)); + VERIFY_IS_EQUAL((internal::cast(internal::cast(T(0.0)))), T(0.0)); +} + +void test_conversion() +{ + using Eigen::bfloat16_impl::__bfloat16_raw; + + // Round-trip casts + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(bfloat16(1.0f))), + bfloat16(1.0f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(bfloat16(0.5f))), + bfloat16(0.5f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(bfloat16(-0.33333f))), + bfloat16(-0.33333f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(bfloat16(0.0f))), + bfloat16(0.0f)); + + // Conversion from float. + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity. + + // Verify round-to-nearest-even behavior. + float val1 = static_cast(bfloat16(__bfloat16_raw(0x3c00))); + float val2 = static_cast(bfloat16(__bfloat16_raw(0x3c01))); + float val3 = static_cast(bfloat16(__bfloat16_raw(0x3c02))); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02); + + // Conversion from int. + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140); + + // Conversion from bool. + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80); + + // Conversion to bool + VERIFY_IS_EQUAL(static_cast(bfloat16(3)), true); + VERIFY_IS_EQUAL(static_cast(bfloat16(0.33333f)), true); + VERIFY_IS_EQUAL(bfloat16(-0.0), false); + VERIFY_IS_EQUAL(static_cast(bfloat16(0.0)), false); + + // Explicit conversion to float. + VERIFY_IS_EQUAL(static_cast(bfloat16(__bfloat16_raw(0x0000))), 0.0f); + VERIFY_IS_EQUAL(static_cast(bfloat16(__bfloat16_raw(0x3f80))), 1.0f); + + // Implicit conversion to float + VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x0000)), 0.0f); + VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x3f80)), 1.0f); + + // Zero representations + VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f)); + VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f)); + VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f)); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000); + + // Default is zero + VERIFY_IS_EQUAL(static_cast(bfloat16()), 0.0f); + + // Representable floats round trip via bfloat16 + test_roundtrip(); + test_roundtrip(); + test_roundtrip >(); + test_roundtrip >(); + + // Conversion + Array a; + for (int i = 0; i < 100; i++) a(i) = i + 1.25; + Array b = a.cast(); + Array c = b.cast(); + for (int i = 0; i < 100; ++i) { + VERIFY_LE(numext::abs(c(i) - a(i)), a(i) / 128); + } + + // Epsilon + VERIFY_LE(1.0f, static_cast((std::numeric_limits::epsilon)() + bfloat16(1.0f))); + VERIFY_IS_EQUAL(1.0f, static_cast((std::numeric_limits::epsilon)() / bfloat16(2.0f) + bfloat16(1.0f))); + + // Negate + VERIFY_IS_EQUAL(static_cast(-bfloat16(3.0f)), -3.0f); + VERIFY_IS_EQUAL(static_cast(-bfloat16(-4.5f)), 4.5f); + + +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(static_cast(bfloat16(0.0 / 0.0)))); + VERIFY((numext::isinf)(static_cast(bfloat16(1.0 / 0.0)))); + VERIFY((numext::isinf)(static_cast(bfloat16(-1.0 / 0.0)))); + + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(bfloat16(0.0 / 0.0))); + VERIFY((numext::isinf)(bfloat16(1.0 / 0.0))); + VERIFY((numext::isinf)(bfloat16(-1.0 / 0.0))); +#endif + + // NaNs and infinities. + VERIFY(!(numext::isinf)(static_cast(bfloat16(3.38e38f)))); // Largest finite number. + VERIFY(!(numext::isnan)(static_cast(bfloat16(0.0f)))); + VERIFY((numext::isinf)(static_cast(bfloat16(__bfloat16_raw(0xff80))))); + VERIFY((numext::isnan)(static_cast(bfloat16(__bfloat16_raw(0xffc0))))); + VERIFY((numext::isinf)(static_cast(bfloat16(__bfloat16_raw(0x7f80))))); + VERIFY((numext::isnan)(static_cast(bfloat16(__bfloat16_raw(0x7fc0))))); + + // Exactly same checks as above, just directly on the bfloat16 representation. + VERIFY(!(numext::isinf)(bfloat16(__bfloat16_raw(0x7bff)))); + VERIFY(!(numext::isnan)(bfloat16(__bfloat16_raw(0x0000)))); + VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0xff80)))); + VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0xffc0)))); + VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80)))); + VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0)))); + + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0); + VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0); +} + +void test_numtraits() +{ + std::cout << "epsilon = " << NumTraits::epsilon() << " (0x" << std::hex << numext::bit_cast(NumTraits::epsilon()) << ")" << std::endl; + std::cout << "highest = " << NumTraits::highest() << " (0x" << std::hex << numext::bit_cast(NumTraits::highest()) << ")" << std::endl; + std::cout << "lowest = " << NumTraits::lowest() << " (0x" << std::hex << numext::bit_cast(NumTraits::lowest()) << ")" << std::endl; + std::cout << "min = " << (std::numeric_limits::min)() << " (0x" << std::hex << numext::bit_cast((std::numeric_limits::min)()) << ")" << std::endl; + std::cout << "denorm min = " << (std::numeric_limits::denorm_min)() << " (0x" << std::hex << numext::bit_cast((std::numeric_limits::denorm_min)()) << ")" << std::endl; + std::cout << "infinity = " << NumTraits::infinity() << " (0x" << std::hex << numext::bit_cast(NumTraits::infinity()) << ")" << std::endl; + std::cout << "quiet nan = " << NumTraits::quiet_NaN() << " (0x" << std::hex << numext::bit_cast(NumTraits::quiet_NaN()) << ")" << std::endl; + std::cout << "signaling nan = " << std::numeric_limits::signaling_NaN() << " (0x" << std::hex << numext::bit_cast(std::numeric_limits::signaling_NaN()) << ")" << std::endl; + + VERIFY(NumTraits::IsSigned); + + VERIFY_IS_EQUAL( + numext::bit_cast(std::numeric_limits::infinity()), + numext::bit_cast(bfloat16(std::numeric_limits::infinity())) ); + // There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise + // bit pattern. We test that it is in fact a NaN, then test the signaling + // bit (msb of significand is 1 for quiet, 0 for signaling). + const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040; + VERIFY( + (numext::isnan)(std::numeric_limits::quiet_NaN()) + && (numext::isnan)(bfloat16(std::numeric_limits::quiet_NaN())) + && ((numext::bit_cast(std::numeric_limits::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0) + && ((numext::bit_cast(bfloat16(std::numeric_limits::quiet_NaN())) & BFLOAT16_QUIET_BIT) > 0) ); + // After a cast to bfloat16, a signaling NaN may become non-signaling. Thus, + // we check that both are NaN, and that only the `numeric_limits` version is + // signaling. + VERIFY( + (numext::isnan)(std::numeric_limits::signaling_NaN()) + && (numext::isnan)(bfloat16(std::numeric_limits::signaling_NaN())) + && ((numext::bit_cast(std::numeric_limits::signaling_NaN()) & BFLOAT16_QUIET_BIT) == 0) ); + + VERIFY( (std::numeric_limits::min)() > bfloat16(0.f) ); + VERIFY( (std::numeric_limits::denorm_min)() > bfloat16(0.f) ); + VERIFY_IS_EQUAL( (std::numeric_limits::denorm_min)()/bfloat16(2), bfloat16(0.f) ); +} + +void test_arithmetic() +{ + VERIFY_IS_EQUAL(static_cast(bfloat16(2) + bfloat16(2)), 4); + VERIFY_IS_EQUAL(static_cast(bfloat16(2) + bfloat16(-2)), 0); + VERIFY_IS_APPROX(static_cast(bfloat16(0.33333f) + bfloat16(0.66667f)), 1.0f); + VERIFY_IS_EQUAL(static_cast(bfloat16(2.0f) * bfloat16(-5.5f)), -11.0f); + VERIFY_IS_APPROX(static_cast(bfloat16(1.0f) / bfloat16(3.0f)), 0.3339f); + VERIFY_IS_EQUAL(static_cast(-bfloat16(4096.0f)), -4096.0f); + VERIFY_IS_EQUAL(static_cast(-bfloat16(-4096.0f)), 4096.0f); +} + +void test_comparison() +{ + VERIFY(bfloat16(1.0f) > bfloat16(0.5f)); + VERIFY(bfloat16(0.5f) < bfloat16(1.0f)); + VERIFY(!(bfloat16(1.0f) < bfloat16(0.5f))); + VERIFY(!(bfloat16(0.5f) > bfloat16(1.0f))); + + VERIFY(!(bfloat16(4.0f) > bfloat16(4.0f))); + VERIFY(!(bfloat16(4.0f) < bfloat16(4.0f))); + + VERIFY(!(bfloat16(0.0f) < bfloat16(-0.0f))); + VERIFY(!(bfloat16(-0.0f) < bfloat16(0.0f))); + VERIFY(!(bfloat16(0.0f) > bfloat16(-0.0f))); + VERIFY(!(bfloat16(-0.0f) > bfloat16(0.0f))); + + VERIFY(bfloat16(0.2f) > bfloat16(-1.0f)); + VERIFY(bfloat16(-1.0f) < bfloat16(0.2f)); + VERIFY(bfloat16(-16.0f) < bfloat16(-15.0f)); + + VERIFY(bfloat16(1.0f) == bfloat16(1.0f)); + VERIFY(bfloat16(1.0f) != bfloat16(2.0f)); + + // Comparisons with NaNs and infinities. +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY(!(bfloat16(0.0 / 0.0) == bfloat16(0.0 / 0.0))); + VERIFY(bfloat16(0.0 / 0.0) != bfloat16(0.0 / 0.0)); + + VERIFY(!(bfloat16(1.0) == bfloat16(0.0 / 0.0))); + VERIFY(!(bfloat16(1.0) < bfloat16(0.0 / 0.0))); + VERIFY(!(bfloat16(1.0) > bfloat16(0.0 / 0.0))); + VERIFY(bfloat16(1.0) != bfloat16(0.0 / 0.0)); + + VERIFY(bfloat16(1.0) < bfloat16(1.0 / 0.0)); + VERIFY(bfloat16(1.0) > bfloat16(-1.0 / 0.0)); +#endif +} + +void test_basic_functions() +{ + VERIFY_IS_EQUAL(static_cast(numext::abs(bfloat16(3.5f))), 3.5f); + VERIFY_IS_EQUAL(static_cast(abs(bfloat16(3.5f))), 3.5f); + VERIFY_IS_EQUAL(static_cast(numext::abs(bfloat16(-3.5f))), 3.5f); + VERIFY_IS_EQUAL(static_cast(abs(bfloat16(-3.5f))), 3.5f); + + VERIFY_IS_EQUAL(static_cast(numext::floor(bfloat16(3.5f))), 3.0f); + VERIFY_IS_EQUAL(static_cast(floor(bfloat16(3.5f))), 3.0f); + VERIFY_IS_EQUAL(static_cast(numext::floor(bfloat16(-3.5f))), -4.0f); + VERIFY_IS_EQUAL(static_cast(floor(bfloat16(-3.5f))), -4.0f); + + VERIFY_IS_EQUAL(static_cast(numext::ceil(bfloat16(3.5f))), 4.0f); + VERIFY_IS_EQUAL(static_cast(ceil(bfloat16(3.5f))), 4.0f); + VERIFY_IS_EQUAL(static_cast(numext::ceil(bfloat16(-3.5f))), -3.0f); + VERIFY_IS_EQUAL(static_cast(ceil(bfloat16(-3.5f))), -3.0f); + + VERIFY_IS_APPROX(static_cast(numext::sqrt(bfloat16(0.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(sqrt(bfloat16(0.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(numext::sqrt(bfloat16(4.0f))), 2.0f); + VERIFY_IS_APPROX(static_cast(sqrt(bfloat16(4.0f))), 2.0f); + + VERIFY_IS_APPROX(static_cast(numext::pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(numext::pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f); + VERIFY_IS_APPROX(static_cast(pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f); + + VERIFY_IS_EQUAL(static_cast(numext::exp(bfloat16(0.0f))), 1.0f); + VERIFY_IS_EQUAL(static_cast(exp(bfloat16(0.0f))), 1.0f); + VERIFY_IS_APPROX(static_cast(numext::exp(bfloat16(EIGEN_PI))), 20.f + static_cast(EIGEN_PI)); + VERIFY_IS_APPROX(static_cast(exp(bfloat16(EIGEN_PI))), 20.f + static_cast(EIGEN_PI)); + + VERIFY_IS_EQUAL(static_cast(numext::expm1(bfloat16(0.0f))), 0.0f); + VERIFY_IS_EQUAL(static_cast(expm1(bfloat16(0.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(numext::expm1(bfloat16(2.0f))), 6.375f); + VERIFY_IS_APPROX(static_cast(expm1(bfloat16(2.0f))), 6.375f); + + VERIFY_IS_EQUAL(static_cast(numext::log(bfloat16(1.0f))), 0.0f); + VERIFY_IS_EQUAL(static_cast(log(bfloat16(1.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(numext::log(bfloat16(10.0f))), 2.296875f); + VERIFY_IS_APPROX(static_cast(log(bfloat16(10.0f))), 2.296875f); + + VERIFY_IS_EQUAL(static_cast(numext::log1p(bfloat16(0.0f))), 0.0f); + VERIFY_IS_EQUAL(static_cast(log1p(bfloat16(0.0f))), 0.0f); + VERIFY_IS_APPROX(static_cast(numext::log1p(bfloat16(10.0f))), 2.390625f); + VERIFY_IS_APPROX(static_cast(log1p(bfloat16(10.0f))), 2.390625f); +} + +void test_trigonometric_functions() +{ + VERIFY_IS_APPROX(numext::cos(bfloat16(0.0f)), bfloat16(cosf(0.0f))); + VERIFY_IS_APPROX(cos(bfloat16(0.0f)), bfloat16(cosf(0.0f))); + VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI)), bfloat16(cosf(EIGEN_PI))); + // VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI/2)), bfloat16(cosf(EIGEN_PI/2))); + // VERIFY_IS_APPROX(numext::cos(bfloat16(3*EIGEN_PI/2)), bfloat16(cosf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::cos(bfloat16(3.5f)), bfloat16(cosf(3.5f))); + + VERIFY_IS_APPROX(numext::sin(bfloat16(0.0f)), bfloat16(sinf(0.0f))); + VERIFY_IS_APPROX(sin(bfloat16(0.0f)), bfloat16(sinf(0.0f))); + // VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI)), bfloat16(sinf(EIGEN_PI))); + VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI/2)), bfloat16(sinf(EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(bfloat16(3*EIGEN_PI/2)), bfloat16(sinf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(bfloat16(3.5f)), bfloat16(sinf(3.5f))); + + VERIFY_IS_APPROX(numext::tan(bfloat16(0.0f)), bfloat16(tanf(0.0f))); + VERIFY_IS_APPROX(tan(bfloat16(0.0f)), bfloat16(tanf(0.0f))); + // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI)), bfloat16(tanf(EIGEN_PI))); + // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI/2)), bfloat16(tanf(EIGEN_PI/2))); + // VERIFY_IS_APPROX(numext::tan(bfloat16(3*EIGEN_PI/2)), bfloat16(tanf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::tan(bfloat16(3.5f)), bfloat16(tanf(3.5f))); +} + +void test_array() +{ + typedef Array ArrayXh; + Index size = internal::random(1,10); + Index i = internal::random(0,size-1); + ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size); + VERIFY_IS_APPROX( a1+a1, bfloat16(2)*a1 ); + VERIFY( (a1.abs() >= bfloat16(0)).all() ); + VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() ); + + VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() ); + a1(i) = bfloat16(-10.); + VERIFY_IS_EQUAL( a1.minCoeff(), bfloat16(-10.) ); + a1(i) = bfloat16(10.); + VERIFY_IS_EQUAL( a1.maxCoeff(), bfloat16(10.) ); + + std::stringstream ss; + ss << a1; +} + +void test_product() +{ + typedef Matrix MatrixXh; + Index rows = internal::random(1,EIGEN_TEST_MAX_SIZE); + Index cols = internal::random(1,EIGEN_TEST_MAX_SIZE); + Index depth = internal::random(1,EIGEN_TEST_MAX_SIZE); + MatrixXh Ah = MatrixXh::Random(rows,depth); + MatrixXh Bh = MatrixXh::Random(depth,cols); + MatrixXh Ch = MatrixXh::Random(rows,cols); + MatrixXf Af = Ah.cast(); + MatrixXf Bf = Bh.cast(); + MatrixXf Cf = Ch.cast(); + VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast()); +} + +EIGEN_DECLARE_TEST(bfloat16_float) +{ + CALL_SUBTEST(test_numtraits()); + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST(test_conversion()); + CALL_SUBTEST(test_arithmetic()); + CALL_SUBTEST(test_comparison()); + CALL_SUBTEST(test_basic_functions()); + CALL_SUBTEST(test_trigonometric_functions()); + CALL_SUBTEST(test_array()); + CALL_SUBTEST(test_product()); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bicgstab.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bicgstab.cpp new file mode 100644 index 0000000000000000000000000000000000000000..59c4b501c20e6f51ec688c65c38ecfdf70a5a1ec --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bicgstab.cpp @@ -0,0 +1,34 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "sparse_solver.h" +#include + +template void test_bicgstab_T() +{ + BiCGSTAB, DiagonalPreconditioner > bicgstab_colmajor_diag; + BiCGSTAB, IdentityPreconditioner > bicgstab_colmajor_I; + BiCGSTAB, IncompleteLUT > bicgstab_colmajor_ilut; + //BiCGSTAB, SSORPreconditioner > bicgstab_colmajor_ssor; + + bicgstab_colmajor_diag.setTolerance(NumTraits::epsilon()*4); + bicgstab_colmajor_ilut.setTolerance(NumTraits::epsilon()*4); + + CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_diag) ); +// CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_I) ); + CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ilut) ); + //CALL_SUBTEST( check_sparse_square_solving(bicgstab_colmajor_ssor) ); +} + +EIGEN_DECLARE_TEST(bicgstab) +{ + CALL_SUBTEST_1((test_bicgstab_T()) ); + CALL_SUBTEST_2((test_bicgstab_T, int>())); + CALL_SUBTEST_3((test_bicgstab_T())); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/blasutil.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/blasutil.cpp new file mode 100644 index 0000000000000000000000000000000000000000..845a498d675f589a4a526834fd693f024392c07b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/blasutil.cpp @@ -0,0 +1,210 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2020 Everton Constantino +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/ + +#include "main.h" + +// Disable "ignoring attributes on template argument" +// for packet_traits +// => The only workaround would be to wrap _m128 and the likes +// within wrappers. +#if EIGEN_GNUC_AT_LEAST(6,0) + #pragma GCC diagnostic ignored "-Wignored-attributes" +#endif + +#define GET(i,j) (StorageOrder == RowMajor ? (i)*stride + (j) : (i) + (j)*stride) +#define SCATTER(i,j,k) (StorageOrder == RowMajor ? ((i)+(k))*stride + (j) : (i) + ((j)+(k))*stride) + +template +void compare(const Packet& a, const Packet& b) +{ + int pktsz = internal::packet_traits::size; + Scalar *buffA = new Scalar[pktsz]; + Scalar *buffB = new Scalar[pktsz]; + + internal::pstoreu(buffA, a); + internal::pstoreu(buffB, b); + + for(int i = 0; i < pktsz; i++) + { + VERIFY_IS_EQUAL(buffA[i], buffB[i]); + } + + delete[] buffA; + delete[] buffB; +} + +template +struct PacketBlockSet +{ + typedef typename internal::packet_traits::type Packet; + + void setPacketBlock(internal::PacketBlock& block, Scalar value) + { + for(int idx = 0; idx < n; idx++) + { + block.packet[idx] = internal::pset1(value); + } + } + + void comparePacketBlock(Scalar *data, int i, int j, int stride, internal::PacketBlock& block) + { + for(int idx = 0; idx < n; idx++) + { + Packet line = internal::ploadu(data + SCATTER(i,j,idx)); + compare(block.packet[idx], line); + } + } +}; + +template +void run_bdmp_spec_1() +{ + typedef internal::blas_data_mapper BlasDataMapper; + int packetSize = internal::packet_traits::size; + int minSize = std::max(packetSize, BlockSize); + typedef typename internal::packet_traits::type Packet; + + int szm = internal::random(minSize,500), szn = internal::random(minSize,500); + int stride = StorageOrder == RowMajor ? szn : szm; + Scalar *d = new Scalar[szn*szm]; + + // Initializing with random entries + for(int i = 0; i < szm*szn; i++) + { + d[i] = internal::random(static_cast(3), static_cast(10)); + } + + BlasDataMapper bdm(d, stride); + + // Testing operator() + for(int i = 0; i < szm; i++) + { + for(int j = 0; j < szn; j++) + { + VERIFY_IS_EQUAL(d[GET(i,j)], bdm(i,j)); + } + } + + // Testing getSubMapper and getLinearMapper + int i0 = internal::random(0,szm-2); + int j0 = internal::random(0,szn-2); + for(int i = i0; i < szm; i++) + { + for(int j = j0; j < szn; j++) + { + const BlasDataMapper& bdmSM = bdm.getSubMapper(i0,j0); + const internal::BlasLinearMapper& bdmLM = bdm.getLinearMapper(i0,j0); + + Scalar v = bdmSM(i - i0, j - j0); + Scalar vd = d[GET(i,j)]; + VERIFY_IS_EQUAL(vd, v); + VERIFY_IS_EQUAL(vd, bdmLM(GET(i-i0, j-j0))); + } + } + + // Testing loadPacket + for(int i = 0; i < szm - minSize; i++) + { + for(int j = 0; j < szn - minSize; j++) + { + Packet pktBDM = bdm.template loadPacket(i,j); + Packet pktD = internal::ploadu(d + GET(i,j)); + + compare(pktBDM, pktD); + } + } + + // Testing gatherPacket + Scalar *buff = new Scalar[packetSize]; + for(int i = 0; i < szm - minSize; i++) + { + for(int j = 0; j < szn - minSize; j++) + { + Packet p = bdm.template gatherPacket(i,j); + internal::pstoreu(buff, p); + + for(int k = 0; k < packetSize; k++) + { + VERIFY_IS_EQUAL(d[SCATTER(i,j,k)], buff[k]); + } + + } + } + delete[] buff; + + // Testing scatterPacket + for(int i = 0; i < szm - minSize; i++) + { + for(int j = 0; j < szn - minSize; j++) + { + Packet p = internal::pset1(static_cast(1)); + bdm.template scatterPacket(i,j,p); + for(int k = 0; k < packetSize; k++) + { + VERIFY_IS_EQUAL(d[SCATTER(i,j,k)], static_cast(1)); + } + } + } + + //Testing storePacketBlock + internal::PacketBlock block; + + PacketBlockSet pbs; + pbs.setPacketBlock(block, static_cast(2)); + + for(int i = 0; i < szm - minSize; i++) + { + for(int j = 0; j < szn - minSize; j++) + { + bdm.template storePacketBlock(i, j, block); + + pbs.comparePacketBlock(d, i, j, stride, block); + } + } + + delete[] d; +} + +template +void run_test() +{ + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); + run_bdmp_spec_1(); +} + +EIGEN_DECLARE_TEST(blasutil) +{ + for(int i = 0; i < g_repeat; i++) + { + CALL_SUBTEST_1(run_test()); + CALL_SUBTEST_2(run_test()); + CALL_SUBTEST_3(run_test()); + +// TODO: Replace this by a call to numext::int64_t as soon as we have a way to +// detect the typedef for int64_t on all platforms +#if EIGEN_HAS_CXX11 + CALL_SUBTEST_4(run_test()); +#else + CALL_SUBTEST_4(run_test()); +#endif + + CALL_SUBTEST_5(run_test()); + CALL_SUBTEST_6(run_test()); + CALL_SUBTEST_7(run_test >()); + CALL_SUBTEST_8(run_test >()); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/block.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/block.cpp new file mode 100644 index 0000000000000000000000000000000000000000..84124aba642b38521d864a5b130ac3cab8b86684 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/block.cpp @@ -0,0 +1,316 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT // otherwise we fail at compile time on unused paths +#include "main.h" + +template +typename Eigen::internal::enable_if::IsComplex,typename MatrixType::Scalar>::type +block_real_only(const MatrixType &m1, Index r1, Index r2, Index c1, Index c2, const Scalar& s1) { + // check cwise-Functions: + VERIFY_IS_APPROX(m1.row(r1).cwiseMax(s1), m1.cwiseMax(s1).row(r1)); + VERIFY_IS_APPROX(m1.col(c1).cwiseMin(s1), m1.cwiseMin(s1).col(c1)); + + VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMin(s1), m1.cwiseMin(s1).block(r1,c1,r2-r1+1,c2-c1+1)); + VERIFY_IS_APPROX(m1.block(r1,c1,r2-r1+1,c2-c1+1).cwiseMax(s1), m1.cwiseMax(s1).block(r1,c1,r2-r1+1,c2-c1+1)); + + return Scalar(0); +} + +template +typename Eigen::internal::enable_if::IsComplex,typename MatrixType::Scalar>::type +block_real_only(const MatrixType &, Index, Index, Index, Index, const Scalar&) { + return Scalar(0); +} + +// Check at compile-time that T1==T2, and at runtime-time that a==b +template +typename internal::enable_if::value,bool>::type +is_same_block(const T1& a, const T2& b) +{ + return a.isApprox(b); +} + +template void block(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix VectorType; + typedef Matrix RowVectorType; + typedef Matrix DynamicMatrixType; + typedef Matrix DynamicVectorType; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m1_copy = m1, + m2 = MatrixType::Random(rows, cols), + m3(rows, cols), + ones = MatrixType::Ones(rows, cols); + VectorType v1 = VectorType::Random(rows); + + Scalar s1 = internal::random(); + + Index r1 = internal::random(0,rows-1); + Index r2 = internal::random(r1,rows-1); + Index c1 = internal::random(0,cols-1); + Index c2 = internal::random(c1,cols-1); + + block_real_only(m1, r1, r2, c1, c1, s1); + + //check row() and col() + VERIFY_IS_EQUAL(m1.col(c1).transpose(), m1.transpose().row(c1)); + //check operator(), both constant and non-constant, on row() and col() + m1 = m1_copy; + m1.row(r1) += s1 * m1_copy.row(r2); + VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + s1 * m1_copy.row(r2)); + // check nested block xpr on lhs + m1.row(r1).row(0) += s1 * m1_copy.row(r2); + VERIFY_IS_APPROX(m1.row(r1), m1_copy.row(r1) + Scalar(2) * s1 * m1_copy.row(r2)); + m1 = m1_copy; + m1.col(c1) += s1 * m1_copy.col(c2); + VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + s1 * m1_copy.col(c2)); + m1.col(c1).col(0) += s1 * m1_copy.col(c2); + VERIFY_IS_APPROX(m1.col(c1), m1_copy.col(c1) + Scalar(2) * s1 * m1_copy.col(c2)); + + + //check block() + Matrix b1(1,1); b1(0,0) = m1(r1,c1); + + RowVectorType br1(m1.block(r1,0,1,cols)); + VectorType bc1(m1.block(0,c1,rows,1)); + VERIFY_IS_EQUAL(b1, m1.block(r1,c1,1,1)); + VERIFY_IS_EQUAL(m1.row(r1), br1); + VERIFY_IS_EQUAL(m1.col(c1), bc1); + //check operator(), both constant and non-constant, on block() + m1.block(r1,c1,r2-r1+1,c2-c1+1) = s1 * m2.block(0, 0, r2-r1+1,c2-c1+1); + m1.block(r1,c1,r2-r1+1,c2-c1+1)(r2-r1,c2-c1) = m2.block(0, 0, r2-r1+1,c2-c1+1)(0,0); + + const Index BlockRows = 2; + const Index BlockCols = 5; + + if (rows>=5 && cols>=8) + { + // test fixed block() as lvalue + m1.template block(1,1) *= s1; + // test operator() on fixed block() both as constant and non-constant + m1.template block(1,1)(0, 3) = m1.template block<2,5>(1,1)(1,2); + // check that fixed block() and block() agree + Matrix b = m1.template block(3,3); + VERIFY_IS_EQUAL(b, m1.block(3,3,BlockRows,BlockCols)); + + // same tests with mixed fixed/dynamic size + m1.template block(1,1,BlockRows,BlockCols) *= s1; + m1.template block(1,1,BlockRows,BlockCols)(0,3) = m1.template block<2,5>(1,1)(1,2); + Matrix b2 = m1.template block(3,3,2,5); + VERIFY_IS_EQUAL(b2, m1.block(3,3,BlockRows,BlockCols)); + + VERIFY(is_same_block(m1.block(3,3,BlockRows,BlockCols), m1.block(3,3,fix(BlockRows),fix(BlockCols)))); + VERIFY(is_same_block(m1.template block(1,1,BlockRows,BlockCols), m1.block(1,1,fix,BlockCols))); + VERIFY(is_same_block(m1.template block(1,1,BlockRows,BlockCols), m1.block(1,1,fix(),fix))); + VERIFY(is_same_block(m1.template block(1,1,BlockRows,BlockCols), m1.block(1,1,fix,fix(BlockCols)))); + } + + if (rows>2) + { + // test sub vectors + VERIFY_IS_EQUAL(v1.template head<2>(), v1.block(0,0,2,1)); + VERIFY_IS_EQUAL(v1.template head<2>(), v1.head(2)); + VERIFY_IS_EQUAL(v1.template head<2>(), v1.segment(0,2)); + VERIFY_IS_EQUAL(v1.template head<2>(), v1.template segment<2>(0)); + Index i = rows-2; + VERIFY_IS_EQUAL(v1.template tail<2>(), v1.block(i,0,2,1)); + VERIFY_IS_EQUAL(v1.template tail<2>(), v1.tail(2)); + VERIFY_IS_EQUAL(v1.template tail<2>(), v1.segment(i,2)); + VERIFY_IS_EQUAL(v1.template tail<2>(), v1.template segment<2>(i)); + i = internal::random(0,rows-2); + VERIFY_IS_EQUAL(v1.segment(i,2), v1.template segment<2>(i)); + } + + // stress some basic stuffs with block matrices + VERIFY(numext::real(ones.col(c1).sum()) == RealScalar(rows)); + VERIFY(numext::real(ones.row(r1).sum()) == RealScalar(cols)); + + VERIFY(numext::real(ones.col(c1).dot(ones.col(c2))) == RealScalar(rows)); + VERIFY(numext::real(ones.row(r1).dot(ones.row(r2))) == RealScalar(cols)); + + // check that linear acccessors works on blocks + m1 = m1_copy; + if((MatrixType::Flags&RowMajorBit)==0) + VERIFY_IS_EQUAL(m1.leftCols(c1).coeff(r1+c1*rows), m1(r1,c1)); + else + VERIFY_IS_EQUAL(m1.topRows(r1).coeff(c1+r1*cols), m1(r1,c1)); + + + // now test some block-inside-of-block. + + // expressions with direct access + VERIFY_IS_EQUAL( (m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , (m1.block(r2,c2,rows-r2,cols-c2)) ); + VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , (m1.row(r1).segment(c1,c2-c1+1)) ); + VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , (m1.col(c1).segment(r1,r2-r1+1)) ); + VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() ); + VERIFY_IS_EQUAL( (m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , (m1.row(r1).segment(c1,c2-c1+1)).transpose() ); + + // expressions without direct access + VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , ((m1+m2).block(r2,c2,rows-r2,cols-c2)) ); + VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) ); + VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).eval().row(r1).segment(c1,c2-c1+1)) ); + VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , ((m1+m2).col(c1).segment(r1,r2-r1+1)) ); + VERIFY_IS_APPROX( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() ); + VERIFY_IS_APPROX( ((m1+m2).transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)).transpose() ); + VERIFY_IS_APPROX( ((m1+m2).template block(r1,c1,r2-r1+1,1)) , ((m1+m2).eval().col(c1).eval().segment(r1,r2-r1+1)) ); + VERIFY_IS_APPROX( ((m1+m2).template block<1,Dynamic>(r1,c1,1,c2-c1+1)) , ((m1+m2).eval().row(r1).eval().segment(c1,c2-c1+1)) ); + VERIFY_IS_APPROX( ((m1+m2).transpose().template block<1,Dynamic>(c1,r1,1,r2-r1+1)) , ((m1+m2).eval().col(c1).eval().segment(r1,r2-r1+1)).transpose() ); + VERIFY_IS_APPROX( (m1+m2).row(r1).eval(), (m1+m2).eval().row(r1) ); + VERIFY_IS_APPROX( (m1+m2).adjoint().col(r1).eval(), (m1+m2).adjoint().eval().col(r1) ); + VERIFY_IS_APPROX( (m1+m2).adjoint().row(c1).eval(), (m1+m2).adjoint().eval().row(c1) ); + VERIFY_IS_APPROX( (m1*1).row(r1).segment(c1,c2-c1+1).eval(), m1.row(r1).eval().segment(c1,c2-c1+1).eval() ); + VERIFY_IS_APPROX( m1.col(c1).reverse().segment(r1,r2-r1+1).eval(),m1.col(c1).reverse().eval().segment(r1,r2-r1+1).eval() ); + + VERIFY_IS_APPROX( (m1*1).topRows(r1), m1.topRows(r1) ); + VERIFY_IS_APPROX( (m1*1).leftCols(c1), m1.leftCols(c1) ); + VERIFY_IS_APPROX( (m1*1).transpose().topRows(c1), m1.transpose().topRows(c1) ); + VERIFY_IS_APPROX( (m1*1).transpose().leftCols(r1), m1.transpose().leftCols(r1) ); + VERIFY_IS_APPROX( (m1*1).transpose().middleRows(c1,c2-c1+1), m1.transpose().middleRows(c1,c2-c1+1) ); + VERIFY_IS_APPROX( (m1*1).transpose().middleCols(r1,r2-r1+1), m1.transpose().middleCols(r1,r2-r1+1) ); + + // evaluation into plain matrices from expressions with direct access (stress MapBase) + DynamicMatrixType dm; + DynamicVectorType dv; + dm.setZero(); + dm = m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2); + VERIFY_IS_EQUAL(dm, (m1.block(r2,c2,rows-r2,cols-c2))); + dm.setZero(); + dv.setZero(); + dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0).transpose(); + dv = m1.row(r1).segment(c1,c2-c1+1); + VERIFY_IS_EQUAL(dv, dm); + dm.setZero(); + dv.setZero(); + dm = m1.col(c1).segment(r1,r2-r1+1); + dv = m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0); + VERIFY_IS_EQUAL(dv, dm); + dm.setZero(); + dv.setZero(); + dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0); + dv = m1.row(r1).segment(c1,c2-c1+1); + VERIFY_IS_EQUAL(dv, dm); + dm.setZero(); + dv.setZero(); + dm = m1.row(r1).segment(c1,c2-c1+1).transpose(); + dv = m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0); + VERIFY_IS_EQUAL(dv, dm); + + VERIFY_IS_EQUAL( (m1.template block(1,0,0,1)), m1.block(1,0,0,1)); + VERIFY_IS_EQUAL( (m1.template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0)); + VERIFY_IS_EQUAL( ((m1*1).template block(1,0,0,1)), m1.block(1,0,0,1)); + VERIFY_IS_EQUAL( ((m1*1).template block<1,Dynamic>(0,1,1,0)), m1.block(0,1,1,0)); + + if (rows>=2 && cols>=2) + { + VERIFY_RAISES_ASSERT( m1 += m1.col(0) ); + VERIFY_RAISES_ASSERT( m1 -= m1.col(0) ); + VERIFY_RAISES_ASSERT( m1.array() *= m1.col(0).array() ); + VERIFY_RAISES_ASSERT( m1.array() /= m1.col(0).array() ); + } + + VERIFY_IS_EQUAL( m1.template subVector(r1), m1.row(r1) ); + VERIFY_IS_APPROX( (m1+m1).template subVector(r1), (m1+m1).row(r1) ); + VERIFY_IS_EQUAL( m1.template subVector(c1), m1.col(c1) ); + VERIFY_IS_APPROX( (m1+m1).template subVector(c1), (m1+m1).col(c1) ); + VERIFY_IS_EQUAL( m1.template subVectors(), m1.rows() ); + VERIFY_IS_EQUAL( m1.template subVectors(), m1.cols() ); + + if (rows>=2 || cols>=2) { + VERIFY_IS_EQUAL( int(m1.middleCols(0,0).IsRowMajor), int(m1.IsRowMajor) ); + VERIFY_IS_EQUAL( m1.middleCols(0,0).outerSize(), m1.IsRowMajor ? rows : 0); + VERIFY_IS_EQUAL( m1.middleCols(0,0).innerSize(), m1.IsRowMajor ? 0 : rows); + + VERIFY_IS_EQUAL( int(m1.middleRows(0,0).IsRowMajor), int(m1.IsRowMajor) ); + VERIFY_IS_EQUAL( m1.middleRows(0,0).outerSize(), m1.IsRowMajor ? 0 : cols); + VERIFY_IS_EQUAL( m1.middleRows(0,0).innerSize(), m1.IsRowMajor ? cols : 0); + } +} + + +template +void compare_using_data_and_stride(const MatrixType& m) +{ + Index rows = m.rows(); + Index cols = m.cols(); + Index size = m.size(); + Index innerStride = m.innerStride(); + Index outerStride = m.outerStride(); + Index rowStride = m.rowStride(); + Index colStride = m.colStride(); + const typename MatrixType::Scalar* data = m.data(); + + for(int j=0;j +void data_and_stride(const MatrixType& m) +{ + Index rows = m.rows(); + Index cols = m.cols(); + + Index r1 = internal::random(0,rows-1); + Index r2 = internal::random(r1,rows-1); + Index c1 = internal::random(0,cols-1); + Index c2 = internal::random(c1,cols-1); + + MatrixType m1 = MatrixType::Random(rows, cols); + compare_using_data_and_stride(m1.block(r1, c1, r2-r1+1, c2-c1+1)); + compare_using_data_and_stride(m1.transpose().block(c1, r1, c2-c1+1, r2-r1+1)); + compare_using_data_and_stride(m1.row(r1)); + compare_using_data_and_stride(m1.col(c1)); + compare_using_data_and_stride(m1.row(r1).transpose()); + compare_using_data_and_stride(m1.col(c1).transpose()); +} + +EIGEN_DECLARE_TEST(block) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( block(Matrix()) ); + CALL_SUBTEST_1( block(Matrix(internal::random(2,50))) ); + CALL_SUBTEST_1( block(Matrix(internal::random(2,50))) ); + CALL_SUBTEST_2( block(Matrix4d()) ); + CALL_SUBTEST_3( block(MatrixXcf(internal::random(2,50), internal::random(2,50))) ); + CALL_SUBTEST_4( block(MatrixXi(internal::random(2,50), internal::random(2,50))) ); + CALL_SUBTEST_5( block(MatrixXcd(internal::random(2,50), internal::random(2,50))) ); + CALL_SUBTEST_6( block(MatrixXf(internal::random(2,50), internal::random(2,50))) ); + CALL_SUBTEST_7( block(Matrix(internal::random(2,50), internal::random(2,50))) ); + + CALL_SUBTEST_8( block(Matrix(3, 4)) ); + +#ifndef EIGEN_DEFAULT_TO_ROW_MAJOR + CALL_SUBTEST_6( data_and_stride(MatrixXf(internal::random(5,50), internal::random(5,50))) ); + CALL_SUBTEST_7( data_and_stride(Matrix(internal::random(5,50), internal::random(5,50))) ); +#endif + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/boostmultiprec.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/boostmultiprec.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7c79ded23bc49639ded9cda751c10bdae0fe0ee0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/boostmultiprec.cpp @@ -0,0 +1,208 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include + +#ifdef EIGEN_TEST_MAX_SIZE +#undef EIGEN_TEST_MAX_SIZE +#endif + +#define EIGEN_TEST_MAX_SIZE 50 + +#ifdef EIGEN_TEST_PART_1 +#include "cholesky.cpp" +#endif + +#ifdef EIGEN_TEST_PART_2 +#include "lu.cpp" +#endif + +#ifdef EIGEN_TEST_PART_3 +#include "qr.cpp" +#endif + +#ifdef EIGEN_TEST_PART_4 +#include "qr_colpivoting.cpp" +#endif + +#ifdef EIGEN_TEST_PART_5 +#include "qr_fullpivoting.cpp" +#endif + +#ifdef EIGEN_TEST_PART_6 +#include "eigensolver_selfadjoint.cpp" +#endif + +#ifdef EIGEN_TEST_PART_7 +#include "eigensolver_generic.cpp" +#endif + +#ifdef EIGEN_TEST_PART_8 +#include "eigensolver_generalized_real.cpp" +#endif + +#ifdef EIGEN_TEST_PART_9 +#include "jacobisvd.cpp" +#endif + +#ifdef EIGEN_TEST_PART_10 +#include "bdcsvd.cpp" +#endif + +#ifdef EIGEN_TEST_PART_11 +#include "simplicial_cholesky.cpp" +#endif + +#include + +#undef min +#undef max +#undef isnan +#undef isinf +#undef isfinite +#undef I + +#include +#include +#include +#include +#include + +namespace mp = boost::multiprecision; +typedef mp::number, mp::et_on> Real; + +namespace Eigen { + template<> struct NumTraits : GenericNumTraits { + static inline Real dummy_precision() { return 1e-50; } + }; + + template + struct NumTraits > : NumTraits {}; + + template<> + Real test_precision() { return 1e-50; } + + // needed in C++93 mode where number does not support explicit cast. + namespace internal { + template + struct cast_impl { + static inline NewType run(const Real& x) { + return x.template convert_to(); + } + }; + + template<> + struct cast_impl > { + static inline std::complex run(const Real& x) { + return std::complex(x); + } + }; + } +} + +namespace boost { +namespace multiprecision { + // to make ADL works as expected: + using boost::math::isfinite; + using boost::math::isnan; + using boost::math::isinf; + using boost::math::copysign; + using boost::math::hypot; + + // The following is needed for std::complex: + Real fabs(const Real& a) { return abs EIGEN_NOT_A_MACRO (a); } + Real fmax(const Real& a, const Real& b) { using std::max; return max(a,b); } + + // some specialization for the unit tests: + inline bool test_isMuchSmallerThan(const Real& a, const Real& b) { + return internal::isMuchSmallerThan(a, b, test_precision()); + } + + inline bool test_isApprox(const Real& a, const Real& b) { + return internal::isApprox(a, b, test_precision()); + } + + inline bool test_isApproxOrLessThan(const Real& a, const Real& b) { + return internal::isApproxOrLessThan(a, b, test_precision()); + } + + Real get_test_precision(const Real&) { + return test_precision(); + } + + Real test_relative_error(const Real &a, const Real &b) { + using Eigen::numext::abs2; + return sqrt(abs2(a-b)/Eigen::numext::mini(abs2(a),abs2(b))); + } +} +} + +namespace Eigen { + +} + +EIGEN_DECLARE_TEST(boostmultiprec) +{ + typedef Matrix Mat; + typedef Matrix,Dynamic,Dynamic> MatC; + + std::cout << "NumTraits::epsilon() = " << NumTraits::epsilon() << std::endl; + std::cout << "NumTraits::dummy_precision() = " << NumTraits::dummy_precision() << std::endl; + std::cout << "NumTraits::lowest() = " << NumTraits::lowest() << std::endl; + std::cout << "NumTraits::highest() = " << NumTraits::highest() << std::endl; + std::cout << "NumTraits::digits10() = " << NumTraits::digits10() << std::endl; + + // check stream output + { + Mat A(10,10); + A.setRandom(); + std::stringstream ss; + ss << A; + } + { + MatC A(10,10); + A.setRandom(); + std::stringstream ss; + ss << A; + } + + for(int i = 0; i < g_repeat; i++) { + int s = internal::random(1,EIGEN_TEST_MAX_SIZE); + + CALL_SUBTEST_1( cholesky(Mat(s,s)) ); + + CALL_SUBTEST_2( lu_non_invertible() ); + CALL_SUBTEST_2( lu_invertible() ); + CALL_SUBTEST_2( lu_non_invertible() ); + CALL_SUBTEST_2( lu_invertible() ); + + CALL_SUBTEST_3( qr(Mat(internal::random(1,EIGEN_TEST_MAX_SIZE),internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_3( qr_invertible() ); + + CALL_SUBTEST_4( qr() ); + CALL_SUBTEST_4( cod() ); + CALL_SUBTEST_4( qr_invertible() ); + + CALL_SUBTEST_5( qr() ); + CALL_SUBTEST_5( qr_invertible() ); + + CALL_SUBTEST_6( selfadjointeigensolver(Mat(s,s)) ); + + CALL_SUBTEST_7( eigensolver(Mat(s,s)) ); + + CALL_SUBTEST_8( generalized_eigensolver_real(Mat(s,s)) ); + + TEST_SET_BUT_UNUSED_VARIABLE(s) + } + + CALL_SUBTEST_9(( jacobisvd(Mat(internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + CALL_SUBTEST_10(( bdcsvd(Mat(internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE), internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + + CALL_SUBTEST_11(( test_simplicial_cholesky_T() )); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.cpp new file mode 100644 index 0000000000000000000000000000000000000000..581760c1a67e2f88eae29de5b18fd10f8ac23cab --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.cpp @@ -0,0 +1,13 @@ + +// This anonymous enum is essential to trigger the linking issue +enum { + Foo +}; + +#include "bug1213.h" + +bool bug1213_1(const Eigen::Vector3f& x) +{ + return bug1213_2(x); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.h new file mode 100644 index 0000000000000000000000000000000000000000..040e5a470d3a3e005d24ec52089a1e4aa89bc1b3 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213.h @@ -0,0 +1,8 @@ + +#include + +template +bool bug1213_2(const Eigen::Matrix& x); + +bool bug1213_1(const Eigen::Vector3f& x); + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213_main.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213_main.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4802c00032f18f39e866cc59711b61036012bcdd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/bug1213_main.cpp @@ -0,0 +1,18 @@ + +// This is a regression unit regarding a weird linking issue with gcc. + +#include "bug1213.h" + +int main() +{ + return 0; +} + + +template +bool bug1213_2(const Eigen::Matrix& ) +{ + return true; +} + +template bool bug1213_2(const Eigen::Vector3f&); diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholesky.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholesky.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0b1a7b45b2c2b8d93ad03030fa195e3ac97fb6b8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholesky.cpp @@ -0,0 +1,532 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define TEST_ENABLE_TEMPORARY_TRACKING + +#include "main.h" +#include +#include +#include "solverbase.h" + +template +typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) { + if(m.cols()==0) return typename MatrixType::RealScalar(0); + MatrixType symm = m.template selfadjointView(); + return symm.cwiseAbs().colwise().sum().maxCoeff(); +} + +template class CholType> void test_chol_update(const MatrixType& symm) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix VectorType; + + MatrixType symmLo = symm.template triangularView(); + MatrixType symmUp = symm.template triangularView(); + MatrixType symmCpy = symm; + + CholType chollo(symmLo); + CholType cholup(symmUp); + + for (int k=0; k<10; ++k) + { + VectorType vec = VectorType::Random(symm.rows()); + RealScalar sigma = internal::random(); + symmCpy += sigma * vec * vec.adjoint(); + + // we are doing some downdates, so it might be the case that the matrix is not SPD anymore + CholType chol(symmCpy); + if(chol.info()!=Success) + break; + + chollo.rankUpdate(vec, sigma); + VERIFY_IS_APPROX(symmCpy, chollo.reconstructedMatrix()); + + cholup.rankUpdate(vec, sigma); + VERIFY_IS_APPROX(symmCpy, cholup.reconstructedMatrix()); + } +} + +template void cholesky(const MatrixType& m) +{ + /* this test covers the following files: + LLT.h LDLT.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix SquareMatrixType; + typedef Matrix VectorType; + + MatrixType a0 = MatrixType::Random(rows,cols); + VectorType vecB = VectorType::Random(rows), vecX(rows); + MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols); + SquareMatrixType symm = a0 * a0.adjoint(); + // let's make sure the matrix is not singular or near singular + for (int k=0; k<3; ++k) + { + MatrixType a1 = MatrixType::Random(rows,cols); + symm += a1 * a1.adjoint(); + } + + { + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + + SquareMatrixType symmUp = symm.template triangularView(); + SquareMatrixType symmLo = symm.template triangularView(); + + LLT chollo(symmLo); + VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix()); + + check_solverbase(symm, chollo, rows, rows, 1); + check_solverbase(symm, chollo, rows, cols, rows); + + const MatrixType symmLo_inverse = chollo.solve(MatrixType::Identity(rows,cols)); + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(symmLo)) / + matrix_l1_norm(symmLo_inverse); + RealScalar rcond_est = chollo.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10); + + // test the upper mode + LLT cholup(symmUp); + VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix()); + vecX = cholup.solve(vecB); + VERIFY_IS_APPROX(symm * vecX, vecB); + matX = cholup.solve(matB); + VERIFY_IS_APPROX(symm * matX, matB); + + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + const MatrixType symmUp_inverse = cholup.solve(MatrixType::Identity(rows,cols)); + rcond = (RealScalar(1) / matrix_l1_norm(symmUp)) / + matrix_l1_norm(symmUp_inverse); + rcond_est = cholup.rcond(); + VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10); + + + MatrixType neg = -symmLo; + chollo.compute(neg); + VERIFY(neg.size()==0 || chollo.info()==NumericalIssue); + + VERIFY_IS_APPROX(MatrixType(chollo.matrixL().transpose().conjugate()), MatrixType(chollo.matrixU())); + VERIFY_IS_APPROX(MatrixType(chollo.matrixU().transpose().conjugate()), MatrixType(chollo.matrixL())); + VERIFY_IS_APPROX(MatrixType(cholup.matrixL().transpose().conjugate()), MatrixType(cholup.matrixU())); + VERIFY_IS_APPROX(MatrixType(cholup.matrixU().transpose().conjugate()), MatrixType(cholup.matrixL())); + + // test some special use cases of SelfCwiseBinaryOp: + MatrixType m1 = MatrixType::Random(rows,cols), m2(rows,cols); + m2 = m1; + m2 += symmLo.template selfadjointView().llt().solve(matB); + VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView().llt().solve(matB)); + m2 = m1; + m2 -= symmLo.template selfadjointView().llt().solve(matB); + VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView().llt().solve(matB)); + m2 = m1; + m2.noalias() += symmLo.template selfadjointView().llt().solve(matB); + VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView().llt().solve(matB)); + m2 = m1; + m2.noalias() -= symmLo.template selfadjointView().llt().solve(matB); + VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView().llt().solve(matB)); + } + + // LDLT + { + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + + int sign = internal::random()%2 ? 1 : -1; + + if(sign == -1) + { + symm = -symm; // test a negative matrix + } + + SquareMatrixType symmUp = symm.template triangularView(); + SquareMatrixType symmLo = symm.template triangularView(); + + LDLT ldltlo(symmLo); + VERIFY(ldltlo.info()==Success); + VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix()); + + check_solverbase(symm, ldltlo, rows, rows, 1); + check_solverbase(symm, ldltlo, rows, cols, rows); + + const MatrixType symmLo_inverse = ldltlo.solve(MatrixType::Identity(rows,cols)); + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(symmLo)) / + matrix_l1_norm(symmLo_inverse); + RealScalar rcond_est = ldltlo.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10); + + + LDLT ldltup(symmUp); + VERIFY(ldltup.info()==Success); + VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix()); + vecX = ldltup.solve(vecB); + VERIFY_IS_APPROX(symm * vecX, vecB); + matX = ldltup.solve(matB); + VERIFY_IS_APPROX(symm * matX, matB); + + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + const MatrixType symmUp_inverse = ldltup.solve(MatrixType::Identity(rows,cols)); + rcond = (RealScalar(1) / matrix_l1_norm(symmUp)) / + matrix_l1_norm(symmUp_inverse); + rcond_est = ldltup.rcond(); + VERIFY(rcond_est >= rcond / 10 && rcond_est <= rcond * 10); + + VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU())); + VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL())); + VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU())); + VERIFY_IS_APPROX(MatrixType(ldltup.matrixU().transpose().conjugate()), MatrixType(ldltup.matrixL())); + + if(MatrixType::RowsAtCompileTime==Dynamic) + { + // note : each inplace permutation requires a small temporary vector (mask) + + // check inplace solve + matX = matB; + VERIFY_EVALUATION_COUNT(matX = ldltlo.solve(matX), 0); + VERIFY_IS_APPROX(matX, ldltlo.solve(matB).eval()); + + + matX = matB; + VERIFY_EVALUATION_COUNT(matX = ldltup.solve(matX), 0); + VERIFY_IS_APPROX(matX, ldltup.solve(matB).eval()); + } + + // restore + if(sign == -1) + symm = -symm; + + // check matrices coming from linear constraints with Lagrange multipliers + if(rows>=3) + { + SquareMatrixType A = symm; + Index c = internal::random(0,rows-2); + A.bottomRightCorner(c,c).setZero(); + // Make sure a solution exists: + vecX.setRandom(); + vecB = A * vecX; + vecX.setZero(); + ldltlo.compute(A); + VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix()); + vecX = ldltlo.solve(vecB); + VERIFY_IS_APPROX(A * vecX, vecB); + } + + // check non-full rank matrices + if(rows>=3) + { + Index r = internal::random(1,rows-1); + Matrix a = Matrix::Random(rows,r); + SquareMatrixType A = a * a.adjoint(); + // Make sure a solution exists: + vecX.setRandom(); + vecB = A * vecX; + vecX.setZero(); + ldltlo.compute(A); + VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix()); + vecX = ldltlo.solve(vecB); + VERIFY_IS_APPROX(A * vecX, vecB); + } + + // check matrices with a wide spectrum + if(rows>=3) + { + using std::pow; + using std::sqrt; + RealScalar s = (std::min)(16,std::numeric_limits::max_exponent10/8); + Matrix a = Matrix::Random(rows,rows); + Matrix d = Matrix::Random(rows); + for(Index k=0; k(-s,s)); + SquareMatrixType A = a * d.asDiagonal() * a.adjoint(); + // Make sure a solution exists: + vecX.setRandom(); + vecB = A * vecX; + vecX.setZero(); + ldltlo.compute(A); + VERIFY_IS_APPROX(A, ldltlo.reconstructedMatrix()); + vecX = ldltlo.solve(vecB); + + if(ldltlo.vectorD().real().cwiseAbs().minCoeff()>RealScalar(0)) + { + VERIFY_IS_APPROX(A * vecX,vecB); + } + else + { + RealScalar large_tol = sqrt(test_precision()); + VERIFY((A * vecX).isApprox(vecB, large_tol)); + + ++g_test_level; + VERIFY_IS_APPROX(A * vecX,vecB); + --g_test_level; + } + } + } + + // update/downdate + CALL_SUBTEST(( test_chol_update(symm) )); + CALL_SUBTEST(( test_chol_update(symm) )); +} + +template void cholesky_cplx(const MatrixType& m) +{ + // classic test + cholesky(m); + + // test mixing real/scalar types + + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix RealMatrixType; + typedef Matrix VectorType; + + RealMatrixType a0 = RealMatrixType::Random(rows,cols); + VectorType vecB = VectorType::Random(rows), vecX(rows); + MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols); + RealMatrixType symm = a0 * a0.adjoint(); + // let's make sure the matrix is not singular or near singular + for (int k=0; k<3; ++k) + { + RealMatrixType a1 = RealMatrixType::Random(rows,cols); + symm += a1 * a1.adjoint(); + } + + { + RealMatrixType symmLo = symm.template triangularView(); + + LLT chollo(symmLo); + VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix()); + + check_solverbase(symm, chollo, rows, rows, 1); + //check_solverbase(symm, chollo, rows, cols, rows); + } + + // LDLT + { + int sign = internal::random()%2 ? 1 : -1; + + if(sign == -1) + { + symm = -symm; // test a negative matrix + } + + RealMatrixType symmLo = symm.template triangularView(); + + LDLT ldltlo(symmLo); + VERIFY(ldltlo.info()==Success); + VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix()); + + check_solverbase(symm, ldltlo, rows, rows, 1); + //check_solverbase(symm, ldltlo, rows, cols, rows); + } +} + +// regression test for bug 241 +template void cholesky_bug241(const MatrixType& m) +{ + eigen_assert(m.rows() == 2 && m.cols() == 2); + + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + + MatrixType matA; + matA << 1, 1, 1, 1; + VectorType vecB; + vecB << 1, 1; + VectorType vecX = matA.ldlt().solve(vecB); + VERIFY_IS_APPROX(matA * vecX, vecB); +} + +// LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal. +// This test checks that LDLT reports correctly that matrix is indefinite. +// See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736 +template void cholesky_definiteness(const MatrixType& m) +{ + eigen_assert(m.rows() == 2 && m.cols() == 2); + MatrixType mat; + LDLT ldlt(2); + + { + mat << 1, 0, 0, -1; + ldlt.compute(mat); + VERIFY(ldlt.info()==Success); + VERIFY(!ldlt.isNegative()); + VERIFY(!ldlt.isPositive()); + VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix()); + } + { + mat << 1, 2, 2, 1; + ldlt.compute(mat); + VERIFY(ldlt.info()==Success); + VERIFY(!ldlt.isNegative()); + VERIFY(!ldlt.isPositive()); + VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix()); + } + { + mat << 0, 0, 0, 0; + ldlt.compute(mat); + VERIFY(ldlt.info()==Success); + VERIFY(ldlt.isNegative()); + VERIFY(ldlt.isPositive()); + VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix()); + } + { + mat << 0, 0, 0, 1; + ldlt.compute(mat); + VERIFY(ldlt.info()==Success); + VERIFY(!ldlt.isNegative()); + VERIFY(ldlt.isPositive()); + VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix()); + } + { + mat << -1, 0, 0, 0; + ldlt.compute(mat); + VERIFY(ldlt.info()==Success); + VERIFY(ldlt.isNegative()); + VERIFY(!ldlt.isPositive()); + VERIFY_IS_APPROX(mat,ldlt.reconstructedMatrix()); + } +} + +template +void cholesky_faillure_cases() +{ + MatrixXd mat; + LDLT ldlt; + + { + mat.resize(2,2); + mat << 0, 1, 1, 0; + ldlt.compute(mat); + VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix()); + VERIFY(ldlt.info()==NumericalIssue); + } +#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE_SSE2) + { + mat.resize(3,3); + mat << -1, -3, 3, + -3, -8.9999999999999999999, 1, + 3, 1, 0; + ldlt.compute(mat); + VERIFY(ldlt.info()==NumericalIssue); + VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix()); + } +#endif + { + mat.resize(3,3); + mat << 1, 2, 3, + 2, 4, 1, + 3, 1, 0; + ldlt.compute(mat); + VERIFY(ldlt.info()==NumericalIssue); + VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix()); + } + + { + mat.resize(8,8); + mat << 0.1, 0, -0.1, 0, 0, 0, 1, 0, + 0, 4.24667, 0, 2.00333, 0, 0, 0, 0, + -0.1, 0, 0.2, 0, -0.1, 0, 0, 0, + 0, 2.00333, 0, 8.49333, 0, 2.00333, 0, 0, + 0, 0, -0.1, 0, 0.1, 0, 0, 1, + 0, 0, 0, 2.00333, 0, 4.24667, 0, 0, + 1, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 1, 0, 0, 0; + ldlt.compute(mat); + VERIFY(ldlt.info()==NumericalIssue); + VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix()); + } + + // bug 1479 + { + mat.resize(4,4); + mat << 1, 2, 0, 1, + 2, 4, 0, 2, + 0, 0, 0, 1, + 1, 2, 1, 1; + ldlt.compute(mat); + VERIFY(ldlt.info()==NumericalIssue); + VERIFY_IS_NOT_APPROX(mat,ldlt.reconstructedMatrix()); + } +} + +template void cholesky_verify_assert() +{ + MatrixType tmp; + + LLT llt; + VERIFY_RAISES_ASSERT(llt.matrixL()) + VERIFY_RAISES_ASSERT(llt.matrixU()) + VERIFY_RAISES_ASSERT(llt.solve(tmp)) + VERIFY_RAISES_ASSERT(llt.transpose().solve(tmp)) + VERIFY_RAISES_ASSERT(llt.adjoint().solve(tmp)) + VERIFY_RAISES_ASSERT(llt.solveInPlace(tmp)) + + LDLT ldlt; + VERIFY_RAISES_ASSERT(ldlt.matrixL()) + VERIFY_RAISES_ASSERT(ldlt.transpositionsP()) + VERIFY_RAISES_ASSERT(ldlt.vectorD()) + VERIFY_RAISES_ASSERT(ldlt.isPositive()) + VERIFY_RAISES_ASSERT(ldlt.isNegative()) + VERIFY_RAISES_ASSERT(ldlt.solve(tmp)) + VERIFY_RAISES_ASSERT(ldlt.transpose().solve(tmp)) + VERIFY_RAISES_ASSERT(ldlt.adjoint().solve(tmp)) + VERIFY_RAISES_ASSERT(ldlt.solveInPlace(tmp)) +} + +EIGEN_DECLARE_TEST(cholesky) +{ + int s = 0; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( cholesky(Matrix()) ); + CALL_SUBTEST_3( cholesky(Matrix2d()) ); + CALL_SUBTEST_3( cholesky_bug241(Matrix2d()) ); + CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) ); + CALL_SUBTEST_4( cholesky(Matrix3f()) ); + CALL_SUBTEST_5( cholesky(Matrix4d()) ); + + s = internal::random(1,EIGEN_TEST_MAX_SIZE); + CALL_SUBTEST_2( cholesky(MatrixXd(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + + s = internal::random(1,EIGEN_TEST_MAX_SIZE/2); + CALL_SUBTEST_6( cholesky_cplx(MatrixXcd(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + } + // empty matrix, regression test for Bug 785: + CALL_SUBTEST_2( cholesky(MatrixXd(0,0)) ); + + // This does not work yet: + // CALL_SUBTEST_2( cholesky(Matrix()) ); + + CALL_SUBTEST_4( cholesky_verify_assert() ); + CALL_SUBTEST_7( cholesky_verify_assert() ); + CALL_SUBTEST_8( cholesky_verify_assert() ); + CALL_SUBTEST_2( cholesky_verify_assert() ); + + // Test problem size constructors + CALL_SUBTEST_9( LLT(10) ); + CALL_SUBTEST_9( LDLT(10) ); + + CALL_SUBTEST_2( cholesky_faillure_cases() ); + + TEST_SET_BUT_UNUSED_VARIABLE(nb_temporaries) +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholmod_support.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholmod_support.cpp new file mode 100644 index 0000000000000000000000000000000000000000..89b9cf41e0fed1f45268056058b2dbd0a5ab3ef1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/cholmod_support.cpp @@ -0,0 +1,69 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS +#include "sparse_solver.h" + +#include + +template void test_cholmod_ST() +{ + CholmodDecomposition g_chol_colmajor_lower; g_chol_colmajor_lower.setMode(CholmodSupernodalLLt); + CholmodDecomposition g_chol_colmajor_upper; g_chol_colmajor_upper.setMode(CholmodSupernodalLLt); + CholmodDecomposition g_llt_colmajor_lower; g_llt_colmajor_lower.setMode(CholmodSimplicialLLt); + CholmodDecomposition g_llt_colmajor_upper; g_llt_colmajor_upper.setMode(CholmodSimplicialLLt); + CholmodDecomposition g_ldlt_colmajor_lower; g_ldlt_colmajor_lower.setMode(CholmodLDLt); + CholmodDecomposition g_ldlt_colmajor_upper; g_ldlt_colmajor_upper.setMode(CholmodLDLt); + + CholmodSupernodalLLT chol_colmajor_lower; + CholmodSupernodalLLT chol_colmajor_upper; + CholmodSimplicialLLT llt_colmajor_lower; + CholmodSimplicialLLT llt_colmajor_upper; + CholmodSimplicialLDLT ldlt_colmajor_lower; + CholmodSimplicialLDLT ldlt_colmajor_upper; + + check_sparse_spd_solving(g_chol_colmajor_lower); + check_sparse_spd_solving(g_chol_colmajor_upper); + check_sparse_spd_solving(g_llt_colmajor_lower); + check_sparse_spd_solving(g_llt_colmajor_upper); + check_sparse_spd_solving(g_ldlt_colmajor_lower); + check_sparse_spd_solving(g_ldlt_colmajor_upper); + + check_sparse_spd_solving(chol_colmajor_lower); + check_sparse_spd_solving(chol_colmajor_upper); + check_sparse_spd_solving(llt_colmajor_lower); + check_sparse_spd_solving(llt_colmajor_upper); + check_sparse_spd_solving(ldlt_colmajor_lower); + check_sparse_spd_solving(ldlt_colmajor_upper); + + check_sparse_spd_determinant(chol_colmajor_lower); + check_sparse_spd_determinant(chol_colmajor_upper); + check_sparse_spd_determinant(llt_colmajor_lower); + check_sparse_spd_determinant(llt_colmajor_upper); + check_sparse_spd_determinant(ldlt_colmajor_lower); + check_sparse_spd_determinant(ldlt_colmajor_upper); +} + +template void test_cholmod_T() +{ + test_cholmod_ST >(); +} + +EIGEN_DECLARE_TEST(cholmod_support) +{ + CALL_SUBTEST_11( (test_cholmod_T()) ); + CALL_SUBTEST_12( (test_cholmod_T()) ); + CALL_SUBTEST_13( (test_cholmod_T()) ); + CALL_SUBTEST_14( (test_cholmod_T()) ); + CALL_SUBTEST_21( (test_cholmod_T, ColMajor, int >()) ); + CALL_SUBTEST_22( (test_cholmod_T, ColMajor, long>()) ); + // TODO complex row-major matrices do not work at the moment: + // CALL_SUBTEST_23( (test_cholmod_T, RowMajor, int >()) ); + // CALL_SUBTEST_24( (test_cholmod_T, RowMajor, long>()) ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/commainitializer.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/commainitializer.cpp new file mode 100644 index 0000000000000000000000000000000000000000..eb275be9cf4527e8fac96cb1f25b2c929695d800 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/commainitializer.cpp @@ -0,0 +1,118 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + + +template +void test_blocks() +{ + Matrix m_fixed; + MatrixXi m_dynamic(M1+M2, N1+N2); + + Matrix mat11; mat11.setRandom(); + Matrix mat12; mat12.setRandom(); + Matrix mat21; mat21.setRandom(); + Matrix mat22; mat22.setRandom(); + + MatrixXi matx11 = mat11, matx12 = mat12, matx21 = mat21, matx22 = mat22; + + { + VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat21, matx22).finished(), (m_dynamic << mat11, matx12, mat21, matx22).finished()); + VERIFY_IS_EQUAL((m_fixed.template topLeftCorner()), mat11); + VERIFY_IS_EQUAL((m_fixed.template topRightCorner()), mat12); + VERIFY_IS_EQUAL((m_fixed.template bottomLeftCorner()), mat21); + VERIFY_IS_EQUAL((m_fixed.template bottomRightCorner()), mat22); + VERIFY_IS_EQUAL((m_fixed << mat12, mat11, matx21, mat22).finished(), (m_dynamic << mat12, matx11, matx21, mat22).finished()); + } + + if(N1 > 0) + { + if(M1 > 0) + { + VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat11, mat21, mat22)); + } + if(M2 > 0) + { + VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat21, mat21, mat22)); + } + } + else + { + // allow insertion of zero-column blocks: + VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat11, mat11, mat21, mat21, mat22).finished(), (m_dynamic << mat12, mat22).finished()); + } + if(M1 != M2) + { + VERIFY_RAISES_ASSERT((m_fixed << mat11, mat21, mat12, mat22)); + } +} + + +template +struct test_block_recursion +{ + static void run() + { + test_block_recursion::run(); + test_block_recursion::run(); + } +}; + +template +struct test_block_recursion<0,N> +{ + static void run() { + test_blocks<(N>>6)&3, (N>>4)&3, (N>>2)&3, N & 3>(); + } +}; + +void test_basics() { + Matrix3d m3; + Matrix4d m4; + + VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8) ); + + #ifndef _MSC_VER + VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) ); + #endif + + double data[] = {1, 2, 3, 4, 5, 6, 7, 8, 9}; + Matrix3d ref = Map >(data); + + m3 = Matrix3d::Random(); + m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9; + VERIFY_IS_APPROX(m3, ref ); + + Vector3d vec[3]; + vec[0] << 1, 4, 7; + vec[1] << 2, 5, 8; + vec[2] << 3, 6, 9; + m3 = Matrix3d::Random(); + m3 << vec[0], vec[1], vec[2]; + VERIFY_IS_APPROX(m3, ref); + + vec[0] << 1, 2, 3; + vec[1] << 4, 5, 6; + vec[2] << 7, 8, 9; + m3 = Matrix3d::Random(); + m3 << vec[0].transpose(), + 4, 5, 6, + vec[2].transpose(); + VERIFY_IS_APPROX(m3, ref); +} + +EIGEN_DECLARE_TEST(commainitializer) +{ + + CALL_SUBTEST_1(test_basics()); + + // recursively test all block-sizes from 0 to 3: + CALL_SUBTEST_2(test_block_recursion<8>::run()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conjugate_gradient.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conjugate_gradient.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b076a126b7cd8352eeb3199d8bb07640dc82a3f6 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conjugate_gradient.cpp @@ -0,0 +1,34 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "sparse_solver.h" +#include + +template void test_conjugate_gradient_T() +{ + typedef SparseMatrix SparseMatrixType; + ConjugateGradient cg_colmajor_lower_diag; + ConjugateGradient cg_colmajor_upper_diag; + ConjugateGradient cg_colmajor_loup_diag; + ConjugateGradient cg_colmajor_lower_I; + ConjugateGradient cg_colmajor_upper_I; + + CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_diag) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_diag) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_loup_diag) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_lower_I) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_colmajor_upper_I) ); +} + +EIGEN_DECLARE_TEST(conjugate_gradient) +{ + CALL_SUBTEST_1(( test_conjugate_gradient_T() )); + CALL_SUBTEST_2(( test_conjugate_gradient_T, int>() )); + CALL_SUBTEST_3(( test_conjugate_gradient_T() )); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conservative_resize.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conservative_resize.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d48eb126fdb1fca779981e258f0c82430c1a01d1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/conservative_resize.cpp @@ -0,0 +1,167 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +#include +#include "AnnoyingScalar.h" + +using namespace Eigen; + +template +void run_matrix_tests() +{ + typedef Matrix MatrixType; + + MatrixType m, n; + + // boundary cases ... + m = n = MatrixType::Random(50,50); + m.conservativeResize(1,50); + VERIFY_IS_APPROX(m, n.block(0,0,1,50)); + + m = n = MatrixType::Random(50,50); + m.conservativeResize(50,1); + VERIFY_IS_APPROX(m, n.block(0,0,50,1)); + + m = n = MatrixType::Random(50,50); + m.conservativeResize(50,50); + VERIFY_IS_APPROX(m, n.block(0,0,50,50)); + + // random shrinking ... + for (int i=0; i<25; ++i) + { + const Index rows = internal::random(1,50); + const Index cols = internal::random(1,50); + m = n = MatrixType::Random(50,50); + m.conservativeResize(rows,cols); + VERIFY_IS_APPROX(m, n.block(0,0,rows,cols)); + } + + // random growing with zeroing ... + for (int i=0; i<25; ++i) + { + const Index rows = internal::random(50,75); + const Index cols = internal::random(50,75); + m = n = MatrixType::Random(50,50); + m.conservativeResizeLike(MatrixType::Zero(rows,cols)); + VERIFY_IS_APPROX(m.block(0,0,n.rows(),n.cols()), n); + VERIFY( rows<=50 || m.block(50,0,rows-50,cols).sum() == Scalar(0) ); + VERIFY( cols<=50 || m.block(0,50,rows,cols-50).sum() == Scalar(0) ); + } +} + +template +void run_vector_tests() +{ + typedef Matrix VectorType; + + VectorType m, n; + + // boundary cases ... + m = n = VectorType::Random(50); + m.conservativeResize(1); + VERIFY_IS_APPROX(m, n.segment(0,1)); + + m = n = VectorType::Random(50); + m.conservativeResize(50); + VERIFY_IS_APPROX(m, n.segment(0,50)); + + m = n = VectorType::Random(50); + m.conservativeResize(m.rows(),1); + VERIFY_IS_APPROX(m, n.segment(0,1)); + + m = n = VectorType::Random(50); + m.conservativeResize(m.rows(),50); + VERIFY_IS_APPROX(m, n.segment(0,50)); + + // random shrinking ... + for (int i=0; i<50; ++i) + { + const int size = internal::random(1,50); + m = n = VectorType::Random(50); + m.conservativeResize(size); + VERIFY_IS_APPROX(m, n.segment(0,size)); + + m = n = VectorType::Random(50); + m.conservativeResize(m.rows(), size); + VERIFY_IS_APPROX(m, n.segment(0,size)); + } + + // random growing with zeroing ... + for (int i=0; i<50; ++i) + { + const int size = internal::random(50,100); + m = n = VectorType::Random(50); + m.conservativeResizeLike(VectorType::Zero(size)); + VERIFY_IS_APPROX(m.segment(0,50), n); + VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) ); + + m = n = VectorType::Random(50); + m.conservativeResizeLike(Matrix::Zero(1,size)); + VERIFY_IS_APPROX(m.segment(0,50), n); + VERIFY( size<=50 || m.segment(50,size-50).sum() == Scalar(0) ); + } +} + +// Basic memory leak check with a non-copyable scalar type +template void noncopyable() +{ + typedef Eigen::Matrix VectorType; + typedef Eigen::Matrix MatrixType; + + { +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW + AnnoyingScalar::dont_throw = true; +#endif + int n = 50; + VectorType v0(n), v1(n); + MatrixType m0(n,n), m1(n,n), m2(n,n); + v0.setOnes(); v1.setOnes(); + m0.setOnes(); m1.setOnes(); m2.setOnes(); + VERIFY(m0==m1); + m0.conservativeResize(2*n,2*n); + VERIFY(m0.topLeftCorner(n,n) == m1); + + VERIFY(v0.head(n) == v1); + v0.conservativeResize(2*n); + VERIFY(v0.head(n) == v1); + } + VERIFY(AnnoyingScalar::instances==0 && "global memory leak detected in noncopyable"); +} + +EIGEN_DECLARE_TEST(conservative_resize) +{ + for(int i=0; i())); + CALL_SUBTEST_1((run_matrix_tests())); + CALL_SUBTEST_2((run_matrix_tests())); + CALL_SUBTEST_2((run_matrix_tests())); + CALL_SUBTEST_3((run_matrix_tests())); + CALL_SUBTEST_3((run_matrix_tests())); + CALL_SUBTEST_4((run_matrix_tests, Eigen::RowMajor>())); + CALL_SUBTEST_4((run_matrix_tests, Eigen::ColMajor>())); + CALL_SUBTEST_5((run_matrix_tests, Eigen::RowMajor>())); + CALL_SUBTEST_5((run_matrix_tests, Eigen::ColMajor>())); + CALL_SUBTEST_1((run_matrix_tests())); + + CALL_SUBTEST_1((run_vector_tests())); + CALL_SUBTEST_2((run_vector_tests())); + CALL_SUBTEST_3((run_vector_tests())); + CALL_SUBTEST_4((run_vector_tests >())); + CALL_SUBTEST_5((run_vector_tests >())); + +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW + AnnoyingScalar::dont_throw = true; +#endif + CALL_SUBTEST_6(( run_vector_tests() )); + CALL_SUBTEST_6(( noncopyable<0>() )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/constructor.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/constructor.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ffd5e802abfb04a7fb28a8316ab065a9fa6ee9b5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/constructor.cpp @@ -0,0 +1,98 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2017 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#define TEST_ENABLE_TEMPORARY_TRACKING + +#include "main.h" + +template struct Wrapper +{ + MatrixType m_mat; + inline Wrapper(const MatrixType &x) : m_mat(x) {} + inline operator const MatrixType& () const { return m_mat; } + inline operator MatrixType& () { return m_mat; } +}; + +enum my_sizes { M = 12, N = 7}; + +template void ctor_init1(const MatrixType& m) +{ + // Check logic in PlainObjectBase::_init1 + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m0 = MatrixType::Random(rows,cols); + + VERIFY_EVALUATION_COUNT( MatrixType m1(m0), 1); + VERIFY_EVALUATION_COUNT( MatrixType m2(m0+m0), 1); + VERIFY_EVALUATION_COUNT( MatrixType m2(m0.block(0,0,rows,cols)) , 1); + + Wrapper wrapper(m0); + VERIFY_EVALUATION_COUNT( MatrixType m3(wrapper) , 1); +} + + +EIGEN_DECLARE_TEST(constructor) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( ctor_init1(Matrix()) ); + CALL_SUBTEST_1( ctor_init1(Matrix4d()) ); + CALL_SUBTEST_1( ctor_init1(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_1( ctor_init1(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } + { + Matrix a(123); + VERIFY_IS_EQUAL(a[0], 123); + } + { + Matrix a(123.0); + VERIFY_IS_EQUAL(a[0], 123); + } + { + Matrix a(123); + VERIFY_IS_EQUAL(a[0], 123.f); + } + { + Array a(123); + VERIFY_IS_EQUAL(a[0], 123); + } + { + Array a(123.0); + VERIFY_IS_EQUAL(a[0], 123); + } + { + Array a(123); + VERIFY_IS_EQUAL(a[0], 123.f); + } + { + Array a(123); + VERIFY_IS_EQUAL(a(4), 123); + } + { + Array a(123.0); + VERIFY_IS_EQUAL(a(4), 123); + } + { + Array a(123); + VERIFY_IS_EQUAL(a(4), 123.f); + } + { + MatrixXi m1(M,N); + VERIFY_IS_EQUAL(m1.rows(),M); + VERIFY_IS_EQUAL(m1.cols(),N); + ArrayXXi a1(M,N); + VERIFY_IS_EQUAL(a1.rows(),M); + VERIFY_IS_EQUAL(a1.cols(),N); + VectorXi v1(M); + VERIFY_IS_EQUAL(v1.size(),M); + ArrayXi a2(M); + VERIFY_IS_EQUAL(a2.size(),M); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/corners.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/corners.cpp new file mode 100644 index 0000000000000000000000000000000000000000..73342a8ddb692d0ce0a60ffa1d1f547881896761 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/corners.cpp @@ -0,0 +1,117 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +#define COMPARE_CORNER(A,B) \ + VERIFY_IS_EQUAL(matrix.A, matrix.B); \ + VERIFY_IS_EQUAL(const_matrix.A, const_matrix.B); + +template void corners(const MatrixType& m) +{ + Index rows = m.rows(); + Index cols = m.cols(); + + Index r = internal::random(1,rows); + Index c = internal::random(1,cols); + + MatrixType matrix = MatrixType::Random(rows,cols); + const MatrixType const_matrix = MatrixType::Random(rows,cols); + + COMPARE_CORNER(topLeftCorner(r,c), block(0,0,r,c)); + COMPARE_CORNER(topRightCorner(r,c), block(0,cols-c,r,c)); + COMPARE_CORNER(bottomLeftCorner(r,c), block(rows-r,0,r,c)); + COMPARE_CORNER(bottomRightCorner(r,c), block(rows-r,cols-c,r,c)); + + Index sr = internal::random(1,rows) - 1; + Index nr = internal::random(1,rows-sr); + Index sc = internal::random(1,cols) - 1; + Index nc = internal::random(1,cols-sc); + + COMPARE_CORNER(topRows(r), block(0,0,r,cols)); + COMPARE_CORNER(middleRows(sr,nr), block(sr,0,nr,cols)); + COMPARE_CORNER(bottomRows(r), block(rows-r,0,r,cols)); + COMPARE_CORNER(leftCols(c), block(0,0,rows,c)); + COMPARE_CORNER(middleCols(sc,nc), block(0,sc,rows,nc)); + COMPARE_CORNER(rightCols(c), block(0,cols-c,rows,c)); +} + +template void corners_fixedsize() +{ + MatrixType matrix = MatrixType::Random(); + const MatrixType const_matrix = MatrixType::Random(); + + enum { + rows = MatrixType::RowsAtCompileTime, + cols = MatrixType::ColsAtCompileTime, + r = CRows, + c = CCols, + sr = SRows, + sc = SCols + }; + + VERIFY_IS_EQUAL((matrix.template topLeftCorner()), (matrix.template block(0,0))); + VERIFY_IS_EQUAL((matrix.template topRightCorner()), (matrix.template block(0,cols-c))); + VERIFY_IS_EQUAL((matrix.template bottomLeftCorner()), (matrix.template block(rows-r,0))); + VERIFY_IS_EQUAL((matrix.template bottomRightCorner()), (matrix.template block(rows-r,cols-c))); + + VERIFY_IS_EQUAL((matrix.template topLeftCorner()), (matrix.template topLeftCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template topRightCorner()), (matrix.template topRightCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template bottomLeftCorner()), (matrix.template bottomLeftCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template bottomRightCorner()), (matrix.template bottomRightCorner(r,c))); + + VERIFY_IS_EQUAL((matrix.template topLeftCorner()), (matrix.template topLeftCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template topRightCorner()), (matrix.template topRightCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template bottomLeftCorner()), (matrix.template bottomLeftCorner(r,c))); + VERIFY_IS_EQUAL((matrix.template bottomRightCorner()), (matrix.template bottomRightCorner(r,c))); + + VERIFY_IS_EQUAL((matrix.template topRows()), (matrix.template block(0,0))); + VERIFY_IS_EQUAL((matrix.template middleRows(sr)), (matrix.template block(sr,0))); + VERIFY_IS_EQUAL((matrix.template bottomRows()), (matrix.template block(rows-r,0))); + VERIFY_IS_EQUAL((matrix.template leftCols()), (matrix.template block(0,0))); + VERIFY_IS_EQUAL((matrix.template middleCols(sc)), (matrix.template block(0,sc))); + VERIFY_IS_EQUAL((matrix.template rightCols()), (matrix.template block(0,cols-c))); + + VERIFY_IS_EQUAL((const_matrix.template topLeftCorner()), (const_matrix.template block(0,0))); + VERIFY_IS_EQUAL((const_matrix.template topRightCorner()), (const_matrix.template block(0,cols-c))); + VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner()), (const_matrix.template block(rows-r,0))); + VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner()), (const_matrix.template block(rows-r,cols-c))); + + VERIFY_IS_EQUAL((const_matrix.template topLeftCorner()), (const_matrix.template topLeftCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template topRightCorner()), (const_matrix.template topRightCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner()), (const_matrix.template bottomLeftCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner()), (const_matrix.template bottomRightCorner(r,c))); + + VERIFY_IS_EQUAL((const_matrix.template topLeftCorner()), (const_matrix.template topLeftCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template topRightCorner()), (const_matrix.template topRightCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template bottomLeftCorner()), (const_matrix.template bottomLeftCorner(r,c))); + VERIFY_IS_EQUAL((const_matrix.template bottomRightCorner()), (const_matrix.template bottomRightCorner(r,c))); + + VERIFY_IS_EQUAL((const_matrix.template topRows()), (const_matrix.template block(0,0))); + VERIFY_IS_EQUAL((const_matrix.template middleRows(sr)), (const_matrix.template block(sr,0))); + VERIFY_IS_EQUAL((const_matrix.template bottomRows()), (const_matrix.template block(rows-r,0))); + VERIFY_IS_EQUAL((const_matrix.template leftCols()), (const_matrix.template block(0,0))); + VERIFY_IS_EQUAL((const_matrix.template middleCols(sc)), (const_matrix.template block(0,sc))); + VERIFY_IS_EQUAL((const_matrix.template rightCols()), (const_matrix.template block(0,cols-c))); +} + +EIGEN_DECLARE_TEST(corners) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( corners(Matrix()) ); + CALL_SUBTEST_2( corners(Matrix4d()) ); + CALL_SUBTEST_3( corners(Matrix()) ); + CALL_SUBTEST_4( corners(MatrixXcf(5, 7)) ); + CALL_SUBTEST_5( corners(MatrixXf(21, 20)) ); + + CALL_SUBTEST_1(( corners_fixedsize, 1, 1, 0, 0>() )); + CALL_SUBTEST_2(( corners_fixedsize() )); + CALL_SUBTEST_3(( corners_fixedsize,4,7,5,2>() )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/ctorleak.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/ctorleak.cpp new file mode 100644 index 0000000000000000000000000000000000000000..73904176bf0d9f1b37e0324eb6ba611cfb68b851 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/ctorleak.cpp @@ -0,0 +1,81 @@ +#include "main.h" + +#include // std::exception + +struct Foo +{ + static Index object_count; + static Index object_limit; + int dummy; + + Foo() : dummy(0) + { +#ifdef EIGEN_EXCEPTIONS + // TODO: Is this the correct way to handle this? + if (Foo::object_count > Foo::object_limit) { std::cout << "\nThrow!\n"; throw Foo::Fail(); } +#endif + std::cout << '+'; + ++Foo::object_count; + } + + ~Foo() + { + std::cout << '-'; + --Foo::object_count; + } + + class Fail : public std::exception {}; +}; + +Index Foo::object_count = 0; +Index Foo::object_limit = 0; + +#undef EIGEN_TEST_MAX_SIZE +#define EIGEN_TEST_MAX_SIZE 3 + +EIGEN_DECLARE_TEST(ctorleak) +{ + typedef Matrix MatrixX; + typedef Matrix VectorX; + + Foo::object_count = 0; + for(int i = 0; i < g_repeat; i++) { + Index rows = internal::random(2,EIGEN_TEST_MAX_SIZE), cols = internal::random(2,EIGEN_TEST_MAX_SIZE); + Foo::object_limit = rows*cols; + { + MatrixX r(rows, cols); + Foo::object_limit = r.size()+internal::random(0, rows*cols - 2); + std::cout << "object_limit =" << Foo::object_limit << std::endl; +#ifdef EIGEN_EXCEPTIONS + try + { +#endif + if(internal::random()) { + std::cout << "\nMatrixX m(" << rows << ", " << cols << ");\n"; + MatrixX m(rows, cols); + } + else { + std::cout << "\nMatrixX m(r);\n"; + MatrixX m(r); + } +#ifdef EIGEN_EXCEPTIONS + VERIFY(false); // not reached if exceptions are enabled + } + catch (const Foo::Fail&) { /* ignore */ } +#endif + } + VERIFY_IS_EQUAL(Index(0), Foo::object_count); + + { + Foo::object_limit = (rows+1)*(cols+1); + MatrixX A(rows, cols); + VERIFY_IS_EQUAL(Foo::object_count, rows*cols); + VectorX v=A.row(0); + VERIFY_IS_EQUAL(Foo::object_count, (rows+1)*cols); + v = A.col(0); + VERIFY_IS_EQUAL(Foo::object_count, rows*(cols+1)); + } + VERIFY_IS_EQUAL(Index(0), Foo::object_count); + } + std::cout << "\n"; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/denseLM.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/denseLM.cpp new file mode 100644 index 0000000000000000000000000000000000000000..afb8004b1e35fe909d580133c1736ec4bf19179b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/denseLM.cpp @@ -0,0 +1,190 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Desire Nuentsa +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include +#include +#include + +#include "main.h" +#include +using namespace std; +using namespace Eigen; + +template +struct DenseLM : DenseFunctor +{ + typedef DenseFunctor Base; + typedef typename Base::JacobianType JacobianType; + typedef Matrix VectorType; + + DenseLM(int n, int m) : DenseFunctor(n,m) + { } + + VectorType model(const VectorType& uv, VectorType& x) + { + VectorType y; // Should change to use expression template + int m = Base::values(); + int n = Base::inputs(); + eigen_assert(uv.size()%2 == 0); + eigen_assert(uv.size() == n); + eigen_assert(x.size() == m); + y.setZero(m); + int half = n/2; + VectorBlock u(uv, 0, half); + VectorBlock v(uv, half, half); + for (int j = 0; j < m; j++) + { + for (int i = 0; i < half; i++) + y(j) += u(i)*std::exp(-(x(j)-i)*(x(j)-i)/(v(i)*v(i))); + } + return y; + + } + void initPoints(VectorType& uv_ref, VectorType& x) + { + m_x = x; + m_y = this->model(uv_ref, x); + } + + int operator()(const VectorType& uv, VectorType& fvec) + { + + int m = Base::values(); + int n = Base::inputs(); + eigen_assert(uv.size()%2 == 0); + eigen_assert(uv.size() == n); + eigen_assert(fvec.size() == m); + int half = n/2; + VectorBlock u(uv, 0, half); + VectorBlock v(uv, half, half); + for (int j = 0; j < m; j++) + { + fvec(j) = m_y(j); + for (int i = 0; i < half; i++) + { + fvec(j) -= u(i) *std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i))); + } + } + + return 0; + } + int df(const VectorType& uv, JacobianType& fjac) + { + int m = Base::values(); + int n = Base::inputs(); + eigen_assert(n == uv.size()); + eigen_assert(fjac.rows() == m); + eigen_assert(fjac.cols() == n); + int half = n/2; + VectorBlock u(uv, 0, half); + VectorBlock v(uv, half, half); + for (int j = 0; j < m; j++) + { + for (int i = 0; i < half; i++) + { + fjac.coeffRef(j,i) = -std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i))); + fjac.coeffRef(j,i+half) = -2.*u(i)*(m_x(j)-i)*(m_x(j)-i)/(std::pow(v(i),3)) * std::exp(-(m_x(j)-i)*(m_x(j)-i)/(v(i)*v(i))); + } + } + return 0; + } + VectorType m_x, m_y; //Data Points +}; + +template +int test_minimizeLM(FunctorType& functor, VectorType& uv) +{ + LevenbergMarquardt lm(functor); + LevenbergMarquardtSpace::Status info; + + info = lm.minimize(uv); + + VERIFY_IS_EQUAL(info, 1); + //FIXME Check other parameters + return info; +} + +template +int test_lmder(FunctorType& functor, VectorType& uv) +{ + typedef typename VectorType::Scalar Scalar; + LevenbergMarquardtSpace::Status info; + LevenbergMarquardt lm(functor); + info = lm.lmder1(uv); + + VERIFY_IS_EQUAL(info, 1); + //FIXME Check other parameters + return info; +} + +template +int test_minimizeSteps(FunctorType& functor, VectorType& uv) +{ + LevenbergMarquardtSpace::Status info; + LevenbergMarquardt lm(functor); + info = lm.minimizeInit(uv); + if (info==LevenbergMarquardtSpace::ImproperInputParameters) + return info; + do + { + info = lm.minimizeOneStep(uv); + } while (info==LevenbergMarquardtSpace::Running); + + VERIFY_IS_EQUAL(info, 1); + //FIXME Check other parameters + return info; +} + +template +void test_denseLM_T() +{ + typedef Matrix VectorType; + + int inputs = 10; + int values = 1000; + DenseLM dense_gaussian(inputs, values); + VectorType uv(inputs),uv_ref(inputs); + VectorType x(values); + + // Generate the reference solution + uv_ref << -2, 1, 4 ,8, 6, 1.8, 1.2, 1.1, 1.9 , 3; + + //Generate the reference data points + x.setRandom(); + x = 10*x; + x.array() += 10; + dense_gaussian.initPoints(uv_ref, x); + + // Generate the initial parameters + VectorBlock u(uv, 0, inputs/2); + VectorBlock v(uv, inputs/2, inputs/2); + + // Solve the optimization problem + + //Solve in one go + u.setOnes(); v.setOnes(); + test_minimizeLM(dense_gaussian, uv); + + //Solve until the machine precision + u.setOnes(); v.setOnes(); + test_lmder(dense_gaussian, uv); + + // Solve step by step + v.setOnes(); u.setOnes(); + test_minimizeSteps(dense_gaussian, uv); + +} + +EIGEN_DECLARE_TEST(denseLM) +{ + CALL_SUBTEST_2(test_denseLM_T()); + + // CALL_SUBTEST_2(test_sparseLM_T()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dense_storage.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dense_storage.cpp new file mode 100644 index 0000000000000000000000000000000000000000..45c2bd728a993ee4747901536aea2876cbf18126 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dense_storage.cpp @@ -0,0 +1,190 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2013 Hauke Heibel +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include "AnnoyingScalar.h" +#include "SafeScalar.h" + +#include + +#if EIGEN_HAS_TYPE_TRAITS && EIGEN_HAS_CXX11 +using DenseStorageD3x3 = Eigen::DenseStorage; +static_assert(std::is_trivially_move_constructible::value, "DenseStorage not trivially_move_constructible"); +static_assert(std::is_trivially_move_assignable::value, "DenseStorage not trivially_move_assignable"); +#if !defined(EIGEN_DENSE_STORAGE_CTOR_PLUGIN) +static_assert(std::is_trivially_copy_constructible::value, "DenseStorage not trivially_copy_constructible"); +static_assert(std::is_trivially_copy_assignable::value, "DenseStorage not trivially_copy_assignable"); +static_assert(std::is_trivially_copyable::value, "DenseStorage not trivially_copyable"); +#endif +#endif + +template +void dense_storage_copy(int rows, int cols) +{ + typedef DenseStorage DenseStorageType; + + const int size = rows*cols; + DenseStorageType reference(size, rows, cols); + T* raw_reference = reference.data(); + for (int i=0; i(i); + + DenseStorageType copied_reference(reference); + const T* raw_copied_reference = copied_reference.data(); + for (int i=0; i +void dense_storage_assignment(int rows, int cols) +{ + typedef DenseStorage DenseStorageType; + + const int size = rows*cols; + DenseStorageType reference(size, rows, cols); + T* raw_reference = reference.data(); + for (int i=0; i(i); + + DenseStorageType copied_reference; + copied_reference = reference; + const T* raw_copied_reference = copied_reference.data(); + for (int i=0; i +void dense_storage_swap(int rows0, int cols0, int rows1, int cols1) +{ + typedef DenseStorage DenseStorageType; + + const int size0 = rows0*cols0; + DenseStorageType a(size0, rows0, cols0); + for (int i=0; i(i); + } + + const int size1 = rows1*cols1; + DenseStorageType b(size1, rows1, cols1); + for (int i=0; i(-i); + } + + a.swap(b); + + for (int i=0; i(i)); + } + + for (int i=0; i(-i)); + } +} + +template +void dense_storage_alignment() +{ + #if EIGEN_HAS_ALIGNAS + + struct alignas(Alignment) Empty1 {}; + VERIFY_IS_EQUAL(std::alignment_of::value, Alignment); + + struct EIGEN_ALIGN_TO_BOUNDARY(Alignment) Empty2 {}; + VERIFY_IS_EQUAL(std::alignment_of::value, Alignment); + + struct Nested1 { EIGEN_ALIGN_TO_BOUNDARY(Alignment) T data[Size]; }; + VERIFY_IS_EQUAL(std::alignment_of::value, Alignment); + + VERIFY_IS_EQUAL( (std::alignment_of >::value), Alignment); + + const std::size_t default_alignment = internal::compute_default_alignment::value; + + VERIFY_IS_EQUAL( (std::alignment_of >::value), default_alignment); + VERIFY_IS_EQUAL( (std::alignment_of >::value), default_alignment); + struct Nested2 { Matrix mat; }; + VERIFY_IS_EQUAL(std::alignment_of::value, default_alignment); + + #endif +} + +template +void dense_storage_tests() { + // Dynamic Storage. + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + // Fixed Storage. + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + // Fixed Storage with Uninitialized Elements. + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + dense_storage_copy(4, 3); + + // Dynamic Storage. + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + // Fixed Storage. + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + // Fixed Storage with Uninitialized Elements. + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + dense_storage_assignment(4, 3); + + // Dynamic Storage. + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 1); + dense_storage_swap(2, 1, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 3); + dense_storage_swap(2, 3, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 4, 1); + dense_storage_swap(4, 1, 4, 3); + // Fixed Storage. + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 1); + dense_storage_swap(2, 1, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 4, 1); + dense_storage_swap(4, 1, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 3); + dense_storage_swap(2, 3, 4, 3); + // Fixed Storage with Uninitialized Elements. + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 1); + dense_storage_swap(2, 1, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 4, 1); + dense_storage_swap(4, 1, 4, 3); + dense_storage_swap(4, 3, 4, 3); + dense_storage_swap(4, 3, 2, 3); + dense_storage_swap(2, 3, 4, 3); + + dense_storage_alignment(); + dense_storage_alignment(); + dense_storage_alignment(); + dense_storage_alignment(); +} + +EIGEN_DECLARE_TEST(dense_storage) +{ + dense_storage_tests(); + dense_storage_tests(); + dense_storage_tests >(); + dense_storage_tests(); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/determinant.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/determinant.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7dd33c37389aa6b6ccdb8768a26696d3159e67b9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/determinant.cpp @@ -0,0 +1,66 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template void determinant(const MatrixType& m) +{ + /* this test covers the following files: + Determinant.h + */ + Index size = m.rows(); + + MatrixType m1(size, size), m2(size, size); + m1.setRandom(); + m2.setRandom(); + typedef typename MatrixType::Scalar Scalar; + Scalar x = internal::random(); + VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1)); + VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant()); + if(size==1) return; + Index i = internal::random(0, size-1); + Index j; + do { + j = internal::random(0, size-1); + } while(j==i); + m2 = m1; + m2.row(i).swap(m2.row(j)); + VERIFY_IS_APPROX(m2.determinant(), -m1.determinant()); + m2 = m1; + m2.col(i).swap(m2.col(j)); + VERIFY_IS_APPROX(m2.determinant(), -m1.determinant()); + VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant()); + VERIFY_IS_APPROX(numext::conj(m2.determinant()), m2.adjoint().determinant()); + m2 = m1; + m2.row(i) += x*m2.row(j); + VERIFY_IS_APPROX(m2.determinant(), m1.determinant()); + m2 = m1; + m2.row(i) *= x; + VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x); + + // check empty matrix + VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1)); +} + +EIGEN_DECLARE_TEST(determinant) +{ + for(int i = 0; i < g_repeat; i++) { + int s = 0; + CALL_SUBTEST_1( determinant(Matrix()) ); + CALL_SUBTEST_2( determinant(Matrix()) ); + CALL_SUBTEST_3( determinant(Matrix()) ); + CALL_SUBTEST_4( determinant(Matrix()) ); + CALL_SUBTEST_5( determinant(Matrix, 10, 10>()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_6( determinant(MatrixXd(s, s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4e8c4b3c97a05145202856626c2f6dd41c451f68 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal.cpp @@ -0,0 +1,105 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void diagonal(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols); + + Scalar s1 = internal::random(); + + //check diagonal() + VERIFY_IS_APPROX(m1.diagonal(), m1.transpose().diagonal()); + m2.diagonal() = 2 * m1.diagonal(); + m2.diagonal()[0] *= 3; + + if (rows>2) + { + enum { + N1 = MatrixType::RowsAtCompileTime>2 ? 2 : 0, + N2 = MatrixType::RowsAtCompileTime>1 ? -1 : 0 + }; + + // check sub/super diagonal + if(MatrixType::SizeAtCompileTime!=Dynamic) + { + VERIFY(m1.template diagonal().RowsAtCompileTime == m1.diagonal(N1).size()); + VERIFY(m1.template diagonal().RowsAtCompileTime == m1.diagonal(N2).size()); + } + + m2.template diagonal() = 2 * m1.template diagonal(); + VERIFY_IS_APPROX(m2.template diagonal(), static_cast(2) * m1.diagonal(N1)); + m2.template diagonal()[0] *= 3; + VERIFY_IS_APPROX(m2.template diagonal()[0], static_cast(6) * m1.template diagonal()[0]); + + + m2.template diagonal() = 2 * m1.template diagonal(); + m2.template diagonal()[0] *= 3; + VERIFY_IS_APPROX(m2.template diagonal()[0], static_cast(6) * m1.template diagonal()[0]); + + m2.diagonal(N1) = 2 * m1.diagonal(N1); + VERIFY_IS_APPROX(m2.template diagonal(), static_cast(2) * m1.diagonal(N1)); + m2.diagonal(N1)[0] *= 3; + VERIFY_IS_APPROX(m2.diagonal(N1)[0], static_cast(6) * m1.diagonal(N1)[0]); + + m2.diagonal(N2) = 2 * m1.diagonal(N2); + VERIFY_IS_APPROX(m2.template diagonal(), static_cast(2) * m1.diagonal(N2)); + m2.diagonal(N2)[0] *= 3; + VERIFY_IS_APPROX(m2.diagonal(N2)[0], static_cast(6) * m1.diagonal(N2)[0]); + + m2.diagonal(N2).x() = s1; + VERIFY_IS_APPROX(m2.diagonal(N2).x(), s1); + m2.diagonal(N2).coeffRef(0) = Scalar(2)*s1; + VERIFY_IS_APPROX(m2.diagonal(N2).coeff(0), Scalar(2)*s1); + } + + VERIFY( m1.diagonal( cols).size()==0 ); + VERIFY( m1.diagonal(-rows).size()==0 ); +} + +template void diagonal_assert(const MatrixType& m) { + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols); + + if (rows>=2 && cols>=2) + { + VERIFY_RAISES_ASSERT( m1 += m1.diagonal() ); + VERIFY_RAISES_ASSERT( m1 -= m1.diagonal() ); + VERIFY_RAISES_ASSERT( m1.array() *= m1.diagonal().array() ); + VERIFY_RAISES_ASSERT( m1.array() /= m1.diagonal().array() ); + } + + VERIFY_RAISES_ASSERT( m1.diagonal(cols+1) ); + VERIFY_RAISES_ASSERT( m1.diagonal(-(rows+1)) ); +} + +EIGEN_DECLARE_TEST(diagonal) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( diagonal(Matrix()) ); + CALL_SUBTEST_1( diagonal(Matrix()) ); + CALL_SUBTEST_1( diagonal(Matrix()) ); + CALL_SUBTEST_2( diagonal(Matrix4d()) ); + CALL_SUBTEST_2( diagonal(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_2( diagonal(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_2( diagonal(MatrixXcd(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_1( diagonal(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_1( diagonal(Matrix(3, 4)) ); + CALL_SUBTEST_1( diagonal_assert(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal_matrix_variadic_ctor.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal_matrix_variadic_ctor.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fbc8f8470c702e73957232625c6364e52e6a94af --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonal_matrix_variadic_ctor.cpp @@ -0,0 +1,185 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2019 David Tellenbach +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT + +#include "main.h" + +template +void assertionTest() +{ + typedef DiagonalMatrix DiagMatrix5; + typedef DiagonalMatrix DiagMatrix7; + typedef DiagonalMatrix DiagMatrixX; + + Scalar raw[6]; + for (int i = 0; i < 6; ++i) { + raw[i] = internal::random(); + } + + VERIFY_RAISES_ASSERT((DiagMatrix5{raw[0], raw[1], raw[2], raw[3]})); + VERIFY_RAISES_ASSERT((DiagMatrix5{raw[0], raw[1], raw[3]})); + VERIFY_RAISES_ASSERT((DiagMatrix7{raw[0], raw[1], raw[2], raw[3]})); + + VERIFY_RAISES_ASSERT((DiagMatrixX { + {raw[0], raw[1], raw[2]}, + {raw[3], raw[4], raw[5]} + })); +} + +#define VERIFY_IMPLICIT_CONVERSION_3(DIAGTYPE, V0, V1, V2) \ + DIAGTYPE d(V0, V1, V2); \ + DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \ + VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \ + VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \ + VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2); + +#define VERIFY_IMPLICIT_CONVERSION_4(DIAGTYPE, V0, V1, V2, V3) \ + DIAGTYPE d(V0, V1, V2, V3); \ + DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \ + VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \ + VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \ + VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2); \ + VERIFY_IS_APPROX(Dense(3, 3), (Scalar)V3); + +#define VERIFY_IMPLICIT_CONVERSION_5(DIAGTYPE, V0, V1, V2, V3, V4) \ + DIAGTYPE d(V0, V1, V2, V3, V4); \ + DIAGTYPE::DenseMatrixType Dense = d.toDenseMatrix(); \ + VERIFY_IS_APPROX(Dense(0, 0), (Scalar)V0); \ + VERIFY_IS_APPROX(Dense(1, 1), (Scalar)V1); \ + VERIFY_IS_APPROX(Dense(2, 2), (Scalar)V2); \ + VERIFY_IS_APPROX(Dense(3, 3), (Scalar)V3); \ + VERIFY_IS_APPROX(Dense(4, 4), (Scalar)V4); + +template +void constructorTest() +{ + typedef DiagonalMatrix DiagonalMatrix0; + typedef DiagonalMatrix DiagonalMatrix3; + typedef DiagonalMatrix DiagonalMatrix4; + typedef DiagonalMatrix DiagonalMatrixX; + + Scalar raw[7]; + for (int k = 0; k < 7; ++k) raw[k] = internal::random(); + + // Fixed-sized matrices + { + DiagonalMatrix0 a {{}}; + VERIFY(a.rows() == 0); + VERIFY(a.cols() == 0); + typename DiagonalMatrix0::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrix3 a {{raw[0], raw[1], raw[2]}}; + VERIFY(a.rows() == 3); + VERIFY(a.cols() == 3); + typename DiagonalMatrix3::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrix4 a {{raw[0], raw[1], raw[2], raw[3]}}; + VERIFY(a.rows() == 4); + VERIFY(a.cols() == 4); + typename DiagonalMatrix4::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + + // dynamically sized matrices + { + DiagonalMatrixX a{{}}; + VERIFY(a.rows() == 0); + VERIFY(a.rows() == 0); + typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrixX a{{raw[0], raw[1], raw[2], raw[3], raw[4], raw[5], raw[6]}}; + VERIFY(a.rows() == 7); + VERIFY(a.rows() == 7); + typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } +} + +template<> +void constructorTest() +{ + typedef float Scalar; + + typedef DiagonalMatrix DiagonalMatrix0; + typedef DiagonalMatrix DiagonalMatrix3; + typedef DiagonalMatrix DiagonalMatrix4; + typedef DiagonalMatrix DiagonalMatrix5; + typedef DiagonalMatrix DiagonalMatrixX; + + Scalar raw[7]; + for (int k = 0; k < 7; ++k) raw[k] = internal::random(); + + // Fixed-sized matrices + { + DiagonalMatrix0 a {{}}; + VERIFY(a.rows() == 0); + VERIFY(a.cols() == 0); + typename DiagonalMatrix0::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrix3 a {{raw[0], raw[1], raw[2]}}; + VERIFY(a.rows() == 3); + VERIFY(a.cols() == 3); + typename DiagonalMatrix3::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrix4 a {{raw[0], raw[1], raw[2], raw[3]}}; + VERIFY(a.rows() == 4); + VERIFY(a.cols() == 4); + typename DiagonalMatrix4::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + + // dynamically sized matrices + { + DiagonalMatrixX a{{}}; + VERIFY(a.rows() == 0); + VERIFY(a.rows() == 0); + typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { + DiagonalMatrixX a{{raw[0], raw[1], raw[2], raw[3], raw[4], raw[5], raw[6]}}; + VERIFY(a.rows() == 7); + VERIFY(a.rows() == 7); + typename DiagonalMatrixX::DenseMatrixType m = a.toDenseMatrix(); + for (Index k = 0; k < a.rows(); ++k) VERIFY(m(k, k) == raw[k]); + } + { VERIFY_IMPLICIT_CONVERSION_3(DiagonalMatrix3, 1.2647, 2.56f, -3); } + { VERIFY_IMPLICIT_CONVERSION_4(DiagonalMatrix4, 1.2647, 2.56f, -3, 3.23f); } + { VERIFY_IMPLICIT_CONVERSION_5(DiagonalMatrix5, 1.2647, 2.56f, -3, 3.23f, 2); } +} + +EIGEN_DECLARE_TEST(diagonal_matrix_variadic_ctor) +{ + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest()); + CALL_SUBTEST_1(assertionTest>()); + + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest()); + CALL_SUBTEST_2(constructorTest>()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonalmatrices.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonalmatrices.cpp new file mode 100644 index 0000000000000000000000000000000000000000..276beade05ee7fd8b93e36006cdeece3580cc55d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/diagonalmatrices.cpp @@ -0,0 +1,173 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +using namespace std; +template void diagonalmatrices(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; + typedef Matrix VectorType; + typedef Matrix RowVectorType; + typedef Matrix SquareMatrixType; + typedef Matrix DynMatrixType; + typedef DiagonalMatrix LeftDiagonalMatrix; + typedef DiagonalMatrix RightDiagonalMatrix; + typedef Matrix BigMatrix; + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols); + VectorType v1 = VectorType::Random(rows), + v2 = VectorType::Random(rows); + RowVectorType rv1 = RowVectorType::Random(cols), + rv2 = RowVectorType::Random(cols); + + LeftDiagonalMatrix ldm1(v1), ldm2(v2); + RightDiagonalMatrix rdm1(rv1), rdm2(rv2); + + Scalar s1 = internal::random(); + + SquareMatrixType sq_m1 (v1.asDiagonal()); + VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix()); + sq_m1 = v1.asDiagonal(); + VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix()); + SquareMatrixType sq_m2 = v1.asDiagonal(); + VERIFY_IS_APPROX(sq_m1, sq_m2); + + ldm1 = v1.asDiagonal(); + LeftDiagonalMatrix ldm3(v1); + VERIFY_IS_APPROX(ldm1.diagonal(), ldm3.diagonal()); + LeftDiagonalMatrix ldm4 = v1.asDiagonal(); + VERIFY_IS_APPROX(ldm1.diagonal(), ldm4.diagonal()); + + sq_m1.block(0,0,rows,rows) = ldm1; + VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix()); + sq_m1.transpose() = ldm1; + VERIFY_IS_APPROX(sq_m1, ldm1.toDenseMatrix()); + + Index i = internal::random(0, rows-1); + Index j = internal::random(0, cols-1); + + VERIFY_IS_APPROX( ((ldm1 * m1)(i,j)) , ldm1.diagonal()(i) * m1(i,j) ); + VERIFY_IS_APPROX( ((ldm1 * (m1+m2))(i,j)) , ldm1.diagonal()(i) * (m1+m2)(i,j) ); + VERIFY_IS_APPROX( ((m1 * rdm1)(i,j)) , rdm1.diagonal()(j) * m1(i,j) ); + VERIFY_IS_APPROX( ((v1.asDiagonal() * m1)(i,j)) , v1(i) * m1(i,j) ); + VERIFY_IS_APPROX( ((m1 * rv1.asDiagonal())(i,j)) , rv1(j) * m1(i,j) ); + VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * m1)(i,j)) , (v1+v2)(i) * m1(i,j) ); + VERIFY_IS_APPROX( (((v1+v2).asDiagonal() * (m1+m2))(i,j)) , (v1+v2)(i) * (m1+m2)(i,j) ); + VERIFY_IS_APPROX( ((m1 * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * m1(i,j) ); + VERIFY_IS_APPROX( (((m1+m2) * (rv1+rv2).asDiagonal())(i,j)) , (rv1+rv2)(j) * (m1+m2)(i,j) ); + + if(rows>1) + { + DynMatrixType tmp = m1.topRows(rows/2), res; + VERIFY_IS_APPROX( (res = m1.topRows(rows/2) * rv1.asDiagonal()), tmp * rv1.asDiagonal() ); + VERIFY_IS_APPROX( (res = v1.head(rows/2).asDiagonal()*m1.topRows(rows/2)), v1.head(rows/2).asDiagonal()*tmp ); + } + + BigMatrix big; + big.setZero(2*rows, 2*cols); + + big.block(i,j,rows,cols) = m1; + big.block(i,j,rows,cols) = v1.asDiagonal() * big.block(i,j,rows,cols); + + VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , v1.asDiagonal() * m1 ); + + big.block(i,j,rows,cols) = m1; + big.block(i,j,rows,cols) = big.block(i,j,rows,cols) * rv1.asDiagonal(); + VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , m1 * rv1.asDiagonal() ); + + + // scalar multiple + VERIFY_IS_APPROX(LeftDiagonalMatrix(ldm1*s1).diagonal(), ldm1.diagonal() * s1); + VERIFY_IS_APPROX(LeftDiagonalMatrix(s1*ldm1).diagonal(), s1 * ldm1.diagonal()); + + VERIFY_IS_APPROX(m1 * (rdm1 * s1), (m1 * rdm1) * s1); + VERIFY_IS_APPROX(m1 * (s1 * rdm1), (m1 * rdm1) * s1); + + // Diagonal to dense + sq_m1.setRandom(); + sq_m2 = sq_m1; + VERIFY_IS_APPROX( (sq_m1 += (s1*v1).asDiagonal()), sq_m2 += (s1*v1).asDiagonal().toDenseMatrix() ); + VERIFY_IS_APPROX( (sq_m1 -= (s1*v1).asDiagonal()), sq_m2 -= (s1*v1).asDiagonal().toDenseMatrix() ); + VERIFY_IS_APPROX( (sq_m1 = (s1*v1).asDiagonal()), (s1*v1).asDiagonal().toDenseMatrix() ); + + sq_m1.setRandom(); + sq_m2 = v1.asDiagonal(); + sq_m2 = sq_m1 * sq_m2; + VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).col(i), sq_m2.col(i) ); + VERIFY_IS_APPROX( (sq_m1*v1.asDiagonal()).row(i), sq_m2.row(i) ); + + sq_m1 = v1.asDiagonal(); + sq_m2 = v2.asDiagonal(); + SquareMatrixType sq_m3 = v1.asDiagonal(); + VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() + v2.asDiagonal(), sq_m1 + sq_m2); + VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - v2.asDiagonal(), sq_m1 - sq_m2); + VERIFY_IS_APPROX( sq_m3 = v1.asDiagonal() - 2*v2.asDiagonal() + v1.asDiagonal(), sq_m1 - 2*sq_m2 + sq_m1); +} + +template void as_scalar_product(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + typedef Matrix DynMatrixType; + typedef Matrix DynVectorType; + typedef Matrix DynRowVectorType; + + Index rows = m.rows(); + Index depth = internal::random(1,EIGEN_TEST_MAX_SIZE); + + VectorType v1 = VectorType::Random(rows); + DynVectorType dv1 = DynVectorType::Random(depth); + DynRowVectorType drv1 = DynRowVectorType::Random(depth); + DynMatrixType dm1 = dv1; + DynMatrixType drm1 = drv1; + + Scalar s = v1(0); + + VERIFY_IS_APPROX( v1.asDiagonal() * drv1, s*drv1 ); + VERIFY_IS_APPROX( dv1 * v1.asDiagonal(), dv1*s ); + + VERIFY_IS_APPROX( v1.asDiagonal() * drm1, s*drm1 ); + VERIFY_IS_APPROX( dm1 * v1.asDiagonal(), dm1*s ); +} + +template +void bug987() +{ + Matrix3Xd points = Matrix3Xd::Random(3, 3); + Vector2d diag = Vector2d::Random(); + Matrix2Xd tmp1 = points.topRows<2>(), res1, res2; + VERIFY_IS_APPROX( res1 = diag.asDiagonal() * points.topRows<2>(), res2 = diag.asDiagonal() * tmp1 ); + Matrix2d tmp2 = points.topLeftCorner<2,2>(); + VERIFY_IS_APPROX(( res1 = points.topLeftCorner<2,2>()*diag.asDiagonal()) , res2 = tmp2*diag.asDiagonal() ); +} + +EIGEN_DECLARE_TEST(diagonalmatrices) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( diagonalmatrices(Matrix()) ); + CALL_SUBTEST_1( as_scalar_product(Matrix()) ); + + CALL_SUBTEST_2( diagonalmatrices(Matrix3f()) ); + CALL_SUBTEST_3( diagonalmatrices(Matrix()) ); + CALL_SUBTEST_4( diagonalmatrices(Matrix4d()) ); + CALL_SUBTEST_5( diagonalmatrices(Matrix()) ); + CALL_SUBTEST_6( diagonalmatrices(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( as_scalar_product(MatrixXcf(1,1)) ); + CALL_SUBTEST_7( diagonalmatrices(MatrixXi(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_8( diagonalmatrices(Matrix(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_9( diagonalmatrices(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_9( diagonalmatrices(MatrixXf(1,1)) ); + CALL_SUBTEST_9( as_scalar_product(MatrixXf(1,1)) ); + } + CALL_SUBTEST_10( bug987<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dontalign.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dontalign.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2e4102b86f63ad8c0e96b2ab1c039e4c08b4fe23 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dontalign.cpp @@ -0,0 +1,62 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_4 +#define EIGEN_DONT_ALIGN +#elif defined EIGEN_TEST_PART_5 || defined EIGEN_TEST_PART_6 || defined EIGEN_TEST_PART_7 || defined EIGEN_TEST_PART_8 +#define EIGEN_DONT_ALIGN_STATICALLY +#endif + +#include "main.h" +#include + +template +void dontalign(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + typedef Matrix SquareMatrixType; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType a = MatrixType::Random(rows,cols); + SquareMatrixType square = SquareMatrixType::Random(rows,rows); + VectorType v = VectorType::Random(rows); + + VERIFY_IS_APPROX(v, square * square.colPivHouseholderQr().solve(v)); + square = square.inverse().eval(); + a = square * a; + square = square*square; + v = square * v; + v = a.adjoint() * v; + VERIFY(square.determinant() != Scalar(0)); + + // bug 219: MapAligned() was giving an assert with EIGEN_DONT_ALIGN, because Map Flags were miscomputed + Scalar* array = internal::aligned_new(rows); + v = VectorType::MapAligned(array, rows); + internal::aligned_delete(array, rows); +} + +EIGEN_DECLARE_TEST(dontalign) +{ +#if defined EIGEN_TEST_PART_1 || defined EIGEN_TEST_PART_5 + dontalign(Matrix3d()); + dontalign(Matrix4f()); +#elif defined EIGEN_TEST_PART_2 || defined EIGEN_TEST_PART_6 + dontalign(Matrix3cd()); + dontalign(Matrix4cf()); +#elif defined EIGEN_TEST_PART_3 || defined EIGEN_TEST_PART_7 + dontalign(Matrix()); + dontalign(Matrix, 32, 32>()); +#elif defined EIGEN_TEST_PART_4 || defined EIGEN_TEST_PART_8 + dontalign(MatrixXd(32, 32)); + dontalign(MatrixXcf(32, 32)); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dynalloc.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dynalloc.cpp new file mode 100644 index 0000000000000000000000000000000000000000..23c90a7b5e901a2916b2ff7a418bcf51dad98a36 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/dynalloc.cpp @@ -0,0 +1,177 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +#if EIGEN_MAX_ALIGN_BYTES>0 +#define ALIGNMENT EIGEN_MAX_ALIGN_BYTES +#else +#define ALIGNMENT 1 +#endif + +typedef Matrix Vector16f; +typedef Matrix Vector8f; + +void check_handmade_aligned_malloc() +{ + for(int i = 1; i < 1000; i++) + { + char *p = (char*)internal::handmade_aligned_malloc(i); + VERIFY(internal::UIntPtr(p)%ALIGNMENT==0); + // if the buffer is wrongly allocated this will give a bad write --> check with valgrind + for(int j = 0; j < i; j++) p[j]=0; + internal::handmade_aligned_free(p); + } +} + +void check_aligned_malloc() +{ + for(int i = ALIGNMENT; i < 1000; i++) + { + char *p = (char*)internal::aligned_malloc(i); + VERIFY(internal::UIntPtr(p)%ALIGNMENT==0); + // if the buffer is wrongly allocated this will give a bad write --> check with valgrind + for(int j = 0; j < i; j++) p[j]=0; + internal::aligned_free(p); + } +} + +void check_aligned_new() +{ + for(int i = ALIGNMENT; i < 1000; i++) + { + float *p = internal::aligned_new(i); + VERIFY(internal::UIntPtr(p)%ALIGNMENT==0); + // if the buffer is wrongly allocated this will give a bad write --> check with valgrind + for(int j = 0; j < i; j++) p[j]=0; + internal::aligned_delete(p,i); + } +} + +void check_aligned_stack_alloc() +{ + for(int i = ALIGNMENT; i < 400; i++) + { + ei_declare_aligned_stack_constructed_variable(float,p,i,0); + VERIFY(internal::UIntPtr(p)%ALIGNMENT==0); + // if the buffer is wrongly allocated this will give a bad write --> check with valgrind + for(int j = 0; j < i; j++) p[j]=0; + } +} + + +// test compilation with both a struct and a class... +struct MyStruct +{ + EIGEN_MAKE_ALIGNED_OPERATOR_NEW + char dummychar; + Vector16f avec; +}; + +class MyClassA +{ + public: + EIGEN_MAKE_ALIGNED_OPERATOR_NEW + char dummychar; + Vector16f avec; +}; + +template void check_dynaligned() +{ + // TODO have to be updated once we support multiple alignment values + if(T::SizeAtCompileTime % ALIGNMENT == 0) + { + T* obj = new T; + VERIFY(T::NeedsToAlign==1); + VERIFY(internal::UIntPtr(obj)%ALIGNMENT==0); + delete obj; + } +} + +template void check_custom_new_delete() +{ + { + T* t = new T; + delete t; + } + + { + std::size_t N = internal::random(1,10); + T* t = new T[N]; + delete[] t; + } + +#if EIGEN_MAX_ALIGN_BYTES>0 && (!EIGEN_HAS_CXX17_OVERALIGN) + { + T* t = static_cast((T::operator new)(sizeof(T))); + (T::operator delete)(t, sizeof(T)); + } + + { + T* t = static_cast((T::operator new)(sizeof(T))); + (T::operator delete)(t); + } +#endif +} + +EIGEN_DECLARE_TEST(dynalloc) +{ + // low level dynamic memory allocation + CALL_SUBTEST(check_handmade_aligned_malloc()); + CALL_SUBTEST(check_aligned_malloc()); + CALL_SUBTEST(check_aligned_new()); + CALL_SUBTEST(check_aligned_stack_alloc()); + + for (int i=0; i() ); + CALL_SUBTEST( check_custom_new_delete() ); + CALL_SUBTEST( check_custom_new_delete() ); + CALL_SUBTEST( check_custom_new_delete() ); + } + + // check static allocation, who knows ? + #if EIGEN_MAX_STATIC_ALIGN_BYTES + for (int i=0; i() ); + CALL_SUBTEST(check_dynaligned() ); + CALL_SUBTEST(check_dynaligned() ); + CALL_SUBTEST(check_dynaligned() ); + CALL_SUBTEST(check_dynaligned() ); + CALL_SUBTEST(check_dynaligned() ); + CALL_SUBTEST(check_dynaligned() ); + } + + { + MyStruct foo0; VERIFY(internal::UIntPtr(foo0.avec.data())%ALIGNMENT==0); + MyClassA fooA; VERIFY(internal::UIntPtr(fooA.avec.data())%ALIGNMENT==0); + } + + // dynamic allocation, single object + for (int i=0; iavec.data())%ALIGNMENT==0); + MyClassA *fooA = new MyClassA(); VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0); + delete foo0; + delete fooA; + } + + // dynamic allocation, array + const int N = 10; + for (int i=0; iavec.data())%ALIGNMENT==0); + MyClassA *fooA = new MyClassA[N]; VERIFY(internal::UIntPtr(fooA->avec.data())%ALIGNMENT==0); + delete[] foo0; + delete[] fooA; + } + #endif + +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigen2support.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigen2support.cpp new file mode 100644 index 0000000000000000000000000000000000000000..49d7328e9e15db9509d2777288820b487bad33cd --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigen2support.cpp @@ -0,0 +1,65 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN2_SUPPORT + +#include "main.h" + +template void eigen2support(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m3(rows, cols); + + Scalar s1 = internal::random(), + s2 = internal::random(); + + // scalar addition + VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise()); + VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1); + VERIFY_IS_APPROX((m1*Scalar(2)).cwise() - s2, (m1+m1) - MatrixType::Constant(rows,cols,s2) ); + m3 = m1; + m3.cwise() += s2; + VERIFY_IS_APPROX(m3, m1.cwise() + s2); + m3 = m1; + m3.cwise() -= s1; + VERIFY_IS_APPROX(m3, m1.cwise() - s1); + + VERIFY_IS_EQUAL((m1.corner(TopLeft,1,1)), (m1.block(0,0,1,1))); + VERIFY_IS_EQUAL((m1.template corner<1,1>(TopLeft)), (m1.template block<1,1>(0,0))); + VERIFY_IS_EQUAL((m1.col(0).start(1)), (m1.col(0).segment(0,1))); + VERIFY_IS_EQUAL((m1.col(0).template start<1>()), (m1.col(0).segment(0,1))); + VERIFY_IS_EQUAL((m1.col(0).end(1)), (m1.col(0).segment(rows-1,1))); + VERIFY_IS_EQUAL((m1.col(0).template end<1>()), (m1.col(0).segment(rows-1,1))); + + using std::cos; + using numext::real; + using numext::abs2; + VERIFY_IS_EQUAL(ei_cos(s1), cos(s1)); + VERIFY_IS_EQUAL(ei_real(s1), real(s1)); + VERIFY_IS_EQUAL(ei_abs2(s1), abs2(s1)); + + m1.minor(0,0); +} + +EIGEN_DECLARE_TEST(eigen2support) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( eigen2support(Matrix()) ); + CALL_SUBTEST_2( eigen2support(MatrixXd(1,1)) ); + CALL_SUBTEST_4( eigen2support(Matrix3f()) ); + CALL_SUBTEST_5( eigen2support(Matrix4d()) ); + CALL_SUBTEST_2( eigen2support(MatrixXf(200,200)) ); + CALL_SUBTEST_6( eigen2support(MatrixXcd(100,100)) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_complex.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_complex.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c5373f420e482f390f5efdfea516462840cffee9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_complex.cpp @@ -0,0 +1,176 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// Copyright (C) 2010 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +template bool find_pivot(typename MatrixType::Scalar tol, MatrixType &diffs, Index col=0) +{ + bool match = diffs.diagonal().sum() <= tol; + if(match || col==diffs.cols()) + { + return match; + } + else + { + Index n = diffs.cols(); + std::vector > transpositions; + for(Index i=col; i tol) + break; + + best_index += col; + + diffs.row(col).swap(diffs.row(best_index)); + if(find_pivot(tol,diffs,col+1)) return true; + diffs.row(col).swap(diffs.row(best_index)); + + // move current pivot to the end + diffs.row(n-(i-col)-1).swap(diffs.row(best_index)); + transpositions.push_back(std::pair(n-(i-col)-1,best_index)); + } + // restore + for(Index k=transpositions.size()-1; k>=0; --k) + diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second)); + } + return false; +} + +/* Check that two column vectors are approximately equal up to permutations. + * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(), + * however this strategy is numerically inacurate because of numerical cancellation issues. + */ +template +void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2) +{ + typedef typename VectorType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + VERIFY(vec1.cols() == 1); + VERIFY(vec2.cols() == 1); + VERIFY(vec1.rows() == vec2.rows()); + + Index n = vec1.rows(); + RealScalar tol = test_precision()*test_precision()*numext::maxi(vec1.squaredNorm(),vec2.squaredNorm()); + Matrix diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2(); + + VERIFY( find_pivot(tol, diffs) ); +} + + +template void eigensolver(const MatrixType& m) +{ + /* this test covers the following files: + ComplexEigenSolver.h, and indirectly ComplexSchur.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + MatrixType a = MatrixType::Random(rows,cols); + MatrixType symmA = a.adjoint() * a; + + ComplexEigenSolver ei0(symmA); + VERIFY_IS_EQUAL(ei0.info(), Success); + VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal()); + + ComplexEigenSolver ei1(a); + VERIFY_IS_EQUAL(ei1.info(), Success); + VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); + // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus + // another algorithm so results may differ slightly + verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues()); + + ComplexEigenSolver ei2; + ei2.setMaxIterations(ComplexSchur::m_maxIterationsPerRow * rows).compute(a); + VERIFY_IS_EQUAL(ei2.info(), Success); + VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); + VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); + if (rows > 2) { + ei2.setMaxIterations(1).compute(a); + VERIFY_IS_EQUAL(ei2.info(), NoConvergence); + VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1); + } + + ComplexEigenSolver eiNoEivecs(a, false); + VERIFY_IS_EQUAL(eiNoEivecs.info(), Success); + VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); + + // Regression test for issue #66 + MatrixType z = MatrixType::Zero(rows,cols); + ComplexEigenSolver eiz(z); + VERIFY((eiz.eigenvalues().cwiseEqual(0)).all()); + + MatrixType id = MatrixType::Identity(rows, cols); + VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1)); + + if (rows > 1 && rows < 20) + { + // Test matrix with NaN + a(0,0) = std::numeric_limits::quiet_NaN(); + ComplexEigenSolver eiNaN(a); + VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence); + } + + // regression test for bug 1098 + { + ComplexEigenSolver eig(a.adjoint() * a); + eig.compute(a.adjoint() * a); + } + + // regression test for bug 478 + { + a.setZero(); + ComplexEigenSolver ei3(a); + VERIFY_IS_EQUAL(ei3.info(), Success); + VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); + VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); + } +} + +template void eigensolver_verify_assert(const MatrixType& m) +{ + ComplexEigenSolver eig; + VERIFY_RAISES_ASSERT(eig.eigenvectors()); + VERIFY_RAISES_ASSERT(eig.eigenvalues()); + + MatrixType a = MatrixType::Random(m.rows(),m.cols()); + eig.compute(a, false); + VERIFY_RAISES_ASSERT(eig.eigenvectors()); +} + +EIGEN_DECLARE_TEST(eigensolver_complex) +{ + int s = 0; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( eigensolver(Matrix4cf()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_2( eigensolver(MatrixXcd(s,s)) ); + CALL_SUBTEST_3( eigensolver(Matrix, 1, 1>()) ); + CALL_SUBTEST_4( eigensolver(Matrix3f()) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + } + CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4cf()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXcd(s,s)) ); + CALL_SUBTEST_3( eigensolver_verify_assert(Matrix, 1, 1>()) ); + CALL_SUBTEST_4( eigensolver_verify_assert(Matrix3f()) ); + + // Test problem size constructors + CALL_SUBTEST_5(ComplexEigenSolver tmp(s)); + + TEST_SET_BUT_UNUSED_VARIABLE(s) +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generalized_real.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generalized_real.cpp new file mode 100644 index 0000000000000000000000000000000000000000..95ed431db70a040e63f1183a9ccfce8cb41ed76c --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generalized_real.cpp @@ -0,0 +1,103 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012-2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_RUNTIME_NO_MALLOC +#include "main.h" +#include +#include +#include + +template void generalized_eigensolver_real(const MatrixType& m) +{ + /* this test covers the following files: + GeneralizedEigenSolver.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef std::complex ComplexScalar; + typedef Matrix VectorType; + + MatrixType a = MatrixType::Random(rows,cols); + MatrixType b = MatrixType::Random(rows,cols); + MatrixType a1 = MatrixType::Random(rows,cols); + MatrixType b1 = MatrixType::Random(rows,cols); + MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1; + MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1; + + // lets compare to GeneralizedSelfAdjointEigenSolver + { + GeneralizedSelfAdjointEigenSolver symmEig(spdA, spdB); + GeneralizedEigenSolver eig(spdA, spdB); + + VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0); + + VectorType realEigenvalues = eig.eigenvalues().real(); + std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size()); + VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues()); + + // check eigenvectors + typename GeneralizedEigenSolver::EigenvectorsType D = eig.eigenvalues().asDiagonal(); + typename GeneralizedEigenSolver::EigenvectorsType V = eig.eigenvectors(); + VERIFY_IS_APPROX(spdA*V, spdB*V*D); + } + + // non symmetric case: + { + GeneralizedEigenSolver eig(rows); + // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition + //Eigen::internal::set_is_malloc_allowed(false); + eig.compute(a,b); + //Eigen::internal::set_is_malloc_allowed(true); + for(Index k=0; k tmp = (eig.betas()(k)*a).template cast() - eig.alphas()(k)*b; + if(tmp.size()>1 && tmp.norm()>(std::numeric_limits::min)()) + tmp /= tmp.norm(); + VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) ); + } + // check eigenvectors + typename GeneralizedEigenSolver::EigenvectorsType D = eig.eigenvalues().asDiagonal(); + typename GeneralizedEigenSolver::EigenvectorsType V = eig.eigenvectors(); + VERIFY_IS_APPROX(a*V, b*V*D); + } + + // regression test for bug 1098 + { + GeneralizedSelfAdjointEigenSolver eig1(a.adjoint() * a,b.adjoint() * b); + eig1.compute(a.adjoint() * a,b.adjoint() * b); + GeneralizedEigenSolver eig2(a.adjoint() * a,b.adjoint() * b); + eig2.compute(a.adjoint() * a,b.adjoint() * b); + } + + // check without eigenvectors + { + GeneralizedEigenSolver eig1(spdA, spdB, true); + GeneralizedEigenSolver eig2(spdA, spdB, false); + VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues()); + } +} + +EIGEN_DECLARE_TEST(eigensolver_generalized_real) +{ + for(int i = 0; i < g_repeat; i++) { + int s = 0; + CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) ); + + // some trivial but implementation-wise special cases + CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) ); + CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) ); + CALL_SUBTEST_3( generalized_eigensolver_real(Matrix()) ); + CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generic.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generic.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7adb986658675525847cf40eb9b74cbb18d52f08 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_generic.cpp @@ -0,0 +1,247 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2010,2012 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include + +template +void check_eigensolver_for_given_mat(const EigType &eig, const MatType& a) +{ + typedef typename NumTraits::Real RealScalar; + typedef Matrix RealVectorType; + typedef typename std::complex Complex; + Index n = a.rows(); + VERIFY_IS_EQUAL(eig.info(), Success); + VERIFY_IS_APPROX(a * eig.pseudoEigenvectors(), eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()); + VERIFY_IS_APPROX(a.template cast() * eig.eigenvectors(), + eig.eigenvectors() * eig.eigenvalues().asDiagonal()); + VERIFY_IS_APPROX(eig.eigenvectors().colwise().norm(), RealVectorType::Ones(n).transpose()); + VERIFY_IS_APPROX(a.eigenvalues(), eig.eigenvalues()); +} + +template void eigensolver(const MatrixType& m) +{ + /* this test covers the following files: + EigenSolver.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef typename std::complex Complex; + + MatrixType a = MatrixType::Random(rows,cols); + MatrixType a1 = MatrixType::Random(rows,cols); + MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; + + EigenSolver ei0(symmA); + VERIFY_IS_EQUAL(ei0.info(), Success); + VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix()); + VERIFY_IS_APPROX((symmA.template cast()) * (ei0.pseudoEigenvectors().template cast()), + (ei0.pseudoEigenvectors().template cast()) * (ei0.eigenvalues().asDiagonal())); + + EigenSolver ei1(a); + CALL_SUBTEST( check_eigensolver_for_given_mat(ei1,a) ); + + EigenSolver ei2; + ei2.setMaxIterations(RealSchur::m_maxIterationsPerRow * rows).compute(a); + VERIFY_IS_EQUAL(ei2.info(), Success); + VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); + VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); + if (rows > 2) { + ei2.setMaxIterations(1).compute(a); + VERIFY_IS_EQUAL(ei2.info(), NoConvergence); + VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1); + } + + EigenSolver eiNoEivecs(a, false); + VERIFY_IS_EQUAL(eiNoEivecs.info(), Success); + VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); + VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix()); + + MatrixType id = MatrixType::Identity(rows, cols); + VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1)); + + if (rows > 2 && rows < 20) + { + // Test matrix with NaN + a(0,0) = std::numeric_limits::quiet_NaN(); + EigenSolver eiNaN(a); + VERIFY_IS_NOT_EQUAL(eiNaN.info(), Success); + } + + // regression test for bug 1098 + { + EigenSolver eig(a.adjoint() * a); + eig.compute(a.adjoint() * a); + } + + // regression test for bug 478 + { + a.setZero(); + EigenSolver ei3(a); + VERIFY_IS_EQUAL(ei3.info(), Success); + VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); + VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); + } +} + +template void eigensolver_verify_assert(const MatrixType& m) +{ + EigenSolver eig; + VERIFY_RAISES_ASSERT(eig.eigenvectors()); + VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors()); + VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix()); + VERIFY_RAISES_ASSERT(eig.eigenvalues()); + + MatrixType a = MatrixType::Random(m.rows(),m.cols()); + eig.compute(a, false); + VERIFY_RAISES_ASSERT(eig.eigenvectors()); + VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors()); +} + + +template +Matrix +make_companion(const CoeffType& coeffs) +{ + Index n = coeffs.size()-1; + Matrix res(n,n); + res.setZero(); + res.row(0) = -coeffs.tail(n) / coeffs(0); + res.diagonal(-1).setOnes(); + return res; +} + +template +void eigensolver_generic_extra() +{ + { + // regression test for bug 793 + MatrixXd a(3,3); + a << 0, 0, 1, + 1, 1, 1, + 1, 1e+200, 1; + Eigen::EigenSolver eig(a); + double scale = 1e-200; // scale to avoid overflow during the comparisons + VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale); + VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale); + } + { + // check a case where all eigenvalues are null. + MatrixXd a(2,2); + a << 1, 1, + -1, -1; + Eigen::EigenSolver eig(a); + VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.); + VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.); + VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.); + VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.); + VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.); + } + + // regression test for bug 933 + { + { + VectorXd coeffs(5); coeffs << 1, -3, -175, -225, 2250; + MatrixXd C = make_companion(coeffs); + EigenSolver eig(C); + CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) ); + } + { + // this test is tricky because it requires high accuracy in smallest eigenvalues + VectorXd coeffs(5); coeffs << 6.154671e-15, -1.003870e-10, -9.819570e-01, 3.995715e+03, 2.211511e+08; + MatrixXd C = make_companion(coeffs); + EigenSolver eig(C); + CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) ); + Index n = C.rows(); + for(Index i=0;i Complex; + MatrixXcd ac = C.cast(); + ac.diagonal().array() -= eig.eigenvalues()(i); + VectorXd sv = ac.jacobiSvd().singularValues(); + // comparing to sv(0) is not enough here to catch the "bug", + // the hard-coded 1.0 is important! + VERIFY_IS_MUCH_SMALLER_THAN(sv(n-1), 1.0); + } + } + } + // regression test for bug 1557 + { + // this test is interesting because it contains zeros on the diagonal. + MatrixXd A_bug1557(3,3); + A_bug1557 << 0, 0, 0, 1, 0, 0.5887907064808635127, 0, 1, 0; + EigenSolver eig(A_bug1557); + CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1557) ); + } + + // regression test for bug 1174 + { + Index n = 12; + MatrixXf A_bug1174(n,n); + A_bug1174 << 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432, + 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432, + 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432, + 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0, + 0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0; + EigenSolver eig(A_bug1174); + CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1174) ); + } +} + +EIGEN_DECLARE_TEST(eigensolver_generic) +{ + int s = 0; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( eigensolver(Matrix4f()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + + // some trivial but implementation-wise tricky cases + CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) ); + CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) ); + CALL_SUBTEST_3( eigensolver(Matrix()) ); + CALL_SUBTEST_4( eigensolver(Matrix2d()) ); + } + + CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) ); + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) ); + CALL_SUBTEST_3( eigensolver_verify_assert(Matrix()) ); + CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) ); + + // Test problem size constructors + CALL_SUBTEST_5(EigenSolver tmp(s)); + + // regression test for bug 410 + CALL_SUBTEST_2( + { + MatrixXd A(1,1); + A(0,0) = std::sqrt(-1.); // is Not-a-Number + Eigen::EigenSolver solver(A); + VERIFY_IS_EQUAL(solver.info(), NumericalIssue); + } + ); + + CALL_SUBTEST_2( eigensolver_generic_extra<0>() ); + + TEST_SET_BUT_UNUSED_VARIABLE(s) +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_selfadjoint.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_selfadjoint.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0fb2f4da766209ab394459bdc969e97bba1d6bb5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/eigensolver_selfadjoint.cpp @@ -0,0 +1,281 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2010 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include "svd_fill.h" +#include +#include +#include + + +template void selfadjointeigensolver_essential_check(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + RealScalar eival_eps = numext::mini(test_precision(), NumTraits::dummy_precision()*20000); + + SelfAdjointEigenSolver eiSymm(m); + VERIFY_IS_EQUAL(eiSymm.info(), Success); + + RealScalar scaling = m.cwiseAbs().maxCoeff(); + + if(scaling<(std::numeric_limits::min)()) + { + VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits::min)()); + } + else + { + VERIFY_IS_APPROX((m.template selfadjointView() * eiSymm.eigenvectors())/scaling, + (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling); + } + VERIFY_IS_APPROX(m.template selfadjointView().eigenvalues(), eiSymm.eigenvalues()); + VERIFY_IS_UNITARY(eiSymm.eigenvectors()); + + if(m.cols()<=4) + { + SelfAdjointEigenSolver eiDirect; + eiDirect.computeDirect(m); + VERIFY_IS_EQUAL(eiDirect.info(), Success); + if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) ) + { + std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n" + << "obtained eigenvalues: " << eiDirect.eigenvalues().transpose() << "\n" + << "diff: " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << "\n" + << "error (eps): " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << " (" << eival_eps << ")\n"; + } + if(scaling<(std::numeric_limits::min)()) + { + VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits::min)()); + } + else + { + VERIFY_IS_APPROX(eiSymm.eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + VERIFY_IS_APPROX((m.template selfadjointView() * eiDirect.eigenvectors())/scaling, + (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling); + VERIFY_IS_APPROX(m.template selfadjointView().eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + } + + VERIFY_IS_UNITARY(eiDirect.eigenvectors()); + } +} + +template void selfadjointeigensolver(const MatrixType& m) +{ + /* this test covers the following files: + EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h) + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + + RealScalar largerEps = 10*test_precision(); + + MatrixType a = MatrixType::Random(rows,cols); + MatrixType a1 = MatrixType::Random(rows,cols); + MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; + MatrixType symmC = symmA; + + svd_fill_random(symmA,Symmetric); + + symmA.template triangularView().setZero(); + symmC.template triangularView().setZero(); + + MatrixType b = MatrixType::Random(rows,cols); + MatrixType b1 = MatrixType::Random(rows,cols); + MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; + symmB.template triangularView().setZero(); + + CALL_SUBTEST( selfadjointeigensolver_essential_check(symmA) ); + + SelfAdjointEigenSolver eiSymm(symmA); + // generalized eigen pb + GeneralizedSelfAdjointEigenSolver eiSymmGen(symmC, symmB); + + SelfAdjointEigenSolver eiSymmNoEivecs(symmA, false); + VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); + VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); + + // generalized eigen problem Ax = lBx + eiSymmGen.compute(symmC, symmB,Ax_lBx); + VERIFY_IS_EQUAL(eiSymmGen.info(), Success); + VERIFY((symmC.template selfadjointView() * eiSymmGen.eigenvectors()).isApprox( + symmB.template selfadjointView() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); + + // generalized eigen problem BAx = lx + eiSymmGen.compute(symmC, symmB,BAx_lx); + VERIFY_IS_EQUAL(eiSymmGen.info(), Success); + VERIFY((symmB.template selfadjointView() * (symmC.template selfadjointView() * eiSymmGen.eigenvectors())).isApprox( + (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); + + // generalized eigen problem ABx = lx + eiSymmGen.compute(symmC, symmB,ABx_lx); + VERIFY_IS_EQUAL(eiSymmGen.info(), Success); + VERIFY((symmC.template selfadjointView() * (symmB.template selfadjointView() * eiSymmGen.eigenvectors())).isApprox( + (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); + + + eiSymm.compute(symmC); + MatrixType sqrtSymmA = eiSymm.operatorSqrt(); + VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView()), sqrtSymmA*sqrtSymmA); + VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView()*eiSymm.operatorInverseSqrt()); + + MatrixType id = MatrixType::Identity(rows, cols); + VERIFY_IS_APPROX(id.template selfadjointView().operatorNorm(), RealScalar(1)); + + SelfAdjointEigenSolver eiSymmUninitialized; + VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); + + eiSymmUninitialized.compute(symmA, false); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); + VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); + + // test Tridiagonalization's methods + Tridiagonalization tridiag(symmC); + VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal()); + VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>()); + Matrix T = tridiag.matrixT(); + if(rows>1 && cols>1) { + // FIXME check that upper and lower part are 0: + //VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView().isZero()); + } + VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal()); + VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>()); + VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); + VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView()), tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint()); + + // Test computation of eigenvalues from tridiagonal matrix + if(rows > 1) + { + SelfAdjointEigenSolver eiSymmTridiag; + eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors); + VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues()); + VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose()); + } + + if (rows > 1 && rows < 20) + { + // Test matrix with NaN + symmC(0,0) = std::numeric_limits::quiet_NaN(); + SelfAdjointEigenSolver eiSymmNaN(symmC); + VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); + } + + // regression test for bug 1098 + { + SelfAdjointEigenSolver eig(a.adjoint() * a); + eig.compute(a.adjoint() * a); + } + + // regression test for bug 478 + { + a.setZero(); + SelfAdjointEigenSolver ei3(a); + VERIFY_IS_EQUAL(ei3.info(), Success); + VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); + VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); + } +} + +template +void bug_854() +{ + Matrix3d m; + m << 850.961, 51.966, 0, + 51.966, 254.841, 0, + 0, 0, 0; + selfadjointeigensolver_essential_check(m); +} + +template +void bug_1014() +{ + Matrix3d m; + m << 0.11111111111111114658, 0, 0, + 0, 0.11111111111111109107, 0, + 0, 0, 0.11111111111111107719; + selfadjointeigensolver_essential_check(m); +} + +template +void bug_1225() +{ + Matrix3d m1, m2; + m1.setRandom(); + m1 = m1*m1.transpose(); + m2 = m1.triangularView(); + SelfAdjointEigenSolver eig1(m1); + SelfAdjointEigenSolver eig2(m2.selfadjointView()); + VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues()); +} + +template +void bug_1204() +{ + SparseMatrix A(2,2); + A.setIdentity(); + SelfAdjointEigenSolver > eig(A); +} + +EIGEN_DECLARE_TEST(eigensolver_selfadjoint) +{ + int s = 0; + for(int i = 0; i < g_repeat; i++) { + + // trivial test for 1x1 matrices: + CALL_SUBTEST_1( selfadjointeigensolver(Matrix())); + CALL_SUBTEST_1( selfadjointeigensolver(Matrix())); + CALL_SUBTEST_1( selfadjointeigensolver(Matrix, 1, 1>())); + + // very important to test 3x3 and 2x2 matrices since we provide special paths for them + CALL_SUBTEST_12( selfadjointeigensolver(Matrix2f()) ); + CALL_SUBTEST_12( selfadjointeigensolver(Matrix2d()) ); + CALL_SUBTEST_12( selfadjointeigensolver(Matrix2cd()) ); + CALL_SUBTEST_13( selfadjointeigensolver(Matrix3f()) ); + CALL_SUBTEST_13( selfadjointeigensolver(Matrix3d()) ); + CALL_SUBTEST_13( selfadjointeigensolver(Matrix3cd()) ); + CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); + CALL_SUBTEST_2( selfadjointeigensolver(Matrix4cd()) ); + + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); + CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); + CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); + CALL_SUBTEST_9( selfadjointeigensolver(Matrix,Dynamic,Dynamic,RowMajor>(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + + // some trivial but implementation-wise tricky cases + CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); + CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) ); + CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(1,1)) ); + CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(2,2)) ); + CALL_SUBTEST_6( selfadjointeigensolver(Matrix()) ); + CALL_SUBTEST_7( selfadjointeigensolver(Matrix()) ); + } + + CALL_SUBTEST_13( bug_854<0>() ); + CALL_SUBTEST_13( bug_1014<0>() ); + CALL_SUBTEST_13( bug_1204<0>() ); + CALL_SUBTEST_13( bug_1225<0>() ); + + // Test problem size constructors + s = internal::random(1,EIGEN_TEST_MAX_SIZE/4); + CALL_SUBTEST_8(SelfAdjointEigenSolver tmp1(s)); + CALL_SUBTEST_8(Tridiagonalization tmp2(s)); + + TEST_SET_BUT_UNUSED_VARIABLE(s) +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/evaluator_common.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/evaluator_common.h new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/evaluators.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/evaluators.cpp new file mode 100644 index 0000000000000000000000000000000000000000..2810cd265187c27c669ee055f9a04528571a3664 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/evaluators.cpp @@ -0,0 +1,525 @@ + +#include "main.h" + +namespace Eigen { + + template + const Product + prod(const Lhs& lhs, const Rhs& rhs) + { + return Product(lhs,rhs); + } + + template + const Product + lazyprod(const Lhs& lhs, const Rhs& rhs) + { + return Product(lhs,rhs); + } + + template + EIGEN_STRONG_INLINE + DstXprType& copy_using_evaluator(const EigenBase &dst, const SrcXprType &src) + { + call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op()); + return dst.const_cast_derived(); + } + + template class StorageBase, typename SrcXprType> + EIGEN_STRONG_INLINE + const DstXprType& copy_using_evaluator(const NoAlias& dst, const SrcXprType &src) + { + call_assignment(dst, src.derived(), internal::assign_op()); + return dst.expression(); + } + + template + EIGEN_STRONG_INLINE + DstXprType& copy_using_evaluator(const PlainObjectBase &dst, const SrcXprType &src) + { + #ifdef EIGEN_NO_AUTOMATIC_RESIZING + eigen_assert((dst.size()==0 || (IsVectorAtCompileTime ? (dst.size() == src.size()) + : (dst.rows() == src.rows() && dst.cols() == src.cols()))) + && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined"); + #else + dst.const_cast_derived().resizeLike(src.derived()); + #endif + + call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op()); + return dst.const_cast_derived(); + } + + template + void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src) + { + typedef typename DstXprType::Scalar Scalar; + call_assignment(const_cast(dst), src.derived(), internal::add_assign_op()); + } + + template + void subtract_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src) + { + typedef typename DstXprType::Scalar Scalar; + call_assignment(const_cast(dst), src.derived(), internal::sub_assign_op()); + } + + template + void multiply_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src) + { + typedef typename DstXprType::Scalar Scalar; + call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op()); + } + + template + void divide_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src) + { + typedef typename DstXprType::Scalar Scalar; + call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op()); + } + + template + void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src) + { + typedef typename DstXprType::Scalar Scalar; + call_assignment(dst.const_cast_derived(), src.const_cast_derived(), internal::swap_assign_op()); + } + + namespace internal { + template class StorageBase, typename Src, typename Func> + EIGEN_DEVICE_FUNC void call_assignment(const NoAlias& dst, const Src& src, const Func& func) + { + call_assignment_no_alias(dst.expression(), src, func); + } + + template class StorageBase, typename Src, typename Func> + EIGEN_DEVICE_FUNC void call_restricted_packet_assignment(const NoAlias& dst, const Src& src, const Func& func) + { + call_restricted_packet_assignment_no_alias(dst.expression(), src, func); + } + } + +} + +template long get_cost(const XprType& ) { return Eigen::internal::evaluator::CoeffReadCost; } + +using namespace std; + +#define VERIFY_IS_APPROX_EVALUATOR(DEST,EXPR) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (EXPR).eval()); +#define VERIFY_IS_APPROX_EVALUATOR2(DEST,EXPR,REF) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (REF).eval()); + +EIGEN_DECLARE_TEST(evaluators) +{ + // Testing Matrix evaluator and Transpose + Vector2d v = Vector2d::Random(); + const Vector2d v_const(v); + Vector2d v2; + RowVector2d w; + + VERIFY_IS_APPROX_EVALUATOR(v2, v); + VERIFY_IS_APPROX_EVALUATOR(v2, v_const); + + // Testing Transpose + VERIFY_IS_APPROX_EVALUATOR(w, v.transpose()); // Transpose as rvalue + VERIFY_IS_APPROX_EVALUATOR(w, v_const.transpose()); + + copy_using_evaluator(w.transpose(), v); // Transpose as lvalue + VERIFY_IS_APPROX(w,v.transpose().eval()); + + copy_using_evaluator(w.transpose(), v_const); + VERIFY_IS_APPROX(w,v_const.transpose().eval()); + + // Testing Array evaluator + { + ArrayXXf a(2,3); + ArrayXXf b(3,2); + a << 1,2,3, 4,5,6; + const ArrayXXf a_const(a); + + VERIFY_IS_APPROX_EVALUATOR(b, a.transpose()); + + VERIFY_IS_APPROX_EVALUATOR(b, a_const.transpose()); + + // Testing CwiseNullaryOp evaluator + copy_using_evaluator(w, RowVector2d::Random()); + VERIFY((w.array() >= -1).all() && (w.array() <= 1).all()); // not easy to test ... + + VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Zero()); + + VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Constant(3)); + + // mix CwiseNullaryOp and transpose + VERIFY_IS_APPROX_EVALUATOR(w, Vector2d::Zero().transpose()); + } + + { + // test product expressions + int s = internal::random(1,100); + MatrixXf a(s,s), b(s,s), c(s,s), d(s,s); + a.setRandom(); + b.setRandom(); + c.setRandom(); + d.setRandom(); + VERIFY_IS_APPROX_EVALUATOR(d, (a + b)); + VERIFY_IS_APPROX_EVALUATOR(d, (a + b).transpose()); + VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b), a*b); + VERIFY_IS_APPROX_EVALUATOR2(d.noalias(), prod(a,b), a*b); + VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + c, a*b + c); + VERIFY_IS_APPROX_EVALUATOR2(d, s * prod(a,b), s * a*b); + VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b).transpose(), (a*b).transpose()); + VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + prod(b,c), a*b + b*c); + + // check that prod works even with aliasing present + c = a*a; + copy_using_evaluator(a, prod(a,a)); + VERIFY_IS_APPROX(a,c); + + // check compound assignment of products + d = c; + add_assign_using_evaluator(c.noalias(), prod(a,b)); + d.noalias() += a*b; + VERIFY_IS_APPROX(c, d); + + d = c; + subtract_assign_using_evaluator(c.noalias(), prod(a,b)); + d.noalias() -= a*b; + VERIFY_IS_APPROX(c, d); + } + + { + // test product with all possible sizes + int s = internal::random(1,100); + Matrix m11, res11; m11.setRandom(1,1); + Matrix m14, res14; m14.setRandom(1,4); + Matrix m1X, res1X; m1X.setRandom(1,s); + Matrix m41, res41; m41.setRandom(4,1); + Matrix m44, res44; m44.setRandom(4,4); + Matrix m4X, res4X; m4X.setRandom(4,s); + Matrix mX1, resX1; mX1.setRandom(s,1); + Matrix mX4, resX4; mX4.setRandom(s,4); + Matrix mXX, resXX; mXX.setRandom(s,s); + + VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m11,m11), m11*m11); + VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m14,m41), m14*m41); + VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m1X,mX1), m1X*mX1); + VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m11,m14), m11*m14); + VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m14,m44), m14*m44); + VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m1X,mX4), m1X*mX4); + VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m11,m1X), m11*m1X); + VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m14,m4X), m14*m4X); + VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m1X,mXX), m1X*mXX); + VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m41,m11), m41*m11); + VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m44,m41), m44*m41); + VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m4X,mX1), m4X*mX1); + VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m41,m14), m41*m14); + VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m44,m44), m44*m44); + VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m4X,mX4), m4X*mX4); + VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m41,m1X), m41*m1X); + VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m44,m4X), m44*m4X); + VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m4X,mXX), m4X*mXX); + VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX1,m11), mX1*m11); + VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX4,m41), mX4*m41); + VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mXX,mX1), mXX*mX1); + VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX1,m14), mX1*m14); + VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX4,m44), mX4*m44); + VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mXX,mX4), mXX*mX4); + VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX1,m1X), mX1*m1X); + VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX4,m4X), mX4*m4X); + VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mXX,mXX), mXX*mXX); + } + + { + ArrayXXf a(2,3); + ArrayXXf b(3,2); + a << 1,2,3, 4,5,6; + const ArrayXXf a_const(a); + + // this does not work because Random is eval-before-nested: + // copy_using_evaluator(w, Vector2d::Random().transpose()); + + // test CwiseUnaryOp + VERIFY_IS_APPROX_EVALUATOR(v2, 3 * v); + VERIFY_IS_APPROX_EVALUATOR(w, (3 * v).transpose()); + VERIFY_IS_APPROX_EVALUATOR(b, (a + 3).transpose()); + VERIFY_IS_APPROX_EVALUATOR(b, (2 * a_const + 3).transpose()); + + // test CwiseBinaryOp + VERIFY_IS_APPROX_EVALUATOR(v2, v + Vector2d::Ones()); + VERIFY_IS_APPROX_EVALUATOR(w, (v + Vector2d::Ones()).transpose().cwiseProduct(RowVector2d::Constant(3))); + + // dynamic matrices and arrays + MatrixXd mat1(6,6), mat2(6,6); + VERIFY_IS_APPROX_EVALUATOR(mat1, MatrixXd::Identity(6,6)); + VERIFY_IS_APPROX_EVALUATOR(mat2, mat1); + copy_using_evaluator(mat2.transpose(), mat1); + VERIFY_IS_APPROX(mat2.transpose(), mat1); + + ArrayXXd arr1(6,6), arr2(6,6); + VERIFY_IS_APPROX_EVALUATOR(arr1, ArrayXXd::Constant(6,6, 3.0)); + VERIFY_IS_APPROX_EVALUATOR(arr2, arr1); + + // test automatic resizing + mat2.resize(3,3); + VERIFY_IS_APPROX_EVALUATOR(mat2, mat1); + arr2.resize(9,9); + VERIFY_IS_APPROX_EVALUATOR(arr2, arr1); + + // test direct traversal + Matrix3f m3; + Array33f a3; + VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity()); // matrix, nullary + // TODO: find a way to test direct traversal with array + VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Identity().transpose()); // transpose + VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Identity()); // unary + VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity() + Matrix3f::Zero()); // binary + VERIFY_IS_APPROX_EVALUATOR(m3.block(0,0,2,2), Matrix3f::Identity().block(1,1,2,2)); // block + + // test linear traversal + VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero()); // matrix, nullary + VERIFY_IS_APPROX_EVALUATOR(a3, Array33f::Zero()); // array + VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Zero().transpose()); // transpose + VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Zero()); // unary + VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero() + m3); // binary + + // test inner vectorization + Matrix4f m4, m4src = Matrix4f::Random(); + Array44f a4, a4src = Matrix4f::Random(); + VERIFY_IS_APPROX_EVALUATOR(m4, m4src); // matrix + VERIFY_IS_APPROX_EVALUATOR(a4, a4src); // array + VERIFY_IS_APPROX_EVALUATOR(m4.transpose(), m4src.transpose()); // transpose + // TODO: find out why Matrix4f::Zero() does not allow inner vectorization + VERIFY_IS_APPROX_EVALUATOR(m4, 2 * m4src); // unary + VERIFY_IS_APPROX_EVALUATOR(m4, m4src + m4src); // binary + + // test linear vectorization + MatrixXf mX(6,6), mXsrc = MatrixXf::Random(6,6); + ArrayXXf aX(6,6), aXsrc = ArrayXXf::Random(6,6); + VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc); // matrix + VERIFY_IS_APPROX_EVALUATOR(aX, aXsrc); // array + VERIFY_IS_APPROX_EVALUATOR(mX.transpose(), mXsrc.transpose()); // transpose + VERIFY_IS_APPROX_EVALUATOR(mX, MatrixXf::Zero(6,6)); // nullary + VERIFY_IS_APPROX_EVALUATOR(mX, 2 * mXsrc); // unary + VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc + mXsrc); // binary + + // test blocks and slice vectorization + VERIFY_IS_APPROX_EVALUATOR(m4, (mXsrc.block<4,4>(1,0))); + VERIFY_IS_APPROX_EVALUATOR(aX, ArrayXXf::Constant(10, 10, 3.0).block(2, 3, 6, 6)); + + Matrix4f m4ref = m4; + copy_using_evaluator(m4.block(1, 1, 2, 3), m3.bottomRows(2)); + m4ref.block(1, 1, 2, 3) = m3.bottomRows(2); + VERIFY_IS_APPROX(m4, m4ref); + + mX.setIdentity(20,20); + MatrixXf mXref = MatrixXf::Identity(20,20); + mXsrc = MatrixXf::Random(9,12); + copy_using_evaluator(mX.block(4, 4, 9, 12), mXsrc); + mXref.block(4, 4, 9, 12) = mXsrc; + VERIFY_IS_APPROX(mX, mXref); + + // test Map + const float raw[3] = {1,2,3}; + float buffer[3] = {0,0,0}; + Vector3f v3; + Array3f a3f; + VERIFY_IS_APPROX_EVALUATOR(v3, Map(raw)); + VERIFY_IS_APPROX_EVALUATOR(a3f, Map(raw)); + Vector3f::Map(buffer) = 2*v3; + VERIFY(buffer[0] == 2); + VERIFY(buffer[1] == 4); + VERIFY(buffer[2] == 6); + + // test CwiseUnaryView + mat1.setRandom(); + mat2.setIdentity(); + MatrixXcd matXcd(6,6), matXcd_ref(6,6); + copy_using_evaluator(matXcd.real(), mat1); + copy_using_evaluator(matXcd.imag(), mat2); + matXcd_ref.real() = mat1; + matXcd_ref.imag() = mat2; + VERIFY_IS_APPROX(matXcd, matXcd_ref); + + // test Select + VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc)); + + // test Replicate + mXsrc = MatrixXf::Random(6, 6); + VectorXf vX = VectorXf::Random(6); + mX.resize(6, 6); + VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc.colwise() + vX); + matXcd.resize(12, 12); + VERIFY_IS_APPROX_EVALUATOR(matXcd, matXcd_ref.replicate(2,2)); + VERIFY_IS_APPROX_EVALUATOR(matXcd, (matXcd_ref.replicate<2,2>())); + + // test partial reductions + VectorXd vec1(6); + VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.rowwise().sum()); + VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.colwise().sum().transpose()); + + // test MatrixWrapper and ArrayWrapper + mat1.setRandom(6,6); + arr1.setRandom(6,6); + VERIFY_IS_APPROX_EVALUATOR(mat2, arr1.matrix()); + VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array()); + VERIFY_IS_APPROX_EVALUATOR(mat2, (arr1 + 2).matrix()); + VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array() + 2); + mat2.array() = arr1 * arr1; + VERIFY_IS_APPROX(mat2, (arr1 * arr1).matrix()); + arr2.matrix() = MatrixXd::Identity(6,6); + VERIFY_IS_APPROX(arr2, MatrixXd::Identity(6,6).array()); + + // test Reverse + VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.reverse()); + VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.colwise().reverse()); + VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.rowwise().reverse()); + arr2.reverse() = arr1; + VERIFY_IS_APPROX(arr2, arr1.reverse()); + mat2.array() = mat1.array().reverse(); + VERIFY_IS_APPROX(mat2.array(), mat1.array().reverse()); + + // test Diagonal + VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal()); + vec1.resize(5); + VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal(1)); + VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal<-1>()); + vec1.setRandom(); + + mat2 = mat1; + copy_using_evaluator(mat1.diagonal(1), vec1); + mat2.diagonal(1) = vec1; + VERIFY_IS_APPROX(mat1, mat2); + + copy_using_evaluator(mat1.diagonal<-1>(), mat1.diagonal(1)); + mat2.diagonal<-1>() = mat2.diagonal(1); + VERIFY_IS_APPROX(mat1, mat2); + } + + { + // test swapping + MatrixXd mat1, mat2, mat1ref, mat2ref; + mat1ref = mat1 = MatrixXd::Random(6, 6); + mat2ref = mat2 = 2 * mat1 + MatrixXd::Identity(6, 6); + swap_using_evaluator(mat1, mat2); + mat1ref.swap(mat2ref); + VERIFY_IS_APPROX(mat1, mat1ref); + VERIFY_IS_APPROX(mat2, mat2ref); + + swap_using_evaluator(mat1.block(0, 0, 3, 3), mat2.block(3, 3, 3, 3)); + mat1ref.block(0, 0, 3, 3).swap(mat2ref.block(3, 3, 3, 3)); + VERIFY_IS_APPROX(mat1, mat1ref); + VERIFY_IS_APPROX(mat2, mat2ref); + + swap_using_evaluator(mat1.row(2), mat2.col(3).transpose()); + mat1.row(2).swap(mat2.col(3).transpose()); + VERIFY_IS_APPROX(mat1, mat1ref); + VERIFY_IS_APPROX(mat2, mat2ref); + } + + { + // test compound assignment + const Matrix4d mat_const = Matrix4d::Random(); + Matrix4d mat, mat_ref; + mat = mat_ref = Matrix4d::Identity(); + add_assign_using_evaluator(mat, mat_const); + mat_ref += mat_const; + VERIFY_IS_APPROX(mat, mat_ref); + + subtract_assign_using_evaluator(mat.row(1), 2*mat.row(2)); + mat_ref.row(1) -= 2*mat_ref.row(2); + VERIFY_IS_APPROX(mat, mat_ref); + + const ArrayXXf arr_const = ArrayXXf::Random(5,3); + ArrayXXf arr, arr_ref; + arr = arr_ref = ArrayXXf::Constant(5, 3, 0.5); + multiply_assign_using_evaluator(arr, arr_const); + arr_ref *= arr_const; + VERIFY_IS_APPROX(arr, arr_ref); + + divide_assign_using_evaluator(arr.row(1), arr.row(2) + 1); + arr_ref.row(1) /= (arr_ref.row(2) + 1); + VERIFY_IS_APPROX(arr, arr_ref); + } + + { + // test triangular shapes + MatrixXd A = MatrixXd::Random(6,6), B(6,6), C(6,6), D(6,6); + A.setRandom();B.setRandom(); + VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView(), MatrixXd(A.triangularView())); + + A.setRandom();B.setRandom(); + VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView(), MatrixXd(A.triangularView())); + + A.setRandom();B.setRandom(); + VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView(), MatrixXd(A.triangularView())); + + A.setRandom();B.setRandom(); + C = B; C.triangularView() = A; + copy_using_evaluator(B.triangularView(), A); + VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView(), A)"); + + A.setRandom();B.setRandom(); + C = B; C.triangularView() = A.triangularView(); + copy_using_evaluator(B.triangularView(), A.triangularView()); + VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView(), A.triangularView())"); + + + A.setRandom();B.setRandom(); + C = B; C.triangularView() = A.triangularView().transpose(); + copy_using_evaluator(B.triangularView(), A.triangularView().transpose()); + VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView(), A.triangularView().transpose())"); + + + A.setRandom();B.setRandom(); C = B; D = A; + C.triangularView().swap(D.triangularView()); + swap_using_evaluator(B.triangularView(), A.triangularView()); + VERIFY(B.isApprox(C) && "swap_using_evaluator(B.triangularView(), A.triangularView())"); + + + VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.triangularView(),A), MatrixXd(A.triangularView()*A)); + + VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.selfadjointView(),A), MatrixXd(A.selfadjointView()*A)); + } + + { + // test diagonal shapes + VectorXd d = VectorXd::Random(6); + MatrixXd A = MatrixXd::Random(6,6), B(6,6); + A.setRandom();B.setRandom(); + + VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(d.asDiagonal(),A), MatrixXd(d.asDiagonal()*A)); + VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(A,d.asDiagonal()), MatrixXd(A*d.asDiagonal())); + } + + { + // test CoeffReadCost + Matrix4d a, b; + VERIFY_IS_EQUAL( get_cost(a), 1 ); + VERIFY_IS_EQUAL( get_cost(a+b), 3); + VERIFY_IS_EQUAL( get_cost(2*a+b), 4); + VERIFY_IS_EQUAL( get_cost(a*b), 1); + VERIFY_IS_EQUAL( get_cost(a.lazyProduct(b)), 15); + VERIFY_IS_EQUAL( get_cost(a*(a*b)), 1); + VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a*b)), 15); + VERIFY_IS_EQUAL( get_cost(a*(a+b)), 1); + VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a+b)), 15); + } + + // regression test for PR 544 and bug 1622 (introduced in #71609c4) + { + // test restricted_packet_assignment with an unaligned destination + const size_t M = 2; + const size_t K = 2; + const size_t N = 5; + float *destMem = new float[(M*N) + 1]; + float *dest = (internal::UIntPtr(destMem)%EIGEN_MAX_ALIGN_BYTES) == 0 ? destMem+1 : destMem; + + const Matrix a = Matrix::Random(M, K); + const Matrix b = Matrix::Random(K, N); + + Map > z(dest, M, N);; + Product, Matrix, LazyProduct> tmp(a,b); + internal::call_restricted_packet_assignment(z.noalias(), tmp.derived(), internal::assign_op()); + + VERIFY_IS_APPROX(z, a*b); + delete[] destMem; + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/exceptions.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/exceptions.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3d93060aba2c31e028624b087cede4ffa6054c24 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/exceptions.cpp @@ -0,0 +1,49 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +// Various sanity tests with exceptions and non trivially copyable scalar type. +// - no memory leak when a custom scalar type trow an exceptions +// - todo: complete the list of tests! + +#define EIGEN_STACK_ALLOCATION_LIMIT 100000000 + +#include "main.h" +#include "AnnoyingScalar.h" + +#define CHECK_MEMLEAK(OP) { \ + AnnoyingScalar::countdown = 100; \ + int before = AnnoyingScalar::instances; \ + bool exception_thrown = false; \ + try { OP; } \ + catch (my_exception) { \ + exception_thrown = true; \ + VERIFY(AnnoyingScalar::instances==before && "memory leak detected in " && EIGEN_MAKESTRING(OP)); \ + } \ + VERIFY( (AnnoyingScalar::dont_throw) || (exception_thrown && " no exception thrown in " && EIGEN_MAKESTRING(OP)) ); \ + } + +EIGEN_DECLARE_TEST(exceptions) +{ + typedef Eigen::Matrix VectorType; + typedef Eigen::Matrix MatrixType; + + { + AnnoyingScalar::dont_throw = false; + int n = 50; + VectorType v0(n), v1(n); + MatrixType m0(n,n), m1(n,n), m2(n,n); + v0.setOnes(); v1.setOnes(); + m0.setOnes(); m1.setOnes(); m2.setOnes(); + CHECK_MEMLEAK(v0 = m0 * m1 * v1); + CHECK_MEMLEAK(m2 = m0 * m1 * m2); + CHECK_MEMLEAK((v0+v1).dot(v0+v1)); + } + VERIFY(AnnoyingScalar::instances==0 && "global memory leak detected in " && EIGEN_MAKESTRING(OP)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/fastmath.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/fastmath.cpp new file mode 100644 index 0000000000000000000000000000000000000000..00a1a59b8b51b72b88611585706da5b1cb6b1221 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/fastmath.cpp @@ -0,0 +1,99 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +void check(bool b, bool ref) +{ + std::cout << b; + if(b==ref) + std::cout << " OK "; + else + std::cout << " BAD "; +} + +#if EIGEN_COMP_MSVC && EIGEN_COMP_MSVC < 1800 +namespace std { + template bool (isfinite)(T x) { return _finite(x); } + template bool (isnan)(T x) { return _isnan(x); } + template bool (isinf)(T x) { return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF; } +} +#endif + +template +void check_inf_nan(bool dryrun) { + Matrix m(10); + m.setRandom(); + m(3) = std::numeric_limits::quiet_NaN(); + + if(dryrun) + { + std::cout << "std::isfinite(" << m(3) << ") = "; check((std::isfinite)(m(3)),false); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(3)), false); std::cout << "\n"; + std::cout << "std::isinf(" << m(3) << ") = "; check((std::isinf)(m(3)),false); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(3)), false); std::cout << "\n"; + std::cout << "std::isnan(" << m(3) << ") = "; check((std::isnan)(m(3)),true); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(3)), true); std::cout << "\n"; + std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n"; + std::cout << "hasNaN: "; check(m.hasNaN(), 1); std::cout << "\n"; + std::cout << "\n"; + } + else + { + if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !(numext::isfinite)(m(3)) ); g_test_level=0; + if( (std::isinf) (m(3))) g_test_level=1; VERIFY( !(numext::isinf)(m(3)) ); g_test_level=0; + if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( (numext::isnan)(m(3)) ); g_test_level=0; + if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0; + if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( m.hasNaN() ); g_test_level=0; + } + T hidden_zero = (std::numeric_limits::min)()*(std::numeric_limits::min)(); + m(4) /= hidden_zero; + if(dryrun) + { + std::cout << "std::isfinite(" << m(4) << ") = "; check((std::isfinite)(m(4)),false); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(4)), false); std::cout << "\n"; + std::cout << "std::isinf(" << m(4) << ") = "; check((std::isinf)(m(4)),true); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(4)), true); std::cout << "\n"; + std::cout << "std::isnan(" << m(4) << ") = "; check((std::isnan)(m(4)),false); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(4)), false); std::cout << "\n"; + std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n"; + std::cout << "hasNaN: "; check(m.hasNaN(), 1); std::cout << "\n"; + std::cout << "\n"; + } + else + { + if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !(numext::isfinite)(m(4)) ); g_test_level=0; + if(!(std::isinf) (m(3))) g_test_level=1; VERIFY( (numext::isinf)(m(4)) ); g_test_level=0; + if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !(numext::isnan)(m(4)) ); g_test_level=0; + if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0; + if(!(std::isnan) (m(3))) g_test_level=1; VERIFY( m.hasNaN() ); g_test_level=0; + } + m(3) = 0; + if(dryrun) + { + std::cout << "std::isfinite(" << m(3) << ") = "; check((std::isfinite)(m(3)),true); std::cout << " ; numext::isfinite = "; check((numext::isfinite)(m(3)), true); std::cout << "\n"; + std::cout << "std::isinf(" << m(3) << ") = "; check((std::isinf)(m(3)),false); std::cout << " ; numext::isinf = "; check((numext::isinf)(m(3)), false); std::cout << "\n"; + std::cout << "std::isnan(" << m(3) << ") = "; check((std::isnan)(m(3)),false); std::cout << " ; numext::isnan = "; check((numext::isnan)(m(3)), false); std::cout << "\n"; + std::cout << "allFinite: "; check(m.allFinite(), 0); std::cout << "\n"; + std::cout << "hasNaN: "; check(m.hasNaN(), 0); std::cout << "\n"; + std::cout << "\n\n"; + } + else + { + if(!(std::isfinite)(m(3))) g_test_level=1; VERIFY( (numext::isfinite)(m(3)) ); g_test_level=0; + if( (std::isinf) (m(3))) g_test_level=1; VERIFY( !(numext::isinf)(m(3)) ); g_test_level=0; + if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !(numext::isnan)(m(3)) ); g_test_level=0; + if( (std::isfinite)(m(3))) g_test_level=1; VERIFY( !m.allFinite() ); g_test_level=0; + if( (std::isnan) (m(3))) g_test_level=1; VERIFY( !m.hasNaN() ); g_test_level=0; + } +} + +EIGEN_DECLARE_TEST(fastmath) { + std::cout << "*** float *** \n\n"; check_inf_nan(true); + std::cout << "*** double ***\n\n"; check_inf_nan(true); + std::cout << "*** long double *** \n\n"; check_inf_nan(true); + + check_inf_nan(false); + check_inf_nan(false); + check_inf_nan(false); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/first_aligned.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/first_aligned.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ed9945077b97129414b63e27eef65d403f23310a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/first_aligned.cpp @@ -0,0 +1,51 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template +void test_first_aligned_helper(Scalar *array, int size) +{ + const int packet_size = sizeof(Scalar) * internal::packet_traits::size; + VERIFY(((size_t(array) + sizeof(Scalar) * internal::first_default_aligned(array, size)) % packet_size) == 0); +} + +template +void test_none_aligned_helper(Scalar *array, int size) +{ + EIGEN_UNUSED_VARIABLE(array); + EIGEN_UNUSED_VARIABLE(size); + VERIFY(internal::packet_traits::size == 1 || internal::first_default_aligned(array, size) == size); +} + +struct some_non_vectorizable_type { float x; }; + +EIGEN_DECLARE_TEST(first_aligned) +{ + EIGEN_ALIGN16 float array_float[100]; + test_first_aligned_helper(array_float, 50); + test_first_aligned_helper(array_float+1, 50); + test_first_aligned_helper(array_float+2, 50); + test_first_aligned_helper(array_float+3, 50); + test_first_aligned_helper(array_float+4, 50); + test_first_aligned_helper(array_float+5, 50); + + EIGEN_ALIGN16 double array_double[100]; + test_first_aligned_helper(array_double, 50); + test_first_aligned_helper(array_double+1, 50); + test_first_aligned_helper(array_double+2, 50); + + double *array_double_plus_4_bytes = (double*)(internal::UIntPtr(array_double)+4); + test_none_aligned_helper(array_double_plus_4_bytes, 50); + test_none_aligned_helper(array_double_plus_4_bytes+1, 50); + + some_non_vectorizable_type array_nonvec[100]; + test_first_aligned_helper(array_nonvec, 100); + test_none_aligned_helper(array_nonvec, 100); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_alignedbox.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_alignedbox.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7b1684f292cdefc934c015b52f4c6c71ed03f6e9 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_alignedbox.cpp @@ -0,0 +1,531 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +using namespace std; + +// NOTE the following workaround was needed on some 32 bits builds to kill extra precision of x87 registers. +// It seems that it is not needed anymore, but let's keep it here, just in case... + +template EIGEN_DONT_INLINE +void kill_extra_precision(T& /* x */) { + // This one worked but triggered a warning: + /* eigen_assert((void*)(&x) != (void*)0); */ + // An alternative could be: + /* volatile T tmp = x; */ + /* x = tmp; */ +} + + +template void alignedbox(const BoxType& box) +{ + /* this test covers the following files: + AlignedBox.h + */ + typedef typename BoxType::Scalar Scalar; + typedef NumTraits ScalarTraits; + typedef typename ScalarTraits::Real RealScalar; + typedef Matrix VectorType; + + const Index dim = box.dim(); + + VectorType p0 = VectorType::Random(dim); + VectorType p1 = VectorType::Random(dim); + while( p1 == p0 ){ + p1 = VectorType::Random(dim); } + RealScalar s1 = internal::random(0,1); + + BoxType b0(dim); + BoxType b1(VectorType::Random(dim),VectorType::Random(dim)); + BoxType b2; + + kill_extra_precision(b1); + kill_extra_precision(p0); + kill_extra_precision(p1); + + b0.extend(p0); + b0.extend(p1); + VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1)); + VERIFY(b0.contains(b0.center())); + VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2)); + + (b2 = b0).extend(b1); + VERIFY(b2.contains(b0)); + VERIFY(b2.contains(b1)); + VERIFY_IS_APPROX(b2.clamp(b0), b0); + + // intersection + BoxType box1(VectorType::Random(dim)); + box1.extend(VectorType::Random(dim)); + BoxType box2(VectorType::Random(dim)); + box2.extend(VectorType::Random(dim)); + + VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty()); + + // alignment -- make sure there is no memory alignment assertion + BoxType *bp0 = new BoxType(dim); + BoxType *bp1 = new BoxType(dim); + bp0->extend(*bp1); + delete bp0; + delete bp1; + + // sampling + for( int i=0; i<10; ++i ) + { + VectorType r = b0.sample(); + VERIFY(b0.contains(r)); + } + +} + +template void alignedboxTranslatable(const BoxType& box) +{ + typedef typename BoxType::Scalar Scalar; + typedef Matrix VectorType; + typedef Transform IsometryTransform; + typedef Transform AffineTransform; + + alignedbox(box); + + const VectorType Ones = VectorType::Ones(); + const VectorType UnitX = VectorType::UnitX(); + const Index dim = box.dim(); + + // box((-1, -1, -1), (1, 1, 1)) + BoxType a(-Ones, Ones); + + VERIFY_IS_APPROX(a.sizes(), Ones * Scalar(2)); + + BoxType b = a; + VectorType translate = Ones; + translate[0] = Scalar(2); + b.translate(translate); + // translate by (2, 1, 1) -> box((1, 0, 0), (3, 2, 2)) + + VERIFY_IS_APPROX(b.sizes(), Ones * Scalar(2)); + VERIFY_IS_APPROX((b.min)(), UnitX); + VERIFY_IS_APPROX((b.max)(), Ones * Scalar(2) + UnitX); + + // Test transform + + IsometryTransform tf = IsometryTransform::Identity(); + tf.translation() = -translate; + + BoxType c = b.transformed(tf); + // translate by (-2, -1, -1) -> box((-1, -1, -1), (1, 1, 1)) + VERIFY_IS_APPROX(c.sizes(), a.sizes()); + VERIFY_IS_APPROX((c.min)(), (a.min)()); + VERIFY_IS_APPROX((c.max)(), (a.max)()); + + c.transform(tf); + // translate by (-2, -1, -1) -> box((-3, -2, -2), (-1, 0, 0)) + VERIFY_IS_APPROX(c.sizes(), a.sizes()); + VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) - UnitX); + VERIFY_IS_APPROX((c.max)(), -UnitX); + + // Scaling + + AffineTransform atf = AffineTransform::Identity(); + atf.scale(Scalar(3)); + c.transform(atf); + // scale by 3 -> box((-9, -6, -6), (-3, 0, 0)) + VERIFY_IS_APPROX(c.sizes(), Scalar(3) * a.sizes()); + VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-6) - UnitX * Scalar(3)); + VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(-3)); + + atf = AffineTransform::Identity(); + atf.scale(Scalar(-3)); + c.transform(atf); + // scale by -3 -> box((27, 18, 18), (9, 0, 0)) + VERIFY_IS_APPROX(c.sizes(), Scalar(9) * a.sizes()); + VERIFY_IS_APPROX((c.min)(), UnitX * Scalar(9)); + VERIFY_IS_APPROX((c.max)(), Ones * Scalar(18) + UnitX * Scalar(9)); + + // Check identity transform within numerical precision. + BoxType transformedC = c.transformed(IsometryTransform::Identity()); + VERIFY_IS_APPROX(transformedC, c); + + for (size_t i = 0; i < 10; ++i) + { + VectorType minCorner; + VectorType maxCorner; + for (Index d = 0; d < dim; ++d) + { + minCorner[d] = internal::random(-10,10); + maxCorner[d] = minCorner[d] + internal::random(0, 10); + } + + c = BoxType(minCorner, maxCorner); + + translate = VectorType::Random(); + c.translate(translate); + + VERIFY_IS_APPROX((c.min)(), minCorner + translate); + VERIFY_IS_APPROX((c.max)(), maxCorner + translate); + } +} + +template +Rotation rotate2D(Scalar angle) { + return Rotation2D(angle); +} + +template +Rotation rotate2DIntegral(typename NumTraits::NonInteger angle) { + typedef typename NumTraits::NonInteger NonInteger; + return Rotation2D(angle).toRotationMatrix(). + template cast(); +} + +template +Rotation rotate3DZAxis(Scalar angle) { + return AngleAxis(angle, Matrix(0, 0, 1)); +} + +template +Rotation rotate3DZAxisIntegral(typename NumTraits::NonInteger angle) { + typedef typename NumTraits::NonInteger NonInteger; + return AngleAxis(angle, Matrix(0, 0, 1)). + toRotationMatrix().template cast(); +} + +template +Rotation rotate4DZWAxis(Scalar angle) { + Rotation result = Matrix::Identity(); + result.block(0, 0, 3, 3) = rotate3DZAxis(angle).toRotationMatrix(); + return result; +} + +template +MatrixType randomRotationMatrix() +{ + // algorithm from + // https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-7/103/2016/isprs-annals-III-7-103-2016.pdf + const MatrixType rand = MatrixType::Random(); + const MatrixType q = rand.householderQr().householderQ(); + const JacobiSVD svd = q.jacobiSvd(ComputeFullU | ComputeFullV); + const typename MatrixType::Scalar det = (svd.matrixU() * svd.matrixV().transpose()).determinant(); + MatrixType diag = rand.Identity(); + diag(MatrixType::RowsAtCompileTime - 1, MatrixType::ColsAtCompileTime - 1) = det; + const MatrixType rotation = svd.matrixU() * diag * svd.matrixV().transpose(); + return rotation; +} + +template +Matrix boxGetCorners(const Matrix& min_, const Matrix& max_) +{ + Matrix result; + for(Index i=0; i<(1< void alignedboxRotatable( + const BoxType& box, + Rotation (*rotate)(typename NumTraits::NonInteger /*_angle*/)) +{ + alignedboxTranslatable(box); + + typedef typename BoxType::Scalar Scalar; + typedef typename NumTraits::NonInteger NonInteger; + typedef Matrix VectorType; + typedef Transform IsometryTransform; + typedef Transform AffineTransform; + + const VectorType Zero = VectorType::Zero(); + const VectorType Ones = VectorType::Ones(); + const VectorType UnitX = VectorType::UnitX(); + const VectorType UnitY = VectorType::UnitY(); + // this is vector (0, 0, -1, -1, -1, ...), i.e. with zeros at first and second dimensions + const VectorType UnitZ = Ones - UnitX - UnitY; + + // in this kind of comments the 3D case values will be illustrated + // box((-1, -1, -1), (1, 1, 1)) + BoxType a(-Ones, Ones); + + // to allow templating this test for both 2D and 3D cases, we always set all + // but the first coordinate to the same value; so basically 3D case works as + // if you were looking at the scene from top + + VectorType minPoint = -2 * Ones; + minPoint[0] = -3; + VectorType maxPoint = Zero; + maxPoint[0] = -1; + BoxType c(minPoint, maxPoint); + // box((-3, -2, -2), (-1, 0, 0)) + + IsometryTransform tf2 = IsometryTransform::Identity(); + // for some weird reason the following statement has to be put separate from + // the following rotate call, otherwise precision problems arise... + Rotation rot = rotate(NonInteger(EIGEN_PI)); + tf2.rotate(rot); + + c.transform(tf2); + // rotate by 180 deg around origin -> box((1, 0, -2), (3, 2, 0)) + + VERIFY_IS_APPROX(c.sizes(), a.sizes()); + VERIFY_IS_APPROX((c.min)(), UnitX - UnitZ * Scalar(2)); + VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(3) + UnitY * Scalar(2)); + + rot = rotate(NonInteger(EIGEN_PI / 2)); + tf2.setIdentity(); + tf2.rotate(rot); + + c.transform(tf2); + // rotate by 90 deg around origin -> box((-2, 1, -2), (0, 3, 0)) + + VERIFY_IS_APPROX(c.sizes(), a.sizes()); + VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) + UnitY * Scalar(3)); + VERIFY_IS_APPROX((c.max)(), UnitY * Scalar(3)); + + // box((-1, -1, -1), (1, 1, 1)) + AffineTransform atf = AffineTransform::Identity(); + atf.linearExt()(0, 1) = Scalar(1); + c = BoxType(-Ones, Ones); + c.transform(atf); + // 45 deg shear in x direction -> box((-2, -1, -1), (2, 1, 1)) + + VERIFY_IS_APPROX(c.sizes(), Ones * Scalar(2) + UnitX * Scalar(2)); + VERIFY_IS_APPROX((c.min)(), -Ones - UnitX); + VERIFY_IS_APPROX((c.max)(), Ones + UnitX); +} + +template void alignedboxNonIntegralRotatable( + const BoxType& box, + Rotation (*rotate)(typename NumTraits::NonInteger /*_angle*/)) +{ + alignedboxRotatable(box, rotate); + + typedef typename BoxType::Scalar Scalar; + typedef typename NumTraits::NonInteger NonInteger; + enum { Dim = BoxType::AmbientDimAtCompileTime }; + typedef Matrix VectorType; + typedef Matrix CornersType; + typedef Transform IsometryTransform; + typedef Transform AffineTransform; + + const Index dim = box.dim(); + const VectorType Zero = VectorType::Zero(); + const VectorType Ones = VectorType::Ones(); + + VectorType minPoint = -2 * Ones; + minPoint[1] = 1; + VectorType maxPoint = Zero; + maxPoint[1] = 3; + BoxType c(minPoint, maxPoint); + // ((-2, 1, -2), (0, 3, 0)) + + VectorType cornerBL = (c.min)(); + VectorType cornerTR = (c.max)(); + VectorType cornerBR = (c.min)(); cornerBR[0] = cornerTR[0]; + VectorType cornerTL = (c.max)(); cornerTL[0] = cornerBL[0]; + + NonInteger angle = NonInteger(EIGEN_PI/3); + Rotation rot = rotate(angle); + IsometryTransform tf2; + tf2.setIdentity(); + tf2.rotate(rot); + + c.transform(tf2); + // rotate by 60 deg -> box((-3.59, -1.23, -2), (-0.86, 1.5, 0)) + + cornerBL = tf2 * cornerBL; + cornerBR = tf2 * cornerBR; + cornerTL = tf2 * cornerTL; + cornerTR = tf2 * cornerTR; + + VectorType minCorner = Ones * Scalar(-2); + VectorType maxCorner = Zero; + minCorner[0] = (min)((min)(cornerBL[0], cornerBR[0]), (min)(cornerTL[0], cornerTR[0])); + maxCorner[0] = (max)((max)(cornerBL[0], cornerBR[0]), (max)(cornerTL[0], cornerTR[0])); + minCorner[1] = (min)((min)(cornerBL[1], cornerBR[1]), (min)(cornerTL[1], cornerTR[1])); + maxCorner[1] = (max)((max)(cornerBL[1], cornerBR[1]), (max)(cornerTL[1], cornerTR[1])); + + for (Index d = 2; d < dim; ++d) + VERIFY_IS_APPROX(c.sizes()[d], Scalar(2)); + + VERIFY_IS_APPROX((c.min)(), minCorner); + VERIFY_IS_APPROX((c.max)(), maxCorner); + + VectorType minCornerValue = Ones * Scalar(-2); + VectorType maxCornerValue = Zero; + minCornerValue[0] = Scalar(Scalar(-sqrt(2*2 + 3*3)) * Scalar(cos(Scalar(atan(2.0/3.0)) - angle/2))); + minCornerValue[1] = Scalar(Scalar(-sqrt(1*1 + 2*2)) * Scalar(sin(Scalar(atan(2.0/1.0)) - angle/2))); + maxCornerValue[0] = Scalar(-sin(angle)); + maxCornerValue[1] = Scalar(3 * cos(angle)); + VERIFY_IS_APPROX((c.min)(), minCornerValue); + VERIFY_IS_APPROX((c.max)(), maxCornerValue); + + // randomized test - translate and rotate the box and compare to a box made of transformed vertices + for (size_t i = 0; i < 10; ++i) + { + for (Index d = 0; d < dim; ++d) + { + minCorner[d] = internal::random(-10,10); + maxCorner[d] = minCorner[d] + internal::random(0, 10); + } + + c = BoxType(minCorner, maxCorner); + + CornersType corners = boxGetCorners(minCorner, maxCorner); + + typename AffineTransform::LinearMatrixType rotation = + randomRotationMatrix(); + + tf2.setIdentity(); + tf2.rotate(rotation); + tf2.translate(VectorType::Random()); + + c.transform(tf2); + corners = tf2 * corners; + + minCorner = corners.rowwise().minCoeff(); + maxCorner = corners.rowwise().maxCoeff(); + + VERIFY_IS_APPROX((c.min)(), minCorner); + VERIFY_IS_APPROX((c.max)(), maxCorner); + } + + // randomized test - transform the box with a random affine matrix and compare to a box made of transformed vertices + for (size_t i = 0; i < 10; ++i) + { + for (Index d = 0; d < dim; ++d) + { + minCorner[d] = internal::random(-10,10); + maxCorner[d] = minCorner[d] + internal::random(0, 10); + } + + c = BoxType(minCorner, maxCorner); + + CornersType corners = boxGetCorners(minCorner, maxCorner); + + AffineTransform atf = AffineTransform::Identity(); + atf.linearExt() = AffineTransform::LinearPart::Random(); + atf.translate(VectorType::Random()); + + c.transform(atf); + corners = atf * corners; + + minCorner = corners.rowwise().minCoeff(); + maxCorner = corners.rowwise().maxCoeff(); + + VERIFY_IS_APPROX((c.min)(), minCorner); + VERIFY_IS_APPROX((c.max)(), maxCorner); + } +} + +template +void alignedboxCastTests(const BoxType& box) +{ + // casting + typedef typename BoxType::Scalar Scalar; + typedef Matrix VectorType; + + const Index dim = box.dim(); + + VectorType p0 = VectorType::Random(dim); + VectorType p1 = VectorType::Random(dim); + + BoxType b0(dim); + + b0.extend(p0); + b0.extend(p1); + + const int Dim = BoxType::AmbientDimAtCompileTime; + typedef typename GetDifferentType::type OtherScalar; + AlignedBox hp1f = b0.template cast(); + VERIFY_IS_APPROX(hp1f.template cast(),b0); + AlignedBox hp1d = b0.template cast(); + VERIFY_IS_APPROX(hp1d.template cast(),b0); +} + + +void specificTest1() +{ + Vector2f m; m << -1.0f, -2.0f; + Vector2f M; M << 1.0f, 5.0f; + + typedef AlignedBox2f BoxType; + BoxType box( m, M ); + + Vector2f sides = M-m; + VERIFY_IS_APPROX(sides, box.sizes() ); + VERIFY_IS_APPROX(sides[1], box.sizes()[1] ); + VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() ); + VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() ); + + VERIFY_IS_APPROX( 14.0f, box.volume() ); + VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() ); + VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() ); + + VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) ); + VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) ); + Vector2f bottomRight; bottomRight << M[0], m[1]; + Vector2f topLeft; topLeft << m[0], M[1]; + VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) ); + VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) ); +} + + +void specificTest2() +{ + Vector3i m; m << -1, -2, 0; + Vector3i M; M << 1, 5, 3; + + typedef AlignedBox3i BoxType; + BoxType box( m, M ); + + Vector3i sides = M-m; + VERIFY_IS_APPROX(sides, box.sizes() ); + VERIFY_IS_APPROX(sides[1], box.sizes()[1] ); + VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() ); + VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() ); + + VERIFY_IS_APPROX( 42, box.volume() ); + VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() ); + + VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) ); + VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) ); + Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2]; + Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2]; + VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) ); + VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) ); +} + + +EIGEN_DECLARE_TEST(geo_alignedbox) +{ + for(int i = 0; i < g_repeat; i++) + { + CALL_SUBTEST_1( (alignedboxNonIntegralRotatable(AlignedBox2f(), &rotate2D)) ); + CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) ); + + CALL_SUBTEST_3( (alignedboxNonIntegralRotatable(AlignedBox3f(), &rotate3DZAxis)) ); + CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) ); + + CALL_SUBTEST_5( (alignedboxNonIntegralRotatable(AlignedBox4d(), &rotate4DZWAxis)) ); + CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) ); + + CALL_SUBTEST_7( alignedboxTranslatable(AlignedBox1d()) ); + CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) ); + + CALL_SUBTEST_9( alignedboxTranslatable(AlignedBox1i()) ); + CALL_SUBTEST_10( (alignedboxRotatable(AlignedBox2i(), &rotate2DIntegral)) ); + CALL_SUBTEST_11( (alignedboxRotatable(AlignedBox3i(), &rotate3DZAxisIntegral)) ); + + CALL_SUBTEST_14( alignedbox(AlignedBox(4)) ); + } + CALL_SUBTEST_12( specificTest1() ); + CALL_SUBTEST_13( specificTest2() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_eulerangles.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_eulerangles.cpp new file mode 100644 index 0000000000000000000000000000000000000000..693c627a9a451cdebf9c447d4729ed10ec64689a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_eulerangles.cpp @@ -0,0 +1,112 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + + +template +void verify_euler(const Matrix& ea, int i, int j, int k) +{ + typedef Matrix Matrix3; + typedef Matrix Vector3; + typedef AngleAxis AngleAxisx; + using std::abs; + Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k))); + Vector3 eabis = m.eulerAngles(i, j, k); + Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k))); + VERIFY_IS_APPROX(m, mbis); + /* If I==K, and ea[1]==0, then there no unique solution. */ + /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ + if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision())) ) + VERIFY((ea-eabis).norm() <= test_precision()); + + // approx_or_less_than does not work for 0 + VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); + VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI)); + VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]); + VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI)); + VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]); + VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI)); +} + +template void check_all_var(const Matrix& ea) +{ + verify_euler(ea, 0,1,2); + verify_euler(ea, 0,1,0); + verify_euler(ea, 0,2,1); + verify_euler(ea, 0,2,0); + + verify_euler(ea, 1,2,0); + verify_euler(ea, 1,2,1); + verify_euler(ea, 1,0,2); + verify_euler(ea, 1,0,1); + + verify_euler(ea, 2,0,1); + verify_euler(ea, 2,0,2); + verify_euler(ea, 2,1,0); + verify_euler(ea, 2,1,2); +} + +template void eulerangles() +{ + typedef Matrix Matrix3; + typedef Matrix Vector3; + typedef Array Array3; + typedef Quaternion Quaternionx; + typedef AngleAxis AngleAxisx; + + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + Quaternionx q1; + q1 = AngleAxisx(a, Vector3::Random().normalized()); + Matrix3 m; + m = q1; + + Vector3 ea = m.eulerAngles(0,1,2); + check_all_var(ea); + ea = m.eulerAngles(0,1,0); + check_all_var(ea); + + // Check with purely random Quaternion: + q1.coeffs() = Quaternionx::Coefficients::Random().normalized(); + m = q1; + ea = m.eulerAngles(0,1,2); + check_all_var(ea); + ea = m.eulerAngles(0,1,0); + check_all_var(ea); + + // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi]. + ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1); + check_all_var(ea); + + ea[2] = ea[0] = internal::random(0,Scalar(EIGEN_PI)); + check_all_var(ea); + + ea[0] = ea[1] = internal::random(0,Scalar(EIGEN_PI)); + check_all_var(ea); + + ea[1] = 0; + check_all_var(ea); + + ea.head(2).setZero(); + check_all_var(ea); + + ea.setZero(); + check_all_var(ea); +} + +EIGEN_DECLARE_TEST(geo_eulerangles) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( eulerangles() ); + CALL_SUBTEST_2( eulerangles() ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_homogeneous.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_homogeneous.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9aebe6226ff23907cb202c590cdc2b247ac09506 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_homogeneous.cpp @@ -0,0 +1,125 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template void homogeneous(void) +{ + /* this test covers the following files: + Homogeneous.h + */ + + typedef Matrix MatrixType; + typedef Matrix VectorType; + + typedef Matrix HMatrixType; + typedef Matrix HVectorType; + + typedef Matrix T1MatrixType; + typedef Matrix T2MatrixType; + typedef Matrix T3MatrixType; + + VectorType v0 = VectorType::Random(), + ones = VectorType::Ones(); + + HVectorType hv0 = HVectorType::Random(); + + MatrixType m0 = MatrixType::Random(); + + HMatrixType hm0 = HMatrixType::Random(); + + hv0 << v0, 1; + VERIFY_IS_APPROX(v0.homogeneous(), hv0); + VERIFY_IS_APPROX(v0, hv0.hnormalized()); + + VERIFY_IS_APPROX(v0.homogeneous().sum(), hv0.sum()); + VERIFY_IS_APPROX(v0.homogeneous().minCoeff(), hv0.minCoeff()); + VERIFY_IS_APPROX(v0.homogeneous().maxCoeff(), hv0.maxCoeff()); + + hm0 << m0, ones.transpose(); + VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0); + VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized()); + hm0.row(Size-1).setRandom(); + for(int j=0; j aff; + Transform caff; + Transform proj; + Matrix pts; + Matrix pts1, pts2; + + aff.affine().setRandom(); + proj = caff = aff; + pts.setRandom(Size,internal::random(1,20)); + + pts1 = pts.colwise().homogeneous(); + VERIFY_IS_APPROX(aff * pts.colwise().homogeneous(), (aff * pts1).colwise().hnormalized()); + VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized()); + VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1)); + + VERIFY_IS_APPROX((aff * pts1).colwise().hnormalized(), aff * pts); + VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts); + + pts2 = pts1; + pts2.row(Size).setRandom(); + VERIFY_IS_APPROX((aff * pts2).colwise().hnormalized(), aff * pts2.colwise().hnormalized()); + VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized()); + VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized()); + + // Test combination of homogeneous + + VERIFY_IS_APPROX( (t2 * v0.homogeneous()).hnormalized(), + (t2.template topLeftCorner() * v0 + t2.template topRightCorner()) + / ((t2.template bottomLeftCorner<1,Size>()*v0).value() + t2(Size,Size)) ); + + VERIFY_IS_APPROX( (t2 * pts.colwise().homogeneous()).colwise().hnormalized(), + (Matrix(t2 * pts1).colwise().hnormalized()) ); + + VERIFY_IS_APPROX( (t2 .lazyProduct( v0.homogeneous() )).hnormalized(), (t2 * v0.homogeneous()).hnormalized() ); + VERIFY_IS_APPROX( (t2 .lazyProduct ( pts.colwise().homogeneous() )).colwise().hnormalized(), (t2 * pts1).colwise().hnormalized() ); + + VERIFY_IS_APPROX( (v0.transpose().homogeneous() .lazyProduct( t2 )).hnormalized(), (v0.transpose().homogeneous()*t2).hnormalized() ); + VERIFY_IS_APPROX( (pts.transpose().rowwise().homogeneous() .lazyProduct( t2 )).rowwise().hnormalized(), (pts1.transpose()*t2).rowwise().hnormalized() ); + + VERIFY_IS_APPROX( (t2.template triangularView() * v0.homogeneous()).eval(), (t2.template triangularView()*hv0) ); +} + +EIGEN_DECLARE_TEST(geo_homogeneous) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( homogeneous() )); + CALL_SUBTEST_2(( homogeneous() )); + CALL_SUBTEST_3(( homogeneous() )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_hyperplane.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_hyperplane.cpp new file mode 100644 index 0000000000000000000000000000000000000000..44b2f2aecb3e8e9b239f93cc586778f0b11b779d --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_hyperplane.cpp @@ -0,0 +1,192 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +template void hyperplane(const HyperplaneType& _plane) +{ + /* this test covers the following files: + Hyperplane.h + */ + using std::abs; + const Index dim = _plane.dim(); + enum { Options = HyperplaneType::Options }; + typedef typename HyperplaneType::Scalar Scalar; + typedef typename HyperplaneType::RealScalar RealScalar; + typedef Matrix VectorType; + typedef Matrix MatrixType; + + VectorType p0 = VectorType::Random(dim); + VectorType p1 = VectorType::Random(dim); + + VectorType n0 = VectorType::Random(dim).normalized(); + VectorType n1 = VectorType::Random(dim).normalized(); + + HyperplaneType pl0(n0, p0); + HyperplaneType pl1(n1, p1); + HyperplaneType pl2 = pl1; + + Scalar s0 = internal::random(); + Scalar s1 = internal::random(); + + VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) ); + + VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) ); + if(numext::abs2(s0)>RealScalar(1e-6)) + VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0); + else + VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) ); + VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); + VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); + + // transform + if (!NumTraits::IsComplex) + { + MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); + DiagonalMatrix scaling(VectorType::Random()); + Translation translation(VectorType::Random()); + + while(scaling.diagonal().cwiseAbs().minCoeff()::type OtherScalar; + Hyperplane hp1f = pl1.template cast(); + VERIFY_IS_APPROX(hp1f.template cast(),pl1); + Hyperplane hp1d = pl1.template cast(); + VERIFY_IS_APPROX(hp1d.template cast(),pl1); +} + +template void lines() +{ + using std::abs; + typedef Hyperplane HLine; + typedef ParametrizedLine PLine; + typedef Matrix Vector; + typedef Matrix CoeffsType; + + for(int i = 0; i < 10; i++) + { + Vector center = Vector::Random(); + Vector u = Vector::Random(); + Vector v = Vector::Random(); + Scalar a = internal::random(); + while (abs(a-1) < Scalar(1e-4)) a = internal::random(); + while (u.norm() < Scalar(1e-4)) u = Vector::Random(); + while (v.norm() < Scalar(1e-4)) v = Vector::Random(); + + HLine line_u = HLine::Through(center + u, center + a*u); + HLine line_v = HLine::Through(center + v, center + a*v); + + // the line equations should be normalized so that a^2+b^2=1 + VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); + VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); + + Vector result = line_u.intersection(line_v); + + // the lines should intersect at the point we called "center" + if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized())) void planes() +{ + using std::abs; + typedef Hyperplane Plane; + typedef Matrix Vector; + + for(int i = 0; i < 10; i++) + { + Vector v0 = Vector::Random(); + Vector v1(v0), v2(v0); + if(internal::random(0,1)>0.25) + v1 += Vector::Random(); + if(internal::random(0,1)>0.25) + v2 += v1 * std::pow(internal::random(0,1),internal::random(1,16)); + if(internal::random(0,1)>0.25) + v2 += Vector::Random() * std::pow(internal::random(0,1),internal::random(1,16)); + + Plane p0 = Plane::Through(v0, v1, v2); + + VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1)); + } +} + +template void hyperplane_alignment() +{ + typedef Hyperplane Plane3a; + typedef Hyperplane Plane3u; + + EIGEN_ALIGN_MAX Scalar array1[4]; + EIGEN_ALIGN_MAX Scalar array2[4]; + EIGEN_ALIGN_MAX Scalar array3[4+1]; + Scalar* array3u = array3+1; + + Plane3a *p1 = ::new(reinterpret_cast(array1)) Plane3a; + Plane3u *p2 = ::new(reinterpret_cast(array2)) Plane3u; + Plane3u *p3 = ::new(reinterpret_cast(array3u)) Plane3u; + + p1->coeffs().setRandom(); + *p2 = *p1; + *p3 = *p1; + + VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); + VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); +} + + +EIGEN_DECLARE_TEST(geo_hyperplane) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( hyperplane(Hyperplane()) ); + CALL_SUBTEST_2( hyperplane(Hyperplane()) ); + CALL_SUBTEST_2( hyperplane(Hyperplane()) ); + CALL_SUBTEST_2( hyperplane_alignment() ); + CALL_SUBTEST_3( hyperplane(Hyperplane()) ); + CALL_SUBTEST_4( hyperplane(Hyperplane,5>()) ); + CALL_SUBTEST_1( lines() ); + CALL_SUBTEST_3( lines() ); + CALL_SUBTEST_2( planes() ); + CALL_SUBTEST_5( planes() ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_orthomethods.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_orthomethods.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b7b660740284d3bb94b14693a4a1134bfb8f6eac --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_orthomethods.cpp @@ -0,0 +1,133 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +/* this test covers the following files: + Geometry/OrthoMethods.h +*/ + +template void orthomethods_3() +{ + typedef typename NumTraits::Real RealScalar; + typedef Matrix Matrix3; + typedef Matrix Vector3; + + typedef Matrix Vector4; + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(), + v2 = Vector3::Random(); + + // cross product + VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1)); + Matrix3 mat3; + mat3 << v0.normalized(), + (v0.cross(v1)).normalized(), + (v0.cross(v1).cross(v0)).normalized(); + VERIFY(mat3.isUnitary()); + + mat3.setRandom(); + VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0)); + VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0)); + + // colwise/rowwise cross product + mat3.setRandom(); + Vector3 vec3 = Vector3::Random(); + Matrix3 mcross; + int i = internal::random(0,2); + mcross = mat3.colwise().cross(vec3); + VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); + + VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1)); + + VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1)); + + mcross = mat3.rowwise().cross(vec3); + VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); + + // cross3 + Vector4 v40 = Vector4::Random(), + v41 = Vector4::Random(), + v42 = Vector4::Random(); + v40.w() = v41.w() = v42.w() = 0; + v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>()); + VERIFY_IS_APPROX(v40.cross3(v41), v42); + VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1)); + + // check mixed product + typedef Matrix RealVector3; + RealVector3 rv1 = RealVector3::Random(); + VERIFY_IS_APPROX(v1.cross(rv1.template cast()), v1.cross(rv1)); + VERIFY_IS_APPROX(rv1.template cast().cross(v1), rv1.cross(v1)); +} + +template void orthomethods(int size=Size) +{ + typedef typename NumTraits::Real RealScalar; + typedef Matrix VectorType; + typedef Matrix Matrix3N; + typedef Matrix MatrixN3; + typedef Matrix Vector3; + + VectorType v0 = VectorType::Random(size); + + // unitOrthogonal + VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1)); + VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1)); + + if (size>=3) + { + v0.template head<2>().setZero(); + v0.tail(size-2).setRandom(); + + VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1)); + VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1)); + } + + // colwise/rowwise cross product + Vector3 vec3 = Vector3::Random(); + int i = internal::random(0,size-1); + + Matrix3N mat3N(3,size), mcross3N(3,size); + mat3N.setRandom(); + mcross3N = mat3N.colwise().cross(vec3); + VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3)); + + MatrixN3 matN3(size,3), mcrossN3(size,3); + matN3.setRandom(); + mcrossN3 = matN3.rowwise().cross(vec3); + VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3)); +} + +EIGEN_DECLARE_TEST(geo_orthomethods) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( orthomethods_3() ); + CALL_SUBTEST_2( orthomethods_3() ); + CALL_SUBTEST_4( orthomethods_3 >() ); + CALL_SUBTEST_1( (orthomethods()) ); + CALL_SUBTEST_2( (orthomethods()) ); + CALL_SUBTEST_1( (orthomethods()) ); + CALL_SUBTEST_2( (orthomethods()) ); + CALL_SUBTEST_3( (orthomethods()) ); + CALL_SUBTEST_4( (orthomethods,8>()) ); + CALL_SUBTEST_5( (orthomethods(36)) ); + CALL_SUBTEST_6( (orthomethods(35)) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_parametrizedline.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_parametrizedline.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e4b194abc407a7b45bbc437688462051b1132864 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_parametrizedline.cpp @@ -0,0 +1,125 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +template void parametrizedline(const LineType& _line) +{ + /* this test covers the following files: + ParametrizedLine.h + */ + using std::abs; + const Index dim = _line.dim(); + typedef typename LineType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix VectorType; + typedef Hyperplane HyperplaneType; + typedef Matrix MatrixType; + + VectorType p0 = VectorType::Random(dim); + VectorType p1 = VectorType::Random(dim); + + VectorType d0 = VectorType::Random(dim).normalized(); + + LineType l0(p0, d0); + + Scalar s0 = internal::random(); + Scalar s1 = abs(internal::random()); + + VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0), RealScalar(1) ); + VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0+s0*d0), RealScalar(1) ); + VERIFY_IS_APPROX( (l0.projection(p1)-p1).norm(), l0.distance(p1) ); + VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(l0.projection(p1)), RealScalar(1) ); + VERIFY_IS_APPROX( Scalar(l0.distance((p0+s0*d0) + d0.unitOrthogonal() * s1)), s1 ); + + // casting + const int Dim = LineType::AmbientDimAtCompileTime; + typedef typename GetDifferentType::type OtherScalar; + ParametrizedLine hp1f = l0.template cast(); + VERIFY_IS_APPROX(hp1f.template cast(),l0); + ParametrizedLine hp1d = l0.template cast(); + VERIFY_IS_APPROX(hp1d.template cast(),l0); + + // intersections + VectorType p2 = VectorType::Random(dim); + VectorType n2 = VectorType::Random(dim).normalized(); + HyperplaneType hp(p2,n2); + Scalar t = l0.intersectionParameter(hp); + VectorType pi = l0.pointAt(t); + VERIFY_IS_MUCH_SMALLER_THAN(hp.signedDistance(pi), RealScalar(1)); + VERIFY_IS_MUCH_SMALLER_THAN(l0.distance(pi), RealScalar(1)); + VERIFY_IS_APPROX(l0.intersectionPoint(hp), pi); + + // transform + if (!NumTraits::IsComplex) + { + MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); + DiagonalMatrix scaling(VectorType::Random()); + Translation translation(VectorType::Random()); + + while(scaling.diagonal().cwiseAbs().minCoeff() void parametrizedline_alignment() +{ + typedef ParametrizedLine Line4a; + typedef ParametrizedLine Line4u; + + EIGEN_ALIGN_MAX Scalar array1[16]; + EIGEN_ALIGN_MAX Scalar array2[16]; + EIGEN_ALIGN_MAX Scalar array3[16+1]; + Scalar* array3u = array3+1; + + Line4a *p1 = ::new(reinterpret_cast(array1)) Line4a; + Line4u *p2 = ::new(reinterpret_cast(array2)) Line4u; + Line4u *p3 = ::new(reinterpret_cast(array3u)) Line4u; + + p1->origin().setRandom(); + p1->direction().setRandom(); + *p2 = *p1; + *p3 = *p1; + + VERIFY_IS_APPROX(p1->origin(), p2->origin()); + VERIFY_IS_APPROX(p1->origin(), p3->origin()); + VERIFY_IS_APPROX(p1->direction(), p2->direction()); + VERIFY_IS_APPROX(p1->direction(), p3->direction()); +} + +EIGEN_DECLARE_TEST(geo_parametrizedline) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( parametrizedline(ParametrizedLine()) ); + CALL_SUBTEST_2( parametrizedline(ParametrizedLine()) ); + CALL_SUBTEST_2( parametrizedline_alignment() ); + CALL_SUBTEST_3( parametrizedline(ParametrizedLine()) ); + CALL_SUBTEST_3( parametrizedline_alignment() ); + CALL_SUBTEST_4( parametrizedline(ParametrizedLine,5>()) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_quaternion.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_quaternion.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c561fc89d0e8f314354468824cce8a3bfd8d3511 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_quaternion.cpp @@ -0,0 +1,332 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// Copyright (C) 2009 Mathieu Gautier +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include +#include "AnnoyingScalar.h" + +template T bounded_acos(T v) +{ + using std::acos; + using std::min; + using std::max; + return acos((max)(T(-1),(min)(v,T(1)))); +} + +template void check_slerp(const QuatType& q0, const QuatType& q1) +{ + using std::abs; + typedef typename QuatType::Scalar Scalar; + typedef AngleAxis AA; + + Scalar largeEps = test_precision(); + + Scalar theta_tot = AA(q1*q0.inverse()).angle(); + if(theta_tot>Scalar(EIGEN_PI)) + theta_tot = Scalar(2.)*Scalar(EIGEN_PI)-theta_tot; + for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1)) + { + QuatType q = q0.slerp(t,q1); + Scalar theta = AA(q*q0.inverse()).angle(); + VERIFY(abs(q.norm() - 1) < largeEps); + if(theta_tot==0) VERIFY(theta_tot==0); + else VERIFY(abs(theta - t * theta_tot) < largeEps); + } +} + +template void quaternion(void) +{ + /* this test covers the following files: + Quaternion.h + */ + using std::abs; + typedef Matrix Vector3; + typedef Matrix Matrix3; + typedef Quaternion Quaternionx; + typedef AngleAxis AngleAxisx; + + Scalar largeEps = test_precision(); + if (internal::is_same::value) + largeEps = Scalar(1e-3); + + Scalar eps = internal::random() * Scalar(1e-2); + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(), + v2 = Vector3::Random(), + v3 = Vector3::Random(); + + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)), + b = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + + // Quaternion: Identity(), setIdentity(); + Quaternionx q1, q2; + q2.setIdentity(); + VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs()); + q1.coeffs().setRandom(); + VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs()); + +#ifndef EIGEN_NO_IO + // Printing + std::ostringstream ss; + ss << q2; + VERIFY(ss.str() == "0i + 0j + 0k + 1"); +#endif + + // concatenation + q1 *= q2; + + q1 = AngleAxisx(a, v0.normalized()); + q2 = AngleAxisx(a, v1.normalized()); + + // angular distance + Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle()); + if (refangle>Scalar(EIGEN_PI)) + refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle; + + if((q1.coeffs()-q2.coeffs()).norm() > Scalar(10)*largeEps) + { + VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1)); + } + + // rotation matrix conversion + VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2); + VERIFY_IS_APPROX(q1 * q2 * v2, + q1.toRotationMatrix() * q2.toRotationMatrix() * v2); + + VERIFY( (q2*q1).isApprox(q1*q2, largeEps) + || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2)); + + q2 = q1.toRotationMatrix(); + VERIFY_IS_APPROX(q1*v1,q2*v1); + + Matrix3 rot1(q1); + VERIFY_IS_APPROX(q1*v1,rot1*v1); + Quaternionx q3(rot1.transpose()*rot1); + VERIFY_IS_APPROX(q3*v1,v1); + + + // angle-axis conversion + AngleAxisx aa = AngleAxisx(q1); + VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); + + // Do not execute the test if the rotation angle is almost zero, or + // the rotation axis and v1 are almost parallel. + if (abs(aa.angle()) > Scalar(5)*test_precision() + && (aa.axis() - v1.normalized()).norm() < Scalar(1.99) + && (aa.axis() + v1.normalized()).norm() < Scalar(1.99)) + { + VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); + } + + // from two vector creation + VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized()); + VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized()); + VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized()); + if (internal::is_same::value) + { + v3 = (v1.array()+eps).matrix(); + VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized()); + VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized()); + } + + // from two vector creation static function + VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized()); + VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized()); + VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized()); + if (internal::is_same::value) + { + v3 = (v1.array()+eps).matrix(); + VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized()); + VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized()); + } + + // inverse and conjugate + VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1); + VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1); + + // test casting + Quaternion q1f = q1.template cast(); + VERIFY_IS_APPROX(q1f.template cast(),q1); + Quaternion q1d = q1.template cast(); + VERIFY_IS_APPROX(q1d.template cast(),q1); + + // test bug 369 - improper alignment. + Quaternionx *q = new Quaternionx; + delete q; + + q1 = Quaternionx::UnitRandom(); + q2 = Quaternionx::UnitRandom(); + check_slerp(q1,q2); + + q1 = AngleAxisx(b, v1.normalized()); + q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized()); + check_slerp(q1,q2); + + q1 = AngleAxisx(b, v1.normalized()); + q2 = AngleAxisx(-b, -v1.normalized()); + check_slerp(q1,q2); + + q1 = Quaternionx::UnitRandom(); + q2.coeffs() = -q1.coeffs(); + check_slerp(q1,q2); +} + +template void mapQuaternion(void){ + typedef Map, Aligned> MQuaternionA; + typedef Map, Aligned> MCQuaternionA; + typedef Map > MQuaternionUA; + typedef Map > MCQuaternionUA; + typedef Quaternion Quaternionx; + typedef Matrix Vector3; + typedef AngleAxis AngleAxisx; + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(); + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + + EIGEN_ALIGN_MAX Scalar array1[4]; + EIGEN_ALIGN_MAX Scalar array2[4]; + EIGEN_ALIGN_MAX Scalar array3[4+1]; + Scalar* array3unaligned = array3+1; + + MQuaternionA mq1(array1); + MCQuaternionA mcq1(array1); + MQuaternionA mq2(array2); + MQuaternionUA mq3(array3unaligned); + MCQuaternionUA mcq3(array3unaligned); + +// std::cerr << array1 << " " << array2 << " " << array3 << "\n"; + mq1 = AngleAxisx(a, v0.normalized()); + mq2 = mq1; + mq3 = mq1; + + Quaternionx q1 = mq1; + Quaternionx q2 = mq2; + Quaternionx q3 = mq3; + Quaternionx q4 = MCQuaternionUA(array3unaligned); + + VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs()); + VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs()); + VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs()); + + VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1); + VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1); + + VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1); + VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1); + + VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1); + VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1); + + VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1); + VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1); + + VERIFY_IS_APPROX(mq1*mq2, q1*q2); + VERIFY_IS_APPROX(mq3*mq2, q3*q2); + VERIFY_IS_APPROX(mcq1*mq2, q1*q2); + VERIFY_IS_APPROX(mcq3*mq2, q3*q2); + + // Bug 1461, compilation issue with Map::w(), and other reference/constness checks: + VERIFY_IS_APPROX(mcq3.coeffs().x() + mcq3.coeffs().y() + mcq3.coeffs().z() + mcq3.coeffs().w(), mcq3.coeffs().sum()); + VERIFY_IS_APPROX(mcq3.x() + mcq3.y() + mcq3.z() + mcq3.w(), mcq3.coeffs().sum()); + mq3.w() = 1; + const Quaternionx& cq3(q3); + VERIFY( &cq3.x() == &q3.x() ); + const MQuaternionUA& cmq3(mq3); + VERIFY( &cmq3.x() == &mq3.x() ); + // FIXME the following should be ok. The problem is that currently the LValueBit flag + // is used to determine whether we can return a coeff by reference or not, which is not enough for Map. + //const MCQuaternionUA& cmcq3(mcq3); + //VERIFY( &cmcq3.x() == &mcq3.x() ); + + // test cast + { + Quaternion q1f = mq1.template cast(); + VERIFY_IS_APPROX(q1f.template cast(),mq1); + Quaternion q1d = mq1.template cast(); + VERIFY_IS_APPROX(q1d.template cast(),mq1); + } +} + +template void quaternionAlignment(void){ + typedef Quaternion QuaternionA; + typedef Quaternion QuaternionUA; + + EIGEN_ALIGN_MAX Scalar array1[4]; + EIGEN_ALIGN_MAX Scalar array2[4]; + EIGEN_ALIGN_MAX Scalar array3[4+1]; + Scalar* arrayunaligned = array3+1; + + QuaternionA *q1 = ::new(reinterpret_cast(array1)) QuaternionA; + QuaternionUA *q2 = ::new(reinterpret_cast(array2)) QuaternionUA; + QuaternionUA *q3 = ::new(reinterpret_cast(arrayunaligned)) QuaternionUA; + + q1->coeffs().setRandom(); + *q2 = *q1; + *q3 = *q1; + + VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs()); + VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs()); +} + +template void check_const_correctness(const PlainObjectType&) +{ + // there's a lot that we can't test here while still having this test compile! + // the only possible approach would be to run a script trying to compile stuff and checking that it fails. + // CMake can help with that. + + // verify that map-to-const don't have LvalueBit + typedef typename internal::add_const::type ConstPlainObjectType; + VERIFY( !(internal::traits >::Flags & LvalueBit) ); + VERIFY( !(internal::traits >::Flags & LvalueBit) ); + VERIFY( !(Map::Flags & LvalueBit) ); + VERIFY( !(Map::Flags & LvalueBit) ); +} + +#if EIGEN_HAS_RVALUE_REFERENCES + +// Regression for bug 1573 +struct MovableClass { + // The following line is a workaround for gcc 4.7 and 4.8 (see bug 1573 comments). + static_assert(std::is_nothrow_move_constructible::value,""); + MovableClass() = default; + MovableClass(const MovableClass&) = default; + MovableClass(MovableClass&&) noexcept = default; + MovableClass& operator=(const MovableClass&) = default; + MovableClass& operator=(MovableClass&&) = default; + Quaternionf m_quat; +}; + +#endif + +EIGEN_DECLARE_TEST(geo_quaternion) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( quaternion() )); + CALL_SUBTEST_1( check_const_correctness(Quaternionf()) ); + CALL_SUBTEST_1(( quaternion() )); + CALL_SUBTEST_1(( quaternionAlignment() )); + CALL_SUBTEST_1( mapQuaternion() ); + + CALL_SUBTEST_2(( quaternion() )); + CALL_SUBTEST_2( check_const_correctness(Quaterniond()) ); + CALL_SUBTEST_2(( quaternion() )); + CALL_SUBTEST_2(( quaternionAlignment() )); + CALL_SUBTEST_2( mapQuaternion() ); + +#ifndef EIGEN_TEST_ANNOYING_SCALAR_DONT_THROW + AnnoyingScalar::dont_throw = true; +#endif + CALL_SUBTEST_3(( quaternion() )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_transformations.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_transformations.cpp new file mode 100644 index 0000000000000000000000000000000000000000..72c6edac14708ffb3969855dd7096ca94504773f --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/geo_transformations.cpp @@ -0,0 +1,731 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +template +Matrix angleToVec(T a) +{ + return Matrix(std::cos(a), std::sin(a)); +} + +// This permits to workaround a bug in clang/llvm code generation. +template +EIGEN_DONT_INLINE +void dont_over_optimize(T& x) { volatile typename T::Scalar tmp = x(0); x(0) = tmp; } + +template void non_projective_only() +{ + /* this test covers the following files: + Cross.h Quaternion.h, Transform.cpp + */ + typedef Matrix Vector3; + typedef Quaternion Quaternionx; + typedef AngleAxis AngleAxisx; + typedef Transform Transform3; + typedef DiagonalMatrix AlignedScaling3; + typedef Translation Translation3; + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(); + + Transform3 t0, t1, t2; + + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + + Quaternionx q1, q2; + + q1 = AngleAxisx(a, v0.normalized()); + + t0 = Transform3::Identity(); + VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); + + t0.linear() = q1.toRotationMatrix(); + + v0 << 50, 2, 1; + t0.scale(v0); + + VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x()); + + t0.setIdentity(); + t1.setIdentity(); + v1 << 1, 2, 3; + t0.linear() = q1.toRotationMatrix(); + t0.pretranslate(v0); + t0.scale(v1); + t1.linear() = q1.conjugate().toRotationMatrix(); + t1.prescale(v1.cwiseInverse()); + t1.translate(-v0); + + VERIFY((t0 * t1).matrix().isIdentity(test_precision())); + + t1.fromPositionOrientationScale(v0, q1, v1); + VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); + VERIFY_IS_APPROX(t1*v1, t0*v1); + + // translation * vector + t0.setIdentity(); + t0.translate(v0); + VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1); + + // AlignedScaling * vector + t0.setIdentity(); + t0.scale(v0); + VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1); +} + +template void transformations() +{ + /* this test covers the following files: + Cross.h Quaternion.h, Transform.cpp + */ + using std::cos; + using std::abs; + typedef Matrix Matrix3; + typedef Matrix Matrix4; + typedef Matrix Vector2; + typedef Matrix Vector3; + typedef Matrix Vector4; + typedef Quaternion Quaternionx; + typedef AngleAxis AngleAxisx; + typedef Transform Transform2; + typedef Transform Transform3; + typedef typename Transform3::MatrixType MatrixType; + typedef DiagonalMatrix AlignedScaling3; + typedef Translation Translation2; + typedef Translation Translation3; + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(); + Matrix3 matrot1, m; + + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + Scalar s0 = internal::random(), s1 = internal::random(); + + while(v0.norm() < test_precision()) v0 = Vector3::Random(); + while(v1.norm() < test_precision()) v1 = Vector3::Random(); + + VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); + VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0); + if(abs(cos(a)) > test_precision()) + { + VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0)); + } + m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint(); + VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized())); + VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m); + + Quaternionx q1, q2; + q1 = AngleAxisx(a, v0.normalized()); + q2 = AngleAxisx(a, v1.normalized()); + + // rotation matrix conversion + matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX()) + * AngleAxisx(Scalar(0.2), Vector3::UnitY()) + * AngleAxisx(Scalar(0.3), Vector3::UnitZ()); + VERIFY_IS_APPROX(matrot1 * v1, + AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix() + * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix() + * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1))); + + // angle-axis conversion + AngleAxisx aa = AngleAxisx(q1); + VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); + + // The following test is stable only if 2*angle != angle and v1 is not colinear with axis + if( (abs(aa.angle()) > test_precision()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision())) ) + { + VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) ); + } + + aa.fromRotationMatrix(aa.toRotationMatrix()); + VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); + // The following test is stable only if 2*angle != angle and v1 is not colinear with axis + if( (abs(aa.angle()) > test_precision()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision())) ) + { + VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) ); + } + + // AngleAxis + VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(), + Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix()); + + AngleAxisx aa1; + m = q1.toRotationMatrix(); + aa1 = m; + VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(), + Quaternionx(m).toRotationMatrix()); + + // Transform + // TODO complete the tests ! + a = 0; + while (abs(a)(-Scalar(0.4)*Scalar(EIGEN_PI), Scalar(0.4)*Scalar(EIGEN_PI)); + q1 = AngleAxisx(a, v0.normalized()); + Transform3 t0, t1, t2; + + // first test setIdentity() and Identity() + t0.setIdentity(); + VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); + t0.matrix().setZero(); + t0 = Transform3::Identity(); + VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); + + t0.setIdentity(); + t1.setIdentity(); + v1 << 1, 2, 3; + t0.linear() = q1.toRotationMatrix(); + t0.pretranslate(v0); + t0.scale(v1); + t1.linear() = q1.conjugate().toRotationMatrix(); + t1.prescale(v1.cwiseInverse()); + t1.translate(-v0); + + VERIFY((t0 * t1).matrix().isIdentity(test_precision())); + + t1.fromPositionOrientationScale(v0, q1, v1); + VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); + + t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix()); + t1.setIdentity(); t1.scale(v0).rotate(q1); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix()); + VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix()); + + // More transform constructors, operator=, operator*= + + Matrix3 mat3 = Matrix3::Random(); + Matrix4 mat4; + mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose(); + Transform3 tmat3(mat3), tmat4(mat4); + if(Mode!=int(AffineCompact)) + tmat4.matrix()(3,3) = Scalar(1); + VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); + + Scalar a3 = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + Vector3 v3 = Vector3::Random().normalized(); + AngleAxisx aa3(a3, v3); + Transform3 t3(aa3); + Transform3 t4; + t4 = aa3; + VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); + t4.rotate(AngleAxisx(-a3,v3)); + VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity()); + t4 *= aa3; + VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); + + do { + v3 = Vector3::Random(); + dont_over_optimize(v3); + } while (v3.cwiseAbs().minCoeff()::epsilon()); + Translation3 tv3(v3); + Transform3 t5(tv3); + t4 = tv3; + VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); + t4.translate((-v3).eval()); + VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity()); + t4 *= tv3; + VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); + + AlignedScaling3 sv3(v3); + Transform3 t6(sv3); + t4 = sv3; + VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); + t4.scale(v3.cwiseInverse()); + VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity()); + t4 *= sv3; + VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); + + // matrix * transform + VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix()); + + // chained Transform product + VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix()); + + // check that Transform product doesn't have aliasing problems + t5 = t4; + t5 = t5*t5; + VERIFY_IS_APPROX(t5, t4*t4); + + // 2D transformation + Transform2 t20, t21; + Vector2 v20 = Vector2::Random(); + Vector2 v21 = Vector2::Random(); + for (int k=0; k<2; ++k) + if (abs(v21[k])(a).toRotationMatrix(); + VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(), + t21.pretranslate(v20).scale(v21).matrix()); + + t21.setIdentity(); + t21.linear() = Rotation2D(-a).toRotationMatrix(); + VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) + * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision()) ); + + // Transform - new API + // 3D + t0.setIdentity(); + t0.rotate(q1).scale(v0).translate(v0); + // mat * aligned scaling and mat * translation + t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + // mat * transformation and aligned scaling * translation + t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + + t0.setIdentity(); + t0.scale(s0).translate(v0); + t1 = Eigen::Scaling(s0) * Translation3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t0.prescale(s0); + t1 = Eigen::Scaling(s0) * t1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + t0 = t3; + t0.scale(s0); + t1 = t3 * Eigen::Scaling(s0,s0,s0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t0.prescale(s0); + t1 = Eigen::Scaling(s0,s0,s0) * t1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + t0 = t3; + t0.scale(s0); + t1 = t3 * Eigen::Scaling(s0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t0.prescale(s0); + t1 = Eigen::Scaling(s0) * t1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + t0.setIdentity(); + t0.prerotate(q1).prescale(v0).pretranslate(v0); + // translation * aligned scaling and transformation * mat + t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + // scaling * mat and translation * mat + t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + t0.setIdentity(); + t0.scale(v0).translate(v0).rotate(q1); + // translation * mat and aligned scaling * transformation + t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + // transformation * aligned scaling + t0.scale(v0); + t1 *= AlignedScaling3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1)); + t1 = t1 * v0.asDiagonal(); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + // transformation * translation + t0.translate(v0); + t1 = t1 * Translation3(v0); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + // translation * transformation + t0.pretranslate(v0); + t1 = Translation3(v0) * t1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // transform * quaternion + t0.rotate(q1); + t1 = t1 * q1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // translation * quaternion + t0.translate(v1).rotate(q1); + t1 = t1 * (Translation3(v1) * q1); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // aligned scaling * quaternion + t0.scale(v1).rotate(q1); + t1 = t1 * (AlignedScaling3(v1) * q1); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // quaternion * transform + t0.prerotate(q1); + t1 = q1 * t1; + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // quaternion * translation + t0.rotate(q1).translate(v1); + t1 = t1 * (q1 * Translation3(v1)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // quaternion * aligned scaling + t0.rotate(q1).scale(v1); + t1 = t1 * (q1 * AlignedScaling3(v1)); + VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); + + // test transform inversion + t0.setIdentity(); + t0.translate(v0); + do { + t0.linear().setRandom(); + } while(t0.linear().jacobiSvd().singularValues()(2)()); + Matrix4 t044 = Matrix4::Zero(); + t044(3,3) = 1; + t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); + VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); + t0.setIdentity(); + t0.translate(v0).rotate(q1); + t044 = Matrix4::Zero(); + t044(3,3) = 1; + t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); + VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); + + Matrix3 mat_rotation, mat_scaling; + t0.setIdentity(); + t0.translate(v0).rotate(q1).scale(v1); + t0.computeRotationScaling(&mat_rotation, &mat_scaling); + VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling); + VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); + VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); + t0.computeScalingRotation(&mat_scaling, &mat_rotation); + VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation); + VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); + VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); + + // test casting + Transform t1f = t1.template cast(); + VERIFY_IS_APPROX(t1f.template cast(),t1); + Transform t1d = t1.template cast(); + VERIFY_IS_APPROX(t1d.template cast(),t1); + + Translation3 tr1(v0); + Translation tr1f = tr1.template cast(); + VERIFY_IS_APPROX(tr1f.template cast(),tr1); + Translation tr1d = tr1.template cast(); + VERIFY_IS_APPROX(tr1d.template cast(),tr1); + + AngleAxis aa1f = aa1.template cast(); + VERIFY_IS_APPROX(aa1f.template cast(),aa1); + AngleAxis aa1d = aa1.template cast(); + VERIFY_IS_APPROX(aa1d.template cast(),aa1); + + Rotation2D r2d1(internal::random()); + Rotation2D r2d1f = r2d1.template cast(); + VERIFY_IS_APPROX(r2d1f.template cast(),r2d1); + Rotation2D r2d1d = r2d1.template cast(); + VERIFY_IS_APPROX(r2d1d.template cast(),r2d1); + + for(int k=0; k<100; ++k) + { + Scalar angle = internal::random(-100,100); + Rotation2D rot2(angle); + VERIFY( rot2.smallestPositiveAngle() >= 0 ); + VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) ); + VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) ); + + VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) ); + VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) ); + VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) ); + + Matrix rot2_as_mat(rot2); + Rotation2D rot3(rot2_as_mat); + VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot3.angle()) ); + } + + s0 = internal::random(-100,100); + s1 = internal::random(-100,100); + Rotation2D R0(s0), R1(s1); + + t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0)); + t21 = Translation2(v20) * R0 * Eigen::Scaling(s0); + VERIFY_IS_APPROX(t20,t21); + + t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0)); + t21 = Translation2(v20) * Eigen::Scaling(s0); + VERIFY_IS_APPROX(t20,t21); + + VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle()); + VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) ); + VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle()); + + if(std::cos(s0)>0) + VERIFY_IS_MUCH_SMALLER_THAN((R0.slerp(0.5, R0.inverse())).smallestAngle(), Scalar(1)); + else + VERIFY_IS_APPROX(Scalar(EIGEN_PI), (R0.slerp(0.5, R0.inverse())).smallestPositiveAngle()); + + // Check path length + Scalar l = 0; + int path_steps = 100; + for(int k=0; k::epsilon()*Scalar(path_steps/2))); + + // check basic features + { + Rotation2D r1; // default ctor + r1 = Rotation2D(s0); // copy assignment + VERIFY_IS_APPROX(r1.angle(),s0); + Rotation2D r2(r1); // copy ctor + VERIFY_IS_APPROX(r2.angle(),s0); + } + + { + Transform3 t32(Matrix4::Random()), t33, t34; + t34 = t33 = t32; + t32.scale(v0); + t33*=AlignedScaling3(v0); + VERIFY_IS_APPROX(t32.matrix(), t33.matrix()); + t33 = t34 * AlignedScaling3(v0); + VERIFY_IS_APPROX(t32.matrix(), t33.matrix()); + } + +} + +template +void transform_associativity_left(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h) +{ + VERIFY_IS_APPROX( q*(a1*v), (q*a1)*v ); + VERIFY_IS_APPROX( q*(a2*v), (q*a2)*v ); + VERIFY_IS_APPROX( q*(p*h).hnormalized(), ((q*p)*h).hnormalized() ); +} + +template +void transform_associativity2(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h) +{ + VERIFY_IS_APPROX( a1*(q*v), (a1*q)*v ); + VERIFY_IS_APPROX( a2*(q*v), (a2*q)*v ); + VERIFY_IS_APPROX( p *(q*v).homogeneous(), (p *q)*v.homogeneous() ); + + transform_associativity_left(a1, a2,p, q, v, h); +} + +template +void transform_associativity(const RotationType& R) +{ + typedef Matrix VectorType; + typedef Matrix HVectorType; + typedef Matrix LinearType; + typedef Matrix MatrixType; + typedef Transform AffineCompactType; + typedef Transform AffineType; + typedef Transform ProjectiveType; + typedef DiagonalMatrix ScalingType; + typedef Translation TranslationType; + + AffineCompactType A1c; A1c.matrix().setRandom(); + AffineCompactType A2c; A2c.matrix().setRandom(); + AffineType A1(A1c); + AffineType A2(A2c); + ProjectiveType P1; P1.matrix().setRandom(); + VectorType v1 = VectorType::Random(); + VectorType v2 = VectorType::Random(); + HVectorType h1 = HVectorType::Random(); + Scalar s1 = internal::random(); + LinearType L = LinearType::Random(); + MatrixType M = MatrixType::Random(); + + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2, v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2c, v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, v1.asDiagonal(), v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, ScalingType(v1), v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(v1), v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(s1), v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, TranslationType(v1), v2, h1) ); + CALL_SUBTEST( transform_associativity_left(A1c, A1, P1, L, v2, h1) ); + CALL_SUBTEST( transform_associativity2(A1c, A1, P1, R, v2, h1) ); + + VERIFY_IS_APPROX( A1*(M*h1), (A1*M)*h1 ); + VERIFY_IS_APPROX( A1c*(M*h1), (A1c*M)*h1 ); + VERIFY_IS_APPROX( P1*(M*h1), (P1*M)*h1 ); + + VERIFY_IS_APPROX( M*(A1*h1), (M*A1)*h1 ); + VERIFY_IS_APPROX( M*(A1c*h1), (M*A1c)*h1 ); + VERIFY_IS_APPROX( M*(P1*h1), ((M*P1)*h1) ); +} + +template void transform_alignment() +{ + typedef Transform Projective3a; + typedef Transform Projective3u; + + EIGEN_ALIGN_MAX Scalar array1[16]; + EIGEN_ALIGN_MAX Scalar array2[16]; + EIGEN_ALIGN_MAX Scalar array3[16+1]; + Scalar* array3u = array3+1; + + Projective3a *p1 = ::new(reinterpret_cast(array1)) Projective3a; + Projective3u *p2 = ::new(reinterpret_cast(array2)) Projective3u; + Projective3u *p3 = ::new(reinterpret_cast(array3u)) Projective3u; + + p1->matrix().setRandom(); + *p2 = *p1; + *p3 = *p1; + + VERIFY_IS_APPROX(p1->matrix(), p2->matrix()); + VERIFY_IS_APPROX(p1->matrix(), p3->matrix()); + + VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3)); +} + +template void transform_products() +{ + typedef Matrix Mat; + typedef Transform Proj; + typedef Transform Aff; + typedef Transform AffC; + + Proj p; p.matrix().setRandom(); + Aff a; a.linear().setRandom(); a.translation().setRandom(); + AffC ac = a; + + Mat p_m(p.matrix()), a_m(a.matrix()); + + VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m); + VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m); + VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m); + VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m); + VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m); + VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m); + VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m); + VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m); +} + +template void transformations_no_scale() +{ + /* this test covers the following files: + Cross.h Quaternion.h, Transform.h + */ + typedef Matrix Vector3; + typedef Matrix Vector4; + typedef Quaternion Quaternionx; + typedef AngleAxis AngleAxisx; + typedef Transform Transform3; + typedef Translation Translation3; + typedef Matrix Matrix4; + + Vector3 v0 = Vector3::Random(), + v1 = Vector3::Random(); + + Transform3 t0, t1, t2; + + Scalar a = internal::random(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)); + + Quaternionx q1, q2; + + q1 = AngleAxisx(a, v0.normalized()); + + t0 = Transform3::Identity(); + VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); + + t0.setIdentity(); + t1.setIdentity(); + v1 = Vector3::Ones(); + t0.linear() = q1.toRotationMatrix(); + t0.pretranslate(v0); + t1.linear() = q1.conjugate().toRotationMatrix(); + t1.translate(-v0); + + VERIFY((t0 * t1).matrix().isIdentity(test_precision())); + + t1.fromPositionOrientationScale(v0, q1, v1); + VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); + VERIFY_IS_APPROX(t1*v1, t0*v1); + + // translation * vector + t0.setIdentity(); + t0.translate(v0); + VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1); + + // Conversion to matrix. + Transform3 t3; + t3.linear() = q1.toRotationMatrix(); + t3.translation() = v1; + Matrix4 m3 = t3.matrix(); + VERIFY((m3 * m3.inverse()).isIdentity(test_precision())); + // Verify implicit last row is initialized. + VERIFY_IS_APPROX(Vector4(m3.row(3)), Vector4(0.0, 0.0, 0.0, 1.0)); + + VERIFY_IS_APPROX(t3.rotation(), t3.linear()); + if(Mode==Isometry) + VERIFY(t3.rotation().data()==t3.linear().data()); +} + +template void transformations_computed_scaling_continuity() +{ + typedef Matrix Vector3; + typedef Transform Transform3; + typedef Matrix Matrix3; + + // Given: two transforms that differ by '2*eps'. + Scalar eps(1e-3); + Vector3 v0 = Vector3::Random().normalized(), + v1 = Vector3::Random().normalized(), + v3 = Vector3::Random().normalized(); + Transform3 t0, t1; + // The interesting case is when their determinants have different signs. + Matrix3 rank2 = 50 * v0 * v0.adjoint() + 20 * v1 * v1.adjoint(); + t0.linear() = rank2 + eps * v3 * v3.adjoint(); + t1.linear() = rank2 - eps * v3 * v3.adjoint(); + + // When: computing the rotation-scaling parts + Matrix3 r0, s0, r1, s1; + t0.computeRotationScaling(&r0, &s0); + t1.computeRotationScaling(&r1, &s1); + + // Then: the scaling parts should differ by no more than '2*eps'. + const Scalar c(2.1); // 2 + room for rounding errors + VERIFY((s0 - s1).norm() < c * eps); +} + +EIGEN_DECLARE_TEST(geo_transformations) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( transformations() )); + CALL_SUBTEST_1(( non_projective_only() )); + CALL_SUBTEST_1(( transformations_computed_scaling_continuity() )); + + CALL_SUBTEST_2(( transformations() )); + CALL_SUBTEST_2(( non_projective_only() )); + CALL_SUBTEST_2(( transform_alignment() )); + + CALL_SUBTEST_3(( transformations() )); + CALL_SUBTEST_3(( transformations() )); + CALL_SUBTEST_3(( transform_alignment() )); + + CALL_SUBTEST_4(( transformations() )); + CALL_SUBTEST_4(( non_projective_only() )); + + CALL_SUBTEST_5(( transformations() )); + CALL_SUBTEST_5(( non_projective_only() )); + + CALL_SUBTEST_6(( transformations() )); + CALL_SUBTEST_6(( transformations() )); + + + CALL_SUBTEST_7(( transform_products() )); + CALL_SUBTEST_7(( transform_products() )); + + CALL_SUBTEST_8(( transform_associativity(Rotation2D(internal::random()*double(EIGEN_PI))) )); + CALL_SUBTEST_8(( transform_associativity(Quaterniond::UnitRandom()) )); + + CALL_SUBTEST_9(( transformations_no_scale() )); + CALL_SUBTEST_9(( transformations_no_scale() )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_basic.cu b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_basic.cu new file mode 100644 index 0000000000000000000000000000000000000000..4298da3bb6e12138cbd3e2e3ccb77e42e2df7c39 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_basic.cu @@ -0,0 +1,461 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015-2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// workaround issue between gcc >= 4.7 and cuda 5.5 +#if (defined __GNUC__) && (__GNUC__>4 || __GNUC_MINOR__>=7) + #undef _GLIBCXX_ATOMIC_BUILTINS + #undef _GLIBCXX_USE_INT128 +#endif + +#define EIGEN_TEST_NO_LONGDOUBLE +#define EIGEN_DEFAULT_DENSE_INDEX_TYPE int + +#include "main.h" +#include "gpu_common.h" + +// Check that dense modules can be properly parsed by nvcc +#include + +// struct Foo{ +// EIGEN_DEVICE_FUNC +// void operator()(int i, const float* mats, float* vecs) const { +// using namespace Eigen; +// // Matrix3f M(data); +// // Vector3f x(data+9); +// // Map(data+9) = M.inverse() * x; +// Matrix3f M(mats+i/16); +// Vector3f x(vecs+i*3); +// // using std::min; +// // using std::sqrt; +// Map(vecs+i*3) << x.minCoeff(), 1, 2;// / x.dot(x);//(M.inverse() * x) / x.x(); +// //x = x*2 + x.y() * x + x * x.maxCoeff() - x / x.sum(); +// } +// }; + +template +struct coeff_wise { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + T x1(in+i); + T x2(in+i+1); + T x3(in+i+2); + Map res(out+i*T::MaxSizeAtCompileTime); + + res.array() += (in[0] * x1 + x2).array() * x3.array(); + } +}; + +template +struct complex_sqrt { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + typedef typename T::Scalar ComplexType; + typedef typename T::Scalar::value_type ValueType; + const int num_special_inputs = 18; + + if (i == 0) { + const ValueType nan = std::numeric_limits::quiet_NaN(); + typedef Eigen::Vector SpecialInputs; + SpecialInputs special_in; + special_in.setZero(); + int idx = 0; + special_in[idx++] = ComplexType(0, 0); + special_in[idx++] = ComplexType(-0, 0); + special_in[idx++] = ComplexType(0, -0); + special_in[idx++] = ComplexType(-0, -0); + // GCC's fallback sqrt implementation fails for inf inputs. + // It is called when _GLIBCXX_USE_C99_COMPLEX is false or if + // clang includes the GCC header (which temporarily disables + // _GLIBCXX_USE_C99_COMPLEX) + #if !defined(_GLIBCXX_COMPLEX) || \ + (_GLIBCXX_USE_C99_COMPLEX && !defined(__CLANG_CUDA_WRAPPERS_COMPLEX)) + const ValueType inf = std::numeric_limits::infinity(); + special_in[idx++] = ComplexType(1.0, inf); + special_in[idx++] = ComplexType(nan, inf); + special_in[idx++] = ComplexType(1.0, -inf); + special_in[idx++] = ComplexType(nan, -inf); + special_in[idx++] = ComplexType(-inf, 1.0); + special_in[idx++] = ComplexType(inf, 1.0); + special_in[idx++] = ComplexType(-inf, -1.0); + special_in[idx++] = ComplexType(inf, -1.0); + special_in[idx++] = ComplexType(-inf, nan); + special_in[idx++] = ComplexType(inf, nan); + #endif + special_in[idx++] = ComplexType(1.0, nan); + special_in[idx++] = ComplexType(nan, 1.0); + special_in[idx++] = ComplexType(nan, -1.0); + special_in[idx++] = ComplexType(nan, nan); + + Map special_out(out); + special_out = special_in.cwiseSqrt(); + } + + T x1(in + i); + Map res(out + num_special_inputs + i*T::MaxSizeAtCompileTime); + res = x1.cwiseSqrt(); + } +}; + +template +struct complex_operators { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + typedef typename T::Scalar ComplexType; + typedef typename T::Scalar::value_type ValueType; + const int num_scalar_operators = 24; + const int num_vector_operators = 23; // no unary + operator. + int out_idx = i * (num_scalar_operators + num_vector_operators * T::MaxSizeAtCompileTime); + + // Scalar operators. + const ComplexType a = in[i]; + const ComplexType b = in[i + 1]; + + out[out_idx++] = +a; + out[out_idx++] = -a; + + out[out_idx++] = a + b; + out[out_idx++] = a + numext::real(b); + out[out_idx++] = numext::real(a) + b; + out[out_idx++] = a - b; + out[out_idx++] = a - numext::real(b); + out[out_idx++] = numext::real(a) - b; + out[out_idx++] = a * b; + out[out_idx++] = a * numext::real(b); + out[out_idx++] = numext::real(a) * b; + out[out_idx++] = a / b; + out[out_idx++] = a / numext::real(b); + out[out_idx++] = numext::real(a) / b; + + out[out_idx] = a; out[out_idx++] += b; + out[out_idx] = a; out[out_idx++] -= b; + out[out_idx] = a; out[out_idx++] *= b; + out[out_idx] = a; out[out_idx++] /= b; + + const ComplexType true_value = ComplexType(ValueType(1), ValueType(0)); + const ComplexType false_value = ComplexType(ValueType(0), ValueType(0)); + out[out_idx++] = (a == b ? true_value : false_value); + out[out_idx++] = (a == numext::real(b) ? true_value : false_value); + out[out_idx++] = (numext::real(a) == b ? true_value : false_value); + out[out_idx++] = (a != b ? true_value : false_value); + out[out_idx++] = (a != numext::real(b) ? true_value : false_value); + out[out_idx++] = (numext::real(a) != b ? true_value : false_value); + + // Vector versions. + T x1(in + i); + T x2(in + i + 1); + const int res_size = T::MaxSizeAtCompileTime * num_scalar_operators; + const int size = T::MaxSizeAtCompileTime; + int block_idx = 0; + + Map> res(out + out_idx, res_size); + res.segment(block_idx, size) = -x1; + block_idx += size; + + res.segment(block_idx, size) = x1 + x2; + block_idx += size; + res.segment(block_idx, size) = x1 + x2.real(); + block_idx += size; + res.segment(block_idx, size) = x1.real() + x2; + block_idx += size; + res.segment(block_idx, size) = x1 - x2; + block_idx += size; + res.segment(block_idx, size) = x1 - x2.real(); + block_idx += size; + res.segment(block_idx, size) = x1.real() - x2; + block_idx += size; + res.segment(block_idx, size) = x1.array() * x2.array(); + block_idx += size; + res.segment(block_idx, size) = x1.array() * x2.real().array(); + block_idx += size; + res.segment(block_idx, size) = x1.real().array() * x2.array(); + block_idx += size; + res.segment(block_idx, size) = x1.array() / x2.array(); + block_idx += size; + res.segment(block_idx, size) = x1.array() / x2.real().array(); + block_idx += size; + res.segment(block_idx, size) = x1.real().array() / x2.array(); + block_idx += size; + + res.segment(block_idx, size) = x1; res.segment(block_idx, size) += x2; + block_idx += size; + res.segment(block_idx, size) = x1; res.segment(block_idx, size) -= x2; + block_idx += size; + res.segment(block_idx, size) = x1; res.segment(block_idx, size).array() *= x2.array(); + block_idx += size; + res.segment(block_idx, size) = x1; res.segment(block_idx, size).array() /= x2.array(); + block_idx += size; + + const T true_vector = T::Constant(true_value); + const T false_vector = T::Constant(false_value); + res.segment(block_idx, size) = (x1 == x2 ? true_vector : false_vector); + block_idx += size; + // Mixing types in equality comparison does not work. + // res.segment(block_idx, size) = (x1 == x2.real() ? true_vector : false_vector); + // block_idx += size; + // res.segment(block_idx, size) = (x1.real() == x2 ? true_vector : false_vector); + // block_idx += size; + res.segment(block_idx, size) = (x1 != x2 ? true_vector : false_vector); + block_idx += size; + // res.segment(block_idx, size) = (x1 != x2.real() ? true_vector : false_vector); + // block_idx += size; + // res.segment(block_idx, size) = (x1.real() != x2 ? true_vector : false_vector); + // block_idx += size; + } +}; + +template +struct replicate { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + T x1(in+i); + int step = x1.size() * 4; + int stride = 3 * step; + + typedef Map > MapType; + MapType(out+i*stride+0*step, x1.rows()*2, x1.cols()*2) = x1.replicate(2,2); + MapType(out+i*stride+1*step, x1.rows()*3, x1.cols()) = in[i] * x1.colwise().replicate(3); + MapType(out+i*stride+2*step, x1.rows(), x1.cols()*3) = in[i] * x1.rowwise().replicate(3); + } +}; + +template +struct alloc_new_delete { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + int offset = 2*i*T::MaxSizeAtCompileTime; + T* x = new T(in + offset); + Eigen::Map u(out + offset); + u = *x; + delete x; + + offset += T::MaxSizeAtCompileTime; + T* y = new T[1]; + y[0] = T(in + offset); + Eigen::Map v(out + offset); + v = y[0]; + delete[] y; + } +}; + +template +struct redux { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + int N = 10; + T x1(in+i); + out[i*N+0] = x1.minCoeff(); + out[i*N+1] = x1.maxCoeff(); + out[i*N+2] = x1.sum(); + out[i*N+3] = x1.prod(); + out[i*N+4] = x1.matrix().squaredNorm(); + out[i*N+5] = x1.matrix().norm(); + out[i*N+6] = x1.colwise().sum().maxCoeff(); + out[i*N+7] = x1.rowwise().maxCoeff().sum(); + out[i*N+8] = x1.matrix().colwise().squaredNorm().sum(); + } +}; + +template +struct prod_test { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const + { + using namespace Eigen; + typedef Matrix T3; + T1 x1(in+i); + T2 x2(in+i+1); + Map res(out+i*T3::MaxSizeAtCompileTime); + res += in[i] * x1 * x2; + } +}; + +template +struct diagonal { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T1::Scalar* in, typename T1::Scalar* out) const + { + using namespace Eigen; + T1 x1(in+i); + Map res(out+i*T2::MaxSizeAtCompileTime); + res += x1.diagonal(); + } +}; + +template +struct eigenvalues_direct { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + typedef Matrix Vec; + T M(in+i); + Map res(out+i*Vec::MaxSizeAtCompileTime); + T A = M*M.adjoint(); + SelfAdjointEigenSolver eig; + eig.computeDirect(A); + res = eig.eigenvalues(); + } +}; + +template +struct eigenvalues { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + typedef Matrix Vec; + T M(in+i); + Map res(out+i*Vec::MaxSizeAtCompileTime); + T A = M*M.adjoint(); + SelfAdjointEigenSolver eig; + eig.compute(A); + res = eig.eigenvalues(); + } +}; + +template +struct matrix_inverse { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + using namespace Eigen; + T M(in+i); + Map res(out+i*T::MaxSizeAtCompileTime); + res = M.inverse(); + } +}; + +template +struct numeric_limits_test { + EIGEN_DEVICE_FUNC + void operator()(int i, const typename T::Scalar* in, typename T::Scalar* out) const + { + EIGEN_UNUSED_VARIABLE(in) + int out_idx = i * 5; + out[out_idx++] = numext::numeric_limits::epsilon(); + out[out_idx++] = (numext::numeric_limits::max)(); + out[out_idx++] = (numext::numeric_limits::min)(); + out[out_idx++] = numext::numeric_limits::infinity(); + out[out_idx++] = numext::numeric_limits::quiet_NaN(); + } +}; + +template +bool verifyIsApproxWithInfsNans(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only +{ + if (a.rows() != b.rows()) { + return false; + } + if (a.cols() != b.cols()) { + return false; + } + for (Index r = 0; r < a.rows(); ++r) { + for (Index c = 0; c < a.cols(); ++c) { + if (a(r, c) != b(r, c) + && !((numext::isnan)(a(r, c)) && (numext::isnan)(b(r, c))) + && !test_isApprox(a(r, c), b(r, c))) { + return false; + } + } + } + return true; +} + +template +void test_with_infs_nans(const Kernel& ker, int n, const Input& in, Output& out) +{ + Output out_ref, out_gpu; + #if !defined(EIGEN_GPU_COMPILE_PHASE) + out_ref = out_gpu = out; + #else + EIGEN_UNUSED_VARIABLE(in); + EIGEN_UNUSED_VARIABLE(out); + #endif + run_on_cpu (ker, n, in, out_ref); + run_on_gpu(ker, n, in, out_gpu); + #if !defined(EIGEN_GPU_COMPILE_PHASE) + verifyIsApproxWithInfsNans(out_ref, out_gpu); + #endif +} + +EIGEN_DECLARE_TEST(gpu_basic) +{ + ei_test_init_gpu(); + + int nthreads = 100; + Eigen::VectorXf in, out; + Eigen::VectorXcf cfin, cfout; + + #if !defined(EIGEN_GPU_COMPILE_PHASE) + int data_size = nthreads * 512; + in.setRandom(data_size); + out.setConstant(data_size, -1); + cfin.setRandom(data_size); + cfout.setConstant(data_size, -1); + #endif + + CALL_SUBTEST( run_and_compare_to_gpu(coeff_wise(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(coeff_wise(), nthreads, in, out) ); + +#if !defined(EIGEN_USE_HIP) + // FIXME + // These subtests result in a compile failure on the HIP platform + // + // eigen-upstream/Eigen/src/Core/Replicate.h:61:65: error: + // base class 'internal::dense_xpr_base, -1, -1> >::type' + // (aka 'ArrayBase, -1, -1> >') has protected default constructor + CALL_SUBTEST( run_and_compare_to_gpu(replicate(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(replicate(), nthreads, in, out) ); + + // HIP does not support new/delete on device. + CALL_SUBTEST( run_and_compare_to_gpu(alloc_new_delete(), nthreads, in, out) ); +#endif + + CALL_SUBTEST( run_and_compare_to_gpu(redux(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(redux(), nthreads, in, out) ); + + CALL_SUBTEST( run_and_compare_to_gpu(prod_test(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(prod_test(), nthreads, in, out) ); + + CALL_SUBTEST( run_and_compare_to_gpu(diagonal(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(diagonal(), nthreads, in, out) ); + + CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(matrix_inverse(), nthreads, in, out) ); + + CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues_direct(), nthreads, in, out) ); + CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues_direct(), nthreads, in, out) ); + + // Test std::complex. + CALL_SUBTEST( run_and_compare_to_gpu(complex_operators(), nthreads, cfin, cfout) ); + CALL_SUBTEST( test_with_infs_nans(complex_sqrt(), nthreads, cfin, cfout) ); + + // numeric_limits + CALL_SUBTEST( test_with_infs_nans(numeric_limits_test(), 1, in, out) ); + +#if defined(__NVCC__) + // FIXME + // These subtests compiles only with nvcc and fail with HIPCC and clang-cuda + CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues(), nthreads, in, out) ); + typedef Matrix Matrix6f; + CALL_SUBTEST( run_and_compare_to_gpu(eigenvalues(), nthreads, in, out) ); +#endif +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_common.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_common.h new file mode 100644 index 0000000000000000000000000000000000000000..c37eaa13fc372c792d9ff5ee97fafb0007055e92 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/gpu_common.h @@ -0,0 +1,176 @@ +#ifndef EIGEN_TEST_GPU_COMMON_H +#define EIGEN_TEST_GPU_COMMON_H + +#ifdef EIGEN_USE_HIP + #include + #include +#else + #include + #include + #include +#endif + +#include + +#define EIGEN_USE_GPU +#include + +#if !defined(__CUDACC__) && !defined(__HIPCC__) +dim3 threadIdx, blockDim, blockIdx; +#endif + +template +void run_on_cpu(const Kernel& ker, int n, const Input& in, Output& out) +{ + for(int i=0; i +__global__ +EIGEN_HIP_LAUNCH_BOUNDS_1024 +void run_on_gpu_meta_kernel(const Kernel ker, int n, const Input* in, Output* out) +{ + int i = threadIdx.x + blockIdx.x*blockDim.x; + if(i +void run_on_gpu(const Kernel& ker, int n, const Input& in, Output& out) +{ + typename Input::Scalar* d_in; + typename Output::Scalar* d_out; + std::ptrdiff_t in_bytes = in.size() * sizeof(typename Input::Scalar); + std::ptrdiff_t out_bytes = out.size() * sizeof(typename Output::Scalar); + + gpuMalloc((void**)(&d_in), in_bytes); + gpuMalloc((void**)(&d_out), out_bytes); + + gpuMemcpy(d_in, in.data(), in_bytes, gpuMemcpyHostToDevice); + gpuMemcpy(d_out, out.data(), out_bytes, gpuMemcpyHostToDevice); + + // Simple and non-optimal 1D mapping assuming n is not too large + // That's only for unit testing! + dim3 Blocks(128); + dim3 Grids( (n+int(Blocks.x)-1)/int(Blocks.x) ); + + gpuDeviceSynchronize(); + +#ifdef EIGEN_USE_HIP + hipLaunchKernelGGL(HIP_KERNEL_NAME(run_on_gpu_meta_kernel::type, + typename std::decay::type>), + dim3(Grids), dim3(Blocks), 0, 0, ker, n, d_in, d_out); +#else + run_on_gpu_meta_kernel<<>>(ker, n, d_in, d_out); +#endif + // Pre-launch errors. + gpuError_t err = gpuGetLastError(); + if (err != gpuSuccess) { + printf("%s: %s\n", gpuGetErrorName(err), gpuGetErrorString(err)); + gpu_assert(false); + } + + // Kernel execution errors. + err = gpuDeviceSynchronize(); + if (err != gpuSuccess) { + printf("%s: %s\n", gpuGetErrorName(err), gpuGetErrorString(err)); + gpu_assert(false); + } + + + // check inputs have not been modified + gpuMemcpy(const_cast(in.data()), d_in, in_bytes, gpuMemcpyDeviceToHost); + gpuMemcpy(out.data(), d_out, out_bytes, gpuMemcpyDeviceToHost); + + gpuFree(d_in); + gpuFree(d_out); +} + + +template +void run_and_compare_to_gpu(const Kernel& ker, int n, const Input& in, Output& out) +{ + Input in_ref, in_gpu; + Output out_ref, out_gpu; + #if !defined(EIGEN_GPU_COMPILE_PHASE) + in_ref = in_gpu = in; + out_ref = out_gpu = out; + #else + EIGEN_UNUSED_VARIABLE(in); + EIGEN_UNUSED_VARIABLE(out); + #endif + run_on_cpu (ker, n, in_ref, out_ref); + run_on_gpu(ker, n, in_gpu, out_gpu); + #if !defined(EIGEN_GPU_COMPILE_PHASE) + VERIFY_IS_APPROX(in_ref, in_gpu); + VERIFY_IS_APPROX(out_ref, out_gpu); + #endif +} + +struct compile_time_device_info { + EIGEN_DEVICE_FUNC + void operator()(int i, const int* /*in*/, int* info) const + { + if (i == 0) { + EIGEN_UNUSED_VARIABLE(info) + #if defined(__CUDA_ARCH__) + info[0] = int(__CUDA_ARCH__ +0); + #endif + #if defined(EIGEN_HIP_DEVICE_COMPILE) + info[1] = int(EIGEN_HIP_DEVICE_COMPILE +0); + #endif + } + } +}; + +void ei_test_init_gpu() +{ + int device = 0; + gpuDeviceProp_t deviceProp; + gpuGetDeviceProperties(&deviceProp, device); + + ArrayXi dummy(1), info(10); + info = -1; + run_on_gpu(compile_time_device_info(),10,dummy,info); + + + std::cout << "GPU compile-time info:\n"; + + #ifdef EIGEN_CUDACC + std::cout << " EIGEN_CUDACC: " << int(EIGEN_CUDACC) << "\n"; + #endif + + #ifdef EIGEN_CUDA_SDK_VER + std::cout << " EIGEN_CUDA_SDK_VER: " << int(EIGEN_CUDA_SDK_VER) << "\n"; + #endif + + #ifdef EIGEN_COMP_NVCC + std::cout << " EIGEN_COMP_NVCC: " << int(EIGEN_COMP_NVCC) << "\n"; + #endif + + #ifdef EIGEN_HIPCC + std::cout << " EIGEN_HIPCC: " << int(EIGEN_HIPCC) << "\n"; + #endif + + std::cout << " EIGEN_CUDA_ARCH: " << info[0] << "\n"; + std::cout << " EIGEN_HIP_DEVICE_COMPILE: " << info[1] << "\n"; + + std::cout << "GPU device info:\n"; + std::cout << " name: " << deviceProp.name << "\n"; + std::cout << " capability: " << deviceProp.major << "." << deviceProp.minor << "\n"; + std::cout << " multiProcessorCount: " << deviceProp.multiProcessorCount << "\n"; + std::cout << " maxThreadsPerMultiProcessor: " << deviceProp.maxThreadsPerMultiProcessor << "\n"; + std::cout << " warpSize: " << deviceProp.warpSize << "\n"; + std::cout << " regsPerBlock: " << deviceProp.regsPerBlock << "\n"; + std::cout << " concurrentKernels: " << deviceProp.concurrentKernels << "\n"; + std::cout << " clockRate: " << deviceProp.clockRate << "\n"; + std::cout << " canMapHostMemory: " << deviceProp.canMapHostMemory << "\n"; + std::cout << " computeMode: " << deviceProp.computeMode << "\n"; +} + +#endif // EIGEN_TEST_GPU_COMMON_H diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/half_float.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/half_float.cpp new file mode 100644 index 0000000000000000000000000000000000000000..729de1bc725d2b0d4db43c7f9e48f90de92b50be --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/half_float.cpp @@ -0,0 +1,349 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include + +#include "main.h" + +#include + +#define VERIFY_HALF_BITS_EQUAL(h, bits) \ + VERIFY_IS_EQUAL((numext::bit_cast(h)), (static_cast(bits))) + +// Make sure it's possible to forward declare Eigen::half +namespace Eigen { +struct half; +} + +using Eigen::half; + +void test_conversion() +{ + using Eigen::half_impl::__half_raw; + + // Round-trip bit-cast with uint16. + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(half(1.0f))), + half(1.0f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(half(0.5f))), + half(0.5f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(half(-0.33333f))), + half(-0.33333f)); + VERIFY_IS_EQUAL( + numext::bit_cast(numext::bit_cast(half(0.0f))), + half(0.0f)); + + // Conversion from float. + VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00); + VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800); + VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555); + VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000); + VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000); + VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff); + VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00); // Becomes infinity. + + // Denormals. + VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001); + VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001); + VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002); + + // Verify round-to-nearest-even behavior. + float val1 = float(half(__half_raw(0x3c00))); + float val2 = float(half(__half_raw(0x3c01))); + float val3 = float(half(__half_raw(0x3c02))); + VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00); + VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02); + + // Conversion from int. + VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00); + VERIFY_HALF_BITS_EQUAL(half(0), 0x0000); + VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00); + VERIFY_HALF_BITS_EQUAL(half(2), 0x4000); + VERIFY_HALF_BITS_EQUAL(half(3), 0x4200); + + // Conversion from bool. + VERIFY_HALF_BITS_EQUAL(half(false), 0x0000); + VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00); + + // Conversion to float. + VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f); + VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f); + + // Denormals. + VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f); + VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f); + VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f); + + // NaNs and infinities. + VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number. + VERIFY(!(numext::isnan)(float(half(0.0f)))); + VERIFY((numext::isinf)(float(half(__half_raw(0xfc00))))); + VERIFY((numext::isnan)(float(half(__half_raw(0xfc01))))); + VERIFY((numext::isinf)(float(half(__half_raw(0x7c00))))); + VERIFY((numext::isnan)(float(half(__half_raw(0x7c01))))); + +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(float(half(0.0 / 0.0)))); + VERIFY((numext::isinf)(float(half(1.0 / 0.0)))); + VERIFY((numext::isinf)(float(half(-1.0 / 0.0)))); +#endif + + // Exactly same checks as above, just directly on the half representation. + VERIFY(!(numext::isinf)(half(__half_raw(0x7bff)))); + VERIFY(!(numext::isnan)(half(__half_raw(0x0000)))); + VERIFY((numext::isinf)(half(__half_raw(0xfc00)))); + VERIFY((numext::isnan)(half(__half_raw(0xfc01)))); + VERIFY((numext::isinf)(half(__half_raw(0x7c00)))); + VERIFY((numext::isnan)(half(__half_raw(0x7c01)))); + +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY((numext::isnan)(half(0.0 / 0.0))); + VERIFY((numext::isinf)(half(1.0 / 0.0))); + VERIFY((numext::isinf)(half(-1.0 / 0.0))); +#endif + + // Conversion to bool + VERIFY(!static_cast(half(0.0))); + VERIFY(!static_cast(half(-0.0))); + VERIFY(static_cast(half(__half_raw(0x7bff)))); + VERIFY(static_cast(half(-0.33333))); + VERIFY(static_cast(half(1.0))); + VERIFY(static_cast(half(-1.0))); + VERIFY(static_cast(half(-5.96046e-08f))); +} + +void test_numtraits() +{ + std::cout << "epsilon = " << NumTraits::epsilon() << " (0x" << std::hex << numext::bit_cast(NumTraits::epsilon()) << ")" << std::endl; + std::cout << "highest = " << NumTraits::highest() << " (0x" << std::hex << numext::bit_cast(NumTraits::highest()) << ")" << std::endl; + std::cout << "lowest = " << NumTraits::lowest() << " (0x" << std::hex << numext::bit_cast(NumTraits::lowest()) << ")" << std::endl; + std::cout << "min = " << (std::numeric_limits::min)() << " (0x" << std::hex << numext::bit_cast(half((std::numeric_limits::min)())) << ")" << std::endl; + std::cout << "denorm min = " << (std::numeric_limits::denorm_min)() << " (0x" << std::hex << numext::bit_cast(half((std::numeric_limits::denorm_min)())) << ")" << std::endl; + std::cout << "infinity = " << NumTraits::infinity() << " (0x" << std::hex << numext::bit_cast(NumTraits::infinity()) << ")" << std::endl; + std::cout << "quiet nan = " << NumTraits::quiet_NaN() << " (0x" << std::hex << numext::bit_cast(NumTraits::quiet_NaN()) << ")" << std::endl; + std::cout << "signaling nan = " << std::numeric_limits::signaling_NaN() << " (0x" << std::hex << numext::bit_cast(std::numeric_limits::signaling_NaN()) << ")" << std::endl; + + VERIFY(NumTraits::IsSigned); + + VERIFY_IS_EQUAL( + numext::bit_cast(std::numeric_limits::infinity()), + numext::bit_cast(half(std::numeric_limits::infinity())) ); + // There is no guarantee that casting a 32-bit NaN to 16-bit has a precise + // bit pattern. We test that it is in fact a NaN, then test the signaling + // bit (msb of significand is 1 for quiet, 0 for signaling). + const numext::uint16_t HALF_QUIET_BIT = 0x0200; + VERIFY( + (numext::isnan)(std::numeric_limits::quiet_NaN()) + && (numext::isnan)(half(std::numeric_limits::quiet_NaN())) + && ((numext::bit_cast(std::numeric_limits::quiet_NaN()) & HALF_QUIET_BIT) > 0) + && ((numext::bit_cast(half(std::numeric_limits::quiet_NaN())) & HALF_QUIET_BIT) > 0) ); + // After a cast to half, a signaling NaN may become non-signaling + // (e.g. in the case of casting float to native __fp16). Thus, we check that + // both are NaN, and that only the `numeric_limits` version is signaling. + VERIFY( + (numext::isnan)(std::numeric_limits::signaling_NaN()) + && (numext::isnan)(half(std::numeric_limits::signaling_NaN())) + && ((numext::bit_cast(std::numeric_limits::signaling_NaN()) & HALF_QUIET_BIT) == 0) ); + + VERIFY( (std::numeric_limits::min)() > half(0.f) ); + VERIFY( (std::numeric_limits::denorm_min)() > half(0.f) ); + VERIFY( (std::numeric_limits::min)()/half(2) > half(0.f) ); + VERIFY_IS_EQUAL( (std::numeric_limits::denorm_min)()/half(2), half(0.f) ); +} + +void test_arithmetic() +{ + VERIFY_IS_EQUAL(float(half(2) + half(2)), 4); + VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0); + VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f); + VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f); + VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f); + VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f); + VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f); + + half x(3); + half y = ++x; + VERIFY_IS_EQUAL(x, half(4)); + VERIFY_IS_EQUAL(y, half(4)); + y = --x; + VERIFY_IS_EQUAL(x, half(3)); + VERIFY_IS_EQUAL(y, half(3)); + y = x++; + VERIFY_IS_EQUAL(x, half(4)); + VERIFY_IS_EQUAL(y, half(3)); + y = x--; + VERIFY_IS_EQUAL(x, half(3)); + VERIFY_IS_EQUAL(y, half(4)); +} + +void test_comparison() +{ + VERIFY(half(1.0f) > half(0.5f)); + VERIFY(half(0.5f) < half(1.0f)); + VERIFY(!(half(1.0f) < half(0.5f))); + VERIFY(!(half(0.5f) > half(1.0f))); + + VERIFY(!(half(4.0f) > half(4.0f))); + VERIFY(!(half(4.0f) < half(4.0f))); + + VERIFY(!(half(0.0f) < half(-0.0f))); + VERIFY(!(half(-0.0f) < half(0.0f))); + VERIFY(!(half(0.0f) > half(-0.0f))); + VERIFY(!(half(-0.0f) > half(0.0f))); + + VERIFY(half(0.2f) > half(-1.0f)); + VERIFY(half(-1.0f) < half(0.2f)); + VERIFY(half(-16.0f) < half(-15.0f)); + + VERIFY(half(1.0f) == half(1.0f)); + VERIFY(half(1.0f) != half(2.0f)); + + // Comparisons with NaNs and infinities. +#if !EIGEN_COMP_MSVC + // Visual Studio errors out on divisions by 0 + VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0))); + VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0)); + + VERIFY(!(half(1.0) == half(0.0 / 0.0))); + VERIFY(!(half(1.0) < half(0.0 / 0.0))); + VERIFY(!(half(1.0) > half(0.0 / 0.0))); + VERIFY(half(1.0) != half(0.0 / 0.0)); + + VERIFY(half(1.0) < half(1.0 / 0.0)); + VERIFY(half(1.0) > half(-1.0 / 0.0)); +#endif +} + +void test_basic_functions() +{ + VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f); + VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f); + + VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f); + VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f); + VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f); + VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f); + + VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f); + VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f); + VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f); + VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f); + + VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f); + VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f); + + VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f); + VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f); + + VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f); + VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f); + VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI)); + VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI)); + + VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f); + VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f); + VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f); + + VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f); + VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f); + VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f); + + VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f); + VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f); + VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f); + VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f); + + VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f)); + VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f)); + VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f)); + VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f)); +} + +void test_trigonometric_functions() +{ + VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f))); + VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f))); + VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI))); + // VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2))); + // VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f))); + + VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f))); + VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f))); + // VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI))); + VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f))); + + VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f))); + VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f))); + // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI))); + // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2))); + //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2))); + VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f))); +} + +void test_array() +{ + typedef Array ArrayXh; + Index size = internal::random(1,10); + Index i = internal::random(0,size-1); + ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size); + VERIFY_IS_APPROX( a1+a1, half(2)*a1 ); + VERIFY( (a1.abs() >= half(0)).all() ); + VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() ); + + VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() ); + a1(i) = half(-10.); + VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) ); + a1(i) = half(10.); + VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) ); + + std::stringstream ss; + ss << a1; +} + +void test_product() +{ + typedef Matrix MatrixXh; + Index rows = internal::random(1,EIGEN_TEST_MAX_SIZE); + Index cols = internal::random(1,EIGEN_TEST_MAX_SIZE); + Index depth = internal::random(1,EIGEN_TEST_MAX_SIZE); + MatrixXh Ah = MatrixXh::Random(rows,depth); + MatrixXh Bh = MatrixXh::Random(depth,cols); + MatrixXh Ch = MatrixXh::Random(rows,cols); + MatrixXf Af = Ah.cast(); + MatrixXf Bf = Bh.cast(); + MatrixXf Cf = Ch.cast(); + VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast()); +} + +EIGEN_DECLARE_TEST(half_float) +{ + CALL_SUBTEST(test_numtraits()); + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST(test_conversion()); + CALL_SUBTEST(test_arithmetic()); + CALL_SUBTEST(test_comparison()); + CALL_SUBTEST(test_basic_functions()); + CALL_SUBTEST(test_trigonometric_functions()); + CALL_SUBTEST(test_array()); + CALL_SUBTEST(test_product()); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/hessenberg.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/hessenberg.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0e1b0098dacd12ea9cef0648ca8212a8906450f5 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/hessenberg.cpp @@ -0,0 +1,62 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Gael Guennebaud +// Copyright (C) 2010 Jitse Niesen +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template void hessenberg(int size = Size) +{ + typedef Matrix MatrixType; + + // Test basic functionality: A = U H U* and H is Hessenberg + for(int counter = 0; counter < g_repeat; ++counter) { + MatrixType m = MatrixType::Random(size,size); + HessenbergDecomposition hess(m); + MatrixType Q = hess.matrixQ(); + MatrixType H = hess.matrixH(); + VERIFY_IS_APPROX(m, Q * H * Q.adjoint()); + for(int row = 2; row < size; ++row) { + for(int col = 0; col < row-1; ++col) { + VERIFY(H(row,col) == (typename MatrixType::Scalar)0); + } + } + } + + // Test whether compute() and constructor returns same result + MatrixType A = MatrixType::Random(size, size); + HessenbergDecomposition cs1; + cs1.compute(A); + HessenbergDecomposition cs2(A); + VERIFY_IS_EQUAL(cs1.matrixH().eval(), cs2.matrixH().eval()); + MatrixType cs1Q = cs1.matrixQ(); + MatrixType cs2Q = cs2.matrixQ(); + VERIFY_IS_EQUAL(cs1Q, cs2Q); + + // Test assertions for when used uninitialized + HessenbergDecomposition hessUninitialized; + VERIFY_RAISES_ASSERT( hessUninitialized.matrixH() ); + VERIFY_RAISES_ASSERT( hessUninitialized.matrixQ() ); + VERIFY_RAISES_ASSERT( hessUninitialized.householderCoefficients() ); + VERIFY_RAISES_ASSERT( hessUninitialized.packedMatrix() ); + + // TODO: Add tests for packedMatrix() and householderCoefficients() +} + +EIGEN_DECLARE_TEST(hessenberg) +{ + CALL_SUBTEST_1(( hessenberg,1>() )); + CALL_SUBTEST_2(( hessenberg,2>() )); + CALL_SUBTEST_3(( hessenberg,4>() )); + CALL_SUBTEST_4(( hessenberg(internal::random(1,EIGEN_TEST_MAX_SIZE)) )); + CALL_SUBTEST_5(( hessenberg,Dynamic>(internal::random(1,EIGEN_TEST_MAX_SIZE)) )); + + // Test problem size constructors + CALL_SUBTEST_6(HessenbergDecomposition(10)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/householder.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/householder.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cad8138a2aa11701d2b14a5ccf3d864539c6eb37 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/householder.cpp @@ -0,0 +1,148 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template void householder(const MatrixType& m) +{ + static bool even = true; + even = !even; + /* this test covers the following files: + Householder.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix VectorType; + typedef Matrix::ret, 1> EssentialVectorType; + typedef Matrix SquareMatrixType; + typedef Matrix HBlockMatrixType; + typedef Matrix HCoeffsVectorType; + + typedef Matrix TMatrixType; + + Matrix _tmp((std::max)(rows,cols)); + Scalar* tmp = &_tmp.coeffRef(0,0); + + Scalar beta; + RealScalar alpha; + EssentialVectorType essential; + + VectorType v1 = VectorType::Random(rows), v2; + v2 = v1; + v1.makeHouseholder(essential, beta, alpha); + v1.applyHouseholderOnTheLeft(essential,beta,tmp); + VERIFY_IS_APPROX(v1.norm(), v2.norm()); + if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows-1).norm(), v1.norm()); + v1 = VectorType::Random(rows); + v2 = v1; + v1.applyHouseholderOnTheLeft(essential,beta,tmp); + VERIFY_IS_APPROX(v1.norm(), v2.norm()); + + // reconstruct householder matrix: + SquareMatrixType id, H1, H2; + id.setIdentity(rows, rows); + H1 = H2 = id; + VectorType vv(rows); + vv << Scalar(1), essential; + H1.applyHouseholderOnTheLeft(essential, beta, tmp); + H2.applyHouseholderOnTheRight(essential, beta, tmp); + VERIFY_IS_APPROX(H1, H2); + VERIFY_IS_APPROX(H1, id - beta * vv*vv.adjoint()); + + MatrixType m1(rows, cols), + m2(rows, cols); + + v1 = VectorType::Random(rows); + if(even) v1.tail(rows-1).setZero(); + m1.colwise() = v1; + m2 = m1; + m1.col(0).makeHouseholder(essential, beta, alpha); + m1.applyHouseholderOnTheLeft(essential,beta,tmp); + VERIFY_IS_APPROX(m1.norm(), m2.norm()); + if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1,0,rows-1,cols).norm(), m1.norm()); + VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0,0)), numext::real(m1(0,0))); + VERIFY_IS_APPROX(numext::real(m1(0,0)), alpha); + + v1 = VectorType::Random(rows); + if(even) v1.tail(rows-1).setZero(); + SquareMatrixType m3(rows,rows), m4(rows,rows); + m3.rowwise() = v1.transpose(); + m4 = m3; + m3.row(0).makeHouseholder(essential, beta, alpha); + m3.applyHouseholderOnTheRight(essential.conjugate(),beta,tmp); + VERIFY_IS_APPROX(m3.norm(), m4.norm()); + if(rows>=2) VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0,1,rows,rows-1).norm(), m3.norm()); + VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0,0)), numext::real(m3(0,0))); + VERIFY_IS_APPROX(numext::real(m3(0,0)), alpha); + + // test householder sequence on the left with a shift + + Index shift = internal::random(0, std::max(rows-2,0)); + Index brows = rows - shift; + m1.setRandom(rows, cols); + HBlockMatrixType hbm = m1.block(shift,0,brows,cols); + HouseholderQR qr(hbm); + m2 = m1; + m2.block(shift,0,brows,cols) = qr.matrixQR(); + HCoeffsVectorType hc = qr.hCoeffs().conjugate(); + HouseholderSequence hseq(m2, hc); + hseq.setLength(hc.size()).setShift(shift); + VERIFY(hseq.length() == hc.size()); + VERIFY(hseq.shift() == shift); + + MatrixType m5 = m2; + m5.block(shift,0,brows,cols).template triangularView().setZero(); + VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly + m3 = hseq; + VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying + + SquareMatrixType hseq_mat = hseq; + SquareMatrixType hseq_mat_conj = hseq.conjugate(); + SquareMatrixType hseq_mat_adj = hseq.adjoint(); + SquareMatrixType hseq_mat_trans = hseq.transpose(); + SquareMatrixType m6 = SquareMatrixType::Random(rows, rows); + VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj); + VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj); + VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans); + VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6); + VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6); + VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6); + VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6); + VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat); + VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj); + VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj); + VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans); + + // test householder sequence on the right with a shift + + TMatrixType tm2 = m2.transpose(); + HouseholderSequence rhseq(tm2, hc); + rhseq.setLength(hc.size()).setShift(shift); + VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly + m3 = rhseq; + VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying +} + +EIGEN_DECLARE_TEST(householder) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( householder(Matrix()) ); + CALL_SUBTEST_2( householder(Matrix()) ); + CALL_SUBTEST_3( householder(Matrix()) ); + CALL_SUBTEST_4( householder(Matrix()) ); + CALL_SUBTEST_5( householder(MatrixXd(internal::random(1,EIGEN_TEST_MAX_SIZE),internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( householder(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE),internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_7( householder(MatrixXf(internal::random(1,EIGEN_TEST_MAX_SIZE),internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_8( householder(Matrix()) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/incomplete_cholesky.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/incomplete_cholesky.cpp new file mode 100644 index 0000000000000000000000000000000000000000..ecc17f5c3582cbf3d39089ac0496dfec197b737b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/incomplete_cholesky.cpp @@ -0,0 +1,69 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015-2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +// #define EIGEN_DONT_VECTORIZE +// #define EIGEN_MAX_ALIGN_BYTES 0 +#include "sparse_solver.h" +#include +#include + +template void test_incomplete_cholesky_T() +{ + typedef SparseMatrix SparseMatrixType; + ConjugateGradient > > cg_illt_lower_amd; + ConjugateGradient > > cg_illt_lower_nat; + ConjugateGradient > > cg_illt_upper_amd; + ConjugateGradient > > cg_illt_upper_nat; + ConjugateGradient > > cg_illt_uplo_amd; + + + CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_amd) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_illt_lower_nat) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_amd) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_illt_upper_nat) ); + CALL_SUBTEST( check_sparse_spd_solving(cg_illt_uplo_amd) ); +} + +template +void bug1150() +{ + // regression for bug 1150 + for(int N = 1; N<20; ++N) + { + Eigen::MatrixXd b( N, N ); + b.setOnes(); + + Eigen::SparseMatrix m( N, N ); + m.reserve(Eigen::VectorXi::Constant(N,4)); + for( int i = 0; i < N; ++i ) + { + m.insert( i, i ) = 1; + m.coeffRef( i, i / 2 ) = 2; + m.coeffRef( i, i / 3 ) = 2; + m.coeffRef( i, i / 4 ) = 2; + } + + Eigen::SparseMatrix A; + A = m * m.transpose(); + + Eigen::ConjugateGradient, + Eigen::Lower | Eigen::Upper, + Eigen::IncompleteCholesky > solver( A ); + VERIFY(solver.preconditioner().info() == Eigen::Success); + VERIFY(solver.info() == Eigen::Success); + } +} + +EIGEN_DECLARE_TEST(incomplete_cholesky) +{ + CALL_SUBTEST_1(( test_incomplete_cholesky_T() )); + CALL_SUBTEST_2(( test_incomplete_cholesky_T, int>() )); + CALL_SUBTEST_3(( test_incomplete_cholesky_T() )); + + CALL_SUBTEST_1(( bug1150<0>() )); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/indexed_view.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/indexed_view.cpp new file mode 100644 index 0000000000000000000000000000000000000000..72c54af6845ec34de338a34222738b50dab7838b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/indexed_view.cpp @@ -0,0 +1,473 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2017 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifdef EIGEN_TEST_PART_2 +// Make sure we also check c++11 max implementation +#define EIGEN_MAX_CPP_VER 11 +#endif + +#ifdef EIGEN_TEST_PART_3 +// Make sure we also check c++98 max implementation +#define EIGEN_MAX_CPP_VER 03 + +// We need to disable this warning when compiling with c++11 while limiting Eigen to c++98 +// Ideally we would rather configure the compiler to build in c++98 mode but this needs +// to be done at the CMakeLists.txt level. +#if defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 8)) + #pragma GCC diagnostic ignored "-Wdeprecated" +#endif + +#if defined(__GNUC__) && (__GNUC__ >=9) + #pragma GCC diagnostic ignored "-Wdeprecated-copy" +#endif +#if defined(__clang__) && (__clang_major__ >= 10) + #pragma clang diagnostic ignored "-Wdeprecated-copy" +#endif + +#endif + +#include +#include +#include "main.h" + +#if EIGEN_HAS_CXX11 +#include +#endif + +typedef std::pair IndexPair; + +int encode(Index i, Index j) { + return int(i*100 + j); +} + +IndexPair decode(Index ij) { + return IndexPair(ij / 100, ij % 100); +} + +template +bool match(const T& xpr, std::string ref, std::string str_xpr = "") { + EIGEN_UNUSED_VARIABLE(str_xpr); + std::stringstream str; + str << xpr; + if(!(str.str() == ref)) + std::cout << str_xpr << "\n" << xpr << "\n\n"; + return str.str() == ref; +} + +#define MATCH(X,R) match(X, R, #X) + +template +typename internal::enable_if::value,bool>::type +is_same_eq(const T1& a, const T2& b) +{ + return (a == b).all(); +} + +template +bool is_same_seq(const T1& a, const T2& b) +{ + bool ok = a.first()==b.first() && a.size() == b.size() && Index(a.incrObject())==Index(b.incrObject());; + if(!ok) + { + std::cerr << "seqN(" << a.first() << ", " << a.size() << ", " << Index(a.incrObject()) << ") != "; + std::cerr << "seqN(" << b.first() << ", " << b.size() << ", " << Index(b.incrObject()) << ")\n"; + } + return ok; +} + +template +typename internal::enable_if::value,bool>::type +is_same_seq_type(const T1& a, const T2& b) +{ + return is_same_seq(a,b); +} + + + +#define VERIFY_EQ_INT(A,B) VERIFY_IS_APPROX(int(A),int(B)) + +// C++03 does not allow local or unnamed enums as index +enum DummyEnum { XX=0, YY=1 }; + +void check_indexed_view() +{ + Index n = 10; + + ArrayXd a = ArrayXd::LinSpaced(n,0,n-1); + Array b = a.transpose(); + + #if EIGEN_COMP_CXXVER>=14 + ArrayXXi A = ArrayXXi::NullaryExpr(n,n, std::ref(encode)); + #else + ArrayXXi A = ArrayXXi::NullaryExpr(n,n, std::ptr_fun(&encode)); + #endif + + for(Index i=0; i vali(4); Map(&vali[0],4) = eii; + std::vector veci(4); Map(veci.data(),4) = eii; + + VERIFY( MATCH( A(3, seq(9,3,-1)), + "309 308 307 306 305 304 303") + ); + + VERIFY( MATCH( A(seqN(2,5), seq(9,3,-1)), + "209 208 207 206 205 204 203\n" + "309 308 307 306 305 304 303\n" + "409 408 407 406 405 404 403\n" + "509 508 507 506 505 504 503\n" + "609 608 607 606 605 604 603") + ); + + VERIFY( MATCH( A(seqN(2,5), 5), + "205\n" + "305\n" + "405\n" + "505\n" + "605") + ); + + VERIFY( MATCH( A(seqN(last,5,-1), seq(2,last)), + "902 903 904 905 906 907 908 909\n" + "802 803 804 805 806 807 808 809\n" + "702 703 704 705 706 707 708 709\n" + "602 603 604 605 606 607 608 609\n" + "502 503 504 505 506 507 508 509") + ); + + VERIFY( MATCH( A(eii, veci), + "303 301 306 305\n" + "103 101 106 105\n" + "603 601 606 605\n" + "503 501 506 505") + ); + + VERIFY( MATCH( A(eii, all), + "300 301 302 303 304 305 306 307 308 309\n" + "100 101 102 103 104 105 106 107 108 109\n" + "600 601 602 603 604 605 606 607 608 609\n" + "500 501 502 503 504 505 506 507 508 509") + ); + + // take row number 3, and repeat it 5 times + VERIFY( MATCH( A(seqN(3,5,0), all), + "300 301 302 303 304 305 306 307 308 309\n" + "300 301 302 303 304 305 306 307 308 309\n" + "300 301 302 303 304 305 306 307 308 309\n" + "300 301 302 303 304 305 306 307 308 309\n" + "300 301 302 303 304 305 306 307 308 309") + ); + + VERIFY( MATCH( a(seqN(3,3),0), "3\n4\n5" ) ); + VERIFY( MATCH( a(seq(3,5)), "3\n4\n5" ) ); + VERIFY( MATCH( a(seqN(3,3,1)), "3\n4\n5" ) ); + VERIFY( MATCH( a(seqN(5,3,-1)), "5\n4\n3" ) ); + + VERIFY( MATCH( b(0,seqN(3,3)), "3 4 5" ) ); + VERIFY( MATCH( b(seq(3,5)), "3 4 5" ) ); + VERIFY( MATCH( b(seqN(3,3,1)), "3 4 5" ) ); + VERIFY( MATCH( b(seqN(5,3,-1)), "5 4 3" ) ); + + VERIFY( MATCH( b(all), "0 1 2 3 4 5 6 7 8 9" ) ); + VERIFY( MATCH( b(eii), "3 1 6 5" ) ); + + Array44i B; + B.setRandom(); + VERIFY( (A(seqN(2,5), 5)).ColsAtCompileTime == 1); + VERIFY( (A(seqN(2,5), 5)).RowsAtCompileTime == Dynamic); + VERIFY_EQ_INT( (A(seqN(2,5), 5)).InnerStrideAtCompileTime , A.InnerStrideAtCompileTime); + VERIFY_EQ_INT( (A(seqN(2,5), 5)).OuterStrideAtCompileTime , A.col(5).OuterStrideAtCompileTime); + + VERIFY_EQ_INT( (A(5,seqN(2,5))).InnerStrideAtCompileTime , A.row(5).InnerStrideAtCompileTime); + VERIFY_EQ_INT( (A(5,seqN(2,5))).OuterStrideAtCompileTime , A.row(5).OuterStrideAtCompileTime); + VERIFY_EQ_INT( (B(1,seqN(1,2))).InnerStrideAtCompileTime , B.row(1).InnerStrideAtCompileTime); + VERIFY_EQ_INT( (B(1,seqN(1,2))).OuterStrideAtCompileTime , B.row(1).OuterStrideAtCompileTime); + + VERIFY_EQ_INT( (A(seqN(2,5), seq(1,3))).InnerStrideAtCompileTime , A.InnerStrideAtCompileTime); + VERIFY_EQ_INT( (A(seqN(2,5), seq(1,3))).OuterStrideAtCompileTime , A.OuterStrideAtCompileTime); + VERIFY_EQ_INT( (B(seqN(1,2), seq(1,3))).InnerStrideAtCompileTime , B.InnerStrideAtCompileTime); + VERIFY_EQ_INT( (B(seqN(1,2), seq(1,3))).OuterStrideAtCompileTime , B.OuterStrideAtCompileTime); + VERIFY_EQ_INT( (A(seqN(2,5,2), seq(1,3,2))).InnerStrideAtCompileTime , Dynamic); + VERIFY_EQ_INT( (A(seqN(2,5,2), seq(1,3,2))).OuterStrideAtCompileTime , Dynamic); + VERIFY_EQ_INT( (A(seqN(2,5,fix<2>), seq(1,3,fix<3>))).InnerStrideAtCompileTime , 2); + VERIFY_EQ_INT( (A(seqN(2,5,fix<2>), seq(1,3,fix<3>))).OuterStrideAtCompileTime , Dynamic); + VERIFY_EQ_INT( (B(seqN(1,2,fix<2>), seq(1,3,fix<3>))).InnerStrideAtCompileTime , 2); + VERIFY_EQ_INT( (B(seqN(1,2,fix<2>), seq(1,3,fix<3>))).OuterStrideAtCompileTime , 3*4); + + VERIFY_EQ_INT( (A(seqN(2,fix<5>), seqN(1,fix<3>))).RowsAtCompileTime, 5); + VERIFY_EQ_INT( (A(seqN(2,fix<5>), seqN(1,fix<3>))).ColsAtCompileTime, 3); + VERIFY_EQ_INT( (A(seqN(2,fix<5>(5)), seqN(1,fix<3>(3)))).RowsAtCompileTime, 5); + VERIFY_EQ_INT( (A(seqN(2,fix<5>(5)), seqN(1,fix<3>(3)))).ColsAtCompileTime, 3); + VERIFY_EQ_INT( (A(seqN(2,fix(5)), seqN(1,fix(3)))).RowsAtCompileTime, Dynamic); + VERIFY_EQ_INT( (A(seqN(2,fix(5)), seqN(1,fix(3)))).ColsAtCompileTime, Dynamic); + VERIFY_EQ_INT( (A(seqN(2,fix(5)), seqN(1,fix(3)))).rows(), 5); + VERIFY_EQ_INT( (A(seqN(2,fix(5)), seqN(1,fix(3)))).cols(), 3); + + VERIFY( is_same_seq_type( seqN(2,5,fix<-1>), seqN(2,5,fix<-1>(-1)) ) ); + VERIFY( is_same_seq_type( seqN(2,5), seqN(2,5,fix<1>(1)) ) ); + VERIFY( is_same_seq_type( seqN(2,5,3), seqN(2,5,fix(3)) ) ); + VERIFY( is_same_seq_type( seq(2,7,fix<3>), seqN(2,2,fix<3>) ) ); + VERIFY( is_same_seq_type( seqN(2,fix(5),3), seqN(2,5,fix(3)) ) ); + VERIFY( is_same_seq_type( seqN(2,fix<5>(5),fix<-2>), seqN(2,fix<5>,fix<-2>()) ) ); + + VERIFY( is_same_seq_type( seq(2,fix<5>), seqN(2,4) ) ); +#if EIGEN_HAS_CXX11 + VERIFY( is_same_seq_type( seq(fix<2>,fix<5>), seqN(fix<2>,fix<4>) ) ); + VERIFY( is_same_seq( seqN(2,std::integral_constant(),std::integral_constant()), seqN(2,fix<5>,fix<-2>()) ) ); + VERIFY( is_same_seq( seq(std::integral_constant(),std::integral_constant(),std::integral_constant()), + seq(fix<1>,fix<5>,fix<2>()) ) ); + VERIFY( is_same_seq_type( seqN(2,std::integral_constant(),std::integral_constant()), seqN(2,fix<5>,fix<-2>()) ) ); + VERIFY( is_same_seq_type( seq(std::integral_constant(),std::integral_constant(),std::integral_constant()), + seq(fix<1>,fix<5>,fix<2>()) ) ); + + VERIFY( is_same_seq_type( seqN(2,std::integral_constant()), seqN(2,fix<5>) ) ); + VERIFY( is_same_seq_type( seq(std::integral_constant(),std::integral_constant()), seq(fix<1>,fix<5>) ) ); +#else + // sorry, no compile-time size recovery in c++98/03 + VERIFY( is_same_seq( seq(fix<2>,fix<5>), seqN(fix<2>,fix<4>) ) ); +#endif + + VERIFY( (A(seqN(2,fix<5>), 5)).RowsAtCompileTime == 5); + VERIFY( (A(4, all)).ColsAtCompileTime == Dynamic); + VERIFY( (A(4, all)).RowsAtCompileTime == 1); + VERIFY( (B(1, all)).ColsAtCompileTime == 4); + VERIFY( (B(1, all)).RowsAtCompileTime == 1); + VERIFY( (B(all,1)).ColsAtCompileTime == 1); + VERIFY( (B(all,1)).RowsAtCompileTime == 4); + + VERIFY(int( (A(all, eii)).ColsAtCompileTime) == int(eii.SizeAtCompileTime)); + VERIFY_EQ_INT( (A(eii, eii)).Flags&DirectAccessBit, (unsigned int)(0)); + VERIFY_EQ_INT( (A(eii, eii)).InnerStrideAtCompileTime, 0); + VERIFY_EQ_INT( (A(eii, eii)).OuterStrideAtCompileTime, 0); + + VERIFY_IS_APPROX( A(seq(n-1,2,-2), seqN(n-1-6,3,-1)), A(seq(last,2,fix<-2>), seqN(last-6,3,fix<-1>)) ); + + VERIFY_IS_APPROX( A(seq(n-1,2,-2), seqN(n-1-6,4)), A(seq(last,2,-2), seqN(last-6,4)) ); + VERIFY_IS_APPROX( A(seq(n-1-6,n-1-2), seqN(n-1-6,4)), A(seq(last-6,last-2), seqN(6+last-6-6,4)) ); + VERIFY_IS_APPROX( A(seq((n-1)/2,(n)/2+3), seqN(2,4)), A(seq(last/2,(last+1)/2+3), seqN(last+2-last,4)) ); + VERIFY_IS_APPROX( A(seq(n-2,2,-2), seqN(n-8,4)), A(seq(lastp1-2,2,-2), seqN(lastp1-8,4)) ); + + // Check all combinations of seq: + VERIFY_IS_APPROX( A(seq(1,n-1-2,2), seq(1,n-1-2,2)), A(seq(1,last-2,2), seq(1,last-2,fix<2>)) ); + VERIFY_IS_APPROX( A(seq(n-1-5,n-1-2,2), seq(n-1-5,n-1-2,2)), A(seq(last-5,last-2,2), seq(last-5,last-2,fix<2>)) ); + VERIFY_IS_APPROX( A(seq(n-1-5,7,2), seq(n-1-5,7,2)), A(seq(last-5,7,2), seq(last-5,7,fix<2>)) ); + VERIFY_IS_APPROX( A(seq(1,n-1-2), seq(n-1-5,7)), A(seq(1,last-2), seq(last-5,7)) ); + VERIFY_IS_APPROX( A(seq(n-1-5,n-1-2), seq(n-1-5,n-1-2)), A(seq(last-5,last-2), seq(last-5,last-2)) ); + + VERIFY_IS_APPROX( A.col(A.cols()-1), A(all,last) ); + VERIFY_IS_APPROX( A(A.rows()-2, A.cols()/2), A(last-1, lastp1/2) ); + VERIFY_IS_APPROX( a(a.size()-2), a(last-1) ); + VERIFY_IS_APPROX( a(a.size()/2), a((last+1)/2) ); + + // Check fall-back to Block + { + VERIFY( is_same_eq(A.col(0), A(all,0)) ); + VERIFY( is_same_eq(A.row(0), A(0,all)) ); + VERIFY( is_same_eq(A.block(0,0,2,2), A(seqN(0,2),seq(0,1))) ); + VERIFY( is_same_eq(A.middleRows(2,4), A(seqN(2,4),all)) ); + VERIFY( is_same_eq(A.middleCols(2,4), A(all,seqN(2,4))) ); + + VERIFY( is_same_eq(A.col(A.cols()-1), A(all,last)) ); + + const ArrayXXi& cA(A); + VERIFY( is_same_eq(cA.col(0), cA(all,0)) ); + VERIFY( is_same_eq(cA.row(0), cA(0,all)) ); + VERIFY( is_same_eq(cA.block(0,0,2,2), cA(seqN(0,2),seq(0,1))) ); + VERIFY( is_same_eq(cA.middleRows(2,4), cA(seqN(2,4),all)) ); + VERIFY( is_same_eq(cA.middleCols(2,4), cA(all,seqN(2,4))) ); + + VERIFY( is_same_eq(a.head(4), a(seq(0,3))) ); + VERIFY( is_same_eq(a.tail(4), a(seqN(last-3,4))) ); + VERIFY( is_same_eq(a.tail(4), a(seq(lastp1-4,last))) ); + VERIFY( is_same_eq(a.segment<4>(3), a(seqN(3,fix<4>))) ); + } + + ArrayXXi A1=A, A2 = ArrayXXi::Random(4,4); + ArrayXi range25(4); range25 << 3,2,4,5; + A1(seqN(3,4),seq(2,5)) = A2; + VERIFY_IS_APPROX( A1.block(3,2,4,4), A2 ); + A1 = A; + A2.setOnes(); + A1(seq(6,3,-1),range25) = A2; + VERIFY_IS_APPROX( A1.block(3,2,4,4), A2 ); + + // check reverse + { + VERIFY( is_same_seq_type( seq(3,7).reverse(), seqN(7,5,fix<-1>) ) ); + VERIFY( is_same_seq_type( seq(7,3,fix<-2>).reverse(), seqN(3,3,fix<2>) ) ); + VERIFY_IS_APPROX( a(seqN(2,last/2).reverse()), a(seqN(2+(last/2-1)*1,last/2,fix<-1>)) ); + VERIFY_IS_APPROX( a(seqN(last/2,fix<4>).reverse()),a(seqN(last/2,fix<4>)).reverse() ); + VERIFY_IS_APPROX( A(seq(last-5,last-1,2).reverse(), seqN(last-3,3,fix<-2>).reverse()), + A(seq(last-5,last-1,2), seqN(last-3,3,fix<-2>)).reverse() ); + } + +#if EIGEN_HAS_CXX11 + // check lastN + VERIFY_IS_APPROX( a(lastN(3)), a.tail(3) ); + VERIFY( MATCH( a(lastN(3)), "7\n8\n9" ) ); + VERIFY_IS_APPROX( a(lastN(fix<3>())), a.tail<3>() ); + VERIFY( MATCH( a(lastN(3,2)), "5\n7\n9" ) ); + VERIFY( MATCH( a(lastN(3,fix<2>())), "5\n7\n9" ) ); + VERIFY( a(lastN(fix<3>())).SizeAtCompileTime == 3 ); + + VERIFY( (A(all, std::array{{1,3,2,4}})).ColsAtCompileTime == 4); + + VERIFY_IS_APPROX( (A(std::array{{1,3,5}}, std::array{{9,6,3,0}})), A(seqN(1,3,2), seqN(9,4,-3)) ); + +#if EIGEN_HAS_STATIC_ARRAY_TEMPLATE + VERIFY_IS_APPROX( A({3, 1, 6, 5}, all), A(std::array{{3, 1, 6, 5}}, all) ); + VERIFY_IS_APPROX( A(all,{3, 1, 6, 5}), A(all,std::array{{3, 1, 6, 5}}) ); + VERIFY_IS_APPROX( A({1,3,5},{3, 1, 6, 5}), A(std::array{{1,3,5}},std::array{{3, 1, 6, 5}}) ); + + VERIFY_IS_EQUAL( A({1,3,5},{3, 1, 6, 5}).RowsAtCompileTime, 3 ); + VERIFY_IS_EQUAL( A({1,3,5},{3, 1, 6, 5}).ColsAtCompileTime, 4 ); + + VERIFY_IS_APPROX( a({3, 1, 6, 5}), a(std::array{{3, 1, 6, 5}}) ); + VERIFY_IS_EQUAL( a({1,3,5}).SizeAtCompileTime, 3 ); + + VERIFY_IS_APPROX( b({3, 1, 6, 5}), b(std::array{{3, 1, 6, 5}}) ); + VERIFY_IS_EQUAL( b({1,3,5}).SizeAtCompileTime, 3 ); +#endif + +#endif + + // check mat(i,j) with weird types for i and j + { + VERIFY_IS_APPROX( A(B.RowsAtCompileTime-1, 1), A(3,1) ); + VERIFY_IS_APPROX( A(B.RowsAtCompileTime, 1), A(4,1) ); + VERIFY_IS_APPROX( A(B.RowsAtCompileTime-1, B.ColsAtCompileTime-1), A(3,3) ); + VERIFY_IS_APPROX( A(B.RowsAtCompileTime, B.ColsAtCompileTime), A(4,4) ); + const Index I_ = 3, J_ = 4; + VERIFY_IS_APPROX( A(I_,J_), A(3,4) ); + } + + // check extended block API + { + VERIFY( is_same_eq( A.block<3,4>(1,1), A.block(1,1,fix<3>,fix<4>)) ); + VERIFY( is_same_eq( A.block<3,4>(1,1,3,4), A.block(1,1,fix<3>(),fix<4>(4))) ); + VERIFY( is_same_eq( A.block<3,Dynamic>(1,1,3,4), A.block(1,1,fix<3>,4)) ); + VERIFY( is_same_eq( A.block(1,1,3,4), A.block(1,1,fix(3),fix<4>)) ); + VERIFY( is_same_eq( A.block(1,1,3,4), A.block(1,1,fix(3),fix(4))) ); + + VERIFY( is_same_eq( A.topLeftCorner<3,4>(), A.topLeftCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( A.bottomLeftCorner<3,4>(), A.bottomLeftCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( A.bottomRightCorner<3,4>(), A.bottomRightCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( A.topRightCorner<3,4>(), A.topRightCorner(fix<3>,fix<4>)) ); + + VERIFY( is_same_eq( A.leftCols<3>(), A.leftCols(fix<3>)) ); + VERIFY( is_same_eq( A.rightCols<3>(), A.rightCols(fix<3>)) ); + VERIFY( is_same_eq( A.middleCols<3>(1), A.middleCols(1,fix<3>)) ); + + VERIFY( is_same_eq( A.topRows<3>(), A.topRows(fix<3>)) ); + VERIFY( is_same_eq( A.bottomRows<3>(), A.bottomRows(fix<3>)) ); + VERIFY( is_same_eq( A.middleRows<3>(1), A.middleRows(1,fix<3>)) ); + + VERIFY( is_same_eq( a.segment<3>(1), a.segment(1,fix<3>)) ); + VERIFY( is_same_eq( a.head<3>(), a.head(fix<3>)) ); + VERIFY( is_same_eq( a.tail<3>(), a.tail(fix<3>)) ); + + const ArrayXXi& cA(A); + VERIFY( is_same_eq( cA.block(1,1,3,4), cA.block(1,1,fix(3),fix<4>)) ); + + VERIFY( is_same_eq( cA.topLeftCorner<3,4>(), cA.topLeftCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( cA.bottomLeftCorner<3,4>(), cA.bottomLeftCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( cA.bottomRightCorner<3,4>(), cA.bottomRightCorner(fix<3>,fix<4>)) ); + VERIFY( is_same_eq( cA.topRightCorner<3,4>(), cA.topRightCorner(fix<3>,fix<4>)) ); + + VERIFY( is_same_eq( cA.leftCols<3>(), cA.leftCols(fix<3>)) ); + VERIFY( is_same_eq( cA.rightCols<3>(), cA.rightCols(fix<3>)) ); + VERIFY( is_same_eq( cA.middleCols<3>(1), cA.middleCols(1,fix<3>)) ); + + VERIFY( is_same_eq( cA.topRows<3>(), cA.topRows(fix<3>)) ); + VERIFY( is_same_eq( cA.bottomRows<3>(), cA.bottomRows(fix<3>)) ); + VERIFY( is_same_eq( cA.middleRows<3>(1), cA.middleRows(1,fix<3>)) ); + } + + // Check compilation of enums as index type: + a(XX) = 1; + A(XX,YY) = 1; + // Anonymous enums only work with C++11 +#if EIGEN_HAS_CXX11 + enum { X=0, Y=1 }; + a(X) = 1; + A(X,Y) = 1; + A(XX,Y) = 1; + A(X,YY) = 1; +#endif + + // Check compilation of varying integer types as index types: + Index i = n/2; + short i_short(i); + std::size_t i_sizet(i); + VERIFY_IS_EQUAL( a(i), a.coeff(i_short) ); + VERIFY_IS_EQUAL( a(i), a.coeff(i_sizet) ); + + VERIFY_IS_EQUAL( A(i,i), A.coeff(i_short, i_short) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(i_short, i) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(i, i_short) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(i, i_sizet) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(i_sizet, i) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(i_sizet, i_short) ); + VERIFY_IS_EQUAL( A(i,i), A.coeff(5, i_sizet) ); + + // Regression test for Max{Rows,Cols}AtCompileTime + { + Matrix3i A3 = Matrix3i::Random(); + ArrayXi ind(5); ind << 1,1,1,1,1; + VERIFY_IS_EQUAL( A3(ind,ind).eval(), MatrixXi::Constant(5,5,A3(1,1)) ); + } + + // Regression for bug 1736 + { + VERIFY_IS_APPROX(A(all, eii).col(0).eval(), A.col(eii(0))); + A(all, eii).col(0) = A.col(eii(0)); + } + + // bug 1815: IndexedView should allow linear access + { + VERIFY( MATCH( b(eii)(0), "3" ) ); + VERIFY( MATCH( a(eii)(0), "3" ) ); + VERIFY( MATCH( A(1,eii)(0), "103")); + VERIFY( MATCH( A(eii,1)(0), "301")); + VERIFY( MATCH( A(1,all)(1), "101")); + VERIFY( MATCH( A(all,1)(1), "101")); + } + +#if EIGEN_HAS_CXX11 + //Bug IndexView with a single static row should be RowMajor: + { + // A(1, seq(0,2,1)).cwiseAbs().colwise().replicate(2).eval(); + STATIC_CHECK(( (internal::evaluator::Flags & RowMajorBit) == RowMajorBit )); + } +#endif + +} + +EIGEN_DECLARE_TEST(indexed_view) +{ +// for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( check_indexed_view() ); + CALL_SUBTEST_2( check_indexed_view() ); + CALL_SUBTEST_3( check_indexed_view() ); +// } + + // static checks of some internals: + STATIC_CHECK(( internal::is_valid_index_type::value )); + STATIC_CHECK(( internal::is_valid_index_type::value )); + STATIC_CHECK(( internal::is_valid_index_type::value )); + STATIC_CHECK(( internal::is_valid_index_type::value )); + STATIC_CHECK(( internal::is_valid_index_type::value )); + STATIC_CHECK(( !internal::valid_indexed_view_overload::value )); + STATIC_CHECK(( !internal::valid_indexed_view_overload::value )); + STATIC_CHECK(( !internal::valid_indexed_view_overload::value )); + STATIC_CHECK(( !internal::valid_indexed_view_overload::value )); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/initializer_list_construction.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/initializer_list_construction.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7a9c49e8d476e60cf1103f930319298bf7f81304 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/initializer_list_construction.cpp @@ -0,0 +1,385 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2019 David Tellenbach +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT + +#include "main.h" + +template::IsInteger> +struct TestMethodDispatching { + static void run() {} +}; + +template +struct TestMethodDispatching { + static void run() + { + { + Matrix m {3, 4}; + Array a {3, 4}; + VERIFY(m.rows() == 3); + VERIFY(m.cols() == 4); + VERIFY(a.rows() == 3); + VERIFY(a.cols() == 4); + } + { + Matrix m {3, 4}; + Array a {3, 4}; + VERIFY(m(0) == 3); + VERIFY(m(1) == 4); + VERIFY(a(0) == 3); + VERIFY(a(1) == 4); + } + { + Matrix m {3, 4}; + Array a {3, 4}; + VERIFY(m(0) == 3); + VERIFY(m(1) == 4); + VERIFY(a(0) == 3); + VERIFY(a(1) == 4); + } + } +}; + +template void fixedsizeVariadicVectorConstruction2() +{ + { + Vec4 ref = Vec4::Random(); + Vec4 v{ ref[0], ref[1], ref[2], ref[3] }; + VERIFY_IS_APPROX(v, ref); + VERIFY_IS_APPROX(v, (Vec4( ref[0], ref[1], ref[2], ref[3] ))); + VERIFY_IS_APPROX(v, (Vec4({ref[0], ref[1], ref[2], ref[3]}))); + + Vec4 v2 = { ref[0], ref[1], ref[2], ref[3] }; + VERIFY_IS_APPROX(v2, ref); + } + { + Vec5 ref = Vec5::Random(); + Vec5 v{ ref[0], ref[1], ref[2], ref[3], ref[4] }; + VERIFY_IS_APPROX(v, ref); + VERIFY_IS_APPROX(v, (Vec5( ref[0], ref[1], ref[2], ref[3], ref[4] ))); + VERIFY_IS_APPROX(v, (Vec5({ref[0], ref[1], ref[2], ref[3], ref[4]}))); + + Vec5 v2 = { ref[0], ref[1], ref[2], ref[3], ref[4] }; + VERIFY_IS_APPROX(v2, ref); + } +} + +#define CHECK_MIXSCALAR_V5_APPROX(V, A0, A1, A2, A3, A4) { \ + VERIFY_IS_APPROX(V[0], Scalar(A0) ); \ + VERIFY_IS_APPROX(V[1], Scalar(A1) ); \ + VERIFY_IS_APPROX(V[2], Scalar(A2) ); \ + VERIFY_IS_APPROX(V[3], Scalar(A3) ); \ + VERIFY_IS_APPROX(V[4], Scalar(A4) ); \ +} + +#define CHECK_MIXSCALAR_V5(VEC5, A0, A1, A2, A3, A4) { \ + typedef VEC5::Scalar Scalar; \ + VEC5 v = { A0 , A1 , A2 , A3 , A4 }; \ + CHECK_MIXSCALAR_V5_APPROX(v, A0 , A1 , A2 , A3 , A4); \ +} + +template void fixedsizeVariadicVectorConstruction3() +{ + typedef Matrix Vec5; + typedef Array Arr5; + CHECK_MIXSCALAR_V5(Vec5, 1, 2., -3, 4.121, 5.53252); + CHECK_MIXSCALAR_V5(Arr5, 1, 2., 3.12f, 4.121, 5.53252); +} + +template void fixedsizeVariadicVectorConstruction() +{ + CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2, Matrix >() )); + CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2, Matrix >() )); + CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2, Array >() )); + CALL_SUBTEST(( fixedsizeVariadicVectorConstruction2, Array >() )); +} + + +template void initializerListVectorConstruction() +{ + Scalar raw[4]; + for(int k = 0; k < 4; ++k) { + raw[k] = internal::random(); + } + { + Matrix m { {raw[0]}, {raw[1]},{raw[2]},{raw[3]} }; + Array a { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }; + for(int k = 0; k < 4; ++k) { + VERIFY(m(k) == raw[k]); + } + for(int k = 0; k < 4; ++k) { + VERIFY(a(k) == raw[k]); + } + VERIFY_IS_EQUAL(m, (Matrix({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))); + VERIFY((a == (Array({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))).all()); + } + { + Matrix m { {raw[0], raw[1], raw[2], raw[3]} }; + Array a { {raw[0], raw[1], raw[2], raw[3]} }; + for(int k = 0; k < 4; ++k) { + VERIFY(m(k) == raw[k]); + } + for(int k = 0; k < 4; ++k) { + VERIFY(a(k) == raw[k]); + } + VERIFY_IS_EQUAL(m, (Matrix({{raw[0],raw[1],raw[2],raw[3]}}))); + VERIFY((a == (Array({{raw[0],raw[1],raw[2],raw[3]}}))).all()); + } + { + Matrix m { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }; + Array a { {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }; + for(int k=0; k < 4; ++k) { + VERIFY(m(k) == raw[k]); + } + for(int k=0; k < 4; ++k) { + VERIFY(a(k) == raw[k]); + } + VERIFY_IS_EQUAL(m, (Matrix({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))); + VERIFY((a == (Array({ {raw[0]}, {raw[1]}, {raw[2]}, {raw[3]} }))).all()); + } + { + Matrix m {{raw[0],raw[1],raw[2],raw[3]}}; + Array a {{raw[0],raw[1],raw[2],raw[3]}}; + for(int k=0; k < 4; ++k) { + VERIFY(m(k) == raw[k]); + } + for(int k=0; k < 4; ++k) { + VERIFY(a(k) == raw[k]); + } + VERIFY_IS_EQUAL(m, (Matrix({{raw[0],raw[1],raw[2],raw[3]}}))); + VERIFY((a == (Array({{raw[0],raw[1],raw[2],raw[3]}}))).all()); + } +} + +template void initializerListMatrixConstruction() +{ + const Index RowsAtCompileTime = 5; + const Index ColsAtCompileTime = 4; + const Index SizeAtCompileTime = RowsAtCompileTime * ColsAtCompileTime; + + Scalar raw[SizeAtCompileTime]; + for (int i = 0; i < SizeAtCompileTime; ++i) { + raw[i] = internal::random(); + } + { + Matrix m {}; + VERIFY(m.cols() == 0); + VERIFY(m.rows() == 0); + VERIFY_IS_EQUAL(m, (Matrix())); + } + { + Matrix m { + {raw[0], raw[1], raw[2], raw[3]}, + {raw[4], raw[5], raw[6], raw[7]}, + {raw[8], raw[9], raw[10], raw[11]}, + {raw[12], raw[13], raw[14], raw[15]}, + {raw[16], raw[17], raw[18], raw[19]} + }; + + Matrix m2; + m2 << raw[0], raw[1], raw[2], raw[3], + raw[4], raw[5], raw[6], raw[7], + raw[8], raw[9], raw[10], raw[11], + raw[12], raw[13], raw[14], raw[15], + raw[16], raw[17], raw[18], raw[19]; + + int k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + VERIFY(m(i, j) == raw[k]); + ++k; + } + } + VERIFY_IS_EQUAL(m, m2); + } + { + Matrix m{ + {raw[0], raw[1], raw[2], raw[3]}, + {raw[4], raw[5], raw[6], raw[7]}, + {raw[8], raw[9], raw[10], raw[11]}, + {raw[12], raw[13], raw[14], raw[15]}, + {raw[16], raw[17], raw[18], raw[19]} + }; + + VERIFY(m.cols() == 4); + VERIFY(m.rows() == 5); + int k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + VERIFY(m(i, j) == raw[k]); + ++k; + } + } + + Matrix m2(RowsAtCompileTime, ColsAtCompileTime); + k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + m2(i, j) = raw[k]; + ++k; + } + } + VERIFY_IS_EQUAL(m, m2); + } +} + +template void initializerListArrayConstruction() +{ + const Index RowsAtCompileTime = 5; + const Index ColsAtCompileTime = 4; + const Index SizeAtCompileTime = RowsAtCompileTime * ColsAtCompileTime; + + Scalar raw[SizeAtCompileTime]; + for (int i = 0; i < SizeAtCompileTime; ++i) { + raw[i] = internal::random(); + } + { + Array a {}; + VERIFY(a.cols() == 0); + VERIFY(a.rows() == 0); + } + { + Array m { + {raw[0], raw[1], raw[2], raw[3]}, + {raw[4], raw[5], raw[6], raw[7]}, + {raw[8], raw[9], raw[10], raw[11]}, + {raw[12], raw[13], raw[14], raw[15]}, + {raw[16], raw[17], raw[18], raw[19]} + }; + + Array m2; + m2 << raw[0], raw[1], raw[2], raw[3], + raw[4], raw[5], raw[6], raw[7], + raw[8], raw[9], raw[10], raw[11], + raw[12], raw[13], raw[14], raw[15], + raw[16], raw[17], raw[18], raw[19]; + + int k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + VERIFY(m(i, j) == raw[k]); + ++k; + } + } + VERIFY_IS_APPROX(m, m2); + } + { + Array m { + {raw[0], raw[1], raw[2], raw[3]}, + {raw[4], raw[5], raw[6], raw[7]}, + {raw[8], raw[9], raw[10], raw[11]}, + {raw[12], raw[13], raw[14], raw[15]}, + {raw[16], raw[17], raw[18], raw[19]} + }; + + VERIFY(m.cols() == 4); + VERIFY(m.rows() == 5); + int k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + VERIFY(m(i, j) == raw[k]); + ++k; + } + } + + Array m2(RowsAtCompileTime, ColsAtCompileTime); + k = 0; + for(int i = 0; i < RowsAtCompileTime; ++i) { + for (int j = 0; j < ColsAtCompileTime; ++j) { + m2(i, j) = raw[k]; + ++k; + } + } + VERIFY_IS_APPROX(m, m2); + } +} + +template void dynamicVectorConstruction() +{ + const Index size = 4; + Scalar raw[size]; + for (int i = 0; i < size; ++i) { + raw[i] = internal::random(); + } + + typedef Matrix VectorX; + + { + VectorX v {{raw[0], raw[1], raw[2], raw[3]}}; + for (int i = 0; i < size; ++i) { + VERIFY(v(i) == raw[i]); + } + VERIFY(v.rows() == size); + VERIFY(v.cols() == 1); + VERIFY_IS_EQUAL(v, (VectorX {{raw[0], raw[1], raw[2], raw[3]}})); + } + + { + VERIFY_RAISES_ASSERT((VectorX {raw[0], raw[1], raw[2], raw[3]})); + } + { + VERIFY_RAISES_ASSERT((VectorX { + {raw[0], raw[1], raw[2], raw[3]}, + {raw[0], raw[1], raw[2], raw[3]}, + })); + } +} + +EIGEN_DECLARE_TEST(initializer_list_construction) +{ + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction()); + CALL_SUBTEST_1(initializerListVectorConstruction>()); + CALL_SUBTEST_1(initializerListVectorConstruction>()); + + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction()); + CALL_SUBTEST_2(initializerListMatrixConstruction>()); + CALL_SUBTEST_2(initializerListMatrixConstruction>()); + + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction()); + CALL_SUBTEST_3(initializerListArrayConstruction>()); + CALL_SUBTEST_3(initializerListArrayConstruction>()); + + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction>()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction>()); + CALL_SUBTEST_4(fixedsizeVariadicVectorConstruction3<0>()); + + CALL_SUBTEST_5(TestMethodDispatching::run()); + CALL_SUBTEST_5(TestMethodDispatching::run()); + + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction()); + CALL_SUBTEST_6(dynamicVectorConstruction>()); + CALL_SUBTEST_6(dynamicVectorConstruction>()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inplace_decomposition.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inplace_decomposition.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e3aa9957d0338463b1b8c5a602965d362aabf1c1 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inplace_decomposition.cpp @@ -0,0 +1,110 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include +#include + +// This file test inplace decomposition through Ref<>, as supported by Cholesky, LU, and QR decompositions. + +template void inplace(bool square = false, bool SPD = false) +{ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix RhsType; + typedef Matrix ResType; + + Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random(2,EIGEN_TEST_MAX_SIZE/2) : Index(MatrixType::RowsAtCompileTime); + Index cols = MatrixType::ColsAtCompileTime==Dynamic ? (square?rows:internal::random(2,rows)) : Index(MatrixType::ColsAtCompileTime); + + MatrixType A = MatrixType::Random(rows,cols); + RhsType b = RhsType::Random(rows); + ResType x(cols); + + if(SPD) + { + assert(square); + A.topRows(cols) = A.topRows(cols).adjoint() * A.topRows(cols); + A.diagonal().array() += 1e-3; + } + + MatrixType A0 = A; + MatrixType A1 = A; + + DecType dec(A); + + // Check that the content of A has been modified + VERIFY_IS_NOT_APPROX( A, A0 ); + + // Check that the decomposition is correct: + if(rows==cols) + { + VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } + + // Check that modifying A breaks the current dec: + A.setRandom(); + if(rows==cols) + { + VERIFY_IS_NOT_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_NOT_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } + + // Check that calling compute(A1) does not modify A1: + A = A0; + dec.compute(A1); + VERIFY_IS_EQUAL(A0,A1); + VERIFY_IS_NOT_APPROX( A, A0 ); + if(rows==cols) + { + VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b ); + } + else + { + VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b ); + } +} + + +EIGEN_DECLARE_TEST(inplace_decomposition) +{ + EIGEN_UNUSED typedef Matrix Matrix43d; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( inplace >, MatrixXd>(true,true) )); + CALL_SUBTEST_1(( inplace >, Matrix4d>(true,true) )); + + CALL_SUBTEST_2(( inplace >, MatrixXd>(true,true) )); + CALL_SUBTEST_2(( inplace >, Matrix4d>(true,true) )); + + CALL_SUBTEST_3(( inplace >, MatrixXd>(true,false) )); + CALL_SUBTEST_3(( inplace >, Matrix4d>(true,false) )); + + CALL_SUBTEST_4(( inplace >, MatrixXd>(true,false) )); + CALL_SUBTEST_4(( inplace >, Matrix4d>(true,false) )); + + CALL_SUBTEST_5(( inplace >, MatrixXd>(false,false) )); + CALL_SUBTEST_5(( inplace >, Matrix43d>(false,false) )); + + CALL_SUBTEST_6(( inplace >, MatrixXd>(false,false) )); + CALL_SUBTEST_6(( inplace >, Matrix43d>(false,false) )); + + CALL_SUBTEST_7(( inplace >, MatrixXd>(false,false) )); + CALL_SUBTEST_7(( inplace >, Matrix43d>(false,false) )); + + CALL_SUBTEST_8(( inplace >, MatrixXd>(false,false) )); + CALL_SUBTEST_8(( inplace >, Matrix43d>(false,false) )); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/integer_types.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/integer_types.cpp new file mode 100644 index 0000000000000000000000000000000000000000..31f4100c5ad05bf213c1844eb263e45dcc7e633a --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/integer_types.cpp @@ -0,0 +1,173 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_STATIC_ASSERT + +#include "main.h" + +#undef VERIFY_IS_APPROX +#define VERIFY_IS_APPROX(a, b) VERIFY((a)==(b)); +#undef VERIFY_IS_NOT_APPROX +#define VERIFY_IS_NOT_APPROX(a, b) VERIFY((a)!=(b)); + +template void signed_integer_type_tests(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 }; + VERIFY(is_signed == 1); + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1(rows, cols), + m2 = MatrixType::Random(rows, cols), + mzero = MatrixType::Zero(rows, cols); + + do { + m1 = MatrixType::Random(rows, cols); + } while(m1 == mzero || m1 == m2); + + // check linear structure + + Scalar s1; + do { + s1 = internal::random(); + } while(s1 == 0); + + VERIFY_IS_EQUAL(-(-m1), m1); + VERIFY_IS_EQUAL(-m2+m1+m2, m1); + VERIFY_IS_EQUAL((-m1+m2)*s1, -s1*m1+s1*m2); +} + +template void integer_type_tests(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + VERIFY(NumTraits::IsInteger); + enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 }; + VERIFY(int(NumTraits::IsSigned) == is_signed); + + typedef Matrix VectorType; + + Index rows = m.rows(); + Index cols = m.cols(); + + // this test relies a lot on Random.h, and there's not much more that we can do + // to test it, hence I consider that we will have tested Random.h + MatrixType m1(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols), + mzero = MatrixType::Zero(rows, cols); + + typedef Matrix SquareMatrixType; + SquareMatrixType identity = SquareMatrixType::Identity(rows, rows), + square = SquareMatrixType::Random(rows, rows); + VectorType v1(rows), + v2 = VectorType::Random(rows), + vzero = VectorType::Zero(rows); + + do { + m1 = MatrixType::Random(rows, cols); + } while(m1 == mzero || m1 == m2); + + do { + v1 = VectorType::Random(rows); + } while(v1 == vzero || v1 == v2); + + VERIFY_IS_APPROX( v1, v1); + VERIFY_IS_NOT_APPROX( v1, 2*v1); + VERIFY_IS_APPROX( vzero, v1-v1); + VERIFY_IS_APPROX( m1, m1); + VERIFY_IS_NOT_APPROX( m1, 2*m1); + VERIFY_IS_APPROX( mzero, m1-m1); + + VERIFY_IS_APPROX(m3 = m1,m1); + MatrixType m4; + VERIFY_IS_APPROX(m4 = m1,m1); + + m3.real() = m1.real(); + VERIFY_IS_APPROX(static_cast(m3).real(), static_cast(m1).real()); + VERIFY_IS_APPROX(static_cast(m3).real(), m1.real()); + + // check == / != operators + VERIFY(m1==m1); + VERIFY(m1!=m2); + VERIFY(!(m1==m2)); + VERIFY(!(m1!=m1)); + m1 = m2; + VERIFY(m1==m2); + VERIFY(!(m1!=m2)); + + // check linear structure + + Scalar s1; + do { + s1 = internal::random(); + } while(s1 == 0); + + VERIFY_IS_EQUAL(m1+m1, 2*m1); + VERIFY_IS_EQUAL(m1+m2-m1, m2); + VERIFY_IS_EQUAL(m1*s1, s1*m1); + VERIFY_IS_EQUAL((m1+m2)*s1, s1*m1+s1*m2); + m3 = m2; m3 += m1; + VERIFY_IS_EQUAL(m3, m1+m2); + m3 = m2; m3 -= m1; + VERIFY_IS_EQUAL(m3, m2-m1); + m3 = m2; m3 *= s1; + VERIFY_IS_EQUAL(m3, s1*m2); + + // check matrix product. + + VERIFY_IS_APPROX(identity * m1, m1); + VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2); + VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square); + VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1)); +} + +template +void integer_types_extra() +{ + VERIFY_IS_EQUAL(int(internal::scalar_div_cost::value), 8); + VERIFY_IS_EQUAL(int(internal::scalar_div_cost::value), 8); + if(sizeof(long)>sizeof(int)) { + VERIFY(int(internal::scalar_div_cost::value) > int(internal::scalar_div_cost::value)); + VERIFY(int(internal::scalar_div_cost::value) > int(internal::scalar_div_cost::value)); + } +} + +EIGEN_DECLARE_TEST(integer_types) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( integer_type_tests(Matrix()) ); + CALL_SUBTEST_1( integer_type_tests(Matrix()) ); + + CALL_SUBTEST_2( integer_type_tests(Matrix()) ); + CALL_SUBTEST_2( signed_integer_type_tests(Matrix()) ); + + CALL_SUBTEST_3( integer_type_tests(Matrix(2, 10)) ); + CALL_SUBTEST_3( signed_integer_type_tests(Matrix(2, 10)) ); + + CALL_SUBTEST_4( integer_type_tests(Matrix()) ); + CALL_SUBTEST_4( integer_type_tests(Matrix(20, 20)) ); + + CALL_SUBTEST_5( integer_type_tests(Matrix(7, 4)) ); + CALL_SUBTEST_5( signed_integer_type_tests(Matrix(7, 4)) ); + + CALL_SUBTEST_6( integer_type_tests(Matrix()) ); + +#if EIGEN_HAS_CXX11 + CALL_SUBTEST_7( integer_type_tests(Matrix()) ); + CALL_SUBTEST_7( signed_integer_type_tests(Matrix()) ); + + CALL_SUBTEST_8( integer_type_tests(Matrix(1, 5)) ); +#endif + } + CALL_SUBTEST_9( integer_types_extra<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inverse.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inverse.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9cedfa1e1069ce7a15e4056a6ab95fe4cccc7405 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/inverse.cpp @@ -0,0 +1,150 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template +void inverse_for_fixed_size(const MatrixType&, typename internal::enable_if::type* = 0) +{ +} + +template +void inverse_for_fixed_size(const MatrixType& m1, typename internal::enable_if::type* = 0) +{ + using std::abs; + + MatrixType m2, identity = MatrixType::Identity(); + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef Matrix VectorType; + + //computeInverseAndDetWithCheck tests + //First: an invertible matrix + bool invertible; + Scalar det; + + m2.setZero(); + m1.computeInverseAndDetWithCheck(m2, det, invertible); + VERIFY(invertible); + VERIFY_IS_APPROX(identity, m1*m2); + VERIFY_IS_APPROX(det, m1.determinant()); + + m2.setZero(); + m1.computeInverseWithCheck(m2, invertible); + VERIFY(invertible); + VERIFY_IS_APPROX(identity, m1*m2); + + //Second: a rank one matrix (not invertible, except for 1x1 matrices) + VectorType v3 = VectorType::Random(); + MatrixType m3 = v3*v3.transpose(), m4; + m3.computeInverseAndDetWithCheck(m4, det, invertible); + VERIFY( m1.rows()==1 ? invertible : !invertible ); + VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1)); + m3.computeInverseWithCheck(m4, invertible); + VERIFY( m1.rows()==1 ? invertible : !invertible ); + + // check with submatrices + { + Matrix m5; + m5.setRandom(); + m5.topLeftCorner(m1.rows(),m1.rows()) = m1; + m2 = m5.template topLeftCorner().inverse(); + VERIFY_IS_APPROX( (m5.template topLeftCorner()), m2.inverse() ); + } +} + +template void inverse(const MatrixType& m) +{ + /* this test covers the following files: + Inverse.h + */ + Index rows = m.rows(); + Index cols = m.cols(); + + typedef typename MatrixType::Scalar Scalar; + + MatrixType m1(rows, cols), + m2(rows, cols), + identity = MatrixType::Identity(rows, rows); + createRandomPIMatrixOfRank(rows,rows,rows,m1); + m2 = m1.inverse(); + VERIFY_IS_APPROX(m1, m2.inverse() ); + + VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5)); + + VERIFY_IS_APPROX(identity, m1.inverse() * m1 ); + VERIFY_IS_APPROX(identity, m1 * m1.inverse() ); + + VERIFY_IS_APPROX(m1, m1.inverse().inverse() ); + + // since for the general case we implement separately row-major and col-major, test that + VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose())); + + inverse_for_fixed_size(m1); + + // check in-place inversion + if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4) + { + // in-place is forbidden + VERIFY_RAISES_ASSERT(m1 = m1.inverse()); + } + else + { + m2 = m1.inverse(); + m1 = m1.inverse(); + VERIFY_IS_APPROX(m1,m2); + } +} + +template +void inverse_zerosized() +{ + Matrix A(0,0); + { + Matrix b, x; + x = A.inverse() * b; + } + { + Matrix b(0,1), x; + x = A.inverse() * b; + VERIFY_IS_EQUAL(x.rows(), 0); + VERIFY_IS_EQUAL(x.cols(), 1); + } +} + +EIGEN_DECLARE_TEST(inverse) +{ + int s = 0; + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( inverse(Matrix()) ); + CALL_SUBTEST_2( inverse(Matrix2d()) ); + CALL_SUBTEST_3( inverse(Matrix3f()) ); + CALL_SUBTEST_4( inverse(Matrix4f()) ); + CALL_SUBTEST_4( inverse(Matrix()) ); + + s = internal::random(50,320); + CALL_SUBTEST_5( inverse(MatrixXf(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + CALL_SUBTEST_5( inverse_zerosized() ); + CALL_SUBTEST_5( inverse(MatrixXf(0, 0)) ); + CALL_SUBTEST_5( inverse(MatrixXf(1, 1)) ); + + s = internal::random(25,100); + CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) + + CALL_SUBTEST_7( inverse(Matrix4d()) ); + CALL_SUBTEST_7( inverse(Matrix()) ); + + CALL_SUBTEST_8( inverse(Matrix4cd()) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/io.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/io.cpp new file mode 100644 index 0000000000000000000000000000000000000000..aa14e76e9b984d922e09fb743d78648e92de6bdb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/io.cpp @@ -0,0 +1,71 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2019 Joel Holdsworth +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include + +#include "main.h" + +template +struct check_ostream_impl +{ + static void run() + { + const Array array(123); + std::ostringstream ss; + ss << array; + VERIFY(ss.str() == "123"); + + check_ostream_impl< std::complex >::run(); + }; +}; + +template<> +struct check_ostream_impl +{ + static void run() + { + const Array array(1, 0); + std::ostringstream ss; + ss << array; + VERIFY(ss.str() == "1 0"); + }; +}; + +template +struct check_ostream_impl< std::complex > +{ + static void run() + { + const Array,1,1> array(std::complex(12, 34)); + std::ostringstream ss; + ss << array; + VERIFY(ss.str() == "(12,34)"); + }; +}; + +template +static void check_ostream() +{ + check_ostream_impl::run(); +} + +EIGEN_DECLARE_TEST(rand) +{ + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); + CALL_SUBTEST(check_ostream()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/is_same_dense.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/is_same_dense.cpp new file mode 100644 index 0000000000000000000000000000000000000000..23dd806ebd9941b6c5477cbed2eb37749e4d7156 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/is_same_dense.cpp @@ -0,0 +1,41 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +using internal::is_same_dense; + +EIGEN_DECLARE_TEST(is_same_dense) +{ + typedef Matrix ColMatrixXd; + typedef Matrix,Dynamic,Dynamic,ColMajor> ColMatrixXcd; + ColMatrixXd m1(10,10); + ColMatrixXcd m2(10,10); + Ref ref_m1(m1); + Ref > ref_m2_real(m2.real()); + Ref const_ref_m1(m1); + + VERIFY(is_same_dense(m1,m1)); + VERIFY(is_same_dense(m1,ref_m1)); + VERIFY(is_same_dense(const_ref_m1,m1)); + VERIFY(is_same_dense(const_ref_m1,ref_m1)); + + VERIFY(is_same_dense(m1.block(0,0,m1.rows(),m1.cols()),m1)); + VERIFY(!is_same_dense(m1.row(0),m1.col(0))); + + Ref const_ref_m1_row(m1.row(1)); + VERIFY(!is_same_dense(m1.row(1),const_ref_m1_row)); + + Ref const_ref_m1_col(m1.col(1)); + VERIFY(is_same_dense(m1.col(1),const_ref_m1_col)); + + + VERIFY(!is_same_dense(m1, ref_m2_real)); + VERIFY(!is_same_dense(m2, ref_m2_real)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobi.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobi.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5604797f526089176bb061f86ab1503b162985c8 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobi.cpp @@ -0,0 +1,80 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template +void jacobi(const MatrixType& m = MatrixType()) +{ + Index rows = m.rows(); + Index cols = m.cols(); + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + typedef Matrix JacobiVector; + + const MatrixType a(MatrixType::Random(rows, cols)); + + JacobiVector v = JacobiVector::Random().normalized(); + JacobiScalar c = v.x(), s = v.y(); + JacobiRotation rot(c, s); + + { + Index p = internal::random(0, rows-1); + Index q; + do { + q = internal::random(0, rows-1); + } while (q == p); + + MatrixType b = a; + b.applyOnTheLeft(p, q, rot); + VERIFY_IS_APPROX(b.row(p), c * a.row(p) + numext::conj(s) * a.row(q)); + VERIFY_IS_APPROX(b.row(q), -s * a.row(p) + numext::conj(c) * a.row(q)); + } + + { + Index p = internal::random(0, cols-1); + Index q; + do { + q = internal::random(0, cols-1); + } while (q == p); + + MatrixType b = a; + b.applyOnTheRight(p, q, rot); + VERIFY_IS_APPROX(b.col(p), c * a.col(p) - s * a.col(q)); + VERIFY_IS_APPROX(b.col(q), numext::conj(s) * a.col(p) + numext::conj(c) * a.col(q)); + } +} + +EIGEN_DECLARE_TEST(jacobi) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(( jacobi() )); + CALL_SUBTEST_2(( jacobi() )); + CALL_SUBTEST_3(( jacobi() )); + CALL_SUBTEST_3(( jacobi >() )); + + int r = internal::random(2, internal::random(1,EIGEN_TEST_MAX_SIZE)/2), + c = internal::random(2, internal::random(1,EIGEN_TEST_MAX_SIZE)/2); + CALL_SUBTEST_4(( jacobi(MatrixXf(r,c)) )); + CALL_SUBTEST_5(( jacobi(MatrixXcd(r,c)) )); + CALL_SUBTEST_5(( jacobi >(MatrixXcd(r,c)) )); + // complex is really important to test as it is the only way to cover conjugation issues in certain unaligned paths + CALL_SUBTEST_6(( jacobi(MatrixXcf(r,c)) )); + CALL_SUBTEST_6(( jacobi >(MatrixXcf(r,c)) )); + + TEST_SET_BUT_UNUSED_VARIABLE(r); + TEST_SET_BUT_UNUSED_VARIABLE(c); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobisvd.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobisvd.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5b15c5a27bff8996be7ab66dc49581fcfd226840 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/jacobisvd.cpp @@ -0,0 +1,147 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2014 Gael Guennebaud +// Copyright (C) 2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// discard stack allocation as that too bypasses malloc +#define EIGEN_STACK_ALLOCATION_LIMIT 0 +#define EIGEN_RUNTIME_NO_MALLOC +#include "main.h" +#include + +#define SVD_DEFAULT(M) JacobiSVD +#define SVD_FOR_MIN_NORM(M) JacobiSVD +#include "svd_common.h" + +// Check all variants of JacobiSVD +template +void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true) +{ + MatrixType m = a; + if(pickrandom) + svd_fill_random(m); + + CALL_SUBTEST(( svd_test_all_computation_options >(m, true) )); // check full only + CALL_SUBTEST(( svd_test_all_computation_options >(m, false) )); + CALL_SUBTEST(( svd_test_all_computation_options >(m, false) )); + if(m.rows()==m.cols()) + CALL_SUBTEST(( svd_test_all_computation_options >(m, false) )); +} + +template void jacobisvd_verify_assert(const MatrixType& m) +{ + svd_verify_assert >(m); + svd_verify_assert >(m, true); + svd_verify_assert >(m); + svd_verify_assert >(m); + Index rows = m.rows(); + Index cols = m.cols(); + + enum { + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + + MatrixType a = MatrixType::Zero(rows, cols); + a.setZero(); + + if (ColsAtCompileTime == Dynamic) + { + JacobiSVD svd_fullqr; + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV)) + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV)) + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV)) + } +} + +template +void jacobisvd_method() +{ + enum { Size = MatrixType::RowsAtCompileTime }; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix RealVecType; + MatrixType m = MatrixType::Identity(); + VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones()); + VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU()); + VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV()); + VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m); + VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).transpose().solve(m), m); + VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).adjoint().solve(m), m); +} + +namespace Foo { +// older compiler require a default constructor for Bar +// cf: https://stackoverflow.com/questions/7411515/ +class Bar {public: Bar() {}}; +bool operator<(const Bar&, const Bar&) { return true; } +} +// regression test for a very strange MSVC issue for which simply +// including SVDBase.h messes up with std::max and custom scalar type +void msvc_workaround() +{ + const Foo::Bar a; + const Foo::Bar b; + std::max EIGEN_NOT_A_MACRO (a,b); +} + +EIGEN_DECLARE_TEST(jacobisvd) +{ + CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) )); + CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) )); + CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) )); + CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) )); + + CALL_SUBTEST_11(svd_all_trivial_2x2(jacobisvd)); + CALL_SUBTEST_12(svd_all_trivial_2x2(jacobisvd)); + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_3(( jacobisvd() )); + CALL_SUBTEST_4(( jacobisvd() )); + CALL_SUBTEST_5(( jacobisvd >() )); + CALL_SUBTEST_6(( jacobisvd >(Matrix(10,2)) )); + + int r = internal::random(1, 30), + c = internal::random(1, 30); + + TEST_SET_BUT_UNUSED_VARIABLE(r) + TEST_SET_BUT_UNUSED_VARIABLE(c) + + CALL_SUBTEST_10(( jacobisvd(MatrixXd(r,c)) )); + CALL_SUBTEST_7(( jacobisvd(MatrixXf(r,c)) )); + CALL_SUBTEST_8(( jacobisvd(MatrixXcd(r,c)) )); + (void) r; + (void) c; + + // Test on inf/nan matrix + CALL_SUBTEST_7( (svd_inf_nan, MatrixXf>()) ); + CALL_SUBTEST_10( (svd_inf_nan, MatrixXd>()) ); + + // bug1395 test compile-time vectors as input + CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix()) )); + CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix()) )); + CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix(r)) )); + CALL_SUBTEST_13(( jacobisvd_verify_assert(Matrix(c)) )); + } + + CALL_SUBTEST_7(( jacobisvd(MatrixXf(internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + CALL_SUBTEST_8(( jacobisvd(MatrixXcd(internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) )); + + // test matrixbase method + CALL_SUBTEST_1(( jacobisvd_method() )); + CALL_SUBTEST_3(( jacobisvd_method() )); + + // Test problem size constructors + CALL_SUBTEST_7( JacobiSVD(10,10) ); + + // Check that preallocation avoids subsequent mallocs + CALL_SUBTEST_9( svd_preallocate() ); + + CALL_SUBTEST_2( svd_underoverflow() ); + + msvc_workaround(); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/klu_support.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/klu_support.cpp new file mode 100644 index 0000000000000000000000000000000000000000..f806ad50ef566bdb569fae6776a90323ee2076ca --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/klu_support.cpp @@ -0,0 +1,32 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS +#include "sparse_solver.h" + +#include + +template void test_klu_support_T() +{ + KLU > klu_colmajor; + KLU > klu_rowmajor; + + check_sparse_square_solving(klu_colmajor); + check_sparse_square_solving(klu_rowmajor); + + //check_sparse_square_determinant(umfpack_colmajor); + //check_sparse_square_determinant(umfpack_rowmajor); +} + +EIGEN_DECLARE_TEST(klu_support) +{ + CALL_SUBTEST_1(test_klu_support_T()); + CALL_SUBTEST_2(test_klu_support_T >()); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/linearstructure.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/linearstructure.cpp new file mode 100644 index 0000000000000000000000000000000000000000..46ee5162b84049103500e2997814923f5bfa0243 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/linearstructure.cpp @@ -0,0 +1,147 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2014 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +static bool g_called; +#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same::value); } + +#include "main.h" + +template void linearStructure(const MatrixType& m) +{ + using std::abs; + /* this test covers the following files: + CwiseUnaryOp.h, CwiseBinaryOp.h, SelfCwiseBinaryOp.h + */ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + // this test relies a lot on Random.h, and there's not much more that we can do + // to test it, hence I consider that we will have tested Random.h + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols); + + Scalar s1 = internal::random(); + while (abs(s1)(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + VERIFY_IS_APPROX(-(-m1), m1); + VERIFY_IS_APPROX(m1+m1, 2*m1); + VERIFY_IS_APPROX(m1+m2-m1, m2); + VERIFY_IS_APPROX(-m2+m1+m2, m1); + VERIFY_IS_APPROX(m1*s1, s1*m1); + VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2); + VERIFY_IS_APPROX((-m1+m2)*s1, -s1*m1+s1*m2); + m3 = m2; m3 += m1; + VERIFY_IS_APPROX(m3, m1+m2); + m3 = m2; m3 -= m1; + VERIFY_IS_APPROX(m3, m2-m1); + m3 = m2; m3 *= s1; + VERIFY_IS_APPROX(m3, s1*m2); + if(!NumTraits::IsInteger) + { + m3 = m2; m3 /= s1; + VERIFY_IS_APPROX(m3, m2/s1); + } + + // again, test operator() to check const-qualification + VERIFY_IS_APPROX((-m1)(r,c), -(m1(r,c))); + VERIFY_IS_APPROX((m1-m2)(r,c), (m1(r,c))-(m2(r,c))); + VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c))); + VERIFY_IS_APPROX((s1*m1)(r,c), s1*(m1(r,c))); + VERIFY_IS_APPROX((m1*s1)(r,c), (m1(r,c))*s1); + if(!NumTraits::IsInteger) + VERIFY_IS_APPROX((m1/s1)(r,c), (m1(r,c))/s1); + + // use .block to disable vectorization and compare to the vectorized version + VERIFY_IS_APPROX(m1+m1.block(0,0,rows,cols), m1+m1); + VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), m1.cwiseProduct(m1)); + VERIFY_IS_APPROX(m1 - m1.block(0,0,rows,cols), m1 - m1); + VERIFY_IS_APPROX(m1.block(0,0,rows,cols) * s1, m1 * s1); +} + +// Make sure that complex * real and real * complex are properly optimized +template void real_complex(DenseIndex rows = MatrixType::RowsAtCompileTime, DenseIndex cols = MatrixType::ColsAtCompileTime) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + + RealScalar s = internal::random(); + MatrixType m1 = MatrixType::Random(rows, cols); + + g_called = false; + VERIFY_IS_APPROX(s*m1, Scalar(s)*m1); + VERIFY(g_called && "real * matrix not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(m1*s, m1*Scalar(s)); + VERIFY(g_called && "matrix * real not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(m1/s, m1/Scalar(s)); + VERIFY(g_called && "matrix / real not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(s+m1.array(), Scalar(s)+m1.array()); + VERIFY(g_called && "real + matrix not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(m1.array()+s, m1.array()+Scalar(s)); + VERIFY(g_called && "matrix + real not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(s-m1.array(), Scalar(s)-m1.array()); + VERIFY(g_called && "real - matrix not properly optimized"); + + g_called = false; + VERIFY_IS_APPROX(m1.array()-s, m1.array()-Scalar(s)); + VERIFY(g_called && "matrix - real not properly optimized"); +} + +template +void linearstructure_overflow() +{ + // make sure that /=scalar and /scalar do not overflow + // rational: 1.0/4.94e-320 overflow, but m/4.94e-320 should not + Matrix4d m2, m3; + m3 = m2 = Matrix4d::Random()*1e-20; + m2 = m2 / 4.9e-320; + VERIFY_IS_APPROX(m2.cwiseQuotient(m2), Matrix4d::Ones()); + m3 /= 4.9e-320; + VERIFY_IS_APPROX(m3.cwiseQuotient(m3), Matrix4d::Ones()); +} + +EIGEN_DECLARE_TEST(linearstructure) +{ + g_called = true; + VERIFY(g_called); // avoid `unneeded-internal-declaration` warning. + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( linearStructure(Matrix()) ); + CALL_SUBTEST_2( linearStructure(Matrix2f()) ); + CALL_SUBTEST_3( linearStructure(Vector3d()) ); + CALL_SUBTEST_4( linearStructure(Matrix4d()) ); + CALL_SUBTEST_5( linearStructure(MatrixXcf(internal::random(1,EIGEN_TEST_MAX_SIZE/2), internal::random(1,EIGEN_TEST_MAX_SIZE/2))) ); + CALL_SUBTEST_6( linearStructure(MatrixXf (internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_7( linearStructure(MatrixXi (internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_8( linearStructure(MatrixXcd(internal::random(1,EIGEN_TEST_MAX_SIZE/2), internal::random(1,EIGEN_TEST_MAX_SIZE/2))) ); + CALL_SUBTEST_9( linearStructure(ArrayXXf (internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_10( linearStructure(ArrayXXcf (internal::random(1,EIGEN_TEST_MAX_SIZE), internal::random(1,EIGEN_TEST_MAX_SIZE))) ); + + CALL_SUBTEST_11( real_complex() ); + CALL_SUBTEST_11( real_complex(10,10) ); + CALL_SUBTEST_11( real_complex(10,10) ); + } + CALL_SUBTEST_4( linearstructure_overflow<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lscg.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lscg.cpp new file mode 100644 index 0000000000000000000000000000000000000000..feb2347a8fc7c20400bbbc9c170cf54690279788 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lscg.cpp @@ -0,0 +1,37 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "sparse_solver.h" +#include + +template void test_lscg_T() +{ + LeastSquaresConjugateGradient > lscg_colmajor_diag; + LeastSquaresConjugateGradient, IdentityPreconditioner> lscg_colmajor_I; + LeastSquaresConjugateGradient > lscg_rowmajor_diag; + LeastSquaresConjugateGradient, IdentityPreconditioner> lscg_rowmajor_I; + + CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_diag) ); + CALL_SUBTEST( check_sparse_square_solving(lscg_colmajor_I) ); + + CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_diag) ); + CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_colmajor_I) ); + + CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_diag) ); + CALL_SUBTEST( check_sparse_square_solving(lscg_rowmajor_I) ); + + CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_diag) ); + CALL_SUBTEST( check_sparse_leastsquare_solving(lscg_rowmajor_I) ); +} + +EIGEN_DECLARE_TEST(lscg) +{ + CALL_SUBTEST_1(test_lscg_T()); + CALL_SUBTEST_2(test_lscg_T >()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lu.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lu.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1bbadcbf0ff6b65479cba01849503f7c7dc33117 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/lu.cpp @@ -0,0 +1,252 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include +#include "solverbase.h" +using namespace std; + +template +typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) { + return m.cwiseAbs().colwise().sum().maxCoeff(); +} + +template void lu_non_invertible() +{ + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + + typedef typename MatrixType::RealScalar RealScalar; + /* this test covers the following files: + LU.h + */ + Index rows, cols, cols2; + if(MatrixType::RowsAtCompileTime==Dynamic) + { + rows = internal::random(2,EIGEN_TEST_MAX_SIZE); + } + else + { + rows = MatrixType::RowsAtCompileTime; + } + if(MatrixType::ColsAtCompileTime==Dynamic) + { + cols = internal::random(2,EIGEN_TEST_MAX_SIZE); + cols2 = internal::random(2,EIGEN_TEST_MAX_SIZE); + } + else + { + cols2 = cols = MatrixType::ColsAtCompileTime; + } + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + typedef typename internal::kernel_retval_base >::ReturnType KernelMatrixType; + typedef typename internal::image_retval_base >::ReturnType ImageMatrixType; + typedef Matrix + CMatrixType; + typedef Matrix + RMatrixType; + + Index rank = internal::random(1, (std::min)(rows, cols)-1); + + // The image of the zero matrix should consist of a single (zero) column vector + VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1)); + + // The kernel of the zero matrix is the entire space, and thus is an invertible matrix of dimensions cols. + KernelMatrixType kernel = MatrixType::Zero(rows,cols).fullPivLu().kernel(); + VERIFY((kernel.fullPivLu().isInvertible())); + + MatrixType m1(rows, cols), m3(rows, cols2); + CMatrixType m2(cols, cols2); + createRandomPIMatrixOfRank(rank, rows, cols, m1); + + FullPivLU lu; + + // The special value 0.01 below works well in tests. Keep in mind that we're only computing the rank + // of singular values are either 0 or 1. + // So it's not clear at all that the epsilon should play any role there. + lu.setThreshold(RealScalar(0.01)); + lu.compute(m1); + + MatrixType u(rows,cols); + u = lu.matrixLU().template triangularView(); + RMatrixType l = RMatrixType::Identity(rows,rows); + l.block(0,0,rows,(std::min)(rows,cols)).template triangularView() + = lu.matrixLU().block(0,0,rows,(std::min)(rows,cols)); + + VERIFY_IS_APPROX(lu.permutationP() * m1 * lu.permutationQ(), l*u); + + KernelMatrixType m1kernel = lu.kernel(); + ImageMatrixType m1image = lu.image(m1); + + VERIFY_IS_APPROX(m1, lu.reconstructedMatrix()); + VERIFY(rank == lu.rank()); + VERIFY(cols - lu.rank() == lu.dimensionOfKernel()); + VERIFY(!lu.isInjective()); + VERIFY(!lu.isInvertible()); + VERIFY(!lu.isSurjective()); + VERIFY_IS_MUCH_SMALLER_THAN((m1 * m1kernel), m1); + VERIFY(m1image.fullPivLu().rank() == rank); + VERIFY_IS_APPROX(m1 * m1.adjoint() * m1image, m1image); + + check_solverbase(m1, lu, rows, cols, cols2); + + m2 = CMatrixType::Random(cols,cols2); + m3 = m1*m2; + m2 = CMatrixType::Random(cols,cols2); + // test that the code, which does resize(), may be applied to an xpr + m2.block(0,0,m2.rows(),m2.cols()) = lu.solve(m3); + VERIFY_IS_APPROX(m3, m1*m2); +} + +template void lu_invertible() +{ + /* this test covers the following files: + FullPivLU.h + */ + typedef typename NumTraits::Real RealScalar; + Index size = MatrixType::RowsAtCompileTime; + if( size==Dynamic) + size = internal::random(1,EIGEN_TEST_MAX_SIZE); + + MatrixType m1(size, size), m2(size, size), m3(size, size); + FullPivLU lu; + lu.setThreshold(RealScalar(0.01)); + do { + m1 = MatrixType::Random(size,size); + lu.compute(m1); + } while(!lu.isInvertible()); + + VERIFY_IS_APPROX(m1, lu.reconstructedMatrix()); + VERIFY(0 == lu.dimensionOfKernel()); + VERIFY(lu.kernel().cols() == 1); // the kernel() should consist of a single (zero) column vector + VERIFY(size == lu.rank()); + VERIFY(lu.isInjective()); + VERIFY(lu.isSurjective()); + VERIFY(lu.isInvertible()); + VERIFY(lu.image(m1).fullPivLu().isInvertible()); + + check_solverbase(m1, lu, size, size, size); + + MatrixType m1_inverse = lu.inverse(); + m3 = MatrixType::Random(size,size); + m2 = lu.solve(m3); + VERIFY_IS_APPROX(m2, m1_inverse*m3); + + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse); + const RealScalar rcond_est = lu.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); + + // Regression test for Bug 302 + MatrixType m4 = MatrixType::Random(size,size); + VERIFY_IS_APPROX(lu.solve(m3*m4), lu.solve(m3)*m4); +} + +template void lu_partial_piv(Index size = MatrixType::ColsAtCompileTime) +{ + /* this test covers the following files: + PartialPivLU.h + */ + typedef typename NumTraits::Real RealScalar; + + MatrixType m1(size, size), m2(size, size), m3(size, size); + m1.setRandom(); + PartialPivLU plu(m1); + + STATIC_CHECK(( internal::is_same::StorageIndex,int>::value )); + + VERIFY_IS_APPROX(m1, plu.reconstructedMatrix()); + + check_solverbase(m1, plu, size, size, size); + + MatrixType m1_inverse = plu.inverse(); + m3 = MatrixType::Random(size,size); + m2 = plu.solve(m3); + VERIFY_IS_APPROX(m2, m1_inverse*m3); + + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse); + const RealScalar rcond_est = plu.rcond(); + // Verify that the estimate is within a factor of 10 of the truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); +} + +template void lu_verify_assert() +{ + MatrixType tmp; + + FullPivLU lu; + VERIFY_RAISES_ASSERT(lu.matrixLU()) + VERIFY_RAISES_ASSERT(lu.permutationP()) + VERIFY_RAISES_ASSERT(lu.permutationQ()) + VERIFY_RAISES_ASSERT(lu.kernel()) + VERIFY_RAISES_ASSERT(lu.image(tmp)) + VERIFY_RAISES_ASSERT(lu.solve(tmp)) + VERIFY_RAISES_ASSERT(lu.transpose().solve(tmp)) + VERIFY_RAISES_ASSERT(lu.adjoint().solve(tmp)) + VERIFY_RAISES_ASSERT(lu.determinant()) + VERIFY_RAISES_ASSERT(lu.rank()) + VERIFY_RAISES_ASSERT(lu.dimensionOfKernel()) + VERIFY_RAISES_ASSERT(lu.isInjective()) + VERIFY_RAISES_ASSERT(lu.isSurjective()) + VERIFY_RAISES_ASSERT(lu.isInvertible()) + VERIFY_RAISES_ASSERT(lu.inverse()) + + PartialPivLU plu; + VERIFY_RAISES_ASSERT(plu.matrixLU()) + VERIFY_RAISES_ASSERT(plu.permutationP()) + VERIFY_RAISES_ASSERT(plu.solve(tmp)) + VERIFY_RAISES_ASSERT(plu.transpose().solve(tmp)) + VERIFY_RAISES_ASSERT(plu.adjoint().solve(tmp)) + VERIFY_RAISES_ASSERT(plu.determinant()) + VERIFY_RAISES_ASSERT(plu.inverse()) +} + +EIGEN_DECLARE_TEST(lu) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( lu_non_invertible() ); + CALL_SUBTEST_1( lu_invertible() ); + CALL_SUBTEST_1( lu_verify_assert() ); + CALL_SUBTEST_1( lu_partial_piv() ); + + CALL_SUBTEST_2( (lu_non_invertible >()) ); + CALL_SUBTEST_2( (lu_verify_assert >()) ); + CALL_SUBTEST_2( lu_partial_piv() ); + CALL_SUBTEST_2( lu_partial_piv() ); + CALL_SUBTEST_2( (lu_partial_piv >()) ); + + CALL_SUBTEST_3( lu_non_invertible() ); + CALL_SUBTEST_3( lu_invertible() ); + CALL_SUBTEST_3( lu_verify_assert() ); + + CALL_SUBTEST_4( lu_non_invertible() ); + CALL_SUBTEST_4( lu_invertible() ); + CALL_SUBTEST_4( lu_partial_piv(internal::random(1,EIGEN_TEST_MAX_SIZE)) ); + CALL_SUBTEST_4( lu_verify_assert() ); + + CALL_SUBTEST_5( lu_non_invertible() ); + CALL_SUBTEST_5( lu_invertible() ); + CALL_SUBTEST_5( lu_verify_assert() ); + + CALL_SUBTEST_6( lu_non_invertible() ); + CALL_SUBTEST_6( lu_invertible() ); + CALL_SUBTEST_6( lu_partial_piv(internal::random(1,EIGEN_TEST_MAX_SIZE)) ); + CALL_SUBTEST_6( lu_verify_assert() ); + + CALL_SUBTEST_7(( lu_non_invertible >() )); + + // Test problem size constructors + CALL_SUBTEST_9( PartialPivLU(10) ); + CALL_SUBTEST_9( FullPivLU(10, 20); ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/main.h b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/main.h new file mode 100644 index 0000000000000000000000000000000000000000..01667388b2e2a4c4569a7ec0ad850c57075d9808 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/main.h @@ -0,0 +1,1058 @@ + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +// The following includes of STL headers have to be done _before_ the +// definition of macros min() and max(). The reason is that many STL +// implementations will not work properly as the min and max symbols collide +// with the STL functions std:min() and std::max(). The STL headers may check +// for the macro definition of min/max and issue a warning or undefine the +// macros. +// +// Still, Windows defines min() and max() in windef.h as part of the regular +// Windows system interfaces and many other Windows APIs depend on these +// macros being available. To prevent the macro expansion of min/max and to +// make Eigen compatible with the Windows environment all function calls of +// std::min() and std::max() have to be written with parenthesis around the +// function name. +// +// All STL headers used by Eigen should be included here. Because main.h is +// included before any Eigen header and because the STL headers are guarded +// against multiple inclusions, no STL header will see our own min/max macro +// definitions. +#include +#include +// Disable ICC's std::complex operator specializations so we can use our own. +#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1 +#include +#include +#include +#include +#include +#if __cplusplus >= 201103L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201103L) +#include +#include +#ifdef EIGEN_USE_THREADS +#include +#endif +#endif + +// Same for cuda_fp16.h +#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA) + // Means the compiler is either nvcc or clang with CUDA enabled + #define EIGEN_CUDACC __CUDACC__ +#endif +#if defined(EIGEN_CUDACC) +#include + #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10) +#else + #define EIGEN_CUDA_SDK_VER 0 +#endif +#if EIGEN_CUDA_SDK_VER >= 70500 +#include +#endif + +// To test that all calls from Eigen code to std::min() and std::max() are +// protected by parenthesis against macro expansion, the min()/max() macros +// are defined here and any not-parenthesized min/max call will cause a +// compiler error. +#if !defined(__HIPCC__) && !defined(EIGEN_USE_SYCL) + // + // HIP header files include the following files + // + // + // + // which seem to contain not-parenthesized calls to "max"/"min", triggering the following check and causing the compile to fail + // + // Including those header files before the following macro definition for "min" / "max", only partially resolves the issue + // This is because other HIP header files also define "isnan" / "isinf" / "isfinite" functions, which are needed in other + // headers. + // + // So instead choosing to simply disable this check for HIP + // + #define min(A,B) please_protect_your_min_with_parentheses + #define max(A,B) please_protect_your_max_with_parentheses + #define isnan(X) please_protect_your_isnan_with_parentheses + #define isinf(X) please_protect_your_isinf_with_parentheses + #define isfinite(X) please_protect_your_isfinite_with_parentheses +#endif + + +// test possible conflicts +struct real {}; +struct imag {}; + +#ifdef M_PI +#undef M_PI +#endif +#define M_PI please_use_EIGEN_PI_instead_of_M_PI + +#define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes +// B0 is defined in POSIX header termios.h +#define B0 FORBIDDEN_IDENTIFIER +// `I` may be defined by complex.h: +#define I FORBIDDEN_IDENTIFIER + +// Unit tests calling Eigen's blas library must preserve the default blocking size +// to avoid troubles. +#ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS +#define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS +#endif + +// shuts down ICC's remark #593: variable "XXX" was set but never used +#define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X) + +#ifdef TEST_ENABLE_TEMPORARY_TRACKING + +static long int nb_temporaries; +static long int nb_temporaries_on_assert = -1; + +inline void on_temporary_creation(long int size) { + // here's a great place to set a breakpoint when debugging failures in this test! + if(size!=0) nb_temporaries++; + if(nb_temporaries_on_assert>0) assert(nb_temporaries if NDEBUG is not defined. +#ifndef DEBUG +#define DEBUG +#endif + +// bounds integer values for AltiVec +#if defined(__ALTIVEC__) || defined(__VSX__) +#define EIGEN_MAKING_DOCS +#endif + +#define DEFAULT_REPEAT 10 + +namespace Eigen +{ + static std::vector g_test_stack; + // level == 0 <=> abort if test fail + // level >= 1 <=> warning message to std::cerr if test fail + static int g_test_level = 0; + static int g_repeat = 1; + static unsigned int g_seed = 0; + static bool g_has_set_repeat = false, g_has_set_seed = false; + + class EigenTest + { + public: + EigenTest() : m_func(0) {} + EigenTest(const char* a_name, void (*func)(void)) + : m_name(a_name), m_func(func) + { + get_registered_tests().push_back(this); + } + const std::string& name() const { return m_name; } + void operator()() const { m_func(); } + + static const std::vector& all() { return get_registered_tests(); } + protected: + static std::vector& get_registered_tests() + { + static std::vector* ms_registered_tests = new std::vector(); + return *ms_registered_tests; + } + std::string m_name; + void (*m_func)(void); + }; + + // Declare and register a test, e.g.: + // EIGEN_DECLARE_TEST(mytest) { ... } + // will create a function: + // void test_mytest() { ... } + // that will be automatically called. + #define EIGEN_DECLARE_TEST(X) \ + void EIGEN_CAT(test_,X) (); \ + static EigenTest EIGEN_CAT(test_handler_,X) (EIGEN_MAKESTRING(X), & EIGEN_CAT(test_,X)); \ + void EIGEN_CAT(test_,X) () +} + +#define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl +// #define TRACK while() + +#define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, " ", "\n", "", "", "", "") + +#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__) + #define EIGEN_EXCEPTIONS +#endif + +#ifndef EIGEN_NO_ASSERTION_CHECKING + + namespace Eigen + { + static const bool should_raise_an_assert = false; + + // Used to avoid to raise two exceptions at a time in which + // case the exception is not properly caught. + // This may happen when a second exceptions is triggered in a destructor. + static bool no_more_assert = false; + static bool report_on_cerr_on_assert_failure = true; + + struct eigen_assert_exception + { + eigen_assert_exception(void) {} + ~eigen_assert_exception() { Eigen::no_more_assert = false; } + }; + + struct eigen_static_assert_exception + { + eigen_static_assert_exception(void) {} + ~eigen_static_assert_exception() { Eigen::no_more_assert = false; } + }; + } + // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while + // one should have been, then the list of executed assertions is printed out. + // + // EIGEN_DEBUG_ASSERTS is not enabled by default as it + // significantly increases the compilation time + // and might even introduce side effects that would hide + // some memory errors. + #ifdef EIGEN_DEBUG_ASSERTS + + namespace Eigen + { + namespace internal + { + static bool push_assert = false; + } + static std::vector eigen_assert_list; + } + #define eigen_assert(a) \ + if( (!(a)) && (!no_more_assert) ) \ + { \ + if(report_on_cerr_on_assert_failure) \ + std::cerr << #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \ + Eigen::no_more_assert = true; \ + EIGEN_THROW_X(Eigen::eigen_assert_exception()); \ + } \ + else if (Eigen::internal::push_assert) \ + { \ + eigen_assert_list.push_back(std::string(EIGEN_MAKESTRING(__FILE__) " (" EIGEN_MAKESTRING(__LINE__) ") : " #a) ); \ + } + + #ifdef EIGEN_EXCEPTIONS + #define VERIFY_RAISES_ASSERT(a) \ + { \ + Eigen::no_more_assert = false; \ + Eigen::eigen_assert_list.clear(); \ + Eigen::internal::push_assert = true; \ + Eigen::report_on_cerr_on_assert_failure = false; \ + try { \ + a; \ + std::cerr << "One of the following asserts should have been triggered:\n"; \ + for (uint ai=0 ; ai // required for createRandomPIMatrixOfRank and generateRandomMatrixSvs + +inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string) +{ + if (!condition) + { + if(Eigen::g_test_level>0) + std::cerr << "WARNING: "; + std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")" + << std::endl << " " << condition_as_string << std::endl; + std::cerr << "Stack:\n"; + const int test_stack_size = static_cast(Eigen::g_test_stack.size()); + for(int i=test_stack_size-1; i>=0; --i) + std::cerr << " - " << Eigen::g_test_stack[i] << "\n"; + std::cerr << "\n"; + if(Eigen::g_test_level==0) + abort(); + } +} + +#define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a)) + +#define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a >= b)) +#define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a <= b)) + + +#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true)) +#define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false)) +#define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b)) +#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b)) +#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b)) +#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b)) +#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b)) +#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b)) + +#define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a)) + +#define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT ) + +#define CALL_SUBTEST(FUNC) do { \ + g_test_stack.push_back(EIGEN_MAKESTRING(FUNC)); \ + FUNC; \ + g_test_stack.pop_back(); \ + } while (0) + + + namespace Eigen { + +// Forward declarations to avoid ICC warnings +template +bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true); + +template +void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m); + +template +void randomPermutationVector(PermutationVectorType& v, Index size); + +template +MatrixType generateRandomUnitaryMatrix(const Index dim); + +template +void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M); + +template +VectorType setupRandomSvs(const Index dim, const RealScalar max); + +template +VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max); + +} // end namespace Eigen + +// Forward declaration to avoid ICC warnings +template std::string type_name(); + + +namespace Eigen { + +template +typename internal::enable_if::value,bool>::type +is_same_type(const T1&, const T2&) +{ + return true; +} + +template inline typename NumTraits::Real test_precision() { return NumTraits::dummy_precision(); } +template<> inline float test_precision() { return 1e-3f; } +template<> inline double test_precision() { return 1e-6; } +template<> inline long double test_precision() { return 1e-6l; } +template<> inline float test_precision >() { return test_precision(); } +template<> inline double test_precision >() { return test_precision(); } +template<> inline long double test_precision >() { return test_precision(); } + +#define EIGEN_TEST_SCALAR_TEST_OVERLOAD(TYPE) \ + inline bool test_isApprox(TYPE a, TYPE b) \ + { return internal::isApprox(a, b, test_precision()); } \ + inline bool test_isMuchSmallerThan(TYPE a, TYPE b) \ + { return internal::isMuchSmallerThan(a, b, test_precision()); } \ + inline bool test_isApproxOrLessThan(TYPE a, TYPE b) \ + { return internal::isApproxOrLessThan(a, b, test_precision()); } + +EIGEN_TEST_SCALAR_TEST_OVERLOAD(short) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned short) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(int) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned int) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(long) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long) +#if EIGEN_HAS_CXX11 +EIGEN_TEST_SCALAR_TEST_OVERLOAD(long long) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long long) +#endif +EIGEN_TEST_SCALAR_TEST_OVERLOAD(float) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(double) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(half) +EIGEN_TEST_SCALAR_TEST_OVERLOAD(bfloat16) + +#undef EIGEN_TEST_SCALAR_TEST_OVERLOAD + +#ifndef EIGEN_TEST_NO_COMPLEX +inline bool test_isApprox(const std::complex& a, const std::complex& b) +{ return internal::isApprox(a, b, test_precision >()); } +inline bool test_isMuchSmallerThan(const std::complex& a, const std::complex& b) +{ return internal::isMuchSmallerThan(a, b, test_precision >()); } + +inline bool test_isApprox(const std::complex& a, const std::complex& b) +{ return internal::isApprox(a, b, test_precision >()); } +inline bool test_isMuchSmallerThan(const std::complex& a, const std::complex& b) +{ return internal::isMuchSmallerThan(a, b, test_precision >()); } + +#ifndef EIGEN_TEST_NO_LONGDOUBLE +inline bool test_isApprox(const std::complex& a, const std::complex& b) +{ return internal::isApprox(a, b, test_precision >()); } +inline bool test_isMuchSmallerThan(const std::complex& a, const std::complex& b) +{ return internal::isMuchSmallerThan(a, b, test_precision >()); } +#endif +#endif + +#ifndef EIGEN_TEST_NO_LONGDOUBLE +inline bool test_isApprox(const long double& a, const long double& b) +{ + bool ret = internal::isApprox(a, b, test_precision()); + if (!ret) std::cerr + << std::endl << " actual = " << a + << std::endl << " expected = " << b << std::endl << std::endl; + return ret; +} + +inline bool test_isMuchSmallerThan(const long double& a, const long double& b) +{ return internal::isMuchSmallerThan(a, b, test_precision()); } +inline bool test_isApproxOrLessThan(const long double& a, const long double& b) +{ return internal::isApproxOrLessThan(a, b, test_precision()); } +#endif // EIGEN_TEST_NO_LONGDOUBLE + +// test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox. +template +typename NumTraits::NonInteger test_relative_error(const EigenBase &a, const EigenBase &b) +{ + using std::sqrt; + typedef typename NumTraits::NonInteger RealScalar; + typename internal::nested_eval::type ea(a.derived()); + typename internal::nested_eval::type eb(b.derived()); + return sqrt(RealScalar((ea-eb).cwiseAbs2().sum()) / RealScalar((std::min)(eb.cwiseAbs2().sum(),ea.cwiseAbs2().sum()))); +} + +template +typename T1::RealScalar test_relative_error(const T1 &a, const T2 &b, const typename T1::Coefficients* = 0) +{ + return test_relative_error(a.coeffs(), b.coeffs()); +} + +template +typename T1::Scalar test_relative_error(const T1 &a, const T2 &b, const typename T1::MatrixType* = 0) +{ + return test_relative_error(a.matrix(), b.matrix()); +} + +template +S test_relative_error(const Translation &a, const Translation &b) +{ + return test_relative_error(a.vector(), b.vector()); +} + +template +S test_relative_error(const ParametrizedLine &a, const ParametrizedLine &b) +{ + return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin())); +} + +template +S test_relative_error(const AlignedBox &a, const AlignedBox &b) +{ + return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)())); +} + +template class SparseMatrixBase; +template +typename T1::RealScalar test_relative_error(const MatrixBase &a, const SparseMatrixBase &b) +{ + return test_relative_error(a,b.toDense()); +} + +template class SparseMatrixBase; +template +typename T1::RealScalar test_relative_error(const SparseMatrixBase &a, const MatrixBase &b) +{ + return test_relative_error(a.toDense(),b); +} + +template class SparseMatrixBase; +template +typename T1::RealScalar test_relative_error(const SparseMatrixBase &a, const SparseMatrixBase &b) +{ + return test_relative_error(a.toDense(),b.toDense()); +} + +template +typename NumTraits::Real>::NonInteger test_relative_error(const T1 &a, const T2 &b, typename internal::enable_if::Real>::value, T1>::type* = 0) +{ + typedef typename NumTraits::Real>::NonInteger RealScalar; + return numext::sqrt(RealScalar(numext::abs2(a-b))/(numext::mini)(RealScalar(numext::abs2(a)),RealScalar(numext::abs2(b)))); +} + +template +T test_relative_error(const Rotation2D &a, const Rotation2D &b) +{ + return test_relative_error(a.angle(), b.angle()); +} + +template +T test_relative_error(const AngleAxis &a, const AngleAxis &b) +{ + return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis())); +} + +template +inline bool test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only +{ + return a.isApprox(b, test_precision()); +} + +// get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or expressions +template +typename NumTraits::Real get_test_precision(const T&, const typename T::Scalar* = 0) +{ + return test_precision::Real>(); +} + +template +typename NumTraits::Real get_test_precision(const T&,typename internal::enable_if::Real>::value, T>::type* = 0) +{ + return test_precision::Real>(); +} + +// verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails. +template +inline bool verifyIsApprox(const Type1& a, const Type2& b) +{ + bool ret = test_isApprox(a,b); + if(!ret) + { + std::cerr << "Difference too large wrt tolerance " << get_test_precision(a) << ", relative error is: " << test_relative_error(a,b) << std::endl; + } + return ret; +} + +// The idea behind this function is to compare the two scalars a and b where +// the scalar ref is a hint about the expected order of magnitude of a and b. +// WARNING: the scalar a and b must be positive +// Therefore, if for some reason a and b are very small compared to ref, +// we won't issue a false negative. +// This test could be: abs(a-b) <= eps * ref +// However, it seems that simply comparing a+ref and b+ref is more sensitive to true error. +template +inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref) +{ + return test_isApprox(a+ref, b+ref); +} + +template +inline bool test_isMuchSmallerThan(const MatrixBase& m1, + const MatrixBase& m2) +{ + return m1.isMuchSmallerThan(m2, test_precision::Scalar>()); +} + +template +inline bool test_isMuchSmallerThan(const MatrixBase& m, + const typename NumTraits::Scalar>::Real& s) +{ + return m.isMuchSmallerThan(s, test_precision::Scalar>()); +} + +template +inline bool test_isUnitary(const MatrixBase& m) +{ + return m.isUnitary(test_precision::Scalar>()); +} + +template +bool test_is_equal(const T& actual, const U& expected, bool expect_equal) +{ + if ((actual==expected) == expect_equal) + return true; + // false: + std::cerr + << "\n actual = " << actual + << "\n expected " << (expect_equal ? "= " : "!=") << expected << "\n\n"; + return false; +} + +// Forward declaration to avoid ICC warning +template +void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m); +/** + * Creates a random partial isometry matrix of given rank. + * + * A partial isometry is a matrix all of whose singular values are either 0 or 1. + * This is very useful to test rank-revealing algorithms. + * + * @tparam MatrixType type of random partial isometry matrix + * @param desired_rank rank requested for the random partial isometry matrix + * @param rows row dimension of requested random partial isometry matrix + * @param cols column dimension of requested random partial isometry matrix + * @param m random partial isometry matrix + */ +template +void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m) +{ + typedef typename internal::traits::Scalar Scalar; + enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; + + typedef Matrix VectorType; + typedef Matrix MatrixAType; + typedef Matrix MatrixBType; + + if(desired_rank == 0) + { + m.setZero(rows,cols); + return; + } + + if(desired_rank == 1) + { + // here we normalize the vectors to get a partial isometry + m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose(); + return; + } + + MatrixAType a = MatrixAType::Random(rows,rows); + MatrixType d = MatrixType::Identity(rows,cols); + MatrixBType b = MatrixBType::Random(cols,cols); + + // set the diagonal such that only desired_rank non-zero entries remain + const Index diag_size = (std::min)(d.rows(),d.cols()); + if(diag_size != desired_rank) + d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank); + + HouseholderQR qra(a); + HouseholderQR qrb(b); + m = qra.householderQ() * d * qrb.householderQ(); +} + +// Forward declaration to avoid ICC warning +template +void randomPermutationVector(PermutationVectorType& v, Index size); +/** + * Generate random permutation vector. + * + * @tparam PermutationVectorType type of vector used to store permutation + * @param v permutation vector + * @param size length of permutation vector + */ +template +void randomPermutationVector(PermutationVectorType& v, Index size) +{ + typedef typename PermutationVectorType::Scalar Scalar; + v.resize(size); + for(Index i = 0; i < size; ++i) v(i) = Scalar(i); + if(size == 1) return; + for(Index n = 0; n < 3 * size; ++n) + { + Index i = internal::random(0, size-1); + Index j; + do j = internal::random(0, size-1); while(j==i); + std::swap(v(i), v(j)); + } +} + +/** + * Generate a random unitary matrix of prescribed dimension. + * + * The algorithm is using a random Householder sequence to produce + * a random unitary matrix. + * + * @tparam MatrixType type of matrix to generate + * @param dim row and column dimension of the requested square matrix + * @return random unitary matrix + */ +template +MatrixType generateRandomUnitaryMatrix(const Index dim) +{ + typedef typename internal::traits::Scalar Scalar; + typedef Matrix VectorType; + + MatrixType v = MatrixType::Identity(dim, dim); + VectorType h = VectorType::Zero(dim); + for (Index i = 0; i < dim; ++i) + { + v.col(i).tail(dim - i - 1) = VectorType::Random(dim - i - 1); + h(i) = 2 / v.col(i).tail(dim - i).squaredNorm(); + } + + const Eigen::HouseholderSequence HSeq(v, h); + return MatrixType(HSeq); +} + +/** + * Generation of random matrix with prescribed singular values. + * + * We generate random matrices with given singular values by setting up + * a singular value decomposition. By choosing the number of zeros as + * singular values we can specify the rank of the matrix. + * Moreover, we also control its spectral norm, which is the largest + * singular value, as well as its condition number with respect to the + * l2-norm, which is the quotient of the largest and smallest singular + * value. + * + * Reference: For details on the method see e.g. Section 8.1 (pp. 62 f) in + * + * C. C. Paige, M. A. Saunders, + * LSQR: An algorithm for sparse linear equations and sparse least squares. + * ACM Transactions on Mathematical Software 8(1), pp. 43-71, 1982. + * https://web.stanford.edu/group/SOL/software/lsqr/lsqr-toms82a.pdf + * + * and also the LSQR webpage https://web.stanford.edu/group/SOL/software/lsqr/. + * + * @tparam MatrixType matrix type to generate + * @tparam RealScalarVectorType vector type with real entries used for singular values + * @param svs vector of desired singular values + * @param rows row dimension of requested random matrix + * @param cols column dimension of requested random matrix + * @param M generated matrix with prescribed singular values + */ +template +void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M) +{ + enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime }; + typedef typename internal::traits::Scalar Scalar; + typedef Matrix MatrixAType; + typedef Matrix MatrixBType; + + const Index min_dim = (std::min)(rows, cols); + + const MatrixAType U = generateRandomUnitaryMatrix(rows); + const MatrixBType V = generateRandomUnitaryMatrix(cols); + + M = U.block(0, 0, rows, min_dim) * svs.asDiagonal() * V.block(0, 0, cols, min_dim).transpose(); +} + +/** + * Setup a vector of random singular values with prescribed upper limit. + * For use with generateRandomMatrixSvs(). + * + * Singular values are non-negative real values. By convention (to be consistent with + * singular value decomposition) we sort them in decreasing order. + * + * This strategy produces random singular values in the range [0, max], in particular + * the singular values can be zero or arbitrarily close to zero. + * + * @tparam VectorType vector type with real entries used for singular values + * @tparam RealScalar data type used for real entry + * @param dim number of singular values to generate + * @param max upper bound for singular values + * @return vector of singular values + */ +template +VectorType setupRandomSvs(const Index dim, const RealScalar max) +{ + VectorType svs = max / RealScalar(2) * (VectorType::Random(dim) + VectorType::Ones(dim)); + std::sort(svs.begin(), svs.end(), std::greater()); + return svs; +} + +/** + * Setup a vector of random singular values with prescribed range. + * For use with generateRandomMatrixSvs(). + * + * Singular values are non-negative real values. By convention (to be consistent with + * singular value decomposition) we sort them in decreasing order. + * + * For dim > 1 this strategy generates a vector with largest entry max, smallest entry + * min, and remaining entries in the range [min, max]. For dim == 1 the only entry is + * min. + * + * @tparam VectorType vector type with real entries used for singular values + * @tparam RealScalar data type used for real entry + * @param dim number of singular values to generate + * @param min smallest singular value to use + * @param max largest singular value to use + * @return vector of singular values + */ +template +VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max) +{ + VectorType svs = VectorType::Random(dim); + if(dim == 0) + return svs; + if(dim == 1) + { + svs(0) = min; + return svs; + } + std::sort(svs.begin(), svs.end(), std::greater()); + + // scale to range [min, max] + const RealScalar c_min = svs(dim - 1), c_max = svs(0); + svs = (svs - VectorType::Constant(dim, c_min)) / (c_max - c_min); + return min * (VectorType::Ones(dim) - svs) + max * svs; +} + +/** + * Check if number is "not a number" (NaN). + * + * @tparam T input type + * @param x input value + * @return true, if input value is "not a number" (NaN) + */ +template bool isNotNaN(const T& x) +{ + return x==x; +} + +/** + * Check if number is plus infinity. + * + * @tparam T input type + * @param x input value + * @return true, if input value is plus infinity + */ +template bool isPlusInf(const T& x) +{ + return x > NumTraits::highest(); +} + +/** + * Check if number is minus infinity. + * + * @tparam T input type + * @param x input value + * @return true, if input value is minus infinity + */ +template bool isMinusInf(const T& x) +{ + return x < NumTraits::lowest(); +} + +} // end namespace Eigen + +template struct GetDifferentType; + +template<> struct GetDifferentType { typedef double type; }; +template<> struct GetDifferentType { typedef float type; }; +template struct GetDifferentType > +{ typedef std::complex::type> type; }; + +template std::string type_name() { return "other"; } +template<> std::string type_name() { return "float"; } +template<> std::string type_name() { return "double"; } +template<> std::string type_name() { return "long double"; } +template<> std::string type_name() { return "int"; } +template<> std::string type_name >() { return "complex"; } +template<> std::string type_name >() { return "complex"; } +template<> std::string type_name >() { return "complex"; } +template<> std::string type_name >() { return "complex"; } + +using namespace Eigen; + +/** + * Set number of repetitions for unit test from input string. + * + * @param str input string + */ +inline void set_repeat_from_string(const char *str) +{ + errno = 0; + g_repeat = int(strtoul(str, 0, 10)); + if(errno || g_repeat <= 0) + { + std::cout << "Invalid repeat value " << str << std::endl; + exit(EXIT_FAILURE); + } + g_has_set_repeat = true; +} + +/** + * Set seed for randomized unit tests from input string. + * + * @param str input string + */ +inline void set_seed_from_string(const char *str) +{ + errno = 0; + g_seed = int(strtoul(str, 0, 10)); + if(errno || g_seed == 0) + { + std::cout << "Invalid seed value " << str << std::endl; + exit(EXIT_FAILURE); + } + g_has_set_seed = true; +} + +int main(int argc, char *argv[]) +{ + g_has_set_repeat = false; + g_has_set_seed = false; + bool need_help = false; + + for(int i = 1; i < argc; i++) + { + if(argv[i][0] == 'r') + { + if(g_has_set_repeat) + { + std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl; + return 1; + } + set_repeat_from_string(argv[i]+1); + } + else if(argv[i][0] == 's') + { + if(g_has_set_seed) + { + std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl; + return 1; + } + set_seed_from_string(argv[i]+1); + } + else + { + need_help = true; + } + } + + if(need_help) + { + std::cout << "This test application takes the following optional arguments:" << std::endl; + std::cout << " rN Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl; + std::cout << " sN Use N as seed for random numbers (default: based on current time)" << std::endl; + std::cout << std::endl; + std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl; + std::cout << "will be used as default values for these parameters." << std::endl; + return 1; + } + + char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT"); + if(!g_has_set_repeat && env_EIGEN_REPEAT) + set_repeat_from_string(env_EIGEN_REPEAT); + char *env_EIGEN_SEED = getenv("EIGEN_SEED"); + if(!g_has_set_seed && env_EIGEN_SEED) + set_seed_from_string(env_EIGEN_SEED); + + if(!g_has_set_seed) g_seed = (unsigned int) time(NULL); + if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT; + + std::cout << "Initializing random number generator with seed " << g_seed << std::endl; + std::stringstream ss; + ss << "Seed: " << g_seed; + g_test_stack.push_back(ss.str()); + srand(g_seed); + std::cout << "Repeating each test " << g_repeat << " times" << std::endl; + + VERIFY(EigenTest::all().size()>0); + + for(std::size_t i=0; i this warning is raised even for legal usage as: g_test_stack.push_back("foo"); where g_test_stack is a std::vector + // remark #1418: external function definition with no prior declaration + // -> this warning is raised for all our test functions. Declaring them static would fix the issue. + // warning #279: controlling expression is constant + // remark #1572: floating-point equality and inequality comparisons are unreliable + #pragma warning disable 279 383 1418 1572 +#endif + +#ifdef _MSC_VER + // 4503 - decorated name length exceeded, name was truncated + #pragma warning( disable : 4503) +#endif diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapped_matrix.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapped_matrix.cpp new file mode 100644 index 0000000000000000000000000000000000000000..0ea136ae6293b7d224db9745001e91f1157d5325 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapped_matrix.cpp @@ -0,0 +1,207 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_NO_STATIC_ASSERT +#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them +#endif + +#include "main.h" + +#define EIGEN_TESTMAP_MAX_SIZE 256 + +template void map_class_vector(const VectorType& m) +{ + typedef typename VectorType::Scalar Scalar; + + Index size = m.size(); + + Scalar* array1 = internal::aligned_new(size); + Scalar* array2 = internal::aligned_new(size); + Scalar* array3 = new Scalar[size+1]; + Scalar* array3unaligned = (internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES) == 0 ? array3+1 : array3; + Scalar array4[EIGEN_TESTMAP_MAX_SIZE]; + + Map(array1, size) = VectorType::Random(size); + Map(array2, size) = Map(array1, size); + Map(array3unaligned, size) = Map(array1, size); + Map(array4, size) = Map(array1, size); + VectorType ma1 = Map(array1, size); + VectorType ma2 = Map(array2, size); + VectorType ma3 = Map(array3unaligned, size); + VectorType ma4 = Map(array4, size); + VERIFY_IS_EQUAL(ma1, ma2); + VERIFY_IS_EQUAL(ma1, ma3); + VERIFY_IS_EQUAL(ma1, ma4); + #ifdef EIGEN_VECTORIZE + if(internal::packet_traits::Vectorizable && size>=AlignedMax) + VERIFY_RAISES_ASSERT((Map(array3unaligned, size))) + #endif + + internal::aligned_delete(array1, size); + internal::aligned_delete(array2, size); + delete[] array3; +} + +template void map_class_matrix(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + + Index rows = m.rows(), cols = m.cols(), size = rows*cols; + Scalar s1 = internal::random(); + + // array1 and array2 -> aligned heap allocation + Scalar* array1 = internal::aligned_new(size); + for(int i = 0; i < size; i++) array1[i] = Scalar(1); + Scalar* array2 = internal::aligned_new(size); + for(int i = 0; i < size; i++) array2[i] = Scalar(1); + // array3unaligned -> unaligned pointer to heap + Scalar* array3 = new Scalar[size+1]; + Index sizep1 = size + 1; // <- without this temporary MSVC 2103 generates bad code + for(Index i = 0; i < sizep1; i++) array3[i] = Scalar(1); + Scalar* array3unaligned = (internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES) == 0 ? array3+1 : array3; + Scalar array4[256]; + if(size<=256) + for(int i = 0; i < size; i++) array4[i] = Scalar(1); + + Map map1(array1, rows, cols); + Map map2(array2, rows, cols); + Map map3(array3unaligned, rows, cols); + Map map4(array4, rows, cols); + + VERIFY_IS_EQUAL(map1, MatrixType::Ones(rows,cols)); + VERIFY_IS_EQUAL(map2, MatrixType::Ones(rows,cols)); + VERIFY_IS_EQUAL(map3, MatrixType::Ones(rows,cols)); + map1 = MatrixType::Random(rows,cols); + map2 = map1; + map3 = map1; + MatrixType ma1 = map1; + MatrixType ma2 = map2; + MatrixType ma3 = map3; + VERIFY_IS_EQUAL(map1, map2); + VERIFY_IS_EQUAL(map1, map3); + VERIFY_IS_EQUAL(ma1, ma2); + VERIFY_IS_EQUAL(ma1, ma3); + VERIFY_IS_EQUAL(ma1, map3); + + VERIFY_IS_APPROX(s1*map1, s1*map2); + VERIFY_IS_APPROX(s1*ma1, s1*ma2); + VERIFY_IS_EQUAL(s1*ma1, s1*ma3); + VERIFY_IS_APPROX(s1*map1, s1*map3); + + map2 *= s1; + map3 *= s1; + VERIFY_IS_APPROX(s1*map1, map2); + VERIFY_IS_APPROX(s1*map1, map3); + + if(size<=256) + { + VERIFY_IS_EQUAL(map4, MatrixType::Ones(rows,cols)); + map4 = map1; + MatrixType ma4 = map4; + VERIFY_IS_EQUAL(map1, map4); + VERIFY_IS_EQUAL(ma1, map4); + VERIFY_IS_EQUAL(ma1, ma4); + VERIFY_IS_APPROX(s1*map1, s1*map4); + + map4 *= s1; + VERIFY_IS_APPROX(s1*map1, map4); + } + + internal::aligned_delete(array1, size); + internal::aligned_delete(array2, size); + delete[] array3; +} + +template void map_static_methods(const VectorType& m) +{ + typedef typename VectorType::Scalar Scalar; + + Index size = m.size(); + + Scalar* array1 = internal::aligned_new(size); + Scalar* array2 = internal::aligned_new(size); + Scalar* array3 = new Scalar[size+1]; + Scalar* array3unaligned = internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES == 0 ? array3+1 : array3; + + VectorType::MapAligned(array1, size) = VectorType::Random(size); + VectorType::Map(array2, size) = VectorType::Map(array1, size); + VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size); + VectorType ma1 = VectorType::Map(array1, size); + VectorType ma2 = VectorType::MapAligned(array2, size); + VectorType ma3 = VectorType::Map(array3unaligned, size); + VERIFY_IS_EQUAL(ma1, ma2); + VERIFY_IS_EQUAL(ma1, ma3); + + internal::aligned_delete(array1, size); + internal::aligned_delete(array2, size); + delete[] array3; +} + +template void check_const_correctness(const PlainObjectType&) +{ + // there's a lot that we can't test here while still having this test compile! + // the only possible approach would be to run a script trying to compile stuff and checking that it fails. + // CMake can help with that. + + // verify that map-to-const don't have LvalueBit + typedef typename internal::add_const::type ConstPlainObjectType; + VERIFY( !(internal::traits >::Flags & LvalueBit) ); + VERIFY( !(internal::traits >::Flags & LvalueBit) ); + VERIFY( !(Map::Flags & LvalueBit) ); + VERIFY( !(Map::Flags & LvalueBit) ); +} + +template +void map_not_aligned_on_scalar() +{ + typedef Matrix MatrixType; + Index size = 11; + Scalar* array1 = internal::aligned_new((size+1)*(size+1)+1); + Scalar* array2 = reinterpret_cast(sizeof(Scalar)/2+std::size_t(array1)); + Map > map2(array2, size, size, OuterStride<>(size+1)); + MatrixType m2 = MatrixType::Random(size,size); + map2 = m2; + VERIFY_IS_EQUAL(m2, map2); + + typedef Matrix VectorType; + Map map3(array2, size); + MatrixType v3 = VectorType::Random(size); + map3 = v3; + VERIFY_IS_EQUAL(v3, map3); + + internal::aligned_delete(array1, (size+1)*(size+1)+1); +} + +EIGEN_DECLARE_TEST(mapped_matrix) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( map_class_vector(Matrix()) ); + CALL_SUBTEST_1( check_const_correctness(Matrix()) ); + CALL_SUBTEST_2( map_class_vector(Vector4d()) ); + CALL_SUBTEST_2( map_class_vector(VectorXd(13)) ); + CALL_SUBTEST_2( check_const_correctness(Matrix4d()) ); + CALL_SUBTEST_3( map_class_vector(RowVector4f()) ); + CALL_SUBTEST_4( map_class_vector(VectorXcf(8)) ); + CALL_SUBTEST_5( map_class_vector(VectorXi(12)) ); + CALL_SUBTEST_5( check_const_correctness(VectorXi(12)) ); + + CALL_SUBTEST_1( map_class_matrix(Matrix()) ); + CALL_SUBTEST_2( map_class_matrix(Matrix4d()) ); + CALL_SUBTEST_11( map_class_matrix(Matrix()) ); + CALL_SUBTEST_4( map_class_matrix(MatrixXcf(internal::random(1,10),internal::random(1,10))) ); + CALL_SUBTEST_5( map_class_matrix(MatrixXi(internal::random(1,10),internal::random(1,10))) ); + + CALL_SUBTEST_6( map_static_methods(Matrix()) ); + CALL_SUBTEST_7( map_static_methods(Vector3f()) ); + CALL_SUBTEST_8( map_static_methods(RowVector3d()) ); + CALL_SUBTEST_9( map_static_methods(VectorXcd(8)) ); + CALL_SUBTEST_10( map_static_methods(VectorXf(12)) ); + CALL_SUBTEST_11( map_not_aligned_on_scalar() ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstaticmethods.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstaticmethods.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d0128ba94f9b702a3105e76b287662a51dd2d5b2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstaticmethods.cpp @@ -0,0 +1,177 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +// GCC<=4.8 has spurious shadow warnings, because `ptr` re-appears inside template instantiations +// workaround: put these in an anonymous namespace +namespace { +float *ptr; +const float *const_ptr; +} + +template +struct mapstaticmethods_impl {}; + +template +struct mapstaticmethods_impl +{ + static void run(const PlainObjectType& m) + { + mapstaticmethods_impl::run(m); + + int i = internal::random(2,5), j = internal::random(2,5); + + PlainObjectType::Map(ptr).setZero(); + PlainObjectType::MapAligned(ptr).setZero(); + PlainObjectType::Map(const_ptr).sum(); + PlainObjectType::MapAligned(const_ptr).sum(); + + PlainObjectType::Map(ptr, InnerStride<>(i)).setZero(); + PlainObjectType::MapAligned(ptr, InnerStride<>(i)).setZero(); + PlainObjectType::Map(const_ptr, InnerStride<>(i)).sum(); + PlainObjectType::MapAligned(const_ptr, InnerStride<>(i)).sum(); + + PlainObjectType::Map(ptr, InnerStride<2>()).setZero(); + PlainObjectType::MapAligned(ptr, InnerStride<3>()).setZero(); + PlainObjectType::Map(const_ptr, InnerStride<4>()).sum(); + PlainObjectType::MapAligned(const_ptr, InnerStride<5>()).sum(); + + PlainObjectType::Map(ptr, OuterStride<>(i)).setZero(); + PlainObjectType::MapAligned(ptr, OuterStride<>(i)).setZero(); + PlainObjectType::Map(const_ptr, OuterStride<>(i)).sum(); + PlainObjectType::MapAligned(const_ptr, OuterStride<>(i)).sum(); + + PlainObjectType::Map(ptr, OuterStride<2>()).setZero(); + PlainObjectType::MapAligned(ptr, OuterStride<3>()).setZero(); + PlainObjectType::Map(const_ptr, OuterStride<4>()).sum(); + PlainObjectType::MapAligned(const_ptr, OuterStride<5>()).sum(); + + PlainObjectType::Map(ptr, Stride(i,j)).setZero(); + PlainObjectType::MapAligned(ptr, Stride<2,Dynamic>(2,i)).setZero(); + PlainObjectType::Map(const_ptr, Stride(i,3)).sum(); + PlainObjectType::MapAligned(const_ptr, Stride(i,j)).sum(); + + PlainObjectType::Map(ptr, Stride<2,3>()).setZero(); + PlainObjectType::MapAligned(ptr, Stride<3,4>()).setZero(); + PlainObjectType::Map(const_ptr, Stride<2,4>()).sum(); + PlainObjectType::MapAligned(const_ptr, Stride<5,3>()).sum(); + } +}; + +template +struct mapstaticmethods_impl +{ + static void run(const PlainObjectType& m) + { + Index rows = m.rows(), cols = m.cols(); + + int i = internal::random(2,5), j = internal::random(2,5); + + PlainObjectType::Map(ptr, rows, cols).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols).setZero(); + PlainObjectType::Map(const_ptr, rows, cols).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols).sum(); + + PlainObjectType::Map(ptr, rows, cols, InnerStride<>(i)).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<>(i)).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, InnerStride<>(i)).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<>(i)).sum(); + + PlainObjectType::Map(ptr, rows, cols, InnerStride<2>()).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, InnerStride<3>()).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, InnerStride<4>()).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, InnerStride<5>()).sum(); + + PlainObjectType::Map(ptr, rows, cols, OuterStride<>(i)).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<>(i)).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, OuterStride<>(i)).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<>(i)).sum(); + + PlainObjectType::Map(ptr, rows, cols, OuterStride<2>()).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, OuterStride<3>()).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, OuterStride<4>()).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, OuterStride<5>()).sum(); + + PlainObjectType::Map(ptr, rows, cols, Stride(i,j)).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, Stride<2,Dynamic>(2,i)).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, Stride(i,3)).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, Stride(i,j)).sum(); + + PlainObjectType::Map(ptr, rows, cols, Stride<2,3>()).setZero(); + PlainObjectType::MapAligned(ptr, rows, cols, Stride<3,4>()).setZero(); + PlainObjectType::Map(const_ptr, rows, cols, Stride<2,4>()).sum(); + PlainObjectType::MapAligned(const_ptr, rows, cols, Stride<5,3>()).sum(); + } +}; + +template +struct mapstaticmethods_impl +{ + static void run(const PlainObjectType& v) + { + Index size = v.size(); + + int i = internal::random(2,5); + + PlainObjectType::Map(ptr, size).setZero(); + PlainObjectType::MapAligned(ptr, size).setZero(); + PlainObjectType::Map(const_ptr, size).sum(); + PlainObjectType::MapAligned(const_ptr, size).sum(); + + PlainObjectType::Map(ptr, size, InnerStride<>(i)).setZero(); + PlainObjectType::MapAligned(ptr, size, InnerStride<>(i)).setZero(); + PlainObjectType::Map(const_ptr, size, InnerStride<>(i)).sum(); + PlainObjectType::MapAligned(const_ptr, size, InnerStride<>(i)).sum(); + + PlainObjectType::Map(ptr, size, InnerStride<2>()).setZero(); + PlainObjectType::MapAligned(ptr, size, InnerStride<3>()).setZero(); + PlainObjectType::Map(const_ptr, size, InnerStride<4>()).sum(); + PlainObjectType::MapAligned(const_ptr, size, InnerStride<5>()).sum(); + } +}; + +template +void mapstaticmethods(const PlainObjectType& m) +{ + mapstaticmethods_impl::run(m); + VERIFY(true); // just to avoid 'unused function' warning +} + +EIGEN_DECLARE_TEST(mapstaticmethods) +{ + ptr = internal::aligned_new(1000); + for(int i = 0; i < 1000; i++) ptr[i] = float(i); + + const_ptr = ptr; + + CALL_SUBTEST_1(( mapstaticmethods(Matrix()) )); + CALL_SUBTEST_1(( mapstaticmethods(Vector2f()) )); + CALL_SUBTEST_2(( mapstaticmethods(Vector3f()) )); + CALL_SUBTEST_2(( mapstaticmethods(Matrix2f()) )); + CALL_SUBTEST_3(( mapstaticmethods(Matrix4f()) )); + CALL_SUBTEST_3(( mapstaticmethods(Array4f()) )); + CALL_SUBTEST_4(( mapstaticmethods(Array3f()) )); + CALL_SUBTEST_4(( mapstaticmethods(Array33f()) )); + CALL_SUBTEST_5(( mapstaticmethods(Array44f()) )); + CALL_SUBTEST_5(( mapstaticmethods(VectorXf(1)) )); + CALL_SUBTEST_5(( mapstaticmethods(VectorXf(8)) )); + CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(1,1)) )); + CALL_SUBTEST_6(( mapstaticmethods(MatrixXf(5,7)) )); + CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(1)) )); + CALL_SUBTEST_7(( mapstaticmethods(ArrayXf(5)) )); + CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(1,1)) )); + CALL_SUBTEST_8(( mapstaticmethods(ArrayXXf(8,6)) )); + + internal::aligned_delete(ptr, 1000); +} + diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstride.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstride.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fde73f2eccf62f48907812f16acbfad31bb03d91 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mapstride.cpp @@ -0,0 +1,260 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void map_class_vector(const VectorType& m) +{ + typedef typename VectorType::Scalar Scalar; + + Index size = m.size(); + + VectorType v = VectorType::Random(size); + + Index arraysize = 3*size; + + Scalar* a_array = internal::aligned_new(arraysize+1); + Scalar* array = a_array; + if(Alignment!=Aligned) + array = (Scalar*)(internal::IntPtr(a_array) + (internal::packet_traits::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits::Real))); + + { + Map > map(array, size); + map = v; + for(int i = 0; i < size; ++i) + { + VERIFY(array[3*i] == v[i]); + VERIFY(map[i] == v[i]); + } + } + + { + Map > map(array, size, InnerStride(2)); + map = v; + for(int i = 0; i < size; ++i) + { + VERIFY(array[2*i] == v[i]); + VERIFY(map[i] == v[i]); + } + } + + internal::aligned_delete(a_array, arraysize+1); +} + +template void map_class_matrix(const MatrixType& _m) +{ + typedef typename MatrixType::Scalar Scalar; + + Index rows = _m.rows(), cols = _m.cols(); + + MatrixType m = MatrixType::Random(rows,cols); + Scalar s1 = internal::random(); + + Index arraysize = 4*(rows+4)*(cols+4); + + Scalar* a_array1 = internal::aligned_new(arraysize+1); + Scalar* array1 = a_array1; + if(Alignment!=Aligned) + array1 = (Scalar*)(internal::IntPtr(a_array1) + (internal::packet_traits::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits::Real))); + + Scalar a_array2[256]; + Scalar* array2 = a_array2; + if(Alignment!=Aligned) + array2 = (Scalar*)(internal::IntPtr(a_array2) + (internal::packet_traits::AlignedOnScalar?sizeof(Scalar):sizeof(typename NumTraits::Real))); + else + array2 = (Scalar*)(((internal::UIntPtr(a_array2)+EIGEN_MAX_ALIGN_BYTES-1)/EIGEN_MAX_ALIGN_BYTES)*EIGEN_MAX_ALIGN_BYTES); + Index maxsize2 = a_array2 - array2 + 256; + + // test no inner stride and some dynamic outer stride + for(int k=0; k<2; ++k) + { + if(k==1 && (m.innerSize()+1)*m.outerSize() > maxsize2) + break; + Scalar* array = (k==0 ? array1 : array2); + + Map > map(array, rows, cols, OuterStride(m.innerSize()+1)); + map = m; + VERIFY(map.outerStride() == map.innerSize()+1); + for(int i = 0; i < m.outerSize(); ++i) + for(int j = 0; j < m.innerSize(); ++j) + { + VERIFY(array[map.outerStride()*i+j] == m.coeffByOuterInner(i,j)); + VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j)); + } + VERIFY_IS_APPROX(s1*map,s1*m); + map *= s1; + VERIFY_IS_APPROX(map,s1*m); + } + + // test no inner stride and an outer stride of +4. This is quite important as for fixed-size matrices, + // this allows to hit the special case where it's vectorizable. + for(int k=0; k<2; ++k) + { + if(k==1 && (m.innerSize()+4)*m.outerSize() > maxsize2) + break; + Scalar* array = (k==0 ? array1 : array2); + + enum { + InnerSize = MatrixType::InnerSizeAtCompileTime, + OuterStrideAtCompileTime = InnerSize==Dynamic ? Dynamic : InnerSize+4 + }; + Map > + map(array, rows, cols, OuterStride(m.innerSize()+4)); + map = m; + VERIFY(map.outerStride() == map.innerSize()+4); + for(int i = 0; i < m.outerSize(); ++i) + for(int j = 0; j < m.innerSize(); ++j) + { + VERIFY(array[map.outerStride()*i+j] == m.coeffByOuterInner(i,j)); + VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j)); + } + VERIFY_IS_APPROX(s1*map,s1*m); + map *= s1; + VERIFY_IS_APPROX(map,s1*m); + } + + // test both inner stride and outer stride + for(int k=0; k<2; ++k) + { + if(k==1 && (2*m.innerSize()+1)*(m.outerSize()*2) > maxsize2) + break; + Scalar* array = (k==0 ? array1 : array2); + + Map > map(array, rows, cols, Stride(2*m.innerSize()+1, 2)); + map = m; + VERIFY(map.outerStride() == 2*map.innerSize()+1); + VERIFY(map.innerStride() == 2); + for(int i = 0; i < m.outerSize(); ++i) + for(int j = 0; j < m.innerSize(); ++j) + { + VERIFY(array[map.outerStride()*i+map.innerStride()*j] == m.coeffByOuterInner(i,j)); + VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j)); + } + VERIFY_IS_APPROX(s1*map,s1*m); + map *= s1; + VERIFY_IS_APPROX(map,s1*m); + } + + // test inner stride and no outer stride + for(int k=0; k<2; ++k) + { + if(k==1 && (m.innerSize()*2)*m.outerSize() > maxsize2) + break; + Scalar* array = (k==0 ? array1 : array2); + + Map > map(array, rows, cols, InnerStride(2)); + map = m; + VERIFY(map.outerStride() == map.innerSize()*2); + for(int i = 0; i < m.outerSize(); ++i) + for(int j = 0; j < m.innerSize(); ++j) + { + VERIFY(array[map.innerSize()*i*2+j*2] == m.coeffByOuterInner(i,j)); + VERIFY(map.coeffByOuterInner(i,j) == m.coeffByOuterInner(i,j)); + } + VERIFY_IS_APPROX(s1*map,s1*m); + map *= s1; + VERIFY_IS_APPROX(map,s1*m); + } + + // test negative strides + { + Matrix::Map(a_array1, arraysize+1).setRandom(); + Index outerstride = m.innerSize()+4; + Scalar* array = array1; + + { + Map > map1(array, rows, cols, OuterStride<>( outerstride)); + Map > map2(array+(m.outerSize()-1)*outerstride, rows, cols, OuterStride<>(-outerstride)); + if(MatrixType::IsRowMajor) VERIFY_IS_APPROX(map1.colwise().reverse(), map2); + else VERIFY_IS_APPROX(map1.rowwise().reverse(), map2); + } + + { + Map > map1(array, rows, cols, OuterStride<>( outerstride)); + Map > map2(array+(m.outerSize()-1)*outerstride+m.innerSize()-1, rows, cols, Stride(-outerstride,-1)); + VERIFY_IS_APPROX(map1.reverse(), map2); + } + + { + Map > map1(array, rows, cols, OuterStride<>( outerstride)); + Map > map2(array+(m.outerSize()-1)*outerstride+m.innerSize()-1, rows, cols, Stride(-outerstride,-1)); + VERIFY_IS_APPROX(map1.reverse(), map2); + } + } + + internal::aligned_delete(a_array1, arraysize+1); +} + +// Additional tests for inner-stride but no outer-stride +template +void bug1453() +{ + const int data[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}; + typedef Matrix RowMatrixXi; + typedef Matrix ColMatrix23i; + typedef Matrix ColMatrix32i; + typedef Matrix RowMatrix23i; + typedef Matrix RowMatrix32i; + + VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>())); + VERIFY_IS_APPROX(MatrixXi::Map(data, 2, 3, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>())); + VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>())); + VERIFY_IS_APPROX(MatrixXi::Map(data, 3, 2, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>())); + + VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>())); + VERIFY_IS_APPROX(RowMatrixXi::Map(data, 2, 3, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>())); + VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>())); + VERIFY_IS_APPROX(RowMatrixXi::Map(data, 3, 2, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>())); + + VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 2, 3, Stride<4,2>())); + VERIFY_IS_APPROX(ColMatrix23i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 2, 3, Stride<4,2>())); + VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<2>()), MatrixXi::Map(data, 3, 2, Stride<6,2>())); + VERIFY_IS_APPROX(ColMatrix32i::Map(data, InnerStride<>(2)), MatrixXi::Map(data, 3, 2, Stride<6,2>())); + + VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 2, 3, Stride<6,2>())); + VERIFY_IS_APPROX(RowMatrix23i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 2, 3, Stride<6,2>())); + VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<2>()), RowMatrixXi::Map(data, 3, 2, Stride<4,2>())); + VERIFY_IS_APPROX(RowMatrix32i::Map(data, InnerStride<>(2)), RowMatrixXi::Map(data, 3, 2, Stride<4,2>())); +} + +EIGEN_DECLARE_TEST(mapstride) +{ + for(int i = 0; i < g_repeat; i++) { + int maxn = 3; + CALL_SUBTEST_1( map_class_vector(Matrix()) ); + CALL_SUBTEST_1( map_class_vector(Matrix()) ); + CALL_SUBTEST_2( map_class_vector(Vector4d()) ); + CALL_SUBTEST_2( map_class_vector(Vector4d()) ); + CALL_SUBTEST_3( map_class_vector(RowVector4f()) ); + CALL_SUBTEST_3( map_class_vector(RowVector4f()) ); + CALL_SUBTEST_4( map_class_vector(VectorXcf(internal::random(1,maxn))) ); + CALL_SUBTEST_4( map_class_vector(VectorXcf(internal::random(1,maxn))) ); + CALL_SUBTEST_5( map_class_vector(VectorXi(internal::random(1,maxn))) ); + CALL_SUBTEST_5( map_class_vector(VectorXi(internal::random(1,maxn))) ); + + CALL_SUBTEST_1( map_class_matrix(Matrix()) ); + CALL_SUBTEST_1( map_class_matrix(Matrix()) ); + CALL_SUBTEST_2( map_class_matrix(Matrix4d()) ); + CALL_SUBTEST_2( map_class_matrix(Matrix4d()) ); + CALL_SUBTEST_3( map_class_matrix(Matrix()) ); + CALL_SUBTEST_3( map_class_matrix(Matrix()) ); + CALL_SUBTEST_3( map_class_matrix(Matrix()) ); + CALL_SUBTEST_3( map_class_matrix(Matrix()) ); + CALL_SUBTEST_4( map_class_matrix(MatrixXcf(internal::random(1,maxn),internal::random(1,maxn))) ); + CALL_SUBTEST_4( map_class_matrix(MatrixXcf(internal::random(1,maxn),internal::random(1,maxn))) ); + CALL_SUBTEST_5( map_class_matrix(MatrixXi(internal::random(1,maxn),internal::random(1,maxn))) ); + CALL_SUBTEST_5( map_class_matrix(MatrixXi(internal::random(1,maxn),internal::random(1,maxn))) ); + CALL_SUBTEST_6( map_class_matrix(MatrixXcd(internal::random(1,maxn),internal::random(1,maxn))) ); + CALL_SUBTEST_6( map_class_matrix(MatrixXcd(internal::random(1,maxn),internal::random(1,maxn))) ); + + CALL_SUBTEST_5( bug1453<0>() ); + + TEST_SET_BUT_UNUSED_VARIABLE(maxn); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/meta.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/meta.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7a8b93c3d8bd78e5d0dae361988f17e35293dd0b --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/meta.cpp @@ -0,0 +1,158 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template +bool check_is_convertible(const From&, const To&) +{ + return internal::is_convertible::value; +} + +struct FooReturnType { + typedef int ReturnType; +}; + +struct MyInterface { + virtual void func() = 0; + virtual ~MyInterface() {} +}; +struct MyImpl : public MyInterface { + void func() {} +}; + +EIGEN_DECLARE_TEST(meta) +{ + VERIFY((internal::conditional<(3<4),internal::true_type, internal::false_type>::type::value)); + VERIFY(( internal::is_same::value)); + VERIFY((!internal::is_same::value)); + VERIFY((!internal::is_same::value)); + VERIFY((!internal::is_same::value)); + + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + + // test add_const + VERIFY(( internal::is_same< internal::add_const::type, const float >::value)); + VERIFY(( internal::is_same< internal::add_const::type, float* const>::value)); + VERIFY(( internal::is_same< internal::add_const::type, float const* const>::value)); + VERIFY(( internal::is_same< internal::add_const::type, float& >::value)); + + // test remove_const + VERIFY(( internal::is_same< internal::remove_const::type, float const* >::value)); + VERIFY(( internal::is_same< internal::remove_const::type, float const* >::value)); + VERIFY(( internal::is_same< internal::remove_const::type, float* >::value)); + + // test add_const_on_value_type + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, float const& >::value)); + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, float const* >::value)); + + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, const float >::value)); + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, const float >::value)); + + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, const float* const>::value)); + VERIFY(( internal::is_same< internal::add_const_on_value_type::type, const float* const>::value)); + + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + VERIFY(( internal::is_same::type >::value)); + + + // is_convertible + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible >::value )); + STATIC_CHECK((!internal::is_convertible,double>::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + STATIC_CHECK((!internal::is_convertible::value )); + STATIC_CHECK((!internal::is_convertible::value )); + STATIC_CHECK(!( internal::is_convertible::value )); + + STATIC_CHECK(!( internal::is_convertible::value )); + STATIC_CHECK(( internal::is_convertible::value )); + + //STATIC_CHECK((!internal::is_convertible::value )); //does not even compile because the conversion is prevented by a static assertion + STATIC_CHECK((!internal::is_convertible::value )); + STATIC_CHECK((!internal::is_convertible::value )); + { + float f = 0.0f; + MatrixXf A, B; + VectorXf a, b; + VERIFY(( check_is_convertible(a.dot(b), f) )); + VERIFY(( check_is_convertible(a.transpose()*b, f) )); + VERIFY((!check_is_convertible(A*B, f) )); + VERIFY(( check_is_convertible(A*B, A) )); + } + + #if (EIGEN_COMP_GNUC && EIGEN_COMP_GNUC <= 99) \ + || (EIGEN_COMP_CLANG && EIGEN_COMP_CLANG <= 909) \ + || (EIGEN_COMP_MSVC && EIGEN_COMP_MSVC <=1914) + // See http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1752, + // basically, a fix in the c++ standard breaks our c++98 implementation + // of is_convertible for abstract classes. + // So the following tests are expected to fail with recent compilers. + + STATIC_CHECK(( !internal::is_convertible::value )); + #if (!EIGEN_COMP_GNUC_STRICT) || (EIGEN_GNUC_AT_LEAST(4,8)) + // GCC prior to 4.8 fails to compile this test: + // error: cannot allocate an object of abstract type 'MyInterface' + // In other word, it does not obey SFINAE. + // Nevertheless, we don't really care about supporting abstract type as scalar type! + STATIC_CHECK(( !internal::is_convertible::value )); + #endif + STATIC_CHECK(( internal::is_convertible::value )); + + #endif + + { + int i = 0; + VERIFY(( check_is_convertible(fix<3>(), i) )); + VERIFY((!check_is_convertible(i, fix()) )); + } + + + VERIFY(( internal::has_ReturnType::value )); + VERIFY(( internal::has_ReturnType >::value )); + VERIFY(( !internal::has_ReturnType::value )); + VERIFY(( !internal::has_ReturnType::value )); + + VERIFY(internal::meta_sqrt<1>::ret == 1); + #define VERIFY_META_SQRT(X) VERIFY(internal::meta_sqrt::ret == int(std::sqrt(double(X)))) + VERIFY_META_SQRT(2); + VERIFY_META_SQRT(3); + VERIFY_META_SQRT(4); + VERIFY_META_SQRT(5); + VERIFY_META_SQRT(6); + VERIFY_META_SQRT(8); + VERIFY_META_SQRT(9); + VERIFY_META_SQRT(15); + VERIFY_META_SQRT(16); + VERIFY_META_SQRT(17); + VERIFY_META_SQRT(255); + VERIFY_META_SQRT(256); + VERIFY_META_SQRT(257); + VERIFY_META_SQRT(1023); + VERIFY_META_SQRT(1024); + VERIFY_META_SQRT(1025); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/metis_support.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/metis_support.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b490dacde9839aaf51d67ceaa6e846d745db52db --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/metis_support.cpp @@ -0,0 +1,25 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "sparse_solver.h" +#include +#include +#include + +template void test_metis_T() +{ + SparseLU, MetisOrdering > sparselu_metis; + + check_sparse_square_solving(sparselu_metis); +} + +EIGEN_DECLARE_TEST(metis_support) +{ + CALL_SUBTEST_1(test_metis_T()); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/miscmatrices.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/miscmatrices.cpp new file mode 100644 index 0000000000000000000000000000000000000000..e71712f33290ae1c716d198e53b922530f3fcf10 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/miscmatrices.cpp @@ -0,0 +1,46 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template void miscMatrices(const MatrixType& m) +{ + /* this test covers the following files: + DiagonalMatrix.h Ones.h + */ + typedef typename MatrixType::Scalar Scalar; + typedef Matrix VectorType; + Index rows = m.rows(); + Index cols = m.cols(); + + Index r = internal::random(0, rows-1), r2 = internal::random(0, rows-1), c = internal::random(0, cols-1); + VERIFY_IS_APPROX(MatrixType::Ones(rows,cols)(r,c), static_cast(1)); + MatrixType m1 = MatrixType::Ones(rows,cols); + VERIFY_IS_APPROX(m1(r,c), static_cast(1)); + VectorType v1 = VectorType::Random(rows); + v1[0]; + Matrix + square(v1.asDiagonal()); + if(r==r2) VERIFY_IS_APPROX(square(r,r2), v1[r]); + else VERIFY_IS_MUCH_SMALLER_THAN(square(r,r2), static_cast(1)); + square = MatrixType::Zero(rows, rows); + square.diagonal() = VectorType::Ones(rows); + VERIFY_IS_APPROX(square, MatrixType::Identity(rows, rows)); +} + +EIGEN_DECLARE_TEST(miscmatrices) +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1( miscMatrices(Matrix()) ); + CALL_SUBTEST_2( miscMatrices(Matrix4d()) ); + CALL_SUBTEST_3( miscMatrices(MatrixXcf(3, 3)) ); + CALL_SUBTEST_4( miscMatrices(MatrixXi(8, 12)) ); + CALL_SUBTEST_5( miscMatrices(MatrixXcd(20, 20)) ); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mixingtypes.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mixingtypes.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d450dbff8bbfd324e5b7b19b0329dbebef52ba45 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mixingtypes.cpp @@ -0,0 +1,329 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2015 Gael Guennebaud +// Copyright (C) 2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#if defined(EIGEN_TEST_PART_7) + +#ifndef EIGEN_NO_STATIC_ASSERT +#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them +#endif + +// ignore double-promotion diagnostic for clang and gcc, if we check for static assertion anyway: +// TODO do the same for MSVC? +#if defined(__clang__) +# if (__clang_major__ * 100 + __clang_minor__) >= 308 +# pragma clang diagnostic ignored "-Wdouble-promotion" +# endif +#elif defined(__GNUC__) + // TODO is there a minimal GCC version for this? At least g++-4.7 seems to be fine with this. +# pragma GCC diagnostic ignored "-Wdouble-promotion" +#endif + +#endif + + + +#if defined(EIGEN_TEST_PART_1) || defined(EIGEN_TEST_PART_2) || defined(EIGEN_TEST_PART_3) + +#ifndef EIGEN_DONT_VECTORIZE +#define EIGEN_DONT_VECTORIZE +#endif + +#endif + +static bool g_called; +#define EIGEN_SCALAR_BINARY_OP_PLUGIN { g_called |= (!internal::is_same::value); } + +#include "main.h" + +using namespace std; + +#define VERIFY_MIX_SCALAR(XPR,REF) \ + g_called = false; \ + VERIFY_IS_APPROX(XPR,REF); \ + VERIFY( g_called && #XPR" not properly optimized"); + +template +void raise_assertion(Index size = SizeAtCompileType) +{ + // VERIFY_RAISES_ASSERT(mf+md); // does not even compile + Matrix vf; vf.setRandom(size); + Matrix vd; vd.setRandom(size); + VERIFY_RAISES_ASSERT(vf=vd); + VERIFY_RAISES_ASSERT(vf+=vd); + VERIFY_RAISES_ASSERT(vf-=vd); + VERIFY_RAISES_ASSERT(vd=vf); + VERIFY_RAISES_ASSERT(vd+=vf); + VERIFY_RAISES_ASSERT(vd-=vf); + + // vd.asDiagonal() * mf; // does not even compile + // vcd.asDiagonal() * mf; // does not even compile + +#if 0 // we get other compilation errors here than just static asserts + VERIFY_RAISES_ASSERT(vd.dot(vf)); +#endif +} + + +template void mixingtypes(int size = SizeAtCompileType) +{ + typedef std::complex CF; + typedef std::complex CD; + typedef Matrix Mat_f; + typedef Matrix Mat_d; + typedef Matrix, SizeAtCompileType, SizeAtCompileType> Mat_cf; + typedef Matrix, SizeAtCompileType, SizeAtCompileType> Mat_cd; + typedef Matrix Vec_f; + typedef Matrix Vec_d; + typedef Matrix, SizeAtCompileType, 1> Vec_cf; + typedef Matrix, SizeAtCompileType, 1> Vec_cd; + + Mat_f mf = Mat_f::Random(size,size); + Mat_d md = mf.template cast(); + //Mat_d rd = md; + Mat_cf mcf = Mat_cf::Random(size,size); + Mat_cd mcd = mcf.template cast >(); + Mat_cd rcd = mcd; + Vec_f vf = Vec_f::Random(size,1); + Vec_d vd = vf.template cast(); + Vec_cf vcf = Vec_cf::Random(size,1); + Vec_cd vcd = vcf.template cast >(); + float sf = internal::random(); + double sd = internal::random(); + complex scf = internal::random >(); + complex scd = internal::random >(); + + mf+mf; + + float epsf = std::sqrt(std::numeric_limits ::min EIGEN_EMPTY ()); + double epsd = std::sqrt(std::numeric_limits::min EIGEN_EMPTY ()); + + while(std::abs(sf )(); + while(std::abs(sd )(); + while(std::abs(scf)(); + while(std::abs(scd)(); + + // check scalar products + VERIFY_MIX_SCALAR(vcf * sf , vcf * complex(sf)); + VERIFY_MIX_SCALAR(sd * vcd , complex(sd) * vcd); + VERIFY_MIX_SCALAR(vf * scf , vf.template cast >() * scf); + VERIFY_MIX_SCALAR(scd * vd , scd * vd.template cast >()); + + VERIFY_MIX_SCALAR(vcf * 2 , vcf * complex(2)); + VERIFY_MIX_SCALAR(vcf * 2.1 , vcf * complex(2.1)); + VERIFY_MIX_SCALAR(2 * vcf, vcf * complex(2)); + VERIFY_MIX_SCALAR(2.1 * vcf , vcf * complex(2.1)); + + // check scalar quotients + VERIFY_MIX_SCALAR(vcf / sf , vcf / complex(sf)); + VERIFY_MIX_SCALAR(vf / scf , vf.template cast >() / scf); + VERIFY_MIX_SCALAR(vf.array() / scf, vf.template cast >().array() / scf); + VERIFY_MIX_SCALAR(scd / vd.array() , scd / vd.template cast >().array()); + + // check scalar increment + VERIFY_MIX_SCALAR(vcf.array() + sf , vcf.array() + complex(sf)); + VERIFY_MIX_SCALAR(sd + vcd.array(), complex(sd) + vcd.array()); + VERIFY_MIX_SCALAR(vf.array() + scf, vf.template cast >().array() + scf); + VERIFY_MIX_SCALAR(scd + vd.array() , scd + vd.template cast >().array()); + + // check scalar subtractions + VERIFY_MIX_SCALAR(vcf.array() - sf , vcf.array() - complex(sf)); + VERIFY_MIX_SCALAR(sd - vcd.array(), complex(sd) - vcd.array()); + VERIFY_MIX_SCALAR(vf.array() - scf, vf.template cast >().array() - scf); + VERIFY_MIX_SCALAR(scd - vd.array() , scd - vd.template cast >().array()); + + // check scalar powers + VERIFY_MIX_SCALAR( pow(vcf.array(), sf), Eigen::pow(vcf.array(), complex(sf)) ); + VERIFY_MIX_SCALAR( vcf.array().pow(sf) , Eigen::pow(vcf.array(), complex(sf)) ); + VERIFY_MIX_SCALAR( pow(sd, vcd.array()), Eigen::pow(complex(sd), vcd.array()) ); + VERIFY_MIX_SCALAR( Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast >().array(), scf) ); + VERIFY_MIX_SCALAR( vf.array().pow(scf) , Eigen::pow(vf.template cast >().array(), scf) ); + VERIFY_MIX_SCALAR( Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast >().array()) ); + + // check dot product + vf.dot(vf); + VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast >())); + + // check diagonal product + VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast >().asDiagonal() * mcf); + VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast >()); + VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast >().asDiagonal()); + VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast >() * vcd.asDiagonal()); + + // check inner product + VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast >().transpose() * vcf).value()); + + // check outer product + VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast >() * vcf.transpose()).eval()); + + // coeff wise product + + VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast >() * vcf.transpose()).eval()); + + Mat_cd mcd2 = mcd; + VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast >()); + + // check matrix-matrix products + VERIFY_IS_APPROX(sd*md*mcd, (sd*md).template cast().eval()*mcd); + VERIFY_IS_APPROX(sd*mcd*md, sd*mcd*md.template cast()); + VERIFY_IS_APPROX(scd*md*mcd, scd*md.template cast().eval()*mcd); + VERIFY_IS_APPROX(scd*mcd*md, scd*mcd*md.template cast()); + + VERIFY_IS_APPROX(sf*mf*mcf, sf*mf.template cast()*mcf); + VERIFY_IS_APPROX(sf*mcf*mf, sf*mcf*mf.template cast()); + VERIFY_IS_APPROX(scf*mf*mcf, scf*mf.template cast()*mcf); + VERIFY_IS_APPROX(scf*mcf*mf, scf*mcf*mf.template cast()); + + VERIFY_IS_APPROX(sd*md.adjoint()*mcd, (sd*md).template cast().eval().adjoint()*mcd); + VERIFY_IS_APPROX(sd*mcd.adjoint()*md, sd*mcd.adjoint()*md.template cast()); + VERIFY_IS_APPROX(sd*md.adjoint()*mcd.adjoint(), (sd*md).template cast().eval().adjoint()*mcd.adjoint()); + VERIFY_IS_APPROX(sd*mcd.adjoint()*md.adjoint(), sd*mcd.adjoint()*md.template cast().adjoint()); + VERIFY_IS_APPROX(sd*md*mcd.adjoint(), (sd*md).template cast().eval()*mcd.adjoint()); + VERIFY_IS_APPROX(sd*mcd*md.adjoint(), sd*mcd*md.template cast().adjoint()); + + VERIFY_IS_APPROX(sf*mf.adjoint()*mcf, (sf*mf).template cast().eval().adjoint()*mcf); + VERIFY_IS_APPROX(sf*mcf.adjoint()*mf, sf*mcf.adjoint()*mf.template cast()); + VERIFY_IS_APPROX(sf*mf.adjoint()*mcf.adjoint(), (sf*mf).template cast().eval().adjoint()*mcf.adjoint()); + VERIFY_IS_APPROX(sf*mcf.adjoint()*mf.adjoint(), sf*mcf.adjoint()*mf.template cast().adjoint()); + VERIFY_IS_APPROX(sf*mf*mcf.adjoint(), (sf*mf).template cast().eval()*mcf.adjoint()); + VERIFY_IS_APPROX(sf*mcf*mf.adjoint(), sf*mcf*mf.template cast().adjoint()); + + VERIFY_IS_APPROX(sf*mf*vcf, (sf*mf).template cast().eval()*vcf); + VERIFY_IS_APPROX(scf*mf*vcf,(scf*mf.template cast()).eval()*vcf); + VERIFY_IS_APPROX(sf*mcf*vf, sf*mcf*vf.template cast()); + VERIFY_IS_APPROX(scf*mcf*vf,scf*mcf*vf.template cast()); + + VERIFY_IS_APPROX(sf*vcf.adjoint()*mf, sf*vcf.adjoint()*mf.template cast().eval()); + VERIFY_IS_APPROX(scf*vcf.adjoint()*mf, scf*vcf.adjoint()*mf.template cast().eval()); + VERIFY_IS_APPROX(sf*vf.adjoint()*mcf, sf*vf.adjoint().template cast().eval()*mcf); + VERIFY_IS_APPROX(scf*vf.adjoint()*mcf, scf*vf.adjoint().template cast().eval()*mcf); + + VERIFY_IS_APPROX(sd*md*vcd, (sd*md).template cast().eval()*vcd); + VERIFY_IS_APPROX(scd*md*vcd,(scd*md.template cast()).eval()*vcd); + VERIFY_IS_APPROX(sd*mcd*vd, sd*mcd*vd.template cast().eval()); + VERIFY_IS_APPROX(scd*mcd*vd,scd*mcd*vd.template cast().eval()); + + VERIFY_IS_APPROX(sd*vcd.adjoint()*md, sd*vcd.adjoint()*md.template cast().eval()); + VERIFY_IS_APPROX(scd*vcd.adjoint()*md, scd*vcd.adjoint()*md.template cast().eval()); + VERIFY_IS_APPROX(sd*vd.adjoint()*mcd, sd*vd.adjoint().template cast().eval()*mcd); + VERIFY_IS_APPROX(scd*vd.adjoint()*mcd, scd*vd.adjoint().template cast().eval()*mcd); + + VERIFY_IS_APPROX( sd*vcd.adjoint()*md.template triangularView(), sd*vcd.adjoint()*md.template cast().eval().template triangularView()); + VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template triangularView(), scd*vcd.adjoint()*md.template cast().eval().template triangularView()); + VERIFY_IS_APPROX( sd*vcd.adjoint()*md.transpose().template triangularView(), sd*vcd.adjoint()*md.transpose().template cast().eval().template triangularView()); + VERIFY_IS_APPROX(scd*vcd.adjoint()*md.transpose().template triangularView(), scd*vcd.adjoint()*md.transpose().template cast().eval().template triangularView()); + VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.template triangularView(), sd*vd.adjoint().template cast().eval()*mcd.template triangularView()); + VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template triangularView(), scd*vd.adjoint().template cast().eval()*mcd.template triangularView()); + VERIFY_IS_APPROX( sd*vd.adjoint()*mcd.transpose().template triangularView(), sd*vd.adjoint().template cast().eval()*mcd.transpose().template triangularView()); + VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.transpose().template triangularView(), scd*vd.adjoint().template cast().eval()*mcd.transpose().template triangularView()); + + // Not supported yet: trmm +// VERIFY_IS_APPROX(sd*mcd*md.template triangularView(), sd*mcd*md.template cast().eval().template triangularView()); +// VERIFY_IS_APPROX(scd*mcd*md.template triangularView(), scd*mcd*md.template cast().eval().template triangularView()); +// VERIFY_IS_APPROX(sd*md*mcd.template triangularView(), sd*md.template cast().eval()*mcd.template triangularView()); +// VERIFY_IS_APPROX(scd*md*mcd.template triangularView(), scd*md.template cast().eval()*mcd.template triangularView()); + + // Not supported yet: symv +// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView(), sd*vcd.adjoint()*md.template cast().eval().template selfadjointView()); +// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView(), scd*vcd.adjoint()*md.template cast().eval().template selfadjointView()); +// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView(), sd*vd.adjoint().template cast().eval()*mcd.template selfadjointView()); +// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView(), scd*vd.adjoint().template cast().eval()*mcd.template selfadjointView()); + + // Not supported yet: symm +// VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView(), sd*vcd.adjoint()*md.template cast().eval().template selfadjointView()); +// VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template selfadjointView(), scd*vcd.adjoint()*md.template cast().eval().template selfadjointView()); +// VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView(), sd*vd.adjoint().template cast().eval()*mcd.template selfadjointView()); +// VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template selfadjointView(), scd*vd.adjoint().template cast().eval()*mcd.template selfadjointView()); + + rcd.setZero(); + VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView() = sd * mcd * md), + Mat_cd((sd * mcd * md.template cast().eval()).template triangularView())); + VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView() = sd * md * mcd), + Mat_cd((sd * md.template cast().eval() * mcd).template triangularView())); + VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView() = scd * mcd * md), + Mat_cd((scd * mcd * md.template cast().eval()).template triangularView())); + VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView() = scd * md * mcd), + Mat_cd((scd * md.template cast().eval() * mcd).template triangularView())); + + + VERIFY_IS_APPROX( md.array() * mcd.array(), md.template cast().eval().array() * mcd.array() ); + VERIFY_IS_APPROX( mcd.array() * md.array(), mcd.array() * md.template cast().eval().array() ); + + VERIFY_IS_APPROX( md.array() + mcd.array(), md.template cast().eval().array() + mcd.array() ); + VERIFY_IS_APPROX( mcd.array() + md.array(), mcd.array() + md.template cast().eval().array() ); + + VERIFY_IS_APPROX( md.array() - mcd.array(), md.template cast().eval().array() - mcd.array() ); + VERIFY_IS_APPROX( mcd.array() - md.array(), mcd.array() - md.template cast().eval().array() ); + + if(mcd.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( md.array() / mcd.array(), md.template cast().eval().array() / mcd.array() ); + } + if(md.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( mcd.array() / md.array(), mcd.array() / md.template cast().eval().array() ); + } + + if(md.array().abs().minCoeff()>epsd || mcd.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( md.array().pow(mcd.array()), md.template cast().eval().array().pow(mcd.array()) ); + VERIFY_IS_APPROX( mcd.array().pow(md.array()), mcd.array().pow(md.template cast().eval().array()) ); + + VERIFY_IS_APPROX( pow(md.array(),mcd.array()), md.template cast().eval().array().pow(mcd.array()) ); + VERIFY_IS_APPROX( pow(mcd.array(),md.array()), mcd.array().pow(md.template cast().eval().array()) ); + } + + rcd = mcd; + VERIFY_IS_APPROX( rcd = md, md.template cast().eval() ); + rcd = mcd; + VERIFY_IS_APPROX( rcd += md, mcd + md.template cast().eval() ); + rcd = mcd; + VERIFY_IS_APPROX( rcd -= md, mcd - md.template cast().eval() ); + rcd = mcd; + VERIFY_IS_APPROX( rcd.array() *= md.array(), mcd.array() * md.template cast().eval().array() ); + rcd = mcd; + if(md.array().abs().minCoeff()>epsd) + { + VERIFY_IS_APPROX( rcd.array() /= md.array(), mcd.array() / md.template cast().eval().array() ); + } + + rcd = mcd; + VERIFY_IS_APPROX( rcd.noalias() += md + mcd*md, mcd + (md.template cast().eval()) + mcd*(md.template cast().eval())); + + VERIFY_IS_APPROX( rcd.noalias() = md*md, ((md*md).eval().template cast()) ); + rcd = mcd; + VERIFY_IS_APPROX( rcd.noalias() += md*md, mcd + ((md*md).eval().template cast()) ); + rcd = mcd; + VERIFY_IS_APPROX( rcd.noalias() -= md*md, mcd - ((md*md).eval().template cast()) ); + + VERIFY_IS_APPROX( rcd.noalias() = mcd + md*md, mcd + ((md*md).eval().template cast()) ); + rcd = mcd; + VERIFY_IS_APPROX( rcd.noalias() += mcd + md*md, mcd + mcd + ((md*md).eval().template cast()) ); + rcd = mcd; + VERIFY_IS_APPROX( rcd.noalias() -= mcd + md*md, - ((md*md).eval().template cast()) ); +} + +EIGEN_DECLARE_TEST(mixingtypes) +{ + g_called = false; // Silence -Wunneeded-internal-declaration. + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(mixingtypes<3>()); + CALL_SUBTEST_2(mixingtypes<4>()); + CALL_SUBTEST_3(mixingtypes(internal::random(1,EIGEN_TEST_MAX_SIZE))); + + CALL_SUBTEST_4(mixingtypes<3>()); + CALL_SUBTEST_5(mixingtypes<4>()); + CALL_SUBTEST_6(mixingtypes(internal::random(1,EIGEN_TEST_MAX_SIZE))); + CALL_SUBTEST_7(raise_assertion(internal::random(1,EIGEN_TEST_MAX_SIZE))); + } + CALL_SUBTEST_7(raise_assertion<0>()); + CALL_SUBTEST_7(raise_assertion<3>()); + CALL_SUBTEST_7(raise_assertion<4>()); + CALL_SUBTEST_7(raise_assertion(0)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mpl2only.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mpl2only.cpp new file mode 100644 index 0000000000000000000000000000000000000000..296350d082fdf7d3e989ae56afe0d01c54786a11 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/mpl2only.cpp @@ -0,0 +1,24 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MPL2_ONLY +#define EIGEN_MPL2_ONLY +#endif +#include +#include +#include +#include +#include +#include +#include + +int main() +{ + return 0; +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nestbyvalue.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nestbyvalue.cpp new file mode 100644 index 0000000000000000000000000000000000000000..c5356bc24cb8e571309b5cb674aecc41602fedd2 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nestbyvalue.cpp @@ -0,0 +1,37 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2019 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define TEST_ENABLE_TEMPORARY_TRACKING + +#include "main.h" + +typedef NestByValue CpyMatrixXd; +typedef CwiseBinaryOp,const CpyMatrixXd,const CpyMatrixXd> XprType; + +XprType get_xpr_with_temps(const MatrixXd& a) +{ + MatrixXd t1 = a.rowwise().reverse(); + MatrixXd t2 = a+a; + return t1.nestByValue() + t2.nestByValue(); +} + +EIGEN_DECLARE_TEST(nestbyvalue) +{ + for(int i = 0; i < g_repeat; i++) { + Index rows = internal::random(1,EIGEN_TEST_MAX_SIZE); + Index cols = internal::random(1,EIGEN_TEST_MAX_SIZE); + MatrixXd a = MatrixXd(rows,cols); + nb_temporaries = 0; + XprType x = get_xpr_with_temps(a); + VERIFY_IS_EQUAL(nb_temporaries,6); + MatrixXd b = x; + VERIFY_IS_EQUAL(nb_temporaries,6+1); + VERIFY_IS_APPROX(b, a.rowwise().reverse().eval() + (a+a).eval()); + } +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nesting_ops.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nesting_ops.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4b5fc21f259d13570e979d31086511007fa6a358 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nesting_ops.cpp @@ -0,0 +1,107 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Hauke Heibel +// Copyright (C) 2015 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#define TEST_ENABLE_TEMPORARY_TRACKING + +#include "main.h" + +template +void use_n_times(const XprType &xpr) +{ + typename internal::nested_eval::type mat(xpr); + typename XprType::PlainObject res(mat.rows(), mat.cols()); + nb_temporaries--; // remove res + res.setZero(); + for(int i=0; i +bool verify_eval_type(const XprType &, const ReferenceType&) +{ + typedef typename internal::nested_eval::type EvalType; + return internal::is_same::type, typename internal::remove_all::type>::value; +} + +template void run_nesting_ops_1(const MatrixType& _m) +{ + typename internal::nested_eval::type m(_m); + + // Make really sure that we are in debug mode! + VERIFY_RAISES_ASSERT(eigen_assert(false)); + + // The only intention of these tests is to ensure that this code does + // not trigger any asserts or segmentation faults... more to come. + VERIFY_IS_APPROX( (m.transpose() * m).diagonal().sum(), (m.transpose() * m).diagonal().sum() ); + VERIFY_IS_APPROX( (m.transpose() * m).diagonal().array().abs().sum(), (m.transpose() * m).diagonal().array().abs().sum() ); + + VERIFY_IS_APPROX( (m.transpose() * m).array().abs().sum(), (m.transpose() * m).array().abs().sum() ); +} + +template void run_nesting_ops_2(const MatrixType& _m) +{ + typedef typename MatrixType::Scalar Scalar; + Index rows = _m.rows(); + Index cols = _m.cols(); + MatrixType m1 = MatrixType::Random(rows,cols); + Matrix m2; + + if((MatrixType::SizeAtCompileTime==Dynamic)) + { + VERIFY_EVALUATION_COUNT( use_n_times<1>(m1 + m1*m1), 1 ); + VERIFY_EVALUATION_COUNT( use_n_times<10>(m1 + m1*m1), 1 ); + + VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.template triangularView().solve(m1.col(0))), 1 ); + VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.template triangularView().solve(m1.col(0))), 1 ); + + VERIFY_EVALUATION_COUNT( use_n_times<1>(Scalar(2)*m1.template triangularView().solve(m1.col(0))), 2 ); // FIXME could be one by applying the scaling in-place on the solve result + VERIFY_EVALUATION_COUNT( use_n_times<1>(m1.col(0)+m1.template triangularView().solve(m1.col(0))), 2 ); // FIXME could be one by adding m1.col() inplace + VERIFY_EVALUATION_COUNT( use_n_times<10>(m1.col(0)+m1.template triangularView().solve(m1.col(0))), 2 ); + } + + { + VERIFY( verify_eval_type<10>(m1, m1) ); + if(!NumTraits::IsComplex) + { + VERIFY( verify_eval_type<3>(2*m1, 2*m1) ); + VERIFY( verify_eval_type<4>(2*m1, m1) ); + } + else + { + VERIFY( verify_eval_type<2>(2*m1, 2*m1) ); + VERIFY( verify_eval_type<3>(2*m1, m1) ); + } + VERIFY( verify_eval_type<2>(m1+m1, m1+m1) ); + VERIFY( verify_eval_type<3>(m1+m1, m1) ); + VERIFY( verify_eval_type<1>(m1*m1.transpose(), m2) ); + VERIFY( verify_eval_type<1>(m1*(m1+m1).transpose(), m2) ); + VERIFY( verify_eval_type<2>(m1*m1.transpose(), m2) ); + VERIFY( verify_eval_type<1>(m1+m1*m1, m1) ); + + VERIFY( verify_eval_type<1>(m1.template triangularView().solve(m1), m1) ); + VERIFY( verify_eval_type<1>(m1+m1.template triangularView().solve(m1), m1) ); + } +} + + +EIGEN_DECLARE_TEST(nesting_ops) +{ + CALL_SUBTEST_1(run_nesting_ops_1(MatrixXf::Random(25,25))); + CALL_SUBTEST_2(run_nesting_ops_1(MatrixXcd::Random(25,25))); + CALL_SUBTEST_3(run_nesting_ops_1(Matrix4f::Random())); + CALL_SUBTEST_4(run_nesting_ops_1(Matrix2d::Random())); + + Index s = internal::random(1,EIGEN_TEST_MAX_SIZE); + CALL_SUBTEST_1( run_nesting_ops_2(MatrixXf(s,s)) ); + CALL_SUBTEST_2( run_nesting_ops_2(MatrixXcd(s,s)) ); + CALL_SUBTEST_3( run_nesting_ops_2(Matrix4f()) ); + CALL_SUBTEST_4( run_nesting_ops_2(Matrix2d()) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nomalloc.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nomalloc.cpp new file mode 100644 index 0000000000000000000000000000000000000000..cb4c073e941895b9e72f6d39cdb8ae70f707598e --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nomalloc.cpp @@ -0,0 +1,228 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2006-2008 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// discard stack allocation as that too bypasses malloc +#define EIGEN_STACK_ALLOCATION_LIMIT 0 +// heap allocation will raise an assert if enabled at runtime +#define EIGEN_RUNTIME_NO_MALLOC + +#include "main.h" +#include +#include +#include +#include +#include + +template void nomalloc(const MatrixType& m) +{ + /* this test check no dynamic memory allocation are issued with fixed-size matrices + */ + typedef typename MatrixType::Scalar Scalar; + + Index rows = m.rows(); + Index cols = m.cols(); + + MatrixType m1 = MatrixType::Random(rows, cols), + m2 = MatrixType::Random(rows, cols), + m3(rows, cols); + + Scalar s1 = internal::random(); + + Index r = internal::random(0, rows-1), + c = internal::random(0, cols-1); + + VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2); + VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c))); + VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix()); + VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); + + m2.col(0).noalias() = m1 * m1.col(0); + m2.col(0).noalias() -= m1.adjoint() * m1.col(0); + m2.col(0).noalias() -= m1 * m1.row(0).adjoint(); + m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint(); + + m2.row(0).noalias() = m1.row(0) * m1; + m2.row(0).noalias() -= m1.row(0) * m1.adjoint(); + m2.row(0).noalias() -= m1.col(0).adjoint() * m1; + m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint(); + VERIFY_IS_APPROX(m2,m2); + + m2.col(0).noalias() = m1.template triangularView() * m1.col(0); + m2.col(0).noalias() -= m1.adjoint().template triangularView() * m1.col(0); + m2.col(0).noalias() -= m1.template triangularView() * m1.row(0).adjoint(); + m2.col(0).noalias() -= m1.adjoint().template triangularView() * m1.row(0).adjoint(); + + m2.row(0).noalias() = m1.row(0) * m1.template triangularView(); + m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView(); + m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView(); + m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView(); + VERIFY_IS_APPROX(m2,m2); + + m2.col(0).noalias() = m1.template selfadjointView() * m1.col(0); + m2.col(0).noalias() -= m1.adjoint().template selfadjointView() * m1.col(0); + m2.col(0).noalias() -= m1.template selfadjointView() * m1.row(0).adjoint(); + m2.col(0).noalias() -= m1.adjoint().template selfadjointView() * m1.row(0).adjoint(); + + m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView(); + m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView(); + m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView(); + m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView(); + VERIFY_IS_APPROX(m2,m2); + + m2.template selfadjointView().rankUpdate(m1.col(0),-1); + m2.template selfadjointView().rankUpdate(m1.row(0),-1); + m2.template selfadjointView().rankUpdate(m1.col(0), m1.col(0)); // rank-2 + + // The following fancy matrix-matrix products are not safe yet regarding static allocation + m2.template selfadjointView().rankUpdate(m1); + m2 += m2.template triangularView() * m1; + m2.template triangularView() = m2 * m2; + m1 += m1.template selfadjointView() * m2; + VERIFY_IS_APPROX(m2,m2); +} + +template +void ctms_decompositions() +{ + const int maxSize = 16; + const int size = 12; + + typedef Eigen::Matrix Matrix; + + typedef Eigen::Matrix Vector; + + typedef Eigen::Matrix, + Eigen::Dynamic, Eigen::Dynamic, + 0, + maxSize, maxSize> ComplexMatrix; + + const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size)); + Matrix X(size,size); + const ComplexMatrix complexA(ComplexMatrix::Random(size, size)); + const Matrix saA = A.adjoint() * A; + const Vector b(Vector::Random(size)); + Vector x(size); + + // Cholesky module + Eigen::LLT LLT; LLT.compute(A); + X = LLT.solve(B); + x = LLT.solve(b); + Eigen::LDLT LDLT; LDLT.compute(A); + X = LDLT.solve(B); + x = LDLT.solve(b); + + // Eigenvalues module + Eigen::HessenbergDecomposition hessDecomp; hessDecomp.compute(complexA); + Eigen::ComplexSchur cSchur(size); cSchur.compute(complexA); + Eigen::ComplexEigenSolver cEigSolver; cEigSolver.compute(complexA); + Eigen::EigenSolver eigSolver; eigSolver.compute(A); + Eigen::SelfAdjointEigenSolver saEigSolver(size); saEigSolver.compute(saA); + Eigen::Tridiagonalization tridiag; tridiag.compute(saA); + + // LU module + Eigen::PartialPivLU ppLU; ppLU.compute(A); + X = ppLU.solve(B); + x = ppLU.solve(b); + Eigen::FullPivLU fpLU; fpLU.compute(A); + X = fpLU.solve(B); + x = fpLU.solve(b); + + // QR module + Eigen::HouseholderQR hQR; hQR.compute(A); + X = hQR.solve(B); + x = hQR.solve(b); + Eigen::ColPivHouseholderQR cpQR; cpQR.compute(A); + X = cpQR.solve(B); + x = cpQR.solve(b); + Eigen::FullPivHouseholderQR fpQR; fpQR.compute(A); + // FIXME X = fpQR.solve(B); + x = fpQR.solve(b); + + // SVD module + Eigen::JacobiSVD jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV); +} + +void test_zerosized() { + // default constructors: + Eigen::MatrixXd A; + Eigen::VectorXd v; + // explicit zero-sized: + Eigen::ArrayXXd A0(0,0); + Eigen::ArrayXd v0(0); + + // assigning empty objects to each other: + A=A0; + v=v0; +} + +template void test_reference(const MatrixType& m) { + typedef typename MatrixType::Scalar Scalar; + enum { Flag = MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor}; + enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor}; + Index rows = m.rows(), cols=m.cols(); + typedef Eigen::Matrix MatrixX; + typedef Eigen::Matrix MatrixXT; + // Dynamic reference: + typedef Eigen::Ref Ref; + typedef Eigen::Ref RefT; + + Ref r1(m); + Ref r2(m.block(rows/3, cols/4, rows/2, cols/2)); + RefT r3(m.transpose()); + RefT r4(m.topLeftCorner(rows/2, cols/2).transpose()); + + VERIFY_RAISES_ASSERT(RefT r5(m)); + VERIFY_RAISES_ASSERT(Ref r6(m.transpose())); + VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m)); + + // Copy constructors shall also never malloc + Ref r8 = r1; + RefT r9 = r3; + + // Initializing from a compatible Ref shall also never malloc + Eigen::Ref > r10=r8, r11=m; + + // Initializing from an incompatible Ref will malloc: + typedef Eigen::Ref RefAligned; + VERIFY_RAISES_ASSERT(RefAligned r12=r10); + VERIFY_RAISES_ASSERT(Ref r13=r10); // r10 has more dynamic strides + +} + +EIGEN_DECLARE_TEST(nomalloc) +{ + // create some dynamic objects + Eigen::MatrixXd M1 = MatrixXd::Random(3,3); + Ref R1 = 2.0*M1; // Ref requires temporary + + // from here on prohibit malloc: + Eigen::internal::set_is_malloc_allowed(false); + + // check that our operator new is indeed called: + VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3))); + CALL_SUBTEST_1(nomalloc(Matrix()) ); + CALL_SUBTEST_2(nomalloc(Matrix4d()) ); + CALL_SUBTEST_3(nomalloc(Matrix()) ); + + // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms) + CALL_SUBTEST_4(ctms_decompositions()); + + CALL_SUBTEST_5(test_zerosized()); + + CALL_SUBTEST_6(test_reference(Matrix())); + CALL_SUBTEST_7(test_reference(R1)); + CALL_SUBTEST_8(Ref R2 = M1.topRows<2>(); test_reference(R2)); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nullary.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nullary.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9b25ea4f36b6be5b02af2f52e7268250d91862cb --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/nullary.cpp @@ -0,0 +1,341 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010-2011 Jitse Niesen +// Copyright (C) 2016 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" + +template +bool equalsIdentity(const MatrixType& A) +{ + typedef typename MatrixType::Scalar Scalar; + Scalar zero = static_cast(0); + + bool offDiagOK = true; + for (Index i = 0; i < A.rows(); ++i) { + for (Index j = i+1; j < A.cols(); ++j) { + offDiagOK = offDiagOK && (A(i,j) == zero); + } + } + for (Index i = 0; i < A.rows(); ++i) { + for (Index j = 0; j < (std::min)(i, A.cols()); ++j) { + offDiagOK = offDiagOK && (A(i,j) == zero); + } + } + + bool diagOK = (A.diagonal().array() == 1).all(); + return offDiagOK && diagOK; + +} + +template +void check_extremity_accuracy(const VectorType &v, const typename VectorType::Scalar &low, const typename VectorType::Scalar &high) +{ + typedef typename VectorType::Scalar Scalar; + typedef typename VectorType::RealScalar RealScalar; + + RealScalar prec = internal::is_same::value ? NumTraits::dummy_precision()*10 : NumTraits::dummy_precision()/10; + Index size = v.size(); + + if(size<20) + return; + + for (int i=0; isize-6) + { + Scalar ref = (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1); + if(std::abs(ref)>1) + { + if(!internal::isApprox(v(i), ref, prec)) + std::cout << v(i) << " != " << ref << " ; relative error: " << std::abs((v(i)-ref)/ref) << " ; required precision: " << prec << " ; range: " << low << "," << high << " ; i: " << i << "\n"; + VERIFY(internal::isApprox(v(i), (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1), prec)); + } + } + } +} + +template +void testVectorType(const VectorType& base) +{ + typedef typename VectorType::Scalar Scalar; + typedef typename VectorType::RealScalar RealScalar; + + const Index size = base.size(); + + Scalar high = internal::random(-500,500); + Scalar low = (size == 1 ? high : internal::random(-500,500)); + if (numext::real(low)>numext::real(high)) std::swap(low,high); + + // check low==high + if(internal::random(0.f,1.f)<0.05f) + low = high; + // check abs(low) >> abs(high) + else if(size>2 && std::numeric_limits::max_exponent10>0 && internal::random(0.f,1.f)<0.1f) + low = -internal::random(1,2) * RealScalar(std::pow(RealScalar(10),std::numeric_limits::max_exponent10/2)); + + const Scalar step = ((size == 1) ? 1 : (high-low)/RealScalar(size-1)); + + // check whether the result yields what we expect it to do + VectorType m(base); + m.setLinSpaced(size,low,high); + + if(!NumTraits::IsInteger) + { + VectorType n(size); + for (int i=0; i::IsInteger) || (range_length>=size && (Index(range_length)%(size-1))==0) || (Index(range_length+1)::IsInteger) || (range_length>=size)) + for (int i=0; i::IsInteger) + CALL_SUBTEST( check_extremity_accuracy(m, low, high) ); + } + + VERIFY( numext::real(m(m.size()-1)) <= numext::real(high) ); + VERIFY( (m.array().real() <= numext::real(high)).all() ); + VERIFY( (m.array().real() >= numext::real(low)).all() ); + + + VERIFY( numext::real(m(m.size()-1)) >= numext::real(low) ); + if(size>=1) + { + VERIFY( internal::isApprox(m(0),low) ); + VERIFY_IS_EQUAL(m(0) , low); + } + + // check whether everything works with row and col major vectors + Matrix row_vector(size); + Matrix col_vector(size); + row_vector.setLinSpaced(size,low,high); + col_vector.setLinSpaced(size,low,high); + // when using the extended precision (e.g., FPU) the relative error might exceed 1 bit + // when computing the squared sum in isApprox, thus the 2x factor. + VERIFY( row_vector.isApprox(col_vector.transpose(), RealScalar(2)*NumTraits::epsilon())); + + Matrix size_changer(size+50); + size_changer.setLinSpaced(size,low,high); + VERIFY( size_changer.size() == size ); + + typedef Matrix ScalarMatrix; + ScalarMatrix scalar; + scalar.setLinSpaced(1,low,high); + VERIFY_IS_APPROX( scalar, ScalarMatrix::Constant(high) ); + VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) ); + + // regression test for bug 526 (linear vectorized transversal) + if (size > 1 && (!NumTraits::IsInteger)) { + m.tail(size-1).setLinSpaced(low, high); + VERIFY_IS_APPROX(m(size-1), high); + } + + // regression test for bug 1383 (LinSpaced with empty size/range) + { + Index n0 = VectorType::SizeAtCompileTime==Dynamic ? 0 : VectorType::SizeAtCompileTime; + low = internal::random(); + m = VectorType::LinSpaced(n0,low,low-RealScalar(1)); + VERIFY(m.size()==n0); + + if(VectorType::SizeAtCompileTime==Dynamic) + { + VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,0,Scalar(n0-1)).sum(),Scalar(0)); + VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,low,low-RealScalar(1)).sum(),Scalar(0)); + } + + m.setLinSpaced(n0,0,Scalar(n0-1)); + VERIFY(m.size()==n0); + m.setLinSpaced(n0,low,low-RealScalar(1)); + VERIFY(m.size()==n0); + + // empty range only: + VERIFY_IS_APPROX(VectorType::LinSpaced(size,low,low),VectorType::Constant(size,low)); + m.setLinSpaced(size,low,low); + VERIFY_IS_APPROX(m,VectorType::Constant(size,low)); + + if(NumTraits::IsInteger) + { + VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar(size-1)), VectorType::LinSpaced(size,low+Scalar(size-1),low).reverse() ); + + if(VectorType::SizeAtCompileTime==Dynamic) + { + // Check negative multiplicator path: + for(Index k=1; k<5; ++k) + VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar((size-1)*k)), VectorType::LinSpaced(size,low+Scalar((size-1)*k),low).reverse() ); + // Check negative divisor path: + for(Index k=1; k<5; ++k) + VERIFY_IS_APPROX( VectorType::LinSpaced(size*k,low,low+Scalar(size-1)), VectorType::LinSpaced(size*k,low+Scalar(size-1),low).reverse() ); + } + } + } + + // test setUnit() + if(m.size()>0) + { + for(Index k=0; k<10; ++k) + { + Index i = internal::random(0,m.size()-1); + m.setUnit(i); + VERIFY_IS_APPROX( m, VectorType::Unit(m.size(), i) ); + } + if(VectorType::SizeAtCompileTime==Dynamic) + { + Index i = internal::random(0,2*m.size()-1); + m.setUnit(2*m.size(),i); + VERIFY_IS_APPROX( m, VectorType::Unit(m.size(),i) ); + } + } + +} + +template +void testMatrixType(const MatrixType& m) +{ + using std::abs; + const Index rows = m.rows(); + const Index cols = m.cols(); + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + + Scalar s1; + do { + s1 = internal::random(); + } while(abs(s1)::IsInteger)); + + MatrixType A; + A.setIdentity(rows, cols); + VERIFY(equalsIdentity(A)); + VERIFY(equalsIdentity(MatrixType::Identity(rows, cols))); + + + A = MatrixType::Constant(rows,cols,s1); + Index i = internal::random(0,rows-1); + Index j = internal::random(0,cols-1); + VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1)(i,j), s1 ); + VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1).coeff(i,j), s1 ); + VERIFY_IS_APPROX( A(i,j), s1 ); +} + +template +void bug79() +{ + // Assignment of a RowVectorXd to a MatrixXd (regression test for bug #79). + VERIFY( (MatrixXd(RowVectorXd::LinSpaced(3, 0, 1)) - RowVector3d(0, 0.5, 1)).norm() < std::numeric_limits::epsilon() ); +} + +template +void bug1630() +{ + Array4d x4 = Array4d::LinSpaced(0.0, 1.0); + Array3d x3(Array4d::LinSpaced(0.0, 1.0).head(3)); + VERIFY_IS_APPROX(x4.head(3), x3); +} + +template +void nullary_overflow() +{ + // Check possible overflow issue + int n = 60000; + ArrayXi a1(n), a2(n); + a1.setLinSpaced(n, 0, n-1); + for(int i=0; i +void nullary_internal_logic() +{ + // check some internal logic + VERIFY(( internal::has_nullary_operator >::value )); + VERIFY(( !internal::has_unary_operator >::value )); + VERIFY(( !internal::has_binary_operator >::value )); + VERIFY(( internal::functor_has_linear_access >::ret )); + + VERIFY(( !internal::has_nullary_operator >::value )); + VERIFY(( !internal::has_unary_operator >::value )); + VERIFY(( internal::has_binary_operator >::value )); + VERIFY(( !internal::functor_has_linear_access >::ret )); + + VERIFY(( !internal::has_nullary_operator >::value )); + VERIFY(( internal::has_unary_operator >::value )); + VERIFY(( !internal::has_binary_operator >::value )); + VERIFY(( internal::functor_has_linear_access >::ret )); + + // Regression unit test for a weird MSVC bug. + // Search "nullary_wrapper_workaround_msvc" in CoreEvaluators.h for the details. + // See also traits::match. + { + MatrixXf A = MatrixXf::Random(3,3); + Ref R = 2.0*A; + VERIFY_IS_APPROX(R, A+A); + + Ref R1 = MatrixXf::Random(3,3)+A; + + VectorXi V = VectorXi::Random(3); + Ref R2 = VectorXi::LinSpaced(3,1,3)+V; + VERIFY_IS_APPROX(R2, V+Vector3i(1,2,3)); + + VERIFY(( internal::has_nullary_operator >::value )); + VERIFY(( !internal::has_unary_operator >::value )); + VERIFY(( !internal::has_binary_operator >::value )); + VERIFY(( internal::functor_has_linear_access >::ret )); + + VERIFY(( !internal::has_nullary_operator >::value )); + VERIFY(( internal::has_unary_operator >::value )); + VERIFY(( !internal::has_binary_operator >::value )); + VERIFY(( internal::functor_has_linear_access >::ret )); + } +} + +EIGEN_DECLARE_TEST(nullary) +{ + CALL_SUBTEST_1( testMatrixType(Matrix2d()) ); + CALL_SUBTEST_2( testMatrixType(MatrixXcf(internal::random(1,300),internal::random(1,300))) ); + CALL_SUBTEST_3( testMatrixType(MatrixXf(internal::random(1,300),internal::random(1,300))) ); + + for(int i = 0; i < g_repeat*10; i++) { + CALL_SUBTEST_3( testVectorType(VectorXcd(internal::random(1,30000))) ); + CALL_SUBTEST_4( testVectorType(VectorXd(internal::random(1,30000))) ); + CALL_SUBTEST_5( testVectorType(Vector4d()) ); // regression test for bug 232 + CALL_SUBTEST_6( testVectorType(Vector3d()) ); + CALL_SUBTEST_7( testVectorType(VectorXf(internal::random(1,30000))) ); + CALL_SUBTEST_8( testVectorType(Vector3f()) ); + CALL_SUBTEST_8( testVectorType(Vector4f()) ); + CALL_SUBTEST_8( testVectorType(Matrix()) ); + CALL_SUBTEST_8( testVectorType(Matrix()) ); + + CALL_SUBTEST_9( testVectorType(VectorXi(internal::random(1,10))) ); + CALL_SUBTEST_9( testVectorType(VectorXi(internal::random(9,300))) ); + CALL_SUBTEST_9( testVectorType(Matrix()) ); + } + + CALL_SUBTEST_6( bug79<0>() ); + CALL_SUBTEST_6( bug1630<0>() ); + CALL_SUBTEST_9( nullary_overflow<0>() ); + CALL_SUBTEST_10( nullary_internal_logic<0>() ); +} diff --git a/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/num_dimensions.cpp b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/num_dimensions.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7ad7ef6979d67cf3390bb4ce609f688d183cfea0 --- /dev/null +++ b/slahmr/third-party/DROID-SLAM/thirdparty/eigen/test/num_dimensions.cpp @@ -0,0 +1,90 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2018 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#include "main.h" +#include + +template +void check_dim(const Xpr& ) { + STATIC_CHECK( Xpr::NumDimensions == ExpectedDim ); +} + +#if EIGEN_HAS_CXX11 +template