././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/0000755000175000017500000000000000000000000015060 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/AUTHORS0000644000175000017500000000036000000000000016127 0ustar00shreyasshreyas00000000000000* Shreyas Bapat Primary Author * Bhavya Bhatt Primary Author * Ritwik Saha Primary Author * Priyanshu Khandelwal Primary Author ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/COPYING0000644000175000017500000000210600000000000016112 0ustar00shreyasshreyas00000000000000The MIT License (MIT) Copyright (c) 2019-2020 The EinsteinPy Project 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. ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/MANIFEST.in0000644000175000017500000000030100000000000016610 0ustar00shreyasshreyas00000000000000graft docs include COPYING include AUTHORS recursive-include src/einsteinpy/tests *.py *.html prune docs/source/examples/.ipynb_checkpoints global-exclude *.py[cod] __pycache__ *.so *.dylib ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/PKG-INFO0000644000175000017500000003024500000000000016161 0ustar00shreyasshreyas00000000000000Metadata-Version: 2.1 Name: einsteinpy Version: 0.3.0 Summary: Python package for General Relativity Home-page: https://einsteinpy.org/ Author: Shreyas Bapat Author-email: bapat.shreyas@gmail.com License: MIT Download-URL: https://github.com/einsteinpy/einsteinpy Description: .. einsteinpy .. image:: https://blog.einsteinpy.org/img/logo.png :target: https://einsteinpy.org/ :alt: EinsteinPy logo :width: 675px :align: center .. |astropy| image:: http://img.shields.io/badge/powered%20by-AstroPy-orange.svg?style=flat-square :target: http://www.astropy.org/ .. |mailing| image:: https://img.shields.io/badge/mailing%20list-groups.io-8cbcd1.svg?style=flat-square :target: https://groups.io/g/einsteinpy-dev .. |doi| image:: https://zenodo.org/badge/168302584.svg?style=flat-square :target: https://zenodo.org/badge/latestdoi/168302584 .. |gitter| image:: https://img.shields.io/gitter/room/EinsteinPy-Project/EinsteinPy.svg?logo=gitter&style=flat-square :alt: Join the chat at https://gitter.im/EinsteinPy-Project/EinsteinPy :target: https://gitter.im/EinsteinPy-Project/EinsteinPy?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge .. |riotchat| image:: https://img.shields.io/matrix/einsteinpy:matrix.org.svg?logo=riot&style=flat-square :target: https://riot.im/app/#/room/#einsteinpy:matrix.org .. |license| image:: https://img.shields.io/badge/license-MIT-blue.svg?style=flat-square :target: https://github.com/einsteinpy/einsteinpy/raw/0.3.x/COPYING .. |docs| image:: https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat-square :target: https://docs.einsteinpy.org/en/v0.3.0/?badge=latest .. |codeclimate| image:: https://img.shields.io/codeclimate/maintainability/einsteinpy/einsteinpy.svg?logo=code-climate&style=flat-square :target: https://codeclimate.com/github/einsteinpy/einsteinpy/maintainability :alt: Maintainability .. |circleci| image:: https://img.shields.io/circleci/project/github/einsteinpy/einsteinpy/0.3.x.svg?style=flat-square&logo=circleci :target: https://circleci.com/gh/einsteinpy/einsteinpy .. |ghactions| image:: https://img.shields.io/github/workflow/status/einsteinpy/einsteinpy/Test_MacOS?logo=github&style=flat-square :target: https://github.com/einsteinpy/einsteinpy/actions?query=branch%3A0.3.x .. |codecov| image:: https://img.shields.io/codecov/c/github/einsteinpy/einsteinpy.svg?style=flat-square :target: https://codecov.io/github/einsteinpy/einsteinpy?branch=0.3.x .. |appveyor| image:: https://img.shields.io/appveyor/ci/shreyasbapat/einsteinpy/0.3.x?logo=appveyor&style=flat-square :target: https://ci.appveyor.com/project/shreyasbapat/einsteinpy/branch/0.3.x .. |orcid-shreyas| image:: https://img.shields.io/badge/id-0000--0002--0870--4665-a6ce39.svg :target: https://orcid.org/0000-0002-0870-4665 :Name: EinsteinPy :Website: https://einsteinpy.org/ :Version: 0.3.0 |astropy| |mailing| |gitter| |riotchat| |license| |docs| |circleci| |ghactions| |appveyor| |codecov| |codeclimate| **EinsteinPy** is an open source pure Python package dedicated to problems arising in General Relativity and gravitational physics, such as geodesics plotting for Schwarzschild, Kerr and Kerr Newman space-time model, calculation of Schwarzschild radius, calculation of Event Horizon and Ergosphere for Kerr space-time. Symbolic Manipulations of various tensors like Metric, Riemann, Ricci, Ricci Scalar, Weyl, Schouten, Stress-Energy-Momentum, Einstein and Christoffel Symbols is also possible using the library. EinsteinPy also features Hypersurface Embedding of Schwarzschild space-time, which will soon lead to modelling of Gravitational Lensing! It is released under the MIT license. Documentation ============= |docs| Complete documentation, including a user guide and an API reference, can be read on the wonderful `Read the Docs`_. https://docs.einsteinpy.org/ .. _`Read the Docs`: https://readthedocs.org/ Examples ======== .. |mybinder| image:: https://img.shields.io/badge/launch-binder-e66581.svg?style=flat-square :target: https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb |mybinder| In the examples directory, you can find several Jupyter notebooks with specific applications of einsteinpy. You can consider theses Jupyter Notebooks as tutorials for einsteinpy. You can launch a cloud Jupyter server using `binder`_ to edit the notebooks without installing anything. Try it out! https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb .. _binder: https://beta.mybinder.org/ Requirements ============ EinsteinPy requires the following Python packages: * NumPy, for basic numerical routines * Astropy, for physical units and time handling * Matplotlib, for static geodesics plotting and visualizations. * Plotly, for interactive geodesics plotting and visualizations. * SciPy, for solving ordinary differential equations. * SymPy, for symbolic calculations related to GR. * Numba, for accelerating the code EinsteinPy is usually tested on Linux, Windows and OS X on Python 3.6, 3.7 and 3.8 against latest NumPy. ============== =============== =================== Platform Site Status ============== =============== =================== Linux CircleCI |circleci| OS X Github Actions |ghactions| Windows x64 Appveyor |appveyor| ============== =============== =================== Installation ============ The easiest and fastest way to get the package up and running is to install EinsteinPy using `conda `_:: $ conda install einsteinpy --channel conda-forge Or you can simply install it from `PyPI `_:: $ pip install einsteinpy Or for Debian/Ubuntu/Mint users, the package is installable (Ubuntu 19.04 onwards) from `apt `_:: $ sudo apt install python3-einsteinpy Please note that the package version in Debian Repositories might not be the latest. But it will be definitely the most stable version of EinsteinPy available till date. Please check out the `guide for alternative installation methods`_. .. _`guide for alternative installation methods`: https://einsteinpy.github.io/installation/ Testing ======= |codecov| If installed correctly, the tests can be run using pytest:: $ python -c "import einsteinpy.testing; einsteinpy.testing.test()" ============================= test session starts ============================== platform linux -- Python 3.7.1, pytest-4.3.1, py-1.8.0, pluggy-0.9.0 rootdir: /home/shreyas/Local Forks/einsteinpy, inifile: setup.cfg plugins: remotedata-0.3.1, openfiles-0.3.1, doctestplus-0.3.0, cov-2.5.1, arraydiff-0.3 collected 56 items [...] ==================== 56 passed, 1 warnings in 28.19 seconds ==================== $ Problems ======== If the installation fails or you find something that doesn't work as expected, please open an issue in the `issue tracker`_. .. _`issue tracker`: https://github.com/einsteinpy/einsteinpy/issues Contributing ============ EinsteinPy is a community project, hence all contributions are more than welcome! For more information, head to `CONTRIBUTING.rst`_. .. _`CONTRIBUTING.rst`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/CONTRIBUTING.rst Developers Documentation can be found here. Support ======= |mailing| Release announcements and general discussion take place on our `mailing list`_. Feel free to join! .. _`mailing list`: https://groups.io/g/einsteinpy-dev https://groups.io/g/einsteinpy-dev Please join our `[matrix]`_ channel or `gitter`_ chat room for further queries. .. _`[matrix]`: https://matrix.to/#/#einsteinpy:matrix.org .. _`gitter`: https://gitter.im/EinsteinPy-Project/EinsteinPy If you still have a doubt, write a mail directly to `all@einsteinpy.org `_. Citing ====== If you use EinsteinPy on your project, please `drop us a line `_. You can also use the DOI to cite it in your publications. This is the latest one: |doi| And this is an example citation format:: Shreyas Bapat et al.. (2019). EinsteinPy: einsteinpy 0.1.0. Zenodo. 10.5281/zenodo.2582388 License ======= |license| EinsteinPy is released under the MIT license, hence allowing commercial use of the library. Please refer to `COPYING`_. .. _`COPYING`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/COPYING FAQ === Why Einstein-Py? ---------------- EinsteinPy comes from the name of the famous physicist, Nobel laureate, revolutionary person, Prof. Albert Einstein. This is a small tribute from our part for the amazing work he did for the humanity! Can I do with EinsteinPy? ---------------------------------------------- EinsteinPy is focused on general relativity. One can always discuss probable features on the mailing list and try to implement it. We welcome every contribution and will be happy to include it in EinsteinPy. What's the future of the project? --------------------------------- EinsteinPy is actively maintained and we hope to receive an influx of new contributors. The best way to get an idea of the roadmap is to see the `Milestones`_ of the project. .. _`Milestones`: https://github.com/einsteinpy/einsteinpy/milestones Inspiration ----------- The whole documentation and code structure is shamelessly inspired by `poliastro`_ . We really thank the poliastro developers to make this possible. EinsteinPy is nothing without it's supporters. .. _`poliastro`: https://docs.poliastro.space/ Keywords: general relativity,geodesics,relativity,kerr,black-hole,kerr-newman,schwarzschild Platform: UNKNOWN Classifier: Development Status :: 4 - Beta Classifier: Intended Audience :: Education Classifier: Intended Audience :: Science/Research Classifier: License :: OSI Approved :: MIT License Classifier: Operating System :: OS Independent Classifier: Programming Language :: Python Classifier: Programming Language :: Python :: 3 Classifier: Programming Language :: Python :: 3.6 Classifier: Programming Language :: Python :: 3.7 Classifier: Programming Language :: Python :: 3.8 Classifier: Topic :: Scientific/Engineering Classifier: Topic :: Scientific/Engineering :: Physics Classifier: Topic :: Scientific/Engineering :: Astronomy Requires-Python: >=3.5 Provides-Extra: dev ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588632684.0 einsteinpy-0.3.0/README.rst0000644000175000017500000002217700000000000016560 0ustar00shreyasshreyas00000000000000.. einsteinpy .. image:: https://blog.einsteinpy.org/img/logo.png :target: https://einsteinpy.org/ :alt: EinsteinPy logo :width: 675px :align: center .. |astropy| image:: http://img.shields.io/badge/powered%20by-AstroPy-orange.svg?style=flat-square :target: http://www.astropy.org/ .. |mailing| image:: https://img.shields.io/badge/mailing%20list-groups.io-8cbcd1.svg?style=flat-square :target: https://groups.io/g/einsteinpy-dev .. |doi| image:: https://zenodo.org/badge/168302584.svg?style=flat-square :target: https://zenodo.org/badge/latestdoi/168302584 .. |gitter| image:: https://img.shields.io/gitter/room/EinsteinPy-Project/EinsteinPy.svg?logo=gitter&style=flat-square :alt: Join the chat at https://gitter.im/EinsteinPy-Project/EinsteinPy :target: https://gitter.im/EinsteinPy-Project/EinsteinPy?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge .. |riotchat| image:: https://img.shields.io/matrix/einsteinpy:matrix.org.svg?logo=riot&style=flat-square :target: https://riot.im/app/#/room/#einsteinpy:matrix.org .. |license| image:: https://img.shields.io/badge/license-MIT-blue.svg?style=flat-square :target: https://github.com/einsteinpy/einsteinpy/raw/0.3.x/COPYING .. |docs| image:: https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat-square :target: https://docs.einsteinpy.org/en/v0.3.0/?badge=latest .. |codeclimate| image:: https://img.shields.io/codeclimate/maintainability/einsteinpy/einsteinpy.svg?logo=code-climate&style=flat-square :target: https://codeclimate.com/github/einsteinpy/einsteinpy/maintainability :alt: Maintainability .. |circleci| image:: https://img.shields.io/circleci/project/github/einsteinpy/einsteinpy/0.3.x.svg?style=flat-square&logo=circleci :target: https://circleci.com/gh/einsteinpy/einsteinpy .. |ghactions| image:: https://img.shields.io/github/workflow/status/einsteinpy/einsteinpy/Test_MacOS?logo=github&style=flat-square :target: https://github.com/einsteinpy/einsteinpy/actions?query=branch%3A0.3.x .. |codecov| image:: https://img.shields.io/codecov/c/github/einsteinpy/einsteinpy.svg?style=flat-square :target: https://codecov.io/github/einsteinpy/einsteinpy?branch=0.3.x .. |appveyor| image:: https://img.shields.io/appveyor/ci/shreyasbapat/einsteinpy/0.3.x?logo=appveyor&style=flat-square :target: https://ci.appveyor.com/project/shreyasbapat/einsteinpy/branch/0.3.x .. |orcid-shreyas| image:: https://img.shields.io/badge/id-0000--0002--0870--4665-a6ce39.svg :target: https://orcid.org/0000-0002-0870-4665 :Name: EinsteinPy :Website: https://einsteinpy.org/ :Version: 0.3.0 |astropy| |mailing| |gitter| |riotchat| |license| |docs| |circleci| |ghactions| |appveyor| |codecov| |codeclimate| **EinsteinPy** is an open source pure Python package dedicated to problems arising in General Relativity and gravitational physics, such as geodesics plotting for Schwarzschild, Kerr and Kerr Newman space-time model, calculation of Schwarzschild radius, calculation of Event Horizon and Ergosphere for Kerr space-time. Symbolic Manipulations of various tensors like Metric, Riemann, Ricci, Ricci Scalar, Weyl, Schouten, Stress-Energy-Momentum, Einstein and Christoffel Symbols is also possible using the library. EinsteinPy also features Hypersurface Embedding of Schwarzschild space-time, which will soon lead to modelling of Gravitational Lensing! It is released under the MIT license. Documentation ============= |docs| Complete documentation, including a user guide and an API reference, can be read on the wonderful `Read the Docs`_. https://docs.einsteinpy.org/ .. _`Read the Docs`: https://readthedocs.org/ Examples ======== .. |mybinder| image:: https://img.shields.io/badge/launch-binder-e66581.svg?style=flat-square :target: https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb |mybinder| In the examples directory, you can find several Jupyter notebooks with specific applications of einsteinpy. You can consider theses Jupyter Notebooks as tutorials for einsteinpy. You can launch a cloud Jupyter server using `binder`_ to edit the notebooks without installing anything. Try it out! https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb .. _binder: https://beta.mybinder.org/ Requirements ============ EinsteinPy requires the following Python packages: * NumPy, for basic numerical routines * Astropy, for physical units and time handling * Matplotlib, for static geodesics plotting and visualizations. * Plotly, for interactive geodesics plotting and visualizations. * SciPy, for solving ordinary differential equations. * SymPy, for symbolic calculations related to GR. * Numba, for accelerating the code EinsteinPy is usually tested on Linux, Windows and OS X on Python 3.6, 3.7 and 3.8 against latest NumPy. ============== =============== =================== Platform Site Status ============== =============== =================== Linux CircleCI |circleci| OS X Github Actions |ghactions| Windows x64 Appveyor |appveyor| ============== =============== =================== Installation ============ The easiest and fastest way to get the package up and running is to install EinsteinPy using `conda `_:: $ conda install einsteinpy --channel conda-forge Or you can simply install it from `PyPI `_:: $ pip install einsteinpy Or for Debian/Ubuntu/Mint users, the package is installable (Ubuntu 19.04 onwards) from `apt `_:: $ sudo apt install python3-einsteinpy Please note that the package version in Debian Repositories might not be the latest. But it will be definitely the most stable version of EinsteinPy available till date. Please check out the `guide for alternative installation methods`_. .. _`guide for alternative installation methods`: https://einsteinpy.github.io/installation/ Testing ======= |codecov| If installed correctly, the tests can be run using pytest:: $ python -c "import einsteinpy.testing; einsteinpy.testing.test()" ============================= test session starts ============================== platform linux -- Python 3.7.1, pytest-4.3.1, py-1.8.0, pluggy-0.9.0 rootdir: /home/shreyas/Local Forks/einsteinpy, inifile: setup.cfg plugins: remotedata-0.3.1, openfiles-0.3.1, doctestplus-0.3.0, cov-2.5.1, arraydiff-0.3 collected 56 items [...] ==================== 56 passed, 1 warnings in 28.19 seconds ==================== $ Problems ======== If the installation fails or you find something that doesn't work as expected, please open an issue in the `issue tracker`_. .. _`issue tracker`: https://github.com/einsteinpy/einsteinpy/issues Contributing ============ EinsteinPy is a community project, hence all contributions are more than welcome! For more information, head to `CONTRIBUTING.rst`_. .. _`CONTRIBUTING.rst`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/CONTRIBUTING.rst Developers Documentation can be found here. Support ======= |mailing| Release announcements and general discussion take place on our `mailing list`_. Feel free to join! .. _`mailing list`: https://groups.io/g/einsteinpy-dev https://groups.io/g/einsteinpy-dev Please join our `[matrix]`_ channel or `gitter`_ chat room for further queries. .. _`[matrix]`: https://matrix.to/#/#einsteinpy:matrix.org .. _`gitter`: https://gitter.im/EinsteinPy-Project/EinsteinPy If you still have a doubt, write a mail directly to `all@einsteinpy.org `_. Citing ====== If you use EinsteinPy on your project, please `drop us a line `_. You can also use the DOI to cite it in your publications. This is the latest one: |doi| And this is an example citation format:: Shreyas Bapat et al.. (2019). EinsteinPy: einsteinpy 0.1.0. Zenodo. 10.5281/zenodo.2582388 License ======= |license| EinsteinPy is released under the MIT license, hence allowing commercial use of the library. Please refer to `COPYING`_. .. _`COPYING`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/COPYING FAQ === Why Einstein-Py? ---------------- EinsteinPy comes from the name of the famous physicist, Nobel laureate, revolutionary person, Prof. Albert Einstein. This is a small tribute from our part for the amazing work he did for the humanity! Can I do with EinsteinPy? ---------------------------------------------- EinsteinPy is focused on general relativity. One can always discuss probable features on the mailing list and try to implement it. We welcome every contribution and will be happy to include it in EinsteinPy. What's the future of the project? --------------------------------- EinsteinPy is actively maintained and we hope to receive an influx of new contributors. The best way to get an idea of the roadmap is to see the `Milestones`_ of the project. .. _`Milestones`: https://github.com/einsteinpy/einsteinpy/milestones Inspiration ----------- The whole documentation and code structure is shamelessly inspired by `poliastro`_ . We really thank the poliastro developers to make this possible. EinsteinPy is nothing without it's supporters. .. _`poliastro`: https://docs.poliastro.space/ ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1873431 einsteinpy-0.3.0/docs/0000755000175000017500000000000000000000000016010 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/Makefile0000644000175000017500000001520300000000000017451 0ustar00shreyasshreyas00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line. SPHINXOPTS = SPHINXBUILD = sphinx-build PAPER = BUILDDIR = build # User-friendly check for sphinx-build ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1) $(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/) endif # Internal variables. PAPEROPT_a4 = -D latex_paper_size=a4 PAPEROPT_letter = -D latex_paper_size=letter ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source # the i18n builder cannot share the environment and doctrees with the others I18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source .PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext help: @echo "Please use \`make ' where is one of" @echo " html to make standalone HTML files" @echo " dirhtml to make HTML files named index.html in directories" @echo " singlehtml to make a single large HTML file" @echo " pickle to make pickle files" @echo " json to make JSON files" @echo " htmlhelp to make HTML files and a HTML help project" @echo " qthelp to make HTML files and a qthelp project" @echo " devhelp to make HTML files and a Devhelp project" @echo " epub to make an epub" @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" @echo " latexpdf to make LaTeX files and run them through pdflatex" @echo " latexpdfja to make LaTeX files and run them through platex/dvipdfmx" @echo " text to make text files" @echo " man to make manual pages" @echo " texinfo to make Texinfo files" @echo " info to make Texinfo files and run them through makeinfo" @echo " gettext to make PO message catalogs" @echo " changes to make an overview of all changed/added/deprecated items" @echo " xml to make Docutils-native XML files" @echo " pseudoxml to make pseudoxml-XML files for display purposes" @echo " linkcheck to check all external links for integrity" @echo " doctest to run all doctests embedded in the documentation (if enabled)" clean: rm -rf $(BUILDDIR)/* html: $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html @echo @echo "Build finished. The HTML pages are in $(BUILDDIR)/html." dirhtml: $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml @echo @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml." singlehtml: $(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml @echo @echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml." pickle: $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle @echo @echo "Build finished; now you can process the pickle files." json: $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json @echo @echo "Build finished; now you can process the JSON files." htmlhelp: $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp @echo @echo "Build finished; now you can run HTML Help Workshop with the" \ ".hhp project file in $(BUILDDIR)/htmlhelp." qthelp: $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp @echo @echo "Build finished; now you can run "qcollectiongenerator" with the" \ ".qhcp project file in $(BUILDDIR)/qthelp, like this:" @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/einsteinpy.qhcp" @echo "To view the help file:" @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/einsteinpy.qhc" devhelp: $(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp @echo @echo "Build finished." @echo "To view the help file:" @echo "# mkdir -p $$HOME/.local/share/devhelp/einsteinpy" @echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/einsteinpy" @echo "# devhelp" epub: $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub @echo @echo "Build finished. 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er._er>Ɂw/5s6P{^ FX sR* "BAfClˑ#s.^^}mG1w2_x(ܫ)7ͯj'cΗo++M1u7T Qo穩sirI?'w)c:eΔ.;I6z%}MWj~~ 䯿L&M\u4|yꞫKMlrJ|{s'tz\R*@Io#B@8k{/I9oo%އo8W^s9rYY˓e(vP*@+@ T`(#NDE?o>G.;HzuҰ.ʍ,mܥ!*קKøYa(QgT QOygϝg-7GOϔ֖1¦|q6EޫnC{i T Ph xT 4?y$TJN?1cFdr W slGP%kUnS*(@]QfT Qp.(rD'o;GV-T Px xT |K̦ȣ<~Ε)'}# T P &,(T`QpɇBx$Ӥ-LT P**@ୢl P*@T x?T P*@@ VQ\6MT P*P P*@T x(.T P*@{@T P*PEUMS*@T _o=T P*@*˦T P*@sP*@T TQoeT P*@W[9`T P*@i*@T P+@T P*@UT[Eq4T P*@@ *@T P**@ୢl P*@T x?T P*@@ VQ\6MT P*P P*@T x(.T P*@{@T P*PEUMS*@T _o=T P*@*˦T P*@sP*@T TQoeT P*@W[9`T P*@i*@T P+@T P*@UT[Eq4T P*@@ *@T P**@ୢl P*@T x?T P*@@ VQ\6MT P*P P*@T x(.T P*@ה=6IENDB`././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/0000755000175000017500000000000000000000000020061 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/bodies.rst0000644000175000017500000000014400000000000022057 0ustar00shreyasshreyas00000000000000Bodies module ============= .. automodule:: einsteinpy.bodies :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/constant.rst0000644000175000017500000000015200000000000022442 0ustar00shreyasshreyas00000000000000Constant module =============== .. automodule:: einsteinpy.constant :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/coordinates/0000755000175000017500000000000000000000000022373 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/coordinates/coordinates_index.rst0000644000175000017500000000031600000000000026626 0ustar00shreyasshreyas00000000000000Coordinates module ================== This module contains the classes for various coordinate systems and their position and velocity transformations. .. toctree:: :maxdepth: 2 core velocity ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/coordinates/core.rst0000644000175000017500000000031400000000000024053 0ustar00shreyasshreyas00000000000000core module =========== This module contains the basic classes for coordinate systems and their position transformation: .. automodule:: einsteinpy.coordinates.core :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/coordinates/velocity.rst0000644000175000017500000000034400000000000024764 0ustar00shreyasshreyas00000000000000velocity module =============== This module contains the basic classes for time differentials of coordinate systems and the transformations: .. automodule:: einsteinpy.coordinates.velocity :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/geodesic.rst0000644000175000017500000000015200000000000022373 0ustar00shreyasshreyas00000000000000Geodesic module =============== .. automodule:: einsteinpy.geodesic :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/hypersurface/0000755000175000017500000000000000000000000022561 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/hypersurface/hypersurface_index.rst0000644000175000017500000000027500000000000027206 0ustar00shreyasshreyas00000000000000Hypersurface module =================== This module contains Classes to calculate and plot hypersurfaces of various geometries. .. toctree:: :maxdepth: 2 schwarzschildembedding ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/hypersurface/schwarzschildembedding.rst0000644000175000017500000000041000000000000030015 0ustar00shreyasshreyas00000000000000Schwarzschild Embedding Module ============================== Class for Utility functions for Schwarzschild Embedding surface to implement gravitational lensing: .. automodule:: einsteinpy.hypersurface.schwarzschildembedding :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/index.rst0000644000175000017500000000147300000000000021727 0ustar00shreyasshreyas00000000000000EinsteinPy API ============== Welcome to the API documenatation of EinsteinPy. Please navigate through the given modules to get to know the API of the classes and methods. If you find anything missing, please open an `issue in the repo`_ . .. _`issue in the repo` : https://github.com/einsteinpy/einsteinpy .. graphviz:: digraph { "einsteinpy" -> "integrators", "metric", "utils", "plotting", "constant", "units", "coordinates", "geodesic", "bodies", "hypersurface", "symbolic", "rays" } .. toctree:: :hidden: :maxdepth: 2 integrators/integrators_index metric/metric_index symbolic/symbolic_index hypersurface/hypersurface_index rays/rays_index utils/utils_index plotting/plotting_index coordinates/coordinates_index constant units bodies geodesic ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/integrators/0000755000175000017500000000000000000000000022422 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/integrators/integrators_index.rst0000644000175000017500000000024400000000000026704 0ustar00shreyasshreyas00000000000000Integrators module ================== This module contains the methods of solving Ordinary Differential Equations. .. toctree:: :maxdepth: 2 runge_kutta ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/integrators/runge_kutta.rst0000644000175000017500000000017700000000000025511 0ustar00shreyasshreyas00000000000000Runge Kutta module ================== .. automodule:: einsteinpy.integrators.runge_kutta :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/metric/0000755000175000017500000000000000000000000021344 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/metric/kerr.rst0000644000175000017500000000030300000000000023035 0ustar00shreyasshreyas00000000000000kerr module =========== This module contains the basic class for calculating time-like geodesics in Kerr Space-Time: .. automodule:: einsteinpy.metric.kerr :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/metric/kerrnewman.rst0000644000175000017500000000033600000000000024251 0ustar00shreyasshreyas00000000000000kerr-newman module ================== This module contains the basic class for calculating time-like geodesics in Kerr-Newman Space-Time: .. automodule:: einsteinpy.metric.kerrnewman :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/metric/metric_index.rst0000644000175000017500000000035000000000000024546 0ustar00shreyasshreyas00000000000000Metric module ============= This module contains the basic classes of different metrics for various space-time geometries including schwarzschild, kerr etc. .. toctree:: :maxdepth: 2 schwarzschild kerr kerrnewman ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/metric/schwarzschild.rst0000644000175000017500000000034700000000000024752 0ustar00shreyasshreyas00000000000000schwarzschild module ==================== This module contains the basic class for calculating time-like geodesics in Schwarzschild Space-Time: .. automodule:: einsteinpy.metric.schwarzschild :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1913433 einsteinpy-0.3.0/docs/source/api/plotting/0000755000175000017500000000000000000000000021721 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/plotting/geodesics/0000755000175000017500000000000000000000000023666 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/geodesics/core.rst0000644000175000017500000000031000000000000025342 0ustar00shreyasshreyas00000000000000Core plotting module ==================== This module contains the advanced backend switching while plotting. .. automodule:: einsteinpy.plotting.geodesics.core :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/geodesics/geodesics_index.rst0000644000175000017500000000023700000000000027556 0ustar00shreyasshreyas00000000000000Geodesics Plotting module ========================= This module contains Classes to plot geodesics. .. toctree:: :maxdepth: 2 core interactive ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/geodesics/interactive.rst0000644000175000017500000000031400000000000026733 0ustar00shreyasshreyas00000000000000Interactive plotting module =========================== This module contains interactive plotting backend. .. automodule:: einsteinpy.plotting.geodesics.interactive :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/hypersurface.rst0000644000175000017500000000030700000000000025153 0ustar00shreyasshreyas00000000000000Hypersurface plotting module ============================ This module contains the hypersurface plotting. .. automodule:: einsteinpy.plotting.hypersurface.core :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/plotting_index.rst0000644000175000017500000000040600000000000025502 0ustar00shreyasshreyas00000000000000Plotting module =============== This module contains the basic classes for static and interactive 3-D and 2-D geodesic, hypersurface and shadow plotting modules. .. toctree:: :maxdepth: 2 geodesics/geodesics_index hypersurface rays/rays_index ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/plotting/rays/0000755000175000017500000000000000000000000022677 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/rays/rays_index.rst0000644000175000017500000000025400000000000025577 0ustar00shreyasshreyas00000000000000Rays Plotting module ==================== This module contains classes and sub-modules for light interactions with heavy bodies. .. toctree:: :maxdepth: 2 shadow././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/plotting/rays/shadow.rst0000644000175000017500000000030000000000000024707 0ustar00shreyasshreyas00000000000000Shadow plotting module ====================== This module contains the black hole shadow plotting class. .. automodule:: einsteinpy.plotting.rays.shadow :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/rays/0000755000175000017500000000000000000000000021037 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/rays/rays_index.rst0000644000175000017500000000027000000000000023735 0ustar00shreyasshreyas00000000000000Rays module =========== This module contains Classes to calculate and plot trajectories and other interactions of light with heavy objects. .. toctree:: :maxdepth: 2 shadow ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/rays/shadow.rst0000644000175000017500000000030600000000000023055 0ustar00shreyasshreyas00000000000000Shadow Module ============= Module for calculating Shadow cast by an thin emission disk around schwarzschild spacetime. .. automodule:: einsteinpy.rays.shadow :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/symbolic/0000755000175000017500000000000000000000000021702 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/christoffel.rst0000644000175000017500000000042700000000000024747 0ustar00shreyasshreyas00000000000000Christoffel Symbols Module ========================== This module contains the class for obtaining Christoffel Symbols related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.christoffel :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/constants.rst0000644000175000017500000000035400000000000024452 0ustar00shreyasshreyas00000000000000Symbolic Constants Module ========================= This module contains common constants used in physics/relativity and classes used to define them: .. automodule:: einsteinpy.symbolic.constants :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/einstein.rst0000644000175000017500000000040700000000000024253 0ustar00shreyasshreyas00000000000000Einstein Tensor Module ====================== This module contains the class for obtaining Einstein Tensor related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.einstein :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/helpers.rst0000644000175000017500000000021200000000000024071 0ustar00shreyasshreyas00000000000000Helper Function and Classes =========================== .. automodule:: einsteinpy.symbolic.helpers :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/metric.rst0000644000175000017500000000034500000000000023721 0ustar00shreyasshreyas00000000000000Metric Tensor Module ==================== This module contains the class for defining a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.metric :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/symbolic/predefined/0000755000175000017500000000000000000000000024007 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/predefined/find.rst0000644000175000017500000000023500000000000025461 0ustar00shreyasshreyas00000000000000find ==== This module contains the function find to search for list of possible metrics. .. automodule:: einsteinpy.symbolic.predefined.find :members: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/predefined/full_list.rst0000644000175000017500000000264600000000000026546 0ustar00shreyasshreyas00000000000000All Available Metrics ===================== All the currently available pre-defined metrics are listed here. Minkowski Space-Time -------------------- .. automodule:: einsteinpy.symbolic.predefined.minkowski :members: Vacuum Solutions ---------------- .. automodule:: einsteinpy.symbolic.predefined.vacuum_solutions :members: De Sitter and Anti De Sitter ---------------------------- This module contains pre-defined functions to obtain instances of various forms of Anti-De-Sitter and De-Sitter space-times. .. automodule:: einsteinpy.symbolic.predefined.de_sitter :members: C-Metric -------- .. automodule:: einsteinpy.symbolic.predefined.cmetric :members: Godel ----- .. automodule:: einsteinpy.symbolic.predefined.godel :members: Davidson -------- .. automodule:: einsteinpy.symbolic.predefined.davidson :members: Bessel Gravitational Wave ------------------------- .. automodule:: einsteinpy.symbolic.predefined.bessel_gravitational_wave :members: Barriola Vilekin ---------------- .. automodule:: einsteinpy.symbolic.predefined.barriola_vilenkin :members: Bertotti Kasner --------------- .. automodule:: einsteinpy.symbolic.predefined.bertotti_kasner :members: Ernst ----- .. automodule:: einsteinpy.symbolic.predefined.ernst :members: Janis Newman Winicour --------------------- .. automodule:: einsteinpy.symbolic.predefined.janis_newman_winicour :members:././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/predefined/predefined_index.rst0000644000175000017500000000026200000000000030035 0ustar00shreyasshreyas00000000000000Predefined Metrics ================== This module contains various pre-defined space-time metrics in General Relativity. .. toctree:: :maxdepth: 2 full_list find ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/ricci.rst0000644000175000017500000000040600000000000023525 0ustar00shreyasshreyas00000000000000Ricci Module ============ This module contains the basic classes for obtaining Ricci Tensor and Ricci Scalar related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.ricci :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/riemann.rst0000644000175000017500000000041500000000000024065 0ustar00shreyasshreyas00000000000000Riemann Tensor Module ===================== This module contains the class for obtaining Riemann Curvature Tensor related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.riemann :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/schouten.rst0000644000175000017500000000040100000000000024257 0ustar00shreyasshreyas00000000000000Schouten Module =============== This module contains the basic classes for obtaining Schouten Tensor related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.schouten :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/stress_energy_momentum.rst0000644000175000017500000000047700000000000027261 0ustar00shreyasshreyas00000000000000Stress Energy Momentum Tensor Module ==================================== This module contains the class for obtaining Stress Energy Momentum Tensor related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.stress_energy_momentum :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/symbolic_index.rst0000644000175000017500000000057300000000000025451 0ustar00shreyasshreyas00000000000000Symbolic Relativity Module ========================== This module contains the classes for performing symbolic calculations related to General Relativity. .. toctree:: :maxdepth: 2 predefined/predefined_index helpers constants tensor vector metric christoffel riemann ricci einstein stress_energy_momentum weyl schouten ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/tensor.rst0000644000175000017500000000034000000000000023743 0ustar00shreyasshreyas00000000000000Tensor Module ============= This module contains Tensor class which serves as the base class for more specific Tensors in General Relativity: .. automodule:: einsteinpy.symbolic.tensor :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/vector.rst0000644000175000017500000000032600000000000023737 0ustar00shreyasshreyas00000000000000Vector module ============= This module contains the class GenericVector to represent a vector in arbitrary space-time symbolically .. automodule:: einsteinpy.symbolic.vector :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/symbolic/weyl.rst0000644000175000017500000000036700000000000023422 0ustar00shreyasshreyas00000000000000Weyl Tensor Module ================== This module contains the class for obtaining Weyl Tensor related to a Metric belonging to any arbitrary space-time symbolically: .. automodule:: einsteinpy.symbolic.weyl :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/units.rst0000644000175000017500000000014100000000000021751 0ustar00shreyasshreyas00000000000000Units module ============ .. automodule:: einsteinpy.units :members: :show-inheritance: ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1953435 einsteinpy-0.3.0/docs/source/api/utils/0000755000175000017500000000000000000000000021221 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/utils/kerr_utils.rst0000644000175000017500000000015300000000000024135 0ustar00shreyasshreyas00000000000000Kerr Geometry Utilities ======================= .. automodule:: einsteinpy.utils.kerr_utils :members: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/utils/kerrnewman_utils.rst0000644000175000017500000000017700000000000025351 0ustar00shreyasshreyas00000000000000Kerr-Newman Geometry Utilities ============================== .. automodule:: einsteinpy.utils.kerrnewman_utils :members: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/utils/scalar_factor.rst0000644000175000017500000000013200000000000024552 0ustar00shreyasshreyas00000000000000Scalar Factor ============= .. automodule:: einsteinpy.utils.scalar_factor :members: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/utils/schwarzschild_utils.rst0000644000175000017500000000020600000000000026041 0ustar00shreyasshreyas00000000000000Schwarzschild Geometry Utilities ================================ .. automodule:: einsteinpy.utils.schwarzschild_utils :members: ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/api/utils/utils_index.rst0000644000175000017500000000053700000000000024307 0ustar00shreyasshreyas00000000000000Utils module ============ The common utilities of the project are included in this module. This includes easy methods for calculation of the schwartzschild radius, calculation of the rate of expansion of the universe, velocity of time etc. .. toctree:: :maxdepth: 2 scalar_factor schwarzschild_utils kerr_utils kerrnewman_utils ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588631229.0 einsteinpy-0.3.0/docs/source/changelog.rst0000644000175000017500000001762100000000000022000 0ustar00shreyasshreyas00000000000000What's new ========== einsteinpy 0.3.0 - 2020-05-05 ----------------------------- This major release would bring some very important improvements. This release fixes a very crucial bug with sympy. Fixes coordinate conversions so they don't fail on edge cases anymore. EinsteinPy now uses GitHub Actions for macOS builds. Big changes to the plotting module. The release comes for the paper of EinsteinPy. The release marks the beginning of Google Summer of Code 2020. The release also brings a new rays module, which will form the base for null geodesics in future releases. Features ........ * Loads of Predefined Metrics * Sympy version incompatibilities handled * Numba as a default installation * Lorentz Transform for Einstein Tensor * Lorentz Transform to Tensor Class * Hypersurface Plotting API similar to the common plotting API * Find Function in Predefined Metrics * Increased Code Coverage * New rays module * Plotting Black Hole Shadows * Coordinate Subscripting * Supports Python 3.8, dropping support fpr Python 3.5 * numpy moveaxis replaced with sympy permutedims * name parameter in Metric Tensor * Tags to Tensor names Contributors ............ This is the complete list of the people that contributed to this release, with a + sign indicating first contribution. * Shreyas Bapat * Ritwik Saha * Manvi Gupta * Micky Yun Chan+ * DylanBrdt+ (GitHub Username) * Vineet Gandham+ * Pratyush Kerhalkar+ * Bhavam Vidyarthi+ * Khalid Shaikh+ * Rohit Sanjay+ * Saurabh+ * Raahul Singh+ * Nimesh Vashishtha+ * Shamanth R Nayak K+ * Arnav Das+ * Gim Seng Ng+ * Nihar Gupte+ * Suyash Salampuria+ * Atul Mangat+ * Ganesh Tarone+ * Shreyas Kalvankar+ * Swastik Singh+ * Jyotirmaya Shivottam+ * Sitara Srinivasan+ * Aayush Gautam+ * Zac Yauney+ * Gagan-Shenoy+ * Bibek Gautam+ * Erin Allard+ * Suyog Garg+ einsteinpy 0.2.1 - 2019-11-02 ----------------------------- This minor release would bring improvements and new feature additions to the already existing symbolic calculations module along with performance boosts of order of 15x. This release concludes the SOCIS 2019 projects of Sofía Ortín Vela (ortinvela.sofia@gmail.com) and Varun Singh(varunsinghs2021@gmail.com). Part of this release is sponsored by European Space Agency, through Summer of Code in Space (SOCIS) 2019 program. Features ........ * New tensors in symbolic module * Ricci Scalar * Weyl Tensor * Stress-Energy-Momentum Tensor * Einstein Tensor * Schouten Tensor * Improvement in performance of current tensors * Lambdify option for tensors * Support for vectors at arbitrary space-time symbolically as 1\ :sup:`st` order tensor. * Support for scalars at arbitrary space-time symbolically as 0\ :sup:`th` order tensor. * Addition of constants sub-module to symbolic module * Improvement in speed of Geodesic plotting * Move away from Jupyter and Plotly Widgets * New Plotting Framework Contributors ............ This is the complete list of the people that contributed to this release, with a + sign indicating first contribution. * Shreyas Bapat * Ritwik Saha * Sofía Ortín Vela * Varun Singh * Arnav Das+ * Calvin Jay Ross+ einsteinpy 0.2.0 - 2019-07-15 ----------------------------- This release brings a lot of new features for the EinsteinPy Users. A better API, intuitive structure and easy coordinates handling! This major release comes before Python in Astronomy 2019 workshop and brings a lots of cool stuff. Part of this release is sponsored by ESA/ESTEC – Adv. Concepts & Studies Office (European Space Agency), through Summer of Code in Space (SOCIS) 2019 program. This is a short-term supported version and will be supported only until December 2019. For any feature request, write a mail to developers@einsteinpy.org describing what you need. Features ........ * Kerr Metric * Kerr-Newman Metric * Coordinates Module with Boyer Lindquist Coordinates and transformation * Bodies Module * Defining Geodesics with ease! * Animated plots * Intuitive API for plotting * Schwarzschild Hypersurface Embedding * Interactive Plotting * Environment-aware plotting and exceptional support for iPython Notebooks! * Support for Tensor Algebra in General Relativity * Symbolic Manipulation of Metric Tensor, Riemann Tensor and Ricci Tensor * Support for Index Raising and Lowering in Tensors * Numerical Calculation and Symbolic Manipulation of Christoffel Symbols * Calculations of Event Horizon and Ergosphere of Kerr Black holes! Contributors ............ This is the complete list of the people that contributed to this release, with a + sign indicating first contribution. * Shreyas Bapat * Ritwik Saha * Bhavya Bhatt * Sofía Ortín Vela+ * Raphael Reyna+ * Prithvi Manoj Krishna+ * Manvi Gupta+ * Divya Gupta+ * Yash Sharma+ * Shilpi Jain+ * Rishi Sharma+ * Varun Singh+ * Alpesh Jamgade+ * Saurabh Bansal+ * Tanmay Rustagi+ * Abhijeet Manhas+ * Ankit Khandelwal+ * Tushar Tyagi+ * Hrishikesh Sarode * Naman Tayal+ * Ratin Kumar+ * Govind Dixit+ * Jialin Ma+ Bugs Fixed .......... * `Issue #115`_: Coordinate Conversion had naming issues that made them confusing! * `Issue #185`_: Isort had conflicts with Black * `Issue #210`_: Same notebook had two different listings in Example Gallery * `Issue #264`_: Removing all relative imports * `Issue #265`_: New modules were lacking API Docs * `Issue #266`_: The logo on documentation was not rendering * `Issue #267`_: Docs were not present for Ricci Tensor and Vacuum Metrics * `Issue #277`_: Coordinate Conversion in plotting module was handled incorrectly .. _`Issue #115`: https://github.com/einsteinpy/einsteinpy/issues/115 .. _`Issue #185`: https://github.com/einsteinpy/einsteinpy/issues/185 .. _`Issue #210`: https://github.com/einsteinpy/einsteinpy/issues/210 .. _`Issue #264`: https://github.com/einsteinpy/einsteinpy/issues/264 .. _`Issue #265`: https://github.com/einsteinpy/einsteinpy/issues/265 .. _`Issue #266`: https://github.com/einsteinpy/einsteinpy/issues/266 .. _`Issue #267`: https://github.com/einsteinpy/einsteinpy/issues/267 .. _`Issue #277`: https://github.com/einsteinpy/einsteinpy/issues/277 Backwards incompatible changes .............................. * The old :code:`StaticGeodesicPlotter` has been renamed to :py:class:`einsteinpy.plotting.senile.StaticGeodesicPlotter`, please adjust your imports accordingly * The old :code:`ScatterGeodesicPlotter` has been renamed to :py:class:`einsteinpy.plotting.senile.ScatterGeodesicPlotter`, please adjust your imports accordingly. * :py:class:`einsteinpy.metric.Schwarzschild`, :py:class:`einsteinpy.metric.Kerr`, and :py:class:`einsteinpy.metric.KerrNewman` now have different signatures for class methods, and they now explicitly support :py:mod:`einsteinpy.coordinates` coordinate objects. Check out the notebooks and their respective documentation. * The old `coordinates` conversion in :py:mod:`einsteinpy.utils` has been deprecated. * The old `symbolic` module in :py:mod:`einsteinpy.utils` has been moved to :py:mod:`einsteinpy.symbolic`. einsteinpy 0.1.0 - 2019-03-08 ----------------------------- This is a major first release for world's first actively maintained python library for General Relativity and Numerical methods. This major release just comes before the Annual AstroMeet of IIT Mandi, AstraX. This will be a short term support version and will be supported only until late 2019. Features ........ * Schwarzschild Geometry Analysis and trajectory calculation * Symbolic Calculation of various tensors in GR * Christoffel Symbols * Riemann Curvature Tensor * Static Geodesic Plotting * Velocity of Coordinate time w.r.t proper time * Easy Calculation of Schwarzschild Radius * Coordinate conversion with unit handling * Spherical/Cartesian Coordinates * Boyer-Lindquist/Cartesian Coordinates Contributors ............ This is the complete list of the people that contributed to this release, with a + sign indicating first contribution. * Shreyas Bapat+ * Ritwik Saha+ * Bhavya Bhatt+ * Priyanshu Khandelwal+ * Gaurav Kumar+ * Hrishikesh Sarode+ * Sashank Mishra+ ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/codeofconduct.rst0000644000175000017500000000604300000000000022664 0ustar00shreyasshreyas00000000000000Code of Conduct =============== The community of participants in einsteinpy is made up of members from around the globe with a diverse set of skills, personalities, and experiences. It is through these differences that our community experiences success and continued growth. We expect everyone in our community to follow these guidelines when interacting with others both inside and outside of our community. Our goal is to keep ours a positive, inclusive, successful, and growing community. As members of the community, * We pledge to treat all people with respect and provide a harassment- and bullying-free environment, regardless of sex, sexual orientation and/or gender identity, disability, physical appearance, body size, race, nationality, ethnicity, and religion. In particular, sexual language and imagery, sexist, racist, or otherwise exclusionary jokes are not appropriate. * We pledge to respect the work of others by recognizing acknowledgment/citation requests of original authors. As authors, we pledge to be explicit about how we want our own work to be cited or acknowledged. * We pledge to welcome those interested in joining the community, and realize that including people with a variety of opinions and backgrounds will only serve to enrich our community. In particular, discussions relating to pros/cons of various technologies, programming languages, and so on are welcome, but these should be done with respect, taking proactive measure to ensure that all participants are heard and feel confident that they can freely express their opinions. * We pledge to welcome questions and answer them respectfully, paying particular attention to those new to the community. We pledge to provide respectful criticisms and feedback in forums, especially in discussion threads resulting from code contributions. * We pledge to be conscientious of the perceptions of the wider community and to respond to criticism respectfully. We will strive to model behaviors that encourage productive debate and disagreement, both within our community and where we are criticized. We will treat those outside our community with the same respect as people within our community. * We pledge to help the entire community follow the code of conduct, and to not remain silent when we see violations of the code of conduct. We will take action when members of our community violate this code such as contacting shreyas@einsteinpy.org (all emails sent to this address will be treated with the strictest confidence) or talking privately with the person. This code of conduct applies to all community situations online and offline, including mailing lists, forums, social media, conferences, meetings, associated social events, and one-to-one interactions. Parts of this code of conduct have been adapted from the Astropy code of conduct. The Code of Conduct for the einsteinpy community is licensed under a Creative Commons Attribution 4.0 International License. We encourage other communities related to ours to use or adapt this code as they see fit. ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588631767.0 einsteinpy-0.3.0/docs/source/conf.py0000644000175000017500000000426000000000000020611 0ustar00shreyasshreyas00000000000000from datetime import datetime import alabaster project = "EinsteinPy" year = datetime.now().year copyright = "%d EinsteinPy Development Team" % year version = "0.3" release = "0.3.0" highlight_language = "python" pygments_style = "sphinx" autoclass_content = "both" intersphinx_mapping = { "python": ("https://docs.python.org/3", None), "astropy": ("http://docs.astropy.org/en/stable/", None), "numpy": ("https://docs.scipy.org/doc/numpy/", None), "scipy": ("https://docs.scipy.org/doc/scipy/reference", None), "matplotlib": ("https://matplotlib.org", None), "sympy": ("https://docs.sympy.org/latest", None), } def setup(app): app.add_js_file('https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js') autodoc_member_order = "bysource" html_theme_options = { "logo": "logo_small.png", "logo_name": True, "logo_text_align": "center", "codecov_button": True, "description": "General Relativity in Python", "body_text_align": "left", "github_user": "einsteinpy", "github_repo": "einsteinpy", "show_relbars": True, "show_powered_by": False, "page_width": "80%", "github_banner": True, "donate_url": "https://opencollective.com/einsteinpy", "github_button": True, "extra_nav_links": {"Blog": "https://docs.einsteinpy.org/"}, } add_function_parentheses = True add_module_names = True needs_sphinx = "1.3" extensions = [ "alabaster", "sphinx.ext.autodoc", "sphinx.ext.napoleon", "sphinx.ext.todo", "sphinx.ext.mathjax", "sphinx.ext.intersphinx", "nbsphinx", "IPython.sphinxext.ipython_console_highlighting", "sphinx.ext.mathjax", # New module for matrix visualization "sphinx.ext.graphviz", # For creating the diagrams "sphinx.ext.viewcode", # View Source button ] templates_path = ["_templates"] source_suffix = ".rst" master_doc = "index" html_theme = "alabaster" html_theme_path = [alabaster.get_path()] html_title = "EinsteinPy" html_static_path = ["_static"] htmlhelp_basename = "einsteinpydoc" html_sidebars = { "**": [ "about.html", "navigation.html", "relations.html", "searchbox.html", "donate.html", ] } ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/dev_guide.rst0000644000175000017500000001216700000000000022004 0ustar00shreyasshreyas00000000000000Developer Guide =============== Einsteinpy is a community project, hence all contributions are more than welcome! Bug reporting ------------- Not only things break all the time, but also different people have different use cases for the project. If you find anything that doesn't work as expected or have suggestions, please refer to the `issue tracker`_ on GitHub. .. _`issue tracker`: https://github.com/einsteinpy/einsteinpy/issues Documentation ------------- Documentation can always be improved and made easier to understand for newcomers. The docs are stored in text files under the `docs/source` directory, so if you think anything can be improved there please edit the files and proceed in the same way as with `code writing`_. The Python classes and methods also feature inline docs: if you detect any inconsistency or opportunity for improvement, you can edit those too. Besides, the `wiki`_ is open for everybody to edit, so feel free to add new content. To build the docs, you must first create a development environment (see below) and then in the ``docs/`` directory run: .. code:: bash $ cd docs $ make html After this, the new docs will be inside ``build/html``. You can open them by running an HTTP server: .. code:: bash $ cd build/html $ python -m http.server Serving HTTP on 0.0.0.0 port 8000 ... And point your browser to http://0.0.0.0:8000. Code writing ------------ Code contributions are welcome! If you are looking for a place to start, help us fixing bugs in einsteinpy and check out the `"easy" tag`_. Those should be easier to fix than the others and require less knowledge about the library. .. _`"easy" tag`: https://github.com/einsteinpy/einsteinpy/issues?q=is%3Aissue+is%3Aopen+label%3Aeasy If you are hesitant on what IDE or editor to use, just choose one that you find comfortable and stick to it while you are learning. People have strong opinions on which editor is better so I recommend you to ignore the crowd for the time being - again, choose one that you like :) If you ask me for a recommendation, I would suggest PyCharm (complete IDE, free and gratis, RAM-hungry) or vim (powerful editor, very lightweight, steep learning curve). Other people use Spyder, emacs, gedit, Notepad++, Sublime, Atom... You will also need to understand how git works. git is a decentralized version control system that preserves the history of the software, helps tracking changes and allows for multiple versions of the code to exist at the same time. If you are new to git and version control, I recommend following `the Try Git tutorial`_. .. _`the Try Git tutorial`: https://try.github.io/ If you already know how all this works and would like to contribute new features then that's awesome! Before rushing out though please make sure it is within the scope of the library so you don't waste your time - `email`_ us or `chat`_ with us on Riot!. .. _`email`: all@einsteinpy.org .. _`chat`: https://riot.im/app/#/room/#einsteinpy:matrix.org If the feature you suggest happens to be useful and within scope, you will probably be advised to create a new `wiki`_ page with some information about what problem you are trying to solve, how do you plan to do it and a sketch or idea of how the API is going to look like. You can go there to read other good examples on how to do it. The purpose is to describe without too much code what you are trying to accomplish to justify the effort and to make it understandable to a broader audience. .. _`wiki`: https://github.com/einsteinpy/einsteinpy/wiki All new features should be thoroughly tested, and in the ideal case the coverage rate should increase or stay the same. Automatic services will ensure your code works on all the operative systems and package combinations einsteinpy support - specifically, note that einsteinpy is a Python 3 only library. Development environment ----------------------- These are some succint steps to set up a development environment: 1. `Install git `_ on your computer. 2. `Register to GitHub `_. 3. `Fork einsteinpy `_. 4. `Clone your fork `_. 5. Install it in development mode using :code:`pip install --editable /path/to/einsteinpy/[dev]` (this means that the installed code will change as soon as you change it in the download location). 6. Create a new branch. 7. Make changes and commit. 8. `Push to your fork `_. 9. `Open a pull request! `_ Code Linting ------------ To get the quality checks passed, the code should follow some standards listed below: 1. `Black `_ for code formatting. 2. `isort `_ for imports sorting. 3. `mypy `_ for static type checking. But to avoid confusion, we have setup `tox `_ for doing this in one command and doing it properly! Run: .. code:: bash $ cd einsteinpy/ $ tox -e reformat And it will format all your code! ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.203344 einsteinpy-0.3.0/docs/source/examples/0000755000175000017500000000000000000000000021126 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588627193.0 einsteinpy-0.3.0/docs/source/examples/Analysing Earth using EinsteinPy!.ipynb0000644000175000017500002307417400000000000030403 0ustar00shreyasshreyas00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analysing Earth using EinsteinPy!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the eccentricity and speed at apehelion of Earth's orbit\n", "\n", "Various parameters of Earth's orbit considering Sun as schwarzschild body and solving geodesic equations are calculated\n", "\n", "### 1. Defining the initial parameters" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from astropy import units as u\n", "import numpy as np\n", "from einsteinpy.metric import Schwarzschild\n", "from einsteinpy.coordinates import SphericalDifferential" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Define position and velocity vectors in spherical coordinates\n", "# Earth is at perihelion\n", "M = 1.989e30 * u.kg # mass of sun\n", "distance = 147.09e6 * u.km\n", "speed_at_perihelion = 30.29 * u.km / u.s\n", "omega = (u.rad * speed_at_perihelion) / distance\n", "\n", "sph_obj = SphericalDifferential(distance, np.pi / 2 * u.rad, np.pi * u.rad,\n", " 0 * u.km / u.s, 0 * u.rad / u.s, omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " - Defining $\\lambda$ (or $\\tau$) for which to calculate trajectory\n", " - $\\lambda$ is proper time and is approximately equal to coordinate time in non-relativistic limits" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Set lambda to complete an year.\n", "# Lambda is always specified in secs\n", "end_lambda = ((1 * u.year).to(u.s)).value\n", "# Choosing stepsize for ODE solver to be 5 minutes\n", "stepsize = ((5 * u.min).to(u.s)).value" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Making a class instance to get the trajectory in cartesian coordinates" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "obj = Schwarzschild.from_coords(sph_obj, M)\n", "ans = obj.calculate_trajectory(\n", " end_lambda=end_lambda, OdeMethodKwargs={\"stepsize\": stepsize}, return_cartesian=True\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " - Return value is a tuple consisting of 2 numpy array\n", " - First one contains list of $\\lambda$\n", " - Seconds is array of shape (n,8) where each component is:\n", " - t - coordinate time\n", " - x - position in m\n", " - y - position in m\n", " - z - position in m\n", " - dt/d$\\lambda$\n", " - dx/d$\\lambda$\n", " - dy/d$\\lambda$\n", " - dz/d$\\lambda$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((13150,), (13150, 8))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ans[0].shape, ans[1].shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating distance at aphelion\n", " - Should be 152.10 million km" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$1.5204947 \\times 10^{8} \\; \\mathrm{km}$" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = np.sqrt(np.square(ans[1][:, 1]) + np.square(ans[1][:, 2]))\n", "i = np.argmax(r)\n", "(r[i] * u.m).to(u.km)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Speed at aphelion should be 29.29 km/s and should be along y-axis" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$29.302016 \\; \\mathrm{\\frac{km}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((ans[1][i][6]) * u.m / u.s).to(u.km / u.s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating the eccentricity\n", " - Should be 0.0167" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.016709664332073014" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xlist, ylist = ans[1][:, 1], ans[1][:, 2]\n", "i = np.argmax(ylist)\n", "x, y = xlist[i], ylist[i]\n", "eccentricity = x / (np.sqrt(x ** 2 + y ** 2))\n", "eccentricity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the trajectory with time" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "marker": { "color": "#ffcc00", "size": 0 }, "mode": "markers", "name": "attractor", "type": "scatter", "x": [ 0 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"white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "xaxis": { "constrain": "domain", "title": { "text": "x (m)" } }, "yaxis": { "scaleanchor": "x", "title": { "text": "y (m)" } } } }, "text/html": [ "

\n", " \n", " \n", "
\n", " \n", "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from einsteinpy.bodies import Body\n", "from einsteinpy.geodesic import Geodesic\n", "Sun = Body(name=\"Sun\", mass=M, parent=None)\n", "Object = Body(name=\"Earth\", differential=sph_obj, parent=Sun)\n", "geodesic = Geodesic(body=Object, time=0 * u.s, end_lambda=end_lambda, step_size=stepsize)\n", "from einsteinpy.plotting import GeodesicPlotter\n", "sgp = GeodesicPlotter()\n", "sgp.plot(geodesic)\n", "sgp.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " All data regarding earth's orbit is taken from https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html" ] } ], "metadata": { "file_extension": ".py", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": 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"x", "title": { "text": "y (m)" } } }, "_model_module_version": "0.9.1", "_py2js_animate": {}, "_py2js_deleteTraces": {}, "_py2js_moveTraces": {}, "_py2js_removeLayoutProps": {}, "_py2js_removeTraceProps": {}, "_py2js_restyle": {}, "_view_count": 1, "_view_module_version": "0.9.1" } } }, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 2 } ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/examples/Animations in EinsteinPy.ipynb0000644000175000017500000025100700000000000026737 0ustar00shreyasshreyas00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Animations in EinsteinPy\n", "### Import the required modules" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "\n", "from einsteinpy.plotting import StaticGeodesicPlotter\n", "from einsteinpy.coordinates import SphericalDifferential\n", "from einsteinpy.bodies import Body\n", "from einsteinpy.geodesic import Geodesic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining various parameters\n", " - Mass of the attractor (M)\n", " - Initial position and velocity vectors of test partcle" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "Attractor = Body(name=\"BH\", mass=6e24 * u.kg, parent=None)\n", "sph_obj = SphericalDifferential(130*u.m, np.pi/2*u.rad, -np.pi/8*u.rad,\n", " 0*u.m/u.s, 0*u.rad/u.s, 1900*u.rad/u.s)\n", "Object = Body(differential=sph_obj, parent=Attractor)\n", "geodesic = Geodesic(body=Object, time=0 * u.s, end_lambda=0.002, step_size=5e-8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the animation" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global 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././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/getting_started.rst0000644000175000017500000000624500000000000023240 0ustar00shreyasshreyas00000000000000Getting started =============== Overview -------- EinsteinPy is a easy-to-use python library which provides a user-friendly interface for supporting numerical relativity and relativistic astrophysics research. The library is an attempt to provide programming and numerical environment for a lot of numerical relativity problems like geodesics plotter, gravitational lensing and ray tracing, solving and simulating relativistic hydrodynamical equations, plotting of black hole event horizons, solving Einstein’s field equations and simulating various dynamical systems like binary merger etc. Who can use? ------------ Most of the numerical relativity platforms currently available in the gravitational physics research community demands a heavy programming experience in languages like C, C++ or their wrappers on some other non popular platforms. Many of the people working in the field of gravitational physics have theoretical background and does not have any or have little programming experience and they find using these libraries mind-boggling. EinsteinPy is motivated by this problem and provide a high level of abstraction that shed away from user all the programming and algorithmic view of the implemented numerical methods and enables anyone to simulate complicated system like binary merger with just 20-25 lines of python code. Even people who does not know any python programming can also follow up with the help of tutorials and documentation given for the library. We aim to provide all steps, from setting up your library environment to running your first geodesic plotter with example jupyter notebooks. So now you are motivated enough so let’s first start with installing the library. Installation ------------ It’s as easy as running one command! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Stable Versions: ~~~~~~~~~~~~~~~~ For installation of the latest ``stable`` version of EinsteinPy: - Using pip: .. code-block:: sh $ pip install einsteinpy - Using conda: .. code-block:: sh $ conda install -c conda-forge einsteinpy Latest Versions ~~~~~~~~~~~~~~~ For installing the development version, you can do two things: - Installation from clone: .. code-block:: sh $ git clone https://github.com/einsteinpy/einsteinpy.git $ cd einsteinpy/ $ pip install . - Install using pip: .. code-block:: sh $ pip install git+https://github.com/einsteinpy/einsteinpy.git Development Version ~~~~~~~~~~~~~~~~~~~ .. code-block:: sh $ git clone your_account/einsteinpy.git $ pip install --editable /path/to/einsteinpy[dev] Please open an issue `here`_ if you feel any difficulty in installation! .. _`here` : https://github.com/einsteinpy/einsteinpy/issues Running your first code using the library ----------------------------------------- Various examples can be found in the `examples`_ folder. .. _`examples` : https://einsteinpy-project.readthedocs.io/en/latest/jupyter.html Contribute ---------- EinsteinPy is an open source library which is under heavy development. To contribute kindly do visit : https://github.com/einsteinpy/einsteinpy/ and also check out current posted issues and help us expand this awesome library. ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/index.rst0000644000175000017500000000661100000000000021155 0ustar00shreyasshreyas00000000000000EinsteinPy - Making Einstein possible in Python =============================================== .. image:: https://einsteinpy.org/img/wordmark.png :target: https://einsteinpy.org/ :alt: EinsteinPy logo :width: 675px :align: center **EinsteinPy** is an open source pure Python package dedicated to problems arising in General Relativity and gravitational physics, such as goedesics plotting for Schwarzschild, Kerr and Kerr Newman space-time model, calculation of Schwarzschild radius, calculation of Event Horizon and Ergosphere for Kerr space-time. Symbolic Manipulations of various tensors like Metric, Riemann, Ricci and Christoffel Symbols is also possible using the library. EinsteinPy also features Hypersurface Embedding of Schwarzschild space-time, which will soon lead to modelling of Gravitational Lensing! It is released under the MIT license. View `source code`_ of EinsteinPy! .. _`source code`: https://github.com/einsteinpy/einsteinpy Key features of EinsteinPy are: * Geometry analysis and trajectory calculation in vacuum solutions of Einstein's field equations * Schwarzschild space-time * Kerr space-time * Kerr-Newman space-time * Various utilities related to above geometry models * Schwarzschild Radius * Event horizon and ergosphere for Kerr black hole * Maxwell Tensor and electromagnetic potential in Kerr-Newman space-time * And much more! * Symbolic Calculation of various quantities * Christoffel Symbols * Riemann Curvature Tensor * Ricci Tensor * Index uppering and lowering! * Simplification of symbolic expressions * Geodesic Plotting * Static Plotting using Matplotlib * Interactive 2D plotting * Environment aware plotting! * Coordinate conversion with unit handling * Spherical/Cartesian Coordinates * Boyer-Lindquist/Cartesian Coordinates * Hypersurface Embedding of Schwarzschild Space-Time * Shadow cast by an thin emission disk around a Schwarzschild Black Hole And more to come! Einsteinpy is developed by an open community. Release announcements and general discussion take place on our `mailing list`_ and `chat`_. .. _`mailing list`: https://groups.io/g/einsteinpy-dev .. _`chat`: https://riot.im/app/#/room/#einsteinpy:matrix.org .. include:: form.rst The `source code`_, `issue tracker`_ and `wiki`_ are hosted on GitHub, and all contributions and feedback are more than welcome. You can test EinsteinPy in your browser using binder, a cloud Jupyter notebook server: .. image:: https://img.shields.io/badge/launch-binder-e66581.svg?style=flat-square :target: https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/master?filepath=index.ipynb .. _`source code`: https://github.com/einsteinpy/einsteinpy .. _`issue tracker`: https://github.com/einsteinpy/einsteinpy/issues .. _`wiki`: https://github.com/einsteinpy/einsteinpy/wiki/ EinsteinPy works on recent versions of Python and is released under the MIT license, hence allowing commercial use of the library. .. code-block:: python from einsteinpy.plotting import GeodesicPlotter from einsteinpy.examples import perihelion a = GeodesicPlotter() a.plot(perihelion()) a.show() .. figure:: _static/perihelion.png :align: center :figwidth: 650px :alt: Advancement of perihelion in Schwarzschild space-time Contents -------- .. toctree:: :maxdepth: 2 getting_started user_guide metric jupyter changelog dev_guide api/index codeofconduct ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/jupyter.rst0000644000175000017500000000250200000000000021543 0ustar00shreyasshreyas00000000000000Jupyter notebooks ================= .. toctree:: :maxdepth: 1 :caption: hypersurface /examples/Plotting spacial hypersurface embedding for schwarzschild spacetime.ipynb .. toctree:: :maxdepth: 1 :caption: rays /examples/Shadow cast by an thin emission disk around a black hole.ipynb .. toctree:: :maxdepth: 1 :caption: utils /examples/Visualizing event horizon and ergosphere of Kerr black hole.ipynb .. toctree:: :maxdepth: 1 :caption: metric, bodies, geodesic, coordinates /examples/Visualizing frame dragging in Kerr spacetime.ipynb /examples/Analysing Earth using EinsteinPy!.ipynb /examples/Animations in EinsteinPy.ipynb /examples/Visualizing advance of perihelion of a test particle in Schwarzschild space-time.ipynb .. toctree:: :maxdepth: 1 :caption: symbolic /examples/Einstein Tensor symbolic calculation.ipynb /examples/Lambdify symbolic calculation.ipynb /examples/Playing with Contravariant and Covariant Indices in Tensors(Symbolic).ipynb /examples/Predefined Metrics in Symbolic Module.ipynb /examples/Ricci Tensor and Scalar Curvature symbolic calculation.ipynb /examples/Symbolically Understanding Christoffel Symbol and Riemann Curvature Tensor using EinsteinPy.ipynb /examples/Weyl Tensor symbolic calculation.ipynb ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/metric.rst0000644000175000017500000001215500000000000021331 0ustar00shreyasshreyas00000000000000Vacuum Solutions to Einstein's Field Equations ============================================== Einstein's Equation ------------------- Einstein's Field Equation(EFE) is a ten component tensor equation which relates local space-time curvature with local energy and momentum. In short, they determine the metric tensor of a spacetime given arrangement of stress-energy in space-time. The EFE is given by .. image:: ./_static/metric/EFE.PNG :align: center Here, :math:`R_{\mu\nu}` is the Ricci Tensor, :math:`R` is the curvature scalar(contraction of Ricci Tensor), :math:`g_{\mu\nu}` is the metric tensor, :math:`\Lambda` is the cosmological constant and lastly, :math:`T_{\mu\nu}` is the stress-energy tensor. All the other variables hold their usual meaning. Metric Tensor ------------- The metric tensor gives us the differential length element for each durection of space. Small distance in a N-dimensional space is given by : * :math:`ds^2 = g_{ij}dx_{i}dx_{j}` The tensor is constructed when each :math:`g_{ij}` is put in it's position in a rank-2 tensor. For example, metric tensor in a spherical coordinate system is given by: * :math:`g_{00} = 1` * :math:`g_{11} = r^2` * :math:`g_{22} = r^2sin^2\theta` * :math:`g_{ij} = 0` when :math:`i{\neq}j` We can see the off-diagonal component of the metric to be equal to `0` as it is an orthogonal coordinate system, i.e. all the axis are perpendicular to each other. However it is not always the case. For example, a euclidean space defined by vectors `i`, `j` and `j+k` is a flat space but the metric tensor would surely contain off-diagonal components. Notion of Curved Space ---------------------- Imagine a bug travelling across a 2-D paper folded into a cone. The bug can't see up and down, so he lives in a 2d world, but still he can experience the curvature, as after a long journey, he would come back at the position where he started. For him space is not infinite. Mathematically, curvature of a space is given by Riemann Curvature Tensor, whose contraction is Ricii Tensor, and taking its trace yields a scalar called Ricci Scalar or Curvature Scalar. Straight lines in Curved Space ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Imagine driving a car on a hilly terrain keeping the steering absolutely straight. The trajectory followed by the car, gives us the notion of geodesics. Geodesics are like straight lines in higher dimensional(maybe curved) space. Mathematically, geodesics are calculated by solving set of differential equation for each space(time) component using the equation: * :math:`\ddot{x}_i+0.5*g^{im}*(\partial_{l}g_{mk}+\partial_{k}g_{ml}-\partial_{m}g_{kl})\dot{x}_k\dot{x}_l = 0` which can be re-written as * :math:`\ddot{x}_i+\Gamma_{kl}^i \dot{x}_k\dot{x}_l = 0` where :math:`\Gamma` is Christoffel symbol of the second kind. Christoffel symbols can be encapsulated in a rank-3 tensor which is symmetric over it's lower indices. Coming back to Riemann Curvature Tensor, which is derived from Christoffel symbols using the equation * :math:`R_{abc}^i=\partial_b\Gamma_{ca}^i-\partial_c\Gamma_{ba}^i+\Gamma_{bm}^i\Gamma_{ca}^m-\Gamma_{cm}^i\Gamma_{ba}^m` Of course, Einstein's indicial notation applies everywhere. Contraction of Riemann Tensor gives us Ricci Tensor, on which taking trace gives Ricci or Curvature scalar. A space with no curvature has Riemann Tensor as zero. Exact Solutions of EFE ---------------------- Schwarzschild Metric ^^^^^^^^^^^^^^^^^^^^ It is the first exact solution of EFE given by Karl Schwarzschild, for a limited case of single spherical non-rotating mass. The metric is given as: * :math:`d\tau^2 = -(1-r_s/r)dt^2+(1-r_s/r)^{-1}dr^2+r^2d\theta^2/c^2+r^2sin^2\theta d\phi^2/c^2` where :math:`r_s=2*G*M/c^2` and is called the Schwarzschild Radius, a point beyond where space and time flips and any object inside the radius would require speed greater than speed of light to escape singularity, where the curvature of space becomes infinite and so is the case with the tidal forces. Putting :math:`r=\infty`, we see that the metric transforms to a metric for a flat space defined by spherical coordinates. :math:`\tau` is the proper time, the time experienced by the particle in motion in the space-time while :math:`t` is the coordinate time observed by an observer at infinity. Using the metric in the above discussed geodesic equation gives the four-position and four-velocity of a particle for a given range of :math:`\tau`. The differential equations can be solved by supplying the initial positions and velocities. Kerr Metric and Kerr-Newman Metric ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Kerr-Newman metric is also an exact solution of EFE. It deals with spinning, charged massive body as the solution has axial symettry. A quick search on google would give the exact metric as it is quite exhaustive. Kerr-Newman metric is the most general vacuum solution consisting of a single body at the center. Kerr metric is a specific case of Kerr-Newman where charge on the body :math:`Q=0`. Schwarzschild metric can be derived from Kerr-Newman solution by putting charge and spin as zero :math:`Q=0`, :math:`a=0`. ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/docs/source/user_guide.rst0000644000175000017500000002015600000000000022201 0ustar00shreyasshreyas00000000000000User guide ########## Defining the geometry: :py:class:`~einsteinpy.metric` objects ************************************************************* EinsteinPy provides a way to define the background geometry on which the code would deal with the dynamics. These geometry has a central operating quantity known as metric tensor and encapsulate all the geometrical and topological information about the 4d spacetime in them. * The central quantity required to simulate trajectory of a particle in a gravitational field is christoffel symbols. * EinsteinPy provides an easy to use interface to calculate these symbols. Schwarzschild metric ==================== EinsteinPy provides an easy interface for calculating time-like geodesics in Schwarzschild Geometry. First of all, we import all the relevant modules and classes : .. code-block:: python import numpy as np from astropy import units as u from einsteinpy.coordinates import SphericalDifferential, CartesianDifferential from einsteinpy.metric import Schwarzschild From position and velocity in Spherical Coordinates --------------------------------------------------- There are several methods available to create :py:class:`~einsteinpy.metric.schwarzschild.Schwarzschild` objects. For example, if we have the position and velocity vectors we can use :py:meth:`~einsteinpy.metric.schwarzschild.Schwarzschild.from_spherical`: .. code-block:: python M = 5.972e24 * u.kg sph_coord = SphericalDifferential(306.0 * u.m, np.pi/2 * u.rad, -np.pi/6*u.rad, 0*u.m/u.s, 0*u.rad/u.s, 1900*u.rad/u.s) obj = Schwarzschild.from_coords(sph_coord, M , 0* u.s) From position and velocity in Cartesian Coordinates --------------------------------------------------- For initializing with Cartesian Coordinates, we can use :py:class:`~einsteinpy.metric.schwarzschild.Schwarzschild.from_cartesian`: .. code-block:: python cartsn_coord = CartesianDifferential(.265003774 * u.km, -153.000000e-03 * u.km, 0 * u.km, 145.45557 * u.km/u.s, 251.93643748389 * u.km/u.s, 0 * u.km/u.s) obj = Schwarzschild.from_coords(cartsn_coord, M , 0* u.s) Calculating Trajectory/Time-like Geodesics ------------------------------------------ After creating the object we can call :py:class:`~einsteinpy.metric.schwarzschild.Schwarzschild.calculate_trajectory` .. code-block:: python end_tau = 0.01 # approximately equal to coordinate time stepsize = 0.3e-6 ans = obj.calculate_trajectory(end_lambda=end_tau, OdeMethodKwargs={"stepsize":stepsize}) print(ans) .. code-block:: python (array([0.00000000e+00, 2.40000000e-07, 2.64000000e-06, ..., 9.99367909e-03, 9.99607909e-03, 9.99847909e-03]), array([[ 0.00000000e+00, 3.06000000e+02, 1.57079633e+00, ..., 0.00000000e+00, 0.00000000e+00, 9.50690000e+02], [ 2.39996635e-07, 3.05999885e+02, 1.57079633e+00, ..., -9.55164950e+02, 1.32822112e-17, 9.50690712e+02], [ 2.63996298e-06, 3.05986131e+02, 1.57079633e+00, ..., -1.05071184e+04, 1.46121838e-16, 9.50776184e+02], ..., [ 9.99381048e-03, 3.05156192e+02, 1.57079633e+00, ..., 8.30642520e+04, -1.99760372e-12, 9.55955926e+02], [ 9.99621044e-03, 3.05344028e+02, 1.57079633e+00, ..., 7.34673728e+04, -2.01494258e-12, 9.54780155e+02], [ 9.99861041e-03, 3.05508844e+02, 1.57079633e+00, ..., 6.38811856e+04, -2.03252073e-12, 9.53750261e+02]])) Return value can be obtained in Cartesian Coordinates by : .. code-block:: python ans = obj.calculate_trajectory(end_lambda=end_tau, OdeMethodKwargs={"stepsize":stepsize}, return_cartesian=True) Bodies Module: :py:class:`~einsteinpy.bodies` ********************************************* EinsteinPy has a module to define the attractor and revolving bodies, using which plotting and geodesic calculation becomes much easier. Importing all the relevant modules and classes : .. code-block:: python import numpy as np from astropy import units as u from einsteinpy.coordinates import BoyerLindquistDifferential from einsteinpy.metric import Kerr from einsteinpy.bodies import Body from einsteinpy.geodesic import Geodesic Defining various astronomical bodies : .. code-block:: python spin_factor = 0.3 * u.m Attractor = Body(name="BH", mass = 1.989e30 * u.kg, a = spin_factor) BL_obj = BoyerLindquistDifferential(50e5 * u.km, np.pi / 2 * u.rad, np.pi * u.rad, 0 * u.km / u.s, 0 * u.rad / u.s, 0 * u.rad / u.s, spin_factor) Particle = Body(differential = BL_obj, parent = Attractor) geodesic = Geodesic(body = Particle, end_lambda = ((1 * u.year).to(u.s)).value / 930, step_size = ((0.02 * u.min).to(u.s)).value, metric=Kerr) geodesic.trajectory # get the values of the trajectory Plotting the trajectory : .. code-block:: python from einsteinpy.plotting import GeodesicPlotter obj = GeodesicPlotter() obj.plot(geodesic) obj.show() Utilities: :py:class:`~einsteinpy.utils` **************************************** EinsteinPy provides a great set of utility functions which are frequently used in general and numerical relativity. * Conversion of Coordinates (both position & velocity) * Cartesian/Spherical * Cartesian/Boyer-Lindquist * Calculation of Schwarzschild Geometry related quantities * Schwarzschild Radius * Rate of change of coordinate time w.r.t. proper time Coordinate Conversion ===================== In a short example, we would see coordinate conversion between Cartesian and Boyer-Lindquist Coordinates. Using the functions: * :py:class:`~einsteinpy.coordinates.BoyerLindquistDifferential.to_cartesian` * :py:class:`~einsteinpy.coordinates.CartesianDifferential.to_bl` .. code-block:: python import numpy as np from astropy import units as u from einsteinpy.coordinates import BoyerLindquistDifferential, CartesianDifferential, Cartesian, BoyerLindquist a = 0.5 * u.km pos_vec = Cartesian(.265003774 * u.km, -153.000000e-03 * u.km, 0 * u.km) bl_pos = pos_vec.to_bl(a) print(bl_pos) cartsn_pos = bl_pos.to_cartesian(a) print(cartsn_pos) pos_vel_coord = CartesianDifferential(.265003774 * u.km, -153.000000e-03 * u.km, 0 * u.km, 145.45557 * u.km/u.s, 251.93643748389 * u.km/u.s, 0 * u.km/u.s) bl_coord = pos_vel_coord.bl_differential(a) bl_coord = bl_coord.si_values() bl_vel = bl_coord[3:] print(bl_vel) cartsn_coord = bl_coord.cartesian_differential(a) cartsn_coord = cartsn_coord.si_values() cartsn_vel = cartsn_coord[3:] print(cartsn_vel) .. code-block:: python [ 200. -100. 20.5] [224.54398697 1.47937288 -0.46364761] Symbolic Calculations ===================== EinsteinPy also supports symbolic calculations in :py:class:`~einsteinpy.symbolic` .. code-block:: python import sympy from einsteinpy.symbolic import SchwarzschildMetric, ChristoffelSymbols m = SchwarzschildMetric() ch = ChristoffelSymbols.from_metric(m) print(ch[1,2,:]) .. code-block:: python [0, 0, -r*(-a/r + 1), 0] .. code-block:: python import sympy from einsteinpy.symbolic import SchwarzschildMetric, EinsteinTensor m = SchwarzschildMetric() G1 = EinsteinTensor.from_metric(m) print(G1.arr) .. code-block:: python [[a*c**2*(-a + r)/r**4 + a*c**2*(a - r)/r**4, 0, 0, 0], [0, a/(r**2*(a - r)) + a/(r**2*(-a + r)), 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]] Future Plans ============ * Support for null-geodesics in different geometries * Ultimate goal is providing numerical solutions for Einstein's equations for arbitrarily complex matter distribution. * Relativistic hydrodynamics ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/pyproject.toml0000644000175000017500000000011200000000000017766 0ustar00shreyasshreyas00000000000000[build-system] requires = [ "setuptools", "wheel", "numpy", ] ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.219345 einsteinpy-0.3.0/setup.cfg0000644000175000017500000000334600000000000016707 0ustar00shreyasshreyas00000000000000[metadata] name = einsteinpy version = 0.3.0 author = Shreyas Bapat author_email = bapat.shreyas@gmail.com license = MIT description = Python package for General Relativity keywords = general relativity geodesics relativity kerr black-hole kerr-newman schwarzschild url = https://einsteinpy.org/ download_url = https://github.com/einsteinpy/einsteinpy long_description = file: README.rst classifiers = Development Status :: 4 - Beta Intended Audience :: Education Intended Audience :: Science/Research License :: OSI Approved :: MIT License Operating System :: OS Independent Programming Language :: Python Programming Language :: Python :: 3 Programming Language :: Python :: 3.6 Programming Language :: Python :: 3.7 Programming Language :: Python :: 3.8 Topic :: Scientific/Engineering Topic :: Scientific/Engineering :: Physics Topic :: Scientific/Engineering :: Astronomy [options] package_dir = = src packages = find: zip_safe = False install_requires = numpy astropy matplotlib scipy>=1.0 plotly>=4.0 sympy>=1.1 numba >=0.46,!=0.49.0 ; implementation_name=='cpython' include_package_data = True python_requires = >=3.5 [options.packages.find] where = src [options.extras_require] dev = black ; python_version>="3.6" coverage isort pytest pytest-xdist pytest-cov<2.6.0 pycodestyle sphinx alabaster nbsphinx ipython>=5.0 jupyter-client ipykernel ipywidgets tox jupyter_sphinx [tool:pytest] norecursedirs = .git dist build python_files = test_*.py doctest_plus = disabled addopts = --strict markers = slow remote_data filterwarnings mpl_image_compare [flake8] ignore = E203, E266, E501, W503 max-line-length = 80 max-complexity = 18 select = B,C,E,F,W,T4,B9 [egg_info] tag_build = tag_date = 0 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/setup.py0000644000175000017500000000031100000000000016565 0ustar00shreyasshreyas00000000000000#!/usr/bin/env python from setuptools import setup # https://packaging.python.org/guides/single-sourcing-package-version/ # http://blog.ionelmc.ro/2014/05/25/python-packaging/ setup(setup_cfg=True) ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.1873431 einsteinpy-0.3.0/src/0000755000175000017500000000000000000000000015647 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/0000755000175000017500000000000000000000000020036 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588631731.0 einsteinpy-0.3.0/src/einsteinpy/__init__.py0000644000175000017500000000014000000000000022142 0ustar00shreyasshreyas00000000000000""" ========== einsteinpy ========== Python for General Relativity """ __version__ = "0.3.0" ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/bodies.py0000644000175000017500000001277200000000000021666 0ustar00shreyasshreyas00000000000000"""Important Bodies. Contains some predefined bodies of the Solar System: * Sun (☉) * Earth (♁) * Moon (☾) * Mercury (☿) * Venus (♀) * Mars (♂) * Jupiter (♃) * Saturn (♄) * Uranus (⛢) * Neptune (♆) * Pluto (♇) and a way to define new bodies (:py:class:`~Body` class). Data references can be found in :py:mod:`~einsteinpy.constant` """ import astropy.units as u from einsteinpy import constant from einsteinpy.coordinates import CartesianDifferential class Body: """ Class to create a generic Body """ @u.quantity_input(mass=u.kg, R=u.km) def __init__( self, name="Generic Body", mass=0 * u.kg, R=0 * u.km, differential=None, a=0 * u.m, q=0 * u.C, parent=None, ): """ Parameters ---------- name : str Name/ID of the body mass : ~astropy.units.kg Mass of the body R : ~astropy.units Radius of the body differential : ~einsteinpy.coordinates, optional Complete coordinates of the body a : ~astropy.units.m, optional Spin factor of massive body. Should be less than half of schwarzschild radius. q : ~astropy.units.C, optional Charge on the massive body is_attractor : Bool, optional To denote is this body is acting as attractor or not parent : Body, optional The parent object of the body. """ if differential: if differential.system == "Cartesian": self.pos_vec = [differential.x, differential.y, differential.z] self.vel_vec = [differential.v_x, differential.v_y, differential.v_z] else: self.pos_vec = [differential.r, differential.theta, differential.phi] self.vel_vec = [differential.v_r, differential.v_t, differential.v_p] self.a = a self.R = R self.q = q self.mass = mass self.name = name self.coordinates = differential self.parent = parent def __repr__(self): return ( "'Body ( name: ({0}), mass: ({1}), radius: ({2}), coordinates: ({3}), spin factor: ({4}), charge: ({" "5}) )'".format( self.name, self.mass, self.R, self.coordinates, self.a, self.q ) ) def __str__(self): return ( "Body ( name: ({0}), mass: ({1}), radius: ({2}), coordinates: ({3}), spin factor: ({4}), charge: ({" "5}) )".format( self.name, self.mass, self.R, self.coordinates, self.a, self.q ) ) class _Sun(Body): def __init__(self): parent = None name = "Sun" R = constant.R_sun mass = constant.Solar_Mass super(_Sun, self).__init__(name=name, mass=mass, R=R, parent=parent) Sun = _Sun() class _Earth(Body): def __init__(self): parent = Sun name = "Earth" R = 6731 * u.km mass = 5.97219e24 * u.kg super(_Earth, self).__init__(name=name, mass=mass, R=R, parent=parent) Earth = _Earth() class _Moon(Body): def __init__(self): parent = Earth name = "Moon" R = 1737.5 * u.km mass = 7.34767309e22 * u.kg super(_Moon, self).__init__(name=name, mass=mass, R=R, parent=parent) Moon = _Moon() class _Mercury(Body): def __init__(self): parent = Sun name = "Mercury" R = 2439.7 * u.km mass = 3.285e23 * u.kg super(_Mercury, self).__init__(name=name, mass=mass, R=R, parent=parent) Mercury = _Mercury() class _Venus(Body): def __init__(self): parent = Sun name = "Venus" R = 6051.8 * u.km mass = 4.867e24 * u.kg super(_Venus, self).__init__(name=name, mass=mass, R=R, parent=parent) Venus = _Venus() class _Mars(Body): def __init__(self): parent = Sun name = "Mars" R = 3389.5 * u.km mass = 6.39e23 * u.kg super(_Mars, self).__init__(name=name, mass=mass, R=R, parent=parent) Mars = _Mars() class _Jupiter(Body): def __init__(self): parent = Sun name = "Jupiter" R = 69911 * u.km mass = 1.89813e27 * u.kg super(_Jupiter, self).__init__(name=name, mass=mass, R=R, parent=parent) Jupiter = _Jupiter() class _Saturn(Body): def __init__(self): parent = Sun name = "Saturn" R = 58232 * u.km mass = 5.683e26 * u.kg super(_Saturn, self).__init__(name=name, mass=mass, R=R, parent=parent) Saturn = _Saturn() class _Uranus(Body): def __init__(self): parent = Sun name = "Uranus" R = 25362 * u.km mass = 8.681e25 * u.kg super(_Uranus, self).__init__(name=name, mass=mass, R=R, parent=parent) Uranus = _Uranus() class _Neptune(Body): def __init__(self): parent = Sun name = "Neptune" R = 24622 * u.km mass = 1.024e26 * u.kg super(_Neptune, self).__init__(name=name, mass=mass, R=R, parent=parent) Neptune = _Neptune() class _Pluto(Body): def __init__(self): parent = Sun name = "Pluto" R = 1183.3 * u.km mass = 1.309e22 * u.kg super(_Pluto, self).__init__(name=name, mass=mass, R=R, parent=parent) Pluto = _Pluto() ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/constant.py0000644000175000017500000000067100000000000022245 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from astropy import constants c = constants.c G = constants.G eps0 = constants.eps0 coulombs_const = 1 / (4 * np.pi * eps0) Cosmo_Const_base = constants.Constant( "lambda", "Cosmological Constant", 2.036e-35, "1 / s2", 0.000081e-35, "Wikipedia", system="si", ) Cosmo_Const = Cosmo_Const_base.value * (u.s ** -2) Solar_Mass = 1.9891e30 * u.kg R_sun = 695510 * u.km ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/coordinates/0000755000175000017500000000000000000000000022350 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/coordinates/__init__.py0000644000175000017500000000042300000000000024460 0ustar00shreyasshreyas00000000000000from .conversion import ( BoyerLindquistConversion, CartesianConversion, SphericalConversion, ) from .core import BoyerLindquist, Cartesian, Spherical from .velocity import ( BoyerLindquistDifferential, CartesianDifferential, SphericalDifferential, ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/coordinates/conversion.py0000644000175000017500000000662200000000000025115 0ustar00shreyasshreyas00000000000000import numpy as np from einsteinpy.coordinates.utils import ( bl_to_cartesian_fast, cartesian_to_bl_fast, cartesian_to_spherical_fast, spherical_to_cartesian_fast, ) class CartesianConversion: def __init__(self, x, y, z, v_x=None, v_y=None, v_z=None): self.x_si = x self.y_si = y self.z_si = z self.vx_si = v_x self.vy_si = v_y self.vz_si = v_z self._velocities_provided = not ( (v_x is None) or (v_y is None) or (v_z is None) ) def values(self): if self._velocities_provided: return self.x_si, self.y_si, self.z_si, self.vx_si, self.vy_si, self.vz_si return self.x_si, self.y_si, self.z_si def convert_spherical(self): return cartesian_to_spherical_fast( self.x_si, self.y_si, self.z_si, self.vx_si, self.vy_si, self.vz_si, self._velocities_provided, ) def convert_bl(self, a): return cartesian_to_bl_fast( self.x_si, self.y_si, self.z_si, a, self.vx_si, self.vy_si, self.vz_si, self._velocities_provided, ) class SphericalConversion: def __init__(self, r, theta, phi, v_r=None, v_t=None, v_p=None): self.r_si = r self.t_si = theta self.p_si = phi self.vr_si = v_r self.vt_si = v_t self.vp_si = v_p self._velocities_provided = not ( (v_r is None) or (v_t is None) or (v_p is None) ) def values(self): if self._velocities_provided: return self.r_si, self.t_si, self.p_si, self.vr_si, self.vt_si, self.vp_si return self.r_si, self.t_si, self.p_si def convert_cartesian(self): return spherical_to_cartesian_fast( self.r_si, self.t_si, self.p_si, self.vr_si, self.vt_si, self.vp_si, self._velocities_provided, ) def convert_bl(self, a): transformed_cartesian = self.convert_cartesian() cart = CartesianConversion(*transformed_cartesian) return cart.convert_bl(a) class BoyerLindquistConversion: def __init__(self, r, theta, phi, v_r=None, v_t=None, v_p=None, a=0.0): self.r_si = r self.t_si = theta self.p_si = phi self.vr_si = v_r self.vt_si = v_t self.vp_si = v_p self.a_si = a self._velocities_provided = not ( (v_r is None) or (v_t is None) or (v_p is None) ) def values(self): if self._velocities_provided: return ( self.r_si, self.t_si, self.p_si, self.vr_si, self.vt_si, self.vp_si, self.a_si, ) return self.r_si, self.t_si, self.p_si, self.a_si def convert_cartesian(self): return bl_to_cartesian_fast( self.r_si, self.t_si, self.p_si, self.a_si, self.vr_si, self.vt_si, self.vp_si, self._velocities_provided, ) def convert_spherical(self): transformed_cartesian = self.convert_cartesian() cart = CartesianConversion(*transformed_cartesian) return cart.convert_spherical() ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/coordinates/core.py0000644000175000017500000002213400000000000023654 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy.coordinates.conversion import ( BoyerLindquistConversion, CartesianConversion, SphericalConversion, ) class Cartesian(CartesianConversion): """ Class for Cartesian Coordinates and related transformations. """ @u.quantity_input(x=u.km, y=u.km, z=u.km) def __init__(self, x, y, z): """ Constructor. Parameters ---------- x : ~astropy.units.quantity.Quantity y : ~astropy.units.quantity.Quantity z : ~astropy.units.quantity.Qauntity """ self.x = x self.y = y self.z = z super().__init__(x.si.value, y.si.value, z.si.value) self.system = "Cartesian" self._dimension = {"x": self.x, "y": self.y, "z": self.z, "system": self.system} self._dimension_order = ("x", "y", "z") def __repr__(self): return "Cartesian x: {}, y: {}, z: {}".format(self.x, self.y, self.z) def __str__(self): return self.__repr__() def __getitem__(self, item): """ Method to return coordinates. Objects are subsctiptable with both explicit names of parameters and integer indices. Parameters ---------- item : str or int Name of the parameter or its index. If ``'system'``, Name of coordinate is returned. """ if isinstance(item, (int, np.integer)): return self._dimension[self._dimension_order[item]] return self._dimension[item] def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, m, m) """ element_list = [self.x.to(u.m), self.y.to(u.m), self.z.to(u.m)] return np.array([e.value for e in element_list], dtype=float) def norm(self): """ Function for finding euclidean norm of a vector. Returns ------- ~astropy.units.quantity.Quantity Euclidean norm with units. """ return np.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2) def dot(self, target): """ Dot product of two vectors. Parameters ---------- target: ~einsteipy.coordinates.core.Cartesian Returns ------- ~astropy.units.quantity.Quantity Dot product with units """ x = self.x * target.x y = self.y * target.y z = self.z * target.z return x + y + z def to_spherical(self): """ Method for conversion to spherical coordinates. Returns ------- ~einsteinpy.coordinates.core.Spherical Spherical representation of the Cartesian Coordinates. """ r, theta, phi = self.convert_spherical() return Spherical(r * u.m, theta * u.rad, phi * u.rad) @u.quantity_input(a=u.km) def to_bl(self, a): """ Method for conversion to boyer-lindquist coordinates. Parameters ---------- a : ~astropy.units.quantity.Quantity a = J/Mc , the angular momentum per unit mass of the black hole per speed of light. Returns ------- ~einsteinpy.coordinates.core.BoyerLindquist BL representation of the Cartesian Coordinates. """ r, theta, phi, a = self.convert_bl(a.si.value) return BoyerLindquist(r * u.m, theta * u.rad, phi * u.rad, a * u.m) class Spherical(SphericalConversion): """ Class for Spherical Coordinates and related transformations. """ @u.quantity_input(r=u.km, theta=u.rad, phi=u.rad) def __init__(self, r, theta, phi): """ Constructor. Parameters ---------- r : ~astropy.units.quantity.Quantity theta : ~astropy.units.quantity.Quantity phi : ~astropy.units.quantity.Quantity """ self.r = r self.theta = theta self.phi = phi super().__init__(r.si.value, theta.si.value, phi.si.value) self.system = "Spherical" self._dimension = { "r": self.r, "theta": self.theta, "phi": self.phi, "system": self.system, } self._dimension_order = ("r", "theta", "phi") def __repr__(self): return "Spherical r: {}, theta: {}, phi: {}".format( self.r, self.theta, self.phi ) def __str__(self): return self.__repr__() def __getitem__(self, item): """ Method to return coordinates. Objects are subsctiptable with both explicit names of parameters and integer indices. Parameters ---------- item : str or int Name of the parameter or its index. If ``'system'``, Name of coordinate is returned. """ if isinstance(item, (int, np.integer)): return self._dimension[self._dimension_order[item]] return self._dimension[item] def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, rad, rad) """ element_list = [self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad)] return np.array([e.value for e in element_list], dtype=float) def to_cartesian(self): """ Method for conversion to cartesian coordinates. Returns ------- ~einsteinpy.coordinates.core.Cartesian Cartesian representation of the Spherical Coordinates. """ x, y, z = self.convert_cartesian() return Cartesian(x * u.m, y * u.m, z * u.m) @u.quantity_input(a=u.km) def to_bl(self, a): """ Method for conversion to boyer-lindquist coordinates. Parameters ---------- a : ~astropy.units.quantity.Quantity a = J/Mc , the angular momentum per unit mass of the black hole per speed of light. Returns ------- ~einsteinpy.coordinates.core.BoyerLindquist BL representation of the Spherical Coordinates. """ r, theta, phi, a = self.convert_bl(a.si.value) return BoyerLindquist(r * u.m, theta * u.rad, phi * u.rad, a * u.m) class BoyerLindquist(BoyerLindquistConversion): """ Class for Spherical Coordinates and related transformations. """ @u.quantity_input(r=u.km, theta=u.rad, phi=u.rad, a=u.km) def __init__(self, r, theta, phi, a): """ Constructor. Parameters ---------- r : ~astropy.units.quantity.Quantity theta : ~astropy.units.quantity.Quantity phi : ~astropy.units.quantity.Quantity a : ~astropy.units.quantity.Quantity """ self.r = r self.theta = theta self.phi = phi self.a = a super().__init__(r.si.value, theta.si.value, phi.si.value, a=a.si.value) self.system = "BoyerLindquist" self._dimension = { "r": self.r, "theta": self.theta, "phi": self.phi, "a": self.a, "system": self.system, } self._dimension_order = ("r", "theta", "phi") def __repr__(self): return "Boyer-Lindquist r: {}, theta: {}, phi: {} | a: {}".format( self.r, self.theta, self.phi, self.a ) def __str__(self): return self.__repr__() def __getitem__(self, item): """ Method to return coordinates. Objects are subsctiptable with both explicit names of parameters and integer indices. Parameters ---------- item : str or int Name of the parameter or its index. If ``'system'``, Name of coordinate is returned. If ``'a'``, spin factor of the body, ``self.a`` is returned. """ if isinstance(item, (int, np.integer)): return self._dimension[self._dimension_order[item]] return self._dimension[item] def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, rad, rad) """ element_list = [self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad)] return np.array([e.value for e in element_list], dtype=float) def to_cartesian(self): """ Method for conversion to cartesian coordinates. Returns ------- ~einsteinpy.coordinates.core.Cartesian Cartesian representation of the BL Coordinates. """ x, y, z = self.convert_cartesian() return Cartesian(x * u.m, y * u.m, z * u.m) def to_spherical(self): """ Method for conversion to spherical coordinates. Returns ------- ~einsteinpy.coordinates.core.Spherical Spherical representation of the BL Coordinates. """ r, theta, phi = self.convert_spherical() return Spherical(r * u.m, theta * u.rad, phi * u.rad) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/coordinates/utils.py0000644000175000017500000001224100000000000024062 0ustar00shreyasshreyas00000000000000import numpy as np from einsteinpy.ijit import jit def cartesian_to_spherical_fast( x, y, z, v_x=None, v_y=None, v_z=None, velocities_provided=False ): if velocities_provided: return cartesian_to_spherical(x, y, z, v_x, v_y, v_z) return cartesian_to_spherical_novel(x, y, z) @jit def cartesian_to_spherical(x, y, z, v_x, v_y, v_z): """ Utility function (jitted) to convert cartesian to spherical. This function should eventually result in Coordinate Transformation Graph! """ hxy = np.hypot(x, y) r = np.hypot(hxy, z) theta = np.arctan2(hxy, z) phi = np.arctan2(y, x) n1 = x ** 2 + y ** 2 n2 = n1 + z ** 2 v_r = (x * v_x + y * v_y + z * v_z) / np.sqrt(n2) v_t = (z * (x * v_x + y * v_y) - n1 * v_z) / (n2 * np.sqrt(n1)) v_p = -1 * (v_x * y - x * v_y) / n1 return r, theta, phi, v_r, v_t, v_p @jit def cartesian_to_spherical_novel(x, y, z): """ Utility function (jitted) to convert cartesian to spherical. This function should eventually result in Coordinate Transformation Graph! """ hxy = np.hypot(x, y) r = np.hypot(hxy, z) theta = np.arctan2(hxy, z) phi = np.arctan2(y, x) return r, theta, phi def cartesian_to_bl_fast( x, y, z, a, v_x=None, v_y=None, v_z=None, velocities_provided=False ): if velocities_provided: return cartesian_to_bl(x, y, z, a, v_x, v_y, v_z) return cartesian_to_bl_novel(x, y, z, a) @jit def cartesian_to_bl(x, y, z, a, v_x, v_y, v_z): """ Utility function (jitted) to convert cartesian to boyer lindquist. This function should eventually result in Coordinate Transformation Graph! """ w = (x ** 2 + y ** 2 + z ** 2) - (a ** 2) r = np.sqrt(0.5 * (w + np.sqrt((w ** 2) + (4 * (a ** 2) * (z ** 2))))) theta = np.arccos(z / r) phi = np.arctan2(y, x) dw_dt = 2 * (x * v_x + y * v_y + z * v_z) v_r = (1 / (2 * r)) * ( (dw_dt / 2) + ( (w * dw_dt + 4 * (a ** 2) * z * v_z) / (2 * np.sqrt((w ** 2) + (4 * (a ** 2) * (z ** 2)))) ) ) v_t = (-1 / np.sqrt(1 - np.square(z / r))) * ((v_z * r - v_r * z) / (r ** 2)) v_p = (1 / (1 + np.square(y / x))) * ((v_y * x - v_x * y) / (x ** 2)) return r, theta, phi, v_r, v_t, v_p, a @jit def cartesian_to_bl_novel(x, y, z, a): """ Utility function (jitted) to convert cartesian to boyer lindquist. This function should eventually result in Coordinate Transformation Graph! """ w = (x ** 2 + y ** 2 + z ** 2) - (a ** 2) r = np.sqrt(0.5 * (w + np.sqrt((w ** 2) + (4 * (a ** 2) * (z ** 2))))) theta = np.arccos(z / r) phi = np.arctan2(y, x) return r, theta, phi, a def spherical_to_cartesian_fast( r, t, p, v_r=None, v_t=None, v_p=None, velocities_provided=False ): if velocities_provided: return spherical_to_cartesian(r, t, p, v_r, v_t, v_p) return spherical_to_cartesian_novel(r, t, p) @jit def spherical_to_cartesian(r, t, p, v_r, v_t, v_p): """ Utility function (jitted) to convert spherical to cartesian. This function should eventually result in Coordinate Transformation Graph! """ x = r * np.cos(p) * np.sin(t) y = r * np.sin(p) * np.sin(t) z = r * np.cos(t) v_x = ( np.sin(t) * np.cos(p) * v_r - r * np.sin(t) * np.sin(p) * v_p + r * np.cos(t) * np.cos(p) * v_t ) v_y = ( np.sin(t) * np.sin(p) * v_r + r * np.cos(t) * np.sin(p) * v_t + r * np.sin(t) * np.cos(p) * v_p ) v_z = np.cos(t) * v_r - r * np.sin(t) * v_t return x, y, z, v_x, v_y, v_z @jit def spherical_to_cartesian_novel(r, t, p): """ Utility function (jitted) to convert spherical to cartesian. This function should eventually result in Coordinate Transformation Graph! """ x = r * np.cos(p) * np.sin(t) y = r * np.sin(p) * np.sin(t) z = r * np.cos(t) return x, y, z def bl_to_cartesian_fast( r, t, p, a, v_r=None, v_t=None, v_p=None, velocities_provided=False ): if velocities_provided: return bl_to_cartesian(r, t, p, a, v_r, v_t, v_p) return bl_to_cartesian_novel(r, t, p, a) @jit def bl_to_cartesian(r, t, p, a, v_r, v_t, v_p): """ Utility function (jitted) to convert bl to cartesian. This function should eventually result in Coordinate Transformation Graph! """ xa = np.sqrt(r ** 2 + a ** 2) sin_norm = xa * np.sin(t) x = sin_norm * np.cos(p) y = sin_norm * np.sin(p) z = r * np.cos(t) v_x = ( (r * v_r * np.sin(t) * np.cos(p) / xa) + (xa * np.cos(t) * np.cos(p) * v_t) - (xa * np.sin(t) * np.sin(p) * v_p) ) v_y = ( (r * v_r * np.sin(t) * np.sin(p) / xa) + (xa * np.cos(t) * np.sin(p) * v_t) + (xa * np.sin(t) * np.cos(p) * v_p) ) v_z = (v_r * np.cos(t)) - (r * np.sin(t) * v_t) return x, y, z, v_x, v_y, v_z @jit def bl_to_cartesian_novel(r, t, p, a): """ Utility function (jitted) to convert bl to cartesian. This function should eventually result in Coordinate Transformation Graph! """ xa = np.sqrt(r ** 2 + a ** 2) sin_norm = xa * np.sin(t) x = sin_norm * np.cos(p) y = sin_norm * np.sin(p) z = r * np.cos(t) return x, y, z ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/coordinates/velocity.py0000644000175000017500000002570500000000000024571 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy.coordinates.conversion import ( BoyerLindquistConversion, CartesianConversion, SphericalConversion, ) class CartesianDifferential(CartesianConversion): """ Class for calculating and transforming the velocity in Cartesian coordinates. """ @u.quantity_input( x=u.km, y=u.km, z=u.km, v_x=u.km / u.s, v_y=u.km / u.s, v_z=u.km / u.s ) def __init__(self, x, y, z, v_x, v_y, v_z): """ Constructor. Parameters ---------- x : ~astropy.units.quantity.Quantity y : ~astropy.units.quantity.Quantity z : ~astropy.units.quantity.Quantity v_x : ~astropy.units.quantity.Quantity v_y : ~astropy.units.quantity.Quantity v_z : ~astropy.units.quantity.Quantity """ self.x = x self.y = y self.z = z self.v_x = v_x self.v_y = v_y self.v_z = v_z super().__init__( x.si.value, y.si.value, z.si.value, v_x.si.value, v_y.si.value, v_z.si.value ) self.system = "Cartesian" def __repr__(self): return "Cartesian x: {}, y: {}, z: {}\n" "vx: {}, vy: {}, vz: {}".format( self.x, self.y, self.z, self.v_x, self.v_y, self.v_z ) def __str__(self): return self.__repr__() def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, m, m, m/s, m/s, m/s) """ element_list = [ self.x.to(u.m), self.y.to(u.m), self.z.to(u.m), self.v_x.to(u.m / u.s), self.v_y.to(u.m / u.s), self.v_z.to(u.m / u.s), ] return np.array([e.value for e in element_list], dtype=float) def velocities(self, return_np=False): """ Function for returning velocity. Parameters ---------- return_np : bool True for numpy array with SI values, False for list with astropy units. Defaults to False Returns ------- ~numpy.ndarray or list Array or list containing velocity. """ if return_np: return self.si_values()[3:] return [self.v_x, self.v_y, self.v_z] def spherical_differential(self): """ Function to convert velocity to spherical coordinates velocity Returns ------- ~einsteinpy.coordinates.velocity.SphericalDifferential Spherical representation of the velocity in Cartesian Coordinates. """ r, theta, phi, v_r, v_t, v_p = self.convert_spherical() return SphericalDifferential( r * u.m, theta * u.rad, phi * u.rad, v_r * u.m / u.s, v_t * u.rad / u.s, v_p * u.rad / u.s, ) @u.quantity_input(a=u.km) def bl_differential(self, a): """ Function to convert velocity to Boyer-Lindquist coordinates Parameters ---------- a : ~astropy.units.quantity.Quantity a = J/Mc , the angular momentum per unit mass of the black hole per speed of light. Returns ------- ~einsteinpy.coordinates.velocity.BoyerLindquistDifferential Boyer-Lindquist representation of the velocity in Cartesian Coordinates. """ r, theta, phi, v_r, v_t, v_p, a = self.convert_bl(a.si.value) return BoyerLindquistDifferential( r * u.m, theta * u.rad, phi * u.rad, v_r * u.m / u.s, v_t * u.rad / u.s, v_p * u.rad / u.s, a * u.m, ) class SphericalDifferential(SphericalConversion): """ Class for calculating and transforming the velocity in Spherical coordinates. """ @u.quantity_input( r=u.km, theta=u.rad, phi=u.rad, v_r=u.km / u.s, v_t=u.rad / u.s, v_p=u.rad / u.s ) def __init__(self, r, theta, phi, v_r, v_t, v_p): """ Constructor. Parameters ---------- r : ~astropy.units.quantity.Quantity theta : ~astropy.units.quantity.Quantity phi : ~astropy.units.quantity.Quantity v_r : ~astropy.units.quantity.Quantity v_t : ~astropy.units.quantity.Quantity v_p : ~astropy.units.quantity.Quantity """ self.r = r self.theta = theta self.phi = phi self.v_r = v_r self.v_t = v_t self.v_p = v_p super().__init__( r.si.value, theta.si.value, phi.si.value, v_r.si.value, v_t.si.value, v_p.si.value, ) self.system = "Spherical" def __repr__(self): return "Spherical r: {}, theta: {}, phi: {}\n" "vr: {}, vt: {}, vp: {}".format( self.r, self.theta, self.phi, self.v_r, self.v_t, self.v_p ) def __str__(self): return self.__repr__() def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, rad, rad, m/s, rad/s, rad/s) """ element_list = [ self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad), self.v_r.to(u.m / u.s), self.v_t.to(u.rad / u.s), self.v_p.to(u.rad / u.s), ] return np.array([e.value for e in element_list], dtype=float) def velocities(self, return_np=False): """ Function for returning velocity. Parameters ---------- return_np : bool True for numpy array with SI values, False for list with astropy units. Defaults to False Returns ------- ~numpy.ndarray or list Array or list containing velocity. """ if return_np: return self.si_values()[3:] return [self.v_r, self.v_t, self.v_p] def cartesian_differential(self): """ Function to convert velocity to cartesian coordinates Returns ------- ~einsteinpy.coordinates.velocity.CartesianDifferential Cartesian representation of the velocity in Spherical Coordinates. """ x, y, z, v_x, v_y, v_z = self.convert_cartesian() return CartesianDifferential( x * u.m, y * u.m, z * u.m, v_x * u.m / u.s, v_y * u.m / u.s, v_z * u.m / u.s ) @u.quantity_input(a=u.km) def bl_differential(self, a): """ Function to convert velocity to Boyer-Lindquist coordinates Parameters ---------- a : ~astropy.units.quantity.Quantity a = J/Mc , the angular momentum per unit mass of the black hole per speed of light. Returns ------- ~einsteinpy.coordinates.velocity.BoyerLindquistDifferential Boyer-Lindquist representation of the velocity in Spherical Coordinates. """ r, theta, phi, v_r, v_t, v_p, a = self.convert_bl(a.si.value) return BoyerLindquistDifferential( r * u.m, theta * u.rad, phi * u.rad, v_r * u.m / u.s, v_t * u.rad / u.s, v_p * u.rad / u.s, a * u.m, ) class BoyerLindquistDifferential(BoyerLindquistConversion): """ Class for calculating and transforming the velocity in Boyer-Lindquist coordinates """ @u.quantity_input( r=u.km, theta=u.rad, phi=u.rad, v_r=u.km / u.s, v_t=u.rad / u.s, v_p=u.rad / u.s, a=u.km, ) def __init__(self, r, theta, phi, v_r, v_t, v_p, a): """ Constructor. Parameters ---------- r : ~astropy.units.quantity.Quantity theta : ~astropy.units.quantity.Quantity phi : ~astropy.units.quantity.Quantity v_r : ~astropy.units.quantity.Quantity v_t : ~astropy.units.quantity.Quantity v_p : ~astropy.units.quantity.Quantity a : ~astropy.units.quantity.Quantity """ self.r = r self.theta = theta self.phi = phi self.a = a self.v_r = v_r self.v_t = v_t self.v_p = v_p super().__init__( r.si.value, theta.si.value, phi.si.value, v_r.si.value, v_t.si.value, v_p.si.value, a.si.value, ) self.system = "BoyerLindquist" def __repr__(self): return ( "Boyer-Lindquist r: {}, theta: {}, phi: {}\n" "vr: {}, vt: {}, vp: {}\n" "a: {}".format( self.r, self.theta, self.phi, self.v_r, self.v_t, self.v_p, self.a ) ) def __str__(self): return self.__repr__() def si_values(self): """ Function for returning values in SI units. Returns ------- ~numpy.ndarray Array containing values in SI units (m, rad, rad, m/s, rad/s, rad/s) """ element_list = [ self.r.to(u.m), self.theta.to(u.rad), self.phi.to(u.rad), self.v_r.to(u.m / u.s), self.v_t.to(u.rad / u.s), self.v_p.to(u.rad / u.s), ] return np.array([e.value for e in element_list], dtype=float) def velocities(self, return_np=False): """ Function for returning velocity. Parameters ---------- return_np : bool True for numpy array with SI values, False for list with astropy units. Defaults to False Returns ------- ~numpy.ndarray or list Array or list containing velocity. """ if return_np: return self.si_values()[3:6] return [self.v_r, self.v_t, self.v_p] def cartesian_differential(self): """ Function to convert velocity to cartesian coordinates Returns ------- ~einsteinpy.coordinates.velocity.CartesianDifferential Cartesian representation of the velocity in Boyer-Lindquist Coordinates. """ x, y, z, v_x, v_y, v_z = self.convert_cartesian() return CartesianDifferential( x * u.m, y * u.m, z * u.m, v_x * u.m / u.s, v_y * u.m / u.s, v_z * u.m / u.s ) def spherical_differential(self): """ Function to convert velocity to spherical coordinates Returns ------- ~einsteinpy.coordinates.velocity.SphericalDifferential Spherical representation of the velocity in Boyer-Lindquist Coordinates. """ r, theta, phi, v_r, v_t, v_p = self.convert_spherical() return SphericalDifferential( r * u.m, theta * u.rad, phi * u.rad, v_r * u.m / u.s, v_t * u.rad / u.s, v_p * u.rad / u.s, ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/examples.py0000644000175000017500000000117700000000000022234 0ustar00shreyasshreyas00000000000000"""Example data. """ import astropy.units as u import numpy as np from einsteinpy.bodies import Body from einsteinpy.coordinates import SphericalDifferential from einsteinpy.geodesic import Geodesic def perihelion(): Attractor = Body(name="BH", mass=6e24 * u.kg, parent=None) sph_obj = SphericalDifferential( 130 * u.m, np.pi / 2 * u.rad, -np.pi / 8 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 1900 * u.rad / u.s, ) Object = Body(differential=sph_obj, parent=Attractor) geodesic = Geodesic(body=Object, time=0 * u.s, end_lambda=0.002, step_size=5e-8) return geodesic ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/geodesic.py0000644000175000017500000000435600000000000022202 0ustar00shreyasshreyas00000000000000""" In differential geometry, a geodesic is a curve representing in some sense the shortest path between two points in a surface. """ import astropy.units as u from einsteinpy.metric import Schwarzschild class Geodesic: """ Class for defining geodesics of different geometries. """ def __init__( self, body, end_lambda, step_size=1e-3, time=0 * u.s, metric=Schwarzschild ): """ Parameters ---------- body : ~einsteinpy.bodies.Body Test particle for which geodesics is to be calculated. end_lambda : float Lambda(proper time in seconds) where iterations will stop step_size : float, optional Size of each increment in proper time. Defaults to ``1e-3``. time : ~astropy.units.s, optional Time of start, Defaults to 0 seconds. metric : ~einsteinpy.metric.schwarzschild.Schwarzschild or ~einsteinpy.metric.kerr.Kerr or ~einsteinpy.metric.kerrnewman.KerrNewman, optional Class of the spacetime metric in which geodesics are to be calculated. Defaults to ``Schwarzschild``. """ self.body = body self.attractor = body.parent self.metric = metric.from_coords( coords=self.body.coordinates, M=self.attractor.mass, q=self.body.q, Q=self.attractor.q, time=time, a=self.attractor.a, ) self._trajectory = self.metric.calculate_trajectory( end_lambda=end_lambda, OdeMethodKwargs={"stepsize": step_size}, return_cartesian=True, )[1] def __repr__(self): return "Geodesic object body name= ({0}) , metric=({1}) , parent name=({2}) , parent mass=({3})".format( self.body.name, self.metric.name, self.body.parent.name, self.body.parent.mass, ) def __str__(self): return "Geodesic object body name= ({0}) , metric=({1}) , parent name=({2}) , parent mass=({3})".format( self.body.name, self.metric.name, self.body.parent.name, self.body.parent.mass, ) @property def trajectory(self): return self._trajectory ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/hypersurface/0000755000175000017500000000000000000000000022536 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/hypersurface/__init__.py0000644000175000017500000000007300000000000024647 0ustar00shreyasshreyas00000000000000from .schwarzschildembedding import SchwarzschildEmbedding ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/hypersurface/schwarzschildembedding.py0000644000175000017500000001145100000000000027621 0ustar00shreyasshreyas00000000000000import warnings import astropy.units as u import numpy as np from matplotlib import pyplot as plt class SchwarzschildEmbedding: """ Class for Utility functions for Schwarzschild Embedding surface to implement gravitational lensing Attributes ---------- input_units : list list of input units of M units_list : list customized units to handle values of M and render plots within grid range r_init : ~astropy.units.m """ def __init__(self, M): """ Constructor Initialize mass and embedding initial radial coordinate in appropiate units in order to render the plots of the surface in finite grid. The initial r is taken to be just greater than schwarzschild radius but it is important to note that the embedding breaks at r < 9m/4. Parameters ---------- M : ~astropy.units.kg Mass of the body """ self.input_units = [M.unit] self.units_list = [u.kg * 10e22, u.m / M.to(u.kg * 10e22).value] M = M.to(self.units_list[0]) self.M = M self.r_init = (((3 * self.M.value + 0.0001) / self.M.value) * u.m).to( self.units_list[1] ) def gradient(self, r): """ Calculate gradient of Z coordinate w.r.t r to update the value of r and thereby get value of spherical radial coordinate R. Parameters ---------- r : float schwarzschild coordinate at which gradient is supposed to be obtained Returns ------- float gradient of Z w.r.t r at the point r (passed as argument) """ R = r / np.sqrt(1 - (2 * self.M.value / r)) num_one = 1 - (3 * self.M.value / r) num_two = np.sqrt( ((4 * self.M.value * r - 9 * self.M.value * self.M.value) * R) / (r - 3 * self.M.value) ** 2 ) deno = np.sqrt(1 - (2 * self.M.value / r)) ** 3 return num_one * num_two / deno def radial_coord(self, r): """ Returns spherical radial coordinate (of the embedding) from given schwarzschild coordinate. Parameters ---------- r : float Returns ------- float spherical radial coordinate of the 3d embedding """ return r / np.sqrt(1 - (2 * self.M.value / r)) def get_values(self, alpha): """ Obtain the Z coordinate values and corrosponding R values for range of r as 9m/4 < r < 9m. Parameters ---------- alpha : float scaling factor to obtain the step size for incrementing r Returns ------- tuple (list, list) : values of R (x_axis) and Z (y_axis) """ x_axis = [] y_axis = [] r_initial = self.r_init.value r_step = self.M.value / alpha z = 0 r = r_initial while r < 9 * self.M.value: x_axis.append(self.radial_coord(r)) y_axis.append(z) z = z + self.gradient(r) * r_step r = r + r_step z = 0 r = r_initial while r > (9 * self.M.value / 4): x_axis.append(self.radial_coord(r)) y_axis.append(z) z = z + self.gradient(r) * r_step r = r - r_step return x_axis, y_axis def get_values_surface(self, alpha): """ Obtain the same values as of the get_values function but reshapes them to obtain values for all points on the solid of revolution about Z axis (as the embedding is symmetric in angular coordinates). Parameters ---------- alpha : float scaling factor to obtain the step size for incrementing r Returns ------- tuple (~numpy.array of X, ~numpy.array of Y, ~numpy.array of Z) values in cartesian coordinates obtained after applying solid of revolution """ r_initial = self.r_init.value r_step = self.M.value / alpha phi_values = np.linspace(0, 2 * np.pi, 60) R_values = [] z_values = [] z = 0 r = r_initial while r < 20 * self.M.value: R_values.append(self.radial_coord(r)) z_values.append(z) z = z + self.gradient(r) * r_step r = r + r_step R_values = np.array(R_values) R_values, phi_values = np.meshgrid(R_values, phi_values) X = R_values * np.cos(phi_values) Y = R_values * np.sin(phi_values) x_len = X.shape[0] Z = np.array(z_values) z_values = np.array(z_values) for i in range(0, x_len - 1): Z = np.concatenate((Z, z_values), axis=0) Z.reshape((X.shape[0], X.shape[1])) return X, Y, Z ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/ijit.py0000644000175000017500000000125300000000000021350 0ustar00shreyasshreyas00000000000000"""Just-in-time compiler. Wraps numba if it is available as a module, uses an identity decorator instead. """ import inspect import warnings def ijit(first=None, *args, **kwargs): """Identity JIT, returns unchanged function. """ def _jit(f): return f if inspect.isfunction(first): return first else: return _jit try: import numba jit = numba.njit except ImportError: warnings.warn( "Could not import numba package. All einsteinpy " "functions will work properly but the CPU intensive " "algorithms will be slow. Consider installing numba to " "boost performance." ) jit = ijit ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/integrators/0000755000175000017500000000000000000000000022377 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/integrators/__init__.py0000644000175000017500000000005000000000000024503 0ustar00shreyasshreyas00000000000000from .runge_kutta import RK45, RK4naive ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/integrators/runge_kutta.py0000644000175000017500000000650700000000000025311 0ustar00shreyasshreyas00000000000000import warnings import numpy as np from scipy import integrate class RK4naive: """ Class for Defining Runge-Kutta 4th Order ODE solving method """ def __init__(self, fun, t0, y0, t_bound, stepsize): """ Initialization Parameters ---------- fun : function Should accept t, y as parameters, and return same type as y t0 : float Initial t y0 : ~numpy.array or float Initial y t_bound : float Boundary time - the integration won’t continue beyond it. It also determines the direction of the integration. stepsize : float Size of each increment in t """ self.t = t0 self.y = y0 self.t_bound = t_bound self.step_size = stepsize self._fun = fun self.direction = 1 * (self.t_bound >= t0) - 1 * (not self.t_bound < t0) def step(self): """ Updates the value of self.t and self.y """ if (self.t >= self.t_bound and self.direction == 1) or ( self.t <= self.t_bound and self.direction == -1 ): warnings.warn("Out of bounds set by t_bound. ", RuntimeWarning) return k0 = self._fun(self.t, self.y) k1 = self._fun( self.t + (self.step_size / 2.0), self.y + (self.step_size / 2.0) * k0 ) k2 = self._fun( self.t + (self.step_size / 2.0), self.y + (self.step_size / 2.0) * k1 ) k3 = self._fun(self.t + self.step_size, self.y + (self.step_size) * k2) self.y = self.y + ((self.step_size / 6.0) * (k0 + 2 * k1 + 2 * k2 + k3)) self.t = self.t + self.step_size class RK45(integrate.RK45): """ This Class inherits ~scipy.integrate.RK45 Class """ def __init__(self, fun, t0, y0, t_bound, stepsize, rtol=None, atol=None): """ Initialization Parameters ---------- fun : function Should accept t, y as parameters, and return same type as y t0 : float Initial t y0 : ~numpy.array or float Initial y t_bound : float Boundary time - the integration won’t continue beyond it. It also determines the direction of the integration. stepsize : float Size of each increment in t rtol : float Relative tolerance, defaults to 0.2*stepsize atol : float Absolute tolerance, defaults to rtol/0.8e3 """ vectorized = not isinstance(y0, float) self._t_bound = t_bound if rtol is None: rtol = 0.2 * stepsize if atol is None: atol = rtol / 0.8e3 super(RK45, self).__init__( fun=fun, t0=t0, y0=y0, t_bound=self._t_bound, first_step=0.8 * stepsize, max_step=8.0 * stepsize, rtol=rtol, atol=atol, vectorized=vectorized, ) def step(self): """ Updates the value of self.t and self.y """ try: super(RK45, self).step() except RuntimeError: warnings.warn( "Attempt to step on a failed or finished solver. (Invalid Value or out of bounds of t_bound)", RuntimeWarning, ) ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/metric/0000755000175000017500000000000000000000000021321 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/metric/__init__.py0000644000175000017500000000014300000000000023430 0ustar00shreyasshreyas00000000000000from .kerr import Kerr from .kerrnewman import KerrNewman from .schwarzschild import Schwarzschild ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/metric/kerr.py0000644000175000017500000001740000000000000022640 0ustar00shreyasshreyas00000000000000import warnings import astropy.units as u import numpy as np from einsteinpy import constant from einsteinpy.coordinates import BoyerLindquistConversion from einsteinpy.integrators import RK45 from einsteinpy.utils import kerr_utils, schwarzschild_radius _G = constant.G.value _c = constant.c.value class Kerr: """ Class for defining Kerr Geometry Methods """ @u.quantity_input(time=u.s, M=u.kg) def __init__(self, bl_coords, M, time): self.input_coords = bl_coords self.name = "Kerr" self.M = M self.a = self.input_coords.a.to(u.m) self.time = time pos_vec, vel_vec = ( self.input_coords.si_values()[:3], self.input_coords.si_values()[3:], ) time_vel = kerr_utils.kerr_time_velocity(pos_vec, vel_vec, self.M, self.a.value) self.initial_vec = np.hstack( (self.time.value, pos_vec, time_vel.value, vel_vec) ) self.scr = schwarzschild_radius(M) @classmethod @u.quantity_input(time=u.s, M=u.kg, a=u.m) def from_coords(cls, coords, M, q=None, Q=None, time=0 * u.s, a=0 * u.m): """ Constructor Parameters ---------- coords : ~einsteinpy.coordinates.velocity.CartesianDifferential Object having both initial positions and velocities of particle in Cartesian Coordinates M : ~astropy.units.quantity.Quantity Mass of the body a : ~astropy.units.quantity.Quantity Spin factor of the massive body. Angular momentum divided by mass divided by speed of light. time : ~astropy.units.quantity.Quantity Time of start, defaults to 0 seconds. """ if coords.system == "Cartesian": bl_coords = coords.bl_differential(a) return cls(bl_coords, M, time) if coords.system == "Spherical": bl_coords = coords.bl_differential(a) return cls(bl_coords, M, time) return cls(coords, M, time) def f_vec(self, ld, vec): chl = kerr_utils.christoffels(vec[1], vec[2], self.M.value, self.a.value) vals = np.zeros(shape=(8,), dtype=float) for i in range(4): vals[i] = vec[i + 4] vals[4] = -2.0 * ( chl[0, 0, 1] * vec[4] * vec[5] + chl[0, 0, 2] * vec[4] * vec[6] + chl[0, 1, 3] * vec[5] * vec[7] + chl[0, 2, 3] * vec[6] * vec[7] ) vals[5] = -1.0 * ( chl[1, 0, 0] * vec[4] * vec[4] + 2 * chl[1, 0, 3] * vec[4] * vec[7] + chl[1, 1, 1] * vec[5] * vec[5] + 2 * chl[1, 1, 2] * vec[5] * vec[6] + chl[1, 2, 2] * vec[6] * vec[6] + chl[1, 3, 3] * vec[7] * vec[7] ) vals[6] = -1.0 * ( chl[2, 0, 0] * vec[4] * vec[4] + 2 * chl[2, 0, 3] * vec[4] * vec[7] + chl[2, 1, 1] * vec[5] * vec[5] + 2 * chl[2, 1, 2] * vec[5] * vec[6] + chl[2, 2, 2] * vec[6] * vec[6] + chl[2, 3, 3] * vec[7] * vec[7] ) vals[7] = -2.0 * ( chl[3, 0, 1] * vec[4] * vec[5] + chl[3, 0, 2] * vec[4] * vec[6] + chl[3, 1, 3] * vec[5] * vec[7] + chl[3, 2, 3] * vec[6] * vec[7] ) return vals def calculate_trajectory( self, start_lambda=0.0, end_lambda=10.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation Parameters ---------- start_lambda : float Starting lambda(proper time), defaults to 0, (lambda ~= t) end_lamdba : float Lambda(proper time) where iteartions will stop, defaults to 100000 stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to False Returns ------- ~numpy.ndarray N-element array containing proper time. ~numpy.ndarray (n,8) shape array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ vecs = list() lambdas = list() crossed_event_horizon = False ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=end_lambda, **OdeMethodKwargs ) _event_hor = kerr_utils.event_horizon(self.M.value, self.a.value)[0] * 1.001 while ODE.t < end_lambda: vecs.append(ODE.y) lambdas.append(ODE.t) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _event_hor): warnings.warn("particle reached event horizon. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True vecs, lambdas = np.array(vecs), np.array(lambdas) if not return_cartesian: return lambdas, vecs else: cart_vecs = list() for v in vecs: si_vals = BoyerLindquistConversion( v[1], v[2], v[3], v[5], v[6], v[7], self.a.value ).convert_cartesian() cart_vecs.append(np.hstack((v[0], si_vals[:3], v[4], si_vals[3:]))) return lambdas, np.array(cart_vecs) def calculate_trajectory_iterator( self, start_lambda=0.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation. Yields an iterator. Parameters ---------- start_lambda : float Starting lambda, defaults to 0.0, (lambda ~= t) stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to Falsed Yields ------ float proper time ~numpy.ndarray array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=1e300, **OdeMethodKwargs ) crossed_event_horizon = False _event_hor = kerr_utils.event_horizon(self.M.value, self.a.value)[0] * 1.001 while True: if not return_cartesian: yield ODE.t, ODE.y else: v = ODE.y si_vals = BoyerLindquistConversion( v[1], v[2], v[3], v[5], v[6], v[7], self.a.value ).convert_cartesian() yield ODE.t, np.hstack((v[0], si_vals[:3], v[4], si_vals[3:])) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _event_hor): warnings.warn("particle reached event horizon. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/metric/kerrnewman.py0000644000175000017500000002134100000000000024045 0ustar00shreyasshreyas00000000000000import warnings import astropy.units as u import numpy as np from einsteinpy import constant from einsteinpy.coordinates import BoyerLindquistConversion from einsteinpy.integrators import RK45 from einsteinpy.utils import kerrnewman_utils, schwarzschild_radius _G = constant.G.value _c = constant.c.value _Cc = constant.coulombs_const.value # q = 11604461683.91822052001953125*q This comment is not to be removed. This is a hack. class KerrNewman: """ Class for defining Kerr-Newman Goemetry Methods """ @u.quantity_input(time=u.s, M=u.kg, Q=u.C) def __init__(self, bl_coords, q, M, Q, time): self.input_coords = bl_coords self.name = "KerrNewman" self.M = M self.a = self.input_coords.a.to(u.m) self.Q = Q self.q = q pos_vec, vel_vec = ( self.input_coords.si_values()[:3], self.input_coords.si_values()[3:], ) self.time = time time_vel = kerrnewman_utils.kerrnewman_time_velocity( pos_vec, vel_vec, self.M, self.a.value, Q ) self.initial_vec = np.hstack( (self.time.value, pos_vec, time_vel.value, vel_vec) ) self.scr = schwarzschild_radius(M) @classmethod @u.quantity_input(q=u.C / u.kg, time=u.s, M=u.kg, Q=u.C, a=u.m) def from_coords(cls, coords, M, q, Q, time=0 * u.s, a=0 * u.m): """ Constructor. Parameters ---------- coords : ~einsteinpy.coordinates.velocity.BoyerLindquistDifferential Initial positions and velocities of particle in BL Coordinates, and spin factor of massive body. q : ~astropy.units.quantity.Quantity Charge per unit mass of test particle M : ~astropy.units.quantity.Quantity Mass of the massive body Q : ~astropy.units.quantity.Quantity Charge on the massive body a : ~astropy.units.quantity.Quantity Spin factor of the massive body(Angular Momentum per unit mass per speed of light) time : ~astropy.units.quantity.Quantity Time of start, defaults to 0 seconds. """ if coords.system == "Cartesian": bl_coords = coords.bl_differential(a) return cls(bl_coords, q, M, Q, time) if coords.system == "Spherical": bl_coords = coords.bl_differential(a) return cls(bl_coords, q, M, Q, time) return cls(coords, q, M, Q, time) def f_vec(self, ld, vec): chl = kerrnewman_utils.christoffels( vec[1], vec[2], self.M.value, self.a.value, self.Q.value ) maxwell = kerrnewman_utils.maxwell_tensor_contravariant( vec[1], vec[2], self.a.value, self.Q.value, self.M.value ) metric = kerrnewman_utils.metric( vec[1], vec[2], self.M.value, self.a.value, self.Q.value ) vals = np.zeros(shape=(8,), dtype=float) for i in range(4): vals[i] = vec[i + 4] vals[4] = -2.0 * ( chl[0, 0, 1] * vec[4] * vec[5] + chl[0, 0, 2] * vec[4] * vec[6] + chl[0, 1, 3] * vec[5] * vec[7] + chl[0, 2, 3] * vec[6] * vec[7] ) vals[5] = -1.0 * ( chl[1, 0, 0] * vec[4] * vec[4] + 2 * chl[1, 0, 3] * vec[4] * vec[7] + chl[1, 1, 1] * vec[5] * vec[5] + 2 * chl[1, 1, 2] * vec[5] * vec[6] + chl[1, 2, 2] * vec[6] * vec[6] + chl[1, 3, 3] * vec[7] * vec[7] ) vals[6] = -1.0 * ( chl[2, 0, 0] * vec[4] * vec[4] + 2 * chl[2, 0, 3] * vec[4] * vec[7] + chl[2, 1, 1] * vec[5] * vec[5] + 2 * chl[2, 1, 2] * vec[5] * vec[6] + chl[2, 2, 2] * vec[6] * vec[6] + chl[2, 3, 3] * vec[7] * vec[7] ) vals[7] = -2.0 * ( chl[3, 0, 1] * vec[4] * vec[5] + chl[3, 0, 2] * vec[4] * vec[6] + chl[3, 1, 3] * vec[5] * vec[7] + chl[3, 2, 3] * vec[6] * vec[7] ) vals[4:] -= self.q.value * np.dot( vec[4:].reshape((4,)), np.matmul(metric, maxwell) ) return vals def calculate_trajectory( self, start_lambda=0.0, end_lambda=10.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation Parameters ---------- start_lambda : float Starting lambda(proper time), defaults to 0.0, (lambda ~= t) end_lamdba : float Lambda(proper time) where iteartions will stop, defaults to 100000 stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to False Returns ------- ~numpy.ndarray N-element array containing proper time. ~numpy.ndarray (n,8) shape array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ vecs = list() lambdas = list() crossed_event_horizon = False ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=end_lambda, **OdeMethodKwargs ) _event_hor = ( kerrnewman_utils.event_horizon(self.M.value, self.a.value, self.Q.value)[0] * 1.001 ) while ODE.t < end_lambda: vecs.append(ODE.y) lambdas.append(ODE.t) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _event_hor): warnings.warn("particle reached Event horizon. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True vecs, lambdas = np.array(vecs), np.array(lambdas) if not return_cartesian: return lambdas, vecs else: cart_vecs = list() for v in vecs: si_vals = BoyerLindquistConversion( v[1], v[2], v[3], v[5], v[6], v[7], self.a.value ).convert_cartesian() cart_vecs.append(np.hstack((v[0], si_vals[:3], v[4], si_vals[3:]))) return lambdas, np.array(cart_vecs) def calculate_trajectory_iterator( self, start_lambda=0.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation. Yields an iterator. Parameters ---------- start_lambda : float Starting lambda, defaults to 0.0, (lambda ~= t) stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to Falsed Yields ------ float proper time ~numpy.ndarray array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=1e300, **OdeMethodKwargs ) crossed_event_horizon = False _event_hor = ( kerrnewman_utils.event_horizon(self.M.value, self.a.value, self.Q.value)[0] * 1.001 ) while True: if not return_cartesian: yield ODE.t, ODE.y else: v = ODE.y si_vals = BoyerLindquistConversion( v[1], v[2], v[3], v[5], v[6], v[7], self.a.value ).convert_cartesian() yield ODE.t, np.hstack((v[0], si_vals[:3], v[4], si_vals[3:])) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _event_hor): warnings.warn("particle reached event horizon. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/metric/schwarzschild.py0000644000175000017500000001530100000000000024543 0ustar00shreyasshreyas00000000000000import warnings import astropy.units as u import numpy as np from einsteinpy import constant from einsteinpy.coordinates import SphericalConversion from einsteinpy.integrators import RK45 from einsteinpy.utils import schwarzschild_radius, schwarzschild_utils _G = constant.G.value _c = constant.c.value class Schwarzschild: """ Class for defining a Schwarzschild Geometry methods """ @u.quantity_input(time=u.s, M=u.kg) def __init__(self, sph_coords, M, time): self.name = "Schwarzschild" self.M = M self.input_coords = sph_coords self.time = time pos_vec, vel_vec = ( self.input_coords.si_values()[:3], self.input_coords.si_values()[3:], ) time_vel = schwarzschild_utils.time_velocity(pos_vec, vel_vec, M) self.initial_vec = np.hstack( (self.time.value, pos_vec, time_vel.value, vel_vec) ) self.scr = schwarzschild_radius(M) @classmethod @u.quantity_input(time=u.s, M=u.kg, a=u.m) def from_coords(cls, coords, M, q=None, Q=None, time=0 * u.s, a=0 * u.m): """ Constructor Parameters ---------- coords : ~einsteinpy.coordinates.velocity.CartesianDifferential Object having both initial positions and velocities of particle in Cartesian Coordinates M : ~astropy.units.quantity.Quantity Mass of the body time : ~astropy.units.quantity.Quantity Time of start, defaults to 0 seconds. """ if coords.system == "Spherical": return cls(coords, M, time) sph_coords = coords.spherical_differential() return cls(sph_coords, M, time) def f_vec(self, ld, vec): vals = np.zeros(shape=vec.shape, dtype=vec.dtype) chl = schwarzschild_utils.christoffels(vec[1], vec[2], self.M.value) vals[:4] = vec[4:8] vals[4] = -2 * chl[0, 0, 1] * vec[4] * vec[5] vals[5] = -1 * ( chl[1, 0, 0] * (vec[4] ** 2) + chl[1, 1, 1] * (vec[5] ** 2) + chl[1, 2, 2] * (vec[6] ** 2) + chl[1, 3, 3] * (vec[7] ** 2) ) vals[6] = -2 * chl[2, 2, 1] * vec[6] * vec[5] - 1 * chl[2, 3, 3] * (vec[7] ** 2) vals[7] = -2 * (chl[3, 3, 1] * vec[7] * vec[5] + chl[3, 3, 2] * vec[7] * vec[6]) return vals def calculate_trajectory( self, start_lambda=0.0, end_lambda=10.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation Parameters ---------- start_lambda : float Starting lambda(proper time), defaults to 0, (lambda ~= t) end_lamdba : float Lambda(proper time) where iteartions will stop, defaults to 100000 stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to False Returns ------- ~numpy.ndarray N-element array containing proper time. ~numpy.ndarray (n,8) shape array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=end_lambda, **OdeMethodKwargs ) vecs = list() lambdas = list() crossed_event_horizon = False _scr = self.scr.value * 1.001 while ODE.t < end_lambda: vecs.append(ODE.y) lambdas.append(ODE.t) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _scr): warnings.warn("particle reached Schwarzchild Radius. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True vecs, lambdas = np.array(vecs), np.array(lambdas) if not return_cartesian: return lambdas, vecs else: cart_vecs = list() for v in vecs: si_vals = SphericalConversion( v[1], v[2], v[3], v[5], v[6], v[7] ).convert_cartesian() cart_vecs.append(np.hstack((v[0], si_vals[:3], v[4], si_vals[3:]))) return lambdas, np.array(cart_vecs) def calculate_trajectory_iterator( self, start_lambda=0.0, stop_on_singularity=True, OdeMethodKwargs={"stepsize": 1e-3}, return_cartesian=False, ): """ Calculate trajectory in manifold according to geodesic equation Yields an iterator Parameters ---------- start_lambda : float Starting lambda, defaults to 0.0, (lambda ~= t) stop_on_singularity : bool Whether to stop further computation on reaching singularity, defaults to True OdeMethodKwargs : dict Kwargs to be supplied to the ODESolver, defaults to {'stepsize': 1e-3} Dictionary with key 'stepsize' along with an float value is expected. return_cartesian : bool True if coordinates and velocities are required in cartesian coordinates(SI units), defaults to Falsed Yields ------ float proper time ~numpy.ndarray array of [t, x1, x2, x3, velocity_of_time, v1, v2, v3] for each proper time(lambda). """ ODE = RK45( fun=self.f_vec, t0=start_lambda, y0=self.initial_vec, t_bound=1e300, **OdeMethodKwargs ) crossed_event_horizon = False _scr = self.scr.value * 1.001 while True: if not return_cartesian: yield ODE.t, ODE.y else: v = ODE.y si_vals = SphericalConversion( v[1], v[2], v[3], v[5], v[6], v[7] ).convert_cartesian() yield ODE.t, np.hstack((v[0], si_vals[:3], v[4], si_vals[3:])) ODE.step() if (not crossed_event_horizon) and (ODE.y[1] <= _scr): warnings.warn("particle reached Schwarzchild Radius. ", RuntimeWarning) if stop_on_singularity: break else: crossed_event_horizon = True ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy/plotting/0000755000175000017500000000000000000000000021676 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/__init__.py0000644000175000017500000000060700000000000024012 0ustar00shreyasshreyas00000000000000from einsteinpy.plotting.fractal import fractal from einsteinpy.plotting.geodesics.core import GeodesicPlotter from einsteinpy.plotting.geodesics.interactive import InteractiveGeodesicPlotter from einsteinpy.plotting.geodesics.static import StaticGeodesicPlotter from einsteinpy.plotting.hypersurface.core import HypersurfacePlotter from einsteinpy.plotting.rays.shadow import ShadowPlotter ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/fractal.py0000644000175000017500000000644400000000000023674 0ustar00shreyasshreyas00000000000000"""Easter Egg. This module was added before ``0.3.0`` release as an Easter Egg. Contains a simple implementation of fractal. """ import numpy as np import plotly.graph_objects as go from einsteinpy.ijit import jit @jit def _julia(A, c, zabs_max, i, j, dims, x_range, y_range, iter_max): width, height = dims xmin, xmax = x_range ymin, ymax = y_range xwidth, ywidth = xmax - xmin, ymax - ymin it = 0 z = np.complex((i / width) * xwidth + xmin + 1j * ((j / height) * ywidth + ymin)) while abs(z) < zabs_max and it < iter_max: z = z ** 2 + c it += 1 A[i, j] = (it / iter_max) ** 0.2 def _fractal_img( dims=(384, 384), angle=2.75, zabs_max=20, iter_max=64, x_range=(-1.6, 1.6), y_range=(-1.6, 1.6), ): width, height = dims A = np.zeros((width, height), dtype=float) c = 0.80 * np.exp(1j * angle) for i in range(width): for j in range(height): _julia(A, c, zabs_max, i, j, dims, x_range, y_range, iter_max) return A def fractal(start_angle=(np.pi / 3), end_angle=np.pi, divs=12, show=True): """ It's an Easter Egg. This function plots fractals arising out of a specific class of functions from Julia set. The plot also provides a slider to visualize various angles which can act as parameters for the complex function. Parameters ---------- start_angle : float Starting angle for the slider. Defaults to ``pi/3``. end_angle : float Ending angle for the slider. Defaults to ``pi``. divs : int Number of divisions between ``start_angle`` and ``end_angle``. Defaults to ``12``. show : bool Shows plot if ``True``. Defaults to ``True``. Returns ------- ~plotly.graph_objects.Figure Instance of plot created. """ active = divs - 1 fig = go.Figure() # Add traces, one for each slider step for step in np.linspace(start_angle, end_angle, num=divs): fig.add_trace( go.Heatmap(z=_fractal_img(angle=step, dims=(400, 400)), showscale=False) ) fig.data[active].visible = True text = """ A fractal is a never ending pattern. We are generating fractals out of Julia set with different angles as parameters. """ print(text) steps = list() for i in range(len(fig.data)): step = dict(method="restyle", args=["visible", [False] * len(fig.data)]) step["args"][1][i] = True # Toggle i'th trace to "visible" steps.append(step) sliders = [ dict( active=active, currentvalue={ "prefix": "Angle between %.2f & %.2f : " % (start_angle, end_angle) }, pad={"t": divs}, steps=steps, ) ] fig.update_layout( sliders=sliders, width=600, height=600, xaxis=dict( autorange=True, showgrid=False, ticks="", showticklabels=False, fixedrange=True, ), yaxis=dict( autorange=True, showgrid=False, ticks="", showticklabels=False, fixedrange=True, ), ) text = """ Waiting for plotly object to load. """ if show: print(text) fig.show() return fig ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/plotting/geodesics/0000755000175000017500000000000000000000000023643 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/geodesics/__init__.py0000644000175000017500000000032700000000000025756 0ustar00shreyasshreyas00000000000000from einsteinpy.plotting.geodesics.core import GeodesicPlotter from einsteinpy.plotting.geodesics.interactive import InteractiveGeodesicPlotter from einsteinpy.plotting.geodesics.static import StaticGeodesicPlotter ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/geodesics/core.py0000644000175000017500000000127200000000000025147 0ustar00shreyasshreyas00000000000000import random from einsteinpy.plotting.geodesics.interactive import InteractiveGeodesicPlotter from einsteinpy.plotting.geodesics.static import StaticGeodesicPlotter def in_ipynb(): try: shell = get_ipython().__class__.__name__ # type: ignore if shell == "ZMQInteractiveShell": return InteractiveGeodesicPlotter if shell == "TerminalInteractiveShell": return StaticGeodesicPlotter return StaticGeodesicPlotter except NameError: return StaticGeodesicPlotter class GeodesicPlotter(in_ipynb()): # type: ignore """ Class for automatically switching between Matplotlib and Plotly depending on platform used. """ ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/geodesics/interactive.py0000644000175000017500000000677000000000000026544 0ustar00shreyasshreyas00000000000000import os import random import numpy as np import plotly.graph_objects as go from plotly.offline import plot as saveplot class InteractiveGeodesicPlotter: def __init__(self, attractor_radius_scale=-1.0, attractor_color="#ffcc00"): """ Constructor. Parameters ---------- attractor_color : string, optional Color which is used to denote the attractor. Defaults to #ffcc00. """ self.fig = go.Figure() self.attractor_radius_scale = attractor_radius_scale self.attractor_color = attractor_color self.attractor_present = False self._layout = go.Layout( autosize=True, xaxis=dict(title="x (m)", constrain="domain"), yaxis=dict(title="y (m)", scaleanchor="x"), ) def _mindist(self, x, y, z=0): return np.sqrt(x * x + y * y + z * z) def _draw_attractor(self, radius, xarr, yarr): self.attractor_present = True if self.attractor_radius_scale == -1.0: minrad_nooverlap = self._mindist(xarr[0], yarr[0]) for i, _ in enumerate(xarr): minrad_nooverlap = min( minrad_nooverlap, self._mindist(xarr[i], yarr[i]) ) xlen = max(xarr) - min(xarr) ylen = max(yarr) - min(yarr) minlen_plot = min(xlen, ylen) min_radius = minlen_plot / 12 radius = min(min_radius, minrad_nooverlap) else: radius = radius.value * self.attractor_radius_scale self.fig.add_trace( go.Scatter( x=[0], y=[0], mode="markers", name="attractor", marker=dict(size=0, color=self.attractor_color), ) ) self._layout.shapes = [ go.layout.Shape( type="circle", xref="x", yref="y", fillcolor=self.attractor_color, x0=-radius, y0=-radius, x1=radius, y1=radius, line_width=0, ) ] def plot(self, geodesic, color="#{:06x}".format(random.randint(0, 0xFFFFFF))): """ Parameters ---------- geodesic : ~einsteinpy.geodesic.Geodesic Geodesic of the body color : hex code RGB, optional Color of the dashed lines. Picks a random color by default. """ vals = geodesic.trajectory x = np.array([coord[1] for coord in vals]) y = np.array([coord[2] for coord in vals]) if not self.attractor_present: self._draw_attractor(geodesic.metric.scr, x, y) self.fig.add_trace( go.Scatter( x=x, y=y, mode="lines", name="geodesic", marker=dict(size=5, color=color, line=dict(width=2)), ) ) def show(self): """ Method to show plots during runtime. Returns ------- ~plotly.graph_objects.Figure """ self.fig.layout.update(self._layout) return self.fig def save(self, name="geodesic.png"): """ Method to save plots locally. Parameters ---------- name : str, optional Name of the file with extension. """ basename, ext = os.path.splitext(name) saveplot(self.fig, image=ext[1:], image_filename=basename, show_link=False) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/geodesics/static.py0000644000175000017500000001231500000000000025506 0ustar00shreyasshreyas00000000000000import random import matplotlib.pyplot as plt import numpy as np from matplotlib.animation import FuncAnimation from matplotlib.patches import Circle from mpl_toolkits import mplot3d class StaticGeodesicPlotter: def __init__( self, ax=None, attractor_radius_scale=-1.0, attractor_color="#ffcc00", use_3d=False, ): """ Constructor. Parameters ---------- ax: ~matplotlib.axes.Axes Matplotlib Axes object. attractor_radius_scale : float, optional Scales the attractor radius by the value given. Default is 1. It is used to make plots look more clear if needed. attractor_color : string, optional Color which is used to denote the attractor. Defaults to #ffcc00. """ self.ax = ax self.use_3d = use_3d if not self.ax: self.fig, self.ax = plt.subplots(figsize=(6, 6)) self.ax.set_aspect(1) if self.use_3d: self.ax = plt.axes(projection="3d") self.ax.set_zlabel("$z$ (m)") self.ax.set_xlabel("$x$ (m)") self.ax.set_ylabel("$y$ (m)") self.attractor_radius_scale = attractor_radius_scale self.attractor_color = attractor_color self.attractor_present = False def _mindist(self, x, y, z=0): return np.sqrt(x * x + y * y + z * z) def _draw_attractor(self, radius, xarr, yarr): self.attractor_present = True if self.use_3d: self.ax.plot([0], [0], [0], "o", mew=0, color=self.attractor_color) elif self.attractor_radius_scale == -1.0: minrad_nooverlap = self._mindist(xarr[0], yarr[0]) for i, _ in enumerate(xarr): minrad_nooverlap = min( minrad_nooverlap, self._mindist(xarr[i], yarr[i]) ) xlen = max(xarr) - min(xarr) ylen = max(yarr) - min(yarr) minlen_plot = min(xlen, ylen) min_radius = minlen_plot / 12 radius = min(min_radius, minrad_nooverlap) self.get_curr_plot_radius = radius self.ax.add_patch(Circle((0, 0), radius, lw=0, color=self.attractor_color)) else: radius = radius * self.attractor_radius_scale self.get_curr_plot_radius = radius self.ax.add_patch( Circle((0, 0), radius.value, lw=0, color=self.attractor_color) ) def _set_scaling(self, x_range, y_range, z_range, lim): if x_range < lim and y_range < lim and z_range < lim: return if x_range < lim: self.ax.set_xlim([-lim, lim]) if y_range < lim: self.ax.set_ylim([-lim, lim]) if z_range < lim: self.ax.set_zlim([-lim, lim]) def plot(self, geodesic, color="#{:06x}".format(random.randint(0, 0xFFFFFF))): """ Parameters ---------- geodesic : ~einsteinpy.geodesic.Geodesic Geodesic of the body color : hex code RGB, optional Color of the dashed lines. Picks a random color by default. """ vals = geodesic.trajectory x = np.array(vals[:, 1]) y = np.array(vals[:, 2]) z = np.array(vals[:, 3]) if not self.use_3d: self.ax.plot(x, y, "--", color=color) self.ax.plot(x[-1], y[-1], "o", mew=0, color=color) else: x_range = max(x) - min(x) y_range = max(y) - min(y) z_range = max(z) - min(z) self._set_scaling(x_range, y_range, z_range, 1e-5) self.ax.plot(x, y, z, "--", color=color) self.ax.plot(x[-1:], y[-1:], z[-1:], "o", mew=0, color=color) if not self.attractor_present: self._draw_attractor(geodesic.metric.scr, x, y) def animate( self, geodesic, color="#{:06x}".format(random.randint(0, 0xFFFFFF)), interval=50 ): """ Parameters ---------- geodesic : ~einsteinpy.geodesic.Geodesic Geodesic of the body. color : hex code RGB, optional Color of the dashed lines. Picks a random color by default. interval : int, optional Control the time between frames. Add time in milliseconds. """ vals = geodesic.trajectory x = np.array([coord[1] for coord in vals]) y = np.array([coord[2] for coord in vals]) x_max, x_min = max(x), min(x) y_max, y_min = max(y), min(y) margin_x = (x_max - x_min) * 0.1 margin_y = (y_max - y_min) * 0.2 frames = x.shape[0] (pic,) = self.ax.plot([], [], "--", color=color) plt.xlim(x_min - margin_x, x_max + margin_x) plt.ylim(y_min - margin_y, y_max + margin_y) if not self.attractor_present: self._draw_attractor(geodesic.metric.scr, x, y) def _update(frame): pic.set_xdata(x[: frame + 1]) pic.set_ydata(y[: frame + 1]) return (pic,) self.ani = FuncAnimation( self.fig, _update, frames=frames, interval=interval, blit=True ) def show(self): plt.show() def save(self, name="geodesic.png"): plt.savefig(name) ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/plotting/hypersurface/0000755000175000017500000000000000000000000024376 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/hypersurface/__init__.py0000644000175000017500000000010600000000000026504 0ustar00shreyasshreyas00000000000000from einsteinpy.plotting.hypersurface.core import HypersurfacePlotter ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/hypersurface/core.py0000644000175000017500000000261500000000000025704 0ustar00shreyasshreyas00000000000000import matplotlib.pyplot as plt class HypersurfacePlotter: """ Class for plotting and visualising hypersurfaces """ def __init__(self, embedding, plot_type="wireframe", alpha=100): """ Constructor for plotter. Parameters ---------- embedding : ~einsteinpy.hypersurface.SchwarzschildEmbedding The embedding of the hypersurface. plot_type : str, optional type of texture for the plots - wireframe / surface, defaults to 'wireframe' alpha : float, optional scaling factor to obtain the step size for incrementing r, defaults to 100 """ self.embedding = embedding self.plot_type = plot_type self.alpha = alpha def plot(self): """ Plots the surface thus obtained for the embedding. """ fig = plt.figure() ax = plt.axes(projection="3d") X, Y, Z = self.embedding.get_values_surface(self.alpha) shape_tuple = X.shape Z = Z.reshape((shape_tuple[0], shape_tuple[1])) if self.plot_type == "wireframe": ax.plot_wireframe(X, Y, Z, color="black") elif self.plot_type == "surface": ax.plot_surface( X, Y, Z, rstride=1, cstride=1, cmap="cubehelix", edgecolor="none" ) def show(self): """ Shows the plot. """ plt.show() ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/plotting/rays/0000755000175000017500000000000000000000000022654 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/rays/__init__.py0000644000175000017500000000004200000000000024761 0ustar00shreyasshreyas00000000000000from .shadow import ShadowPlotter ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/plotting/rays/shadow.py0000644000175000017500000000321200000000000024511 0ustar00shreyasshreyas00000000000000import matplotlib.pyplot as plt import numpy as np class ShadowPlotter: """ Class for plotting and visualising shadows """ def __init__(self, shadow, is_line_plot=True): """ Constructor for plotter. Parameters ---------- shadow : ~einsteinpy.rays.Shadow The shadow object is_line_plot : bool, optional If the plot is a line plot or a contour plot. Defaults to True. """ self.shadow = shadow self.is_intensity_plot = is_line_plot def plot(self): """ Plots the shadow. """ if self.is_intensity_plot: plt.plot(self.shadow.fb1, self.shadow.intensity, "r") plt.plot(self.shadow.fb2, self.shadow.intensity, "r") plt.xlabel("Impact Paramter (b)") plt.ylabel("Intensity (Emissivity)") plt.title("Intensity Plot") else: theta1 = np.linspace(0, 2 * np.pi, len(self.shadow.fb1)) self.r1, self.theta1 = np.meshgrid(self.shadow.fb1, theta1) self.values1, self.values2 = np.meshgrid( self.shadow.intensity, self.shadow.intensity ) def show(self): """ Shows the plot. """ if self.is_intensity_plot: plt.show() else: xx = self.r1 * np.cos(self.theta1) yy = self.r1 * np.sin(self.theta1) plt.figure(figsize=(7, 7)) plt.pcolormesh(xx, yy, self.values1, cmap=plt.cm.afmhot, shading="gouraud") plt.title("Schwarzschild Black Hole") plt.gca().set_aspect("equal", adjustable="box") ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/rays/0000755000175000017500000000000000000000000021014 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/rays/__init__.py0000644000175000017500000000003300000000000023121 0ustar00shreyasshreyas00000000000000from .shadow import Shadow ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/rays/shadow.py0000644000175000017500000001122000000000000022647 0ustar00shreyasshreyas00000000000000import warnings import astropy.units as u import numpy as np from scipy.integrate import fixed_quad from scipy.interpolate import interp1d from scipy.optimize import newton class Shadow: """ Class for plotting the shadow of Schwarzschild Black Hole surrounded by a thin accreting emission disk as seen by a distant observer. """ @u.quantity_input(mass=u.kg, fov=u.km) def __init__(self, mass, n_rays, fov, limit=0.001): self.mass = mass.to(u.kg) self.limit = limit self.n_rays = n_rays self.fov = fov.to(u.km) self.horizon = 2 * self.mass.value # To be changed after 0.3.0 self.b_crit = 3 * np.sqrt(3) * self.mass self.b = self._compute_B() self.z = list() self.bfin = list() warnings.filterwarnings("ignore") for i in self.b: root = newton(self._root_equation, 0.1, args=(i,)) if np.isreal(root): self.bfin.append(i) self.z.append([i, np.real(root)]) self.z = np.array(self.z) self.k0 = self._intensity() self.k1 = self._intensity_from_event_horizon() self.intensity = self.k1 + self.k0 # Just to make the plot symmetric on -x axis self.fb1 = list(self.b2) + list(self.bfin) self.fb2 = np.asarray(list(-np.asarray(self.b2)) + list(-np.asarray(self.bfin))) def _compute_B(self): """ Returns an array of impact parameters """ return np.linspace(self.b_crit.value, self.fov.value, self.n_rays) def _root_equation(self, r_tp, i): """ Returns the root of the equation for ``r_tp`` (turning points) for some impact parameter """ return r_tp / ((1 - (2 * int(self.mass.value) / r_tp))) ** 0.5 - i def _intensity_blue_sch(self, r, b): """ Returns the integrand for the blue shifted intensity to be integrated. Reference : Cosimo Bambi, 10.1103/PhysRevD.87.107501 """ GTT = 1 - (2 * self.mass.value / r) GRR = (1 - (2 * self.mass.value / r)) ** (-1) KRKText = ((GTT / GRR) * (1 - (b ** 2 * GTT / (r ** 2)))) ** 0.5 Gblue = ( (1 / GTT) - KRKText * (GRR / GTT) * ((1 - GTT) / (GTT * GRR)) ** 0.5 ) ** (-1) Iblue = -(Gblue ** 3) * (GTT / (r ** 2)) * (1 / KRKText) return Iblue def _intensity_red_sch(self, r, b): """ Returns the integrand for the red shifted intensity to be integrated. Reference : Cosimo Bambi, 10.1103/PhysRevD.87.107501 """ GTT = 1 - (2 * self.mass.value / r) GRR = (1 - (2 * self.mass.value / r)) ** (-1) KRKText = ((GTT / GRR) * (1 - (b ** 2 * GTT / (r ** 2)))) ** 0.5 Gred = ( (1 / GTT) + KRKText * (GRR / GTT) * ((1 - GTT) / (GTT * GRR)) ** 0.5 ) ** (-1) Ired = (Gred ** 3) * (GTT / (r ** 2)) * (1 / KRKText) return Ired def _intensity(self): """ Returns an array of the integrated values using ~scipy.integrate.quadrature as the intensities for the blue shifted and red shifted rays above the critical impact paratmeter from the distance to the emitter """ intensity = [] for i in np.arange(len(self.z)): b = self.z[i][0] val1, _ = fixed_quad( self._intensity_blue_sch, self.fov.value, self.z[i][1], args=(b,) ) val2, _ = fixed_quad( self._intensity_red_sch, self.z[i][1], self.fov.value, args=(b,) ) intensity.append(val1 + val2) return intensity def _intensity_from_event_horizon(self): """ Returns an array of the integrated values using ~scipy.integrate.quadrature as the intensities for the blue shifted and red shifted rays below the critical impact paratmeter from the event horizon to the distance given. """ self.b2 = np.linspace(self.limit, self.b_crit.value, len(self.bfin)) k1 = list() for i in self.b2: arg = i val3, _ = fixed_quad( self._intensity_red_sch, self.horizon, self.fov.value, args=(arg,) ) k1.append(val3) return k1 def smoothen(self, points=500): """ Sets the interpolated values for the intensities for smoothening of the plot using ~scipy.interpolate.interp1d """ b_new = np.linspace(np.min(self.fb1), np.max(self.fb1), points) interpolation = interp1d(self.fb1, self.intensity, kind="cubic") smoothened = interpolation(b_new) self.intensity = smoothened self.fb1 = b_new self.fb2 = -1 * b_new ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/symbolic/0000755000175000017500000000000000000000000021657 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/__init__.py0000644000175000017500000000102400000000000023765 0ustar00shreyasshreyas00000000000000from .christoffel import ChristoffelSymbols from .constants import SymbolicConstant, get_constant from .einstein import EinsteinTensor from .helpers import TransformationMatrix, simplify_sympy_array from .metric import MetricTensor from .ricci import RicciScalar, RicciTensor from .riemann import RiemannCurvatureTensor from .schouten import SchoutenTensor from .stress_energy_momentum import StressEnergyMomentumTensor from .tensor import BaseRelativityTensor, Tensor from .vector import GenericVector from .weyl import WeylTensor ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/christoffel.py0000644000175000017500000001205000000000000024537 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class ChristoffelSymbols(BaseRelativityTensor): """ Class for defining christoffel symbols. """ def __init__( self, arr, syms, config="ull", parent_metric=None, name="ChristoffelSymbols" ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'ull'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor Metric Tensor from which Christoffel symbol is calculated. Defaults to None. name : str Name of the Christoffel Symbols Tensor. Defaults to "ChristoffelSymbols". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 3 indices """ super(ChristoffelSymbols, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 3 if not len(self.config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_metric(cls, metric): """ Get Christoffel symbols calculated from a metric tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Space-time Metric from which Christoffel Symbols are to be calculated """ dims = metric.dims tmplist = np.zeros((dims, dims, dims), dtype=int).tolist() mat, syms = metric.lower_config().tensor(), metric.symbols() matinv = sympy.Matrix(mat.tolist()).inv() for t in range(dims ** 3): # i,j,k each goes from 0 to (dims-1) # hack for codeclimate. Could be done with 3 nested for loops k = t % dims j = (int(t / dims)) % (dims) i = (int(t / (dims ** 2))) % (dims) if k <= j: tmpvar = 0 for n in range(dims): tmpvar += (matinv[i, n] / 2) * ( sympy.diff(mat[n, j], syms[k]) + sympy.diff(mat[n, k], syms[j]) - sympy.diff(mat[j, k], syms[n]) ) tmplist[i][j][k] = tmplist[i][k][j] = tmpvar return cls(tmplist, syms, config="ull", parent_metric=metric) def change_config(self, newconfig="lll", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'lll' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if not initialized with 'from_metric'. Defaults to None. Returns ------- ~einsteinpy.symbolic.christoffel.ChristoffelSymbols New tensor with new configuration. Defaults to 'lll' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = ChristoffelSymbols( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.christoffel.ChristoffelSymbols lorentz transformed tensor """ t = super(ChristoffelSymbols, self).lorentz_transform(transformation_matrix) return ChristoffelSymbols( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/constants.py0000644000175000017500000000312500000000000024246 0ustar00shreyasshreyas00000000000000from sympy.core.symbol import Symbol class SymbolicConstant(Symbol): """ This class inherits from ~sympy.core.symbol.Symbol """ def __new__(cls, name, descriptive_name=None, **assumptions): """ Constructor and Initializer Parameters ---------- name : str Short, commonly accepted name of the constant. For example, 'c' for Speed of light. descriptive_name : str The extended name of the constant. For example, 'Speed of Light' for 'c'. Defaults to None. """ instance = super(SymbolicConstant, cls).__new__(cls, name, **assumptions) instance._descriptive_name = descriptive_name return instance @property def descriptive_name(self): """ Returns the extended name of the constant """ return self._descriptive_name c = SymbolicConstant("c", "Speed Of Light") G = SymbolicConstant("G", "Gravitational Constant") Cosmo_Const = SymbolicConstant("Lambda", "Cosmological Constant") eps_0 = SymbolicConstant("eps_0", "Permittivity of free space") def get_constant(name): """ Returns a symbolic instance of the constant Parameters ---------- name : str Name of the constant. Currently available names are 'c', 'G', 'Cosmo_Const', 'eps_0'. Returns ------- ~einsteinpy.symbolic.constants.SymbolicConstant An instance of the required constant """ const_dict = {"c": c, "G": G, "Cosmo_Const": Cosmo_Const, "eps_0": eps_0} return const_dict[name] ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/einstein.py0000644000175000017500000001032600000000000024051 0ustar00shreyasshreyas00000000000000import sympy from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.ricci import RicciScalar, RicciTensor from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class EinsteinTensor(BaseRelativityTensor): """ Class for defining Einstein Tensor """ def __init__( self, arr, syms, config="ll", parent_metric=None, name="EinsteinTensor" ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Einstein Tensor. Defaults to None. name : str Name of the Tensor. Defaults to "EinsteinTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 2 indices """ super(EinsteinTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 2 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_metric(cls, metric): t_ricci = RicciTensor.from_metric(metric) r_scalar = RicciScalar.from_riccitensor(t_ricci, t_ricci.parent_metric) einstein_tensor = ( t_ricci.tensor() - (1 / 2) * metric.lower_config().tensor() * r_scalar.expr ) return cls( einstein_tensor, metric.syms, config="ll", parent_metric=t_ricci.parent_metric, ) def change_config(self, newconfig="ul", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'ul' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if somehow does not have a parent metric. Defaults to None. Returns ------- ~einsteinpy.symbolic.einstein.EinsteinTensor New tensor with new configuration. Defaults to 'ul' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = EinsteinTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.einstein.EinsteinTensor lorentz transformed tensor """ t = super(EinsteinTensor, self).lorentz_transform(transformation_matrix) return EinsteinTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/helpers.py0000644000175000017500000001333300000000000023676 0ustar00shreyasshreyas00000000000000import warnings import numpy as np import sympy from sympy import ImmutableDenseNDimArray, derive_by_array def raise_warning(WarningType, message): warnings.warn(message, WarningType) def _flatten_list(seq): # flatten an arbitarily nested list if not seq: return [] if not isinstance(seq[0], list): return [seq[0]] + _flatten_list(seq[1:]) return _flatten_list(seq[0]) + _flatten_list(seq[1:]) def simplify_sympy_array(arr): """ Function to simplify sympy expression or array. This function is explicitely defined as native ``simplify`` function within sympy stopped working with sympy version change. Parameters ---------- arr : ~sympy.tensor.array.ndim_array.NDimArray or ~sympy.core.expr.Expr Any sympy array or expression. Returns ------- sympy.tensor.array.ndim_array.NDimArray or ~sympy.core.expr.Expr Simplified sympy array or expression. """ try: flattened_list = _flatten_list(arr.tolist()) simplified_flattened_list = [sympy.simplify(e) for e in flattened_list] return sympy.Array(simplified_flattened_list, arr.shape) except AttributeError: return sympy.simplify(arr) except IndexError: return sympy.Array(sympy.simplify(sum(arr))) def sympy_to_np_array(arr): """ Function to convert sympy to numpy array Parameters ---------- arr : ~sympy.tensor.array.ndim_array.NDimArray Sympy Array Returns ------- ~numpy.ndarray Numpy Array """ return np.array(arr.tolist()).reshape(arr.shape) class TransformationMatrix(ImmutableDenseNDimArray): """ Class for defining transformation matrix for basis change of vectors and tensors. """ def __init__( self, iterable, old_coords, new_coords, shape=None, old2new=None, new2old=None, **kwargs ): """ Constructor. Parameters ---------- iterable : iterable-object 2D list or array to pass a matrix. old_coords : list or tuple list of old coordinates. For example, ``[x, y]``. new_coords : list or tuple list of new coordinates. For example, ``[r, theta]``. shape : tuple, optional shape of the transformation matrix. Usually, not required. Defaults to ``None``. old2new : list or tuple, optional List of expressions for new coordinates in terms of old coordinates. For example, ``[x**2+y**2, atan2(y, x)]``. new2old : list or tuple, optional List of expressions for old coordinates in terms of new coordinates. For example, ``[r*cos(theta), r*sin(theta)]``. Raises ------ ValueError Raised when tensor has a rank not equal to 2. This is because, a matrix is expected. """ # __new__() is called after __init__() automatically self._inv = None self.old_coords, self.new_coords = old_coords, new_coords self.old2new, self.new2old = old2new, new2old def __new__( cls, iterable, old_coords, new_coords, shape=None, old2new=None, new2old=None, **kwargs ): obj = super(TransformationMatrix, cls).__new__(cls, iterable, shape, **kwargs) if not obj.rank() == 2: raise ValueError("Expected a tensor with rank 2") return obj @classmethod def from_new2old(cls, old_coords, new_coords, new2old, **kwargs): """ Classmethod to obtain transformation matrix from old coordinates expressed as a function of new coordinates. Parameters ---------- old_coords : list or tuple list of old coordinates. For example, ``[x, y]``. new_coords : list or tuple list of new coordinates. For example, ``[r, theta]``. new2old : list or tuple, optional List of expressions for old coordinates in terms of new coordinates. For example, ``[r*cos(theta), r*sin(theta)]``. """ tmp_array = derive_by_array(new2old, new_coords) tmp_array = sympy_to_np_array(tmp_array) derivative_array = np.reciprocal(tmp_array) return cls( derivative_array, old_coords, new_coords, old2new=None, new2old=new2old, **kwargs ) @classmethod def from_old2new(cls, old_coords, new_coords, old2new=None, new2old=None, **kwrags): raise NotImplementedError def inv(self): """ Returns inverse of the transformation matrix Returns ------- ~sympy.tensor.array.ndim_array.NDimArray Inverse of the matrix. """ if self._inv is not None: return self._inv tmp_array = sympy_to_np_array(self) tmp_array = np.reciprocal(tmp_array) self._inv = ImmutableDenseNDimArray(tmp_array) return self._inv def _change_name(curr_name: str, context: str) -> str: """ Function to add descriptive tags to Tensor name, after the tensor is modified. Currently handles Lorentz Transformation and Config Changes. Parameters ---------- curr_name : str Current name of the tensor context : str Context of name change - '__lt', for lorentz_transformation - '__' + newconfig, for config_change (cc) Returns ------- str Altered name of the tensor, with appropriate tags """ return curr_name + context if (curr_name is not None) else None ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/metric.py0000644000175000017500000001046500000000000023522 0ustar00shreyasshreyas00000000000000import sympy from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.tensor import BaseRelativityTensor class MetricTensor(BaseRelativityTensor): """ Class to define a metric tensor for a space-time """ def __init__(self, arr, syms, config="ll", name="GenericMetricTensor"): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. name : str Name of the Metric Tensor. Defaults to "GenericMetricTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 2 indices """ super(MetricTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=self, name=name ) self._order = 2 self._invmetric = None if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) def change_config(self, newconfig="uu"): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'uu' Returns ------- ~einsteinpy.symbolic.metric.MetricTensor New Metric with new configuration. Defaults to 'uu' Raises ------ ValueError Raised when new configuration is not 'll' or 'uu'. This constraint is in place because we are dealing with Metric Tensor. """ if newconfig == self.config: return self if newconfig == "uu" or newconfig == "ll": inv_met = MetricTensor( sympy.simplify(sympy.Matrix(self.arr.tolist()).inv()).tolist(), self.syms, config=newconfig, name=_change_name(self.name, context="__" + newconfig), ) inv_met._invmetric = self return inv_met raise ValueError( "Configuration can't have one upper and one lower index in Metric Tensor." ) def inv(self): """ Returns the inverse of the Metric. Returns contravariant Metric if it is originally covariant or vice-versa. Returns ------- ~einsteinpy.symbolic.metric.MetricTensor New Metric which is the inverse of original Metric. """ if self._invmetric is None: if self.config == "ll": self._invmetric = self.change_config("uu") else: self._invmetric = self.change_config("ll") return self._invmetric def lower_config(self): """ Returns a covariant instance of the given metric tensor. Returns ------- ~einsteinpy.symbolic.metric.MetricTensor same instance if the configuration is already lower or inverse of given metric if configuration is upper """ if self.config == "ll": return self return self.inv() def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.metric.MetricTensor lorentz transformed tensor """ t = super(MetricTensor, self).lorentz_transform(transformation_matrix) return MetricTensor( t.tensor(), syms=self.syms, config=self._config, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/0000755000175000017500000000000000000000000023764 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/__init__.py0000644000175000017500000000105600000000000026077 0ustar00shreyasshreyas00000000000000from .barriola_vilenkin import BarriolaVilekin from .bertotti_kasner import BertottiKasner from .bessel_gravitational_wave import BesselGravitationalWave from .cmetric import CMetric from .davidson import Davidson from .de_sitter import AntiDeSitter, AntiDeSitterStatic, DeSitter from .ernst import Ernst from .find import find from .godel import Godel from .janis_newman_winicour import JanisNewmanWinicour from .minkowski import Minkowski, MinkowskiCartesian, MinkowskiPolar from .vacuum_solutions import Kerr, KerrNewman, ReissnerNordstorm, Schwarzschild ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/barriola_vilenkin.py0000644000175000017500000000162000000000000030027 0ustar00shreyasshreyas00000000000000from sympy import diag, sin, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def BarriolaVilekin(c=constants.c, k=symbols("k")): """ Barriola-Vilekin monopol metric Phys. Rev. Lett. 63, 341 Manuel Barriola and Alexander Vilenkin Published 24 July 1989 Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to 'c'. k : ~sympy.core.basic.Basic or int or float The scaling factor responsible for the deficit/surplus angle Defaults to ``k``. """ coords = symbols("t r theta phi") t, r, th, ph = coords # define the metric metric = diag( -1, 1 / (c ** 2), ((k * r) ** 2) / (c ** 2), ((k * r * sin(th)) ** 2) / (c ** 2) ).tolist() return MetricTensor(metric, coords, "ll", name="BarriolaVilekinMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/bertotti_kasner.py0000644000175000017500000000171000000000000027534 0ustar00shreyasshreyas00000000000000from sympy import diag, exp, sin, sqrt, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def BertottiKasner(c=constants.c, k=symbols("k"), lambd=symbols("l")): """ Birkhoff’s theorem with Λ-term and Bertotti-Kasner space Phys. Lett. A, 245:363–365, 1998 W. Rindler Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to 'c'. lambd : ~sympy.core.basic.Basic or int or float The cosmological constant, note it must be postive. Defaults to ``l``. """ coords = symbols("t r theta phi") t, r, th, ph = coords # define the metric metric = diag( -1, exp(2 * sqrt(lambd) * c * t) / (c ** 2), 1 / (lambd * (c ** 2)), (sin(th) ** 2) / (lambd * (c ** 2)), ).tolist() return MetricTensor(metric, coords, "ll", name="BertottiKasnerMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/bessel_gravitational_wave.py0000644000175000017500000000315400000000000031564 0ustar00shreyasshreyas00000000000000from sympy import Function, Symbol, besselj, cos, diag, exp, sin, sqrt, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def BesselGravitationalWave(C=symbols("C")): """ Exact gravitational wave solution without diffraction. Class. Quantum Grav., 16:L75–78, 1999. D. Kramer. An exact solution describing an axisymmetric gravitational wave propagating in the z-direction in closed form. This solution to Einstein’s vacuum field equations has the remarkable property that the curvature invariants decrease monotonically with increasing radial distance from the axis and vanish at infinity. The solution is regular at the symmetry axis. Parameters ---------- C : ~sympy.core.basic.Basic or int or float Constant for Bessel metric, the choice of the constant is not really relavent for details see the paper. Defaults to 'C'. """ coords = symbols("t rho phi z") t, rho, ph, z = coords # Useful helper functions, these wrap the Bessel functions that are used. C is some constant here U = C * besselj(rho, 0) * cos(t) K = ( (1 / 2) * (C ** 2) * rho * ( (rho * ((besselj(rho, 0) ** 2) + (besselj(rho, 1) ** 2))) - (2 * besselj(rho, 0) * besselj(rho, 1) * (cos(t) ** 2)) ) ) # define the metric metric = diag( -1 * exp(-2 * U) * exp(2 * K), exp(-2 * U) * exp(2 * K), exp(-2 * U) * (rho ** 2), exp(2 * U), ).tolist() return MetricTensor(metric, coords, "ll", name="BesselGravitationalWaveMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/cmetric.py0000644000175000017500000000076600000000000025775 0ustar00shreyasshreyas00000000000000from sympy import Function, diag, symbols from einsteinpy.symbolic.metric import MetricTensor def CMetric(): """ The C-metric Stephani (Table 16.2) p188 """ coords = symbols("t x y phi") x, y = coords[1], coords[2] f, h = Function("f")(x), Function("h")(y) metric = diag( -h / (x + y) ** 2, 1 / ((x + y) ** 2 * f), 1 / ((x + y) ** 2 * h), f / (x + y) ** 2, ).tolist() return MetricTensor(metric, coords, "ll", name="CMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/davidson.py0000644000175000017500000000112300000000000026142 0ustar00shreyasshreyas00000000000000from sympy import Rational, diag, symbols from einsteinpy.symbolic.metric import MetricTensor def Davidson(): """ Davidson's cylindrically symmetric radiation perfect fluid universe Davidson, J. Math. Phys., v32, p1560, (1991) """ coords = symbols("t r z phi") t, r, z, phi = coords expr = (1 + r ** 2) ** Rational(2, 5) metric = diag( -(expr ** 3), t ** Rational(4, 3) * expr, t ** Rational(-2, 3) / expr, t ** Rational(4, 3) * r ** 2 / expr, ).tolist() return MetricTensor(metric, coords, "ll", name="DavidsonMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/de_sitter.py0000644000175000017500000000221400000000000026317 0ustar00shreyasshreyas00000000000000from sympy import cos, cosh, diag, exp, sin, sinh, symbols from einsteinpy.symbolic.metric import MetricTensor def AntiDeSitter(): """ Anti-de Sitter space Hawking and Ellis (5.9) p131 """ coords = symbols("t chi theta phi") t, ch, th, ph = coords metric = diag( -1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2, ).tolist() return MetricTensor(metric, coords, "ll", name="AntiDeSitterMetric") def AntiDeSitterStatic(): """ Static form of Anti-de Sitter space Hawking and Ellis (5.9) p131 """ coords = symbols("t r theta phi") t, r, th, ph = coords metric = diag(-cosh(r) ** 2, 1, sinh(r) ** 2, sinh(r) ** 2 * sin(th) ** 2).tolist() return MetricTensor(metric, coords, "ll", name="AntiDeSitterStaticMetric") def DeSitter(): """ de Sitter space Hawking and Ellis p125 """ coords = symbols("t x y z") t = coords[1] al = symbols("alpha") expr = exp(2 * t / al) metric = diag(-1, expr, expr, expr).tolist() return MetricTensor(metric, coords, "ll", name="DeSitterMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/ernst.py0000644000175000017500000000166700000000000025503 0ustar00shreyasshreyas00000000000000from sympy import diag, exp, sin, sqrt, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def Ernst(B=symbols("B"), M=symbols("M")): """ Black holes in a magnetic universe. J. Math. Phys., 17:54–56, 1976. Frederick J. Ernst. Parameters ---------- M : ~sympy.core.basic.Basic or int or float Mass of the black hole. Defaults to ``M``. B : ~sympy.core.basic.Basic or int or float The magnetic field strength Defaults to ``B``. """ coords = symbols("t r theta phi") t, r, th, ph = coords # Helper functions lambd = 1 + ((B * r * sin(th)) ** 2) w = 1 - ((2 * M) / r) # define the metric metric = diag( -1 * (lambd ** 2) * w, (lambd ** 2) / w, ((r * lambd) ** 2), (((r * sin(th)) / lambd) ** 2), ).tolist() return MetricTensor(metric, coords, "ll", name="ErnstMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/find.py0000644000175000017500000000114400000000000025256 0ustar00shreyasshreyas00000000000000import importlib def find(search_string): """ Performs a find operation on available functions. Parameters ---------- search_string : str Name of the function to be searched. Returns ------- list A list of available functions related to ``search_string``. """ search_string = search_string.lower() current_module = "einsteinpy.symbolic.predefined" predefined = importlib.import_module(current_module) return [ fname for fname in dir(predefined) if ((search_string in fname.lower()) and (not fname.islower())) ] ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/godel.py0000644000175000017500000000104500000000000025430 0ustar00shreyasshreyas00000000000000from sympy import Rational, diag, exp, sqrt, symbols from einsteinpy.symbolic.metric import MetricTensor def Godel(): """ Godel metric Rev. Mod. Phys., v21, p447, (1949) Stephani (10.25) 122 """ coords = symbols("t x y z") om = symbols("omega") t, x, y, z = coords # define the metric metric = diag(-1, 1, -Rational(1, 2) * exp(2 * sqrt(2) * om * x), 1) metric[0, 2] = metric[2, 0] = -exp(sqrt(2) * om * x) metric = metric.tolist() return MetricTensor(metric, coords, "ll", name="GodelMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/janis_newman_winicour.py0000644000175000017500000000226400000000000030732 0ustar00shreyasshreyas00000000000000from sympy import diag, sin, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def JanisNewmanWinicour( c=constants.c, G=constants.G, gam=symbols("gam"), M=symbols("M") ): """ Reality of the Schwarzschild singularity. Phys. Rev. Lett., 20:878–880, 1968. A. I. Janis, E. T. Newman, and J. Winicour. Parameters ---------- M : ~sympy.core.basic.Basic or int or float Mass parameter, this is used for defining the schwarzschild metric. Defaults to ``M``. gam : ~sympy.core.basic.Basic or int or float Parameter for scaling Schwarzschild radius, for gamma=1 this will return the Schwarzschild metric Defaults to ``gam``. """ coords = symbols("t r theta phi") t, r, th, ph = coords # Helper functions r_s = (2 * G * M) / (c ** 2) alpha = 1 - (r_s / (gam * r)) # define the metric metric = diag( -1 * (alpha ** gam), (alpha ** -gam) / (c ** 2), (r ** 2) * (alpha ** (-gam + 1)), (r ** 2) * (alpha ** (-gam + 1)) * (sin(th) ** 2), ).tolist() return MetricTensor(metric, coords, "ll", name="JanisNewmanWinicourMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/minkowski.py0000644000175000017500000000223500000000000026353 0ustar00shreyasshreyas00000000000000from sympy import diag, sin, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def MinkowskiCartesian(c=constants.c): """ Minkowski(flat) space-time in Cartesian coordinates. Space-time without any curvature or matter. Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to 'c'. """ coords = symbols("t x y z") metric = diag(-1, 1 / (c ** 2), 1 / (c ** 2), 1 / (c ** 2)).tolist() return MetricTensor(metric, coords, "ll", name="MinkowskiMetric") Minkowski = MinkowskiCartesian def MinkowskiPolar(c=constants.c): """ Minkowski(flat) space-time in Polar coordinates. Space-time without any curvature or matter. Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to 'c'. """ coords = symbols("t r theta phi") t, r, th, ph = coords c2 = c ** 2 metric = diag(-1, 1 / c2, (r ** 2) / c2, (r ** 2 * sin(th) ** 2) / c2).tolist() return MetricTensor(metric, coords, "ll", name="MinkowskiMetricPolar") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/predefined/vacuum_solutions.py0000644000175000017500000001250700000000000027762 0ustar00shreyasshreyas00000000000000from sympy import cos, diag, pi, sin, symbols from einsteinpy.symbolic import constants from einsteinpy.symbolic.metric import MetricTensor def Schwarzschild(c=constants.c, sch=symbols("r_s")): """ Schwarzschild exterior metric in curvature coordinates Schwarzschild, Sitz. Preuss. Akad. Wiss., p189, (1916) Stephani (13.19) p157 Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to ``c``. sch : ~sympy.core.basic.Basic or int or float Any value to assign to Schwarzschild Radius of the central object. Defaults to ``r_s``. """ coords = symbols("t r theta phi") t, r, theta, phi = coords val1, c2 = 1 - sch / r, c ** 2 metric = diag( val1, -1 / (val1 * c2), -(r ** 2) / c2, -((r * sin(theta)) ** 2) / c2 ).tolist() return MetricTensor(metric, coords, "ll", name="SchwarzschildMetric") def Kerr(c=constants.c, sch=symbols("r_s"), a=symbols("a")): """ Kerr Metric in Boyer Lindquist coordinates. Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to ``c``. sch : ~sympy.core.basic.Basic or int or float Any value to assign to Schwarzschild Radius of the central object. Defaults to ``r_s``. a : ~sympy.core.basic.Basic or int or float Spin factor of the heavy body. Usually, given by ``J/(Mc)``, where ``J`` is the angular momentum. Defaults to ``a``. """ coords = symbols("t r theta phi") t, r, theta, phi = coords Sigma = r ** 2 + (a ** 2 * cos(theta) ** 2) Delta = r ** 2 - sch * r + a ** 2 c2 = c ** 2 metric = diag( 1 - (sch * r / Sigma), -Sigma / (Delta * c2), -Sigma / c2, -( (r ** 2 + a ** 2 + (sch * r * (a ** 2) * (sin(theta) ** 2) / Sigma)) * (sin(theta) ** 2) ) / c2, ).tolist() metric[0][3] = metric[3][0] = sch * r * a * (sin(theta) ** 2) / (Sigma * c) return MetricTensor(metric, coords, "ll", name="KerrMetric") def KerrNewman( c=constants.c, G=constants.G, eps_0=constants.eps_0, sch=symbols("r_s"), a=symbols("a"), Q=symbols("Q"), ): """ Kerr-Newman Metric in Boyer Lindquist coordinates. Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to ``c``. G : ~sympy.core.basic.Basic or int or float Any value to assign to the Newton's (or gravitational) constant. Defaults to ``G``. eps_0 : ~sympy.core.basic.Basic or int or float Any value to assign to the electric constant or permittivity of free space. Defaults to ``eps_0``. sch : ~sympy.core.basic.Basic or int or float Any value to assign to Schwarzschild Radius of the central object. Defaults to ``r_s``. a : ~sympy.core.basic.Basic or int or float Spin factor of the heavy body. Usually, given by ``J/(Mc)``, where ``J`` is the angular momentum. Defaults to ``a``. Q: ~sympy.core.basic.Basic or int or float Any value to assign to eletric charge of the central object. Defaults to ``Q``. """ coords = symbols("t r theta phi") t, r, theta, phi = coords Sigma = r ** 2 + (a ** 2 * cos(theta) ** 2) rQsq = ((Q ** 2) * G) / (4 * pi * eps_0 * (c ** 4)) Delta = r ** 2 - sch * r + a ** 2 + rQsq c2 = c ** 2 metric = diag( 1 + ((rQsq - sch * r) / Sigma), -Sigma / (Delta * c2), -Sigma / c2, (Delta * a ** 2 * sin(theta) ** 2 - (r ** 2 + a ** 2) ** 2) * sin(theta) ** 2 / (Sigma * c2), ).tolist() metric[0][3] = metric[3][0] = (sch * r - rQsq) * a * (sin(theta) ** 2) / (Sigma * c) return MetricTensor(metric, coords, "ll", name="KerrNewmanMetric") def ReissnerNordstorm( c=constants.c, G=constants.G, eps_0=constants.eps_0, sch=symbols("r_s"), Q=symbols("Q"), ): """" The Reissner–Nordström metric in spherical coordinates A static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. Parameters ---------- c : ~sympy.core.basic.Basic or int or float Any value to assign to speed of light. Defaults to ``c``. G : ~sympy.core.basic.Basic or int or float Any value to assign to the Newton's (or gravitational) constant. Defaults to ``G``. eps_0 : ~sympy.core.basic.Basic or int or float Any value to assign to the electric constant or permittivity of free space. Defaults to ``eps_0``. sch : ~sympy.core.basic.Basic or int or float Any value to assign to Schwarzschild Radius of the central object. Defaults to ``r_s``. Q: ~sympy.core.basic.Basic or int or float Any value to assign to eletric charge of the central object. Defaults to ``Q``. """ coords = symbols("t r theta phi") t, r, theta, phi = coords rQsq = ((Q ** 2) * G) / (4 * pi * eps_0 * (c ** 4)) Arn = 1 - sch / r + rQsq / r ** 2 c2 = c ** 2 metric = diag( Arn, -1 / (Arn * c2), -(r ** 2) / c2, -(r ** 2) * sin(theta) ** 2 / c2 ).tolist() return MetricTensor(metric, coords, "ll", name="ReissnerNordstormMetric") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/ricci.py0000644000175000017500000002255400000000000023332 0ustar00shreyasshreyas00000000000000import sympy from sympy import tensorcontraction, tensorproduct from einsteinpy.symbolic.christoffel import ChristoffelSymbols from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.metric import MetricTensor from einsteinpy.symbolic.riemann import RiemannCurvatureTensor from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class RicciTensor(BaseRelativityTensor): """ Class for defining Ricci Tensor """ def __init__(self, arr, syms, config="ll", parent_metric=None, name="RicciTensor"): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Tensor. Defaults to None. name : str Name of the Tensor. Defaults to "RicciTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 2 indices """ super(RicciTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 2 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_riemann(cls, riemann, parent_metric=None): """ Get Ricci Tensor calculated from Riemann Tensor Parameters ---------- riemann : ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor Riemann Tensor parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Tensor. None if it should inherit the Parent Metric of Riemann Tensor. Defaults to None. """ if not riemann.config == "ulll": riemann = riemann.change_config(newconfig="ulll", metric=parent_metric) if parent_metric is None: parent_metric = riemann.parent_metric return cls( sympy.tensorcontraction(riemann.tensor(), (0, 2)), riemann.syms, config="ll", parent_metric=parent_metric, ) @classmethod def from_christoffels(cls, chris, parent_metric=None): """ Get Ricci Tensor calculated from Christoffel Tensor Parameters ---------- chris : ~einsteinpy.symbolic.christoffel.ChristoffelSymbols Christoffel Tensor parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Tensor. None if it should inherit the Parent Metric of Christoffel Symbols. Defaults to None. """ rt = RiemannCurvatureTensor.from_christoffels( chris, parent_metric=parent_metric ) return cls.from_riemann(rt) @classmethod def from_metric(cls, metric): """ Get Ricci Tensor calculated from Metric Tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Metric Tensor """ ch = ChristoffelSymbols.from_metric(metric) return cls.from_christoffels(ch, parent_metric=None) def change_config(self, newconfig="ul", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'ul' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if somehow does not have a parent metric. Defaults to None. Returns ------- ~einsteinpy.symbolic.ricci.RicciTensor New tensor with new configuration. Defaults to 'ul' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = RicciTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.ricci.RicciTensor lorentz transformed tensor """ t = super(RicciTensor, self).lorentz_transform(transformation_matrix) return RicciTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) class RicciScalar(BaseRelativityTensor): """ Class for defining Ricci Scalar """ def __init__(self, arr, syms, parent_metric=None): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array, multi-dimensional list containing Sympy Expressions, or Sympy Expressions or int or float scalar syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Scalar. Defaults to None. Raises ------ TypeError Raised when syms is not a list or tuple """ super(RicciScalar, self).__init__( arr=arr, syms=syms, config="", parent_metric=parent_metric, name="RicciScalar", ) self._order = 0 @property def expr(self): """ Retuns the symbolic expression of the Ricci Scalar """ val = sum(self.arr) # sympy not allowing indexing, temporary fix! return val @classmethod def from_riccitensor(cls, riccitensor, parent_metric=None): """ Get Ricci Scalar calculated from Ricci Tensor Parameters ---------- riccitensor: ~einsteinpy.symbolic.metric.RicciTensor Ricci Tensor parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Scalar. Defaults to None. """ if not riccitensor.config == "ul": riccitensor = riccitensor.change_config( newconfig="ul", metric=parent_metric ) if parent_metric is None: parent_metric = riccitensor.parent_metric ricci_scalar = tensorcontraction(riccitensor.tensor(), (0, 1)) return cls(ricci_scalar, riccitensor.syms, parent_metric=parent_metric) @classmethod def from_riemann(cls, riemann, parent_metric=None): """ Get Ricci Scalar calculated from Riemann Tensor Parameters ---------- riemann : ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor Riemann Tensor parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Scalar. Defaults to None. """ cg = RicciTensor.from_riemann(riemann, parent_metric=parent_metric) return cls.from_riccitensor(cg) @classmethod def from_christoffels(cls, chris, parent_metric=None): """ Get Ricci Scalar calculated from Christoffel Tensor Parameters ---------- chris : ~einsteinpy.symbolic.christoffel.ChristoffelSymbols Christoffel Tensor parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Ricci Scalar. Defaults to None. """ rt = RiemannCurvatureTensor.from_christoffels( chris, parent_metric=parent_metric ) return cls.from_riemann(rt) @classmethod def from_metric(cls, metric): """ Get Ricci Scalar calculated from Metric Tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Metric Tensor """ ch = ChristoffelSymbols.from_metric(metric) return cls.from_christoffels(ch, parent_metric=None) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/riemann.py0000644000175000017500000001366100000000000023671 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from einsteinpy.symbolic.christoffel import ChristoffelSymbols from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class RiemannCurvatureTensor(BaseRelativityTensor): """ Class for defining Riemann Curvature Tensor """ def __init__( self, arr, syms, config="ulll", parent_metric=None, name="RiemannCurvatureTensor", ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'ulll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor Metric Tensor related to this Riemann Curvature Tensor. name : str Name of the Tensor. Defaults to "RiemannCurvatureTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 4 indices """ super(RiemannCurvatureTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 4 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_christoffels(cls, chris, parent_metric=None): """ Get Riemann Tensor calculated from a Christoffel Symbols Parameters ---------- chris : ~einsteinpy.symbolic.christoffel.ChristoffelSymbols Christoffel Symbols from which Riemann Curvature Tensor to be calculated parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Riemann Tensor. None if it should inherit the Parent Metric of Christoffel Symbols. Defaults to None. """ if not chris.config == "ull": chris = chris.change_config(newconfig="ull", metric=parent_metric) arr, syms = chris.tensor(), chris.symbols() dims = len(syms) riemann_list = (np.zeros(shape=(dims, dims, dims, dims), dtype=int)).tolist() for i in range(dims ** 4): # t,s,r,n each goes from 0 to (dims-1) # hack for codeclimate. Could be done with 4 nested for loops n = i % dims r = (int(i / dims)) % (dims) s = (int(i / (dims ** 2))) % (dims) t = (int(i / (dims ** 3))) % (dims) temp = sympy.diff(arr[t, s, n], syms[r]) - sympy.diff(arr[t, r, n], syms[s]) for p in range(dims): temp += arr[p, s, n] * arr[t, p, r] - arr[p, r, n] * arr[t, p, s] riemann_list[t][s][r][n] = sympy.simplify(temp) if parent_metric is None: parent_metric = chris.parent_metric return cls(riemann_list, syms, config="ulll", parent_metric=parent_metric) @classmethod def from_metric(cls, metric): """ Get Riemann Tensor calculated from a Metric Tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Metric Tensor from which Riemann Curvature Tensor to be calculated """ ch = ChristoffelSymbols.from_metric(metric) return cls.from_christoffels(ch, parent_metric=None) def change_config(self, newconfig="llll", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'llll' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if not initialized with 'from_metric'. Defaults to None. Returns ------- ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor New tensor with new configuration. Configuration defaults to 'llll' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = RiemannCurvatureTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.riemann.RiemannCurvatureTensor lorentz transformed tensor """ t = super(RiemannCurvatureTensor, self).lorentz_transform(transformation_matrix) return RiemannCurvatureTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/schouten.py0000644000175000017500000001136300000000000024065 0ustar00shreyasshreyas00000000000000from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.ricci import RicciScalar, RicciTensor from einsteinpy.symbolic.riemann import RiemannCurvatureTensor from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class SchoutenTensor(BaseRelativityTensor): """ Class for defining Schouten Tensor """ def __init__( self, arr, syms, config="ll", parent_metric=None, name="SchoutenTensor" ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor Corresponding Metric for the Schouten Tensor. Defaults to None. name : str Name of the Tensor. Defaults to "SchoutenTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 2 indices """ super(SchoutenTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 2 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_metric(cls, metric): """ Get Schouten tensor calculated from a metric tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Space-time Metric from which Christoffel Symbols are to be calculated Raises ------ ValueError Raised when the dimension of the tensor is less than 3 """ if metric.dims >= 3: t_ricci = RicciTensor.from_metric(metric) r_scalar = RicciScalar.from_riccitensor(t_ricci, parent_metric=None) dims = metric.dims t_schouten = ( t_ricci.tensor() - (r_scalar.expr * metric.lower_config().tensor() / (2 * (dims - 1))) ) / (dims - 2) return cls(t_schouten, metric.syms, config="ll", parent_metric=metric) raise ValueError("Dimension of the space/space-time should be 3 or more") def change_config(self, newconfig="ul", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'ul' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if not initialized with 'from_metric'. Defaults to None. Returns ------- ~einsteinpy.symbolic.schouten.SchoutenTensor New tensor with new configuration. Configuration defaults to 'ul' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = SchoutenTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.schouten.SchoutenTensor lorentz transformed tensor """ t = super(SchoutenTensor, self).lorentz_transform(transformation_matrix) return SchoutenTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/stress_energy_momentum.py0000644000175000017500000001060200000000000027045 0ustar00shreyasshreyas00000000000000import numpy as np from einsteinpy.symbolic.constants import Cosmo_Const, G, c from einsteinpy.symbolic.einstein import EinsteinTensor from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class StressEnergyMomentumTensor(BaseRelativityTensor): """ Class for defining Stress-Energy Coefficient Tensor """ def __init__( self, arr, syms, config="ll", parent_metric=None, name="StressEnergyMomentumTensor", ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Stress-Energy Coefficient Tensor. Defaults to None. name : str Name of the Tensor. Defaults to "StressEnergyMomentumTensor". Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 2 indices """ super(StressEnergyMomentumTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 2 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_metric(cls, metric): t_einstein = EinsteinTensor.from_metric(metric) stress_tensor = ( c ** 4 / (8 * np.pi * G) * (t_einstein.tensor() - Cosmo_Const * metric.lower_config().tensor()) ) return cls(stress_tensor, metric.syms, config="ll", parent_metric=metric) def change_config(self, newconfig="ul", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'ul' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if somehow does not have a parent metric. Defaults to None. Returns ------- ~einsteinpy.symbolic.stress_energy_momentum.StressEnergyMomentumTensor New tensor with new configuration. Defaults to 'ul' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = EinsteinTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.stress_energy_momentum.StressEnergyMomentumTensor lorentz transformed tensor """ t = super(StressEnergyMomentumTensor, self).lorentz_transform( transformation_matrix ) return StressEnergyMomentumTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/tensor.py0000644000175000017500000003240200000000000023544 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import simplify, tensorcontraction, tensorproduct from sympy.core.expr import Expr from sympy.core.function import AppliedUndef, UndefinedFunction from einsteinpy.symbolic.helpers import ( _change_name, simplify_sympy_array, sympy_to_np_array, ) def _config_checker(config): # check if the string for config contains 'u' and 'l' only if not isinstance(config, str): return False for ch in config: if (not ch == "l") and (not ch == "u"): return False return True def _difference_list(newconfig, oldconfig): # defines a list of actions to be taken on a tensor difflist = list() for n_ch, o_ch in zip(newconfig, oldconfig): if n_ch == o_ch: difflist.append(0) elif n_ch == "u": difflist.append(1) else: difflist.append(-1) return difflist def _change_config(tensor, metric, newconfig): # check length and validity of new configuration if not (len(newconfig) == len(tensor.config) and _config_checker(newconfig)): raise ValueError # seperate the contravariant & covariant metric tensors met_dict = { -1: metric.lower_config().tensor(), 1: metric.lower_config().inv().tensor(), } # main code def chain_config_change(): t = sympy.Array(tensor.tensor()) difflist = _difference_list(newconfig, tensor.config) for i, action in enumerate(difflist): if action == 0: continue else: t = simplify( tensorcontraction(tensorproduct(met_dict[action], t), (1, 2 + i)) ) # reshuffle the indices dest = list(range(len(t.shape))) dest.remove(0) dest.insert(i, 0) t = sympy.permutedims(t, dest) return t return chain_config_change() class Tensor: """ Base Class for Tensor manipulation """ def __init__(self, arr, config="ll", name=None): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array, multi-dimensional list containing Sympy Expressions, or Sympy Expressions or int or float scalar config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. name : str or None Name of the tensor. Raises ------ TypeError Raised when arr is not a list or sympy array TypeError Raised when config is not of type str or contains characters other than 'l' or 'u' ValueError Raised when ``config`` implies order of Tensor different than that indicated by shape of ``arr`` """ if isinstance(arr, (list, tuple, np.ndarray, int, float, np.number, Expr)): self.arr = sympy.Array(arr) elif isinstance(arr, sympy.Array): self.arr = arr else: raise TypeError("Only multi-dimensional list or Sympy Array is expected") if _config_checker(config): self._config = config self._order = len(config) else: raise TypeError( "config is either not of type 'str' or does contain characters other than 'l' or 'u'" ) if len(self.arr.shape) != len(config): raise ValueError( "invalid shape of array for tensor of order implied by config: '{}'".format( config ) ) self.name = name @property def order(self): """ Returns the order of the Tensor """ return self._order @property def config(self): """ Returns the configuration of covariant and contravariant indices """ return self._config def __getitem__(self, index): return self.arr[index] def __str__(self): """ Returns a String with a readable representation of the object of class Tensor """ representation = "Tensor" if self.name is not None: representation = " ".join((representation, self.name)) representation += "\n" representation += self.arr.__str__() return representation def __repr__(self): """ Returns a String with a representation of the state of the object of class Tensor """ interpretable_representation = self.__class__.__name__ interpretable_representation += self.arr.__repr__() return interpretable_representation def tensor(self): """ Returns the sympy Array Returns ------- ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray Sympy Array object """ return self.arr def subs(self, *args): """ Substitute the variables/expressions in a Tensor with other sympy variables/expressions. Parameters ---------- args : one argument or two argument - two arguments, e.g foo.subs(old, new) - one iterable argument, e.g foo.subs([(old1, new1), (old2, new2)]) for multiple substitutions at once. Returns ------- ~einsteinpy.symbolic.tensor.Tensor: Tensor with substituted values """ return Tensor(self.tensor().subs(*args)) def simplify(self, set_self=True): """ Returns a simplified Tensor Parameters ---------- set_self : bool Replaces the tensor contained the class with its simplified version, if ``True``. Defaults to ``True``. Returns ------- ~einsteinpy.symbolic.tensor.Tensor Simplified Tensor """ if set_self: self.arr = simplify_sympy_array(self.tensor()) return self.tensor() # return sympy.simplify(self.tensor()) # this used to work with older sympy versions return simplify_sympy_array(self.tensor()) class BaseRelativityTensor(Tensor): """ Generic class for defining tensors in General Relativity. This would act as a base class for other Tensorial quantities in GR. Attributes ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray Raw Tensor in sympy array syms : list or tuple List of symbols denoting space and time axis dims : int dimension of the space-time. variables : list free variables in the tensor expression other than the variables describing space-time axis. functions : list Undefined functions in the tensor expression. name : str or None Name of the tensor. Defaults to "GenericTensor". """ def __init__( self, arr, syms, config="ll", parent_metric=None, variables=list(), functions=list(), name="GenericTensor", ): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list List of crucial symbols dentoting time-axis and/or spacial axis. For example, in case of 4D space-time, the arrangement would look like [t, x1, x2, x3]. config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'll'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Metric Tensor for some particular space-time which is associated with this Tensor. variables : tuple or list or set List of symbols used in expressing the tensor other than symbols associated with denoting the space-time axis. Calculates in real-time if left blank. functions : tuple or list or set List of symbolic functions used in epressing the tensor. Calculates in real-time if left blank. name : str or None Name of the Tensor. Defaults to "GenericTensor". Raises ------ TypeError Raised when arr is not a list, sympy array or numpy array. TypeError Raised when config is not of type str or contains characters other than 'l' or 'u' TypeError Raised when arguments syms, variables, functions have data type other than list, tuple or set. TypeError Raised when argument parent_metric does not belong to MetricTensor class and isn't None. ValueError Raised when argument ``syms`` does not agree with shape of argument ``arr`` """ super(BaseRelativityTensor, self).__init__(arr=arr, config=config, name=name) if len(self.arr.shape) != 0 and self.arr.shape[0] != len(syms): raise ValueError("invalid shape of argument arr for syms: {}".format(syms)) # Cannot implement the check that parent metric belongs to the class MetricTensor # Due to the issue of cyclic imports, would find a workaround self._parent_metric = parent_metric if isinstance(syms, (list, tuple)): self.syms = syms self.dims = len(self.syms) else: raise TypeError("syms should be a list or tuple") if isinstance(variables, (list, tuple, set)) and isinstance( functions, (list, tuple, set) ): # compute free variables and functions if list if empty if not variables: self.variables = [ v for v in self.arr.free_symbols if v not in self.syms ] self.variables.sort(key=(lambda var: var.name)) else: self.variables = list(variables) if not functions: self.functions = [ f for f in self.arr.atoms(AppliedUndef).union( self.arr.atoms(UndefinedFunction) ) ] else: self.functions = list(functions) else: raise TypeError( "arguments variables and functions should be a list, tuple or set" ) @property def parent_metric(self): """ Returns the Metric from which Tensor was derived/associated, if available. """ return self._parent_metric def symbols(self): """ Returns the symbols used for defining the time & spacial axis Returns ------- tuple tuple containing (t,x1,x2,x3) in case of 4D space-time """ return self.syms def tensor_lambdify(self, *args): """ Returns lambdified function of symbolic tensors. This means that the returned functions can accept numerical values and return numerical quantities. Parameters ---------- *args The variable number of arguments accept sympy symbols. The returned function accepts arguments in same order as initially defined in ``*args``. Uses sympy symbols from class attributes ``syms`` and ``variables`` (in the same order) if no ``*args`` is passed Leaving ``*args`` empty is recommended. Returns ------- tuple arguments to be passed in the returned function in exact order. function Lambdified function which accepts and returns numerical quantities. """ if len(args) == 0: numeric_arr = sympy.lambdify([*self.syms, *self.variables], self.arr, np) arg_list = (*self.syms, *self.variables) else: numeric_arr = sympy.lambdify(args, self.arr, np) arg_list = tuple(args) return arg_list, numeric_arr def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.tensor.BaseRelativityTensor lorentz transformed tensor(or vector) """ tm = sympy.Array(transformation_matrix) t = self.tensor() for i in range(self.order): if self.config[i] == "u": t = simplify(tensorcontraction(tensorproduct(tm, t), (1, 2 + i))) else: t = simplify(tensorcontraction(tensorproduct(tm, t), (0, 2 + i))) dest = list(range(len(t.shape))) dest.remove(0) dest.insert(i, 0) t = sympy.permutedims(t, dest) return BaseRelativityTensor( t, syms=self.syms, config=self.config, parent_metric=None, variables=self.variables, functions=self.functions, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/vector.py0000644000175000017500000000716700000000000023546 0ustar00shreyasshreyas00000000000000from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class GenericVector(BaseRelativityTensor): """ Class to represent a vector in arbitrary space-time symbolically """ def __init__(self, arr, syms, config="u", parent_metric=None, name="GenericVector"): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray Sympy Array containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'u'. parent_metric : ~einsteinpy.symbolic.metric.MetricTensor or None Corresponding Metric for the Generic Vector. Defaults to None. name : str Name of the Vector. Defaults to "GenericVector". Raises ------ ValueError config has more than 1 index ValueError Dimension should be equal to 1 """ super(GenericVector, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) if self.arr.rank() == 1: self._order = 1 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) else: raise ValueError("Dimension should be equal to 1") def change_config(self, newconfig="u", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'u' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Defaults to None. Returns ------- ~einsteinpy.symbolic.vector.GenericVector New tensor with new configuration. Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = GenericVector( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the vector. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.vector.GenericVector lorentz transformed vector """ t = super(GenericVector, self).lorentz_transform(transformation_matrix) return GenericVector( t.tensor(), syms=self.syms, config=self.config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/symbolic/weyl.py0000644000175000017500000001415600000000000023220 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from einsteinpy.symbolic.helpers import _change_name from einsteinpy.symbolic.ricci import RicciScalar, RicciTensor from einsteinpy.symbolic.riemann import RiemannCurvatureTensor from einsteinpy.symbolic.tensor import BaseRelativityTensor, _change_config class WeylTensor(BaseRelativityTensor): """ Class for defining Weyl Tensor """ def __init__(self, arr, syms, config="ulll", parent_metric=None, name="WeylTensor"): """ Constructor and Initializer Parameters ---------- arr : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions syms : tuple or list Tuple of crucial symbols denoting time-axis, 1st, 2nd, and 3rd axis (t,x1,x2,x3) config : str Configuration of contravariant and covariant indices in tensor. 'u' for upper and 'l' for lower indices. Defaults to 'ulll'. parent_metric : ~einsteinpy.symbolic.metric.WeylTensor Corresponding Metric for the Weyl Tensor. Defaults to None. name : str Name of the Tensor. Defaults to "WeylTensor" Raises ------ TypeError Raised when arr is not a list or sympy Array TypeError syms is not a list or tuple ValueError config has more or less than 4 indices """ super(WeylTensor, self).__init__( arr=arr, syms=syms, config=config, parent_metric=parent_metric, name=name ) self._order = 4 if not len(config) == self._order: raise ValueError("config should be of length {}".format(self._order)) @classmethod def from_metric(cls, metric): """ Get Weyl tensor calculated from a metric tensor Parameters ---------- metric : ~einsteinpy.symbolic.metric.MetricTensor Space-time Metric from which Christoffel Symbols are to be calculated Raises ------ ValueError Raised when the dimension of the tensor is less than 3 """ if metric.dims > 3: metric_cov = metric.lower_config() t_riemann = RiemannCurvatureTensor.from_metric(metric) # Riemann Tensor with covariant indices is needed t_riemann_cov = t_riemann.change_config("llll", metric=None) t_ricci = RicciTensor.from_riemann(t_riemann, parent_metric=None) r_scalar = RicciScalar.from_riccitensor(t_ricci, parent_metric=None) g = metric_cov dims = g.dims # Indexing for resultant Weyl Tensor is iklm C = np.zeros(shape=(dims, dims, dims, dims), dtype=int).tolist() for t in range(dims ** 4): i, k, l, m = ( t % dims, (int(t / dims)) % (dims), (int(t / (dims ** 2))) % (dims), (int(t / (dims ** 3))) % (dims), ) C[i][k][l][m] = t_riemann_cov[i, k, l, m] + ( ( ( t_ricci[i, m] * g[k, l] - t_ricci[i, l] * g[k, m] + t_ricci[k, l] * g[i, m] - t_ricci[k, m] * g[i, l] ) / (dims - 2) ) + ( r_scalar.expr * (g[i, l] * g[k, m] - g[i, m] * g[k, l]) / ((dims - 1) * (dims - 2)) ) ) C = sympy.simplify(sympy.Array(C)) return cls(C, metric.syms, config="llll", parent_metric=metric) if metric.dims == 3: return cls( sympy.Array(np.zeros((3, 3, 3, 3), dtype=int)), metric.syms, config="llll", parent_metric=metric, ) raise ValueError("Dimension of the space/space-time should be 3 or more") def change_config(self, newconfig="llll", metric=None): """ Changes the index configuration(contravariant/covariant) Parameters ---------- newconfig : str Specify the new configuration. Defaults to 'llll' metric : ~einsteinpy.symbolic.metric.MetricTensor or None Parent metric tensor for changing indices. Already assumes the value of the metric tensor from which it was initialized if passed with None. Compulsory if not initialized with 'from_metric'. Defaults to None. Returns ------- ~einsteinpy.symbolic.weyl.WeylTensor New tensor with new configuration. Configuration defaults to 'llll' Raises ------ Exception Raised when a parent metric could not be found. """ if metric is None: metric = self._parent_metric if metric is None: raise Exception("Parent Metric not found, can't do configuration change") new_tensor = _change_config(self, metric, newconfig) new_obj = WeylTensor( new_tensor, self.syms, config=newconfig, parent_metric=metric, name=_change_name(self.name, context="__" + newconfig), ) return new_obj def lorentz_transform(self, transformation_matrix): """ Performs a Lorentz transform on the tensor. Parameters ---------- transformation_matrix : ~sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray or list Sympy Array or multi-dimensional list containing Sympy Expressions Returns ------- ~einsteinpy.symbolic.weyl.WeylTensor lorentz transformed tensor(or vector) """ t = super(WeylTensor, self).lorentz_transform(transformation_matrix) return WeylTensor( t.tensor(), syms=self.syms, config=self._config, parent_metric=None, name=_change_name(self.name, context="__lt"), ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/testing.py0000644000175000017500000000025700000000000022071 0ustar00shreyasshreyas00000000000000"""Testing utilities. """ import os.path import pytest def test(): """Initiate einsteinpy testing """ pytest.main([os.path.dirname(os.path.abspath(__file__))]) ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2113445 einsteinpy-0.3.0/src/einsteinpy/tests/0000755000175000017500000000000000000000000021200 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_bodies.py0000644000175000017500000000613400000000000024062 0ustar00shreyasshreyas00000000000000import astropy.units as u import pytest from einsteinpy.bodies import ( Body, Earth, Jupiter, Mars, Mercury, Moon, Neptune, Pluto, Saturn, Sun, Uranus, Venus, ) from einsteinpy.coordinates import CartesianDifferential, SphericalDifferential @pytest.mark.parametrize( "obj, parent, R, mass", [ (Mercury, Sun, 2439.7 * u.km, 3.285e23 * u.kg), (Venus, Sun, 6051.8 * u.km, 4.867e24 * u.kg), (Sun, None, 695510 * u.km, 1.9891e30 * u.kg), (Earth, Sun, 6731 * u.km, 5.97219e24 * u.kg), (Moon, Earth, 1737.5 * u.km, 7.34767309e22 * u.kg), (Mars, Sun, 3389.5 * u.km, 6.39e23 * u.kg), (Jupiter, Sun, 69911 * u.km, 1.89813e27 * u.kg), (Saturn, Sun, 58232 * u.km, 5.683e26 * u.kg), (Uranus, Sun, 25362 * u.km, 8.681e25 * u.kg), (Neptune, Sun, 24622 * u.km, 1.024e26 * u.kg), (Pluto, Sun, 1183.3 * u.km, 1.309e22 * u.kg), ], ) def test_predefined_bodies_base_properties(obj, parent, R, mass): assert obj.parent == parent assert obj.R == R assert obj.mass == mass @pytest.mark.parametrize( "obj, a, name, q", [ (Mercury, 0, "Mercury", 0 * u.C), (Venus, 0, "Venus", 0 * u.C), (Sun, 0, "Sun", 0 * u.C), (Earth, 0, "Earth", 0 * u.C), (Moon, 0, "Moon", 0 * u.C), (Mars, 0, "Mars", 0 * u.C), (Jupiter, 0, "Jupiter", 0 * u.C), (Saturn, 0, "Saturn", 0 * u.C), (Uranus, 0, "Uranus", 0 * u.C), (Neptune, 0, "Neptune", 0 * u.C), (Pluto, 0, "Pluto", 0 * u.C), ], ) def test_predefined_bodies_extra(obj, a, name, q): assert obj.a == a assert obj.name == name assert obj.q == q def test_differentials(): parent = Sun name = "Earth" R = 6731 * u.km mass = 5.97219e24 * u.kg differential1 = CartesianDifferential( 0 * u.km, 0 * u.km, 0 * u.km, 0 * u.km / u.s, 0 * u.km / u.s, 0 * u.km / u.s ) differential2 = SphericalDifferential( 0 * u.km, 0 * u.rad, 0 * u.rad, 0 * u.km / u.s, 0 * u.rad / u.s, 0 * u.rad / u.s ) a = Body(name=name, mass=mass, R=R, differential=differential1, parent=parent) b = Body(name=name, mass=mass, R=R, differential=differential2, parent=parent) assert isinstance(a.pos_vec, list) assert isinstance(a.vel_vec, list) assert isinstance(b.pos_vec, list) assert isinstance(b.vel_vec, list) def test_body_str_return(): body = Body(name="BodyTest", mass=1.989e30 * u.kg, a=0.3 * u.m, R=30 * u.km) assert ( body.__str__() == "Body ( name: (BodyTest), " "mass: (1.989e+30 kg), radius: (30.0 km), " "coordinates: (None), spin factor: (0.3 m), charge: (0.0 C) )" ) def test_body_repr_return(): body = Body(name="BodyTest", mass=1.989e30 * u.kg, a=0.3 * u.m, R=30 * u.km) assert ( body.__repr__() == "'Body ( name: (BodyTest), " "mass: (1.989e+30 kg), " "radius: (30.0 km), " "coordinates: (None), spin factor: (0.3 m), charge: (0.0 C) )'" ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_constant.py0000644000175000017500000000153000000000000024441 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np import pytest from astropy import constants from numpy.testing import assert_allclose from einsteinpy.constant import Cosmo_Const, Cosmo_Const_base def test_Cosmo_Const_returns_correct_value_units(): cnst = Cosmo_Const assert cnst.value == 2.036e-35 assert isinstance(cnst.unit, u.core.CompositeUnit) assert isinstance(cnst, u.quantity.Quantity) def test_Cosmo_const_is_astropy_constant_with_unit_and_uncert(): cnst = Cosmo_Const_base assert isinstance(cnst, constants.Constant) assert cnst.uncertainty == 8.1e-40 assert cnst.unit == u.Unit("1 / s2") def test_Cosmo_Const_has_correct_metadata(): cnst = Cosmo_Const_base assert cnst.name == "Cosmological Constant" assert cnst.system == "si" and cnst.abbrev == "lambda" assert cnst.reference == "Wikipedia" ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_coordinates/0000755000175000017500000000000000000000000024551 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_coordinates/test_conversions.py0000644000175000017500000001073200000000000030535 0ustar00shreyasshreyas00000000000000import sys from io import StringIO import astropy.units as u import numpy as np import pytest from numpy.testing import assert_allclose from einsteinpy.coordinates import ( BoyerLindquistConversion, CartesianConversion, SphericalConversion, ) @pytest.fixture() def cartesian_coords(): return CartesianConversion( 10 / np.sqrt(2), 10 / np.sqrt(2), 0, -190 / np.sqrt(2), 210 / np.sqrt(2), 200.0 ) @pytest.fixture() def spherical_coords(): return SphericalConversion( 10.0, 1.5707963267948966, 0.7853981633974483, 10.0, -20.0, 20.0 ) @pytest.fixture() def bl_coords(): return BoyerLindquistConversion( 10.0, 1.5707963267948966, 0.7853981633974483, 10.0, -20.0, 20.0, 0.0 ) def strip_velocities(coords): if isinstance(coords, BoyerLindquistConversion): vals = coords.values() return BoyerLindquistConversion(*vals[:3], a=vals[-1]) elif isinstance(coords, (CartesianConversion, SphericalConversion)): vals = coords.values() return type(coords)(*vals[:3]) return None def test_CartesianToSpherical(cartesian_coords, spherical_coords): to_spherical_coords = cartesian_coords.convert_spherical() assert_allclose(to_spherical_coords, spherical_coords.values(), rtol=0.0, atol=1e-6) cartesian_coords, spherical_coords = ( strip_velocities(cartesian_coords), strip_velocities(spherical_coords), ) to_spherical_coords = cartesian_coords.convert_spherical() assert_allclose(to_spherical_coords, spherical_coords.values(), rtol=0.0, atol=1e-6) def test_CartesianToBoyerLindquistDifferential(cartesian_coords, bl_coords): to_bl_coords = cartesian_coords.convert_bl(bl_coords.a_si) assert_allclose(to_bl_coords, bl_coords.values(), rtol=0.0, atol=1e-6) cartesian_coords, bl_coords = ( strip_velocities(cartesian_coords), strip_velocities(bl_coords), ) to_bl_coords = cartesian_coords.convert_bl(bl_coords.a_si) assert_allclose(to_bl_coords, bl_coords.values(), rtol=0.0, atol=1e-6) def test_SphericalToCartesianDifferential(spherical_coords, cartesian_coords): to_cartesian_coords = spherical_coords.convert_cartesian() assert_allclose(to_cartesian_coords, cartesian_coords.values(), rtol=0.0, atol=1e-6) cartesian_coords, spherical_coords = ( strip_velocities(cartesian_coords), strip_velocities(spherical_coords), ) to_cartesian_coords = spherical_coords.convert_cartesian() assert_allclose(to_cartesian_coords, cartesian_coords.values(), rtol=0.0, atol=1e-6) def test_SphericalToBoyerLindquistDifferential(spherical_coords, bl_coords): to_bl_coords = spherical_coords.convert_bl(bl_coords.a_si) assert_allclose(to_bl_coords, bl_coords.values(), rtol=0.0, atol=1e-6) spherical_coords, bl_coords = ( strip_velocities(spherical_coords), strip_velocities(bl_coords), ) to_bl_coords = spherical_coords.convert_bl(bl_coords.a_si) assert_allclose(to_bl_coords, bl_coords.values(), rtol=0.0, atol=1e-6) def test_BoyerLindquistToCartesianDifferential(bl_coords, cartesian_coords): to_cartesian_coords = bl_coords.convert_cartesian() assert_allclose(to_cartesian_coords, cartesian_coords.values(), rtol=0.0, atol=1e-6) bl_coords, cartesian_coords = ( strip_velocities(bl_coords), strip_velocities(cartesian_coords), ) to_cartesian_coords = bl_coords.convert_cartesian() assert_allclose(to_cartesian_coords, cartesian_coords.values(), rtol=0.0, atol=1e-6) def test_BoyerLindquistToSphericalDifferential(bl_coords, spherical_coords): to_spherical_coords = bl_coords.convert_spherical() assert_allclose(to_spherical_coords, spherical_coords.values(), rtol=0.0, atol=1e-6) bl_coords, spherical_coords = ( strip_velocities(bl_coords), strip_velocities(spherical_coords), ) to_spherical_coords = bl_coords.convert_spherical() assert_allclose(to_spherical_coords, spherical_coords.values(), rtol=0.0, atol=1e-6) def test_cycle_BLSphericalDifferential(bl_coords): bl_diff = bl_coords sph_diff = bl_diff.convert_spherical() bl_diff2 = SphericalConversion(*sph_diff).convert_bl(bl_diff.a_si) assert_allclose(bl_diff2, bl_diff.values(), rtol=0.0, atol=1e-6) def test_cycle_BLCartesianDifferential(bl_coords): bl_diff = bl_coords cart_diff = bl_diff.convert_cartesian() bl_diff2 = CartesianConversion(*cart_diff).convert_bl(bl_diff.a_si) assert_allclose(bl_diff2, bl_diff.values(), rtol=0.0, atol=1e-6) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_coordinates/test_coord_transform.py0000644000175000017500000001050500000000000031364 0ustar00shreyasshreyas00000000000000import sys from io import StringIO from unittest import mock import astropy.units as u import numpy as np import pytest from numpy.testing import assert_allclose from einsteinpy.coordinates import BoyerLindquist, Cartesian, Spherical @pytest.fixture() def cartesian(): return Cartesian(20.0 * u.km, 311e3 * u.m, 210e5 * u.cm) @pytest.fixture() def spherical(): return Spherical( 375.79382645275 * u.km, 0.9778376650369 * u.rad, 1.5065760775947 * u.rad ) @pytest.fixture() def boyerlindquist(): return BoyerLindquist( 375.79382645275 * u.km, 0.9778376650369 * u.rad, 1.5065760775947 * u.rad, 0.0 * u.cm, ) def test_CartesianToSpherical(cartesian, spherical): to_spherical = cartesian.to_spherical() assert_allclose( to_spherical.si_values(), spherical.si_values(), rtol=0.0, atol=1e-6 ) def test_CartesianToBoyerLindquist(cartesian, boyerlindquist): bl = boyerlindquist to_bl = cartesian.to_bl(bl.a) assert_allclose(to_bl.si_values(), bl.si_values(), rtol=0.0, atol=1e-6) def test_SphericalToCartesian(spherical, cartesian): to_cartesian = spherical.to_cartesian() assert_allclose( to_cartesian.si_values(), cartesian.si_values(), rtol=0.0, atol=1e-6 ) def test_SphericalToBoyerLindquist(spherical, boyerlindquist): bl = boyerlindquist to_bl = spherical.to_bl(bl.a) assert_allclose(to_bl.si_values(), bl.si_values(), rtol=0.0, atol=1e-6) def test_BoyerLindquistToCartesian(boyerlindquist, cartesian): bl = boyerlindquist to_cartesian = bl.to_cartesian() assert_allclose( to_cartesian.si_values(), cartesian.si_values(), rtol=0.0, atol=1e-6 ) def test_BoyerLindquistToSpherical(boyerlindquist, spherical): bl = boyerlindquist to_spherical = bl.to_spherical() assert_allclose( to_spherical.si_values(), spherical.si_values(), rtol=0.0, atol=1e-6 ) @pytest.mark.parametrize( "cart, a", [ (Cartesian(10 * u.m, 10 * u.m, 0 * u.m), 0.7 * u.m), (Cartesian(-732.0 * u.km, 456 * u.km, -90 * u.km), 9.0 * u.km), (Cartesian(-0.732 * u.km, -1.456 * u.km, 90 * u.m), 21 * u.m), (Cartesian(2 * u.m, -1 * u.m, 0 * u.cm), 0 * u.cm), ], ) def test_cycle_CartesianBL(cart, a): bl = cart.to_bl(a) cart2 = bl.to_cartesian() assert_allclose(cart2.si_values(), cart.si_values(), rtol=0.0, atol=1e-6) @pytest.mark.parametrize( "bl", [ BoyerLindquist(3 * u.m, 120 * u.deg, 175 * u.deg, 0.3 * u.m), BoyerLindquist(100 * u.m, 1e-3 * u.rad, 0 * u.deg, 6.969 * u.m), ], ) def test_cycle_BLSpherical(bl): sph = bl.to_spherical() bl2 = sph.to_bl(bl.a) assert_allclose(bl2.si_values(), bl.si_values(), rtol=0.0, atol=1e-6) def test_cartesian_norm(): test_data_x = 1 * u.km test_data_y = 1 * u.km test_data_z = 1 * u.km test_obj = Cartesian(x=test_data_x, y=test_data_y, z=test_data_z) assert_allclose( (test_obj.norm()).si.value, (np.sqrt(3) * u.km).si.value, rtol=0, atol=1e-5 ) def test_cartesian_dot(): test_data_x = 3 * u.km test_data_y = 3 * u.km test_data_z = 3 * u.km test_data_x_target = 3 * u.km test_data_y_target = 3 * u.km test_data_z_target = 3 * u.km test_obj = Cartesian(x=test_data_x, y=test_data_y, z=test_data_z) test_target_obj = Cartesian( x=test_data_x_target, y=test_data_y_target, z=test_data_z_target ) assert_allclose( (test_obj.dot(test_target_obj)).si.value, (27 * u.km * u.km).si.value, rtol=0, atol=1e-5, ) # Tests for object.__repr__ and object.__str__ @mock.patch("sys.stdout", new_callable=StringIO) def test_print_core_objects(mock_stdout, cartesian, spherical, boyerlindquist): print(str(cartesian)) assert "object at 0x" not in mock_stdout.getvalue() print(str(spherical)) assert "object at 0x" not in mock_stdout.getvalue() print(str(boyerlindquist)) assert "object at 0x" not in mock_stdout.getvalue() def test_coordinate_subscripting(cartesian, spherical, boyerlindquist): assert cartesian["x"] == cartesian.x == cartesian[0] == cartesian[-3] assert spherical["theta"] == spherical.theta == spherical[1] == spherical[-2] assert ( boyerlindquist["phi"] == boyerlindquist.phi == boyerlindquist[2] == boyerlindquist[-1] ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_coordinates/test_velocity_transform.py0000644000175000017500000001167700000000000032127 0ustar00shreyasshreyas00000000000000import sys from io import StringIO from unittest import mock import astropy.units as u import numpy as np import pytest from numpy.testing import assert_allclose from einsteinpy import coordinates @pytest.fixture() def cartesian_differential(): return coordinates.CartesianDifferential( 10 / np.sqrt(2) * u.km, 10 / np.sqrt(2) * u.km, 0 * u.km, -190 / np.sqrt(2) * u.km / u.s, 210 / np.sqrt(2) * u.km / u.s, 200.0 * u.km / u.s, ) @pytest.fixture() def spherical_differential(): return coordinates.SphericalDifferential( 10.0 * u.km, 1.5707963267948966 * u.rad, 0.7853981633974483 * u.rad, 10.0 * u.km / u.s, -20.0 * u.rad / u.s, 20.0 * u.rad / u.s, ) @pytest.fixture() def bl_differential(): return coordinates.BoyerLindquistDifferential( 10.0 * u.km, 1.5707963267948966 * u.rad, 0.7853981633974483 * u.rad, 10.0 * u.km / u.s, -20.0 * u.rad / u.s, 20.0 * u.rad / u.s, 0.0 * u.km, ) @pytest.fixture() def bl_differential2(): return coordinates.BoyerLindquistDifferential( 4 * u.km, 2 * u.rad, 1 * u.rad, -100 * u.m / u.s, -1 * u.rad / u.s, 10 * u.deg / u.s, 100 * u.m, ) def test_CartesianToSphericalDifferential( cartesian_differential, spherical_differential ): to_spherical_differential = cartesian_differential.spherical_differential() assert_allclose( to_spherical_differential.si_values(), spherical_differential.si_values(), rtol=0.0, atol=1e-6, ) def test_CartesianToBoyerLindquistDifferential(cartesian_differential, bl_differential): to_bl_differential = cartesian_differential.bl_differential(bl_differential.a) assert_allclose( to_bl_differential.si_values(), bl_differential.si_values(), rtol=0.0, atol=1e-6 ) def test_SphericalToCartesianDifferential( spherical_differential, cartesian_differential ): to_cartesian_differential = spherical_differential.cartesian_differential() assert_allclose( to_cartesian_differential.si_values(), cartesian_differential.si_values(), rtol=0.0, atol=1e-6, ) def test_SphericalToBoyerLindquistDifferential(spherical_differential, bl_differential): to_bl_differential = spherical_differential.bl_differential(bl_differential.a) assert_allclose( to_bl_differential.si_values(), bl_differential.si_values(), rtol=0.0, atol=1e-6 ) def test_BoyerLindquistToCartesianDifferential(bl_differential, cartesian_differential): to_cartesian_differential = bl_differential.cartesian_differential() assert_allclose( to_cartesian_differential.si_values(), cartesian_differential.si_values(), rtol=0.0, atol=1e-6, ) def test_BoyerLindquistToSphericalDifferential(bl_differential, spherical_differential): to_spherical_differential = bl_differential.spherical_differential() assert_allclose( to_spherical_differential.si_values(), spherical_differential.si_values(), rtol=0.0, atol=1e-6, ) def test_cycle_BLSphericalDifferential(bl_differential2): bl_diff = bl_differential2 sph_diff = bl_diff.spherical_differential() bl_diff2 = sph_diff.bl_differential(bl_diff.a) assert_allclose(bl_diff2.si_values(), bl_diff.si_values(), rtol=0.0, atol=1e-6) def test_cycle_BLCartesianDifferential(bl_differential2): bl_diff = bl_differential2 cart_diff = bl_diff.cartesian_differential() bl_diff2 = cart_diff.bl_differential(bl_diff.a) assert_allclose(bl_diff2.si_values(), bl_diff.si_values(), rtol=0.0, atol=1e-6) # Tests for object.__repr__ and object.__str__ @mock.patch("sys.stdout", new_callable=StringIO) def test_print_core_objects( mock_stdout, cartesian_differential, spherical_differential, bl_differential ): print(str(cartesian_differential)) assert "object at 0x" not in mock_stdout.getvalue() print(str(spherical_differential)) assert "object at 0x" not in mock_stdout.getvalue() print(str(bl_differential)) assert "object at 0x" not in mock_stdout.getvalue() # Tests for object.velocities() def test_velocities(cartesian_differential, spherical_differential, bl_differential): def with_numpy_array(differential_obj): assert_allclose( differential_obj.si_values()[3:], differential_obj.velocities(return_np=True), 1e-10, 1e-15, ) with_numpy_array(cartesian_differential) with_numpy_array(spherical_differential) with_numpy_array(bl_differential) def test_velocities2(cartesian_differential, spherical_differential, bl_differential): cd, sd, bd = cartesian_differential, spherical_differential, bl_differential assert cd.velocities() == [cd.v_x, cd.v_y, cd.v_z] assert sd.velocities() == [sd.v_r, sd.v_t, sd.v_p] assert bd.velocities() == [bd.v_r, bd.v_t, bd.v_p] ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_examples.py0000644000175000017500000000105100000000000024424 0ustar00shreyasshreyas00000000000000from einsteinpy.bodies import Body from einsteinpy.coordinates import SphericalDifferential from einsteinpy.examples import perihelion from einsteinpy.geodesic import Geodesic from einsteinpy.metric import Schwarzschild def test_perihelion_works(): p = perihelion() assert isinstance(p.attractor, Body) assert isinstance(p, Geodesic) assert p.attractor.name == "BH" def test_perihelion_works_2(): p = perihelion() assert isinstance(p.metric, Schwarzschild) assert isinstance(p.metric.input_coords, SphericalDifferential) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_geodesics.py0000644000175000017500000000350000000000000024554 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np import pytest from numpy.testing import assert_allclose from einsteinpy.bodies import Body from einsteinpy.coordinates import SphericalDifferential from einsteinpy.geodesic import Geodesic @pytest.fixture() def dummy_data(): obj = SphericalDifferential( 130 * u.m, np.pi / 2 * u.rad, -np.pi / 8 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 1900 * u.rad / u.s, ) att = Body(name="attractor", mass=6e24 * u.kg, parent=None) b1 = Body(name="obj", differential=obj, parent=att) t = 0 * u.s start_lambda = 0.0 end_lambda = 0.002 step_size = 5e-8 return b1, t, start_lambda, end_lambda, step_size def test_Geodesics_conserves_the_attractor(dummy_data): body, t, _, end_lambda, stepsize = dummy_data geo = Geodesic(body, time=t, end_lambda=end_lambda, step_size=stepsize) assert geo.attractor == body.parent def test_Geodesics_has_trajectory(dummy_data): body, t, _, end_lambda, stepsize = dummy_data geo = Geodesic(body, time=t, end_lambda=end_lambda, step_size=stepsize) assert isinstance(geo.trajectory, np.ndarray) def test_Geodesics_str_returns_members(dummy_data): body, t, _, end_lambda, stepsize = dummy_data geo = Geodesic(body, time=t, end_lambda=end_lambda, step_size=stepsize) assert ( geo.__str__() == "Geodesic object body name= (obj) , metric=(Schwarzschild) , parent name=(attractor) , parent mass=(6e+24 kg)" ) def test_Geodesics_repr_returns_members(dummy_data): body, t, _, end_lambda, stepsize = dummy_data geo = Geodesic(body, time=t, end_lambda=end_lambda, step_size=stepsize) assert ( geo.__repr__() == "Geodesic object body name= (obj) , metric=(Schwarzschild) , parent name=(attractor) , parent mass=(6e+24 kg)" ) ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_hypersurface/0000755000175000017500000000000000000000000024737 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_hypersurface/test_schwarzschildembedding.py0000644000175000017500000000461700000000000033067 0ustar00shreyasshreyas00000000000000from astropy import units as u from numpy.testing import assert_allclose from einsteinpy.hypersurface import SchwarzschildEmbedding def test_gradient(): M = 4e24 * u.kg r = 1200 obj = SchwarzschildEmbedding(M) grad = obj.gradient(r) grad_test_value = 13.7267 assert_allclose(grad_test_value, grad, 1e-4) def test_radial_coord(): M = 5.972e24 * u.kg r = 170000 obj = SchwarzschildEmbedding(M) R = obj.radial_coord(r) R_test_value = 170059.7514 assert_allclose(R_test_value, R, 1e-4) def test_get_values(): M = 5.972e24 * u.g obj = SchwarzschildEmbedding(M) x_axis, y_axis = obj.get_values(100) x_axis = x_axis[:10] y_axis = y_axis[:10] x_axis_test_value = [ 0.31031436748282454, 0.3103211992691816, 0.31033806032413, 0.3103646908134154, 0.3104008399665836, 0.31044626567977485, 0.3105007341394409, 0.3105640194657007, 0.31063590337413993, 0.3107161748549419, ] y_axis_test_value = [ 0, 0.000996913602540167, 0.001987250685704889, 0.002971124505173177, 0.003948645664953687, 0.004919922187844408, 0.005885059584344937, 0.006844160919989087, 0.00779732688107651, 0.008744655838791766, ] assert_allclose(x_axis_test_value, x_axis, 1e-4) assert_allclose(y_axis_test_value, y_axis, 1e-4) def test_get_values_surface(): M = 5.972e24 * u.g obj = SchwarzschildEmbedding(M) X, Y, Z = obj.get_values_surface(100) X = X[1][:10].tolist() Y = Y[1][:10].tolist() Z = Z[1].tolist() X_test_value = [ 0.3085563745933694, 0.3085631676762918, 0.3085799332099953, 0.3086064128322384, 0.30864235719323163, 0.3086875255606821, 0.30874168544564184, 0.30880461224788464, 0.3088760889196209, 0.3089559056464467, ] Y_test_value = [ 0.03298439576620688, 0.03298512194059198, 0.03298691416089414, 0.03298974480842477, 0.03299358722791822, 0.03299841568531133, 0.03300420532774708, 0.03301093214566557, 0.03301857293685553, 0.03302710527234805, ] Z_test_value = 0.000996913602540167 assert_allclose(X_test_value, X, 1e-4) assert_allclose(Y_test_value, Y, 1e-4) assert_allclose(Z_test_value, Z, 1e-4) ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_ijit/0000755000175000017500000000000000000000000023176 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_ijit/test_ijit_without_numba.py0000644000175000017500000000074600000000000030522 0ustar00shreyasshreyas00000000000000import sys import types import warnings from importlib import reload from unittest import mock import einsteinpy.ijit @mock.patch.dict(sys.modules, {"numba": None}) def test(): with warnings.catch_warnings(record=True) as w: custom_jit = reload(einsteinpy.ijit) @custom_jit.jit def _simple_func(a, b): return a + b assert len(w) >= 1 assert isinstance(_simple_func, types.FunctionType) custom_jit = reload(einsteinpy.ijit) ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_integrators/0000755000175000017500000000000000000000000024600 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_integrators/test_runge_kutta.py0000644000175000017500000000062400000000000030543 0ustar00shreyasshreyas00000000000000import warnings import numpy as np import pytest from einsteinpy import integrators def test_RK45_RuntimeWarning(): def fun(t, y): return 2 * y cl = integrators.RK45(fun, 3.0, np.array([3, 2, 1.0]), 8, 2.0) with warnings.catch_warnings(record=True) as w: for i in range(10): cl.step() assert len(w) == 1 and issubclass(w[-1].category, RuntimeWarning) ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_metric/0000755000175000017500000000000000000000000023522 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_metric/test_kerr.py0000644000175000017500000001443500000000000026105 0ustar00shreyasshreyas00000000000000import warnings import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant from einsteinpy.coordinates import BoyerLindquistDifferential, CartesianDifferential from einsteinpy.metric import Kerr from einsteinpy.utils import kerr_utils, schwarzschild_radius_dimensionless _c = constant.c.value @pytest.mark.parametrize( "coords, time, M, start_lambda, end_lambda, OdeMethodKwargs", [ ( BoyerLindquistDifferential( 306 * u.m, np.pi / 2.05 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 951.0 * u.rad / u.s, 2e-3 * u.m, ), 0 * u.s, 4e24 * u.kg, 0.0, 0.001, {"stepsize": 0.5e-6}, ), ( BoyerLindquistDifferential( 1 * u.km, 0.15 * u.rad, np.pi / 2 * u.rad, 0.1 * _c * u.m / u.s, 0.5e-5 * _c * u.rad / u.s, 0.5e-4 * _c * u.rad / u.s, 2e-3 * u.m, ), 0 * u.s, 5.972e24 * u.kg, 0.0, 0.0001, {"stepsize": 0.5e-6}, ), ( BoyerLindquistDifferential( 50 * u.km, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0.1 * _c * u.m / u.s, 2e-7 * _c * u.rad / u.s, 1e-5 * u.rad / u.s, 0.0 * u.km, ), 0 * u.s, 5.972e24 * u.g, 0.0, 0.001, {"stepsize": 5e-6}, ), ], ) def test_calculate_trajectory( coords, time, M, start_lambda, end_lambda, OdeMethodKwargs ): _scr = schwarzschild_radius_dimensionless(M) obj = Kerr.from_coords(coords, M, time) ans = obj.calculate_trajectory( start_lambda=start_lambda, end_lambda=end_lambda, OdeMethodKwargs=OdeMethodKwargs, ) ans = ans[1] testarray = list() for i in ans: g = kerr_utils.metric(i[1], i[2], M.value, coords.a.to(u.m).value) testarray.append( g[0][0] * (i[4] ** 2) + g[1][1] * (i[5] ** 2) + g[2][2] * (i[6] ** 2) + g[3][3] * (i[7] ** 2) + 2 * g[0][3] * i[4] * i[7] ) testarray = np.array(testarray, dtype=float) comparearray = np.ones(shape=ans[:, 4].shape, dtype=float) assert_allclose(testarray, comparearray, 1e-4) def test_calculate_trajectory3(): # Based on the revolution of earth around sun # Data from https://en.wikipedia.org/wiki/Earth%27s_orbit # Initialialized with cartesian coordinates # Function returning cartesian coordinates M = 1.989e30 * u.kg distance_at_perihelion = 147.10e6 * u.km speed_at_perihelion = 30.29 * u.km / u.s cart_obj = CartesianDifferential( distance_at_perihelion / np.sqrt(2), distance_at_perihelion / np.sqrt(2), 0 * u.km, -1 * speed_at_perihelion / np.sqrt(2), speed_at_perihelion / np.sqrt(2), 0 * u.km / u.h, ) end_lambda = ((1 * u.year).to(u.s)).value a = 0 * u.km cl = Kerr.from_coords(cart_obj, M, a) ans = cl.calculate_trajectory( start_lambda=0.0, end_lambda=end_lambda, return_cartesian=True, OdeMethodKwargs={"stepsize": end_lambda / 2e3}, )[1] # velocity should be 29.29 km/s at apehelion(where r is max) R = np.sqrt(ans[:, 1] ** 2 + ans[:, 2] ** 2 + ans[:, 3] ** 2) i = np.argmax(R) # index whre radial distance is max v_apehelion = ( (np.sqrt(ans[i, 5] ** 2 + ans[i, 6] ** 2 + ans[i, 7] ** 2) * (u.m / u.s)).to( u.km / u.s ) ).value assert_allclose(v_apehelion, 29.29, rtol=0.01) @pytest.mark.parametrize( "coords, time, M, start_lambda, end_lambda, OdeMethodKwargs, return_cartesian", [ ( BoyerLindquistDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0.1 * u.rad / u.s, 951.0 * u.rad / u.s, 2e-3 * u.m, ), 0 * u.s, 4e24 * u.kg, 0.0, 0.0003, {"stepsize": 0.3e-6}, True, ), ( BoyerLindquistDifferential( 1 * u.km, 0.15 * u.rad, np.pi / 2 * u.rad, 0.2 * _c * u.m / u.s, 0.5e-5 * _c * u.rad / u.s, 1e-4 * _c * u.rad / u.s, 0.0 * u.km, ), 0 * u.s, 5.972e24 * u.kg, 0.0, 0.0004, {"stepsize": 0.5e-6}, False, ), ], ) def test_calculate_trajectory_iterator( coords, time, M, start_lambda, end_lambda, OdeMethodKwargs, return_cartesian ): cl1 = Kerr.from_coords(coords, M, time) arr1 = cl1.calculate_trajectory( start_lambda=start_lambda, end_lambda=end_lambda, OdeMethodKwargs=OdeMethodKwargs, return_cartesian=return_cartesian, )[1] cl2 = Kerr.from_coords(coords, M, time) it = cl2.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, return_cartesian=return_cartesian, ) arr2_list = list() for _, val in zip(range(100), it): arr2_list.append(val[1]) arr2 = np.array(arr2_list) assert_allclose(arr1[:100, :], arr2, rtol=1e-10) def test_calculate_trajectory_iterator_RuntimeWarning(): bl_obj = BoyerLindquistDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0.01 * u.rad / u.s, 10 * u.rad / u.s, 0 * u.m, ) M = 1e25 * u.kg start_lambda = 0.0 OdeMethodKwargs = {"stepsize": 0.4e-6} cl = Kerr.from_coords(bl_obj, M) with warnings.catch_warnings(record=True) as w: it = cl.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, stop_on_singularity=True, ) for _, _ in zip(range(1000), it): pass assert len(w) >= 1 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_metric/test_kerrnewman.py0000644000175000017500000001177500000000000027317 0ustar00shreyasshreyas00000000000000import warnings import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant from einsteinpy.coordinates import BoyerLindquistDifferential, CartesianDifferential from einsteinpy.metric import KerrNewman from einsteinpy.utils import kerrnewman_utils, schwarzschild_radius _c = constant.c.value _G = constant.G.value _cc = constant.coulombs_const.value def test_calculate_trajectory0(): # Based on the revolution of earth around sun # Data from https://en.wikipedia.org/wiki/Earth%27s_orbit # Initialialized with cartesian coordinates # Function returning cartesian coordinates M = 1.989e30 * u.kg q = 0 * u.C / u.kg Q = 0 * u.C distance_at_perihelion = 147.10e6 * u.km speed_at_perihelion = 30.29 * u.km / u.s cart_obj = CartesianDifferential( distance_at_perihelion / np.sqrt(2), distance_at_perihelion / np.sqrt(2), 0 * u.km, -1 * speed_at_perihelion / np.sqrt(2), speed_at_perihelion / np.sqrt(2), 0 * u.km / u.h, ) a = 0 * u.m end_lambda = ((1 * u.year).to(u.s)).value cl = KerrNewman.from_coords(coords=cart_obj, M=M, q=q, a=a, Q=Q) ans = cl.calculate_trajectory( start_lambda=0.0, end_lambda=end_lambda, return_cartesian=True, OdeMethodKwargs={"stepsize": end_lambda / 1.5e3}, )[1] # velocity should be 29.29 km/s at apehelion(where r is max) R = np.sqrt(ans[:, 1] ** 2 + ans[:, 2] ** 2 + ans[:, 3] ** 2) i = np.argmax(R) # index whre radial distance is max v_apehelion = ( (np.sqrt(ans[i, 5] ** 2 + ans[i, 6] ** 2 + ans[i, 7] ** 2) * (u.m / u.s)).to( u.km / u.s ) ).value assert_allclose(v_apehelion, 29.29, rtol=0.01) def test_calculate_trajectory1(): # the test particle should not move as gravitational & electromagnetic forces are balanced M = 0.5 * 5.972e24 * u.kg r = 1000.0 * u.km end_lambda = 1000.0 stepsize = 0.5 tmp = _G * M.value / _cc q = tmp * u.C / u.kg a = 0 * u.km Q = 11604461683.91822052001953125 * u.C bl_obj = BoyerLindquistDifferential( r, 0.5 * np.pi * u.rad, 0 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 0.0 * u.rad / u.s, a, ) cl = KerrNewman.from_coords(coords=bl_obj, q=q, M=M, Q=Q) ans = cl.calculate_trajectory( end_lambda=end_lambda, OdeMethodKwargs={"stepsize": stepsize} ) assert_allclose(ans[1][0][1], ans[1][-1][1], 1e-2) @pytest.fixture() def test_input(): q = 1 * u.C / u.g a = 1e-6 * u.m Q = 100 * u.C el = 200.0 ss = 1.0 return q, a, Q, el, ss def test_compare_calculate_trajectory_iterator_bl(test_input): q, a, Q, el, ss = test_input bl_obj = BoyerLindquistDifferential( 1000.0 * u.km, 0.6 * np.pi * u.rad, np.pi / 8 * u.rad, 10000 * u.m / u.s, -0.01 * u.rad / u.s, 0.0 * u.rad / u.s, a, ) M = 0.5 * 5.972e24 * u.kg cl1 = KerrNewman.from_coords(coords=bl_obj, q=q, M=M, Q=Q) cl2 = KerrNewman.from_coords(coords=bl_obj, q=q, M=M, Q=Q) ans1 = cl1.calculate_trajectory(end_lambda=el, OdeMethodKwargs={"stepsize": ss})[1] it = cl2.calculate_trajectory_iterator(OdeMethodKwargs={"stepsize": ss}) ans2 = list() for _, val in zip(range(20), it): ans2.append(val[1]) ans2 = np.array(ans2) assert_allclose(ans1[:20], ans2) def test_compare_calculate_trajectory_iterator_cartesians(test_input): cart_obj = CartesianDifferential( 1000000 * u.m, 1000000 * u.m, 20.5 * u.m, 10000 * u.m / u.s, 10000 * u.m / u.s, -30 * u.m / u.s, ) M = 2e24 * u.kg q, a, Q, el, ss = test_input cl1 = KerrNewman.from_coords(coords=cart_obj, q=q, M=M, a=a, Q=Q) cl2 = KerrNewman.from_coords(coords=cart_obj, q=q, M=M, a=a, Q=Q) ans1 = cl1.calculate_trajectory( end_lambda=el, OdeMethodKwargs={"stepsize": ss}, return_cartesian=True )[1] it = cl2.calculate_trajectory_iterator( OdeMethodKwargs={"stepsize": ss}, return_cartesian=True ) ans2 = list() for _, val in zip(range(20), it): ans2.append(val[1]) ans2 = np.array(ans2) assert_allclose(ans1[:20], ans2) def test_calculate_trajectory_iterator_RuntimeWarning(): bl_obj = BoyerLindquistDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0.01 * u.rad / u.s, 10 * u.rad / u.s, 0 * u.m, ) M = 1e25 * u.kg start_lambda = 0.0 q, Q = 0 * u.C / u.kg, 0 * u.C OdeMethodKwargs = {"stepsize": 0.4e-6} cl = KerrNewman.from_coords(coords=bl_obj, q=q, M=M, Q=Q) with warnings.catch_warnings(record=True) as w: it = cl.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, stop_on_singularity=True, ) for _, _ in zip(range(1000), it): pass assert len(w) >= 1 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_metric/test_schwarzschild.py0000644000175000017500000001723500000000000030013 0ustar00shreyasshreyas00000000000000import warnings import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant from einsteinpy.coordinates import CartesianDifferential, SphericalDifferential from einsteinpy.metric import Schwarzschild from einsteinpy.utils import schwarzschild_radius, schwarzschild_utils _c = constant.c.value @pytest.mark.parametrize( "coords, time, M, start_lambda, end_lambda, OdeMethodKwargs", [ ( SphericalDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 951.0 * u.rad / u.s, ), 0 * u.s, 4e24 * u.kg, 0.0, 0.002, {"stepsize": 0.5e-6}, ), ( SphericalDifferential( 1 * u.km, 0.15 * u.rad, 90 * u.deg, 0.1 * _c * u.m / u.s, 0.5e-5 * _c * u.rad / u.s, 0.5e-4 * _c * u.rad / u.s, ), 0 * u.s, 5.972e24 * u.kg, 0.0, 0.0001, {"stepsize": 0.5e-6}, ), ( SphericalDifferential( 50 * u.km, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0.1 * _c * u.m / u.s, 2e-7 * _c * u.rad / u.s, 1e-5 * u.rad / u.s, ), 0 * u.s, 5.972e24 * u.g, 0.0, 0.001, {"stepsize": 5e-6}, ), ], ) def test_calculate_trajectory( coords, time, M, start_lambda, end_lambda, OdeMethodKwargs ): cl = Schwarzschild.from_coords(coords, M, time) ans = cl.calculate_trajectory( start_lambda=start_lambda, end_lambda=end_lambda, OdeMethodKwargs=OdeMethodKwargs, ) ans = ans[1] testarray = list() for i in ans: g = schwarzschild_utils.metric(i[1], i[2], M.value) testarray.append( g[0][0] * (i[4] ** 2) + g[1][1] * (i[5] ** 2) + g[2][2] * (i[6] ** 2) + g[3][3] * (i[7] ** 2) ) testarray = np.array(testarray, dtype=float) comparearray = np.ones(shape=ans[:, 4].shape, dtype=float) assert_allclose(testarray, comparearray, 1e-4) def test_calculate_trajectory2(): # based on the revolution of earth around sun # data from https://en.wikipedia.org/wiki/Earth%27s_orbit M = 1.989e30 * u.kg distance_at_perihelion = 147.10e6 * u.km speed_at_perihelion = 30.29 * u.km / u.s angular_vel = (speed_at_perihelion / distance_at_perihelion) * u.rad sph_obj = SphericalDifferential( distance_at_perihelion, np.pi / 2 * u.rad, 0 * u.rad, 0 * u.km / u.s, 0 * u.rad / u.s, angular_vel, ) end_lambda = ((1 * u.year).to(u.s)).value cl = Schwarzschild.from_coords(sph_obj, M) ans = cl.calculate_trajectory( start_lambda=0.0, end_lambda=end_lambda, OdeMethodKwargs={"stepsize": end_lambda / 2e3}, )[1] # velocity should be 29.29 km/s at apehelion(where r is max) i = np.argmax(ans[:, 1]) # index whre radial distance is max v_apehelion = (((ans[i][1] * ans[i][7]) * (u.m / u.s)).to(u.km / u.s)).value assert_allclose(v_apehelion, 29.29, rtol=0.01) def test_calculate_trajectory3(): # same test as with test_calculate_trajectory2(), # but initialialized with cartesian coordinates # and function returning cartesian coordinates M = 1.989e30 * u.kg distance_at_perihelion = 147.10e6 * u.km speed_at_perihelion = 30.29 * u.km / u.s cart_obj = CartesianDifferential( distance_at_perihelion / np.sqrt(2), distance_at_perihelion / np.sqrt(2), 0 * u.km, -1 * speed_at_perihelion / np.sqrt(2), speed_at_perihelion / np.sqrt(2), 0 * u.km / u.h, ) end_lambda = ((1 * u.year).to(u.s)).value cl = Schwarzschild.from_coords(cart_obj, M) ans = cl.calculate_trajectory( start_lambda=0.0, end_lambda=end_lambda, return_cartesian=True, OdeMethodKwargs={"stepsize": end_lambda / 2e3}, )[1] # velocity should be 29.29 km/s at apehelion(where r is max) R = np.sqrt(ans[:, 1] ** 2 + ans[:, 2] ** 2 + ans[:, 3] ** 2) i = np.argmax(R) # index whre radial distance is max v_apehelion = ( (np.sqrt(ans[i, 5] ** 2 + ans[i, 6] ** 2 + ans[i, 7] ** 2) * (u.m / u.s)).to( u.km / u.s ) ).value assert_allclose(v_apehelion, 29.29, rtol=0.01) @pytest.mark.parametrize( "coords, time, M, start_lambda, end_lambda, OdeMethodKwargs, return_cartesian", [ ( SphericalDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0.1 * u.rad / u.s, 951.0 * u.rad / u.s, ), 0 * u.s, 4e24 * u.kg, 0.0, 0.0002, {"stepsize": 0.3e-6}, True, ), ( SphericalDifferential( 1 * u.km, 0.15 * u.rad, np.pi / 2 * u.rad, _c * u.m / u.s, 0.5e-5 * _c * u.rad / u.s, 1e-4 * _c * u.rad / u.s, ), 0 * u.s, 5.972e24 * u.kg, 0.0, 0.0002, {"stepsize": 0.5e-6}, False, ), ], ) def test_calculate_trajectory_iterator( coords, time, M, start_lambda, end_lambda, OdeMethodKwargs, return_cartesian ): cl1 = Schwarzschild.from_coords(coords, M, time) arr1 = cl1.calculate_trajectory( start_lambda=start_lambda, end_lambda=end_lambda, OdeMethodKwargs=OdeMethodKwargs, return_cartesian=return_cartesian, )[1] cl2 = Schwarzschild.from_coords(coords, M, time) it = cl2.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, return_cartesian=return_cartesian, ) arr2_list = list() for _, val in zip(range(50), it): arr2_list.append(val[1]) arr2 = np.array(arr2_list) assert_allclose(arr1[:50, :], arr2, rtol=1e-10) def test_calculate_trajectory_iterator_RuntimeWarning(): sph_obj = SphericalDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 2 * u.rad, 0 * u.m / u.s, 0.01 * u.rad / u.s, 10 * u.rad / u.s, ) M = 1e25 * u.kg start_lambda = 0.0 OdeMethodKwargs = {"stepsize": 0.4e-6} cl = Schwarzschild.from_coords(sph_obj, M) with warnings.catch_warnings(record=True) as w: it = cl.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, stop_on_singularity=True, ) for _, _ in zip(range(1000), it): pass assert len(w) >= 1 def test_calculate_trajectory_iterator_RuntimeWarning2(): sph_obj = SphericalDifferential( 306 * u.m, np.pi / 2 * u.rad, np.pi / 3 * u.rad, 0 * u.m / u.s, 0.01 * u.rad / u.s, 10 * u.rad / u.s, ) M = 1e25 * u.kg start_lambda = 0.0 OdeMethodKwargs = {"stepsize": 0.4e-6} cl = Schwarzschild.from_coords(sph_obj, M) with warnings.catch_warnings(record=True) as w: it = cl.calculate_trajectory_iterator( start_lambda=start_lambda, OdeMethodKwargs=OdeMethodKwargs, stop_on_singularity=False, ) for _, _ in zip(range(1000), it): pass assert len(w) >= 1 ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/0000755000175000017500000000000000000000000024077 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_fractal.py0000644000175000017500000000073100000000000027125 0ustar00shreyasshreyas00000000000000from io import StringIO from unittest import mock import plotly.graph_objects as go from einsteinpy.plotting import fractal @mock.patch.object(go.Figure, "show") @mock.patch("sys.stdout", new_callable=StringIO) def test_fractal_shows_figure(mock_stdout, mock_show): fig = fractal(divs=2, show=True) mock_show.assert_any_call() assert "plotly" in mock_stdout.getvalue() def test_fractal_draws_figure(): fig = fractal(divs=2, show=False) assert fig ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_geodesics/0000755000175000017500000000000000000000000027103 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_geodesics/test_interactive.py0000644000175000017500000000403000000000000033026 0ustar00shreyasshreyas00000000000000import os from unittest import mock import astropy.units as u import numpy as np import pytest from plotly.graph_objects import Figure from einsteinpy.bodies import Body from einsteinpy.coordinates import SphericalDifferential from einsteinpy.geodesic import Geodesic from einsteinpy.plotting import InteractiveGeodesicPlotter @pytest.fixture() def dummy_data(): obj = SphericalDifferential( 130 * u.m, np.pi / 2 * u.rad, -np.pi / 8 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 1900 * u.rad / u.s, ) att = Body(name="attractor", mass=6e24 * u.kg, parent=None) b1 = Body(name="obj", differential=obj, parent=att) t = 0 * u.s start_lambda = 0.0 end_lambda = 0.002 step_size = 5e-8 geo = Geodesic(b1, time=t, end_lambda=end_lambda, step_size=step_size) return geo def test_interactive_plotter_has_figure(dummy_data): geodesic = dummy_data cl = InteractiveGeodesicPlotter() assert isinstance(cl.fig, Figure) assert cl.attractor_present is False def test_plot_draws_fig(dummy_data): geodesic = dummy_data cl = InteractiveGeodesicPlotter() cl.plot(geodesic) fig = cl.show() assert cl.attractor_present assert fig @mock.patch("einsteinpy.plotting.geodesics.interactive.saveplot") def test_save_saves_plot(mock_save, dummy_data): geodesic = dummy_data cl = InteractiveGeodesicPlotter() cl.plot(geodesic) name = "test_plot.png" cl.save(name) basename, ext = os.path.splitext(name) mock_save.assert_called_with( cl.fig, image=ext[1:], image_filename=basename, show_link=False ) def test_plot_calls_draw_attractor_Manualscale(dummy_data): geodesic = dummy_data cl = InteractiveGeodesicPlotter(attractor_radius_scale=1500) cl.plot(geodesic) assert cl.attractor_present assert cl.attractor_radius_scale == 1500 def test_plot_calls_draw_attractor_AutoScale(dummy_data): geodesic = dummy_data cl = InteractiveGeodesicPlotter() cl.plot(geodesic) assert cl.attractor_present ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_geodesics/test_static.py0000644000175000017500000000557500000000000032017 0ustar00shreyasshreyas00000000000000from unittest import mock import astropy.units as u import numpy as np import pytest from matplotlib.axes import Axes from einsteinpy.bodies import Body from einsteinpy.coordinates import SphericalDifferential from einsteinpy.geodesic import Geodesic from einsteinpy.plotting import StaticGeodesicPlotter @pytest.fixture() def dummy_data(): obj = SphericalDifferential( 130 * u.m, np.pi / 2 * u.rad, -np.pi / 8 * u.rad, 0 * u.m / u.s, 0 * u.rad / u.s, 1900 * u.rad / u.s, ) att = Body(name="attractor", mass=6e24 * u.kg, parent=None) b1 = Body(name="obj", differential=obj, parent=att) t = 0 * u.s start_lambda = 0.0 end_lambda = 0.002 step_size = 5e-8 geo = Geodesic(b1, time=t, end_lambda=end_lambda, step_size=step_size) return geo def test_staticgeodesicplotter_has_axes(dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter() assert isinstance(cl.ax, Axes) assert cl.attractor_present is False @mock.patch("einsteinpy.plotting.geodesics.static.plt.show") def test_plot_calls_plt_show(mock_show, dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter() cl.plot(geodesic) cl.show() mock_show.assert_called_with() assert cl.attractor_present @mock.patch("einsteinpy.plotting.geodesics.static.plt.savefig") def test_plot_save_saves_plot(mock_save, dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter() cl.plot(geodesic) name = "test_plot.png" cl.save(name) mock_save.assert_called_with(name) def test_animate_creates_ani(dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter() cl.animate(geodesic, interval=10) assert cl.attractor_present assert cl.ani @mock.patch("einsteinpy.plotting.geodesics.static.plt.show") def test_plot_in_3d(mock_show, dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter(use_3d=True) cl.plot(geodesic) cl.show() mock_show.assert_called_with() assert cl.attractor_present assert cl.ax.name == "3d" def test_set_scaling(dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter(use_3d=True) cl.plot(geodesic) cl._set_scaling(10, 1e-6, 10, 1e-5) cl._set_scaling(1e-6, 1e-6, 1e-6, 1e-5) zmin, zmax = cl.ax.get_zlim() ymin, ymax = cl.ax.get_ylim() xmin, xmax = cl.ax.get_xlim() assert xmin != -1e-5 and xmax != 1e-5 assert ymin == -1e-5 and ymax == 1e-5 assert zmin == -1e-5 and zmax == 1e-5 def test_plot_calls_draw_attractor_Manualscale(dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter(attractor_radius_scale=1500) cl.plot(geodesic) assert cl.attractor_present assert cl.attractor_radius_scale == 1500 def test_plot_calls_draw_attractor_AutoScale(dummy_data): geodesic = dummy_data cl = StaticGeodesicPlotter() cl.plot(geodesic) assert cl.attractor_present ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_hypersurface.py0000644000175000017500000000174700000000000030221 0ustar00shreyasshreyas00000000000000from unittest import mock import pytest from astropy import units as u from einsteinpy.hypersurface import SchwarzschildEmbedding from einsteinpy.plotting import HypersurfacePlotter @pytest.fixture() def dummy_data(): surface_obj = SchwarzschildEmbedding(5.927e23 * u.kg) return surface_obj @mock.patch("einsteinpy.plotting.hypersurface.core.plt.show") def test_plot_calls_plt_show(mock_show, dummy_data): surface = dummy_data cl = HypersurfacePlotter(surface) cl.plot() cl.show() mock_show.assert_called_with() assert cl.alpha == 100 assert cl.plot_type == "wireframe" @mock.patch("einsteinpy.plotting.hypersurface.core.HypersurfacePlotter.show") @mock.patch("einsteinpy.plotting.hypersurface.core.HypersurfacePlotter.plot") def test_plot_works_with_different_plot_type(mock_plot, mock_show, dummy_data): surface = dummy_data cl = HypersurfacePlotter(surface, plot_type="surface") cl.plot() cl.show() assert cl.plot_type == "surface" ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_rays/0000755000175000017500000000000000000000000026114 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_plotting/test_rays/test_shadow.py0000644000175000017500000000161600000000000031016 0ustar00shreyasshreyas00000000000000from unittest import mock import pytest from astropy import units as u from matplotlib import pyplot as plt from einsteinpy.plotting import ShadowPlotter from einsteinpy.rays import Shadow @pytest.fixture() def dummy_data(): mass = 1 * u.kg fov = 30 * u.km shadow = Shadow(mass=mass, fov=fov, n_rays=1000) return shadow def test_plotter_has_correct_attributes(dummy_data): shadow = dummy_data cl = ShadowPlotter(shadow=shadow) assert isinstance(cl.shadow, Shadow) assert cl.is_intensity_plot @mock.patch("einsteinpy.plotting.rays.shadow.plt.plot") def test_plot_calls_plt_plot(mock_patch, dummy_data): shadow = dummy_data cl = ShadowPlotter(shadow=shadow) cl.plot() expected = [ mock.call(cl.shadow.fb1, cl.shadow.intensity, "r"), mock.call(cl.shadow.fb2, cl.shadow.intensity, "r"), ] assert mock_patch.call_args_list == expected ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/0000755000175000017500000000000000000000000024060 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_christoffel.py0000644000175000017500000000734700000000000030014 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import cosh, sinh, symbols from einsteinpy.symbolic import ChristoffelSymbols, MetricTensor from einsteinpy.symbolic.predefined import AntiDeSitter def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) # print (sch.tensor()) return sch def test_ChristoffelSymbols(): sch = schwarzschild_metric() chl = ChristoffelSymbols.from_metric(sch) mat = chl.tensor() symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") assert ( sympy.simplify(mat[2, 3, 3] - (-1 * sympy.cos(syms[2]) * sympy.sin(syms[2]))) == 0 ) assert sympy.simplify(mat[3, 3, 1] - syms[1] / (syms[1] ** 2)) == 0 assert ( sympy.simplify( (mat[1, 1, 1].subs({a: (2 * G * M / (c ** 2))})) - (G * M / (2 * G * M * syms[1] - c ** 2 * syms[1] ** 2)) ) == 0 ) assert chl.symbols() == syms def test_TypeError(): testarr = np.ones((4, 4, 4), dtype=int).tolist() syms = 0 try: obj = ChristoffelSymbols(testarr, syms) assert False except TypeError: assert True def test_change_config(): x, y, z = sympy.symbols("x y z") list3d = np.zeros((3, 3, 3), dtype=int).tolist() for i in range(3): list3d[i][i][i] = (x ** i) * (y * (2 - i)) + i * z list3d[1][2][0] = list3d[1][0][2] = x * y * z list3d[2][1][0] = list3d[2][0][1] = 4 * y metriclist = np.identity(3).tolist() metric = MetricTensor(metriclist, (x, y, z), "uu") ch = ChristoffelSymbols(list3d, (x, y, z), "ull", parent_metric=metric) chr_new = ch.change_config("llu") for t in range(3): i, j, k = t % 3, (int(t / 3)) % 3, (int(t / (3 ** 2))) % 3 assert sympy.simplify(ch[i, j, k] - chr_new[i, j, k]) == 0 def test_wrong_number_of_indices_ValueError(): x, y, z = sympy.symbols("x y z") list3d = np.zeros((3, 3, 3), dtype=int).tolist() for i in range(3): list3d[i][i][i] = (x ** i) * (y * (2 - i)) + i * z list3d[1][2][0] = list3d[1][0][2] = x * y * z list3d[2][1][0] = list3d[2][0][1] = 4 * y try: ch = ChristoffelSymbols(list3d, (x, y, z), "ulll") assert False except ValueError: assert True def test_properties(): sch_inv = schwarzschild_metric() ch = ChristoffelSymbols.from_metric(sch_inv) assert ch.parent_metric == ch._parent_metric # test change_config, should raise ValueError ch._parent_metric = None try: ch_new = ch.change_config("lll") assert False except Exception: return True def test_lorentz_transform(): # currently testing correct instance, proper theoretical tests needed def get_lorentz_matrix(): list2d = [[0 for t1 in range(4)] for t2 in range(4)] phi = symbols("phi") list2d[0][0], list2d[0][1], list2d[1][0], list2d[1][1] = ( cosh(phi), -sinh(phi), -sinh(phi), cosh(phi), ) list2d[2][2], list2d[3][3] = 1, 1 return list2d def get_tensor(): metric = AntiDeSitter() return ChristoffelSymbols.from_metric(metric) tm = get_lorentz_matrix() t0 = get_tensor() t1 = t0.lorentz_transform(tm) assert isinstance(t1, ChristoffelSymbols) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_constants.py0000644000175000017500000000044100000000000027504 0ustar00shreyasshreyas00000000000000from einsteinpy.symbolic import constants, get_constant def test_get_constant(): c1 = constants.c c2 = get_constant("c") assert c1 - c2 == 0 def test_SymbolicConstant_descriptive_name(): ld = constants.Cosmo_Const assert ld._descriptive_name == ld.descriptive_name ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_einstein.py0000644000175000017500000000625500000000000027317 0ustar00shreyasshreyas00000000000000import numpy as np import pytest import sympy from sympy import cos, cosh, simplify, sin, sinh, symbols, tensorcontraction from einsteinpy.symbolic import ( EinsteinTensor, MetricTensor, RicciScalar, simplify_sympy_array, ) def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) return sch def anti_de_sitter_metric(): coords = sympy.symbols("t chi theta phi") t, ch, th, ph = coords m = sympy.diag( -1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2, ).tolist() metric = MetricTensor(m, coords) return metric def test_EinsteinTensor_ValueError_wrong_config_length(): testarr = np.ones((4, 4), dtype=int).tolist() syms = sympy.symbols("x y") try: obj = EinsteinTensor(testarr, syms, config="lll", parent_metric=None) assert False except ValueError: assert True @pytest.mark.parametrize("metric", [anti_de_sitter_metric(), schwarzschild_metric()]) def test_EinsteinTensor_trace_negetive_of_Ricci_Scalar_in_4D(metric): # https://en.wikipedia.org/wiki/Einstein_tensor#Trace G1 = EinsteinTensor.from_metric(metric) G2 = G1.change_config("ul") val1 = simplify(tensorcontraction(G2.tensor(), (0, 1))) val2 = RicciScalar.from_metric(metric).expr assert simplify(val1 + val2) == 0 def test_EinsteinTensor_symbols_parent_metric_wrong_change_config(): metric = anti_de_sitter_metric() G = EinsteinTensor.from_metric(metric) assert G.parent_metric == G._parent_metric and G.parent_metric == metric assert G.symbols() == G.syms and G.symbols() == metric.symbols() G._parent_metric = None try: obj = G.change_config("ul") boolstore = False except Exception: boolstore = True assert boolstore def test_lorentz_transform(): # currently testing correct instance, proper theoretical tests needed def get_lorentz_matrix(): list2d = [[0 for t1 in range(4)] for t2 in range(4)] phi = symbols("phi") list2d[0][0], list2d[0][1], list2d[1][0], list2d[1][1] = ( cosh(phi), -sinh(phi), -sinh(phi), cosh(phi), ) list2d[2][2], list2d[3][3] = 1, 1 return list2d def get_tensor(): x, y, z, w = symbols("x y z w") list2d = [[0 for t1 in range(4)] for t2 in range(4)] list2d[0][0], list2d[0][1], list2d[1][0], list2d[1][1] = x, z, z, x list2d[2][2], list2d[3][3] = y, y return EinsteinTensor( list2d, syms=(x, y, z, w), config="lu", parent_metric=None ) tm = get_lorentz_matrix() t0 = get_tensor() t1 = t0.lorentz_transform(tm) assert isinstance(t1, EinsteinTensor) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_helpers.py0000644000175000017500000000455400000000000027143 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from sympy import Array, ImmutableDenseNDimArray, cos, sin, symbols from sympy.abc import p, q, x, y from einsteinpy.symbolic import TransformationMatrix, simplify_sympy_array from einsteinpy.symbolic.helpers import _change_name # tests for TransformationMatrix @pytest.mark.parametrize( "iterable, old_coords, new_coords", [ [[[x, x * y], [1, 2 * y]], (p, q), (x, y)], pytest.param([1, 2 * y], (p, q), (x, y), marks=pytest.mark.xfail), ], ) def test_TransformationMatrix_is_initializing(iterable, old_coords, new_coords): obj = TransformationMatrix(iterable, old_coords, new_coords) assert isinstance(obj, ImmutableDenseNDimArray) assert obj.rank() == 2 and isinstance(obj._array, list) @pytest.fixture def cart2sph_matrix(): old_coords, new_coords = [x, y], [p, q] new2old = [p * cos(q), p * sin(q)] obj = TransformationMatrix.from_new2old(old_coords, new_coords, new2old) return obj def test_TransformationMatrix_classmethod_new2old(cart2sph_matrix): obj = cart2sph_matrix cmp_array = Array([[1 / cos(q), 1 / sin(q)], [-1 / (p * sin(q)), 1 / (p * cos(q))]]) zero_array = Array(np.zeros(shape=cmp_array.shape, dtype=int)) assert simplify_sympy_array(cmp_array - obj) == zero_array def test_TransformationMatrix_inv_function(cart2sph_matrix): assert cart2sph_matrix._inv is None obj = cart2sph_matrix.inv() assert cart2sph_matrix._inv is not None obj = cart2sph_matrix.inv() cmp_array = Array([[cos(q), sin(q)], [-1 * p * sin(q), p * cos(q)]]) zero_array = Array(np.zeros(shape=cmp_array.shape, dtype=int)) assert simplify_sympy_array(cmp_array - obj) == zero_array def test_TransformationMatrix_variables_are_not_None(cart2sph_matrix): # this test was required to mitogate confusion arised # due to usage of both __new__ and __init__ obj = cart2sph_matrix assert (obj.old_coords is not None) and (obj.new_coords is not None) assert obj.new2old is not None @pytest.mark.parametrize( "curr_name, context, expected", [ ["tens", "__lt", "tens__lt"], ["tens__ulu", "__ull", "tens__ulu__ull"], ["tens__lt", "__lt", "tens__lt__lt"], [None, "__lt", None], ], ) def test_change_name(curr_name, context, expected): altered_name = _change_name(curr_name, context) assert altered_name == expected ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_metric.py0000644000175000017500000000367400000000000026766 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from einsteinpy.symbolic import MetricTensor def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) return sch def test_MetricTensor(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) obj = schwarzschild_metric() assert obj.dims == 4 assert obj.symbols() == syms def test_TypeError(): list2d = np.zeros((4, 4), dtype=int).tolist() syms = 100 try: obj = MetricTensor(list2d, syms) assert False except TypeError: assert True def test_properties(): sch = schwarzschild_metric() assert sch.config == "ll" assert sch.order == 2 def test_inv(): sch = schwarzschild_metric() sch_inv = sch.inv() assert sch == sch_inv.inv() assert sch_inv == sch.inv() for i in range(4): # this is because schwarzschild metric is diagonal assert sympy.simplify(sch[i, i] * sch_inv[i, i]) == 1 def test_change_config_ValueError(): sch = schwarzschild_metric() try: sch_new = sch.change_config("ul") assert False except ValueError: assert True def test_check_ValueError_on_incorrect_config_length(): sch = schwarzschild_metric() try: sch_new = MetricTensor(sch.tensor(), sch.syms, config="lll") assert False except ValueError: assert True def test_use_original_config_in_change_config(): sch = schwarzschild_metric() sch_new = sch.change_config("ll") assert sch == sch_new ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_predefined/0000755000175000017500000000000000000000000027224 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_predefined/test_all.py0000644000175000017500000000374500000000000031416 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from sympy import Array from einsteinpy.symbolic import MetricTensor, simplify_sympy_array from einsteinpy.symbolic.predefined import ( AntiDeSitter, AntiDeSitterStatic, BarriolaVilekin, BertottiKasner, BesselGravitationalWave, CMetric, Davidson, DeSitter, Ernst, Godel, JanisNewmanWinicour, Kerr, KerrNewman, Minkowski, MinkowskiCartesian, MinkowskiPolar, ReissnerNordstorm, Schwarzschild, ) @pytest.mark.parametrize( "metric_instance", [ AntiDeSitter(), AntiDeSitterStatic(), DeSitter(), Schwarzschild(), Schwarzschild(c=1, sch=2), Kerr(), KerrNewman(), Minkowski(), MinkowskiCartesian(), MinkowskiPolar(), CMetric(), Davidson(), Godel(), BesselGravitationalWave(), BarriolaVilekin(), BertottiKasner(), Ernst(), JanisNewmanWinicour(), ReissnerNordstorm(), ], ) def test_all_predefined_metrics(metric_instance): assert isinstance(metric_instance, MetricTensor) @pytest.mark.parametrize( "m1, m2", [ (Schwarzschild(), Kerr(a=0)), # Schwarzschild is a special case of Kerr (Kerr(), KerrNewman(Q=0)), # Kerr is a special case of Kerr-Newman ( ReissnerNordstorm(), KerrNewman(a=0), ), # Reissner-Nordstorm is a special case of Kerr-Newman ( Schwarzschild(), ReissnerNordstorm(Q=0), ), # Schwarzschild is a special case of Reissner-Nordstorm ], ) def test_check_two_metrics_are_equal(m1, m2): zero_arr = Array(np.zeros(shape=m1.tensor().shape, dtype=int)) assert simplify_sympy_array(m1.tensor() - m2.tensor()) == zero_arr def test_Minkowski_equality(): # Minkowski and MinkowskiCartesian are same assert simplify_sympy_array(MinkowskiCartesian().tensor()) == simplify_sympy_array( Minkowski().tensor() ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_predefined/test_find.py0000644000175000017500000000073600000000000031563 0ustar00shreyasshreyas00000000000000import pytest from einsteinpy.symbolic.predefined import find def test_find_correct(): names = ["AntiDeSitter", "AntiDeSitterStatic", "DeSitter"] namesMin = ["Minkowski", "MinkowskiCartesian", "MinkowskiPolar"] find_list = find("sit") find_listMin = find("min") assert set(names).issubset(set(find_list)) assert set(namesMin).issubset(set(find_listMin)) def test_find_incorrect(): assert find("doesnotexist") == [] assert find("find") == [] ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_ricci.py0000644000175000017500000000513700000000000026570 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import cos, sin, sinh from einsteinpy.symbolic import ( MetricTensor, RicciScalar, RicciTensor, RiemannCurvatureTensor, ) def spherical_metric(): symbolstr = "r theta phi" syms = sympy.symbols(symbolstr) list2d = (np.zeros(shape=(3, 3), dtype=int)).tolist() list2d[0][0] = 1 list2d[1][1] = syms[0] ** 2 list2d[2][2] = (syms[0] ** 2) * (sympy.sin(syms[1]) ** 2) metric = MetricTensor(list2d, syms) return metric def anti_de_sitter_metric(): coords = sympy.symbols("t chi theta phi") t, ch, th, ph = coords m = sympy.diag( -1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2, ).tolist() metric = MetricTensor(m, coords) return metric def test_Ricci_is_zero_for_spherical_space(): metric = spherical_metric() dims = metric.dims T = RicciTensor.from_metric(metric) arr = T.tensor() for i in range(dims ** 2): n = i % dims r = (int(i / dims)) % (dims) assert sympy.simplify(arr[n, r]) == 0 def test_TypeError(): testarr = np.ones((4, 4), dtype=int).tolist() syms = 0 try: obj = RicciTensor(testarr, syms) assert False except TypeError: assert True def test_RicciTensor_parent_metric_property_and_ValueError(): mt = anti_de_sitter_metric() Rt = RicciTensor.from_metric(mt) assert Rt.parent_metric == Rt._parent_metric and Rt.parent_metric == mt # ValueError test part try: Rt2 = RicciTensor(Rt.tensor(), Rt.syms, config="uuu") assert False except ValueError: assert True def test_RicciTensor_from_riemann_with_arbritary_config(): mt = anti_de_sitter_metric() rm = RiemannCurvatureTensor.from_metric(mt) rm2 = rm.change_config("lulu") try: Rt = RicciTensor.from_riemann(rm2) assert True except Exception: assert False # Tests for Ricci Scalar def test_RicciScalar_is_constant_for_ADS_spacetime(): # R is -12 for anti-de-Sitter spacetime mt = anti_de_sitter_metric() R = RicciScalar.from_metric(mt) assert sympy.simplify(R.expr).is_constant() def test_RicciScalar_raise_TypeError(): x, y = sympy.symbols("x y") try: R = RicciScalar(x ** 2 * y * 3, 0) assert False except TypeError: assert True def test_RicciScalar_inbuilt_simplify_works(): x, y = sympy.symbols("x y") R = RicciScalar((-y) + 2 * sin(x) * cos(x) + y - sin(2 * x), (x, y)) val = R.simplify(set_self=True) assert R.expr == 0 assert sum(val) == 0 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_riemann.py0000644000175000017500000000506200000000000027125 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from einsteinpy.symbolic import ChristoffelSymbols, MetricTensor, RiemannCurvatureTensor def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) # print (sch.tensor()) return sch def spherical_metric(): symbolstr = "r theta phi" syms = sympy.symbols(symbolstr) list2d = (np.zeros(shape=(3, 3), dtype=int)).tolist() list2d[0][0] = 1 list2d[1][1] = syms[0] ** 2 list2d[2][2] = (syms[0] ** 2) * (sympy.sin(syms[1]) ** 2) metric = MetricTensor(list2d, syms) return metric def test_Riemann_is_zero_for_spherical_space(): metric = spherical_metric() dims = metric.dims T = RiemannCurvatureTensor.from_metric(metric) arr = T.tensor() for i in range(dims ** 4): n = i % dims r = (int(i / dims)) % (dims) s = (int(i / (dims ** 2))) % (dims) t = (int(i / (dims ** 3))) % (dims) assert arr[t, s, r, n] == 0 def test_TypeError(): testarr = np.ones((4, 4, 4, 4), dtype=int).tolist() syms = 0 try: obj = RiemannCurvatureTensor(testarr, syms) assert False except TypeError: assert True def test_circular_index_config_same(): sch = schwarzschild_metric() rm0 = RiemannCurvatureTensor.from_metric(sch) rm1 = rm0.change_config("lulu") rm2 = rm1.change_config("uuuu") rm3 = rm2.change_config("ulll") dims = sch.dims for i in range(dims ** 4): # t,s,r,n each goes from 0 to (dims-1) # hack for codeclimate. Could be done with 4 nested for loops n = i % dims r = (int(i / dims)) % (dims) s = (int(i / (dims ** 2))) % (dims) t = (int(i / (dims ** 3))) % (dims) assert sympy.simplify(rm3[n, r, s, t] - rm0[n, r, s, t]) == 0 assert rm0.parent_metric == rm0._parent_metric def test_no_exception_raised_passing_christoffel_with_unconventional_indices(): sch = schwarzschild_metric() ch = ChristoffelSymbols.from_metric(sch) ch2 = ch.change_config("uuu") try: rm = RiemannCurvatureTensor.from_christoffels(ch2) assert True except: assert False ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_schouten.py0000644000175000017500000000500000000000000027314 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import cos, sin, sinh from einsteinpy.symbolic import ( MetricTensor, RicciScalar, RicciTensor, RiemannCurvatureTensor, SchoutenTensor, simplify_sympy_array, ) def anti_de_sitter_metric(): coords = sympy.symbols("t chi theta phi") t, ch, th, ph = coords m = sympy.diag( -1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2, ).tolist() metric = MetricTensor(m, coords) return metric def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) # print (sch.tensor()) return sch def test_SchoutenTensor_parent_metric_property_and_ValueError(): mt = anti_de_sitter_metric() St = SchoutenTensor.from_metric(mt) assert St.parent_metric == St._parent_metric and St.parent_metric == mt # ValueError test part try: St2 = SchoutenTensor(St.tensor(), St.syms, config="uuu") assert False except ValueError: assert True def test_Schouten_dim2(): list_metric = np.zeros((2, 2), dtype=int).tolist() symbolstr = "t r" syms = sympy.symbols(symbolstr) metric = MetricTensor(list_metric, syms) try: obj = SchoutenTensor.from_metric(metric) assert False except ValueError: assert True def test_SchoutenTensor_with_arbritary_config(): sch = schwarzschild_metric() ch = SchoutenTensor.from_metric(sch) assert ch.parent_metric == ch._parent_metric # test change_config, should raise ValueError ch._parent_metric = None try: ch_new = ch.change_config("lll") assert False except Exception: return True def test_SchoutenTensor_config_change(): metric = schwarzschild_metric() t1 = SchoutenTensor.from_metric(metric) t2 = t1.change_config("ul") t3 = t2.change_config("ll") assert t1.config == "ll" and t3.config == "ll" compare = sympy.Array(np.zeros((4, 4), dtype=int)) testarr = simplify_sympy_array(t1.tensor() - t3.tensor()) assert testarr == compare ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_stress_energy_momentum.py0000644000175000017500000000343400000000000032312 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import cos, sin, sinh from einsteinpy.symbolic import ( MetricTensor, StressEnergyMomentumTensor, simplify_sympy_array, ) def schwarzschild_metric(): symbolstr = "t r theta phi" syms = sympy.symbols(symbolstr) G, M, c, a = sympy.symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sympy.sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) return sch def test_StressEnergyMomentumTensor_ValueError_wrong_config_length(): testarr = np.ones((4, 4), dtype=int).tolist() syms = sympy.symbols("t x y z") try: obj = StressEnergyMomentumTensor( testarr, syms, config="lll", parent_metric=None ) assert False except ValueError: assert True def test_StressEnergyMomentumTensor_change_config_no_parent_metric(): testarr = np.ones((4, 4), dtype=int).tolist() syms = sympy.symbols("t x y z") obj = StressEnergyMomentumTensor(testarr, syms, config="ll") try: obj2 = obj.change_config("lu") assert False except Exception: assert True def test_StressEnergyMomentumTensor_cyclic_config_change(): metric = schwarzschild_metric() t1 = StressEnergyMomentumTensor.from_metric(metric) t2 = t1.change_config("ul") t3 = t2.change_config("ll") assert t1.config == "ll" and t3.config == "ll" compare = sympy.Array(np.zeros((4, 4), dtype=int)) testarr = simplify_sympy_array(t1.tensor() - t3.tensor()) assert testarr == compare ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_tensor.py0000644000175000017500000001775500000000000027022 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from numpy.testing import assert_allclose from sympy import Array, Function, cos, simplify, sin, symbols from sympy.abc import y, z from einsteinpy.symbolic import ( BaseRelativityTensor, MetricTensor, Tensor, simplify_sympy_array, ) # Making an xfail marker to indicate that you expect a test to fail xfail = pytest.mark.xfail # Test for simplify_sympy_array() def zero_expression(): return 2 * sin(y * z) * cos(z * y) - sin(2 * z * y) @pytest.mark.parametrize( "target", (Array([zero_expression(), 3]), Array(zero_expression()), zero_expression()), ) # Marking unexpectedly failing test functions def test_simplify_sympy_array_works_for_all(target): try: simplify_sympy_array(target) assert True except Exception: assert False # Tests for Tensor and BaseRelativityTensor def schwarzschild_tensor(): symbolstr = "t r theta phi" syms = symbols(symbolstr) G, M, c, a = symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sin(syms[2]) ** 2) / (c ** 2) sch = Tensor(list2d) return sch def schwarzschild_metric(): symbolstr = "t r theta phi" syms = symbols(symbolstr) G, M, c, a = symbols("G M c a") # using metric values of schwarschild space-time # a is schwarzschild radius list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sin(syms[2]) ** 2) / (c ** 2) sch = MetricTensor(list2d, syms) return sch def arbitrary_tensor1(): symbolstr = "x0 x1 x2 x3" syms = symbols(symbolstr) a, c = symbols("a c") f1, f2, f3 = Function("f1")(a, syms[2]), Function("f2")(c), Function("f3") list2d = np.zeros((4, 4), dtype=int).tolist() list2d[0][0] = 1 - (a * f1 / syms[1]) list2d[1][1] = -1 / ((1 - (a / syms[1])) * (c ** 2)) list2d[2][2] = -1 * (syms[1] ** 2) / (c ** 2) list2d[3][3] = -1 * (syms[1] ** 2) * (sin(syms[2]) ** 2) / (c ** 2) list2d[0][3] = list2d[3][0] = 5 * f2 list2d[2][1] = list2d[1][2] = f3 return BaseRelativityTensor(list2d, syms, config="ll"), [a, c], [f1, f2, f3] def test_Tensor(): x, y, z = symbols("x y z") test_list = [[[x, y], [y, sin(2 * z) - 2 * sin(z) * cos(z)]], [[z ** 2, x], [y, z]]] test_arr = Array(test_list) obj1 = Tensor(test_arr, config="ull") obj2 = Tensor(test_list, config="ull") assert obj1.tensor() == obj2.tensor() assert isinstance(obj1.tensor(), Array) def test_Tensor_simplify(): x, y, z = symbols("x y z") test_list = [[[x, y], [y, sin(2 * z) - 2 * sin(z) * cos(z)]], [[z ** 2, x], [y, z]]] obj = Tensor(test_list, config="ull") # with set_self = False assert obj.simplify(set_self=False)[0, 1, 1] == 0 assert not obj.tensor()[0, 1, 1] == 0 # with set_self = True obj.simplify(set_self=True) assert obj.tensor()[0, 1, 1] == 0 def test_Tensor_getitem(): x, y, z = symbols("x y z") test_list = [[[x, y], [y, sin(2 * z) - 2 * sin(z) * cos(z)]], [[z ** 2, x], [y, z]]] obj = Tensor(test_list, config="ull") n = 2 for i in range(n ** 3): p, q, r = i % n, int(i / n) % n, int(i / n ** 2) % n assert obj[p, q, r] - test_list[p][q][r] == 0 def test_Tensor_str(): x, y, z = symbols("x y z") test_list = [[[x, y], [y, x]], [[z, x], [y, z]]] obj1 = Tensor(test_list, config="ull", name="Test") assert "object at 0x" not in str(obj1) assert "Test" in str(obj1) def test_Tensor_repr(): x, y, z = symbols("x y z") test_list = [[[x, y], [y, sin(2 * z) - 2 * sin(z) * cos(z)]], [[z ** 2, x], [y, z]]] obj1 = Tensor(test_list, config="ull") machine_representation = repr(obj1) assert not "object at 0x" in machine_representation @xfail(raises=TypeError, strict=True) def test_TypeError1(): # pass non array, number or expression in arr obj = Tensor("value", config="ll") @xfail(raises=TypeError, strict=True) def test_TypeError2(): scht = schwarzschild_tensor().tensor() # pass non str object obj = Tensor(scht, config=0) @xfail(raises=TypeError, strict=True) def test_TypeError3(): scht = schwarzschild_tensor().tensor() # pass string containing elements other than 'l' or 'u' obj = Tensor(scht, config="al") @xfail(raises=ValueError, strict=True) def test_ValueError1(): x, y = symbols("x y") test_list = [[x, y], [y, x]] # pass array with shape (2,2) when (2,2,2) implied by argument syms obj = Tensor(test_list, config="lll") @xfail(raises=ValueError, strict=True) def test_ValueError2(): x, y, z = symbols("x y z") test_list = [[x, y], [y, x]] # pass 2x2 array when 3x3 implied by argument syms obj = BaseRelativityTensor(test_list, [x, y, z]) def test_subs_single(): # replacing only schwarzschild radius(a) with 0 T = schwarzschild_tensor() a, c = symbols("a c") test_arr = T.subs(a, 0) assert simplify(test_arr.arr[0, 0] - 1) == 0 assert simplify(test_arr.arr[1, 1] - (-1 / c ** 2)) == 0 def test_subs_multiple(): # replacing a with 0, c with 1 # this should give a metric for spherical coordinates T = schwarzschild_tensor() a, c = symbols("a c") test_arr = T.subs([(a, 0), (c, 1)]) assert simplify(test_arr.arr[0, 0] - 1) == 0 assert simplify(test_arr.arr[1, 1] - (-1)) == 0 def test_check_properties(): T = schwarzschild_tensor() assert T.order == T._order assert T.config == T._config # Tests for BaseRelativityTensor @xfail(raises=TypeError, strict=True) def test_BaseRelativilyTensor_TypeError(): # pass non list, tuple, set to variables t1, _, functions = arbitrary_tensor1() t2 = BaseRelativityTensor( t1.arr, t1.symbols(), config=t1.config, variables="value", functions=functions ) def test_BaseRelativityTensor_automatic_calculation_of_free_variables(): t1, variables, functions = arbitrary_tensor1() t2 = BaseRelativityTensor( t1.arr, t1.symbols(), config=t1.config, variables=variables, functions=functions ) assert len(t1.variables) == len(t2.variables) and len(t1.variables) == len( variables ) assert len(t1.functions) == len(t2.functions) and len(t1.functions) == len( functions ) for v, f in zip(t1.variables, t1.functions): assert ( (v in t2.variables) and (v in variables) and (f in t2.functions) and (f in functions) ) # Tests fot Tensor Class to support scalars and sympy expression type scalars @pytest.mark.parametrize("scalar", [11.89, y * z + 5]) def test_tensor_scalar(scalar): scalar_tensor = Tensor(scalar, config="") assert scalar_tensor.tensor().rank() == 0 # Tests for lambdify def test_lambdify_on_schwarzschild_metric_without_args(): sch = schwarzschild_metric() # values of t, r, theta, phi, a, c vals = (0.0, 3.0, np.pi / 2, np.pi / 3, 2, 1) f = sch.tensor_lambdify()[1] # print(sch.variables) result_arr = np.array(f(*vals)) cmp_arr = np.zeros((4, 4), dtype=float) cmp_arr[0, 0], cmp_arr[1, 1], cmp_arr[2, 2], cmp_arr[3, 3] = ( 1 - (vals[4] / vals[1]), -1 / ((1 - (vals[4] / vals[1])) * (vals[5] ** 2)), -1 * (vals[1] ** 2) / (vals[5] ** 2), -1 * (vals[1] ** 2) * (np.sin(vals[2]) ** 2) / (vals[5] ** 2), ) assert_allclose(cmp_arr, result_arr, atol=1e-7, rtol=0.0) def test_lambdify_with_args(): x, y = symbols("x y") T = BaseRelativityTensor([x + y, x], (x, y), config="l") args, f = T.tensor_lambdify(y, x) arr = np.array(f(2, 1)) cmp_arr = np.array([3, 1]) assert_allclose(arr, cmp_arr, rtol=0.0, atol=1e-7) for e1, e2 in zip(args, (y, x)): assert simplify(e1 - e2) == 0 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_vector.py0000644000175000017500000000523400000000000026777 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from sympy import cos, cosh, simplify, sinh, symbols from einsteinpy.symbolic import GenericVector, MetricTensor # Making an xfail marker to indicate that you expect a test to fail xfail = pytest.mark.xfail def euclidean_space_metric(): symbolstr = "e1 e2" # let angle between e1 & e2 be theta syms = symbols(symbolstr) th = symbols("theta") list2d = np.zeros((2, 2), dtype=int).tolist() # defining the metric tensor when axis are not orthogonal list2d[0][0] = list2d[1][1] = 1 list2d[1][0] = list2d[0][1] = cos(th) metric = MetricTensor(list2d, syms, config="ll") return metric def test_GenericVector_change_config_theoretical_test(): # https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors#Definition a, b, th = symbols("a b theta") metric = euclidean_space_metric() # defining a contravariant vector cnvec = GenericVector([a, b], metric.syms, config="u", parent_metric=metric) covec = cnvec.change_config("l") # get contravariant vector assert simplify(covec.tensor()[0] - (a + b * cos(th))) == 0 assert simplify(covec.tensor()[1] - (b + a * cos(th))) == 0 @xfail(strict=True) def test_GenericVector_check_Metric(): syms = symbols("t x y z") t, x, y, z = syms obj = GenericVector([t, x, y, z], syms=syms, config="u", parent_metric=None) obj.change_config("u", None) def test_GenericVector_check_ValueErrors(): a, b = symbols("a b") syms = symbols("e1 e2") # input a tensor with wring rank try: arr = [[a, b], [b, 1]] v1 = GenericVector(arr, syms, "l") boolstore = False except ValueError: boolstore = True assert boolstore # input a wrong length config try: arr = [a, b] v2 = GenericVector(arr, syms, "uu") boolstore = False except ValueError: boolstore = True assert boolstore def test_lorentz_transform(): def get_vector(): syms = symbols("t x y z") t, x, y, z = syms return GenericVector([t, x, y, z], syms=syms, config="u") def get_lorentz_matrix(): list2d = [[0 for t1 in range(4)] for t2 in range(4)] phi = symbols("phi") list2d[0][0], list2d[0][1], list2d[1][0], list2d[1][1] = ( cosh(phi), -sinh(phi), -sinh(phi), cosh(phi), ) list2d[2][2], list2d[3][3] = 1, 1 return list2d t, x, phi = symbols("t x phi") v = get_vector().lorentz_transform(get_lorentz_matrix()) print(v.tensor()) assert simplify(v[0] - (t * cosh(phi) - x * sinh(phi))) == 0 assert simplify(v[1] - (x * cosh(phi) - t * sinh(phi))) == 0 ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_symbolic/test_weyl.py0000644000175000017500000000554500000000000026462 0ustar00shreyasshreyas00000000000000import numpy as np import sympy from sympy import cos, sin, sinh from einsteinpy.symbolic import ( MetricTensor, RicciScalar, RicciTensor, RiemannCurvatureTensor, WeylTensor, simplify_sympy_array, ) def spherical_metric(): symbolstr = "r theta phi xi" syms = sympy.symbols(symbolstr) list2d = (np.zeros(shape=(4, 4), dtype=int)).tolist() list2d[0][0] = 1 list2d[1][1] = syms[0] ** 2 list2d[2][2] = (syms[0] ** 2) * (sympy.sin(syms[1]) ** 2) list2d[3][3] = (syms[0] ** 2) * (sympy.cos(syms[1]) ** 2) metric = MetricTensor(list2d, syms) return metric def anti_de_sitter_metric(): coords = sympy.symbols("t chi theta phi") t, ch, th, ph = coords m = sympy.diag( -1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2, ).tolist() metric = MetricTensor(m, coords) return metric def test_weyl_TypeError(): testarr = np.ones((4, 4, 4, 4), dtype=int).tolist() syms = 0 try: obj = WeylTensor(testarr, syms) assert False except TypeError: assert True def test_weyl_ValueError_wrong_config_length(): testarr = np.ones((4, 4, 4, 4), dtype=int).tolist() syms = sympy.symbols("x y z w") try: obj = WeylTensor(testarr, syms, config="uuu", parent_metric=None) assert False except ValueError: assert True def test_weyl_dim2(): list_metric = np.zeros((2, 2), dtype=int).tolist() symbolstr = "t r" syms = sympy.symbols(symbolstr) metric = MetricTensor(list_metric, syms) try: obj = WeylTensor.from_metric(metric) assert False except ValueError: assert True def test_weyl_dim3(): list_metric = np.ones((3, 3), dtype=int).tolist() symbolstr = "t r theta" syms = sympy.symbols(symbolstr) metric = MetricTensor(list_metric, syms) obj = WeylTensor.from_metric(metric).arr assert obj == sympy.Array(np.zeros((3, 3, 3, 3), dtype=int)) def test_weyl_conformal_rescaling(): # https://en.wikipedia.org/wiki/Weyl_tensor#Conformal_rescaling a = sympy.symbols("a") mw1 = anti_de_sitter_metric() mw2 = MetricTensor(a * mw1.tensor(), mw1.symbols(), mw1.config) w1 = WeylTensor.from_metric(mw1).change_config("ulll") w2 = WeylTensor.from_metric(mw2).change_config("ulll") cmp_arr = sympy.Array(np.zeros(shape=w1.tensor().shape, dtype=int)) assert simplify_sympy_array(w1.tensor() - w2.tensor()) == cmp_arr assert w1.syms == w1.symbols() assert w1.parent_metric == w1._parent_metric def test_weyl_contraction_1st_3rd_indices_zero(): mw1 = anti_de_sitter_metric() w1 = WeylTensor.from_metric(mw1) t1 = simplify_sympy_array( sympy.tensorcontraction(w1.change_config("ulll").tensor(), (0, 2)) ) t0 = sympy.Array(np.zeros(shape=t1.shape, dtype=int)) assert t1 == t0 ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/tests/test_utils/0000755000175000017500000000000000000000000023377 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_utils/test_kerr_utils.py0000644000175000017500000000461100000000000027175 0ustar00shreyasshreyas00000000000000import collections import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant from einsteinpy.utils import kerr_utils, schwarzschild_radius_dimensionless def test_nonzero_christoffels(): l1 = kerr_utils.nonzero_christoffels() l2 = kerr_utils.nonzero_christoffels_list assert collections.Counter(l1) == collections.Counter(l2) def test_spin_factor(): J, M, c = 9e10, 5e24, constant.c.value assert_allclose(J / (M * c), kerr_utils.spin_factor(J, M, c), rtol=0.0, atol=1e-10) def test_event_horizon_for_nonrotating_case(): M = 5e27 a = 0.0 _scr = schwarzschild_radius_dimensionless(M) a1 = kerr_utils.event_horizon(M, a, np.pi / 4) a2 = kerr_utils.event_horizon(M, a, np.pi / 4, "Spherical") assert_allclose(a1, a2, rtol=1e-4, atol=0.0) assert_allclose(a1[0], _scr, rtol=1e-4, atol=0.0) def test_radius_ergosphere_for_nonrotating_case(): M = 5e27 a = 0.0 _scr = schwarzschild_radius_dimensionless(M) a1 = kerr_utils.radius_ergosphere(M, a, np.pi / 5) a2 = kerr_utils.radius_ergosphere(M, a, np.pi / 5, "Spherical") assert_allclose(a1, a2, rtol=1e-4, atol=0.0) assert_allclose(a1[0], _scr, rtol=1e-4, atol=0.0) def test_christoffels(): # output produced by the optimized function c = 3e8 r = 100.0 theta = np.pi / 5 M = 6.73317655e26 a = 0.2 chl1 = kerr_utils.christoffels(r, theta, M, a, c) # calculate by formula invg = kerr_utils.metric_inv(r, theta, M, a, c) dmdx = kerr_utils.dmetric_dx(r, theta, M, a, c) chl2 = np.zeros(shape=(4, 4, 4), dtype=float) tmp = np.array([i for i in range(4 ** 3)]) for t in tmp: i = int(t / (4 ** 2)) % 4 k = int(t / 4) % 4 l = t % 4 for m in range(4): chl2[i, k, l] += invg[i, m] * ( dmdx[l, m, k] + dmdx[k, m, l] - dmdx[m, k, l] ) chl2 = np.multiply(chl2, 0.5) assert_allclose(chl2, chl1, rtol=1e-8) @pytest.mark.parametrize("a", [1.1, -0.1]) def test_scaled_spin_factor_raises_error(a): try: kerr_utils.scaled_spin_factor(a, 3e20) assert False except ValueError: assert True def test_scaled_spin_factor(): a = 0.8 M = 5e24 a1 = kerr_utils.scaled_spin_factor(a, M) a2 = schwarzschild_radius_dimensionless(M) * a * 0.5 assert_allclose(a2, a1, rtol=1e-9) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_utils/test_kerrnewman_utils.py0000644000175000017500000001344200000000000030405 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant, utils from einsteinpy.utils import ( kerr_utils, kerrnewman_utils, schwarzschild_radius_dimensionless, ) _c = constant.c.value _G = constant.G.value _cc = constant.coulombs_const.value @pytest.fixture() def test_input(): c = _c G = _G Cc = _cc r = 0.1 theta = 4 * np.pi / 5 M = 1e23 a = 0.99 return c, G, Cc, r, theta, M, a def test_compare_kerr_kerrnewman_metric_inv(test_input): c, G, Cc, r, theta, M, a = test_input # the inverse of metric for Kerr and Kerr-Newman metric should be equal when Q=0 scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) m1 = kerr_utils.metric_inv(r, theta, M, a_scaled) m2 = kerrnewman_utils.metric_inv(r, theta, M, a_scaled, 0.0) assert_allclose(m1, m2, rtol=1e-10) def test_compare_kerr_kerrnewman_dmetric_dx(test_input): c, G, Cc, r, theta, M, a = test_input # differentiation of metric for Kerr and Kerr-Newman metric should be equal when Q=0 scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) m1 = kerr_utils.dmetric_dx(r, theta, M, a_scaled) m2 = kerrnewman_utils.dmetric_dx(r, theta, M, a_scaled, 0.0) assert_allclose(m1, m2, rtol=1e-10) def test_christoffels1(test_input): # compare Christoffel symbols output by optimized function and by brute force c, G, Cc, r, theta, M, a = test_input Q = 1.0 scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) chl1 = kerrnewman_utils.christoffels(r, theta, M, a_scaled, Q) # calculate by formula invg = kerrnewman_utils.metric_inv(r, theta, M, a_scaled, Q) dmdx = kerrnewman_utils.dmetric_dx(r, theta, M, a_scaled, Q) chl2 = np.zeros(shape=(4, 4, 4), dtype=float) tmp = np.array([i for i in range(4 ** 3)]) for t in tmp: i = int(t / (4 ** 2)) % 4 k = int(t / 4) % 4 l = t % 4 for m in range(4): chl2[i, k, l] += invg[i, m] * ( dmdx[l, m, k] + dmdx[k, m, l] - dmdx[m, k, l] ) chl2 = np.multiply(chl2, 0.5) assert_allclose(chl2, chl1, rtol=1e-10) def test_compare_kerr_kerrnewman_christoffels(test_input): # christoffel symbols for Kerr and Kerr-Newman metric should be equal when Q=0 c, G, Cc, r, theta, M, a = test_input scr = 2 * M * G / (c ** 2) a_scaled = kerr_utils.scaled_spin_factor(a, M) c1 = kerr_utils.christoffels(r, theta, M, a_scaled) c2 = kerrnewman_utils.christoffels(r, theta, M, a_scaled, 0.0) assert_allclose(c1, c2, rtol=1e-8) def test_electric_magnetic_potential_from_em_potential_vector(test_input): c, G, Cc, r, theta, M, a = test_input Q = 15.5 vec = kerrnewman_utils.em_potential(r, theta, 0.0, Q, M) cmparr = np.zeros((4,), dtype=float) cmparr[0] = (Q / ((c ** 2) * r)) * np.sqrt(G * constant.coulombs_const.value) assert_allclose(cmparr, vec, rtol=1e-8) def test_compare_kerr_kerrnewman_time_velocity(): # time velocity for Kerr & Kerr-Newman should be same when Q=0 pos_vec = np.array([1.0, np.pi / 2, 0.1]) vel_vec = np.array([-0.1, -0.01, 0.05]) mass = 1e24 * u.kg a01 = 0.85 a = kerr_utils.scaled_spin_factor(a01, mass.to(u.kg).value) t1 = kerr_utils.kerr_time_velocity(pos_vec, vel_vec, mass, a) t2 = kerrnewman_utils.kerrnewman_time_velocity(pos_vec, vel_vec, mass, a, 0.0 * u.C) assert_allclose(t1.value, t2.value, rtol=1e-10) def test_maxwell_tensor_covariant_for_natural_units(): # formula for testing from https://arxiv.org/abs/gr-qc/0409025 M = 2e22 r = 1.5 theta = 3 * np.pi / 5 Q = 10.0 a = 0.5 m = kerrnewman_utils.maxwell_tensor_covariant(r, theta, a, Q, M, 1.0, 1.0, 1.0) for t in range(16): i = int(t / 4) % 4 j = t % 4 assert_allclose(0, m[i, j] + m[j, i], rtol=0.0, atol=1e-10) th, r2, a2 = theta, r ** 2, a ** 2 E_r = Q * (r2 - (a * np.cos(th)) ** 2) / ((r2 + (a * np.cos(th)) ** 2) ** 2) E_th = (a2) * (-Q) * np.sin(2 * th) / ((r2 + (a * np.cos(th)) ** 2) ** 2) B_r = 2 * a * Q * (r2 + a2) * np.cos(th) / (r * ((r2 + (a * np.cos(th)) ** 2) ** 2)) B_th = ( a * Q * np.sin(th) * (r2 - (a * np.cos(th)) ** 2) / (r * ((r2 + (a * np.cos(th)) ** 2) ** 2)) ) assert_allclose(E_r, m[0, 1], rtol=1e-8) assert_allclose(r * E_th, m[0, 2], rtol=1e-8) assert_allclose(-r * np.sin(theta) * B_th / M, m[3, 1], rtol=1e-8) assert_allclose((r ** 2) * np.sin(theta) * B_r / M, m[3, 2], rtol=1e-8) def test_maxwell_tensor_contravariant_for_natural_units(): # Theoretical background is required to write extensive tests. Right now only skew-symmetric property is being checked. M = 1e22 r = 5.5 theta = 2 * np.pi / 5 Q = 45.0 a = 0.7 m = kerrnewman_utils.maxwell_tensor_contravariant(r, theta, a, Q, M, 1.0, 1.0, 1.0) for t in range(16): i = int(t / 4) % 4 j = t % 4 assert_allclose(0, m[i, j] + m[j, i], rtol=0.0, atol=1e-10) def test_event_horizon_for_nonrotating_uncharged_case(): M = 5e27 a = 0.0 Q = 0.0 _scr = schwarzschild_radius_dimensionless(M) a1 = kerrnewman_utils.event_horizon(M, a, Q, np.pi / 4, "Spherical") a2 = kerr_utils.event_horizon(M, a, np.pi / 4) assert_allclose(a1, a2, rtol=1e-4, atol=0.0) assert_allclose(a1[0], _scr, rtol=1e-4, atol=0.0) def test_radius_ergosphere_for_nonrotating_uncharged_case(): M = 5e27 a = 0.0 Q = 0.0 _scr = schwarzschild_radius_dimensionless(M) a1 = kerrnewman_utils.radius_ergosphere(M, a, Q, np.pi / 4, "Spherical") a2 = kerr_utils.radius_ergosphere(M, a, np.pi / 4) assert_allclose(a1, a2, rtol=1e-4, atol=0.0) assert_allclose(a1[0], _scr, rtol=1e-4, atol=0.0) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/tests/test_utils/test_schwarzschild_utils.py0000644000175000017500000000107200000000000031100 0ustar00shreyasshreyas00000000000000import numpy as np import pytest from astropy import units as u from numpy.testing import assert_allclose from einsteinpy import constant, utils from einsteinpy.utils import kerr_utils, schwarzschild_utils _c = constant.c.value _G = constant.G.value def test_compare_kerr_and_schwarzschild_metric(): r = 99.9 theta = 5 * np.pi / 6 M = 6.73317655e26 # Kerr metric would reduce to Schwarzschild metric under limits a=0 mk = kerr_utils.metric(r, theta, M, 0.0) ms = schwarzschild_utils.metric(r, theta, M) assert_allclose(mk, ms, rtol=1e-8) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/units.py0000644000175000017500000000101300000000000021545 0ustar00shreyasshreyas00000000000000import astropy.units as u from einsteinpy.constant import G, c def astro_dist(mass): """ Function for turning distance into astronomical perspective. """ value = (G.value * mass) / (c.value ** 2) astro_dist = u.def_unit("astro-m(GM/c2)", u.m / value) return astro_dist def astro_sec(mass): """ Function for turning time into astronomical perspective. """ value = (G.value * mass) / (c.value ** 3) astro_sec = u.def_unit("astro-sec(GM/c3)", u.s / value) return astro_sec ././@PaxHeader0000000000000000000000000000003300000000000011451 xustar000000000000000027 mtime=1588632901.215345 einsteinpy-0.3.0/src/einsteinpy/utils/0000755000175000017500000000000000000000000021176 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/utils/__init__.py0000644000175000017500000000027500000000000023313 0ustar00shreyasshreyas00000000000000from .scalar_factor import scalar_factor, scalar_factor_derivative from .schwarzschild_utils import ( schwarzschild_radius, schwarzschild_radius_dimensionless, time_velocity, ) ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/utils/kerr_utils.py0000644000175000017500000003010500000000000023732 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy import constant, utils from einsteinpy.coordinates import BoyerLindquist, Spherical from einsteinpy.utils import schwarzschild_radius_dimensionless nonzero_christoffels_list = [ (0, 0, 1), (0, 0, 2), (0, 1, 3), (0, 2, 3), (0, 1, 0), (0, 2, 0), (0, 3, 1), (0, 3, 2), (1, 0, 0), (1, 1, 1), (1, 2, 2), (1, 3, 3), (2, 0, 0), (2, 1, 1), (2, 2, 2), (2, 3, 3), (1, 0, 3), (1, 1, 2), (2, 0, 3), (2, 1, 2), (1, 2, 1), (1, 3, 0), (2, 2, 1), (2, 3, 0), (3, 0, 1), (3, 0, 2), (3, 1, 0), (3, 1, 3), (3, 2, 0), (3, 2, 3), (3, 3, 1), (3, 3, 2), ] #: Precomputed list of tuples consisting of indices of christoffel symbols which are non-zero in Kerr Metric def scaled_spin_factor(a, M, c=constant.c.value, G=constant.G.value): """ Returns a scaled version of spin factor(a) Parameters ---------- a : float Number between 0 & 1 M : float Mass of massive body c : float Speed of light. Defaults to speed in SI units. G : float Gravitational constant. Defaults to Gravitaional Constant in SI units. Returns ------- float Scaled spinf factor to consider changed units Raises ------ ValueError If a not between 0 & 1 """ half_scr = (schwarzschild_radius_dimensionless(M, c, G)) / 2 if a < 0 or a > 1: raise ValueError("a to be supplied between 0 and 1") return a * half_scr def sigma(r, theta, a): """ Returns the value r^2 + a^2 * cos^2(theta) Specific to Boyer-Lindquist coordinates Parameters ---------- r : float Component r in vector theta : float Component theta in vector a : float Any constant Returns ------- float The value r^2 + a^2 * cos^2(theta) """ return (r ** 2) + ((a * np.cos(theta)) ** 2) def delta(r, M, a, c=constant.c.value, G=constant.G.value): """ Returns the value r^2 - Rs * r + a^2 Specific to Boyer-Lindquist coordinates Parameters ---------- r : float Component r in vector M : float Mass of massive body a : float Any constant Returns ------- float The value r^2 - Rs * r + a^2 """ Rs = schwarzschild_radius_dimensionless(M, c, G) return (r ** 2) - (Rs * r) + (a ** 2) def metric(r, theta, M, a, c=constant.c.value, G=constant.G.value): """ Returns the Kerr Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of massive body a : float Black Hole spin factor c : float Speed of light Returns ------- ~numpy.array Numpy array of shape (4,4) """ Rs = schwarzschild_radius_dimensionless(M, c, G) m = np.zeros(shape=(4, 4), dtype=float) sg, dl = sigma(r, theta, a), delta(r, M, a, c, G) c2 = c ** 2 # set the diagonal/off-diagonal terms of metric m[0, 0] = 1 - (Rs * r / sg) m[1, 1] = (sg / dl) * (-1 / c2) m[2, 2] = -1 * sg / c2 m[3, 3] = ( (-1 / c2) * ((r ** 2) + (a ** 2) + (Rs * r * (np.sin(theta) ** 2) * ((a ** 2) / sg))) * (np.sin(theta) ** 2) ) m[0, 3] = m[3, 0] = Rs * r * a * (np.sin(theta) ** 2) / (sg * c) return m def metric_inv(r, theta, M, a, c=constant.c.value, G=constant.G.value): """ Returns the inverse of Kerr Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of massive body a : float Black Hole spin factor c : float Speed of light Returns ------- ~numpy.array Numpy array of shape (4,4) """ m = metric(r, theta, M, a, c, G) return np.linalg.inv(m) def dmetric_dx(r, theta, M, a, c=constant.c.value, G=constant.G.value): """ Returns differentiation of each component of Kerr metric tensor w.r.t. t, r, theta, phi Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of massive body a : float Black Hole spin factor c : float Speed of light Returns ------- dmdx : ~numpy.array Numpy array of shape (4,4,4) dmdx[0], dmdx[1], dmdx[2] & dmdx[3] is differentiation of metric w.r.t. t, r, theta & phi respectively """ Rs = schwarzschild_radius_dimensionless(M, c, G) dmdx = np.zeros(shape=(4, 4, 4), dtype=float) sg, dl = sigma(r, theta, a), delta(r, M, a, c, G) c2 = c ** 2 # metric is invariant on t & phi # differentiation of metric wrt r def due_to_r(): nonlocal dmdx dsdr = 2 * r dddr = 2 * r - Rs tmp = (Rs * (sg - r * dsdr) / sg) * (1 / sg) dmdx[1, 0, 0] = -1 * tmp dmdx[1, 1, 1] = (-1 / c2) * (dsdr - (sg * (dddr / dl))) / dl dmdx[1, 2, 2] = (-1 / c2) * dsdr dmdx[1, 3, 3] = ( (-1 / c2) * (2 * r + (a ** 2) * (np.sin(theta) ** 2) * tmp) * (np.sin(theta) ** 2) ) dmdx[1, 0, 3] = dmdx[1, 3, 0] = (1 / c) * (a * (np.sin(theta) ** 2) * tmp) # differentiation of metric wrt theta def due_to_theta(): nonlocal dmdx dsdth = -2 * (a ** 2) * np.cos(theta) * np.sin(theta) tmp = (-1 / sg) * Rs * r * dsdth / sg dmdx[2, 0, 0] = -1 * tmp dmdx[2, 1, 1] = (-1 / c2) * (dsdth / dl) dmdx[2, 2, 2] = (-1 / c2) * dsdth dmdx[2, 3, 3] = (-1 / c2) * ( 2 * np.sin(theta) * np.cos(theta) * ((r ** 2) + (a ** 2)) + tmp * (a ** 2) * (np.sin(theta) ** 4) + (4 * (np.sin(theta) ** 3) * np.cos(theta) * (a ** 2) * r * Rs / sg) ) dmdx[2, 0, 3] = dmdx[2, 3, 0] = (a / c) * ( (np.sin(theta) ** 2) * tmp + (2 * np.sin(theta) * np.cos(theta) * Rs * r / sg) ) due_to_r() due_to_theta() return dmdx def christoffels(r, theta, M, a, c=constant.c.value, G=constant.G.value): """ Returns the 3rd rank Tensor containing Christoffel Symbols for Kerr Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of massive body a : float Black Hole spin factor c : float Speed of light Returns ------- ~numpy.array Numpy array of shape (4,4,4) """ invg = metric_inv(r, theta, M, a, c, G) dmdx = dmetric_dx(r, theta, M, a, c, G) chl = np.zeros(shape=(4, 4, 4), dtype=float) for _, k, l in nonzero_christoffels_list[0:4]: val1 = dmdx[l, 0, k] + dmdx[k, 0, l] val2 = dmdx[l, 3, k] + dmdx[k, 3, l] chl[0, k, l] = chl[0, l, k] = 0.5 * (invg[0, 0] * (val1) + invg[0, 3] * (val2)) chl[3, k, l] = chl[3, l, k] = 0.5 * (invg[3, 0] * (val1) + invg[3, 3] * (val2)) for i, k, l in nonzero_christoffels_list[8:16]: chl[i, k, l] = 0.5 * ( invg[i, i] * (dmdx[l, i, k] + dmdx[k, i, l] - dmdx[i, k, l]) ) for i, k, l in nonzero_christoffels_list[16:20]: chl[i, k, l] = chl[i, l, k] = 0.5 * ( invg[i, i] * (dmdx[l, i, k] + dmdx[k, i, l] - dmdx[i, k, l]) ) return chl @u.quantity_input(mass=u.kg) def kerr_time_velocity(pos_vec, vel_vec, mass, a): """ Velocity of coordinate time wrt proper metric Parameters ---------- pos_vector : ~numpy.array Vector with r, theta, phi components in SI units vel_vector : ~numpy.array Vector with velocities of r, theta, phi components in SI units mass : ~astropy.units.kg Mass of the body a : float Any constant Returns ------- ~astropy.units.one Velocity of time """ g = metric(pos_vec[0], pos_vec[1], mass.value, a) A = g[0, 0] B = 2 * g[0, 3] C = ( g[1, 1] * (vel_vec[0] ** 2) + g[2, 2] * (vel_vec[1] ** 2) + g[3, 3] * (vel_vec[2] ** 2) - 1 ) D = (B ** 2) - (4 * A * C) vt = (B + np.sqrt(D)) / (2 * A) return vt * u.one def nonzero_christoffels(): """ Returns a list of tuples consisting of indices of christoffel symbols which are non-zero in Kerr Metric computed in real-time. Returns ------- list List of tuples each tuple (i,j,k) represent christoffel symbol with i as upper index and j,k as lower indices. """ # Below is the code for algorithmically calculating the indices of nonzero christoffel symbols in Kerr Metric. invg = np.zeros(shape=(4, 4), dtype=bool) dmdx = np.zeros(shape=(4, 4, 4), dtype=bool) invg[3, 0] = invg[0, 3] = True dmdx[1, 3, 0] = dmdx[1, 0, 3] = True dmdx[2, 0, 3] = dmdx[2, 3, 0] = True # Code Climate cyclomatic complexity hack ; Instead of "for i in range(4)" invg[0, 0] = invg[1, 1] = invg[2, 2] = invg[3, 3] = True dmdx[1, 0, 0] = dmdx[1, 1, 1] = dmdx[1, 2, 2] = dmdx[1, 3, 3] = True dmdx[2, 0, 0] = dmdx[2, 1, 1] = dmdx[2, 2, 2] = dmdx[2, 3, 3] = True # hack ends chl = np.zeros(shape=(4, 4, 4), dtype=bool) tmp = np.array([i for i in range(4 ** 3)]) vcl = list() for t in tmp: i = int(t / (4 ** 2)) % 4 k = int(t / 4) % 4 l = t % 4 for m in range(4): chl[i, k, l] |= invg[i, m] & (dmdx[l, m, k] | dmdx[k, m, l] | dmdx[m, k, l]) if chl[i, k, l]: vcl.append((i, k, l)) return vcl def spin_factor(J, M, c): """ Calculate spin factor(a) of kerr body Parameters ---------- J : float Angular momentum in SI units(kg m2 s-2) M : float Mass of body in SI units(kg) c : float Speed of light Returns ------- float Spin factor (J/(Mc)) """ return J / (M * c) def event_horizon( M, a, theta=np.pi / 2, coord="BL", c=constant.c.value, G=constant.G.value ): """ Calculate the radius of event horizon of Kerr black hole Parameters ---------- M : float Mass of massive body a : float Black hole spin factor theta : float Angle from z-axis in Boyer-Lindquist coordinates in radians. Mandatory for coord=='Spherical'. Defaults to pi/2. coord : str Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'. c : float Speed of light G : float Gravitational constant Returns ------- ~numpy.array [Radius of event horizon(R), angle from z axis(theta)] in BL/Spherical coordinates """ Rs = schwarzschild_radius_dimensionless(M, c, G) Rh = 0.5 * (Rs + np.sqrt((Rs ** 2) - 4 * (a ** 2))) if coord == "BL": ans = np.array([Rh, theta], dtype=float) else: ans = ( BoyerLindquist(Rh * u.m, theta * u.rad, 0.0 * u.rad, a * u.m) .to_spherical() .si_values()[:2] ) return ans def radius_ergosphere( M, a, theta=np.pi / 2, coord="BL", c=constant.c.value, G=constant.G.value ): """ Calculate the radius of ergospere of Kerr black hole at a specific azimuthal angle Parameters ---------- M : float Mass of massive body a : float Black hole spin factor theta : float Angle from z-axis in Boyer-Lindquist coordinates in radians. Defaults to pi/2. coord : str Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'. c : float Speed of light G : float Gravitational constant Returns ------- ~numpy.array [Radius of ergosphere(R), angle from z axis(theta)] in BL/Spherical coordinates """ Rs = schwarzschild_radius_dimensionless(M, c, G) Re = 0.5 * (Rs + np.sqrt((Rs ** 2) - 4 * (a ** 2) * (np.cos(theta) ** 2))) if coord == "BL": ans = np.array([Re, theta], dtype=float) else: ans = ( BoyerLindquist(Re * u.m, theta * u.rad, 0.0 * u.rad, a * u.m) .to_spherical() .si_values()[:2] ) return ans ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/utils/kerrnewman_utils.py0000644000175000017500000004001200000000000025136 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy import constant, utils from einsteinpy.coordinates import BoyerLindquist, Spherical from einsteinpy.utils import schwarzschild_radius_dimensionless nonzero_christoffels_list = [ (0, 0, 1), (0, 0, 2), (0, 1, 3), (0, 2, 3), (0, 1, 0), (0, 2, 0), (0, 3, 1), (0, 3, 2), (1, 0, 0), (1, 1, 1), (1, 2, 2), (1, 3, 3), (2, 0, 0), (2, 1, 1), (2, 2, 2), (2, 3, 3), (1, 0, 3), (1, 1, 2), (2, 0, 3), (2, 1, 2), (1, 2, 1), (1, 3, 0), (2, 2, 1), (2, 3, 0), (3, 0, 1), (3, 0, 2), (3, 1, 0), (3, 1, 3), (3, 2, 0), (3, 2, 3), (3, 3, 1), (3, 3, 2), ] #: Precomputed list of tuples consisting of indices of christoffel symbols which are non-zero in Kerr-Newman Metric def charge_length_scale( Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value ): """ Returns a length scale corrosponding to the Electric Charge Q of the mass Parameters ---------- Q : float Charge on the massive body c : float Speed of light. Defaults to 299792458 (SI units) G : float Gravitational constant. Defaults to 6.67408e-11 (SI units) Cc : float Coulumb's constant. Defaults to 8.98755e9 (SI units) Returns ------- float returns (coulomb's constant^0.5)*(Q/c^2)*G^0.5 """ return (Q / (c ** 2)) * np.sqrt(G * Cc) def rho(r, theta, a): """ Returns the value sqrt(r^2 + a^2 * cos^2(theta)). Specific to Boyer-Lindquist coordinates Parameters ---------- r : float Component r in vector theta : float Component theta in vector a : float Any constant Returns ------- float The value sqrt(r^2 + a^2 * cos^2(theta)) """ return np.sqrt((r ** 2) + ((a * np.cos(theta)) ** 2)) def delta( r, M, a, Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value ): """ Returns the value r^2 - Rs * r + a^2 Specific to Boyer-Lindquist coordinates Parameters ---------- r : float Component r in vector M : float Mass of the massive body a : float Any constant Q : float Charge on the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- float The value r^2 - Rs * r + a^2 + Rq^2 """ Rs = utils.schwarzschild_radius_dimensionless(M, c, G) return (r ** 2) - (Rs * r) + (a ** 2) + (charge_length_scale(Q, c, G, Cc) ** 2) def metric( r, theta, M, a, Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns the Kerr-Newman Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body a : float Black Hole spin factor Q : float Charge on the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,4) """ m = np.zeros((4, 4), dtype=float) rh2, dl = rho(r, theta, a) ** 2, delta(r, M, a, Q, c, G, Cc) c2 = c ** 2 # set the diagonal/off-diagonal terms of metric m[0, 0] = (dl - ((a * np.sin(theta)) ** 2)) / (rh2) m[1, 1] = -rh2 / (dl * c2) m[2, 2] = -rh2 / c2 m[3, 3] = ( (((a * np.sin(theta)) ** 2) * dl - ((r ** 2 + a ** 2) ** 2)) * (np.sin(theta) ** 2) / (rh2 * c2) ) m[0, 3] = m[3, 0] = ( -a * (np.sin(theta) ** 2) * (dl - (r ** 2) - (a ** 2)) / (rh2 * c) ) return m def metric_inv( r, theta, M, a, Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns the inverse of Kerr-Newman Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body a : float Black Hole spin factor Q : float Charge on the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,4) """ return np.linalg.inv(metric(r, theta, M, a, Q, c, G, Cc)) def dmetric_dx( r, theta, M, a, Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns differentiation of each component of Kerr-Newman metric tensor w.r.t. t, r, theta, phi Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body a : float Black Hole spin factor Q : float Charge on the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- dmdx : ~numpy.array Numpy array of shape (4,4,4) dmdx[0], dmdx[1], dmdx[2] & dmdx[3] is differentiation of metric w.r.t. t, r, theta & phi respectively """ Rs = utils.schwarzschild_radius_dimensionless(M, c, G) dmdx = np.zeros((4, 4, 4), dtype=float) rh2, dl = rho(r, theta, a) ** 2, delta(r, M, a, Q, c, G, Cc) c2 = c ** 2 # metric is invariant on t & phi # differentiation of metric wrt r def due_to_r(): nonlocal dmdx drh2dr = 2 * r dddr = 2 * r - Rs dmdx[1, 0, 0] = (dddr * rh2 - drh2dr * (dl - (a * np.sin(theta)) ** 2)) / ( rh2 ** 2 ) dmdx[1, 1, 1] = (-1 / (c2 * (dl ** 2))) * (drh2dr * dl - dddr * rh2) dmdx[1, 2, 2] = -drh2dr / c2 dmdx[1, 3, 3] = ((np.sin(theta) ** 2) / (c2 * (rh2 ** 2))) * ( ( (((a * np.sin(theta)) ** 2) * dddr - 4 * (r ** 3) - 4 * (r * (a ** 2))) * rh2 ) - (drh2dr * (((a * np.sin(theta)) ** 2) * dl - ((r ** 2 + a ** 2) ** 2))) ) dmdx[1, 0, 3] = dmdx[1, 3, 0] = ( (-a) * (np.sin(theta) ** 2) / (c * (rh2 ** 2)) ) * ((dddr - 2 * r) * rh2 - drh2dr * (dl - r ** 2 - a ** 2)) # differentiation of metric wrt theta def due_to_theta(): nonlocal dmdx drh2dth = -2 * (a ** 2) * np.cos(theta) * np.sin(theta) dmdx[2, 0, 0] = ( (-2 * (a ** 2) * np.sin(theta) * np.cos(theta)) * rh2 - drh2dth * (dl - ((a * np.sin(theta)) ** 2)) ) / (rh2 ** 2) dmdx[2, 1, 1] = -drh2dth / (c2 * dl) dmdx[2, 2, 2] = -drh2dth / c2 dmdx[2, 3, 3] = (1 / (c2 * (rh2 ** 2))) * ( ( ( (4 * (a ** 2) * (np.sin(theta) ** 3) * np.cos(theta) * dl) - (2 * np.sin(theta) * np.cos(theta) * ((r ** 2 + a ** 2) ** 2)) ) * rh2 ) - ( drh2dth * (((a * np.sin(theta)) ** 2) * dl - ((r ** 2 + a ** 2) ** 2)) * (np.sin(theta) ** 2) ) ) dmdx[2, 0, 3] = dmdx[2, 3, 0] = ( (-a * (dl - r ** 2 - a ** 2)) / (c * (rh2 ** 2)) ) * ( (2 * np.sin(theta) * np.cos(theta) * rh2) - (drh2dth * (np.sin(theta) ** 2)) ) due_to_r() due_to_theta() return dmdx def christoffels( r, theta, M, a, Q, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns the 3rd rank Tensor containing Christoffel Symbols for Kerr-Newman Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body a : float Black Hole spin factor Q : float Charge on the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,4,4) """ invg = metric_inv(r, theta, M, a, Q, c, G, Cc) dmdx = dmetric_dx(r, theta, M, a, Q, c, G, Cc) chl = np.zeros(shape=(4, 4, 4), dtype=float) for _, k, l in nonzero_christoffels_list[0:4]: val1 = dmdx[l, 0, k] + dmdx[k, 0, l] val2 = dmdx[l, 3, k] + dmdx[k, 3, l] chl[0, k, l] = chl[0, l, k] = 0.5 * (invg[0, 0] * (val1) + invg[0, 3] * (val2)) chl[3, k, l] = chl[3, l, k] = 0.5 * (invg[3, 0] * (val1) + invg[3, 3] * (val2)) for i, k, l in nonzero_christoffels_list[8:16]: chl[i, k, l] = 0.5 * ( invg[i, i] * (dmdx[l, i, k] + dmdx[k, i, l] - dmdx[i, k, l]) ) for i, k, l in nonzero_christoffels_list[16:20]: chl[i, k, l] = chl[i, l, k] = 0.5 * ( invg[i, i] * (dmdx[l, i, k] + dmdx[k, i, l] - dmdx[i, k, l]) ) return chl def em_potential( r, theta, a, Q, M, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns a 4-d vector(for each component of 4-d space-time) containing the electromagnetic potential around a Kerr-Newman body Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis a : float Black Hole spin factor Q : float Charge on the massive body M : float Mass of the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,) """ rq, rh2, c2 = charge_length_scale(Q, c, G, Cc), rho(r, theta, a) ** 2, c ** 2 vec = np.zeros((4,), dtype=float) vec[0] = r * rq / rh2 vec[3] = ((-c2) / (rh2 * G * M)) * a * r * rq * (np.sin(theta) ** 2) return vec def maxwell_tensor_covariant( r, theta, a, Q, M, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns a 2nd rank Tensor containing Maxwell Tensor with lower indices for Kerr-Newman Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis a : float Black Hole spin factor Q : float Charge on the massive body M : float Mass of the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,4) """ c2 = c ** 2 m = np.zeros((4, 4), dtype=float) rh2, rq = rho(r, theta, a) ** 2, charge_length_scale(Q, c, G, Cc) drh2dr, drh2dth = 2 * r, -2 * (a ** 2) * np.cos(theta) * np.sin(theta) # set the tensor terms m[0, 1] = ((-rq) / (rh2 ** 2)) * (rh2 - drh2dr * r) m[0, 2] = r * rq * drh2dth / (rh2 ** 2) m[3, 1] = (c2 * a * rq * (np.sin(theta) ** 2) / (G * M * (rh2 ** 2))) * ( rh2 - r * drh2dr ) m[3, 2] = (c2 * a * rq * r / (G * M * (rh2 ** 2))) * ( (2 * np.sin(theta) * np.cos(theta) * rh2) - (drh2dth * (np.sin(theta) ** 2)) ) for i, j in [(0, 1), (0, 2), (3, 1), (3, 2)]: m[j, i] = -m[i, j] return m def maxwell_tensor_contravariant( r, theta, a, Q, M, c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Returns a 2nd rank Tensor containing Maxwell Tensor with upper indices for Kerr-Newman Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis a : float Black Hole spin factor Q : float Charge on the massive body M : float Mass of the massive body c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array Numpy array of shape (4,4) """ mcov = maxwell_tensor_covariant(r, theta, a, Q, M, c, G, Cc) ginv = metric_inv(r, theta, M, a, Q, c, G, Cc) # contravariant F = contravariant g X covariant F X transpose(contravariant g) # but g is symettric return np.matmul(np.matmul(ginv, mcov), ginv) @u.quantity_input(mass=u.kg, Q=u.C) def kerrnewman_time_velocity(pos_vec, vel_vec, mass, a, Q): """ Velocity of coordinate time wrt proper metric Parameters ---------- pos_vector : ~numpy.array Vector with r, theta, phi components in SI units vel_vector : ~numpy.array Vector with velocities of r, theta, phi components in SI units mass : ~astropy.units.kg Mass of the body a : float Any constant Q : ~astropy.units.C Charge on the massive body Returns ------- ~astropy.units.one Velocity of time """ _scr = utils.schwarzschild_radius(mass).value Qc = Q.to(u.C) g = metric(pos_vec[0], pos_vec[1], mass.value, a, Qc.value) A = g[0, 0] B = 2 * g[0, 3] C = ( g[1, 1] * (vel_vec[0] ** 2) + g[2, 2] * (vel_vec[1] ** 2) + g[3, 3] * (vel_vec[2] ** 2) - 1 ) D = (B ** 2) - (4 * A * C) vt = (B + np.sqrt(D)) / (2 * A) return vt * u.one def event_horizon( M, a, Q, theta=np.pi / 2, coord="BL", c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Calculate the radius of event horizon of Kerr-Newman black hole Parameters ---------- M : float Mass of massive body a : float Black hole spin factor Q : float Charge on the black hole theta : float Angle from z-axis in Boyer-Lindquist coordinates in radians. Mandatory for coord=='Spherical'. Defaults to pi/2. coord : str Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'. c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array [Radius of event horizon(R), angle from z axis(theta)] in BL/Spherical coordinates """ Rs = schwarzschild_radius_dimensionless(M, c, G) rQsq = (Q ** 2) * G * Cc / c ** 4 Rh = 0.5 * Rs + np.sqrt((Rs ** 2) / 4 - a ** 2 - rQsq) if coord == "BL": ans = np.array([Rh, theta], dtype=float) else: ans = ( BoyerLindquist(Rh * u.m, theta * u.rad, 0.0 * u.rad, a * u.m) .to_spherical() .si_values()[:2] ) return ans def radius_ergosphere( M, a, Q, theta=np.pi / 2, coord="BL", c=constant.c.value, G=constant.G.value, Cc=constant.coulombs_const.value, ): """ Calculate the radius of ergospere of Kerr-Newman black hole at a specific azimuthal angle Parameters ---------- M : float Mass of massive body a : float Black hole spin factor Q : float Charge on the black hole theta : float Angle from z-axis in Boyer-Lindquist coordinates in radians. Mandatory for coord=='Spherical'. Defaults to pi/2. coord : str Output coordinate system. 'BL' for Boyer-Lindquist & 'Spherical' for spherical. Defaults to 'BL'. c : float Speed of light G : float Gravitational constant Cc : float Coulomb's constant Returns ------- ~numpy.array [Radius of event horizon(R), angle from z axis(theta)] in BL/Spherical coordinates """ Rs = schwarzschild_radius_dimensionless(M, c, G) rQsq = (Q ** 2) * G * Cc / c ** 4 Rh = 0.5 * Rs + np.sqrt((Rs ** 2) / 4 - a ** 2 * np.cos(theta) ** 2 - rQsq) if coord == "BL": ans = np.array([Rh, theta], dtype=float) else: ans = ( BoyerLindquist(Rh * u.m, theta * u.rad, 0.0 * u.rad, a * u.m) .to_spherical() .si_values()[:2] ) return ans ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/utils/scalar_factor.py0000644000175000017500000000430200000000000024352 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy import constant @u.quantity_input(t=u.s) def scalar_factor(t, era="md", tuning_param=1.0): """ Acceleration of the universe in cosmological models of Robertson Walker Flat Universe. Parameters ---------- era : string Can be chosen from 'md' (Matter Dominant), 'rd' (Radiation Dominant) and 'ded' (Dark Energy Dominant) t : ~astropy.units.s Time for the event tuning_param : float, optional Unit scaling factor, defaults to 1 Returns ------- float Value of scalar factor at time t. Raises ------ ValueError : If era is not 'md' , 'rd', and 'ded'. """ T = t.to(u.s).value if era == "md": return tuning_param * (T ** (2 / 3)) elif era == "rd": return tuning_param * (T ** (0.5)) elif era == "ded": hubble_const = (constant.Cosmo_Const / 3) ** 0.5 val = np.e ** (hubble_const.value * T) return tuning_param * val else: raise ValueError("Passed era should be either 'md', 'rd' or 'ded' ") @u.quantity_input(t=u.s) def scalar_factor_derivative(t, era="md", tuning_param=1.0): """ Derivative of acceleration of the universe in cosmological models of Robertson Walker Flat Universe. Parameters ---------- era : string Can be chosen from 'md' (Matter Dominant), 'rd' (Radiation Dominant) and 'ded' (Dark Energy Dominant) t : ~astropy.units.s Time for the event tuning_param : float, optional Unit scaling factor, defaults to 1 Returns ------- float Value of derivative of scalar factor at time t. Raises ------ ValueError : If era is not 'md' , 'rd', and 'ded'. """ T = t.to(u.s).value if era == "md": return (2 / 3) * tuning_param * (T ** (-1 / 3)) elif era == "rd": return 0.5 * tuning_param * (T ** (-0.5)) elif era == "ded": hubble_const = (constant.Cosmo_Const / 3) ** 0.5 val = hubble_const.value * (np.e ** (hubble_const.value * T)) return tuning_param * val else: raise ValueError("Passed era should be either 'md', 'rd' or 'ded' ") ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588625238.0 einsteinpy-0.3.0/src/einsteinpy/utils/schwarzschild_utils.py0000644000175000017500000000773300000000000025652 0ustar00shreyasshreyas00000000000000import astropy.units as u import numpy as np from einsteinpy import constant def schwarzschild_radius(mass, c=constant.c, G=constant.G): """ Schwarzschild radius is the radius defining the event horizon of a Schwarzschild black hole. It is characteristic radius associated with every quantity of mass. Parameters ---------- mass : ~astropy.units.kg Returns ------- r : ~astropy.units.m Schwarzschild radius for a given mass """ if not isinstance(mass, u.quantity.Quantity): mass = mass * u.kg if not isinstance(c, u.quantity.Quantity): c = c * u.m / u.s if not isinstance(G, u.quantity.Quantity): G = G * constant.G.unit M = mass.to(u.kg) num = 2 * G * M deno = c ** 2 return num / deno def schwarzschild_radius_dimensionless(M, c=constant.c.value, G=constant.G.value): """ Parameters ------------ M : float Mass of massive body c : float Speed of light, defaults to value of speed of light in SI units. G : float Gravitational Constant, defaults to its value in SI units Returns ------- Rs : float Schwarzschild radius for a given mass """ Rs = 2 * M * G / c ** 2 return Rs @u.quantity_input(mass=u.kg) def time_velocity(pos_vec, vel_vec, mass): """ Velocity of time calculated from einstein's equation. See http://www.physics.usu.edu/Wheeler/GenRel/Lectures/GRNotesDecSchwarzschildGeodesicsPost.pdf Parameters ---------- pos_vector : ~numpy.array Vector with r, theta, phi components in SI units vel_vector : ~numpy.array Vector with velocities of r, theta, phi components in SI units mass : ~astropy.units.kg Mass of the body Returns ------- ~astropy.units.one Velocity of time """ # this function considers SI units only a = schwarzschild_radius(mass).value c = constant.c.value num1 = (1 / ((c ** 2) * (1 + (a / pos_vec[0])))) * (vel_vec[0] ** 2) num2 = ((pos_vec[0] ** 2) / (c ** 2)) * (vel_vec[1] ** 2) num3 = ( ((pos_vec[0] ** 2) / (c ** 2)) * (np.sin(pos_vec[1]) ** 2) * (vel_vec[2] ** 2) ) deno = 1 + (a / pos_vec[0]) time_vel_squared = (1 + num1 + num2 + num3) / deno time_vel = np.sqrt(time_vel_squared) return time_vel * u.one def metric(r, theta, M, c=constant.c.value, G=constant.G.value): """ Returns the Schwarzschild Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body c : float Speed of light Returns ------- ~numpy.array Numpy array of shape (4,4) """ Rs = schwarzschild_radius_dimensionless(M, c, G) m = np.zeros(shape=(4, 4), dtype=float) tmp, c2 = 1.0 - (Rs / r), c ** 2 m[0, 0] = tmp m[1, 1] = -1.0 / (tmp * c2) m[2, 2] = -1 * (r ** 2) / c2 m[3, 3] = -1 * ((r * np.sin(theta)) ** 2) / c2 return m def christoffels(r, theta, M, c=constant.c.value, G=constant.G.value): """ Returns the 3rd rank Tensor containing Christoffel Symbols for Schwarzschild Metric Parameters ---------- r : float Distance from the centre theta : float Angle from z-axis M : float Mass of the massive body c : float Speed of light Returns ------- ~numpy.array Numpy array of shape (4,4,4) """ Rs = schwarzschild_radius_dimensionless(M, c, G) chl = np.zeros(shape=(4, 4, 4), dtype=float) c2 = c ** 2 chl[1, 0, 0] = 0.5 * Rs * (r - Rs) * c2 / (r ** 3) chl[1, 1, 1] = 0.5 * Rs / (Rs * r - r ** 2) chl[1, 2, 2] = Rs - r chl[1, 3, 3] = (Rs - r) * (np.sin(theta) ** 2) chl[0, 0, 1] = chl[0, 1, 0] = -chl[1, 1, 1] chl[2, 2, 1] = chl[2, 1, 2] = chl[3, 3, 1] = chl[3, 1, 3] = 1 / r chl[2, 3, 3] = -np.cos(theta) * np.sin(theta) chl[3, 3, 2] = chl[3, 2, 3] = 1 / np.tan(theta) return chl ././@PaxHeader0000000000000000000000000000003400000000000011452 xustar000000000000000028 mtime=1588632901.2073443 einsteinpy-0.3.0/src/einsteinpy.egg-info/0000755000175000017500000000000000000000000021530 5ustar00shreyasshreyas00000000000000././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588632901.0 einsteinpy-0.3.0/src/einsteinpy.egg-info/PKG-INFO0000644000175000017500000003024500000000000022631 0ustar00shreyasshreyas00000000000000Metadata-Version: 2.1 Name: einsteinpy Version: 0.3.0 Summary: Python package for General Relativity Home-page: https://einsteinpy.org/ Author: Shreyas Bapat Author-email: bapat.shreyas@gmail.com License: MIT Download-URL: https://github.com/einsteinpy/einsteinpy Description: .. einsteinpy .. image:: https://blog.einsteinpy.org/img/logo.png :target: https://einsteinpy.org/ :alt: EinsteinPy logo :width: 675px :align: center .. |astropy| image:: http://img.shields.io/badge/powered%20by-AstroPy-orange.svg?style=flat-square :target: http://www.astropy.org/ .. |mailing| image:: https://img.shields.io/badge/mailing%20list-groups.io-8cbcd1.svg?style=flat-square :target: https://groups.io/g/einsteinpy-dev .. |doi| image:: https://zenodo.org/badge/168302584.svg?style=flat-square :target: https://zenodo.org/badge/latestdoi/168302584 .. |gitter| image:: https://img.shields.io/gitter/room/EinsteinPy-Project/EinsteinPy.svg?logo=gitter&style=flat-square :alt: Join the chat at https://gitter.im/EinsteinPy-Project/EinsteinPy :target: https://gitter.im/EinsteinPy-Project/EinsteinPy?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge .. |riotchat| image:: https://img.shields.io/matrix/einsteinpy:matrix.org.svg?logo=riot&style=flat-square :target: https://riot.im/app/#/room/#einsteinpy:matrix.org .. |license| image:: https://img.shields.io/badge/license-MIT-blue.svg?style=flat-square :target: https://github.com/einsteinpy/einsteinpy/raw/0.3.x/COPYING .. |docs| image:: https://img.shields.io/badge/docs-latest-brightgreen.svg?style=flat-square :target: https://docs.einsteinpy.org/en/v0.3.0/?badge=latest .. |codeclimate| image:: https://img.shields.io/codeclimate/maintainability/einsteinpy/einsteinpy.svg?logo=code-climate&style=flat-square :target: https://codeclimate.com/github/einsteinpy/einsteinpy/maintainability :alt: Maintainability .. |circleci| image:: https://img.shields.io/circleci/project/github/einsteinpy/einsteinpy/0.3.x.svg?style=flat-square&logo=circleci :target: https://circleci.com/gh/einsteinpy/einsteinpy .. |ghactions| image:: https://img.shields.io/github/workflow/status/einsteinpy/einsteinpy/Test_MacOS?logo=github&style=flat-square :target: https://github.com/einsteinpy/einsteinpy/actions?query=branch%3A0.3.x .. |codecov| image:: https://img.shields.io/codecov/c/github/einsteinpy/einsteinpy.svg?style=flat-square :target: https://codecov.io/github/einsteinpy/einsteinpy?branch=0.3.x .. |appveyor| image:: https://img.shields.io/appveyor/ci/shreyasbapat/einsteinpy/0.3.x?logo=appveyor&style=flat-square :target: https://ci.appveyor.com/project/shreyasbapat/einsteinpy/branch/0.3.x .. |orcid-shreyas| image:: https://img.shields.io/badge/id-0000--0002--0870--4665-a6ce39.svg :target: https://orcid.org/0000-0002-0870-4665 :Name: EinsteinPy :Website: https://einsteinpy.org/ :Version: 0.3.0 |astropy| |mailing| |gitter| |riotchat| |license| |docs| |circleci| |ghactions| |appveyor| |codecov| |codeclimate| **EinsteinPy** is an open source pure Python package dedicated to problems arising in General Relativity and gravitational physics, such as geodesics plotting for Schwarzschild, Kerr and Kerr Newman space-time model, calculation of Schwarzschild radius, calculation of Event Horizon and Ergosphere for Kerr space-time. Symbolic Manipulations of various tensors like Metric, Riemann, Ricci, Ricci Scalar, Weyl, Schouten, Stress-Energy-Momentum, Einstein and Christoffel Symbols is also possible using the library. EinsteinPy also features Hypersurface Embedding of Schwarzschild space-time, which will soon lead to modelling of Gravitational Lensing! It is released under the MIT license. Documentation ============= |docs| Complete documentation, including a user guide and an API reference, can be read on the wonderful `Read the Docs`_. https://docs.einsteinpy.org/ .. _`Read the Docs`: https://readthedocs.org/ Examples ======== .. |mybinder| image:: https://img.shields.io/badge/launch-binder-e66581.svg?style=flat-square :target: https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb |mybinder| In the examples directory, you can find several Jupyter notebooks with specific applications of einsteinpy. You can consider theses Jupyter Notebooks as tutorials for einsteinpy. You can launch a cloud Jupyter server using `binder`_ to edit the notebooks without installing anything. Try it out! https://beta.mybinder.org/v2/gh/einsteinpy/einsteinpy/0.3.x?filepath=index.ipynb .. _binder: https://beta.mybinder.org/ Requirements ============ EinsteinPy requires the following Python packages: * NumPy, for basic numerical routines * Astropy, for physical units and time handling * Matplotlib, for static geodesics plotting and visualizations. * Plotly, for interactive geodesics plotting and visualizations. * SciPy, for solving ordinary differential equations. * SymPy, for symbolic calculations related to GR. * Numba, for accelerating the code EinsteinPy is usually tested on Linux, Windows and OS X on Python 3.6, 3.7 and 3.8 against latest NumPy. ============== =============== =================== Platform Site Status ============== =============== =================== Linux CircleCI |circleci| OS X Github Actions |ghactions| Windows x64 Appveyor |appveyor| ============== =============== =================== Installation ============ The easiest and fastest way to get the package up and running is to install EinsteinPy using `conda `_:: $ conda install einsteinpy --channel conda-forge Or you can simply install it from `PyPI `_:: $ pip install einsteinpy Or for Debian/Ubuntu/Mint users, the package is installable (Ubuntu 19.04 onwards) from `apt `_:: $ sudo apt install python3-einsteinpy Please note that the package version in Debian Repositories might not be the latest. But it will be definitely the most stable version of EinsteinPy available till date. Please check out the `guide for alternative installation methods`_. .. _`guide for alternative installation methods`: https://einsteinpy.github.io/installation/ Testing ======= |codecov| If installed correctly, the tests can be run using pytest:: $ python -c "import einsteinpy.testing; einsteinpy.testing.test()" ============================= test session starts ============================== platform linux -- Python 3.7.1, pytest-4.3.1, py-1.8.0, pluggy-0.9.0 rootdir: /home/shreyas/Local Forks/einsteinpy, inifile: setup.cfg plugins: remotedata-0.3.1, openfiles-0.3.1, doctestplus-0.3.0, cov-2.5.1, arraydiff-0.3 collected 56 items [...] ==================== 56 passed, 1 warnings in 28.19 seconds ==================== $ Problems ======== If the installation fails or you find something that doesn't work as expected, please open an issue in the `issue tracker`_. .. _`issue tracker`: https://github.com/einsteinpy/einsteinpy/issues Contributing ============ EinsteinPy is a community project, hence all contributions are more than welcome! For more information, head to `CONTRIBUTING.rst`_. .. _`CONTRIBUTING.rst`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/CONTRIBUTING.rst Developers Documentation can be found here. Support ======= |mailing| Release announcements and general discussion take place on our `mailing list`_. Feel free to join! .. _`mailing list`: https://groups.io/g/einsteinpy-dev https://groups.io/g/einsteinpy-dev Please join our `[matrix]`_ channel or `gitter`_ chat room for further queries. .. _`[matrix]`: https://matrix.to/#/#einsteinpy:matrix.org .. _`gitter`: https://gitter.im/EinsteinPy-Project/EinsteinPy If you still have a doubt, write a mail directly to `all@einsteinpy.org `_. Citing ====== If you use EinsteinPy on your project, please `drop us a line `_. You can also use the DOI to cite it in your publications. This is the latest one: |doi| And this is an example citation format:: Shreyas Bapat et al.. (2019). EinsteinPy: einsteinpy 0.1.0. Zenodo. 10.5281/zenodo.2582388 License ======= |license| EinsteinPy is released under the MIT license, hence allowing commercial use of the library. Please refer to `COPYING`_. .. _`COPYING`: https://github.com/einsteinpy/einsteinpy/blob/0.3.x/COPYING FAQ === Why Einstein-Py? ---------------- EinsteinPy comes from the name of the famous physicist, Nobel laureate, revolutionary person, Prof. Albert Einstein. This is a small tribute from our part for the amazing work he did for the humanity! Can I do with EinsteinPy? ---------------------------------------------- EinsteinPy is focused on general relativity. One can always discuss probable features on the mailing list and try to implement it. We welcome every contribution and will be happy to include it in EinsteinPy. What's the future of the project? --------------------------------- EinsteinPy is actively maintained and we hope to receive an influx of new contributors. The best way to get an idea of the roadmap is to see the `Milestones`_ of the project. .. _`Milestones`: https://github.com/einsteinpy/einsteinpy/milestones Inspiration ----------- The whole documentation and code structure is shamelessly inspired by `poliastro`_ . We really thank the poliastro developers to make this possible. EinsteinPy is nothing without it's supporters. .. _`poliastro`: https://docs.poliastro.space/ Keywords: general relativity,geodesics,relativity,kerr,black-hole,kerr-newman,schwarzschild Platform: UNKNOWN Classifier: Development Status :: 4 - Beta Classifier: Intended Audience :: Education Classifier: Intended Audience :: Science/Research Classifier: License :: OSI Approved :: MIT License Classifier: Operating System :: OS Independent Classifier: Programming Language :: Python Classifier: Programming Language :: Python :: 3 Classifier: Programming Language :: Python :: 3.6 Classifier: Programming Language :: Python :: 3.7 Classifier: Programming Language :: Python :: 3.8 Classifier: Topic :: Scientific/Engineering Classifier: Topic :: Scientific/Engineering :: Physics Classifier: Topic :: Scientific/Engineering :: Astronomy Requires-Python: >=3.5 Provides-Extra: dev ././@PaxHeader0000000000000000000000000000002600000000000011453 xustar000000000000000022 mtime=1588632901.0 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