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cxroots
=======
cxroots is a Python package for finding all the roots of a function, *f(z)*, of a single complex variable within a given contour, *C*, in the complex plane. It requires only that both:
- *f(z)* has no roots or poles on *C*
- *f(z)* is analytic in the interior of *C*
The implementation is primarily based on [KB]_ and evaluates contour integrals involving *f(z)* and its derivative *f'(z)* to determine the roots. If *f'(z)* is not provided then it is approximated using a finite difference method. The roots are further refined using Newton-Raphson if *f'(z)* is given or Muller's method if not. See the `documentation <https://rparini.github.io/cxroots/>`_ for a more details and a tutorial.
With `Python <http://www.python.org/>`_ installed you can install cxroots by entering in the terminal/command line
.. code:: bash
pip install cxroots
Example
-------
.. code:: python
from numpy import exp, cos, sin
f = lambda z: (exp(2*z)*cos(z)-1-sin(z)+z**5)*(z*(z+2))**2
from cxroots import Circle
C = Circle(0,3)
roots = C.roots(f)
roots.show()
.. Relative images do not display on pypi
.. image:: https://github.com/rparini/cxroots/blob/master/README_resources/readme_example.png?raw=true
.. code:: python
print(roots)
.. literalinclude readme_example.txt doesn't work on github
.. code::
Multiplicity | Root
------------------------------------------------
2 | -2.000000000000 +0.000000000000i
1 | -0.651114070264 -0.390425719088i
1 | -0.651114070264 +0.390425719088i
3 | 0.000000000000 +0.000000000000i
1 | 0.648578080954 -1.356622683988i
1 | 0.648578080954 +1.356622683988i
1 | 2.237557782467 +0.000000000000i
See also
--------
The Fortran 90 package `ZEAL <http://cpc.cs.qub.ac.uk/summaries/ADKW>`_ is a direct implementation of [KB]_.
Citing cxroots
--------------
\R. Parini. *cxroots: A Python module to find all the roots of a complex analytic function within a given contour* (2018), https://github.com/rparini/cxroots https://doi.org/10.5281/zenodo.7013117
BibTex:
.. code::
@misc{cxroots,
author = {Robert Parini},
title = {{cxroots: A Python module to find all the roots of a complex analytic function within a given contour}},
doi = {10.5281/zenodo.7013116},
url = {https://github.com/rparini/cxroots},
year = {2018}
}
----------
Development
-----------
- Install the `pre-commit <https://pre-commit.com/>`_ and then run :code:`pre-commit install`. The pre-commit scripts can also be run manually with :code:`pre-commit run --all-files`
- The project uses:
- `Black <https://github.com/psf/black/>`_ to maintain consistent formatting. It is run as part of the pre-commit hook and is recommended to be run on save in the developer's editor.
- `isort <https://pycqa.github.io/isort/>`_ to sensibly order import statements in Python files. It is also run as part of the pre-commit hook.
Release Procedure
-----------------
Making a release on GitHub with the tag vX.Y.Z will update the documentation on `master` and push cxroots at the tagged commit to PyPI.
The documentation can be manually generated by running `./create_docs` in the `docs_src` directory.
References
----------
.. [KB] \P. Kravanja and M. Van Barel. *Computing the Zeros of Analytic Functions*. Springer, Berlin, Heidelberg, 2000.
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"description": "|pkg_img| |doi| |tests| |coverage|\n\n.. |tests| image:: https://github.com/rparini/cxroots/workflows/tests/badge.svg\n :target: https://github.com/rparini/cxroots/actions\n\n.. |doi| image:: https://zenodo.org/badge/79802240.svg\n :target: https://zenodo.org/badge/latestdoi/79802240\n\n.. |pkg_img| image:: https://badge.fury.io/py/cxroots.svg\n :target: https://badge.fury.io/py/cxroots\n\n.. |coverage| image:: https://coveralls.io/repos/github/rparini/cxroots/badge.svg\n\t:target: https://coveralls.io/github/rparini/cxroots\n\n\ncxroots\n=======\n\ncxroots is a Python package for finding all the roots of a function, *f(z)*, of a single complex variable within a given contour, *C*, in the complex plane. It requires only that both:\n\n- *f(z)* has no roots or poles on *C*\n- *f(z)* is analytic in the interior of *C*\n\nThe implementation is primarily based on [KB]_ and evaluates contour integrals involving *f(z)* and its derivative *f'(z)* to determine the roots. If *f'(z)* is not provided then it is approximated using a finite difference method. The roots are further refined using Newton-Raphson if *f'(z)* is given or Muller's method if not. See the `documentation <https://rparini.github.io/cxroots/>`_ for a more details and a tutorial.\n\nWith `Python <http://www.python.org/>`_ installed you can install cxroots by entering in the terminal/command line\n\n.. code:: bash\n\n pip install cxroots\n\nExample\n-------\n\n.. code:: python\n\n from numpy import exp, cos, sin\n f = lambda z: (exp(2*z)*cos(z)-1-sin(z)+z**5)*(z*(z+2))**2\n \n from cxroots import Circle\n C = Circle(0,3)\n roots = C.roots(f)\n roots.show()\n\n\n.. Relative images do not display on pypi\n.. image:: https://github.com/rparini/cxroots/blob/master/README_resources/readme_example.png?raw=true\n\n.. code:: python\n\n print(roots)\n\n\n.. literalinclude readme_example.txt doesn't work on github\n.. code::\n\n\t Multiplicity | Root \n\t------------------------------------------------\n\t 2 | -2.000000000000 +0.000000000000i\n\t 1 | -0.651114070264 -0.390425719088i\n\t 1 | -0.651114070264 +0.390425719088i\n\t 3 | 0.000000000000 +0.000000000000i\n\t 1 | 0.648578080954 -1.356622683988i\n\t 1 | 0.648578080954 +1.356622683988i\n\t 1 | 2.237557782467 +0.000000000000i\n\n\nSee also\n--------\n\nThe Fortran 90 package `ZEAL <http://cpc.cs.qub.ac.uk/summaries/ADKW>`_ is a direct implementation of [KB]_.\n\nCiting cxroots\n--------------\n\n \\R. Parini. *cxroots: A Python module to find all the roots of a complex analytic function within a given contour* (2018), https://github.com/rparini/cxroots https://doi.org/10.5281/zenodo.7013117\n\nBibTex:\n\n.. code::\n\n\t@misc{cxroots,\n\t author = {Robert Parini},\n\t title = {{cxroots: A Python module to find all the roots of a complex analytic function within a given contour}},\n doi = {10.5281/zenodo.7013116},\n url = {https://github.com/rparini/cxroots},\n\t year = {2018}\n\t}\n\n----------\n\nDevelopment\n-----------\n- Install the `pre-commit <https://pre-commit.com/>`_ and then run :code:`pre-commit install`. The pre-commit scripts can also be run manually with :code:`pre-commit run --all-files`\n- The project uses:\n\n - `Black <https://github.com/psf/black/>`_ to maintain consistent formatting. It is run as part of the pre-commit hook and is recommended to be run on save in the developer's editor.\n - `isort <https://pycqa.github.io/isort/>`_ to sensibly order import statements in Python files. It is also run as part of the pre-commit hook.\n\nRelease Procedure\n-----------------\nMaking a release on GitHub with the tag vX.Y.Z will update the documentation on `master` and push cxroots at the tagged commit to PyPI.\n\nThe documentation can be manually generated by running `./create_docs` in the `docs_src` directory.\n\nReferences\n----------\n\n.. [KB] \\P. Kravanja and M. Van Barel. *Computing the Zeros of Analytic Functions*. Springer, Berlin, Heidelberg, 2000.\n\n\n",
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