Welcome to PyZEAL’s documentation!¶
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Welcome to PyZEAL!¶
Welcome to PyZEAL!
This project implements numerical algorithms for the computation of zeros of holomorphic as well as the zeros, poles and residues of meromorphic functions. It aspires to be a successor to and an extension of the original ZEAL (ZEros of AnaLytic functions) package written in Fortran90 by Kravanja, Van Barel, Ragos, Vrahatis, and Zafiropoulos [KVanBarelR+00].
The full documentation of this project is hosted on ReadTheDocs.
While there exists a wealth of theoretical results as well as battle-hardened implementations of such root finding algorithms for e.g. smooth functions (SciPy), the situation in the holomorphic setting is much less comfortable: It appears that most of the algorithms available for holomorphic ones do not possess a readily available, up-to-date, actively maintained implementation.
This (seeming) gap in the software landscape is even more apparant as these types of functions exhibit a rich structure far beyond simple smoothness, opening up the possibility for adapted, more efficient root finding algorithms. The goal of this project then is the practical implementation of such algorithms in an open-source package that is well tested, written in an accessible language, and distributed in a user-friendly manner.
We aim to support two main use cases with this package:
Enabling out-of-the-box usage as a tool within any project which requires the calculation of roots or poles of holomorphic or meromorphic functions. In particular this includes seamless integration into the Python ecosystem and a user experience similar to common packages like SciPy or NumPy.
Providing a platform for the practical implementation, debugging, testing, and benchmarking of newly developed root finding algorithms as well as their comparison with existing procedures. To this end PyZEAL includes a number of framework elements as well as a plugin mechanism for more light-weight implementations of prototypes.
The approach to achieving these goals will be iterative implementation and optimization of a variety of different algorithms and comparing them, while simultaneously exposing an easy-to-use, accessible, and standardized API.
Note
This is an ongoing project. Any contributions such as feature requests, bug reports, or collaborations on documentation, theoretical background, or practical implementation are much appreciated!
Kravanja, Van Barel, Ragos, Vrahatis, and Zafiropoulos. ZEAL: A mathematical software package for computing zeros of analytic functions. Computer Physics Communications, 124(2):212–232, 2000.
How to Contribute¶
If you would like to contribute anything from an improvement of the documentation, a new feature request, bug report or (parts of) a root finding algorithm, please feel free to do so. Any collaborations are welcome and the documentation or the open issues might be a good place to start.
To contribute, either clone or fork the GitHub repository and create a development branch dev/<your_feature>. Once you have completed your work on this branch create a pull request on the main branch of the repo. At this point your PR requires (at least) one positive review from a core contributor. Once you have received such a review, maybe after addressing some comments and suggestions by the reviewer(s), your PR will be merged, effectively making your work part of the mainline PyZEAL package.
Contents of PyZEAL's Documentation: