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 for a more details and a tutorial.

With Python installed you can install cxroots by entering in the terminal/command line

pip install cxroots

Example

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()

print(roots)

 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

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:

@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 and then run pre-commit install. The pre-commit scripts can also be run manually with pre-commit run --all-files
The project uses ruff for formatting and linting. It is run as part of the pre-commit hook and is recommended to be run on save in the developer’s editor.

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] (1,2)

P. Kravanja and M. Van Barel. Computing the Zeros of Analytic Functions. Springer, Berlin, Heidelberg, 2000.

Metadata

Release files for cxroots 3.2.0

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for cxroots 3.2.0
File	Size	Uploaded
cxroots-3.2.0.tar.gz	47.6 MB	Apr 12, 2025	Details

Built distribution (wheel)

Table of built distributions (wheels) for cxroots 3.2.0
File	Interpreter	ABI	Platform	Reset
cxroots-3.2.0-py3-none-any.whl 54.1 kB Apr 12, 2025	Python 3	none	any	Details

Total release size: 47.7 MB

Release files / cxroots-3.2.0.tar.gz

Download URL	cxroots-3.2.0.tar.gz
Size	47.6 MB
Tags	Source
SHA-256 checksum How to use checksums	`c41a81db1080a65de78fa88d471ce8f4f8870b6d9016f3c2607208d027117e39`
BLAKE2b-256 checksum How to use checksums	`ce56e3e75edbcb1818a52a14de87aef4159f298941becc43c1f057c6edd59cd4`
Upload date	Apr 12, 2025
Uploaded using Trusted Publishing? What is trusted publishing?	No
Uploaded via	`twine/6.0.1 CPython/3.13.2`

Release files / cxroots-3.2.0-py3-none-any.whl

Download URL	cxroots-3.2.0-py3-none-any.whl
Size	54.1 kB
Tags	Python 3
SHA-256 checksum How to use checksums	`4b1625919c155da38225147ceeb6042d7bbb22f7f44dfdddb251ab7fa7710373`
BLAKE2b-256 checksum How to use checksums	`d526e5524ef2591d524d430e80df51eb6520eff964c8b2ae0064c4ab724cdcbc`
Upload date	Apr 12, 2025
Uploaded using Trusted Publishing? What is trusted publishing?	No
Uploaded via	`twine/6.0.1 CPython/3.13.2`