Find all the roots (zeros) of a complex analytic function within a given contour in the complex plane.
Project description
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:
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
See also
The Fortran 90 package ZEAL 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
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}},
url = {https://github.com/rparini/cxroots},
year = {2018--}
}
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
References
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