cxroots: rootfinding for complex analytic functions¶
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.
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()