skzeros.find_zeros

skzeros.find_zeros(domain, f, f_z, max_arg_principle, quadrature_args=None, maxiter=50, rng=None)

Find all the zeros of a holomorphic function in a given domain.

First the domain is subdivided into smaller regions until the value of the argument principle is less than max_arg_principle. Then, a AAA approximation of the logarithmic derivative is used to locate the zeros of f.

Parameters:

  • domain (Domain) – The domain in which to search for zeros.

  • f (callable) – The holomorphic function for which to find zeros. It should accept a 1D array and return a 1D array of complex numbers.

  • f_z (callable) – The derivative of the holomorphic function f. It should accept a 1D array and return a 1D array of complex numbers.

  • max_arg_principle (float) – Subdivide domain until the value of the argument principle is less than this value.

  • quadrature_args (dict, optional) – Additional arguments to pass to the quadrature method used in subdivision. See scipy.integrate.quadvec for the supported arguments, by default None.

  • maxiter (int, optional) – The maximum number of attempts at subdivision allowed, by default 50

  • rng (np.random.Generator, optional) – Random number generator to use for sampling points in the domain. If None, the default numpy random generator is used.

Returns:

A ZerosResult object containing the computed zeros and their multiplicities.

Return type:

ZerosResult