Duplication of the Fast Relaxed Vector-Fitting algorithm in python.
To use, put vectfit.py somewhere on your path
import vectfit
import numpy as np
# Create some test data using known poles and residues
# Substitute your source of data as needed
# Note our independent variable lies along the imaginary axis
test_s = 1j*np.linspace(1, 1e5, 800)
# Poles are produced in complex conjugate pairs
test_poles = [
-4500,
-41000,
-100+5000j, -100-5000j,
-120+15000j, -120-15000j,
-3000+35000j, -3000-35000j,
]
# As are the associated resdiues
test_residues = [
-3000,
-83000,
-5+7000j, -5-7000j,
-20+18000j, -20-18000j,
6000+45000j, 6000-45000j,
]
# d == offset, h == slope
test_d = .2
test_h = 2e-5
test_f = vectfit.model(test_s, test_poles, test_residues, test_d, test_h)
# Run algorithm, results hopefully match the known model parameters
poles, residues, d, h = vectfit.vectfit_auto(test_f, test_s, n_poles=5)If you have issues, and perhaps notice warnings about ill-conditioned matrices,
subtitute the vectfit.vectfit_auto method with vectfit.vectfit_auto_rescale,
which rescales the problem before passing it to vectfit_auto, with the intention
of making problem more numerically stable.