TESTING.py

import numpy as np
import scipy as sc
import matplotlib.pyplot as plt
import itertools as itr

w = np.logspace(-5, 3, 1000)
s = 1j*w

def G(s):
    # the matrix transfer function
    G = [[0.001*np.exp(-5*s)*(-34.54*(s+0.0572))/((s+1.72E-04)*(4.32*s+1)),
    0.001*np.exp(-5*s)*(1.913)/((s+1.72E-04)*(4.32*s+1))],
    [0.001*np.exp(-5*s)*(-32.22*s)/((s+1.72E-04)*(4.32*s+1)),
    0.001*np.exp(-5*s)*(-9.188*(s+6.95E-04))/((s+1.72E-04)*(4.32*s+1))]]
    return G

freqresp = map(G, s)

sigmas = np.array([Sigma for U, Sigma, V in map(np.linalg.svd, freqresp)])

#maximum input and output vectors
Umax = np.array([U[:, 0] for U, sigma, V in map(np.linalg.svd, freqresp)])
Vmax = np.array([V[:, 0] for U, sigma, V in map(np.linalg.svd, freqresp)])

#minimum input and output vectors
Umin = np.array([U[:, -1] for U, sigma, V in map(np.linalg.svd, freqresp)])
Vmin = np.array([V[:, -1] for U, sigma, V in map(np.linalg.svd, freqresp)])

def Sing(w_s):
    s = 1j*w_s
    return np.max(np.linalg.svd(G(s))[1])-1

sc.optimize.fsolve(Sing, 0.1)

plt.loglog(w, sigmas)
plt.show()