diagonal_well_conditioning.py

import numpy as np
import math

r = np.random.randint(0, 30, (3, 3)).astype('d')

def spectral_radius(m):
    return max(abs(y) for y in np.linalg.eigvals(m))

def matrix_norm2(m):
    return math.sqrt(spectral_radius(m.dot(m.T)))

def matrix_sensitivity(m):
    return matrix_norm2(m) * matrix_norm2(np.linalg.inv(m))

d = (1 / np.diag(r)) * np.eye(3)

print "Matrix"
print r
print "Condition Number:", matrix_sensitivity(r)
print

print "D"
print d
print

print "Well Conditioned"
print d.dot(r)
print "Condition Number:", matrix_sensitivity(d.dot(r))
print