from numpy import *
import matplotlib.pyplot as plt
from scipy.linalg import hilbert

n = arange(1,21)
ch = zeros(20)
cv = zeros(20)
for k in n:
    ch[k-1] = linalg.cond(hilbert(k))
    gens = linspace(-1,1,k).reshape((1,-1))
    cv[k-1] = linalg.cond(gens**(arange(k).reshape((-1,1))))
    
plt.semilogy(n,ch,n,cv)
plt.legend(['Hilbert','Uniform Vandermonde'])
plt.show()