import random
import matplotlib.pyplot as plt
import math
import numpy as np


x = np.array([random.random() for i in xrange(1000)])
y = np.array([random.random() for i in xrange(1000)])
vec = np.concatenate(( x[:,np.newaxis], y[:,np.newaxis]),1) 

transform = np.matrix([[-.2,1.1],[1.1,-.6]])
trans_vec = np.array((transform* np.matrix(vec).transpose()).transpose())

x_mean = sum(trans_vec[:,0])/ len(trans_vec[:,0])
y_mean = sum(trans_vec[:,1])/ len(trans_vec[:,1])

centered = np.empty_like(vec)
centered[:,0] = [i-x_mean for i in trans_vec[:,0] ] 
centered[:,1] = [i-y_mean for i in trans_vec[:,1] ] 


C = np.cov(centered, rowvar = 1)
eigval, eigenvect = np.linalg.eig(C)

eigenvect[:,0] /= eigval[0]**(1.0/len(eigval))
eigenvect[:,0] /= eigval[1]**(1.0/len(eigval))

M = np.transpose(eigenvect[:,abs(eigval)>1e-8])

xt = np.dot(M,centered)
Cxt = np.cov(xt)
# xt should have a diagonal covariance matrix, with no zero eigenvalues

# plot transformed data:

print xt
plt.scatter(vec[:,0],vec[:,1],c='y')
plt.scatter(trans_vec[:,0],trans_vec[:,1], c="r")
plt.scatter(centered[:,0],centered[:,1])
plt.scatter(xt[:,0],xt[:,1])

plt.axis([-1,2, -1,2])
plt.show()