import random
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import math
import numpy as np

fig = plt.figure()
ax = fig.gca(projection='3d')

x1 = np.array([random.gauss(0,1) for i in xrange(1000)])
x2 = np.array([random.gauss(0,1) for i in xrange(1000)])
x3 = np.array([i+e for i,e in zip(x1,x2)])
vec = np.hstack((x1[:,np.newaxis],x2[:,np.newaxis],x3[:,np.newaxis]))

covariance = np.cov(vec.transpose())
print covariance
eingval, eigenvect = np.linalg.eig(covariance)

y = np.linalg.inv(eigenvect)*np.matrix(vec).transpose()
print  np.linalg.eig(np.cov(y))[0]

y = np.array(y.transpose(),dtype=np.float32)
ax.scatter(vec[:,0],vec[:,1],vec[:,2], c="r")
ax.scatter(y[:,0],y[:,1],y[:,2], c="b")
plt.axis([-4,4, -4,4])
plt.show()