import numpy as np
from numpy import *
import matplotlib
matplotlib.use('TkAgg')
from matplotlib import pyplot as plt
from matplotlib import animation

N = 1000

def f(x):
	return log(cosh(x))

def df(x):
	return tanh(x)

def ddf(x):
	return sech(x)**2

# generate random pairs
s = np.random.rand(N, 2)

# reshape them
A = zeros([2,2])
A[0] = [1, 2]
A[1] = [3, 1]
x = dot(s,A)

# zero mean
xm = x-mean(x)

# diagonalize
cv = cov(xm)
w, v = linalg.eig(cv)
# print shape(diag(1/pow(w,0.5)))
# print v

xd = dot(v.T,xm)
# xfixed = dot(np.diag(1/pow(w,0.5)),xd)
# # d = np.diag([1/pow(i,0.5) for i in w])
# print(d)
# xfixed = dot(d,dot(v.T,xm))
# print xd
# print xn

# wt = random.rand(N,2)
# # print shape(xd)
# nsteps = 1
# for i in range(nsteps):
# 	# w = mean(x*df(w*x)) - w*mean(ddf(w*x))
# 	w_new = df(dot(xd,wt.T)) 
# print shape(w_new)
fig = plt.figure()
ax = plt.axes()
ax.plot(s[:,0],s[:,1],'b.')
ax.plot(x[:,0],x[:,1],'r.')
ax.plot(xm[:,0],xm[:,1],'g.')
# ax.plot(xd[:,0],xd[:,1],'k.')
plt.show()