#!/usr/bin/python
"""
	Contrast function
	
"""
import argparse
import numpy as np
from matplotlib import pyplot as plt


def setup_data():
	mu = 0
	sigma = 1
	samples = 500
	s1 = np.random.random(size=samples)
	s2 = np.random.random(size=samples)
	
	return np.array([s1, s2])

def main(args):
	s = setup_data()
	
	A = np.array([[1,2],[3,1]])

	x = A.dot(s)

	x_mu = 1./len(x[0])*np.sum(x, axis=1)

	Cx = np.zeros((len(x), len(x[0])))
	Cx_intermediate = np.zeros((len(x), len(x[0])))

	# Calculate Error Vectors
	for i in xrange(0, len(Cx[0,:])):
		Cx_intermediate[0,i] = x[0,i]-x_mu[0]
		Cx_intermediate[1,i] = x[1,i]-x_mu[1]
		#Cx_intermediate[2,i] = x[2,i]-x_mu[2]

	# Calculate Covariance matrix based on error vectors
	Cx = np.dot(Cx_intermediate, (Cx_intermediate.T))
	
	# Calc eigen values and vectors
	w, M = np.linalg.eig(Cx)
	M = M.T # try this line

	print x[0]

	print "\n\n"
	print "-- 12.3c --"
	print "Covariance Matrix, Cx"
	print np.around(Cx, decimals=3)
	print "Eigenvalues"
	print np.around(w, decimals=3)
	print "\n"
	print "-- 12.3d --"
	print "Eigenvectors of Covariance matrix"
	print M.T
	# Calculate Covariance Matrix of Transformation
	y = np.dot(M, x)
	Cy = np.dot(np.dot(M, Cx), M.T)

	print len(y)
	print "Cy"
	print np.around(Cy, decimals=3)
	wy, My = np.linalg.eig(Cy)
	My = My.T
	print "Eigenvalues of Cy"
	print np.around(wy, decimals=3)

	fig = plt.figure()
	
	# 12.4a
	#plt.scatter(s[0],s[1])
	# 12.4b
	#plt.scatter(x[0],x[1])
	
	# 12.4c
	plt.scatter(y[0],y[1])
	plt.show()




if __name__ == '__main__':
	parser = argparse.ArgumentParser()
	parser.add_argument("-n", "--n", type=int, default=100, help="number of points")
	parser.add_argument("-s", "--s", type=int, default=0.5, help="standard deviation")
	args = parser.parse_args()
	main(args)