# -*- coding: utf-8 -*-
import numpy as np
import math
import matplotlib.pyplot as plt
import matplotlib.image as mpimg

img = mpimg.imread("images/butter.png")
img_gray = np.mean(img, -1)
#img = mpimg.imread("images/baboon.png")
#img_gray = img #np.mean(img, -1)
plt.clf()
plt.imshow(img_gray, cmap = 'gray')
plt.axis('off')
plt.show()
m, n = img_gray.shape
T = 0

if m < n:
    img_gray = img_gray.T
    m, n = img_gray.shape
    T = 1

M = img_gray.mean(axis = 0)*np.ones((1,n))
h = np.ones((m,1))
X = img_gray - h.dot(M)
Sigma = X.T.dot(X)/(n-1)

s, V = np.linalg.eig(Sigma)

variances = np.diag(s*s)
position = range(0,10)
width = 0.35
plt.figure()
plt.bar(position, s[0:10]*s[0:10], width)
plt.show()

l = 20
D = V[:,0:l]
C = D.T.dot(X.T)

ratio = m/(2.0*l+1)
XX = D.dot(C).T
XX = XX + h.dot(M)

if T == 1:
    XX = XX.T

plt.figure()
plt.imshow(XX, cmap='gray')
plt.axis('off')
plt.show()