#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Mar  2 19:08:12 2021

"""
import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
import scipy.io

Clown=scipy.io.loadmat('clowndata.mat')
X=Clown['X']
map=Clown['map']

cm = mpl.colors.ListedColormap(map)
plt.figure(1)
plt.imshow(X,cmap=cm)
plt.axis('off')
plt.show()

U,S,VT=np.linalg.svd(X,full_matrices=0)

# Look at the singular values
plt.figure(2)
t=np.arange(1,201)
plt.plot(t,S)

# We can consider the plot of the log:
plt.figure(3)
plt.plot(t,np.log(S))

N=50
PartialRecon=U[:,1:N+1] @ np.diag(S[:N]) @ VT[1:N+1,:]
plt.figure(4)
plt.imshow(PartialRecon,cmap=cm)
plt.axis('off')
plt.show()