Homework 6

import scipy.io as io from scipy import signal import numpy as np import matplotlib import matplotlib.image as im import matplotlib.pyplot as plt import time import struct import math from sklearn.metrics.pairwise import cosine_similarity from mpl_toolkits.mplot3d import Axes3D import binascii

# Load X matrix output = io.loadmat("X.mat")['X'] rank = np.linalg.matrix_rank(output) unitary, singular, vunitary = np.linalg.svd(output, full_matrices=True) # print(rank) # print(u.shape) # print(s.shape) # print(vh.shape) # print(s) # original image plt.imshow(output, interpolation='nearest', cmap='gray') plt.title('Original Image') plt.show()

# SVD reconstruction function def reconstruct(u, s, vh): smat = np.zeros((u.shape[0], vh.shape[0])) smat[:vh.shape[0], :vh.shape[0]] = np.diag(s) return np.dot(u, np.dot(smat, vh))

# SVD Truncate Function (cuts down to k SVs) def truncK(s, k): thresholdMat = np.zeros(s.shape) thresholdMat = s > s[k] return s * thresholdMat

# SVD truncate test thresh = truncK(singular, 100) plt.imshow(reconstruct(unitary, thresh, vunitary), interpolation='nearest', cmap='gray') plt.title('Original Image') plt.show()

# SVDs - Image starts to become extremely blurry at 10 SVs values = [100, 50, 30, 20, 10, 1] for value in values: sing = truncK(singular, value) reconstructed = reconstruct(unitary, sing, vunitary) plt.imshow(reconstructed, interpolation='nearest', cmap='gray') plt.title(f'{value} Singular Values Image') plt.show() plt.imsave(f'{value}_Singluar_Values_Image.png', reconstructed, cmap = 'Greys_r')

# Center Matrix def center(matrix): output = np.zeros(matrix.shape) mean = np.mean(matrix, axis=0) for row in range(matrix.shape[0]): for col in range(matrix.shape[1]): output[row][col] = matrix[row][col] - mean[col] return output def print1Matrix(matrix, ptitle=''): fig = plt.figure() x = np.arange(0, matrix.shape[0], 1) plt.scatter(x, matrix) plt.savefig(f'singular_values_{ptitle}.png') plt.show() # print matrix helper function def printMatrix(matrix, ptitle=''): fig = plt.figure() x = np.zeros(matrix.shape[1]) y = np.zeros(matrix.shape[1]) for row in matrix: for col in range(matrix.shape[1]): x[col] = row[col] y[col] = col plt.scatter(y, x) x = np.zeros(matrix.shape[1]) y = np.zeros(matrix.shape[1]) plt.show()

# Load Image eavesdropping = io.loadmat("eavesdropping.mat")["Y"] print(eavesdropping.shape) print(eavesdropping)

eavU, eavS, eavVh = np.linalg.svd(eavesdropping) eaveCenter = center(eavesdropping) ceavU, ceavS, ceavVh = np.linalg.svd(eaveCenter) print1Matrix(eavS, ptitle='not_centered') print1Matrix(ceavS, ptitle='centered') principleMatrix = np.matmul(ceavU, np.diag(ceavS)) printMatrix(principleMatrix) vMat = np.conjugate(np.transpose(ceavVh)) printMatrix(ceavVh[0:2]) principle = np.zeros(eavesdropping.shape) principle[0] = ceavVh[0] principle[1] = ceavVh[1] principle = np.conjugate(np.transpose(principle)) principle2 = np.matmul(eaveCenter, principle) plt.title('principle directions') plt.scatter(principle2.transpose()[0], principle2.transpose()[1]) plt.savefig('principle directions.png') plt.show()

# Decode decode = (principle2.transpose()[0] < 0).astype(int) for b in range(27): currentByte = ''.join(str(n) for n in decode[(7 * b) : (7 * b) + 7]) currentInt = int(currentByte, 2) print(chr(currentInt), end='')