compression_Transforms.py

import numpy import matplotlib.pyplot as plt from scipy import fftpack, linalg class Transforms: def __init__(self, fftfunction, length): self.matrix = [] for i in range(length): self.matrix.append(fftfunction(i)) self.matrix = numpy.array(self.matrix) def fft(self, matrix1): return numpy.fft.fft(matrix1) def absolute(self, matrix1): ans = [] for i in matrix1: ans.append(numpy.abs(i)) return numpy.array(ans) def sorting(self, matrix1): return sorted(enumerate(matrix1), key=lambda x: x[1]) def inversefft(self, matrix): return numpy.fft.ifft(matrix) def dct(self, matrix): return fftpack.dct(matrix, norm='ortho') def idct(self, matrix): return fftpack.idct(matrix, norm='ortho') def hadamard(self, number): return linalg.hadamard(number) def walsh(self, number): if number != 2: base = linalg.hadamard(number/2) ansh = numpy.concatenate((base, base), axis=1) ansb = numpy.concatenate((base, -base), axis=1) hmatrix = numpy.concatenate((ansh, ansb)) changeset = [] l = len(hmatrix) for i in hmatrix: signchanges = 0 for j in reversed(range(l)): if j - 1 >= 0 and i[j - 1] != i[j]: signchanges += 1 changeset.append(signchanges) ans2 = [] for i in sorted(enumerate(changeset), key=lambda x: x[1]): ans2.append(hmatrix[i[0]]) return ans2 def preinverse(self, matrix, k): magnitude = fft.absolute(matrix) sortedresult = fft.sorting(magnitude) for i in range(k): matrix[sortedresult[i][0]] = 0 def meansquareerror(self, mat1, mat2): l = len(mat1) squareerror = pow(mat1 - mat2, 2) mean = numpy.sum(squareerror)/l return mean if __name__ == '__main__': function1 = lambda x: pow(x, 3)/4 function2 = lambda x: numpy.math.cos((3*x + 1)/16*numpy.pi) fft = Transforms(function2, 16) mt = fft.matrix '''walsh = fft.walsh(16) walt = 1/4 * numpy.matmul(walsh, fft.matrix) fft.preinverse(walt) rewal = 1/4 * numpy.matmul(walt, walsh) ftm = fft.fft(mt) fft.preinverse(ftm) iftm = fft.inversefft(ftm)''' errors = [] for i in range(1, 16): dctm = fft.dct(mt) fft.preinverse(dctm, i) idctm = fft.idct(dctm) error = fft.meansquareerror(idctm, mt) errors.append(error) errors = numpy.array(errors) rag = [i for i in range(1, 16)] plt.plot(rag, errors, 'bo-') plt.title('MSE of DCT') plt.xlabel('MSE') plt.ylabel('Last n') plt.legend(('MSE', 'walsh trans', 'fft', 'dct')) plt.show() print('Last n ', 'MSE') for i in range(15): print(' ', i, ' ', errors[i])