zfill ( 6 ) + '.png' ) print 'step: ', count, ' residual norm: ', linalg.

fft ( residual ), label = 'FFT of Ax-b' ) pylab. Residual = Ax - b #plot Ax (or something else, the fft of error should be cool.) astype ( int16 ) #update the reisdual, and get its fft for a nice photo norm ( residual ) > tol ): #update x in place write ( 'initialAx.wav', 44100, Ax ) x = x0 count = 0 while ( linalg. ''' #make noise of the initial approximation to b We should hear the song emerge from the initial guess wav data corresponding to AxĪs Ax gets closer to b (ie the residual gets smaller) X0 is our initial guess for the gauss seidel method (probably random static) wav files and then using Gauss-Seidel to iteratively solve a linear system:įrom TridiagonalMatrix import * from numpy import * from scipy.io import wavfile import scipy.fftpack import pylab import sys import os def musical_gauss_seidel ( A, b, x0, tol ): '''īut output some sound every now and then.Ī is some matrix that lets gauss seidel workī is a vector that represents a. apply ( x ) - b count = count + 1 print count return xĪnd here's the code to handle reading/writing the. norm ( error ) > tol ): #update x in place apply ( x0 ) - b x = x0 count = 0 while ( linalg. upper * v except ( Inde圎rror ): print 'Wrong sizes' return out #solve Ax=b using gauss seidelĭef gauss_seidel ( self, b, x0, tol ): error = self. shape #matrix mulitplicationĭef apply ( self, v ): out = ndarray ( self. Here's the TridiagonalMatrix class I used:įrom numpy import * #a tridiagonal matrix classĬlass TridiagonalMatrix : #initialize with 3 numpy arraysĭef _init_ ( self, upper_in, diag_in, lower_in ): self. wav file needs an array of size 12*44100. A sparse matrix class is neccessary to avoid memory wav files into arrays is not tooīad in scipy. Third iteration: gauss_seidel_out000002.wavįourth iteration: gauss_seidel_out000003.wav Second iteration: gauss_seidel_out000001.wav Plots of the initial Ax, residual, and FFT of residual:Īfter one iteration the high notes become audible gauss_seidel_out000000.wavĪnd some structure is visible in the spectrum: High pitched notes in b become audible first while at the same timeĪudio of the initial 12 second. Initial guess and write out Ax at each iteration we observe that the If we take b to be a song recording, some white noise as our Will approach b with the high frequency parts of Ax getting close to bįirst. Through iterations of Gauss-Seidel the vector Ax wav file can be read into anĪrray (call it b) of length 44100. In both cases, x is the final solution vector and i returns the number of iterations.One second of a 44.1kHz single channel.

I have created the below code for each of them, however my final solution vector does not return the correct answers and i'm really struggling to figure out why. I need to code the Gauss Seidel and Successive over relaxation iterative methods in Matlab.

Gauss seidel algorithm python