% 
% Written by:
% -- 
% John L. Weatherwax                2008-11-24
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear functions; 
clear; 
clc; 
close all; drawnow; 

% now plot the "convergence" or not of these weights
%
n = 0:7;

rx0  = 1.0; 
w0   = -.5; % our initial guess ... 
wopt = 0.5; % the optimal value ... 

figure; hold on; 

% pick some values of mu: 
%
mu = 0.5 * ( 1/(2*rx0) );           % <- we should easily converge ... 
wn = wopt + ( ( 1 - 2*mu*rx0 ).^n ) * ( w0 - wopt );
mu1 = plot( n, wn, 'bo-' ); 

mu = ( 1/(2*rx0) )-1e-6;            % <- we should still converge ...  
wn = wopt + ( ( 1 - 2*mu*rx0 ).^n ) * ( w0 - wopt );
mu2 = plot( n, wn, 'rx-' ); 

mu = 0.5 * ( 1/(2*rx0) + 1/rx0 );   % <- we converge by via osscilations ... 
wn = wopt + ( ( 1 - 2*mu*rx0 ).^n ) * ( w0 - wopt );
mu3 = plot( n, wn, '-gd' ); 

mu = 1.5 * ( 1/rx0 );   % <- we diverge ...
wn = wopt + ( ( 1 - 2*mu*rx0 ).^n ) * ( w0 - wopt );
mu4 = plot( n(1:5), wn(1:5), '-cs' ); 

axis( [0,max(n),-2,+2] ); xlabel('n (index)'); ylabel('w(n)');
legend( [mu1,mu2,mu3,mu4], {'Part (a)','Part (b)','Part (c)','Part (d)'} ); grid on; 

saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_1_2', 'epsc' );