% Lecture 9, Experiment 2
% generating plot showing singular values of a matrix
% affected by roundoff error.

clear;
close all;

% Experiment 2
randn('state',sum(100*clock)); % initialize random number generator
[U,X] = qr(randn(80));
[V,X] = qr(randn(80));

S = diag(2.^(-1:-1:-80));
A = U*S*V;

[QC,RC] = clgs(A);
[QM,RM] = mgs(A);
rc = diag(RC);
rm = diag(RM);

N = 80;
j = 1:1:N;

figure;
hold on;
plot(j',log10(abs(rc)),'o',...
     j',log10(abs(rm)),'x',...
     [1;80],[-8;-8],'r-',...
     [1;80],[-16;-16],'k-');
xlabel('j');
ylabel('log_{10}(r_{jj})');
legend('Classical Gram-Schmidt','Modified Gram-Schmidt',...
       'sqrt(\epsilon_{machine}','\epsilon_{machine}');
grid on;
axis([0 80 -25 0]);