% Script qralgH_test.m
% test out qr iteration algorithm with and without hessenbeg form

n = 100;
% random eigenvalues; all made real.  (cases 4,5,6,7)
D = diag(randn(n,1));
V = randn(n);   % Interesting results if orthogonal matrix here instead!
Ak = V*D/V;

% symmetric A: real eigenvalues  (cases 1,2,3)
% Ak = rand(n);
% Ak = (Ak+Ak')/2;

[dH,iterH] = qralgHt(Ak);
[d,iter] = qralgt(Ak);
[dH,idH] = sort(dH);
[d,id] = sort(d);
norm(d-dH)

plot(1:length(Ak),iter(id),1:length(Ak),iterH(id),'--')
xlabel('n'); ylabel('# of iterations');
legend('without','with','Location','NorthWest');
title('QR iterations with and without Hessenberg Form');