% testQR: tests four QR methods on random matrices
% requires: clgs.m, mgs.m, house.m
%ELB 10/03

clear E F
numtest=20;
sizetest=100;

Ih=eye(sizetest);
for k=1:numtest
    if k==1, tic, end
    A=randn(sizetest); 
    [QC,RC]=clgs(A); E(k,1)=max(max(abs(A-QC*RC))); F(k,1)=max(max(abs(Ih-QC'*QC)));
    [QM,RM]=mgs(A); E(k,2)=max(max(abs(A-QM*RM))); F(k,2)=max(max(abs(Ih-QM'*QM)));
    [QH,RH]=house(A); E(k,3)=max(max(abs(A-QH*RH))); F(k,3)=max(max(abs(Ih-QH'*QH)));
    [QQ,RR]=qr(A,0); E(k,4)=max(max(abs(A-QQ*RR))); F(k,4)=max(max(abs(Ih-QQ'*QQ)));
    
end

subplot(1,2,1)
semilogy(1:numtest,E(:,1),'o',1:numtest,E(:,2),'*',1:numtest,E(:,3),'s',1:numtest,E(:,4),'d')
legend('CLGS','MGS','Householder','Matlab QR'), title('max entry of |A - Q R|')
xlabel('test number'), ylabel error
subplot(1,2,2)
semilogy(1:numtest,F(:,1),'o',1:numtest,F(:,2),'*',1:numtest,F(:,3),'s',1:numtest,F(:,4),'d')
legend('CLGS','MGS','Householder','Matlab QR'), title('max entry of |I - Q* Q|')
xlabel('test number'), ylabel error