% Page 108 Gilbert Strang Example 5
% Linear Algebra 2011
% Donsen 31MAY11

clc;clear;
v(:,1)=[1 0 1];% a
v(:,2)=[1 0 0];% b
v(:,3)=[2 1 0];% c
[m n]=size(v); % m by n

bnorm=norm(v(:,1));
q=zeros(n,m);
q(:,1)=v(:,1)/bnorm; %first one
b=zeros(n,1);
for i=2:n
    a=zeros(n,1);
    for j=1:i-1
    a=a+(q(:,j)'*v(:,i))*q(:,j);
    end
    b=v(:,i)-a;
    bnorm=0;
bnorm=norm(b);
q(:,i)=b/bnorm;
end

for i=1:n
    fprintf('q(%d)         ',i);
end
fprintf('\n')
for i=1:n
    for j=1:m
fprintf('%f    ',q(i,j));
    end
    fprintf('\n')
end
% To verity the result.
    [Q,R] = qr(v); %QR factorization