MATLAB: QR Factorization Using Householder Transformations

Question

function [Q,R]=QRfactor(A)
[m,n]=size(A);
R=A; %Start with R=A
Q=eye(m); %Set Q as the identity matrix
for k=1:m-1
x=zeros(m,1);
x(k:m,1)=R(k:m,k);
g=norm(x);
v=x; v(k)=x(k)+g;
%Orthogonal transformation matrix that eliminates one element
%below the diagonal of the matrix it is post-multiplying:
s=norm(v);
if s~=0, w=v/s; u=2*R'*w;
R=R-w*u'; %Product HR
Q=Q-2*Q*w*w'; %Product QR
end
end

for A=[-2 2 3; 1 3 5; -3 -1 2]

I got the answers Q and R different from when I use [Q,R]=qr(A). Where am I wrong with code.

Answer 1

Hi Hüseyin,

I don't think something is wrong. Q*R gives A (at least for your matrix A). Having different Q and R from MATLAB's implementation does not necessarily mean something is wrong (as long as Q*R=A and Q is orthogonal, i.e. Q'*Q = identity).

Titus