Householder Algorithm finding Q

Hi, i have this algorithm:

function [Q,R] = householder(A)
   % Write your code here.
   [m,n]=size(A);
   Q=eye(m);
for k=1:n
    z = -sign(A(k,k))*norm(A(k:m,k));
    v = [zeros(k-1,1); A(k,k)-z; A(k+1:m,k)];
    f = v'*v;
    if f == 0, continue; end
for j = k:n
     c = v'*A(:,j); 
     A(:,j) = A(:,j)-(2*c/f)*v; 
end
end
R=A;
end

I get the correct R matrix, but I can't seem to find Q correctly. Please let me know ASAP

[Jan]

Terms like "ASAP" are not appropriate, if you ask voluntary members of an internet forum to help you.

What did you try to determine Q?

[Frederick Melanson]

I added an extra forloop at the end like this:

for j=k:m

c = v'*Q(:,j);

Q(:,j) = Q(:,j)-(2*c/f)*v;

end

Q=Q';

I get the lower triangular part of Q correctly, the problem is with the upper half of the matrix

Answer 1

[Athul Prakash]

Hi Frederick,

You may prefer the MATLAB built-in qr() function.

[Q,R] = qr(M);

See this documentation:

https://in.mathworks.com/help/matlab/ref/qr.html

Alternately, you may search the Mathworks File Exchange for alternate implementations of Householder algorithm. For example:

https://in.mathworks.com/matlabcentral/fileexchange/72766-qr-decomposition

These are submissions by other MATLAB users, and not part of the MATLAB product. It is not tested or qualified by Mathworks, so use at your own responsibility.