Nan Mihai - Householder (Metode numerice)

function [R,Q]=Householder(A)
% HouseQR - descompunere QR a lui A cu reflexii Householder
    [m,n]=size(A);
    u=zeros(m,n);

    for k=1:n
            x=A(k:m,k);
            x(1)=semnul(x(1))*norm(x)+x(1);
            u(k:m,k)=x/norm(x);
            A(k:m,k:n)=A(k:m,k:n)-2*u(k:m,k)*(u (k:m,k)'*A(k:m,k:n));
    endfor
    R=triu(A(1:n,:));
    if nargout==2
            Q=eye(m,n);
            for j=1:n
                for k=n:-1:1
                        Q(k:m,j)=Q(k:m,j)-2*u(k:m,k)*(u (k:m,k)'*Q(k:m,j));
                endfor
            endfor
    endif
endfunction

function y=semnul(x)
    if x>=0
            y=1;
    else
            y=-1;
    endif
endfunction