function Q = formQ(W)
% FORMQ forms the matrix Q in the QR factorization
%
%  see also HOUSEHOLDER
%
% tire de: LN Trefethen & D Bau III, Numerical Linear Algebra, 1997 SIAM Philadelphia

[m,n]=size(W);
Q=zeros(m,m);

% compute the product QI = Q, column by column
for i=1:m
    Q(i,i)=1;
    for k=n:-1:1 
        Q(k:m,i)=Q(k:m,i)-2*W(k:m,k)*W(k:m,k)'*Q(k:m,i);
    end
end