function [Q,R]=cgs(X)
%
%  function [Q,R]=cgs(X)
%   Classical Gram-Scmmidt Algorithm for Q--R factorization.
%
[m,n]=size(X);
R= norm(X(:,1));
p=min(m,n);
Q=X(:,1)/R;
for k=2:p
  v=Q'*X(:,k);
  y=X(:,k)-Q*v;
  rkk=norm(y);
  Q=[Q y/rkk ];
  R=[R v ; zeros(1,k-1) rkk ];
end;