function [Q,R] = mgs(A)
% MGS modified Gram-Schmidt algorithm
%
% See also CLGS, QR
%
% tire de: LN Trefethen & D Bau III, Numerical Linear Algebra, 1997 SIAM Philadelphia 


[m,n] = size(A);
v = A;
R = zeros(n,n);
Q = zeros(m,n);

for i=1:n
    v(:,i) = A(:,i);
end

for i=1:n
    R(i,i) = norm(v(:,i),2);
    Q(:,i) = v(:,i)/R(i,i);
    for j = (i+1):n
        R(i,j) = (conj(Q(:,i))')*v(:,j);
        v(:,j) = v(:,j) - R(i,j)*Q(:,i);
    end
end