function Q = mgs(X)
% Modified Gram-Schmidt Algorithm
% -------------------------------
% Usage: Q = mgs(X)
%     Q = New orthonormal basis vectors [q1,q2,...,qM]
%     X = Given M linearly independent vectors [x1,x2,...,xM]
%
%-----------------------------------------------------------
% Copyright 2000, by Dimitris G. Manolakis, Vinay K. Ingle,
% and Stephen M. Kogon.  For use with the book
% "Statistical and Adaptive Signal Processing"
% McGraw-Hill Higher Education.
%-----------------------------------------------------------



% Initialization
[N,M] = size(X);
if M > N
   error('***vector dimension must be greater than or equal to number of vectors***')
end
r = zeros(M);
Q = zeros(size(X));

for m = 1:M
   r(m,m) = norm(X(:,m));
   Q(:,m) = X(:,m)/r(m,m);
   for i = m+1:M
      r(m,i) = Q(:,m)'*X(:,i);
      X(:,i) = X(:,i) - r(m,i)*Q(:,m);
   end
end