function [Q,R] = clgs(A)
% FUNCTION [Q,R] = clgs(A)
% Classical Gram Schmidt Algorithm
% Find Q,R such that A = QR
%  
% Input:    A -- matrix to be factorized
% Output:   Q -- unitary matrix
%           R -- upper triangular matrix

  [m,n] = size(A);
  Q = zeros(m,n);
  R = zeros(n,n);
  for j = 1:n
    v = A(:,j);
    for i = 1:j-1
      R(i,j) = Q(:,i)'*A(:,j);
      v = v - R(i,j)*Q(:,i);
    end
    R(j,j) = norm(v);
    Q(:,j) = v/R(j,j);
  end