%
% Demo for implementing Algorithm 7.7 (page 204)
%
%  input:  A  -- a matrix whose columns are to be orthonormalized
%  output: Q, R -- A = Q*R, Q'*Q = eye(n)
%
function [Q,R] = gs(A)
   [m,n] = size(A);  % get the dimensions of A
   Q = zeros(m,n);   % create space for Q
   R = zeros(n,n);   % create space for R
   %
   for k = 1:n
      for i = 1:k-1
  	 R(i,k) = Q(:,i)'*A(:,k);
      end
      Q(:,k) = A(:,k);
      for i = 1:k-1
	 Q(:,k) = Q(:,k) - R(i,k)*Q(:,i); 
      end
      R(k,k) = norm(Q(:,k));
      Q(:,k) = Q(:,k)/R(k,k);
   end