%Modified Gram-Schmidt
%Usage: [q,r]=mgs(A)
function [q,r]=mgs(A)
[m,n]=size(A);
for i=1:n
   v(:,i)=A(:,i);
end
for i=1:n;
   r(i,i)=norm(v(:,i));
   q(:,i)=v(:,i)/r(i,i);
   for j=i+1:n
      r(i,j)=q(:,i)'*v(:,j);
      v(:,j)=v(:,j)-r(i,j)*q(:,i);
   end
end