[MATLAB] Gram-Schmidt A = QR Factorization

function [Q R] = qr_factorize(A)
% A = QR factorization (Gram-Schmidt)

[n, n] = size(A); 

for j = 1:n;
    v = A(:, j);     % pick a column to orthogonalize
    for i = 1:j-1;
        R(i, j) = Q(:, i)'*v;      
        v = v - Q(:, i)*R(i, j);    % orthogonalize (subtracts earlier projections)
    end
    R(j, j) = norm(v);      % set diagonal of A with the length of orthogonalized column of A
    Q(:, j) = v/R(j, j);
end s

A = [2 0 1; 2 -3 0; -1 3 0];

qr_factorize(A) 
ans =
 
    0.6667    0.6667    0.3333
    0.6667   -0.3333   -0.6667
   -0.3333    0.6667   -0.6667