function [V,R] = house(A)
% usage: [V,R] = house(A)
% description: this function calculates a full QR
% factorizaton of full rank matrix A (this is
% assumed!) by the modified Gram-Schmidt algorithm.
% Q is returned implicitly via the Householder vectors
% in V.

% local variables:
% ii,jj: index variables

[m,n] = size(A);
p = min([m,n]);
V = zeros(m,p);
R = A;
for k = 1:p
  x = R(k:m,k);
  x(1) = (sign(x(1))+(x(1)==0))*norm(x)+x(1);
  V(k:m,k) = x/norm(x);
  R(k:m,k:n) = R(k:m,k:n) - 2*V(k:m,k)*V(k:m,k)'*R(k:m,k:n);
end