function QRdata = basicqr(QR)

  [M, N] = size(QR);
  tau = zeros(1,N);

  for j=1:min(M,N),
    [QR(j:M,j), tau(j), alpha] = make_house(QR(j:M,j));
    if j < N,
      QR(j,j) = 1;

      # The parentheses are necessary for performance...
      QR(j:M, j+1:N) -= \
	  tau(j)*QR(j:M,j) * ( QR(j:M,j)'*QR(j:M,j+1:N) );
    endif
    QR(j,j) = alpha;
  endfor

  QRdata.QR = QR;
  QRdata.tau = tau;

endfunction