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+## Copyright (C) 1996, 1997 John W. Eaton
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2, or (at your option)
+## any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, write to the Free
+## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
+## 02111-1307, USA.
+
+## usage: [BETA, v [,R]] = gls (Y, X, O)
+##
+## Generalized Least Squares (GLS) estimation for the multivariate model
+##
+##   Y = X*B + E,  mean(E) = 0,  cov(vec(E)) = (s^2)*O
+##
+## with Y ...  T x p      As usual, each row of Y and X is an observation
+##      X ...  T x k      and each column a variable.
+##      B ...  k x p
+##      E ...  T x p
+##      O ... Tp x Tp.
+##
+## BETA is the GLS estimator for B.
+## v is the GLS estimator for s^2.
+## R = Y - X*BETA is the matrix of GLS residuals.
+
+## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at>
+## Created: May 1993
+## Adapted-By: jwe
+
+function [BETA, v, R] = gls (Y, X, O)
+
+  if (nargin != 3)
+    usage ("[BETA, v [, R]] = gls (Y, X, O)");
+  endif
+
+  [rx, cx] = size (X);
+  [ry, cy] = size (Y);
+  if (rx != ry)
+    error ("gls: incorrect matrix dimensions");
+  endif
+
+  O = O^(-1/2);
+  Z = kron (eye (cy), X);
+  Z = O * Z;
+  Y1 = O * reshape (Y, ry*cy, 1);
+  U = Z' * Z;
+  r = rank (U);
+
+  if (r == cx*cy)
+    B = inv (U) * Z' * Y1;
+  else
+    B = pinv (Z) * Y1;
+  endif
+
+  BETA = reshape (B, cx, cy);
+  R = Y - X * BETA;
+  v = (reshape (R, ry*cy, 1))' * (O^2) * reshape (R, ry*cy, 1) / (rx*cy - r);
+
+endfunction