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[CreaPhase.git] / octave_packages / m / linear-algebra / vech.m

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+## Copyright (C) 1995-2012 Kurt Hornik
+## Copyright (C) 2009 VZLU Prague
+##
+## 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 3 of the License, 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, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} vech (@var{x})
+## Return the vector obtained by eliminating all supradiagonal elements of
+## the square matrix @var{x} and stacking the result one column above the
+## other.  This has uses in matrix calculus where the underlying matrix
+## is symmetric and it would be pointless to keep values above the main
+## diagonal.
+## @seealso{vec}
+## @end deftypefn
+
+## See Magnus and Neudecker (1988), Matrix differential calculus with
+## applications in statistics and econometrics.
+
+## Author KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 8 May 1995
+## Adapted-By: jwe
+
+function v = vech (x)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (! issquare (x))
+    error ("vech: X must be square");
+  endif
+
+  n = rows (x);
+  slices = cellslices (x(:), (1:n) + n*(0:n-1), n*(1:n));
+  v = vertcat (slices{:});
+
+endfunction
+
+%!assert(all (vech ([1, 2, 3; 4, 5, 6; 7, 8, 9]) == [1; 4; 7; 5; 8; 9]));
+
+%!error vech ();
+
+%!error vech (1, 2);
+