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########################################################################
##
## Copyright (C) 1995-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{v} =} vech (@var{x})
## Return the vector obtained by eliminating all superdiagonal 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.
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 (vech ([1, 2, 3; 4, 5, 6; 7, 8, 9]), [1; 4; 7; 5; 8; 9])
## Test input validation
%!error <Invalid call> vech ()
%!error <X must be square> vech ([1,2,3;4,5,6])
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