1######################################################################## 2## 3## Copyright (C) 1995-2021 The Octave Project Developers 4## 5## See the file COPYRIGHT.md in the top-level directory of this 6## distribution or <https://octave.org/copyright/>. 7## 8## This file is part of Octave. 9## 10## Octave is free software: you can redistribute it and/or modify it 11## under the terms of the GNU General Public License as published by 12## the Free Software Foundation, either version 3 of the License, or 13## (at your option) any later version. 14## 15## Octave is distributed in the hope that it will be useful, but 16## WITHOUT ANY WARRANTY; without even the implied warranty of 17## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18## GNU General Public License for more details. 19## 20## You should have received a copy of the GNU General Public License 21## along with Octave; see the file COPYING. If not, see 22## <https://www.gnu.org/licenses/>. 23## 24######################################################################## 25 26## -*- texinfo -*- 27## @deftypefn {} {} vech (@var{x}) 28## Return the vector obtained by eliminating all superdiagonal elements of 29## the square matrix @var{x} and stacking the result one column above the 30## other. 31## 32## This has uses in matrix calculus where the underlying matrix is symmetric 33## and it would be pointless to keep values above the main diagonal. 34## @seealso{vec} 35## @end deftypefn 36 37## See Magnus and Neudecker (1988), Matrix differential calculus with 38## applications in statistics and econometrics. 39 40## Author KH <Kurt.Hornik@wu-wien.ac.at> 41 42function v = vech (x) 43 44 if (nargin != 1) 45 print_usage (); 46 endif 47 48 if (! issquare (x)) 49 error ("vech: X must be square"); 50 endif 51 52 n = rows (x); 53 slices = cellslices (x(:), (1:n) + n*(0:n-1), n*(1:n)); 54 v = vertcat (slices{:}); 55 56endfunction 57 58 59%!assert (vech ([1, 2, 3; 4, 5, 6; 7, 8, 9]), [1; 4; 7; 5; 8; 9]) 60 61%!error vech () 62%!error vech (1, 2) 63