Mercurial > octave
view scripts/linear-algebra/duplication_matrix.m @ 33584:3fe954c2fd25 default tip @
maint: merge stable to default
author | Rik <rik@octave.org> |
---|---|
date | Mon, 13 May 2024 11:41:11 -0700 |
parents | 2e484f9f1f18 |
children |
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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{d} =} duplication_matrix (@var{n}) ## Return the duplication matrix ## @tex ## $D_n$ ## @end tex ## @ifnottex ## @nospell{@math{Dn}} ## @end ifnottex ## which is the unique ## @tex ## $n^2 \times n(n+1)/2$ ## @end tex ## @ifnottex ## @math{N^2}-by-@math{N*(N+1)/2} ## @end ifnottex ## matrix such that ## @tex ## $D_n * {\rm vech} (A) = {\rm vec} (A)$ ## @end tex ## @ifnottex ## @nospell{@code{Dn * vech (A) = vec (A)}} ## @end ifnottex ## for all symmetric ## @tex ## $n \times n$ ## @end tex ## @ifnottex ## @math{N}-by-@math{N} ## @end ifnottex ## matrices ## @tex ## $A$. ## @end tex ## @ifnottex ## @math{A}. ## @end ifnottex ## ## See @nospell{Magnus and Neudecker} (1988), @cite{Matrix Differential ## Calculus with Applications in Statistics and Econometrics}. ## @end deftypefn function d = duplication_matrix (n) if (nargin < 1) print_usage (); endif if (! (isscalar (n) && n > 0 && n == fix (n))) error ("duplication_matrix: N must be a positive integer"); endif d = zeros (n * n, n * (n + 1) / 2); ## It is clearly possible to make this a LOT faster! count = 0; for j = 1 : n d((j - 1) * n + j, count + j) = 1; for i = (j + 1) : n d((j - 1) * n + i, count + i) = 1; d((i - 1) * n + j, count + i) = 1; endfor count += n - j; endfor endfunction %!test %! N = 2; %! A = rand (N); %! B = A * A'; %! C = A + A'; %! D = duplication_matrix (N); %! assert (D * vech (B), vec (B), 1e-6); %! assert (D * vech (C), vec (C), 1e-6); %!test %! N = 3; %! A = rand (N); %! B = A * A'; %! C = A + A'; %! D = duplication_matrix (N); %! assert (D * vech (B), vec (B), 1e-6); %! assert (D * vech (C), vec (C), 1e-6); %!test %! N = 4; %! A = rand (N); %! B = A * A'; %! C = A + A'; %! D = duplication_matrix (N); %! assert (D * vech (B), vec (B), 1e-6); %! assert (D * vech (C), vec (C), 1e-6); %!error <Invalid call> duplication_matrix () %!error duplication_matrix (0.5) %!error duplication_matrix (-1) %!error duplication_matrix (ones (1,4))