Mercurial > octave
view scripts/linear-algebra/commutation_matrix.m @ 19833:9fc020886ae9
maint: Clean up m-files to follow Octave coding conventions.
Try to trim long lines to < 80 chars.
Use '##' for single line comments.
Use '(...)' around tests for if/elseif/switch/while.
Abut cell indexing operator '{' next to variable.
Abut array indexing operator '(' next to variable.
Use space between negation operator '!' and following expression.
Use two newlines between endfunction and start of %!test or %!demo code.
Remove unnecessary parens grouping between short-circuit operators.
Remove stray extra spaces (typos) between variables and assignment operators.
Remove stray extra spaces from ends of lines.
author | Rik <rik@octave.org> |
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date | Mon, 23 Feb 2015 14:54:39 -0800 |
parents | 4197fc428c7d |
children | 03b9d17a2d95 |
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## Copyright (C) 1995-2015 Kurt Hornik ## ## 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} {} commutation_matrix (@var{m}, @var{n}) ## Return the commutation matrix ## @tex ## $K_{m,n}$ ## @end tex ## @ifnottex ## K(m,n) ## @end ifnottex ## which is the unique ## @tex ## $m n \times m n$ ## @end tex ## @ifnottex ## @var{m}*@var{n} by @var{m}*@var{n} ## @end ifnottex ## matrix such that ## @tex ## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$ ## @end tex ## @ifnottex ## @math{K(m,n) * vec(A) = vec(A')} ## @end ifnottex ## for all ## @tex ## $m\times n$ ## @end tex ## @ifnottex ## @math{m} by @math{n} ## @end ifnottex ## matrices ## @tex ## $A$. ## @end tex ## @ifnottex ## @math{A}. ## @end ifnottex ## ## If only one argument @var{m} is given, ## @tex ## $K_{m,m}$ ## @end tex ## @ifnottex ## @math{K(m,m)} ## @end ifnottex ## is returned. ## ## See @nospell{Magnus and Neudecker} (1988), @cite{Matrix Differential ## Calculus with Applications in Statistics and Econometrics.} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 8 May 1995 ## Adapted-By: jwe function k = commutation_matrix (m, n) if (nargin < 1 || nargin > 2) print_usage (); else if (! (isscalar (m) && m == fix (m) && m > 0)) error ("commutation_matrix: M must be a positive integer"); endif if (nargin == 1) n = m; elseif (! (isscalar (n) && n == fix (n) && n > 0)) error ("commutation_matrix: N must be a positive integer"); endif endif ## It is clearly possible to make this a LOT faster! k = zeros (m * n, m * n); for i = 1 : m for j = 1 : n k((i - 1) * n + j, (j - 1) * m + i) = 1; endfor endfor endfunction %!test %! c = commutation_matrix (1,1); %! assert (c,1); %!test %! A = rand (3,5); %! vc = vec (A); %! vr = vec (A'); %! c = commutation_matrix (3,5); %! assert (c*vc, vr); %!test %! A = rand (4,6); %! vc = vec (A); %! vr = vec (A'); %! c = commutation_matrix (4,6); %! assert (c*vc, vr); %!error <M must be a positive integer> commutation_matrix (0,0) %!error <N must be a positive integer> commutation_matrix (1,0) %!error <M must be a positive integer> commutation_matrix (0,1)