Mercurial > octave
view scripts/linear-algebra/commutation_matrix.m @ 27980:bdad8ca48700
maint: Remove "Created:" lines from code base.
* lin2mu.m, mu2lin.m, bincoeff.m, common_size.m, deal.m, nextpow2.m,
postpad.m, prepad.m, repmat.m, shift.m, xor.m, inpolygon.m, rotx.m, roty.m,
rotz.m, getappdata.m, isappdata.m, rmappdata.m, setappdata.m, colormap.m,
gray.m, gray2ind.m, image.m, imagesc.m, ind2gray.m, ind2rgb.m, ocean.m,
rgb2ind.m, javachk.m, javamem.m, commutation_matrix.m, cross.m,
duplication_matrix.m, gls.m, housh.m, isdefinite.m, ishermitian.m,
issymmetric.m, null.m, ols.m, orth.m, qzhess.m, vech.m, __w2mpth__.m,
expand_rel_paths.m, make_rel_paths.m, daspect.m, pbaspect.m, rticks.m,
thetaticks.m, xticklabels.m, xticks.m, yticklabels.m, yticks.m, zticklabels.m,
zticks.m, comet.m, errorbar.m, loglogerr.m, __errplot__.m, semilogxerr.m,
semilogyerr.m, cla.m, copyobj.m, hdl2struct.m, linkaxes.m, __ghostscript__.m,
__gnuplot_get_var__.m, __gnuplot_has_feature__.m, __gnuplot_has_terminal__.m,
__gnuplot_open_stream__.m, struct2hdl.m, compan.m, conv.m, deconv.m, mpoles.m,
poly.m, polyder.m, polyfit.m, polyint.m, polyout.m, polyreduce.m, polyval.m,
polyvalm.m, residue.m, roots.m, __parse_movargs__.m, detrend.m, fftconv.m,
fftfilt.m, fftshift.m, ifftshift.m, movfun.m, movslice.m, beta.m, betaln.m,
lcm.m, pow2.m, corr.m, kurtosis.m, skewness.m, untabify.m, calendar.m,
datestr.m, datevec.m, eomday.m, now.m, weekday.m:
Remove "Created:" lines from code base.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 21 Jan 2020 13:06:02 -0800 |
parents | bd51beb6205e |
children | 7f1cec12c240 |
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######################################################################## ## ## Copyright (C) 1995-2020 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 {} {} 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> ## 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)