Mercurial > octave-nkf
view scripts/linear-algebra/duplication_matrix.m @ 20266:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 26 May 2015 21:07:42 -0700 |
parents | 03b9d17a2d95 |
children |
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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} {} 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{@math{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 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 8 May 1995 ## Adapged-By: jwe 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 duplication_matrix () %!error duplication_matrix (0.5) %!error duplication_matrix (-1) %!error duplication_matrix (ones (1,4))