Mercurial > octave-nkf
view scripts/linear-algebra/duplication_matrix.m @ 19074:0850b5212619
doc: Add @nospell macro around proper names in documentation.
* aspell-octave.en.pws: Remove proper names from Octave's custom dictionary.
* doc/interpreter/audio.txi, doc/interpreter/diagperm.txi,
doc/interpreter/diffeq.txi, doc/interpreter/emacs.txi,
doc/interpreter/func.txi, doc/interpreter/geometry.txi,
doc/interpreter/intro.txi, doc/interpreter/linalg.txi,
doc/interpreter/numbers.txi, doc/interpreter/preface.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
libinterp/corefcn/colloc.cc, libinterp/corefcn/ellipj.cc,
libinterp/corefcn/gammainc.cc, libinterp/corefcn/hess.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/sqrtm.cc, libinterp/dldfcn/ccolamd.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/dmperm.cc,
libinterp/dldfcn/symrcm.cc, scripts/general/quadgk.m, scripts/general/quadl.m,
scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/condest.m,
scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/onenormest.m, scripts/linear-algebra/qzhess.m,
scripts/optimization/fminsearch.m, scripts/optimization/glpk.m,
scripts/signal/arch_fit.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/diffpara.m,
scripts/signal/durbinlevinson.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/sparse/eigs.m, scripts/sparse/pcg.m,
scripts/sparse/pcr.m, scripts/specfun/ellipke.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/invhilb.m,
scripts/statistics/base/quantile.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m:
Add @nospell macro around proper names in documentation.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 21 Aug 2014 15:57:18 -0700 |
parents | d63878346099 |
children | 4197fc428c7d |
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## Copyright (C) 1995-2013 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 = 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))