Mercurial > octave-antonio
view scripts/linear-algebra/duplication_matrix.m @ 20160:03b9d17a2d95 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed io, java, linear-algebra, prefs, and set script directories.
* scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m,
scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m,
scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m,
scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m,
scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m,
scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m,
scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m,
scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m,
scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m,
scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m,
scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m,
scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m,
scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m,
scripts/set/powerset.m, scripts/set/setdiff.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 15:36:23 -0700 |
parents | 9fc020886ae9 |
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 = 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))