octave-nkf: scripts/linear-algebra/duplication

annotate scripts/linear-algebra/duplication_matrix.m @ 17744:d63878346099

maint: Update copyright notices for release.

author	John W. Eaton <jwe@octave.org>
date	Wed, 23 Oct 2013 22:09:27 -0400
parents	a4969508008e
children	0850b5212619

rev	line source
17744 d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 16826 diff changeset	1 ## Copyright (C) 1995-2013 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	2 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	3 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	4 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	9 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3499 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	13 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	14 ##
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	18
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	19 ## -- texinfo --
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	20 ## @deftypefn {Function File} {} duplication_matrix (@var{n})
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	21 ## Return the duplication matrix
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	22 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	23 ## $D_n$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	24 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	25 ## @ifnottex
16826 a4969508008e doc: Periodic spellcheck of the documentation. Rik <rik@octave.org> parents: 14363 diff changeset	26 ## @nospell{@math{Dn}}
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	27 ## @end ifnottex
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	28 ## which is the unique
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	29 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	30 ## $n^2 \times n(n+1)/2$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	31 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	32 ## @ifnottex
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3426 diff changeset	33 ## @math{n^2} by @math{n*(n+1)/2}
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	34 ## @end ifnottex
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	35 ## matrix such that
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	36 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	37 ## $D_n * {\rm vech} (A) = {\rm vec} (A)$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	38 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	39 ## @ifnottex
16826 a4969508008e doc: Periodic spellcheck of the documentation. Rik <rik@octave.org> parents: 14363 diff changeset	40 ## @nospell{@math{Dn vech (A) = vec (A)}}
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	41 ## @end ifnottex
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	42 ## for all symmetric
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	43 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	44 ## $n \times n$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	45 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	46 ## @ifnottex
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3426 diff changeset	47 ## @math{n} by @math{n}
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	48 ## @end ifnottex
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	49 ## matrices
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	50 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	51 ## $A$.
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	52 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	53 ## @ifnottex
3499 3e3e14ad5149 [project @ 2000-01-31 05:18:07 by jwe] jwe parents: 3426 diff changeset	54 ## @math{A}.
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7017 diff changeset	55 ## @end ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	56 ##
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	57 ## See Magnus and Neudecker (1988), Matrix differential calculus with
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	58 ## applications in statistics and econometrics.
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2540 diff changeset	59 ## @end deftypefn
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	60
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	61 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	62 ## Created: 8 May 1995
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	63 ## Adapged-By: jwe
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	64
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	65 function d = duplication_matrix (n)
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	66
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	67 if (nargin != 1)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	68 print_usage ();
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	69 endif
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	70
13286 49ae6f497171 Use common code idiom x == fix (x) to detect integers Rik <octave@nomad.inbox5.com> parents: 13085 diff changeset	71 if (! (isscalar (n) && n > 0 && n == fix (n)))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	72 error ("duplication_matrix: N must be a positive integer");
2540 c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	73 endif
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	74
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	75 d = zeros (n * n, n * (n + 1) / 2);
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	76
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	77 ## It is clearly possible to make this a LOT faster!
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	78 count = 0;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	79 for j = 1 : n
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	80 d ((j - 1) * n + j, count + j) = 1;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	81 for i = (j + 1) : n
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	82 d ((j - 1) * n + i, count + i) = 1;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	83 d ((i - 1) * n + j, count + i) = 1;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	84 endfor
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	85 count = count + n - j;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	86 endfor
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	87
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe] jwe parents: diff changeset	88 endfunction
13084 60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	89
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	90
13085 0fe1b5d4db56 codesprint: Fix typo Jordi Gutiérrez Hermoso <jordigh@gmail.com> parents: 13084 diff changeset	91 %!test
13084 60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	92 %! N = 2;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	93 %! A = rand (N);
13084 60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	94 %! B = A * A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	95 %! C = A + A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	96 %! D = duplication_matrix (N);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	97 %! assert (D * vech (B), vec (B), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	98 %! assert (D * vech (C), vec (C), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	99
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	100 %!test
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	101 %! N = 3;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	102 %! A = rand (N);
13084 60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	103 %! B = A * A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	104 %! C = A + A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	105 %! D = duplication_matrix (N);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	106 %! assert (D * vech (B), vec (B), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	107 %! assert (D * vech (C), vec (C), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	108
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	109 %!test
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	110 %! N = 4;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	111 %! A = rand (N);
13084 60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	112 %! B = A * A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	113 %! C = A + A';
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	114 %! D = duplication_matrix (N);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	115 %! assert (D * vech (B), vec (B), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	116 %! assert (D * vech (C), vec (C), 1e-6);
60bd7ebb12fc codesprint: 7 tests for duplication_matrix.m Andriy Shinkarchuck <adriano32.gnu@gmail.com> parents: 11523 diff changeset	117
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	118 %!error duplication_matrix ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	119 %!error duplication_matrix (0.5)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	120 %!error duplication_matrix (-1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	121 %!error duplication_matrix (ones (1,4))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	122

Mercurial > octave-nkf

annotate scripts/linear-algebra/duplication_matrix.m @ 17744:d63878346099