Mercurial > octave-antonio

annotate scripts/linear-algebra/commutation_matrix.m @ 2540:c3d634d49ce4

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 1996-11-20 00:20:12 by jwe]
author jwe
date Wed, 20 Nov 1996 00:21:25 +0000
parents
children 6923abb04e16
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
2540
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
1 ## Copyright (C) 1995, 1996 Kurt Hornik
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
2 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
3 ## This program is free software; you can redistribute it and/or modify
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
4 ## it under the terms of the GNU General Public License as published by
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
5 ## the Free Software Foundation; either version 2, or (at your option)
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
6 ## any later version.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
7 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
8 ## This program is distributed in the hope that it will be useful, but
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
9 ## WITHOUT ANY WARRANTY; without even the implied warranty of
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
11 ## General Public License for more details.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
12 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
13 ## You should have received a copy of the GNU General Public License
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
14 ## along with this file. If not, write to the Free Software Foundation,
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
16
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
17 ## usage: commutation_matrix (m [, n])
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
18 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
19 ## Returns the commutation matrix K_{m,n} which is the unique m*n by
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
20 ## m*n matrix such that K_{m,n} * vec (A) = vec (A') for all m by n
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
21 ## matrices A.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
22 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
23 ## If only one argument m is given, K_{m,m} is returned.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
24 ##
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
25 ## See Magnus and Neudecker (1988), Matrix differential calculus with
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
26 ## applications in statistics and econometrics.
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
27
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
28 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
29 ## Created: 8 May 1995
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
30 ## Adapted-By: jwe
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
31
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
32 function k = commutation_matrix (m, n)
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
33
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
34 if (nargin < 1 || nargin > 2)
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
35 usage ("commutation_matrix (m [, n])");
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
36 else
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
37 if (! (is_scalar (m) && m == round (m) && m > 0))
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
38 error ("commutation_matrix: m must be a positive integer");
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
39 endif
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
40 if (nargin == 1)
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
41 n = m;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
42 elseif (! (is_scalar (n) && n == round (n) && n > 0))
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
43 error ("commutation_matrix: n must be a positive integer");
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
44 endif
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
45 endif
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
46
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
47 ## It is clearly possible to make this a LOT faster!
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
48 k = zeros (m * n, m * n);
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
49 for i = 1 : m
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
50 for j = 1 : n
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
51 k ((i - 1) * n + j, (j - 1) * m + i) = 1;
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
52 endfor
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
53 endfor
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
54
c3d634d49ce4 [project @ 1996-11-20 00:20:12 by jwe]
jwe
parents:
diff changeset
55 endfunction