Mercurial > hg > octave-lyh

annotate scripts/special-matrix/sylvester_matrix.m @ 3140:990ea337e950

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
[project @ 1998-02-03 08:07:51 by jwe]
author jwe
date Tue, 03 Feb 1998 08:07:51 +0000
parents
children f37ca3017116
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
3140
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
1 ## Copyright (C) 1996, 1997 John W. Eaton
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
2 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
3 ## This file is part of Octave.
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
4 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
7 ## the Free Software Foundation; either version 2, or (at your option)
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
8 ## any later version.
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
9 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
13 ## General Public License for more details.
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
14 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
16 ## along with Octave; see the file COPYING. If not, write to the Free
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
18 ## 02111-1307, USA.
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
19
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
20 ## usage: sylvester_matrix (k)
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
21 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
22 ## Return the Sylvester matrix of order n = 2^k.
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
23 ##
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
24 ## See also: hankel, vander, hilb, invhilb, toeplitz
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
25
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
26 ## Author: jwe
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
27
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
28 function retval = sylvester_matrix (k)
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
29
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
30 if (nargin != 1)
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
31 usage ("sylvester_matrix (n)");
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
32 endif
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
33
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
34 if (is_scalar (k))
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
35 if (k < 1)
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
36 retval = 1;
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
37 else
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
38 tmp = sylvester_matrix (k-1);
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
39 retval = [tmp, tmp; tmp, -tmp];
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
40 endif
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
41 else
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
42 error ("sylvester_matrix: expecting scalar argument");
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
43 endif
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
44
990ea337e950 [project @ 1998-02-03 08:07:51 by jwe]
jwe
parents:
diff changeset
45 endfunction