Mercurial > hg > octave-nkf

annotate scripts/special-matrix/pascal.m @ 9094:2e35cfcf6a6a

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
fix, optimize & extend pascal
author Jaroslav Hajek <highegg@gmail.com>
date Mon, 06 Apr 2009 11:16:20 +0200
parents 1bf0ce0930be
children 5235caf89e12
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
7017
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe]
jwe
parents: 7016
diff changeset
1 ## Copyright (C) 1999, 2006, 2007 Peter Ekberg
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
2 ## Copyright (C) 2009 VZLU Prague
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
3 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
4 ## This file is part of Octave.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
5 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
6 ## Octave is free software; you can redistribute it and/or modify it
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
7 ## 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: 5827
diff changeset
8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
9 ## your option) any later version.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
10 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
11 ## Octave is distributed in the hope that it will be useful, but
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
14 ## General Public License for more details.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
15 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
16 ## 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: 5827
diff changeset
17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5827
diff changeset
18 ## <http://www.gnu.org/licenses/>.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
19
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
20 ## -*- texinfo -*-
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
21 ## @deftypefn {Function File} {} pascal (@var{n}, @var{t})
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
22 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}.
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
24 ## @var{t} defaults to 0. Return lower triangular Cholesky factor of
9051
1bf0ce0930be Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents: 9041
diff changeset
25 ## the Pascal matrix if @code{@var{t} = 1}. This matrix is its own
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
26 ## inverse, that is @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}.
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
27 ## If @code{@var{t} = -1}, return its absolute value. This is the
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
28 ## standard pascal triangle as a lower-triangular matrix.
9051
1bf0ce0930be Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents: 9041
diff changeset
29 ## If @code{@var{t} = 2}, return a transposed and permuted version of
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
30 ## @code{pascal (@var{n}, 1)}, which is the cube-root of the identity
9041
853f96e8008f Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents: 7017
diff changeset
31 ## matrix. That is @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
32 ##
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
33 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
34 ## hadamard, wilkinson, compan, rosser}
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
35 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
36
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
37 ## Author: Peter Ekberg
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
38 ## (peda)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
39
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40 function retval = pascal (n, t)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
42 if (nargin > 2) || (nargin == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
45
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
46 if (nargin == 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
47 t = 0;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
48 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
49
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
50 if (! isscalar (n) || ! isscalar (t))
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
51 error ("pascal: expecting scalar arguments, found something else");
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
52 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
53
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
54 retval = zeros (n);
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
55 retval(:,1) = 1;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
56
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
57 if (t == -1)
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
58 for j = 2:n-1
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
59 retval(j:n,j) = cumsum (retval (j-1:n-1,j-1));
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
60 endfor
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
61 else
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
62 for j = 2:n-1
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
63 retval(j:n,j) = -cumsum (retval (j-1:n-1,j-1));
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
64 endfor
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
65 endif
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
66
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
67 if (t == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
68 retval = retval*retval';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
69 elseif (t == 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
70 retval = retval';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
71 retval = retval(n:-1:1,:);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
72 retval(:,n) = -retval(:,n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
73 retval(n,:) = -retval(n,:);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
74 if (rem(n,2) != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
75 retval = -retval;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
76 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
77 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
78
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
79 endfunction