Mercurial > octave-antonio

annotate scripts/special-matrix/pascal.m @ 12639:4d777e05d47c stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Review and update documentation for "Matrix Manipulation" chapter. * matrix.txi, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m, bsxfun.cc, find.cc, lookup.cc, rand.cc, tril.cc, data.cc, arrayfun.m, blkdiag.m, fliplr.m, flipud.m, logspace.m, postpad.m, prepad.m, randi.m, repmat.m, rot90.m, rotdim.m, shiftdim.m, sortrows.m, vech.m, xor.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m, sylvester_matrix.m, toeplitz.m, vander.m, wilkinson.m, bsxfun.cc (bsxfun), find.cc (find), lookup.cc (lookup), rand.cc (rand, randn, rande, randg, randp), tril.cc (triu), data.cc (all, any, horzcat, vertcat, cat, permute, ipermute, ones, zeros, eye, linspace, resize, reshape, issorted, diff): Improve docstrings
author Rik <octave@nomad.inbox5.com>
date Sun, 01 May 2011 08:55:15 -0700
parents f5a5e5252b5a
children d4404589498c
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
11523
fd0a3ac60b0e update copyright notices
John W. Eaton <jwe@octave.org>
parents: 11098
diff changeset
1 ## Copyright (C) 1999-2011 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 -*-
10791
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents: 9209
diff changeset
21 ## @deftypefn {Function File} {} pascal (@var{n})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents: 9209
diff changeset
22 ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t})
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. @var{t}
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
24 ## defaults to 0. Return the pseudo-lower triangular Cholesky@tie{}factor of
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
25 ## the Pascal matrix if @code{@var{t} = 1} (The sign of some columns may be
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
26 ## negative). This matrix is its own inverse, that is @code{pascal (@var{n},
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
27 ## 1) ^ 2 == eye (@var{n})}. If @code{@var{t} = -1}, return the true
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
28 ## Cholesky@tie{}factor with strictly positive values on the diagonal. If
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
29 ## @code{@var{t} = 2}, return a transposed and permuted version of @code{pascal
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
30 ## (@var{n}, 1)}, which is the cube root of the identity matrix. That is,
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
31 ## @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 ##
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 12485
diff changeset
33 ## @seealso{chol}
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
34 ## @end deftypefn
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
35
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
36 ## Author: Peter Ekberg
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
37 ## (peda)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
38
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
39 function retval = pascal (n, t)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
40
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
41 if (nargin > 2) || (nargin == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
42 print_usage ();
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
43 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
44
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
45 if (nargin == 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
46 t = 0;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
47 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
48
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
49 if (! isscalar (n) || ! isscalar (t))
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
50 error ("pascal: expecting scalar arguments, found something else");
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
51 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
52
11098
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
53 if (t < -1 || t > 2)
12480
139f993936af Uppercase variables in script error strings.
Rik <octave@nomad.inbox5.com>
parents: 12448
diff changeset
54 error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t);
11098
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
55 endif
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
56
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
57 retval = zeros (n);
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
58 retval(:,1) = 1;
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
59
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
60 if (t == -1)
9096
5235caf89e12 fix typo in pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9094
diff changeset
61 for j = 2:n
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
62 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
63 endfor
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
64 else
9096
5235caf89e12 fix typo in pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9094
diff changeset
65 for j = 2:n
9094
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
66 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
67 endfor
2e35cfcf6a6a fix, optimize & extend pascal
Jaroslav Hajek <highegg@gmail.com>
parents: 9051
diff changeset
68 endif
5827
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
69
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
70 if (t == 0)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
71 retval = retval*retval';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
72 elseif (t == 2)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
73 retval = retval';
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
74 retval = retval(n:-1:1,:);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
75 retval(:,n) = -retval(:,n);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
76 retval(n,:) = -retval(n,:);
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
77 if (rem(n,2) != 1)
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
78 retval = -retval;
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
79 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
80 endif
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
81
1fe78adb91bc [project @ 2006-05-22 06:25:14 by jwe]
jwe
parents:
diff changeset
82 endfunction
11098
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
83
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
84 %!assert (pascal(3,-1), [1,0,0;1,1,0;1,2,1])
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
85 %!assert (pascal(3,0), [1,1,1;1,2,3;1,3,6])
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
86 %!assert (pascal(3,0), pascal(3))
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
87 %!assert (pascal(3,1), [1,0,0;1,-1,0;1,-2,1])
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
88 %!assert (pascal(3,2), [0,0,-1;0,-1,2;-1,-1,1])
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
89 %!error (pascal(3,4))
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
90 %!error (pascal(3,-2))
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
91 %!error (pascal())
dcde7c5a1d29 new tests for special-matrix functions
John W. Eaton <jwe@octave.org>
parents: 10791
diff changeset
92 %!error (pascal(1,2,3))