Mercurial > hg > octave-lyh

annotate scripts/special-matrix/vander.m @ 17508:9b2443f97a3e

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Merge the official development
author LYH <lyh.kernel@gmail.com>
date Thu, 26 Sep 2013 04:47:20 +0800
parents f3d52523cde1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
14138
72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents: 13881
diff changeset
1 ## Copyright (C) 1993-2012 John W. Eaton
9104
e0250e2b60ed optimize vander
Jaroslav Hajek <highegg@gmail.com>
parents: 9041
diff changeset
2 ## Copyright (C) 2009 VZLU Prague
2313
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
3 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
4 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
5 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
6 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
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: 6046
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: 6046
diff changeset
9 ## your option) any later version.
2313
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
10 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
11 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
14 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
15 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
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: 6046
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: 6046
diff changeset
18 ## <http://www.gnu.org/licenses/>.
245
16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe]
jwe
parents: 4
diff changeset
19
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
20 ## -*- texinfo -*-
10791
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents: 9211
diff changeset
21 ## @deftypefn {Function File} {} vander (@var{c})
3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents: 9211
diff changeset
22 ## @deftypefnx {Function File} {} vander (@var{c}, @var{n})
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
23 ## Return the Vandermonde matrix whose next to last column is @var{c}.
9137
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
24 ## If @var{n} is specified, it determines the number of columns;
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
25 ## otherwise, @var{n} is taken to be equal to the length of @var{c}.
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3408
diff changeset
26 ##
5016
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
27 ## A Vandermonde matrix has the form:
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
28 ## @tex
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
29 ## $$
5016
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
30 ## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
31 ## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
32 ## \vdots & \ddots & \vdots & \vdots & \vdots \cr
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
33 ## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right]
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
34 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
35 ## @end tex
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
36 ## @ifnottex
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3408
diff changeset
37 ##
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
38 ## @example
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
39 ## @group
9041
853f96e8008f Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
40 ## c(1)^(n-1) @dots{} c(1)^2 c(1) 1
853f96e8008f Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
41 ## c(2)^(n-1) @dots{} c(2)^2 c(2) 1
5016
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
42 ## . . . . .
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
43 ## . . . . .
bdbee5282954 [project @ 2004-09-22 02:50:35 by jwe]
jwe
parents: 4030
diff changeset
44 ## . . . . .
9041
853f96e8008f Cleanup documentation file matrix.texi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
45 ## c(n)^(n-1) @dots{} c(n)^2 c(n) 1
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
46 ## @end group
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
47 ## @end example
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 10791
diff changeset
48 ##
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
49 ## @end ifnottex
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
50 ## @seealso{polyfit}
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
51 ## @end deftypefn
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
52
2314
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe]
jwe
parents: 2313
diff changeset
53 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe]
jwe
parents: 2313
diff changeset
54
9137
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
55 function retval = vander (c, n)
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
56
9137
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
57 if (nargin == 1)
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
58 n = length (c);
eebc7f8e7398 extend vander to allow specified number of columns
Jaroslav Hajek <highegg@gmail.com>
parents: 9104
diff changeset
59 elseif (nargin != 2)
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5642
diff changeset
60 print_usage ();
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
61 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
62
13881
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
63 if (! isvector (c))
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
64 error ("vander: polynomial C must be a vector");
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
65 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
66
13881
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
67 ## avoiding many ^s appears to be faster for n >= 100.
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
68 retval = zeros (length (c), n, class (c));
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
69 d = 1;
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
70 c = c(:);
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
71 for i = n:-1:1
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
72 retval(:,i) = d;
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
73 d .*= c;
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
74 endfor
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
75
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
76 endfunction
7387
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe]
jwe
parents: 7017
diff changeset
77
13881
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
78
7387
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe]
jwe
parents: 7017
diff changeset
79 %!test
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe]
jwe
parents: 7017
diff changeset
80 %! c = [0,1,2,3];
b429b21abdd4 [project @ 2008-01-15 21:43:11 by jwe]
jwe
parents: 7017
diff changeset
81 %! expect = [0,0,0,1; 1,1,1,1; 8,4,2,1; 27,9,3,1];
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
82 %! assert (vander (c), expect);
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7387
diff changeset
83
13881
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
84 %!assert (vander (1), 1)
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
85 %!assert (vander ([1, 2, 3]), vander ([1; 2; 3]))
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
86 %!assert (vander ([1, 2, 3]), [1, 1, 1; 4, 2, 1; 9, 3, 1])
da929884f51e vander.m: Update coding style
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
87 %!assert (vander ([1, 2, 3]*i), [-1, i, 1; -4, 2i, 1; -9, 3i, 1])
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7387
diff changeset
88
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
89 %!assert (vander (2, 3), [4, 2, 1])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
90 %!assert (vander ([2, 3], 3), [4, 2, 1; 9, 3, 1])
9140
c309e028185e vander.m: update tests
John W. Eaton <jwe@octave.org>
parents: 9137
diff changeset
91
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
92 %!error vander ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
93 %!error vander (1, 2, 3)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
94 %!error <polynomial C must be a vector> vander ([1, 2; 3, 4])
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7387
diff changeset
95