Mercurial > hg > octave-lyh

annotate scripts/special-matrix/hilb.m @ 15806:01d4f742d75d

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Re-organize and improve Java Interface documentation. * doc/interpreter/java.txi: Add usejava, isjava functions, debug_java, java_matrix_autoconversion, java_unsigned_autoconversion to docs. Re-organize to put functions in logical order. Add new "Dialog Box Functions" node. * doc/interpreter/system.txi: Remove usejava from list of system functions. * libinterp/octave-value/ov-java.cc(FjavaObject, FjavaMethod, Fjava_unsigned_autoconversion): Improve docstrings. * scripts/java/javaArray.m: Tweak docstring. * scripts/java/listdlg.m: Wrap long lines in docstring. Improve code example in docstring.
author Rik <rik@octave.org>
date Mon, 17 Dec 2012 10:23:43 -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: 13872
diff changeset
1 ## Copyright (C) 1993-2012 John W. Eaton
2313
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
5 ## 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
6 ## 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
7 ## 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
8 ## your option) any later version.
2313
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
10 ## 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
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
12 ## 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
13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe]
jwe
parents: 2311
diff changeset
15 ## 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
16 ## 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
17 ## <http://www.gnu.org/licenses/>.
245
16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe]
jwe
parents: 4
diff changeset
18
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
19 ## -*- texinfo -*-
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
20 ## @deftypefn {Function File} {} hilb (@var{n})
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
21 ## Return the Hilbert matrix of order @var{n}. The @math{i,j} element
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
22 ## of a Hilbert matrix is defined as
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
23 ## @tex
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
24 ## $$
14327
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
25 ## H(i, j) = {1 \over (i + j - 1)}
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
26 ## $$
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
27 ## @end tex
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
28 ## @ifnottex
3426
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe]
jwe
parents: 3408
diff changeset
29 ##
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
30 ## @example
14327
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
31 ## H(i, j) = 1 / (i + j - 1)
3369
f37ca3017116 [project @ 1999-11-21 16:26:02 by jwe]
jwe
parents: 3140
diff changeset
32 ## @end example
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 9211
diff changeset
33 ##
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7411
diff changeset
34 ## @end ifnottex
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
35 ##
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
36 ## Hilbert matrices are close to being singular which make them difficult to
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
37 ## invert with numerical routines.
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
38 ## Comparing the condition number of a random matrix 5x5 matrix with that of
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
39 ## a Hilbert matrix of order 5 reveals just how difficult the problem is.
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
40 ##
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
41 ## @example
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
42 ## @group
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
43 ## cond (rand (5))
14327
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
44 ## @result{} 14.392
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
45 ## cond (hilb (5))
14327
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
46 ## @result{} 4.7661e+05
12639
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
47 ## @end group
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
48 ## @end example
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
49 ##
4d777e05d47c doc: Review and update documentation for "Matrix Manipulation" chapter.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
50 ## @seealso{invhilb}
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
2311
2b5788792cad [project @ 1996-07-11 20:18:38 by jwe]
jwe
parents: 2303
diff changeset
55 function retval = hilb (n)
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
56
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
57 if (nargin != 1)
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5642
diff changeset
58 print_usage ();
13872
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
59 elseif (! isscalar (n))
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
60 error ("hilb: N must be a scalar integer");
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
13872
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
63 retval = zeros (n);
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
64 tmp = 1:n;
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
65 for i = 1:n
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
66 retval(i, :) = 1.0 ./ tmp;
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
67 tmp++;
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
68 endfor
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
69
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
jwe
parents:
diff changeset
70 endfunction
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
71
13872
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
72
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
73 %!assert (hilb (2), [1, 1/2; 1/2, 1/3])
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
74 %!assert (hilb (3), [1, 1/2, 1/3; 1/2, 1/3, 1/4; 1/3, 1/4, 1/5])
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
75
13872
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
76 %!error hilb ()
779e15b69738 hilb.m: 10% speedup by using in-place accumulation.
Rik <octave@nomad.inbox5.com>
parents: 12639
diff changeset
77 %!error hilb (1, 2)
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
78 %!error <N must be a scalar integer> hilb (ones (2))
7411
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe]
jwe
parents: 7017
diff changeset
79