octave-nkf: scripts/specfun/beta.m annotate

annotate scripts/specfun/beta.m @ 15144:9cc337ced51a

build: Update OCTAVE_UMFPACK_SEPARATE_SPLIT macro to look for SuiteSparse header file. * acinclude.m4: Update OCTAVE_UMFPACK_SEPARATE_SPLIT macro to look for SuiteSparse header file.

author	Rik <rik@octave.org>
date	Fri, 10 Aug 2012 12:56:15 -0700
parents	67897baaa05f
children	d63878346099

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	1 ## Copyright (C) 1994-2012 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 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: 2312 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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: 2312 diff changeset	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2312 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/>.
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	18
3381 69b167451491 [project @ 1999-12-15 20:48:10 by jwe] jwe parents: 3321 diff changeset	19 ## -- texinfo --
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	20 ## @deftypefn {Mapping Function} {} beta (@var{a}, @var{b})
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	21 ## For real inputs, return the Beta function,
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	22 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	23 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	24 ## B (a, b) = {\Gamma (a) \Gamma (b) \over \Gamma (a + b)}.
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	25 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	26 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7601 diff changeset	27 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3381 diff changeset	28 ##
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	29 ## @example
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	30 ## beta (a, b) = gamma (a) * gamma (b) / gamma (a + b).
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	31 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	32 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 7601 diff changeset	33 ## @end ifnottex
14817 67897baaa05f Adapt implementation of betaincinv to Octave. Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	34 ## @seealso{betaln, betainc}
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2847 diff changeset	35 ## @end deftypefn
2311 2b5788792cad [project @ 1996-07-11 20:18:38 by jwe] jwe parents: 2303 diff changeset	36
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	37 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2312 204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	38 ## Created: 13 June 1993
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	39 ## Adapted-By: jwe
204cc7db6f4a [project @ 1996-07-11 21:20:36 by jwe] jwe parents: 2311 diff changeset	40
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	41 function retval = beta (a, b)
2325 b5568c31ee2c [project @ 1996-07-15 22:20:21 by jwe] jwe parents: 2313 diff changeset	42
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	43 if (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	44 print_usage ();
1026 9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	45 endif
9fc405c8c06c [project @ 1995-01-11 21:17:01 by jwe] jwe parents: 904 diff changeset	46
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	47 if (any (size (a) != size (b)) && numel (a) != 1 && numel (b) != 1)
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	48 error ("beta: inputs A and B have inconsistent sizes");
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	49 endif
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	50
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	51 if (! isreal (a) \|\| ! isreal (b))
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 9211 diff changeset	52 error ("beta: inputs A and B must be real");
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	53 endif
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	54
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	55 retval = real (exp (gammaln (a) + gammaln (b) - gammaln (a+b)));
715 6544b83ef9e9 [project @ 1994-09-20 18:40:02 by jwe] jwe parents: diff changeset	56
6544b83ef9e9 [project @ 1994-09-20 18:40:02 by jwe] jwe parents: diff changeset	57 endfunction
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	58
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	59
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	60 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	61 %! a = [1, 1.5, 2, 3];
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	62 %! b = [4, 3, 2, 1];
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	63 %! v1 = beta (a,b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	64 %! v2 = beta (b,a);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	65 %! v3 = gamma (a).*gamma (b) ./ gamma (a+b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	66 %! assert (v1, v2, sqrt (eps));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	67 %! assert (v2, v3, sqrt (eps));
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	68
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	69 %!assert (beta (1, 1), 1)
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	70
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	71 %!test
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	72 %! a = 2:10;
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	73 %! tol = 10 * max (a) * eps;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	74 %! assert (-a, beta (-1./a, 1), tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	75 %! assert (-a, beta (1, -1./a), tol);
7601 8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	76
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	77 %!test
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	78 %! a = 0.25 + (0:5) * 0.5;
8a939b217863 Treat negative values to lgamma and beta correctly David Bateman <dbateman@free.fr> parents: 7385 diff changeset	79 %! tol = 10 * max (a) * eps;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	80 %! assert (zeros (size (a)), beta (a, -a), tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	81 %! assert (zeros (size (a)), beta (-a, a), tol);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	82
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	83 %!error beta ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	84 %!error beta (1)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	85

Mercurial > hg > octave-nkf

annotate scripts/specfun/beta.m @ 15144:9cc337ced51a