octave-nkf: scripts/miscellaneous/bincoeff.m annotate

annotate scripts/miscellaneous/bincoeff.m @ 13169:078729410a0d

bincoeff.m: 15% speed improvement and better input validation * bincoeff.m: Check for complex inputs. Return NaN correctly for bad inputs. Use logical indexing effectively for 15% speed improvement.

author	Rik <octave@nomad.inbox5.com>
date	Tue, 20 Sep 2011 11:41:59 -0700
parents	c792872f8942
children	72c96de7a403

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11472 diff changeset	1 ## Copyright (C) 1995-2011 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	2 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	3 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	4 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 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: 6902 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: 6902 diff changeset	8 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	9 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	13 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	14 ##
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: 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: 6902 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: 6902 diff changeset	17 ## <http://www.gnu.org/licenses/>.
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	18
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	19 ## -- texinfo --
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	20 ## @deftypefn {Mapping Function} {} bincoeff (@var{n}, @var{k})
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	21 ## Return the binomial coefficient of @var{n} and @var{k}, defined as
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	22 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	23 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	24 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	25 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	26 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 8435 diff changeset	27 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	28 ##
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	29 ## @example
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	30 ## @group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	31 ## / \
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	32 ## \| n \| n (n-1) (n-2) @dots{} (n-k+1)
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	33 ## \| \| = -------------------------
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	34 ## \| k \| k!
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	35 ## \ /
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	36 ## @end group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	37 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	38 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 8435 diff changeset	39 ## @end ifnottex
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	40 ## For example:
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	41 ##
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	42 ## @example
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	43 ## @group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	44 ## bincoeff (5, 2)
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	45 ## @result{} 10
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	46 ## @end group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	47 ## @end example
8435 69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	48 ##
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	49 ## In most cases, the @code{nchoosek} function is faster for small
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	50 ## scalar integer arguments. It also warns about loss of precision for
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	51 ## big arguments.
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	52 ##
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	53 ## @seealso{nchoosek}
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	54 ## @end deftypefn
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	55
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	56 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	57 ## Created: 8 October 1994
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	58 ## Adapted-By: jwe
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	59
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	60 function b = bincoeff (n, k)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	61
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	62 if (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5961 diff changeset	63 print_usage ();
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	64 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	65
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	66 [retval, n, k] = common_size (n, k);
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	67 if (retval > 0)
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	68 error ("bincoeff: N and K must be of common size or scalars");
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	69 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	70
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	71 if (iscomplex (n) \|\| iscomplex (k))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	72 error ("bincoeff: N and K must not be complex");
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	73 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	74
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	75 b = zeros (size (n));
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	76
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	77 ok = (k >= 0) & (k == fix (k)) & (! isnan (n));
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	78 b(! ok) = NaN;
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	79
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	80 n_int = (n == fix (n));
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	81 idx = n_int & (n < 0) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	82 b(idx) = (-1) .^ k(idx) .* exp (gammaln (abs (n(idx)) + k(idx))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	83 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	84 - gammaln (abs (n(idx))));
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	85
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	86 idx = (n >= k) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	87 b(idx) = exp (gammaln (n(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	88 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	89 - gammaln (n(idx) - k(idx) + 1));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	90
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	91 idx = (! n_int) & (n < k) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	92 b(idx) = (1/pi) * exp (gammaln (n(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	93 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	94 + gammaln (k(idx) - n(idx))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	95 + log (sin (pi * (n(idx) - k(idx) + 1))));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	96
d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	97 ## Clean up rounding errors.
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	98 b(n_int) = round (b(n_int));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	99
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	100 idx = ! n_int;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	101 b(idx) = real (b(idx));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	102
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	103 endfunction
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	104
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	105
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	106 %!assert(bincoeff (4, 2), 6)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	107 %!assert(bincoeff (2, 4), 0)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	108 %!assert(bincoeff (-4, 2), 10)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	109 %!assert(bincoeff (5, 2), 10)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	110 %!assert(bincoeff (50, 6), 15890700)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	111 %!assert(bincoeff (0.4, 2), -.12, 8*eps)
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	112
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	113 %!assert(bincoeff ([4 NaN 4], [-1, 2, 2.5]), NaN (1, 3))
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	114
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	115 %% Test input validation
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	116 %!error bincoeff ();
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	117 %!error bincoeff (1, 2, 3);
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	118 %!error bincoeff (ones(3),ones(2))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	119 %!error bincoeff (ones(2),ones(3))
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	120

Mercurial > octave-nkf

annotate scripts/miscellaneous/bincoeff.m @ 13169:078729410a0d