Mercurial > octave-nkf
annotate scripts/miscellaneous/bincoeff.m @ 10549:95c3e38098bf
Untabify .m scripts
| author | Rik <code@nomad.inbox5.com> |
|---|---|
| date | Fri, 23 Apr 2010 11:28:50 -0700 |
| parents | f0c3d3fc4903 |
| children | 693e22af08ae |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 1995, 1996, 1999, 2000, 2002, 2004, 2005, 2006, 2007, |
| 2 ## 2008, 2009 Kurt Hornik | |
| 3426 | 3 ## |
| 3922 | 4 ## This file is part of Octave. |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3426 | 10 ## |
| 3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
| 2538 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 14 ## General Public License for more details. |
| 15 ## | |
| 2538 | 16 ## You should have received a copy of the GNU General Public License |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 2538 | 19 |
| 3321 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Mapping Function} {} bincoeff (@var{n}, @var{k}) | |
| 22 ## Return the binomial coefficient of @var{n} and @var{k}, defined as | |
| 23 ## @tex | |
| 24 ## $$ | |
| 25 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} | |
| 26 ## $$ | |
| 27 ## @end tex | |
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28 ## @ifnottex |
| 3426 | 29 ## |
| 3321 | 30 ## @example |
| 31 ## @group | |
| 32 ## / \ | |
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33 ## | n | n (n-1) (n-2) @dots{} (n-k+1) |
| 3321 | 34 ## | | = ------------------------- |
| 35 ## | k | k! | |
| 36 ## \ / | |
| 37 ## @end group | |
| 38 ## @end example | |
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39 ## @end ifnottex |
| 3426 | 40 ## |
| 3321 | 41 ## For example, |
| 3426 | 42 ## |
| 3321 | 43 ## @example |
| 44 ## @group | |
| 45 ## bincoeff (5, 2) | |
| 46 ## @result{} 10 | |
| 47 ## @end group | |
| 48 ## @end example | |
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49 ## |
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50 ## In most cases, the @code{nchoosek} function is faster for small |
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51 ## scalar integer arguments. It also warns about loss of precision for |
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52 ## big arguments. |
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53 ## |
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54 ## @seealso{nchoosek} |
| 3321 | 55 ## @end deftypefn |
| 2538 | 56 |
| 5428 | 57 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2538 | 58 ## Created: 8 October 1994 |
| 59 ## Adapted-By: jwe | |
| 60 | |
| 61 function b = bincoeff (n, k) | |
| 3426 | 62 |
| 2538 | 63 if (nargin != 2) |
| 6046 | 64 print_usage (); |
| 2538 | 65 endif |
| 3426 | 66 |
| 2538 | 67 [retval, n, k] = common_size (n, k); |
| 68 if (retval > 0) | |
| 3458 | 69 error ("bincoeff: n and k must be of common size or scalars"); |
| 2538 | 70 endif |
| 3426 | 71 |
| 4854 | 72 sz = size (n); |
| 73 b = zeros (sz); | |
| 3426 | 74 |
| 5961 | 75 ind = (! (k >= 0) | (k != real (round (k))) | isnan (n)); |
| 76 b(ind) = NaN; | |
| 77 | |
| 78 ind = (k == 0); | |
| 79 b(ind) = 1; | |
| 2538 | 80 |
| 5961 | 81 ind = ((k > 0) & ((n == real (round (n))) & (n < 0))); |
| 6902 | 82 b(ind) = (-1) .^ k(ind) .* exp (gammaln (abs (n(ind)) + k(ind)) |
| 10549 | 83 - gammaln (k(ind) + 1) |
| 84 - gammaln (abs (n(ind)))); | |
| 3426 | 85 |
| 6902 | 86 ind = ((k > 0) & (n >= k)); |
| 87 b(ind) = exp (gammaln (n(ind) + 1) | |
| 10549 | 88 - gammaln (k(ind) + 1) |
| 89 - gammaln (n(ind) - k(ind) + 1)); | |
| 6902 | 90 |
| 91 ind = ((k > 0) & ((n != real (round (n))) & (n < k))); | |
| 92 b(ind) = (1/pi) * exp (gammaln (n(ind) + 1) | |
| 10549 | 93 - gammaln (k(ind) + 1) |
| 94 + gammaln (k(ind) - n(ind)) | |
| 95 + log (sin (pi * (n(ind) - k(ind) + 1)))); | |
| 6902 | 96 |
| 97 ## Clean up rounding errors. | |
| 5961 | 98 ind = (n == round (n)); |
| 99 b(ind) = round (b(ind)); | |
| 6902 | 100 |
| 101 ind = (n != round (n)); | |
| 102 b(ind) = real (b(ind)); | |
| 103 | |
| 2538 | 104 endfunction |
| 105 | |
| 6902 | 106 %!assert(bincoeff(4,2), 6) |
| 107 %!assert(bincoeff(2,4), 0) | |
| 108 %!assert(bincoeff(0.4,2), -.12, 8*eps) | |
| 7385 | 109 |
| 110 %!assert(bincoeff (5, 2) == 10 && bincoeff (50, 6) == 15890700); | |
| 111 | |
| 112 %!error bincoeff (); | |
| 113 | |
| 114 %!error bincoeff (1, 2, 3); |