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1 ## Copyright (C) 1995, 1996 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Mapping Function} {} bincoeff (@var{n}, @var{k}) |
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21 ## Return the binomial coefficient of @var{n} and @var{k}, defined as |
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22 ## @iftex |
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23 ## @tex |
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24 ## $$ |
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25 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} |
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26 ## $$ |
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27 ## @end tex |
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28 ## @end iftex |
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29 ## @ifinfo |
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30 ## |
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31 ## @example |
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32 ## @group |
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33 ## / \ |
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34 ## | n | n (n-1) (n-2) ... (n-k+1) |
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35 ## | | = ------------------------- |
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36 ## | k | k! |
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37 ## \ / |
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38 ## @end group |
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39 ## @end example |
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40 ## @end ifinfo |
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41 ## |
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42 ## For example, |
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43 ## |
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44 ## @example |
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45 ## @group |
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46 ## bincoeff (5, 2) |
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47 ## @result{} 10 |
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48 ## @end group |
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49 ## @end example |
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50 ## @end deftypefn |
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51 |
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52 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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53 ## Created: 8 October 1994 |
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54 ## Adapted-By: jwe |
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55 |
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56 function b = bincoeff (n, k) |
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57 |
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58 if (nargin != 2) |
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59 print_usage (); |
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60 endif |
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61 |
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62 [retval, n, k] = common_size (n, k); |
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63 if (retval > 0) |
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64 error ("bincoeff: n and k must be of common size or scalars"); |
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65 endif |
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66 |
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67 sz = size (n); |
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68 b = zeros (sz); |
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69 |
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70 ind = (! (k >= 0) | (k != real (round (k))) | isnan (n)); |
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71 b(ind) = NaN; |
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72 |
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73 ind = (k == 0); |
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74 b(ind) = 1; |
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75 |
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76 ind = ((k > 0) & ((n == real (round (n))) & (n < 0))); |
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77 b(ind) = (-1) .^ k(ind) .* exp (gammaln (abs (n(ind)) + k(ind)) |
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78 - gammaln (k(ind) + 1) |
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79 - gammaln (abs (n(ind)))); |
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80 |
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81 ind = ((k > 0) & (n >= k)); |
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82 b(ind) = exp (gammaln (n(ind) + 1) |
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83 - gammaln (k(ind) + 1) |
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84 - gammaln (n(ind) - k(ind) + 1)); |
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85 |
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86 ind = ((k > 0) & ((n != real (round (n))) & (n < k))); |
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87 b(ind) = (1/pi) * exp (gammaln (n(ind) + 1) |
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88 - gammaln (k(ind) + 1) |
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89 + gammaln (k(ind) - n(ind)) |
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90 + log (sin (pi * (n(ind) - k(ind) + 1)))); |
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91 |
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92 ## Clean up rounding errors. |
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93 ind = (n == round (n)); |
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94 b(ind) = round (b(ind)); |
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95 |
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96 ind = (n != round (n)); |
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97 b(ind) = real (b(ind)); |
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98 |
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99 endfunction |
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100 |
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101 %!assert(bincoeff(4,2), 6) |
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102 %!assert(bincoeff(2,4), 0) |
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103 %!assert(bincoeff(0.4,2), -.12, 8*eps) |
