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1 ## Copyright (C) 2001 Rolf Fabian and Paul Kienzle |
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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 {Function File} {@var{c} =} nchoosek (@var{n}, @var{k}) |
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21 ## |
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22 ## Compute the binomial coefficient or all combinations of @var{n}. |
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23 ## If @var{n} is a scalar then, calculate the binomial coefficient |
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24 ## of @var{n} and @var{k}, defined as |
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25 ## |
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26 ## @iftex |
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27 ## @tex |
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28 ## $$ |
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29 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} |
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30 ## = {n! \over k! (n-k)!} |
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31 ## $$ |
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32 ## @end tex |
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33 ## @end iftex |
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34 ## @ifinfo |
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35 ## |
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36 ## @example |
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37 ## @group |
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38 ## / \ |
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39 ## | n | n (n-1) (n-2) ... (n-k+1) n! |
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40 ## | | = ------------------------- = --------- |
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41 ## | k | k! k! (n-k)! |
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42 ## \ / |
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43 ## @end group |
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44 ## @end example |
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45 ## @end ifinfo |
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46 ## |
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47 ## If @var{n} is a vector generate all combinations of the elements |
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48 ## of @var{n}, taken @var{k} at a time, one row per combination. The |
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49 ## resulting @var{c} has size @code{[nchoosek (length (@var{n}), |
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50 ## @var{k}), @var{k}]}. |
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51 ## |
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52 ## @seealso{bincoeff} |
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53 ## @end deftypefn |
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54 |
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55 ## Author: Rolf Fabian <fabian@tu-cottbus.de> |
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56 ## Author: Paul Kienzle <pkienzle@users.sf.net> |
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57 |
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58 ## FIXME -- This function is identical to bincoeff for scalar |
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59 ## values, and so should probably be combined with bincoeff. |
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60 |
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61 function A = nchoosek (v, k) |
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62 |
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63 if (nargin != 2) |
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64 print_usage (); |
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65 endif |
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66 |
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67 n = length (v); |
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68 |
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69 if (n == 1) |
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70 A = round (exp (sum (log (k+1:v)) - sum (log (2:v-k)))); |
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71 elseif (k == 0) |
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72 A = []; |
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73 elseif (k == 1) |
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74 A = v(:); |
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75 elseif (k == n) |
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76 A = v(:).'; |
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77 else |
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78 m = round (exp (sum (log (k:n-1)) - sum (log (2:n-k)))); |
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79 A = [v(1)*ones(m,1), nchoosek(v(2:n),k-1); |
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80 nchoosek(v(2:n),k)]; |
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81 endif |
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82 |
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83 endfunction |
