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nchoosek.m: Update documentation, fix input validation, add more %!tests * nchoosek.m: Update documentation, fix input validation, add more %!tests
author Rik <octave@nomad.inbox5.com>
date Wed, 21 Dec 2011 16:53:43 -0800
parents 5b49cafe0599
children 050bc580cb60
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1 ## Copyright (C) 2001-2011 Rolf Fabian and Paul Kienzle
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2 ## Copyright (C) 2008 Jaroslav Hajek
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{c} =} nchoosek (@var{n}, @var{k})
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22 ## @deftypefnx {Function File} {@var{c} =} nchoosek (@var{set}, @var{k})
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23 ##
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24 ## Compute the binomial coefficient or all combinations of a set of items.
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25 ##
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26 ## If @var{n} is a scalar then calculate the binomial coefficient
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27 ## of @var{n} and @var{k} which is defined as
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28 ## @tex
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29 ## $$
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30 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
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31 ## = {n! \over k! (n-k)!}
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32 ## $$
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33 ## @end tex
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34 ## @ifnottex
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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) @dots{} (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 ##
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46 ## @end ifnottex
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47 ## @noindent
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48 ## This is the number of combinations of @var{n} items taken in groups of
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49 ## size @var{k}.
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50 ##
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51 ## If the first argument is a vector, @var{set}, then generate all combinations
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52 ## of the elements of @var{set}, taken @var{k} at a time, with one row per
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53 ## combination. The result @var{c} has @var{k} columns and
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54 ## @w{@code{nchoosek (length (@var{set}), @var{k})}} rows.
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55 ##
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56 ## For example:
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57 ##
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58 ## How many ways can three items be grouped into pairs?
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59 ##
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60 ## @example
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61 ## @group
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62 ## nchoosek (3, 2)
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63 ## @result{} 3
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64 ## @end group
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65 ## @end example
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66 ##
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67 ## What are the possible pairs?
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68 ##
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69 ## @example
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70 ## @group
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71 ## nchoosek (1:3, 2)
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72 ## @result{} 1 2
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73 ## 1 3
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74 ## 2 3
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75 ## @end group
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76 ## @end example
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77 ##
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78 ## @code{nchoosek} works only for non-negative, integer arguments. Use
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79 ## @code{bincoeff} for non-integer and negative scalar arguments, or for
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80 ## computing many binomial coefficients at once with vector inputs for @var{n}
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81 ## or @var{k}.
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82 ##
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83 ## @seealso{bincoeff, perms}
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84 ## @end deftypefn
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85
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86 ## Author: Rolf Fabian <fabian@tu-cottbus.de>
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87 ## Author: Paul Kienzle <pkienzle@users.sf.net>
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88 ## Author: Jaroslav Hajek
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89
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90 function A = nchoosek (v, k)
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91
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92 if (nargin != 2
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93 || !isnumeric (k) || !isnumeric (v)
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94 || !isscalar (k) || ! (isscalar (v) || isvector (v)))
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95 print_usage ();
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96 endif
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97 if (k < 0 || k != fix (k)
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98 || (isscalar (v) && (v < k || v < 0 || v != fix (v))))
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99 error ("nchoosek: args are non-negative integers with V not less than K");
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100 endif
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101
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102 n = length (v);
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103
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104 if (n == 1)
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105 ## Improve precision at next step.
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106 k = min (k, v-k);
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107 A = round (prod ((v-k+1:v)./(1:k)));
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108 if (A*2*k*eps >= 0.5)
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109 warning ("nchoosek", "nchoosek: possible loss of precision");
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110 endif
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111 elseif (k == 0)
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112 A = [];
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113 elseif (k == 1)
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114 A = v(:);
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115 elseif (k == n)
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116 A = v(:).';
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117 elseif (k > n)
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118 A = zeros (0, k, class (v));
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119 elseif (k == 2)
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120 ## Can do it without transpose.
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121 x = repelems (v(1:n-1), [1:n-1; n-1:-1:1]).';
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122 y = cat (1, cellslices (v(:), 2:n, n*ones (1, n-1)){:});
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123 A = [x, y];
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124 elseif (k < n)
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125 v = v(:).';
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126 A = v(k:n);
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127 l = 1:n-k+1;
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128 for j = 2:k
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129 c = columns (A);
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130 cA = cellslices (A, l, c*ones (1, n-k+1), 2);
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131 l = c-l+1;
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132 b = repelems (v(k-j+1:n-j+1), [1:n-k+1; l]);
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133 A = [b; cA{:}];
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134 l = cumsum (l);
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135 l = [1, 1 + l(1:n-k)];
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Jaroslav Hajek <highegg@gmail.com>
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136 endfor
10800
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137 clear cA b;
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138 A = A.';
6318
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jwe
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139 endif
8361
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Francesco Potortì <pot@gnu.org>
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140 endfunction
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jwe
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141
14090
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Rik <octave@nomad.inbox5.com>
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142
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143 %!assert (nchoosek (80,10), bincoeff (80,10))
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144 %!assert (nchoosek(1:5,3), [1:3;1,2,4;1,2,5;1,3,4;1,3,5;1,4,5;2:4;2,3,5;2,4,5;3:5])
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parents: 14062
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145
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parents: 14062
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146 %% Test input validation
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147 %!warning nchoosek (100,45);
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148 %!error nchoosek ("100", 45)
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parents: 14062
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149 %!error nchoosek (100, "45")
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parents: 14062
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150 %!error nchoosek (100, ones (2,2))
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parents: 14062
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151 %!error nchoosek (repmat (100, [2 2]), 45)
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parents: 14062
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152 %!error nchoosek (100, -45)
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153 %!error nchoosek (100, 45.5)
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154 %!error nchoosek (100, 145)
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parents: 14062
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155 %!error nchoosek (-100, 45)
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Rik <octave@nomad.inbox5.com>
parents: 14062
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156 %!error nchoosek (100.5, 45)
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Rik <octave@nomad.inbox5.com>
parents: 14062
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157