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nchoosek.m: Allow struct inputs (bug #61119) * nchoosek.m: Change input validation to avoid numeric checks if input V is scalar but not a number. Add BIST tests for exceptional values of scalar structs and struct arrays.
author Rik <rik@octave.org>
date Thu, 23 Sep 2021 12:19:54 -0700
parents 23a907b2dbd5
children 54774a713d7c
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2001-2021 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{c} =} nchoosek (@var{n}, @var{k})
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28 ## @deftypefnx {} {@var{c} =} nchoosek (@var{set}, @var{k})
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29 ##
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30 ## Compute the binomial coefficient of @var{n} or list all possible
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31 ## combinations of a @var{set} of items.
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32 ##
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33 ## If @var{n} is a scalar then calculate the binomial coefficient
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34 ## of @var{n} and @var{k} which is defined as
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35 ## @tex
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36 ## $$
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37 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
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38 ## = {n! \over k! (n-k)!}
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39 ## $$
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40 ## @end tex
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41 ## @ifnottex
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42 ##
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43 ## @example
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44 ## @group
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45 ## / \
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46 ## | n | n (n-1) (n-2) @dots{} (n-k+1) n!
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47 ## | | = ------------------------- = ---------
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48 ## | k | k! k! (n-k)!
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49 ## \ /
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50 ## @end group
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51 ## @end example
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52 ##
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53 ## @end ifnottex
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54 ## @noindent
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55 ## This is the number of combinations of @var{n} items taken in groups of
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56 ## size @var{k}.
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57 ##
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58 ## If the first argument is a vector, @var{set}, then generate all
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59 ## combinations of the elements of @var{set}, taken @var{k} at a time, with
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60 ## one row per combination. The result @var{c} has @var{k} columns and
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61 ## @w{@code{nchoosek (length (@var{set}), @var{k})}} rows.
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62 ##
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63 ## For example:
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64 ##
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65 ## How many ways can three items be grouped into pairs?
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66 ##
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67 ## @example
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68 ## @group
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69 ## nchoosek (3, 2)
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70 ## @result{} 3
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71 ## @end group
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72 ## @end example
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73 ##
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74 ## What are the possible pairs?
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75 ##
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76 ## @example
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77 ## @group
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78 ## nchoosek (1:3, 2)
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79 ## @result{} 1 2
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80 ## 1 3
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81 ## 2 3
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82 ## @end group
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83 ## @end example
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84 ##
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85 ## Programming Note: When calculating the binomial coefficient @code{nchoosek}
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86 ## works only for non-negative, integer arguments. Use @code{bincoeff} for
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87 ## non-integer and negative scalar arguments, or for computing many binomial
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88 ## coefficients at once with vector inputs for @var{n} or @var{k}.
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89 ##
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90 ## @seealso{bincoeff, perms}
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91 ## @end deftypefn
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92
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93 function C = nchoosek (v, k)
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94
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95 if (nargin != 2)
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96 print_usage ();
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97 endif
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98
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99 if (! isvector (v))
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100 error ("nchoosek: first argument must be a scalar or a vector");
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101 endif
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102 if (! (isreal (k) && isscalar (k) && k >= 0 && k == fix (k)))
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103 error ("nchoosek: K must be an integer >= 0");
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104 endif
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105 if (isscalar (v))
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106 if (isnumeric (v) && (iscomplex (v) || v < k || v < 0 || v != fix (v)))
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107 error ("nchoosek: N must be a non-negative integer >= K");
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108 endif
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109 endif
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110
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111 n = numel (v);
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112
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113 if (n == 1 && isnumeric (v))
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114 ## Improve precision at next step.
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115 k = min (k, v-k);
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116 C = round (prod ((v-k+1:v)./(1:k)));
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117 if (C*2*k*eps >= 0.5)
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118 warning ("nchoosek: possible loss of precision");
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119 endif
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120 elseif (k == 0)
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121 C = v(zeros (1, 0)); # Return 1x0 object for Matlab compatibility
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122 elseif (k == 1)
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123 C = v(:);
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124 elseif (k == n)
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125 C = v(:).';
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126 elseif (k > n)
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127 C = v(zeros (0, k)); # return 0xk object for Matlab compatibility
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128 elseif (k == 2)
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129 ## Can do it without transpose.
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130 x = repelems (v(1:n-1), [1:n-1; n-1:-1:1]).';
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131 y = cat (1, cellslices (v(:), 2:n, n*ones (1, n-1)){:});
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132 C = [x, y];
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133 elseif (k < n)
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134 v = v(:).';
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135 C = v(k:n);
10800
23b3ae008f5e optimize nchoosek
Jaroslav Hajek <highegg@gmail.com>
parents: 10549
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136 l = 1:n-k+1;
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diff changeset
137 for j = 2:k
19059
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138 c = columns (C);
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139 cA = cellslices (C, l, c*ones (1, n-k+1), 2);
10800
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140 l = c-l+1;
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141 b = repelems (v(k-j+1:n-j+1), [1:n-k+1; l]);
19059
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142 C = [b; cA{:}];
10800
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Jaroslav Hajek <highegg@gmail.com>
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143 l = cumsum (l);
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Jaroslav Hajek <highegg@gmail.com>
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144 l = [1, 1 + l(1:n-k)];
8391
343f0fbca6eb implement nchoosek without recursion
Jaroslav Hajek <highegg@gmail.com>
parents: 8361
diff changeset
145 endfor
19059
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146 C = C.';
6318
bae85c1e0e2a [project @ 2007-02-16 08:15:25 by jwe]
jwe
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147 endif
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148
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Francesco Potortì <pot@gnu.org>
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149 endfunction
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150
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151
30205
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152 %!assert (nchoosek (80, 10), bincoeff (80, 10))
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153 %!assert (nchoosek (1:5, 3),
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154 %! [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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155
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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156 # Test basic behavior for various input types
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157 %!assert (nchoosek ('a':'b', 2), 'ab')
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158 %!assert (nchoosek ("a":"b", 2), "ab")
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159 %!assert (nchoosek ({1,2}, 2), {1,2})
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160 %!test
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161 %! s(1).a = 1;
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162 %! s(2).a = 2;
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163 %! assert (nchoosek (s, 1), s(:));
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164 %! assert (nchoosek (s, 2), s);
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165
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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166 # Verify Matlab compatibility of return sizes & types
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167 %!test
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168 %! x = nchoosek (1:2, 0);
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169 %! assert (size (x), [1, 0]);
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170 %! assert (isa (x, "double"));
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171 %! x = nchoosek (1:2, 3);
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172 %! assert (size (x), [0, 3]);
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173 %! assert (isa (x, "double"));
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diff changeset
174
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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175 %!test
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176 %! x = nchoosek (single (1:2), 0);
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177 %! assert (size (x), [1, 0]);
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178 %! assert (isa (x, "single"));
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179 %! x = nchoosek (single (1:2), 3);
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180 %! assert (size (x), [0, 3]);
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181 %! assert (isa (x, "single"));
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182
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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183 %!test
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184 %! x = nchoosek ('a':'b', 0);
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185 %! assert (size (x), [1, 0]);
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186 %! assert (is_sq_string (x));
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187 %! x = nchoosek ('a':'b', 3);
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188 %! assert (size (x), [0, 3]);
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189 %! assert (is_sq_string (x));
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190
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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191 %!test
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192 %! x = nchoosek ("a":"b", 0);
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193 %! assert (size (x), [1, 0]);
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194 %! assert (is_dq_string (x));
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195 %! x = nchoosek ("a":"b", 3);
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196 %! assert (size (x), [0, 3]);
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197 %! assert (is_dq_string (x));
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198
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199 %!test
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200 %! x = nchoosek (uint8(1):uint8(2), 0);
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201 %! assert (size (x), [1, 0]);
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202 %! assert (isa (x, "uint8"));
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203 %! x = nchoosek (uint8(1):uint8(2), 3);
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204 %! assert (size (x), [0, 3]);
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205 %! assert (isa (x, "uint8"));
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diff changeset
206
23a907b2dbd5 nchoosek.m: Allow "char" and other non-numeric inputs (bug #61119)
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207 %!test
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208 %! x = nchoosek ({1, 2}, 0);
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209 %! assert (size (x), [1, 0]);
30206
aaee7b170cb1 nchoosek.m: Allow struct inputs (bug #61119)
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210 %! assert (iscell (x));
30205
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211 %! x = nchoosek ({1, 2}, 3);
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212 %! assert (size (x), [0, 3]);
30206
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213 %! assert (iscell (x));
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214
aaee7b170cb1 nchoosek.m: Allow struct inputs (bug #61119)
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215 %!test
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216 %! s.a = [1 2 3];
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Rik <rik@octave.org>
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217 %! s.b = [4 5 6];
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Rik <rik@octave.org>
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218 %! x = nchoosek (s, 0);
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Rik <rik@octave.org>
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219 %! assert (size (x), [1, 0]);
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Rik <rik@octave.org>
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220 %! assert (isstruct (x));
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221 %! assert (fieldnames (x), {"a"; "b"});
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222 %! x = nchoosek (s, 3);
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Rik <rik@octave.org>
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223 %! assert (size (x), [0, 3]);
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Rik <rik@octave.org>
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224 %! assert (isstruct (x));
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225 %! assert (fieldnames (x), {"a"; "b"});
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226
aaee7b170cb1 nchoosek.m: Allow struct inputs (bug #61119)
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diff changeset
227 %!test
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228 %! s.a = [1 2 3];
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229 %! s.b = [4 5 6];
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230 %! s(2).a = 1; # make s a struct array rather than scalar struct
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231 %! x = nchoosek (s, 0);
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232 %! assert (size (x), [1, 0]);
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Rik <rik@octave.org>
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233 %! assert (isstruct (x));
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234 %! assert (fieldnames (x), {"a"; "b"});
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235 %! x = nchoosek (s, 3);
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236 %! assert (size (x), [0, 3]);
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Rik <rik@octave.org>
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237 %! assert (isstruct (x));
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238 %! assert (fieldnames (x), {"a"; "b"});
14090
281ecc6fb431 nchoosek.m: Update documentation, fix input validation, add more %!tests
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diff changeset
239
19833
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240 ## Test input validation
28886
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241 %!error <Invalid call> nchoosek ()
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242 %!error <Invalid call> nchoosek (1)
30205
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243 %!error <first argument must be a scalar or a vector> nchoosek (ones (3, 3), 1)
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244 %!error <K must be an integer .= 0> nchoosek (100, 2i)
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245 %!error <K must be an integer .= 0> nchoosek (100, [2 3])
19059
83b88e20e9c1 nchoosek.m: Overhaul function.
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246 %!error <K must be an integer .= 0> nchoosek (100, -45)
83b88e20e9c1 nchoosek.m: Overhaul function.
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247 %!error <K must be an integer .= 0> nchoosek (100, 45.5)
83b88e20e9c1 nchoosek.m: Overhaul function.
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248 %!error <N must be a non-negative integer .= K> nchoosek (100i, 2)
83b88e20e9c1 nchoosek.m: Overhaul function.
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diff changeset
249 %!error <N must be a non-negative integer .= K> nchoosek (100, 145)
83b88e20e9c1 nchoosek.m: Overhaul function.
Rik <rik@octave.org>
parents: 18795
diff changeset
250 %!error <N must be a non-negative integer .= K> nchoosek (-100, 45)
83b88e20e9c1 nchoosek.m: Overhaul function.
Rik <rik@octave.org>
parents: 18795
diff changeset
251 %!error <N must be a non-negative integer .= K> nchoosek (100.5, 45)
83b88e20e9c1 nchoosek.m: Overhaul function.
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parents: 18795
diff changeset
252 %!warning <possible loss of precision> nchoosek (100, 45);