annotate scripts/statistics/mode.m @ 26376:00f796120a6d stable

maint: Update copyright dates in all source files.
author John W. Eaton <jwe@octave.org>
date Wed, 02 Jan 2019 16:32:43 -0500
parents 6652d3823428
children b442ec6dda5c
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1 ## Copyright (C) 2007-2019 David Bateman
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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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {} mode (@var{x})
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21 ## @deftypefnx {} {} mode (@var{x}, @var{dim})
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22 ## @deftypefnx {} {[@var{m}, @var{f}, @var{c}] =} mode (@dots{})
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23 ## Compute the most frequently occurring value in a dataset (mode).
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24 ##
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25 ## @code{mode} determines the frequency of values along the first non-singleton
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26 ## dimension and returns the value with the highest frequency. If two, or
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27 ## more, values have the same frequency @code{mode} returns the smallest.
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28 ##
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29 ## If the optional argument @var{dim} is given, operate along this dimension.
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30 ##
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31 ## The return variable @var{f} is the number of occurrences of the mode in
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32 ## the dataset.
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33 ##
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34 ## The cell array @var{c} contains all of the elements with the maximum
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35 ## frequency.
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36 ## @seealso{mean, median}
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37 ## @end deftypefn
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38
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39 function [m, f, c] = mode (x, dim)
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40
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41 if (nargin < 1 || nargin > 2)
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42 print_usage ();
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43 endif
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44
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45 if (! (isnumeric (x) || islogical (x)))
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46 error ("mode: X must be a numeric vector or matrix");
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47 endif
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48
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49 nd = ndims (x);
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50 sz = size (x);
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51 if (nargin < 2)
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52 ## Find the first non-singleton dimension.
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53 (dim = find (sz > 1, 1)) || (dim = 1);
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54 else
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55 if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
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56 error ("mode: DIM must be an integer and a valid dimension");
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57 endif
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58 endif
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59
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60 if (dim > nd)
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61 ## Special case of mode over non-existent dimension.
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62 m = x;
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63 f = ones (size (x));
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64 c = num2cell (x);
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65 return;
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66 endif
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67
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68 sz2 = sz;
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69 sz2(dim) = 1;
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70 sz3 = ones (1, nd);
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71 sz3(dim) = sz(dim);
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72
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73 if (issparse (x))
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74 t2 = sparse (sz(1), sz(2));
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75 else
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76 t2 = zeros (sz);
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77 endif
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78
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79 if (dim != 1)
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80 perm = [dim, 1:dim-1, dim+1:nd];
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81 t2 = permute (t2, perm);
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82 endif
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83
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84 xs = sort (x, dim);
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85 t = cat (dim, true (sz2), diff (xs, 1, dim) != 0);
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86
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87 if (dim != 1)
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88 t2(permute (t != 0, perm)) = diff ([find(permute (t, perm))(:); prod(sz)+1]);
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89 f = max (ipermute (t2, perm), [], dim);
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90 xs = permute (xs, perm);
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91 else
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92 t2(t) = diff ([find(t)(:); prod(sz)+1]);
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93 f = max (t2, [], dim);
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94 endif
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95
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96 c = cell (sz2);
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97 if (issparse (x))
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98 m = sparse (sz2(1), sz2(2));
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99 else
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100 m = zeros (sz2, class (x));
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101 endif
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102 for i = 1 : prod (sz2)
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103 c{i} = xs(t2(:, i) == f(i), i);
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104 m(i) = c{i}(1);
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105 endfor
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106
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107 endfunction
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108
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109
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110 %!test
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111 %! [m, f, c] = mode (toeplitz (1:5));
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112 %! assert (m, [1,2,2,2,1]);
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113 %! assert (f, [1,2,2,2,1]);
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114 %! assert (c, {[1;2;3;4;5],[2],[2;3],[2],[1;2;3;4;5]});
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115 %!test
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116 %! [m, f, c] = mode (toeplitz (1:5), 2);
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117 %! assert (m, [1;2;2;2;1]);
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118 %! assert (f, [1;2;2;2;1]);
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119 %! assert (c, {[1;2;3;4;5];[2];[2;3];[2];[1;2;3;4;5]});
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120 %!test
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121 %! a = sprandn (32, 32, 0.05);
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122 %! sp0 = sparse (0);
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123 %! [m, f, c] = mode (a);
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124 %! [m2, f2, c2] = mode (full (a));
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125 %! assert (m, sparse (m2));
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126 %! assert (f, sparse (f2));
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127 %! c_exp(1:length (a)) = { sp0 };
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128 %! assert (c ,c_exp);
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129 %! assert (c2,c_exp);
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130
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131 %!assert (mode ([2,3,1,2,3,4],1),[2,3,1,2,3,4])
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132 %!assert (mode ([2,3,1,2,3,4],2),2)
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133 %!assert (mode ([2,3,1,2,3,4]),2)
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134 %!assert (mode (single ([2,3,1,2,3,4])), single (2))
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135 %!assert (mode (int8 ([2,3,1,2,3,4])), int8 (2))
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136
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137 %!assert (mode ([2;3;1;2;3;4],1),2)
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138 %!assert (mode ([2;3;1;2;3;4],2),[2;3;1;2;3;4])
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139 %!assert (mode ([2;3;1;2;3;4]),2)
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140
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141 %!test
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142 %! x = magic (3);
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143 %! [m, f, c] = mode (x, 3);
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144 %! assert (m, x);
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145 %! assert (f, ones (3,3));
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146 %! assert (c, num2cell (x));
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147
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148 %!shared x
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149 %! x(:,:,1) = toeplitz (1:3);
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150 %! x(:,:,2) = circshift (toeplitz (1:3), 1);
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151 %! x(:,:,3) = circshift (toeplitz (1:3), 2);
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152 %!test
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153 %! [m, f, c] = mode (x, 1);
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154 %! assert (reshape (m, [3, 3]), [1 1 1; 2 2 2; 1 1 1]);
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155 %! assert (reshape (f, [3, 3]), [1 1 1; 2 2 2; 1 1 1]);
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156 %! c = reshape (c, [3, 3]);
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157 %! assert (c{1}, [1; 2; 3]);
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158 %! assert (c{2}, 2);
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159 %! assert (c{3}, [1; 2; 3]);
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160 %!test
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161 %! [m, f, c] = mode (x, 2);
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162 %! assert (reshape (m, [3, 3]), [1 1 2; 2 1 1; 1 2 1]);
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163 %! assert (reshape (f, [3, 3]), [1 1 2; 2 1 1; 1 2 1]);
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164 %! c = reshape (c, [3, 3]);
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165 %! assert (c{1}, [1; 2; 3]);
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166 %! assert (c{2}, 2);
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167 %! assert (c{3}, [1; 2; 3]);
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168 %!test
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169 %! [m, f, c] = mode (x, 3);
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170 %! assert (reshape (m, [3, 3]), [1 2 1; 1 2 1; 1 2 1]);
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171 %! assert (reshape (f, [3, 3]), [1 2 1; 1 2 1; 1 2 1]);
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172 %! c = reshape (c, [3, 3]);
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173 %! assert (c{1}, [1; 2; 3]);
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174 %! assert (c{2}, [1; 2; 3]);
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175 %! assert (c{3}, [1; 2; 3]);
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176
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177 ## Test input validation
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178 %!error mode ()
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179 %!error mode (1, 2, 3)
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180 %!error <X must be a numeric> mode ({1 2 3})
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181 %!error <DIM must be an integer> mode (1, ones (2,2))
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182 %!error <DIM must be an integer> mode (1, 1.5)
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183 %!error <DIM must be .* a valid dimension> mode (1, 0)