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maint: Merge default to bytecode-interpreter.
author Markus Mützel <markus.muetzel@gmx.de>
date Tue, 21 May 2024 18:29:03 +0200
parents 2e484f9f1f18
children
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 1996-2024 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{y} =} skewness (@var{x})
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28 ## @deftypefnx {} {@var{y} =} skewness (@var{x}, @var{flag})
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29 ## @deftypefnx {} {@var{y} =} skewness (@var{x}, @var{flag}, @var{dim})
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30 ## Compute the sample skewness of the elements of @var{x}.
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31 ##
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32 ## The sample skewness is defined as
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33 ## @tex
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34 ## $$
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35 ## {\rm skewness} (@var{x}) = {{{1\over N}\,
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36 ## \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3},
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37 ## $$
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38 ## where $N$ is the length of @var{x}, $\bar{x}$ its mean and $\sigma$
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39 ## its (uncorrected) standard deviation.
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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 ## mean ((@var{x} - mean (@var{x})).^3)
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46 ## skewness (@var{X}) = ------------------------.
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47 ## std (@var{x}).^3
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48 ## @end group
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49 ## @end example
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50 ##
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51 ## @end ifnottex
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52 ##
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53 ## @noindent
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54 ## The optional argument @var{flag} controls which normalization is used.
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55 ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted
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56 ## or empty), return the sample skewness as defined above. If @var{flag} is
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57 ## equal to 0, return the adjusted skewness coefficient instead:
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58 ## @tex
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59 ## $$
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60 ## {\rm skewness} (@var{x}) = {\sqrt{N (N - 1)} \over N - 2} \times \,
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61 ## {{{1 \over N} \sum_{i=1}^N (x_i - \bar{x})^3} \over \sigma^3}
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62 ## $$
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63 ## @end tex
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64 ## @ifnottex
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65 ##
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66 ## @example
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67 ## @group
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68 ## sqrt (N*(N-1)) mean ((@var{x} - mean (@var{x})).^3)
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69 ## skewness (@var{X}, 0) = -------------- * ------------------------.
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70 ## (N - 2) std (@var{x}).^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 ## @noindent
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75 ## where @math{N} is the length of the @var{x} vector.
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76 ##
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77 ## @end ifnottex
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78 ## The adjusted skewness coefficient is obtained by replacing the sample second
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79 ## and third central moments by their bias-corrected versions.
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80 ##
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81 ## If @var{x} is a matrix, or more generally a multi-dimensional array, return
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82 ## the skewness along the first non-singleton dimension. If the optional
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83 ## @var{dim} argument is given, operate along this dimension.
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84 ##
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85 ## @seealso{var, kurtosis, moment}
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86 ## @end deftypefn
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87
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88 function y = skewness (x, flag, dim)
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89
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90 if (nargin < 1)
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91 print_usage ();
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92 endif
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93
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94 if (! (isnumeric (x) || islogical (x)))
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95 error ("skewness: X must be a numeric vector or matrix");
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96 endif
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97
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98 if (nargin < 2 || isempty (flag))
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99 flag = 1; # default: do not use the "bias corrected" version
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100 elseif (! isscalar (flag) || (flag != 0 && flag != 1))
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101 error ("skewness: FLAG must be 0 or 1");
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102 endif
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103
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104 nd = ndims (x);
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105 sz = size (x);
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106 if (nargin < 3)
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107 ## Find the first non-singleton dimension.
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108 (dim = find (sz > 1, 1)) || (dim = 1);
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109 else
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110 if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
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111 error ("skewness: DIM must be an integer and a valid dimension");
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112 endif
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113 endif
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114
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115 n = size (x, dim);
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116 sz(dim) = 1;
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117
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118 x = center (x, dim); # center also promotes integer, logical to double
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119 s = std (x, 1, dim); # Normalize with 1/N
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120 y = sum (x .^ 3, dim);
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121 idx = (s != 0);
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122 y(idx) ./= (n * s(idx) .^ 3);
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123 y(! idx) = NaN;
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124
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125 ## Apply bias correction to the second and third central sample moment
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126 if (flag == 0)
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127 if (n > 2)
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128 y *= sqrt (n * (n - 1)) / (n - 2);
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129 else
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130 y(:) = NaN;
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131 endif
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132 endif
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133
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134 endfunction
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135
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136
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137 %!assert (skewness ([-1, 0, 1]), 0)
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138 %!assert (skewness ([-2, 0, 1]) < 0)
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139 %!assert (skewness ([-1, 0, 2]) > 0)
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140 %!assert (skewness ([-3, 0, 1]) == -1 * skewness ([-1, 0, 3]))
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141 %!assert (skewness (ones (3, 5)), NaN (1, 5))
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142 %!assert (skewness (1, [], 3), NaN)
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143
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144 %!test
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145 %! x = [0; 0; 0; 1];
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146 %! y = [x, 2*x];
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147 %! assert (skewness (y), 1.154700538379251 * [1 1], 5*eps);
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148
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149 %!assert (skewness ([1:5 10; 1:5 10], 0, 2), 1.439590274527954 * [1; 1], eps)
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150 %!assert (skewness ([1:5 10; 1:5 10], 1, 2), 1.051328089232020 * [1; 1], 2*eps)
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151 %!assert (skewness ([1:5 10; 1:5 10], [], 2), 1.051328089232020 * [1; 1], 2*eps)
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152
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153 ## Test behavior on single input
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154 %!assert (skewness (single ([1:5 10])), single (1.0513283), eps ("single"))
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155 %!assert (skewness (single ([1 2]), 0), single (NaN))
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156
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157 ## Verify no warnings
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158 %!test
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159 %! lastwarn (""); # clear last warning
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160 %! skewness (1);
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161 %! assert (lastwarn (), "");
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162
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163 ## Test input validation
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164 %!error <Invalid call> skewness ()
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165 %!error <X must be a numeric vector or matrix> skewness (['A'; 'B'])
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166 %!error <FLAG must be 0 or 1> skewness (1, 2)
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167 %!error <FLAG must be 0 or 1> skewness (1, [1 0])
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168 %!error <DIM must be an integer> skewness (1, [], ones (2,2))
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169 %!error <DIM must be an integer> skewness (1, [], 1.5)
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170 %!error <DIM must be .* a valid dimension> skewness (1, [], 0)