annotate scripts/statistics/base/mean.m @ 23219:3ac9f9ecfae5 stable

maint: Update copyright dates.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:39:29 -0500
parents e9a0469dedd9
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1 ## Copyright (C) 1995-2017 Kurt Hornik
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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 {} {} mean (@var{x})
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21 ## @deftypefnx {} {} mean (@var{x}, @var{dim})
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22 ## @deftypefnx {} {} mean (@var{x}, @var{opt})
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23 ## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt})
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24 ## Compute the mean of the elements of the vector @var{x}.
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25 ##
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26 ## The mean is defined as
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27 ##
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28 ## @tex
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29 ## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$
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30 ## @end tex
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31 ## @ifnottex
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32 ##
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33 ## @example
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34 ## mean (x) = SUM_i x(i) / N
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35 ## @end example
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36 ##
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37 ## @end ifnottex
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38 ## If @var{x} is a matrix, compute the mean for each column and return them
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39 ## in a row vector.
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40 ##
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41 ## If the optional argument @var{dim} is given, operate along this dimension.
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42 ##
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43 ## The optional argument @var{opt} selects the type of mean to compute.
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44 ## The following options are recognized:
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45 ##
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46 ## @table @asis
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47 ## @item @qcode{"a"}
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48 ## Compute the (ordinary) arithmetic mean. [default]
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49 ##
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50 ## @item @qcode{"g"}
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51 ## Compute the geometric mean.
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52 ##
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53 ## @item @qcode{"h"}
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54 ## Compute the harmonic mean.
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55 ## @end table
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56 ##
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57 ## Both @var{dim} and @var{opt} are optional. If both are supplied, either
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58 ## may appear first.
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59 ## @seealso{median, mode}
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60 ## @end deftypefn
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61
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62 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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63 ## Description: Compute arithmetic, geometric, and harmonic mean
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64
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65 function y = mean (x, opt1, opt2)
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66
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67 if (nargin < 1 || nargin > 3)
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68 print_usage ();
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69 endif
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70
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71 if (! (isnumeric (x) || islogical (x)))
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72 error ("mean: X must be a numeric vector or matrix");
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73 endif
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74
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75 need_dim = false;
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76
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77 if (nargin == 1)
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78 opt = "a";
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79 need_dim = true;
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80 elseif (nargin == 2)
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81 if (ischar (opt1))
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82 opt = opt1;
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83 need_dim = true;
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84 else
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85 dim = opt1;
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86 opt = "a";
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87 endif
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88 elseif (nargin == 3)
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89 if (ischar (opt1))
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90 opt = opt1;
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91 dim = opt2;
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92 elseif (ischar (opt2))
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93 opt = opt2;
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94 dim = opt1;
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95 else
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96 error ("mean: OPT must be a string");
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97 endif
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98 else
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99 print_usage ();
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100 endif
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101
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102 nd = ndims (x);
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103 sz = size (x);
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104 if (need_dim)
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105 ## Find the first non-singleton dimension.
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106 (dim = find (sz > 1, 1)) || (dim = 1);
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107 else
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108 if (! (isscalar (dim) && dim == fix (dim) && dim > 0))
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109 error ("mean: DIM must be an integer and a valid dimension");
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110 endif
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111 endif
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112
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113 n = size (x, dim);
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114
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115 if (strcmp (opt, "a"))
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116 y = sum (x, dim) / n;
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117 elseif (strcmp (opt, "g"))
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118 if (all (x(:) >= 0))
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119 y = exp (sum (log (x), dim) ./ n);
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120 else
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121 error ("mean: X must not contain any negative values");
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122 endif
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123 elseif (strcmp (opt, "h"))
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124 y = n ./ sum (1 ./ x, dim);
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125 else
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126 error ("mean: option '%s' not recognized", opt);
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127 endif
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128
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129 endfunction
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130
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131
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132 %!test
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133 %! x = -10:10;
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134 %! y = x';
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135 %! z = [y, y+10];
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136 %! assert (mean (x), 0);
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137 %! assert (mean (y), 0);
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138 %! assert (mean (z), [0, 10]);
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139
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140 ## Test small numbers
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141 %!assert (mean (repmat (0.1,1,1000), "g"), 0.1, 20*eps)
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142
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143 %!assert (mean (magic (3), 1), [5, 5, 5])
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144 %!assert (mean (magic (3), 2), [5; 5; 5])
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145 %!assert (mean ([2 8], "g"), 4)
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146 %!assert (mean ([4 4 2], "h"), 3)
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147 %!assert (mean (logical ([1 0 1 1])), 0.75)
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148 %!assert (mean (single ([1 0 1 1])), single (0.75))
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149 %!assert (mean ([1 2], 3), [1 2])
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150
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151 ## Test input validation
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152 %!error mean ()
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153 %!error mean (1, 2, 3, 4)
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154 %!error <X must be a numeric> mean ({1:5})
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155 %!error <OPT must be a string> mean (1, 2, 3)
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156 %!error <DIM must be an integer> mean (1, ones (2,2))
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157 %!error <DIM must be an integer> mean (1, 1.5)
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parents: 20852
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158 %!error <DIM must be .* a valid dimension> mean (1, 0)
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parents: 20852
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159 %!error <X must not contain any negative values> mean ([1 -1], "g")
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parents: 20852
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160 %!error <option 'b' not recognized> mean (1, "b")