Mercurial > octave
annotate scripts/statistics/base/mean.m @ 23219:3ac9f9ecfae5 stable
maint: Update copyright dates.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:39:29 -0500 |
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1 ## Copyright (C) 1995-2017 Kurt Hornik |
3426 | 2 ## |
3922 | 3 ## This file is part of Octave. |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
3426 | 9 ## |
3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 13 ## General Public License for more details. |
14 ## | |
3200 | 15 ## You should have received a copy of the GNU General Public License |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
3200 | 18 |
3367 | 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 ## |
3367 | 28 ## @tex |
29 ## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$ | |
30 ## @end tex | |
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31 ## @ifnottex |
3426 | 32 ## |
3367 | 33 ## @example |
34 ## mean (x) = SUM_i x(i) / N | |
35 ## @end example | |
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36 ## |
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37 ## @end ifnottex |
3367 | 38 ## If @var{x} is a matrix, compute the mean for each column and return them |
39 ## in a row vector. | |
3200 | 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: |
3367 | 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] |
3367 | 49 ## |
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50 ## @item @qcode{"g"} |
7001 | 51 ## Compute the geometric mean. |
3367 | 52 ## |
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53 ## @item @qcode{"h"} |
3367 | 54 ## Compute the harmonic mean. |
55 ## @end table | |
4022 | 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} |
3367 | 60 ## @end deftypefn |
3426 | 61 |
5428 | 62 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 63 ## Description: Compute arithmetic, geometric, and harmonic mean |
3200 | 64 |
4022 | 65 function y = mean (x, opt1, opt2) |
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; |
3200 | 76 |
4022 | 77 if (nargin == 1) |
78 opt = "a"; | |
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79 need_dim = true; |
4022 | 80 elseif (nargin == 2) |
5443 | 81 if (ischar (opt1)) |
4022 | 82 opt = opt1; |
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83 need_dim = true; |
4022 | 84 else |
4525 | 85 dim = opt1; |
4022 | 86 opt = "a"; |
87 endif | |
88 elseif (nargin == 3) | |
5443 | 89 if (ischar (opt1)) |
4022 | 90 opt = opt1; |
91 dim = opt2; | |
5443 | 92 elseif (ischar (opt2)) |
4022 | 93 opt = opt2; |
94 dim = opt1; | |
95 else | |
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96 error ("mean: OPT must be a string"); |
4022 | 97 endif |
98 else | |
6046 | 99 print_usage (); |
3200 | 100 endif |
3426 | 101 |
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102 nd = ndims (x); |
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103 sz = size (x); |
4022 | 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"); |
4022 | 110 endif |
3200 | 111 endif |
112 | |
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113 n = size (x, dim); |
3426 | 114 |
3200 | 115 if (strcmp (opt, "a")) |
4022 | 116 y = sum (x, dim) / n; |
3200 | 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 |
3200 | 123 elseif (strcmp (opt, "h")) |
4022 | 124 y = n ./ sum (1 ./ x, dim); |
3200 | 125 else |
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126 error ("mean: option '%s' not recognized", opt); |
3200 | 127 endif |
3426 | 128 |
3200 | 129 endfunction |
7411 | 130 |
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131 |
7411 | 132 %!test |
133 %! x = -10:10; | |
134 %! y = x'; | |
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]); |
7411 | 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) |
7411 | 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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158 %!error <DIM must be .* a valid dimension> mean (1, 0) |
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159 %!error <X must not contain any negative values> mean ([1 -1], "g") |
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160 %!error <option 'b' not recognized> mean (1, "b") |