1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
|
## Copyright (C) 1995-2013 Kurt Hornik
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} mean (@var{x})
## @deftypefnx {Function File} {} mean (@var{x}, @var{dim})
## @deftypefnx {Function File} {} mean (@var{x}, @var{opt})
## @deftypefnx {Function File} {} mean (@var{x}, @var{dim}, @var{opt})
## Compute the mean of the elements of the vector @var{x}.
## @tex
## $$ {\rm mean}(x) = \bar{x} = {1\over N} \sum_{i=1}^N x_i $$
## @end tex
## @ifnottex
##
## @example
## mean (x) = SUM_i x(i) / N
## @end example
##
## @end ifnottex
## If @var{x} is a matrix, compute the mean for each column and return them
## in a row vector.
##
## The optional argument @var{opt} selects the type of mean to compute.
## The following options are recognized:
##
## @table @asis
## @item @qcode{"a"}
## Compute the (ordinary) arithmetic mean. [default]
##
## @item @qcode{"g"}
## Compute the geometric mean.
##
## @item @qcode{"h"}
## Compute the harmonic mean.
## @end table
##
## If the optional argument @var{dim} is given, operate along this dimension.
##
## Both @var{dim} and @var{opt} are optional. If both are supplied,
## either may appear first.
## @seealso{median, mode}
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Compute arithmetic, geometric, and harmonic mean
function y = mean (x, opt1, opt2)
if (nargin < 1 || nargin > 3)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)))
error ("mean: X must be a numeric vector or matrix");
endif
need_dim = false;
if (nargin == 1)
opt = "a";
need_dim = true;
elseif (nargin == 2)
if (ischar (opt1))
opt = opt1;
need_dim = true;
else
dim = opt1;
opt = "a";
endif
elseif (nargin == 3)
if (ischar (opt1))
opt = opt1;
dim = opt2;
elseif (ischar (opt2))
opt = opt2;
dim = opt1;
else
error ("mean: OPT must be a string");
endif
else
print_usage ();
endif
nd = ndims (x);
sz = size (x);
if (need_dim)
## Find the first non-singleton dimension.
(dim = find (sz > 1, 1)) || (dim = 1);
else
if (!(isscalar (dim) && dim == fix (dim))
|| !(1 <= dim && dim <= nd))
error ("mean: DIM must be an integer and a valid dimension");
endif
endif
n = sz(dim);
if (strcmp (opt, "a"))
y = sum (x, dim) / n;
elseif (strcmp (opt, "g"))
if (all (x(:) >= 0))
y = exp (sum (log (x), dim) ./ n);
else
error ("mean: X must not contain any negative values");
endif
elseif (strcmp (opt, "h"))
y = n ./ sum (1 ./ x, dim);
else
error ("mean: option '%s' not recognized", opt);
endif
endfunction
%!test
%! x = -10:10;
%! y = x';
%! z = [y, y+10];
%! assert (mean (x), 0);
%! assert (mean (y), 0);
%! assert (mean (z), [0, 10]);
## Test small numbers
%!assert (mean (repmat (0.1,1,1000), "g"), 0.1, 20*eps)
%!assert (mean (magic (3), 1), [5, 5, 5])
%!assert (mean (magic (3), 2), [5; 5; 5])
%!assert (mean ([2 8], "g"), 4)
%!assert (mean ([4 4 2], "h"), 3)
%!assert (mean (logical ([1 0 1 1])), 0.75)
%!assert (mean (single ([1 0 1 1])), single (0.75))
%% Test input validation
%!error mean ()
%!error mean (1, 2, 3, 4)
%!error mean ({1:5})
%!error mean (1, 2, 3)
%!error mean (1, ones (2,2))
%!error mean (1, 1.5)
%!error mean (1, 0)
%!error mean (1, 3)
%!error mean (1, "b")
|
