## Copyright (C) 1995-2017 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
## .
## -*- texinfo -*-
## @deftypefn {} {} mean (@var{x})
## @deftypefnx {} {} mean (@var{x}, @var{dim})
## @deftypefnx {} {} mean (@var{x}, @var{opt})
## @deftypefnx {} {} mean (@var{x}, @var{dim}, @var{opt})
## Compute the mean of the elements of the vector @var{x}.
##
## The mean is defined as
##
## @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.
##
## If the optional argument @var{dim} is given, operate along this dimension.
##
## 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
##
## Both @var{dim} and @var{opt} are optional. If both are supplied, either
## may appear first.
## @seealso{median, mode}
## @end deftypefn
## Author: KH
## Description: Compute arithmetic, geometric, and harmonic mean
function retval = 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) && dim > 0))
error ("mean: DIM must be an integer and a valid dimension");
endif
endif
n = size (x, dim);
if (isempty (x))
%% codepath for Matlab compatibility. empty x produces NaN output, but
%% for ndim > 2, output depends on size of x and whether DIM is set.
if ((nd == 2) && (max (sz) < 2) && need_dim)
retval = NaN;
else
if (~need_dim)
sz(dim) = 1;
else
sz (find ((sz ~= 1), 1)) = 1;
endif
retval = NaN (sz);
endif
if (isa (x, "single"))
retval = single (retval);
endif
elseif (strcmp (opt, "a"))
retval = sum (x, dim) / n;
elseif (strcmp (opt, "g"))
if (all (x(:) >= 0))
retval = exp (sum (log (x), dim) ./ n);
else
error ("mean: X must not contain any negative values");
endif
elseif (strcmp (opt, "h"))
retval = 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))
%!assert (mean ([1 2], 3), [1 2])
##tests for empty input Matlab compatibility (bug #48690)
%!assert (mean ([]), NaN)
%!assert (mean (single([])), single(NaN))
%!assert (mean (ones (0, 0, 0, 0)), NaN (1, 0, 0, 0))
%!assert (mean (ones (0, 0, 0, 1)), NaN (1, 0, 0, 1))
%!assert (mean (ones (0, 0, 0, 2)), NaN (1, 0, 0, 2))
%!assert (mean (ones (0, 0, 1, 0)), NaN (1, 0, 1, 0))
%!assert (mean (ones (0, 0, 1, 1)), NaN (1, 1, 1, 1))
%!assert (mean (ones (0, 0, 1, 2)), NaN (1, 0, 1, 2))
%!assert (mean (ones (0, 0, 2, 0)), NaN (1, 0, 2, 0))
%!assert (mean (ones (0, 0, 2, 1)), NaN (1, 0, 2, 1))
%!assert (mean (ones (0, 0, 2, 2)), NaN (1, 0, 2, 2))
%!assert (mean (ones (0, 1, 0, 0)), NaN (1, 1, 0, 0))
%!assert (mean (ones (0, 1, 0, 1)), NaN (1, 1, 0, 1))
%!assert (mean (ones (0, 1, 0, 2)), NaN (1, 1, 0, 2))
%!assert (mean (ones (0, 1, 1, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (0, 1, 1, 1)), NaN (1, 1, 1, 1))
%!assert (mean (ones (0, 1, 1, 2)), NaN (1, 1, 1, 2))
%!assert (mean (ones (0, 1, 2, 0)), NaN (1, 1, 2, 0))
%!assert (mean (ones (0, 1, 2, 1)), NaN (1, 1, 2, 1))
%!assert (mean (ones (0, 1, 2, 2)), NaN (1, 1, 2, 2))
%!assert (mean (ones (0, 2, 0, 0)), NaN (1, 2, 0, 0))
%!assert (mean (ones (0, 2, 0, 1)), NaN (1, 2, 0, 1))
%!assert (mean (ones (0, 2, 0, 2)), NaN (1, 2, 0, 2))
%!assert (mean (ones (0, 2, 1, 0)), NaN (1, 2, 1, 0))
%!assert (mean (ones (0, 2, 1, 1)), NaN (1, 2, 1, 1))
%!assert (mean (ones (0, 2, 1, 2)), NaN (1, 2, 1, 2))
%!assert (mean (ones (0, 2, 2, 0)), NaN (1, 2, 2, 0))
%!assert (mean (ones (0, 2, 2, 1)), NaN (1, 2, 2, 1))
%!assert (mean (ones (0, 2, 2, 2)), NaN (1, 2, 2, 2))
%!assert (mean (ones (1, 0, 0, 0)), NaN (1, 1, 0, 0))
%!assert (mean (ones (1, 0, 0, 1)), NaN (1, 1, 0, 1))
%!assert (mean (ones (1, 0, 0, 2)), NaN (1, 1, 0, 2))
%!assert (mean (ones (1, 0, 1, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (1, 0, 1, 1)), NaN (1, 1, 1, 1))
%!assert (mean (ones (1, 0, 1, 2)), NaN (1, 1, 1, 2))
%!assert (mean (ones (1, 0, 2, 0)), NaN (1, 1, 2, 0))
%!assert (mean (ones (1, 0, 2, 1)), NaN (1, 1, 2, 1))
%!assert (mean (ones (1, 0, 2, 2)), NaN (1, 1, 2, 2))
%!assert (mean (ones (1, 1, 0, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (1, 1, 0, 1)), NaN (1, 1, 1, 1))
%!assert (mean (ones (1, 1, 0, 2)), NaN (1, 1, 1, 2))
%!assert (mean (ones (1, 1, 1, 0)), NaN (1, 1, 1, 1))
%!assert (mean (ones (1, 1, 2, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (1, 2, 0, 0)), NaN (1, 1, 0, 0))
%!assert (mean (ones (1, 2, 0, 1)), NaN (1, 1, 0, 1))
%!assert (mean (ones (1, 2, 0, 2)), NaN (1, 1, 0, 2))
%!assert (mean (ones (1, 2, 1, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (1, 2, 2, 0)), NaN (1, 1, 2, 0))
%!assert (mean (ones (2, 0, 0, 0)), NaN (1, 0, 0, 0))
%!assert (mean (ones (2, 0, 0, 1)), NaN (1, 0, 0, 1))
%!assert (mean (ones (2, 0, 0, 2)), NaN (1, 0, 0, 2))
%!assert (mean (ones (2, 0, 1, 0)), NaN (1, 0, 1, 0))
%!assert (mean (ones (2, 0, 1, 1)), NaN (1, 0, 1, 1))
%!assert (mean (ones (2, 0, 1, 2)), NaN (1, 0, 1, 2))
%!assert (mean (ones (2, 0, 2, 0)), NaN (1, 0, 2, 0))
%!assert (mean (ones (2, 0, 2, 1)), NaN (1, 0, 2, 1))
%!assert (mean (ones (2, 0, 2, 2)), NaN (1, 0, 2, 2))
%!assert (mean (ones (2, 1, 0, 0)), NaN (1, 1, 0, 0))
%!assert (mean (ones (2, 1, 0, 1)), NaN (1, 1, 0, 1))
%!assert (mean (ones (2, 1, 0, 2)), NaN (1, 1, 0, 2))
%!assert (mean (ones (2, 1, 1, 0)), NaN (1, 1, 1, 0))
%!assert (mean (ones (2, 1, 2, 0)), NaN (1, 1, 2, 0))
%!assert (mean (ones (2, 2, 0, 0)), NaN (1, 2, 0, 0))
%!assert (mean (ones (2, 2, 0, 1)), NaN (1, 2, 0, 1))
%!assert (mean (ones (2, 2, 0, 2)), NaN (1, 2, 0, 2))
%!assert (mean (ones (2, 2, 1, 0)), NaN (1, 2, 1, 0))
%!assert (mean (ones (2, 2, 2, 0)), NaN (1, 2, 2, 0))
%!assert (mean (ones (1, 1, 0, 0, 0)), NaN (1, 1, 1, 0, 0))
%!assert (mean (ones (1, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 1))
%!assert (mean (ones (2, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 0))
%!assert (mean (ones (1, 2, 1, 1, 0)), NaN (1, 1, 1, 1, 0))
%!assert (mean (ones (1, 3, 0, 2)), NaN (1, 1, 0, 2))
%!assert (mean (single (ones (1, 3, 0, 2))), single (NaN (1, 1, 0, 2)))
%!assert (mean ([], 1), NaN (1, 0))
%!assert (mean ([], 2), NaN (0, 1))
%!assert (mean ([], 3), [])
%!assert (mean (ones (1, 0), 1), NaN (1, 0))
%!assert (mean (ones (1, 0), 2), NaN)
%!assert (mean (ones (1, 0), 3), NaN (1, 0))
%!assert (mean (ones (0, 1), 1), NaN)
%!assert (mean (ones (0, 1), 2), NaN (0, 1))
%!assert (mean (ones (0, 1), 3), NaN (0, 1))
## 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 -1], "g")
%!error