## 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