## Copyright (C) 1996-2017 John W. Eaton ## Copyright (C) 2009-2010 VZLU Prague ## ## 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 {} {} median (@var{x}) ## @deftypefnx {} {} median (@var{x}, @var{dim}) ## Compute the median value of the elements of the vector @var{x}. ## ## When the elements of @var{x} are sorted, the median is defined as ## @tex ## $$ ## {\rm median} (x) = ## \cases{x(\lceil N/2\rceil), & $N$ odd;\cr ## (x(N/2)+x(N/2+1))/2, & $N$ even.} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## x(ceil(N/2)) N odd ## median (x) = ## (x(N/2) + x((N/2)+1))/2 N even ## @end group ## @end example ## ## @end ifnottex ## If @var{x} is of a discrete type such as integer or logical, then ## the case of even N rounds up (or toward @code{true}). ## ## If @var{x} is a matrix, compute the median value for each column and ## return them in a row vector. ## ## If the optional @var{dim} argument is given, operate along this dimension. ## @seealso{mean, mode} ## @end deftypefn ## Author: jwe function retval = median (x, dim) if (nargin != 1 && nargin != 2) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("median: X must be a numeric vector or matrix"); endif nd = ndims (x); sz = size (x); if (nargin < 2) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("median: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); k = floor ((n+1) / 2); if (isempty (x)) %% codepath for Matlab compatibility. empty x produces NaN output, but %% for ndim > 2, output depends on size of x. if ((nd == 2) && (max (sz) < 2) && (nargin ~= 2)) retval = NaN; else if (nargin == 2) sz(dim) = 1; else sz (find ((sz ~= 1), 1)) = 1; endif retval = NaN (sz); endif if (isa (x, "single")) retval = single (retval); endif elseif (mod (n, 2) == 1) retval = nth_element (x, k, dim); else retval = sum (nth_element (x, k:k+1, dim), dim, "native") / 2; if (islogical (x)) retval = logical (retval); endif endif ## Inject NaNs where needed, to be consistent with Matlab. if (isfloat (x)) retval(any (isnan (x), dim)) = NaN; endif endfunction %!test %! x = [1, 2, 3, 4, 5, 6]; %! x2 = x'; %! y = [1, 2, 3, 4, 5, 6, 7]; %! y2 = y'; %! %! assert (median (x) == median (x2) && median (x) == 3.5); %! assert (median (y) == median (y2) && median (y) == 4); %! assert (median ([x2, 2*x2]), [3.5, 7]); %! assert (median ([y2, 3*y2]), [4, 12]); %!assert (median (single ([1, 2, 3])), single (2)) %!assert (median ([1, 2, NaN; 4, 5, 6; NaN, 8, 9]), [NaN, 5, NaN]) %!assert (median ([1, 2], 3), [1,2]) ## Test multidimensional arrays %!shared a, b, x, y %! rand ("seed", 2); %! a = rand (2, 3, 4, 5); %! b = rand (3, 4, 6, 5); %! x = sort (a, 4); %! y = sort (b, 3); %!assert <35679> (median (a, 4), x(:, :, :, 3)) %!assert <35679> (median (b, 3), (y(:, :, 3, :) + y(:, :, 4, :))/2) ##tests for empty input Matlab compatibility (bug #48690) %!assert (median ([]), NaN) %!assert (median (single ([])), single (NaN)) %!assert (median (ones (0, 0, 0, 0)), NaN (1, 0, 0, 0)) %!assert (median (ones (0, 0, 0, 1)), NaN (1, 0, 0, 1)) %!assert (median (ones (0, 0, 0, 2)), NaN (1, 0, 0, 2)) %!assert (median (ones (0, 0, 1, 0)), NaN (1, 0, 1, 0)) %!assert (median (ones (0, 0, 1, 1)), NaN (1, 1, 1, 1)) %!assert (median (ones (0, 0, 1, 2)), NaN (1, 0, 1, 2)) %!assert (median (ones (0, 0, 2, 0)), NaN (1, 0, 2, 0)) %!assert (median (ones (0, 0, 2, 1)), NaN (1, 0, 2, 1)) %!assert (median (ones (0, 0, 2, 2)), NaN (1, 0, 2, 2)) %!assert (median (ones (0, 1, 0, 0)), NaN (1, 1, 0, 0)) %!assert (median (ones (0, 1, 0, 1)), NaN (1, 1, 0, 1)) %!assert (median (ones (0, 1, 0, 2)), NaN (1, 1, 0, 2)) %!assert (median (ones (0, 1, 1, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (0, 1, 1, 1)), NaN (1, 1, 1, 1)) %!assert (median (ones (0, 1, 1, 2)), NaN (1, 1, 1, 2)) %!assert (median (ones (0, 1, 2, 0)), NaN (1, 1, 2, 0)) %!assert (median (ones (0, 1, 2, 1)), NaN (1, 1, 2, 1)) %!assert (median (ones (0, 1, 2, 2)), NaN (1, 1, 2, 2)) %!assert (median (ones (0, 2, 0, 0)), NaN (1, 2, 0, 0)) %!assert (median (ones (0, 2, 0, 1)), NaN (1, 2, 0, 1)) %!assert (median (ones (0, 2, 0, 2)), NaN (1, 2, 0, 2)) %!assert (median (ones (0, 2, 1, 0)), NaN (1, 2, 1, 0)) %!assert (median (ones (0, 2, 1, 1)), NaN (1, 2, 1, 1)) %!assert (median (ones (0, 2, 1, 2)), NaN (1, 2, 1, 2)) %!assert (median (ones (0, 2, 2, 0)), NaN (1, 2, 2, 0)) %!assert (median (ones (0, 2, 2, 1)), NaN (1, 2, 2, 1)) %!assert (median (ones (0, 2, 2, 2)), NaN (1, 2, 2, 2)) %!assert (median (ones (1, 0, 0, 0)), NaN (1, 1, 0, 0)) %!assert (median (ones (1, 0, 0, 1)), NaN (1, 1, 0, 1)) %!assert (median (ones (1, 0, 0, 2)), NaN (1, 1, 0, 2)) %!assert (median (ones (1, 0, 1, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (1, 0, 1, 1)), NaN (1, 1, 1, 1)) %!assert (median (ones (1, 0, 1, 2)), NaN (1, 1, 1, 2)) %!assert (median (ones (1, 0, 2, 0)), NaN (1, 1, 2, 0)) %!assert (median (ones (1, 0, 2, 1)), NaN (1, 1, 2, 1)) %!assert (median (ones (1, 0, 2, 2)), NaN (1, 1, 2, 2)) %!assert (median (ones (1, 1, 0, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (1, 1, 0, 1)), NaN (1, 1, 1, 1)) %!assert (median (ones (1, 1, 0, 2)), NaN (1, 1, 1, 2)) %!assert (median (ones (1, 1, 1, 0)), NaN (1, 1, 1, 1)) %!assert (median (ones (1, 1, 2, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (1, 2, 0, 0)), NaN (1, 1, 0, 0)) %!assert (median (ones (1, 2, 0, 1)), NaN (1, 1, 0, 1)) %!assert (median (ones (1, 2, 0, 2)), NaN (1, 1, 0, 2)) %!assert (median (ones (1, 2, 1, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (1, 2, 2, 0)), NaN (1, 1, 2, 0)) %!assert (median (ones (2, 0, 0, 0)), NaN (1, 0, 0, 0)) %!assert (median (ones (2, 0, 0, 1)), NaN (1, 0, 0, 1)) %!assert (median (ones (2, 0, 0, 2)), NaN (1, 0, 0, 2)) %!assert (median (ones (2, 0, 1, 0)), NaN (1, 0, 1, 0)) %!assert (median (ones (2, 0, 1, 1)), NaN (1, 0, 1, 1)) %!assert (median (ones (2, 0, 1, 2)), NaN (1, 0, 1, 2)) %!assert (median (ones (2, 0, 2, 0)), NaN (1, 0, 2, 0)) %!assert (median (ones (2, 0, 2, 1)), NaN (1, 0, 2, 1)) %!assert (median (ones (2, 0, 2, 2)), NaN (1, 0, 2, 2)) %!assert (median (ones (2, 1, 0, 0)), NaN (1, 1, 0, 0)) %!assert (median (ones (2, 1, 0, 1)), NaN (1, 1, 0, 1)) %!assert (median (ones (2, 1, 0, 2)), NaN (1, 1, 0, 2)) %!assert (median (ones (2, 1, 1, 0)), NaN (1, 1, 1, 0)) %!assert (median (ones (2, 1, 2, 0)), NaN (1, 1, 2, 0)) %!assert (median (ones (2, 2, 0, 0)), NaN (1, 2, 0, 0)) %!assert (median (ones (2, 2, 0, 1)), NaN (1, 2, 0, 1)) %!assert (median (ones (2, 2, 0, 2)), NaN (1, 2, 0, 2)) %!assert (median (ones (2, 2, 1, 0)), NaN (1, 2, 1, 0)) %!assert (median (ones (2, 2, 2, 0)), NaN (1, 2, 2, 0)) %!assert (median (ones (1, 1, 0, 0, 0)), NaN (1, 1, 1, 0, 0)) %!assert (median (ones (1, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 1)) %!assert (median (ones (2, 1, 1, 1, 0)), NaN (1, 1, 1, 1, 0)) %!assert (median (ones (1, 2, 1, 1, 0)), NaN (1, 1, 1, 1, 0)) %!assert (median (ones (1, 3, 0, 2)), NaN (1, 1, 0, 2)) %!assert (median (single (ones (1, 3, 0, 2))), single (NaN (1, 1, 0, 2))) %!assert (median ([], 1), NaN (1, 0)) %!assert (median ([], 2), NaN (0, 1)) %!assert (median ([], 3), []) %!assert (median (ones (1, 0), 1), NaN (1, 0)) %!assert (median (ones (1, 0), 2), NaN) %!assert (median (ones (1, 0), 3), NaN (1, 0)) %!assert (median (ones (0, 1), 1), NaN) %!assert (median (ones (0, 1), 2), NaN (0, 1)) %!assert (median (ones (0, 1), 3), NaN (0, 1)) ## Test non-floating point types %!assert (median ([true, false]), true) %!assert (median (uint8 ([1, 3])), uint8 (2)) %!assert (median (int8 ([1, 3, 4])), int8 (3)) %!assert (median (single ([1, 3, 4])), single (3)) %!assert (median (single ([1, 3, NaN])), single (NaN)) ## Test input validation %!error median () %!error median (1, 2, 3) %!error median ({1:5}) %!error median (1, ones (2, 2)) %!error median (1, 1.5) %!error median (1, 0)