Mercurial > octave
view scripts/statistics/base/median.m @ 24512:3fc1c8ebe5c3
maint: merge stable to default.
author | Rik <rik@octave.org> |
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date | Thu, 04 Jan 2018 09:40:23 -0800 |
parents | 1b4f4ec53b4a 4f0e6ee6c9b8 |
children | 194eb4bd202b |
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## 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 ## <http://www.gnu.org/licenses/>. ## -*- 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, say @code{@var{s} = sort (@var{x})}, ## the median is defined as ## @tex ## $$ ## {\rm median} (x) = ## \cases{s(\lceil N/2\rceil), & $N$ odd;\cr ## (s(N/2)+s(N/2+1))/2, & $N$ even.} ## $$ ## where $N$ is the number of elements of @var{x}. ## ## @end tex ## @ifnottex ## ## @example ## @group ## | @var{s}(ceil(N/2)) N odd ## median (@var{x}) = | ## | (@var{s}(N/2) + @var{s}(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 @math{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 if (isempty (x)) error ("median: X cannot be an empty 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 (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) ## 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 <X must be a numeric> median ({1:5}) %!error <X cannot be an empty matrix> median ([]) %!error <DIM must be an integer> median (1, ones (2,2)) %!error <DIM must be an integer> median (1, 1.5) %!error <DIM must be .* a valid dimension> median (1, 0)