Mercurial > octave
view scripts/statistics/median.m @ 31551:fd29c7a50a78 stable
maint: use commas, semicolons consistently with Octave conventions.
* makeValidName.m: Remove %!test and move BIST %!asserts to column 1.
* base64decode.m, base64encode.m, which.m, logm.m, uniquetol.m, perms.m:
Delete semicolon (';') at end of %!assert BIST.
* lin2mu.m, interp2.m, interpn.m, lsqnonneg.m, pqpnonneg.m, uniquetol.m,
betainc.m, normalize.m: Add semicolon (';') to end of assert statement within
%!test BIST.
* __memoize__.m, tar_is_bsd.m, publish.m: Add semicolon (';') to line with
keyword "persistent".
* stft.m: Use comma (',') after "case" keyword when code immediately follows.
* gallery.m: Align commas used in case statements in massive switch block.
Remove unnecessary parentheses around a numeric case argument.
* ranks.m: Remove semicolon (';') from case statemnt argument.
author | Rik <rik@octave.org> |
---|---|
date | Sat, 26 Nov 2022 06:32:08 -0800 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
line wrap: on
line source
######################################################################## ## ## Copyright (C) 1996-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{y} =} median (@var{x}) ## @deftypefnx {} {@var{y} =} 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 function y = median (x, dim) if (nargin < 1) 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) y = nth_element (x, k, dim); else y = sum (nth_element (x, k:k+1, dim), dim, "native") / 2; if (islogical (x)) y = logical (y); endif endif ## Inject NaNs where needed, to be consistent with Matlab. if (isfloat (x)) y(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 %! old_state = rand ("state"); %! restore_state = onCleanup (@() rand ("state", old_state)); %! rand ("state", 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 <Invalid call> median () %!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)