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view scripts/statistics/median.m @ 27898:4d6d21839dfd
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Files affected: url-transfer.cc, url-transfer.h, acot.m, acoth.m,
acsc.m, acsch.m, asec.m, asech.m, cot.m, coth.m, csc.m, csch.m, sec.m,
sech.m, cart2pol.m, cart2sph.m, deal.m, fliplr.m, flipud.m, int2str.m,
logspace.m, num2str.m, pol2cart.m, rot90.m, sortrows.m, sph2cart.m,
waitbar.m, doc.m, hsv2rgb.m, rgb2hsv.m, beep.m, isstr.m, setstr.m,
strmatch.m, cond.m, rank.m, trace.m, bug_report.m, cast.m, delete.m,
dir.m, list_primes.m, ls.m, ls_command.m, menu.m, pack.m, recycle.m,
substruct.m, version.m, glpk.m, axis.m, box.m, grid.m,
__axis_label__.m, text.m, title.m, view.m, xlabel.m, ylabel.m,
zlabel.m, bar.m, barh.m, comet3.m, hist.m, line.m, loglog.m, mesh.m,
patch.m, plot.m, polar.m, __bar__.m, __line__.m, __plt__.m,
__stem__.m, semilogx.m, semilogy.m, sombrero.m, stairs.m, stem.m,
surface.m, __default_plot_options__.m, __gnuplot_drawnow__.m,
__next_line_color__.m, __plt_get_axis_arg__.m, __pltopt__.m, clf.m,
closereq.m, gca.m, gnuplot_binary.in.m, isfigure.m, meshgrid.m,
__gnuplot_draw_axes__.m, __gnuplot_draw_figure__.m, shg.m, addpref.m,
getpref.m, ispref.m, loadprefs.m, prefsfile.m, saveprefs.m, rmpref.m,
setpref.m, ismember.m, setdiff.m, union.m, hankel.m, hilb.m, vander.m,
median.m, std.m, cstrcat.m, isletter.m, str2num.m, strcat.m,
oruntests.m, rundemos.m, asctime.m, clock.m, ctime.m, date.m, etime.m,
is_leap_year.m.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 02 Jan 2020 15:43:01 -0500 |
parents | 00f796120a6d |
children | b442ec6dda5c |
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## Copyright (C) 1996-2019 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 ## <https://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 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 %! 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 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)