########################################################################
##
## Copyright (C) 1996-2023 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or .
##
## 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.
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## 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.
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## You should have received a copy of the GNU General Public License
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########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{m} =} median (@var{x})
## @deftypefnx {} {@var{m} =} median (@var{x}, @var{dim})
## @deftypefnx {} {@var{m} =} median (@var{x}, @var{vecdim})
## @deftypefnx {} {@var{m} =} median (@var{x}, "all")
## @deftypefnx {} {@var{m} =} median (@dots{}, @var{nanflag})
## @deftypefnx {} {@var{m} =} median (@dots{}, @var{outtype})
## Compute the median value of the elements of @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 a array, then @code{median (@var{x})} operates along the first
## non-singleton dimension of @var{x}.
##
## The optional variable @var{dim} forces @code{median} to operate over the
## specified dimension, which must be a positive integer-valued number.
## Specifying any singleton dimension in @var{x}, including any dimension
## exceeding @code{ndims (@var{x})}, will result in a median equal to @var{x}.
##
## Specifying the dimensions as @var{vecdim}, a vector of non-repeating
## dimensions, will return the median over the array slice defined by
## @var{vecdim}. If @var{vecdim} indexes all dimensions of @var{x}, then it is
## equivalent to the option @qcode{"all"}. Any dimension in @var{vecdim} greater
## than @code{ndims (@var{x})} is ignored.
##
## Specifying the dimension as @qcode{"all"} will force @code{median} to operate
## on all elements of @var{x}, and is equivalent to @code{median (@var{x}(:))}.
##
## @code{median (@dots{}, @var{outtype})} returns the median with a specified
## data type, using any of the input arguments in the previous syntaxes.
## @var{outtype} can take the following values:
##
## @table @asis
## @item "default"
## Output is of type double, unless the input is single in which case the output
## is of type single.
##
## @item "double"
## Output is of type double.
##
## @item "native".
## Output is of the same type as the input (@code{class (@var{x})}), unless the
## input is logical in which case the output is of type double.
## @end table
##
## The optional variable @var{nanflag} specifies whether to include or exclude
## NaN values from the calculation using any of the previously specified input
## argument combinations. The default value for @var{nanflag} is "includenan"
## which keeps NaN values in the calculation. To exclude NaN values set the
## value of @var{nanflag} to "omitnan". The output will still contain NaN
## values if @var{x} consists of all NaN values in the operating dimension.
##
## @seealso{mean, mode, movmedian}
## @end deftypefn
function m = median (x, varargin)
if (nargin < 1 || nargin > 4)
print_usage ();
endif
if (! (isnumeric (x) || islogical (x)))
error ("median: X must be either numeric or logical.");
endif
## Set initial conditions
all_flag = 0;
omitnan = 0;
perm_flag = 0;
out_flag = 0;
vecdim_flag = 0;
dim = [];
nvarg = numel (varargin);
varg_chars = cellfun ("ischar", varargin);
szx = sz_out = size (x);
ndx = ndims (x);
outtype = class (x);
if (nvarg > 1 && ! varg_chars(2:end))
## Only first varargin can be numeric
print_usage ();
endif
## Process any other char arguments.
if (any (varg_chars))
for idx = varargin(varg_chars)
switch (tolower (idx{:}))
case "all"
all_flag = 1;
case "omitnan"
omitnan = 1;
case "includenan"
omitnan = 0;
case "native"
if (out_flag)
error ("median: only one OUTTYPE can be specified.")
endif
if (strcmp (outtype, "logical"))
outtype = "double";
endif
out_flag = 1;
case "default"
if (out_flag)
error ("median: only one OUTTYPE can be specified.")
endif
if (! strcmp (outtype, "single"))
outtype = "double";
endif
out_flag = 1;
case "double"
if (out_flag)
error ("median: only one OUTTYPE can be specified.")
endif
outtype = "double";
out_flag = 1;
otherwise
print_usage ();
endswitch
endfor
varargin(varg_chars) = [];
nvarg = numel (varargin);
endif
if (((nvarg == 1) && ! (isnumeric (varargin{1}))) || (nvarg > 1))
## After trimming char inputs should only be one numeric varargin left
print_usage ();
endif
## Process special cases for in/out size
if (nvarg > 0)
## dim or vecdim provided
if (all_flag)
error ("median: 'all' cannot be used with DIM or VECDIM options.");
endif
dim = varargin{1};
vecdim_flag = ! isscalar (dim);
if (! (isvector (dim) && (dim > 0)) || any (rem (dim, 1)))
error ("median: DIM must be a positive integer scalar or vector.");
endif
## Adjust sz_out, account for possible dim > ndx by appending singletons
sz_out(ndx + 1 : max (dim)) = 1;
sz_out(dim(dim <= ndx)) = 1;
szx(ndx + 1 : max (dim)) = 1;
if (vecdim_flag)
## vecdim - try to simplify first
dim = sort (dim);
if (! all (diff (dim)))
error ("median: VECDIM must contain non-repeating positive integers.");
endif
## dims > ndims(x) and dims only one element long don't affect median
sing_dim_x = find (szx != 1);
dim(dim > ndx | szx(dim) == 1) = [];
if (isempty (dim))
## No dims left to process, return input as output
if (! strcmp (class (x), outtype))
m = outtype_convert (x, outtype);
else
m = x;
endif
return;
elseif ((numel(dim) == numel(sing_dim_x)) ...
&& unique ([dim, sing_dim_x]) == dim)
## If DIMs cover all nonsingleton ndims(x) it's equivalent to "all"
## (check lengths first to reduce unique overhead if not covered)
all_flag = true;
endif
endif
else
## Dim not provided. Determine scalar dimension
if (all_flag)
## Special case 'all': Recast input as dim1 vector, process as normal
x = x(:);
szx = [numel(x), 1];
dim = 1;
sz_out = [1 1];
elseif (isrow (x))
## Special case row vector: Avoid setting dim to 1.
dim = 2;
sz_out = [1, 1];
elseif (ndx == 2 && szx == [0, 0])
## Special case []: Do not apply sz_out(dim)=1 change
dim = 1;
sz_out = [1, 1];
else
## General case: Set dim to first non-singleton, contract sz_out along dim
(dim = find (szx != 1, 1)) || (dim = 1);
sz_out(dim) = 1;
endif
endif
if (isempty (x))
## Empty input - output NaN or class equivalent in pre-determined size
switch (outtype)
case {"double", "single"}
m = NaN (sz_out, outtype);
case ("logical")
m = false (sz_out);
otherwise
m = cast (NaN (sz_out), outtype);
endswitch
return;
endif
if (szx(dim) == 1)
## Operation along singleton dimension - nothing to do
if (! strcmp (class (x), outtype))
m = outtype_convert (x, outtype);
else
m = x;
endif
return;
endif
## Permute dim to simplify all operations along dim1. At func. end ipermute.
## FIXME: for very large data sets, flattening all vecdim dimensions into dim1
## could hit index type limits
if ((numel (dim) > 1) || (dim != 1 && ! isvector (x)))
perm_vect = 1 : ndx;
if (! vecdim_flag)
## Move dim to dim 1
perm_vect([1, dim]) = [dim, 1];
x = permute (x, perm_vect);
szx([1, dim]) = szx([dim, 1]);
dim = 1;
else
## Move vecdims to front
perm_vect(dim) = [];
perm_vect = [dim, perm_vect];
x = permute (x, perm_vect);
## Reshape all vecdims into dim1
num_dim = prod (szx(dim));
szx(dim) = [];
szx = [ones(1, numel(dim)), szx];
szx(1) = num_dim;
x = reshape (x, szx);
dim = 1;
endif
perm_flag = true;
endif
## Find column locations of NaNs
nanfree = ! any (isnan (x), dim);
if (omitnan && nanfree(:))
## Don't use omitnan path if no NaNs are present. Prevents any data types
## without a defined NaN from following slower omitnan codepath.
omitnan = 0;
endif
x = sort (x, dim); # Note: pushes any NaN's to end for omitnan compatability
if (omitnan)
## Ignore any NaN's in data. Each operating vector might have a
## different number of non-NaN data points.
if (isvector (x))
## Checks above ensure either dim1 or dim2 vector
x = x(! isnan (x));
n = numel (x);
k = floor ((n + 1) / 2);
if (mod (n, 2))
## odd
m = x(k);
else
## even
m = (x(k) + x(k + 1)) / 2;
endif
else
n = sum (! isnan (x), 1);
k = floor ((n + 1) ./ 2);
m_idx_odd = mod (n, 2) & n;
m_idx_even = (! m_idx_odd) & n;
m = NaN ([1, szx(2 : end)]);
if (ndims (x) > 2)
szx = [szx(1), prod(szx(2 : end))];
endif
## Grab kth value, k possibly different for each column
if (any (m_idx_odd(:)))
x_idx_odd = sub2ind (szx, k(m_idx_odd), find (m_idx_odd));
m(m_idx_odd) = x(x_idx_odd);
endif
if (any (m_idx_even(:)))
k_even = k(m_idx_even)(:);
x_idx_even = sub2ind (szx, [k_even, k_even + 1], ...
(find (m_idx_even))(:, [1, 1]));
m(m_idx_even) = sum (x(x_idx_even), 2) / 2;
endif
endif
else
## No "omitnan". All 'vectors' uniform length.
## All types without a NaN value will use this path.
if (all (! nanfree))
m = NaN (sz_out);
else
if (isvector (x))
n = numel (x);
k = floor ((n + 1) / 2);
m = x(k);
if (! mod (n, 2))
## Even
if (any (isa (x, "integer")))
## avoid int overflow issues
m2 = x(k + 1);
if (sign (m) != sign (m2))
m += m2;
m /= 2;
else
m += (m2 - m) / 2;
endif
else
m += (x(k + 1) - m) / 2;
endif
endif
else
## Nonvector, all operations were permuted to be along dim 1
n = szx(1);
k = floor ((n + 1) / 2);
if (isfloat (x))
m = NaN ([1, szx(2 : end)]);
else
m = zeros ([1, szx(2 : end)], outtype);
endif
if (! mod (n, 2))
## Even
if (any (isa (x, "integer")))
## avoid int overflow issues
## Use flattened index to simplify n-D operations
m(1, :) = x(k, :);
m2 = x(k + 1, :);
samesign = prod (sign ([m(1, :); m2]), 1) == 1;
m(1, :) = samesign .* m(1, :) + ...
(m2 + !samesign .* m(1, :) - samesign .* m(1, :)) / 2;
else
m(nanfree) = (x(k, nanfree) + x(k + 1, nanfree)) / 2;
endif
else
## Odd. Use flattened index to simplify n-D operations
m(nanfree) = x(k, nanfree);
endif
endif
endif
endif
if (perm_flag)
## Inverse permute back to correct dimensions
m = ipermute (m, perm_vect);
endif
## Convert output type as requested
if (! strcmp (class (m), outtype))
m = outtype_convert (m, outtype);
endif
endfunction
function m = outtype_convert (m, outtype)
switch (outtype)
case "single"
m = single (m);
case "double"
m = double (m);
otherwise
m = cast (m, outtype);
endswitch
endfunction
%!assert (median (1), 1)
%!assert (median ([1,2,3]), 2)
%!assert (median ([1,2,3]'), 2)
%!assert (median (cat(3,3,1,2)), 2)
%!assert (median ([3,1,2]), 2)
%!assert (median ([2,4,6,8]), 5)
%!assert (median ([8,2,6,4]), 5)
%!assert (median (single ([1,2,3])), single (2))
%!assert (median ([1,2], 3), [1,2])
%!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]);
## Test outtype option
%!test
%! in = [1 2 3];
%! out = 2;
%! assert (median (in, "default"), median (in));
%! assert (median (in, "default"), out);
%!test
%! in = single ([1 2 3]);
%! out = 2;
%! assert (median (in, "default"), single (median (in)));
%! assert (median (in, "default"), single (out));
%! assert (median (in, "double"), double (out));
%! assert (median (in, "native"), single (out));
%!test
%! in = uint8 ([1 2 3]);
%! out = 2;
%! assert (median (in, "default"), double (median (in)));
%! assert (median (in, "default"), double (out));
%! assert (median (in, "double"), out);
%! assert (median (in, "native"), uint8 (out));
%!test
%! in = logical ([1 0 1]);
%! out = 1;
%! assert (median (in, "default"), double (median (in)));
%! assert (median (in, "default"), double (out));
%! assert (median (in, "double"), double (out));
%! assert (median (in, "native"), double (out));
## Test single input and optional arguments "all", DIM, "omitnan")
%!test
%! x = repmat ([2 2.1 2.2 2 NaN; 3 1 2 NaN 5; 1 1.1 1.4 5 3], [1, 1, 4]);
%! y = repmat ([2 1.1 2 NaN NaN], [1, 1, 4]);
%! assert (median (x), y);
%! assert (median (x, 1), y);
%! y = repmat ([2 1.1 2 3.5 4], [1, 1, 4]);
%! assert (median (x, "omitnan"), y);
%! assert (median (x, 1, "omitnan"), y);
%! y = repmat ([2.05; 2.5; 1.4], [1, 1, 4]);
%! assert (median (x, 2, "omitnan"), y);
%! y = repmat ([NaN; NaN; 1.4], [1, 1, 4]);
%! assert (median (x, 2), y);
%! assert (median (x, "all"), NaN);
%! assert (median (x, "all", "omitnan"), 2);
%!assert (median (cat (3, 3, 1, NaN, 2), "omitnan"), 2)
%!assert (median (cat (3, 3, 1, NaN, 2), 3, "omitnan"), 2)
# Test boolean input
%!test
%! assert (median (true, "all"), logical (1));
%! assert (median (false), logical (0));
%! assert (median ([true false true]), true);
%! assert (median ([true false true], 2), true);
%! assert (median ([true false true], 1), logical ([1 0 1]));
%! assert (median ([true false NaN], 1), [1 0 NaN]);
%! assert (median ([true false NaN], 2), NaN);
%! assert (median ([true false NaN], 2, "omitnan"), 0.5);
%! assert (median ([true false NaN], 2, "omitnan", "native"), double(0.5));
## Test dimension indexing with vecdim in n-dimensional arrays
%!test
%! x = repmat ([1:20;6:25], [5 2 6 3]);
%! assert (size (median (x, [3 2])), [10 1 1 3]);
%! assert (size (median (x, [1 2])), [1 1 6 3]);
%! assert (size (median (x, [1 2 4])), [1 1 6]);
%! assert (size (median (x, [1 4 3])), [1 40]);
%! assert (size (median (x, [1 2 3 4])), [1 1]);
## Test exceeding dimensions
%!assert (median (ones (2,2), 3), ones (2,2));
%!assert (median (ones (2,2,2), 99), ones (2,2,2));
%!assert (median (magic (3), 3), magic (3));
%!assert (median (magic (3), [1 3]), [4, 5, 6]);
%!assert (median (magic (3), [1 99]), [4, 5, 6]);
## Test results with vecdim in n-dimensional arrays and "omitnan"
%!test
%! x = repmat ([2 2.1 2.2 2 NaN; 3 1 2 NaN 5; 1 1.1 1.4 5 3], [1, 1, 4]);
%! assert (median (x, [3 2]), [NaN NaN 1.4]');
%! assert (median (x, [3 2], "omitnan"), [2.05 2.5 1.4]');
%! assert (median (x, [1 3]), [2 1.1 2 NaN NaN]);
%! assert (median (x, [1 3], "omitnan"), [2 1.1 2 3.5 4]);
## Test empty, NaN, Inf inputs
%!assert (median (NaN), NaN)
%!assert (median (NaN, "omitnan"), NaN)
%!assert (median (NaN (2)), [NaN NaN])
%!assert (median (NaN (2), "omitnan"), [NaN NaN])
%!assert (median ([1 NaN 3]), NaN)
%!assert (median ([1 NaN 3], 1), [1 NaN 3])
%!assert (median ([1 NaN 3], 2), NaN)
%!assert (median ([1 NaN 3]'), NaN)
%!assert (median ([1 NaN 3]', 1), NaN)
%!assert (median ([1 NaN 3]', 2), [1; NaN; 3])
%!assert (median ([1 NaN 3], "omitnan"), 2)
%!assert (median ([1 NaN 3]', "omitnan"), 2)
%!assert (median ([1 NaN 3], 1, "omitnan"), [1 NaN 3])
%!assert (median ([1 NaN 3], 2, "omitnan"), 2)
%!assert (median ([1 NaN 3]', 1, "omitnan"), 2)
%!assert (median ([1 NaN 3]', 2, "omitnan"), [1; NaN; 3])
%!assert (median ([1 2 NaN 3]), NaN)
%!assert (median ([1 2 NaN 3], "omitnan"), 2)
%!assert (median ([1,2,NaN;4,5,6;NaN,8,9]), [NaN, 5, NaN])
%!assert (median ([1 2 ; NaN 4]), [NaN 3])
%!assert (median ([1 2 ; NaN 4], "omitnan"), [1 3])
%!assert (median ([1 2 ; NaN 4], 1, "omitnan"), [1 3])
%!assert (median ([1 2 ; NaN 4], 2, "omitnan"), [1.5; 4], eps)
%!assert (median ([1 2 ; NaN 4], 3, "omitnan"), [1 2 ; NaN 4])
%!assert (median ([NaN 2 ; NaN 4]), [NaN 3])
%!assert (median ([NaN 2 ; NaN 4], "omitnan"), [NaN 3])
%!assert (median (ones (1, 0, 3)), NaN (1, 1, 3))
%!assert (median (NaN("single")), NaN("single"));
%!assert (median (NaN("single"), "omitnan"), NaN("single"));
%!assert (median (NaN("single"), "double"), NaN("double"));
%!assert (median (single([1 2 ; NaN 4])), single([NaN 3]));
%!assert (median (single([1 2 ; NaN 4]), "double"), double([NaN 3]));
%!assert (median (single([1 2 ; NaN 4]), "omitnan"), single([1 3]));
%!assert (median (single([1 2 ; NaN 4]), "omitnan", "double"), double([1 3]));
%!assert (median (single([NaN 2 ; NaN 4]), "double"), double([NaN 3]));
%!assert (median (single([NaN 2 ; NaN 4]), "omitnan"), single([NaN 3]));
%!assert (median (single([NaN 2 ; NaN 4]), "omitnan", "double"), double([NaN 3]));
%!assert (median (Inf), Inf);
%!assert (median (-Inf), -Inf);
%!assert (median ([-Inf Inf]), NaN);
%!assert (median ([3 Inf]), Inf);
%!assert (median ([3 4 Inf]), 4);
%!assert (median ([Inf 3 4]), 4);
%!assert (median ([Inf 3 Inf]), Inf);
%!assert (median ([]), NaN);
%!assert (median (ones(1,0)), NaN);
%!assert (median (ones(0,1)), NaN);
%!assert (median ([], 1), NaN(1,0));
%!assert (median ([], 2), NaN(0,1));
%!assert (median ([], 3), NaN(0,0));
%!assert (median (ones(1,0), 1), NaN(1,0));
%!assert (median (ones(1,0), 2), NaN(1,1));
%!assert (median (ones(1,0), 3), NaN(1,0));
%!assert (median (ones(0,1), 1), NaN(1,1));
%!assert (median (ones(0,1), 2), NaN(0,1));
%!assert (median (ones(0,1), 3), NaN(0,1));
%!assert (median (ones(0,1,0,1), 1), NaN(1,1,0));
%!assert (median (ones(0,1,0,1), 2), NaN(0,1,0));
%!assert (median (ones(0,1,0,1), 3), NaN(0,1,1));
%!assert (median (ones(0,1,0,1), 4), NaN(0,1,0));
## Test complex inputs (should sort by abs(a))
%!assert (median([1 3 3i 2 1i]), 2)
%!assert (median([1 2 4i; 3 2i 4]), [2, 1+1i, 2+2i])
## 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)
%!shared ## Clear shared to prevent variable echo for any later test failures
## Test non-floating point types
%!assert (median ([true, false]), true)
%!assert (median (logical ([])), false)
%!assert (median (uint8 ([1, 3])), uint8 (2))
%!assert (median (uint8 ([])), uint8 (NaN))
%!assert (median (uint8 ([NaN 10])), uint8 (5))
%!assert (median (int8 ([1, 3, 4])), int8 (3))
%!assert (median (int8 ([])), int8 (NaN))
%!assert (median (single ([1, 3, 4])), single (3))
%!assert (median (single ([1, 3, NaN])), single (NaN))
## Test same sign int overflow when getting mean of even number of values
%!assert <*54567> (median (uint8 ([253, 255])), uint8 (254))
%!assert <*54567> (median (uint8 ([253, 254])), uint8 (254))
%!assert <*54567> (median (int8 ([127, 126, 125, 124; 1 3 5 9])), ...
%! int8 ([64 65 65 67]))
%!assert <*54567> (median (int8 ([127, 126, 125, 124; 1 3 5 9]), 2), ...
%! int8 ([126; 4]))
%!assert <*54567> (median (int64 ([intmax("int64"), intmax("int64")-2])), ...
%! intmax ("int64") - 1)
%!assert <*54567> (median ( ...
%! int64 ([intmax("int64"), intmax("int64")-2; 1 2]), 2), ...
%! int64([intmax("int64") - 1; 2]))
%!assert <*54567> (median (uint64 ([intmax("uint64"), intmax("uint64")-2])), ...
%! intmax ("uint64") - 1)
%!assert <*54567> (median ( ...
%! uint64 ([intmax("uint64"), intmax("uint64")-2; 1 2]), 2), ...
%! uint64([intmax("uint64") - 1; 2]))
## Test opposite sign int overflow when getting mean of even number of values
%!assert <*54567> (median (...
%! [intmin('int8') intmin('int8')+5 intmax('int8')-5 intmax('int8')]), ...
%! int8(-1))
%!assert <*54567> (median ([int8([1 2 3 4]); ...
%! intmin('int8') intmin('int8')+5 intmax('int8')-5 intmax('int8')], 2), ...
%! int8([3;-1]))
%!assert <*54567> (median (...
%! [intmin('int64') intmin('int64')+5 intmax('int64')-5 intmax('int64')]), ...
%! int64(-1))
%!assert <*54567> (median ([int64([1 2 3 4]); ...
%! intmin('int64') intmin('int64')+5 intmax('int64')-5 intmax('int64')], 2), ...
%! int64([3;-1]))
## Test int accuracy loss doing mean of close int64/uint64 values as double
%!assert <*54567> (median ([intmax("uint64"), intmax("uint64")-2]), ...
%! intmax("uint64")-1)
%!assert <*54567> (median ([intmax("uint64"), intmax("uint64")-2], "default"), ...
%! double(intmax("uint64")-1))
%!assert <*54567> (median ([intmax("uint64"), intmax("uint64")-2], "double"), ...
%! double(intmax("uint64")-1))
%!assert <*54567> (median ([intmax("uint64"), intmax("uint64")-2], "native"), ...
%! intmax("uint64")-1)
## Test input case insensitivity
%!assert (median ([1 2 3], "aLL"), 2);
%!assert (median ([1 2 3], "OmitNan"), 2);
%!assert (median ([1 2 3], "DOUBle"), 2);
## Test input validation
%!error median ()
%!error median (1, 2, 3)
%!error median (1, 2, 3, 4)
%!error median (1, "all", 3)
%!error median (1, "b")
%!error median (1, 1, "foo")
%!error <'all' cannot be used with> median (1, 3, "all")
%!error <'all' cannot be used with> median (1, [2 3], "all")
%!error median ({1:5})
%!error median ("char")
%!error median(1, "double", "native")
%!error median (1, ones (2,2))
%!error median (1, 1.5)
%!error median (1, 0)
%!error median ([1 2 3], [-1 1])
%!error median(1, [1 2 2])