######################################################################## ## ## 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. ## ## 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 {} {@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])