## Copyright (C) 1996-2011 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  {Function File} {} median (@var{x})
## @deftypefnx {Function File} {} median (@var{x}, @var{dim})
## Compute the median value of the elements of the vector @var{x}.
## If the elements of @var{x} are sorted, the median is defined
## as
## @tex
## $$
## {\rm median} (x) =
##   \cases{x(\lceil N/2\rceil), & $N$ odd;\cr
##           (x(N/2)+x(N/2+1))/2, & $N$ even.}
## $$
## @end tex
## @ifnottex
##
## @example
## @group
##             x(ceil(N/2)),             N odd
## median(x) =
##             (x(N/2) + x((N/2)+1))/2,  N even
## @end group
## @end example
##
## @end ifnottex
## 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))
    error ("median: X must be a numeric vector or matrix");
  endif

  nd = ndims (x);
  sz = size (x);
  if (nargin != 2)
    ## Find the first non-singleton dimension.
    dim = find (sz > 1, 1);
    if (isempty (dim))
      dim = 1;
    endif
  else
    if (!(isscalar (dim) && dim == fix (dim))
        || !(1 <= dim && dim <= nd))
      error ("median: DIM must be an integer and a valid dimension");
    endif
  endif

  if (numel (x) > 0)
    n = size (x, dim);
    k = floor ((n+1) / 2);
    if (mod (n, 2) == 1)
      retval = nth_element (x, k, dim);
    else
      retval = mean (nth_element (x, k:k+1, dim), dim);
    endif
    ## Inject NaNs where needed, to be consistent with Matlab.
    retval(any (isnan (x), dim)) = NaN;
  else
    error ("median: invalid matrix argument");
  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 ([1,2,NaN;4,5,6;NaN,8,9]), [NaN, 5, NaN]);

%% Test input validation
%!error median ();
%!error median (1, 2, 3);
%!error median ({1:5});
%!error median (true(1,5));
%!error median (1, ones(2,2));
%!error median (1, 1.5);
%!error median (1, 0);