## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006,
##               2007, 2008, 2009 John W. Eaton
##
## 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.
##
## 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} {} skewness (@var{x}, @var{dim})
## If @var{x} is a vector of length @math{n}, return the skewness
## @tex
## $$
## {\rm skewness} (x) = {1\over N \sigma(x)^3} \sum_{i=1}^N (x_i-\bar{x})^3
## $$
## where $\bar{x}$ is the mean value of $x$.
## @end tex
## @ifnottex
##
## @example
## skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3)
## @end example
##
## @end ifnottex
##
## @noindent
## of @var{x}.  If @var{x} is a matrix, return the skewness along the
## first non-singleton dimension of the matrix.  If the optional
## @var{dim} argument is given, operate along this dimension.
## @end deftypefn

## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Created: 29 July 1994
## Adapted-By: jwe

function retval = skewness (x, dim)

  if (nargin != 1 && nargin != 2)
    print_usage ();
  endif

  if (!ismatrix(x) || ischar(x))
    error ("skewness: X must be a numeric matrix or vector");
  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 == round (dim)) || 
        !(1 <= dim && dim <= nd))
      error ("skewness: DIM must be an integer and a valid dimension");
    endif
  endif

  c = sz(dim);
  idx = ones (1, nd);
  idx (dim) = c;
  x = x - repmat (mean (x, dim), idx);
  sz(dim) = 1;
  retval = zeros (sz);
  s = std (x, [], dim);
  ind = find (s > 0);
  x = sum (x .^ 3, dim);
  retval(ind) = x(ind) ./ (c * s(ind) .^ 3);
  
endfunction

%!error skewness ();

%!error skewness (1, 2, 3);