## Copyright (C) 1995-2019 Friedrich Leisch
##
## 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 {} {} fractdiff (@var{x}, @var{d})
## Compute the fractional differences @math{(1-L)^d x} where @math{L}
## denotes the lag-operator and @math{d} is greater than -1.
## @end deftypefn

## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description: Compute fractional differences

function retval = fractdiff (x, d)

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

  N = 100;

  if (! isvector (x))
    error ("fractdiff: X must be a vector");
  endif

  if (! isscalar (d))
    error ("fractdiff: D must be a scalar");
  endif


  if (d >= 1)
    for k = 1 : d
      x = x(2 : length (x)) - x(1 : length (x) - 1);
    endfor
  endif

  if (d > -1)

    d = rem (d, 1);

    if (d != 0)
      n = (0 : N)';
      w = real (gamma (-d+n) ./ gamma (-d) ./ gamma (n+1));
      retval = fftfilt (w, x);
      retval = retval(1 : length (x));
    else
      retval = x;
    endif

  else
    error ("fractdiff: D must be > -1");

  endif

endfunction
