## Copyright (C) 2013-2018 Mike Miller
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {} ifwht (@var{x})
## @deftypefnx {Function File} {} ifwht (@var{x}, @var{n})
## @deftypefnx {Function File} {} ifwht (@var{x}, @var{n}, @var{order})
## Compute the inverse Walsh-Hadamard transform of @var{x} using the
## Fast Walsh-Hadamard Transform (FWHT) algorithm.  If the input is a
## matrix, the inverse FWHT is calculated along the columns of @var{x}.
##
## The number of elements of @var{x} must be a power of 2; if not, the
## input will be extended and filled with zeros.  If a second argument
## is given, the input is truncated or extended to have length @var{n}.
##
## The third argument specifies the @var{order} in which the returned
## inverse Walsh-Hadamard transform coefficients should be arranged.
## The @var{order} may be any of the following strings:
##
## @table @asis
## @item "sequency"
## The coefficients are returned in sequency order.  This is the default
## if @var{order} is not given.
##
## @item "hadamard"
## The coefficients are returned in Hadamard order.
##
## @item "dyadic"
## The coefficients are returned in Gray code order.
## @end table
##
## @seealso{fwht}
## @end deftypefn

function y = ifwht (x, n, order)

  if (nargin < 1 || nargin > 3)
    print_usage ();
  elseif (nargin == 1)
    n = order = [];
  elseif (nargin == 2)
    order = [];
  endif

  y = __fwht_opts__ ("ifwht", x, n, order);

endfunction

%!assert (isempty (ifwht ([])));
%!assert (ifwht (zeros (16)), zeros (16));
%!assert (ifwht ([1; (zeros (15, 1))]), ones (16, 1));
%!assert (ifwht (zeros (17, 1)), zeros (32, 1));
%!assert (ifwht ([0 0 0 0 0 0 0 1]), [1 -1 1 -1 1 -1 1 -1]);

%% Test input validation
%!error ifwht ();
%!error ifwht (1, 2, 3, 4);
%!error ifwht (0, 0);
%!error ifwht (0, 5);
%!error ifwht (0, [], "invalid");
