function [y] = gfunc(xx, a)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% G-FUNCTION
%
% Authors: Sonja Surjanovic, Simon Fraser University
%          Derek Bingham, Simon Fraser University
% Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
%
% Copyright 2013. Derek Bingham, Simon Fraser University.
%
% THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
% FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
% derivative works, such modified software should be clearly marked.
% Additionally, 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; version 2.0 of the License. 
% Accordingly, 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.
%
% For function details and reference information, see:
% http://www.sfu.ca/~ssurjano/
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% INPUTS:
%
% xx = [x1, x2, ..., xd]
% a = [a1, a2, ..., ad] (optional), with default values given by Crestaux
%     et al. (2007)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

d = length(xx);

if (nargin == 1)
    a = zeros(1, d);
    for ii = 1:d
        a(ii) = (ii-1) / 2;
    end
end

prod = 1;
for ii = 1:d
    xi = xx(ii);
    ai = a(ii);
    new1 = abs(4*xi-2) + ai;
    new2 = 1 + ai;
    prod = prod * new1/new2;
end

y = prod;

end