function [y] = levy(xx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% LEVY 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/
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% INPUT:
%
% xx = [x1, x2, ..., xd]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

d = length(xx);

for ii = 1:d
	w(ii) = 1 + (xx(ii) - 1)/4;
end

term1 = (sin(pi*w(1)))^2;
term3 = (w(d)-1)^2 * (1+(sin(2*pi*w(d)))^2);

sum = 0;
for ii = 1:(d-1)
	wi = w(ii);
        new = (wi-1)^2 * (1+10*(sin(pi*wi+1))^2);
	sum = sum + new;
end

y = term1 + sum + term3;

end