function [y] = soblev99(xx, b, c0)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SOBOL' & LEVITAN (1999) 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]
% b  = d-dimensional vector (optional), with default value
%      [2, 1.95, 1.9, 1.85, 1.8, 1.75, 1.7, 1.65, 0.4228, 0.3077, 0.2169,
%       0.1471, 0.0951, 0.0577, 0.0323, 0.0161, 0.0068, 0.0021, 0.0004, 0]
%      (when d<=20)
% c0 = constant term (optional), with default value 0
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

d = length(xx);

if (nargin == 1)
    if (d <= 20)
        b = [2, 1.95, 1.9, 1.85, 1.8, 1.75, 1.7, 1.65, 0.4228, 0.3077, 0.2169, 0.1471, 0.0951, 0.0577, 0.0323, 0.0161, 0.0068, 0.0021, 0.0004, 0];
    else
        error('Value of the d-dimensional vector b is required.')
    end
    c0 = 0;
elseif (nargin == 2)
    c0 = 0;
end
    
Id = 1;
for ii = 1:d
    bi = b(ii);
    new = (exp(bi)-1) / bi;
    Id = Id * new;
end

sum = 0;
for ii = 1:d
    bi = b(ii);
    xi = xx(ii);
    sum = sum + bi*xi;
end

y = exp(sum) - Id + c0;

end