function [y] = hart3(xx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% HARTMANN 3-DIMENSIONAL 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, x3]

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

alpha = [1.0, 1.2, 3.0, 3.2]';

A = [3.0, 10, 30;

     0.1, 10, 35;

     3.0, 10, 30;

     0.1, 10, 35];

P = 10^(-4) * [3689, 1170, 2673;

               4699, 4387, 7470;

               1091, 8732, 5547;

               381, 5743, 8828];

outer = 0;

for ii = 1:4

inner = 0;

for jj = 1:3

xj = xx(jj);

Aij = A(ii, jj);

Pij = P(ii, jj);

inner = inner + Aij*(xj-Pij)^2;

end

new = alpha(ii) * exp(-inner);

outer = outer + new;

end

y = -outer;

end