funXinSheYang3

PURPOSE ^

% Xin-She-Yang 3 function

SYNOPSIS ^

function [p,dp] = funXinSheYang3(xx)

DESCRIPTION ^

% Xin-She-Yang 3 function
 L. LAURENT -- 28/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Xin-She-Yang 3 function
0002 % L. LAURENT -- 28/02/2017 -- luc.laurent@lecnam.net
0003 
0004 % sources available here:
0005 % https://bitbucket.org/luclaurent/optigtest/
0006 % https://github.com/luclaurent/optigtest/
0007 
0008 % optiGTest - set of testing functions    A toolbox to easy manipulate functions.
0009 % Copyright (C) 2017  Luc LAURENT <luc.laurent@lecnam.net>
0010 %
0011 % This program is free software: you can redistribute it and/or modify
0012 % it under the terms of the GNU General Public License as published by
0013 % the Free Software Foundation, either version 3 of the License, or
0014 % (at your option) any later version.
0015 %
0016 % This program is distributed in the hope that it will be useful,
0017 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0018 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0019 % GNU General Public License for more details.
0020 %
0021 % You should have received a copy of the GNU General Public License
0022 % along with this program.  If not, see <http://www.gnu.org/licenses/>.
0023 
0024 %1 minimum global: f(0,...,0)=-1
0025 %
0026 %Design space -20<xi<20
0027 
0028 function [p,dp] = funXinSheYang3(xx)
0029 
0030 %constants
0031 a=2;
0032 m=3;
0033 beta=15;
0034 
0035 %evaluation and derivatives
0036 pa=xx./beta;
0037 pA=sum(pa.^(2*m),3);
0038 pAA=exp(-pA);
0039 %
0040 pb=xx.^2;
0041 pB=sum(pb,3);
0042 pBB=exp(-pB);
0043 %
0044 pc=cos(xx).^2;
0045 pCC=prod(pc,3);
0046 %
0047 p=pAA-a*pBB.*pCC;
0048 
0049 if nargout==2
0050     dp=-2*m/beta^(2*m)*xx.^(2*m-1).*pAA ...
0051         + 2*a*xx.*pBB.*pCC ...
0052         +2*a*sin(xx).*pBB.*pCC./cos(xx); %could required specific writing for dealing with NaN values
0053 end
0054 end
0055

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