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