% Schaffer 3 function L. LAURENT -- 15/02/2017 -- luc.laurent@lecnam.net
0001 %% Schaffer 3 function 0002 % L. LAURENT -- 15/02/2017 -- 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(0,1.253115)=0.00123005 0025 % 0026 %Design space -100<xi<100 0027 0028 0029 function [p,dp] = funSchaffer3(xx) 0030 0031 %constants 0032 a=0.5; 0033 b=1; 0034 c=0.001; 0035 0036 %evaluation and derivatives 0037 x=xx(:,:,1); 0038 y=xx(:,:,2); 0039 xay=x.^2+y.^2; 0040 xmy=x.^2-y.^2; 0041 cxy=cos(abs(xmy)); 0042 scxy=sin(cxy); 0043 pa=scxy.^2-a; 0044 pb=b+c*xay.^2; 0045 % 0046 p=a+pa./pb; 0047 0048 if nargout==2 0049 % 0050 dpT=-2*xx.*sign(xmy).*sin(abs(xmy)).*2.*cos(cxy).*scxy; 0051 dpax=dpT(:,:,1); 0052 dpay=-dpT(:,:,2); 0053 dpbx=4*c*x.*xay; 0054 dpby=4*c*y.*xay; 0055 dp(:,:,1)=(dpax.*pb-pa.*dpbx)./pb.^2; 0056 dp(:,:,2)=(dpay.*pb-pa.*dpby)./pb.^2; 0057 end 0058 end