% Schaffer 1 function L. LAURENT -- 15/02/2017 -- luc.laurent@lecnam.net
0001 %% Schaffer 1 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(0,0)=0 0025 % 0026 %Design space -100<xi<100 0027 0028 0029 function [p,dp] = funSchaffer1(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 xy=x.^2+y.^2; 0040 sxy=sin(xy); 0041 pa=sxy.^2-a; 0042 pb=b+c*xy.^2; 0043 % 0044 p=a+pa./pb; 0045 0046 if nargout==2 0047 % 0048 dp=zeros(size(xx)); 0049 cxy=cos(xy); 0050 dpax=4*x.*sxy.*cxy; 0051 dpay=4*y.*sxy.*cxy; 0052 dpbx=4*c*x.*xy; 0053 dpby=4*c*y.*xy; 0054 dp(:,:,1)=(dpax.*pb-pa.*dpbx)./pb.^2; 0055 dp(:,:,2)=(dpay.*pb-pa.*dpby)./pb.^2; 0056 end 0057 end