% Freudenstein Roth function L. LAURENT -- 16/11/2016 -- luc.laurent@lecnam.net
0001 %% Freudenstein Roth function 0002 %L. LAURENT -- 16/11/2016 -- 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 % 0025 %global minimum : f(x1,x2)=0 for (5,4) 0026 % 0027 %Design space: -10<xi<10 0028 0029 function [p,dp]=funFreudensteinRoth(xx) 0030 0031 %constants 0032 a=13; 0033 b=5; 0034 c=2; 0035 d=29; 0036 e=1; 0037 f=14; 0038 0039 %variables 0040 xxx=xx(:,:,1); 0041 yyy=xx(:,:,2); 0042 0043 %evaluation and derivatives 0044 pa=xxx-a+yyy.*((b-yyy).*yyy-c); 0045 pb=xxx-d+((yyy+e).*yyy-f).*yyy; 0046 p=pa.^2+pb.^2; 0047 % 0048 if nargout==2 0049 dp(:,:,1)=2*(pa+pb); 0050 dp(:,:,2)=2*((b-yyy).*yyy... 0051 -c+yyy.*(b-2*yyy)).*pa... 0052 +2*(yyy.*(yyy+e)-f+yyy.*(2*yyy+e)).*pb; 0053 end 0054 end