% Branin's function 2 L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net
0001 %% Branin's function 2 0002 %L. LAURENT -- 13/12/2010 -- 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 %3 global minima : 0026 %f(x1,x2)=5.559037 for (x1,x2)=(-3.2,12.53) 0027 % 0028 %Design space: -5<x1,x2<15 0029 0030 0031 0032 function [p,dp]=funBranin2(xx) 0033 0034 %constants 0035 a=5.1/(4*pi^2); 0036 b=5/pi; 0037 c=6; 0038 d=10; 0039 e=1/(8*pi); 0040 0041 %responses and derivatives 0042 xxx=xx(:,:,1); 0043 yyy=xx(:,:,2); 0044 0045 p = (yyy-a*xxx.^2+b*xxx-c).^2 ... 0046 +d*(1-e)*cos(xxx).*cos(yyy)+log(xxx.^2+yyy.^2+1)+d; 0047 0048 if nargout==2 0049 dp(:,:,1)=2*(yyy-a*xxx.^2+b*xxx-c).*(b-2*a*xxx)... 0050 -d*(1-e)*sin(xxx).*cos(yyy)... 0051 +2*xxx./(xxx.^2+yyy.^2+1); 0052 dp(:,:,2)=2*(yyy-a*xxx.^2+b*xxx-c)... 0053 -d*(1-e)*cos(xxx).*sin(yyy)... 0054 +2*yyy./(xxx.^2+yyy.^2+1); 0055 end 0056 end