% Bird's function L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net
0001 %% Bird's function 0002 %L. LAURENT -- 31/10/2016 -- 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 %one local minimum 0026 %1 global minimum : x={(4.70104,3.15294),(-1.58214, -3.13024)} >> f(x)=-106.764537 0027 % 0028 %design space -2pi<xi<2pi 0029 0030 0031 0032 function [p,dp]=funBird(xx) 0033 0034 %evaluate responses 0035 xxx=xx(:,:,1); 0036 yyy=xx(:,:,2); 0037 sx=sin(xxx); 0038 cy=cos(yyy); 0039 ex1=exp((1-cy).^2); 0040 ex2=exp((1-sx).^2); 0041 fxy=(xxx-yyy).^2; 0042 p=sx.*ex1+cy.*ex2+fxy; 0043 0044 %evaluate derivatives 0045 if nargout==2 0046 cx=cos(xxx); 0047 sy=sin(yyy); 0048 dp(:,:,1)=cx.*ex1-2*cy.*cx.*(1-sx).*ex2+2*(xxx-yyy); 0049 dp(:,:,2)=2*sx.*sy.*(1-cy).*ex1-sy.*ex2-2*(xxx-yyy); 0050 end 0051 end