% Alpine's function 2 L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net
0001 %% Alpine's function 2 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 %numerous local minima 0026 %1 global minimum : x=(7.917,7.917,...,7.917) >> f(x)=2.808^p 0027 % 0028 %design space 0<xi<10 0029 0030 0031 0032 function [p,dp]=funAlpine2(xx) 0033 0034 %number of variables 0035 nbvar=size(xx,3); 0036 0037 %responses and derivatives 0038 fx=sqrt(xx).*sin(xx); 0039 p=prod(fx,3); 0040 0041 if nargout==2 0042 dp=zeros(size(xx)); 0043 for itV=1:nbvar 0044 itF=[1:(itV-1) (itV+1):nbvar]; 0045 dp(:,:,itV)=prod(fx(:,:,itF),3).*... 0046 (0.5./sqrt(xx(:,:,itV)).*sin(xx(:,:,itV))+sqrt(xx(:,:,itV)).*cos(xx(:,:,itV))); 0047 end 0048 end 0049 end