% Deb4's function L. LAURENT -- 06/11/2016 -- luc.laurent@lecnam.net
0001 %% Deb4's function 0002 %L. LAURENT -- 06/11/2016 -- 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 %numerous local minima 0026 %5^np global minimum : 0027 % 0028 %design space -1<xi<1 0029 0030 0031 function [p,dp]=funDeb4(xx) 0032 0033 %constans 0034 a=6; 0035 b=5*pi; 0036 c=3/4; 0037 d=0.05; 0038 e=2*log(2); 0039 f=0.08; 0040 g=0.854; 0041 0042 %evaluation and derivatives 0043 nS=size(xx,3); 0044 sx=sin(b*(xx.^c-d)); 0045 ex=exp(-e*((xx-f)./g).^2); 0046 p=-1/nS*sum(ex.*sx.^a,3); 0047 0048 if nargout==2 0049 cx=cos(b*(xx.^c-d)); 0050 dp=-1/nS*ex.*(b*a*c*xx.^(c-1).*cx.*sx.^(a-1)+sx.^a.*(-2*e/g*(xx-f)./g)); 0051 end 0052 end