% Egg Holder function L. LAURENT -- 16/11/2016 -- luc.laurent@lecnam.net
0001 %% Egg Holder 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 %one local minimum 0026 %1 global minimum : x=(512.0, 404.2319) >> f(x)=-959.640662711 0027 % 0028 %design space -512<xi<512 0029 0030 0031 function [p,dp]=funEggHolder(xx) 0032 0033 %constants 0034 a=47; 0035 b=0.5; 0036 0037 %variables 0038 dim=size(xx,3); 0039 0040 %evaluations and derivatives 0041 pa=xx(:,:,2:end)+a; 0042 pb=xx(:,:,2:end)+xx(:,:,1:end-1).*0.5+a; 0043 pc=xx(:,:,1:end-1)-xx(:,:,2:end)-a; 0044 % 0045 sqpb=sqrt(abs(pb)); 0046 sqpc=sqrt(abs(pc)); 0047 sipb=sin(sqpb); 0048 sipc=sin(sqpc); 0049 % 0050 g=-pa.*sipb-xx(:,:,1:end-1).*sipc; 0051 p=sum(g,3); 0052 0053 if nargout==2 0054 dgi=-b*pa.*sign(pb).*1./(2*sqpb).*cos(sqpb)... 0055 -sipc... 0056 -xx(:,:,1:end-1).*sign(pc).*1./(2*sqpc).*cos(sqpc); 0057 dgii=-sipb... 0058 -pa.*sign(pb).*1./(2*sqpb).*cos(sqpb)... 0059 +xx(:,:,1:end-1).*sign(pc).*1./(2*sqpc).*cos(sqpc); 0060 % 0061 dp=zeros(size(xx)); 0062 dp(:,:,1)=dgi(:,:,1); 0063 for it=2:dim-1 0064 dp(:,:,it)=dgi(:,:,it)+dgii(:,:,it-1); 0065 end 0066 dp(:,:,dim)=dgii(:,:,end); 0067 end 0068 end