% Dixon & Price's function L. LAURENT -- 15/11/2016 -- luc.laurent@lecnam.net
0001 %% Dixon & Price's function 0002 %L. LAURENT -- 15/11/2016 -- 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={(4.70104,3.15294),(?1.58214, ?3.13024)} >> f(x)=?106.764537 0027 % 0028 %design space -10<xi<10 0029 0030 0031 function [p,dp]=funDixonPrice(xx) 0032 0033 %constants 0034 a=1; 0035 b=2; 0036 0037 %evaluations and derivatives 0038 dim=size(xx,3); 0039 pa=(xx(:,:,1)-a).^2; 0040 ii=reshape(2:dim,1,1,[]); 0041 pb=b*xx(:,:,2:end).^2-xx(:,:,1:end-1); 0042 pc=bsxfun(@times,pb.^2,ii); 0043 p=pa+sum(pc,3); 0044 0045 if nargout==2 0046 pd=bsxfun(@times,pb,ii); 0047 % 0048 dp=zeros(size(xx)); 0049 dp(:,:,1)=2*(xx(:,:,1)-a)-2*pd(:,:,1); 0050 for it=2:dim-1 0051 try 0052 dp(:,:,it)=4*b*it*xx(:,:,it).*pb(:,:,it-1)... 0053 -2*(it+1)*pb(:,:,it); 0054 catch 0055 keyboard 0056 end 0057 end 0058 dp(:,:,dim)=4*b*dim.*xx(:,:,end).*pb(:,:,end); 0059 end 0060 end