% Hartmann 3 function L. LAURENT -- 16/11/2016 -- luc.laurent@lecnam.net
0001 %% Hartmann 3 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 %global minimum : f(x1,x2)=-3.86278214782076 for (x1,x2)=[0.114614,0.555649,0.852547] 0026 % 0027 %Design space: 0<xi<10 0028 0029 0030 function [p,dp]=funHartmann3(xx) 0031 %constants 0032 ma=[3.0, 0.1, 3.0, 0.1; 0033 10.0, 10.0, 10.0, 10.0; 0034 30.0, 35.0, 30.0, 35.0]; 0035 mp=[0.36890, 0.46990, 0.10910, 0.03815; 0036 0.11700, 0.43870, 0.87320, 0.57430; 0037 0.26730, 0.74700, 0.55470, 0.88280]; 0038 c=[1,1.2,3,3.2]; 0039 b=4; 0040 dim=3; 0041 0042 %evaluation and derivatives 0043 sX=size(xx); 0044 p=zeros(sX(1),sX(2)); 0045 for it=1:b 0046 pa=bsxfun(@minus,xx,reshape(mp(:,it),1,1,dim)); 0047 pb=bsxfun(@times,reshape(ma(:,it),1,1,dim),pa.^2); 0048 p=p-c(it)*exp(-sum(pb,3)); 0049 end 0050 0051 if nargout==2 0052 dp=zeros(sX); 0053 % 0054 for it=1:b 0055 pa=bsxfun(@minus,xx,reshape(mp(:,it),1,1,dim)); 0056 pb=bsxfun(@times,reshape(ma(:,it),1,1,dim),pa.^2); 0057 pc=exp(-sum(pb,3)); 0058 pe=bsxfun(@times,reshape(ma(:,it),1,1,dim),pa); 0059 % 0060 for itD=1:dim 0061 dp(:,:,itD)=dp(:,:,itD)+2*c(it)*pe(:,:,itD).*pc; 0062 end 0063 end 0064 end 0065 end