% Exp4 function L. LAURENT -- 26/04/2017 -- luc.laurent@lecnam.net
0001 %% Exp4 function 0002 %L. LAURENT -- 26/04/2017 -- 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(x)=0 for x=[1 10 1 5] 0026 % 0027 %Design space: 0<xi<20 0028 % 0029 0030 0031 0032 function [p,dp]=funExp4(xx) 0033 %constants 0034 a=10; 0035 b=5; 0036 0037 %evaluation and derivatives 0038 x=xx(:,:,1); 0039 y=xx(:,:,2); 0040 z=xx(:,:,3); 0041 v=xx(:,:,4); 0042 % 0043 listI=reshape(1:a,1,1,a); 0044 pa=exp(-listI.*x./a); 0045 pb=-exp(-listI.*y./a); 0046 pc=-exp(-listI./a); 0047 pd=b*exp(-listI); 0048 % 0049 pt=z.*pa+v.*pb+pc+pd; 0050 p=sum(pt.^2,3); 0051 0052 % 0053 if nargout==2 0054 % 0055 dp=zeros(size(xx)); 0056 % 0057 dp(:,:,1)=2*z.*sum(-listI./a.*pa.*pt,3); 0058 dp(:,:,2)=2*v.*sum(-listI/a.*pb.*pt,3); 0059 dp(:,:,3)=2*sum(pa.*pt,3); 0060 dp(:,:,4)=2*sum(pb.*pt,3); 0061 end 0062 end