% Biggs EXP 3's function L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net
0001 %% Biggs EXP 3's function 0002 %L. LAURENT -- 31/10/2016 -- 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=(1, 10, 5) >> f(x)=0 0027 % 0028 %design space 0<xi<20 0029 0030 0031 0032 function [p,dp]=funBiggsExp3(xx) 0033 0034 %constants 0035 a=5; 0036 b=10; 0037 nbt=10; 0038 t=0.1.*(1:10); 0039 y=exp(-t)-a*exp(-b*t); 0040 0041 %responses and derivatives 0042 xxx=xx(:,:,1); 0043 yyy=xx(:,:,2); 0044 zzz=xx(:,:,3); 0045 0046 p=zeros(size(xxx)); 0047 for it=1:nbt 0048 p=p+(exp(-t(it).*xxx)-zzz.*exp(-t(it).*yyy)-y(it)).^2; 0049 end 0050 if nargout==2 0051 dp=zeros(size(xxx,1),size(xxx,2),3); 0052 for it=1:nbt 0053 dp(:,:,1)=dp(:,:,1)-2*t(it)*exp(-t(it)*xxx).*(exp(-t(it).*xxx)-zzz.*exp(-t(it).*yyy)-y(it)); 0054 dp(:,:,2)=dp(:,:,2)+2*zzz.*t(it).*exp(-t(it)*yyy).*(exp(-t(it).*xxx)-zzz.*exp(-t(it).*yyy)-y(it)); 0055 dp(:,:,3)=dp(:,:,3)-2.*exp(-t(it)*yyy).*(exp(-t(it).*xxx)-zzz.*exp(-t(it).*yyy)-y(it)); 0056 end 0057 end 0058 end