% Biggs EXP 5's function L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net
0001 %% Biggs EXP 5'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, 1, 5,4) >> f(x)=0 0027 % 0028 %design space 0<xi<20 0029 0030 0031 0032 function [p,dp]=funBiggsExp5(xx) 0033 0034 %constants 0035 a=5; 0036 b=10; 0037 c=3; 0038 d=4; 0039 nbt=11; 0040 t=0.1.*(1:nbt); 0041 y=exp(-t)-a*exp(-b*t)+c*exp(-d*t); 0042 0043 %responses and derivatives 0044 xxx=xx(:,:,1); 0045 yyy=xx(:,:,2); 0046 zzz=xx(:,:,3); 0047 lll=xx(:,:,4); 0048 mmm=xx(:,:,5); 0049 0050 0051 p=zeros(size(xxx)); 0052 for it=1:nbt 0053 p=p+(zzz.*exp(-t(it).*xxx)-lll.*exp(-t(it).*yyy)+c.*exp(-t(it).*mmm)-y(it)).^2; 0054 end 0055 if nargout==2 0056 dp=zeros(size(xxx,1),size(xxx,2),5); 0057 for it=1:nbt 0058 mult=zzz.*exp(-t(it).*xxx)-lll.*exp(-t(it).*yyy)+c.*exp(-t(it).*mmm)-y(it); 0059 dp(:,:,1)=dp(:,:,1)-2.*zzz.*t(it).*exp(-t(it)*xxx).*mult; 0060 dp(:,:,2)=dp(:,:,2)+2*lll.*t(it).*exp(-t(it)*yyy).*mult; 0061 dp(:,:,3)=dp(:,:,3)+2.*exp(-t(it)*xxx).*mult; 0062 dp(:,:,4)=dp(:,:,4)-2.*exp(-t(it)*yyy).*mult; 0063 dp(:,:,5)=dp(:,:,5)-2*c*t(it).*exp(-t(it)*mmm).*mult; 0064 end 0065 end 0066 end