funBiggsExp6

PURPOSE ^

% Biggs EXP 6's function

SYNOPSIS ^

function [p,dp]=funBiggsExp6(xx)

DESCRIPTION ^

% Biggs EXP 6's function
L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Biggs EXP 6'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 ,3) >> f(x)=0
0027 %
0028 %design space 0<xi<20
0029 
0030 
0031 
0032 function [p,dp]=funBiggsExp6(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 nnn=xx(:,:,6);
0050 
0051 
0052 p=zeros(size(xxx));
0053 for it=1:nbt
0054     p=p+(zzz.*exp(-t(it).*xxx)-lll.*exp(-t(it).*yyy)+nnn.*exp(-t(it).*mmm)-y(it)).^2;
0055 end
0056 if nargout==2
0057     dp=zeros(size(xxx,1),size(xxx,2),6);
0058     for it=1:nbt
0059         mult=zzz.*exp(-t(it).*xxx)-lll.*exp(-t(it).*yyy)+nnn.*exp(-t(it).*mmm)-y(it);
0060         dp(:,:,1)=dp(:,:,1)-2.*zzz.*t(it).*exp(-t(it)*xxx).*mult;
0061         dp(:,:,2)=dp(:,:,2)+2*lll.*t(it).*exp(-t(it)*yyy).*mult;
0062         dp(:,:,3)=dp(:,:,3)+2.*exp(-t(it)*xxx).*mult;
0063         dp(:,:,4)=dp(:,:,4)-2.*exp(-t(it)*yyy).*mult;
0064         dp(:,:,5)=dp(:,:,5)-2*nnn*t(it).*exp(-t(it)*mmm).*mult;
0065         dp(:,:,6)=dp(:,:,6)+2.*exp(-t(it)*mmm).*mult;
0066     end
0067 end
0068 end

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