funExp3

PURPOSE ^

% Exp3 function

SYNOPSIS ^

function [p,dp]=funExp3(xx)

DESCRIPTION ^

% Exp3 function
L. LAURENT -- 26/04/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Exp3 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 5]
0026 %
0027 %Design space: 0<xi<20
0028 %
0029 
0030 
0031 
0032 function [p,dp]=funExp3(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 %
0042 listI=reshape(1:a,1,1,a);
0043 pa=exp(-listI.*x./a);
0044 pb=-exp(-listI.*y./a);
0045 pc=-exp(-listI./a);
0046 pd=b*exp(-listI);
0047 %
0048 pt=pa+z.*pb+pc+pd;
0049 p=sum(pt.^2,3);
0050 
0051 %
0052 if nargout==2
0053     %
0054     dp=zeros(size(xx));
0055     %
0056     dp(:,:,1)=2*sum(-listI./a.*pa.*pt,3);
0057     dp(:,:,2)=2*z.*sum(-listI/a.*pb.*pt,3);
0058     dp(:,:,3)=2*sum(pb.*pt,3);
0059 end
0060 end

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