funChenV

PURPOSE ^

% Chen V's function

SYNOPSIS ^

function [p,dp]=funChenV(xx)

DESCRIPTION ^

% Chen V's function
L. LAURENT -- 04/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Chen V's function
0002 %L. LAURENT -- 04/11/2016 -- 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 %1 global minimum
0026 %f(x1,x2)=-2000 for (x1,x2)=(7/18,13/18)
0027 %
0028 %Design space: -500<x1,x2<500
0029 
0030 
0031 
0032 
0033 function [p,dp]=funChenV(xx)
0034 
0035 %constants
0036 a=1e-3;
0037 b=0.4;
0038 c=0.1;
0039 d=2;
0040 e=1.5;
0041 
0042 %variables
0043 xxx=xx(:,:,1);
0044 yyy=xx(:,:,2);
0045 
0046 %evaluations and derivatives
0047 pa=xxx-b*yyy-c;
0048 da=a^2+pa.^2;
0049 pb=d*xxx+yyy-e;
0050 db=a^2+pb.^2;
0051 p=-a./da-a./db; 
0052 
0053 if nargout==2
0054     dp(:,:,1)=2*a*pa./da.^2 ...
0055         +2*a*d*pb./db.^2;
0056     dp(:,:,2)=-2*a*b*pa./da.^2 ...
0057         +2*a*pb./db.^2;
0058 end
0059 end

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