funChenBird

PURPOSE ^

% Chen Bird's function

SYNOPSIS ^

function [p,dp]=funChenBird(xx)

DESCRIPTION ^

% Chen Bird'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 Bird'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 %2 global minima
0026 %f(x1,x2)=-2000 for (x1,x2)={(0.5,0.5),(-0.5,-0.5)}
0027 %
0028 %Design space: -500<x1,x2<500
0029 
0030 
0031 
0032 
0033 function [p,dp]=funChenBird(xx)
0034 
0035 %constants
0036 a=1e-3;
0037 b=1;
0038 c=0.5;
0039 
0040 %variables
0041 xxx=xx(:,:,1);
0042 yyy=xx(:,:,2);
0043 
0044 %evaluations and derivatives
0045 pa=xxx.^2+yyy.^2-b;
0046 da=a^2+pa.^2;
0047 pb=xxx.^2+yyy.^2-c;
0048 db=a^2+pb.^2;
0049 pc=xxx-yyy;
0050 dc=a^2+pc.^2;
0051 p=-a./da-a./db-a./dc; 
0052 
0053 if nargout==2
0054     dp(:,:,1)=4*a*xxx.*pa./da.^2 ...
0055         +4*a*xxx.*pb./db.^2 ...
0056         +2*a.*pc./dc.^2;
0057     dp(:,:,2)=4*a*yyy.*pa./da.^2 ...
0058         +4*a*yyy.*pb./db.^2 ...
0059         -2*a.*pc./dc.^2;
0060 end
0061 end

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