funCamelbackSixHump

PURPOSE ^

% Six-Hump camel back function

SYNOPSIS ^

function [p,dp]=funCamelbackSixHump(xx)

DESCRIPTION ^

% Six-Hump camel back function
L. LAURENT -- 13/12/2010 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Six-Hump camel back function
0002 %L. LAURENT -- 13/12/2010 -- 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 %6 local minima and  2 global:
0026 %f(x1,x2)=-1.0316 for (x1,x2)={(-0.0898,0.7126),(0.0898,0.7126)}
0027 %
0028 %Design space: -3<x1<3 -2<x2<2
0029 %(recommanded: -2<x1<2 -1<x2<1)
0030 
0031 function [p,dp]=funCamelbackSixHump(xx)
0032 
0033 %constants
0034 a=4;
0035 b=2.1;
0036 c=3;
0037 
0038 %variables
0039 xxx=xx(:,:,1);
0040 yyy=xx(:,:,2);
0041 
0042 %evaluations and derivatives
0043 pa=(a-b*xxx.^2+xxx.^4/c);
0044 pb=(-1+yyy.^2);
0045 p=pa.*xxx.^2+...
0046     xxx.*yyy...
0047     +a*pb.*yyy.^2;   
0048     
0049 if nargout==2
0050     dp(:,:,1)=2*xxx.*pa...
0051         +xxx.^2.*(-2*b*xxx+a*xxx.^3/c)...
0052         +yyy;
0053     dp(:,:,2)=xxx...
0054         +2*a*yyy.*pb...
0055         +2*a*yyy.^3;
0056 end
0057 end

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