funFreudensteinRoth

PURPOSE ^

% Freudenstein Roth function

SYNOPSIS ^

function [p,dp]=funFreudensteinRoth(xx)

DESCRIPTION ^

% Freudenstein Roth function
L. LAURENT -- 16/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Freudenstein Roth function
0002 %L. LAURENT -- 16/11/2016 -- 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 %global minimum : f(x1,x2)=0 for (5,4)
0026 %
0027 %Design space: -10<xi<10
0028 
0029 function [p,dp]=funFreudensteinRoth(xx)
0030 
0031 %constants
0032 a=13;
0033 b=5;
0034 c=2;
0035 d=29;
0036 e=1;
0037 f=14;
0038 
0039 %variables
0040 xxx=xx(:,:,1);
0041 yyy=xx(:,:,2);
0042 
0043 %evaluation and derivatives
0044 pa=xxx-a+yyy.*((b-yyy).*yyy-c);
0045 pb=xxx-d+((yyy+e).*yyy-f).*yyy;
0046 p=pa.^2+pb.^2;
0047 %
0048 if nargout==2
0049     dp(:,:,1)=2*(pa+pb);
0050     dp(:,:,2)=2*((b-yyy).*yyy...
0051         -c+yyy.*(b-2*yyy)).*pa...
0052         +2*(yyy.*(yyy+e)-f+yyy.*(2*yyy+e)).*pb;
0053 end
0054 end

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