funSchaffer3

PURPOSE ^

% Schaffer 3 function

SYNOPSIS ^

function [p,dp] = funSchaffer3(xx)

DESCRIPTION ^

% Schaffer 3 function
 L. LAURENT -- 15/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Schaffer 3 function
0002 % L. LAURENT -- 15/02/2017 -- 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 %1 minimum global: f(0,1.253115)=0.00123005
0025 %
0026 %Design space -100<xi<100
0027 
0028 
0029 function [p,dp] = funSchaffer3(xx)
0030 
0031 %constants
0032 a=0.5;
0033 b=1;
0034 c=0.001;
0035 
0036 %evaluation and derivatives
0037 x=xx(:,:,1);
0038 y=xx(:,:,2);
0039 xay=x.^2+y.^2;
0040 xmy=x.^2-y.^2;
0041 cxy=cos(abs(xmy));
0042 scxy=sin(cxy);
0043 pa=scxy.^2-a;
0044 pb=b+c*xay.^2;
0045 %
0046 p=a+pa./pb;
0047 
0048 if nargout==2
0049     %
0050     dpT=-2*xx.*sign(xmy).*sin(abs(xmy)).*2.*cos(cxy).*scxy;
0051     dpax=dpT(:,:,1);
0052     dpay=-dpT(:,:,2);
0053     dpbx=4*c*x.*xay;
0054     dpby=4*c*y.*xay;
0055     dp(:,:,1)=(dpax.*pb-pa.*dpbx)./pb.^2;
0056     dp(:,:,2)=(dpay.*pb-pa.*dpby)./pb.^2;
0057 end
0058 end

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