funCrossInTray

PURPOSE ^

% Cross-in-Tray function

SYNOPSIS ^

function [p,dp]=funCrossInTray(xx)

DESCRIPTION ^

% Cross-in-Tray function
L. LAURENT -- 05/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Cross-in-Tray function
0002 %L. LAURENT -- 05/11/2016 -- 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 %4 global minimas : f(x1,x2,x3,x4)=-2.06261218 for
0026 % {(1.349406685353340,1.349406608602084),
0027 %   (-1.349406685353340,1.349406608602084),
0028 %   (1.349406685353340,-1.349406608602084),
0029 %   (-1.349406685353340,-1.349406608602084)}
0030 %
0031 %Design space: -10<xi<10
0032 
0033 
0034 function [p,dp]=funCrossInTray(xx)
0035 
0036 %constants
0037 a=1e-4;
0038 b=100;
0039 c=pi;
0040 d=1;
0041 e=0.1;
0042 
0043 %variables
0044 xxx=xx(:,:,1);
0045 yyy=xx(:,:,2);
0046 
0047 %evaluation and derivatives
0048 sx=sin(xxx);
0049 sy=sin(yyy);
0050 gxy=sqrt(xxx.^2+yyy.^2);
0051 hxy=exp(abs(b-gxy./c));
0052 kxy=abs(sx.*sy.*hxy);
0053 p=-a*(kxy+d).^e;
0054 %
0055 if nargout==2
0056     cx=cos(xxx);
0057     cy=cos(yyy);
0058     %
0059     dgx=xxx./gxy;
0060     dgy=yyy./gxy;
0061     %
0062     dhx=hxy.*sign(b-gxy./c).*(-1/c.*dgx);
0063     dhy=hxy.*sign(b-gxy./c).*(-1/c.*dgy);
0064     %
0065     dkx=(cx.*sy.*hxy+sx.*sy.*dhx).*sign(sx.*sy.*hxy);
0066     dky=(cy.*sx.*hxy+sx.*sy.*dhy).*sign(sx.*sy.*hxy);
0067     %
0068     dp(:,:,1)=-a*e*dkx.*(kxy+d).^(e-1);
0069     dp(:,:,2)=-a*e*dky.*(kxy+d).^(e-1);
0070 end
0071 end

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