funDamavandi

PURPOSE ^

% Damavandi's function

SYNOPSIS ^

function [p,dp]=funDamavandi(xx)

DESCRIPTION ^

% Damavandi's function
L. LAURENT -- 05/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Damavandi's 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 %1 global minimum : f(2,2)=0
0026 %
0027 %Design space: 0<xi<14
0028 
0029 
0030 function [p,dp]=funDamavandi(xx)
0031 
0032 %constants
0033 a=1;
0034 b=pi;
0035 c=2;
0036 d=7;
0037 
0038 %variables
0039 xxx=xx(:,:,1);
0040 yyy=xx(:,:,2);
0041 
0042 %evaluation and derivatives
0043 pax=xxx-c;
0044 pay=yyy-c;
0045 sx=sin(b*pax);
0046 sy=sin(b*pay);
0047 kxy=sx.*sy./(b^2*pax.*pay);
0048 %
0049 pbx=xxx-d;
0050 pby=yyy-d;
0051 hxy=c+pbx.^2+c*pby.^2;
0052 %
0053 p=(a-abs(kxy).^5).*hxy;
0054 %
0055 if nargout==2
0056     cx=cos(b*pax);
0057     cy=cos(b*pay);
0058     %
0059     dkx=b*cx.*sy./(b^2*pax.*pay)+b^2*pax.*kxy./(b^2*pax.*pay);
0060     dky=b*cy.*sx./(b^2*pax.*pay)+b^2*pbx.*kxy./(b^2*pax.*pay);
0061     %
0062     dhx=2*pbx;
0063     dhy=2*c*pby;
0064     %
0065     dp(:,:,1)=dhx.*(a-abs(kxy).^5)-5*dkx.*sign(kxy).*kxy.^4.*hxy;
0066     dp(:,:,2)=dhy.*(a-abs(kxy).^5)-5*dky.*sign(kxy).*kxy.^4.*hxy;
0067 end
0068 end

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