funKeane

PURPOSE ^

% Keane's function

SYNOPSIS ^

function [p,dp]=funKeane(xx)

DESCRIPTION ^

% Keane's function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Keane's function
0002 %L. LAURENT -- 17/11/2016 -- 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)=-0.673668 for (x1,x2)={(0,1.39325),(1.39325,0)}
0026 %
0027 %Design space: 0<xi<10
0028 
0029 
0030 function [p,dp]=funKeane(xx)
0031 
0032 %variables
0033 xxx=xx(:,:,1);
0034 yyy=xx(:,:,2);
0035 
0036 %evaluation and derivatives
0037 sa=sin(xxx-yyy);
0038 sb=sin(xxx+yyy);
0039 pa=sqrt(xxx.^2+yyy.^2);
0040 %
0041 p=sa.^2.*sb.^2./pa;
0042 
0043 if nargout==2
0044     ca=cos(xxx-yyy);
0045     cb=cos(xxx+yyy);
0046     %
0047     dp(:,:,1)=(2*sa.*ca.*sb.^2+2*sb.*cb.*sa.^2)./pa-xxx.*p./pa.^2;
0048     dp(:,:,2)=(-2*sa.*ca.*sb.^2+2*sb.*cb.*sa.^2)./pa-yyy.*p./pa.^2;
0049 end
0050 end

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