funLevy05

PURPOSE ^

% Levy 05 function

SYNOPSIS ^

function [p,dp]=funLevy05(xx)

DESCRIPTION ^

% Levy 05 function
L. LAURENT -- 17/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Levy 05 function
0002 %L. LAURENT -- 17/03/2017 -- 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 %
0025 %global minimum : f(x)=-176.1375 for x=[-1.3068 -1.4248]
0026 %
0027 %Design space: -10<xi<10
0028 %
0029 
0030 
0031 function [p,dp]=funLevy05(xx)
0032 %constants
0033 m=5;
0034 a=1.42513;
0035 b=0.80032;
0036 
0037 
0038 %evaluation and derivatives
0039 x=xx(:,:,1);
0040 y=xx(:,:,2);
0041 %
0042 lI=reshape(1:m,1,1,m);
0043 %
0044 pa=cos((lI-1).*x+lI);
0045 pb=cos((lI+1).*y+lI);
0046 pc=x+a;
0047 pd=y+b;
0048 %
0049 p=sum(lI.*pa,3).*sum(lI.*pb,3)+pc.^2+pd.^2;
0050 
0051 %
0052 if nargout==2
0053     %
0054     dp=zeros(size(xx));
0055     %
0056     dp(:,:,1)=sum(-lI.*(lI-1).*sin((lI-1).*x+lI),3).*sum(lI.*pb,3)+2*pc;
0057     dp(:,:,2)=sum(-lI.*(lI+1).*sin((lI+1).*y+lI),3).*sum(lI.*pa,3)+2*pd;
0058 end
0059 end

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