funAlpine2

PURPOSE ^

% Alpine's function 2

SYNOPSIS ^

function [p,dp]=funAlpine2(xx)

DESCRIPTION ^

% Alpine's function 2
L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Alpine's function 2
0002 %L. LAURENT -- 31/10/2016 -- 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 %numerous local minima
0026 %1 global minimum : x=(7.917,7.917,...,7.917) >> f(x)=2.808^p
0027 %
0028 %design space 0<xi<10
0029 
0030 
0031 
0032 function [p,dp]=funAlpine2(xx)
0033 
0034 %number of variables
0035 nbvar=size(xx,3);
0036 
0037 %responses and derivatives
0038 fx=sqrt(xx).*sin(xx);
0039 p=prod(fx,3);
0040 
0041 if nargout==2
0042     dp=zeros(size(xx));
0043     for itV=1:nbvar
0044         itF=[1:(itV-1) (itV+1):nbvar];
0045         dp(:,:,itV)=prod(fx(:,:,itF),3).*...
0046             (0.5./sqrt(xx(:,:,itV)).*sin(xx(:,:,itV))+sqrt(xx(:,:,itV)).*cos(xx(:,:,itV)));
0047     end
0048 end
0049 end

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