funGriewank

PURPOSE ^

% Griewank function

SYNOPSIS ^

function [p,dp]=funGriewank(xx)

DESCRIPTION ^

% Griewank function
L. LAURENT -- 16/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Griewank function
0002 %L. LAURENT -- 16/11/2016 -- 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 for (0,...,0)
0026 %
0027 %Design space: -100<xi<100
0028 
0029 function [p,dp]=funGriewank(xx)
0030 
0031 %constants
0032 a=1/4000;
0033 b=1;
0034 
0035 %evaluation and derivatives
0036 dim=size(xx,3);
0037 div=sqrt(reshape(1:dim,1,1,dim));
0038 pa=bsxfun(@times,xx,1./div);
0039 p=a*sum(xx.^2,3)-prod(cos(pa),3)+b;
0040 %
0041 if nargout==2
0042     funP=@(i)prod(cos(pa(:,:,[1:i-1 i+1:end])),3);
0043     pb=arrayfun(funP,1:dim,'UniformOutput',false);
0044     pb=cell2mat(reshape(pb,1,1,dim));
0045     %
0046     dp=2*a*xx...
0047         +bsxfun(@times,sin(pa),1./div).*pb;
0048 end
0049 end

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