funBrown

PURPOSE ^

% Brown's function

SYNOPSIS ^

function [p,dp]=funBrown(xx)

DESCRIPTION ^

% Brown's function
L. LAURENT -- 16/05/2012 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Brown's function
0002 %L. LAURENT -- 16/05/2012 -- 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=(0,0,...,0) >> f(x)=0
0027 %
0028 %design space -1<xi<4
0029 
0030 
0031 
0032 function [p,dp]=funBrown(xx)
0033 
0034 %handle functions
0035 funG=@(x,y)exp((y.^2+1).*log(x.^2))+exp((x.^2+1).*log(y.^2));
0036 funDxG=@(x,y)2*(y.^2+1)./x.*exp((y.^2+1).*log(x.^2))+2*x.*log(y.^2).*exp((x.^2+1).*log(y.^2));
0037 funDyG=@(x,y)2*y.*log(x.^2).*exp((y.^2+1).*log(x.^2))+2*(x.^2+1)./y.*exp((x.^2+1).*log(y.^2));
0038 
0039 %evaluation and derivatives
0040 tSum=funG(xx(:,:,1:end-1),xx(:,:,2:end));
0041 p=sum(tSum,3);
0042 if nargout==2
0043     sX=size(xx);
0044     nbvar=sX(3);
0045     dp=zeros(sX);
0046     for ii=1:nbvar
0047         if ii==1
0048             dp(:,:,ii)=funDxG(xx(:,:,1),xx(:,:,2));
0049         elseif ii==nbvar
0050             dp(:,:,ii)=funDyG(xx(:,:,nbvar-1),xx(:,:,nbvar));
0051         else
0052             dp(:,:,ii)=funDxG(xx(:,:,ii),xx(:,:,ii+1))...
0053                 +funDyG(xx(:,:,ii-1),xx(:,:,ii));
0054         end
0055     end
0056 end
0057 end

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