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