% Paviani function L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net
0001 %% Paviani function 0002 %L. LAURENT -- 17/11/2016 -- 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(x)=-45.778 for x=[9.351,...,9.351] 0026 % 0027 %Design space: 2.0001<xi<10 0028 0029 0030 function [p,dp]=funPaviani(xx) 0031 0032 %constants 0033 a=2; 0034 b=10; 0035 c=0.2; 0036 0037 %evaluation and derivatives 0038 dim=size(xx,3); 0039 xa=xx-a; 0040 xb=b-xx; 0041 la=log(xa); 0042 lb=log(xb); 0043 % 0044 pa=sum(la.^2+lb.^2,3); 0045 pb=prod(xx,3); 0046 p=pa-pb.^c; 0047 0048 if nargout==2 0049 funP=@(i)prod(xx(:,:,[1:i-1 i+1:end]),3); 0050 pd=arrayfun(funP,1:dim,'UniformOutput',false); 0051 pd=cell2mat(reshape(pd,1,1,dim)); 0052 % 0053 dp=2*la./xa-2*lb./xb-c*bsxfun(@times,pb.^(c-1),pd); 0054 end 0055 end