% AMGM function (Arthmetic Mean - Geometric Mean) L. LAURENT -- 13/03/2017 -- luc.laurent@lecnam.net
0001 %% AMGM function (Arthmetic Mean - Geometric Mean) 0002 %L. LAURENT -- 13/03/2017 -- 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)=0 for x1=x2=x3=...=xn 0026 % 0027 %Design space: 0<xi<10 0028 0029 0030 function [p,dp]=funAMGM(xx) 0031 0032 %variables 0033 dim=size(xx,3); 0034 0035 %evaluation and derivatives 0036 pa=sum(xx,3); 0037 pb=prod(xx,3); 0038 pc=1/dim*pa-pb.^(1/dim); 0039 % 0040 p=pc.^2; 0041 0042 if nargout==2 0043 % 0044 funP=@(i)prod(xx(:,:,[1:i-1 i+1:end]),3); 0045 pdA=arrayfun(funP,1:dim,'UniformOutput',false); 0046 pdA=cell2mat(reshape(pdA,1,1,dim)); 0047 % 0048 pdB=1/dim-pdA.*pb.^(1/dim-1)./dim; 0049 % 0050 dp=2*pdB.*pc; 0051 end 0052 end