funAMGM

PURPOSE ^

% AMGM function (Arthmetic Mean - Geometric Mean)

SYNOPSIS ^

function [p,dp]=funAMGM(xx)

DESCRIPTION ^

% AMGM function (Arthmetic Mean - Geometric Mean)
L. LAURENT -- 13/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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

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