funShekel05

PURPOSE ^

% Shekel 5 function

SYNOPSIS ^

function [p,dp] = funShekel05(xx)

DESCRIPTION ^

% Shekel 5 function
 L. LAURENT -- 19/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Shekel 5 function
0002 % L. LAURENT -- 19/02/2017 -- 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 %1 minimum global: f(4,4,4,4)=-10.15270
0025 %
0026 %Design space 0<xi<10
0027 
0028 
0029 function [p,dp] = funShekel05(xx)
0030 
0031 %constants
0032 a=[
0033     4 4 4 4
0034     1 1 1 1
0035     8 8 8 8
0036     6 6 6 6
0037     3 7 3 7
0038     ];
0039 c=0.1*[1 2 2 4 6]';
0040 m=5;
0041 
0042 %evaluation and derivatives
0043 sX=[size(xx,1) size(xx,2) size(xx,3)];
0044 p=zeros(sX(1),sX(2));
0045 for itI=1:m
0046     aI=a(itI,:);
0047     aR=reshape(aI,1,1,[]);
0048     pTmp=xx-aR(ones(1,sX(1)),ones(1:sX(2)),:);
0049     hI=c(itI)+sum(pTmp.^2,3);
0050     p=p-1./hI;
0051 end
0052 
0053 
0054 if nargout==2
0055     %
0056     dp=zeros(sX);
0057     for itI=1:m
0058         aI=a(itI,:);
0059         aR=reshape(aI,1,1,[]);
0060         pTmp=xx-aR(ones(1,sX(1)),ones(1:sX(2)),:);
0061         hI=c(itI)+sum(pTmp.^2,3);
0062         dhI=2*pTmp;
0063         dp=dp+dhI./hI.^2;
0064     end
0065 end
0066 end

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