funDixonPrice

PURPOSE ^

% Dixon & Price's function

SYNOPSIS ^

function [p,dp]=funDixonPrice(xx)

DESCRIPTION ^

% Dixon & Price's function
L. LAURENT -- 15/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Dixon & Price's function
0002 %L. LAURENT -- 15/11/2016 -- 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 %one local minimum
0026 %1 global minimum : x={(4.70104,3.15294),(?1.58214, ?3.13024)} >> f(x)=?106.764537
0027 %
0028 %design space -10<xi<10
0029 
0030 
0031 function [p,dp]=funDixonPrice(xx)
0032 
0033 %constants
0034 a=1;
0035 b=2;
0036 
0037 %evaluations and derivatives
0038 dim=size(xx,3);
0039 pa=(xx(:,:,1)-a).^2;
0040 ii=reshape(2:dim,1,1,[]);
0041 pb=b*xx(:,:,2:end).^2-xx(:,:,1:end-1);
0042 pc=bsxfun(@times,pb.^2,ii);
0043 p=pa+sum(pc,3);
0044 
0045 if nargout==2
0046     pd=bsxfun(@times,pb,ii);
0047     %
0048     dp=zeros(size(xx));
0049     dp(:,:,1)=2*(xx(:,:,1)-a)-2*pd(:,:,1);
0050     for it=2:dim-1
0051         try
0052         dp(:,:,it)=4*b*it*xx(:,:,it).*pb(:,:,it-1)...
0053             -2*(it+1)*pb(:,:,it);
0054         catch
0055             keyboard
0056         end
0057     end    
0058     dp(:,:,dim)=4*b*dim.*xx(:,:,end).*pb(:,:,end);
0059 end
0060 end

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