funSchwefel04

PURPOSE ^

% Schwefel 4 function

SYNOPSIS ^

function [p,dp] = funSchwefel04(xx)

DESCRIPTION ^

% Schwefel 4 function
 L. LAURENT -- 19/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Schwefel 4 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(0,...,0)=0
0025 %
0026 %Design space 0<xi<10
0027 
0028 
0029 function [p,dp] = funSchwefel04(xx)
0030 
0031 %constants
0032 a=1;
0033 
0034 %evaluation and derivatives
0035 x1=xx(:,:,1);
0036 pa=xx-a;
0037 pb=x1-xx.^2;
0038 %
0039 p=sum(pa.^2+pb.^2,3);
0040 
0041 if nargout==2
0042     %
0043     dp=zeros(size(xx));
0044     %
0045     dp(:,:,1)=2*(x1-a) ...
0046         + 2*(1-2*x1).*(x1-x1.^2) ...
0047         + 2*sum(pb(:,:,2:end),3);
0048     dp(:,:,2:end)=2*pa(:,:,2:end) ...
0049         - 4*xx(:,:,2:end).*pb(:,:,2:end);
0050 end
0051 end

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