funShubert3

PURPOSE ^

% Shubert 3 function

SYNOPSIS ^

function [p,dp] = funShubert3(xx)

DESCRIPTION ^

% Shubert 3 function
 L. LAURENT -- 19/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Shubert 3 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(5.791794,5.791794)=-24.062499
0025 %
0026 %Design space -10<xi<10
0027 
0028 
0029 function [p,dp] = funShubert3(xx)
0030 
0031 %constants
0032 a=5;
0033 
0034 %evaluation and derivatives
0035 sX=size(xx);
0036 %
0037 lI=1:a;
0038 lI=reshape(lI,1,1,[]);
0039 lI=lI(ones(1,sX(1)),ones(1,sX(2)),:);
0040 %
0041 fun=@(I,X)I.*sin((I+1).*X+I);
0042 %
0043 p=zeros(sX(1),sX(2));
0044 %
0045 for itX=1:sX(3)
0046     h=fun(lI,xx(:,:,itX));
0047     p=p-sum(h,3);
0048 end
0049 
0050 if nargout==2
0051     %
0052     dp=zeros(sX);
0053     funD=@(I,X)I.*(I+1).*cos((I+1).*X+I);
0054     %
0055     for itX=1:sX(3)
0056         dh=funD(lI,xx(:,:,itX));
0057         dp(:,:,itX)=-sum(dh,3);
0058     end
0059 end
0060 end

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