funShubert1

PURPOSE ^

% Shubert 1 function

SYNOPSIS ^

function [p,dp] = funShubert1(xx)

DESCRIPTION ^

% Shubert 1 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 1 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(7.0835,4.8580)=-186.7309
0025 %
0026 %Design space -10<xi<10
0027 
0028 
0029 function [p,dp] = funShubert1(xx)
0030 
0031 %constants
0032 a=5;
0033 
0034 %evaluation and derivatives
0035 sX=size(xx);
0036 da=ones(1,a);
0037 x=xx(:,:,1);x=x(:,:,da);
0038 y=xx(:,:,2);y=y(:,:,da);
0039 lI=1:a;
0040 lI=reshape(lI,1,1,[]);
0041 lI=lI(ones(1,sX(1)),ones(1,sX(2)),:);
0042 %
0043 fun=@(I,X)I.*cos((I+1).*X+I);
0044 %
0045 h=fun(lI,x);
0046 g=fun(lI,y);
0047 %
0048 p=sum(h,3).*sum(g,3);
0049 
0050 if nargout==2
0051     %
0052     dp=zeros(sX);
0053     funD=@(I,X)-I.*(I+1).*sin((I+1).*X+I);
0054     %
0055     dH=funD(lI,x);
0056     dG=funD(lI,y);
0057     %
0058     dp(:,:,1)=sum(dH,3).*sum(g,3);
0059     dp(:,:,2)=sum(h,3).*sum(dG,3);
0060 end
0061 end

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