funWeierstrass

PURPOSE ^

% Weierstrass function

SYNOPSIS ^

function [p,dp] = funWeierstrass(xx)

DESCRIPTION ^

% Weierstrass function
 L. LAURENT -- 28/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Weierstrass function
0002 % L. LAURENT -- 28/02/2017 -- 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 -1/2<xi<1/2
0027 
0028 function [p,dp] = funWeierstrass(xx)
0029 
0030 %constants
0031 a=1/2;
0032 b=3;
0033 k=20;
0034 c=2*pi;
0035 d=1/2;
0036 e=pi;
0037 nbvar=size(xx,3);
0038 
0039 %evaluation and derivatives
0040 lik=reshape(0:k,1,1,1,[]);
0041 %
0042 pa=a.^lik.*cos(c*b.^lik.*(xx+d));
0043 pb=a.^lik.*cos(e*b.^lik);
0044 %
0045 pAA=sum(pa,4);
0046 pBB=sum(pb,4);
0047 %
0048 p=sum(pAA,3)-nbvar*pBB;
0049 
0050 pp=zeros(size(xx,1),size(xx,2));
0051 for itD=1:nbvar
0052     for itk=0:k
0053         pp=pp+a.^itk.*cos(c*b.^itk.*(xx(:,:,itD)-d));
0054     end
0055 end
0056 for itk=0:k
0057         pp=pp-nbvar*a.^itk.*cos(e*b.^itk);
0058 end
0059 
0060 %keyboard
0061 
0062 if nargout==2
0063     dpd=zeros(size(xx));
0064     for itk=0:k
0065         dpd=dpd-a.^itk.*c.*b^itk.*sin(c*b.^itk.*(xx+d));
0066     end
0067     dp=sum(-a.^lik.*b.^lik.*c.*sin(c*b.^lik.*(xx+d)),4); 
0068     %keyboard
0069 end
0070 end
0071

Generated on Tue 28-May-2019 16:00:34 by m2html © 2005