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