% Watson function L. LAURENT -- 27/02/2017 -- luc.laurent@lecnam.net
0001 %% Watson function 0002 % L. LAURENT -- 27/02/2017 -- 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(-0.0158,1.012,-0.2329,1.26,-1.513,0.9928)=0.002288 0025 % 0026 %Design space 0.25<xi<10 0027 0028 %% NEED TO BE FIXED 0029 0030 function [p,dp] = funWatson(xx) 0031 0032 0033 0034 %constants 0035 a=29; 0036 b=4; 0037 c=5; 0038 d=@(i) i/a; 0039 0040 %evaluation and derivatives 0041 % 0042 liJ=reshape(0:b,1,1,[]); 0043 liL=reshape(0:c,1,1,[]); 0044 % 0045 sX=size(xx); 0046 % 0047 pp=zeros(sX(1),sX(2),a); 0048 for itI=0:a 0049 pA=(liJ-1).*d(itI).^liJ.*xx(:,:,1:b+1); 0050 pB=d(itI).^liL.*xx(:,:,1:c+1); 0051 pp(:,:,itI+1)=sum(pA,3)-sum(pB,3).^2-1; 0052 end 0053 % 0054 p=sum(pp.^2,3)+xx(:,:,1).^2; 0055 0056 if nargout==2 0057 % 0058 dp=zeros(sX); 0059 pdp=zeros(sX(1),sX(2),a); 0060 % 0061 for itI=0:a 0062 pB=d(itI).^liL.*xx(:,:,1:c+1); 0063 pdp(:,:,itI+1)=-pp(:,:,itI+1).*(1+2*sum(pB,3)); 0064 end 0065 dp(:,:,1)=2*xx(:,:,1)+2*sum(pdp,3); 0066 % 0067 pdp=zeros(sX(1),sX(2),a); 0068 % 0069 for itD=2:sX(3) 0070 for itI=0:a 0071 pB=d(itI).^liL.*xx(:,:,1:c+1); 0072 pdp(:,:,itI+1)=pp(:,:,itI+1).*d(itI).^(itD-1).*(itD-2-2*sum(pB,3)); 0073 end 0074 dp(:,:,itD)=2*sum(pdp,3); 0075 end 0076 0077 end 0078 end 0079