% Power Sum function L. LAURENT -- 23/03/2017 -- luc.laurent@lecnam.net
0001 %% Power Sum function 0002 %L. LAURENT -- 23/03/2017 -- 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 % 0025 %global minimum : f(x)=0 for xi=[1,2,2,3] 0026 % 0027 %Design space: 0<xi<4 0028 % 0029 0030 function [p,dp]=funPowerSum(xx) 0031 %constants 0032 b=[8,18,44,114]; 0033 b=reshape(b,1,1,1,4); 0034 0035 %evaluation and derivatives 0036 liK=reshape(1:4,1,1,1,4); 0037 pa=xx.^liK; 0038 % 0039 p=sum((sum(pa,3)-b).^2,4); 0040 % 0041 if nargout==2 0042 % 0043 dp=sum(2*liK.*xx.^(liK-1).*(sum(pa,3)-b),4); 0044 end