funKowalik

PURPOSE ^

% Kowalik function

SYNOPSIS ^

function [p,dp]=funKowalik(xx)

DESCRIPTION ^

% Kowalik function
L. LAURENT -- 17/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Kowalik function
0002 %L. LAURENT -- 17/03/2017 -- 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)=0.00030748610 for x=[0.192833 0.190836 0.123117
0026 %0.135766]
0027 %
0028 %Design space: -5<xi<5
0029 %
0030 
0031 
0032 
0033 function [p,dp]=funKowalik(xx)
0034 %constants
0035 m=11;
0036 a = [0.1957, 0.1947, 0.1735, 0.1600, 0.0844,...
0037     0.0627, 0.0456, 0.0342, 0.0323, 0.0235,...
0038     0.0246];
0039 b =[4,   2,   1,    1/2,  1/4,...
0040     1/6, 1/8, 1/10, 1/12, 1/14,...
0041     1/16];
0042 a=reshape(a,1,1,m);
0043 b=reshape(b,1,1,m);
0044 
0045 
0046 %evaluation and derivatives
0047 x=xx(:,:,1);
0048 y=xx(:,:,2);
0049 z=xx(:,:,3);
0050 w=xx(:,:,4);
0051 %
0052 pa=b.^2+b.*y;
0053 pb=b.^2+b.*z+w;
0054 %
0055 pt=a-x.*pa./pb;
0056 %
0057 p=sum(pt.^2,3);
0058 %
0059 if nargout==2
0060     %
0061     dp=zeros(size(xx));
0062     %
0063     dp(:,:,1)=sum(-2*pa./pb.*pt,3);
0064     dp(:,:,2)=sum(-2*b.*x./pb.*pt,3);
0065     dp(:,:,3)=sum(2*b.*x.*pa./pb.^2.*pt,3);
0066     dp(:,:,4)=sum(2*x.*pa./pb.^2.*pt,3);
0067 end
0068 end

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