funPenHolder

PURPOSE ^

% Pen Holder function

SYNOPSIS ^

function [p,dp]=funPenHolder(xx)

DESCRIPTION ^

% Pen Holder function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Pen Holder function
0002 %L. LAURENT -- 17/11/2016 -- 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 %4 global minimas : f(x)=-1.037845 for x=[9.646167708023526, 9.646167671043401;
0026 %-9.646167708023526, 9.646167671043401;
0027 %9.646167708023526, -9.646167671043401;
0028 %-9.646167708023526, -9.646167671043401];
0029 %
0030 %Design space: -11<xi<11
0031 
0032 
0033 function [p,dp]=funPenHolder(xx)
0034 
0035 %constants
0036 a=1;
0037 b=pi;
0038 
0039 %variables
0040 xxx=xx(:,:,1);
0041 yyy=xx(:,:,2);
0042 
0043 %evaluation and derivatives
0044 sxy=a-sqrt(xxx.^2+yyy.^2)/b;
0045 g=exp(abs(sxy));
0046 h=cos(xxx).*cos(yyy);
0047 %
0048 p=-exp(abs(g.*h).^(-1));
0049 
0050 if nargout==2
0051     dgX=-1/b*sign(sxy).*xxx./sqrt(xxx.^2+yyy.^2).*g;
0052     dgY=-1/b*sign(sxy).*yyy./sqrt(xxx.^2+yyy.^2).*g;
0053     dhX=-cos(yyy).*sin(xxx);
0054     dhY=-sin(yyy).*cos(xxx);
0055     %
0056     dp(:,:,1)=-sign(g.*h).*(g.*h).^(-2)...
0057         .*(dgX.*h+dhX.*g).*p;
0058     dp(:,:,2)=-sign(g.*h).*(g.*h).^(-2)...
0059         .*(dgY.*h+dhY.*g).*p;
0060 end
0061 end

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