funCarromTable

PURPOSE ^

% CarromTable function

SYNOPSIS ^

function [p,dp]=funCarromTable(xx)

DESCRIPTION ^

% CarromTable function 
L. LAURENT -- 14/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% CarromTable function
0002 %L. LAURENT -- 14/03/2017 -- 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)=-24.15681551650653 for xi=+/- 9.646157266348881
0026 %
0027 %Design space: -10<xi<10
0028 
0029 
0030 function [p,dp]=funCarromTable(xx)
0031 %constants
0032 a=30;
0033 b=2;
0034 c=1;
0035 d=pi;
0036 
0037 %evaluation and derivatives
0038 x=xx(:,:,1);
0039 y=xx(:,:,2);
0040 %
0041 xy=sqrt(x.^2+y.^2);
0042 fxy=c-xy./d;
0043 %
0044 pa=exp(b*abs(fxy));
0045 cx=cos(x);
0046 cy=cos(y);
0047 %
0048 p=-1/a*pa.*cx.^2.*cy.^2;
0049 
0050 if nargout==2
0051     %
0052     dp=-b/d*xx./xy.*sign(fxy).*p...
0053         +2*sin(xx).*cos(xx)./a.*pa.*cos(xx(:,:,[2 1])).^2;
0054 end
0055 end

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