funRump

PURPOSE ^

% Rump function

SYNOPSIS ^

function [p,dp] = funRump(xx)

DESCRIPTION ^

% Rump function
 L. LAURENT -- 14/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Rump function
0002 % L. LAURENT -- 14/02/2017 -- 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(0,0)=0
0025 %
0026 %Design space -500<xi<500
0027 
0028 
0029 function [p,dp] = funRump(xx)
0030 
0031 %constants
0032 a=333.75;
0033 b=11;
0034 c=121;
0035 d=2;
0036 e=5.5;
0037 f=2;
0038 
0039 %evaluation and derivatives
0040 x=xx(:,:,1);
0041 y=xx(:,:,2);
0042 p=(a-x.^2).*y.^6 ...
0043     +x.^2.*(b*x.^2.*y.^2-c*y.^4-d) ...
0044     +e*y.^8+x./(f*y);
0045 
0046 if nargout==2
0047     %
0048     dp=zeros(size(xx));
0049     dp(:,:,1)=-2*x.*y.^6 ...
0050         +2*x.*(b*x.^2.*y.^2-c*y.^4-d) ...
0051         +2*b*x.^3.*y.^2 ...
0052         +1./(f*y);
0053     dp(:,:,2)=6*y.^5.*(a-x.^2) ...
0054         +x.^2.*(2*b*x.^2.*y-4*c*y.^3) ...
0055         +8*e*y.^7 ...
0056         -x./(f*y.^2);
0057 end
0058 end

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