funNewFunction3

PURPOSE ^

% New Function 3 function

SYNOPSIS ^

function [p,dp]=funNewFunction3(xx)

DESCRIPTION ^

% New Function 3 function
L. LAURENT -- 21/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% New Function 3 function
0002 %L. LAURENT -- 21/03/2017 -- 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)=-1.019829 for x=[-1.9862 -10]
0026 %
0027 %Design space: -10<xi<10
0028 %
0029 
0030 
0031 function [p,dp]=funNewFunction3(xx)
0032 %constants
0033 a=0.01;
0034 b=0.1;
0035 
0036 %evaluation and derivatives
0037 x=xx(:,:,1);
0038 y=xx(:,:,2);
0039 %
0040 cx=cos(x);
0041 cy=cos(y);
0042 sx=sin(x);
0043 sy=sin(y);
0044 scxy=sin((cx+cy).^2);
0045 csxy=cos((sx+sy).^2);
0046 %
0047 pa=(x+scxy.^2+csxy.^2);
0048 p=a*x+b*y+pa.^2;
0049 %
0050 if nargout==2
0051     %
0052     dp=zeros(size(xx));
0053     %
0054     ccxy=cos((cx+cy).^2);
0055     ssxy=sin((sx+sy).^2);
0056     %
0057     dp(:,:,1)=a+2*pa.*(1-4*sx.*(cx+cy).*scxy.*ccxy-4*cx.*(sx+sy).*ssxy.*csxy);
0058     dp(:,:,2)=b+2*pa.*(-4*sy.*(cx+cy).*ccxy.*scxy-4*cy.*(sx+sy).*ssxy.*csxy);
0059     %
0060 end

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