funRipple01

PURPOSE ^

% Ripple 25 function

SYNOPSIS ^

function [p,dp]=funRipple01(xx)

DESCRIPTION ^

% Ripple 25 function
L. LAURENT -- 12/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Ripple 25 function
0002 %L. LAURENT -- 12/02/2017 -- 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 %
0025 %1 minimum global: x=0 >> f(-0.1,-0.1)=-2.2
0026 %
0027 %Design space 0<xi<1
0028 
0029 function [p,dp]=funRipple01(xx)
0030 
0031 %constants
0032 a=2;
0033 b=0.1;
0034 c=0.8;
0035 d=5*pi;
0036 e=500*pi;
0037 
0038 %evaluation and derivatives
0039 pa=(xx-b)./c;
0040 pb=-a*log(a)*pa.^2;
0041 pc=-exp(pb);
0042 sd=sin(d*xx);
0043 ce=cos(e*xx);
0044 pd=sd.^6+b*ce.^2;
0045 cal=pc.*pd;
0046 %
0047 p=sum(cal,3);
0048 
0049 if nargout==2
0050     dpd=6*d*sd.^5.*cos(d*xx)-2*e*b*ce.*sin(e*xx);
0051     dpb=-2*a*log(a).*pa.*pc./c;
0052     %
0053     dp=dpb.*pd+pc.*dpd;
0054 end
0055 
0056 end

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