funAckley1

PURPOSE ^

% Ackley's function 1

SYNOPSIS ^

function [p,dp]=funAckley1(xx)

DESCRIPTION ^

% Ackley's function 1
L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Ackley's function 1
0002 %L. LAURENT -- 31/10/2016 -- 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 %numerous local minima
0026 %1 global minimum : x=(0,0,...,0) >> f(x)=0
0027 %
0028 %design space -35<xi<35 (small range -2<xi<2)
0029 
0030 function [p,dp]=funAckley1(xx)
0031 
0032 %constants
0033 a=20;
0034 b=0.02;
0035 c=2*pi;
0036 d=exp(1);
0037 
0038 %number of variables
0039 nbvar=size(xx,3);
0040 
0041 %responses and derivatives
0042 normP=sqrt(sum(xx.^2,3));
0043 ex1=exp(-b*normP/sqrt(nbvar));
0044 sco=sum(cos(c*xx),3);
0045 ex2=exp(1/nbvar*sco);
0046 p=-a*ex1-ex2+a+d;
0047 
0048 if nargout==2
0049     dp=a*b*1/sqrt(nbvar)*xx./normP.*ex1+c/nbvar*sin(c*xx).*ex2;
0050 end
0051 end

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