funAckley3

PURPOSE ^

% Ackley's function 3

SYNOPSIS ^

function [p,dp]=funAckley3(xx)

DESCRIPTION ^

% Ackley's function 3
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 3
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 %one local minimum
0026 %1 global minimum : x=(0,-0.4) >> f(x)=-219.1418
0027 %
0028 %design space -32<xi<32
0029 
0030 
0031 
0032 function [p,dp]=funAckley3(xx)
0033 
0034 %constants
0035 a=200;
0036 b=0.02;
0037 c=5;
0038 d=3;
0039 
0040 %responses and derivatives
0041 normP=sqrt(sum(xx.^2,3));
0042 ex1=exp(-b*normP);
0043 ex2=exp(cos(d*xx(:,:,1))+sin(d*xx(:,:,2)));
0044 p=-a*ex1-c*ex2;
0045 
0046 if nargout==2
0047     dp=a*b*xx./normP.*ex1;
0048     %
0049     dp(:,:,1)=dp(:,:,1)+c*d*sin(d*xx(:,:,1)).*ex2;
0050     dp(:,:,2)=dp(:,:,2)-c*d*cos(d*xx(:,:,2)).*ex2;
0051 end
0052 end

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