funAckley4

PURPOSE ^

% Ackley's function 4 (Modified Ackley Function)

SYNOPSIS ^

function [p,dp]=funAckley4(xx)

DESCRIPTION ^

% Ackley's function 4 (Modified Ackley Function)
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 4 (Modified Ackley Function)
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 %xx global minimum : UNDEFINED
0027 % in dimension 2: x{-1.479252, -0.739807), (1.479252, -0.739807)} >> f(x)=-3.917275
0028 %
0029 %design space -35<xi<35 (small range -2<xi<2)
0030 
0031 
0032 
0033 function [p,dp]=funAckley4(xx)
0034 
0035 %constants
0036 a=0.2;
0037 b=3;
0038 c=2;
0039 
0040 %number of variables
0041 nbvar=size(xx,3);
0042 
0043 %responses and derivatives
0044 ex1=exp(-a);
0045 normP=zeros(size(xx,1),size(xx,2),nbvar-1);
0046 for itV=1:nbvar-1
0047     normP(:,:,itV)=sqrt(xx(:,:,itV).^2+xx(:,:,itV+1).^2);
0048 end
0049 cx=cos(c*xx(:,:,1:end-1));
0050 sx=sin(c*xx(:,:,2:end));
0051 p=sum(ex1.*normP+b*(cx+sx),3);
0052 
0053 
0054 if nargout==2
0055     dp=zeros(size(xx));
0056     for ii=1:nbvar
0057         if ii==1
0058             dp(:,:,ii)=ex1*xx(:,:,1)./normP(:,:,1)-c*b*sin(c*xx(:,:,1));
0059         elseif ii==nbvar
0060             dp(:,:,ii)=ex1*xx(:,:,nbvar)./normP(:,:,end)+c*b*cos(c*xx(:,:,nbvar));
0061         else
0062             dp(:,:,ii)=ex1*xx(:,:,ii)./normP(:,:,ii)-c*b*sin(c*xx(:,:,ii))...
0063                 +ex1*xx(:,:,ii+1)./normP(:,:,ii+1)+c*b*cos(c*xx(:,:,ii+1));
0064         end
0065     end
0066 end
0067 end

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