funKatsuura

PURPOSE ^

% Katsuura function

SYNOPSIS ^

function [p,dp]=funKatsuura(xx)

DESCRIPTION ^

% Katsuura function
L. LAURENT -- 17/03/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Katsuura function
0002 %L. LAURENT -- 17/03/2017 -- 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 for xi=0
0026 %
0027 %Design space: 0<xi<100
0028 %
0029 
0030 
0031 
0032 function [p,dp]=funKatsuura(xx)
0033 %constants
0034 d=32;
0035 
0036 %evaluation and derivatives
0037 sX=size(xx,3);
0038 %
0039 lD=reshape(1:d,1,1,1,d);
0040 lI=reshape(1:sX,1,1,sX);
0041 %
0042 pa=2.^lD.*xx;
0043 pbf=floor(pa).*2.^lD;
0044 %
0045 spb=sum(pbf,4);
0046 pt=1+lI.*spb;
0047 %
0048 p=prod(pt,3);
0049 
0050 %
0051 if nargout==2
0052     %
0053     dp=zeros(size(xx));
0054     %
0055     isInteger =@(input) (imag(input) == 0) & (round(input) == input);
0056     %
0057     dp(isInteger(xx))=1/eps;
0058 end
0059 end

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