funTrigonometric1

PURPOSE ^

% Trigonometric 1 function

SYNOPSIS ^

function [p,dp] = funTrigonometric1(xx)

DESCRIPTION ^

% Trigonometric 1 function
 L. LAURENT -- 23/02/2017 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Trigonometric 1 function
0002 % L. LAURENT -- 23/02/2017 -- 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 %1 minimum global: f(0,...,0)=0
0025 %
0026 %Design space 0<xi<pi
0027 
0028 
0029 function [p,dp] = funTrigonometric1(xx)
0030 
0031 %constants
0032 nbvar=size(xx,3);
0033 
0034 %evaluation and derivatives
0035 cx=cos(xx);
0036 sx=sin(xx);
0037 %
0038 lI=reshape(1:nbvar,1,1,nbvar);
0039 %
0040 sumcx=sum(cx+lI.*(1-cx-sx),3);
0041 %
0042 pa=nbvar-sumcx(:,:,ones(1,nbvar));
0043 %
0044 p=sum(pa.^2,3);
0045 
0046 if nargout==2
0047     %
0048     dp=2*pa.*(sx+lI.*(-sx+cx))*nbvar;
0049 end
0050 end

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