funMishra08

PURPOSE ^

% Mishra 8 function

SYNOPSIS ^

function [p,dp]=funMishra08(xx)

DESCRIPTION ^

% Mishra 8 function
L. LAURENT -- 17/11/2016 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Mishra 8 function
0002 %L. LAURENT -- 17/11/2016 -- 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 %global minimum : f(x)=0 for x=(2,-3)
0026 %
0027 %Design space: -10<xi<10
0028 
0029 
0030 function [p,dp]=funMishra08(xx)
0031 
0032 %constants
0033 aa=0.001;
0034 a=[1,-20,180,-960,3360,-8064,1334,-15360,11520,-5120,2624];
0035 b=[1,12,54,108,81];
0036 
0037 %variables
0038 xxx=xx(:,:,1);
0039 yyy=xx(:,:,2);
0040 
0041 %evaluation and derivatives
0042 itg=reshape(10:-1:0,1,1,11);
0043 gt=bsxfun(@power,xxx,itg);
0044 g=bsxfun(@times,gt,reshape(a(11-itg),1,1,11));
0045 ith=reshape(4:-1:0,1,1,5);
0046 ht=bsxfun(@power,yyy,ith);
0047 h=bsxfun(@times,ht,reshape(b(5-ith),1,1,5));
0048 %
0049 pa=abs(sum(h,3)).*abs(sum(g,3));
0050 p=aa*pa.^2;
0051 
0052 if nargout==2
0053     itdg=reshape(10:-1:1,1,1,10);
0054     dgt=bsxfun(@power,xxx,itdg-1);    
0055     dgtt=bsxfun(@times,dgt,itdg);
0056     dg=bsxfun(@times,dgtt,reshape(a(11-itdg),1,1,10));
0057     itdh=reshape(4:-1:1,1,1,4);
0058     dht=bsxfun(@power,yyy,itdh-1);
0059     dhtt=bsxfun(@times,dht,itdh);
0060     dh=bsxfun(@times,dhtt,reshape(b(5-itdh),1,1,4));
0061     %
0062     dp(:,:,1)=2*aa*sign(sum(g,3)).*abs(sum(h,3)).*sum(dg,3).*pa;
0063     dp(:,:,2)=2*aa*sign(sum(h,3)).*abs(sum(g,3)).*sum(dh,3).*pa;
0064 end
0065 end

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