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deriv2

PURPOSE ^

High order partial derivatives of the Gaussian kernel.

SYNOPSIS ^

k=deriv2(x,y,d)

DESCRIPTION ^

 DERIV2  High order partial derivatives of the Gaussian kernel. 
  
  CALL:  k = deriv2(x,y,dstr) 
  
   k   =  partial derivatives of the 2D Gaussian kernel   
          at the point (X,Y). 
  x,y  = evaluation points 
  dstr = string defininfg the type of partial derivative 
  
  Example: 4'th p. derivative wrt. x and 2'nd p. derivative wrt. y at (0,0) 
  
           k42=deriv2(0,0,'42') 
  
  See also  deriv

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function k=deriv2(x,y,d) 
002 %DERIV2  High order partial derivatives of the Gaussian kernel. 
003 % 
004 % CALL:  k = deriv2(x,y,dstr) 
005 % 
006 %  k   =  partial derivatives of the 2D Gaussian kernel   
007 %         at the point (X,Y). 
008 % x,y  = evaluation points 
009 % dstr = string defininfg the type of partial derivative 
010 % 
011 % Example: 4'th p. derivative wrt. x and 2'nd p. derivative wrt. y at (0,0) 
012 % 
013 %          k42=deriv2(0,0,'42') 
014 % 
015 % See also  deriv 
016  
017 %tested on: matlab 5.3 
018 %revised pab 16.10.1999 
019 %  updated to matlab 5.x + documentation 
020 % from kdetools by   Christian C. Beardah 1995 
021  
022 k=zeros(size(x)); 
023  
024 xd=str2num(d(1)); 
025 yd=str2num(d(2)); 
026  
027 switch xd, 
028 case 0, 
029   xterm=1; 
030 case 2, 
031   xterm=x.^2-1;   
032 case 4, 
033   xterm=x.^4-6*x.^2+3; 
034 case 6, 
035   xterm=x.^6-15*x.^4+45*x.^2-15; 
036 case 8, 
037   xterm=x.^8-28*x.^6+210*x.^4-420*x.^2+105; 
038 end; 
039 switch yd, 
040 case 0, 
041   yterm=1; 
042 case 2, 
043   yterm=y.^2-1;   
044 case 4, 
045   yterm=y.^4-6*y.^2+3; 
046 case 6, 
047   yterm=y.^6-15*y.^4+45*y.^2-15; 
048 case 8, 
049   yterm=y.^8-28*y.^6+210*y.^4-420*y.^2+105; 
050 end; 
051  
052 k=xterm.*yterm.*mkernel(x,y,'gauss');

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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