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
L-stage DPI estimate of smoothing parameter for 2D data | |
L-stage DPI estimate of smoothing parameter for 2D data |
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');
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