| Library: | kernel |
| See also: | rkernpq repa rqua rtrian runi tri |
| Quantlet: | rtri | |
| Description: | computes the radial symmetric triweight kernel |
| Usage: | y = rtri (x) | |
| Input: | ||
| x | n x d matrix of user-defined data for which the kernel is to be computed | |
| Output: | ||
| y | n x 1 matrix containing the radial triweight kernel | |
library("kernel") ; load library kernel
d = 3 ; choose dimension
n = 1000 ; choose n points uniformly in [-1,1]^d
x = 2*uniform(n,d)-1
y = rtri(x) ; compute kernel values
; approximate the integral about the kernel
; function in [-1,1]^d
sum(y.*2^d/n)
Independent of d you should get approximately 1 as result. Note that for higher dimensions n has to be increased!
library("kernel") ; load kernel library
library("plot") ; load plot library
d = 2 ; choose dimension
o = matrix(d) ; create uniform grid in [-1,1]^d
n = 50.*o
h = 2/(n-1).*o
x0 = -o
x = grid(x0, h, n)
y = rtri(x) ; compute kernel values
plot(x~y) ; show kernel function(d<3)
Shows the radial triweight kernel. Note that d can only take the values d=1 or d=2 to show something useful!