| Library: | kernel |
| See also: | repa rqua rtri rtrian runi |
| Quantlet: | rkernpq | |
| Description: | Computes the radial kernel of the form: C (1-r^q)^p. |
| Usage: | y = rkernpq (x, p, q) | |
| Input: | ||
| x | n x d matrix of user-defined data | |
| p | scalar, positive integer | |
| q | scalar, positive integer | |
| Output: | ||
| y | n x 1 matrix containing the radial kernel | |
p=1 q=1 triangle
p=0 q=. uniform
p=1 q=2 epanechnikov
p=2 q=2 quartic/biweight
p=3 q=2 triweight
; Quartic kernel in d dimensions
library("kernel")
p = 2
q = 2
d = 3
; choose n points, uniformly distributed in [-1,1]^d
n = 1000
x = 2*uniform(n,d)-1
; compute kernel values
y = rkernpq(x, p, q)
; approximate the integral about the kernel
; function in [-1,1]^d
sum(y.*2^d/n)
Independent of p, q and d you should get approximately 1 as result. Note that for higher dimensions n has to be increased!
; Quartic kernel in d dimensions
library("kernel")
p = 2
q = 2
d = 2
; create uniform grid in [-1,1]^d
o = matrix(d)
n = 50.*o
h = 2/(n-1).*o
x0 = -o
x = grid(x0, h, n)
; compute kernel values
y = rkernpq(x, p, q)
; show kernel function(d<3)
library("plot")
plot(x~y)
Shows the radial kernel. Note that d can only take the values d=1 or d=2 to show something useful!