fields (version 5.02)

Wendland: Wendland family of covariance functions

Description

Computes the compactly supported, stationatry Wendland covariance function as a function ofdistance. This family is useful for creating sparse covariance matrices.

Usage

Wendland(d, theta = 1, dimension, k,derivative=0, phi=1)
Wendland2.2(d, theta=1)
wendland.coef(d,k)

Value

A vector of the covariances or its derivative.

Details

This is the basic function applied to distances and called by the wendland.cov function. It can also be used as the Covariance or Taper specifications in the more general stationary.cov and station.taper.cov functions. The Wendland covariance function is a polynomial on [0,theta] and zero beyond theta. The parameter k detemines the smoothness of the covariance at zero. The polynomial coefficients are computed recursively based on the values of k and dimension in the function wendland.coef. The polynomial is evaluated using fields.evlpoly.

A specific example of the Wendland family is Wendland2.2 and this is included mainly for testing.

See Also

wendland.cov, stationary.taper.cov

Examples

DD<- seq( 0,1.5,, 200)

y<- Wendland( DD, k=2, dimension=2)

plot( DD, y, type="l")

# should agree with 

y.test<- Wendland2.2( DD)