Wendland {fields} | R Documentation

## 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)

### Arguments

`d` | Distances between locations. Or for wendland.coef the dimension of the locations.
`theta` | Scale for distances. This is the same as the range parameter.
`dimension` | Dimension of the locations
`k` | Order of covariance function.
`derivative` | Indicates derivative of covariance function
`phi` | Scale factor to multiply the function. Equivalent to the marginal variance or sill if viewed as a covariance function.

### 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.

### Value

A vector of the covariances or its derivative.

### Author(s)

Doug Nychka

### 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)

[Package fields version 5.02 Index]