R: Covariance functions

Exponential {fields}

R Documentation

Covariance functions

Functional form of covariance function assuming the argument is a distance between locations.

Exponential(d, range = 1, alpha = 1/range, phi = 1)
Matern (d , scale = 1, range = 1,alpha=1/range,
     smoothness = 0.5, nu= smoothness, phi=scale)

`d`	Vector of distances
`range`	Range parameter default is one. Note that the scale can also be specified through the "theta" scaling argument used in fields covariance functions)
`alpha`	1/range
`scale`	Same as phi
`phi`	Marginal variance.
`smoothness`	Smoothness parameter in Matern. Controls the number of derivatives in the process. Default is 1/2 corresponding to an exponential covariance.
`nu`	Same as smoothness

Exponential:

phi* exp( -d/range)

Matern:

phi*con*(d^nu) * besselK(d , nu )

Matern covariance function transcribed from Stein's book page 31 nu==smoothness, alpha == 1/range

GeoR parameters map to kappa==smoothness and phi == range check for negative distances

con is a constant that normalizes the expression to be 1.0 when phi=1.0 and d=0.

A vector of covariances.

Doug Nychka

Stein's book