Exponential, Matern, Radial Basis {fields} | R Documentation

## Covariance functions

### Description

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

### Usage

    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)
    RadialBasis(d,M,dimension)

### Arguments

`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
`M` | Interpreted as a spline M is the order of the derivatives in the penalty.
`dimension` | Dimension of function

### Details

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.

Radial basis functions:

C.m,d d^(2m-dim) dim- odd

C.m,d d^(2m-dim)ln( d) dim-even

where C.m.d is a constant based on spline theory. See `radbas.constant`.

### Value

A vector of covariances.

### Author(s)

Doug Nychka

### References

Stein's book

### See Also

stationary.cov, stationary.image.cov, Wendland,stationary.taper.cov rad.cov

[Package fields version 5.02 Index]