MaternCov: Matern covariance function

In sppmix: Modeling Spatial Poisson and Related Point Processes

Description

Computes the Matern covariance function. Used in the creation of stationary and isotropic Gaussian Random Fields (GRFs).

For examples see

http://faculty.missouri.edu/~micheasa/sppmix/sppmix_all_examples.html#MaternCov

Usage

MaternCov(grid, nu = 0.5, theta = 1, sig = 1)

Arguments

grid	An nx2 matrix of locations over which to compute the covariance matrix or an nxn matrix representing the distances of the n planar points.
nu, theta, sig	Matern model parameters. See details.

Details

The Matern covariance model for two points with Euclidean distance r, is given by

C(r) = sig^2 2^(1-nu) gamma(nu)^(-1) (sqrt(2nu) r/theta)^nu B_nu(sqrt(2nu) r/theta)

where sig, theta, nu>0, and B_nu is the modified Bessel function of second kind. Note that the Matern for nu=.5 reduces to the exponential.

Value

A matrix representing the covariance matrix for a random field (typically a GRF).

Author(s)

Sakis Micheas

See Also

rGRF

Examples

grid=cbind(seq(0,1,length=10), seq(0,1,length=10))
MaternCov(grid)

sppmix documentation built on Jan. 13, 2021, 10:04 p.m.