kernel_matern {SpatialGEV}

Matern covariance function

Description

Matern covariance function

Usage

kernel_matern(x, sigma, kappa, nu = 1, X1 = NULL, X2 = NULL)

Arguments

x

Distance measure.

sigma

Positive parameter. (This is in fact sigma^2)

kappa

Positive parameter.

nu

Range parameter default to 1.

X1

A ⁠n1 x 2⁠ matrix containing the coordinates of location set 1. If x is not provided, X1 and X2 should be provided for calculating their distance.

X2

A ⁠n2 x 2⁠ coordinate matrix.

Details

Let x = dist(x_i, x_j).

cov(i,j) = sigma * 2^(1-nu)/gamma(nu) * (kappa*x)^nu * K_v(kappa*x)

Note that when nu=0.5, the Matern kernel corresponds to the absolute exponential kernel.

Value

A matrix or a scalar of Matern covariance depending on the type of x or whether X1 and X2 are used instead.

Examples

X1 <- cbind(runif(10, 1, 10), runif(10, 10, 20))
X2 <- cbind(runif(5, 1, 10), runif(5, 10, 20))

kernel_matern(sigma=2, kappa=1, X1=X1, X2=X2)

kernel_matern(as.matrix(stats::dist(X1)), sigma=2, kappa=1)