kernel_exp {SpatialGEV}

Exponential covariance function

Description

Exponential covariance function

Usage

kernel_exp(x, sigma, ell, X1 = NULL, X2 = NULL)

Arguments

x

Distance measure.

sigma

The scale parameter with the constraint of sigma > 0

ell

The range/lengthscale parameter with the constraint of ell > 0.

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*exp(-x/ell)

Value

A matrix or a scalar of exponential 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_exp(sigma=2, ell=1, X1=X1, X2=X2)

kernel_exp(as.matrix(stats::dist(X1)), sigma=2, ell=1)