kernel_matern: Matern covariance function In SpatialGEV: Fit Spatial Generalized Extreme Value Models

 kernel_matern R Documentation

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 scale parameter. `kappa` Positive inverse range/lengthscale parameter. `nu` Smoothness 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 * 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)
``````

SpatialGEV documentation built on June 22, 2024, 9:24 a.m.