Matérn covariance kernels

Computes Matérn kernels for smoothness parameters \(\nu = 1/2\), \(3/2\), and \(5/2\). A scalar length scale gives an isotropic distance; one length scale per input dimension gives ARD.

Usage

kernel_matern12(x, y = NULL, variance = 1, length_scale = 1)

kernel_matern32(x, y = NULL, variance = 1, length_scale = 1)

kernel_matern52(x, y = NULL, variance = 1, length_scale = 1)

Arguments

x

Numeric vector or matrix. Matrix rows are observations and columns are input dimensions.

y

Optional numeric vector or matrix with the same number of input dimensions as x. If NULL, computes the covariance of x with itself.

variance

Positive marginal variance.

length_scale

Positive scalar or numeric vector with one value per input dimension. A vector enables ARD.

Value

A numeric covariance matrix.

Stability

Stable: from version 1.0.0 this interface changes incompatibly only in a major release, after a deprecation period. Results and options that concern an experimental model class, kernel, or argument follow that interface's tier. See gaussianprocesses-package for the policy.

See also

matern_kernel_specs for the same kernels as reusable specifications, which can be combined, optimized, and used in models.

Examples

x <- seq(0, 2, by = 0.5)

# Smoothness increases from nu = 1/2 to nu = 5/2.
kernel_matern12(x, length_scale = 0.7)[1, ]
#> [1] 1.00000000 0.48954166 0.23965104 0.11731917 0.05743262
kernel_matern32(x, length_scale = 0.7)[1, ]
#> [1] 1.00000000 0.64923315 0.29260009 0.11514960 0.04219131
kernel_matern52(x, length_scale = 0.7)[1, ]
#> [1] 1.00000000 0.69800227 0.31136332 0.11158216 0.03527718