Rational approximation of the Matern covariance

Computes a rational approximation of the Matern covariance function on intervals.

Usage

matern.rational.cov(
  h,
  order,
  kappa,
  nu,
  sigma,
  type_rational = "brasil",
  type_interp = "linear",
  wl2_table = NULL
)

Arguments

h

Lags at which to compute the covariance. May also be a matrix of lags, in which case a matrix of the same shape is returned.

order

The order of the approximation

kappa

Range parameter

nu

Smoothness parameter

sigma

Standard deviation

type_rational

Method used to compute the coefficients of the rational approximation.

type_interp

Interpolation method for the rational coefficients.

wl2_table

Table of weighted-L2 coefficients, only used for type_rational = "wl2". If NULL, it is taken from the tables stored in the package where there is one for this configuration, and computed otherwise.

Value

The covariance matrix of the approximation

Examples

h <- seq(from = 0, to = 1, length.out = 100)
cov.true <- matern.covariance(h, kappa = 10, sigma = 1, nu = 0.8)
cov.approx <- matern.rational.cov(h, kappa = 10, sigma = 1, nu = 0.8, order = 2)

plot(h, cov.true)
lines(h, cov.approx, col = 2)