Optimized precision matrix of stationary Gaussian Matern random fields with integer covariance exponent

rspde.matern.precision.integer.opt is used for computing the optimized version of the precision matrix of stationary Gaussian random fields on \(R^d\) with a Matern covariance function $$C(h) = \frac{\sigma^2}{2^{\nu-1}\Gamma(\nu)}(\kappa h)^\nu K_\nu(\kappa h),$$ where \(\alpha = \nu + d/2\) is a natural number.

Usage

rspde.matern.precision.integer.opt(
  kappa,
  nu,
  tau,
  d,
  fem_matrices,
  graph = NULL
)

Arguments

kappa

Range parameter of the covariance function.

nu

Shape parameter of the covariance function.

tau

Scale parameter of the covariance function.

d

The dimension of the domain

fem_matrices

A list containing the FEM-related matrices. The list should contain elements C, G, G_2, G_3, etc.

graph

The sparsity graph of the matrices. If NULL, only a vector of the elements will be returned, if non-NULL, a sparse matrix will be returned.

Value

The precision matrix