Optimized precision matrix of the covariance-based rational approximation

rspde.matern.precision is used for computing the optimized version of the precision matrix of the covariance-based rational SPDE approximation of a stationary Gaussian random fields on \(R^d\) with a Matern covariance function $$C(h) = \frac{\sigma^2}{2^{\nu-1}\Gamma(\nu)}(\kappa h)^\nu K_\nu(\kappa h).$$

Usage

rspde.matern.precision.opt(
  kappa,
  nu,
  tau,
  rspde.order,
  dim,
  fem_matrices,
  graph = NULL,
  sharp,
  type_rational_approx
)

Arguments

kappa

Range parameter of the covariance function.

nu

Shape parameter of the covariance function.

tau

Scale parameter of the covariance function.

rspde.order

The order of the rational approximation

dim

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.

sharp

The sparsity graph should have the correct sparsity (costs more to perform a sparsity analysis) or an upper bound for the sparsity?

type_rational_approx

Which type of rational approximation should be used? The current types are "chebfun", "brasil" or "chebfunLB".

Value

The precision matrix