rspde.matern.precision.opt: Optimized precision matrix of the covariance-based rational...

In rSPDE: Rational Approximations of Fractional Stochastic Partial Differential Equations

Optimized precision matrix of the covariance-based rational approximation

Description

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

rSPDE documentation built on Nov. 6, 2023, 1:06 a.m.