matern2d.operators {rSPDE}R Documentation

Rational approximations of stationary anisotropic Gaussian Matern random fields

Description

matern2d.operators is used for computing a 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)}(\sqrt{h^T H^{-1}h})^\nu K_\nu(\sqrt{h^T H^{-1}h})

, based on a SPDE representation of the form

(I - \nabla\cdot(H\nabla))^{(\nu+1)/2}u = c\sigma W

, where $c>0$ is a constant. The matrix H is defined as

\begin{bmatrix} h_x^2 & h_xh_yh_{xy} \\ h_xh_yh_{xy} & h_y^2 \end{bmatrix}

Usage

matern2d.operators(
  hx = NULL,
  hy = NULL,
  hxy = NULL,
  nu = NULL,
  sigma = NULL,
  mesh = NULL,
  fem = NULL,
  m = 1,
  type_rational_approximation = c("brasil", "chebfun", "chebfunLB"),
  return_fem_matrices = FALSE
)

Arguments

hx

Parameter in the H matrix.

hy

Parameter in the H matrix.

hxy

Parameter in the H matrix.

nu

Smoothness parameter.

sigma

standard deviation parameter.

mesh

An fmesher mesh.

fem

Optional precomputed FEM matrices.

m

The order of the rational approximation, which needs to be a positive integer. The default value is 1.

type_rational_approximation

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

return_fem_matrices

Should the FEM matrices be returned?

Value

An object of type CBrSPDEobj2d

See Also

fractional.operators(), spde.matern.operators(), matern.operators()

Examples

library(fmesher)
n_loc <- 2000
loc_2d_mesh <- matrix(runif(n_loc * 2), n_loc, 2)
mesh_2d <- fm_mesh_2d(loc = loc_2d_mesh, cutoff = 0.03, max.edge = c(0.1, 0.5))
op <- matern2d.operators(mesh = mesh_2d)

[Package rSPDE version 2.5.1 Index]