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 |
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)