Rational approximations of stationary anisotropic Gaussian Matern random fields
Source:R/fractional.operators.R
matern2d.operators.Rdmatern2d.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("chebfun", "brasil", "chebfunLB")
)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
fmeshermesh.- 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 "chebfun", "brasil" or "chebfunLB".