# Optimized precision matrix of the covariance-based rational approximation

Source:`R/inla_rspde.R`

`rspde.matern.precision.opt.Rd`

`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".