inla.matern.cov {INLA} | R Documentation

## Numerical evaluation of Matern and related covariance functions.

### Description

Calculates covariance and correlation functions for Matern models and related oscillating SPDE models, on R^d and on the sphere, S^2.

### Usage

    inla.matern.cov(nu, kappa, x,
                    d = 1,
                    corr = FALSE,
                    norm.corr = FALSE,
                    theta,
                    epsilon = 1e-08)

    inla.matern.cov.s2(nu, kappa, x,
                       norm.corr = FALSE,
                       theta = 0)

### Arguments

`nu` | The Matern smoothness parameter.
`kappa` | The spatial scale parameter.
`x` | Distance values.
`d` | Space dimension; the domain is R^d.
`corr` | If `TRUE`, calculate correlations, otherwise calculate covariances. Only used for pure Matern models (i.e. with theta=0).
`norm.corr` | If `TRUE`, normalise by the estimated variance, giving approximate correlations.
`theta` | Oscillation strength parameter.
`epsilon` | Tolerance for detecting points close to distance zero.

### Details

On R^d, the models are defined by the spectral density given by

S(w) = 1 / ( (2π)^d * (kappa^4 + 2 kappa^2 * cos(pi * theta) * |w|^2 + |w|^4)^((nu + d/2)/2) )

On S^2, the models are defined by the spectral coefficients

S(k) = (2k+1) / (4 pi (kappa^4 + 2 kappa^2 cos(pi theta) k(k+1) + k^2(k+1)^2)^((ν + 1)/2) )

### Author(s)

Finn Lindgren finn.lindgren@gmail.com

[Package INLA version 18.07.12 Index]