inla.matern.cov {INLA} | R Documentation |
Calculates covariance and correlation functions for Matern models and related oscillating SPDE models, on R^d and on the sphere, S^2.
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, freq.max = NULL) inla.matern.cov.s2.unstable( nu, kappa, x, norm.corr = FALSE, theta = 0, freq.max = NULL )
nu |
The Matern smoothness parameter. |
kappa |
The spatial scale parameter. |
x |
Distance values. |
d |
Space dimension; the domain is R^d. |
corr |
If |
norm.corr |
If |
theta |
Oscillation strength parameter. |
epsilon |
Tolerance for detecting points close to distance zero. |
freq.max |
The maximum allowed harmonic order. Current default 40, to be changed to a dynamic choice based on error bounds. |
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) )
inla.matern.cov.s2.unstable
is an old implementation using
orthopolynom::legendre.polynomials
and orthopolynom::polynomial.values
Finn Lindgren finn.lindgren@gmail.com