Matern.R
# fields, Tools for spatial data
# Copyright 2004-2013, Institute for Mathematics Applied Geosciences
# University Corporation for Atmospheric Research
# Licensed under the GPL -- www.gpl.org/licenses/gpl.html
"Matern" <- function(d, scale = 1, range = 1, alpha = 1/range,
smoothness = 0.5, nu = smoothness, phi = scale) {
#
# Matern covariance function transcribed from Stein's book page 31
# nu==smoothness, alpha == 1/range
#
# GeoR parameters map to kappa==smoothness and phi == range
# check for negative distances
if (any(d < 0))
stop("distance argument must be nonnegative")
d <- d * alpha
# avoid sending exact zeroes to besselK
d[d == 0] <- 1e-10
#
# the hairy constant ...
# this is different from Stein to make this a correlation function when
# scale =1
con <- (2^(nu - 1)) * gamma(nu)
con <- 1/con
#
# call to Bessel function from R base package
#
return(phi * con * (d^nu) * besselK(d, nu))
}