# fields, Tools for spatial data
# Copyright 2004-2011, 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))
}