R/Matern.R

In fields: Tools for Spatial Data

#
# fields  is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2022 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka,  douglasnychka@gmail.edu,
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with the R software environment if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
# or see http://www.r-project.org/Licenses/GPL-2
##END HEADER
"Matern" <- function(d, range = 1, alpha = 1/range, 
    smoothness = 0.5, nu = smoothness, phi = 1.0) {
    #
    # Matern covariance function transcribed from Stein's book page 31
    # nu==smoothness, alpha ==  1/range == aRange 
    #
    # GeoR parameters map to kappa==smoothness and phi == range
    # check for negative distances
    # phi is accepted as the marginal variance of the process (see below)
    # within fields, however, this parameter is sigma^2 and we recommend
    # not using phi.
    if (any(d < 0)) 
        stop("distance argument must be nonnegative")
    # rescale distances
    d <- d * alpha
    # call some special cases for half fractions of nu
    if( nu ==.5){
        return( phi*exp( -d) )
    }
     if( nu ==1.5){
         return( phi*(1+d)*exp( -d) )
     }
     if( nu ==2.5){
         return( phi*(1+d+d^2/3)*exp( -d) )
     }
    # otherwise .....
    # call to  Bessel function from R base package                                  #
    # avoid sending exact zeroes to besselK
    d[d == 0] <- 1e-10
    #
    # the hairy constant ...
    con <- (2^(nu - 1)) * gamma(nu)
    con <- 1/con
    return(phi * con * (d^nu) * besselK(d, nu))
}