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#
# fields is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2024 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka, douglasnychka@gmail.com,
#
# 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))
}
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