matern.r
"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 ) )
}