"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 ) )
}