RMcutoff: Gneiting's modification towards finite range
Description
RMcutoff is a functional on univariate stationary
isotropic covariance functions $\phi$.
The corresponding function $C$ (which is not necessarily a
covariance function,
see details) only depends on the distance $r$ between two
points in $d$-dimensional space and is given by
$$C(r)=\phi(r), 0\le r \le d$$
$$C(r) = b_0 ((dR)^a - r^a)^{2 a}, d \le r \le dR$$
$$C(r) = 0, dR \le r$$
The parameters $R$ and $b_0$
are chosen internally such that $C$ is a smooth function.
Usage
RMcutoff(phi, diameter, a, var, scale, Aniso, proj)
Arguments
phi
a univariate stationary isotropic covariance model
(see RFgetModelNames(type="positive definite",
domain="single variable", isotropy="isotropy", vdim=1))
which is valid in dimension fulldim.
diameter
a numerical value; should be greater than 0; the
diameter of the domain on which the simulation is done
a
a numerical value; should be greater than 0; has been shown to be
optimal for $a = 1/2$ or $a =1$.
var,scale,Aniso,proj
optional arguments; same meaning for any
RMmodel. If not passed, the above
covariance function remains unmodified.
The algorithm that checks the given parameters knows
only about some few necessary conditions.
Hence it is not ensured that
the cutoff-model is a valid covariance function for any
choice of $\phi$ and the parameters.
For certain models $\phi$, e.g. RMstable,
RMwhittle and RMgencauchy, some
sufficient conditions
are known (cf. Gneiting et al. (2006)).
References
Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M.,
Jiang Y. (2006) Fast and Exact Simulation of Large {G}aussian
Lattice Systems in {$R^2$}: Exploring the Limits.J. Comput. Graph. Stat.15, 483--501.
Stein, M.L. (2002) Fast and exact simulation of fractional
Brownian surfaces.J. Comput. Graph. Statist.11, 587--599
## For examples see the help page of 'RFsimulateAdvanced' ##model <- RMexp()
plot(model, model.cutoff=RMcutoff(model, diameter=1), xlim=c(0, 4))
FinalizeExample()