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 ddimensional space and is given by
C(r)=φ(r), 0≤ r ≤ d
C(r) = b_0 ((dR)^a  r^a)^{2 a}, d ≤ r ≤ dR
C(r) = 0, dR ≤ r
The parameters R and b_0 are chosen internally such that C is a smooth function.
1 
phi 
a univariate stationary isotropic covariance model. See, for instance,

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

The algorithm that checks the given parameters knows only about some few necessary conditions. Hence it is not ensured that the cutoffmodel is a valid covariance function for any choice of φ and the parameters.
For certain models phi, e.g. RMstable
,
RMwhittle
and RMgencauchy
, some
sufficient conditions
are known (cf. Gneiting et al. (2006)).
RMcutoff
returns an object of class RMmodel
Martin Schlather, schlather@math.unimannheim.de
Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M., Jiang Y. (2006) Fast and Exact Simulation of Large Gaussian 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
RMmodel
,
RFsimulate
,
RFfit
.
1 2 3 4 5 6 7 8 9 10 11  RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model < RMexp()
plot(model, model.cutoff=RMcutoff(model, diameter=1), xlim=c(0, 4))
model < RMstable(alpha = 0.8)
plot(model, model.cutoff=RMcutoff(model, diameter=2), xlim=c(0, 5))
x < y < seq(0, 4, 0.05)
plot(RFsimulate(RMcutoff(model), x=x, y = y))

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