Gneiting's modification towards finite range
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)=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.
RMcutoff(phi, diameter, a, var, scale, Aniso, proj)
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 cutoff-model 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)).
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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
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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