RMdampedcos: Exponentially Damped Cosine
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

RMdampedcos is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r) = exp(-λ r) cos(r).

1	RMdampedcos(lambda, var, scale, Aniso, proj)

`lambda`	numeric. The range depends on the dimension of the random field (see details).
`var, scale, Aniso, proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

The model is valid for any dimension d. However, depending on the dimension of the random field the following bound for the argument λ has to be respected:

λ ≥ 1/{tan(π/(2d))}.

This covariance models a hole effect (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 92).

For λ = 0 we obtain the covariance function

C(r)=cos(r)

which is only valid for d=1 and corresponds to RMbessel for ν=-0.5, there.

RMdampedcos returns an object of class RMmodel.

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.
Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

RMbessel, RMmodel, RFsimulate, RFfit.

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMdampedcos(lambda=0.3, scale=0.1)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.