RandomFields (version 3.0.32)

RMwave: Wave Covariance Model / Cardinal Sine

Description

RMwave is a stationary isotropic covariance model, which is valid only for dimension $d \le 3$. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = sin(r)/r 1_{r>0} + 1_{r=0} .$$ It is a special case of RMbessel.

Usage

RMwave(var, scale, Aniso, proj)
RMcardinalsine(var, scale, Aniso, proj)

Arguments

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMwave returns an object of class RMmodel

Details

The model is valid only for dimension $d \le 3$. It is a special case of RMbessel for $\nu = 0.5$.

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

References

• Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley.

See Also

RMbessel RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
model <- RMwave(scale=0.1)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(-0.2, 1))
plot(RFsimulate(model, x=x))
FinalizeExample()