RandomFields (version 3.0.5)

RMcurlfree: Curlfree Covariance Model

Description

RMcurlfree is a multivariate covariance model which depends on a univariate stationary covariance model where the covariance function phi(h) is twice differentiable. The corresponding matrix-valued covariance function C of the model only depends on the difference $h$ between two points and it is given by $$C(h)=( - \nabla_h (\nabla_h)^T ) C_0(h)$$

Usage

RMcurlfree(phi, var, scale, Aniso, proj)

Arguments

phi

a univariate stationary covariance model (2 or 3 dimensional).

var,scale,Aniso,proj

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

Value

• RMcurlfree returns an object of class RMmodel

Details

The model returns the potential field in the first component, the corresponding curlfree field and field of sources and sinks in the last component. See also the models RMdivfree and RMvector.

References

• Scheuerer, M. and Schlather, M. (2012) Covariance Models for Divergence-Free and Curl-Free Random Vector Fields.Stochastic Models28:3.

See Also

RMdivfree, RMvector, 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 <- RMcurlfree(RMgauss(), scale=4)
plot(model, dim=2)

x.seq <- y.seq <- seq(-10, 10, if (interactive()) 0.2 else 5)
simulated <- RFsimulate(model=model, x=x.seq, y=y.seq)
plot(simulated, select.variables=list(1, c(1, 2:3), 4))
FinalizeExample()