Curlfree Covariance Model
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 the following components:
the potential
the vector field given by
C(h)=( - \nabla_h (\nabla_h)^T ) C_0(h)
the field of sinks and sources
RMcurlfree(phi, which, var, scale, Aniso, proj)
phi |
a univariate stationary covariance model (2- or 3-dimensional). |
which |
vector of integers. If not given all components are returned; otherwise the selected components are returned. |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The model returns the potential field in the first component, the corresponding curlfree field and field of sources and sinks in the last component.
RMcurlfree returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Scheuerer, M. and Schlather, M. (2012) Covariance Models for Divergence-Free and Curl-Free Random Vector Fields. Stochastic Models 28:3.
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, 0.2) simulated <- RFsimulate(model=model, x=x.seq, y=y.seq) plot(simulated, select.variables=list(1, c(1, 2:3), 4))
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