R: Curlfree Covariance Model

RMcurlfree {RandomFields} | R Documentation

## 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 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

### Usage

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

### Arguments

`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 `RMmodel`. If not passed, the above covariance function remains unmodified.

### 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`.

### Value

`RMcurlfree` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

- Scheuerer, M. and Schlather, M. (2012) Covariance Models for Divergence-Free and Curl-Free Random Vector Fields. Stochastic Models 28:3.

### 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, 0.2)
    simulated <- RFsimulate(model=model, x=x.seq, y=y.seq)
    plot(simulated, select.variables=list(1, c(1, 2:3), 4))

[Package RandomFields version 3.1.50 Index]