Vector Covariance Model
RMvector is a multivariate covariance model which depends on
a univariate covariance model that is stationary in the first Dspace
coordinates h and where the covariance function phi(h,t)
is twice differentiable in the first component h.
The corresponding matrix-valued covariance function C of the model only depends on the difference h between two points in the first component. It is given by
C(h,t)=( -0.5 * (a + 1) Δ + a \nabla \nabla^T ) C_0(h, t)
where the operator is applied to the first component h only.
RMvector(phi, a, Dspace, var, scale, Aniso, proj)
phi |
an |
a |
a numerical value; should be in the interval [-1,1]. |
Dspace |
an integer; either 2 or 3; the first Dspace coordinates give the first component h. |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
C_0 is either a spatio-temporal model (then t is the time component) or it is an isotropic model. Then, the first Dspace coordinates are considered as h coordinates and the remaining ones as t coordinates. By default, Dspace equals the dimension of the field (and there is no t component). If a=-1 then the field is curl free; if a=1 then the field is divergence free.
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 <- RMvector(RMgauss(), scale=0.3) x <- seq(0, 10, 0.4) plot(RFsimulate(model, x=x, y=x, z=0), select.variables=list(1:2))
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