Vector Covariance Model
Description
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 matrixvalued 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.
Usage
1 
Arguments
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

Details
C_0 is either a spatiotemporal 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.
Value
RMvector
returns an object of class RMmodel
Author(s)
Martin Schlather, schlather@math.unimannheim.de
References
Scheuerer, M. and Schlather, M. (2012) Covariance Models for DivergenceFree and CurlFree Random Vector Fields. Stochastic Models 28:3.
See Also
RMcurlfree
,
RMdivfree
,
RMmodel
,
RFsimulate
,
RFfit
.
Examples
1 2 3 4 5 6 
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 plotmethod: Methods for function 'plot' in package 'RandomFields'
 PrintModelList: Information about the implemented covariance models
 QMath: Transformation of coordinate systems
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 RFspclass: Class 'RFsp'
 RM: Overview over classes of 'RMmodels'
 RMangle: Anisotropy matrix given by angle
 RMaskey: Askey model
 RMave: Spacetime moving average model
 RMball: RMball
 RMbcw: Model bridging stationary and intrinsically stationary...
 RMbernoulli: Covariance Model for binary field based on a Gaussian field
 RMbessel: Bessel Family Covariance Model
 RMbigneiting: GneitingWendland Covariance Models
 RMbiwm: Full Bivariate Whittle Matern Model
 RMbr2: Transformation from BrownResnick to Gauss
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 RMbrownresnick: Tail correlation function of the BrownResnick process
 RMcauchy: Cauchy Family Covariance Model
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 RMcurlfree: Curlfree Covariance Model
 RMcutoff: Gneiting's modification towards finite range
 RMdagum: Dagum Covariance Model Family
 RMdampedcos: Exponentially Damped Cosine
 RMdelay: Bivariate Delay Effect
 RMdewijsian: Modified DeWijsian Variogram Model
 RMdivfree: Divfree Covariance Model
 RMeaxxa: Special models for rotation like fields
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 RMexp: Exponential Covariance Model
 RMexponential: Exponential operator
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 RMintexp: Integral exponential operator
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 RMkolmogorov: Identical Model
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 RMmastein: MaStein operator
 RMmatern: WhittleMatern Covariance Model
 RMmatrix: Matrix operator
 RMmodel: Covariance and Variogram Models in 'RandomFields' (RM...
 RMmodelclass: Class 'RMmodel'
 RMmodelExtclass: Class "RMmodelFit"
 RMmodelgeneratorclass: Class 'RMmodelgenerator'
 RMmodelsAdvanced: Advanced features of the mdoels
 RMmodelsAuxiliary: Auxiliary and other Models
 RMmodelsMultivariate: Multivariate models
 RMmodelsNonstatationary: Nonstationary features of the mdoels
 RMmodelsSpaceTime: Spacetime Covariance Models
 RMmodelsSphere: Covariance models valid on a sphere
 RMmodelsTailcorrelation: Covariance models valid for maxstable random fields
 RMmodelsTrend: Trend Modelling
 RMmppplus: Mixture of shape functions
 RMmqam: multivariate quasiarithmetic mean
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 RMnugget: Nugget Effect Covariance Model
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 RMqam: Quasiarithmetic mean
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 RMrational: Rational function
 RMrotat: Rotation matrices
 RMS: Scaling operator
 RMschlather: Covariance Model for binary field based on Gaussian field
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 RMsinepower: The Sinepower Covariance Model on the Sphere
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 RMtbm: Turning Bands Method
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 RMtrend: Trend Model
 RMtruncsupport: Random sign
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 RMvector: Vector Covariance Model
 RMwave: Wave Covariance Model / Cardinal Sine
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