RMtbm: Turning Bands Method

Description Usage Arguments Details Value References See Also Examples

View source: R/RMmodels.R

Description

RMtbm is a univariate or multivaraiate stationary isotropic covariance model in dimension reduceddim which depends on a univariate or multivariate stationary isotropic covariance phi in a bigger dimension fulldim. For formulas for the covariance function see details.

Usage

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RMtbm(phi, fulldim, reduceddim, layers, var, scale, Aniso, proj)

Arguments

phi, fulldim, reduceddim, layers

See RPtbm.

var,scale,Aniso,proj

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

Details

The turning bands method stems from the 1:1 correspondence between the isotropic covariance functions of different dimensions. See Gneiting (1999) and Strokorb and Schlather (2014).

The standard case is reduceddim=1 and fulldim=3. If only one of the arguments is given, then the difference of the two arguments equals 2.

For d == n + 2, where n=reduceddim and d==fulldim the original dimension, we have

C(r) = phi(r) + r phi'(r) / n

which for n=1 reduces to the standard TBM operator

C(r) = d/dr [ r phi(r) ]

For d == 2 && n == 1 we have

C(r) = d/dr int_0^r [ r phi(r) ] / [ sqrt{r^2 - u^2} ] d u

‘Turning layers’ is a generalization of the turning bands method, see Schlather (2011).

Value

RMtbm returns an object of class RMmodel.

References

Turning bands

Turning layers

See Also

RPtbm, RFsimulate.

Examples

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RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

x <- seq(0, 10, 0.02)
model <- RMspheric()
plot(model, model.on.the.line=RMtbm(RMspheric()), xlim=c(-1.5, 1.5))

z <- RFsimulate(RPtbm(model), x, x)
plot(z)

Example output

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.