RPspectral: Spectral turning bands method
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Value References See Also Examples

The spectral turning bands method is a simulation method for stationary Gaussian random fields (Mantoglou and Wilson, 1982). It makes use of Bochners's theorem and the corresponding spectral measure Ξ for a given covariance function C(h). For x in R^d, the field

Y(x)=√{2} cos(<V,x> + 2 pi U)

with V ~ Ξ and U ~ Ufo((0,1)) is a random field with covariance function C(h). A scaled superposition of many independent realizations of Y gives a Gaussian field according to the central limit theorem. For details see Lantuejoul (2002). The standard method allows for the simulation of 2-dimensional random fields defined on arbitrary points or arbitrary grids.

1	RPspectral(phi, boxcox, sp_lines, sp_grid, prop_factor, sigma)

phi

object of class RMmodel; specifies the covariance model to be simulated.

`boxcox`	the one or two parameters of the box cox transformation. If not given, the globally defined parameters are used. See `RFboxcox` for details.
`sp_lines`	Number of lines used (in total for all additive components of the covariance function). Default: `2500`.
`sp_grid`	Logical. The angle of the lines is random if `grid=FALSE`, and kπ/`sp_lines` for k in `1:sp_lines`, otherwise. This argument is only considered if the spectral measure, not the density is used. Default: `TRUE`.
`prop_factor`	positive real value. Sometimes, the spectral density must be sampled by MCMC. Let p be the average rejection rate. Then the chain is sampled every nth point where n = \|log(p)\| *`prop_factor`. Default: `50`.
`sigma`	real. Considered if the Metropolis algorithm is used. It gives the standard deviation of the multivariate normal distribution of the proposing distribution. If `sigma` is not positive then `RandomFields` tries to find a good choice for `sigma` itself. Default: `0`.

RPspectral returns an object of class RMmodel.

Lantuejoul, C. (2002) Geostatistical Simulation: Models and Algorithms. Springer.
Mantoglou, A. and J. L. Wilson (1982), The Turning Bands Method for simulation of random fields using line generation by a spectral method. Water Resour. Res., 18(5), 1379-1394.

Gaussian, RP, RPtbm.

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

model <- RPspectral(RMmatern(nu=1))
y <- x <- seq(0,10, len=400)
z <- RFsimulate(model, x, y, n=2)
plot(z)

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

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

    RFoptions

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)'.