RandomFields (version 1.0.15)

RFparameters: Control Parameters

Description

RFparameters sets and returns control parameters for the simulation of random fields

Usage

RFparameters(...)
  RFparameters.default(Storing=storing, PrintLevel=printlevel,
                       PracticalRange=practicalrange, CE.force=ce.force,
                       CE.mmin=ce.mmin, CE.tolRe=ce.tolRe,
                       CE.tolIm=ce.tolIm, CE.trials=ce.trials,
                       direct.checkprecision=directcheckprecision,
                       direct.maxvariables=directmaxvariables,
                       direct.method=directmethod,
                       direct.requiredprecision=directrequiredprecision,
                       spectral.lines=spectrallines,
                       spectral.grid=spectralgrid,
                       TBMCE.force=tbmceforce, TBMCE.mmin=tbmcemmin,
                       TBMCE.tolRe=tbmcetolre, TBMCE.tolIm=tbmcetolim,
                       TBMCE.trials=tbmcetrials, TBM2.lines=tbm2lines,
                       TBM2.linesimufactor=tbm2linesimufactor,
                       TBM2.linesimustep=tbm2linesimustep,
                       TBM3D2.lines=tbm3D2lines,
                       TBM3D2.linesimufactor=tbm3D2linesimufactor,
                       TBM3D2.linesimustep=tbm3D2linesimustep,
                       TBM3D3.lines=tbm3D3lines,
                       TBM3D3.linesimufactor=tbm3D3linesimufactor,
                       TBM3D3.linesimustep=tbm3D3linesimustep,
                       MPP.approxzero=mppapproxzero,
                       add.MPP.realisations=addmpprealisations,
                       MPP.radius=mppradius,
                       maxstable.maxGauss=maxstablemaxGauss, pch=pchx)

Arguments

...

arguments as given in RFparameters.default and listed in the following.

Storing

logical. If TRUE then intermediate results are kept after each simulation; if several simulation are made with the same parameters (e.g., by n$>1$ in GaussRF or several calls of

PrintLevel

If PrintLevel$\le0$ there is not any output on the screen. The higher the number the more tracing information. Default: 1 [init, do]. 1 : messages about errors occurred 2 : messages about partial failures of the algorithm

PracticalRange

The range of the covariance functions can be adjusted so that cov(1) is about 0.05 (for scale==1). Default: FALSE [init].

CE.force

logical. Circulant embedding does not work if a certain matrix has negative eigenvalues. Sometimes it is convenient to replace all the negative eigenvalues by zero (CE.force==TRUE) after CE.trials number of trial

CE.mmin

Circulant embedding usually uses the smallest matrix possible; by CE.mmin the minimum number of rows and columns of the matrix are given. Default: 0 [init].

CE.tolRe

Circulant embedding. Threshold above which eigenvalues are considered as non-negative. Default: -1E-5 [init].

CE.tolIm

Circulant embedding. If the modulus of the imaginary part is less than CE.tolIm then the eigenvalue is considered as real. Default: 1E-3 [init].

CE.trials

Circulant embedding. A larger embedding matrix is likely to make more eigenvalues non-negative. If at least one of the thresholds CE.tolRe and CE.tolIm are missed then the matrix size is doubled, and the matrix is

direct.checkprecision

Gaussian random vectors can be generated by means of the square root of the covariance matrix. By default Cholesky decomposition is used. If direct.checkprecision==TRUE then the precision is checked. Default: FALS

direct.maxvariables

Decomposition of the covariance matrix. If the number of variables to generate is greater than direct.maxvariables, then any matrix decomposition method is rejected. It is important that this option is set conveniently if

direct.method

Decomposition of the covariance matrix. If direct.method==1, Cholesky decomposition will not be attempted, but singular value decomposition used instead. Default: 0 [init].

direct.requiredprecision

Decomposition of the covariance matrix. If direct.checkprecision==TRUE and the direct.requiredprecision is not reached then Cholesky decomposition fails, and singular value decomposition is used. Default:

spectral.lines

Spectral turning bands. Number of lines used. Default: 500 [do].

spectral.grid

Logical. Spectral turning bands is implemented for 2 dimensions only. The angle of the lines is random if spectral.grid==FALSE, and $k\pi/$spectral.lines for $k$ in 1:spectral.lines, otherwise.

TBMCE.force

Ordinary TBM methods. At the moment only the circulant embedding method on the line is implemented; this parameter corresponds to CE.force. Default: FALSE [init].

TBMCE.mmin

Ordinary TBM methods. This parameter corresponds to CE.mmin. Default: 0 [init].

TBMCE.tolRe

Ordinary TBM methods. This parameter corresponds to CE.tolRe. Default: -1E-5 [init].

TBMCE.tolIm

Ordinary TBM methods. This parameter corresponds to CE.tolIm. Default: 1E-3 [init].

TBMCE.trials

Ordinary TBM methods. This parameter corresponds to CE.trials. Default: 3 [init].

TBM2.lines

Ordinary 2-dimensional turning bands method. Number of lines used. Default: 60 [do].

TBM2.linesimufactor

Either TBM2.linesimufactor or TBM2.linesimustep must be greater than zero. The parameter that is zero is ignored. The grid on the line is TBM2.linesimufactor-times smaller than the smallest distance

TBM2.linesimustep

The grid on the line has lag TBM2.linesimustep. See also TBM2.linesimufactor. Default: 0.0 [init].

TBM3D2.lines

Ordinary 3-dimensional turning bands method, simulation of a 2-dimensional field. Number of lines used. Default: 500 [do].

TBM3D2.linesimufactor

Either TBM3D2.linesimufactor or TBM2.linesimustep must be greater than zero. The parameter that is zero is ignored. The grid on the line is TBM3D2.linesimufactor-times smaller than the smallest dist

TBM3D2.linesimustep

The grid on the line has lag TBM3D2.linesimustep. See also TBM3D2.linesimufactor. Default: 0.0 [init].

TBM3D3.lines

Ordinary 3-dimensional turning bands method, simulation of a 3-dimensional field. Number of lines used. Default: 500 [do].

TBM3D3.linesimufactor

Either TBM3D3.linesimufactor or TBM2.linesimustep must be greater than zero. The parameter that is zero is ignored. The grid on the line is TBM3D3.linesimufactor-times smaller than the smallest dist

TBM3D3.linesimustep

The grid on the line has lag TBM3D3.linesimustep. See also TBM3D3.linesimufactor. Default: 0.0 [init].

MPP.approxzero

Marked point processes. Functions that do not have compact support are set to zero outside the ball outside which the function has absolute values less than MPP.approxzero. Default: 0.001 [init].

add.MPP.realisations

Random coins. Number of superposed realisations (to approximate the normal distribution). Default: 100 [do].

MPP.radius

Marked point processes. In order avoid edge effects, the simulation area is enlarged by a constant $r$ so that all marks have their (supposed) support in the ball with radius $r$ centred at the origin; see also MPP.approxzero.

maxstable.maxGauss

Max-stable random fields. The simulation of the max-stable process based on random fields uses a stopping rule that necessarily needs a finite upper endpoint of the marginal distribution of the random field. In the case of extremal Gaussia

pch

character. The character is printed after each performed simulation if more than one simulation is performed at once. Default: "#" [do].

Value

• returns NULL if any parameter has been given, and the list of all parameter values otherwise.

Details

The following refers to the simulation of Gaussian random fields (InitGaussRF, GaussRF), but most parts also apply for the simulation of max-stable random fields (InitMaxStableRF, MaxStableRF). Some of the global parameters determine the basic settings of a simulation, e.g. direct.method (which chooses a square root of a positive definite matrix). The values of such parameters are read by InitGaussRF and stored in an internal register. Changing such a parameter between calling InitGaussRF and calling DoSimulateRF will not have any effect. These parameters have the flag "[init]". Parameters like TBM2.lines (which determines the number of i.i.d. proceses to be simulated on the line) are only relevant when generating random numbers. These parameters are read by DoSimulateRF, and are marked by "[do]". Storing has an influence on both, InitGaussRF and DoSimulateRF. InitGaussRF may reserve more memory if Storing==TRUE. DoSimulateRF will free the register if Storing==FALSE, whatever the value of Storing was when InitGaussRF was called.

The distinction between [init] and [do] is relevant even if GaussRF is used, but called a second time with the same parameters for the random field and if RFparameters()$Storing==TRUE. Then GaussRF realises that the second call has the same parameters, and takes over the stored intermediate results (that have been calculated with the RFparameters() at that time). To prevent this put RFparameters(Storing==FALSE) or use DeleteRegister().

A programme that checks whether the parameters are well adapted to a specific simulation problem is given as an example of EmpiricalVariogram().

For further details on the implemented methods, see RFMethods.

References

Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.

See Also

GaussRF, GetPracticalRange, MaxStableRF, RandomFields, and RFMethods.

Examples

RFparameters(Storing=TRUE)
 str(RFparameters())