R: Pseudovariogram

RFpseudovariogram {RandomFields}

R Documentation

Pseudovariogram

Description

Calculates the theoretical and empirical Pseudovariogram.

Usage


RFpseudovariogram(model, x, y=NULL, z = NULL, T=NULL, grid, params, distances,
            dim, ..., data, bin=NULL, phi=NULL, theta = NULL,
            deltaT = NULL, vdim=NULL)

Arguments

`model,params`	object of class `RMmodel`, `RFformula` or `formula`; best is to consider the examples below, first. The argument `params` is a list that specifies free parameters in a formula description, see RMformula.
`x`	vector of x coordinates, or object of class `GridTopology` or `raster`; for more options see RFsimulateAdvanced.
`y,z`	optional vectors of y (z) coordinates, which should not be given if `x` is a matrix.
`T`	optional vector of time coordinates, `T` must always be an equidistant vector. Instead of `T=seq(from=From, by=By, len=Len)`, one may also write `T=c(From, By, Len)`.
`grid`	logical; the function finds itself the correct value in nearly all cases, so that usually `grid` need not be given. See also RFsimulateAdvanced.
`distances,dim`	another alternative for the argument `x` to pass the (relative) coordinates, see RFsimulateAdvanced.
`...`	for advanced use: further options and control arguments for the simulation that are passed to and processed by `RFoptions`. If `params` is given, then `...` may include also the variables used in `params`.
`data`	matrix, data.frame or object of class `RFsp`; If a matrix is given the ordering of the colums is the following: space, time, multivariate, repetitions, i.e. the index for the space runs the fastest and that for repetitions the slowest.
`bin`	a vector giving the borders of the bins; If not specified an array describing the empirical (pseudo-)(cross-) covariance function in every direction is returned.
`phi`	an integer defining the number of sectors one half of the X/Y plane shall be divided into. If not specified, either an array is returned (if bin missing) or isotropy is assumed (if bin specified).
`theta`	an integer defining the number of sectors one half of the X/Z plane shall be divided into. Use only for dimension d=3 if phi is already specified.
`deltaT`	vector of length 2, specifying the temporal bins. The internal bin vector becomes `seq(from=0, to=deltaT[1], by=deltaT[2])`
`vdim`	the number of variables of a multivariate data set. If not given and `data` is an `RFsp` object created by RandomFields, the information there is taken from there. Otherwise `vdim` is assumed to be one. NOTE: still the argument `vdim` is an experimental stage.

Details

RFpseudovariogram computes the empirical pseudovariogram for given (multivariate) spatial data.

The spatial coordinates x, y, z should be vectors. For random fields of spatial dimension d > 3 write all vectors as columns of matrix x. In this case do neither use y, nor z and write the columns in gridtriple notation.

If the data is spatially located on a grid a fast algorithm based on the fast Fourier transformed (fft) will be used. As advanced option the calculation method can also be changed for grid data (see RFoptions.)

Value

an objects of class RFempVariog.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, http://ms.math.uni-mannheim.de

References

Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

Stein, M. L. (1999) Interpolation of Spatial Data. New York: Springer-Verlag

Examples

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


model <- RMbiwm(nudiag=c(1, 2), nured=1, rhored=1, cdiag=c(1, 5), 
                s=c(1, 1, 2))
x <- seq(0, 20, 0.1)
z <- RFsimulate(model, x=x, y=x, n=2)
emp.vario <- RFpseudovariogram(data=z)
plot(emp.vario, model=model)

[Package RandomFields version 3.3.7 Index]