R: Interpolation methods

RFinterpolate {RandomFields}

R Documentation

Interpolation methods

Description

The function allows for different methods of interpolation. Currently only various kinds of kriging are installed.

Usage

RFinterpolate(model, x, y = NULL, z = NULL, T = NULL, grid=NULL,
              distances, dim, data, given=NULL, err.model,
                 ignore.trend = FALSE, ...)

Arguments

`model`	string; covariance model, see `RMmodel`, or type `RFgetModelNames(type="variogram")` to get all options.
`x`	(n x d) matrix or vector of x coordinates, or object of class `GridTopology` or `raster`; coordinates of n points to be kriged. For more options see RFsimulateAdvanced.
`y`	optional vector of y coordinates
`z`	optional vector of z coordinates
`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; determines whether the vectors `x`, `y`, and `z` should be interpreted as a grid definition; `RandomFields` can find itself the correct value in nearly all cases. See also RFsimulateAdvanced.
`distances`	another alternative to pass the (relative) coordinates, see RFsimulateAdvanced.
`dim`	Only used if `distances` are given.
`data`	Matrix, data.frame or object of class `RFsp`; coordinates and response values of measurements; `given` is not given and `data` is a matrix or `data` is a data.frame, the first columns are interpreted as coordinate vectors, and the last column(s) as (multiple) measurement(s) of the field which are kriged separately; if the argument `x` is missing, `data` may contain `NA`s, which are then replaced by the kriged values (imputing); for details on matching of variable names see RFsimulateAdvanced; if of class `RFsp`
`given`	optional, matrix or list. If `given` matrix then the coordinates can be given separately, namely by `given` where, in each row, a single location is given. If `given` is a list, it may consist of `x`, `y`, `z`, `T`, `grid`. If `given` is provided, `data` must be a matrix or an array containing the data only.
`err.model`	For conditional simulation and random imputing only. Usually `err.model=RMnugget(var=var)`, or not given at all (error-free measurements).
`ignore.trend`	logical. If `TRUE` only the covariance model of the given model is considered, without the trend part.
`...`	for options, etc.

Details

In case of intrinsic cokriging (intrinsic kriging for a multivariate random fields) the pseudo-cross-variogram is used (cf. Ver Hoef and Cressie, 1991).

Value

The value depends on the additional argument variance.return, see RFoptions.

If variance.return=FALSE (default), Kriging returns a vector or matrix of kriged values corresponding to the specification of x, y, z, and grid, and data.

data: a vector or matrix with one column
* grid=FALSE. A vector of simulated values is returned (independent of the dimension of the random field)
* grid=TRUE. An array of the dimension of the random field is returned (according to the specification of x, y, and z).

data: a matrix with at least two columns
* grid=FALSE. A matrix with the ncol(data) columns is returned.
* grid=TRUE. An array of dimension d+1, where d is the dimension of the random field, is returned (according to the specification of x, y, and z). The last dimension contains the realisations.

If variance.return=TRUE, a list of two elements, estim and var, i.e. the kriged field and the kriging variances, is returned. The format of estim is the same as described above. The format of var is accordingly.

Note

Important options are

method (overwriting the automatically detected variant of kriging)
return_variance (returning also the kriging variance)
locmaxm (maximum number of conditional values before neighbourhood kriging is performed)
fillall imputing estimates location by default
varnames and coordnames in case data.frames are used to tell which column contains the data and the coordinates, respectively.

Author(s)

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

Marco Oesting, oesting@math.uni-mannheim.de

Author(s) of the code:

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

Alexander Malinowski, malinowski@math.uni-mannheim.de

Marco Oesting, oesting@math.uni-mannheim.de

References

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.

Cressie, N.A.C. (1993) Statistics for Spatial Data. New York: Wiley.

Goovaerts, P. (1997) Geostatistics for Natural Resources Evaluation. New York: Oxford University Press.

Ver Hoef, J.M. and Cressie, N.A.C. (1993) Multivariate Spatial Prediction. Mathematical Geology 25(2), 219-240.

Wackernagel, H. (1998) Multivariate Geostatistics. Berlin: Springer, 2nd edition.

Examples

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

## Preparation of graphics
dev.new(height=7, width=16) 

## creating random variables first
## here, a grid is chosen, but does not matter
p <- 3:8
points <- as.matrix(expand.grid(p,p))
model <- RMexp() + RMtrend(mean=1)
data <- RFsimulate(model, x=points)
plot(data)
x <- seq(0, 9, 0.25)

## Simple kriging with the exponential covariance model
model <- RMexp()
z <- RFinterpolate(model, x=x, y=x, data=data)
plot(z, data)

## Simple kriging with mean=4 and scaled covariance
model <- RMexp(scale=2) + RMtrend(mean=4)
z <- RFinterpolate(model, x=x, y=x, data=data)
plot(z, data)


## Ordinary kriging
model <- RMexp() + RMtrend(mean=NA)
z <- RFinterpolate(model, x=x, y=x, data=data)
plot(z, data)







close.screen(all = TRUE)

[Package RandomFields version 3.1.50 Index]