RFinterpolate: 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, method =
              "ml", ...)

Arguments

model

string; covariance model, see RMmodel, or type RFgetModelNames(type="variogram") to get all options.

$(n \times d)$ matrix or vector of x coordinates, or object of class GridTopology or raster; coordinates of $n$ points t

optional vector of y coordinates

optional vector of z coordinates

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

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

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

err.model

For conditional simulation and random imputing only.
Usually err.model=RMnugget(var=var), or not given at all
 (error-free measurements).

method

character. A single method out of methods or
   sub.methods,
   see RFfit.

...

An intrinsic arguements can be given:
 [object Object]
 For further optional arguments, see RFoptions.

`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.

`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).

`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.

`See Also`

RMmodel,
 RFempiricalvariogram,
 RandomFields,

`Examples`

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

## Preparation of graphics
if (interactive()) dev.new(height=7, width=16)
RFoptions(always_close_screen=FALSE)

## 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)


\dontrun{

## alternatively 

## Intrinsic kriging
model <- RMfbm(a=1)
z <- RFinterpolate(krige.meth="U", model, x, x, data=data)
screen(scr <- scr+1); plot(z, data)


## Interpolation nicht korrekt
## Intrinsic kriging with Polynomial Trend
model <- RMfbm(a=1) + RMtrend(polydeg=2)
z <- RFinterpolate(model, x, x, data=data)
screen(scr <- scr+1); plot(z, data)
}

\dontrun{
## Universal kriging with trend as formula
model <- RMexp() + RMtrend(arbit=function(X1,X2) sin(X1+X2)) +
 RMtrend(mean=1)
z <- RFinterpolate(model, x=x, y=x, data=data)
screen(scr <- scr+1); plot(z, data)

## Universal kriging with several arbitrary functions
model <- RMexp() + RMtrend(arbit=function(x,y) x^2 + y^2) +
 RMtrend(arbit=function(x,y) (x^2 + y^2)^0.5) + RMtrend(mean=1)
z <- RFinterpolate(model, x=x, y=x, data=data)
screen(scr <- scr+1); plot(z, data)
}close.screen(all = TRUE)

RFoptions(always_close_screen=TRUE);
          close.screen(all.screens=TRUE);
          while (length(dev.list()) >= 2) dev.off()
FinalizeExample()
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