| Kriging {RandomFields} | R Documentation |
The function allows for different methods of kriging.
Kriging(krige.method, x, y=NULL, z=NULL, T=NULL, grid,
gridtriple=FALSE, model, param, given, data, trend, pch=".",
return.variance=FALSE, internal=FALSE)
krige.method |
kriging method; currently only 'S' (simple kriging) and 'O' (ordinary kriging) implemented. |
x |
(n x d) matrix or vector of x
coordinates; coordinates of n points to be kriged |
y |
vector of y coordinates. |
z |
vector of z coordinates. |
T |
vector in grid triple form for the time coordinates. |
grid |
logical; determines whether the vectors x,
y, and z should be
interpreted as a grid definition, see Details. |
gridtriple |
logical. Only relevant if grid=TRUE.
If gridtriple=TRUE
then x, y, and z are of the
form c(start,end,step); if
gridtriple=FALSE then x, y, and z
must be vectors of ascending values.
|
model |
string; covariance model, see CovarianceFct, or
type PrintModelList() to get all options. |
param |
parameter vector:
param=c(mean, variance, nugget, scale,...);
the parameters must be given
in this order. Further parameters are to be added in case of a
parametrised class of covariance functions, see
CovarianceFct.
The value of mean must be finite
in the case of simple kriging, and is ignored otherwise. |
given |
matrix or vector of points where data are available. |
data |
the data values given at given; it might be a
vector or a matrix. If a matrix is given multivariate data are
assumed which are kriged separately. |
trend |
not programmed yet (will be used in case of universal kriging) |
pch |
Kriging procedures are quite time consuming in general.
The character pch is printed after roughly
each 80th part of calculation. |
return.variance |
logical. If FALSE the kriged field is
returned. If TRUE a list of two elements, estim and
var, i.e. the kriged field and the kriging variances,
is returned. |
internal |
FALSE. internal should not be set to TRUE
by the user.
(In case internal=TRUE,
various consistency checks for the input variables
are not performed. Further, grid must be FALSE,
and model must be given in the output format of
PrepareModel.)
|
grid=FALSE : the vectors x, y,
and z are interpreted as vectors of coordinates
(grid=TRUE) && (gridtriple=FALSE) : the vectors
x, y, and z
are increasing sequences with identical lags for each sequence.
A corresponding
grid is created (as given by expand.grid).
(grid=TRUE) && (gridtriple=TRUE) : the vectors
x, y, and z
are triples of the form (start,end,step) defining a grid
(as given by expand.grid(seq(x$start,x$end,x$step),
seq(y$start,y$end,y$step),
seq(z$start,z$end,z$step)))
If variance.return=FALSE 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.
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute
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.
Wackernagel, H. (1998) Multivariate Geostatistics. Berlin: Springer, 2nd edition.
CondSimu,
CovarianceFct,
EmpiricalVariogram,
RandomFields,
## creating random variables first
## here, a grid is chosen, but does not matter
step <- 0.25
x <- seq(0,7,step)
param <- c(0,1,0,1)
model <- "exponential"
RFparameters(PracticalRange=FALSE)
p <- 1:7
points <- as.matrix(expand.grid(p,p))
data <- GaussRF(points, grid=FALSE, model=model, param=param)
## visualise generated spatial data
zlim <- c(-2.6,2.6)
colour <- rainbow(100)
image(p, p, xlim=range(x), ylim=range(x),
matrix(data,ncol=length(p)),
col=colour,zlim=zlim)
## now: kriging
krige.method <- "O" ## ordinary kriging
z <- Kriging(krige.method=krige.method,
x=x, y=x, grid=TRUE,
model=model, param=param,
given=points, data=data)
image(x,x,z,col=colour,zlim=zlim)