CondSimu {RandomFields} | R Documentation |
the function returns conditional simulations of a random field
CondSimu(krige.method, x, y=NULL, z=NULL, grid, model, param, method=NULL, n=1, register=0, gridtriple=FALSE, err.model=NULL, err.param=NULL, err.method=NULL, err.register=1, given, data, tol=1e-05, pch=".")
krige.method |
Assumptions on the random field which corresponds to
the respective kriging method;
currently only "S" (simple
kriging) and "O" (ordinary kriging) possible. |
x |
matrix or vector of x coordinates; points to be kriged. |
y |
vector of y coordinates. |
z |
vector of z coordinates. |
grid |
logical; determines whether the vectors x ,
y , and z should be
interpreted as a grid definition, see Details. |
model |
string; covariance model of the random field.
See CovarianceFct , or
type PrintModelList() to get all options for
model . |
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. |
method |
NULL or string; method used for simulating,
see RFMethods , or
type PrintMethodList() to get all options. |
n |
number of realisations to generate. |
register |
0:9; place where intermediate calculations are stored;
the numbers are aliases for 10 internal registers; see
GaussRF for further 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.
|
err.model |
string; covariance model that
describes the measurement error. See CovarianceFct , or
type PrintModelList() to get all options for
err.model . If NULL no measurement error is assumed.
Currently, the only option for err.model is "nugget" .
|
err.param |
parameter vector:
err.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.
Since currently the only option for err.model is
"nugget" , err.param can only be of the form
c(mean,0,nugget,0) .
|
err.method |
Currently, only "nugget" or NULL
is sensible; see method for further information. |
err.register |
see register for details. |
given |
matrix or vector of locations where data are available; note that it is not possible to give the points in form of a grid definition. |
data |
the values measured. |
tol |
considered only if grid=TRUE ;
tolerated distances of a given point to the nearest grid point to
be regarded as being zero; see Details. |
pch |
character.
The included kriging procedure can be quite time consuming.
The character pch is printed after roughly
each 80th part of calculation. |
The same way as GaussRF
the function
CondSimu
allows for simulating on grids or arbitrary
locations. However simulation on a grid is sometimes performed
as if the points were at arbitrary locations, what may
imply a great reduction in speed. This happens when the given
locations do not ly on the specified grid, since in an intermediate
step simulation has to be performed simultaneously on both the grid
defined by x
, y
, z
, and the locations
of given
.
Comments on specific parameters
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==FALSE)
: 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))
)
Martin Schlather, Martin.Schlather@uni-bayreuth.de http://www.geo.uni-bayreuth.de/~martin
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.
CovarianceFct
,
GaussRF
,
Kriging
RandomFields
,
## creating random variables first ## here, a grid is chosen, but any arbitrary points for which ## data are given are fine. Indeed if the data are given on a ## grid, the grid has to be expanded before calling `CondSimu', ## see below. ## However, locations where values are to be simulated, ## should be given in form of a grid definition whenever ## possible param <- c(0, 1, 0, 1) model <- "exponential" RFparameters(PracticalRange=FALSE) p <- 1:7 data <- GaussRF(x=p, y=p, grid=TRUE, model=model, param=param) # another grid, where values are to be simulated step <- 0.25 # or 0.3 x <- seq(0, 7, step) # standardisation of the output lim <- range( c(x, p) ) zlim <- c(-2.6, 2.6) colour <- rainbow(100) ## visualise generated spatial data image(p, p, data, xlim=lim, ylim=lim, zlim=zlim, col=colour) #conditional simulation krige.method <- "O" ## random field assumption corresponding to ## those of ordinary kriging cz <- CondSimu(krige.method, x, x, grid=TRUE, model=model, param=param, given=expand.grid(p,p),# if data are given on a grid # then expand the grid first data=data) image(x, x, cz, col=colour, xlim=lim, ylim=lim, zlim=zlim)