| CondSimu {RandomFields} | R Documentation |
the function returns conditional simulations of a Gaussian random field
CondSimu(krige.method, x, y=NULL, z=NULL, T=NULL, grid,
gridtriple=FALSE, model, param, method=NULL, given, data,
trend, n=1, register=0,
err.model=NULL, err.param=NULL, err.method=NULL,
err.register=1, tol=1E-5, pch=".", paired=FALSE, na.rm=FALSE)
krige.method |
Assumptions on the random field which corresponds to the respective kriging method; currently 'S' (simple kriging) and 'O' (ordinary kriging) are implemented. |
x |
matrix or vector of x coordinates; 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 of the random field.
See CovarianceFct, or
type PrintModelList() to get all options for
model.
See CovarianceFct for model being a list.
|
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.
See CovarianceFct for param being NULL
or list.
|
method |
NULL or string; method used for simulating,
see RFMethods, or
type PrintMethodList() to get all options. |
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. |
trend |
Not programmed yet. (used by universal kriging) |
n |
number of realisations to generate. If paired=TRUE
then n must be even. |
register |
0:9; place where intermediate calculations are stored;
the numbers are aliases for 10 internal registers; see
GaussRF for further details. |
err.model |
covariance function for the error model. String or list.
See model for details.
|
err.param |
parameters for the error model. See also
param.
|
err.method |
Only relevant if err.model is not
NULL.
Then it must be given if and only if method is given;
see method for details. |
err.register |
see register for details. |
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. |
paired |
logical.
logical. If TRUE then every second simulation is obtained by
only changing the signs of the standard Gaussian random variables, the
simulation is based on (“antithetic pairs”).
|
na.rm |
logical. If TRUE then NAs are removed from
the given data. |
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 lay 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=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)))
The returned object depends on the parameters n and
grid:
n=1:
* 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.
n>1:
* grid=FALSE. A matrix is returned. The columns
contain the realisations.
* grid=TRUE. An array of dimension
d+1, where d is the dimension of
the random field as given by x, y, and z,
is returned. The last dimension contains the realisations.
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.
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)
do.call(getOption("device"), list(height=4,width=4))
do.call(getOption("device"), list(height=4,width=4))
do.call(getOption("device"), list(height=4,width=4))
# 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
dev.set(2)
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)
range(cz)
dev.set(3)
image(x, x, cz, col=colour, xlim=lim, ylim=lim, zlim=zlim)
#conditional simulation with error term
cze <- CondSimu(krige.method, x, x, grid=TRUE,
model=model, param=c(0, 1/2, 0, 1),
err.model="gauss", err.param=c(0, 1/2, 0, 1),
given=expand.grid(p,p),
data=data)
range(cze)
dev.set(4)
image(x, x, cze, col=colour, xlim=lim, ylim=lim, zlim=zlim)