| EmpiricalVariogram {RandomFields} | R Documentation |
EmpiricalVariogram calculates the empirical (semi-)variogram
of a random field realisation
EmpiricalVariogram(x, y=NULL, z=NULL, data, grid, bin, gridtriple=FALSE)
x |
vector of coordinates |
y |
vector of coordinates |
z |
vector of coordinates |
data |
vector or matrix of data |
grid |
logical; if TRUE then
x, y, and z define a grid; otherwise
x, y, and z are interpreted as points |
bin |
vector of ascending values giving the bin boundaries |
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 |
Comments on specific parameters:
data: the number of values must match the number of
points (given by x, y, z, grid, and
gridtriple). That is, it must equal the number of points or be
a multiple of it. In case the number of data equals n times the
number of points, the data are interpreted as n independent
realisations for the given set of points.
(grid==FALSE): the vectors x, y, and
z, are interpreted as
vectors of coordinates
(grid==TRUE) && (gridtriple==FALSE): the vectors
code{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$step)))
b[i],bin[i+1]] for
i=1,...,length(bin)-1.
Hence, to include zero, bin[1] must be negative.
The function returns
list(centers,emp.vario) where centers are the central
points of the bins and emp.vario gives the empirical variogram.
Both elements are
vectors of length (length(bin)-1).
Martin Schlather, Martin.Schlather@uni-bayreuth.de http://www.geo.uni-bayreuth.de/~martin
GaussRF and RandomFields
#############################################################
## this example checks whether a certain simulation method ##
## works well for a specified covariance model and ##
## a configuration of points ##
#############################################################
x <- seq(0, 10, 0.5)
y <- seq(0, 10, 0.5)
grid <- TRUE
gridtriple <- FALSE ## see help("GaussRF")
model <- "wh" ## whittlematern
alpha <- 2
mean <- 1
variance <- 10
nugget <- 5
scale <- 2
method <- "TBM3"
bins <- seq(0, 5, 0.001)
repetition <- 20 ## by far too small to get reliable results!!
## It should be of order 500,
## but then it will take some time
## to do the simulations
param <- c(mean, variance, nugget, scale, alpha)
f <- GaussRF(x=x, y=y, grid=grid, gridtriple=gridtriple,
model=model, param=param, meth=method,
n=repetition)
binned <- EmpiricalVariogram(x=x, y=y, data=f,
grid=grid, gridtriple=gridtriple, bin=bins)
truevariogram <- Variogram(binned$c, model, param)
matplot(binned$c, cbind(truevariogram,binned$e), pch=c("*","e"))
##black curve gives the theoretical values