EmpiricalVariogram {RandomFields}R Documentation

Empirical (Semi-)Variogram

Description

EmpiricalVariogram calculates the empirical (semi-)variogram of a random field realisation

Usage

EmpiricalVariogram(x, y=NULL, z=NULL, data, grid, bin, gridtriple=FALSE)

Arguments

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

Details

Comments on specific parameters:

Value

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).

Author(s)

Martin Schlather, Martin.Schlather@uni-bayreuth.de http://www.geo.uni-bayreuth.de/~martin

See Also

GaussRF and RandomFields

Examples

  #############################################################
  ## 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

[Package Contents]