Fast and Exact Simulation of Large Gaussian Lattice Systems in R2

Description

Here the code of the paper on ‘Fast and Exact Simulation of Large Gaussian Lattice Systems in R2’ is given.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software;

References

• Gneiting, T., Sevcikova, H., Percival, D.B., Schlather, M., Jiang, Y. (2006) Fast and Exact Simulation of Large Gaussian Lattice Systems in R2: Exploring the Limits. J. Comput. Graph. Stat., 15, 483-501.

Examples

## Figure 1 
stabletest <- function(alpha, theta, size=if (interactive()) 512 else 20) {
  RFoptions(trials=1, tolIm = 1e-8, tolRe=0, force = FALSE,
            useprimes=TRUE, strategy=0, skipchecks=!FALSE,
             storing=TRUE)
  model <- RMcutoff(diameter=theta, a=1, RMstable(alpha=alpha))
  RFcov(dist=0, model=model, dim=2, seed=0)
  r <- RFgetModelInfo(RFcov, modelname="RMcutoff", level=3)$internalq[5] # theor R
  x <- seq(0, r, by= r / (size - 1)) * theta
  err <- try(RFsimulate(x, x, model=RPcirculant(model), n=0))
  return(if (class(err) == "try-error") NA else r)
}

alphas <- seq(1.52, 2.0, if (interactive()) 0.02 else 0.5) 
thetas <-
  if (interactive()) seq(0.05, 3.5, 0.05) else seq(0.1, 3.5, 2)

m <- matrix(NA, nrow=length(thetas), ncol=length(alphas))
for (it in 1:length(thetas)) {
  theta <- thetas[it]
  for (ia in 1:length(alphas)) {
  alpha <- alphas[ia]
  cat("alpha=", alpha, "theta=", theta,"\n")
  m[it, ia] <- stabletest(alpha=alpha, theta=theta)
  if (is.na(m[it, ia])) break
  }
  if (any(is.finite(m))) image(thetas, alphas, m, col=rainbow(100))
}