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, https://www.wim.uni-mannheim.de/schlather/

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

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

## Figure 1 (pretty time consuming)
stabletest <- function(alpha, theta, size=512) {
  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(modelname="RMcutoff", level=3)$storage$R_theor
  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, 0.02) 
thetas <- seq(0.05, 3.5, 0.05)

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))
}