RandomFields (version 3.0.10)

S10: On some covariance models based on normal scale mixtures

Description

Here the code of the paper on On some covariance models based on normal scale mixtures is given.

References

• Schlather, M. (2010) On some covariance models based on normal scale mixtures.Bernoulli,16, 780-797.

Examples

RFoptions(seed=0)
if (!.C("isAuthor", a=integer(1))$a) {}

\dontrun{
jpg <- jpeg
Plot <- function(basicname, x, y, z, pixels=200, col=col, delay=1,
 basicn=10000, T, redo=TRUE, height=5, zi=1, speed=0.3,
 zlim = range(z)) {
 Print(try(dir.create(basicname)))
 if (length(T)==3) T <- seq(T[1], T[2], T[3])
 cex = 2
 par(mar=c(4,4.3, 0.8, 0.8), cex=0.7)
 for (file in list(TRUE, "jpg")) {
 h <- if (is.logical(file)) height else pixels
 args <- list(TRUE, file, ps=paste(basicname, "/X2", basicname, sep=""),
 quiet=FALSE, height=h, width=h)
 do.call("Dev", args)
 image(x, T, z[,zi,], zlim=zlim, col=col, cex.axis=cex, cex.lab=cex,
 ylab="time")
 Dev(FALSE)
 
 args <- list(TRUE, file, ps=paste(basicname, "/X3", basicname, sep=""),
 quiet=FALSE, height=h, width=h)
 do.call("Dev", args)
 image(x, y, z[,,1], zlim=zlim, col=col, cex.axis=cex, cex.lab=cex)
 Dev(FALSE)
 }
 k <- 0
 time <- length(T)
 if (redo) {
 system(paste("rm ", basicname, "/", basicname, "*.jpg", sep=""))

 par(mar=rep(0, 4))
 Dev(TRUE, "jpg", ps=paste(basicname, "/", basicname, sep=""),
 quiet=FALSE, height=pixels * height, width=pixels * height)
 plot(Inf, Inf, axes=FALSE, xlim=c(0,1), ylim=c(0,1))
 Dev(FALSE)
 
 for (i in 1:(time)) {
 for (j in 1:delay) {
 k <- k + 1
 name <- paste(basicname, "/", basicname, k + basicn, sep="")
 Dev(TRUE, "jpg", ps=name, quiet=FALSE, height=pixels, width=pixels)
 image(x, y, z[,,i], zlim=zlim, col=col, axes=FALSE)
 Dev(FALSE)
 }
 }
 }
 system(paste("cd ", basicname, ";mencoder -mf fps=30 -ffourcc DX50 -ovc lavc ",
 " -speed ", speed,
 " -lavcopts vcodec=mpeg4:vbitrate=9800:aspect=4/3:vhq:keyint=15",
 " -vf scale=720:576 -o ", basicname, ".avi mf://",
 basicname, "*.jpg &", sep=""))

}




### Example 10 in Schlather (2010)
basicname <- "coxisham"
y <- x <- seq(0, 10, len=if (interactive()) 256 else 5)
T <- c(0, 25.5, if (interactive()) 0.02 else 5)
col <- c(topo.colors(300)[1:100], cm.colors(300)[c((1:50) * 2, 101:150)])
model <- RMcoxisham(mu=c(1, 1), D=matrix(nr=2, c(1, 0.5, 0.5, 1)),
                    RMwhittle(nu=1))
z <- RFsimulate(x, y, T=T, grid =TRUE, sp_lines=1500, every=10,
 model = model, printlevel=2)

zlim <- range(z)
time <- dim(z)[3]
for (i in 1:time) {
 cat(i,"\n")
 image(x, y, z[, , i], add=i>1, col=col, zlim=zlim)
} 
# load(paste(basicname, ".dat", sep=""))
Plot(basicname, x, y, z, col=col, T=T)
save(file=paste(basicname, "/", basicname, ".dat", sep=""), z)


### Example 13 in Schlather (2010)
basicname <- "moving"
y <- x <- seq(0, 10,len = if (interactive()) 256 else 10) 
T <- c(0, 25.5, if (interactive()) 0.02 else 10)
col <- c(topo.colors(300)[1:100], cm.colors(300)[c((1:50) * 2, 101:150)]) 
model <- RMave(A = matrix(nc=2,c(0.5, 0, 0, 1)), z= c(2,0),
               RMwhittle(nu=1))
z <- RFsimulate(x, x, T=T, model=model, grid=TRUE, Print=2, me="av",
 every = 10, CE.trial=2, CE.force=TRUE, CE.maxmem=16777216*8)

zlim <- range(z)
time <- dim(z)[3]
for (i in 1:time) {
 Print(i)
 image(x, y, z[, , i], add=i>1, col=col, zlim=zlim)
}
# load(paste(basicname, ".dat", sep=""))
Plot(basicname, x, y, z, col=col, T=T)
save(file=paste(basicname, "/", basicname, ".dat", sep=""), z)



### Example 16 in Schlather (2010)
intens <- if (interactive()) 100 else 3 ## 1000 takes a huge amount
## ## of time; take smaller values
basicname <- "cyclone"
len <- if (interactive()) 81 else 10
y <- x <- seq(-3, 3, len=len)
T <- seq(0, 6, len=len)
col <- c(topo.colors(300)[1:100], cm.colors(300)[c((1:50) * 2, 101:150)])
model <- RMstp(M=matrix(nc=3, rep(0, 9)),
               S=RMetaxxa(E=c(1, 1, 1), alpha = -2 * pi,
                          A=t(matrix(nc=3, c(2, 0, 0, 1, 1 , 0, 0, 0, 0)))),
               Aniso = RMrotation(phi= -2 * pi),
               phi = RMwhittle(nu = 1) )
z <- RFsimulate(x, x, z=T, model=model, grid=TRUE, me="coin", every = 10, 
 mpp.intens=intens, mpp.p = 0.1, mpp.beta=3.5, mpp.plus = 8, Print=3) 
zlim <- c(-3.5, 3.5)
time <- dim(z)[3]
for (i in 1:time) {Print(i);image(x, y, z[,,i], add=i>1, col=col, zlim=zlim)}
# load(paste(basicname, ".dat", sep=""))
Plot(basicname, x, y, z, col=col, T=T, pixels=256, zi=0.5 + dim(z)[2]/2,
 speed=0.2, zlim=zlim)
save(file=paste(basicname, "/", basicname, ".dat", sep=""), z)

}

RFoptions(seed=NA)