#############################################################
## EXAMPLE 1 ##
## The following gives an example on the advantage of ##
## dependent=TRUE for simulating with RPcirculant if, in a ##
## study, most of the time is spent with simulating the ##
## Gaussian random fields. Here, the covariance at a pair ##
## of points is estimated for n independentent repetitions ##
## and 2*n locally dependent dependent repetitions . ##
## To get the precision, the procedure is repeated m times.##
#############################################################
# In the example below, local.dependent speeds up the simulation
# by about factor 16 at the price of an increased variance of
# factor 1.5
x <- seq(0, 1, len=10)
y <- seq(0, 1, len=10)
grid.size <- c(length(x), length(y))
meth <- RPcirculant
model <- RMexp(var=1.1, Aniso=matrix(nc=2, c(2,0.1,1.5,1)))
m <- if (interactive()) 5 else 2
n <- if (interactive()) 100 else 2
# using local.dependent=FALSE (which is the default)
c1 <- numeric(m)
time <- unix.time(
for (i in 1:m) {
cat("", i, "out of", m, "")
z <- RFsimulate(meth(model), x, y, n=n, pch="",
dependent=FALSE, spConform=FALSE, trials=5)
c1[i] <- cov(z[1,length(y), ], z[length(x), 1, ])
}) # many times slower than with local.dependent=TRUE below
cat("\n")
true.cov <- RFcov(model, t(y[c(1, length(y))]), t(x[c(length(x), 1)]))
print(time)
Print(true.cov, mean(c1), sd(c1), empty.lines=1)## true mean is zero
# using local.dependent=TRUE ...
c2 <- numeric(m)
time <- unix.time(
for (i in 1:m) {
cat("", i)
z <- RFsimulate(meth(model), x, y, n=2 * n, pch="",
dependent=TRUE, spConform=FALSE, trials=5)
c2[i] <- cov(z[1,length(y),], z[length(x), 1 , ])
})
cat("\n")
print(time) ## 20 times faster
Print(true.cov, mean(c2), sd(c2), empty.lines=1) ## much better results
## the sd is samller (using more locally dependent realisations)
## but it is (much) faster! Note that for n=n2 instead of n=2 * n,
## the value of sd(c2) would be larger due to the local dependencies
## in the realisations.
#############################################################
## EXAMPLE 2 ##
## This example shows that the same realisation can be ##
## obtained on different grid geometries (or point ##
## configurations, i.e. grid, non-grid) using TBM ##
#############################################################
x1 <- seq(-150,150,1)
y1 <- seq(-15, 15, 1)
x2 <- seq(-50, 50, 1)
model <- RPtbm(RMexp(scale=10))
RFoptions(storing=TRUE)
mar <- c(2.2, 2.2, 0.1, 0.1)
points <- 700
###### simulation of a random field on long thin stripe
z1 <- RFsimulate(model, x1, y1, center=0, seed=0,
points=points, storing=TRUE, spConform=FALSE)
ScreenDevice(height=1.55, width=12)
par(mar=mar)
image(x1, y1, z1, col=rainbow(100))
polygon(range(x2)[c(1,2,2,1)], range(y1)[c(1,1,2,2)],
border="red", lwd=3)
###### definition of a random field on a square of shorter diagonal
z2 <- RFsimulate(model, x2, x2, register=1, seed=0,
center=0, points=points, spConform=FALSE)
ScreenDevice(height=4.3, width=4.3)
par(mar=mar)
image(x2, x2, z2, zlim=range(z1), col=rainbow(100))
polygon(range(x2)[c(1,2,2,1)], range(y1)[c(1,1,2,2)],
border="red", lwd=3)
tbm.points <- RFgetModelInfo(level=3)$loc$totpts
Print(tbm.points, empty.lines=0) # number of points on the line
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