if (!interactive()) RFoptions(modus_operandi="sloppy")
###########################################
## SECTION 4: UNCONDITIONAL SIMULATION ##
###########################################
RFoptions(seed = 0, height = 4, always_close_screen = TRUE)
## seed=0: *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
## height : height of X11
## always_close_screen=FALSE: the pictures are kept on the screen
## Fig. 1: linear model of coregionalization
M1 <- c(0.9, 0.6)
M2 <- c(sqrt(0.19), 0.8)
model <- RMmatrix(M = M1, RMwhittle(nu = 0.3)) +
RMmatrix(M = M2, RMwhittle(nu = 2))
x <- y <- seq(-10, 10, 0.2)
simu <- RFsimulate(model, x, y)
plot(simu)
## Fig. 2: Wackernagel's delay model
model <- RMdelay(RMstable(alpha = 1.9, scale = 2), s = c(4, 4))
simu <- RFsimulate(model, x, y)
plot(simu, zlim = 'joint')
## Fig. 3: extended Wackernagel's delay model
model <- RMdelay(RMstable(alpha = 1.9, scale = 2), s = c(0, 4)) +
RMdelay(RMstable(alpha = 1.9, scale = 2), s = c(4, 0))
simu <- RFsimulate(model, x, y)
plot(simu, zlim = 'joint')
plot(model, dim = 2, xlim = c(-5, 5), main = "Covariance function",
cex = 1.5, col = "brown")
## Fig. 4: latent dimension model
## MARGIN.slices has the effect of choosing the third dimension
## as latend dimension
## n.slices has the effect of choosing a bivariate model
model <- RMgencauchy(alpha = 1.5, beta = 3)
simu <- RFsimulate(model, x, y, z = c(0,1))
plot(simu, MARGIN.slices = 3, n.slices = 2)
## Fig. 5: Gneiting's bivariate Whittle-Matern model
model <- RMbiwm(nudiag = c(1, 2), nured = 1, rhored = 1, cdiag = c(1, 5),
s = c(1, 1, 2))
simu <- RFsimulate(model, x, y)
plot(simu)
## Fig. 6: anisotropic linear model of coregionalisaton
M1 <- c(0.9, 0.6)
M2 <- c(sqrt(0.19), 0.8)
A1 <- RMangle(angle = pi/4, diag = c(0.1, 0.5))
A2 <- RMangle(angle = 0, diag = c(0.1, 0.5))
model <- RMmatrix(M = M1, RMgengneiting(kappa = 0, mu = 2, Aniso = A1)) +
RMmatrix(M = M2, RMgengneiting(kappa = 3, mu = 2, Aniso = A2))
simu <- RFsimulate(model, x, y)
plot(simu)
## Fig. 7: random vector field whose path are curl free
## A 4-variate field is simulated, where the first component
## refers to the potential field, the second and third component
## to the curl free vector field and the forth component to the
## field of sinks and sources
model <- RMcurlfree(RMmatern(nu = 5), scale = 4)
simu <- RFsimulate(model, x, y)
plot(simu, select.variables = list(1, 2 : 3, 4))
plot(model, dim = 2, xlim = c(-3, 3), main = "", cex = 2.3, col="brown")
## Fig. 8: Kolmogorov's model of turbulence
## See the physical literature for its derivation and details
x <- y <- seq(-2, 2, len = 20)
model <- RMkolmogorov()
simu <- RFsimulate(model, x, y, z = 1)
plot(simu, select.variables = list(1 : 2), col = c("red"))
plot(model, dim = 3, xlim = c(-3, 3), MARGIN = 1 : 2, cex = 2.3,
fixed.MARGIN = 1.0, main = "", col = "brown")
###########################################
## SECTION 5: DATA ANALYSIS ##
###########################################
## get the data
data("weather")
All <- if (interactive()) TRUE else 1:10 ## full data set takes more than
## half an hour to be analysed
PT <- weather[All , 1 : 2]
## transformation of earth coordinates to Euclidean coordinates
Dist.mat <- as.vector(RFearth2dist(weather[All , 3 : 4]))
#################################
## model definition ##
#################################
## bivariate pure nugget effect:
nug <- RMmatrix(M = matrix(nc = 2, c(NA, 0, 0, NA)), RMnugget())
## parsimonious bivariate Matern model
pars.model <- nug + RMbiwm(nudiag = c(NA, NA), scale = NA, cdiag = c(NA, NA),
rhored = NA)
## whole bivariate Matern model
whole.model <- nug + RMbiwm(nudiag = c(NA, NA), nured = NA, s = rep(NA, 3),
cdiag = c(NA, NA), rhored = NA)
#################################
## model fitting and testing ##
#################################
## 'parsimoneous model'
## fitting takes a while ( > 10 min)
pars <- RFfit(pars.model, distances = Dist.mat, dim = 3, data = PT)
print(pars)
print(pars, full=TRUE)
RFratiotest(pars)
RFcrossvalidate(pars, x = weather[All , 3 : 4], data = PT, full = TRUE)
## 'whole model'
## fitting takes a while ( > 10 min)
whole <- RFfit(whole.model, distances = Dist.mat, dim = 3, data = PT)
print(whole, full=TRUE)
RFratiotest(whole)
RFcrossvalidate(whole, x = weather[All , 3 : 4], data = PT, full = TRUE)
## compare parsimonious and whole
RFratiotest(nullmodel = pars, alternative = whole)
#################################
## kriging ##
#################################
## First the coordindates are projected on a plane
a <- colMeans(weather[All , 3 : 4]) * pi / 180
P <- cbind(c(-sin(a[1]), cos(a[1]), 0),
c(-cos(a[1]) * sin(a[2]), -sin(a[1]) * sin(a[2]), cos(a[2])),
c(cos(a[1]) * cos(a[2]), sin(a[1]) * cos(a[2]), sin(a[2])))
x <- RFearth2cartesian(weather[All , 3 : 4])
plane <- (t(x) %*%P)[ , 1 : 2]
## here, kriging is performed on a rectangular that covers the
## the projected points above. The rectangular is approximated
## by a grid of length 200 in each direction.
n <- 200
r <- apply(plane, 2, range)
data <- cbind(plane, weather[All , 1 : 2])
z <- RFinterpolate(pars, data = data, dim = 2,
x = seq(r[1, 1], r[2, 1], length = n),
y = seq(r[1, 2], r[2, 2], length = n),
varunits = c("Pa", "K"), spConform = TRUE)
plot(z)
\dontrun{ # OK
dip <- dimnames(installed.packages())
version <- installed.packages()[which(dip[[1]] == "RandomFields")[1],
dip[[2]] == "Version"]
information <- list(date=date(), version=version) # version auf /usr/local !
save(file="/home/schlather/svn/RandomFields/RandomFields/data/weather.rda",# OK
pars.model, pars, whole.model, whole,
weather, information=information)
}
RFoptions(modus_operandi="normal")
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