## Not run:
# ###########################################
# ## SECTION 4: UNCONDITIONAL SIMULATION ##
# ###########################################
#
# RFoptions(seed = 0, height = 4)
# ## 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_device=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")
# PT <- weather[ , 1 : 2] ## full data set takes more than
# ## half an hour to be analysed
# ## transformation of earth coordinates to Euclidean coordinates
# Dist.mat <- as.vector(RFearth2dist(weather[ , 3 : 4]))
# All <- TRUE
# \dontshow{if(RFoptions()$internal$examples_reduced){warning("reduced data set")
# All <- 1:10
# PT <- weather[All , 1 : 2]
# 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)
# ## End(Not run)
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