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RandomFields (version 3.1.16)

jss14: Covariance models for multivariate and vector valued fields

Description

Here the code of the paper on ‘Analysis, simulation and prediction of multivariate random fields with package RandomFields’

Arguments

References

Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 1-25, url = ‘http://www.jstatsoft.org/v63/i08/’

See Also

weather, SS12, S10

Examples

Run this code


## 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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