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GeoModels (version 2.2.1)

GeoSimapprox: Fast simulation of Gaussian and non Gaussian Random Fields.

Description

Simulation of Gaussian and some non Gaussian spatial, spatio-temporal and spatial bivariate random fields using two approximate methods of simulation: circulant embeeding and turning band. (see Examples).

Usage

GeoSimapprox(coordx, coordy=NULL, coordz=NULL,coordt=NULL, 
coordx_dyn=NULL,corrmodel, distance="Eucl",GPU=NULL, 
grid=FALSE,max.ext=1,
method="TB", L=1000,model='Gaussian',parallel=FALSE,ncores=NULL,
n=1,param,anisopars=NULL, radius=6371,X=NULL,spobj=NULL,
nrep=1,progress=TRUE)

Value

Returns an object of class GeoSim. An object of class GeoSim is a list containing at most the following components:

bivariate

Logical:TRUE if the Gaussian RF is bivariate, otherwise FALSE;

coordx

A \(d\)-dimensional vector of spatial coordinates;

coordy

A \(d\)-dimensional vector of spatial coordinates;

coordt

A \(t\)-dimensional vector of temporal coordinates;

coordx_dyn

A list of dynamical (in time) spatial coordinates;

corrmodel

The correlation model; see GeoCovmatrix.

data

The vector or matrix or array of data, see GeoFit;

distance

The type of spatial distance;

method

The method of simulation

model

The type of RF, see GeoFit.

n

The number of trial for Binomial RFs;the number of successes in a negative Binomial RFs;

numcoord

The number of spatial coordinates;

numtime

The number the temporal realisations of the RF;

param

The vector of parameters' estimates;

radius

The radius of the sphere if coordinates are passed in lon/lat format;

spacetime

TRUE if spatio-temporal and FALSE if spatial RF;

nrep

The number of indipendent replicates;

Arguments

coordx

A numeric (\(d \times 2\))-matrix or (\(d \times 3\))-matrix Coordinates on a sphere for a fixed radius radius are passed in lon/lat format expressed in decimal degrees.

coordy

A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

coordz

A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

coordt

A numeric vector giving 1-dimension of temporal coordinates. Optional argument, the default is NULL then a spatial RF is expected.

coordx_dyn

A list of \(m\) numeric (\(d_t \times 2\))-matrices containing dynamical (in time) spatial coordinates. Optional argument, the default is NULL

corrmodel

String; the name of a correlation model, for the description see the Section Details.

parallel

Logical; if TRUE then the TB method is parallelized

ncores

Numeric; number of cores involved in parallelization.

distance

String; the name of the spatial distance. The default is Eucl, the euclidean distance. See the Section Details of GeoFit.

GPU

Numeric; if NULL (the default) no GPU computation is performed.

grid

Logical; if FALSE (the default) the data are interpreted as spatial or spatial-temporal realisations on a set of non-equispaced spatial sites (irregular grid).

max.ext

Numeric; The maximum extension of the simulation window (for the spatial CE method).

method

String; the type of approximation method. Default is TB that is the turning band method. The other possible choice is and CE (circular embeeding).

L

Numeric; the number of lines in the turning band method.

model

String; the type of RF and therefore the densities associated to the likelihood objects. Gaussian is the default, see the Section Details.

n

Numeric; the number of trials for binomial RFs. The number of successes in the negative Binomial RFs. Default is \(1\).

param

A list of parameter values required in the simulation procedure of RFs, see Examples.

anisopars

A list of two elements "angle" and "ratio" i.e. the anisotropy angle and the anisotropy ratio, respectively.

radius

Numeric; a value indicating the radius of the sphere when using the great circle distance. Default value is the radius of the earth in Km (i.e. 6371)

X

Numeric; Matrix of space-time covariates.

spobj

An object of class sp or spacetime

nrep

Numeric; Numbers of indipendent replicates.

progress

Logic; If TRUE then a progress bar is shown.

References

T. Gneiting, H. Sevcikova, D. B. Percival, M. Schlather and Y. Jiang (2006) Fast and Exact Simulation of Large Gaussian Lattice Systems in R2: Exploring the Limits Journal of Computational and Graphical Statistics 15 (3)

D. Arroyo, X. Emery (2020) An R Implementation of a Continuous Spectral Algorithm for Simulating Vector Gaussian Random Fields in Euclidean Spaces ACM Transactions on Mathematical Software 47(1)

Examples

Run this code
library(GeoModels)


################################################################
###
### Example 1. Simulation of a large spatial Gaussian RF 
###            with  Matern  covariance model
###            using circulant embeeding method
###            It works only for regular grid
###############################################################
set.seed(68)
x = seq(0,1,0.005)
y = seq(0,1,0.005)
param=list(smooth=1.5,mean=0,sill=1,scale=0.2/3,nugget=0)
# Simulation of a spatial Gaussian RF with Matern correlation function
data1 <- GeoSimapprox(coordx=x,coordy=y, grid=TRUE,corrmodel="Matern", model="Gaussian",
                      method="CE",param=param)$data
fields::image.plot( matrix(data1, length(x), length(y), byrow = TRUE) )

################################################################
###
### Example 2. Simulation of a large spatial Tukey-h RF 
###            with  GenWend-Matern  covariance model
###            using Turning band method
###            It works for (ir)regular grid
###############################################################
set.seed(68)
x = runif(50000)
y = runif(50000)
coords=cbind(x,y)
param=list(smooth=0.5,mean=0,sill=1,scale=0.04,nugget=0,tail=0.15,power2=1/4)
# Simulation of a spatial Gaussian RF with Matern correlation function
data1 <- GeoSimapprox(coords, corrmodel="GenWend_Matern", model="Tukeyh",
                      method="TB",param=param)$data
quilt.plot(coords,data1)



################################################################
###
### Example 3. Simulation of a large spacetime Gaussian RF 
###            with separable matern  covariance model
###            using  Circular embeeding method
###            It works  for (large) regular time grid
###############################################################
set.seed(68)
coordt <- (0:100)
coords <- cbind( runif(100, 0 ,1), runif(100, 0 ,1))
param <- list(mean  = 0, sill = 1, nugget = 0.25,
              scale_s = 0.05, scale_t = 2, 
              smooth_s = 0.5, smooth_t = 0.5)
# Simulation of a spatial Gaussian RF with Matern correlation function
param<-list(nugget=0,mean=0,scale_s=0.2/3,scale_t=2/3,sill=1,smooth_s=0.5,smooth_t=0.5)

data <- GeoSimapprox(coordx=coords, coordt=coordt, corrmodel="Matern_Matern",
                     model="Gaussian",method="CE",param=param)$data
dim(data)

################################################################
###
### Example 4. Simulation of a large spacetime Gaussian RF 
###            with separable GenWend covariance model
###            using  Circular embeeding method in time
###############################################################
set.seed(68)
# Simulation of a spatial Gaussian RF with Matern correlation function
param<-list(nugget=0,mean=0,scale_s=0.2,scale_t=3,sill=1,
             smooth_s=0,smooth_t=0, power2_s=4,power2_t=4)

data <- GeoSimapprox(coordx=coords, coordt=coordt, corrmodel="GenWend_GenWend",
                     model="Gaussian",method="CE",param=param)$data
dim(data)


################################################################
###
### Example 6. Simulation of a large bivariate Gaussian RF
### with  bivariate Matern correlation model
###
###############################################################

# Define the spatial-coordinates of the points:
#x <- runif(20000, 0, 2)
#y <- runif(20000, 0, 2)
#coords <- cbind(x,y)

# Simulation of a bivariate spatial Gaussian RF:
# with a  Bivariate Matern
#set.seed(12)
#param=list(mean_1=4,mean_2=2,smooth_1=0.5,smooth_2=0.5,smooth_12=0.5,
#           scale_1=0.12,scale_2=0.1,scale_12=0.15,
#           sill_1=1,sill_2=1,nugget_1=0,nugget_2=0,pcol=0.5)
#data <- GeoSimapprox(coordx=coords,corrmodel="Bi_matern",
#              param=param,method="TB",L=1000)$data
#opar=par(no.readonly = TRUE)
#par(mfrow=c(1,2))
#quilt.plot(coords,data[1,],col=terrain.colors(100),main="1",xlab="",ylab="")
#quilt.plot(coords,data[2,],col=terrain.colors(100),main="2",xlab="",ylab="")

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