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

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

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 spectral 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)

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.

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;

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

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)

M. Bevilacqua, X. Emery, F. Cuevas Pacheco (2025) Fast simulation of Gaussian random fields with flexible correlation models in Euclidean spaces arxiv

Examples

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 spectral 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 
### using spectral Turning band method
###############################################################

# 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="")

GeoModels documentation built on April 6, 2026, 5:08 p.m.