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

GeoSimapprox {GeoModels}

R Documentation

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 approximate methods of simulation (circulant embeeding and turning bands) (see Examples).

Usage

GeoSimapprox(coordx, coordy=NULL, coordt=NULL, 
coordx_dyn=NULL,corrmodel, distance="Eucl",GPU=NULL, 
grid=FALSE,local=c(1,1),max.ext=1,
method="TB", L=2000,model='Gaussian',
n=1,param,anisopars=NULL, radius=6371,X=NULL,spobj=NULL,nrep=1)

Arguments

`coordx`	A numeric (`d \times 2`)-matrix (where `d` is the number of spatial sites) giving 2-dimensions of spatial coordinates or a numeric `d`-dimensional vector giving 1-dimension of spatial coordinates. 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; `coordy` is interpreted only if `coordx` is a numeric vector or `grid=TRUE` otherwise it will be ignored. Optional argument, the default is `NULL` then `coordx` is expected to be numeric a (`d \times 2`)-matrix.
`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.
`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).
`local`	Numeric; number of local work-items of the GPU
`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.

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, moreno.bevilacqua89@gmail.com,https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, victor.morales@uv.cl, https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, chcaaman@ubiobio.cl,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)

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)

J. Guiness (2018) Permutation and Grouping Methods for Sharpening Gaussian Process Approximations Technometrics 60(4) 415-429.

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
###            for any typpe of correlation model
###############################################################
set.seed(68)
x = seq(0,1,0.006)
y = seq(0,1,0.006)
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 Gaussian RF 
###            with  Matern  covariance model
###            using Turning band method
###            It works for (ir)regular grid
###            for the Matern model
###############################################################
set.seed(68)
x = runif(8000)
y = runif(8000)
coords=cbind(x,y)
param=list(smooth=0.5,mean=0,sill=1,scale=0.1,nugget=0)
# Simulation of a spatial Gaussian RF with Matern correlation function
data1 <- GeoSimapprox(coords, corrmodel="Matern", model="Gaussian",
                      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="")

[Package GeoModels version 2.0.4 Index]