Simulation of Gaussian and non Gaussian Random Fields.
Simulation of Gaussian and some non Gaussian spatial, spatio-temporal and spatial bivariate random fields. The function return a realization of a random Field for a given covariance model and covariance parameters.Simulation is based on Cholesky decomposition. UTF-8
GeoSim(coordx, coordy=NULL,coordz=NULL, coordt=NULL, coordx_dyn=NULL, corrmodel, distance="Eucl",GPU=NULL, grid=FALSE, local=c(1,1),method="cholesky", model='Gaussian', n=1, param,anisopars=NULL,radius=6371, sparse=FALSE,X=NULL,spobj=NULL,nrep=1,progress=TRUE)
coordx: A numeric ()-matrix or ()-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 numeric ()-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
method: String; the type of matrix decomposition used in the simulation. Default is cholesky. The other possible choices is svd.
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 .
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)
sparse: Logical; if TRUE then cholesky decomposition is performed using sparse matrices algorithms (spam packake). It should be used with compactly supported covariance models.FALSE is the default.
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.
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 -dimensional vector of spatial coordinates;
coordy: A -dimensional vector of spatial coordinates;
coordz: A -dimensional vector of spatial coordinates;
coordt: A -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;
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
library(GeoModels) library(mapproj) ################################################################ ### ### Example 1. Simulation of a spatial Gaussian RF ### with Matern and Generalized Wendland correlations ############################################################### # Define the spatial-coordinates of the points: x <- runif(500);y <- runif(500) coords=cbind(x,y) set.seed(261) # Simulation of a spatial Gaussian RF with Matern correlation function data1 <- GeoSim(coordx=coords, corrmodel="Matern", param=list(smooth=0.5, mean=0,sill=1,scale=0.4/3,nugget=0))$data set.seed(261) data2 <- GeoSim(coordx=coords, corrmodel="GenWend", param=list(smooth=0, power2=4,mean=0,sill=1,scale=0.4,nugget=0))$data opar=par(no.readonly = TRUE) par(mfrow=c(1,2)) quilt.plot(coords,data1,main="Matern",xlab="",ylab="") quilt.plot(coords,data2,main="Wendland",xlab="",ylab="") par(opar) ################################################################ ### ### Example 2. Simulation of a spatial geometric RF ### with underlying Wend0 correlation ### ################################################################ # Define the spatial-coordinates of the points: x <- runif(800);y <- runif(800) coords <- cbind(x,y) set.seed(251) # Simulation of a spatial Binomial RF: sim <- GeoSim(coordx=coords, corrmodel="Wend0", model="BinomialNeg",n=1,sparse=TRUE, param=list(nugget=0,mean=0,scale=.2,power2=4)) quilt.plot(coords,sim$data,nlevel=max(sim$data),col=terrain.colors(max(sim$data+1))) ################################################################ ### ### Example 3. Simulation of a spatial Weibull RF ### with underlying Matern correlation on a regular grid ### ############################################################### # Define the spatial-coordinates of the points: x <- seq(0,1,0.032) y <- seq(0,1,0.032) set.seed(261) # Simulation of a spatial Gaussian RF with Matern correlation function data1 <- GeoSim(x,y,grid=TRUE, corrmodel="Matern",model="Weibull", param=list(shape=1.2,mean=0,scale=0.3/3,nugget=0,smooth=0.5))$data image.plot(x,y,data1,main="Weibull RF",xlab="",ylab="") ################################################################ ### ### Example 4. Simulation of a spatial t RF ### with with underlying Generalized Wendland correlation ### ############################################################### # Define the spatial-coordinates of the points: x <- seq(0,1,0.03) y <- seq(0,1,0.03) set.seed(268) # Simulation of a spatial Gaussian RF with Matern correlation function data1 <- GeoSim(x,y,grid=TRUE, corrmodel="GenWend",model="StudentT", sparse=TRUE, param=list(df=1/4,mean=0,sill=1,scale=0.3,nugget=0,smooth=1,power2=5))$data image.plot(x,y,data1,col=terrain.colors(100),main="Student-t RF",xlab="",ylab="") ################################################################ ### ### Example 5. Simulation of a sinhasinh RF ### with underlying Wend0 correlation. ### ############################################################### # Define the spatial-coordinates of the points: x <- runif(500, 0, 2) y <- runif(500, 0, 2) coords <- cbind(x,y) set.seed(261) corrmodel="Wend0" # Simulation of a spatial Gaussian RF: param=list(power2=4,skew=0,tail=1, mean=0,sill=1,scale=0.2,nugget=0) ## gaussian case data0 <- GeoSim(coordx=coords, corrmodel=corrmodel, model="SinhAsinh", param=param,sparse=TRUE)$data plot(density(data0),xlim=c(-7,7)) param=list(power2=4,skew=0,tail=0.7, mean=0,sill=1,scale=0.2,nugget=0) ## heavy tails data1 <- GeoSim(coordx=coords, corrmodel=corrmodel, model="SinhAsinh", param=param,sparse=TRUE)$data lines(density(data1),lty=2) param=list(power2=4,skew=0.5,tail=1, mean=0,sill=1,scale=0.2,nugget=0) ## asymmetry data2 <- GeoSim(coordx=coords, corrmodel=corrmodel, model="SinhAsinh", param=param,sparse=TRUE)$data lines(density(data2),lty=3) ################################################################ ### ### Example 6. Simulation of a bivariate Gaussian RF ### with bivariate Matern correlation model ### ############################################################### # Define the spatial-coordinates of the points: x <- runif(500, 0, 2) y <- runif(500, 0, 2) coords <- cbind(x,y) # Simulation of a bivariate spatial Gaussian RF: # with a separable Bivariate Matern 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 <- GeoSim(coordx=coords,corrmodel="Bi_matern", param=param)$data opar=par(no.readonly = TRUE) par(mfrow=c(1,2)) quilt.plot(coords,data[1,],col=terrain.colors(100),main="1",xlab="",ylab="") quilt.plot(coords,data[2,],col=terrain.colors(100),main="2",xlab="",ylab="") par(opar) ################################################################ ### ### Example 7. Simulation of a spatio temporal Gaussian RF. ### observed on fixed location sites with double Matern correlation ### ############################################################### coordt=1:5 # Define the spatial-coordinates of the points: x <- runif(50, 0, 2) y <- runif(50, 0, 2) coords <- cbind(x,y) param<-list(nugget=0,mean=0,scale_s=0.2/3,scale_t=2/3,sill=1,smooth_s=0.5,smooth_t=0.5) data <- GeoSim(coordx=coords, coordt=coordt, corrmodel="Matern_Matern", param=param)$data dim(data) ################################################################ ### ### Example 8. Simulation of a spatio temporal Gaussian RF. ### observed on dynamical location sites with double Matern correlation ### ############################################################### # Define the dynamical spatial-coordinates of the points: coordt=1:5 coordx_dyn=list() maxN=30 set.seed(8) for(k in 1:length(coordt)) { NN=sample(1:maxN,size=1) x <- runif(NN, 0, 1) y <- runif(NN, 0, 1) coordx_dyn[[k]]=cbind(x,y) } coordx_dyn 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 <- GeoSim(coordx_dyn=coordx_dyn, coordt=coordt, corrmodel="Matern_Matern", param=param)$data ## spatial realization at first temporal instants data[[1]] ## spatial realization at third temporal instants data[[3]] ################################################################ ### ### Example 9. Simulation of a Gaussian RF ### with a Wend0 correlation in the north emisphere of the planet earth ### using geodesic distance ############################################################### distance="Geod";radius=6371 NN=3000 ## total point on the sphere on lon/lat format set.seed(80) coords=cbind(runif(NN,-180,180),runif(NN,0,90)) ## Set the wendland parameters corrmodel <- "Wend0" param<-list(mean=0,sill=1,nugget=0,scale=1000,power2=3) # Simulation of a spatial Gaussian RF on the sphere #set.seed(2) data <- GeoSim(coordx=coords,corrmodel=corrmodel,sparse=TRUE, distance=distance,radius=radius,param=param)$data #require(globe) #globe::globeearth(eye=place("newyorkcity")) #globe::globepoints(loc=coords,pch=20,col = cm.colors(length(data),alpha=0.4)[rank(data)])