RFsim: Simulation of Gaussian, Binary and Max-stable Random Fields
In CompRandFld: Composite-Likelihood Based Analysis of Random Fields
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Simulation of spatial and spatio-temporal Gaussian, binary and max-stable random fields.
The function returns one or more replications of a random field for a given covariance model and covariance parameters.
Usage
1
2
3
Arguments
coordx
A numeric (d x 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.
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 x 2)-matrix.
coordt
A numeric vector giving 1-dimension of
temporal coordinates. At the moment implemented only for the
Gaussian case. Optional argument, the default is NULL
then a spatial random field is expected.
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 FitComposite.
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).
model
String; the type of random field and therefore the densities associated to the likelihood
objects. Gaussian is the default, see the Section
Details.
numblock
Numeric; the observation size of the underlying random
field. Only in case of max-stable random fields.
param
A list of parameter values required in the
simulation procedure of random fields, see Examples.
replicates
Numeric; a positive integer denoting the number of independent and identically distributed (iid)
replications of a spatial or spatial-temporal random field. Optional argument, the default value is 1 then
a single realisation is considered.
threshold
Numeric; a value indicating a threshold for the
binary random field. Optional in the case that model
is BinaryGauss, see the Section Details.
Details
Note that this function is also interfaced to the R package RandomFields,
using fast routines therein developed for the simulation of random fields.
Value
Returns an object of class RFsim.
An object of class RFsim is a list containing
at most the following components:
coordx
A d-dimensional vector of spatial coordinates;
coordy
A d-dimensional vector of spatial coordinates;
coordt
A t-dimensional vector of temporal coordinates;
corrmodel
The correlation model; see Covmatrix.
data
The vector or matrix or array of data, see
FitComposite;
distance
The type of spatial distance;
model
The type of random field, see FitComposite.
numcoord
The number of spatial coordinates;
numtime
The number the temporal realisations of the random field;
param
The vector of parameters' estimates;
randseed
The seed used for the random simulation;
replicates
The number of the iid replicatations of the random field;
spacetime
TRUE if spatio-temporal and FALSE if
spatial random field;
threshold
The threshold for deriving the binary random field.
Author(s)
Simone Padoan, simone.padoan@unibocconi.it,
http://faculty.unibocconi.it/simonepadoan;
Moreno Bevilacqua, moreno.bevilacqua@uv.cl,
https://sites.google.com/a/uv.cl/moreno-bevilacqua/home.
References
Padoan, S. A. and Bevilacqua, M. (2015). Analysis of Random Fields Using CompRandFld.
Journal of Statistical Software, 63(9), 1–27.
See Also
Examples
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library(CompRandFld)
library(RandomFields)
library(mapproj)
library(fields)
################################################################
###
### Example 1. Simulation of a Gaussian random field.
### Gaussian random fields with Whittle-Matern correlation.
### One spatial replication.
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- runif(500, 0, 2)
y <- runif(500, 0, 2)
set.seed(261)
# Simulation of a spatial Gaussian random field:
data <- RFsim(x, y, corrmodel="matern", param=list(smooth=0.5,
mean=0,sill=1,scale=0.2,nugget=0))$data
################################################################
###
### Example 2. Simulation of a binary random field based on
### the latent Gaussian random field with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.05)
y <- seq(0, 1, 0.05)
set.seed(251)
# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE,
model="BinaryGauss", threshold=0,
param=list(nugget=0,mean=0,scale=.1,sill=1))
image(x,y,sim$data,col=terrain.colors(100))
################################################################
###
### Example 3. Simulation of a max-stable random
### extremal-t type with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################
set.seed(341)
x <- seq(0, 1, 0.02)
y <- seq(0, 1, 0.02)
# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE, model="ExtT",
numblock=500, param=list(nugget=0,mean=0,scale=.1,
sill=1,df=5))
image.plot(x,y,log(sim$data))
################################################################
###
### Example 4. Simulation of a Gaussian random field.
### with double exponential correlation.
### One spatio-temporal replication.
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.1)
y <- seq(0, 1, 0.1)
# Define the temporal-coordinates:
times <- seq(1, 3, 1)
#
# Simulation of a spatial Gaussian random field:
sim <- RFsim(x, y, times, corrmodel="exp_exp", grid=TRUE,
param=list(nugget=0,mean=0,scale_s=0.3,
scale_t=0.5,sill=1))$data
# Spatial simulated data at first temporal instant
sim[,,1]
################################################################
###
### Example 5. Simulation of a Gaussian random field
### with exponential correlation on a portion of the earth surface
### One spatial replication.
###
###
###############################################################
lon_region<-c(-40,40)
lat_region<-c(-40,40)
#
lon<-seq(min(lon_region),max(lon_region),2)
lat<-seq(min(lat_region),max(lat_region),2)
#
data<-RFsim(coordx=lon,coordy=lat,corrmodel="exponential",
distance="Geod",grid=TRUE,param=list(nugget=0,mean=0
,scale=8000,sill=1))$data
image.plot(lon,lat,data,xlab="Longitude",ylab="Latitude")
map(database="world",xlim=lon_region,ylim=lat_region,add=TRUE)
Example output
Loading required package: sp
Loading required package: RandomFieldsUtils
Attaching package: 'RandomFields'
The following object is masked from 'package:RandomFieldsUtils':
RFoptions
Loading required package: maps
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.2-2 (2019-03-07) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
Attaching package: 'spam'
The following objects are masked from 'package:base':
backsolve, forwardsolve
See https://github.com/NCAR/Fields for
an extensive vignette, other supplements and source code
Warning messages:
1: In RandomFields::RFparameters(Storing = TRUE, PrintLevel = 1) :
The function is obsolete. Use 'RFoptions' instead.
2: In RandomFields::GaussRF(x = initparam$coordx, y = initparam$coordy, :
The function is obsolete. Use 'RFsimulate' instead.
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.9223940 0.30095477 0.40964995 0.91663621 1.931617440 1.6026049
[2,] 1.6409078 0.32642028 0.21445962 0.45864417 0.377860017 1.4668482
[3,] 0.7314876 1.10723890 0.07978236 0.61014840 -0.047291793 0.3963501
[4,] 0.3836722 0.36581006 -0.67844116 -0.18028133 -0.002249197 0.1451865
[5,] -0.3351690 0.08378569 -0.48840527 -0.15560243 0.968769420 1.6257795
[6,] 0.1148653 0.32548079 -0.93110371 -0.09962689 0.221159168 0.4808245
[7,] -0.7273573 -0.71882001 -0.41903596 -0.59467175 -0.600302312 -0.3679111
[8,] -0.7700930 -0.38159334 -0.50123552 -0.51089887 -0.597197773 -1.1799146
[9,] 0.0461754 0.21379873 0.71973787 -0.48487066 0.020964399 -0.3270232
[10,] -0.1692514 0.73675199 0.58485622 1.34802440 -0.147042067 -0.2146536
[11,] 2.4904466 2.52227083 1.61567154 0.63179305 -0.015514392 0.8259750
[,7] [,8] [,9] [,10] [,11]
[1,] 1.06404919 1.2124254 0.79459407 1.04054027 0.7369360
[2,] 0.99207459 1.7757777 1.37140622 1.09491858 0.3740511
[3,] 0.49380403 0.8407949 0.86398104 0.23143718 0.6993849
[4,] 0.07859698 1.4913128 1.45786054 0.16451392 1.2432092
[5,] 1.54919931 1.6371512 2.20387253 0.94538811 0.9217018
[6,] 1.68774621 -0.3773446 0.77509517 0.16526951 0.4287533
[7,] 0.29058317 0.5292003 0.09571764 0.01003232 0.7359176
[8,] -0.67686294 0.5683545 1.04658343 1.32212524 1.5057638
[9,] -0.05764332 0.7829094 1.55854845 1.97213767 1.7852469
[10,] -0.01513049 0.2478771 0.84146570 1.26912980 0.6758533
[11,] 0.28541850 0.6895920 1.53725236 0.56494878 1.4580636
CompRandFld documentation built on Jan. 10, 2020, 9:08 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Simulation of spatial and spatio-temporal Gaussian, binary and max-stable random fields. The function returns one or more replications of a random field for a given covariance model and covariance parameters.
Usage
1 2 3 |
Arguments
coordx |
A numeric (d x 2)-matrix (where
|
coordy |
A numeric vector giving 1-dimension of
spatial coordinates; |
coordt |
A numeric vector giving 1-dimension of
temporal coordinates. At the moment implemented only for the
Gaussian case. Optional argument, the default is |
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 |
grid |
Logical; if |
model |
String; the type of random field and therefore the densities associated to the likelihood
objects. |
numblock |
Numeric; the observation size of the underlying random field. Only in case of max-stable random fields. |
param |
A list of parameter values required in the simulation procedure of random fields, see Examples. |
replicates |
Numeric; a positive integer denoting the number of independent and identically distributed (iid) replications of a spatial or spatial-temporal random field. Optional argument, the default value is 1 then a single realisation is considered. |
threshold |
Numeric; a value indicating a threshold for the
binary random field. Optional in the case that |
Details
Note that this function is also interfaced to the R package RandomFields, using fast routines therein developed for the simulation of random fields.
Value
Returns an object of class RFsim.
An object of class RFsim is a list containing
at most the following components:
coordx |
A d-dimensional vector of spatial coordinates; |
coordy |
A d-dimensional vector of spatial coordinates; |
coordt |
A t-dimensional vector of temporal coordinates; |
corrmodel |
The correlation model; see |
data |
The vector or matrix or array of data, see
|
distance |
The type of spatial distance; |
model |
The type of random field, see |
numcoord |
The number of spatial coordinates; |
numtime |
The number the temporal realisations of the random field; |
param |
The vector of parameters' estimates; |
randseed |
The seed used for the random simulation; |
replicates |
The number of the iid replicatations of the random field; |
spacetime |
|
threshold |
The threshold for deriving the binary random field. |
Author(s)
Simone Padoan, simone.padoan@unibocconi.it, http://faculty.unibocconi.it/simonepadoan; Moreno Bevilacqua, moreno.bevilacqua@uv.cl, https://sites.google.com/a/uv.cl/moreno-bevilacqua/home.
References
Padoan, S. A. and Bevilacqua, M. (2015). Analysis of Random Fields Using CompRandFld. Journal of Statistical Software, 63(9), 1–27.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 | library(CompRandFld)
library(RandomFields)
library(mapproj)
library(fields)
################################################################
###
### Example 1. Simulation of a Gaussian random field.
### Gaussian random fields with Whittle-Matern correlation.
### One spatial replication.
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- runif(500, 0, 2)
y <- runif(500, 0, 2)
set.seed(261)
# Simulation of a spatial Gaussian random field:
data <- RFsim(x, y, corrmodel="matern", param=list(smooth=0.5,
mean=0,sill=1,scale=0.2,nugget=0))$data
################################################################
###
### Example 2. Simulation of a binary random field based on
### the latent Gaussian random field with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.05)
y <- seq(0, 1, 0.05)
set.seed(251)
# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE,
model="BinaryGauss", threshold=0,
param=list(nugget=0,mean=0,scale=.1,sill=1))
image(x,y,sim$data,col=terrain.colors(100))
################################################################
###
### Example 3. Simulation of a max-stable random
### extremal-t type with exponential correlation.
### One spatial replication on a regular grid
###
###
###############################################################
set.seed(341)
x <- seq(0, 1, 0.02)
y <- seq(0, 1, 0.02)
# Simulation of a spatial binary random field:
sim <- RFsim(x, y, corrmodel="exponential", grid=TRUE, model="ExtT",
numblock=500, param=list(nugget=0,mean=0,scale=.1,
sill=1,df=5))
image.plot(x,y,log(sim$data))
################################################################
###
### Example 4. Simulation of a Gaussian random field.
### with double exponential correlation.
### One spatio-temporal replication.
###
###
###############################################################
# Define the spatial-coordinates of the points:
x <- seq(0, 1, 0.1)
y <- seq(0, 1, 0.1)
# Define the temporal-coordinates:
times <- seq(1, 3, 1)
#
# Simulation of a spatial Gaussian random field:
sim <- RFsim(x, y, times, corrmodel="exp_exp", grid=TRUE,
param=list(nugget=0,mean=0,scale_s=0.3,
scale_t=0.5,sill=1))$data
# Spatial simulated data at first temporal instant
sim[,,1]
################################################################
###
### Example 5. Simulation of a Gaussian random field
### with exponential correlation on a portion of the earth surface
### One spatial replication.
###
###
###############################################################
lon_region<-c(-40,40)
lat_region<-c(-40,40)
#
lon<-seq(min(lon_region),max(lon_region),2)
lat<-seq(min(lat_region),max(lat_region),2)
#
data<-RFsim(coordx=lon,coordy=lat,corrmodel="exponential",
distance="Geod",grid=TRUE,param=list(nugget=0,mean=0
,scale=8000,sill=1))$data
image.plot(lon,lat,data,xlab="Longitude",ylab="Latitude")
map(database="world",xlim=lon_region,ylim=lat_region,add=TRUE)
|
Example output
Loading required package: sp
Loading required package: RandomFieldsUtils
Attaching package: 'RandomFields'
The following object is masked from 'package:RandomFieldsUtils':
RFoptions
Loading required package: maps
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.2-2 (2019-03-07) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
Attaching package: 'spam'
The following objects are masked from 'package:base':
backsolve, forwardsolve
See https://github.com/NCAR/Fields for
an extensive vignette, other supplements and source code
Warning messages:
1: In RandomFields::RFparameters(Storing = TRUE, PrintLevel = 1) :
The function is obsolete. Use 'RFoptions' instead.
2: In RandomFields::GaussRF(x = initparam$coordx, y = initparam$coordy, :
The function is obsolete. Use 'RFsimulate' instead.
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.9223940 0.30095477 0.40964995 0.91663621 1.931617440 1.6026049
[2,] 1.6409078 0.32642028 0.21445962 0.45864417 0.377860017 1.4668482
[3,] 0.7314876 1.10723890 0.07978236 0.61014840 -0.047291793 0.3963501
[4,] 0.3836722 0.36581006 -0.67844116 -0.18028133 -0.002249197 0.1451865
[5,] -0.3351690 0.08378569 -0.48840527 -0.15560243 0.968769420 1.6257795
[6,] 0.1148653 0.32548079 -0.93110371 -0.09962689 0.221159168 0.4808245
[7,] -0.7273573 -0.71882001 -0.41903596 -0.59467175 -0.600302312 -0.3679111
[8,] -0.7700930 -0.38159334 -0.50123552 -0.51089887 -0.597197773 -1.1799146
[9,] 0.0461754 0.21379873 0.71973787 -0.48487066 0.020964399 -0.3270232
[10,] -0.1692514 0.73675199 0.58485622 1.34802440 -0.147042067 -0.2146536
[11,] 2.4904466 2.52227083 1.61567154 0.63179305 -0.015514392 0.8259750
[,7] [,8] [,9] [,10] [,11]
[1,] 1.06404919 1.2124254 0.79459407 1.04054027 0.7369360
[2,] 0.99207459 1.7757777 1.37140622 1.09491858 0.3740511
[3,] 0.49380403 0.8407949 0.86398104 0.23143718 0.6993849
[4,] 0.07859698 1.4913128 1.45786054 0.16451392 1.2432092
[5,] 1.54919931 1.6371512 2.20387253 0.94538811 0.9217018
[6,] 1.68774621 -0.3773446 0.77509517 0.16526951 0.4287533
[7,] 0.29058317 0.5292003 0.09571764 0.01003232 0.7359176
[8,] -0.67686294 0.5683545 1.04658343 1.32212524 1.5057638
[9,] -0.05764332 0.7829094 1.55854845 1.97213767 1.7852469
[10,] -0.01513049 0.2478771 0.84146570 1.26912980 0.6758533
[11,] 0.28541850 0.6895920 1.53725236 0.56494878 1.4580636
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