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, see
for example
GaussRF,
MaxStableRF, ect.
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
Covmatrix,
GaussRF,
MaxStableRF
Examples
1
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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. 8, 2020, 3:01 p.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, see
for example
GaussRF,
MaxStableRF, ect.
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
Covmatrix,
GaussRF,
MaxStableRF
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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