Description Usage Arguments Details Value Author(s) References See Also Examples
grf()
generates (unconditional)
simulations of Gaussian random fields for
given covariance parameters.
geoR2RF
converts model specification used by geoR
to the correponding one in RandomFields.
1 2 3 4 5 6 7 | grf(n, grid = "irreg", nx, ny, xlims = c(0, 1), ylims = c(0, 1),
borders, nsim = 1, cov.model = "matern",
cov.pars = stop("missing covariance parameters sigmasq and phi"),
kappa = 0.5, nugget = 0, lambda = 1, aniso.pars,
mean = 0, method, RF=TRUE, messages)
geoR2RF(cov.model, cov.pars, nugget = 0, kappa, aniso.pars)
|
n |
number of points (spatial locations) in each simulations. |
grid |
optional. An n x 2 matrix with coordinates of the simulated data. |
nx |
optional. Number of points in the X direction. |
ny |
optional. Number of points in the Y direction. |
xlims |
optional. Limits of the area in the X direction. Defaults to [0,1]. |
ylims |
optional. Limits of the area in the Y direction. Defaults to [0,1]. |
borders |
optional. Typically a two coluns matrix especifying a polygon. See DETAILS below. |
nsim |
Number of simulations. Defaults to 1. |
cov.model |
correlation function. See |
cov.pars |
a vector with 2 elements or an n x 2 matrix with values of the covariance parameters sigma^2 (partial sill) and phi (range parameter). If a vector, the elements are the values of sigma^2 and phi, respectively. If a matrix, corresponding to a model with several structures, the values of sigma^2 are in the first column and the values of phi are in the second. |
kappa |
additional smoothness parameter required only for the
following correlation
functions: |
nugget |
the value of the nugget effect parameter tau^2. |
lambda |
value of the Box-Cox transformation parameter. The value lambda = 1 corresponds to no transformation, the default. For any other value of lambda Gaussian data is simulated and then transformed. |
aniso.pars |
geometric anisotropy parameters. By default an
isotropic field is assumed and this argument is ignored.
If a vector with 2 values is provided, with values for the
anisotropy angle psi_A (in
radians) and
anisotropy ratio psi_A, the coordinates
are transformed,
the simulation is performed on the isotropic (transformed) space
and then the coordinates are back-transformed such that the resulting
field is anisotropic. Coordinates transformation is performed
by the function |
mean |
a numerical vector, scalar or the same length of the data to be simulated. Defaults to zero. |
method |
simulation method with options for
|
RF |
logical, with defaults to TRUE, indicating whether
the algorithm should try to use the function
|
messages |
logical, indicating
whether or not status messages are printed on the screen (or output device)
while the function is running. Defaults to |
For the methods "cholesky"
, "svd"
and "eigen"
the
simulation consists of multiplying a vector of standardized
normal deviates by a square root of the covariance matrix.
The square root of a matrix is not uniquely defined. These
three methods differs in the way they compute the
square root of the (positive definite) covariance matrix.
The previously available
method method = "circular.embedding"
is no longer available
in geoR. For simulations in a fine grid and/or with a large number
of points use the package RandomFields.
The option "RF"
calls internally the function
GaussRF
from the package RandomFields.
The argument borders
, if provides takes a
polygon data set following argument poly
for the splancs' function csr
, in case of
grid="reg"
or gridpts
, in case of
grid="irreg"
. For the latter the simulation will have
approximately “n” points.
grf
returns a list with the components:
coords |
an n x 2 matrix with the coordinates of the simulated data. |
data |
a vector (if |
cov.model |
a string with the name of the correlation function. |
nugget |
the value of the nugget parameter. |
cov.pars |
a vector with the values of sigma^2 and phi, respectively. |
kappa |
value of the parameter kappa. |
lambda |
value of the Box-Cox transformation parameter lambda. |
aniso.pars |
a vector with values of the anisotropy parameters, if provided in the function call. |
method |
a string with the name of the simulation method used. |
sim.dim |
a string "1d" or "2d" indicating the spatial dimension of the simulation. |
.Random.seed |
the random seed by the time the function was called. |
messages |
messages produced by the function describing the simulation. |
call |
the function call. |
geoR2grf
returns a list with the components:
model |
RandomFields name of the correlation model |
param |
RandomFields parameter vector |
Paulo Justiniano Ribeiro Jr. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
Wood, A.T.A. and Chan, G. (1994) Simulation of stationary Gaussian process in [0,1]^d. Journal of Computatinal and Graphical Statistics, 3, 409–432.
Schlather, M. (1999) Introduction to positive definite functions and to unconditional simulation of random fields. Tech. Report ST–99–10, Dept Maths and Stats, Lancaster University.
Schlather, M. (2001) Simulation and Analysis of Random Fields. R-News 1 (2), p. 18-20.
Further information on the package geoR can be found at:
http://www.leg.ufpr.br/geoR.
plot.grf
and image.grf
for
graphical output,
coords.aniso
for anisotropy coordinates transformation
and, chol
,
svd
and eigen
for methods of matrix
decomposition and GaussRF
function
in the package RandomFields.
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 | sim1 <- grf(100, cov.pars = c(1, .25))
# a display of simulated locations and values
points(sim1)
# empirical and theoretical variograms
plot(sim1)
## alternative way
plot(variog(sim1, max.dist=1))
lines.variomodel(sim1)
#
# a "smallish" simulation
sim2 <- grf(441, grid = "reg", cov.pars = c(1, .25))
image(sim2)
##
## 1-D simulations using the same seed and different noise/signal ratios
##
set.seed(234)
sim11 <- grf(100, ny=1, cov.pars=c(1, 0.25), nug=0)
set.seed(234)
sim12 <- grf(100, ny=1, cov.pars=c(0.75, 0.25), nug=0.25)
set.seed(234)
sim13 <- grf(100, ny=1, cov.pars=c(0.5, 0.25), nug=0.5)
##
par.ori <- par(no.readonly = TRUE)
par(mfrow=c(3,1), mar=c(3,3,.5,.5))
yl <- range(c(sim11$data, sim12$data, sim13$data))
image(sim11, type="l", ylim=yl)
image(sim12, type="l", ylim=yl)
image(sim13, type="l", ylim=yl)
par(par.ori)
## simulating within borders
data(parana)
pr1 <- grf(100, cov.pars=c(200, 40), borders=parana$borders, mean=500)
points(pr1)
pr1 <- grf(100, grid="reg", cov.pars=c(200, 40), borders=parana$borders)
points(pr1)
pr1 <- grf(100, grid="reg", nx=10, ny=5, cov.pars=c(200, 40), borders=parana$borders)
points(pr1)
|
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