Draw From a Gaussian Random Field

Fast and intuitive ways to draw from a Gaussian random field.

Usage

rgrf( n,
   locs, nx, ny=nx, xlim=c(0,1), ylim=c(0,1), tau=0,
   Covariance, theta, beta=0, X, 
   method=c('chol'),  method.args=list(sparse=FALSE), 
   eps = getOption("spam.eps"), drop=TRUE, attributes=TRUE, ...)

Arguments

n: number of observations.
locs: locations, the result of as.matrix(locs) will be used.
nx,ny: if no locations are specified, at least one of these to specify the grid dimension.
xlim,ylim: Domain, see ‘Details’.
tau: perturbation degree, see ‘Details’.
Covariance: covariance function name.
theta: covariance parameter.
beta: mean or vector for regression-type mean.
X: design matrix for regression-type mean.
method: based on Choleski factorization.
method.args: list of arguments that can be passed to the corresponding approach. For "chol" it can be, e.g., RStruct, chol.args, cov.args.
eps: small value, anything smaller is considered a collocation.
drop: logical, if a single realization should be returned as a vector.
attributes: logical, if should attributes be passed back.
...: currently not used.

Details

If no locations are given, the function constructs these according a regular or a regular perturbed grid. The perturbation is determined by tau, which has to be greater than zero (no perturbation) and strictly smaller than 1/2 (max perturbation).

The regular grid has spacing (here for x) dx=diff(xlim)/nx and runs from xlim[1]+dx/2 to xlim[2]-dx/2. The locations are at least (1/nx-2*tau*dx) separated.

Currently, the only method implemented is a Cholesky factorization routine, (much as in rmvnorm).

The rdist() from the fields package is awefully fast. Unless one has very sparse covariance matrices, a sparse approach is not bringing a lot of improvements.

The methods may use different covariance construction approaches and thus the nesting of cov.args in method.args.

Author

Reinhard Furrer

Examples

require(fields)
#> Loading required package: fields
#> Loading required package: viridisLite
#> 
#> Try help(fields) to get started.
# Regular grid with constant mean:
nx <- 10
field <- rgrf(1, nx=nx,  Covariance="cov.wend2", theta=c(.5, 1), beta=5)
quilt.plot(cbind(attr(field,"locs"),z=field), nx=nx, ny=nx)
points(attr(field,"locs"))


# Irregluar grid:
field <- rgrf(1, nx=10, tau=0.3, Covariance="cov.mat", theta=c(.2, 1, 1.5))
fields::quilt.plot(attr(field,"locs"), field)