# [R] range and anisotropy with RandomFields

jusin jusinowicz at gmail.com
Fri Feb 10 19:22:12 CET 2012

```Hello,

I am presently trying to get a feel for the various packages out there that
allow me to both analyze and simulate random fields. The package
RandomFields is nice, but there are still a few aspects of its
implementation that are confusing to me and I was hoping someone could help
clarify things for me. It could also be that my questions reflect a lack of
knowledge pertaining to random fields in general and not the RandomFields
package specifically, in which case someone can set me straight.

I like the versatility of the extended definition form that can be used in
RandomFields. For example, specifying an isotropic exponential model with a
nugget of 1 as:

modelA=list("+",
list("\$", var=2, scale=2, list("exp")),
list("\$", var=1, list("nugget"))
)

Ultimately I would like to work with anisotropic models (and data), and this
is where I get confused. I can specify a model with (geographic) anisotropy
by defining an anisotropy matrix, m and incorporating that into the
definition:

m = matrix( c(1,0,0,0.1), nrow=2)
modelA=list("+",
list("\$", var=2, anis=m, list("exp")),
list("\$", var=1, list("nugget"))
)

First, nowhere in the RandomFields documentation does it say how  the
anisotropy matrix is actually defined, so I am assuming it is the usual

A = [  1  0 ]  [  cos(phi)  -sin(phi)]
0  R       sin(phi)    cos(phi)

Where R is the ratio of the major range/minor range, and phi is the angle of
rotation.  Can anyone confirm this?

Also, there now  seems to be no way to explicitly specify the range of the
major axis (it states this in the documentation and an error will be
returned if I do try to set e.g. scale=2 in the definition) .  Thus when I
use e.g. GaussRF() to simulate a field using the above anisotropic model
definition I have no idea how the range (scale) is being determined.  Does
anyone now how RandomFields works in this context?

Thanks.

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```