Description Usage Arguments Details Value References See Also Examples
RFoptions
sets and returns control arguments for the analysis
and the simulation of random fields. It expands the functionality of
RFoptions.
RFoptions(...)
arguments in tag = value
form, or a list of tagged
values.
The subsections below comment on
0. basic
: \RFU
1. general
: General options
2. br
: Options for BrownResnick
Fields
3. circulant
: Options for circulant embedding methods
RPcirculant
4. coords
: Options for coordinates and units, see
coordinate systems
5. direct
: Options for simulating by simple matrix decomposition
6. distr
: Options for distributions, in particular RRrectangular
7. empvario
: Options for calculating the empirical variogram
8. fit
: Options for RFfit
,
RFratiotest
, and RFcrossvalidate
9. gauss
: Options for simulating Gaussian random fields
10. graphics
: Options for graphical output
11. gui
: Options for RFgui
12. hyper
: Options for simulating hyperplane tessellations
13. krige
: Options for Kriging
14. maxstable
: Options for simulating maxstable random fields
15. mpp
: Options for the random coins (shot noise) methods
16. nugget
: Options for the nugget effect
17. registers
: Register numbers
18. sequ
: Options for the sequential method
19. solve
: Options for solving linear systems
20. special
: Options for some special methods
21. spectral
: Options for the spectral (turning bands) method
22. tbm
: Options for the turning bands method
23. internal
: Internal
1. General options
allowdistanceZero
boolean. Only used in
RFinterpolate
and in RFfit
.
If true, then
multiple observations or identical locations
are allowed within a single data set.
In this case, the coordinates are slightly scattered, so that
the points have some tiny distances.
Default: FALSE
.
cPrintlevel
cPrintlevel
is automatically set to printlevel
when printlevel
is changed.
Standard users will never use a value higher than 3.
0 : no messages
1 : messages and warnings when the user's input looks odd
2 : messages (and internal errors) documenting the choice of the
simulation method
3 : further user relevant informations
4 : information on recursive function calls
5 : function flow information of central functions
6 : errors that are internally treated
7 : details on building up the covariance structure
8 : details on taking the square root of the covariance matrix
9 : details on intermediate calculations
10 : further details on intermediate calculations
Note that printlevel
works
on the R level whereas cPrintlevel
works on the C level.
Default: 1
detailed_output
logical.
if TRUE
some function, e.g. RFcrossvalidate
will return additional information.
every
integer.
if greater than zero, then every every
th iteration is
printed if simulated by TBM or random coin method. The value zero
means that nothing is printed.
Default: 0
exactness
logical or NA. Currently only used when simulating Gaussian random fields.
TRUE
: RPcoins
,
RPhyperplane
, RPsequential
,
RPspectral
and RPtbm
and
approximative circulant embedding are excluded.
If the circulant embedding method is considered as badly
behaved, then the matrix decomposition methods are preferred.
FALSE
: all the methods are allowed.
If the circulant embedding method is
considered as badly behaved or the number of points to be
simulated is large, the turning bands methods are
rather preferred.
NA
: Similar to FALSE
, but
some inexact algorithms get less preference.
Default: NA
.
expected_number_simu
positive integer which is usally set
internally as the value of the argument n
in
RFsimulate
. The argument expected_number_simu
should be set only by an advanced users and only if
RFsimulate
will be called with argument n
alone.
gridtolerance
used in RFsimulate
to see if the coordinates build a
grid for x, y, z, Tvalues. This argument is also used
in case of conditional
simulation where the data locations might ly on
a grid.
Default: 1e6
logical. Lists of arguments are treated slightly
different from nonlists. If asList=FALSE
they are treated the
same way as nonlists. This options being set to FALSE
after
calling RFoptions
it should be set as first element of a list.
Default: TRUE
modus_operandi
character. One of the values
"careless"
, "sloppy"
, "easygoing"
,
"normal"
, "precise"
, "pedantic"
,
"neurotic"
.
This argument is in an experimental stage and its definition
and effects will change very likely in near future.
This argument sets a lot of argument at once related to estimation
and simulation. "careless"
prefers rather fast algorithms,
but the results
might be very rough approximations. By way of contrast,
"neurotic"
will try very
hard to return exact result at the cost of hugh computing times.
Default: "normal"
na_rm_lines
logical. If TRUE
then a line of the data that contains a
NA
value is deleted. Otherwise it is tried to deal with the
NA
value at higher costs of computing time. (Only used for
kriging – estimation can fully deal with NA
s.)
Default: FALSE
.
output
character.
one of the values "sp"
(if and only if
spConform=TRUE
),
"RandomFields"
(if and only if spConform=FALSE
),
"geoR"
.
The output mode geoR
currently adds some attributes such as
the call of the function.
NOTE: output
is in an experimental stage, whose effects might
change in future. Currently, output
changes the values of
reportcoord
, returncall
and spConform
.
pch
character.
RFfit
: shown before evaluating any method;
if pch!=""
then one or two
additional steps in the MLE methods are
marked by “+” and “#”.
Simulation:
The character is printed after each
performed simulation if more than one simulation is performed at
once. If pch='!'
then an absolute
counter is shown instead of the character.
If pch='%'
then a
counter of percentages is shown instead of the character.
Note that also ‘^H’s are printed in
the last two cases,
which may have undesirable interactions with some few other R
functions, e.g. Sweave
.
Default: '*'
.
practicalrange
logical or integer.
If not FALSE
the range of primitive
covariance functions is
adjusted so that cov(1) is zero for models with finite range.
(Operators are too complex to be adjusted; for anisotropic
covariance the practical range is not well defined.)
The value of cov(1) is about 0.05 (for scale=1
)
for models without range. See RMmodel
or type
RFgetModelNames(type="positive definite",
domain="single variable", isotropy="isotropic", operator=FALSE, vdim=1)
for the list of primitive models.
FALSE
: the practical range ajustment is not used.
TRUE
: practicalrange
is applicable only if
the value is known exactly, or, at least, can be approximated by
a closed formula.
2
: if the practical range is not known exactly it
is approximated numerically.
Default: FALSE
.
printlevel
If printlevel
<=0
there is not any output on the screen. The
higher the number the more tracing information is given.
Standard users will never use a value higher than 3.
0 : no messages
1 : important (error) messages and warnings
2 : less important messages
3 : details, but still for the user
4 : recursive call tracing (only used within RFfit
)
5 : function flow information of large functions
6 : errors that are internally treated
7 : details on intermediate calculations
8 : further details on intermediate calculations
Default: 1
character.
Current values are "always"
, "important"
,
"warn"
, "never"
,
Both "warn"
and "important"
have any effect only
if the coordinate system is changed internally. In this case
"warn"
yields a displayed warning message whereas
"important"
adds an attribute to the result as in the
case "always"
.
If "always"
or "important"
the reports are added as attribute to the results.
Note that in this case the class of the result may change
(e.g. from "numeric"
to "atomic"
).
Default: "warn"
logical. If TRUE
then the call is returned as an attribute
Default: TRUE
integer. If NULL
or NA
set.seed
is not called.
Otherwise, set.seed(seed)
is set
before simulations are performed, e.g. by
RFsimulate
or RFdistr
.
If the argument is set locally, i.e., within a function,
it has the usual local effect. If it is set globally, i.e. by
RFoptions
the seed
is fixed
for all subsequent calls.
If the number of simulations n
is greater than one
and if RFoptions(seed=seed)
is set, the ith
simulation is started with the seed ‘seed
+i1’.
Note also that RFratiotest
has its own argument
seed
with a slightly different meaning.
(does not work yet)
This argument is important iff RFsimulate
is used within
a function from package parallel.
The value of seed_incr
should be set only locally, i.e. not
by RFoptions()
.
If seed_incr != 0
(or the number of simulations n
is
greater than 1) and !is.na(seed)
then the seed for each simulation is calculated as
seed
+ (k1) * seed_sub_incr
+ seed_incr
* n
where k runs from 1 to n
.
Default: 0
set
integer.
Certain models (e.g. RMfixcov
and
RMcovariate
)
allow for lists as arguments.
set
selects a certain list element.
If necessary the list is recycled.
spConform
logical.
spConform=TRUE
might be used by
a standard user as this allows the comfortable use of plot
,
for instance, while spConform=FALSE
is much faster and
and consumes much less memory, hence might
be used by programmers or advanced users.
Details: if spConform=TRUE
then RFsimulate
and
many other functions
return an sp
object (which is an S4 object). Otherwise, matrices
or lists are
returned as defined in RandomFields 2.0, see the manuals for the
specific functions. Frequently, the latter have now a class attribute
to make the output nicer.
Note: for large data sets (to be generated),
spConform=TRUE
should not be used.
See also output
.
Default: TRUE
skipchecks
logical.
If TRUE
, several checks whether the given parameter values
and the dimension are within the allowed range is skipped.
Do not change the value of this variable except you really
know what you do.
Default: FALSE
$
storing
Logical.
If FALSE
then the intermediate results are
destroyed after the simulation of the random field(s)
or if an error had occured.
If storing=TRUE
, then
additional simulations can be performed by calling
RFsimulate
with at most the argument n
.
This call can then be much faster, but the a rather large
amount of memory could be kept.
When storing
turned from TRUE
to FALSE
by
global call then all registers are deleted.
Advanced:
With RFoptions(storing=list(FALSE, register,
model_register))
single registers can be deleted.
Default: FALSE
Ttriple
Logical or NA
.
If TRUE
, then triple for the time argument T
is
expected, containing start, step (by), length.
If FALSE
a sequence on a grid is expected.
If NA
then the decision is automatic, but will lead to an
error if ambiguous.
vdim_close_together
logical. Used especially in functions that
create covariance matrices. If the model is multivariate, then two
ways of ordering the matrix exist. To consider first all variables at
a certain location (vdim_close_together=TRUE
) or to consider first
all locations keeping the variable fixed
(vdim_close_together=FALSE
).
Note that several simulation methods rely on the value FALSE
,
so that these methods will not work anymore if
vdim_close_together=FALSE
.
Default: FALSE
.
2. Options for BrownResnick Fields
deltaAM
integer; only used for simulation of BR processes via RPbrmixed
with optim_mixed=2
. In this case, deltaAM
is the number
of additionally simulated Gaussian processes used for an update of
areamat
in the optimization pricedure.
Default: 300
maxtrendmem
integer; the maximal number of real valued variables used for intermediate storage:
RPbrshifted: trends for shifted locations that may be stored at the same time when simulating BR processes.
RPbrnormed: Let n be the number of locations. Then a n\times n (covariance) matrix has to be evaluated at random columns.
if maxtrendmem
is large (and n small, n≤ 10^4),
multiple evaluations can be avoided.
Default: 1e7
.
meshsize
positive; width of the grid on which the shape functions in the M3
representation of BR processes are simulated; only used for
simulation of BR processes via RPbrmixed
.
Default: 0.1
.
optim_mixed
0, 1, 2
; only used for simulation of BR
processes via RPbrmixed
.
If optim_mixed=0
, the arguments
lambda
and
areamat
of RPbrmixed
are used for the simulation.
If optim_mixed=1
, lambda
is estimated for
areamat=1
.
If optim_mixed=2
, areamat
is optimized and
lambda
is estimated.
Default: 1
.
optim_mixed_tol
value in [0,1]; only used for simulation of BR processes via
RPbrmixed
with optim_mixed=2
. In this case,
areamat
is optimized under the constraint that the
probability of drawing the shape function incorrectly is bounded by
optim_mixed_tol
(cf. Oesting et al., 2012).
Default: 0.01
.
variobound
positive; the shape functions in the mixed moving maxima
representation are cut off where the variogram belonging
to phi
exceeds variobound
.
Default: 8.0
.
vertnumber
positive integer; for an efficient simulation of the shape functions
in the M3 representation of BR processes, the component E from
of the domain [x_0, Inf] x E of the
underlying Poisson point process is subdividedinto cubes
(cf. Oesting et al., 2012); vertical
is the number of
vertical breaks of E; only used for simulation of BR processes
via RPbrmixed
with optim_mixed=2
.
Default: 7
.
3. circulant
: Options for circulant embedding methods, cf. RPcirculant
These options influence the standard circulant embedding
method, cutoff circulant embedding intrinsic circulant embedding.
It can also influence RPtbm
if the line is simulated
with any circulant embedding method.
approx_maxgrid
See RPcirculant
approx_step
See RPcirculant
dependent
See RPcirculant
force
See RPcirculant
maxGB
See RPcirculant
maxmem
See RPcirculant
mmin
See RPcirculant
strategy
See RPcirculant
tolIm
See RPcirculant
tolRe
See RPcirculant
trials
See RPcirculant
useprimes
See RPcirculant
4. coords
: Options for coordinates and units
coord_system
character. See coordinate systems
coordunits
See coordinate systems
coordnames
See coordinate systems
new_coord_system
See coordinate systems
new_coordunits
See coordinate systems
polar_coord
See coordinate systems
varnames
See coordinate systems
varunits
See coordinate systems
xyz_notation
See coordinate systems
zenit
See coordinate systems
5. direct
: Options for simulating by simple matrix decomposition
max_variab
Maximal size of the covariance matrix.
Default: 12000
6. distr
: Options for distributions, in particular RRrectangular
innermin
Default value to simulate from the
RRrectangular
distribution.
The minimal length of the interval where the Taylor expansion shall
be valid.
Default: 1e20
.
maxit
Default value to simulate from the
RRrectangular
distribution.
The number of iterative steps where the the constant of the Taylor development is increased, to find an upper bound for the given function.
Default: 20
.
maxsteps
Default value to simulate from the
RRrectangular
distribution.
maxsteps
is usually the number of steps in the middle part of
the approximation. From this value and the length between
the determined endpoints for the approximation at the origin and in
the tail, the step length is calculated. If the step length is less
than minsteplen
the number of steps is reduced.
Default: 1000
.
mcmc_n
In case of the use of MCMC it leaves out n1 member of the Markov chain bevor the n member is returned. See also maxsteps.
Default: 15
.
minsteplen
Default value to simulate from the
RRrectangular
distribution.
The minimal step length
for the middle part of approximation, which is a step function,
Default: 0
(i.e. not used as a criterion.)
outermax
Default value to simulate from the
RRrectangular
distribution.
The largest possible endpoint for the middle part that
approximates the function by a step function. See also innermax
.
Default: 20.
parts
Default value to simulate from the
RRrectangular
distribution.
parts
determines the number of tests that are performed to
check whether a proposed power function is an upper bound for
the given function, at the origin and the tail.
Default: 8
.
repetitions
Minimal number of realisations to determine a quantity of the distribution by MCMC. E.g. to determine the integral value c in the paper of Oesting, Schlather, Zhou.
Default: 1000.
safety
Default value to simulate from the
RRrectangular
distribution.
First, at the origin, the first power function of the Taylor
expansion is taken as potential upper function.
The constant of the power function are increased by factor
1 + safety
and the exponent of the function
similarly decreased. A number of test evaluations
is performed to check whether this modified function is indeed
a upper bound. If not, the considered interval at the origin
is reduced iteratively, the constants of the power function
further increased and the exponent decreased.
If maxit
iteration have been performed without success,
the search for an upper bound fails.
The search at the origin also fails if the interval around
the origin has become less than innermin
.
Similar procedure is performed for the tail.
Default: 0.08
.
7. empvario
: Options for calculating the empirical variogram
fft
Logical. Determines whether FFT should be used for data on a grid
Default: TRUE
.
phi0
numeric. In case of anisotropic fields directional cones are
considered. The argument phi0
determines the starting angle.
Default: 0
.
pseudovariogram
logical. Only in the multivariate case. Whether the pseudovariogram or the crossvariogram should be calculated.
Default: FALSE
.
theta0
numeric. In case of anisotropic fields directional cones are
considered. The argument theta0
determines one of the
boundaries, hence all boundaries for a given fixed number of cones.
The argument theta0
determines the starting value of the
second anglue in polar coordinate representation in 3 dimensions.
Default: 0
.
tol0
numeric. Estimated values of the empirical variogram
below tol0
times the grid step in the third dimension
are considered to be zero. Hence the respective values are set
to zero.
Default: 1e13
.
8. fit
: Options for RFfit
,
RFratiotest
, and RFcrossvalidate
algorithm
See RFfitOptimiser.
Default: NULL
approximate_functioncalls
In case the parameter vector is too close to the given
bounds, the ML target function is evaluated on a grid
to get a new initial value for the ML estimation.
The number of points of the grid is approximately
approximate_functioncalls
.
Default: 50
boxcox_lb
lower bound for the BoxCox transformation
Default: 10
.
boxcox_ub
upper bound for the BoxCox transformation
Default: 10
.
bin_dist_factor
numeric. The empirical variogram is calculated up the distance
bin_dist_factor
times (maximum distance among any pair of locations)
Default: 0.5
.
bins
vector of explicit boundaries for the bins or the
number of bins for the empirical variogram (used in the
LSQ target function, which is described at the beginning
of the Details).
Note that for anisotropic models, the value of bins
might
be enlarged.
Default: 20
.
critical
logical or signed integer.
If critical=FALSE
and if the result of
any maximum likelihood method
is on a borderline, then the optimisation is redone
in a modified way (which takes about double extra time)
If critical=TRUE
and if the result of
any maximum likelihood method
is on a borderline, then a kind of profile likelihood
optimization is done (which takes about 10 times extra time)
If critical>=2
then a kind of profile likelihood
optimization is always done (which takes about n_crit
times extra time) for an automatically chosen selection
of the model parameters.
If critical>=3
then a kind of profile likelihood
optimization is always done (which takes about n_crit
times extra time) for all the parameters.
If critical<0
then none of the refined methods
are performed.
Default: TRUE
.
cross_refit
logical.
For each of the subset of the crossvalidation method
the parameters have to be fitted to the given model.
If cross_refit
is TRUE
, this is done, but takes a huge
amount of time. If FALSE
, the model is fitted only once to
the data and the value at
each point is predicted with the same model given
the values of the other points.
Default: FALSE
.
see RFlikelihood
.
See the argument control
in optim.
factr_recall
is used for intermediate calculations.
character – not programmed yet.
types of likelihood are "auto"
, "full"
,
"composite"
, "tesselation"
;
Default: "auto"
lowerbound_scale_factor
The lower bound for the scale is determined as
(minimum distance between different pairs of points) /
lowerbound_scale_factor
.
Default: 3
.
lowerbound_scale_ls_factor
For the LSQ target function a different lower bound for the scale is used. It is determined as
(minimum distance between different pairs of points) /
lowerbound_scale_ls_factor
.
Default: 5
.
lowerbound_var_factor
The lower bound for the nugget and the variance is determined
as var(data
) / lowerbound_var_factor
.
If a standard model definition is given and
either the nugget or the variance is fixed,
the parameter to be estimated
must also be greater than lowerbound_sill
.
Default: 10000
.
maxmixedvar
OBSOLETE. upper bound for variance in a mixed model; so, the covariance model for mixed model part might be calibrated appropriately
max_neighbours
integer. Maximum number of locations (with depending values) that are allowed.
Default: 5000
.
minbounddistance
If any value of the parameter vector
returned from the ML estimation
is closer than minbounddistance
to any of the bounds or if any value
has a relative distance smaller than
minboundreldist
, then it is assumed that
the MLE algorithm has dropped into a local minimum,
and it will be continued with evaluating the
ML target function on a grid, cf. the beginning paragraphs
of the Details.
Default: 0.001
.
minboundreldist
relative distance to the bounds
below which a part of the algorithm is considered as
having failed. See minbounddistance
.
Default: 0.02
.
min_diag
Minimal value of any estimated diagonal matrix element.
Default: 1e7
.
n_crit
integer. The approximate profiles that are considered.
Default: 10
.
nphi
scalar or vector of 2 components.
If it is a vector then the first component gives the first angle
of the xy plane
and the second one gives the number of directions on the half circle.
If scalar then the first angle is assumed to be zero.
Note that a good estimation of the variogramm by LSQ with a
anisotropic model a large value for ntheta
might be needed
(about 20).
Default: 1
.
ntheta
scalar or vector of 2 components. If it is a vector then the first component gives the first angle in the third direction and the second one gives the number of directions on the half circle. If scalar then the first angle is assumed to be zero.
Note that a good estimation of the variogramm by LSQ with a
anisotropic model a large value for ntheta
might be needed
(about 20).
Default: 1
.
ntime
scalar or vector of 2 components.
if ntimes
is a vector, then the first component are the
maximum time distance (in units of the grid length T[3]
) and the
second component gives the step size (in units of the grid length
T[3]
). If scalar then the step size is assumed to 1 (in units
of the grid length T[3]
).
Default: 20
.
only_users
boolean.
If true then only users_guess
is used as a
starting point for the fitting algorithms
Default: FALSE
.
optimiser
See RFfitOptimiser.
Default: "optim"
.
See the argument control
in optim.
pgtol_recall
is used for intermediate calculations.
refine_onborder
logical.
If TRUE
and an estimated parameter of the model
is close to the boundary, a second search for the optimum
is started.
Default: TRUE
minmixedvar
lower bound for variance in a mixed model; so, the covariance model for mixed model part might be calibrated appropriately
Default: 1/1000
ratiotest_approx
logical.
if TRUE
the approximative formula that twice the
difference of the likelihoods follow about a χ^2
distribution is used. The parameter of freedom equals
the number of parameters to be estimated for the covariance
function, including those for the covariates.
Default: TRUE
reoptimise
logical.
If TRUE && !only_users
then at a very last step,
the optimisation is redone with currently best parameters
and likelihood as scale parameter for optim
.
Default: TRUE
.
scale_max_relative_factor
If the initial scale
value for the ML estimation
obtained by the LSQ target function is
less than
(minimum distance
between different pairs of points) /
scale_max_relative_factor
a warning is given that probably a nugget effect
is present.
Note: if scale_max_relative_factor
is greater
than lowerbound_scale_ls_factor
then
no warning is given as
the scale has the lower bound (minimum distance
between different pairs of points) /
lowerbound_scale_ls_factor
.
Default: 1000
scale_ratio
RFfit
uses parscale
and fnscale
in the calls of optim
. As these arguments should
have the magnitude of the estimated values, RFfit
checks this by calculating the absolute log ratios.
If they are larger than scale_ratio
,
parscale
and fnscale
are reset and the optimisation
is redone.
Default: 0.1
.
shortnamelength
The names of the variables in the returned table are
abbreviated by taking the first shortnamelength
letters.
Default: 4
.
smalldataset
If the number of locations is considered as small, then some more data are kept in the storage to accelerate the estimation algorithm.
Default: 2000
.
split
integer.
If the number of parameters to be numerically optimised is larger
than or equal to split
then RFfit
checks whether a
spacetime covariance model or a multivariate covariance model
can be split into components, so that certain parameters
can be estimated separately.
Default: 4
.
cliquesize
integer.
RFfit
tries to split the data set
into parts of size splitn_neighbours[2] or less, but never more than
splitn_neighbours[3]
and never less than
splitn_neighbours[1].
Default: c(200, 1000, 3000)
.
splitfactor_neighbours
The total number of neighbouring boxes in each direction 1 + 2\code{splitfactor}, including the current box itself.
Default: 2
.
split_refined
logical.
If TRUE
then also submodels are fitted if splitted.
This takes more time, but anova
and
RFratiotest
, for instance,
will give additional information.
Default: TRUE
.
upperbound_scale_factor
The upper bound for the scale is determined as
upperbound_scale_factor
* (maximum distance
between all pairs of points).
Default: 3
.
upperbound_var_factor
The upper bound for the
variance and the nugget is determined
as upperbound_var_factor
* var(data
)
Default: 10
.
use_naturalscaling
logical. Only used if model is given in standard (simple) way.
If TRUE
then internally, rescaled
covariance functions will be used for which
cov(1)~=0.05.
use_naturalscaling
has the advantage that scale
and the form parameters of the model get ‘orthogonal’,
but use_naturalscaling
does not work for all models.
Note that this argument does not influence
the output of RFfit
: the parameter vector
returned by RFfit
refers
always to the standard covariance model as given in
RMmodel
. (In contrast to practicalrange
in RFoptions
.)
Advantages if use_naturalscaling=TRUE
:
scale
and the shape parameter of a parameterised
covariance model can be estimated better if they are estimated
simultaneously.
The estimated bounds calculated by means of
upperbound_scale_factor
and lowerbound_scale_factor
,
etc. might be more realistic.
in case of anisotropic models, the inverse of the elements of the anisotropy matrix should be in the above bounds.
Disadvantages if use_naturalscaling=TRUE
:
For some covariance models with additional parameters, the
rescaling factor has to be determined numerically.
Then, more time is needed to perform RFfit
.
note the use_naturalscaling
only affects simple
models, no operators. Also functions that define a parameter of
the model are not changed.
Default: FALSE
.
9. gauss
: Options for simulating Gaussian random fields
approx_zero
Value below which a correlation is considered to be essentially zero. This argument is used to determine the practical range of covariance function with noncompact support.
Default: 0.05
boxcox
real vector of one or two components.
If the first component is Inf
then no transformation
is performed. Otherwise the BoxCox transformation is performed.
Note that Box Cox only works in a Gaussian framework.
Note further that either boxcox
or loggauss
may be given.
Default c(Inf, 0)
direct_bestvar
integer.
When searching for an appropriate simuation method
the matrix decomposition method (method="direct"
)
is preferred if the number of variables is less than or equal to
direct_bestvariables
.
Default is 1200
.
loggauss
logical. Whether a logGauss random fields should be returned.
See also boxcox
for a generalisation.
paired
(“Antithetic pairs”.)
Logical. If TRUE
then the second half of the
simulations is logical. If TRUE
then the second half of the
simulations is obtained by
only changing the signs of all the standard Gaussian random variables,
on which the first half of the
simulations is based. Default is FALSE
.
stationary_only
See RPgauss
10. graphics
: Options for graphical output
always_close_device
logical.
If FALSE
the current device is kept as it is;
otherwise the current device is closed before the next
device is opened. If NA
it closes the preceding device
if the opened device is pdf or jpeg.
Default: NA
.
always_open_device
logical.
If TRUE
a new graphical window is opened for every
plot
if a standard graphical output is
used, trying to respect the aspect ratios for the plots.
The devices pdf and jpeg are always opened.
If NA
then the value is set
to interactive()
.
Default: TRUE
.
close_screen
logical; only relevant if
split_screen = TRUE
and always_close_screen = FALSE
.
If FALSE
the windows opened by
split.screen
are left open.
Default: TRUE
.
file
character; only relevant if
split_screen = TRUE
.
argument file
in pdf
If ""
then no internal naming is performed.
Default: ""
.
filenumber
integer; only relevant if
split_screen = TRUE
. Starting number of the file if
onefile=FALSE
. It is set to 0 whenever file
is
changed and onefile=FALSE
.
Default 0.
grDefault
logical. If FALSE
the graphic style up to Version 3.2
is used. Otherwise, the changes of th graphical style are reduced to
a minimum.
Default: FALSE
grPrintlevel
integer values 0, 1, 2; only relevant when simulations are plotted. The higher the more text is shown in the plot.
Default: 1
.
height
real number; only relevant if
a new device is opened, see alwyas_open_screen
.
height=NA
or height
is not positive: no device
is opened.
width = NA
If height
is greater than zero then it gives the height
of a single figure in a plot created by RandomFields;
See also close_screen
.
If plots with multiple figures are
shown, the height and width of the plot
will be increased by a factor up the
ones given by increase_upto
.
The width is calculated so that the aspect ratio is correct.
width
not NA
height
and width
give the size of the
whole window.
Default: 6
.
increase_upto
See height
.
Default: c(3,4)
.
split_screen
logical.
If TRUE
split.screen
is used to split the screen.
Otherwise par(mfcol)
.
When using split_screen
then the figures tend to be fancier.
Default: TRUE
.
onefile
logical; only relevant if
split_screen = TRUE
.
About the behaviour of argument onefile
in
pdf
Default: FALSE
.
width
real number or NA; only relevant if
always_open_screen=TRUE
. See height
for details.
Default: NA
.
11. gui
: Options for cRFgui
alwaysSimulate
logical. If TRUE
then a new random field is simulated
whenever a parameter is changed. Otherwise only the covariance
function or the variogram is replotted; simulations are performed
only when the correponding button is pressed.
Default: TRUE
.
simu_method
"RPcirculant"
,
"RPcutoff"
,
"RPintrinsic"
,
"RPtbm"
,
"RPspectral"
,
"RPdirect"
,
"RPsequential"
,
"RPaverage"
,
"RPnugget"
,
"RPcoins"
,
"RPhyperplane"
,
"RPspecific"
,
"any method"
.
Default: "RPcirculant"
.
size
vector of 2 components. Grid size of the simulated stochastic processes. The two components of the vector correspond to onedimensional and twodimensional processes, respectively.
Default: c(1024, 64)
.
12. hyper
: Options for simulating hyperplane tessellations
mar_distr
integer. This argument should not be changed yet.
It codes the marginal distribution used in the simulation:
0 : uniform distribution
1 : Frechet distribution with form argument mar_param
2 : Bernoulli distribution (Binomial with n=1) with
argument mar_param
Default: 0
.
mar_param
Argument used for the marginal distribution. The argument should not be changed yet.
Default: NA
.
maxlines
integer. Maximum number of allowed lines.
Default: 1000
.
superpos
integer. number of superposed hyperplane tessellations.
Default: 300
.
13. krige
: Options for Kriging
cholesky_R
obsolete
fillall
logical value for imputing.
If true all the components are estimated whether they are
NA
or not.
Default: TRUE
.
locmaxn
Kriging is conditions on maximal locmaxn
points.
If the data contain more points, neighbourhood kriging is performed.
Default: 8000
.
locsplitfactor
In case of neighbourhood kriging, the area is split into small
boxes. The complete neighbourhood contains (2 *
locsplitfactor
+1) boxes in each direction.
Default: 2
.
locsplitn
vector of 3 components.
A box should contain no more than locsplitn[3]
points, but never less than locsplitn[1]
. If
a box had originally less than locsplitn[1]
points,
then the box is increased until at least locsplitn[2]
points are in the box.
Default: c(200, 1000, 5000)
.
method
obsolete
return.variance
logical.
If FALSE
the kriged field is
returned. If TRUE
a list of two elements, estim
and
var
, i.e. the kriged field and the kriging variances,
is returned.
Default: FALSE
.
14. maxstable
: Options for simulating maxstable random fields
check_every
integer. In order to get a precise simulation result, by definition,
the maximum must be taken, for each shape function, over alle
locations of interest. Clearly, small values will not play a role.
To this end, the global minimum has to be determined.
The calculation of the global minimum is expensive and therefor
should not be done too frequently. On the other hand,
rare updates increases the computing times for taking the maximum
over a single shape functions. Here, after every check_every
considered shape function, the global minimum is calculated.
It is expected that a good choice for check_every
is in
in the interval [10, 100].
(For ease and for concerns of efficiency, the more adequate, local minimum is not considered.)
Default: 30 .
density_ratio
value in [0,1]. This argument is considered only
if flat=1
and the simulation is performed on a grid.
Then, the ratio between the highest and the lowest value is
calculated within the convex hull of the grid. If the
value is less than density_ratio
then the grid points
are considered separately. Else the density is considered to be
constant in the convex hull of the grid.
Default: 0.0.
eps_zhou
positive real number, which
gives the aimed relative precision when the constant c
in the paper of Oesting, Schlather, Zhou (2018) has to be estimated.
E.g. if eps_zhou=0.01
then the first 2 digits should be
correct.
Default: 0.01
flathull
NA, FALSE, TRUE
. Only used in M3
modelling in the algorithm by Oesting, Schlather, Zhou (2018).
The argument is considered only if the simulation is performed on a
grid.
If flat=TRUE
, then the density
is considered to be flat
in the convex hull of the grid,
i.e. the simulation method of Schlather (2002) is used.
If flat=NA
the choice is done automatically.
Default: FALSE .
max_gauss
The simulation of the maxstable process by the oldfashioned
method of Schlather (2002) and by older methods for BrownResnick
processes
uses
a stopping rule that necessarily needs a finite upper endpoint
of the marginal distribution of the random field.
In the case of
BrownResnick processes
,
extremal Gaussian fields
,
and
extremal t fields
,
the upper endpoint is approximated by standardmax
.
Default: 3.0
.
max_n_zhou
positive integer. The overall constant c in the paper of Oesting, Schlather, Zhou (2018) has to be determined by MCMC, if the shape functions are random.
The two arguments, min_n_zhou
and max_n_zhou
,
give the minimal and the maximal
number of simulations that are performed. To economize
computer time the values of c is partially estimated
when the shape functions are simulated. If the number
of shape functions is larger than the number of simulations
given by eps_zhou
then
no further simulation is performed to determine c.
So, it is advantageous to simulate all fields at once by
RFsimulate(..., n = )
.
Default: 1000 and 10000000, respectively.
maxpoints
positive integer; the maximal number of Poisson points to be simulated
for one realization of the maxstable random field. This option will
not be considered for most of the users. This option allows
the simulation to interrupt after maxpoints
shape function
have been placed.
Default: 2e9
(never).
mcmc_zhou
positive integer.
In case of random shape functions, an MCMC step is required.
mcmc_zhou
1 equals the number of members of the MCMC chain
that are left out before the next value of the chain is returned.
Default: 20
min_n_zhou
see max_n_zhou
mcmc_zhou
positive integer.
In case of random shape functions, an MCMC step is required.
mcmc_zhou
1 equals the number of members of the MCMC chain
that are left out before the next value of the chain is returned.
Default: 20
min_n_zhou
see max_n_zhou
min_shape_gumbel
To increase speed,
the minimum field value is assumed to be min_shape_gumbel
for calculation of threshold values for simulation short cuts.
During a simulation, its value becomes void as soon as the real
(current) minimum of the field being simulated exceeds
min_shape_gumbel
Default: 1e15
.
scatter_method
logical. If
Default: NA;
xi
Extreme value index. Default: 2e9
.
While ξ can be set globally, the shift μ and the
scale s can be given only locally within the process
definitions, e.g., RPsmith
.
Default: 1.0
.
15. mpp
: Options for the random coins (shot noise) methods
about_zero
In certain cases (Coins,RMtruncsupport),
functions are assumed to zero if the value is less than about_zero
.
Default: 0.001
.
n_estim_E
integer. Number of draws from the
distribution of the scale to estimate the mean of the distribution.
This is used only if the mean of the scale distribution
is not explicitely given.
Default: 50000
.
scatter_method
scatter_size
, scatter_max
Real valued and integer valued, respectively, or NA
.
Used in the internal function RMscatter
that calculates
∑_{i=1}^n f(x + h_i) for some function f and
for some distances h_i.
Let \varepsilon=about_zero
, s=scatter_size
and m=scatter_max
.
We distinguish 4 cases:
scatter_size > 0
and scatter_max >= 0
Here, n equals (2m)^d.
and h_i \in M = \{ (k s, …, k s),…, (m s, …, m
s)\}
with k=m.
scatter_size > 0
and scatter_max < 0
same as the previous case, but m is chosen such that
f(k_i e_i s_i) \approx \varepsilon, k_i\in N,
i=1,…,d and
f(m_i e_i s_i) \approx \varepsilon, m \in N.
scatter_size <= 0
and scatter_max >= 0
This option is possible only for grids.
Here h_i runs on the given grid i=1,…,d,
but at most scatter_max
steps.
scatter_size <= 0
and scatter_max < 0
this option is possible only for grids.
Here, h_i runs over the whole grid.
shape_power
Shape functions are powered by shape_power
before used as
intensity function for the point process.
Default: 2.0
.
16. nugget
: Options for the nugget effect
Simulating a nugget effect is per se trivial.
However, it gets complicated
and best methods (including direct
and circulant
embedding
!) fail if zonal anisotropies are considered,
where sets of points have to be identified that belong to the
same subspace of eigenvalue 0 of the anisotropy matrix.
tol
The nugget tolerance influences two different kind of models
RPnugget
R.is
See there for more information.
17. registers
: Register numbers
Model for different purposes are or can be stored at
different places. They are called registers and have nonnegative
numbers up to 21 (currently).
The user can use the registers 0..9.
register
number in 0:9; place where intermediate calculation for random field simulation are stored; the number refers to 10 internal registers 0..9.
Changing the register number only makes sense, when
two different random fields, say, are to be simulated
alternatingly, several times in a row. Then the
simlulation speed can be increased if several registers
are used, storing=TRUE
and RFsimulate
is used with the only argument n
.
Default: 0
18. sequ
: Options for the sequential method
back_steps
See RPsequential
initial
See RPsequential
max_variables
See RPsequential
19. solve
: Options for solving linear systems
det_as_log
eigen2zero
max_chol
integer. Maximum number of rows of a matrix in a Cholesky decomposition
Default: 8192
max_svd
integer. Maximum number of rows of a matrix in a svd decomposition
Default: 6555
pivot
Type of pivoting for the Cholesky decomposition. Possible values are
No pivoting.
If the matrix has a size greater than 3x3 and Choleskey fails without pivoting, privoting is done. For matrices of size less than 4x4, no pivoting and no checks are performed.
Do alwaoys pivoting. NOTE: privoted Cholesky decomposition yields only very approximately an upper triangular matrix L, but still L^t L = M holds true.
uses the same pivoting as in the previous pivoted decomposition. This option becomes relevant only when simulations with different parameters or different models shall be performed with the same seed so that also the pivoting must be coupled.
Default: PIVOT_auto
pivot_actual_size
pivot_check
logical. Only used in pivoted Cholesky
decomposition.
If TRUE
and a numerically zero diagonal element is detected,
it is checked whether the offdiagonal elements are numerically zero
as well.
(See also pivot_max_deviation
and
pivot_max_reldeviation
.)
if NA
then, in RPdirect, the value is equivent to
FALSE
if the model is positive (semi)definite.
TRUE
if the model is genuinely negative definite.
Default: NA
pivot_idx
pivot_relerror
pivot_max_deviation
pivot_max_reldeviation
solve_method
spam_factor
spam_min_n
spam_min_p
spam_pivot
spam_sample_n
spam_tol
svdtol
use_spam
20. special
: Options for specific methods
multicopies
Only used by RMmult
.
The covariance functions are multiplied if the corresponding
independent random fields are multiplied. To get
an approximative Gaussian random fields with a multiplicative
covariance functions the average over multicopies
products of random fields is calculated.
21. spectral
: Options for the spectral (turning bands) method
ergodic
In case of an additive model and ergodic=FALSE
,
the additive component are chosen proportional to their
variance. In total lines
are simulated. If
ergodic=TRUE
, the components are simulated
separately and then added.
Default: FALSE
.
prop_factor
see RPspectral
sigma
see RPspectral
sp_grid
see RPspectral
sp_lines
see RPspectral
22. tbm
: Options for the turning bands method
center
Scalar or vector.
If not NA
, the center
is used as the center of
the turning bands for TBM2
and TBM3
.
Otherwise the center is determined
automatically such that the line length is minimal.
See also points
and the examples below.
Default: NA
.
fulldim
positiv integer. The dimension of the space into which the
simulated field is embedded. So, the value fulldim
must be at least the dimension of the field.
Default: 3.
grid
Logical.
The angle of the lines is random if
grid=FALSE
,
and k*pi/lines
for k in 1:lines
,
otherwise.
This option is used by both RPspectral
and RPtbm
, the latter only when the dimension is 2.
Default: TRUE
.
layers
Logical or integer. If TRUE
then the turning layers are used whenever
a time component is given.
If NA
the turning layers are used only when the
traditional TBM is not applicable.
If FALSE
then turning layers may never be used.
Default: TRUE
.
lines
Number of lines used.
Default: 60
.
linesimustep
If linesimustep
is positive the grid on the line has lag
linesimustep
.
See also linesimufactor
.
Default: 0.0
.
linesimufactor
linesimufactor
or
linesimustep
must be nonnegative; if
linesimustep
is positive then linesimufactor
is ignored.
If both
arguments are naught then points
is used (and must be
positive).
The grid on the line is linesimufactor
times
finer than the smallest distance.
See also linesimustep
.
Default: 2.0
.
points
integer. If greater than 0,
points
gives the number of points simulated on the TBM
line, hence
must be greater than the minimal number of points given by
the size of the simulated field and the two paramters
TBMx.linesimufactor
and TBMx.linesimustep
.
If points
is not positive the number of points is
determined automatically.
The use of center
and points
is highlighted
in an example below.
Default: 0
.
reduceddim
if positiv integer, then the value itself. If negativ, then the value is substracted from fulldim.
Default: 2
.
23. internal
: Internal options mostly for warnings and
messages
All these options should not be changed by the user unless he/she really known what he/she is doing.
Most of the options below change their value in a session without the user's notice.
do_tests
Internal variable. Do not use it.
Default: FALSE
.
examples_reduced
nonnegative integer. If positve, then the design of any simulation in RandomFields is internally reduced in size (roughly downto the given value in each direction). Warnings report this behaviour. This option is necessary to run the examples of RandomFields under the time constraint of CRAN.
stored.init
internally used logical argument.
This option is closely related to
storing
which controls whether intermediate calculations
should be stored to have faster repeated simulations.
This user option is internally overwritten if the user calls several
simulations at once. This current value is stored in stored.init
.
Default: FALSE
.
warn_ambiguous
internally used logical argument.
Usually, the argument grid
in RFsimulate
,
for instance, can or should be given. If not given,
the system takes a default definition.
Additionally a message is displayed in this case if
ambiguous=TRUE
.
Default: FALSE
.
warn_aspect_ratio
internally used logical argument.
if TRUE
then a warning is given not a standard graphical
device is used and the package plots try to keep a certain aspect
ratio.
Default: TRUE
warn_colour_palette
internally used logical argument. If none of the packages RColorBrewer and colorspace are available and graphics are displayed, a message is displayed.
Default: TRUE
.
warn_constant
The definition of RMconstant
has changed.
A warning is displayed if the command is used. warn_constant
will become obsolete in future versions.
Default: TRUE
.
warn_coordinates
internally used logical argument.
If TRUE
then a transformation from earth coordinates to
cartesian coordinates is reported.
Default: TRUE
.
allow_duplicated_locations
logical.
If FALSE
duplicated locations are not allowed.
If TRUE
then the (standard) nugget effect becomes a nonstationary
model in an abstract space that cannot be extended outside the given
locations. See also RMnugget for the distinction between
measurement error and spatial nugget.
Default: FALSE
.
warn_missing_zenit
Only for Earth systems: a missing zenit is frequently a cause for errors that are difficult to understand. Therefore, in such cases an additional warning message is displayed.
Default: TRUE
warn_newAniso
obsolete.
internally used logical argument.
If newAniso=TRUE
and the argument Aniso
is used in the model
definition, then a message is displayed that the matrix Aniso
is multiplied from the right by x, where up to Version 2.0
the argument aniso
was available which was multiplied from
the left by x.
Default: TRUE
.
warn_newstyle
internally used logical argument.
If TRUE
a message is displayed the by the argument
spConform=FALSE
oldstyle return values are obtained instead
of S4 objects.
Default: TRUE
.
warn_normal_mode
internally used logical argument.
if TRUE
then the function RFfit
displays the message that other values for the option
modus_operandi
are available.
Default: TRUE
.
warn_oldstyle
internally used logical argument.
If TRUE
a warning is given if an obsolete function
from Version 2 is used.
Default: TRUE
.
warn_on_grid
internally used logical argument.
If a (onedimensional) grid is given, but the argument
grid=FALSE
, e.g. in RFsimulate
, this contraction is
reported if warn_on_grid=TRUE
Default: TRUE
.
warn_scale
internally used logical argument.
If warn_scale=TRUE
then a scale less than 10 [km] is reported
if earth coordinates are transformed to cartesian coordinates.
Default: TRUE
.
warn_var
In some cases, RandomFields cannot detect whether the
variance is nonnegative. If TRUE
then a warning is displayed
in such a case.
Default: TRUE
.
NULL
if any argument is given, and the full list of
arguments, otherwise.
Basic
General
Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 9910, Dept. of Maths and Statistics, Lancaster University.
Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., SpaceTime Processes and Challenges Related to Environmental Problems. New York: Springer.
rectangular distribution; eps_zhou
Oesting, M., Schlather, M. and Zhou, C. (2013) On the Normalized Spectral Representation of MaxStable Processes on a compact set. arXiv, 1310.1813
shape_power
Ballani, F. and Schlather, M. (2015) In preparation.
RFsimulate
,
RFoptionsAdvanced,
RFoptions
,
and RFgetMethodNames
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
RFoptions()
############################################################
## ##
## use of exactness ##
## ##
############################################################
x < seq(0, 1, 1/30)
model < RMgauss()
for (exactness in c(NA, FALSE, TRUE)) {
readline(paste("\n\nexactness: `", exactness, "'; press return"))
z < RFsimulate(model, x, x, exactness=exactness,
stationary_only=NA, storing=TRUE)
print(RFgetModelInfo(which="internal")$internal$name)
}

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