# simulate.dppm

##### Simulation of Determinantal Point Process Model

Generates simulated realisations from a determinantal point process model.

##### Usage

```
# S3 method for dppm
simulate(object, nsim = 1, seed = NULL, …,
W = NULL, trunc = 0.99, correction = "periodic", rbord = reach(object))
``` # S3 method for detpointprocfamily
simulate(object, nsim = 1, seed = NULL, …,
W = NULL, trunc = 0.99, correction = "periodic", rbord = reach(object))

##### Arguments

- object
Determinantal point process model. An object of class

`"detpointprocfamily"`

or`"dppm"`

.- nsim
Number of simulated realisations.

- seed
an object specifying whether and how to initialise the random number generator. Either

`NULL`

or an integer that will be used in a call to`set.seed`

before simulating the point patterns.- …
Arguments passed on to

`rdpp`

.- W
Object specifying the window of simulation (defaults to a unit box if nothing else is sensible -- see Details). Can be any single argument acceptable to

`as.boxx`

(e.g. an`"owin"`

,`"box3"`

or`"boxx"`

object).- trunc
Numeric value specifying how the model truncation is preformed. See Details.

- correction
Character string specifying the type of correction to use. The options are "periodic" (default) and "border". See Details.

- rbord
Numeric value specifying the extent of the border correction if this correction is used. See Details.

##### Details

These functions are methods for the generic function
`simulate`

for the classes `"detpointprocfamily"`

and
`"dppm"`

of determinantal point process models.

The return value is a list of `nsim`

point patterns.
It also carries an attribute `"seed"`

that
captures the initial state of the random number generator.
This follows the convention used in
`simulate.lm`

(see `simulate`

).
It can be used to force a sequence of simulations to be
repeated exactly, as shown in the examples for
`simulate`

.

The exact simulation of a determinantal point process model involves
an infinite series, which typically has no analytical solution. In the
implementation a truncation is performed. The truncation
`trunc`

can be specified either directly as a positive integer
or as a fraction between 0 and 1. In the latter case the truncation is chosen
such that the expected number of points in a simulation is
`trunc`

times the theoretical expected number of points in the
model. The default is 0.99.

The window of the returned point pattern(s) can be specified via the
argument `W`

. For a fitted model (of class `"dppm"`

) it
defaults to the observation window of the data used to fit the
model. For inhomogeneous models it defaults to the window of the
intensity image. Otherwise it defaults to a unit box. For
non-rectangular windows simulation is done in the containing rectangle
and then restricted to the window. For inhomogeneous models a
stationary model is first simulated using the maximum intensity and
then the result is obtained by thinning.

The default is to use periodic edge correction for simulation such
that opposite edges are glued together. If border correction is used
then the simulation is done in an extended window. Edge effects are
theoretically completely removed by doubling the size of the window in
each spatial dimension, but for practical purposes much less extension
may be sufficient. The numeric `rbord`

determines the extent of
the extra space added to the window.

##### Value

A list of length `nsim`

containing simulated point patterns.
If the patterns are two-dimensional, then they are
objects of class `"ppp"`

, and the list has class `"solist"`

.
Otherwise, the patterns are objects of class `"ppx"`

and the
list has class `"anylist"`

.

The return value also carries an attribute `"seed"`

that
captures the initial state of the random number generator.
See Details.

##### References

Lavancier, F. Moller, J. and Rubak, E. (2015)
Determinantal point process models and statistical inference
*Journal of the Royal Statistical Society, Series B*
**77**, 853--977.

##### See Also

##### Examples

```
# NOT RUN {
model <- dppGauss(lambda=100, alpha=.05, d=2)
simulate(model, 2)
# }
```

*Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)*