# alltypes

##### Calculate Statistic for All Types in a Multitype Point Pattern

Given a marked point pattern, this computes the estimates of
a selected summary function ($F$,$G$, $J$ or $K$)
of the pattern, for all possible combinations of marks.
It returns these functions in
a list (an object of class `"fasp"`

) amenable to plotting
by `plot.fasp()`

.

- Keywords
- spatial

##### Usage

`alltypes(pp, fun="K",dataname=NULL,verb=F)`

##### Arguments

- pp
- The observed point pattern, for which summary function
estimates are required. An object of class
`"ppp"`

. If the pattern is not marked, the resulting ``array'' is $1 \times 1$. - fun
- Character string indicating the summary function
required. Must be one of the letters
`"F"`

,`"G"`

,`"J"`

,`"K"`

. - dataname
- Character string giving an optional (alternative)
name to the point pattern, different from what is given
in the call. This name, if supplied, may be used by
`plot.fasp()`

in forming the title - verb
- Logical value, meaning ``verbose''. If verb is true then terse ``progress reports'' (just the values of the mark indices) are printed out when the calculations for that combination of marks are completed.

##### Details

This routine is a convenient way to analyse the dependence between
types in a multitype point pattern.
Suppose that the points have possible types $1,2,\ldots,m$
and let $X_i$ denote the pattern of points of type $i$ only.
If `fun="F"`

then this routine
calculates, for each possible type $i$,
an estimate of the Empty Space Function $F_i(r)$ of
$X_i$.
If `fun`

is `"G"`

, `"J"`

or `"K"`

,
the routine calculates, for each pair of types $(i,j)$,
an estimate of the cross-type function
$G_{ij}(r)$,
$J_{ij}(r)$ or
$K_{ij}(r)$ respectively describing the
dependence between
$X_i$ and $X_j$.

The real work is done by the functions `Fest`

, `Gest`

,
`Kest`

, `Jest`

,
`Gcross`

, `Kcross`

, and `Jcross`

.
One of the first four functions (according to
`fun`

) is invoked if the two marks under consideration are
equal. The latter three are invoked if the marks are distinct.
(There is no `Fcross`

; for the empty space function $F(r)$
there is no cross-type version.)

##### Value

- A function array (an object of class
`"fasp"`

, see`fasp.object`

). This can be plotted using`plot.fasp`

.If

`fun="F"`

, the function array has dimensions $m \times 1$ where $m$ is the number of different marks in the point pattern. The entry at position`[i,1]`

in this array is the result of applying`Fest`

to the points of type`i`

only.If

`fun`

is`"G"`

,`"J"`

or`"K"`

, the function array has dimensions $m \times m$. The`[i,j]`

entry of the function array (for $i \neq j$) is the result of applying the function`Gcross`

,`Jcross`

or`Kcross`

to the pair of types`(i,j)`

. The diagonal`[i,i]`

entry of the function array is the result of applying the univariate function`Gest`

,`Jest`

or`Kest`

to the points of type`i`

only. Each function entry`fns[[i]]`

retains the format of the output of the relevant estimating routine`Fest`

,`Gest`

,`Jest`

,`Kest`

,`Gcross`

,`Jcross`

, or`Kcross`

.The default formulae for plotting these functions are

`cbind(km,theo) ~ r`

for F, G, and J, and`cbind(border,theo) ~ r`

for K.

##### Note

Sizeable amounts of memory may be needed during the calculation.

##### See Also

`plot.fasp`

,
`fasp.object`

,
`allstats`

,
`Fest`

,
`Gest`

,
`Jest`

,
`Kest`

,
`Gcross`

,
`Jcross`

,
`Kcross`

##### Examples

```
library(spatstat)
# bramblecanes (3 marks).
data(bramblecanes)
X.F <- alltypes(bramblecanes,fun="F",verb=T)
plot(X.F)
X.G <- alltypes(bramblecanes,fun="G",verb=T)
X.J <- alltypes(bramblecanes,fun="J",verb=T)
X.K <- alltypes(bramblecanes,fun="K",verb=T)
<testonly># smaller dataset
bram <- bramblecanes[seq(1, bramblecanes$n, by=20), ]
X.F <- alltypes(bram,fun="F",verb=T)
X.G <- alltypes(bram,fun="G",verb=T)
X.J <- alltypes(bram,fun="J",verb=T)
X.K <- alltypes(bram,fun="K",verb=T)</testonly>
# Swedishpines (unmarked).
data(swedishpines)
X.F <- alltypes(swedishpines,fun="F")
X.G <- alltypes(swedishpines,fun="G")
X.J <- alltypes(swedishpines,fun="J")
X.K <- alltypes(swedishpines,fun="K")
# simulated data
pp <- runifpoint(350, owin(c(0,1),c(0,1)))
pp$marks <- factor(c(rep(1,50),rep(2,100),rep(3,200)))
X.F <- alltypes(pp,fun="F",verb=T,dataname="Fake Data")
X.G <- alltypes(pp,fun="G",verb=T,dataname="Fake Data")
X.J <- alltypes(pp,fun="J",verb=T,dataname="Fake Data")
X.K <- alltypes(pp,fun="K",verb=T,dataname="Fake Data")
# A setting where you might REALLY want to use dataname:
xxx <- alltypes(ppp(Melvin$x,Melvin$y,
window=as.owin(c(5,20,15,50)),marks=clyde),
fun="F",verb=T,dataname="Melvin")
```

*Documentation reproduced from package spatstat, version 1.0-1, License: GPL version 2 or newer*