alltypes  R Documentation 
Given a marked point pattern, this computes the estimates of
a selected summary function (F
,G
, J
, K
etc)
of the pattern, for all possible combinations of marks,
and returns these functions in an array.
alltypes(X, fun="K", ...,
dataname=NULL,verb=FALSE,envelope=FALSE,reuse=TRUE)
X 
The observed point pattern, for which summary function
estimates are required. An object of class 
fun 
The summary function. Either an R function,
or a character string indicating the summary function
required. Options for strings are

... 
Arguments passed to the summary function
(and to the function 
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

verb 
Logical value. If 
envelope 
Logical value. If 
reuse 
Logical value indicating whether the envelopes in each panel
should be based on the same set of simulated patterns
( 
This routine is a convenient way to analyse the dependence between
types in a multitype point pattern.
It computes the estimates of a selected summary function of the
pattern, for all possible combinations of marks.
It returns these functions in an array
(an object of class "fasp"
) amenable to plotting
by plot.fasp()
.
The argument fun
specifies the summary function that will
be evaluated for each type of point, or for each pair of types.
It may be either an R function or a character string.
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
. See Fest
for explanation of the empty space function.
The estimate is computed by applying Fest
to X_i
with the optional arguments ...
.
If fun
is
"Gcross"
, "Jcross"
, "Kcross"
or "Lcross"
,
the routine calculates, for each pair of types (i,j)
,
an estimate of the “i
toj
” crosstype function
G_{ij}(r)
,
J_{ij}(r)
,
K_{ij}(r)
or
L_{ij}(r)
respectively describing the
dependence between
X_i
and X_j
.
See Gcross
, Jcross
, Kcross
or Lcross
respectively for explanation of these
functions.
The estimate is computed by applying the relevant function
(Gcross
etc)
to X
using each possible value of the arguments i,j
,
together with the optional arguments ...
.
If fun
is "pcf"
the routine calculates
the crosstype pair correlation function pcfcross
between each pair of types.
If fun
is
"Gdot"
, "Jdot"
, "Kdot"
or "Ldot"
,
the routine calculates, for each type i
,
an estimate of the “i
toany” dottype function
G_{i\bullet}(r)
,
J_{i\bullet}(r)
or
K_{i\bullet}(r)
or
L_{i\bullet}(r)
respectively describing the
dependence between X_i
and X
.
See Gdot
, Jdot
, Kdot
or Ldot
respectively for explanation of these functions.
The estimate is computed by applying the relevant function
(Gdot
etc)
to X
using each possible value of the argument i
,
together with the optional arguments ...
.
The letters "G"
, "J"
, "K"
and "L"
are interpreted as abbreviations for Gcross
,
Jcross
, Kcross
and Lcross
respectively, assuming the point pattern is
marked. If the point pattern is unmarked, the appropriate
function Fest
, Jest
,
Kest
or Lest
is invoked instead.
If envelope=TRUE
, then as well as computing the value of the
summary function for each combination of types, the algorithm also
computes simulation envelopes of the summary function for each
combination of types. The arguments ...
are passed to the function
envelope
to control the number of
simulations, the random process generating the simulations,
the construction of envelopes, and so on.
When envelope=TRUE
it is possible that errors could occur
because the simulated point patterns do not satisfy the requirements
of the summary function (for example, because the simulated pattern
is empty and fun
requires at least one point). If the number
of such errors exceeds the maximum permitted number maxnerr
,
then the envelope algorithm will give up, and will return
the empirical summary function for the data point pattern,
fun(X)
, in place of the envelope.
A function array (an object of class "fasp"
,
see fasp.object
). This can be plotted
using plot.fasp
.
If the pattern is not marked, the resulting “array” has dimensions
1 \times 1
. Otherwise the following is true:
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 "Gdot"
, "Jdot"
, "Kdot"
or "Ldot"
, the function array
again has dimensions m \times 1
.
The entry at position [i,1]
in this array
is the result of Gdot(X, i)
, Jdot(X, i)
Kdot(X, i)
or Ldot(X, i)
respectively.
If fun
is "Gcross"
, "Jcross"
, "Kcross"
or "Lcross"
(or their abbreviations "G"
, "J"
, "K"
or "L"
),
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
, Kcross
orLcross
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
, Kest
or Lest
to the
points of type i
only.
If envelope=FALSE
, then
each function entry fns[[i]]
retains the format
of the output of the relevant estimating routine
Fest
, Gest
, Jest
,
Kest
, Lest
, Gcross
,
Jcross
,Kcross
, Lcross
,
Gdot
, Jdot
, Kdot
or
Ldot
The default formulae for plotting these functions are
cbind(km,theo) ~ r
for F, G, and J functions, and
cbind(trans,theo) ~ r
for K and L functions.
If envelope=TRUE
, then each function entry fns[[i]]
has the same format as the output of the envelope
command.
Sizeable amounts of memory may be needed during the calculation.
and \rolf.
plot.fasp
,
fasp.object
,
Fest
,
Gest
,
Jest
,
Kest
,
Lest
,
Gcross
,
Jcross
,
Kcross
,
Lcross
,
Gdot
,
Jdot
,
Kdot
,
envelope
.
# bramblecanes (3 marks).
bram < bramblecanes
bF < alltypes(bram,"F",verb=TRUE)
plot(bF)
if(interactive()) {
plot(alltypes(bram,"G"))
plot(alltypes(bram,"Gdot"))
}
# Swedishpines (unmarked).
swed < swedishpines
plot(alltypes(swed,"K"))
plot(alltypes(amacrine, "pcf"), ylim=c(0,1.3))
# envelopes
bKE < alltypes(bram,"K",envelope=TRUE,nsim=19)
# global version:
bFE < alltypes(bram,"F",envelope=TRUE,nsim=19,global=TRUE)
# extract one entry
as.fv(bKE[1,1])
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