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 Rfunction 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'' cross-type 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 cross-type 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-to-any'' dot-type 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.