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#
#
# fiksel.R
#
# $Revision: 1.20 $ $Date: 2022/03/07 02:05:50 $
#
# Fiksel interaction
#
# ee Stoyan Kendall Mcke 1987 p 161
#
# -------------------------------------------------------------------
#
Fiksel <- local({
# ......... auxiliary functions ...........
fikselterms <- function(U, X, r, kappa, EqualPairs=NULL) {
answer <- crossfikselterms(U, X, r, kappa)
nU <- npoints(U)
# subtract contrinbutions from identical pairs (exp(-0) = 1 for each)
if(length(EqualPairs) > 0) {
idcount <- as.integer(table(factor(EqualPairs[,2L], levels=1:nU)))
answer <- answer - idcount
}
return(answer)
}
crossfikselterms <- function(X, Y, r, kappa) {
stopifnot(is.numeric(r))
# sort in increasing order of x coordinate
oX <- fave.order(X$x)
oY <- fave.order(Y$x)
Xsort <- X[oX]
Ysort <- Y[oY]
nX <- npoints(X)
nY <- npoints(Y)
# call C routine
out <- .C(SC_Efiksel,
nnsource = as.integer(nX),
xsource = as.double(Xsort$x),
ysource = as.double(Xsort$y),
nntarget = as.integer(nY),
xtarget = as.double(Ysort$x),
ytarget = as.double(Ysort$y),
rrmax = as.double(r),
kkappa = as.double(kappa),
values = as.double(double(nX)),
PACKAGE="spatstat.core")
answer <- integer(nX)
answer[oX] <- out$values
return(answer)
}
# ........ template object ..............
BlankFiksel <-
list(
name = "Fiksel process",
creator = "Fiksel",
family = "pairwise.family", # evaluated later
pot = function(d, par) {
v <- (d <= par$r) * exp( - d * par$kappa)
v[ d <= par$hc ] <- (-Inf)
v
},
par = list(r = NULL, hc = NULL, kappa=NULL), # filled in later
parnames = c("interaction distance",
"hard core distance",
"rate parameter"),
hasInf = TRUE,
selfstart = function(X, self) {
# self starter for Fiksel
nX <- npoints(X)
if(nX < 2) {
# not enough points to make any decisions
return(self)
}
md <- minnndist(X)
if(!is.na(hc <- self$par$hc)) {
# value fixed by user or previous invocation
# check it
if(md < hc)
warning(paste("Hard core distance is too large;",
"some data points will have zero probability"))
return(self)
}
if(md == 0)
warning(paste("Pattern contains duplicated points:",
"hard core must be zero"))
# take hc = minimum interpoint distance * n/(n+1)
hcX <- md * nX/(nX+1)
Fiksel(r=self$par$r, hc = hcX, kappa=self$par$kappa)
},
init = function(self) {
r <- self$par$r
hc <- self$par$hc
kappa <- self$par$kappa
check.1.real(r)
check.1.real(kappa)
if(!is.na(hc)) {
check.1.real(hc)
stopifnot(hc > 0)
stopifnot(r > hc)
} else stopifnot(r > 0)
},
update = NULL, # default OK
print = NULL, # default OK
interpret = function(coeffs, self) {
a <- as.numeric(coeffs[1L])
return(list(param=list(a=a),
inames="interaction strength a",
printable=signif(a)))
},
valid = function(coeffs, self) {
a <- (self$interpret)(coeffs, self)$param$a
return(is.finite(a))
},
project = function(coeffs, self) {
if((self$valid)(coeffs, self))
return(NULL)
hc <- self$par$hc
if(hc > 0) return(Hardcore(hc)) else return(Poisson())
},
irange = function(self, coeffs=NA, epsilon=0, ...) {
r <- self$par$r
hc <- self$par$hc
if(anyNA(coeffs))
return(r)
a <- coeffs[1L]
if(abs(a) <= epsilon)
return(hc)
else
return(r)
},
hardcore = function(self, coeffs=NA, epsilon=0, ...) {
return(self$par$hc)
},
version=NULL, # evaluated later
# fast evaluation is available for the border correction only
can.do.fast=function(X,correction,par) {
return(all(correction %in% c("border", "none")))
},
fasteval=function(X,U,EqualPairs,pairpot,potpars,correction,
splitInf=FALSE, ...) {
## fast evaluator for Fiksel interaction
if(!all(correction %in% c("border", "none")))
return(NULL)
if(spatstat.options("fasteval") == "test")
message("Using fast eval for Fiksel")
r <- potpars$r
hc <- potpars$hc
kappa <- potpars$kappa
hclose <- (strausscounts(U, X, hc, EqualPairs) != 0)
fikselbit <- fikselterms(U, X, r, kappa, EqualPairs)
if(!splitInf) {
answer <- ifelseAX(hclose, -Inf, fikselbit)
answer <- matrix(answer, ncol=1L)
} else {
answer <- fikselbit
answer <- matrix(answer, ncol=1L)
attr(answer, "-Inf") <- hclose
}
return(answer)
},
Mayer=function(coeffs, self) {
# second Mayer cluster integral
a <- as.numeric(coeffs[1L])
r <- self$par$r
hc <- self$par$hc
kappa <- self$par$kappa
f <- function(x, kappa, a){ 2 * pi * x *
(1 - exp(a * exp(-x * kappa))) }
hardbit <- integrate(f=f, lower=hc, upper=r,
a=a, kappa=kappa)
mess <- hardbit[["message"]]
if(!identical(mess, "OK")) {
warning(mess)
return(NA)
}
return(pi * hc^2 + hardbit$value)
}
)
class(BlankFiksel) <- "interact"
Fiksel <- function(r, hc=NA, kappa) {
instantiate.interact(BlankFiksel, list(r = r, hc = hc, kappa=kappa))
}
Fiksel <- intermaker(Fiksel, BlankFiksel)
Fiksel
})
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