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#'
#' FGmultiInhom.R
#'
#' inhomogeneous multitype G and F functions
#'
#' Original code by Ottmar Cronie and Marie-Colette van Lieshout
#'
#' Rewritten for spatstat by Adrian Baddeley
#'
#' GmultiInhom
#' FmultiInhom
#'
#' $Revision: 1.8 $ $Date: 2021/01/07 03:16:28 $
GmultiInhom <- function(X, I, J,
lambda=NULL, lambdaI=NULL, lambdaJ=NULL,
lambdamin=NULL,
...,
r=NULL,
ReferenceMeasureMarkSetI=NULL,
ratio=FALSE){
if(!is.ppp(X) || !is.marked(X))
stop("X should be a marked point pattern")
W <- Window(X)
nX <- npoints(X)
#' handle r argument
rmax <- rmax.rule("G", W, intensity(X))
bks <- handle.r.b.args(r, NULL, W, rmaxdefault=rmax)
r <- bks$r
rmax <- bks$max
nr <- length(r)
#' Accept any kind of index for I; convert it to a logical index
I <- ppsubset(X, I)
if(is.null(I))
stop("I must be a valid subset index")
XI <- X[I]
nI <- sum(I)
if (nI == 0)
stop("No points satisfy condition I")
if(!is.null(ReferenceMeasureMarkSetI)) {
check.1.real(ReferenceMeasureMarkSetI)
stopifnot(ReferenceMeasureMarkSetI >= 0)
}
#' likewise for J
if(missing(J) || is.null(J)) {
J <- rep(TRUE, nX)
} else {
J <- ppsubset(X, J)
}
XJ <- X[J]
nJ <- sum(J)
if (nJ == 0)
stop("No points satisfy condition J")
#' supply either lambda, or lambdaI and lambdaJ
lam.given <- !is.null(lambda)
lamIJ.given <- !is.null(lambdaI) || !is.null(lambdaJ)
if(lam.given == lamIJ.given || is.null(lambdaI) != is.null(lambdaJ))
stop(paste("Supply either a vector lambda of length equal to npoints(X),",
"or two vectors lambdaI, lambdaJ of lengths",
"equal to npoints(X[I]) and npoints(X[J]) respectively"),
call.=FALSE)
if(lamIJ.given) {
#' lambdaI and lambdaJ given
check.nvector(lambdaI, nI, things="points of X[I]", vname="lambdaI")
stopifnot(all(lambdaI > 0))
check.nvector(lambdaJ, nJ, things="points of X[J]", vname="lambdaJ")
stopifnot(all(lambdaJ > 0))
if(is.null(lambdamin)){
stop(paste("Supply lambdamin - a single positive number which is",
"smaller than the values in lambdaJ"),
call.=FALSE)
}
check.1.real(lambdamin)
stopifnot(lambdamin > 0)
stopifnot(lambdamin <= min(lambdaJ))
} else {
#' lambda given
check.nvector(lambda, nX, things="points of X", vname="lambda")
stopifnot(all(lambda > 0))
lambdaI <- lambda[I]
lambdaJ <- lambda[J]
if(is.null(lambdamin)){
stop(paste("Supply lambdamin - a single positive number which is",
"smaller than the values in lambda"),
call.=FALSE)
}
check.1.real(lambdamin)
stopifnot(lambdamin > 0)
stopifnot(lambdamin <= min(lambda))
}
#' Calculate 1/lambda(x_i,y_i,m_i))
#' for all (x_i,y_i,m_i) with m_i in I
invlambdaI <- 1/lambdaI
#' Calculate (1 - lambda_min/lambda(x_i,y_i,m_i))
#' for all (x_i,y_i,m_i) with m_i in J
Coeff <- 1-(lambdamin/lambdaJ)
## CoeffMatrix <- matrix(rep(Coeff,times=nI), nrow=nI, byrow=TRUE)
#' distances
## DistanceXItoXJ <- crossdist(XI,XJ)
#' eroded areas and boundary distances
areaWr <- eroded.areas(W, r)
bdistXI <- bdist.points(XI)
#' for each point x in XI, determine largest r such that x \in W-r
ibI <- fastFindInterval(bdistXI, r, labels=TRUE)
#' count of points inside W-r for each r
## NumberEroded <- revcumsum(table(ibI))
#' denominator
#' sum invlambdaI for all points x \in W-r
DenominatorN <- c(sum(invlambdaI),
revcumsum(natozero(tapply(invlambdaI, ibI, sum))))
if(!is.null(ReferenceMeasureMarkSetI))
DenominatorA <- areaWr * ReferenceMeasureMarkSetI
#' local products of weights
#' sort data points in order of increasing x coordinate
xxI <- XI$x
yyI <- XI$y
oXI <- fave.order(xxI)
xIord <- xxI[oXI]
yIord <- yyI[oXI]
#'
xxJ <- XJ$x
yyJ <- XJ$y
vvJ <- Coeff
oXJ <- fave.order(xxJ)
xJord <- xxJ[oXJ]
yJord <- yyJ[oXJ]
vJord <- vvJ[oXJ]
# compute local cumulative products
z <- .C(SC_locxprod,
ntest = as.integer(nI),
xtest = as.double(xIord),
ytest = as.double(yIord),
ndata = as.integer(nJ),
xdata = as.double(xJord),
ydata = as.double(yJord),
vdata = as.double(vJord),
nr = as.integer(nr),
rmax = as.double(rmax),
ans = as.double(numeric(nI * nr)),
PACKAGE="spatstat.core")
ans <- matrix(z$ans, nrow=nr, ncol=nI)
#' revert to original ordering
loccumprod <- matrix(, nrow=nr, ncol=nI)
loccumprod[, oXI] <- ans
#' border correction
outside <- outer(r, bdistXI, ">")
loccumprod[outside] <- 0
#' weight by 1/lambdaI
wlcp <- loccumprod * matrix(invlambdaI, byrow=TRUE, nr, nI)
#' sum over I for each fixed r
numer <- .rowSums(wlcp, nr, nI)
# pack up
Gdf <- data.frame(r=r, theo = 1 - exp(- lambdamin * pi * r^2))
desc <- c("distance argument r", "theoretical Poisson %s")
theo.denom <- rep.int(nI, nr)
fname <- c("G", "list(inhom,I,J)")
G <- ratfv(Gdf, NULL, theo.denom,
"r", quote(G[inhom, I, J](r)),
"theo", NULL, c(0,rmax),
c("r", makefvlabel(NULL, NULL, fname, "pois")),
desc,
fname=fname,
yexp=quote(G[list(inhom,I,J)](r)),
ratio=ratio)
# add border corrected (Hamilton Principle) estimate
G <- bind.ratfv(G,
data.frame(bord=DenominatorN-numer), DenominatorN,
makefvlabel(NULL, "hat", fname, "bord"),
"border estimate of %s",
"bord",
ratio=ratio)
fvnames(G, ".") <- c("bord", "theo")
# add modified border corrected (non-Hamilton-Principle) estimate
if(!is.null(ReferenceMeasureMarkSetI)) {
G <- bind.ratfv(G,
data.frame(bordm=DenominatorA-numer),
DenominatorA,
makefvlabel(NULL, "hat", fname, "bordm"),
"modified border estimate of %s",
"bordm",
ratio=ratio)
fvnames(G, ".") <- c("bord", "bordm", "theo")
}
#
formula(G) <- . ~ r
unitname(G) <- unitname(X)
if(ratio)
G <- conform.ratfv(G)
return(G)
}
#' marked inhomogeneous F
FmultiInhom <- function(X, J,
lambda=NULL,lambdaJ=NULL,
lambdamin=NULL,
...,
r=NULL) {
if(!is.ppp(X) || !is.marked(X))
stop("X should be a marked point pattern")
nX <- npoints(X)
#' Accept any kind of index for J; convert it to a logical index
J <- ppsubset(X, J)
if(is.null(J))
stop("J must be a valid subset index")
XJ <- X[J]
nJ <- sum(J)
if (nJ == 0)
stop("No points satisfy condition J")
if(is.null(lambda) == is.null(lambdaJ))
stop(paste("Supply either a vector lambda of length equal to npoints(X),",
"or a vector lambdaJ of length equal to npoints(X[J])"),
call.=FALSE)
if(is.null(lambdamin))
stop("Supply a value for lambdamin", call.=FALSE)
check.1.real(lambdamin)
if(!is.null(lambda)) {
check.nvector(lambda, nX, vname="lambda")
stopifnot(all(lambda > 0))
stopifnot(lambdamin <= min(lambda[J]))
lambdaJ <- lambda[J]
} else {
check.nvector(lambdaJ, nJ, vname="lambdaJ")
stopifnot(all(lambdaJ > 0))
stopifnot(lambdamin <= min(lambdaJ))
}
FJ <- Finhom(XJ, lambda=lambdaJ, lmin=lambdamin, r=r)
FJ <- rebadge.fv(FJ,
new.ylab = quote(F[inhom, J](r)),
new.fname = c("F", "list(inhom,J)"),
new.yexp = quote(F[list(inhom,J)](r)))
return(FJ)
}
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