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#
# Kinhom.S Estimation of K function for inhomogeneous patterns
#
# $Revision: 1.100 $ $Date: 2021/10/26 07:12:00 $
#
# Kinhom() compute estimate of K_inhom
#
#
# Reference:
# Non- and semiparametric estimation of interaction
# in inhomogeneous point patterns
# A.Baddeley, J.Moller, R.Waagepetersen
# Statistica Neerlandica 54 (2000) 329--350.
#
# -------- functions ----------------------------------------
# Kinhom() compute estimate of K
# using various edge corrections
#
# Kwtsum() internal routine for border correction
#
# -------- standard arguments ------------------------------
# X point pattern (of class 'ppp')
#
# r distance values at which to compute K
#
# lambda vector of intensity values for points of X
#
# -------- standard output ------------------------------
# A data frame (class "fv") with columns named
#
# r: same as input
#
# trans: K function estimated by translation correction
#
# iso: K function estimated by Ripley isotropic correction
#
# theo: K function for Poisson ( = pi * r ^2 )
#
# border: K function estimated by border method
# (denominator = sum of weights of points)
#
# bord.modif: K function estimated by border method
# (denominator = area of eroded window)
#
# ------------------------------------------------------------------------
"Linhom" <- function(X, ..., correction) {
if(missing(correction)) correction <- NULL
K <- Kinhom(X, ..., correction=correction)
L <- eval.fv(sqrt(pmax.int(K,0)/pi))
# relabel the fv object
L <- rebadge.fv(L, quote(L[inhom](r)), c("L", "inhom"),
names(K), new.labl=attr(K, "labl"))
attr(L, "labl") <- attr(K, "labl")
attr(L, "dangerous") <- attr(K, "dangerous")
#
return(L)
}
"Kinhom"<-
function (X, lambda=NULL, ..., r = NULL, breaks = NULL,
correction=c("border", "bord.modif", "isotropic", "translate"),
renormalise=TRUE,
normpower=1,
update = TRUE,
leaveoneout = TRUE,
nlarge = 1000,
lambda2=NULL,
reciplambda=NULL, reciplambda2=NULL,
diagonal=TRUE,
sigma=NULL, varcov=NULL,
ratio=FALSE)
{
verifyclass(X, "ppp")
nlarge.given <- !missing(nlarge)
rfixed <- !missing(r) || !missing(breaks)
# determine basic parameters
W <- X$window
npts <- npoints(X)
areaW <- area(W)
diamW <- diameter(W)
rmaxdefault <- rmax.rule("K", W, npts/areaW)
breaks <- handle.r.b.args(r, breaks, W, rmaxdefault=rmaxdefault)
r <- breaks$r
rmax <- breaks$max
# match corrections
correction.given <- !missing(correction) && !is.null(correction)
if(is.null(correction))
correction <- c("border", "bord.modif", "isotropic", "translate")
correction <- pickoption("correction", correction,
c(none="none",
border="border",
"bord.modif"="bord.modif",
isotropic="isotropic",
Ripley="isotropic",
trans="translate",
translate="translate",
translation="translate",
good="good",
best="best"),
multi=TRUE)
# best.wanted <- ("best" %in% correction)
## replace 'good' by the optimal choice for this size of dataset
if("good" %in% correction)
correction[correction == "good"] <- good.correction.K(X)
## retain only corrections that are implemented for the window
correction <- implemented.for.K(correction, W$type, correction.given)
###########################################################
# DETERMINE WEIGHTS AND VALIDATE
#
# The matrix 'lambda2' or 'reciplambda2' is sufficient information
# unless we want the border correction.
lambda2.given <- !is.null(lambda2) || !is.null(reciplambda2)
lambda2.suffices <- !any(correction %in% c("bord", "bord.modif"))
## Arguments that are 'dangerous' for envelope, if fixed
dangerous <- c("lambda", "reciplambda", "lambda2", "reciplambda2")
danger <- TRUE
# Use matrix of weights if it was provided and if it is sufficient
if(lambda2.suffices && lambda2.given) {
if(!is.null(reciplambda2)) {
check.nmatrix(reciplambda2, npts)
validate.weights(reciplambda2, recip=TRUE)
} else {
check.nmatrix(lambda2, npts)
validate.weights(lambda2)
reciplambda2 <- 1/lambda2
}
# renormalise
if(renormalise) {
check.1.real(normpower)
stopifnot(normpower %in% 1:2)
rlam2 <- reciplambda2
if(!diagonal) diag(rlam2) <- 0
renorm.factor <- (areaW^2/sum(rlam2))^(normpower/2)
}
} else {
# Vector lambda or reciplambda is required
if(missing(lambda) && is.null(reciplambda)) {
# No intensity data provided
danger <- FALSE
# Estimate density by leave-one-out kernel smoothing
lambda <- density(X, ..., sigma=sigma, varcov=varcov,
at="points", leaveoneout=leaveoneout)
lambda <- as.numeric(lambda)
validate.weights(lambda, how="density estimation")
reciplambda <- 1/lambda
} else if(!is.null(reciplambda)) {
# 1/lambda values provided
if(is.im(reciplambda))
reciplambda <- safelookup(reciplambda, X)
else if(is.function(reciplambda))
reciplambda <- reciplambda(X$x, X$y)
else if(is.numeric(reciplambda) && is.vector(as.numeric(reciplambda)))
check.nvector(reciplambda, npts, vname="reciplambda")
else stop(paste(sQuote("reciplambda"),
"should be a vector, a pixel image, or a function"))
validate.weights(reciplambda, recip=TRUE)
} else {
# lambda values provided
if(is.im(lambda))
lambda <- safelookup(lambda, X)
else if(is.ppm(lambda) || is.kppm(lambda) || is.dppm(lambda)) {
model <- lambda
if(!update) {
## just use intensity of fitted model
lambda <- predict(model, locations=X, type="trend")
} else {
## re-fit model to data X
if(is.ppm(model)) {
model <- update(model, Q=X)
lambda <- fitted(model, dataonly=TRUE, leaveoneout=leaveoneout)
} else {
model <- update(model, X=X)
lambda <- fitted(model, dataonly=TRUE, leaveoneout=leaveoneout)
}
danger <- FALSE
}
} else if(is.function(lambda))
lambda <- lambda(X$x, X$y)
else if(is.numeric(lambda) && is.vector(as.numeric(lambda)))
check.nvector(lambda, npts, vname="lambda")
else stop(paste(sQuote("lambda"),
"should be a vector, a pixel image, or a function"))
validate.weights(lambda)
# evaluate reciprocal
reciplambda <- 1/lambda
}
# renormalise
if(renormalise) {
check.1.real(normpower)
stopifnot(normpower %in% 1:2)
if(!diagonal && normpower == 2) {
renorm.factor <- (areaW^2)/(sum(reciplambda)^2 - sum(reciplambda^2))
} else {
renorm.factor <- (areaW/sum(reciplambda))^normpower
}
}
}
# recommended range of r values
alim <- c(0, min(rmax, rmaxdefault))
###########################################
# Efficient code for border correction and no correction
# Usable only if r values are evenly spaced from 0 to rmax
# Invoked automatically if number of points is large
can.do.fast <- breaks$even && !lambda2.given
large.n <- (npts >= nlarge)
# demand.best <- correction.given && best.wanted
large.n.trigger <- large.n && !correction.given
fastcorrections <- c("border", "bord.modif", "none")
fastdefault <- "border"
correction.fast <- all(correction %in% fastcorrections)
will.do.fast <- can.do.fast && (correction.fast || large.n.trigger)
asked.fast <- (correction.given && correction.fast) ||
(nlarge.given && large.n.trigger)
if(!can.do.fast && asked.fast) {
whynot <-
if(!(breaks$even)) "r values not evenly spaced" else
if(!missing(lambda)) "matrix lambda2 was given" else NULL
warning(paste("cannot use efficient code", whynot, sep="; "))
}
if(will.do.fast) {
## Compute Kinhom using fast algorithm(s)
## determine correction(s)
ok <- correction %in% fastcorrections
correction <- if(any(ok)) correction[ok] else fastdefault
bord <- any(correction %in% c("border", "bord.modif"))
none <- any(correction =="none")
if(!all(ok)) {
## some corrections were overridden; notify user
corx <- c(if(bord) "border correction estimate" else NULL,
if(none) "uncorrected estimate" else NULL)
corx <- paste(corx, collapse=" and ")
message(paste("number of data points exceeds",
nlarge, "- computing", corx , "only"))
}
## restrict r values to recommended range, unless specifically requested
if(!rfixed)
r <- seq(from=0, to=alim[2], length.out=length(r))
## border method
if(bord) {
Kb <- Kborder.engine(X, max(r), length(r), correction,
weights=reciplambda, ratio=ratio)
if(renormalise) {
ynames <- setdiff(fvnames(Kb, "*"), "theo")
Kb <- adjust.ratfv(Kb, ynames, denfactor=1/renorm.factor)
}
Kb <- tweak.ratfv.entry(Kb, "border", new.labl="{hat(%s)[%s]^{bord}} (r)")
Kb <- tweak.ratfv.entry(Kb, "bord.modif", new.labl="{hat(%s)[%s]^{bordm}} (r)")
}
## uncorrected
if(none) {
Kn <- Knone.engine(X, max(r), length(r), weights=reciplambda,
ratio=ratio)
if(renormalise)
Kn <- adjust.ratfv(Kn, "un", denfactor=1/renorm.factor)
Kn <- tweak.ratfv.entry(Kn, "un", new.labl="{hat(%s)[%s]^{un}} (r)")
}
K <-
if(bord && !none) Kb else
if(!bord && none) Kn else
if(!ratio) cbind.fv(Kb, Kn[, c("r", "un")]) else
bind.ratfv(Kb, Kn[, c("r", "un")], ratio=TRUE)
## tweak labels
K <- rebadge.fv(K, quote(K[inhom](r)), c("K", "inhom"))
if(danger)
attr(K, "dangerous") <- dangerous
return(K)
}
###########################################
# Fast code for rectangular window
###########################################
if(can.do.fast && is.rectangle(W) && spatstat.options("use.Krect")) {
K <- Krect.engine(X, rmax, length(r), correction,
weights=reciplambda,
ratio=ratio, fname=c("K", "inhom"))
if(renormalise) {
allfun <- setdiff(fvnames(K, "*"), "theo")
K <- adjust.ratfv(K, allfun, denfactor=1/renorm.factor)
}
K <- rebadge.fv(K, quote(K[inhom](r)), c("K", "inhom"))
attr(K, "alim") <- alim
if(danger)
attr(K, "dangerous") <- dangerous
return(K)
}
###########################################
# Slower code
###########################################
# this will be the output data frame
K <- data.frame(r=r, theo= pi * r^2)
desc <- c("distance argument r", "theoretical Poisson %s")
denom <- if(renormalise) (areaW / renorm.factor) else areaW
K <- ratfv(K, NULL, denom,
argu="r",
ylab=quote(K[inhom](r)),
valu="theo",
fmla=NULL,
alim=alim,
labl=c("r","{%s[%s]^{pois}}(r)"),
desc=desc,
fname=c("K", "inhom"),
ratio=ratio)
# identify all close pairs
rmax <- max(r)
what <- if(any(correction == "translate")) "all" else "ijd"
close <- closepairs(X, rmax, what=what)
dIJ <- close$d
# compute weights for these pairs
I <- close$i
J <- close$j
# wI <- reciplambda[I]
wIJ <-
if(!lambda2.given)
reciplambda[I] * reciplambda[J]
else
reciplambda2[cbind(I,J)]
#
# compute edge corrected estimates
if(any(correction == "border" | correction == "bord.modif")) {
# border method
# Compute distances to boundary
b <- bdist.points(X)
bI <- b[I]
# apply reduced sample algorithm
RS <- Kwtsum(dIJ, bI, wIJ, b, w=reciplambda, breaks)
if(any(correction == "border")) {
Kb <- RS$ratio
if(renormalise)
Kb <- Kb * renorm.factor
K <- bind.ratfv(K,
quotient = data.frame(border=Kb),
denominator = denom,
labl = "{hat(%s)[%s]^{bord}}(r)",
desc = "border-corrected estimate of %s",
preferred = "border",
ratio=ratio)
}
if(any(correction == "bord.modif")) {
Kbm <- RS$numerator/eroded.areas(W, r)
if(renormalise)
Kbm <- Kbm * renorm.factor
K <- bind.ratfv(K,
quotient = data.frame(bord.modif=Kbm),
denominator = denom,
labl = "{hat(%s)[%s]^{bordm}}(r)",
desc = "modified border-corrected estimate of %s",
preferred = "bord.modif",
ratio=ratio)
}
}
if(any(correction == "translate")) {
# translation correction
edgewt <- edge.Trans(dx=close$dx, dy=close$dy, W=W, paired=TRUE)
allweight <- edgewt * wIJ
wh <- whist(dIJ, breaks$val, allweight)
Ktrans <- cumsum(wh)/areaW
if(renormalise)
Ktrans <- Ktrans * renorm.factor
rmax <- diamW/2
Ktrans[r >= rmax] <- NA
K <- bind.ratfv(K,
quotient = data.frame(trans=Ktrans),
denominator = denom,
labl ="{hat(%s)[%s]^{trans}}(r)",
desc = "translation-correction estimate of %s",
preferred = "trans",
ratio=ratio)
}
if(any(correction == "isotropic" | correction == "Ripley")) {
# Ripley isotropic correction
edgewt <- edge.Ripley(X[I], matrix(dIJ, ncol=1))
allweight <- edgewt * wIJ
wh <- whist(dIJ, breaks$val, allweight)
Kiso <- cumsum(wh)/areaW
if(renormalise)
Kiso <- Kiso * renorm.factor
rmax <- diamW/2
Kiso[r >= rmax] <- NA
K <- bind.ratfv(K,
quotient = data.frame(iso=Kiso),
denominator = denom,
labl = "{hat(%s)[%s]^{iso}}(r)",
desc = "Ripley isotropic correction estimate of %s",
preferred = "iso",
ratio=ratio)
}
# default is to display them all
formula(K) <- . ~ r
unitname(K) <- unitname(X)
if(danger)
attr(K, "dangerous") <- dangerous
return(K)
}
Kwtsum <- function(dIJ, bI, wIJ, b, w, breaks, fatal=TRUE) {
#
# "internal" routine to compute border-correction estimates of Kinhom
#
# dIJ: vector containing pairwise distances for selected I,J pairs
# bI: corresponding vector of boundary distances for I
# wIJ: product weight for selected I, J pairs
#
# b: vector of ALL distances to window boundary
# w: weights for ALL points
#
# breaks : breakpts object
#
stopifnot(length(dIJ) == length(bI))
stopifnot(length(bI) == length(wIJ))
stopifnot(length(w) == length(b))
if(!is.finite(sum(w, wIJ))) {
if(fatal)
stop("Weights in K-function were infinite or NA", call.=FALSE)
#' set non-finite weights to zero
if(any(bad <- !is.finite(w))) {
warning(paste(sum(bad), "out of", length(bad),
paren(percentage(bad)),
"of the boundary weights",
"in the K-function were NA or NaN or Inf",
"and were reset to zero"),
call.=FALSE)
w[bad] <- 0
}
if(any(bad <- !is.finite(wIJ))) {
warning(paste(sum(bad), "out of", length(bad),
paren(percentage(bad)),
"of the weights for pairwise distances",
"in the K-function were NA or NaN or Inf",
"and were reset to zero"),
call.=FALSE)
wIJ[bad] <- 0
}
}
bkval <- breaks$val
# determine which distances d_{ij} were observed without censoring
uncen <- (dIJ <= bI)
#
# histogram of noncensored distances
nco <- whist(dIJ[uncen], bkval, wIJ[uncen])
# histogram of censoring times for noncensored distances
ncc <- whist(bI[uncen], bkval, wIJ[uncen])
# histogram of censoring times (yes, this is a different total size)
cen <- whist(b, bkval, w)
# total weight of censoring times beyond rightmost breakpoint
uppercen <- sum(w[b > breaks$max])
# go
RS <- reduced.sample(nco, cen, ncc, show=TRUE, uppercen=uppercen)
# extract results
numerator <- RS$numerator
denominator <- RS$denominator
ratio <- RS$numerator/RS$denominator
# check
if(length(numerator) != breaks$ncells)
stop("internal error: length(numerator) != breaks$ncells")
if(length(denominator) != breaks$ncells)
stop("internal error: length(denom.count) != breaks$ncells")
return(list(numerator=numerator, denominator=denominator, ratio=ratio))
}
validate.weights <- function(x, recip=FALSE, how = NULL,
allowzero = recip,
allowinf = !recip) {
xname <- deparse(substitute(x))
ra <- range(x)
offence <-
if(!allowinf && !all(is.finite(ra))) "infinite" else
if(ra[1] < 0) "negative" else
if(!allowzero && ra[1] == 0) "zero" else NULL
if(!is.null(offence)) {
offenders <- paste(offence, "values of", sQuote(xname))
if(is.null(how))
stop(paste(offenders, "are not allowed"), call.=FALSE)
stop(paste(how, "yielded", offenders), call.=FALSE)
}
return(TRUE)
}
resolve.lambda <- function(X, lambda=NULL, ...,
sigma=NULL, varcov=varcov,
leaveoneout=TRUE, update=TRUE) {
dangerous <- "lambda"
danger <- TRUE
if(is.null(lambda)) {
## No intensity data provided
## Estimate density by leave-one-out kernel smoothing
lambda <- density(X, ..., sigma=sigma, varcov=varcov,
at="points", leaveoneout=leaveoneout)
lambda <- as.numeric(lambda)
danger <- FALSE
} else if(is.im(lambda)) {
lambda <- safelookup(lambda, X)
} else if(is.function(lambda)) {
lambda <- lambda(X$x, X$y)
} else if(is.numeric(lambda) && is.vector(as.numeric(lambda))) {
check.nvector(lambda, npoints(X), vname="lambda")
} else if(is.ppm(lambda) || is.kppm(lambda) || is.dppm(lambda)) {
model <- lambda
if(!update) {
## use intensity of model
lambda <- predict(model, locations=X, type="trend")
} else {
## re-fit model to data X
model <- if(is.ppm(model)) update(model, Q=X) else update(model, X=X)
lambda <- fitted(model, dataonly=TRUE, leaveoneout=leaveoneout)
danger <- FALSE
}
} else stop(paste(sQuote("lambda"),
"should be a vector, a pixel image,",
"a fitted model, or a function"))
return(list(lambda=lambda,
danger=danger,
dangerous=if(danger) dangerous else NULL))
}
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