Kinhom.S
#
# Kinhom.S Estimation of K function for inhomogeneous patterns
#
# $Revision: 1.36 $ $Date: 2009/04/15 01:44:06 $
#
# 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(...) {
K <- Kinhom(...)
L <- eval.fv(sqrt(K/pi))
# relabel the fv object
L <- rebadge.fv(L, substitute(Linhom(r), NULL), "Linhom")
return(L)
}
"Kinhom"<-
function (X, lambda, ..., r = NULL, breaks = NULL,
correction=c("border", "bord.modif", "isotropic", "translate"),
nlarge = 1000,
lambda2=NULL,
reciplambda=NULL, reciplambda2=NULL,
sigma=NULL, varcov=NULL)
{
verifyclass(X, "ppp")
nlarge.given <- !missing(nlarge)
rfixed <- !missing(r) || !missing(breaks)
# determine basic parameters
W <- X$window
npoints <- X$n
area <- area.owin(W)
rmaxdefault <- rmax.rule("K", W, npoints/area)
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)
correction <- pickoption("correction", correction,
c(none="none",
border="border",
"bord.modif"="bord.modif",
isotropic="isotropic",
Ripley="isotropic",
translate="translate"),
multi=TRUE)
# available selection of edge corrections depends on window
if(W$type == "mask") {
iso <- (correction == "isotropic")
if(any(iso)) {
if(correction.given)
warning("Isotropic correction not implemented for binary masks")
correction <- correction[!iso]
}
}
###########################################################
# DETERMINE WEIGHTS AND VALIDATE
#
# The matrix 'lambda2' or 'reciplambda2' is sufficient information
# unless we want the border correction.
lambda2.given <- !is.null(lambda2) || !is.null(reciplambda2)
lambda2.suffices <- !any(correction %in% c("bord", "bord.modif"))
validate.vector <- function(v, npoints) {
# vector of values for each point
vname <- sQuote(deparse(substitute(v)))
if(length(v) != npoints)
stop(paste("The length of", vname,
"should equal the number of data points"))
if(any(is.na(v)))
stop(paste("Some values of", vname, "are NA or NaN"))
}
validate.matrix <- function(m, npoints) {
# matrix of values for each pair of points
mname <- sQuote(deparse(substitute(m)))
if(!is.matrix(m))
stop(paste(mname, "should be a matrix"))
if(nrow(m) != ncol(m))
stop(paste(mname, "should be a square matrix"))
if(nrow(m) != npoints)
stop(paste("Dimensions of", mname,
"do not match number of data points"))
}
# Use matrix of weights if it was provided and if it is sufficient
if(lambda2.suffices && lambda2.given) {
if(!is.null(reciplambda2))
validate.matrix(reciplambda2, npoints)
else {
validate.matrix(lambda2, npoints)
reciplambda2 <- 1/lambda2
}
} else {
# Vector lambda or reciplambda is required
if(missing(lambda) && is.null(reciplambda)) {
# No intensity data provided
# Estimate density by leave-one-out kernel smoothing
kerndens <- density(X, ..., sigma=sigma, varcov=varcov, spill=TRUE)
sigma <- kerndens$sigma
varcov <- kerndens$varcov
raw <- kerndens$raw
edg <- kerndens$edg
# Leave-one-out in numerator
SqrtDetSigma <- if(!is.null(sigma)) sigma^2 else sqrt(det(varcov))
peakvalue <- 1/(2 * pi * SqrtDetSigma)
lambda <- safelookup(raw, X) - rep(peakvalue, npoints)
# Edge correction if invoked
if(!is.null(edg))
lambda <- lambda/safelookup(edg, X)
# validate
if(length(lambda) != npoints)
stop(paste("Internal error: incorrect number of lambda values",
"in leave-one-out method:",
"length(lambda) = ", length(lambda),
"!=", npoints, "= npoints"))
if(any(is.na(lambda))) {
nwrong <- sum(is.na(lambda))
stop(paste("Internal error:", nwrong, "NA or NaN",
ngettext(nwrong, "value", "values"),
"generated in leave-one-out method"))
}
reciplambda <- 1/lambda
} else if(!is.null(reciplambda)) {
# 1/lambda values provided
if(is.vector(reciplambda))
validate.vector(reciplambda, npoints)
else if(is.im(reciplambda))
reciplambda <- safelookup(reciplambda, X)
else stop(paste(sQuote("reciplambda"),
"should be a vector or a pixel image"))
} else {
# lambda values provided
if(is.vector(lambda)) {
validate.vector(lambda, npoints)
reciplambda <- 1/lambda
} else if(is.im(lambda)) {
lambda <- safelookup(lambda, X)
reciplambda <- 1/lambda
} else
stop(paste(sQuote("lambda"),
"should be a vector or a pixel image"))
}
}
# recommended range of r values
alim <- c(0, min(rmax, rmaxdefault))
###########################################
# Efficient code for border method
# Usable only if r values are evenly spaced from 0 to rmax
# Invoked automatically if number of points is large
can.do.fast <- breaks$even && missing(lambda2)
borderonly <- all(correction == "border" | correction == "bord.modif")
large.n <- (npoints >= nlarge)
will.do.fast <- can.do.fast && (borderonly || large.n)
asked <- borderonly || (nlarge.given && large.n)
if(will.do.fast && !asked)
message(paste("number of data points exceeds",
nlarge, "- computing border estimate only"))
if(asked && !can.do.fast) {
whynot <-
if(!(breaks$even)) "r values not evenly spaced" else
if(!missing(lambda)) "matrix lambda2 was given" else NULL
warning(paste(c("cannot use efficient code", whynot), sep="; "))
}
if(will.do.fast) {
# restrict r values to recommended range, unless specifically requested
if(!rfixed)
r <- seq(0, alim[2], length=length(r))
return(Kborder.engine(X, max(r), length(r), correction, reciplambda))
}
###########################################
# Slower code
###########################################
# this will be the output data frame
K <- data.frame(r=r, theo= pi * r^2)
desc <- c("distance argument r", "theoretical Poisson %s")
K <- fv(K, "r", substitute(Kinhom(r), NULL),
"theo", , alim, c("r","%spois(r)"), desc, fname="Kinhom")
# identify all close pairs
rmax <- max(r)
close <- closepairs(X, rmax)
dIJ <- close$d
# compute weights for these pairs
I <- close$i
J <- close$j
wI <- reciplambda[I]
wIJ <-
if(is.null(lambda2))
reciplambda[I] * reciplambda[J]
else
reciplambda2[cbind(I,J)]
#
XI <- X[I]
# compute edge corrected estimates
if(any(correction == "border" | correction == "bord.modif")) {
# border method
# Compute distances to boundary
b <- bdist.points(X)
I <- close$i
bI <- b[I]
# apply reduced sample algorithm
RS <- Kwtsum(dIJ, bI, wIJ, b, w=reciplambda, breaks)
if(any(correction == "border")) {
Kb <- RS$ratio
K <- bind.fv(K, data.frame(border=Kb), "%sbord(r)",
"border-corrected estimate of %s",
"border")
}
if(any(correction == "bord.modif")) {
Kbm <- RS$numerator/eroded.areas(W, r)
K <- bind.fv(K, data.frame(bord.modif=Kbm), "%sbord*(r)",
"modified border-corrected estimate of %s",
"bord.modif")
}
}
if(any(correction == "translate")) {
# translation correction
XJ <- X[J]
edgewt <- edge.Trans(XI, XJ, paired=TRUE)
allweight <- edgewt * wIJ
wh <- whist(dIJ, breaks$val, allweight)
Ktrans <- cumsum(wh)/area
rmax <- diameter(W)/2
Ktrans[r >= rmax] <- NA
K <- bind.fv(K, data.frame(trans=Ktrans), "%strans(r)",
"translation-correction estimate of %s",
"trans")
}
if(any(correction == "isotropic" | correction == "Ripley")) {
# Ripley isotropic correction
edgewt <- edge.Ripley(XI, matrix(dIJ, ncol=1))
allweight <- edgewt * wIJ
wh <- whist(dIJ, breaks$val, allweight)
Kiso <- cumsum(wh)/area
rmax <- diameter(W)/2
Kiso[r >= rmax] <- NA
K <- bind.fv(K, data.frame(iso=Kiso), "%siso(r)",
"Ripley isotropic correction estimate of %s",
"iso")
}
# default is to display them all
attr(K, "fmla") <- . ~ r
unitname(K) <- unitname(X)
return(K)
}
Kwtsum <- function(dIJ, bI, wIJ, b, w, breaks) {
#
# "internal" routine to compute border-correction estimates of Kinhom
#
# dIJ: vector containing pairwise distances for selected I,J pairs
# bI: corresponding vector of boundary distances for I
# wIJ: product weight for selected I, J pairs
#
# b: vector of ALL distances to window boundary
# w: weights for ALL points
#
# breaks : breakpts object
#
stopifnot(length(dIJ) == length(bI))
stopifnot(length(bI) == length(wIJ))
stopifnot(length(w) == length(b))
# determine which distances d_{ij} were observed without censoring
uncen <- (dIJ <= bI)
#
# histogram of noncensored distances
nco <- whist(dIJ[uncen], breaks$val, wIJ[uncen])
# histogram of censoring times for noncensored distances
ncc <- whist(bI[uncen], breaks$val, wIJ[uncen])
# histogram of censoring times (yes, this is a different total size)
cen <- whist(b, breaks$val, w)
# total weight of censoring times beyond rightmost breakpoint
uppercen <- sum(w[b > max(breaks$val)])
# go
RS <- reduced.sample(nco, cen, ncc, show=TRUE, uppercen=uppercen)
# extract results
numerator <- RS$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))
}
