pcf.R
#
# pcf.R
#
# $Revision: 1.30 $ $Date: 2009/04/07 07:50:30 $
#
#
# calculate pair correlation function
# from point pattern (pcf.ppp)
# or from estimate of K or Kcross (pcf.fv)
# or from fasp object
#
#
pcf <- function(X, ...) {
UseMethod("pcf")
}
pcf.ppp <- function(X, ..., r=NULL,
kernel="epanechnikov", bw=NULL, stoyan=0.15,
correction=c("translate", "Ripley"))
{
verifyclass(X, "ppp")
r.override <- !is.null(r)
win <- X$window
area <- area.owin(win)
lambda <- X$n/area
correction <- pickoption("correction", correction,
c(isotropic="isotropic",
Ripley="isotropic",
translate="translate"),
multi=TRUE)
if(is.null(bw) && kernel=="epanechnikov") {
# Stoyan & Stoyan 1995, eq (15.16), page 285
h <- stoyan /sqrt(lambda)
# conversion to standard deviation
bw <- h/sqrt(5)
}
########## r values ############################
# handle arguments r and breaks
rmaxdefault <- rmax.rule("K", win, lambda)
breaks <- handle.r.b.args(r, NULL, win, rmaxdefault=rmaxdefault)
if(!(breaks$even))
stop("r values must be evenly spaced")
# extract r values
r <- breaks$r
rmax <- breaks$max
# recommended range of r values for plotting
alim <- c(0, min(rmax, rmaxdefault))
# arguments for 'density'
from <- 0
to <- max(r)
nr <- length(r)
#################################################
# compute pairwise distances
close <- closepairs(X, max(r))
dIJ <- close$d
XI <- ppp(close$xi, close$yi, window=win, check=FALSE)
# how to process the distances
doit <- function(w, d, out, symb, desc, key, otherargs, lambda, area) {
wtot <- sum(w)
kden <- do.call("density.default",
append(list(x=d, weights=w/wtot), otherargs))
r <- kden$x
y <- kden$y * wtot
g <- y/(2 * pi * r * (lambda^2) * area)
if(is.null(out)) {
df <- data.frame(r=r, theo=rep(1,length(r)), g)
colnames(df)[3] <- key
out <- fv(df, "r", substitute(g(r), NULL), key, ,
alim, c("r","%sPois(r)", symb),
c("distance argument r", "theoretical Poisson %s", desc),
fname="g")
} else {
df <- data.frame(g)
colnames(df) <- key
out <- bind.fv(out, df, symb, desc, key)
}
return(out)
}
otherargs <- resolve.defaults(list(kernel=kernel, bw=bw),
list(...),
list(n=nr, from=from, to=to))
###### compute #######
out <- NULL
if(any(correction=="translate")) {
# translation correction
XJ <- ppp(close$xj, close$yj, window=win, check=FALSE)
edgewt <- edge.Trans(XI, XJ, paired=TRUE)
out <- doit(edgewt, dIJ, out, "%sTrans(r)",
"translation-corrected estimate of %s", "trans", otherargs,
lambda, area)
}
if(any(correction=="isotropic")) {
# Ripley isotropic correction
edgewt <- edge.Ripley(XI, matrix(dIJ, ncol=1))
out <- doit(edgewt, dIJ, out, "%sRipley(r)",
"Ripley isotropic-corrected estimate of %s", "iso", otherargs,
lambda, area)
}
# sanity check
if(is.null(out)) {
warning("Nothing computed - no edge corrections chosen")
return(NULL)
}
# which corrections have been computed?
nama2 <- names(out)
corrxns <- rev(nama2[nama2 != "r"])
# default is to display them all
attr(out, "fmla") <- deparse(as.formula(paste(
"cbind(",
paste(corrxns, collapse=","),
") ~ r")))
unitname(out) <- unitname(X)
return(out)
}
"pcf.fasp" <- function(X, ..., method="c") {
verifyclass(X, "fasp")
Y <- X
Y$title <- paste("Array of pair correlation functions",
if(!is.null(X$dataname)) "for",
X$dataname)
# go to work on each function
for(i in seq(X$fns)) {
Xi <- X$fns[[i]]
PCFi <- pcf.fv(Xi, ..., method=method)
Y$fns[[i]] <- as.fv(PCFi)
if(is.fv(PCFi))
Y$default.formula[[i]] <- attr(PCFi, "fmla")
}
return(Y)
}
"pcf.fv" <-
function(X, ..., method="c") {
verifyclass(X, "fv")
callmatched <- function(fun, argue) {
formalnames <- names(formals(fun))
formalnames <- formalnames[formalnames != "..."]
do.call("fun", argue[names(argue) %in% formalnames])
}
# extract r and the recommended estimate of K
r <- X[[attr(X, "argu")]]
K <- X[[attr(X, "valu")]]
alim <- attr(X, "alim")
# remove NA's
ok <- !is.na(K)
K <- K[ok]
r <- r[ok]
switch(method,
a = {
ss <- callmatched(smooth.spline,
list(x=r, y=K, ...))
dK <- predict(ss, r, deriv=1)$y
g <- dK/(2 * pi * r)
},
b = {
y <- K/(2 * pi * r)
y[!is.finite(y)] <- 0
ss <- callmatched(smooth.spline,
list(x=r, y=y, ...))
dy <- predict(ss, r, deriv=1)$y
g <- dy + y/r
},
c = {
z <- K/(pi * r^2)
z[!is.finite(z)] <- 1
ss <- callmatched(smooth.spline,
list(x=r, y=z, ...))
dz <- predict(ss, r, deriv=1)$y
g <- (r/2) * dz + z
},
d = {
z <- sqrt(K)
z[!is.finite(z)] <- 0
ss <- callmatched(smooth.spline,
list(x=r, y=z, ...))
dz <- predict(ss, r, deriv=1)$y
g <- z * dz/(pi * r)
},
stop(paste("unrecognised method", sQuote(method)))
)
# pack result into "fv" data frame
Z <- fv(data.frame(r=r, pcf=g, theo=rep(1, length(r))),
"r", substitute(pcf(r), NULL), "pcf", cbind(pcf, theo) ~ r, alim,
c("r", "%s(r)", "%stheo"),
c("distance argument r",
"estimate of %s by numerical differentiation",
"theoretical Poisson value of %s"),
fname="g")
unitname(Z) <- unitname(X)
return(Z)
}