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#
# varblock.R
#
# Variance estimation using block subdivision
#
# $Revision: 1.22 $ $Date: 2022/01/04 05:30:06 $
#
varblock <- local({
getrvalues <- function(z) { with(z, .x) }
stepsize <- function(z) { mean(diff(z)) }
dofun <- function(domain, fun, Xpp, ...) { fun(Xpp, ..., domain=domain) }
varblock <- function(X, fun=Kest,
blocks=quadrats(X, nx=nx, ny=ny), ...,
nx=3, ny=nx,
confidence=0.95) {
stopifnot(is.ppp(X))
stopifnot(is.tess(blocks))
stopifnot(is.function(fun) || is.character(fun))
if(is.character(fun))
fun <- get(fun, mode="function")
## validate confidence level
stopifnot(confidence > 0.5 && confidence < 1)
alpha <- 1 - confidence
probs <- c(alpha/2, 1-alpha/2)
## determine whether 'fun' has an argument called 'domain'
canrestrict <- ("domain" %in% names(formals(fun))) ||
samefunction(fun, pcf) ||
samefunction(fun, Lest)
## check there's at least one point in each block
Y <- split(X, blocks)
nums <- sapply(Y, npoints)
blockok <- (nums > 0)
if(some.zeroes <- any(!blockok))
warning("Some tiles contain no data: they are discarded")
if(!canrestrict) {
## divide data into disjoint blocks
if(some.zeroes)
Y <- Y[blockok]
n <- length(Y)
if(n <= 1) stop("Need at least 2 blocks")
## apply 'fun' to each block
if(any(c("r", "breaks") %in% names(list(...)))) {
## r vector specified
fX <- fun(X, ...)
z <- lapply(Y, fun, ...)
} else {
## need to ensure compatible fv objects
z <- lapply(Y, fun, ...)
rlist <- lapply(z, getrvalues)
rmax <- min(sapply(rlist, max))
rstep <- min(sapply(rlist, stepsize))
r <- seq(0, rmax, by=rstep)
z <- lapply(Y, fun, ..., r=r)
fX <- fun(X, ..., r=r)
}
} else {
## use 'domain' argument of 'fun' to compute contributions from each tile
B <- tiles(blocks)
if(some.zeroes)
B <- B[blockok]
n <- length(B)
if(any(c("r", "breaks") %in% names(list(...)))) {
## r vector specified
fX <- fun(X, ...)
z <- lapply(B, dofun, ..., fun=fun, Xpp=X)
} else {
## need to ensure compatible fv objects
z <- lapply(B, dofun, ..., fun=fun, Xpp=X)
rlist <- lapply(z, getrvalues)
rmax <- min(sapply(rlist, max))
rstep <- min(sapply(rlist, stepsize))
r <- seq(0, rmax, by=rstep)
z <- lapply(B, dofun, ..., fun=fun, Xpp=X, r=r)
fX <- fun(X, ..., r=r)
}
}
## find columns that are common to all estimates
zzz <- reconcile.fv(append(list(fX), z))
fX <- zzz[[1]]
z <- zzz[-1]
## sample mean
m <- meanlistfv(z)
## sample variance
sqdev <- lapply(z, sqdev.fv, m=m)
v <- meanlistfv(sqdev)
v <- eval.fv(v * n/(n-1), dotonly=FALSE)
## sample standard deviation
sd <- eval.fv(sqrt(v), dotonly=FALSE)
## upper and lower limits
sem <- eval.fv(sd/sqrt(n), dotonly=FALSE)
zcrit <- qnorm(probs)
lower <- eval.fv(m + zcrit[1] * sem, dotonly=FALSE)
upper <- eval.fv(m + zcrit[2] * sem, dotonly=FALSE)
## rebadge
fva <- .Spatstat.FvAttrib
fva <- fva[fva %in% names(attributes(fX))]
attributes(m)[fva] <- attributes(v)[fva] <- attributes(sd)[fva] <-
attributes(upper)[fva] <- attributes(lower)[fva] <- attributes(fX)[fva]
m <- prefixfv(m, "mean", "sample mean of", "bold(mean)~")
v <- prefixfv(v, "var", "estimated variance of", "bold(var)~")
sd <- prefixfv(sd, "sd", "estimated standard deviation of", "bold(sd)~")
CItext <- paste(c("lower", "upper"),
paste0(100 * confidence, "%%"),
"CI limit for")
lower <- prefixfv(lower, "lo", CItext[1], "bold(lo)~")
upper <- prefixfv(upper, "hi", CItext[2], "bold(hi)~")
## tack together
out <- cbind(fX,m,v,sd,upper,lower)
## restrict r domain
bad <- matrowall(!is.finite(as.matrix(as.data.frame(out))))
rmax <- max(getrvalues(out)[!bad])
alim <- c(0, rmax)
if(!canrestrict) alim <- intersect.ranges(attr(out, "alim"), alim)
attr(out, "alim") <- alim
## sensible default plot formula
ybase <- fvnames(fX, ".y")
xname <- fvnames(fX, ".x")
tname <- intersect("theo", fvnames(fX, "."))
fvnames(out, ".y") <- yname <- paste0("mean", ybase)
fvnames(out, ".s") <- snames <- paste0(c("lo", "hi"), ybase)
fvnames(out, ".") <- c(yname, tname, snames)
attr(out, "fmla") <- paste(". ~ ", xname)
return(out)
}
sqdev.fv <- function(x,m){ eval.fv((x-m)^2, dotonly=FALSE) }
varblock
})
meanlistfv <- local({
getYmatrix <- function(x, yn=ynames) { as.matrix(as.data.frame(x)[,yn]) }
meanlistfv <- function(z, ...) {
## compute sample mean of a list of fv objects
if(!is.list(z) || !all(unlist(lapply(z, is.fv))))
stop("z should be a list of fv objects")
if(!do.call(compatible, unname(z)))
stop("Objects are not compatible")
result <- template <- z[[1]]
## extract each object's function values as a matrix
ynames <- fvnames(template, "*")
matlist <- unname(lapply(z, getYmatrix, yn=ynames))
## stack matrices into an array
y <- do.call(abind, append(matlist, list(along=3)))
## take mean
ymean <- apply(y, 1:2, mean, ...)
result[,ynames] <- ymean
return(result)
}
meanlistfv
})
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