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#
# edgeRipley.R
#
# $Revision: 1.20 $ $Date: 2021/10/25 10:26:05 $
#
# Ripley isotropic edge correction weights
#
# edge.Ripley(X, r, W) compute isotropic correction weights
# for centres X[i], radii r[i,j], window W
#
# To estimate the K-function see the idiom in "Kest.S"
#
#######################################################################
edge.Ripley <- local({
small <- function(x) { abs(x) < .Machine$double.eps }
hang <- function(d, r) {
nr <- nrow(r)
nc <- ncol(r)
answer <- matrix(0, nrow=nr, ncol=nc)
# replicate d[i] over j index
d <- matrix(d, nrow=nr, ncol=nc)
hit <- (d < r)
answer[hit] <- acos(d[hit]/r[hit])
answer
}
edge.Ripley <- function(X, r, W=Window(X),
method=c("C", "interpreted"),
maxweight=100, internal=list()) {
# X is a point pattern, or equivalent
X <- as.ppp(X, W)
W <- X$window
method <- match.arg(method)
debug <- resolve.1.default(list(debug=FALSE), internal)
repair <- resolve.1.default(list(repair=TRUE), internal)
switch(W$type,
rectangle={},
polygonal={
if(method != "C")
stop(paste("Ripley isotropic correction for polygonal windows",
"requires method = ", dQuote("C")))
},
mask={
stop(paste("sorry, Ripley isotropic correction",
"is not implemented for binary masks"))
}
)
n <- npoints(X)
if(is.matrix(r) && nrow(r) != n)
stop("the number of rows of r should match the number of points in X")
if(!is.matrix(r)) {
if(length(r) != n)
stop("length of r is incompatible with the number of points in X")
r <- matrix(r, nrow=n)
}
#
Nr <- nrow(r)
Nc <- ncol(r)
if(Nr * Nc == 0) return(r)
##########
x <- X$x
y <- X$y
switch(method,
interpreted = {
######## interpreted R code for rectangular case #########
# perpendicular distance from point to each edge of rectangle
# L = left, R = right, D = down, U = up
dL <- x - W$xrange[1L]
dR <- W$xrange[2L] - x
dD <- y - W$yrange[1L]
dU <- W$yrange[2L] - y
# detect whether any points are corners of the rectangle
corner <- (small(dL) + small(dR) + small(dD) + small(dU) >= 2)
# angle between (a) perpendicular to edge of rectangle
# and (b) line from point to corner of rectangle
bLU <- atan2(dU, dL)
bLD <- atan2(dD, dL)
bRU <- atan2(dU, dR)
bRD <- atan2(dD, dR)
bUL <- atan2(dL, dU)
bUR <- atan2(dR, dU)
bDL <- atan2(dL, dD)
bDR <- atan2(dR, dD)
# The above are all vectors [i]
# Now we compute matrices [i,j]
# half the angle subtended by the intersection between
# the circle of radius r[i,j] centred on point i
# and each edge of the rectangle (prolonged to an infinite line)
aL <- hang(dL, r)
aR <- hang(dR, r)
aD <- hang(dD, r)
aU <- hang(dU, r)
# apply maxima
# note: a* are matrices; b** are vectors;
# b** are implicitly replicated over j index
cL <- pmin.int(aL, bLU) + pmin.int(aL, bLD)
cR <- pmin.int(aR, bRU) + pmin.int(aR, bRD)
cU <- pmin.int(aU, bUL) + pmin.int(aU, bUR)
cD <- pmin.int(aD, bDL) + pmin.int(aD, bDR)
# total exterior angle
ext <- cL + cR + cU + cD
ext <- matrix(ext, Nr, Nc)
# add pi/2 for corners
if(any(corner))
ext[corner,] <- ext[corner,] + pi/2
# OK, now compute weight
weight <- 1 / (1 - ext/(2 * pi))
},
C = {
############ C code #############################
switch(W$type,
rectangle={
if(!debug) {
z <- .C(SC_ripleybox,
nx=as.integer(n),
x=as.double(x),
y=as.double(y),
rmat=as.double(r),
nr=as.integer(Nc), #sic
xmin=as.double(W$xrange[1L]),
ymin=as.double(W$yrange[1L]),
xmax=as.double(W$xrange[2L]),
ymax=as.double(W$yrange[2L]),
epsilon=as.double(.Machine$double.eps),
out=as.double(numeric(Nr * Nc)),
PACKAGE="spatstat.core")
} else {
z <- .C(SC_ripboxDebug,
nx=as.integer(n),
x=as.double(x),
y=as.double(y),
rmat=as.double(r),
nr=as.integer(Nc), #sic
xmin=as.double(W$xrange[1L]),
ymin=as.double(W$yrange[1L]),
xmax=as.double(W$xrange[2L]),
ymax=as.double(W$yrange[2L]),
epsilon=as.double(.Machine$double.eps),
out=as.double(numeric(Nr * Nc)),
PACKAGE="spatstat.core")
}
weight <- matrix(z$out, nrow=Nr, ncol=Nc)
},
polygonal={
Y <- edges(W)
bd <- bdist.points(X)
if(!debug) {
z <- .C(SC_ripleypoly,
nc=as.integer(n),
xc=as.double(x),
yc=as.double(y),
bd=as.double(bd),
nr=as.integer(Nc),
rmat=as.double(r),
nseg=as.integer(Y$n),
x0=as.double(Y$ends$x0),
y0=as.double(Y$ends$y0),
x1=as.double(Y$ends$x1),
y1=as.double(Y$ends$y1),
out=as.double(numeric(Nr * Nc)),
PACKAGE="spatstat.core")
} else {
z <- .C(SC_rippolDebug,
nc=as.integer(n),
xc=as.double(x),
yc=as.double(y),
bd=as.double(bd),
nr=as.integer(Nc),
rmat=as.double(r),
nseg=as.integer(Y$n),
x0=as.double(Y$ends$x0),
y0=as.double(Y$ends$y0),
x1=as.double(Y$ends$x1),
y1=as.double(Y$ends$y1),
out=as.double(numeric(Nr * Nc)),
PACKAGE="spatstat.core")
}
angles <- matrix(z$out, nrow = Nr, ncol = Nc)
weight <- 2 * pi/angles
}
)
}
)
## eliminate wild values
if(repair)
weight <- matrix(pmax.int(1, pmin.int(maxweight, weight)),
nrow=Nr, ncol=Nc)
return(weight)
}
edge.Ripley
})
rmax.Ripley <- function(W) {
W <- as.owin(W)
if(is.rectangle(W))
return(boundingradius(W))
if(is.polygonal(W) && length(W$bdry) == 1L)
return(boundingradius(W))
## could have multiple connected components
pieces <- tiles(tess(image=connected(W)))
answer <- sapply(pieces, boundingradius)
return(as.numeric(answer))
}
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