#' Anisotropic and Inhomogeneous T function
#'
#' Estimate a Sector-T function for second order reweighted ("inhomogeneous") pattern.
#'
#' @param x pp, list with $x~coordinates $bbox~bounding box
#' @param u unit vector(s) of direction, as row vectors. Default: x and y axes, viz. c(1,0) and c(0,1).
#' @param epsilon Central half angle for the directed sector/cone (total angle of the rotation cone is 2*epsilon). Default: pi/4.
#' @param r radius vector at which to evaluate K
#' @param lambda optional vector of intensity estimates at points
#' @param lambda_h if lambda missing, use this bandwidth in a kernel estimate of lambda(x)
#' @param renormalise See details.
#' @param border Use border correction? Default=1, yes.
#' @param ... passed on to e.g. \link{intensity_at_points}
#' @details
#'
#' Computes a second order reweighted version of the Sector-T. In short, we count how many triplets of points in the pattern
#' have both a) their difference vector's angle less than 'epsilon' radians from direction 'u' and
#' b) difference vector lengths less than range r. Usually r is a vector and the output is then a vector as well.
#'
#' An estimate of the intensity Lambda(x) at points can be given ('lambda'). If it is a single value, the pattern is assumed to be homogeneous.
#' If it is a vector the same length as there are points, the pattern is taken to be second-order stationary. In this case the
#' the sum over the pairs (i,j) is weighted with 1/(lambda[i]*lambda[j]). If 'lambda' is missing, 'lambda_h', a single positive number,
#' should be given, which is then used for estimating the non-constant Lambda(x) via Epanechnikov kernel smoothing (see \link{intensity_at_points}).
#' If 'renormalise=TRUE', we normalise the intensity estimate so that sum(1/lambda(x))=|W|. This corresponds in \code{spatstat}'s \code{Kinhom} to setting 'normpower=2'.
#'
#' About border correction: If x$bbox is a a simple bounding box, the algorithm uses the translation corrected weighting 1/area(Wx intersect Wy) with Wx=W+x. If x$bbox is a bbquad-object, for example rotated polygon, the algorithm uses simple minus border correction.
#'
#'
#' @return
#' Returns a dataframe.
#'
#' @useDynLib Kdirectional
Test_anin <- function(x, u, epsilon, r, lambda=NULL, lambda_h,
renormalise=TRUE, border=1, ...) {
stop("Not implemented.")
x <- check_pp(x)
bbox <- x$bbox
trans <- !is.bbquad(bbox)
dim <- bbox_dim(bbox)
V <- bbox_volume(bbox)
# directions
if(missing(u)){
u <- diag(1, dim)
}
#
# make sure unit vectors
u <- rbind(u)
u <- t(apply(u, 1, function(ui) ui/c(sqrt(t(ui)%*%ui))))
#
# central half-angle
if(missing(epsilon)){
epsilon <- pi/4
}
if(abs(epsilon)>pi/2) stop("epsilon should be in range [0, pi/2]")
#
# ranges
if(missing(r)) {
sidelengths <- bbox_sideLengths(bbox)
bl <- min(sidelengths)*0.3
r <- seq(0, bl, length=50)
}
# check intensity
if(!missing(lambda)){
err <- paste("lambda should be a single positive number or a vector of length", nrow(x$x))
if(!is.vector(lambda)) stop(err)
if(length(lambda) != nrow(x$x)){
if(length(lambda)!= 1) stop(err)
lambda <- rep(lambda, nrow(x$x))
}
}
else{
# estimate lambda
if(missing(lambda_h)) stop("Need lambda_h to estimate the intensity function")
lambda <- intensity_at_points(x, bw=lambda_h, ...)
}
# Check the lambda's positive
if(!all(lambda>0)) stop("Check your parameters. Lambda's need to be positive.")
# if renormalisation of the intensity is in order
if(renormalise) {
S <- V/sum(1/lambda)
normpower <- 2
S <- S^normpower
} else {
S<-1
}
#
# we got everything, let's compute.
coord <- x$x
if(trans){
stop("Not implemented.")
out <- Kest_anin_c(coord, lambda, bbox, r, u, epsilon, border)
out <- out * 2 # double sum
}
if(!trans){ # minus border correction
bd <- bbox_distance(coord, bbox)
bbox0 <- bbquad2bbox(bbox)
xout <- Kest_anin_border_c(coord, lambda, bbox0, bd, r, u, epsilon, border)
# need to correct due to minus sampling
if(border){
w <- sapply(r, function(r) sum(bd > r))
out <- out*nrow(coord)/w
}
}
# scaling
#
out <- S * out
# in case translation weights are not applied
if(border==0 | !trans ) out <- out/V
#
# compile output
# direction names
dir_names <- apply(u, 1, function(ui) paste0("(", paste0(round(ui, 3), collapse=","), ")" ))
# theoretical
theo <- if(dim==2) (2 * epsilon * r^2) else (4/3 * r^3 * pi * (1-cos(epsilon)))
#
Kest <- data.frame(r=r, theo=theo, out)
names(Kest)[] <- c("r", "theo", dir_names)
rownames(Kest) <- NULL
attr(Kest, "epsilon") <- epsilon
attr(Kest, "fun_name") <- "Kest_anin"
attr(Kest, "theo_name") <- "CSR"
#done
class(Kest) <- c("K_anin", is(Kest))
Kest
}
#' Plot Kest_anin object
#'
#' @param x Output from Kest_anin
#' @param r_scale Plot with x-axis r*r_scale
#' @param rmax plot upto this range
#' @param legpos legend position
#' @param ... passed on to plot
#' @export
plot.K_anin <- function(x, r_scale=1, rmax, legpos="topleft", lwd = 1, ...) {
# cut r
if(!missing(rmax)) x <- x[x$r<rmax,]
#
plot(x$r*r_scale, x$theo, col=1, xlab="r",
ylab=attr(x, "fun_name"), type="l", lty=3, lwd = lwd, ...)
n <- ncol(x)
for(i in 3:n){
lines(x$r*r_scale, x[,i], col=i-1, lwd = lwd)
}
nam <- names(x)[-1]
tn <- attr(x, "theo_name")
if(!is.null(tn)) nam[1] <- tn
legend(legpos, nam, lty=c(3,rep(1,n-2)), col=c(1:(n-1)), lwd = lwd)
}
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