Nothing

```
#' Overlap between Two Empirical Density Estimates
#'
#' This function generates kernel density estimates for two datasets on a common
#' grid to calculate the area of overlap between the two estimates.
#' For the univariate case,
#' See \url{http://stats.stackexchange.com/questions/97596/how-to-calculate-overlap-between-empirical-probability-densities},
#' this function is derived from code posted in the answer by user mmk.
#'
#' @param a a numeric vector or matrix. Overlap is calculated between a and b.
#' If a and b are vectors, \code{\link[stats]{density}} is used to calculate unidimensional overlap.
#' If a and b are matrices, with each column representing a trait or dimension,
#' \code{\link[hypervolume]{hypervolume}} is used to calculate multidimensional overlap.
#' @param b a numeric vector or matrix. The number of columns of a and b must be equal.
#' @param density_args Additional arguments to pass to \code{\link[stats]{density}}
#' in the univariate case, or \code{\link[hypervolume]{hypervolume}} in
#' the multivariate case.
#' See \code{\link{Ostats}} and \code{\link{Ostats_multivariate}}.
#' @param hypervolume_set_args Additional arguments to pass to
#' \code{\link[hypervolume]{hypervolume_set}}. See
#' \code{\link{Ostats_multivariate}}.
#'
#' @details This is an internal function not intended to be called directly.
#'
#' @return A single numeric value that may range between 0 and 1.
#'
#' @noRd
pairwise_overlap <- function(a, b, discrete, density_args = list(), hypervolume_set_args = list()) {
# Check structure of inputs a and b.
# If they are unidimensional use density(), if >1 dimension use hypervolume()
# If the dimensions don't match (number of columns in a != number of columns in b), return error.
if (!inherits(a, "Hypervolume")) {
# Univariate case
# calculate intersection density
w <- pmin(a$y, b$y)
if (!discrete) {
# If continuous, integrate the areas under curves
total <- sfsmisc::integrate.xy(a$x, a$y) + sfsmisc::integrate.xy(b$x, b$y)
intersection <- sfsmisc::integrate.xy(a$x, w)
} else {
# If discrete, take the overlaps at each discrete point
total <- sum(a$y + b$y)
intersection <- sum(w)
}
# compute overlap coefficient (Sorensen)
overlap_average <- 2 * intersection / total
return(overlap_average)
} else {
# Multivariate case
# Set to verbose = FALSE if that argument is not provided.
if (!'verbose' %in% names(density_args)) {
density_args[['verbose']] <- FALSE
}
# If num.points.max and distance.factor are not provided to pass to hypervolume_set, use default.
if (!'num.points.max' %in% names(hypervolume_set_args)) {
hypervolume_set_args[['num.points.max']] <- NULL
}
if (!'distance.factor' %in% names(hypervolume_set_args)) {
hypervolume_set_args[['distance.factor']] <- 1
}
# Suppress all progress messages from hypervolume functions, including those from underlying C functions.
invisible(utils::capture.output(suppressWarnings(suppressMessages({
# Calculate hypervolume set operations
hv_set_ab <- do.call(hypervolume::hypervolume_set,
c(list(hv1 = a,
hv2 = b,
verbose = density_args[['verbose']],
check.memory = FALSE
),
hypervolume_set_args)
)
# Calculate hypervolume overlap statistic
hv_overlap_ab <- hypervolume::hypervolume_overlap_statistics(hv_set_ab)
}))))
# Return Sorensen similarity (equivalent to univariate overlap statistic)
return(hv_overlap_ab['sorensen'])
}
}
```

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