#' SIDI (landscape level)
#'
#' @description Simpson's diversity index (Diversity metric)
#'
#' @param landscape A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.
#' @param directions The number of directions in which patches should be
#' connected: 4 (rook's case) or 8 (queen's case).
#'
#' @details
#' \deqn{SIDI = 1 - \sum \limits_{i = 1}^{m} P_{i}^{2}}
#' where \eqn{P_{i}} is the proportion of class i and \eqn{m} is the
#' number of classes.
#'
#' SIDI is a 'Diversity metric'. It is widely used in biodiversity and ecology. It is
#' less sensitive to rare class types than \code{\link{lsm_l_shdi}}. It can be interpreted
#' as the probability that two randomly selected cells belong to the same class.
#'
#' \subsection{Units}{None}
#' \subsection{Range}{0 <= SIDI < 1}
#' \subsection{Behaviour}{Equals SIDI = 0 when only one patch is present and approaches
#' SIDI < 1 when the number of class types increases while the proportions are equally
#' distributed}
#'
#' @seealso
#' \code{\link{lsm_c_pland}},
#' \code{\link{lsm_l_pr}}
#'
#' @return tibble
#'
#' @examples
#' landscape <- terra::rast(landscapemetrics::landscape)
#' lsm_l_sidi(landscape)
#'
#' @references
#' McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis
#' Program for Categorical Maps. Computer software program produced by the authors;
#' available at the following web site: https://www.fragstats.org
#'
#' Simpson, E. H. 1949. Measurement of diversity. Nature 163:688
#'
#' @export
lsm_l_sidi <- function(landscape, directions = 8) {
landscape <- landscape_as_list(landscape)
result <- lapply(X = landscape,
FUN = lsm_l_sidi_calc,
directions = directions)
layer <- rep(seq_along(result),
vapply(result, nrow, FUN.VALUE = integer(1)))
result <- do.call(rbind, result)
tibble::add_column(result, layer, .before = TRUE)
}
lsm_l_sidi_calc <- function(landscape, directions, resolution, extras = NULL) {
sidi <- lsm_c_pland_calc(landscape,
directions = directions,
resolution = resolution,
extras = extras)
# all values NA
if (all(is.na(sidi$value))) {
return(tibble::new_tibble(list(level = "landscape",
class = as.integer(NA),
id = as.integer(NA),
metric = "sidi",
value = as.double(NA))))
}
sidi <- 1 - sum((sidi$value / 100) ^ 2)
return(tibble::new_tibble(list(level = rep("landscape", length(sidi)),
class = rep(as.integer(NA), length(sidi)),
id = rep(as.integer(NA), length(sidi)),
metric = rep("sidi", length(sidi)),
value = as.double(sidi))))
}
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