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#' CAI_SD (class level)
#'
#' @description Standard deviation of core area index (Core area 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).
#' @param consider_boundary Logical if cells that only neighbour the landscape
#' boundary should be considered as core
#' @param edge_depth Distance (in cells) a cell has the be away from the patch
#' edge to be considered as core cell
#'
#' @details
#' \deqn{CAI_{SD} = sd(CAI[patch_{ij}]}
#' where \eqn{CAI[patch_{ij}]} is the core area index of each patch.
#'
#' CAI_SD is a 'Core area metric'. The metric summarises each class
#' as the standard deviation of the core area index of all patches belonging to class i.
#' The core area index is the percentage of core area in relation to patch area.
#' A cell is defined as core area if the cell has no neighbour with a different
#' value than itself (rook's case). The metric describes the differences among patches
#' of the same class i in the landscape.
#'
#' Because the metric is based on distances or areas please make sure your data
#' is valid using \code{\link{check_landscape}}.
#'
#' \subsection{Units}{Percent}
#' \subsection{Range}{CAI_SD >= 0}
#' \subsection{Behaviour}{Equals CAI_SD = 0 if the core area index is identical
#' for all patches. Increases, without limit, as the variation of core area
#' indices increases.}
#'
#' @seealso
#' \code{\link{lsm_p_cai}},
#' \code{\link[stats]{sd}} \cr
#' \code{\link{lsm_c_cai_mn}},
#' \code{\link{lsm_c_cai_cv}}, \cr
#' \code{\link{lsm_l_cai_mn}},
#' \code{\link{lsm_l_cai_sd}},
#' \code{\link{lsm_l_cai_cv}}
#'
#' @return tibble
#'
#' @examples
#' landscape <- terra::rast(landscapemetrics::landscape)
#' lsm_c_cai_sd(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
#'
#' @export
lsm_c_cai_sd <- function(landscape, directions = 8, consider_boundary = FALSE, edge_depth = 1) {
landscape <- landscape_as_list(landscape)
result <- lapply(X = landscape,
FUN = lsm_c_cai_sd_calc,
directions = directions,
consider_boundary = consider_boundary,
edge_depth = edge_depth)
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_c_cai_sd_calc <- function(landscape, directions, consider_boundary, edge_depth, resolution, extras = NULL){
# calculate core area index for each patch
cai <- lsm_p_cai_calc(landscape,
directions = directions,
consider_boundary = consider_boundary,
edge_depth = edge_depth,
resolution = resolution,
extras = extras)
# all values NA
if (all(is.na(cai$value))) {
return(tibble::new_tibble(list(level = "class",
class = as.integer(NA),
id = as.integer(NA),
metric = "cai_sd",
value = as.double(NA))))
}
# summarise for classes
cai_sd <- stats::aggregate(x = cai[, 5], by = cai[, 2], FUN = stats::sd)
return(tibble::new_tibble(list(level = rep("class", nrow(cai_sd)),
class = as.integer(cai_sd$class),
id = rep(as.integer(NA), nrow(cai_sd)),
metric = rep("cai_sd", nrow(cai_sd)),
value = as.double(cai_sd$value))))
}
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