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##############################################################################
#' Prediction of potential regeneration densities
#'
#' @description Prediction of the potential regeneration density as a function
#' of the distance to the nearest seed tree.
#'
#' @param distmap A SpatRaster with distances to the nearest seed tree is used
#' for the prediction of the potential regeneration densities. Usually a
#' result of the `seed_tree_distmap()` function
#' @param quax A quax object is used for the prediction. This is a parameterised
#' dispersal function using quantile regression.
#'
#' @details , defined by the study area. The potential regeneration density is
#' calculated and given for each raster cell.
#'
#' @return A SpatRaster with the same resolution as the input raster containing
#' the regeneration density on the same scale (e.g. numbers per hectare) as in
#' the input data.
#'
#' @export
#'
#' @examples
#' ## Prepare artificial data:
#' set.seed(0)
#' r <- rgamma(200, shape=2, scale=150)
#' simulated.data <- data.frame(distance = r, density = rpois(length(r),
#' k_lognormal(r, par=c(6,0), N=1000000, d=2)))
#'
#' ## Run quax function:
#' f1 <- quax(x = simulated.data$distance, y = simulated.data$density,
#' tau = 0.9, fun = k_lognormal)
#'
#' ## Create raster data set
#' rr <- terra::rast(
#' matrix(sample(0:10, 20 * 20, replace = TRUE),
#' nrow = 20, ncol = 20))
#'
#' ## Compute distance for prediction area
#' distance <- seed_tree_distmap(raster = rr, species = "10")
#'
#' ## Prediction
#' p <- predict_quax(distmap = distance, quax = f1)
#' terra::plot(p)
predict_quax <- function(distmap, quax) {
prediction <- quax(terra::values(distmap))
terra::values(distmap) <- prediction
return(distmap)
}
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