R/obs-intensity.R

In antiphon/Kdirectional: Analysis of anisotropy in point patterns using second order statistics

#' #' Estimate intensity of point pattern at given locations
#' #' 
#' #' @param x points, list with $x and $bbox or just a matrix of coordinates.
#' #' @param loc Matrix of locations to estimate the intensity at
#' #' @param bw bandwidth, Epanechnikov kernel domain [-bw,bw]
#' #' @param b Type of border correction estimate.
#' #' @param ... ignored
#' #' @details 
#' #' Uses Epanechnikov kernel smoothing. Border corrections controlled by what b is:
#' #' 0: 2D exact, not available for 3D atm; 
#' #' 1: Box rectangle approximation; 
#' #' 2: 2D Biased box integral, 3D none;
#' #' >3: fine grid sum with resolution b^dim (slow). 
#' #' 
#' #' if b < 0 no edge correction is applied.
#' #' 
#' #' @export
#' 
#' intensity_somewhere <- function(x, loc, bw, b=0, ...) {
#'   x <- check_pp(x)
#'   bbox <- x$bbox
#'   coord <- x$x
#'   if(ncol(loc)!=ncol(coord)) stop("pattern and locations of different dimension.")
#'   intensity_at_other_points_c(coord, loc, bbox, bw, b)
#' }
#' 
#' #' Estimate intensity of point pattern at the points of the pattern
#' #' 
#' #' @param x points, list with $x and $bbox or just a matrix of coordinates.
#' #' @param bw bandwidth, Epanechnikov kernel domain [-bw,bw]
#' #' @param b Type of border correction estimate.
#' #' @param ... ignored
#' #' @details 
#' #' Uses Epanechnikov kernel smoothing. Border corrections controlled by what b is:
#' #' 0: 2D exact, not available for 3D atm; 
#' #' 1: Box rectangle approximation; 
#' #' 2: 2D Biased box integral, 3D none;
#' #' >3: fine grid sum with resolution b^dim (slow). 
#' #' 
#' #' if b < 0 no edge correction is applied.
#' #' 
#' #' @export
#' 
#' intensity_at_points <- function(x, bw, b=0, ...) {
#'   x <- check_pp(x)
#'   bbox <- x$bbox
#'   coord <- x$x
#'   intensity_at_points_c(coord, bbox, bw, b)
#' }
#' 
#' #' Find the optimal smoothing for intensity estimation kernel width
#' #' 
#' #' @param x point pattern
#' #' @param bw_vector Vector of bandwidth values to optimize over
#' #' @param keep_min if true, keep the intensity_at_points for the best bw
#' #' @param ... passed on to \code{intensity_at_points}
#' #' @details 
#' #' 
#' #' Optimize bandwidth $h$ of the Epanechnikov kernel using loss function
#' #' \deqn{latex}{\sum 1/\hat\lambda_h(x_i) - |W|)^2}
#' #' 
#' #' @return 
#' #' 
#' #' Vector of losses, or if keep_min=TRUE, list with vector of losses and vector of intensity values with the bw that gives the minimum loss.
#' #' 
#' #' @export
#' 
#' intensity_bandwidth_profile <- function(x, bw_vector, keep_min=FALSE, ...){
#'   x <- check_pp(x)
#'   V <- bbox_volume(x$bbox)
#'   err <- NULL
#'   for(bw in bw_vector) {
#'       o <- intensity_at_points(x, bw=bw, ...)
#'       # discrepancy
#'       err1 <- (sum(1/o)-V)^2
#'       if(keep_min) if(err1 <= min(err)) i <- o
#'       err <- c(err, err1)
#'   }
#'   if(keep_min) list(err=err, intensity_best=i)
#'   else err
#' }