R/kde.torus.R

In Hong-Seungki/routine: The Clustering Methods on the Surface of Torus

#' Kernel density estimation using circular von Mises distribution
#'
#' \code{kde.torus()} returns a kde using independent bivariate von mises kernel.
#'
#' @param data n x 2 matrix of toroidal data on \eqn{[-\pi, \pi)^2}
#' @param eval.point N x N numeric matrix on \eqn{[-\pi, \pi)^2}. Default input is
#'  \code{grid.torus}.
#' @param concentration positive number which has the role of \eqn{\kappa} of
#'   von Mises distribution. Default value is 25.
#' @return \code{kde.torus} returns N-vector of kdes evaluated at eval.point
#' @export
#' @seealso \code{\link{grid.torus}}
#' @examples
#' \dontrun{
#' data <- matrix(c(-pi/3, -pi/3, pi/2, pi/4),
#'                nrow = 2, byrow = TRUE)
#'
#' kde.torus(data)
#' }

kde.torus <- function(data, eval.point = grid.torus(),
                      concentration = 25){
  # Computes kde using independent bivariate von mises kernel.
  # evaluated at eval.point, a N x 2 matrix of points on torus
  # returns N-vector of kdes evaluated at eval.point
  # used in cp.torus.kde()

  n <- nrow(data)
  N <- nrow(eval.point)

  summand <- rep(0, N)
  for (i in 1:n){
    summand <- summand + exp(concentration *
                               rowSums( cos( sweep(eval.point, 2, data[i, ], "-")) ))
  }
  return( summand / n / (2 * pi * besselI(concentration, 0))^2 )
}