R/kinhat.R

In spatialkernel: Non-Parametric Estimation of Spatial Segregation in a Multivariate Point Process

#' Inhomogeneous K-function Estimation
#' Estimate the inhomogeneous K function of a non-stationary point pattern.
#' @param pts matrix of the \code{x,y}-coordinates of the point locations.
#' @param lambda intensity function evaluated at the above point locations.
#' @param poly matrix of the \code{x,y}-coordinates of the polygon boundary.
#' @param s vector of distances at which to calculate the K function.
#' @return A list with components
#' \describe{
#'   \item{k}{values of estimated K at the distances \code{s}.}
#'   \item{s}{copy of \code{s}.}
#' }
#' @details
#'   The inhomogeneous K function is a generalization of the usual K
#'   function defined for a second-order intensity-reweighted stationary
#'   point process, proposed by Baddeley \emph{et\ al} (2000). 
#'   
#'   When the true intensity function is unknown, and is to be estimated
#'   from the same data as been used to estimate the K function,
#'   a modified kernel density estimation implemented in \code{\link{lambdahat}}
#'   with argument \code{gpts=NULL}
#'   can be used to calculate the estimated intensity at data points.
#'   See Baddeley \emph{et al} (2000) for details,
#'   and Diggle, P.J., \emph{et al} (2006) for a cautious note.
#' @note This code is adapted from \pkg{splancs} (Rowlingson and Diggle, 1993)
#'   fortran code for the estimation of homogeneous K function
#'   \code{\link[splancs]{khat}}, with edge correction inherited
#'   for a general polygonal area.
#' @seealso \code{\link[splancs]{khat}}, \code{\link{lambdahat}} 
#' @references
#' \enumerate{
#'   \item Baddeley, A. J. and M?ller, J. and Waagepetersen R.
#'   (2000) Non and semi-parametric estimation of interaction in
#'   inhomogeneous point patterns, \emph{Statistica Neerlandica}, \bold{54},
#'   3, 329--350.
#'   \item Diggle, P.J., V. G\eqn{\acute{\mathrm{o}}}mez-Rubio,
#'   P.E. Brown, A.G. Chetwynd and S. Gooding (2006) Second-order
#'   analysis of inhomogeneous spatial point processes using case-control
#'   data, \emph{submitted to Biometrics}.
#'   \item Rowlingson, B. and Diggle, P. (1993) Splancs: spatial point pattern
#'   analysis code in S-Plus.  \emph{Computers and Geosciences}, \bold{19},
#'   627--655.
#' }
#' @keywords spatial
#' @export
kinhat <- function (pts, lambda, poly, s)
{
    ptsx <- pts[, 1]
    ptsy <- pts[, 2]
    npt <- length(ptsx)
    ns <- length(s)
    s <- sort(s)
    np <- length(poly[, 1])
    polyx <- c(poly[, 1], poly[1, 1])
    polyy <- c(poly[, 2], poly[1, 2])
    hkhat <- rep(0, times = ns)
    klist <- .Fortran("dokinhat", as.double(ptsx), as.double(ptsy),
        as.integer(npt), as.double(lambda), as.double(polyx), as.double(polyy),
        as.integer(np), as.double(s), as.integer(ns), as.double(hkhat), 
      PACKAGE="spatialkernel")
    res <- list(k = as.numeric(klist[[10]]), s = s)
}