R/stlg.R

In Moradii/stlnpp: Spatio-Temporal Analysis of Point Patterns on Linear Networks

#' Pair correlation function for spatio-temporal point processes on linear networks
#'
#' This function computes the pair correlation function for spatio-temporal point patterns on linear networks.
#'
#' @usage STLg(X,r=NULL,t=NULL,nxy=10)
#'
#' @param X a spatio-temporal point pattern of class \code{\link{stlpp}}
#' @param r values of argument r where pair correlation function will be evaluated. optional
#' @param t values of argument t where pair correlation function will be evaluated. optional
#' @param nxy pixel array dimensions. optional
#' 
#' @seealso \code{\link{pcf}}, \code{\link{STLK}}
#' 
#' @author Mehdi Moradi <m2.moradi@yahoo.com> 
#' 
#' @returns 
#' An object of class \code{sumstlpp}.
#'
#' @details 
#' This function calculates the pair correlation function for a homogeneous spatio-temporal point patterns on a linear network.
#' 
#' @references Moradi, M., & Mateu, J. (2020). First-and second-order characteristics of spatio-temporal point processes on linear networks. Journal of Computational and Graphical Statistics, 29(3), 432-443.
#' 
#' 
#' @examples
#' X <- rpoistlpp(.2,a=0,b=5,L=easynet)
#' g <- STLg(X)
#' plot(g)
#'
#' @export
STLg <- function(X,r=NULL,t=NULL,nxy=10){

  if (!inherits(X, "stlpp")) stop("X should be from class stlpp")

  Y <- as.lpp.stlpp(X)
  l <- domain(Y)
  tleng <- summary(l)$totlength
  n <- npoints(Y)
  a <- X$time[1]
  b <- X$time[2]
  trange <- b-a
  timev <- X$data$t

  denom <- (trange*tleng)/(n*(n-1))

  sdist <- pairdist(Y)
  tdist <- as.matrix(dist(timev))

  ##
  toler <- default.linnet.tolerance(l)
  ml <- matrix(1, n, n)
  for(j in 1:n) {
    ml[ -j, j] <- countends(l, Y[-j], sdist[-j,j], toler=toler)
  }

  mtplus <- matrix(timev,n,n,byrow = T)+tdist
  mtminus <- matrix(timev,n,n,byrow = T)-tdist
  mtedge <- (mtplus<=b) + (mtminus>=a)
  diag(mtedge) <- 1

  edgetl <- mtedge*ml

  maxs <- 0.7*max(sdist[!is.infinite(sdist)])
  maxt <- 0.7*(trange/2)

  if(is.null(r)) r <- seq((maxs/nxy),maxs,by=(maxs-(maxs/nxy))/(nxy-1))
  if(is.null(t)) t <- seq((maxt/nxy),maxt,by=(maxt-(maxt/nxy))/(nxy-1))


  g <- matrix(NA, nrow = nxy, ncol = nxy)
  no <- sdist == 0 & tdist == 0 | sdist==Inf | sdist>maxs | tdist>maxt
  bwl <- bw.nrd0(as.numeric(sdist[!no]))
  bwt <- bw.nrd0(as.numeric(tdist[!no]))

  for (i in 1:length(r)) {
    for (j in 1:length(t)) {

      outl <- dkernel(as.numeric(sdist[!no] - r[i]),
                      sd = bwl)
      outt <- dkernel(as.numeric(tdist[!no] - t[j]),
                      sd = bwt)
      g1 <- outl * outt/(edgetl[!no])
      g[i, j] <- sum(g1[!is.na(g1) & !is.infinite(g1)])
    }
  }

  gval <- g* denom

  gout <- list(gest=gval,gtheo=matrix(rep(1,length(t)*length(r)),ncol = nxy),r=r,t=t)
  class(gout) <- c("sumstlpp")
  attr(gout,"nxy") <- nxy
  return(gout)
}