R/ExpDistMat.R

In RozetaSimonovska/SDPDmod: Spatial Dynamic Panel Data Modeling

#' @name ExpDistMat
#' @title Exponential distance matrix
#'
#' @description This function calculates the (negative) exponential distance matrix,
#' with a given cutoff distance and a positive exponent value.
#'
#' @param distMat distance matrix
#' @param distCutOff cutoff distance. Default = the maximal value from the distance matrix.
#' @param expn positive exponent, default = 0.01
#' @param mevn logical, default FALSE. If TRUE, max-eigenvalue normalization is performed.
#'
#' @return
#' \item{W}{spatial weights matrix (Default, not normalized)}
#'
#' @details
#' W is an \emph{nxn} matrix with elements \eqn{w_{ij}}, \emph{i, j = 1,..n}, where
#' \eqn{w_{ij}=e^{-\alpha d_{ij}}}, if \eqn{0 <= d_{ij} < D} and
#' \eqn{w_{ij}=0}, if \eqn{d_{ij} > D} or \eqn{i = j}.
#' \emph{D} is the distance cutoff point (maximum radius of influence),
#' \eqn{d_{ij}} is the distance between spatial units \emph{i} and \emph{j}, and
#' \eqn{\alpha} is the positive exponent (e.g. \eqn{\alpha}= 0.01, 0.02,...).
#'
#' @author Rozeta Simonovska
#'
#' @examples
#' data(gN3dist) ##distance in meters
#' W1    <- ExpDistMat(distMat = gN3dist, distCutOff = 100000)
#' dist2 <- gN3dist/1000 ##in km
#' W2    <- ExpDistMat(distMat = dist2, distCutOff = 100, expn = 0.02)
#' W2nor <- ExpDistMat(distMat = dist2, 100000, 0.001, mevn = TRUE)
#'
#' @export


ExpDistMat<-function(distMat, distCutOff = NULL, expn = 0.01, mevn = FALSE){
  if(isSymmetric(distMat) & all(diag(distMat)==0)){

    if(is.null(distCutOff)){distCutOff <- max(distMat) }
    n<-nrow(distMat)
    W<-matrix(0,nrow = n,ncol = n)

    for(i in 1:(n-1)){
      for(j in which(distMat[i,]<distCutOff & distMat[i,]!=0)){
          if(j>i){
              temp <- exp(-distMat[i,j]*expn)
              W[i,j]<- temp
              W[j,i]<- temp
          }
      }
    }

    if(mevn){ W <- eignor(W) }

  } else { stop("Error in distMat! Not a distance matrix.")}

  return(W)
}