R/locational.Gini.curve.r

In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

#' Plot a locational Gini curve from regions - industries matrices
#'
#' This function plots a locational Gini curve following Krugman from regions - industries matrices.
#' @param mat An incidence matrix with regions in rows and industries in columns. The input can also be a vector of industrial regional count (a matrix with n regions in rows and a single column).
#' @param pop A vector of population regional count
#' @param pdf Logical; shall a pdf be saved to your current working directory? Defaults to FALSE. If set to TRUE, a pdf with all locational Gini curves will be compiled and saved to your current working directory.
#' @keywords concentration inequality
#' @export
#' @examples
#'
#' ## generate a region - industry matrix
#' mat = matrix (
#' c (100, 0, 0, 0, 0,
#' 0, 15, 5, 70, 10,
#' 0, 20, 10, 20, 50,
#' 0, 25, 30, 5, 40,
#' 0, 40, 55, 5, 0), ncol = 5, byrow = T)
#' rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c ("I1", "I2", "I3", "I4", "I5")
#'
#' ## run the function (shows industry #5)
#' locational.Gini.curve (mat)
#' locational.Gini.curve (mat, pdf = TRUE)
#'
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{Hoover.Gini}}, \code{\link{locational.Gini}}, \code{\link{Hoover.curve}}, \code{\link{Lorenz.curve}}, \code{\link{Gini}}
#' @references Krugman P. (1991) \emph{Geography and Trade}, MIT Press, Cambridge (chapter 2 - p.56)


locational.Gini.curve <- function (mat, pdf = FALSE) {

  mat = as.matrix (mat)

  LGC <- function(mat, pop, col = 1) {

  share_city_total = rowSums (mat) / sum (mat)
  ind <- mat[,col]
  pop <- share_city_total
  o = ind/pop
  o[is.na(o)] = 0
  oind <- order(o)
  ind <- ind[oind]
  pop <- pop[oind]
  ind <- c(0, ind)
  pop <- c(0, pop)
  cind <- cumsum(ind)/max(cumsum(ind))
  cpop <- cumsum(pop)/max(cumsum(pop))
  plot(cpop, cind, type = "l", main = paste0("Locational Gini curve ", colnames(mat)[col]), xlab = "Cumulative distribution of total industrial shares",
       ylab = "Cumulative distribution shares in the focal industry",
       xlim = c(0, 1), ylim = c(0, 1))
  return(abline(0, 1, col = "red"))

  }

  if (!pdf) {

    for (i in unique(1:ncol(mat)))
    {
      LGC(mat, pop, i)
    }


  } else {

    pdf("locational.Gini.curve.pdf")
    for (i in unique(1:ncol(mat)))
    {
      LGC(mat, pop, i)
    }
    dev.off()
    print ("locational.Gini.curve.pdf has been saved to your current working directory")

  }

}