R/kantorovich_lpsolve.R

Defines functions kantorovich_lp

Documented in kantorovich_lp

#' Computes Kantorovich distance with lp_solve
#'
#' Kantorovich distance using the \code{lpSolve} package
#'
#' @param mu (row margins) probability measure in numeric mode
#' @param nu (column margins) probability measure in numeric mode
#' @param dist matrix, the distance to be minimized on average;
#' if \code{NULL}, the 0-1 distance is used.
#' @param lp.object logical, if \code{FALSE}, the output is the Kantorovich
#' distance; if \code{TRUE}, the output is a \code{\link[lpSolve]{lp.object}}
#' @param solution logical, to use only if \code{lp.object=FALSE};
#' if \code{TRUE} the solution is returned in the \code{"solution"} attributes
#' of the output
#' @param ... arguments passed to \code{\link[lpSolve]{lp}}
#'
#' @examples
#' mu <- c(1/7,2/7,4/7)
#' nu <- c(1/4,1/4,1/2)
#' kantorovich_lp(mu, nu)
#'
#' @import lpSolve
#' @importFrom methods is
#' @export
#'
kantorovich_lp <- function(mu, nu, dist=NULL, solution=FALSE, lp.object=FALSE, ...){
  m <- length(mu)
  n <- length(nu)
  # checks
  if(m != n) stop("mu and nu do not have the same length")
  if(!is.null(dist)){
    if(!is(dist, "matrix") || mode(dist) != "numeric")
      stop("dist must be a numeric matrix")
    if(nrow(dist)!=m || ncol(dist)!=m)
      stop("invalid dimensions of the dist matrix")
  }
  if(sum(mu)!=1 || sum(nu)!=1 || any(mu<0) || any(nu<0)){
    message("Warning: mu and/or nu are not probability measures")
  }
  #
  if(is.null(dist)) dist <- 1-diag(m)
  kanto <-
    lpSolve::lp(
      direction = "min",
      objective.in = c(t(dist)),
      const.mat = rbind(-diag(m*n),
                        rbind(t(model.matrix(~0+gl(m,n)))[,],
                              t(model.matrix(~0+factor(rep(1:n,m))))[,])),
      const.dir = c(rep("<=", m*n), rep("==", m+n)),
      const.rhs = c(rep(0,m*n), c(mu, nu)), ...)
  # status
  if(lp.object==FALSE){
    if(kanto$status != 0){
      if(kanto$status == 2){
        message("Error: no feasible solution found")
      }else{
        message("Error: status ", kanto$status)
      }
    }
  }
  # output
  out <- if(lp.object) kanto else kanto$objval
  if(!lp.object && solution)
    attr(out, "solution") <- matrix(kanto$solution, nrow=m, byrow=TRUE)
  out
}

Try the kantorovich package in your browser

Any scripts or data that you put into this service are public.

kantorovich documentation built on Oct. 29, 2020, 1:06 a.m.