R/centroid.R

In swarm-lab/swaRm: Processing Collective Movement Data

#' @title Centroid
#' 
#' @description This function computes the centroid (or center of mass) of a set 
#'  of x-y (or longitude-latitude) coordinates. 
#' 
#' @param x A vector of x (or longitude) coordinates.
#' 
#' @param y A vector of y (or latitude) coordinates.
#' 
#' @param robust A logical value indicating whether to compute the centroid as a
#'  simple average of the coordinates (FALSE, the default), or as the average of 
#'  the coordinates weighted by the inverse of their mean pairwise distance to 
#'  all other coordinates in the set (TRUE).  
#' 
#' @param geo A logical value indicating whether the locations are defined by 
#'  geographic coordinates (pairs of longitude/latitude values). Default: FALSE.
#' 
#' @return A two-element list corresponding to the location of the centroid.
#' 
#' @author Simon Garnier, \email{garnier@@njit.edu}
#' 
#' @seealso \code{\link{dist2centroid}}
#' 
#' @examples
#' x <- rnorm(25)
#' y <- rnorm(25, sd = 3)
#' centroid(x, y)
#' 
#' @export
centroid <- function(x, y, robust = FALSE, geo = FALSE) {
  if (length(x) != length(y)) 
    stop("x and y should have the same length.")
  
  if (!is.numeric(x) | !is.numeric(y))
    stop("x and y should be numeric.")
  
  if (robust) {
    pd <- pdist(x, y, geo = geo)
    diag(pd) <- NA
    w <- 1 / colMeans(pd, na.rm = TRUE)
  }
  
  if (geo) {
    if (length(x) > 1) {
      if (robust) {
        centrd <- as.list(geosphere::geomean(cbind(x, y), w))
      } else {
        centrd <- as.list(geosphere::geomean(cbind(x, y)))
      }
      names(centrd) <- c("lon", "lat")
    } else {
      centrd <- list(lon = x, lat = y)
    }
  } else {
    if (robust) {
      centrd <- list(x = stats::weighted.mean(x, w, na.rm = TRUE), 
                     y = stats::weighted.mean(y, w, na.rm = TRUE))
    } else {
      centrd <- list(x = mean(x, na.rm = TRUE), 
                     y = mean(y, na.rm = TRUE))
    }
  }
  
  centrd
}

#' @title Distances to the Centroid
#' 
#' @description Given a set of x-y (or longitude-latitude) coordinates, this 
#'  function computes their respective distance to the centroid (or center of 
#'  mass) of the set.
#' 
#' @param x A vector of x (or longitude) coordinates.
#' 
#' @param y A vector of y (or latitude) coordinates.
#' 
#' @param robust A logical value indicating whether to compute the centroid as a
#'  simple average of the coordinates (FALSE, the default), or as the average of 
#'  the coordinates weighted by the inverse of their mean pairwise distance to 
#'  all other coordinates in the set (TRUE).    
#' 
#' @param geo A logical value indicating whether the locations are defined by 
#'  geographic coordinates (pairs of longitude/latitude values). Default: FALSE.
#' 
#' @return A vector of the same length as x and y corresponding to the 
#'  individual distance of each point to the centroid of the set.
#' 
#' @author Simon Garnier, \email{garnier@@njit.edu}
#' 
#' @seealso \code{\link{centroid}}
#'  
#' @examples
#' x <- rnorm(25)
#' y <- rnorm(25, sd = 3)
#' dist2centroid(x, y)
#' 
#' @export
dist2centroid <- function(x, y, robust = FALSE, geo = FALSE) {
  centrd <- simplify2array(centroid(x, y, robust = robust, geo = geo))
  
  if (geo) {
    m1 <- matrix(centrd, nrow = length(x), ncol = 2, byrow = TRUE)
    m2 <- cbind(x, y)
    geosphere::distGeo(m1, m2)
  } else {
    sqrt((x - centrd[1]) ^ 2 + (y - centrd[2]) ^ 2)
  }
}