R/maxDelW.R

In treebalance: Computation of Tree (Im)Balance Indices

#' Calculation of the maximal difference in widths for a rooted tree
#'
#' This function calculates the maximal difference in widths \eqn{maxDelW(T)} for a
#' given rooted tree \eqn{T}. The tree must not necessarily be binary.
#' \eqn{maxDelW(T)} is defined as \deqn{maxDelW(T)=\max_{i=0,...,h(T)-1} w(i+1)-w(i)}{maxDelW(T)=max_{i=0,...,h(T)-1} w(i+1)-w(i)}
#' in which \eqn{h(T)} denotes the height of the tree \eqn{T} and \eqn{w(i)} denotes
#' the number of vertices in \eqn{T} that have depth \eqn{i}. The maximal difference
#' in widths is a balance index.
#'
#' @param tree A rooted tree in phylo format.
#'
#' @return \code{maxDelW} returns the maximal difference in widths of a tree.
#'
#' @author Sophie Kersting, Luise Kuehn
#'
#' @references C. Colijn and J. Gardy. Phylogenetic tree shapes resolve disease transmission patterns. Evolution, Medicine, and Public Health, 2014(1):96-108, 2014. ISSN 2050-6201. doi: 10.1093/emph/eou018.
#'
#' @examples
#' tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
#' maxDelW(tree)
#' tree <- ape::read.tree(text="((,),((((,),),),(,)));")
#' maxDelW(tree)
#'
#'@export
maxDelW <- function(tree){
  if (!inherits(tree,"phylo")) stop("The input tree must be in phylo-format.")
  n <- length(tree$tip.label)
  if(n==1){
    return(0)
  }
  Descs <- getDescMatrix(tree)
  depthResults <- getNodesOfDepth(mat=Descs,root=n+1,n=n)
  widths <- sapply(1:(depthResults$maxdepth+1),
                   function(x) length(stats::na.omit(depthResults$nodesOfDepth[x,])))
  return(max(widths[2:(depthResults$maxdepth+1)]-widths[1:depthResults$maxdepth]))
}