R/RF_FFT.R

In MarHayat/RF_Distribution:

library("ape")
library("phangorn")
library("readtext")

#Beta function
Beta=function(m){
  if(m<0){return(1)}
  return(dfactorial(2*m+1))
}

# the function for computing the number of internal edges

internaledges <- function(tree,ntip){
  intedges=array(0,c(1,ntip-1))
  edges=tree$edge
  for (i in (2*ntip-1):(ntip+1)) {
    children=which(edges[,1]==i)
    child1=edges[children[1],2]
    child2=edges[children[2],2]
    if((child1 <= ntip)&(child2 <= ntip)){intedges[i-ntip]=0}
    else if((child1<= ntip) & (child2 > ntip)) {intedges[i-ntip]=intedges[child2-ntip]+1}
    else if((child2<= ntip )& (child1 > ntip)){intedges[i-ntip]=intedges[child1-ntip]+1}
    else {intedges[i-ntip]=intedges[child2-ntip]+intedges[child1-ntip]+2}
  }
  return(intedges)
}


internalchildren <- function(tree,v,ntip){
  edges=tree$edge
  children=which(edges[,1]==v)
  child1=edges[children[1],2]
  child2=edges[children[2],2]
  if((child1 > ntip) & (child2 > ntip)){result=c(2,child1,child2)}
  else if((child1 > ntip) & (child2 <= ntip)){result=c(1,child1)}
  else if((child2 > ntip) & (child1 <= ntip)){result=c(1,child2)}
  else {result=0}
  return(result)
}


RF_Convolve=function(tree,n){
  ntip=n-1
  N=tree$Nnode
  R=rep(list(matrix(0,(ntip-1),(ntip-1))),N)
  edges=internaledges(tree)
  B=c()
  for (k in 0:(n-2)) {
    B[k+1]=Beta(k)
  }
  for (v in N:1) {
    intchild=internalchildren(tree,v+ntip)
    intedges=edges[v]
    if(intchild[1]==0){
      R[[v]][1,1]=1
    }
    else if(intchild[1]==1){
      Rchild=R[[intchild[2]-ntip]]
      R[[v]][1,intedges+1]=1
      R[[v]][2:(ntip-1),1]=rowSums(t(t(Rchild[1:(ntip-2),])*B[1:(ntip-1)]))
      R[[v]][2:(ntip-1),2:(ntip-1)]=Rchild[2:(ntip-1),1:((ntip-2))]
    }
    else {
      Rchild1=R[[intchild[2]-ntip]]
      Rchild2=R[[intchild[3]-ntip]]
      R[[v]][1,intedges+1]=1
      R[[v]][3,1]=sum(t(t(Rchild1[1,])*B[1:(ntip-1)]))*sum(t(t(Rchild2[1,])*B[1:(ntip-1)]))
      for (s in 4:(ntip-1)) {
        R[[v]][s,1]=sum(rowSums(t(t(Rchild1[1:(s-2),])*B[1:(ntip-1)]))*rowSums(t(t(Rchild2[(s-2):1,])*B[1:(ntip-1)])))
      }
      sum1=matrix(0,(ntip-2),(ntip-2))
      sum1[1,1:(ntip-2)]=sum(t(t(Rchild1[1,])*B[1:(ntip-1)]))*Rchild2[1,1:(ntip-2)]
      for (s in 3:(ntip-1)) {
        temp=colSums(rowSums(t(t(Rchild1[1:(s-1),])*B[1:(ntip-1)]))*Rchild2[(s-1):1,1:(ntip-2)])
        sum1[s-1,1:(ntip-2)]=temp
      }
      sum2=matrix(0,(ntip-2),(ntip-2))
      sum2[1,1:(ntip-2)]=sum(t(t(Rchild2[1,])*B[1:(ntip-1)]))*Rchild1[1,1:(ntip-2)]
      for (s in 3:(ntip-1)) {
        temp=colSums(rowSums(t(t(Rchild2[1:(s-1),])*B[1:(ntip-1)]))*Rchild1[(s-1):1,1:(ntip-2)])
        sum2[s-1,1:(ntip-2)]=temp
      }

      R1=Rchild1[1:(ntip-1),1:(ntip-3)]
      R2=Rchild2[1:(ntip-1),1:(ntip-3)]
      R1aug=cbind(R1,matrix(0,nrow(R1),ncol(R1)))
      R2aug=cbind(R2,matrix(0,nrow(R2),ncol(R2)))
      U=round(convolve(t(R1aug), rev(t(R2aug)), type="open"),0)
      sum3=t(matrix(c(U,0),2*ncol(R1),2*nrow(R1))[1:ncol(R1),1:nrow(R1)])
      sum3=cbind(array(0, dim=c(nrow(R1)-1,1)),sum3[2:nrow(R1),])
      R[[v]][2:(ntip-1),2:(ntip-1)]=sum1+sum2+sum3
    }
  }
  return(R)
}



#==========================================
RsT=function(R,n,s){
  B=c()
  for (k in 0:(n-2)) {
    B[k+1]=Beta(k)
  }
  rst =sum(t(t(R[[1]][s+1,1:(n-2-s)])*B[1:(n-2-s)]))
  return(rst)
}

#Compute the value of q_m(T)
qmT=function(R,n,m){
  qmt=0
  for (s in m:(n-3)) {
    rst=RsT(R,n,s)
    qmt=qmt+(factorial(s)/(factorial(m)*factorial(s-m)))*rst*(-1)^(s-m)
  }
  return(qmt)
}

fft_polynomial=function(tree,n){
  R=RF_Convolve(tree,n)
  for (i in seq(0,2*(n-3),2)) {
    print(qmT(R,n,n-3-(i/2)))
  }
}