library("ape")
library("phangorn")
library("readtext")
#==================================================
#we need to convert the unrooted tree to the rooted tree with one tip less
#unrooted_tree=rtree(n,rooted=FALSE)
#plot(unrooted_tree)
#rooted_tree=reroot(unrooted_tree,n)
#plot(rooted_tree)
#rooted_tree=drop.tip(rooted_tree,n)
#plot(rooted_tree)
#tree=rooted_tree
#==================================================
#Beta function
Beta=function(m){
if(m<=0){ans=1}
else {
ans=1
for (i in 1:m) {
ans=ans*(2*i+1)
}
}
return(ans)
}
# the function for computing the number of internal edges for each internal node
internaledges <- function(tree){
ntip=length(tree$tip.label)
intedges=array(0,c(1,ntip-1))
edges=tree$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)
}
#this function computes the number of internal children of each node. v is the node, ntip is the number of tips of th tree
internalchildren <- function(tree,v){
ntip=length(tree$tip.label)
edges=tree$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_old=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
}
sum3=matrix(0,(ntip-2),(ntip-2))
for (s in 1:(ntip-2)){
for (k in 2:(ntip-2)) {
total3=0
for (s1 in 0:(s)) {
for (k1 in 0:(k-2)) {
total3=total3+Rchild1[s1+1,k1+1]*Rchild2[s-s1+1,k-2-k1+1]
}
sum3[s,k]=total3
}
}
}
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)
}
#this function computes the RF distribution
polynomial=function(tree,n){
Coef=numeric()
R=RF_old(tree,n)
for (i in seq(0,2*(n-3),2)) {
Coef=c(Coef,qmT(R,n,n-3-(i/2)))
}
return(Coef)
}
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