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RF_NTTfromPy.R
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RF_NTTfromPy.R
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#note to chanage the options to options("digits"=22) and options("scipen"=100)
library("ape")
library("phangorn")
library("readtext")
options("digits"=22)
options("scipen"=100)
#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
internaledges <- function(tree,ntip){
intedges=array(0,c(1,ntip-1))
edges=tree$edge
for (i in (2*ntip-1):(ntip+1)) {
children=which(edges[,1]==i)
child1=edges[children[1],2]
child2=edges[children[2],2]
if(child1 <= ntip&child2 <= ntip){intedges[i-ntip]=0}
else if(child1<= ntip & child2 > ntip){intedges[i-ntip]=intedges[child2-ntip]+1}
else if(child2<= ntip & child1 > ntip){intedges[i-ntip]=intedges[child1-ntip]+1}
else {intedges[i-ntip]=intedges[child2-ntip]+intedges[child1-ntip]+2}
}
return(intedges)
}
# the function for computing the number of internal children
internalchildren <- function(tree,v,ntip){
edges=tree$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){
tt=0
t=(n-4)*(n-2)*3
L= 2^ceiling(log(t)/log(2))
#L=16384
ntip=n-1
N=tree$Nnode
R=rep(list(matrix(0,(ntip-1),(ntip-1))),N)
edges=internaledges(tree,ntip)
B=c()
for (k in 0:(n-2)) {
B[k+1]=Beta(k)
}
for (v in N:1) {
intchild=internalchildren(tree,v+ntip,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)]
#R1aug=numeric(nrow(R1)*(2*ncol(R1)-1))
R1aug=numeric(L)
t=1
for(i in 1:ncol(R1)){
R1aug[t:(t+nrow(R1)-1)]=R1[,i]
t=t+3*nrow(R1)
}
R2=Rchild2[1:(ntip-1),1:(ntip-3)]
#R2aug=numeric(nrow(R2)*(2*ncol(R2)-1))
R2aug=numeric(L)
t=1
for(i in 1:ncol(R2)){
R2aug[t:(t+nrow(R2)-1)]=R2[,i]
t=t+3*nrow(R2)
}
#write(L,"testNTT.txt",ncolumns=L,append = TRUE)
write(R1aug,"testNTT.txt",ncolumns=L,append = TRUE)
write(R2aug,"testNTT.txt",ncolumns=L,append = TRUE)
#read the output of Python
system('python /python_code/ntt_fromR.py')
U=as.matrix(read.csv("outNTT.txt",header = FALSE, quote=""))
Matc=ceiling(length(R1aug)/(3*nrow(R1)))
sum3=matrix(c(U,numeric(Matc*3*nrow(R1)-length(R1aug))),nrow=3*nrow(R1))[1:nrow(R1),1:ncol(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
file.remove("testNTT.txt")
}
}
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_Convolve(tree,n)
for (i in seq(0,2*(n-3),2)) {
Coef=c(Coef,qmT(R,n,n-3-(i/2)))
}
return(Coef)
}