EBMultiTest <-
function(Data,NgVector=NULL,Conditions, sizeFactors, uc = 0, AllParti=NULL,fast = T,Alpha=NULL, Beta=NULL, Qtrm=1, QtrmCut=0
,maxround = 50, step1 = 1e-6,step2 = 0.01, thre = log(2), sthre = 0, filter = 10, stopthre = 1e-4, nequal = 2)
{
 expect_is(sizeFactors, c("numeric","integer"))
 expect_is(maxround,  c("numeric","integer"))
 if(!is.factor(Conditions))Conditions=as.factor(Conditions)
 if(is.null(rownames(Data)))stop("Please add gene/isoform names to the data matrix")
 if(!is.matrix(Data))stop("The input Data is not a matrix")
 if(length(Conditions)!=ncol(Data))stop("The number of conditions is not the same as the number of samples! ")
 if(nlevels(Conditions)==2)stop("Only 2 conditions - Please use EBTest() function")
 if(nlevels(Conditions)<2)stop("Less than 2 conditions - Please check your input")
 if(length(sizeFactors)!=length(Data) &  length(sizeFactors)!=ncol(Data))
 stop("The number of library size factors is not the same as the number of samples!")
 
 if(length(unique(Conditions)) < 2){
     stop("there is only one condition")
 }
 if(length(unique(Conditions)) <= uc){
     stop("uncertain positison must be smaller than number of conditions")
 }

	#Normalized
	DataNorm=GetNormalizedMat(Data, sizeFactors)

	QuantileFor0=apply(DataNorm,1,function(i)quantile(i,Qtrm))
	AllZeroNames=which(QuantileFor0<=QtrmCut)
	NotAllZeroNames=which(QuantileFor0>QtrmCut)
    
	if(length(AllZeroNames)>0)
					    cat(paste0("Removing transcripts with ",Qtrm*100,
							    " th quantile < = ",QtrmCut," \n",
									length(NotAllZeroNames)," transcripts will be tested \n"))
                                    
	if(length(NotAllZeroNames)==0)stop("0 transcript passed")
    
	Data=Data[NotAllZeroNames,]
	
    if(!is.null(NgVector))
    {
        if(length(NgVector) != nrow(DataNorm))
        {
            stop("NgVector should have same size as number of genes")
        }
        NgVector = NgVector[NotAllZeroNames]
        NgVector = as.factor(NgVector)
        levels(NgVector) = 1:length(levels(NgVector))
    }
    
    # determine whether to use fast or regular EBSeq
    if(fast){
        # fast EBSeq method
        
        # default setting for isoform label, when no input
        if(is.null(NgVector)){NgVector = 1}
        
        # default setting for hyper-parameters alpha and beta (beta prior)
        if(is.null(Alpha))
        {
            Alpha = 0.4
        }
        if(is.null(Beta))
        {
            # for EBSeqTest to set up initial value of beta
            Beta = 0
        }
        
        # gene-level mean
        MeanList=rowMeans(DataNorm)
        
        # gene-level variance
        VarList=apply(DataNorm, 1, var)
        
        # conditions
        cd = Conditions
        levels(cd) = 1:length(levels(cd))
        
        # check if AllParti is valid
        if(!is.null(AllParti)){
            if(!is.matrix(AllParti)){
                stop("AllParti should be matrix")
            }
            if(ncol(AllParti) != length(levels(cd))){
                stop("AllParti should have same number of columns as the number of conditions(groups)")
            }
        }
        
        ## default to have K - 1 position uncertain
        if(uc == 0){
            uc = length(levels(cd)) - 1
        }
        
        # run the Test, c++ based
        res = EBSeqTest(Data,cd,uc,AllParti,iLabel = NgVector,sizefactor = sizeFactors,
        iter = maxround,alpha = Alpha, beta = Beta, step1 = step1,step2 = step2,
        thre = thre, sthre = sthre, filter = filter, stopthre = stopthre, nequal = nequal)
        
        # DE patterns
        parti = res$DEpattern
        rownames(parti) = sapply(1:nrow(parti),function(x) paste0("Pattern",x))
        colnames(parti) = levels(Conditions)
        
        # renames
        colnames(res$Posterior) = sapply(1:ncol(res$Posterior) ,function(i) paste0("pattern",i))
        rownames(res$Posterior) = rownames(DataNorm[NotAllZeroNames,])
        
        
        # Result
        Result=list(Alpha=res$Alpha,Beta=res$Beta,P=res$prop,
        RList=res$r, MeanList=MeanList,
        VarList=VarList, QList = res$q,
        Mean = res$mean,Var = res$var, PoolVar=res$poolVar,
        DataNorm=DataNorm,Iso = as.numeric(NgVector),
        AllZeroIndex=AllZeroNames,PPMat=res$Posterior,AllParti = parti,
        Conditions=Conditions, NumUC = res$nuc)
    }else{
        # regular (old) EBSeq
        Pool = F
        tau=CI=CIthre=NULL
        ApproxVal = 10^-10
        Dataraw = Data
        # size factor and isoform vector
        if(is.null(NgVector))NgVector=rep(1,nrow(Data))
        if(length(sizeFactors)!=ncol(Data))sizeFactors=sizeFactors[NotAllZeroNames,]
        
        #ReNameThem
        IsoNamesIn=rownames(Data)
        Names=paste("I",c(1:dim(Data)[1]),sep="")
        names(IsoNamesIn)=Names
        rownames(Data)=paste("I",c(1:dim(Data)[1]),sep="")
        names(NgVector)=paste("I",c(1:dim(Data)[1]),sep="")
        
        # If PossibleCond==NULL, use all combinations
        NumCond=nlevels(Conditions)
        CondLevels=levels(Conditions)
        #library(blockmodeling)
        if(is.null(AllParti)){
            AllPartiList=sapply(1:NumCond,function(i)nkpartitions(NumCond,i))
            AllParti=do.call(rbind,AllPartiList)
            colnames(AllParti)=CondLevels
            rownames(AllParti)=paste("Pattern",1:nrow(AllParti),sep="")
        }
        if(length(sizeFactors)==length(Data)){
            rownames(sizeFactors)=rownames(Data)
            colnames(sizeFactors)=Conditions
        }
        
        NoneZeroLength=nlevels(as.factor(NgVector))
        NameList=sapply(1:NoneZeroLength,function(i)names(NgVector)[NgVector==i],simplify=F)
        DataList=sapply(1:NoneZeroLength , function(i) Data[NameList[[i]],],simplify=F)
        names(DataList)=names(NameList)
        
        NumEachGroup=sapply(1:NoneZeroLength , function(i)dim(DataList)[i])
        # Unlist
        DataList.unlist=do.call(rbind, DataList)

        # Divide by SampleSize factor
        
        if(length(sizeFactors)==ncol(Data))
        DataList.unlist.dvd=t(t( DataList.unlist)/sizeFactors)
        
        if(length(sizeFactors)==length(Data))
        DataList.unlist.dvd=DataList.unlist/sizeFactors
        
        # Pool or Not
        if(Pool==T){
        DataforPoolSP.dvd=MeanforPoolSP.dvd=vector("list",NumCond)
        for(lv in 1:NumCond){
            DataforPoolSP.dvd[[lv]]=matrix(DataList.unlist.dvd[,Conditions==levels(Conditions)[lv]],nrow=dim(DataList.unlist)[1])
            MeanforPoolSP.dvd[[lv]]=rowMeans(DataforPoolSP.dvd[[lv]])
        }
        MeanforPool.dvd=rowMeans(DataList.unlist.dvd)
        NumInBin=floor(dim(DataList.unlist)[1]/NumBin)
        StartSeq=c(0:(NumBin-1))*NumInBin+1
        EndSeq=c(StartSeq[-1]-1,dim(DataList.unlist)[1])
        MeanforPool.dvd.Sort=sort(MeanforPool.dvd,decreasing=T)
        MeanforPool.dvd.Order=order(MeanforPool.dvd,decreasing=T)
        PoolGroups=sapply(1:NumBin,function(i)(names(MeanforPool.dvd.Sort)[StartSeq[i]:EndSeq[i]]),simplify=F)
        #FCforPool=MeanforPoolSP.dvd1/MeanforPoolSP.dvd2
        # Use GeoMean of every two-group partition
        Parti2=nkpartitions(NumCond,2)
        FCForPoolList=sapply(1:nrow(Parti2),function(i)rowMeans(do.call(cbind,
                                MeanforPoolSP.dvd[Parti2[i,]==1]))/
                                rowMeans(do.call(cbind,MeanforPoolSP.dvd[Parti2[i,]==2])),
                                simplify=F)
        FCForPoolMat=do.call(cbind,FCForPoolList)
        FCforPool=apply(FCForPoolMat,1,function(i)exp(mean(log(i))))
        names(FCforPool)=names(MeanforPool.dvd)
        FC_Use=names(FCforPool)[which(FCforPool>=quantile(FCforPool[!is.na(FCforPool)],PoolLower) & FCforPool<=quantile(FCforPool[!is.na(FCforPool)],PoolUpper))]
        PoolGroupVar=sapply(1:NumBin,function(i)(mean(apply(matrix(DataList.unlist[PoolGroups[[i]][PoolGroups[[i]]%in%FC_Use],],ncol=ncol(DataList.unlist)),1,var))))
        PoolGroupVarInList=sapply(1:NumBin,function(i)(rep(PoolGroupVar[i],length(PoolGroups[[i]]))),simplify=F)
        PoolGroupVarVector=unlist(PoolGroupVarInList)
        VarPool=PoolGroupVarVector[MeanforPool.dvd.Order]
        names(VarPool)=names(MeanforPool.dvd)
            }

        DataListSP=vector("list",nlevels(Conditions))
        DataListSP.dvd=vector("list",nlevels(Conditions))
        SizeFSP=DataListSP
        MeanSP=DataListSP
        VarSP=DataListSP
        GetPSP=DataListSP
        RSP=DataListSP
        CISP=DataListSP
        tauSP=DataListSP
        
        NumEachCondLevel=summary(Conditions)
        if(Pool==F & is.null(CI)) CondLevelsUse=CondLevels[NumEachCondLevel>1]
        if(Pool==T | !is.null(CI)) CondLevelsUse=CondLevels
        NumCondUse=length(CondLevelsUse)

        for (lv in 1:nlevels(Conditions)){
        DataListSP[[lv]]= matrix(DataList.unlist[,Conditions==levels(Conditions)[lv]],nrow=dim(DataList.unlist)[1])
        rownames(DataListSP[[lv]])=rownames(DataList.unlist)
        DataListSP.dvd[[lv]]= matrix(DataList.unlist.dvd[,Conditions==levels(Conditions)[lv]],nrow=dim(DataList.unlist.dvd)[1])
        if(ncol(DataListSP[[lv]])==1 & Pool==F & !is.null(CI)){
        CISP[[lv]]=matrix(CI[,Conditions==levels(Conditions)[lv]],nrow=dim(DataList.unlist.dvd)[1])
        tauSP[[lv]]=matrix(tau[,Conditions==levels(Conditions)[lv]],nrow=dim(DataList.unlist.dvd)[1])
        }
        # no matter sizeFactors is a vector or a matrix. Matrix should be columns are the normalization factors
        # may input one for each
        if(length(sizeFactors)==ncol(Data))SizeFSP[[lv]]=sizeFactors[Conditions==levels(Conditions)[lv]]
        if(length(sizeFactors)==length(Data))SizeFSP[[lv]]=sizeFactors[,Conditions==levels(Conditions)[lv]]
            
        MeanSP[[lv]]=rowMeans(DataListSP.dvd[[lv]])
        names(MeanSP[[lv]])=rownames(DataListSP[[lv]])
            
        if(length(sizeFactors)==ncol(Data))PrePareVar=sapply(1:ncol( DataListSP[[lv]]),function(i)( DataListSP[[lv]][,i]- SizeFSP[[lv]][i]*MeanSP[[lv]])^2 /SizeFSP[[lv]][i])
        if(length(sizeFactors)==length(Data))PrePareVar=sapply(1:ncol( DataListSP[[lv]]),function(i)( DataListSP[[lv]][,i]- SizeFSP[[lv]][,i]*MeanSP[[lv]])^2 /SizeFSP[[lv]][,i])

        if(ncol(DataListSP[[lv]])==1 & Pool==F & !is.null(CI))
            VarSP[[lv]]=as.vector(((DataListSP[[lv]]/tauSP[[lv]]) * CISP[[lv]]/(CIthre*2))^2)
        if( Pool==T){
            VarSP[[lv]]=VarPool
            }
        if(ncol(DataListSP[[lv]])!=1){
            VarSP[[lv]]=rowSums(PrePareVar)/ncol( DataListSP[[lv]])
            names(VarSP[[lv]])=rownames(DataList.unlist)
            GetPSP[[lv]]=MeanSP[[lv]]/VarSP[[lv]]
            RSP[[lv]]=MeanSP[[lv]]*GetPSP[[lv]]/(1-GetPSP[[lv]])
        }
        names(MeanSP[[lv]])=rownames(DataList.unlist)
        }

        # Get Empirical R
        # POOL R???
        MeanList=rowMeans(DataList.unlist.dvd)
        VarList=apply(DataList.unlist.dvd, 1, var)

        if(NumCondUse!=0){
            Varcbind=do.call(cbind,VarSP[CondLevels%in%CondLevelsUse])
          PoolVarSpeedUp_MDFPoi_NoNormVarList=rowMeans(Varcbind)
          VarrowMin=apply(Varcbind,1,min)

        }
        if(NumCondUse==0)
        {
        NumFCgp=choose(NumCond,2)
        FC_Use_tmp=vector("list",NumFCgp)
        aa=1
        for(k1 in 1:(NumCond-1)){
            for(k2 in (k1+1):NumCond){
        FCforPool=DataList.unlist.dvd[,k1]/DataList.unlist.dvd[,k2]
        names(FCforPool)=rownames(DataList.unlist.dvd)
        FC_Use_tmp[[aa]]=names(FCforPool)[which(FCforPool>=quantile(FCforPool[!is.na(FCforPool)],.25) &
                                        FCforPool<=quantile(FCforPool[!is.na(FCforPool)],.75))]
        aa=aa+1
        }}
        FC_Use=Reduce(intersect,FC_Use_tmp)
        if(length(FC_Use)==0){
            All_candi=unlist(FC_Use_tmp)
            FC_Use=names(table(All_candi))[1:3]

        }
        Var_FC_Use=apply( DataList.unlist.dvd[FC_Use,],1,var )
        MeanforPool=apply( DataList.unlist.dvd,1,mean )
        Mean_FC_Use=apply( DataList.unlist.dvd[FC_Use,],1,mean )
        FC_Use2=which(Var_FC_Use>=Mean_FC_Use)
        Var_FC_Use2=Var_FC_Use[FC_Use2]
        Mean_FC_Use2=Mean_FC_Use[FC_Use2]
        Phi=mean((Var_FC_Use2-Mean_FC_Use2)/Mean_FC_Use2^2)
        VarEst=    MeanforPool*(1+MeanforPool*Phi)
        if(Print==T)message(paste("No Replicate - estimate phi",round(Phi,5), "\n"))
        Varcbind=VarEst
        PoolVarSpeedUp_MDFPoi_NoNormVarList=VarEst
        VarrowMin=VarEst

        }

        
        
        GetP=MeanList/PoolVarSpeedUp_MDFPoi_NoNormVarList
        
        EmpiricalRList=MeanList*GetP/(1-GetP)
        # sep
        #Rcb=cbind(RSP[[1]],RSP[[2]])
        #Rbest=apply(Rcb,1,function(i)max(i[!is.na(i) & i!=Inf]))
        EmpiricalRList[EmpiricalRList==Inf]    =max(EmpiricalRList[EmpiricalRList!=Inf])
        # fine
        #
        GoodData=names(MeanList)[EmpiricalRList>0 &  VarrowMin!=0 & EmpiricalRList!=Inf & !is.na(VarrowMin) & !is.na(EmpiricalRList)]
        NotIn=names(MeanList)[EmpiricalRList<=0 | VarrowMin==0 | EmpiricalRList==Inf |  is.na(VarrowMin) | is.na(EmpiricalRList)]
        #NotIn.BestR=Rbest[NotIn.raw]
        #NotIn.fix=NotIn.BestR[which(NotIn.BestR>0)]
        #EmpiricalRList[names(NotIn.fix)]=NotIn.fix
        #print(paste("ZeroVar",sum(VarrowMin==0), "InfR", length(which(EmpiricalRList==Inf)), "Poi", length(which(EmpiricalRList<0)), ""))
        #GoodData=c(GoodData.raw,names(NotIn.fix))
        #NotIn=NotIn.raw[!NotIn.raw%in%names(NotIn.fix)]
        EmpiricalRList.NotIn=EmpiricalRList[NotIn]
        EmpiricalRList.Good=EmpiricalRList[GoodData]
        EmpiricalRList.Good[EmpiricalRList.Good<1]=1+EmpiricalRList.Good[EmpiricalRList.Good<1]
        if(length(sizeFactors)==ncol(Data))
        EmpiricalRList.Good.mat= outer(EmpiricalRList.Good, sizeFactors)
        if(length(sizeFactors)==length(Data))
        EmpiricalRList.Good.mat=EmpiricalRList.Good* sizeFactors[GoodData,]


        # Only Use Data has Good q's
        DataList.In=sapply(1:NoneZeroLength, function(i)DataList[[i]][GoodData[GoodData%in%rownames(DataList[[i]])],],simplify=F)
        DataList.NotIn=sapply(1:NoneZeroLength, function(i)DataList[[i]][NotIn[NotIn%in%rownames(DataList[[i]])],],simplify=F)
        DataListIn.unlist=do.call(rbind, DataList.In)
        DataListNotIn.unlist=do.call(rbind, DataList.NotIn)
        
        DataListSPIn=vector("list",nlevels(Conditions))
        DataListSPNotIn=vector("list",nlevels(Conditions))
        EmpiricalRList.Good.mat.SP=vector("list",nlevels(Conditions))
        for (lv in 1:nlevels(Conditions)){
            DataListSPIn[[lv]]= matrix(DataListIn.unlist[,Conditions==levels(Conditions)[lv]],nrow=dim(DataListIn.unlist)[1])
            if(length(NotIn)>0)    DataListSPNotIn[[lv]]= matrix(DataListNotIn.unlist[,Conditions==levels(Conditions)[lv]],nrow=dim(DataListNotIn.unlist)[1])
            rownames(DataListSPIn[[lv]])=rownames(DataListIn.unlist)
            if(length(NotIn)>0)rownames(DataListSPNotIn[[lv]])=rownames(DataListNotIn.unlist)
            EmpiricalRList.Good.mat.SP[[lv]]=matrix(EmpiricalRList.Good.mat[,Conditions==levels(Conditions)[lv]],nrow=dim(EmpiricalRList.Good.mat)[1])
        }

        NumOfEachGroupIn=sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.In[[i]])[1]))
        NumOfEachGroupNotIn=sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.NotIn[[i]])[1]))

        #Initialize SigIn & ...
        AlphaIn=0.5
        BetaIn=rep(0.5,NoneZeroLength)
        PIn=rep(1/nrow(AllParti),nrow(AllParti))

        ####use while to make an infinity round?
        UpdateAlpha=NULL
        UpdateBeta=NULL
        UpdateP=NULL
        UpdatePFromZ=NULL
        Timeperround=NULL
        for (times in 1:maxround){
            temptime1=proc.time()
            UpdateOutput=suppressWarnings(LogNMulti(DataListIn.unlist,DataListSPIn, EmpiricalRList.Good.mat ,EmpiricalRList.Good.mat.SP,
                                   NumOfEachGroupIn, AlphaIn, BetaIn, PIn, NoneZeroLength, AllParti,Conditions))
            message(paste("iteration", times, "done \n",sep=" "))
            AlphaIn=UpdateOutput$AlphaNew
            BetaIn=UpdateOutput$BetaNew
            PIn=UpdateOutput$PNew
            PFromZ=UpdateOutput$PFromZ
            FOut=UpdateOutput$FGood
            UpdateAlpha=rbind(UpdateAlpha,AlphaIn)
               UpdateBeta=rbind(UpdateBeta,BetaIn)
            UpdateP=rbind(UpdateP,PIn)
            UpdatePFromZ=rbind(UpdatePFromZ,PFromZ)
            temptime2=proc.time()
            Timeperround=c(Timeperround,temptime2[3]-temptime1[3])
            message(paste("time" ,round(Timeperround[times],2),"\n",sep=" "))
            Z.output=UpdateOutput$ZEachGood
               Z.NA.Names=UpdateOutput$zNaNName
            }
            #Remove this } after testing!!
             
    #        if (times!=1){
    #            if((UpdateAlpha[times]-UpdateAlpha[times-1])^2+UpdateBeta[times]-UpdateBeta[times-1])^2+UpdateR[times]-UpdateR[times-1])^2+UpdateP[times]-UpdateP[times-1])^2<=10^(-6)){
    #                   Result=list(Sig=SigIn, Miu=MiuIn, Tau=TauIn)
    #                   break
    #        }
    #    }
    #}

    ##########Change Names############
    ## Only z are for Good Ones
    ## Others are for ALL Data
    GoodData=GoodData[!GoodData%in%Z.NA.Names]
    IsoNamesIn.Good=as.vector(IsoNamesIn[GoodData])
    RealName.Z.output=Z.output
    RealName.F=FOut
    rownames(RealName.Z.output)=IsoNamesIn.Good
    rownames(RealName.F)=IsoNamesIn.Good

    RealName.EmpiricalRList=sapply(1:NoneZeroLength,function(i)EmpiricalRList[names(EmpiricalRList)%in%NameList[[i]]], simplify=F)
    RealName.MeanList=sapply(1:NoneZeroLength,function(i)MeanList[names(MeanList)%in%NameList[[i]]], simplify=F)
    RealName.SPMeanList=sapply(1:NoneZeroLength,function(i)sapply(1:length(MeanSP), function(j)MeanSP[[j]][names(MeanSP[[j]])%in%NameList[[i]]],simplify=F), simplify=F)
    RealName.SPVarList=sapply(1:NoneZeroLength,function(i)sapply(1:length(VarSP), function(j)VarSP[[j]][names(VarSP[[j]])%in%NameList[[i]]],simplify=F), simplify=F)
    RealName.DataList=sapply(1:NoneZeroLength,function(i)DataList[[i]][rownames(DataList[[i]])%in%NameList[[i]],], simplify=F)

    RealName.VarList=sapply(1:NoneZeroLength,function(i)VarList[names(VarList)%in%NameList[[i]]], simplify=F)
    RealName.PoolVarList=sapply(1:NoneZeroLength,function(i)PoolVarSpeedUp_MDFPoi_NoNormVarList[names(PoolVarSpeedUp_MDFPoi_NoNormVarList)%in%NameList[[i]]], simplify=F)
    RealName.QList=sapply(1:NoneZeroLength,function(i)sapply(1:length(GetPSP), function(j)GetPSP[[j]][names(GetPSP[[j]])%in%NameList[[i]]],simplify=F), simplify=F)


    for (i in 1:NoneZeroLength){
    tmp=NameList[[i]]
    Names=IsoNamesIn[tmp]
    RealName.MeanList[[i]]=RealName.MeanList[[i]][NameList[[i]]]
    RealName.VarList[[i]]=RealName.VarList[[i]][NameList[[i]]]
        for(j in 1:NumCond){
            RealName.SPMeanList[[i]][[j]]=RealName.SPMeanList[[i]][[j]][NameList[[i]]]
            if(!is.null(RealName.QList[[i]][[j]])){
                RealName.QList[[i]][[j]]=RealName.QList[[i]][[j]][NameList[[i]]]
                RealName.SPVarList[[i]][[j]]=RealName.SPVarList[[i]][[j]][NameList[[i]]]
                names(RealName.QList[[i]][[j]])=Names
                names(RealName.SPVarList[[i]][[j]])=Names
            }
            names(RealName.SPMeanList[[i]][[j]])=Names
        }
    RealName.EmpiricalRList[[i]]=RealName.EmpiricalRList[[i]][NameList[[i]]]
    RealName.PoolVarList[[i]]=RealName.PoolVarList[[i]][NameList[[i]]]
    RealName.DataList[[i]]=RealName.DataList[[i]][NameList[[i]],]

    names(RealName.MeanList[[i]])=Names
    names(RealName.VarList[[i]])=Names

    names(RealName.EmpiricalRList[[i]])=Names
    names(RealName.PoolVarList[[i]])=Names
    rownames(RealName.DataList[[i]])=Names

    }


    #########posterior part for other data set here later############
    AllNA=unique(c(Z.NA.Names,NotIn))
    AllZ=NULL
    AllF=NULL
    if(length(AllNA)==0){
        AllZ=RealName.Z.output[IsoNamesIn,]
        AllF=RealName.F[IsoNamesIn,]
    }
    ZEachNA=NULL
    if (length(AllNA)>0){
        Ng.NA=NgVector[AllNA]
        AllNA.Ngorder=AllNA[order(Ng.NA)]
        NumOfEachGroupNA=rep(0,NoneZeroLength)
        NumOfEachGroupNA.tmp=tapply(Ng.NA,Ng.NA,length)
        names(NumOfEachGroupNA)=c(1:NoneZeroLength)
        NumOfEachGroupNA[names(NumOfEachGroupNA.tmp)]=NumOfEachGroupNA.tmp
        PNotIn=rep(1-ApproxVal,length(AllNA.Ngorder))
        MeanList.NotIn=MeanList[AllNA.Ngorder]
        R.NotIn.raw=MeanList.NotIn*PNotIn/(1-PNotIn)
        if(length(sizeFactors)==ncol(Data))
        R.NotIn=matrix(outer(R.NotIn.raw,sizeFactors),nrow=length(AllNA.Ngorder))
        if(length(sizeFactors)==length(Data))
        R.NotIn=matrix(R.NotIn.raw*sizeFactors[names(R.NotIn.raw),],nrow=length(AllNA.Ngorder))
        
        DataListNotIn.unlistWithZ=matrix(DataList.unlist[AllNA.Ngorder,],
                                                                         nrow=length(AllNA.Ngorder))
        rownames(DataListNotIn.unlistWithZ)=AllNA.Ngorder
        DataListSPNotInWithZ=vector("list",nlevels(Conditions))
        RListSPNotInWithZ=vector("list",nlevels(Conditions))
        for (lv in 1:nlevels(Conditions)) {
            DataListSPNotInWithZ[[lv]] = matrix(DataListSP[[lv]][AllNA.Ngorder,],nrow=length(AllNA.Ngorder))
            RListSPNotInWithZ[[lv]]=matrix(R.NotIn[,Conditions==levels(Conditions)[lv]],nrow=length(AllNA.Ngorder))
        }

        FListNA=sapply(1:nrow(AllParti),function(i)sapply(1:nlevels(as.factor(AllParti[i,])),
                    function(j)f0(do.call(cbind, DataListSPNotInWithZ[AllParti[i,]==j]),AlphaIn, BetaIn,
                    do.call(cbind,RListSPNotInWithZ[AllParti[i,]==j]), NumOfEachGroupNA, log=T)),
                                           simplify=F)
        for(ii in 1:length(FListNA))
            FListNA[[ii]]=matrix(FListNA[[ii]],nrow=length(AllNA.Ngorder))
        FPartiLogNA=matrix(sapply(FListNA,rowSums),nrow=length(AllNA.Ngorder))
        FMatNA=exp(FPartiLogNA+600)
        
        rownames(FMatNA)=rownames(DataListNotIn.unlistWithZ)
        PMatNA=matrix(rep(1,nrow(DataListNotIn.unlistWithZ)),ncol=1)%*%matrix(PIn,nrow=1)
        FmultiPNA=matrix(FMatNA*PMatNA,nrow=length(AllNA.Ngorder))
      DenomNA=rowSums(FmultiPNA)
        ZEachNA=matrix(apply(FmultiPNA,2,function(i)i/DenomNA),nrow=length(AllNA.Ngorder))

        rownames(ZEachNA)=IsoNamesIn[AllNA.Ngorder]

        AllZ=rbind(RealName.Z.output,ZEachNA)
        AllZ=AllZ[IsoNamesIn,]
        
        F.NotIn=FPartiLogNA
        rownames(F.NotIn)=IsoNamesIn[rownames(FMatNA)]
        AllF=rbind(RealName.F,F.NotIn)
        AllF=AllF[IsoNamesIn,]

    }
    colnames(AllZ)=rownames(AllParti)
    colnames(AllF)=rownames(AllParti)
    rownames(UpdateAlpha)=paste("iter",1:nrow(UpdateAlpha),sep="")
    rownames(UpdateBeta)=paste("iter",1:nrow(UpdateBeta),sep="")
    rownames(UpdateP)=paste("iter",1:nrow(UpdateP),sep="")
    rownames(UpdatePFromZ)=paste("iter",1:nrow(UpdatePFromZ),sep="")
    colnames(UpdateBeta)=paste("Ng",1:ncol(UpdateBeta),sep="")

    CondOut=levels(Conditions)
    names(CondOut)=paste("Condition",c(1:length(CondOut)),sep="")

    AllZWith0=matrix(NA,ncol=ncol(AllZ),nrow=nrow(Dataraw))
    rownames(AllZWith0)=rownames(Dataraw)
    colnames(AllZWith0)=colnames(AllZ)
    if(is.null(AllZeroNames))AllZWith0=AllZ
    if(!is.null(AllZeroNames))AllZWith0[names(NotAllZeroNames),]=AllZ[names(NotAllZeroNames),]

    #############Result############################
    Result=list(Alpha=UpdateAlpha,Beta=UpdateBeta,P=UpdateP, RList=RealName.EmpiricalRList
    , MeanList=RealName.MeanList
    ,VarList=RealName.VarList
    , QList=RealName.QList
    ,Mean=unlist(RealName.SPMeanList)
    ,Var=RealName.SPVarList
    ,PoolVar=RealName.PoolVarList
    ,DataNorm = DataNorm
    ,Iso = as.numeric(NgVector)
    ,AllZeoIndex =AllZeroNames
    ,PPMat=AllZ
    , AllParti=AllParti
    , Conditions=CondOut
    ,NumUC = NA)
        
    }
	
    return(Result)
    

	
}

