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#' @export
#' @title
#' Get SNP data (Geuvadis)
#' 
#' @description
#' This function transforms SNP data (local machine).
#' 
#' @param chr
#' chromosome: integer \eqn{1-22}
#' 
#' @param path
#' local directory for VCF (variant call format) and SDRF (sample and data relationship format) files
#' 
#' @examples
#' path <- "C:/Users/a.rauschenbe/Desktop/spliceQTL/data"
#' 
get.snps.geuvadis <- function(chr,path=getwd()){
    
    # download SNP data
    file <- paste0("GEUVADIS.chr",chr,".PH1PH2_465.IMPFRQFILT_BIALLELIC_PH.annotv2.genotypes.vcf.gz")
    url <- paste0("http://www.ebi.ac.uk/arrayexpress/files/E-GEUV-1/genotypes/",file)
    destfile <- file.path(path,file)
    if(!file.exists(destfile)){
        utils::download.file(url=url,destfile=destfile,method="auto")
    }
    
    # transform with PLINK
    setwd(path)
    system(paste0("plink --vcf GEUVADIS.chr",chr,".PH1PH2_465.IMPFRQFILT_BIALLELIC_PH.annotv2.genotypes.vcf.gz",
                  " --maf 0.05 --geno 0 --make-bed --out snps",chr),invisible=FALSE)
    
    # read into R
    bed <- file.path(path,paste("snps",chr,".bed",sep=""))
    bim <- file.path(path,paste("snps",chr,".bim",sep=""))
    fam <- file.path(path,paste("snps",chr,".fam",sep=""))
    X <- snpStats::read.plink(bed=bed,bim=bim,fam=fam)
    X$fam <- NULL; all(diff(X$map$position) > 0)
    
    # fitler MAF
    maf <- snpStats::col.summary(X$genotypes)$MAF
    cond <- maf >= 0.05
    X$genotypes <- X$genotypes[,cond]
    X$map <- X$map[cond,]
    
    # format
    colnames(X$genotypes) <- paste0(X$map$chromosome,":",X$map$position)
    snps <- methods::as(object=X$genotypes,Class="numeric")
    class(snps) <- "integer"
    
    # change identifiers
    file <- "E-GEUV-1.sdrf.txt"
    url <- paste("http://www.ebi.ac.uk/arrayexpress/files/E-GEUV-1/",file,sep="")
    destfile <- file.path(path$data,file)
    if(!file.exists(destfile)){
        utils::download.file(url=url,destfile=destfile,method="auto")
    }
    samples <- utils::read.delim(file=file.path(path,"E-GEUV-1.sdrf.txt"))
    match <- match(rownames(snps),samples$Source.Name)
    rownames(snps) <- samples$Comment.ENA_RUN.[match]
    snps <- snps[!is.na(rownames(snps)),]
    
    save(object=snps,file=file.path(path,paste0("Geuvadis.chr",chr,".RData")))
}


#' @export
#' @title
#' Get SNP data (BBMRI)
#' 
#' @description
#' This function transforms SNP data (virtual machine).
#' 
#' @param chr
#' chromosome: integer \eqn{1-22}
#' 
#' @param biobank
#' character "CODAM", "LL", "LLS", "NTR", "PAN", "RS", or NULL (all)
#' 
#' @param path
#' data directory
#' 
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#' @param size
#' maximum number of SNPs to read in at once
#' 
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#' @examples
#' path <- "/virdir/Scratch/arauschenberger/trial"
#'
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get.snps.bbmri <- function(chr,biobank=NULL,path=getwd(),size=500*10^3){
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    start <- Sys.time()
    message(rep("-",times=20)," chromosome ",chr," ",rep("-",times=20))
    
    p <- 5*10^6 # (maximum number of SNPs per chromosome, before filtering)
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    # size <- 60*10^3 # (originally 100*10^3, decrease: slower but less memory)
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    skip <- seq(from=0,to=p,by=size)
    if(is.null(biobank)){
        study <- c("CODAM","LL","LLS0","LLS1","NTR0","NTR1","PAN","RS")
    } else if(biobank=="LLS"){
        study <- c("LLS0","LLS1")
    } else if(biobank=="NTR"){
        study <- c("NTR0","NTR1")
    } else if(!biobank %in% c("CODAM","LL","PAN","RS")){
        study <- biobank
    } else{
        stop("Invalid biobank.",call.=FALSE)
    }
    collect <- matrix(list(),nrow=length(skip),ncol=length(study))
    colnames(collect) <- study
    
    for(i in seq_along(skip)){
        message("\n","chunk ",i,": ",appendLF=FALSE)
        for(j in seq_along(study)){
            message(study[j],"  ",appendLF=FALSE)
            
            # Locating files on virtual machine.
            dir <- study[j]
            if(study[j]=="LLS0"){dir <- "LLS/660Q"}
            if(study[j]=="LLS1"){dir <- "LLS/OmniExpr"}
            if(study[j]=="NTR0"){dir <- "NTR/Affy6"}
            if(study[j]=="NTR1"){dir <- "NTR/GoNL"}
            path0 <- file.path("/mnt/virdir/Backup/RP3_data/HRCv1.1_Imputation",dir)
            path1 <- "/virdir/Scratch/arauschenberger/trial"
            file0 <- paste0("chr",chr,".dose.vcf.gz")
            file1 <- paste0(study[j],".chr",chr,".dose.vcf.gz")
            file2 <- paste0(study[j],".chr",chr,".dose.vcf")
            
            # Decompressing missing files in personal folder.
            if(!file.exists(file.path(path1,file2))){
                file.copy(from=file.path(path0,file0),to=file.path(path1,file1))
                R.utils::gunzip(filename=file.path(path1,file1),remove=TRUE,overwrite=TRUE)
            }
            
            # Reading in files.
            vcf <- vcfR::read.vcfR(file=file.path(path1,file2),skip=skip[i],nrows=size,verbose=FALSE)
            vcf <- vcf[vcf@fix[,"CHROM"]!="",] # bug fix
            vcf@fix[,"ID"] <- paste0(vcf@fix[,"ID"],"_",seq_len(dim(vcf)["variants"]))
            collect[i,j][[1]] <- vcf
            stop <- dim(vcf)["variants"]==0
            final <- dim(vcf)["variants"]<size
            if(stop){break}
        }
        print(utils::object.size(collect),units="Gb")
        end <- Sys.time()
        if(stop){break}
        
        # Calculating minor allele frequency.
        num <- numeric(); maf <- list()
        for(j in seq_along(study)){
            num[j] <- dim(collect[i,j][[1]])["gt_cols"] # replace by adjusted sample sizes?
            maf[[j]] <- num[j]*vcfR::maf(collect[i,j][[1]])[,"Frequency"]
        }
        cond <- rowSums(do.call(what="cbind",args=maf))/sum(num)>0.05
        if(sum(cond)==0){if(final){break}else{next}}
        
        # Filtering out genotypes.
        for(j in seq_along(study)){
            gt <- vcfR::extract.gt(collect[i,j][[1]][cond,])
            gt[gt=="0|0"] <- 0
            gt[gt=="0|1"|gt=="1|0"] <- 1
            gt[gt=="1|1"] <- 2
            storage.mode(gt) <- "integer"
            collect[i,j][[1]] <- gt
        }
        
        if(final){break}
    }
    
    # Removing empty rows.
    cond <- apply(collect,1,function(x) all(sapply(x,length)==0))
    collect <- collect[!cond,,drop=FALSE]
    save(object=collect,file=file.path(path1,paste0("temp.chr",chr,".RData")))
    #load(file.path(path1,paste0("temp.chr",chr,".RData")))
    
    # Fusing all matrices.
    snps <- NULL
    for(i in seq_len(nrow(collect))){
        inner <- NULL
        for(j in seq_len(ncol(collect))){
            add <- collect[i,j][[1]]
            colnames(add) <- paste0(colnames(collect)[j],":",colnames(add))
            inner <- cbind(inner,add)
        }
        snps <- rbind(snps,inner)
    }
    attributes(snps)$time <- end-start
    rownames(snps) <- sapply(strsplit(x=rownames(snps),split="_"),function(x) x[[1]])
    snps <- t(snps)
    
    # Filter samples.
    rownames(snps) <- sub(x=rownames(snps),pattern="LLS0|LLS1",replacement="LLS")
    rownames(snps) <- sub(x=rownames(snps),pattern="NTR0|NTR1",replacement="NTR")
    #split <- strsplit(x=colnames(snps),split=":")
    #bio <- sapply(split,function(x) x[[1]])
    #id <- sapply(split,function(x) x[[2]])
    #cond <- rep(NA,times=ncol(snps))
    #for(j in seq_along(study)){
    #  cond[bio==study[j]] <- duplicated(id[bio==study[j]])
    #}
    
    if(is.null(biobank)){
        save(object=snps,file=file.path(path1,paste0("BBMRI.chr",chr,".RData")))
    } else {
        save(object=snps,file=file.path(path1,paste0(biobank,".chr",chr,".RData")))
    }
}


#' @export
#' @title
#' Get exon data (Geuvadis)
#' 
#' @description
#' This function transforms exon data (virtual machine).
#' 
#' @param path
#' data directory 
#' 
#' @examples
#' path <- "/virdir/Scratch/arauschenberger/trial"
#' 
get.exons.geuvadis <- function(path=getwd()){

    nrows <- 303544
    file <-"/virdir/Scratch/rmenezes/data_counts.txt"
    exons <- utils::read.table(file=file,header=TRUE,nrows=nrows)
    exons <- exons[exons[,"chr"] %in% 1:22,] # autosomes
    rownames(exons) <- exon_id <- paste0(exons[,"chr"],"_",exons[,"start"],"_",exons[,"end"])
    gene_id <- as.character(exons[,4])
    exons <- t(exons[,-c(1:4)])

    save(list=c("exons","exon_id","gene_id"),file=file.path(path,"Geuvadis.exons.RData"))
}


#' @export
#' @title
#' Get exon data (BBMRI)
#' 
#' @description
#' This function transforms exon data (virtual machine).
#' 
#' @param path
#' data directory 
#' 
#' @examples
#' path <- "/virdir/Scratch/arauschenberger/trial"
#' 
get.exons.bbmri <- function(path=getwd()){
    
    # sample identifiers:
    # (1) loading quality controlled gene expression data 
    # (2) extracting sample identifiers
    # (3) removing identifiers without SNP data
    # (4) translating identifiers
    utils::data(rnaSeqData_ReadCounts_BIOS_cleaned,package="BBMRIomics") # (1)
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    cd <- SummarizedExperiment::colData(counts)[,c("biobank_id","imputation_id","run_id")] # (2)
    counts <- NULL
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    names(cd) <- substr(names(cd),start=1,stop=3) # abbreviate names
    cd <- cd[!is.na(cd$imp),] # (3)
    cd$id <- NA # (4)
    cd$id[cd$bio=="CODAM"] <- sapply(strsplit(x=cd$imp[cd$bio=="CODAM"],split="_"),function(x) x[[2]])
    cd$id[cd$bio=="LL"] <- sub(pattern="1_LLDeep_",replacement="",x=cd$imp[cd$bio=="LL"])
    cd$id[cd$bio=="LLS"] <- sapply(strsplit(x=cd$imp[cd$bio=="LLS"],split="_"),function(x) x[[2]])
    cd$id[cd$bio=="NTR"] <- sapply(strsplit(x=cd$imp[cd$bio=="NTR"],split="_"),function(x) x[[2]])
    cd$id[cd$bio=="PAN"] <- cd$imp[cd$bio=="PAN"]
    cd$id[cd$bio=="RS"] <- sub(pattern="RS1_|RS2_|RS3_",replacement="",x=cd$imp[cd$bio=="RS"])
    
    # Identify individual not with "id" but with "bio:id".
    any(duplicated(cd$id)) # TRUE
    sapply(unique(cd$bio),function(x) any(duplicated(cd$id[x]))) # FALSE
    
    # exon data:
    # (1) loading exon expression data
    # (2) extracting sample identifiers
    # (3) retaining autosomes
    # (4) retaining samples from above
    load("/virdir/Backup/RP3_data/RNASeq/v2.1.3/exon_base/exon_base_counts.RData") # (1)
    colnames(counts) <- sub(pattern=".exon.base.count.gz",replacement="",x=colnames(counts)) # (2)
    autosomes <- sapply(strsplit(x=rownames(counts),split="_"),function(x) x[[1]] %in% 1:22) # (3)
    exons <- counts[autosomes,cd$run] # (3) and (4)
    exon_id <- exon_id[autosomes] # (3)
    gene_id <- gene_id[autosomes] # (3)
    colnames(exons) <- paste0(cd$bio,":",cd$id)
    exons <- t(exons)
    
    save(list=c("exons","exon_id","gene_id"),file=file.path(path,"BBMRI.exons.RData"))
}


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#' @export
#' @title
#' Prepare data matrices
#' 
#' @description
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#' This function removes duplicate samples from each matrix,
#' only retains samples appearing in all matrices,
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#' and brings samples into the same order.
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#' 
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#' @param ...
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#' matrices with samples in the rows and variables in the columns,
#' with sample identifiers as rows names
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#' 
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#' @param message
#' display messages\strong{:} logical
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#' 
#' @examples
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#' X <- matrix(rnorm(6),nrow=3,ncol=2,dimnames=list(c("A","B","C")))
#' Z <- matrix(rnorm(9),nrow=3,ncol=3,dimnames=list(c("B","A","B")))
#' match.samples(X,Z)
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#' 
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match.samples <- function(...,message=TRUE){
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    list <- list(...)
    if(length(list)==1 & is.list(list[[1]])){list <- list[[1]]}
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    if(is.null(names(list))){
        names(list) <- sapply(substitute(list(...))[-1],deparse)
    }
    names <- names(list)
    
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    # check input
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    cond <- sapply(list,function(x) !is.matrix(x))
    if(any(cond)){
        stop("Provide matrices!",call.=FALSE)
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    }
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    cond <- sapply(list,function(x) is.null(rownames(x)))
    if(any(cond)){
        stop("Provide row names!",call.=FALSE)
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    }
    
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    # remove duplicated samples
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    duplic <- lapply(list,function(x) duplicated(rownames(x)))
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    for(i in seq_along(list)){
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        number <- round(100*mean(duplic[[i]]))
        if(message){message(number," duplicates in \"",names[i],"\"")}
        list[[i]] <- list[[i]][!duplic[[i]],,drop=FALSE]
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    }
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    # retain overlapping samples
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    all <- Reduce(f=intersect,x=lapply(list,rownames))
    for(i in seq_along(list)){
        percent <- round(100*mean(rownames(list[[i]]) %in% all))
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        if(message){message(percent,"% overlap in \"",names[i],"\"")}
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        list[[i]] <- list[[i]][all,,drop=FALSE]
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    }
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    # check output
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    cond <- sapply(list,function(x) any(duplicated(rownames(x))))
    if(any(cond)){
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        stop("Duplicate samples!",call.=FALSE)
    }
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    cond <- sapply(list,function(x) nrow(x)!=nrow(list[[1]]))
    if(any(cond)){
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        stop("Different sample sizes!",call.=FALSE)
    }
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    cond <- sapply(list,function(x) any(rownames(x)!=rownames(list[[1]])))
    if(any(cond)){
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        stop("Different sample names!",call.=FALSE)
    }
    
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    return(list)
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}

#' @export
#' @title
#' Adjust library sizes
#' 
#' @description
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#' This function adjusts RNA-seq expression data for different library sizes.
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#' 
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#' @param x
#' matrix with \eqn{n} rows (samples) and \eqn{p} columns (variables)
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#' 
#' @examples
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#' n <- 5; p <- 10
#' x <- matrix(rnbinom(n=n*p,mu=5,size=1/0.5),nrow=n,ncol=p)
#' x[1,] <- 10*x[1,]
#' adjust.samples(x)
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#' 
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adjust.samples <- function(x){
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    if(!is.matrix(x)){
        stop("no matrix argument",call.=FALSE)
    }
    if(!is.numeric(x)){
        stop("no numeric argument",call.=FALSE)
    }
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    if(!is.integer(x)&&any(round(x)!=x)){
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        warning("non-integer values",call.=FALSE)
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    }
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    if(any(x<0)){
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        warning("negative values",call.=FALSE)
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    }
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    n <- nrow(x); p <- ncol(x)
    lib.size <- rowSums(x)
    norm.factors <- edgeR::calcNormFactors(object=t(x),lib.size=lib.size)
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    gamma <- norm.factors*lib.size/mean(lib.size)
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    gamma <- matrix(gamma,nrow=n,ncol=p,byrow=FALSE)
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    x <- x/gamma
    return(x)
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}

#' @export
#' @title
#' Adjust exon length
#' 
#' @description
#' This function adjusts exon expression data for different exon lengths.
#' 
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#' @param x
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#' matrix with \eqn{n} rows (samples) and \eqn{p} columns (exons)
#' 
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#' @param offset
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#' exon length\strong{:} vector of length \eqn{p}
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#' 
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#' @param group
#' gene names\strong{:} vector of length \eqn{p}
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#' 
#' @examples
#' NA
#' 
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adjust.covariates <- function(x,offset,group){
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    if(!is.numeric(x)|!is.matrix(x)){
        stop("Argument \"x\" is no numeric matrix.",call.=FALSE)
    }
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    if(!is.numeric(offset)|!is.vector(offset)){
        stop("Argument \"offset\" is no numeric vector.",call.=FALSE)
    }
    if(any(offset<0)){
        stop("Argument \"offset\" takes negative values",call.=FALSE)   
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    }
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    if(!is.character(group)|!is.vector(group)){
        stop("Argument \"group\" is no character vector.",call.=FALSE)
    }
    if(ncol(x)!=length(group)|ncol(x)!=length(offset)){
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        stop("Contradictory dimensions.",call.=FALSE)
    }
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    n <- nrow(x); p <- ncol(x); names <- dimnames(x)
    x <- as.numeric(x)
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    offset <- rep(offset,each=n)
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    group <- strsplit(group,split=",")
    group <- sapply(group,function(x) x[[1]][1])
    group <- rep(group,each=n)
    lmer <- lme4::lmer(x ~ offset + (1|group))
    x <- matrix(stats::residuals(lmer),nrow=n,ncol=p,dimnames=names)
    x <- x-min(x)
    return(x)
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}

#' @export
#' @title
#' Search for genes
#' 
#' @description
#' This function retrieves all genes on a chromosome.
#' 
#' @param chr
#' chromosome\strong{:} integer 1-22
#' 
#' @param path
#' path to gene transfer format files (.gtf)
#' 
#' @param release
#' character "NCBI36", "GRCh37", or "GRCh38"
#' 
#' @param build
#' integer 49-91
#' 
#' @examples
#' NA
#' 
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map.genes <- function(chr,path=getwd(),release="GRCh37",build=71){
    
    # check input
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    if(!chr %in% 1:22){
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        stop("Invalid argument \"chr\".",call.=FALSE)
    }
    if(!release %in% c("NCBI36","GRCh37","GRCh38")){
        stop("Invalid argument \"release\".",call.=FALSE)
    }
    if(!build %in% 49:91){
        stop("Invalid argument \"build\".",call.=FALSE)
    }
    
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    file <- paste0("Homo_sapiens.",release,".",build,".gtf")
    if(!file.exists(file.path(path,file))){
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        url <- paste0("ftp://ftp.ensembl.org/pub/release-",build,
                      "/gtf/homo_sapiens/",file,".gz")
        destfile <- file.path(path,paste0(file,".gz"))
        utils::download.file(url=url,destfile=destfile,method="auto")
        R.utils::gunzip(filename=destfile,remove=FALSE,overwrite=TRUE)
    }
    object <- refGenome::ensemblGenome()
    refGenome::basedir(object) <- path
    refGenome::read.gtf(object,filename=file)
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    x <- refGenome::getGenePositions(object=object,by="gene_id")
    x <- x[x$seqid==chr & x$gene_biotype=="protein_coding",]
    x <- x[,c("gene_id","seqid","start","end")]
    rownames(x) <- NULL
    colnames(x)[colnames(x)=="seqid"] <- "chr"
    return(x)
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}

#' @export
#' @title
#' Search for exons
#' 
#' @description
#' This function
#' 
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#' @param gene
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#' gene names\strong{:} vector with one entry per gene,
#' including the gene names
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#' 
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#' @param exon
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#' exon names\strong{:} vector with one entry per exon,
#' including the corresponding \emph{gene} names
#' (separated by comma if multiple gene names)
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#' 
#' @details
#' The exon names should contain the gene names. For each gene, this function
#' returns the indices of the exons.
#' 
#' @examples
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#' gene <- c("A","B","C")
#' exon <- c("A","A,B","B","B,C","C")
#' map.exons(gene,exon)
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#'
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map.exons <- function(gene,exon){
    p <- length(gene)
    x <- list()
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    pb <- utils::txtProgressBar(min=0,max=p,style=3)
    for(i in seq_len(p)){
        utils::setTxtProgressBar(pb=pb,value=i)
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        which <- as.integer(grep(pattern=gene[i],x=exon))
        x[[i]] <- which
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    }
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    close(con=pb)
    names(x) <- gene
    return(x)
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}

#' @export
#' @title
#' Search for SNPs
#' 
#' @description
#' This function
#' 
#' @param gene.chr
#' chromosome\strong{:}
#' numeric vector with one entry per gene
#' 
#' @param gene.start
#' start position\strong{:}
#' numeric vector with one entry per gene
#' 
#' @param gene.end
#' end position\strong{:}
#' numeric vector with one entry per gene
#' 
#' @param snp.chr
#' integer 1-22
#' 
#' @param snp.pos
#' chromosomal position of SNPs\strong{:}
#' numeric vector with one entry per SNP
#' 
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#' @param dist
#' number of base pairs before start position\strong{:}
#' integer
#' 
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#' @examples
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#' gene.chr <- rep(1,times=5)
#' gene.start <- 1:5
#' gene.end <- 2:6
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#'
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#' snp.chr <- rep(1,times=100)
#' snp.pos <- seq(from=1,to=4.9,length.out=100)
#' 
#' map.snps(gene.chr,gene.start,gene.end,snp.chr,snp.pos,dist=0)
#'
map.snps <- function(gene.chr,gene.start,gene.end,snp.chr,snp.pos,dist=10^3){
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    if(length(gene.chr)!=length(gene.start)|length(gene.chr)!=length(gene.end)){
        stop("Invalid.",call.=FALSE)
    }
    p <- length(gene.start)
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    x <- data.frame(from=integer(length=p),to=integer(length=p))
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    pb <- utils::txtProgressBar(min=0,max=p,style=3)
    for(i in seq_len(p)){ # 
        utils::setTxtProgressBar(pb=pb,value=i)
        chr <- snp.chr == gene.chr[i]
        if(!any(chr)){next}
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        start <- snp.pos >= (gene.start[i] - dist)
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        end <- snp.pos <= gene.end[i] + 0
        which <- as.integer(which(chr & start & end))
        if(length(which)==0){next}
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        x$from[i] <- min(which)
        x$to[i] <- max(which)
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        if(length(which)==1){next}
        if(!all(diff(which)==1)){stop("SNPs are in wrong order!")}
    }
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    close(con=pb)
    return(x)
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}

#' @export
#' @title
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#' Drop trivial test
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#' 
#' @description
#' This function
#' 
#' @param map
#' list with names "genes", "exons", and "snps"
#' (output from \code{map.genes}, \code{map.exons}, and \code{map.snps})
#' 
#' @details
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#' This functions drops tests for genes without SNPs or with a single exon.
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#' 
#' @examples
#' NA
#' 
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drop.trivial <- function(map){
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    # check input
    if(length(map)!=3){
        stop("Unexpected argument length.",call.=FALSE)
    }
    if(any(names(map)!=c("genes","exons","snps"))){
        stop("Unexpected argument names.",call.=FALSE)
    }
    
    # search
    p <- nrow(map$genes)
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    pass <- rep(NA,times=p)
    pb <- utils::txtProgressBar(min=0,max=p,style=3)
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    for(i in seq_len(p)){
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        utils::setTxtProgressBar(pb=pb,value=i)
        ys <- map$exons[[i]]
        check <- logical()
        # Exclude genes without SNPs:
        check[1] <- map$snps$from[i] > 0
        check[2] <- map$snps$to[i] > 0
        # Exclude genes with single exon:
        check[3] <- length(ys) > 1
        pass[i] <- all(check)
    }
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    close(con=pb)
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    # check output
    if(any(pass[map$snps$to==0 & map$snps$from==0])){
        stop("Genes without any SNPs.",call.=FALSE)
    }
    if(any(pass[sapply(map$exons,length)<2])){
        stop("Genes without multiple exons.",call.=FALSE)
    }
    
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    map$genes <- map$genes[pass,]
    map$exons <- map$exons[pass]
    map$snps <- map$snps[pass,]
    return(map)
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}


#' @export
#' @title
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#' Conduct single tests
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#' 
#' @description
#' This function
#' 
#' @param Y
#' exon expression\strong{:}
#' matrix with \eqn{n} rows (samples) and \eqn{p} columns (exons)
#' 
#' @param X
#' SNP genotype\strong{:}
#' matrix with \eqn{n} rows (samples) and \eqn{q} columns (SNPs)
#' 
#' @param map
#' list with names "genes", "exons", and "snps"
#' (output from \code{map.genes}, \code{map.exons}, and \code{map.snps})
#' 
#' @param i
#' gene index\strong{:}
#' integer between \eqn{1} and \code{nrow(map$genes)}
#' 
#' @param limit
#' cutoff for rounding \code{p}-values
#' 
#' @param steps
#' size of permutation chunks\strong{:}
#' integer vector
#' 
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#' @param rho
#' correlation\strong{:}
#' numeric vector with values between \eqn{0} and \eqn{1}
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#' 
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#' @details
#' The maximum number of permutations equals \code{sum(steps)}. Permutations is
#' interrupted if at least \code{limit} test statistics for the permuted data
#' are larger than the test statistic for the observed data.
#' 
#' @examples
#' NA
#' 
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test.single <- function(Y,X,map,i,limit=NULL,steps=NULL,rho=c(0,0.5,1)){
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    if(is.null(limit)){limit <- 5}
    if(is.null(steps)){steps <- c(10,20,20,50)}
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    # check input
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    if(!is.numeric(limit)){
        stop("Argument \"limit\" is not numeric.",call.=FALSE)
    }
    if(limit<1){
        stop("Argument \"limit\" is below one.",call.=FALSE)
    }
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    if(!is.numeric(steps)|!is.vector(steps)){
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        stop("Argument \"steps\" is no numeric vector.",call.=FALSE)
    }
    if(sum(steps)<2){
        stop("Too few permutations \"sum(steps)\".",call.=FALSE)
    }
    
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    # extract data
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    ys <- map$exons[[i]]
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    y <- Y[,ys,drop=FALSE]
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    xs <- seq(from=map$snps$from[i],to=map$snps$to[i],by=1)
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    x <- X[,xs,drop=FALSE]
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    # test effects
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    pvalue <- rep(x=NA,times=length(rho))
    for(j in seq_along(rho)){
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        tstat <- spliceQTL:::G2.multin(
            dep.data=y,indep.data=x,nperm=steps[1]-1,rho=rho[j])$Sg
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        for(nperm in steps[-1]){
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            tstat <- c(tstat,spliceQTL:::G2.multin(
                dep.data=y,indep.data=x,nperm=nperm,rho=rho[j])$Sg[-1])
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            if(sum(tstat >= tstat[1]) >= limit){break}
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        }
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        pvalue[j] <- mean(tstat >= tstat[1],na.rm=TRUE)
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    }
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    return(pvalue)
}


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#' @export
#' @title
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#' Conduct multiple tests
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#' 
#' @description
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#' This function ...
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#' 
#' @param Y
#' exon expression\strong{:}
#' matrix with \eqn{n} rows (samples) and \eqn{p} columns (exons)
#' 
#' @param X
#' SNP genotype\strong{:}
#' matrix with \eqn{n} rows (samples) and \eqn{q} columns (SNPs)
#' 
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#' @param map
#' list with names "genes", "exons", and "snps"
#' (output from \code{map.genes}, \code{map.exons}, and \code{map.snps})
#' 
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#' @param rho
#' correlation\strong{:}
#' numeric vector with values between \eqn{0} and \eqn{1}
#' 
#' @details
#' Automatic adjustment of the number of permutations
#' such that Bonferroni-significant p-values are possible.
#' 
#' @examples
#' NA
#' 
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test.multiple <- function(Y,X,map,rho=c(0,0.5,1)){
    
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    p <- nrow(map$genes)
    
    # permutations
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    if(FALSE){
        min <- 5
        max <- p/0.05+1
        limit <- ceiling(0.05*max/p)
        base <- 1.5 # adjust sequence
        from <- log(min,base=base)
        to <- log(max,base=base)
        steps <- c(min,diff(unique(round(base^(seq(from=from,to=to,length.out=20))))))
    }
    
    if(TRUE){
        max <- p/0.05+1
        limit <- ceiling(0.05*max/p)
        steps <- diff(limit^seq(from=1,to=log(max)/log(limit),length.out=pmin(p,20)))
        steps <- c(limit,round(steps))
        steps[length(steps)] <- max-sum(steps[-length(steps)])
    }
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    if(max != sum(steps)){stop("Invalid combination?",call.=FALSE)}
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    # parallel computation
    type <- ifelse(test=.Platform$OS.type=="windows",yes="PSOCK",no="FORK")
    cluster <- parallel::makeCluster(spec=8,type=type)
    parallel::clusterSetRNGStream(cl=cluster,iseed=1)
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    parallel::clusterExport(cl=cluster,varlist=c("Y","X","map","limit","steps","rho"),envir=environment())
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    start <- Sys.time()
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    pvalue <- parallel::parLapply(cl=cluster,X=seq_len(p),fun=function(i) spliceQTL::test.single(Y=Y,X=X,map=map,i=i,limit=limit,steps=steps,rho=rho))
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    end <- Sys.time()
    parallel::stopCluster(cluster)
    rm(cluster)
    
    # tyding up
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    pvalue <- do.call(what=rbind,args=pvalue)
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    colnames(pvalue) <- paste0("rho=",rho)
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    rownames(pvalue) <- map$genes$gene_id
    
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    return(pvalue)
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}



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#--- spliceQTL test functions --------------------------------------------------

# Function: G2.multin
# This is to compute the G2 test statistic under the assumption that the response follows a multinomial distribution
### Input 
### dep data and indep data with samples on the rows and genes on the columns
### grouping: Either a logical value = F or a matrix with a single column and same number of rows as samples. 
###         Column name should be defined.
###         Contains clinical information of the samples. 
###         Should have two groups only. 
### nperm : number of permutations 
### rho: the null correlation between SNPs
### mu: the null correlation between observations corresponding to different exons and different individuals

### Output
### A list containing G2 p.values and G2 test statistics

### Example : G2T = G2(dep.data = cgh, indep.data = expr, grouping=F, stand=TRUE, nperm=1000)
### G2 p.values : G2T$G2p
### G2 TS : G2T$$Sg

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G2.multin <- function(dep.data,indep.data,stand=TRUE,nperm=100,grouping=F,rho=0,mu=0){
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    nperm = nperm
    ## check for the number of samples in dep and indep data
    
    
    if (nrow(dep.data)!=nrow(indep.data)){
        cat("number of samples not same in dep and indep data","\n")
    }
    
    if(any(abs(rho)>1)){
        cat("correlations rho larger than abs(1) are not allowed")
    }
    
    nresponses <- ncol(dep.data)
    ncovariates <- ncol(indep.data)
    ### centering and standardizing the data are not done in this case
    
    #  dep.data = scale(dep.data,center=T,scale=stand)
    #  indep.data = scale(indep.data,center=T,scale=stand)
    
    #### No  grouping of the samples.
    
    ## Calculate U=(I-H)Y and UU', where Y has observations on rows; also tau.mat=X*W.rho*X', 
    ##   where X has observations on rows and variables on columns
    ##  and W.rho = I + rho*(J-I), a square matrix with as many rows as columns in X
    ## NOTE: this formulation uses X with n obs on the rows and m covariates no the columns, so it is the transpose of the first calculations
    nsamples <- nrow(dep.data)
    n.persample <- rowSums(dep.data)
    n.all <- sum(dep.data)
    H <- (1/n.all)*matrix( rep(n.persample,each=nsamples),nrow=nsamples,byrow=T)
    U <- (diag(rep(1,nsamples)) - H) %*% dep.data
    ## Now we may have a vector of values for rho - so we define tau.mat as an array, with the 3rd index corresponding to the value of rho
    tau.mat <- array(0,dim=c(nsamples,nsamples,length(rho)))
    for(xk in 1:length(rho))  
    {  
        if (rho[xk]==0) { tau.mat[,,xk] <- tcrossprod(indep.data) } 
        else { w.rho <- diag(rep(1,ncovariates)) + rho[xk]*(tcrossprod(rep(1,ncovariates)) -diag(rep(1,ncovariates))  )
        tau.mat[,,xk] <- indep.data %*% w.rho %*% t(indep.data)}
        
    }
    ######################################
    ### NOTES ARMIN START ################
    # all(X %*% t(X) == tau.mat[,,1]) # rho = 0 -> TRUE
    # all(X %*% (t(X) %*% X) %*% t(X) == tau.mat[,,1]) # rho = 1
    # plot(as.numeric(X %*% (t(X) %*% X) %*% t(X)),as.numeric(tau.mat[,,1]))
    ### NOTES ARMIN END ##################
    ######################################
    samp_names = 1:nsamples ## this was rownames(indep.data), but I now do this so that rownames do not have to be added to the array tau.mat
    Sg = get.g2stat.multin(U,mu=mu,rho=rho,tau.mat)
    ### now we will have a vector as result, with one value per combination of values of rho and mu
    #
    ### G2 
    ### Permutations
    # When using permutations: only the rows of tau.mat are permuted
    # To check how the permutations can be efficiently applied, see tests_permutation_g2_multin.R
    
    
    perm_samp = matrix(0, nrow=nrow(indep.data), ncol=nperm)   ## generate the permutation matrix
    for(i in 1:ncol(perm_samp)){
        perm_samp[,i] = samp_names[sample(1:length(samp_names),length(samp_names))]
    }
    
    ## permutation starts - recompute tau.mat  (or recompute U each time)
    for (perm in 1:nperm){
        tau.mat.perm = tau.mat[perm_samp[,perm],,,drop=FALSE]          # permute rows
        tau.mat.perm = tau.mat.perm[,perm_samp[,perm],,drop=FALSE]     # permute columns
        
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        Sg = c(Sg,spliceQTL:::get.g2stat.multin(U, mu=mu,rho=rho,tau.mat.perm) )
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    }
    
    
    ########################################################################
    
    #### G2 test statistic
    # *** recompute for a vector of values for each case - just reformat the result with as many rows as permutations + 1,
    # and as many columns as combinations of values of rho and mu
    Sg = matrix(Sg,nrow=nperm+1,ncol=length(mu)*length(rho))
    colnames(Sg) <- paste(rep("rho",ncol(Sg)),rep(1:length(rho),each=length(mu)),rep("mu",ncol(Sg)),rep(1:length(mu),length(rho)) )
    
    ### Calculte G2 pval
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    G2p =  apply(Sg,2,spliceQTL:::get.pval.percol) 
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    return (list(perm = perm_samp,G2p = G2p,Sg = Sg))
}

# Function: get.g2stat.multin
# Computes the G2 test statistic given two data matrices, under a multinomial distribution
# This is used internally by the G2 function
# Inputs: 
#  U = (I-H)Y, a n*K matrix where n=number obs and K=number multinomial responses possible
#  tau.mat = X' W.rho X, a n*n matrix : both square, symmetric matrices with an equal number of rows
# Output: test statistic (single value)
# 
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get.g2stat.multin <- function(U, mu, rho, tau.mat){
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    g2tstat <- NULL
    for(xk in 1:length(rho))
    {
        for(xj in 1:length(mu))
        {
            if(mu[xj]==0) { g2tstat <- c(g2tstat, sum( diag( tcrossprod(U) %*% tau.mat[,,xk] ) ) )
            } else {
                g2tstat <- c(g2tstat, (1-mu[xj])*sum(diag( tcrossprod(U) %*% tau.mat[,,xk] ) ) + mu[xj]*sum( t(U) %*% tau.mat[,,xk] %*% U )  )
            }
            
        }
    }
    g2tstat
}

# Function: get.pval.percol
# This function takes a vector containing the observed test stat as the first entry, followed by values generated by permutation,
# and computed the estimated p-value
# Input
# x: a vector with length nperm+1
# Output
# the pvalue computed
get.pval.percol <- function(x){
    pval = mean(x[1]<= c(Inf , x[2:length(x)]))
    pval
}