loessF <- function(datVn, qcaVi, preVi, spnN) {

    if(length(qcaVi) < 5) {

        return(predict(lm(datVn[qcaVi] ~ qcaVi),
                       newdata = data.frame(qcaVi = preVi)))

    } else {

        return(predict(loess(datVn[qcaVi] ~ qcaVi,
                             control = loess.control(surface = "direct"),
                             span = spnN),
                       newdata = data.frame(qcaVi = preVi)))

    }

    ## Note:
    ##  the surface = 'direct' argument allows extrapolation

} ## loessF

plotBatchF <- function(datMN, samDF.arg, spnN.arg) {

    maiC <- switch(gsub("MN", "", deparse(substitute(datMN))),
                   raw = "Raw",
                   nrm = "Normalized")

    colVc <- c(sample = "green4",
               pool = "red",
               blank = "black",
               other = "yellow")

    par(font = 2, font.axis = 2, font.lab = 2, lwd = 2, pch = 18)

    layout(matrix(c(1, 1, 2, 3), nrow = 2),
           widths = c(0.7, 0.3))

    obsNamVc <- rownames(datMN)

    obsColVc <- sapply(samDF.arg[, "sampleType"],
                       function(typC)
                       ifelse(typC %in% names(colVc), colVc[typC], colVc["other"]))

    ## Graphic 1: Sum of intensities for each sample

    par(mar = c(3.6, 3.6, 3.1, 0.6))

    batTab <- table(samDF.arg[, "batch"])

    sumVn <- rowSums(datMN, na.rm = TRUE)

    plot(sumVn,
         cex = 1.2,
         col = obsColVc,
         pch = 18,
         xaxs = "i",
         xlab = "",
         ylab = "")

    mtext("Injection order",
          line = 2.2,
          side = 1)
    mtext("Sum of variable intensities",
          line = 2.2,
          side = 2)

    mtext(maiC, cex = 1.2, line = 1.5, side = 3)

    abline(v = cumsum(batTab) + 0.5,
           col = "red")

    mtext(names(batTab),
          at = batTab / 2 + c(0, cumsum(batTab[-length(batTab)])))

    obsColVuc <- obsColVc[sort(unique(names(obsColVc)))]

    text(rep(batTab[1], times = length(obsColVuc)),
         par("usr")[3] + (0.97 - length(obsColVuc) * 0.03 + 1:length(obsColVuc) * 0.03) * diff(par("usr")[3:4]),
         col = obsColVuc,
         font = 2,
         labels = names(obsColVuc),
         pos = 2)

    for(batC in names(batTab)) {

        batSeqVi <- which(samDF.arg[, "batch"] == batC)
        batPooVi <- intersect(batSeqVi,
                              grep("pool", samDF.arg[, "sampleType"]))
        batSamVi <- intersect(batSeqVi,
                              grep("sample", samDF.arg[, "sampleType"]))
        if(length(batPooVi))
            lines(batSeqVi,
                  loessF(sumVn, batPooVi, batSeqVi, spnN=spnN.arg),
                  col = colVc["pool"])
        lines(batSeqVi,
              loessF(sumVn, batSamVi, batSeqVi, spnN=spnN.arg),
              col = colVc["sample"])

    }

    ## Graphics 2 and 3 (right): PCA score plots of components 1-4

    radVn <- seq(0, 2 * pi, length.out = 100)
    epsN <- .Machine[["double.eps"]] ## [1] 2.22e-16

    pcaMN <- datMN

    if(any(is.na(pcaMN))) {
        minN <- min(pcaMN, na.rm = TRUE)
        pcaMN[is.na(pcaMN)] <- minN
    }

    pcaLs <- opls(pcaMN, predI = 4, algoC = "svd", printL = FALSE, plotL = FALSE)
    tMN <- getScoreMN(pcaLs)
    vRelVn <- pcaLs@modelDF[, "R2X"]

    n <- nrow(tMN)
    hotN <- 2 * (n - 1) * (n^2 - 1) / (n^2 * (n - 2))

    hotFisN <- hotN * qf(0.95, 2, n - 2)

    pcsLs <- list(c(1, 2), c(3, 4))

    par(mar = c(3.6, 3.6, 0.6, 1.1))

    for(pcsN in 1:length(pcsLs)) {

        pcsVn <- pcsLs[[pcsN]]

        tcsMN <- tMN[, pcsVn]

        micMN <- solve(cov(tcsMN))

        n <- nrow(tMN)
        hotN <- 2 * (n - 1) * (n^2 - 1) / (n^2 * (n - 2))

        hotFisN <- hotN * qf(0.95, 2, n - 2)

        hotVn <- apply(tcsMN,
                       1,
                       function(x) 1 - pf(1 / hotN * t(as.matrix(x)) %*% micMN %*% as.matrix(x), 2, n - 2))

        obsHotVi <- which(hotVn < 0.05)

        xLabC <- paste("t",
                       pcsVn[1],
                       "(",
                       round(vRelVn[pcsVn[1]] * 100),
                       "%)",
                       sep = "")

        yLabC <- paste("t",
                       pcsVn[2],
                       "(",
                       round(vRelVn[pcsVn[2]] * 100),
                       "%)",
                       sep = "")

        xLimVn <- c(-1, 1) * max(sqrt(var(tcsMN[, 1]) * hotFisN), max(abs(tcsMN[, 1])))
        yLimVn <- c(-1, 1) * max(sqrt(var(tcsMN[, 2]) * hotFisN), max(abs(tcsMN[, 2])))

        plot(tcsMN,
             main = "",
             type = "n",
             xlab = "",
             ylab = "",
             xlim = xLimVn,
             ylim = yLimVn)

        mtext(xLabC,
              line = 2.2,
              side = 1)
        mtext(yLabC,
              line = 2.2,
              side = 2)

        par(lwd = 1)

        abline(v = axTicks(1),
               col = "grey")

        abline(h = axTicks(2),
               col = "grey")

        abline(v = 0)
        abline(h = 0)

        lines(sqrt(var(tcsMN[, 1]) * hotFisN) * cos(radVn),
              sqrt(var(tcsMN[, 2]) * hotFisN) * sin(radVn))

        points(tcsMN,
               col = obsColVc,
               pch = 18)

        if(length(obsHotVi))
            text(tcsMN[obsHotVi, 1],
                 tcsMN[obsHotVi, 2],
                 col = obsColVc[obsHotVi],
                 labels = obsNamVc[obsHotVi],
                 pos = 3)

    } ## for(pcsN in 1:length(pcsLs)) {

    return(invisible(list(sumVn = sumVn,
                          tcsMN = tcsMN)))

} ## plotBatchF

shiftBatchCorrectF <- function(rawMN.arg,
                               samDF.arg,
                               refC.arg,
                               spnN.arg) {

    cat("\nReference observations are: ", refC.arg, "\n")

    ## computing median off all pools (or samples) for each variable

    refMeaVn <- apply(rawMN.arg[samDF.arg[, "sampleType"] == refC.arg, ],
                      2,
                      function(feaRefVn) mean(feaRefVn, na.rm = TRUE))

    ## splitting data and sample metadata from each batch

    batRawLs <- split(as.data.frame(rawMN.arg),
                      f = samDF.arg[, "batch"])
    batRawLs <- lapply(batRawLs, function(inpDF) as.matrix(inpDF))

    batSamLs <- split(as.data.frame(samDF.arg),
                      f = samDF.arg[, "batch"])

    ## checking extrapolation: are there pools at the first and last observations of each batch

    if(refC.arg == "pool") {
        pooExtML <- matrix(FALSE, nrow = 2, ncol = length(batRawLs),
                           dimnames = list(c("first", "last"), names(batRawLs)))
        for(batC in names(batSamLs)) {
            batSamTypVc <- batSamLs[[batC]][, "sampleType"]
            pooExtML["first", batC] <- head(batSamTypVc, 1) == "pool"
            pooExtML["last", batC] <- tail(batSamTypVc, 1) == "pool"
        }
        if(!all(c(pooExtML))) {
            cat("\nWarning: Pools are missing at the first and/or last position of the following batches:\n")
            pooExtBatVi <- which(!apply(pooExtML, 2, all))
            for(i in 1:length(pooExtBatVi))
                cat(names(pooExtBatVi)[i], ": ",
                    paste(rownames(pooExtML)[!pooExtML[, pooExtBatVi[i]]], collapse = ", "), "\n", sep = "")
            cat("Extrapolating loess fits for these batches may result in inaccurate modeling!\n")
        }
    }

    ## normalizing

    nrmMN <- NULL ## normalized data matrix to be computed

    cat("\nProcessing batch:")

    for(batC in names(batRawLs)) { ## processing each batch individually

        cat("\n", batC)

        batRawMN <- batRawLs[[batC]]
        batSamDF <- batSamLs[[batC]]

        batAllVi <- 1:nrow(batRawMN)

        batRefVi <- grep(refC.arg, batSamDF[, "sampleType"])

        if(length(batRefVi) < 5)
            cat("\nWarning: less than 5 '", refC.arg, "'; linear regression will be performed instead of loess regression for this batch\n", sep="")

        ## prediction of the loess fit

        batLoeMN <- apply(batRawMN,
                          2,
                          function(rawVn) loessF(rawVn, batRefVi, batAllVi, spnN=spnN.arg))

        ## normalization

        batLoeMN[batLoeMN <= 0] <- NA

        batNrmMN <- batRawMN / batLoeMN

        nrmMN <- rbind(nrmMN,
                       batNrmMN)

    }

    cat("\n")

    nrmMN <- sweep(nrmMN, MARGIN = 2, STATS = refMeaVn, FUN = "*")

    return(nrmMN)

} ## shiftBatchCorrectF