R/cwTools.R

In xiaodfeng/DynamicXCMS: LC-MS and GC-MS Data Analysis

MSW.cwt <- function (ms, scales = 1, wavelet = "mexh")
{ ## modified from package MassSpecWavelet
    if (wavelet == "mexh") {
        psi_xval <- seq(-6, 6, length = 256)
        psi <- (2/sqrt(3) * pi^(-0.25)) * (1 - psi_xval^2) *
            exp(-psi_xval^2/2)
    }
    else if (is.matrix(wavelet)) {
        if (nrow(wavelet) == 2) {
            psi_xval <- wavelet[1, ]
            psi <- wavelet[2, ]
        }
        else if (ncol(wavelet) == 2) {
            psi_xval <- wavelet[, 1]
            psi <- wavelet[, 2]
        }
        else {
            stop("Unsupported wavelet format!")
        }
    }
    else {
        stop("Unsupported wavelet!")
    }
    oldLen <- length(ms)
    ms <- MSW.extendNBase(ms, nLevel = NULL, base = 2)
    len <- length(ms)
    nbscales <- length(scales)
    wCoefs <- NULL
    psi_xval <- psi_xval - psi_xval[1]
    dxval <- psi_xval[2]
    xmax <- psi_xval[length(psi_xval)]
    for (i in 1:length(scales)) {
        scale.i <- scales[i]
        f <- rep(0, len)
        j <- 1 + floor((0:(scale.i * xmax))/(scale.i * dxval))
        if (length(j) == 1)
            j <- c(1, 1)
        lenWave <- length(j)
        f[1:lenWave] <- rev(psi[j]) - mean(psi[j])
        if (length(f) > len)
        {i<-i-1;break;}   ##  stop(paste("scale", scale.i, "is too large!"))
        wCoefs.i <- 1/sqrt(scale.i) * convolve(ms, f)
        wCoefs.i <- c(wCoefs.i[(len - floor(lenWave/2) + 1):len],
                      wCoefs.i[1:(len - floor(lenWave/2))])
        wCoefs <- cbind(wCoefs, wCoefs.i)
    }
    if (i < 1) return(NA)
    scales <- scales[1:i]
    if (length(scales) == 1)
        wCoefs <- matrix(wCoefs, ncol = 1)
    colnames(wCoefs) <- scales
    wCoefs <- wCoefs[1:oldLen, , drop = FALSE]
    wCoefs
}

MSW.extendNBase <- function(x, nLevel=1, base=2, ...)
{ ## from package MassSpecWavelet
    if (!is.matrix(x)) x <- matrix(x, ncol=1)

    nR <- nrow(x)
    if (is.null(nLevel)) {
        nR1 <- nextn(nR, base)
    } else {
        nR1 <- ceiling(nR / base^nLevel) * base^nLevel
    }
    if (nR != nR1) {
        x <- MSW.extendLength(x, addLength=nR1-nR, ...)
    }
    x
}

MSW.extendLength <-
    function(x, addLength=NULL, method=c('reflection', 'open', 'circular'), direction=c('right', 'left', 'both'))
{       ## from package MassSpecWavelet
    if (is.null(addLength)) stop('Please provide the length to be added!')
    if (!is.matrix(x)) x <- matrix(x, ncol=1)
    method <- match.arg(method)
    direction <- match.arg(direction)

    nR <- nrow(x)
    nR1 <- nR + addLength
    if (direction == 'both') {
        left <- right <- addLength
    } else if (direction == 'right') {
        left <- 0
        right <- addLength
    } else if (direction == 'left') {
        left <- addLength
        right <- 0
    }

    if (right > 0) {
        x <- switch(method,
                    reflection =rbind(x, x[nR:(2 * nR - nR1 + 1), , drop=FALSE]),
                    open = rbind(x, matrix(rep(x[nR,], addLength), ncol=ncol(x), byrow=TRUE)),
                    circular = rbind(x, x[1:(nR1 - nR),, drop=FALSE]))
    }

    if (left > 0) {
        x <- switch(method,
                    reflection =rbind(x[addLength:1, , drop=FALSE], x),
                    open = rbind(matrix(rep(x[1,], addLength), ncol=ncol(x), byrow=TRUE), x),
                    circular = rbind(x[(2 * nR - nR1 + 1):nR,, drop=FALSE], x))
    }
    if (ncol(x) == 1)  x <- as.vector(x)

    x
}

MSW.getLocalMaximumCWT <-
    function(wCoefs, minWinSize=5, amp.Th=0)
{        ## from package MassSpecWavelet
    localMax <- NULL
    scales <- as.numeric(colnames(wCoefs))

    for (i in 1:length(scales)) {
        scale.i <- scales[i]
        winSize.i <- scale.i * 2 + 1
        if (winSize.i < minWinSize) {
            winSize.i <- minWinSize
        }
        temp <- MSW.localMaximum(wCoefs[,i], winSize.i)
        localMax <- cbind(localMax, temp)
    }
    ## Set the values less than peak threshold as 0
    localMax[wCoefs < amp.Th] <- 0
    colnames(localMax) <- colnames(wCoefs)
    rownames(localMax) <- rownames(wCoefs)
    localMax
}

MSW.localMaximum <-
    function (x, winSize = 5)
{   ## from package MassSpecWavelet
    len <- length(x)
    rNum <- ceiling(len/winSize)

    ## Transform the vector as a matrix with column length equals winSize
    ##		and find the maximum position at each row.
    y <- matrix(c(x, rep(x[len], rNum * winSize - len)), nrow=winSize)
    y.maxInd <- apply(y, 2, which.max)
    ## Only keep the maximum value larger than the boundary values
    selInd <- which(apply(y, 2, function(x) max(x) > x[1] & max(x) > x[winSize]))

    ## keep the result
    localMax <- rep(0, len)
    localMax[(selInd-1) * winSize + y.maxInd[selInd]] <- 1

    ## Shift the vector with winSize/2 and do the same operation
    shift <- floor(winSize/2)
    rNum <- ceiling((len + shift)/winSize)
    y <- matrix(c(rep(x[1], shift), x, rep(x[len], rNum * winSize - len - shift)), nrow=winSize)
    y.maxInd <- apply(y, 2, which.max)
    ## Only keep the maximum value larger than the boundary values
    selInd <- which(apply(y, 2, function(x) max(x) > x[1] & max(x) > x[winSize]))
    localMax[(selInd-1) * winSize + y.maxInd[selInd] - shift] <- 1

    ## Check whether there is some local maxima have in between distance less than winSize
    maxInd <- which(localMax > 0)
    selInd <- which(diff(maxInd) < winSize)
    if (length(selInd) > 0) {
        selMaxInd1 <- maxInd[selInd]
        selMaxInd2 <- maxInd[selInd + 1]
        temp <- x[selMaxInd1] - x[selMaxInd2]
        localMax[selMaxInd1[temp <= 0]] <- 0
        localMax[selMaxInd2[temp > 0]] <- 0
    }

    localMax
}

MSW.getRidge <-
    function(localMax, iInit=ncol(localMax), step=-1, iFinal=1, minWinSize=3, gapTh=3, skip=NULL)
{  ## modified from package MassSpecWavelet

    scales <- as.numeric(colnames(localMax))
    if (is.null(scales))  scales <- 1:ncol(localMax)

    maxInd_curr <- which(localMax[, iInit] > 0)
    nMz <- nrow(localMax)

    if (is.null(skip))	{
        skip <- iInit + 1
    }

    ## Identify all the peak pathes from the coarse level to detail levels (high column to low column)
    ## Only consider the shortest path
    if ( ncol(localMax) > 1 ) colInd <- seq(iInit+step, iFinal, step)
    else colInd <- 1
    ridgeList <- as.list(maxInd_curr)
    names(ridgeList) <- maxInd_curr
    peakStatus <- as.list(rep(0, length(maxInd_curr)))
    names(peakStatus) <- maxInd_curr

    ## orphanRidgeList keep the ridges disconnected at certain scale level
    ## Changed by Pan Du 05/11/06
    orphanRidgeList <- NULL
    orphanRidgeName <- NULL
    nLevel <- length(colInd)

    for (j in 1:nLevel) {
        col.j <- colInd[j]
        scale.j <- scales[col.j]

        if (colInd[j] == skip) {
            oldname <- names(ridgeList)
            ridgeList <- lapply(ridgeList, function(x) c(x, x[length(x)]))
            ##peakStatus <- lapply(peakStatus, function(x) c(x, x[length(x)]))
            names(ridgeList) <- oldname
            ##names(peakStatus) <- oldname
            next
        }

        if (length(maxInd_curr) == 0) {
            maxInd_curr <- which(localMax[, col.j] > 0)
            next
        }

        ## The slide window size is proportional to the CWT scale
        ## winSize.j <- scale.j / 2 + 1
        winSize.j <- floor(scale.j/2)
        if (winSize.j < minWinSize) {
            winSize.j <- minWinSize
        }

        selPeak.j <- NULL
        remove.j <- NULL
        for (k in 1:length(maxInd_curr)) {
            ind.k <- maxInd_curr[k]
            start.k <- ifelse(ind.k-winSize.j < 1, 1, ind.k-winSize.j)
            end.k <- ifelse(ind.k+winSize.j > nMz, nMz, ind.k+winSize.j)
            ind.curr <- which(localMax[start.k:end.k, col.j] > 0) + start.k - 1
            ##ind.curr <- which(localMax[, col.j] > 0)
            if (length(ind.curr) == 0) {
                status.k <- peakStatus[[as.character(ind.k)]]
                ## bug  work-around
                if (is.null(status.k)) status.k <- gapTh +1
                ##
                if (status.k > gapTh & scale.j >= 2) {
                    temp <- ridgeList[[as.character(ind.k)]]
                    orphanRidgeList <- c(orphanRidgeList, list(temp[1:(length(temp)-status.k)]))
                    orphanRidgeName <- c(orphanRidgeName, paste(col.j + status.k + 1, ind.k, sep='_'))
                    remove.j <- c(remove.j, as.character(ind.k))
                    next
                } else {
                    ind.curr <- ind.k
                    peakStatus[[as.character(ind.k)]] <- status.k + 1
                }
            } else {
                peakStatus[[as.character(ind.k)]] <- 0
                if (length(ind.curr) >= 2)  ind.curr <- ind.curr[which.min(abs(ind.curr - ind.k))]
            }
            ridgeList[[as.character(ind.k)]] <- c(ridgeList[[as.character(ind.k)]], ind.curr)
            selPeak.j <- c(selPeak.j, ind.curr)
        }
        ## Remove the disconnected lines from the currrent list
        if (length(remove.j) > 0) {
            removeInd <- which(names(ridgeList) %in% remove.j)
            ridgeList <- ridgeList[-removeInd]
            peakStatus <- peakStatus[-removeInd]
        }

        ## Check for duplicated selected peaks and only keep the one with the longest path.
        dupPeak.j <- unique(selPeak.j[duplicated(selPeak.j)])
        if (length(dupPeak.j) > 0) {
            removeInd <- NULL
            for (dupPeak.jk in dupPeak.j) {
                selInd <- which(selPeak.j == dupPeak.jk)
                selLen <- sapply(ridgeList[selInd], length)
                removeInd.jk <- which.max(selLen)
                removeInd <- c(removeInd, selInd[-removeInd.jk])
                orphanRidgeList <- c(orphanRidgeList, ridgeList[removeInd.jk])
                orphanRidgeName <- c(orphanRidgeName, paste(col.j, selPeak.j[removeInd.jk], sep='_'))
            }
            selPeak.j <- selPeak.j[-removeInd]
            ridgeList <- ridgeList[-removeInd]
            peakStatus <- peakStatus[-removeInd]
        }

        ## Update the names of the ridgeList as the new selected peaks
        ##if (scale.j >= 2) {
        if (length(ridgeList) > 0) names(ridgeList) <- selPeak.j
        if (length(peakStatus) > 0) names(peakStatus) <- selPeak.j
        ##}

        ## If the level is larger than 3, expand the peak list by including other unselected peaks at that level
        if (scale.j >= 2) {
            maxInd_next <- which(localMax[, col.j] > 0)
            unSelPeak.j <- maxInd_next[!(maxInd_next %in% selPeak.j)]
            newPeak.j <- as.list(unSelPeak.j)
            names(newPeak.j) <- unSelPeak.j
            ## Update ridgeList
            ridgeList <- c(ridgeList, newPeak.j)
            maxInd_curr <- c(selPeak.j, unSelPeak.j)
            ## Update peakStatus
            newPeakStatus <- as.list(rep(0, length(newPeak.j)))
            names(newPeakStatus) <- newPeak.j
            peakStatus <- c(peakStatus, newPeakStatus)
        } else {
            maxInd_curr <- selPeak.j
        }
    }

    ## Attach the peak level at the beginning of the ridge names
    if (length(ridgeList) > 0) names(ridgeList) <- paste(1, names(ridgeList), sep='_')
    if (length(orphanRidgeList) > 0) names(orphanRidgeList) <- orphanRidgeName
    ## Combine ridgeList and orphanRidgeList
    ridgeList <- c(ridgeList, orphanRidgeList)
    if (length(ridgeList) == 0) return(NULL)

    ## Reverse the order as from the low level to high level.
    ridgeList <- lapply(ridgeList, rev)
    ## order the ridgeList in increasing order
    ##ord <- order(selPeak.j)
    ##ridgeList <- ridgeList[ord]

    ## Remove possible duplicated ridges
    ridgeList <- ridgeList[!duplicated(names(ridgeList))]

    attr(ridgeList, 'class') <- 'ridgeList'
    attr(ridgeList, 'scales') <- scales
    return(ridgeList)
}

running <- function (X, Y = NULL, fun = mean, width = min(length(X), 20),
                     allow.fewer = FALSE, pad = FALSE, align = c("right", "center",
                                                       "left"), simplify = TRUE, by, ...)
{   ## from package gtools
    align = match.arg(align)
    n <- length(X)
    if (align == "left") {
        from <- 1:n
        to <- pmin((1:n) + width - 1, n)
    }
    else if (align == "right") {
        from <- pmax((1:n) - width + 1, 1)
        to <- 1:n
    }
    else {
        from <- pmax((2 - width):n, 1)
        to <- pmin(1:(n + width - 1), n)
        if (!odd(width))
            stop("width must be odd for center alignment")
    }
    elements <- apply(cbind(from, to), 1, function(x) seq(x[1],
                                                          x[2]))
    if (is.matrix(elements))
        elements <- as.data.frame(elements)
    names(elements) <- paste(from, to, sep = ":")
    if (!allow.fewer) {
        len <- sapply(elements, length)
        skip <- (len < width)
    }
    else {
        skip <- 0
    }
    run.elements <- elements[!skip]
    if (!invalid(by))
        run.elements <- run.elements[seq(from = 1, to = length(run.elements),
                                         by = by)]
    if (is.null(Y)) {
        funct <- function(which, what, fun, ...) fun(what[which],
                                                     ...)
        if (simplify)
            Xvar <- sapply(run.elements, funct, what = X, fun = fun,
                           ...)
        else Xvar <- lapply(run.elements, funct, what = X, fun = fun,
                            ...)
    } else {
        funct <- function(which, XX, YY, fun, ...) fun(XX[which],
                                                       YY[which], ...)
        if (simplify)
            Xvar <- sapply(run.elements, funct, XX = X, YY = Y,
                           fun = fun, ...)
        else Xvar <- lapply(run.elements, funct, XX = X, YY = Y,
                            fun = fun, ...)
    }
    if (allow.fewer || !pad)
        return(Xvar)
    if (simplify)
        if (is.matrix(Xvar)) {
            wholemat <- matrix(new(class(Xvar[1, 1]), NA), ncol = length(to),
                               nrow = nrow(Xvar))
            colnames(wholemat) <- paste(from, to, sep = ":")
            wholemat[, -skip] <- Xvar
            Xvar <- wholemat
        }
        else {
            wholelist <- rep(new(class(Xvar[1]), NA), length(from))
            names(wholelist) <- names(elements)
            wholelist[names(Xvar)] <- Xvar
            Xvar <- wholelist
        }
    return(Xvar)
}

invalid <- function (x)
{   ## from package gtools
    if (missing(x) || is.null(x) || length(x) == 0)
        return(TRUE)
    if (is.list(x))
        return(all(sapply(x, invalid)))
    else if (is.vector(x))
        return(all(is.na(x)))
    else return(FALSE)
}

odd <- function (x) x != as.integer(x/2) * 2;

gauss <- function(x, h, mu, sigma){
    h*exp(-(x-mu)^2/(2*sigma^2))
}

fitGauss <- function(td, d, pgauss = NA) {
    if (length(d) < 3) return(rep(NA,3))
    if (!any(is.na(pgauss))) { mu <- pgauss$mu; sigma <- pgauss$sigma;h <- pgauss$h }
    fit <- try(nls(d ~ SSgauss(td,mu,sigma,h)), silent = TRUE)
    if (class(fit) == "try-error")
        fit <- try(nls(d ~ SSgauss(td, mu, sigma, h), algorithm = 'port'),
                   silent = TRUE)
    if (class(fit) == "try-error")  return(rep(NA, 3))

    as.data.frame(t(fit$m$getPars()))
}

## ' @param
## ' @param d numeric vector with intensities of centroids within the peak.
## ' @param otd
## ' @param omz
## ' @param od
## ' @param scantime
## ' @param scan.range
## ' @param peaks
## ' @noRd
joinOverlappingPeaks <- function(td, d, otd, omz, od, scantime, scan.range,
                                 peaks, maxGaussOverlap=0.5, mzCenterFun) {
    ## Fix issue #284: avoid having identical peaks multiple times in this
    ## matrix.
    peaks <- unique(peaks)
    gausspeaksidx <- which(!is.na(peaks[,"mu"]))
    Ngp <- length(gausspeaksidx)
    if (Ngp == 0)
        return(peaks)

    newpeaks <- NULL

    gpeaks <- peaks[gausspeaksidx, , drop = FALSE]
    if (nrow(peaks) - Ngp > 0)
        notgausspeaks <- peaks[-gausspeaksidx, , drop = FALSE]

    if (Ngp > 1) {
        comb <- which(upper.tri(matrix(0, Ngp, Ngp)), arr.ind = TRUE)
        overlap <- logical(nrow(comb))
        overlap <- rep(FALSE, dim(comb)[1])
        for (k in seq_len(nrow(comb))) {
            p1 <- comb[k, 1]
            p2 <- comb[k, 2]
            overlap[k] <- gaussCoverage(xlim = scan.range,
                                        h1 = gpeaks[p1, "h"],
                                        mu1 = gpeaks[p1, "mu"],
                                        s1 = gpeaks[p1, "sigma"],
                                        h2 = gpeaks[p2, "h"],
                                        mu2 = gpeaks[p2, "mu"],
                                        s2 = gpeaks[p2, "sigma"]) >=
                maxGaussOverlap
        }
    } else overlap <- FALSE
    
    if (any(overlap) && (Ngp > 1)) {
        jlist <- list()
        if (length(which(overlap)) > 1) {
            gm <- comb[overlap, ]
            ## create list of connected components
            cc <- list()
            cc[[1]] <- gm[1,] ## copy first entry
            for (j in 2:dim(gm)[1]) { ## search for connections
                ccl <- unlist(cc)
                nl <- sapply(cc, function(x) length(x))
                ccidx <- rep(1:length(nl),nl)
                idx <- match(gm[j,],ccl)
                if (any(!is.na(idx))) { ## connection found, add to list
                    pos <- ccidx[idx[which(!is.na(idx))[1]]]
                    cc[[pos]] <- c(cc[[pos]],gm[j,])
                } else  ## create new list element
                    cc[[length(cc) + 1]] <- gm[j,]

            }
            ccn <- list()
            lcc <- length(cc)
            ins <- rep(FALSE,lcc)
            if (lcc > 1) {
                jcomb <- which(upper.tri(matrix(0,lcc,lcc)),arr.ind = TRUE)
                for (j in 1:dim(jcomb)[1]) {
                    j1 <- jcomb[j,1]; j2 <- jcomb[j,2]
                    if (any(cc[[j1]] %in% cc[[j2]]))
                        ccn[[length(ccn) +1]] <- unique(c(cc[[j1]],cc[[j2]]))
                    else {
                        if (!ins[j1]) {
                            ccn[[length(ccn) +1]] <- unique(cc[[j1]])
                            ins[j1] <- TRUE
                        }
                        if (!ins[j2]) {
                            ccn[[length(ccn) +1]] <- unique(cc[[j2]])
                            ins[j2] <- TRUE
                        }
                    }
                }
            } else ccn <- cc;

            size <- sapply(ccn, function(x) length(x))
            s2idx <- which(size >= 2)

            if (length(s2idx) > 0) {
                for (j in 1:length(s2idx)) {
                    pgroup <- unique(ccn[[ s2idx[j] ]])
                    jlist[[j]] <- pgroup
                }
            } else stop('(length(s2idx) = 0) ?!?')
        } else jlist[[1]] <- comb[overlap, ]

        ## join all peaks belonging to one cc
        for (j in seq_along(jlist)) {
            jidx <- jlist[[j]]
            newpeak <- gpeaks[jidx[1], , drop = FALSE]
            newmin <- min(gpeaks[jidx, "lmin"])
            newmax <- max(gpeaks[jidx, "lmax"])
            newpeak[1, "scpos"] <- -1 ## not defined after join
            newpeak[1, "scmin"] <- -1 ##    ..
            newpeak[1, "scmax"] <- -1 ##    ..
            newpeak[1, "scale"] <- -1 ##    ..

            newpeak[1, "maxo"] <- max(gpeaks[jidx, "maxo"])
            newpeak[1, "sn"]   <- max(gpeaks[jidx, "sn"])
            newpeak[1, "lmin"] <- newmin
            newpeak[1, "lmax"] <- newmax
            newpeak[1, "rtmin"] <- scantime[td[newmin]]
            newpeak[1, "rtmax"] <- scantime[td[newmax]]
            newpeak[1,"rt"] <- weighted.mean(gpeaks[jidx, "rt"],
                                             w = gpeaks[jidx, "maxo"])

            ## Re-assign m/z values
            p1 <- match(td[newmin], otd)[1]
            p2 <- match(td[newmax], otd)
            p2 <- p2[length(p2)]
            if (is.na(p1)) p1 <- 1
            if (is.na(p2)) p2 <- length(omz)
            mz.value <- omz[p1:p2]
            mz.int <- od[p1:p2]

            ## re-calculate m/z value for peak range
            mzmean <- do.call(mzCenterFun, list(mz = mz.value,
                                                intensity = mz.int))
            mzrange <- range(mz.value)
            newpeak[1, "mz"] <- mzmean
            newpeak[1, c("mzmin","mzmax")] <- mzrange

            ## re-fit gaussian
            md <- max(d[newmin:newmax])
            d1 <- d[newmin:newmax] / md
            pgauss <- fitGauss(td[newmin:newmax],
                               d[newmin:newmax],
                               pgauss = list(mu = td[newmin] +
                                                 (td[newmax] - td[newmin])/2,
                                             sigma = td[newmax] - td[newmin],
                                             h = max(gpeaks[jidx, "h"])))
            if (!any(is.na(pgauss)) && all(pgauss > 0)) {
                newpeak[1, "mu"]    <- pgauss$mu
                newpeak[1, "sigma"] <- pgauss$sigma
                newpeak[1, "h"]     <- pgauss$h
                newpeak[1, "egauss"]<- sqrt((1/length(td[newmin:newmax])) *
                                            sum(((d1 - gauss(td[newmin:newmax],
                                                           pgauss$h/md,
                                                           pgauss$mu,
                                                           pgauss$sigma))^2)))
            } else { ## re-fit after join failed
                newpeak[1, "mu"]       <- NA
                newpeak[1, "sigma"]    <- NA
                newpeak[1, "h"]        <- NA
                newpeak[1, "egauss"]   <- NA
            }

            newpeaks <- rbind(newpeaks, newpeak)
        }
        ## add the remaining peaks
        jp <- unique(unlist(jlist))
        if (dim(peaks)[1] - length(jp) > 0)
            newpeaks <- rbind(newpeaks, gpeaks[-jp, ])

    } else
        newpeaks <- gpeaks

    grt.min <- newpeaks[, "rtmin"]
    grt.max <- newpeaks[, "rtmax"]

    if (nrow(peaks) - Ngp > 0) { ## notgausspeaks
        for (k in 1:nrow(notgausspeaks)) {
            ## here we can only check if they are completely overlapped
            ## by other peaks
            if (!any((notgausspeaks[k, "rtmin"] >= grt.min) &
                     (notgausspeaks[k,"rtmax"] <= grt.max)))
                newpeaks <- rbind(newpeaks,notgausspeaks[k,])
        }
    }

    rownames(newpeaks) <- NULL
    newpeaks
}

descendMinTol <- function(d,startpos,maxDescOutlier) {
    l <- startpos[1]; r <- startpos[2]; outl <- 0; N <- length(d)
    ## left
    while ((l > 1) && (d[l] > 0) && outl <= maxDescOutlier) {
        if (outl > 0) vpos <- opos else vpos <- l
        if (d[l-1] > d[vpos]) outl <- outl + 1 else outl <- 0
        if (outl == 1) opos <- l
        l <- l -1
    }
    if (outl > 0) l <- l + outl
    ## right
    outl <- 0;
    while ((r < N) && (d[r] > 0) && outl <= maxDescOutlier) {
        if (outl > 0) vpos <- opos else vpos <- r
        if (d[r+1] > d[vpos]) outl <- outl + 1 else outl <- 0
        if (outl == 1) opos <- r
        r <- r + 1
    }
    if (outl > 0) r <- r - outl
    c(l,r)
}

cent <- function(x) {
    N <- length(x)
    if (N == 1) return(1)
    floor(N/2)
}

gaussCoverage <- function(xlim,h1,mu1,s1,h2,mu2,s2) {
    overlap <- NA
    by = 0.05
    ## Calculate points of intersection
    a <- s2^2 - s1^2
    cc <- -( 2 * s1^2 * s2^2 * (log(h1) - log(h2)) + (s1^2 * mu2^2) - (s2^2 * mu1^2) )
    b <- ((2 * s1^2 *mu2) - (2 * s2^2 * mu1))
    D <- b^2 - (a*cc)
    if (a==0) {
        S1 <- -cc/b
        S2 <- NA
    } else if ((D < 0) || ((b^2 - (4*a*cc)) < 0)) {
        S1 <- S2 <- NA
    } else {
        S1 <- (-b + sqrt(b^2 - (4*a*cc))) / (2*a)
        S2 <- (-b - sqrt(b^2 - (4*a*cc))) / (2*a)
        if (S2 < S1)
        {
            tmp <- S1
            S1 <- S2
            S2 <- tmp
        }
    }
    if (!is.na(S1)) if (S1 < xlim[1] || S1 > xlim[2]) S1 <- NA
    if (!is.na(S2)) if (S2 < xlim[1] || S2 > xlim[2]) S2 <- NA

    x <- seq(xlim[1],xlim[2],by=by)
    vsmall <- min(sum(gauss(x,h1,mu1,s1)), sum(gauss(x,h2,mu2,s2)))

    if (!is.na(S1) && !is.na(S2)) {
        x0 <- seq(xlim[1],S1,by=by)
        xo <- seq(S1,S2,by=by)
        x1 <- seq(S2,xlim[2],by=by)
        if (gauss(x0[cent(x0)],h1,mu1,s1) < gauss(x0[cent(x0)],h2,mu2,s2)) {
            ov1 <- sum(gauss(x0,h1,mu1,s1))
        } else {
            ov1 <- sum(gauss(x0,h2,mu2,s2))
        }
        if (gauss(xo[cent(xo)],h1,mu1,s1) < gauss(xo[cent(xo)],h2,mu2,s2)) {
            ov <- sum(gauss(xo,h1,mu1,s1))
        } else {
            ov <- sum(gauss(xo,h2,mu2,s2))
        }
        if (gauss(x1[cent(x1)],h1,mu1,s1) < gauss(x1[cent(x1)],h2,mu2,s2)) {
            ov2 <- sum(gauss(x1,h1,mu1,s1))
        } else {
            ov2 <- sum(gauss(x1,h2,mu2,s2))
        }
        overlap <- ov1 + ov + ov2
    } else
        if (is.na(S1) && is.na(S2)) { ## no overlap -> intergrate smaller function
            if (gauss(x[cent(x)],h1,mu1,s1) < gauss(x[cent(x)],h2,mu2,s2)) {
                overlap <- sum(gauss(x,h1,mu1,s1))
            } else {
                overlap <- sum(gauss(x,h2,mu2,s2))
            }
        } else
            if (!is.na(S1) || !is.na(S2)) {
                if (is.na(S1)) S0 <- S2 else S0 <- S1
                x0 <- seq(xlim[1],S0,by=by)
                x1 <- seq(S0,xlim[2],by=by)
                g01 <- gauss(x0[cent(x0)],h1,mu1,s1)
                g02 <- gauss(x0[cent(x0)],h2,mu2,s2)
                g11 <- gauss(x1[cent(x1)],h1,mu1,s1)
                g12 <- gauss(x1[cent(x1)],h2,mu2,s2)
                if (g01 < g02) ov1 <- sum(gauss(x0,h1,mu1,s1)) else ov1 <- sum(gauss(x0,h2,mu2,s2))
                if (g11 < g12) ov2 <- sum(gauss(x1,h1,mu1,s1)) else ov2 <- sum(gauss(x1,h2,mu2,s2))
                if ((g01 == g02) && (g01==0)) ov1 <- 0
                if ((g11 == g12) && (g11==0)) ov2 <- 0
                overlap <- ov1 + ov2
            }

    overlap / vsmall
}

mzCenter.wMean <- function(mz,intensity) {
    weighted.mean(mz, intensity)
}

mzCenter.mean <- function(mz,intensity) {
    mean(mz)
}

mzCenter.apex <- function(mz,intensity) {
    mz[which.max(intensity)]
}

mzCenter.wMeanApex3 <- function(mz,intensity) {
    iap <- which.max(intensity)
    st <- max(1,iap-1)
    en <- min(iap+1,length(mz))
    weighted.mean(mz[st:en], intensity[st:en])
}

mzCenter.meanApex3 <- function(mz,intensity) {
    iap <- which.max(intensity)
    st <- max(1,iap-1)
    en <- min(iap+1,length(mz))
    mean(mz[st:en])
}

trimm <- function(x, trim=c(0.05,0.95)) {
    a <- sort(x[x>0])
    Na <- length(a)
    quant <- round((Na*trim[1])+1):round(Na*trim[2])
    a[quant]
}

estimateChromNoise <- function(x, trim=0.05, minPts=20) {
    gz <- which(x > 0)
    if (length(gz) < minPts)
        return(mean(x))

    mean(x[gz], trim=trim)
}

getLocalNoiseEstimate <- function(d, td, ftd, noiserange, Nscantime, threshold, num) {

    if (length(d) < Nscantime) {

        ## noiserange[2] is full d-range
        drange <- which(td %in% ftd)
        n1 <- d[-drange] ## region outside the detected ROI (wide)
        n1.cp <- continuousPtsAboveThresholdIdx(n1, threshold=threshold,num=num) ## continousPtsAboveThreshold (probably peak) are subtracted from data for local noise estimation
        n1 <- n1[!n1.cp]
        if (length(n1) > 1)  {
            baseline1 <- mean(n1)
            sdnoise1 <- sd(n1)
        } else
            baseline1 <- sdnoise1 <- 1

        ## noiserange[1]
        d1 <- drange[1]
        d2 <- drange[length(drange)]
        nrange2 <- c(max(1,d1 - noiserange[1]) : d1, d2 : min(length(d),d2 + noiserange[1]))
        n2 <- d[nrange2] ## region outside the detected ROI (narrow)
        n2.cp <- continuousPtsAboveThresholdIdx(n2, threshold=threshold,num=num) ## continousPtsAboveThreshold (probably peak) are subtracted from data for local noise estimation
        n2 <- n2[!n2.cp]
        if (length(n2) > 1)  {
            baseline2 <- mean(n2)
            sdnoise2 <- sd(n2)
        } else
            baseline2 <- sdnoise2 <- 1

    } else {
        trimmed <- trimm(d,c(0.05,0.95))
        baseline1 <- baseline2 <- mean(trimmed)
        sdnoise1 <- sdnoise2 <- sd(trimmed)
    }

    c(min(baseline1,baseline2),min(sdnoise1,sdnoise2))
}