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# Source code for samsifter.tools.filter_ref_coverage

    #!/usr/bin/env python3
    # -*- coding: utf-8 -*-
    """Identify reference accessions with uneven coverage in MALT'ed SAM files.

    Comes with several methods to create optional plots of coverage and read length
    distributions.

    Warning
    -------
    Activating the plotting of these distributions for a large input dataset can
    create I/O problems due to the large amounts of PNG files generated. It will
    also decrease the performance of this filter considerably and should only be
    used to troubleshoot filter parameters for small subsets of the data.

    .. moduleauthor:: Florian Aldehoff <faldehoff@student.uni-tuebingen.de>
    """

    import sys
    if not (sys.version_info[0] >= 3):
        print("Error, I need python 3.x or newer")
        exit(1)

    import argparse
    import logging as log
    import fileinput
    import tempfile
    from os.path import basename, splitext
    import re
    import matplotlib as mpl
    mpl.use('Agg')       # before importing numpy, else trouble on headless server
    import matplotlib.pyplot as plt
    import numpy as np

    """ custom libraries """
    from samsifter.models.filter import FilterItem
    from samsifter.models.parameter import (FilterParameter, FilterSwitch,
                                            FilterThreshold, FilterFilepath)
    from samsifter.util.arg_sanitation import (check_pos_float,
                                               check_pos_float_max1,
                                               check_pos_int, check_sam)
    from samsifter.util.filters import line_filter
    from samsifter.util.papertrail import modify_header
    from samsifter.version import samsifter_version

    __version__ = samsifter_version

    """ global variables """
    TEXT = "Filter references by evenness of coverage"
    DESC = ("Filters reference accessions exceeding a Gini Index threshold.")

    def item():
        """Create item representing this tool in list and tree views.

        Returns
        -------
        FilterItem
            Item for use in item-based list and tree views.
        """
        item = FilterItem(text=TEXT, desc=DESC)
        item.set_command(splitext(basename(__file__))[0])

        item.add_parameter(FilterThreshold(
            text="min. Gini",
            desc="minimum Gini coefficient",
            cli_name='--min_gini',
            default=0.00,
            maximum=1.00
        ))

        item.add_parameter(FilterThreshold(
            text="max. Gini",
            desc="maximum Gini coefficient",
            cli_name='--max_gini',
            default=0.90,
            maximum=1.00,
            required=True,
            active=True
        ))

        item.add_parameter(FilterParameter(
            text="read lengths",
            desc="analyze read length distributions",
            cli_name="--read_lengths",
            default=False
        ))

        item.add_parameter(FilterParameter(
            text="covered bases only",
            desc="covered bases only, ignore uncovered bases",
            cli_name="--covered",
            default=False
        ))

        item.add_parameter(FilterFilepath(
            text="statistics file",
            desc=("override filename for tab-separated statistics "
                  "[${filename}.stats.csv]"),
            cli_name='--stats_file',
            default="${filename}.stats.csv"
        ))

        item.add_parameter(FilterParameter(
            text="plot distribution(s)",
            desc="plot coverage and/or read length distributions",
            cli_name="--plot",
            default=False
        ))

    #    item.add_parameter(FilterThreshold(
    #        text="LCI argument",
    #        desc="fraction of mean coverage to use for LCI integration",
    #        cli_name='--lci_arg',
    #        default=0.50,
    #        maximum=1.00
    #    ))
    #
    #    item.add_parameter(FilterThreshold(
    #        text="min. LCI",
    #        desc="minimum low-coverage index",
    #        cli_name='--min_lci',
    #        default=0.0,
    #        maximum=1000.0
    #    ))
    #
    #    item.add_parameter(FilterThreshold(
    #        text="max. LCI",
    #        desc="maximum low coverage index",
    #        cli_name='--max_lci',
    #        default=1000.0,
    #        maximum=1000.0
    #    ))

        item.add_parameter(FilterThreshold(
            text="min. coverage",
            desc="minimum average coverage",
            cli_name='--min_cov',
            default=0,
            maximum=9999,
            precision=0
        ))

        item.add_parameter(FilterThreshold(
            text="max. coverage",
            desc="maximum average coverage",
            cli_name='--max_cov',
            default=9999,
            maximum=9999,
            precision=0
        ))

        item.add_parameter(FilterSwitch(
            text="filter direction",
            desc="Keep or discard entries passing the filter criteria?",
            cli_name="--discard",
            default=0,
            options=["discard", "keep"]
        ))

        item.add_parameter(FilterParameter(
            text="verbose",
            desc="print additional information to STDERR",
            cli_name="--verbose",
            default=True,
            active=True
        ))

        item.add_parameter(FilterParameter(
            text="debug",
            desc="print debug messages to STDERR",
            cli_name="--debug",
            default=False
        ))

        item.add_parameter(FilterParameter(
            text="write PG tag",
            desc="annotate the filtered SAM file by adding a PG tag to the header",
            cli_name="--modify",
            default=True,
            active=True
        ))

        return item

    """ plotting methods """

    def plot_rld(ax, length_dist, min_length, max_length, read_count,
                 length_dist_total):
        """Creates a bar plot of a read length distribution.

        Includes scaled expected distribution based on all reads in file.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        length_dist : array_like
            Read length distribution of subset of reads.
        min_length : int
            Minimum read length.
        max_length : int
            Maximum read length.
        read_count : int
            Total number of reads.
        length_dist_total : array_like
            Read length distribution of all reads.
        """
        ax.set_title('RLD')
        ax.bar(np.arange(length_dist.size),
               length_dist,
               align='center',
               width=0.8,
               color='gray',
               label='actual')
        ax.plot(np.arange(min_length, max_length + 1, dtype=np.int),
                # scale expected dist down
                (length_dist_total * 1.0 / read_count) * np.sum(length_dist),
                color='red',
                linestyle='dashed',
                label='expected')
        ax.axis([min_length, max_length, 0, None])
        ax.set_xlabel("read length [bp]")
        ax.set_ylabel("number of reads")

    def plot_cd(ax, depth_dist, avg_depth):
        """Creates a bar plot of a coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        depth_dist : array_like
            Coverage depth distribution.
        avg_depth : float
            Mean coverage.
        """
        ax.set_title("CD")
        ax.bar(np.arange(depth_dist.size, dtype=np.int),
               depth_dist,
               align='center',
               width=0.8,
               color='gray')
        ax.axis([-0.5, depth_dist.size - 0.5, 0, None])
        ax.axvline(x=avg_depth,
                   color='green',
                   label="avg. coverage: %.2fx" % (avg_depth,))
        ax.set_xlabel("coverage")
        ax.set_ylabel("reference bases")
        ax.legend(loc=1)  # upper right

    def plot_scd(ax, depth_dist, avg_depth, ref_length, max_depth):
        """Creates a bar plot of a scaled coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        depth_dist : array_like
            coverage depth distribution.
        avg_depth : float
            Mean coverage.
        ref_length : int
            Length of reference in nucleotides.
        max_depth : int
            Maximum coverage depth.
        """
        depth_dist = depth_dist * 1.0 / ref_length

        ax.set_title("SCD")
        ax.bar(np.arange(depth_dist.size, dtype=np.int),
               depth_dist,
               align='center',
               width=0.8,
               color='gray')
        ax.axis([-0.5, depth_dist.size - 0.5, 0, 1])
        ax.axvline(x=avg_depth,
                   color='green',
                   label="avg. coverage: %.2fx" % (avg_depth,))
        ax.set_xlabel("coverage")
        ax.set_ylabel("fraction of reference bases")
        ax.legend(loc=1)  # upper right

    def plot_ccd(ax, depth_dist_cumsum, avg_depth):
        """Creates a bar plot of a cumulative coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        depth_dist_cumsum : array_like
            Cumulative coverage depth distribution.
        avg_depth : float
            Mean coverage.
        """
        ax.set_title("CCD")
        ax.bar(np.arange(depth_dist_cumsum.size, dtype=np.int),
               depth_dist_cumsum,
               align='center',
               width=0.8,
               color='gray')
        ax.axis([-0.5, depth_dist_cumsum.size - 0.5, 0, None])
    #    ax.axis([None, None, 0, None])

        ax.axvline(x=avg_depth,
                   color='green',
                   label="avg. coverage: %.2fx" % (avg_depth,))
        ax.set_xlabel("coverage")
    #    ax.set_xticks(None, None, 1.0)
        ax.set_ylabel("cumulative bases")

    def plot_sccd(ax, depth_dist_cumperc, avg_depth):
        """Creates a bar plot of a scaled cumulative coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        depth_dist_cumperc : array_like
            Scaled cumulative coverage depth distribution.
        avg_depth : float
            Mean coverage.
        """
        ax.set_title("SCCD")
        ax.bar(np.arange(depth_dist_cumperc.size),
               depth_dist_cumperc,
               align='edge',
               width=1,
               color='gray')
        ax.axis([0, depth_dist_cumperc.size - 1, 0, None])
        ax.axvline(x=avg_depth,
                   color='green',
                   label="avg. coverage: %.2fx" % (avg_depth,))
        ax.set_xlabel("coverage")
        ax.set_ylabel("cumulative fraction of alignment")

    def plot_nccd(ax, depth_dist_cumperc, avg_depth, max_depth, avg_depth_scaled,
                  lci, color):
        """Creates a bar plot of a normalized cumulative coverage distribution.

        Includes legend stating average scaled and total depth.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        depth_dist_cumperc : array_like
            Scaled cumulative coverage depth distribution.
        avg_depth : float
            Mean coverage.
        max_depth : int
            Maximum coverage depth.
        avg_depth_scaled : float
            Scaled mean coverage.
        lci : float
            LCI parameter.
        color : str
            Color name to be used for the bar plot.
        """
        ax.set_title("NCCD")
        ax.bar(np.arange(depth_dist_cumperc.size) * 1.0 / max_depth,
               depth_dist_cumperc,
               align='edge',
               width=1.0 / (depth_dist_cumperc.size - 1),
               color=color)
        ax.axis([0, 1, 0, 1])
        ax.axvline(x=avg_depth_scaled,
                   color='green',
                   label="avg. coverage: %.2f [%.2fx]" % (avg_depth_scaled,
                                                          avg_depth))
        ax.axvline(x=lci * avg_depth_scaled,
                   linestyle='dashed',
                   color='green',
                   label="%.2f x avg. cov.: %.2f [%.2fx]" % (
                       lci, lci * avg_depth_scaled, lci * avg_depth))
        ax.set_xlabel("fraction of max coverage")
        ax.set_ylabel("cumulative fraction of alignment")
        ax.legend(loc=4)  # lower right

    def plot_lorenz(ax, x, y):
        """Creates a Lorenz curve plot of a coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        x : array_like
            Coverage bins.
        Y : array_like
            Aligned bases per coverage bin.
        """
        (gini, auc) = get_gini_auc(x, y)

        ax.set_title("Lorenz")

        # show equal distribution
        ax.plot([0, 1],
                [0, 1],
                color='green',
                label="equal distribution")

        # show actual distribution
        ax.plot(x, y, label="actual distribution")
        ax.fill(x, y, color='gray', alpha=0.2)

        ax.axis([0, 1, 0, 1])

        ax.set_xlabel("fraction of coverage bins")
        ax.set_ylabel("fraction of alignment")
        ax.text(0.05, 0.75, "Gini = %.2f" % (gini,), transform=ax.transAxes)

        ax.legend(loc=2)  # upper left

    def plot_lorenz_b2b(ax, x, y):
        """Creates a Lorenz curve plot of a base2base coverage distribution.

        Parameters
        ----------
        ax : Axes
            Axes instance of current plot.
        x : array_like
            reference base positions.
        Y : array_like
            Aligned bases per reference base.
        """
        (gini, auc) = get_gini_auc(x, y)

        ax.set_title("Lorenz base2base")

        # show equal distribution
        ax.plot([0, 1],
                [0, 1],
                color='green',
                label="equal distribution")

        # show actual distribution
        ax.plot(x, y, label="actual distribution")
        ax.fill(x, y, color='gray', alpha=0.2)

        ax.axis([0, 1, 0, 1])

        ax.set_xlabel("fraction of reference bases")
        ax.set_ylabel("fraction of aligned read bases")
        ax.text(0.05, 0.75, "Gini = %.2f" % (gini,), transform=ax.transAxes)

        ax.legend(loc=2)  # upper left

    """ Integration methods """

    def integral_discrete(dist, limit):
        """Integrate discrete distribution with stepsize 1 by adding up values.

        Parameters
        ----------
        dist : array_like
            Discrete distribution with stepsize 1.
        limit : int
            Upper limit (exclusive).

        Returns
        -------
        float
            Integral of the distribution between 0 and upper limit.
        """
        return np.sum(dist[0:limit]) / 100.0

    def integral_scaled(dist, limit):
        """Integrates scaled discrete distribution with arbitrary stepsize.

        Parameters
        ----------
        dist : array_like
            Scaled discrete distribution with arbitrary stepsize.
        limit : float
            Upper limit (exclusive).

        Returns
        -------
        float
            Integral of the distribution between 0 and upper limit.
        """
        area = 0

        # prevent division by zero (for cases with 100% 1x coverage)
        if dist.size == 1:
            return 1.0 * limit

        # scale limit by max depth
        if limit <= dist.size - 1:
            limit_scaled = limit * 1.0 / (dist.size - 1)
        else:
            limit_scaled = 1.0

        stepsize = 1.0 / (dist.size - 1)
        x = stepsize
        for y in np.nditer(dist):
            if limit_scaled > x:
                area += stepsize * y
            else:
                area += (limit_scaled - (x - stepsize)) * y
                break
            x += stepsize

        return area

    def lorenzify(depth_dist):
        """Calculates Lorenz curve from coverage distribution.

        Parameters
        ----------
        depth_dist : array_like
            Coverage depth distribution.

        Returns
        -------
        x : array_like
            X coordinates of Lorenz curve.
        y : array_like
            Y coordinates of Lorenz curve.
        """
        reads_sum = np.sum(depth_dist)
        dd_scaled = depth_dist * 1.0 / reads_sum
        dd_sorted = np.sort(dd_scaled)
        dd_cum = np.cumsum(dd_sorted)

        # append (0|0) origin to beginning of arrays
        y = np.append(np.array([0.0]), dd_cum)
        x = np.append(np.array([0.0]),
                      (np.arange(depth_dist.size) + 1) * 1.0 / depth_dist.size)

        return (x, y)

    def lorenzify_b2b(depth_dist, ignore_uncovered=True):
        """Calculate Lorenz curve from base2base coverage distribution.

        Parameters
        ----------
        depth_dist : array_like
            Coverage depth distribution.
        ignore_uncovered : bool
            Ignore bases with zero coverage, defaults to True.

        Returns
        -------
        x : array_like
            X coordinates of Lorenz curve.
        y : array_like
            Y coordinates of Lorenz curve.
        """
        ali_total = 0
        ref_total = 0

        ali_bases_list = []
        ref_bases_list = []
        for (coverage, count) in enumerate(depth_dist):
            if ignore_uncovered:
                if coverage == 0:
                    continue
            ali_bases = count * coverage
            ali_bases_list.append(ali_bases)
            ref_bases_list.append(count)

            ali_total += ali_bases
            ref_total += count

        # turn lists into arrays and scale them
        b = np.array(ref_bases_list) * 1.0 / ref_total
        v = np.array(ali_bases_list) * 1.0 / ali_total

        triples = np.array([b, v, v/b])
        ttriples = np.transpose(triples)
        tttriples = np.transpose(ttriples[ttriples[:, 2].argsort()])

        x = np.cumsum(tttriples[0])
        y = np.cumsum(tttriples[1])

        # append (0|0) origin to beginning of arrays, scale both axes on the fly
        x = np.append(np.array([0]), x)
        y = np.append(np.array([0]), y)

        return (x, y)

    def get_gini_auc(x, y):
        """Calculates Gini coefficient and area under Lorenz curve.

        The Gini coefficient (also known as the Gini index) is a measure of
        statistical dispersion. When applied to the distribution of aligned read
        bases per reference base an even distribution of reads across the reference
        should have a low Gini coefficient (towards 0) while an alignment with all
        reads covering the same reference region should have a high Gini
        coefficient (towards 1).

        Parameters
        ----------
        x : array_like
            X coordinates of a normalized Lorenz distribution.
        y : array_like
            Y coordinates of a normalized Lorenz distribution.

        Returns
        -------
        float
            Gini coefficient. Ranges from 0 for a perfectly even distribution to 1
            for a maximally uneven distribution.
        float
            Integral of the Lorenz curve (area under curve). Maximal value is 0.5
            if the given distribution is uniform.
        """
        # calculate area under curve
        auc = 0.0
        for (idx, value) in enumerate(x):
            # no area at origin (0|0)
            if idx == 0:
                continue
            square = (x[idx] - x[idx - 1]) * y[idx - 1]
            triangle = ((x[idx] - x[idx - 1]) * (y[idx] - y[idx - 1])) / 2.0
            auc = auc + square + triangle

        # calculate Gini coefficient (area under normalized uniform dist is 0.5)
        gini = 1.0 - (2 * auc)

        return (gini, auc)

    def covered_length_from_cigar(cigar):
        """Calculates length of reference covered by read from CIGAR operations.

        Note
        ----
        * not counting padding, skipping or insertions into the reference.
        * not counting hard or soft clipped bases of the read

        Parameters
        ----------
        cigar : str
            Unmodified CIGAR string from SAM file.

        Returns
        -------
        int
            Length of the reference sequence.
        """
        regex = re.compile("(\d+)([MIDNSHP=X])")
        length = 0
        for match in regex.finditer(cigar):
            if match.group(2) in ("M", "=", "X", "D"):
                length += int(match.group(1))
        return length

    def calc_avg_depth(depth_dist, ignore_uncovered=True):
        """Calculate average depth from a coverage distribution.

        Optionally ignores uncovered bases (first array element).

        Parameters
        ----------
        depth_dist : array_like
            Sorted coverage depth distribution.
        ignore_uncovered : bool, optional
            Ignore bases with zero coverage (first array element), defaults to
            True.
        """
        sum_bases = 0
        sum_cover = 0

        for (coverage, count) in enumerate(depth_dist):
            if ignore_uncovered:
                if coverage == 0:
                    continue
            sum_bases += count
            sum_cover += coverage * count

        return sum_cover / (sum_bases * 1.0)

    def main():
        """Executable to filter SAM files for references with uneven coverage.

        See ``--help`` for details on expected arguments. Takes input from
        either STDIN, or optional, or positional arguments. Logs messages to
        STDERR and writes processed SAM files to STDOUT.
        """
        # parse arguments
        parser = argparse.ArgumentParser(description=DESC)
        parser.add_argument('-i', '--input',
                            type=check_sam,
                            help="specify SAM file to be analysed (default: "
                            "STDIN)",
                            required=False)
        parser.add_argument('--discard',
                            type=int,
                            help="keep or discard entries passing the filter "
                                 "criteria?",
                            required=False,
                            default=0)
        parser.add_argument('-v', '--verbose',
                            required=False,
                            action='store_true',
                            help='print additional information to stderr')
        parser.add_argument('-d', '--debug',
                            required=False,
                            action='store_true',
                            help='print debug messages to stderr')
        parser.add_argument('-m', '--modify',
                            required=False,
                            action='store_true',
                            help='modify header by adding PG record')
        parser.add_argument('-r', '--read_lengths',
                            required=False,
                            action='store_true',
                            help='analyze read length distributions')
        parser.add_argument('-c', '--covered',
                            required=False,
                            action='store_true',
                            help='covered bases only, ignore uncovered bases')
        parser.add_argument('-p', '--plot',
                            required=False,
                            action='store_true',
                            help='plot distribution(s)')
        parser.add_argument('-l', '--lci_arg',
                            required=False,
                            type=check_pos_float_max1,
                            help='fraction of mean coverage to use for LCI \
                            integration',
                            default=0.5)
        parser.add_argument('-s', '--stats_file',
                            required=False,
                            help="override filename for tab-separated statistics")

        acc_thresholds = parser.add_mutually_exclusive_group(required=False)
        acc_thresholds.add_argument('--min_cov',
                                    type=check_pos_int,
                                    help='minimum average coverage',
                                    default=0)
        acc_thresholds.add_argument('--max_cov',
                                    type=check_pos_int,
                                    help='maximum average coverage',
                                    default=sys.maxsize)
        acc_thresholds.add_argument('--min_lci',
                                    type=check_pos_float,
                                    help='minimum LCI',
                                    default=0.0)
        acc_thresholds.add_argument('--max_lci',
                                    type=check_pos_float,
                                    help='maximum LCI',
                                    default=1000.0)
        acc_thresholds.add_argument('--min_gini',
                                    type=check_pos_float_max1,
                                    help='minimum Gini coefficient',
                                    default=0.0)
        acc_thresholds.add_argument('--max_gini',
                                    type=check_pos_float_max1,
                                    help='maximum Gini coefficient',
                                    default=1.0)

        (args, remainArgs) = parser.parse_known_args()

        # configure logging
        if args.verbose:
            log.basicConfig(format="%(levelname)s: %(message)s", level=log.DEBUG)
        else:
            log.basicConfig(format="%(levelname)s: %(message)s")

    #    if args.debug:
    #        from pprint import pprint

        # set filename for statistics output
        if args.stats_file:
            stats_filename = args.stats_file
        elif args.input:
            stats_filename = args.input + ".stats.csv"
        else:
            # this assumes that filename was explicitly set by calling batch script
            stats_filename = "${filename}.stats.csv"

        # initialize dicts
        header = []                     # SAM header lines, unmodified
        depths = {}                     # dict of np.array of ints
        ref_lengths = {}                # dict of ints
        read_counts = {}                # dict of ints
        if args.read_lengths:
            read_lenghts = {}           # dict of dict of ints
            read_lenghtsTotal = {}      # dict of ints
        line_count = 0
        positions = {}   # dict of list for references and their line numbers
        buffer = None    # file handle used to buffer complete STDIN
        byte_offset = 0  # offset of first line after end of header
        line_offset = 0

        # parse SAM file and divide reads by reference accession
        log.info("START of filtering reads by conservation.")

        # parse SAM file
        log.info("STEP 1: parsing SAM records.")
        try:
            """
            open SAM file from either command line argument or STDIN
            use temporary file as buffer if reading from STDIN
            """
            if args.input:
                handle = open(args.input, 'r')
            else:
                handle = fileinput.input(remainArgs)
                buffer = tempfile.TemporaryFile(mode='w+')

            for line_nr, line in enumerate(handle, 0):
                line_count = line_nr + 1
                if buffer is not None:
                    buffer.write(line)

                # assuming that headers always precede alignments (SAMv1)
                if line.startswith("@"):
                    if args.modify:
                        line_offset = line_nr + 1
                        # store header lines for later modification
                        header.append(line)
                        # increase offset until reaching end of header
                        byte_offset += len(line)

                else:
                    fields = line.split("\t")
                    """
                    #   content     description
                    ===========================
                    0   QNAME
                    1   FLAG
                    2   RNAME
                    3   POS
                    4   MAPQ
                    5   CIGAR
                    6   RNEXT
                    7   PNEXT
                    8   TLEN
                    9   SEQ
                    10  QUAL
                    ...optional fields...
                    11  AS          alignment score
                    12  NM          edit distance to reference
                    13  ZL          reference length
                    14  ZR          "raw score"
                    15  ZE          "expected"
                    16  ZI          percent identify (incl. indels and deaminated)
                    17  MD          mismatching positions
                    18  NS          PMD score
                    """

                    # extract accession from required RNAME field
                    # (as written by MALT 0.0.3)
                    rname_parts = fields[2].split("|")
                    """
                    #   content
                    ===============
                    0   gi
                    1   GenBank ID
                    2   ref
                    3   accession
                    4   tax
                    5   taxonomy ID
                    """

                    accession = ""
                    try:
                        accession = rname_parts[3]
                    except IndexError:
                        accession = "unknown"
                        log.warn("no accession in line %s, assigning read to "
                                 "accession 'unknown'" % (line_nr + 1))

                    # extract reference sequence length from optional ZL field
                    ref_length = 0
                    try:
                        zl_parts = fields[13].split(":")
                        ref_length = int(zl_parts[2])
                    except IndexError:
                        log.error("no ZL field in line" % (line_nr + 1))
                        exit(1)

                    """
                    read                ------------------------------
                    ref     -----------------------------------------------------
                    cover   00000000000011111111111111111111111111111100000000000
                                pre    |         covered              |   post
                                     start                           stop
                    """

                    # get 1-based start position of read from required POS field
                    pre = int(fields[3]) - 1

                    # obtain stop position from required CIGAR field
                    covered = covered_length_from_cigar(fields[5])
                    stop = pre + covered

                    if accession in depths:
                        read_counts[accession] += 1
                        for position in range(pre, stop + 1):
                            if position in depths[accession]:
                                depths[accession][position] += 1
                            else:
                                depths[accession][position] = 1
                    else:
                        ref_lengths[accession] = ref_length
                        read_counts[accession] = 1
                        for position in range(pre, stop + 1):
                            depths[accession] = {position: 1}

                    # optional: read length distribution
                    if args.read_lengths:
                        readLen = len(fields[9])

                        if readLen in read_lenghtsTotal:
                            read_lenghtsTotal[readLen] += 1
                        else:
                            read_lenghtsTotal[readLen] = 1

                        if accession in read_lenghts:
                            if readLen in read_lenghts[accession]:
                                read_lenghts[accession][readLen] += 1
                            else:
                                read_lenghts[accession][readLen] = 1
                        else:
                            read_lenghts[accession] = {readLen: 1}

                    # remember occurence of accession and line number(s)
                    try:
                        positions[accession].append(line_nr)
                    except KeyError:
                        positions[accession] = [line_nr, ]
        finally:
            handle.close()
            buffer.seek(0)

        log.info("%i reads are aligned to %i references"
                 % (line_count, len(depths)))

        # get overall read length statistics
        if args.read_lengths:
            max_length_total = max(read_lenghtsTotal.keys())
            min_length_total = min(read_lenghtsTotal.keys())
            length_dist_total = np.zeros(
                (max_length_total - min_length_total + 1, ), dtype=np.int)
            for (length, count) in read_lenghtsTotal.items():
                length_dist_total[length - min_length_total] = count

            log.info("read lengths range from %i to %i bp"
                     % (min_length_total, max_length_total))

        # iterate over accessions and calculate statistics for filtering
        log.info("STEP 2: determining accessions matching the filter criteria.")
        lines = []
        max_depths = []
        max_lengths = []
        with open(stats_filename, "w") as handle:
            # create statistics header
            header = "accession\treference length [bp]\treads"
            if args.read_lengths:
                header += "\tmin length [bp]\tmax length [bp]\tmean length [bp]"
            header += "\tmin coverage\tmax coverage\tmean coverage"
            if args.covered:
                header += "\tmin coverage*\tmax coverage*\tmean coverage*"
            header += "\tLCI(%.2f)\tGini" % (args.lci_arg)
            if args.covered:
                header += "\tLCI(%.2f)*\tGini*" % (args.lci_arg)
            print(header, file=handle)

            for accession in depths:
                ref_length = ref_lengths[accession]
                read_count = read_counts[accession]

                # calculate coverage statistics
                max_depth = max(depths[accession].values())
                max_depths.append(max_depth)

                # determine depth distribution
                uncovered_bases = ref_length
                depth_dist = np.zeros((max_depth + 1,), dtype=np.int)
                for (pos, depth) in depths[accession].items():
                    depth_dist[depth] += 1
                    uncovered_bases -= 1
                depth_dist[0] = uncovered_bases
                if args.debug:
                    print(depth_dist)

                min_depth = 0
                if uncovered_bases == 0:
                    min_depth = min(depths[accession].values())
                avg_depth = calc_avg_depth(depth_dist, False)
                avg_depth_scaled = avg_depth * 1.0 / max_depth

                # convert counts to percentage of total reads (normalize y)
                depth_dist_cumsum = np.cumsum(depth_dist)
                depth_dist_cumperc = depth_dist_cumsum * 1.0 / (ref_length)

                # integrate distribution as lci(0.5)
                limit = args.lci_arg * avg_depth
    #            lci = integral_discrete(depth_dist_cumperc, limit)
                lci = integral_scaled(depth_dist_cumperc, limit)

    #            # calculate Gini coefficient from Lorenz curve
    #            (x,y) = lorenzify(depth_dist)
    #            (gini, auc) = get_gini_auc(x, y)

                # alternative Lorenz curve using base to base assignments
                (u, v) = lorenzify_b2b(depth_dist, False)
                if args.debug:
                    print("x (%i entries): %s" % (len(u), u))
                    print("y (%i entries): %s" % (len(v), v))
                (gini_b2b, auc_b2b) = get_gini_auc(u, v)

                # TODO also calculate Theil index, see
                # https://en.wikipedia.org/wiki/Theil_Index

                # optional: coverage stats for covered bases only
                if args.covered:
                    min_depth_covered = min(depths[accession].values())
                    if uncovered_bases == 0:
                        min_depth_covered = min_depth
                    avg_depth_covered = calc_avg_depth(depth_dist, True)
    #                avg_depth_covered_scaled = avg_depth_covered * 1.0 / max_depth

                    depth_dist_covered_cumsum = np.cumsum(depth_dist[1:])
                    depth_dist_covered_cumperc = (depth_dist_covered_cumsum * 1.0
                                                  / (ref_length - uncovered_bases))

                    limit_covered = args.lci_arg * avg_depth_covered
                    lci_covered = integral_scaled(depth_dist_covered_cumperc,
                                                  limit_covered)

                    (m, n) = lorenzify_b2b(depth_dist, True)
                    if args.debug:
                        print("x (%i entries): %s" % (len(m), m))
                        print("y (%i entries): %s" % (len(n), n))
                    (gini_b2b_covered, auc_b2b_covered) = get_gini_auc(m, n)

                # optional: read length stats
                if args.read_lengths:
                    max_length = max(read_lenghts[accession].keys())
                    min_length = min(read_lenghts[accession].keys())
                    avg_length = np.mean(np.fromiter(
                        read_lenghts[accession].keys(), dtype=np.int,
                        count=len(read_lenghts[accession])))
                    max_lengths.append(max_length)

                    # determine length distribution
                    length_dist = np.zeros((max_length + 1,), dtype=np.int)
                    for (length, count) in read_lenghts[accession].items():
                        length_dist[length] = count

                # compile accession statistics
                stats = "%s\t%i\t%i" % (accession, ref_length, read_count)
                if args.read_lengths:
                    stats += "\t%i\t%i\t%f" % (min_length, max_length, avg_length)
                stats += "\t%i\t%i\t%f" % (min_depth, max_depth, avg_depth)
                if args.covered:
                    stats += "\t%i\t%i\t%f" % (min_depth_covered, max_depth,
                                               avg_depth_covered)
                stats += "\t%f\t%f" % (lci, gini_b2b)
                if args.covered:
                    stats += "\t%f\t%f" % (lci_covered, gini_b2b_covered)
                print(stats, file=handle)

                # apply filters before time-consuming plotting steps
                if ((avg_depth < args.min_cov)
                   or (avg_depth > args.max_cov)
                   or (lci < args.min_lci)
                   or (lci > args.max_lci)
                   or (gini_b2b < args.min_gini)
                   or (gini_b2b > args.max_gini)):
                    continue

                color = 'blue'

                if args.plot:
                    fig_cover = plt.figure(num=1,
                                           figsize=(24, 12),  # inch x inch
                                           dpi=80,            # 1 inch = 80 pixels
                                           facecolor='white',
                                           edgecolor='black')
    #                x = np.arange(depth_dist_cumperc.size) * 1.0 / max_depth

                    # CD = coverage distribution plot
                    ax_cd = fig_cover.add_subplot(2, 4, 1)
                    plot_cd(ax_cd, depth_dist, avg_depth)

                    # SCD = scaled coverage distribution plot
                    ax_scd = fig_cover.add_subplot(2, 4, 2)
                    plot_scd(ax_scd, depth_dist, avg_depth, ref_length, max_depth)

                    # SCD = scaled coverage distribution plot
                    ax_scd_covered = fig_cover.add_subplot(2, 4, 3)
                    plot_scd(ax_scd_covered,
                             np.append(np.array([0]), depth_dist[1:]),
                             avg_depth_covered,
                             ref_length - uncovered_bases,
                             max_depth)

    #                # CCD = cumulative coverage distribution plot
    #                ax_ccd = fig_cover.add_subplot(2, 4, 2)
    #                plot_ccd(ax_ccd, depth_dist_cumsum, avg_depth)

    #                # SCCD = scaled cumulative coverage distribution plot
    #                ax_sccd = fig_cover.add_subplot(2, 4, 3)
    #                plot_sccd(ax_sccd, depth_dist_cumperc, avg_depth)

                    # NCCD = normalized cumulative coverage distribution
                    ax_nccd = fig_cover.add_subplot(2, 4, 4)
                    plot_nccd(ax_nccd, depth_dist_cumperc, avg_depth, max_depth,
                              avg_depth_scaled, args.lci_arg, color)
                    ax_nccd.text(0.05, 0.95,
                                 "lci(%.2f) = %.2f" % (args.lci_arg, lci),
                                 transform=ax_nccd.transAxes)

    #                # Lorenz curve
    #                ax_lorenz = fig_cover.add_subplot(2, 4, 5)
    #                plot_lorenz(ax_lorenz, x, y)

                    # Lorenz curve base2base
                    ax_b2b = fig_cover.add_subplot(2, 4, 6)
                    plot_lorenz_b2b(ax_b2b, u, v)

                    if args.covered:
                        ax_b2b_covered = fig_cover.add_subplot(2, 4, 7)
                        plot_lorenz_b2b(ax_b2b_covered, m, n)

                    # save plot to png
                    fig_cover.tight_layout()
                    fig_cover.savefig(accession + "_coverage.png")
                    plt.close(fig_cover)

                    if args.read_lengths:
                        fig_readlength = plt.figure(num=2,
                                                    figsize=(6, 6),  # inch x inch
                                                    dpi=80,        # 1 inch = 80px
                                                    facecolor='white',
                                                    edgecolor='black')

                        # RLD = read length distribution
                        ax_rld = fig_readlength.add_subplot(1, 1, 1)
                        plot_rld(ax_rld, length_dist, min_length_total,
                                 max_length_total, line_nr + 1, length_dist_total)

                        # save plot to png
                        fig_readlength.savefig(accession + "_readlengths.png")
                        plt.close(fig_readlength)

                log.info("accession %s: reference has a length of %i bp and %i "
                         "aligned reads" % (accession, ref_length, read_count))
                log.info("accession %s: coverage ranges from %ix to %ix, average "
                         "is %.3fx" % (accession, min_depth, max_depth, avg_depth))
                if args.covered:
                    log.info("accession %s: coverage for covered bases only "
                             "ranges from %ix to %ix, average is %.3fx"
                             % (accession, min_depth_covered, max_depth,
                                avg_depth_covered))
                if args.read_lengths:
                    log.info("accession %s: read length ranges from %i bp to %i "
                             "bp, average is %.3f bp" % (accession, min_length,
                                                         max_length, avg_length))

                # finally print accession for later filtering steps
                lines.extend(positions[accession])
                if args.debug:
                    log.info("filtering accession: %s" % (accession,))

        # re-open file if not a buffered stream
        if buffer is None:
            buffer = open(args.input, 'r')

        # skip original headers and sneak in modified headers instead
        if args.modify:
            log.info("Writing new @PG record to SAM header.")
            cl = " ".join(sys.argv[1:])
            modified_header = modify_header(
                header,
                name=splitext(basename(__file__))[0],
                version=__version__,
                command_line=cl,
                description=TEXT
            )
            extra_headers = len(modified_header) - len(header)    # should be 1
            for record in modified_header:
                print(record.rstrip(), file=sys.stdout)
            # fast forward buffer to beginning of alignments
            buffer.seek(byte_offset)

            if args.debug:
                log.info("%i new line added to header lines." % extra_headers)
        # keep or remove accessions from SAM file
        alt = ["discarding", "keeping"]
        log.info("STEP 3: %s %i unevenly covered references from SAM file." %
                 (alt[args.discard], len(lines)))

        line_filter(lines, buffer, discard=(args.discard == 0),
                    offset=line_offset)
        buffer.close()

        log.info("END of filtering references by coverage, statistics saved to "
                 "file %s" % (stats_filename, ))

        exit()

    if __name__ == "__main__":
        main()

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