# Copyright 2002 by Jeffrey Chang.
# Copyright 2016 by Markus Piotrowski.
# All rights reserved.
# This code is part of the Biopython distribution and governed by its
# license.  Please see the LICENSE file that should have been included
# as part of this package.

"""This package implements pairwise sequence alignment using a dynamic
programming algorithm.

This provides functions to get global and local alignments between two
sequences. A global alignment finds the best concordance between all
characters in two sequences. A local alignment finds just the
subsequences that align the best.

When doing alignments, you can specify the match score and gap
penalties.  The match score indicates the compatibility between an
alignment of two characters in the sequences. Highly compatible
characters should be given positive scores, and incompatible ones
should be given negative scores or 0.  The gap penalties should be
negative.

The names of the alignment functions in this module follow the
convention
<alignment type>XX
where <alignment type> is either "global" or "local" and XX is a 2
character code indicating the parameters it takes.  The first
character indicates the parameters for matches (and mismatches), and
the second indicates the parameters for gap penalties.

The match parameters are::

    CODE  DESCRIPTION
    x     No parameters. Identical characters have score of 1, otherwise 0.
    m     A match score is the score of identical chars, otherwise mismatch
          score.
    d     A dictionary returns the score of any pair of characters.
    c     A callback function returns scores.

The gap penalty parameters are::

    CODE  DESCRIPTION
    x     No gap penalties.
    s     Same open and extend gap penalties for both sequences.
    d     The sequences have different open and extend gap penalties.
    c     A callback function returns the gap penalties.

All the different alignment functions are contained in an object
``align``. For example:

    >>> from Bio import pairwise2
    >>> alignments = pairwise2.align.globalxx("ACCGT", "ACG")

will return a list of the alignments between the two strings. For a nice
printout, use the ``format_alignment`` method of the module:

    >>> from Bio.pairwise2 import format_alignment
    >>> print(format_alignment(*alignments[0]))
    ACCGT
    |||||
    A-CG-
      Score=3
    <BLANKLINE>

All alignment functions have the following arguments:

- Two sequences: strings, Biopython sequence objects or lists.
  Lists are useful for suppling sequences which contain residues that are
  encoded by more than one letter.

- ``penalize_extend_when_opening``: boolean (default: False).
  Whether to count an extension penalty when opening a gap. If false, a gap of
  1 is only penalized an "open" penalty, otherwise it is penalized
  "open+extend".

- ``penalize_end_gaps``: boolean.
  Whether to count the gaps at the ends of an alignment. By default, they are
  counted for global alignments but not for local ones. Setting
  ``penalize_end_gaps`` to (boolean, boolean) allows you to specify for the
  two sequences separately whether gaps at the end of the alignment should be
  counted.

- ``gap_char``: string (default: ``'-'``).
  Which character to use as a gap character in the alignment returned. If your
  input sequences are lists, you must change this to ``['-']``.

- ``force_generic``: boolean (default: False).
  Always use the generic, non-cached, dynamic programming function (slow!).
  For debugging.

- ``score_only``: boolean (default: False).
  Only get the best score, don't recover any alignments. The return value of
  the function is the score. Faster and uses less memory.

- ``one_alignment_only``: boolean (default: False).
  Only recover one alignment.

The other parameters of the alignment function depend on the function called.
Some examples:

- Find the best global alignment between the two sequences. Identical
  characters are given 1 point. No points are deducted for mismatches or gaps.

    >>> for a in pairwise2.align.globalxx("ACCGT", "ACG"):
    ...     print(format_alignment(*a))
    ACCGT
    |||||
    A-CG-
      Score=3
    <BLANKLINE>
    ACCGT
    |||||
    AC-G-
      Score=3
    <BLANKLINE>

- Same thing as before, but with a local alignment.

    >>> for a in pairwise2.align.localxx("ACCGT", "ACG"):
    ...     print(format_alignment(*a))
    ACCGT
    ||||
    A-CG-
      Score=3
    <BLANKLINE>
    ACCGT
    ||||
    AC-G-
      Score=3
    <BLANKLINE>

- Do a global alignment. Identical characters are given 2 points, 1 point is
  deducted for each non-identical character. Don't penalize gaps.

    >>> for a in pairwise2.align.globalmx("ACCGT", "ACG", 2, -1):
    ...     print(format_alignment(*a))
    ACCGT
    |||||
    A-CG-
      Score=6
    <BLANKLINE>
    ACCGT
    |||||
    AC-G-
      Score=6
    <BLANKLINE>

- Same as above, except now 0.5 points are deducted when opening a gap, and
  0.1 points are deducted when extending it.

    >>> for a in pairwise2.align.globalms("ACCGT", "ACG", 2, -1, -.5, -.1):
    ...     print(format_alignment(*a))
    ACCGT
    |||||
    A-CG-
      Score=5
    <BLANKLINE>
    ACCGT
    |||||
    AC-G-
      Score=5
    <BLANKLINE>

- Depending on the penalties, a gap in one sequence may be followed by a gap in
  the other sequence.If you don't like this behaviour, increase the gap-open
  penalty:

    >>> for a in pairwise2.align.globalms("A", "T", 5, -4, -1, -.1):
    ...     print(format_alignment(*a))
    A-
    ||
    -T
      Score=-2
    <BLANKLINE>
    >>> for a in pairwise2.align.globalms("A", "T", 5, -4, -3, -.1):
    ...	    print(format_alignment(*a))
    A
    |
    T
      Score=-4
    <BLANKLINE>

- The alignment function can also use known matrices already included in
  Biopython (``MatrixInfo`` from ``Bio.SubsMat``):

    >>> from Bio.SubsMat import MatrixInfo as matlist
    >>> matrix = matlist.blosum62
    >>> for a in pairwise2.align.globaldx("KEVLA", "EVL", matrix):
    ...     print(format_alignment(*a))
    KEVLA
    |||||
    -EVL-
      Score=13
    <BLANKLINE>

- With the parameter ``c`` you can define your own match- and gap functions.
  E.g. to define an affine logarithmic gap function and using it:

    >>> from math import log
    >>> def gap_function(x, y):  # x is gap position in seq, y is gap length
    ...     if y == 0:  # No gap
    ...         return 0
    ...     elif y == 1:  # Gap open penalty
    ...         return -2
    ...     return - (2 + y/4.0 + log(y)/2.0)
    ...
    >>> alignment = pairwise2.align.globalmc("ACCCCCGT", "ACG", 5, -4,
    ...                                      gap_function, gap_function)

  You can define different gap functions for each sequence.
  Self-defined match functions must take the two residues to be compared and
  return a score.

To see a description of the parameters for a function, please look at
the docstring for the function via the help function, e.g.
type ``help(pairwise2.align.localds``) at the Python prompt.

"""
from __future__ import print_function

import warnings

from Bio import BiopythonWarning


MAX_ALIGNMENTS = 1000   # maximum alignments recovered in traceback


class align(object):
    """This class provides functions that do alignments."""

    class alignment_function(object):
        """This class is callable impersonates an alignment function.
        The constructor takes the name of the function.  This class
        will decode the name of the function to figure out how to
        interpret the parameters.

        """
        # match code -> tuple of (parameters, docstring)
        match2args = {
            'x': ([], ''),
            'm': (['match', 'mismatch'],
                  "match is the score to given to identical characters. "
                  "mismatch is the score given to non-identical ones."),
            'd': (['match_dict'],
                  "match_dict is a dictionary where the keys are tuples "
                  "of pairs of characters and the values are the scores, "
                  "e.g. ('A', 'C') : 2.5."),
            'c': (['match_fn'],
                  "match_fn is a callback function that takes two "
                  "characters and returns the score between them."),
        }
        # penalty code -> tuple of (parameters, docstring)
        penalty2args = {
            'x': ([], ''),
            's': (['open', 'extend'],
                  "open and extend are the gap penalties when a gap is "
                  "opened and extended.  They should be negative."),
            'd': (['openA', 'extendA', 'openB', 'extendB'],
                  "openA and extendA are the gap penalties for sequenceA, "
                  "and openB and extendB for sequeneB.  The penalties "
                  "should be negative."),
            'c': (['gap_A_fn', 'gap_B_fn'],
                  "gap_A_fn and gap_B_fn are callback functions that takes "
                  "(1) the index where the gap is opened, and (2) the length "
                  "of the gap.  They should return a gap penalty."),
        }

        def __init__(self, name):
            # Check to make sure the name of the function is
            # reasonable.
            if name.startswith("global"):
                if len(name) != 8:
                    raise AttributeError("function should be globalXX")
            elif name.startswith("local"):
                if len(name) != 7:
                    raise AttributeError("function should be localXX")
            else:
                raise AttributeError(name)
            align_type, match_type, penalty_type = \
                name[:-2], name[-2], name[-1]
            try:
                match_args, match_doc = self.match2args[match_type]
            except KeyError:
                raise AttributeError("unknown match type %r" % match_type)
            try:
                penalty_args, penalty_doc = self.penalty2args[penalty_type]
            except KeyError:
                raise AttributeError("unknown penalty type %r" % penalty_type)

            # Now get the names of the parameters to this function.
            param_names = ['sequenceA', 'sequenceB']
            param_names.extend(match_args)
            param_names.extend(penalty_args)
            self.function_name = name
            self.align_type = align_type
            self.param_names = param_names

            self.__name__ = self.function_name
            # Set the doc string.
            doc = "%s(%s) -> alignments\n" % (
                self.__name__, ', '.join(self.param_names))
            if match_doc:
                doc += "\n%s\n" % match_doc
            if penalty_doc:
                doc += "\n%s\n" % penalty_doc
            doc += ("""\
\nalignments is a list of tuples (seqA, seqB, score, begin, end).
seqA and seqB are strings showing the alignment between the
sequences.  score is the score of the alignment.  begin and end
are indexes into seqA and seqB that indicate the where the
alignment occurs.
""")
            self.__doc__ = doc

        def decode(self, *args, **keywds):
            # Decode the arguments for the _align function.  keywds
            # will get passed to it, so translate the arguments to
            # this function into forms appropriate for _align.
            keywds = keywds.copy()
            if len(args) != len(self.param_names):
                raise TypeError("%s takes exactly %d argument (%d given)"
                                % (self.function_name, len(self.param_names),
                                   len(args)))
            i = 0
            while i < len(self.param_names):
                if self.param_names[i] in [
                   'sequenceA', 'sequenceB',
                   'gap_A_fn', 'gap_B_fn', 'match_fn']:
                    keywds[self.param_names[i]] = args[i]
                    i += 1
                elif self.param_names[i] == 'match':
                    assert self.param_names[i + 1] == 'mismatch'
                    match, mismatch = args[i], args[i + 1]
                    keywds['match_fn'] = identity_match(match, mismatch)
                    i += 2
                elif self.param_names[i] == 'match_dict':
                    keywds['match_fn'] = dictionary_match(args[i])
                    i += 1
                elif self.param_names[i] == 'open':
                    assert self.param_names[i + 1] == 'extend'
                    open, extend = args[i], args[i + 1]
                    pe = keywds.get('penalize_extend_when_opening', 0)
                    keywds['gap_A_fn'] = affine_penalty(open, extend, pe)
                    keywds['gap_B_fn'] = affine_penalty(open, extend, pe)
                    i += 2
                elif self.param_names[i] == 'openA':
                    assert self.param_names[i + 3] == 'extendB'
                    openA, extendA, openB, extendB = args[i:i + 4]
                    pe = keywds.get('penalize_extend_when_opening', 0)
                    keywds['gap_A_fn'] = affine_penalty(openA, extendA, pe)
                    keywds['gap_B_fn'] = affine_penalty(openB, extendB, pe)
                    i += 4
                else:
                    raise ValueError("unknown parameter %r"
                                     % self.param_names[i])

            # Here are the default parameters for _align.  Assign
            # these to keywds, unless already specified.
            pe = keywds.get('penalize_extend_when_opening', 0)
            default_params = [
                ('match_fn', identity_match(1, 0)),
                ('gap_A_fn', affine_penalty(0, 0, pe)),
                ('gap_B_fn', affine_penalty(0, 0, pe)),
                ('penalize_extend_when_opening', 0),
                ('penalize_end_gaps', self.align_type == 'global'),
                ('align_globally', self.align_type == 'global'),
                ('gap_char', '-'),
                ('force_generic', 0),
                ('score_only', 0),
                ('one_alignment_only', 0),
            ]
            for name, default in default_params:
                keywds[name] = keywds.get(name, default)
            value = keywds['penalize_end_gaps']
            try:
                n = len(value)
            except TypeError:
                keywds['penalize_end_gaps'] = tuple([value] * 2)
            else:
                assert n == 2
            return keywds

        def __call__(self, *args, **keywds):
            keywds = self.decode(*args, **keywds)
            return _align(**keywds)

    def __getattr__(self, attr):
        return self.alignment_function(attr)
align = align()


def _align(sequenceA, sequenceB, match_fn, gap_A_fn, gap_B_fn,
           penalize_extend_when_opening, penalize_end_gaps,
           align_globally, gap_char, force_generic, score_only,
           one_alignment_only):
    """Return a list of alignments between two sequences or its score"""
    if not sequenceA or not sequenceB:
        return []
    try:
        sequenceA + gap_char
        sequenceB + gap_char
    except TypeError:
        raise TypeError('both sequences must be of the same type, either ' +
                        'string/sequence object or list. Gap character must ' +
                        'fit the sequence type (string or list)')

    if not isinstance(sequenceA, list):
        sequenceA = str(sequenceA)
    if not isinstance(sequenceB, list):
        sequenceB = str(sequenceB)

    if (not force_generic) and isinstance(gap_A_fn, affine_penalty) \
       and isinstance(gap_B_fn, affine_penalty):
        open_A, extend_A = gap_A_fn.open, gap_A_fn.extend
        open_B, extend_B = gap_B_fn.open, gap_B_fn.extend
        x = _make_score_matrix_fast(
            sequenceA, sequenceB, match_fn, open_A, extend_A, open_B,
            extend_B, penalize_extend_when_opening, penalize_end_gaps,
            align_globally, score_only)
    else:
        x = _make_score_matrix_generic(
            sequenceA, sequenceB, match_fn, gap_A_fn, gap_B_fn,
            penalize_end_gaps, align_globally, score_only)
    score_matrix, trace_matrix = x

    # print("SCORE %s" % print_matrix(score_matrix))
    # print("TRACEBACK %s" % print_matrix(trace_matrix))

    # Look for the proper starting point. Get a list of all possible
    # starting points.
    starts = _find_start(score_matrix, align_globally)
    # Find the highest score.
    best_score = max([x[0] for x in starts])

    # If they only want the score, then return it.
    if score_only:
        return best_score

    tolerance = 0  # XXX do anything with this?
    # Now find all the positions within some tolerance of the best
    # score.
    starts = [(score, pos) for score, pos in starts
              if rint(abs(score - best_score)) <= rint(tolerance)]

    # Recover the alignments and return them.
    return _recover_alignments(sequenceA, sequenceB, starts, score_matrix,
                               trace_matrix, align_globally, gap_char,
                               one_alignment_only, gap_A_fn, gap_B_fn)


def _make_score_matrix_generic(sequenceA, sequenceB, match_fn, gap_A_fn,
                               gap_B_fn, penalize_end_gaps, align_globally,
                               score_only):
    """Generate a score and traceback matrix according to Needleman-Wunsch

    This implementation allows the usage of general gap functions and is rather
    slow. It is automatically called if you define your own gap functions. You
    can force the usage of this method with ``force_generic=True``.
    """
    # Create the score and traceback matrices. These should be in the
    # shape:
    # sequenceA (down) x sequenceB (across)
    lenA, lenB = len(sequenceA), len(sequenceB)
    score_matrix, trace_matrix = [], []
    for i in range(lenA + 1):
        score_matrix.append([None] * (lenB + 1))
        if not score_only:
            trace_matrix.append([None] * (lenB + 1))

    # Initialize first row and column with gap scores. This is like opening up
    # i gaps at the beginning of sequence A or B.
    for i in range(lenA + 1):
        if penalize_end_gaps[1]:  # [1]:gap in sequence B
            score = gap_B_fn(0, i)
        else:
            score = 0
        score_matrix[i][0] = score
    for i in range(lenB + 1):
        if penalize_end_gaps[0]:  # [0]:gap in sequence A
            score = gap_A_fn(0, i)
        else:
            score = 0
        score_matrix[0][i] = score

    # Fill in the score matrix.  Each position in the matrix
    # represents an alignment between a character from sequence A to
    # one in sequence B.  As I iterate through the matrix, find the
    # alignment by choose the best of:
    #    1) extending a previous alignment without gaps
    #    2) adding a gap in sequenceA
    #    3) adding a gap in sequenceB
    for row in range(1, lenA + 1):
        for col in range(1, lenB + 1):
            # First, calculate the score that would occur by extending
            # the alignment without gaps.
            nogap_score = score_matrix[row - 1][col - 1] + \
                match_fn(sequenceA[row - 1], sequenceB[col - 1])

            # Try to find a better score by opening gaps in sequenceA.
            # Do this by checking alignments from each column in the row.
            # Each column represents a different character to align from,
            # and thus a different length gap.
            # Although the gap function does not distinguish between opening
            # and extending a gap, we distinguish them for the backtrace.
            if not penalize_end_gaps[0] and row == lenA:
                row_open = score_matrix[row][col - 1]
                row_extend = max([score_matrix[row][x] for x in range(col)])
            else:
                row_open = score_matrix[row][col - 1] + gap_A_fn(row, 1)
                row_extend = max([score_matrix[row][x] + gap_A_fn(row, col - x)
                                  for x in range(col)])

            # Try to find a better score by opening gaps in sequenceB.
            if not penalize_end_gaps[1] and col == lenB:
                col_open = score_matrix[row - 1][col]
                col_extend = max([score_matrix[x][col] for x in range(row)])
            else:
                col_open = score_matrix[row - 1][col] + gap_B_fn(col, 1)
                col_extend = max([score_matrix[x][col] + gap_B_fn(col, row - x)
                                  for x in range(row)])

            best_score = max(nogap_score, row_open, row_extend, col_open,
                             col_extend)
            if not align_globally and best_score < 0:
                score_matrix[row][col] = 0
            else:
                score_matrix[row][col] = best_score

            # The backtrace is encoded binary. See _make_score_matrix_fast
            # for details.
            if not score_only:
                trace_score = 0
                if rint(nogap_score) == rint(best_score):
                    trace_score += 2
                if rint(row_open) == rint(best_score):
                    trace_score += 1
                if rint(row_extend) == rint(best_score):
                    trace_score += 8
                if rint(col_open) == rint(best_score):
                    trace_score += 4
                if rint(col_extend) == rint(best_score):
                    trace_score += 16
                trace_matrix[row][col] = trace_score

    return score_matrix, trace_matrix


def _make_score_matrix_fast(sequenceA, sequenceB, match_fn, open_A, extend_A,
                            open_B, extend_B, penalize_extend_when_opening,
                            penalize_end_gaps, align_globally, score_only):
    """Generate a score and traceback matrix according to Gotoh"""
    # This is an implementation of the Needleman-Wunsch dynamic programming
    # algorithm as modified by Gotoh, implementing affine gap penalties.
    # In short, we have three matrices, holding scores for alignments ending
    # in (1) a match/mismatch, (2) a gap in sequence A, and (3) a gap in
    # sequence B, respectively. However, we can combine them in one matrix,
    # which holds the best scores, and store only those values from the
    # other matrices that are actually used for the next step of calculation.
    # The traceback matrix holds the positions for backtracing the alignment.

    first_A_gap = calc_affine_penalty(1, open_A, extend_A,
                                      penalize_extend_when_opening)
    first_B_gap = calc_affine_penalty(1, open_B, extend_B,
                                      penalize_extend_when_opening)

    # Create the score and traceback matrices. These should be in the
    # shape:
    # sequenceA (down) x sequenceB (across)
    lenA, lenB = len(sequenceA), len(sequenceB)
    score_matrix, trace_matrix = [], []
    for i in range(lenA + 1):
        score_matrix.append([None] * (lenB + 1))
        if not score_only:
            trace_matrix.append([None] * (lenB + 1))

    # Initialize first row and column with gap scores. This is like opening up
    # i gaps at the beginning of sequence A or B.
    for i in range(lenA + 1):
        if penalize_end_gaps[1]:  # [1]:gap in sequence B
            score = calc_affine_penalty(i, open_B, extend_B,
                                        penalize_extend_when_opening)
        else:
            score = 0
        score_matrix[i][0] = score
    for i in range(lenB + 1):
        if penalize_end_gaps[0]:  # [0]:gap in sequence A
            score = calc_affine_penalty(i, open_A, extend_A,
                                        penalize_extend_when_opening)
        else:
            score = 0
        score_matrix[0][i] = score

    # Now initialize the col 'matrix'. Actually this is only a one dimensional
    # list, since we only need the col scores from the last row.
    col_score = [0]  # Best score, if actual alignment ends with gap in seqB
    for i in range(1, lenB + 1):
        col_score.append(calc_affine_penalty(i, 2 * open_B, extend_B,
                                             penalize_extend_when_opening))

    # The row 'matrix' is calculated on the fly. Here we only need the actual
    # score.
    # Now, filling up the score and traceback matrices:
    for row in range(1, lenA + 1):
        row_score = calc_affine_penalty(row, 2 * open_A, extend_A,
                                        penalize_extend_when_opening)
        for col in range(1, lenB + 1):
            # Calculate the score that would occur by extending the
            # alignment without gaps.
            nogap_score = score_matrix[row - 1][col - 1] + \
                match_fn(sequenceA[row - 1], sequenceB[col - 1])

            # Check the score that would occur if there were a gap in
            # sequence A. This could come from opening a new gap or
            # extending an existing one.
            # A gap in sequence A can also be opened if it follows a gap in
            # sequence B:  A-
            #              -B
            if not penalize_end_gaps[0] and row == lenA:
                row_open = score_matrix[row][col - 1]
                row_extend = row_score
            else:
                row_open = score_matrix[row][col - 1] + first_A_gap
                row_extend = row_score + extend_A
            row_score = max(row_open, row_extend)

            # The same for sequence B:
            if not penalize_end_gaps[1] and col == lenB:
                col_open = score_matrix[row - 1][col]
                col_extend = col_score[col]
            else:
                col_open = score_matrix[row - 1][col] + first_B_gap
                col_extend = col_score[col] + extend_B
            col_score[col] = max(col_open, col_extend)

            best_score = max(nogap_score, col_score[col], row_score)
            if not align_globally and best_score < 0:
                score_matrix[row][col] = 0
            else:
                score_matrix[row][col] = best_score

            # Now the trace_matrix. The edges of the backtrace are encoded
            # binary: 1 = open gap in seqA, 2 = match/mismatch of seqA and
            # seqB, 4 = open gap in seqB, 8 = extend gap in seqA, and
            # 16 = extend gap in seqA. This values can be summed up.
            # Thus, the trace score 7 means that the best score can either
            # come from opening a gap in seqA (=1), pairing two characters
            # of seqA and seqB (+2=3) or opening a gap in seqB (+4=7).
            # However, if we only want the score we don't care about the trace.
            if not score_only:
                row_score_rint = rint(row_score)
                col_score_rint = rint(col_score[col])
                row_trace_score = 0
                col_trace_score = 0
                if rint(row_open) == row_score_rint:
                    row_trace_score += 1  # Open gap in seqA
                if rint(row_extend) == row_score_rint:
                    row_trace_score += 8  # Extend gap in seqA
                if rint(col_open) == col_score_rint:
                    col_trace_score += 4  # Open gap in seqB
                if rint(col_extend) == col_score_rint:
                    col_trace_score += 16  # Extend gap in seqB

                trace_score = 0
                best_score_rint = rint(best_score)
                if rint(nogap_score) == best_score_rint:
                    trace_score += 2  # Align seqA with seqB
                if row_score_rint == best_score_rint:
                    trace_score += row_trace_score
                if col_score_rint == best_score_rint:
                    trace_score += col_trace_score
                trace_matrix[row][col] = trace_score

    return score_matrix, trace_matrix


def _recover_alignments(sequenceA, sequenceB, starts, score_matrix,
                        trace_matrix, align_globally, gap_char,
                        one_alignment_only, gap_A_fn, gap_B_fn):
    """Do the backtracing and return a list of alignments"""
    # Recover the alignments by following the traceback matrix.  This
    # is a recursive procedure, but it's implemented here iteratively
    # with a stack.
    lenA, lenB = len(sequenceA), len(sequenceB)
    ali_seqA, ali_seqB = sequenceA[0:0], sequenceB[0:0]
    tracebacks = []
    in_process = []

    for start in starts:
        score, (row, col) = start
        begin = 0
        if align_globally:
            end = None
        else:
            # Local alignments should start with a positive score!
            if score <= 0:
                continue
            # Local alignments should not end with a gap!:
            trace = trace_matrix[row][col]
            if (trace - trace % 2) % 4 == 2:  # Trace contains 'nogap', fine!
                trace_matrix[row][col] = 2
            # If not, don't start here!
            else:
                continue
            end = -max(lenA - row, lenB - col)
            if not end:
                end = None
            col_distance = lenB - col
            row_distance = lenA - row
            ali_seqA = ((col_distance - row_distance) * gap_char +
                        sequenceA[lenA - 1:row - 1:-1])
            ali_seqB = ((row_distance - col_distance) * gap_char +
                        sequenceB[lenB - 1:col - 1:-1])
        in_process += [(ali_seqA, ali_seqB, end, row, col, False,
                        trace_matrix[row][col])]
    while in_process and len(tracebacks) < MAX_ALIGNMENTS:
        # Although we allow a gap in seqB to be followed by a gap in seqA,
        # we don't want to allow it the other way round, since this would
        # give redundant alignments of type: A-  vs.  -A
        #                                    -B       B-
        # Thus we need to keep track if a gap in seqA was opened (col_gap)
        # and stop the backtrace (dead_end) if a gap in seqB follows.
        dead_end = False
        ali_seqA, ali_seqB, end, row, col, col_gap, trace = in_process.pop()

        while (row > 0 or col > 0) and not dead_end:
            cache = (ali_seqA[:], ali_seqB[:], end, row, col, col_gap)

            # If trace is empty we have reached at least one border of the
            # matrix or the end of a local aligment. Just add the rest of
            # the sequence(s) and fill with gaps if neccessary.
            if not trace:
                if col and col_gap:
                    dead_end = True
                else:
                    ali_seqA, ali_seqB = _finish_backtrace(
                        sequenceA, sequenceB, ali_seqA, ali_seqB,
                        row, col, gap_char)
                break
            elif trace % 2 == 1:  # = row open = open gap in seqA
                trace -= 1
                if col_gap:
                    dead_end = True
                else:
                    col -= 1
                    ali_seqA += gap_char
                    ali_seqB += sequenceB[col]
                    col_gap = False
            elif trace % 4 == 2:  # = match/mismatch of seqA with seqB
                trace -= 2
                row -= 1
                col -= 1
                ali_seqA += sequenceA[row]
                ali_seqB += sequenceB[col]
                col_gap = False
            elif trace % 8 == 4:  # = col open = open gap in seqB
                trace -= 4
                row -= 1
                ali_seqA += sequenceA[row]
                ali_seqB += gap_char
                col_gap = True
            elif trace in (8, 24):  # = row extend = extend gap in seqA
                trace -= 8
                if col_gap:
                    dead_end = True
                else:
                    col_gap = False
                    # We need to find the starting point of the extended gap
                    x = _find_gap_open(sequenceA, sequenceB, ali_seqA,
                                       ali_seqB, end, row, col, col_gap,
                                       gap_char, score_matrix, trace_matrix,
                                       in_process, gap_A_fn, col, row, 'col')
                    ali_seqA, ali_seqB, row, col, in_process, dead_end = x
            elif trace == 16:  # = col extend = extend gap in seqB
                trace -= 16
                col_gap = True
                x = _find_gap_open(sequenceA, sequenceB, ali_seqA, ali_seqB,
                                   end, row, col, col_gap, gap_char,
                                   score_matrix, trace_matrix, in_process,
                                   gap_B_fn, row, col, 'row')
                ali_seqA, ali_seqB, row, col, in_process, dead_end = x

            if trace:  # There is another path to follow...
                cache += (trace,)
                in_process.append(cache)
            trace = trace_matrix[row][col]
            if not align_globally and score_matrix[row][col] <= 0:
                begin = max(row, col)
                trace = 0
        if not dead_end:
            tracebacks.append((ali_seqA[::-1], ali_seqB[::-1], score, begin,
                               end))
            if one_alignment_only:
                break
    return _clean_alignments(tracebacks)


def _find_start(score_matrix, align_globally):
    """Return a list of starting points (score, (row, col)).

    Indicating every possible place to start the tracebacks.
    """
    nrows, ncols = len(score_matrix), len(score_matrix[0])
    # In this implementation of the global algorithm, the start will always be
    # the bottom right corner of the matrix.
    if align_globally:
        starts = [(score_matrix[-1][-1], (nrows - 1, ncols - 1))]
    else:
        starts = []
        for row in range(nrows):
            for col in range(ncols):
                score = score_matrix[row][col]
                starts.append((score, (row, col)))
    return starts


def _clean_alignments(alignments):
    """Take a list of alignments and return a cleaned version."""
    # Remove duplicates, make sure begin and end are set correctly, remove
    # empty alignments.
    unique_alignments = []
    for align in alignments:
        if align not in unique_alignments:
            unique_alignments.append(align)
    i = 0
    while i < len(unique_alignments):
        seqA, seqB, score, begin, end = unique_alignments[i]
        # Make sure end is set reasonably.
        if end is None:   # global alignment
            end = len(seqA)
        elif end < 0:
            end = end + len(seqA)
        # If there's no alignment here, get rid of it.
        if begin >= end:
            del unique_alignments[i]
            continue
        unique_alignments[i] = seqA, seqB, score, begin, end
        i += 1
    return unique_alignments


def _finish_backtrace(sequenceA, sequenceB, ali_seqA, ali_seqB, row, col,
                      gap_char):
    """Add remaining sequences and fill with gaps if neccessary"""
    if row:
        ali_seqA += sequenceA[row - 1::-1]
    if col:
        ali_seqB += sequenceB[col - 1::-1]
    if row > col:
            ali_seqB += gap_char * (len(ali_seqA) - len(ali_seqB))
    elif col > row:
            ali_seqA += gap_char * (len(ali_seqB) - len(ali_seqA))
    return ali_seqA, ali_seqB


def _find_gap_open(sequenceA, sequenceB, ali_seqA, ali_seqB, end, row, col,
                   col_gap, gap_char, score_matrix, trace_matrix, in_process,
                   gap_fn, target, index, direction):
    """Find the starting point(s) of the extended gap"""
    dead_end = False
    target_score = score_matrix[row][col]
    for n in range(target):
        if direction == 'col':
            col -= 1
            ali_seqA += gap_char
            ali_seqB += sequenceB[col]
        else:
            row -= 1
            ali_seqA += sequenceA[row]
            ali_seqB += gap_char
        actual_score = score_matrix[row][col] + gap_fn(index, n + 1)
        if rint(actual_score) == rint(target_score) and n > 0:
            if not trace_matrix[row][col]:
                break
            else:
                in_process.append((ali_seqA[:], ali_seqB[:], end, row, col,
                                   col_gap, trace_matrix[row][col]))
        if not trace_matrix[row][col]:
            dead_end = True
    return ali_seqA, ali_seqB, row, col, in_process, dead_end


_PRECISION = 1000


def rint(x, precision=_PRECISION):
    return int(x * precision + 0.5)


class identity_match(object):
    """identity_match([match][, mismatch]) -> match_fn

    Create a match function for use in an alignment.  match and
    mismatch are the scores to give when two residues are equal or
    unequal.  By default, match is 1 and mismatch is 0.
    """
    def __init__(self, match=1, mismatch=0):
        self.match = match
        self.mismatch = mismatch

    def __call__(self, charA, charB):
        if charA == charB:
            return self.match
        return self.mismatch


class dictionary_match(object):
    """dictionary_match(score_dict[, symmetric]) -> match_fn

    Create a match function for use in an alignment. score_dict is a
    dictionary where the keys are tuples (residue 1, residue 2) and
    the values are the match scores between those residues.  symmetric
    is a flag that indicates whether the scores are symmetric.  If
    true, then if (res 1, res 2) doesn't exist, I will use the score
    at (res 2, res 1).
    """
    def __init__(self, score_dict, symmetric=1):
        self.score_dict = score_dict
        self.symmetric = symmetric

    def __call__(self, charA, charB):
        if self.symmetric and (charA, charB) not in self.score_dict:
            # If the score dictionary is symmetric, then look up the
            # score both ways.
            charB, charA = charA, charB
        return self.score_dict[(charA, charB)]


class affine_penalty(object):
    """affine_penalty(open, extend[, penalize_extend_when_opening]) -> gap_fn

    Create a gap function for use in an alignment.
    """
    def __init__(self, open, extend, penalize_extend_when_opening=0):
        if open > 0 or extend > 0:
            raise ValueError("Gap penalties should be non-positive.")
        if not penalize_extend_when_opening and (extend < open):
            raise ValueError("Gap opening penalty should be higher than " +
                             "gap extension penalty (or equal)")
        self.open, self.extend = open, extend
        self.penalize_extend_when_opening = penalize_extend_when_opening

    def __call__(self, index, length):
        return calc_affine_penalty(
            length, self.open, self.extend, self.penalize_extend_when_opening)


def calc_affine_penalty(length, open, extend, penalize_extend_when_opening):
    if length <= 0:
        return 0
    penalty = open + extend * length
    if not penalize_extend_when_opening:
        penalty -= extend
    return penalty


def print_matrix(matrix):
    """print_matrix(matrix)

    Print out a matrix.  For debugging purposes.
    """
    # Transpose the matrix and get the length of the values in each column.
    matrixT = [[] for x in range(len(matrix[0]))]
    for i in range(len(matrix)):
        for j in range(len(matrix[i])):
            matrixT[j].append(len(str(matrix[i][j])))
    ndigits = [max(x) for x in matrixT]
    for i in range(len(matrix)):
        # Using string formatting trick to add leading spaces,
        print(" ".join("%*s " % (ndigits[j], matrix[i][j])
                       for j in range(len(matrix[i]))))


def format_alignment(align1, align2, score, begin, end):
    """format_alignment(align1, align2, score, begin, end) -> string

    Format the alignment prettily into a string.
    """
    s = []
    s.append("%s\n" % align1)
    s.append("%s%s\n" % (" " * begin, "|" * (end - begin)))
    s.append("%s\n" % align2)
    s.append("  Score=%g\n" % score)
    return ''.join(s)


# Try and load C implementations of functions. If I can't,
# then throw a warning and use the pure Python implementations.
try:
    from .cpairwise2 import rint, _make_score_matrix_fast
except ImportError:
    warnings.warn('Import of C module failed. Falling back to pure Python ' +
                  'implementation. This may be slooow...', BiopythonWarning)
