matrix.py

# This source code is part of the Biotite package and is distributed
# under the 3-Clause BSD License. Please see 'LICENSE.rst' for further
# information.

__name__ = "biotite.sequence.align"
__author__ = "Patrick Kunzmann"

from ..sequence import Sequence
from ..seqtypes import NucleotideSequence, ProteinSequence
from ..alphabet import Alphabet
import numpy as np
import os

__all__ = ["SubstitutionMatrix"]


class SubstitutionMatrix(object):
    """
    A :class:`SubstitutionMatrix` is the foundation for scoring in
    sequence alignments.
    A :class:`SubstitutionMatrix` maps each possible pairing of a symbol
    of a first alphabet with a symbol of a second alphabet to a score
    (integer).
    
    The class uses a 2-D (m x n) :class:`ndarray`
    (dtype=:attr:`numpy.int32`),
    where each element stores the score for a symbol pairing, indexed
    by the symbol codes of the respective symbols in an *m*-length
    alphabet 1 and an *n*-length alphabet 2.
    
    There are 3 ways to creates instances:
    
    At first a 2-D :class:`ndarray` containing the scores can be
    directly provided.
    
    Secondly a dictionary can be provided, where the keys are pairing
    tuples and values are the corresponding scores.
    The pairing tuples consist of a symbol of alphabet 1 as first
    element and a symbol of alphabet 2 as second element. Parings have
    to be provided for each possible combination.
    
    At last a valid matrix name can be given, which is loaded from the
    internal matrix database. The following matrices are avaliable:
        
        - Nucleotide substitution matrices from NCBI database
            - **NUC** - Also usable with ambiguous alphabet
        
        - Protein substitution matrices from NCBI database
        
            - **PAM<n>**
            - **BLOSUM<n>**
            - **MATCH** - Only differentiates between match and mismatch
            - **IDENTITY** - Strongly penalizes mismatches
            - **GONNET** - Not usable with default protein alphabet
            - **DAYHOFF**
        
        - Corrected protein substitution matrices :footcite:`Hess2016`,
          **<BLOCKS>** is the BLOCKS version, the matrix is based on
            
            - **BLOSUM<n>_<BLOCKS>**
            - **RBLOSUM<n>_<BLOCKS>**
            - **CorBLOSUM<n>_<BLOCKS>**
    
    A list of all available matrix names is returned by
    :meth:`list_db()`.
    
    Since this class can handle two different alphabets, it is possible
    to align two different types of sequences.
    
    Objects of this class are immutable.
    
    Parameters
    ----------
    alphabet1 : Alphabet, length=m
        The first alphabet of the substitution matrix.
    alphabet2 : Alphabet, length=n
        The second alphabet of the substitution matrix.
    score_matrix : ndarray, shape=(m,n) or dict or str
        Either a symbol code indexed :class:`ndarray` containing the scores,
        or a dictionary mapping the symbol pairing to scores,
        or a string referencing a matrix in the internal database.
    
    Raises
    ------
    KeyError
        If the matrix dictionary misses a symbol given in the alphabet.
    
    References
    ----------
    
    .. footbibliography::
    
    Examples
    --------
    
    Creating a matrix for two different (nonsense) alphabets
    via a matrix dictionary:
    
    >>> alph1 = Alphabet(["foo","bar"])
    >>> alph2 = Alphabet([1,2,3])
    >>> matrix_dict = {("foo",1):5,  ("foo",2):10, ("foo",3):15,
    ...                ("bar",1):42, ("bar",2):42, ("bar",3):42}
    >>> matrix = SubstitutionMatrix(alph1, alph2, matrix_dict)
    >>> print(matrix.score_matrix())
    [[ 5 10 15]
     [42 42 42]]
    >>> print(matrix.get_score("foo", 2))
    10
    >>> print(matrix.get_score_by_code(0, 1))
    10

    Creating an identity substitution matrix via the score matrix:

    >>> alph = NucleotideSequence.alphabet_unamb
    >>> matrix = SubstitutionMatrix(alph, alph, np.identity(len(alph)))
    >>> print(matrix)
        A   C   G   T
    A   1   0   0   0
    C   0   1   0   0
    G   0   0   1   0
    T   0   0   0   1
    
    Creating a matrix via database name:
        
    >>> alph = ProteinSequence.alphabet
    >>> matrix = SubstitutionMatrix(alph, alph, "BLOSUM50")
    """
    
    # Directory of matrix files
    _db_dir = os.path.join(os.path.dirname(os.path.realpath(__file__)),
                                           "matrix_data")
    
    def __init__(self, alphabet1, alphabet2, score_matrix):
        self._alph1 = alphabet1
        self._alph2 = alphabet2
        if isinstance(score_matrix, dict):
            self._fill_with_matrix_dict(score_matrix)
        elif isinstance(score_matrix, np.ndarray):
            alph_shape = (len(alphabet1), len(alphabet2))
            if score_matrix.shape != alph_shape:
                raise ValueError(
                    f"Matrix has shape {score_matrix.shape}, "
                    f"but {alph_shape} is required"
                )
            self._matrix = score_matrix.astype(np.int32)
        elif isinstance(score_matrix, str):
            matrix_dict = SubstitutionMatrix.dict_from_db(score_matrix)
            self._fill_with_matrix_dict(matrix_dict)
        else:
            raise TypeError("Matrix must be either a dictionary, "
                            "an 2-D ndarray or a string")
        # This class is immutable and has a getter function for the
        # score matrix -> make the score matrix read-only
        self._matrix.setflags(write=False)

    def __repr__(self):
        """Represent SubstitutionMatrix as a string for debugging."""
        return f"SubstitutionMatrix({self._alph1.__repr__()}, {self._alph2.__repr__()}, " \
               f"np.{np.array_repr(self._matrix)})"

    def __eq__(self, item):
        if not isinstance(item, SubstitutionMatrix):
            return False
        if self._alph1 != item.get_alphabet1():
            return False
        if self._alph2 != item.get_alphabet2():
            return False
        if not np.array_equal(self.score_matrix(), item.score_matrix()):
            return False
        return True

    def __ne__(self, item):
        return not self == item

    def _fill_with_matrix_dict(self, matrix_dict):
        self._matrix = np.zeros(( len(self._alph1), len(self._alph2) ),
                                dtype=np.int32)
        for i in range(len(self._alph1)):
            for j in range(len(self._alph2)):
                sym1 = self._alph1.decode(i)
                sym2 = self._alph2.decode(j)
                self._matrix[i,j] = int(matrix_dict[sym1, sym2])
    
    def get_alphabet1(self):
        """
        Get the first alphabet. 
        
        Returns
        -------
        alphabet : Alphabet
            The first alphabet.
        """
        return self._alph1
    
    def get_alphabet2(self):
        """
        Get the second alphabet. 
        
        Returns
        -------
        alphabet : Alphabet
            The second alphabet.
        """
        return self._alph2
    
    def score_matrix(self):
        """
        Get the 2-D :class:`ndarray` containing the score values.
        
        Returns
        -------
        matrix : ndarray, shape=(m,n), dtype=np.int32
            The symbol code indexed score matrix.
            The array is read-only.
        """
        return self._matrix
    
    def transpose(self):
        """
        Get a copy of this instance, where the alphabets are
        interchanged.
        
        Returns
        -------
        transposed : SubstitutionMatrix
            The transposed substitution matrix.
        """
        new_alph1 = self._alph2
        new_alph2 = self._alph1
        new_matrix = np.transpose(self._matrix)
        return SubstitutionMatrix(new_alph1, new_alph2, new_matrix)
    
    def is_symmetric(self):
        """
        Check whether the substitution matrix is symmetric,
        i.e. both alphabets are identical
        and the score matrix is symmetric.

        Returns
        -------
        is_symmetric : bool
            True, if both alphabets are identical and the score matrix
            is symmetric, false otherwise.
        """
        return     self._alph1 == self._alph2 \
               and np.array_equal(self._matrix, np.transpose(self._matrix))
    
    def get_score_by_code(self, code1, code2):
        """
        Get the substitution score of two symbols,
        represented by their code.
        
        Parameters
        ----------
        code1, code2 : int
            Symbol codes of the two symbols to be aligned.
        
        Returns
        -------
        score : int
            The substitution / alignment score.
        """
        return self._matrix[code1, code2]
    
    def get_score(self, symbol1, symbol2):
        """
        Get the substitution score of two symbols.
        
        Parameters
        ----------
        symbol1, symbol2 : object
            Symbols to be aligned.
        
        Returns
        -------
        score : int
            The substitution / alignment score.
        """
        code1 = self._alph1.encode(symbol1)
        code2 = self._alph2.encode(symbol2)
        return self._matrix[code1, code2]
    
    def shape(self):
        """
        Get the shape (i.e. the length of both alphabets)
        of the subsitution matrix.
        
        Returns
        -------
        shape : tuple
            Matrix shape.
        """
        return (len(self._alph1), len(self._alph2))
    
    def __str__(self):
        # Create matrix in NCBI format
        string = " "
        for symbol in self._alph2:
            string += f" {symbol:>3}"
        string += "\n"
        for i, symbol in enumerate(self._alph1):
            string += f"{symbol:>1}"
            for j in range(len(self._alph2)):
                string += f" {int(self._matrix[i,j]):>3d}"
            string += "\n"
        # Remove terminal line break
        string = string[:-1]
        return string
    
    @staticmethod
    def dict_from_str(string):
        """
        Create a matrix dictionary from a string in NCBI matrix format.
        
        Symbols of the first alphabet are taken from the left column,
        symbols of the second alphabet are taken from the top row.
        
        The keys of the dictionary consist of tuples containing the
        aligned symbols and the values are the corresponding scores.
        
        Returns
        -------
        matrix_dict : dict
            A dictionary representing the substitution matrix.
        """
        lines = [line.strip() for line in string.split("\n")]
        lines = [line for line in lines if len(line) != 0 and line[0] != "#"]
        symbols1 = [line.split()[0] for line in lines[1:]]
        symbols2 = [e for e in lines[0].split()]
        scores = np.array([line.split()[1:] for line in lines[1:]]).astype(int)
        scores = np.transpose(scores)
        
        matrix_dict = {}
        for i in range(len(symbols1)):
            for j in range(len(symbols2)):
                matrix_dict[(symbols1[i], symbols2[j])] = scores[i,j]
        return matrix_dict
    
    @staticmethod
    def dict_from_db(matrix_name):
        """
        Create a matrix dictionary from a valid matrix name in the
        internal matrix database.
        
        The keys of the dictionary consist of tuples containing the
        aligned symbols and the values are the corresponding scores.
        
        Returns
        -------
        matrix_dict : dict
            A dictionary representing the substitution matrix.
        """
        filename = SubstitutionMatrix._db_dir + os.sep + matrix_name + ".mat"
        with open(filename, "r") as f:
            return SubstitutionMatrix.dict_from_str(f.read())
    
    @staticmethod
    def list_db():
        """
        List all matrix names in the internal database.
        
        Returns
        -------
        db_list : list
            List of matrix names in the internal database.
        """
        files = os.listdir(SubstitutionMatrix._db_dir)
        # Remove '.mat' from files
        return [file[:-4] for file in sorted(files)]
        
    
    @staticmethod
    def std_protein_matrix():
        """
        Get the default :class:`SubstitutionMatrix` for protein sequence
        alignments, which is BLOSUM62.
        
        Returns
        -------
        matrix : SubstitutionMatrix
            Default matrix.
        """
        return _matrix_blosum62
    
    @staticmethod
    def std_nucleotide_matrix():
        """
        Get the default :class:`SubstitutionMatrix` for DNA sequence
        alignments.
        
        Returns
        -------
        matrix : SubstitutionMatrix
            Default matrix.
        """
        return _matrix_nuc

# Preformatted BLOSUM62 and NUC substitution matrix from NCBI
_matrix_blosum62 = SubstitutionMatrix(ProteinSequence.alphabet,
                                      ProteinSequence.alphabet,
                                      "BLOSUM62")
_matrix_nuc = SubstitutionMatrix(NucleotideSequence.alphabet_amb,
                                 NucleotideSequence.alphabet_amb,
                                 "NUC")