# Copyright 2018-2020 by Christopher C. Little.
# This file is part of Abydos.
#
# Abydos is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Abydos is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Abydos. If not, see <http://www.gnu.org/licenses/>.

"""abydos.distance._minkowski.

Minkowski distance & similarity
"""

from typing import (
    Any,
    Counter as TCounter,
    Optional,
    Sequence,
    Set,
    Union,
    cast,
)

from abydos.distance._token_distance import _TokenDistance
from abydos.tokenizer import _Tokenizer

__all__ = ['Minkowski']


class Minkowski(_TokenDistance):
    """Minkowski distance.

    The Minkowski distance :cite:`Minkowski:1910` is a distance metric in
    :math:`L^p-space`.

    .. versionadded:: 0.3.6
    """

    def __init__(
        self,
        pval: float = 1,
        alphabet: Optional[
            Union[TCounter[str], Sequence[str], Set[str], int]
        ] = 0,
        tokenizer: Optional[_Tokenizer] = None,
        intersection_type: str = 'crisp',
        **kwargs: Any
    ) -> None:
        """Initialize Euclidean instance.

        Parameters
        ----------
        pval : int
            The :math:`p`-value of the :math:`L^p`-space
        alphabet : collection or int
            The values or size of the alphabet
        tokenizer : _Tokenizer
            A tokenizer instance from the :py:mod:`abydos.tokenizer` package
        intersection_type : str
            Specifies the intersection type, and set type as a result:
            See :ref:`intersection_type <intersection_type>` description in
            :py:class:`_TokenDistance` for details.
        **kwargs
            Arbitrary keyword arguments

        Other Parameters
        ----------------
        qval : int
            The length of each q-gram. Using this parameter and tokenizer=None
            will cause the instance to use the QGram tokenizer with this
            q value.
        metric : _Distance
            A string distance measure class for use in the ``soft`` and
            ``fuzzy`` variants.
        threshold : float
            A threshold value, similarities above which are counted as
            members of the intersection for the ``fuzzy`` variant.


        .. versionadded:: 0.4.0

        """
        super(Minkowski, self).__init__(
            tokenizer=tokenizer,
            alphabet=alphabet,
            intersection_type=intersection_type,
            **kwargs
        )
        self.set_params(pval=pval)

    def dist_abs(self, src: str, tar: str, normalized: bool = False) -> float:
        """Return the Minkowski distance (:math:`L^p`-norm) of two strings.

        Parameters
        ----------
        src : str
            Source string (or QGrams/Counter objects) for comparison
        tar : str
            Target string (or QGrams/Counter objects) for comparison
        normalized : bool
            Normalizes to [0, 1] if True

        Returns
        -------
        float
            The Minkowski distance

        Examples
        --------
        >>> cmp = Minkowski()
        >>> cmp.dist_abs('cat', 'hat')
        4.0
        >>> cmp.dist_abs('Niall', 'Neil')
        7.0
        >>> cmp.dist_abs('Colin', 'Cuilen')
        9.0
        >>> cmp.dist_abs('ATCG', 'TAGC')
        10.0


        .. versionadded:: 0.3.0
        .. versionchanged:: 0.3.6
            Encapsulated in class

        """
        self._tokenize(src, tar)
        diffs = self._symmetric_difference().values()

        normalizer = 1
        if normalized:
            totals = self._total().values()
            if self.params['alphabet']:
                normalizer = self.params['alphabet']
            elif self.params['pval'] == 0:
                normalizer = len(totals)
            else:
                normalizer = sum(_ ** self.params['pval'] for _ in totals) ** (
                    1 / self.params['pval']
                )

        if len(diffs) == 0:
            return 0.0
        if self.params['pval'] == float('inf'):
            # Chebyshev distance
            return max(diffs) / normalizer
        if self.params['pval'] == 0:
            # This is the l_0 "norm" as developed by David Donoho
            return sum(_ != 0 for _ in diffs) / normalizer
        return cast(
            float,
            sum(_ ** self.params['pval'] for _ in diffs)
            ** (1 / self.params['pval'])
            / normalizer,
        )

    def dist(self, src: str, tar: str) -> float:
        """Return normalized Minkowski distance of two strings.

        The normalized Minkowski distance :cite:`Minkowski:1910` is a distance
        metric in :math:`L^p`-space, normalized to [0, 1].

        Parameters
        ----------
        src : str
            Source string (or QGrams/Counter objects) for comparison
        tar : str
            Target string (or QGrams/Counter objects) for comparison

        Returns
        -------
        float
            The normalized Minkowski distance

        Examples
        --------
        >>> cmp = Minkowski()
        >>> cmp.dist('cat', 'hat')
        0.5
        >>> round(cmp.dist('Niall', 'Neil'), 12)
        0.636363636364
        >>> round(cmp.dist('Colin', 'Cuilen'), 12)
        0.692307692308
        >>> cmp.dist('ATCG', 'TAGC')
        1.0


        .. versionadded:: 0.3.0
        .. versionchanged:: 0.3.6
            Encapsulated in class

        """
        return self.dist_abs(src, tar, normalized=True)


if __name__ == '__main__':
    import doctest

    doctest.testmod()
