# Copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from collections import namedtuple

import numpy as np

try:
    from scipy.stats import distributions as sp_distributions
except ImportError:
    sp_distributions = None

from ...core import ExecutableTuple
from ...utils import require_not_none
from .. import special
from ..datasource import asarray


# Map from names to lambda_ values used in power_divergence().
_power_div_lambda_names = {
    "pearson": 1,
    "log-likelihood": 0,
    "freeman-tukey": -0.5,
    "mod-log-likelihood": -1,
    "neyman": -2,
    "cressie-read": 2 / 3,
}


def _count(a, axis=None):
    if axis is None:
        return a.size
    else:
        return a.shape[axis]


Power_divergenceResult = namedtuple("Power_divergenceResult", ("statistic", "pvalue"))


@require_not_none(sp_distributions)
def power_divergence(f_obs, f_exp=None, ddof=0, axis=0, lambda_=None):
    """
    Cressie-Read power divergence statistic and goodness of fit test.

    This function tests the null hypothesis that the categorical data
    has the given frequencies, using the Cressie-Read power divergence
    statistic.

    Parameters
    ----------
    f_obs : array_like
        Observed frequencies in each category.
    f_exp : array_like, optional
        Expected frequencies in each category.  By default the categories are
        assumed to be equally likely.
    ddof : int, optional
        "Delta degrees of freedom": adjustment to the degrees of freedom
        for the p-value.  The p-value is computed using a chi-squared
        distribution with ``k - 1 - ddof`` degrees of freedom, where `k`
        is the number of observed frequencies.  The default value of `ddof`
        is 0.
    axis : int or None, optional
        The axis of the broadcast result of `f_obs` and `f_exp` along which to
        apply the test.  If axis is None, all values in `f_obs` are treated
        as a single data set.  Default is 0.
    lambda_ : float or str, optional
        The power in the Cressie-Read power divergence statistic.  The default
        is 1.  For convenience, `lambda_` may be assigned one of the following
        strings, in which case the corresponding numerical value is used::

            String              Value   Description
            "pearson"             1     Pearson's chi-squared statistic.
                                        In this case, the function is
                                        equivalent to `stats.chisquare`.
            "log-likelihood"      0     Log-likelihood ratio. Also known as
                                        the G-test [3]_.
            "freeman-tukey"      -1/2   Freeman-Tukey statistic.
            "mod-log-likelihood" -1     Modified log-likelihood ratio.
            "neyman"             -2     Neyman's statistic.
            "cressie-read"        2/3   The power recommended in [5]_.

    Returns
    -------
    statistic : float or ndarray
        The Cressie-Read power divergence test statistic.  The value is
        a float if `axis` is None or if` `f_obs` and `f_exp` are 1-D.
    pvalue : float or ndarray
        The p-value of the test.  The value is a float if `ddof` and the
        return value `stat` are scalars.

    See Also
    --------
    chisquare

    Notes
    -----
    This test is invalid when the observed or expected frequencies in each
    category are too small.  A typical rule is that all of the observed
    and expected frequencies should be at least 5.

    When `lambda_` is less than zero, the formula for the statistic involves
    dividing by `f_obs`, so a warning or error may be generated if any value
    in `f_obs` is 0.

    Similarly, a warning or error may be generated if any value in `f_exp` is
    zero when `lambda_` >= 0.

    The default degrees of freedom, k-1, are for the case when no parameters
    of the distribution are estimated. If p parameters are estimated by
    efficient maximum likelihood then the correct degrees of freedom are
    k-1-p. If the parameters are estimated in a different way, then the
    dof can be between k-1-p and k-1. However, it is also possible that
    the asymptotic distribution is not a chisquare, in which case this
    test is not appropriate.

    This function handles masked arrays.  If an element of `f_obs` or `f_exp`
    is masked, then data at that position is ignored, and does not count
    towards the size of the data set.

    .. versionadded:: 0.13.0

    References
    ----------
    .. [1] Lowry, Richard.  "Concepts and Applications of Inferential
           Statistics". Chapter 8.
           https://web.archive.org/web/20171015035606/http://faculty.vassar.edu/lowry/ch8pt1.html
    .. [2] "Chi-squared test", https://en.wikipedia.org/wiki/Chi-squared_test
    .. [3] "G-test", https://en.wikipedia.org/wiki/G-test
    .. [4] Sokal, R. R. and Rohlf, F. J. "Biometry: the principles and
           practice of statistics in biological research", New York: Freeman
           (1981)
    .. [5] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
           pp. 440-464.

    Examples
    --------
    (See `chisquare` for more examples.)

    When just `f_obs` is given, it is assumed that the expected frequencies
    are uniform and given by the mean of the observed frequencies.  Here we
    perform a G-test (i.e. use the log-likelihood ratio statistic):

    >>> import mars.tensor as mt
    >>> from mars.tensor.stats import power_divergence
    >>> power_divergence([16, 18, 16, 14, 12, 12], lambda_='log-likelihood').execute()
    (2.006573162632538, 0.84823476779463769)

    The expected frequencies can be given with the `f_exp` argument:

    >>> power_divergence([16, 18, 16, 14, 12, 12],
    ...                  f_exp=[16, 16, 16, 16, 16, 8],
    ...                  lambda_='log-likelihood').execute()
    (3.3281031458963746, 0.6495419288047497)

    When `f_obs` is 2-D, by default the test is applied to each column.

    >>> obs = mt.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T
    >>> obs.shape
    (6, 2)
    >>> power_divergence(obs, lambda_="log-likelihood").execute()
    (array([ 2.00657316,  6.77634498]), array([ 0.84823477,  0.23781225]))

    By setting ``axis=None``, the test is applied to all data in the array,
    which is equivalent to applying the test to the flattened array.

    >>> power_divergence(obs, axis=None).execute()
    (23.31034482758621, 0.015975692534127565)
    >>> power_divergence(obs.ravel()).execute()
    (23.31034482758621, 0.015975692534127565)

    `ddof` is the change to make to the default degrees of freedom.

    >>> power_divergence([16, 18, 16, 14, 12, 12], ddof=1).execute()
    (2.0, 0.73575888234288467)

    `f_obs` and `f_exp` are also broadcast.  In the following, `f_obs` has
    shape (6,) and `f_exp` has shape (2, 6), so the result of broadcasting
    `f_obs` and `f_exp` has shape (2, 6).  To compute the desired chi-squared
    statistics, we must use ``axis=1``:

    >>> power_divergence([16, 18, 16, 14, 12, 12],
    ...                  f_exp=[[16, 16, 16, 16, 16, 8],
    ...                         [8, 20, 20, 16, 12, 12]],
    ...                  axis=1)
    (array([ 3.5 ,  9.25]), array([ 0.62338763,  0.09949846]))
    """
    # Convert the input argument `lambda_` to a numerical value.
    if isinstance(lambda_, str):
        if lambda_ not in _power_div_lambda_names:
            names = repr(list(_power_div_lambda_names.keys()))[1:-1]
            raise ValueError(
                "invalid string for lambda_: {0!r}.  Valid strings "
                "are {1}".format(lambda_, names)
            )
        lambda_ = _power_div_lambda_names[lambda_]
    elif lambda_ is None:
        lambda_ = 1

    f_obs = asarray(f_obs)

    if f_exp is not None:
        f_exp = asarray(f_exp)
    else:
        f_exp = f_obs.mean(axis=axis, keepdims=True)

    # `terms` is the array of terms that are summed along `axis` to create
    # the test statistic.  We use some specialized code for a few special
    # cases of lambda_.
    if lambda_ == 1:
        # Pearson's chi-squared statistic
        terms = (f_obs.astype(np.float64) - f_exp) ** 2 / f_exp
    elif lambda_ == 0:
        # Log-likelihood ratio (i.e. G-test)
        terms = 2.0 * special.xlogy(f_obs, f_obs / f_exp)
    elif lambda_ == -1:
        # Modified log-likelihood ratio
        terms = 2.0 * special.xlogy(f_exp, f_exp / f_obs)
    else:
        # General Cressie-Read power divergence.
        terms = f_obs * ((f_obs / f_exp) ** lambda_ - 1)
        terms /= 0.5 * lambda_ * (lambda_ + 1)

    stat = terms.sum(axis=axis)

    num_obs = _count(terms, axis=axis)
    # we decide not to support ddof for multiple dimensions
    # ddof = asarray(ddof)
    p = stat.map_chunk(
        sp_distributions.chi2.sf, (num_obs - 1 - ddof,), elementwise=True
    )

    return ExecutableTuple(Power_divergenceResult(stat, p))
