"""Base class for mixture models."""

# Author: Wei Xue <xuewei4d@gmail.com>
# Modified by Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause

import warnings
from abc import ABCMeta, abstractmethod
from time import time

import numpy as np
from scipy.special import logsumexp

from .. import cluster
from ..base import BaseEstimator
from ..base import DensityMixin
from ..exceptions import ConvergenceWarning
from ..utils import check_array, check_random_state
from ..utils.validation import check_is_fitted


def _check_shape(param, param_shape, name):
    """Validate the shape of the input parameter 'param'.

    Parameters
    ----------
    param : array

    param_shape : tuple

    name : string
    """
    param = np.array(param)
    if param.shape != param_shape:
        raise ValueError("The parameter '%s' should have the shape of %s, "
                         "but got %s" % (name, param_shape, param.shape))


def _check_X(X, n_components=None, n_features=None, ensure_min_samples=1):
    """Check the input data X.

    Parameters
    ----------
    X : array-like, shape (n_samples, n_features)

    n_components : int

    Returns
    -------
    X : array, shape (n_samples, n_features)
    """
    X = check_array(X, dtype=[np.float64, np.float32],
                    ensure_min_samples=ensure_min_samples)
    if n_components is not None and X.shape[0] < n_components:
        raise ValueError('Expected n_samples >= n_components '
                         'but got n_components = %d, n_samples = %d'
                         % (n_components, X.shape[0]))
    if n_features is not None and X.shape[1] != n_features:
        raise ValueError("Expected the input data X have %d features, "
                         "but got %d features"
                         % (n_features, X.shape[1]))
    return X


class BaseMixture(DensityMixin, BaseEstimator, metaclass=ABCMeta):
    """Base class for mixture models.

    This abstract class specifies an interface for all mixture classes and
    provides basic common methods for mixture models.
    """

    def __init__(self, n_components, tol, reg_covar,
                 max_iter, n_init, init_params, random_state, warm_start,
                 verbose, verbose_interval):
        self.n_components = n_components
        self.tol = tol
        self.reg_covar = reg_covar
        self.max_iter = max_iter
        self.n_init = n_init
        self.init_params = init_params
        self.random_state = random_state
        self.warm_start = warm_start
        self.verbose = verbose
        self.verbose_interval = verbose_interval

    def _check_initial_parameters(self, X):
        """Check values of the basic parameters.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
        """
        if self.n_components < 1:
            raise ValueError("Invalid value for 'n_components': %d "
                             "Estimation requires at least one component"
                             % self.n_components)

        if self.tol < 0.:
            raise ValueError("Invalid value for 'tol': %.5f "
                             "Tolerance used by the EM must be non-negative"
                             % self.tol)

        if self.n_init < 1:
            raise ValueError("Invalid value for 'n_init': %d "
                             "Estimation requires at least one run"
                             % self.n_init)

        if self.max_iter < 1:
            raise ValueError("Invalid value for 'max_iter': %d "
                             "Estimation requires at least one iteration"
                             % self.max_iter)

        if self.reg_covar < 0.:
            raise ValueError("Invalid value for 'reg_covar': %.5f "
                             "regularization on covariance must be "
                             "non-negative"
                             % self.reg_covar)

        # Check all the parameters values of the derived class
        self._check_parameters(X)

    @abstractmethod
    def _check_parameters(self, X):
        """Check initial parameters of the derived class.

        Parameters
        ----------
        X : array-like, shape  (n_samples, n_features)
        """
        pass

    def _initialize_parameters(self, X, random_state):
        """Initialize the model parameters.

        Parameters
        ----------
        X : array-like, shape  (n_samples, n_features)

        random_state : RandomState
            A random number generator instance that controls the random seed
            used for the method chosen to initialize the parameters.
        """
        n_samples, _ = X.shape

        if self.init_params == 'kmeans':
            resp = np.zeros((n_samples, self.n_components))
            label = cluster.KMeans(n_clusters=self.n_components, n_init=1,
                                   random_state=random_state).fit(X).labels_
            resp[np.arange(n_samples), label] = 1
        elif self.init_params == 'random':
            resp = random_state.rand(n_samples, self.n_components)
            resp /= resp.sum(axis=1)[:, np.newaxis]
        else:
            raise ValueError("Unimplemented initialization method '%s'"
                             % self.init_params)

        self._initialize(X, resp)

    @abstractmethod
    def _initialize(self, X, resp):
        """Initialize the model parameters of the derived class.

        Parameters
        ----------
        X : array-like, shape  (n_samples, n_features)

        resp : array-like, shape (n_samples, n_components)
        """
        pass

    def fit(self, X, y=None):
        """Estimate model parameters with the EM algorithm.

        The method fits the model ``n_init`` times and sets the parameters with
        which the model has the largest likelihood or lower bound. Within each
        trial, the method iterates between E-step and M-step for ``max_iter``
        times until the change of likelihood or lower bound is less than
        ``tol``, otherwise, a ``ConvergenceWarning`` is raised.
        If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
        initialization is performed upon the first call. Upon consecutive
        calls, training starts where it left off.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        Returns
        -------
        self
        """
        self.fit_predict(X, y)
        return self

    def fit_predict(self, X, y=None):
        """Estimate model parameters using X and predict the labels for X.

        The method fits the model n_init times and sets the parameters with
        which the model has the largest likelihood or lower bound. Within each
        trial, the method iterates between E-step and M-step for `max_iter`
        times until the change of likelihood or lower bound is less than
        `tol`, otherwise, a :class:`~sklearn.exceptions.ConvergenceWarning` is
        raised. After fitting, it predicts the most probable label for the
        input data points.

        .. versionadded:: 0.20

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        Returns
        -------
        labels : array, shape (n_samples,)
            Component labels.
        """
        X = _check_X(X, self.n_components, ensure_min_samples=2)
        self._check_n_features(X, reset=True)
        self._check_initial_parameters(X)

        # if we enable warm_start, we will have a unique initialisation
        do_init = not(self.warm_start and hasattr(self, 'converged_'))
        n_init = self.n_init if do_init else 1

        max_lower_bound = -np.infty
        self.converged_ = False

        random_state = check_random_state(self.random_state)

        n_samples, _ = X.shape
        for init in range(n_init):
            self._print_verbose_msg_init_beg(init)

            if do_init:
                self._initialize_parameters(X, random_state)

            lower_bound = (-np.infty if do_init else self.lower_bound_)

            for n_iter in range(1, self.max_iter + 1):
                prev_lower_bound = lower_bound

                log_prob_norm, log_resp = self._e_step(X)
                self._m_step(X, log_resp)
                lower_bound = self._compute_lower_bound(
                    log_resp, log_prob_norm)

                change = lower_bound - prev_lower_bound
                self._print_verbose_msg_iter_end(n_iter, change)

                if abs(change) < self.tol:
                    self.converged_ = True
                    break

            self._print_verbose_msg_init_end(lower_bound)

            if lower_bound > max_lower_bound:
                max_lower_bound = lower_bound
                best_params = self._get_parameters()
                best_n_iter = n_iter

        if not self.converged_:
            warnings.warn('Initialization %d did not converge. '
                          'Try different init parameters, '
                          'or increase max_iter, tol '
                          'or check for degenerate data.'
                          % (init + 1), ConvergenceWarning)

        self._set_parameters(best_params)
        self.n_iter_ = best_n_iter
        self.lower_bound_ = max_lower_bound

        # Always do a final e-step to guarantee that the labels returned by
        # fit_predict(X) are always consistent with fit(X).predict(X)
        # for any value of max_iter and tol (and any random_state).
        _, log_resp = self._e_step(X)

        return log_resp.argmax(axis=1)

    def _e_step(self, X):
        """E step.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)

        Returns
        -------
        log_prob_norm : float
            Mean of the logarithms of the probabilities of each sample in X

        log_responsibility : array, shape (n_samples, n_components)
            Logarithm of the posterior probabilities (or responsibilities) of
            the point of each sample in X.
        """
        log_prob_norm, log_resp = self._estimate_log_prob_resp(X)
        return np.mean(log_prob_norm), log_resp

    @abstractmethod
    def _m_step(self, X, log_resp):
        """M step.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)

        log_resp : array-like, shape (n_samples, n_components)
            Logarithm of the posterior probabilities (or responsibilities) of
            the point of each sample in X.
        """
        pass

    @abstractmethod
    def _get_parameters(self):
        pass

    @abstractmethod
    def _set_parameters(self, params):
        pass

    def score_samples(self, X):
        """Compute the weighted log probabilities for each sample.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        Returns
        -------
        log_prob : array, shape (n_samples,)
            Log probabilities of each data point in X.
        """
        check_is_fitted(self)
        X = _check_X(X, None, self.means_.shape[1])

        return logsumexp(self._estimate_weighted_log_prob(X), axis=1)

    def score(self, X, y=None):
        """Compute the per-sample average log-likelihood of the given data X.

        Parameters