"""

=============================================================
Online Latent Dirichlet Allocation with variational inference
=============================================================

This implementation is modified from Matthew D. Hoffman's onlineldavb code
Link: https://github.com/blei-lab/onlineldavb
"""

# Author: Chyi-Kwei Yau
# Author: Matthew D. Hoffman (original onlineldavb implementation)

import numpy as np
import scipy.sparse as sp
from scipy.special import gammaln, logsumexp
from joblib import Parallel, delayed, effective_n_jobs

from ..base import BaseEstimator, TransformerMixin
from ..utils import check_random_state, gen_batches, gen_even_slices
from ..utils.validation import check_non_negative
from ..utils.validation import check_is_fitted
from ..utils.validation import _deprecate_positional_args

from ._online_lda_fast import (mean_change, _dirichlet_expectation_1d,
                               _dirichlet_expectation_2d)

EPS = np.finfo(np.float).eps


def _update_doc_distribution(X, exp_topic_word_distr, doc_topic_prior,
                             max_iters,
                             mean_change_tol, cal_sstats, random_state):
    """E-step: update document-topic distribution.

    Parameters
    ----------
    X : array-like or sparse matrix, shape=(n_samples, n_features)
        Document word matrix.

    exp_topic_word_distr : dense matrix, shape=(n_topics, n_features)
        Exponential value of expectation of log topic word distribution.
        In the literature, this is `exp(E[log(beta)])`.

    doc_topic_prior : float
        Prior of document topic distribution `theta`.

    max_iters : int
        Max number of iterations for updating document topic distribution in
        the E-step.

    mean_change_tol : float
        Stopping tolerance for updating document topic distribution in E-setp.

    cal_sstats : boolean
        Parameter that indicate to calculate sufficient statistics or not.
        Set `cal_sstats` to `True` when we need to run M-step.

    random_state : RandomState instance or None
        Parameter that indicate how to initialize document topic distribution.
        Set `random_state` to None will initialize document topic distribution
        to a constant number.

    Returns
    -------
    (doc_topic_distr, suff_stats) :
        `doc_topic_distr` is unnormalized topic distribution for each document.
        In the literature, this is `gamma`. we can calculate `E[log(theta)]`
        from it.
        `suff_stats` is expected sufficient statistics for the M-step.
            When `cal_sstats == False`, this will be None.

    """
    is_sparse_x = sp.issparse(X)
    n_samples, n_features = X.shape
    n_topics = exp_topic_word_distr.shape[0]

    if random_state:
        doc_topic_distr = random_state.gamma(100., 0.01, (n_samples, n_topics))
    else:
        doc_topic_distr = np.ones((n_samples, n_topics))

    # In the literature, this is `exp(E[log(theta)])`
    exp_doc_topic = np.exp(_dirichlet_expectation_2d(doc_topic_distr))

    # diff on `component_` (only calculate it when `cal_diff` is True)
    suff_stats = np.zeros(exp_topic_word_distr.shape) if cal_sstats else None

    if is_sparse_x:
        X_data = X.data
        X_indices = X.indices
        X_indptr = X.indptr

    for idx_d in range(n_samples):
        if is_sparse_x:
            ids = X_indices[X_indptr[idx_d]:X_indptr[idx_d + 1]]
            cnts = X_data[X_indptr[idx_d]:X_indptr[idx_d + 1]]
        else:
            ids = np.nonzero(X[idx_d, :])[0]
            cnts = X[idx_d, ids]

        doc_topic_d = doc_topic_distr[idx_d, :]
        # The next one is a copy, since the inner loop overwrites it.
        exp_doc_topic_d = exp_doc_topic[idx_d, :].copy()
        exp_topic_word_d = exp_topic_word_distr[:, ids]

        # Iterate between `doc_topic_d` and `norm_phi` until convergence
        for _ in range(0, max_iters):
            last_d = doc_topic_d

            # The optimal phi_{dwk} is proportional to
            # exp(E[log(theta_{dk})]) * exp(E[log(beta_{dw})]).
            norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS

            doc_topic_d = (exp_doc_topic_d *
                           np.dot(cnts / norm_phi, exp_topic_word_d.T))
            # Note: adds doc_topic_prior to doc_topic_d, in-place.
            _dirichlet_expectation_1d(doc_topic_d, doc_topic_prior,
                                      exp_doc_topic_d)

            if mean_change(last_d, doc_topic_d) < mean_change_tol:
                break
        doc_topic_distr[idx_d, :] = doc_topic_d

        # Contribution of document d to the expected sufficient
        # statistics for the M step.
        if cal_sstats:
            norm_phi = np.dot(exp_doc_topic_d, exp_topic_word_d) + EPS
            suff_stats[:, ids] += np.outer(exp_doc_topic_d, cnts / norm_phi)

    return (doc_topic_distr, suff_stats)


class LatentDirichletAllocation(TransformerMixin, BaseEstimator):
    """Latent Dirichlet Allocation with online variational Bayes algorithm

    .. versionadded:: 0.17

    Read more in the :ref:`User Guide <LatentDirichletAllocation>`.

    Parameters
    ----------
    n_components : int, optional (default=10)
        Number of topics.

        .. versionchanged:: 0.19
            ``n_topics `` was renamed to ``n_components``

    doc_topic_prior : float, optional (default=None)
        Prior of document topic distribution `theta`. If the value is None,
        defaults to `1 / n_components`.
        In [1]_, this is called `alpha`.

    topic_word_prior : float, optional (default=None)
        Prior of topic word distribution `beta`. If the value is None, defaults
        to `1 / n_components`.
        In [1]_, this is called `eta`.

    learning_method : 'batch' | 'online', default='batch'
        Method used to update `_component`. Only used in :meth:`fit` method.
        In general, if the data size is large, the online update will be much
        faster than the batch update.

        Valid options::

            'batch': Batch variational Bayes method. Use all training data in
                each EM update.
                Old `components_` will be overwritten in each iteration.
            'online': Online variational Bayes method. In each EM update, use
                mini-batch of training data to update the ``components_``
                variable incrementally. The learning rate is controlled by the
                ``learning_decay`` and the ``learning_offset`` parameters.

        .. versionchanged:: 0.20
            The default learning method is now ``"batch"``.

    learning_decay : float, optional (default=0.7)
        It is a parameter that control learning rate in the online learning
        method. The value should be set between (0.5, 1.0] to guarantee
        asymptotic convergence. When the value is 0.0 and batch_size is
        ``n_samples``, the update method is same as batch learning. In the
        literature, this is called kappa.

    learning_offset : float, optional (default=10.)
        A (positive) parameter that downweights early iterations in online
        learning.  It should be greater than 1.0. In the literature, this is
        called tau_0.

    max_iter : integer, optional (default=10)
        The maximum number of iterations.

    batch_size : int, optional (default=128)
        Number of documents to use in each EM iteration. Only used in online
        learning.

    evaluate_every : int, optional (default=0)
        How often to evaluate perplexity. Only used in `fit` method.
        set it to 0 or negative number to not evaluate perplexity in
        training at all. Evaluating perplexity can help you check convergence
        in training process, but it will also increase total training time.
        Evaluating perplexity in every iteration might increase training time
        up to two-fold.

    total_samples : int, optional (default=1e6)
        Total number of documents. Only used in the :meth:`partial_fit` method.

    perp_tol : float, optional (default=1e-1)
        Perplexity tolerance in batch learning. Only used when
        ``evaluate_every`` is greater than 0.

    mean_change_tol : float, optional (default=1e-3)
        Stopping tolerance for updating document topic distribution in E-step.

    max_doc_update_iter : int (default=100)
        Max number of iterations for updating document topic distribution in
        the E-step.

    n_jobs : int or None, optional (default=None)
        The number of jobs to use in the E-step.
        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
        for more details.

    verbose : int, optional (default=0)
        Verbosity level.

    random_state : int, RandomState instance, default=None
        Pass an int for reproducible results across multiple function calls.
        See :term:`Glossary <random_state>`.

    Attributes
    ----------
    components_ : array, [n_components, n_features]
        Variational parameters for topic word distribution. Since the complete
        conditional for topic word distribution is a Dirichlet,
        ``components_[i, j]`` can be viewed as pseudocount that represents the
        number of times word `j` was assigned to topic `i`.
        It can also be viewed as distribution over the words for each topic
        after normalization:
        ``model.components_ / model.components_.sum(axis=1)[:, np.newaxis]``.

    n_batch_iter_ : int
        Number of iterations of the EM step.

    n_iter_ : int
        Number of passes over the dataset.

    bound_ : float
        Final perplexity score on training set.

    doc_topic_prior_ : float
        Prior of document topic distribution `theta`. If the value is None,
        it is `1 / n_components`.

    topic_word_prior_ : float
        Prior of topic word distribution `beta`. If the value is None, it is
        `1 / n_components`.

    Examples
    --------
    >>> from sklearn.decomposition import LatentDirichletAllocation
    >>> from sklearn.datasets import make_multilabel_classification
    >>> # This produces a feature matrix of token counts, similar to what
    >>> # CountVectorizer would produce on text.
    >>> X, _ = make_multilabel_classification(random_state=0)
    >>> lda = LatentDirichletAllocation(n_components=5,
    ...     random_state=0)
    >>> lda.fit(X)
    LatentDirichletAllocation(...)
    >>> # get topics for some given samples:
    >>> lda.transform(X[-2:])
    array([[0.00360392, 0.25499205, 0.0036211 , 0.64236448, 0.09541846],
           [0.15297572, 0.00362644, 0.44412786, 0.39568399, 0.003586  ]])

    References
    ----------
    .. [1] "Online Learning for Latent Dirichlet Allocation", Matthew D.
        Hoffman, David M. Blei, Francis Bach, 2010

    [2] "Stochastic Variational Inference", Matthew D. Hoffman, David M. Blei,
        Chong Wang, John Paisley, 2013

    [3] Matthew D. Hoffman's onlineldavb code. Link:
        https://github.com/blei-lab/onlineldavb

    """
    @_deprecate_positional_args
    def __init__(self, n_components=10, *, doc_topic_prior=None,
                 topic_word_prior=None, learning_method='batch',
                 learning_decay=.7, learning_offset=10., max_iter=10,
                 batch_size=128, evaluate_every=-1, total_samples=1e6,
                 perp_tol=1e-1, mean_change_tol=1e-3, max_doc_update_iter=100,
                 n_jobs=None, verbose=0, random_state=None):
        self.n_components = n_components
        self.doc_topic_prior = doc_topic_prior
        self.topic_word_prior = topic_word_prior
        self.learning_method = learning_method
        self.learning_decay = learning_decay
        self.learning_offset = learning_offset
        self.max_iter = max_iter
        self.batch_size = batch_size
        self.evaluate_every = evaluate_every
        self.total_samples = total_samples
        self.perp_tol = perp_tol
        self.mean_change_tol = mean_change_tol
        self.max_doc_update_iter = max_doc_update_iter
        self.n_jobs = n_jobs
        self.verbose = verbose
        self.random_state = random_state

    def _check_params(self):
        """Check model parameters."""
        if self.n_components <= 0:
            raise ValueError("Invalid 'n_components' parameter: %r"
                             % self.n_components)

        if self.total_samples <= 0:
            raise ValueError("Invalid 'total_samples' parameter: %r"
                             % self.total_samples)

        if self.learning_offset < 0:
            raise ValueError("Invalid 'learning_offset' parameter: %r"
                             % self.learning_offset)

        if self.learning_method not in ("batch", "online"):
            raise ValueError("Invalid 'learning_method' parameter: %r"
                             % self.learning_method)

    def _init_latent_vars(self, n_features):
        """Initialize latent variables."""

        self.random_state_ = check_random_state(self.random_state)
        self.n_batch_iter_ = 1
        self.n_iter_ = 0

        if self.doc_topic_prior is None:
            self.doc_topic_prior_ = 1. / self.n_components
        else:
            self.doc_topic_prior_ = self.doc_topic_prior

        if self.topic_word_prior is None:
            self.topic_word_prior_ = 1. / self.n_components
        else:
            self.topic_word_prior_ = self.topic_word_prior