# Authors: Manoj Kumar <manojkumarsivaraj334@gmail.com>
#          Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
#          Joel Nothman <joel.nothman@gmail.com>
# License: BSD 3 clause

import warnings
import numbers
import numpy as np
from scipy import sparse
from math import sqrt

from ..metrics import pairwise_distances_argmin
from ..metrics.pairwise import euclidean_distances
from ..base import TransformerMixin, ClusterMixin, BaseEstimator
from ..utils import check_array
from ..utils.extmath import row_norms
from ..utils.validation import check_is_fitted, _deprecate_positional_args
from ..exceptions import ConvergenceWarning
from . import AgglomerativeClustering


def _iterate_sparse_X(X):
    """This little hack returns a densified row when iterating over a sparse
    matrix, instead of constructing a sparse matrix for every row that is
    expensive.
    """
    n_samples = X.shape[0]
    X_indices = X.indices
    X_data = X.data
    X_indptr = X.indptr

    for i in range(n_samples):
        row = np.zeros(X.shape[1])
        startptr, endptr = X_indptr[i], X_indptr[i + 1]
        nonzero_indices = X_indices[startptr:endptr]
        row[nonzero_indices] = X_data[startptr:endptr]
        yield row


def _split_node(node, threshold, branching_factor):
    """The node has to be split if there is no place for a new subcluster
    in the node.
    1. Two empty nodes and two empty subclusters are initialized.
    2. The pair of distant subclusters are found.
    3. The properties of the empty subclusters and nodes are updated
       according to the nearest distance between the subclusters to the
       pair of distant subclusters.
    4. The two nodes are set as children to the two subclusters.
    """
    new_subcluster1 = _CFSubcluster()
    new_subcluster2 = _CFSubcluster()
    new_node1 = _CFNode(
        threshold=threshold, branching_factor=branching_factor,
        is_leaf=node.is_leaf,
        n_features=node.n_features)
    new_node2 = _CFNode(
        threshold=threshold, branching_factor=branching_factor,
        is_leaf=node.is_leaf,
        n_features=node.n_features)
    new_subcluster1.child_ = new_node1
    new_subcluster2.child_ = new_node2

    if node.is_leaf:
        if node.prev_leaf_ is not None:
            node.prev_leaf_.next_leaf_ = new_node1
        new_node1.prev_leaf_ = node.prev_leaf_
        new_node1.next_leaf_ = new_node2
        new_node2.prev_leaf_ = new_node1
        new_node2.next_leaf_ = node.next_leaf_
        if node.next_leaf_ is not None:
            node.next_leaf_.prev_leaf_ = new_node2

    dist = euclidean_distances(
        node.centroids_, Y_norm_squared=node.squared_norm_, squared=True)
    n_clusters = dist.shape[0]

    farthest_idx = np.unravel_index(
        dist.argmax(), (n_clusters, n_clusters))
    node1_dist, node2_dist = dist[(farthest_idx,)]

    node1_closer = node1_dist < node2_dist
    for idx, subcluster in enumerate(node.subclusters_):
        if node1_closer[idx]:
            new_node1.append_subcluster(subcluster)
            new_subcluster1.update(subcluster)
        else:
            new_node2.append_subcluster(subcluster)
            new_subcluster2.update(subcluster)
    return new_subcluster1, new_subcluster2


class _CFNode:
    """Each node in a CFTree is called a CFNode.

    The CFNode can have a maximum of branching_factor
    number of CFSubclusters.

    Parameters
    ----------
    threshold : float
        Threshold needed for a new subcluster to enter a CFSubcluster.

    branching_factor : int
        Maximum number of CF subclusters in each node.

    is_leaf : bool
        We need to know if the CFNode is a leaf or not, in order to
        retrieve the final subclusters.

    n_features : int
        The number of features.

    Attributes
    ----------
    subclusters_ : list
        List of subclusters for a particular CFNode.

    prev_leaf_ : _CFNode
        Useful only if is_leaf is True.

    next_leaf_ : _CFNode
        next_leaf. Useful only if is_leaf is True.
        the final subclusters.

    init_centroids_ : ndarray of shape (branching_factor + 1, n_features)
        Manipulate ``init_centroids_`` throughout rather than centroids_ since
        the centroids are just a view of the ``init_centroids_`` .

    init_sq_norm_ : ndarray of shape (branching_factor + 1,)
        manipulate init_sq_norm_ throughout. similar to ``init_centroids_``.

    centroids_ : ndarray of shape (branching_factor + 1, n_features)
        View of ``init_centroids_``.

    squared_norm_ : ndarray of shape (branching_factor + 1,)
        View of ``init_sq_norm_``.

    """
    def __init__(self, *, threshold, branching_factor, is_leaf, n_features):
        self.threshold = threshold
        self.branching_factor = branching_factor
        self.is_leaf = is_leaf
        self.n_features = n_features

        # The list of subclusters, centroids and squared norms
        # to manipulate throughout.
        self.subclusters_ = []
        self.init_centroids_ = np.zeros((branching_factor + 1, n_features))
        self.init_sq_norm_ = np.zeros((branching_factor + 1))
        self.squared_norm_ = []
        self.prev_leaf_ = None
        self.next_leaf_ = None

    def append_subcluster(self, subcluster):
        n_samples = len(self.subclusters_)
        self.subclusters_.append(subcluster)
        self.init_centroids_[n_samples] = subcluster.centroid_
        self.init_sq_norm_[n_samples] = subcluster.sq_norm_

        # Keep centroids and squared norm as views. In this way
        # if we change init_centroids and init_sq_norm_, it is
        # sufficient,
        self.centroids_ = self.init_centroids_[:n_samples + 1, :]
        self.squared_norm_ = self.init_sq_norm_[:n_samples + 1]

    def update_split_subclusters(self, subcluster,
                                 new_subcluster1, new_subcluster2):
        """Remove a subcluster from a node and update it with the
        split subclusters.
        """
        ind = self.subclusters_.index(subcluster)
        self.subclusters_[ind] = new_subcluster1
        self.init_centroids_[ind] = new_subcluster1.centroid_
        self.init_sq_norm_[ind] = new_subcluster1.sq_norm_
        self.append_subcluster(new_subcluster2)

    def insert_cf_subcluster(self, subcluster):
        """Insert a new subcluster into the node."""
        if not self.subclusters_:
            self.append_subcluster(subcluster)
            return False

        threshold = self.threshold
        branching_factor = self.branching_factor
        # We need to find the closest subcluster among all the
        # subclusters so that we can insert our new subcluster.
        dist_matrix = np.dot(self.centroids_, subcluster.centroid_)
        dist_matrix *= -2.
        dist_matrix += self.squared_norm_
        closest_index = np.argmin(dist_matrix)
        closest_subcluster = self.subclusters_[closest_index]

        # If the subcluster has a child, we need a recursive strategy.
        if closest_subcluster.child_ is not None:
            split_child = closest_subcluster.child_.insert_cf_subcluster(
                subcluster)

            if not split_child:
                # If it is determined that the child need not be split, we
                # can just update the closest_subcluster
                closest_subcluster.update(subcluster)
                self.init_centroids_[closest_index] = \
                    self.subclusters_[closest_index].centroid_
                self.init_sq_norm_[closest_index] = \
                    self.subclusters_[closest_index].sq_norm_
                return False

            # things not too good. we need to redistribute the subclusters in
            # our child node, and add a new subcluster in the parent
            # subcluster to accommodate the new child.
            else:
                new_subcluster1, new_subcluster2 = _split_node(
                    closest_subcluster.child_, threshold, branching_factor)
                self.update_split_subclusters(
                    closest_subcluster, new_subcluster1, new_subcluster2)

                if len(self.subclusters_) > self.branching_factor:
                    return True
                return False

        # good to go!
        else:
            merged = closest_subcluster.merge_subcluster(
                subcluster, self.threshold)
            if merged:
                self.init_centroids_[closest_index] = \
                    closest_subcluster.centroid_
                self.init_sq_norm_[closest_index] = \
                    closest_subcluster.sq_norm_
                return False

            # not close to any other subclusters, and we still
            # have space, so add.
            elif len(self.subclusters_) < self.branching_factor:
                self.append_subcluster(subcluster)
                return False

            # We do not have enough space nor is it closer to an
            # other subcluster. We need to split.
            else:
                self.append_subcluster(subcluster)
                return True


class _CFSubcluster:
    """Each subcluster in a CFNode is called a CFSubcluster.

    A CFSubcluster can have a CFNode has its child.

    Parameters
    ----------
    linear_sum : ndarray of shape (n_features,), default=None
        Sample. This is kept optional to allow initialization of empty
        subclusters.

    Attributes
    ----------
    n_samples_ : int
        Number of samples that belong to each subcluster.

    linear_sum_ : ndarray
        Linear sum of all the samples in a subcluster. Prevents holding
        all sample data in memory.

    squared_sum_ : float
        Sum of the squared l2 norms of all samples belonging to a subcluster.

    centroid_ : ndarray of shape (branching_factor + 1, n_features)
        Centroid of the subcluster. Prevent recomputing of centroids when
        ``CFNode.centroids_`` is called.

    child_ : _CFNode
        Child Node of the subcluster. Once a given _CFNode is set as the child
        of the _CFNode, it is set to ``self.child_``.

    sq_norm_ : ndarray of shape (branching_factor + 1,)
        Squared norm of the subcluster. Used to prevent recomputing when
        pairwise minimum distances are computed.
    """
    def __init__(self, *, linear_sum=None):
        if linear_sum is None:
            self.n_samples_ = 0
            self.squared_sum_ = 0.0
            self.centroid_ = self.linear_sum_ = 0
        else:
            self.n_samples_ = 1
            self.centroid_ = self.linear_sum_ = linear_sum
            self.squared_sum_ = self.sq_norm_ = np.dot(
                self.linear_sum_, self.linear_sum_)
        self.child_ = None

    def update(self, subcluster):
        self.n_samples_ += subcluster.n_samples_
        self.linear_sum_ += subcluster.linear_sum_
        self.squared_sum_ += subcluster.squared_sum_
        self.centroid_ = self.linear_sum_ / self.n_samples_
        self.sq_norm_ = np.dot(self.centroid_, self.centroid_)

    def merge_subcluster(self, nominee_cluster, threshold):
        """Check if a cluster is worthy enough to be merged. If
        yes then merge.
        """
        new_ss = self.squared_sum_ + nominee_cluster.squared_sum_
        new_ls = self.linear_sum_ + nominee_cluster.linear_sum_
        new_n = self.n_samples_ + nominee_cluster.n_samples_
        new_centroid = (1 / new_n) * new_ls
        new_norm = np.dot(new_centroid, new_centroid)
        dot_product = (-2 * new_n) * new_norm
        sq_radius = (new_ss + dot_product) / new_n + new_norm
        if sq_radius <= threshold ** 2:
            (self.n_samples_, self.linear_sum_, self.squared_sum_,
             self.centroid_, self.sq_norm_) = \
                new_n, new_ls, new_ss, new_centroid, new_norm
            return True
        return False

    @property
    def radius(self):
        """Return radius of the subcluster"""
        dot_product = -2 * np.dot(self.linear_sum_, self.centroid_)
        return sqrt(
            ((self.squared_sum_ + dot_product) / self.n_samples_) +
            self.sq_norm_)


class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
    """Implements the Birch clustering algorithm.

    It is a memory-efficient, online-learning algorithm provided as an
    alternative to :class:`MiniBatchKMeans`. It constructs a tree
    data structure with the cluster centroids being read off the leaf.
    These can be either the final cluster centroids or can be provided as input
    to another clustering algorithm such as :class:`AgglomerativeClustering`.

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

    .. versionadded:: 0.16

    Parameters
    ----------
    threshold : float, default=0.5
        The radius of the subcluster obtained by merging a new sample and the
        closest subcluster should be lesser than the threshold. Otherwise a new
        subcluster is started. Setting this value to be very low promotes
        splitting and vice-versa.