# -*- coding: utf-8 -*-
from __future__ import print_function
'''
Copyright (c) 2009, Thomas Aynaud <thomas.aynaud@lip6.fr>
All rights reserved.

Redistribution and use in source and binary forms, with or without 
modification, are permitted provided that the following conditions 
are met:

* Redistributions of source code must retain the above copyright 
notice, this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright 
notice, this list of conditions and the following disclaimer in the 
documentation and/or other materials provided with the distribution.

* Neither the name of the NetworkX Developers nor the names of its 
contributors may be used to endorse or promote products derived from 
this software without specific prior written permission.


THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 
FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 
BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 
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'''

"""
This module implements community detection.
"""

__author__ = """Thomas Aynaud (thomas.aynaud@lip6.fr)"""
#    Copyright (C) 2009 by
#    Thomas Aynaud <thomas.aynaud@lip6.fr>
#    All rights reserved.
#    BSD license.

__PASS_MAX = -1
__MIN = 0.0000001
import array
import random

import networkx as nx

#from .community_status import Status

class Status(object):
    """
    To handle several data in one struct.
    Could be replaced by named tuple, but don't want to depend on python 2.6
    """
    node2com = {}
    total_weight = 0
    internals = {}
    degrees = {}
    gdegrees = {}

    def __init__(self):
        self.node2com = dict([])
        self.total_weight = 0
        self.degrees = dict([])
        self.gdegrees = dict([])
        self.internals = dict([])
        self.loops = dict([])

    def __str__(self):
        return ("node2com : " + str(self.node2com) + " degrees : "
                + str(self.degrees) + " internals : " + str(self.internals)
                + " total_weight : " + str(self.total_weight))

    def copy(self):
        """Perform a deep copy of status"""
        new_status = Status()
        new_status.node2com = self.node2com.copy()
        new_status.internals = self.internals.copy()
        new_status.degrees = self.degrees.copy()
        new_status.gdegrees = self.gdegrees.copy()
        new_status.total_weight = self.total_weight

    def init(self, graph, weight, part=None):
        """Initialize the status of a graph with every node in one community"""
        count = 0
        self.node2com = dict([])
        self.total_weight = 0
        self.degrees = dict([])
        self.gdegrees = dict([])
        self.internals = dict([])
        self.total_weight = graph.size(weight=weight)
        if part is None:
            for node in graph.nodes():
                self.node2com[node] = count
                deg = float(graph.degree(node, weight=weight))
                if deg < 0:
                    error = "Bad node degree ({})".format(deg)
                    raise ValueError(error)
                self.degrees[count] = deg
                self.gdegrees[node] = deg
                edge_data = graph.get_edge_data(node, node, default={weight: 0})
                self.loops[node] = float(edge_data.get(weight, 1))
                self.internals[count] = self.loops[node]
                count += 1
        else:
            for node in graph.nodes():
                com = part[node]
                self.node2com[node] = com
                deg = float(graph.degree(node, weight=weight))
                self.degrees[com] = self.degrees.get(com, 0) + deg
                self.gdegrees[node] = deg
                inc = 0.
                for neighbor, datas in graph[node].items():
                    edge_weight = datas.get(weight, 1)
                    if edge_weight <= 0:
                        error = "Bad graph type ({})".format(type(graph))
                        raise ValueError(error)
                    if part[neighbor] == com:
                        if neighbor == node:
                            inc += float(edge_weight)
                        else:
                            inc += float(edge_weight) / 2.
                self.internals[com] = self.internals.get(com, 0) + inc

def partition_at_level(dendrogram, level):
    """Return the partition of the nodes at the given level
    A dendrogram is a tree and each level is a partition of the graph nodes.
    Level 0 is the first partition, which contains the smallest communities,
    and the best is len(dendrogram) - 1.
    The higher the level is, the bigger are the communities
    Parameters
    ----------
    dendrogram : list of dict
       a list of partitions, ie dictionnaries where keys of the i+1 are the
       values of the i.
    level : int
       the level which belongs to [0..len(dendrogram)-1]
    Returns
    -------
    partition : dictionnary
       A dictionary where keys are the nodes and the values are the set it
       belongs to
    Raises
    ------
    KeyError
       If the dendrogram is not well formed or the level is too high
    See Also
    --------
    best_partition which directly combines partition_at_level and
    generate_dendrogram to obtain the partition of highest modularity
    Examples
    --------
    >>> G=nx.erdos_renyi_graph(100, 0.01)
    >>> dendrogram = generate_dendrogram(G)
    >>> for level in range(len(dendrogram) - 1) :
    >>>     print("partition at level", level, "is", partition_at_level(dendrogram, level))  # NOQA
    """
    partition = dendrogram[0].copy()
    for index in range(1, level + 1):
        for node, community in partition.items():
            partition[node] = dendrogram[index][community]
    return partition


def modularity(partition, graph, weight='weight'):
    """Compute the modularity of a partition of a graph
    Parameters
    ----------
    partition : dict
       the partition of the nodes, i.e a dictionary where keys are their nodes
       and values the communities
    graph : networkx.Graph
       the networkx graph which is decomposed
    weight : str, optional
        the key in graph to use as weight. Default to 'weight'
    Returns
    -------
    modularity : float
       The modularity
    Raises
    ------
    KeyError
       If the partition is not a partition of all graph nodes
    ValueError
        If the graph has no link
    TypeError
        If graph is not a networkx.Graph
    References
    ----------
    .. 1. Newman, M.E.J. & Girvan, M. Finding and evaluating community
    structure in networks. Physical Review E 69, 26113(2004).
    Examples
    --------
    >>> G=nx.erdos_renyi_graph(100, 0.01)
    >>> part = best_partition(G)
    >>> modularity(part, G)
    """
    if graph.is_directed():
        raise TypeError("Bad graph type, use only non directed graph")

    inc = dict([])
    deg = dict([])
    links = graph.size(weight=weight)
    if links == 0:
        raise ValueError("A graph without link has an undefined modularity")

    for node in graph:
        com = partition[node]
        deg[com] = deg.get(com, 0.) + graph.degree(node, weight=weight)
        for neighbor, datas in graph[node].items():
            edge_weight = datas.get(weight, 1)
            if partition[neighbor] == com:
                if neighbor == node:
                    inc[com] = inc.get(com, 0.) + float(edge_weight)
                else:
                    inc[com] = inc.get(com, 0.) + float(edge_weight) / 2.

    res = 0.
    for com in set(partition.values()):
        res += (inc.get(com, 0.) / links) - \
               (deg.get(com, 0.) / (2. * links)) ** 2
    return res


def best_partition(graph, partition=None,
                   weight='weight', resolution=1., randomize=False):
    """Compute the partition of the graph nodes which maximises the modularity
    (or try..) using the Louvain heuristices
    This is the partition of highest modularity, i.e. the highest partition
    of the dendrogram generated by the Louvain algorithm.
    Parameters
    ----------
    graph : networkx.Graph
       the networkx graph which is decomposed
    partition : dict, optional
       the algorithm will start using this partition of the nodes.
       It's a dictionary where keys are their nodes and values the communities
    weight : str, optional
        the key in graph to use as weight. Default to 'weight'
    resolution :  double, optional
        Will change the size of the communities, default to 1.
        represents the time described in
        "Laplacian Dynamics and Multiscale Modular Structure in Networks",
        R. Lambiotte, J.-C. Delvenne, M. Barahona
    randomize :  boolean, optional
        Will randomize the node evaluation order and the community evaluation
        order to get different partitions at each call
    Returns
    -------
    partition : dictionnary
       The partition, with communities numbered from 0 to number of communities
    Raises
    ------
    NetworkXError
       If the graph is not Eulerian.
    See Also
    --------
    generate_dendrogram to obtain all the decompositions levels
    Notes
    -----
    Uses Louvain algorithm
    References
    ----------
    .. 1. Blondel, V.D. et al. Fast unfolding of communities in
    large networks. J. Stat. Mech 10008, 1-12(2008).
    Examples
    --------
    >>>  #Basic usage
    >>> G=nx.erdos_renyi_graph(100, 0.01)
    >>> part = best_partition(G)
    >>> #other example to display a graph with its community :
    >>> #better with karate_graph() as defined in networkx examples
    >>> #erdos renyi don't have true community structure
    >>> G = nx.erdos_renyi_graph(30, 0.05)
    >>> #first compute the best partition
    >>> partition = community.best_partition(G)
    >>>  #drawing
    >>> size = float(len(set(partition.values())))
    >>> pos = nx.spring_layout(G)
    >>> count = 0.
    >>> for com in set(partition.values()) :
    >>>     count += 1.
    >>>     list_nodes = [nodes for nodes in partition.keys()
    >>>                                 if partition[nodes] == com]
    >>>     nx.draw_networkx_nodes(G, pos, list_nodes, node_size = 20,
                                    node_color = str(count / size))
    >>> nx.draw_networkx_edges(G, pos, alpha=0.5)
    >>> plt.show()
    """
    dendo = generate_dendrogram(graph,
                                partition,
                                weight,
                                resolution,
                                randomize)
    return partition_at_level(dendo, len(dendo) - 1)


def generate_dendrogram(graph,
                        part_init=None,
                        weight='weight',
                        resolution=1.,
                        randomize=False):
    """Find communities in the graph and return the associated dendrogram
    A dendrogram is a tree and each level is a partition of the graph nodes.
    Level 0 is the first partition, which contains the smallest communities,
    and the best is len(dendrogram) - 1. The higher the level is, the bigger
    are the communities
    Parameters
    ----------
    graph : networkx.Graph
        the networkx graph which will be decomposed
    part_init : dict, optional
        the algorithm will start using this partition of the nodes. It's a
        dictionary where keys are their nodes and values the communities
    weight : str, optional
        the key in graph to use as weight. Default to 'weight'
    resolution :  double, optional
        Will change the size of the communities, default to 1.
        represents the time described in
        "Laplacian Dynamics and Multiscale Modular Structure in Networks",
        R. Lambiotte, J.-C. Delvenne, M. Barahona
    Returns
    -------
    dendrogram : list of dictionaries
        a list of partitions, ie dictionnaries where keys of the i+1 are the
        values of the i. and where keys of the first are the nodes of graph
    Raises
    ------
    TypeError
        If the graph is not a networkx.Graph
    See Also
    --------
    best_partition
    Notes
    -----
    Uses Louvain algorithm
    References
    ----------
    .. 1. Blondel, V.D. et al. Fast unfolding of communities in large
    networks. J. Stat. Mech 10008, 1-12(2008).
    Examples
    --------
    >>> G=nx.erdos_renyi_graph(100, 0.01)
    >>> dendo = generate_dendrogram(G)
    >>> for level in range(len(dendo) - 1) :
    >>>     print("partition at level", level,
    >>>           "is", partition_at_level(dendo, level))
    :param weight:
    :type weight:
    """
    if graph.is_directed():
        raise TypeError("Bad graph type, use only non directed graph")

    # special case, when there is no link
    # the best partition is everyone in its community
    if graph.number_of_edges() == 0:
        part = dict([])
        for node in graph.nodes():
            part[node] = node
        return [part]

    current_graph = graph.copy()
    status = Status()
    status.init(current_graph, weight, part_init)
    status_list = list()
    __one_level(current_graph, status, weight, resolution, randomize)
    new_mod = __modularity(status)
    partition = __renumber(status.node2com)
    status_list.append(partition)
    mod = new_mod
    current_graph = induced_graph(partition, current_graph, weight)
    status.init(current_graph, weight)

    while True:
        __one_level(current_graph, status, weight, resolution, randomize)
        new_mod = __modularity(status)
        if new_mod - mod < __MIN:
            break
        partition = __renumber(status.node2com)
        status_list.append(partition)
        mod = new_mod
        current_graph = induced_graph(partition, current_graph, weight)
        status.init(current_graph, weight)
    return status_list[:]


def induced_graph(partition, graph, weight="weight"):
    """Produce the graph where nodes are the communities
    there is a link of weight w between communities if the sum of the weights
    of the links between their elements is w
    Parameters
    ----------
    partition : dict
       a dictionary where keys are graph nodes and  values the part the node
       belongs to
    graph : networkx.Graph
        the initial graph
    weight : str, optional
        the key in graph to use as weight. Default to 'weight'
    Returns
    -------
    g : networkx.Graph
       a networkx graph where nodes are the parts
    Examples
    --------
    >>> n = 5
    >>> g = nx.complete_graph(2*n)
    >>> part = dict([])
    >>> for node in g.nodes() :
    >>>     part[node] = node % 2
    >>> ind = induced_graph(part, g)
    >>> goal = nx.Graph()
    >>> goal.add_weighted_edges_from([(0,1,n*n),(0,0,n*(n-1)/2), (1, 1, n*(n-1)/2)])  # NOQA
    >>> nx.is_isomorphic(int, goal)
    True
    """
    ret = nx.Graph()
    ret.add_nodes_from(partition.values())

    for node1, node2, datas in graph.edges(data=True):
        edge_weight = datas.get(weight, 1)
        com1 = partition[node1]
        com2 = partition[node2]
        w_prec = ret.get_edge_data(com1, com2, {weight: 0}).get(weight, 1)
        ret.add_edge(com1, com2, **{weight: w_prec + edge_weight})

    return ret


def __renumber(dictionary):
    """Renumber the values of the dictionary from 0 to n
    """
    count = 0
    ret = dictionary.copy()
    new_values = dict([])

    for key in dictionary.keys():
        value = dictionary[key]
        new_value = new_values.get(value, -1)
        if new_value == -1:
            new_values[value] = count
            new_value = count
            count += 1
        ret[key] = new_value

    return ret


def load_binary(data):
    """Load binary graph as used by the cpp implementation of this algorithm
    """
    data = open(data, "rb")

    reader = array.array("I")
    reader.fromfile(data, 1)
    num_nodes = reader.pop()
    reader = array.array("I")
    reader.fromfile(data, num_nodes)
    cum_deg = reader.tolist()
    num_links = reader.pop()
    reader = array.array("I")
    reader.fromfile(data, num_links)
    links = reader.tolist()
    graph = nx.Graph()
    graph.add_nodes_from(range(num_nodes))
    prec_deg = 0

    for index in range(num_nodes):
        last_deg = cum_deg[index]
        neighbors = links[prec_deg:last_deg]
        graph.add_edges_from([(index, int(neigh)) for neigh in neighbors])
        prec_deg = last_deg

    return graph


def __randomly(seq, randomize):
    """ Convert sequence or iterable to an iterable in random order if
    randomize """
    if randomize:
        shuffled = list(seq)
        random.shuffle(shuffled)
        return iter(shuffled)
    return seq


def __one_level(graph, status, weight_key, resolution, randomize):
    """Compute one level of communities
    """
    modified = True
    nb_pass_done = 0
    cur_mod = __modularity(status)
    new_mod = cur_mod

    while modified and nb_pass_done != __PASS_MAX:
        cur_mod = new_mod
        modified = False
        nb_pass_done += 1

        for node in __randomly(graph.nodes(), randomize):
            com_node = status.node2com[node]
            degc_totw = status.gdegrees.get(node, 0.) / (status.total_weight * 2.)  # NOQA
            neigh_communities = __neighcom(node, graph, status, weight_key)
            remove_cost = - resolution * neigh_communities.get(com_node,0) + \
                (status.degrees.get(com_node, 0.) - status.gdegrees.get(node, 0.)) * degc_totw
            __remove(node, com_node,
                     neigh_communities.get(com_node, 0.), status)
            best_com = com_node
            best_increase = 0
            for com, dnc in __randomly(neigh_communities.items(),
                                       randomize):
                incr = remove_cost + resolution * dnc - \
                       status.degrees.get(com, 0.) * degc_totw
                if incr > best_increase:
                    best_increase = incr
                    best_com = com
            __insert(node, best_com,
                     neigh_communities.get(best_com, 0.), status)
            if best_com != com_node:
                modified = True
        new_mod = __modularity(status)
        if new_mod - cur_mod < __MIN:
            break


def __neighcom(node, graph, status, weight_key):
    """
    Compute the communities in the neighborhood of node in the graph given
    with the decomposition node2com
    """
    weights = {}
    for neighbor, datas in graph[node].items():
        if neighbor != node:
            edge_weight = datas.get(weight_key, 1)
            neighborcom = status.node2com[neighbor]
            weights[neighborcom] = weights.get(neighborcom, 0) + edge_weight

    return weights


def __remove(node, com, weight, status):
    """ Remove node from community com and modify status"""
    status.degrees[com] = (status.degrees.get(com, 0.)
                           - status.gdegrees.get(node, 0.))
    status.internals[com] = float(status.internals.get(com, 0.) -
                                  weight - status.loops.get(node, 0.))
    status.node2com[node] = -1


def __insert(node, com, weight, status):
    """ Insert node into community and modify status"""
    status.node2com[node] = com
    status.degrees[com] = (status.degrees.get(com, 0.) +
                           status.gdegrees.get(node, 0.))
    status.internals[com] = float(status.internals.get(com, 0.) +
                                  weight + status.loops.get(node, 0.))


def __modularity(status):
    """
    Fast compute the modularity of the partition of the graph using
    status precomputed
    """
    links = float(status.total_weight)
    result = 0.
    for community in set(status.node2com.values()):
        in_degree = status.internals.get(community, 0.)
        degree = status.degrees.get(community, 0.)
        if links > 0:
            result += in_degree / links - ((degree / (2. * links)) ** 2)
    return result
