blockmodel.py 119 KB
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#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# graph_tool -- a general graph manipulation python module
#
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# Copyright (C) 2006-2015 Tiago de Paula Peixoto <tiago@skewed.de>
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#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

from __future__ import division, absolute_import, print_function
import sys
if sys.version_info < (3,):
    range = xrange

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from .. import _degree, _prop, Graph, GraphView, libcore, _get_rng, PropertyMap
from .. stats import label_self_loops
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from .. spectral import adjacency
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import random
from numpy import *
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import numpy
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from scipy.optimize import fsolve, fminbound
import scipy.special
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from collections import defaultdict
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import copy
import heapq
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from .. dl_import import dl_import
dl_import("from . import libgraph_tool_community as libcommunity")

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__test__ = False
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def set_test(test):
    global __test__
    __test__ = test

def _bm_test():
    global __test__
    return __test__

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def get_block_graph(g, B, b, vcount, ecount):
    cg, br, vcount, ecount = condensation_graph(g, b,
                                                vweight=vcount,
                                                eweight=ecount,
                                                self_loops=True)[:4]
    cg.vp["count"] = vcount
    cg.ep["count"] = ecount
    cg = Graph(cg, vorder=br)

    cg.add_vertex(B - cg.num_vertices())
    return cg

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class BlockState(object):
    r"""This class encapsulates the block state of a given graph.

    This must be instantiated and used by functions such as :func:`mcmc_sweep`.

    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
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        Graph to be modelled.
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    eweight : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
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        Edge multiplicities (for multigraphs or block graphs).
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    vweight : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
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        Vertex multiplicities (for block graphs).
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    b : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
        Initial block labels on the vertices. If not supplied, it will be
        randomly sampled.
    B : ``int`` (optional, default: ``None``)
        Number of blocks. If not supplied it will be either obtained from the
        parameter ``b``, or set to the maximum possible value according to the
        minimum description length.
    clabel : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
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        Constraint labels on the vertices. If supplied, vertices with different
        label values will not be clustered in the same group.
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    deg_corr : ``bool`` (optional, default: ``True``)
        If ``True``, the degree-corrected version of the blockmodel ensemble will
        be assumed, otherwise the traditional variant will be used.
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    max_BE : ``int`` (optional, default: ``1000``)
        If the number of blocks exceeds this number, a sparse representation of
        the block graph is used, which is slightly less efficient, but uses less
        memory,
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    """

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    _state_ref_count = 0

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    def __init__(self, g, eweight=None, vweight=None, b=None,
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                 B=None, clabel=None, deg_corr=True,
                 max_BE=1000, **kwargs):

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        BlockState._state_ref_count += 1

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        # initialize weights to unity, if necessary
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        if eweight is None:
            eweight = g.new_edge_property("int")
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            eweight.fa = 1
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        elif eweight.value_type() != "int32_t":
            eweight = eweight.copy(value_type="int32_t")
        if vweight is None:
            vweight = g.new_vertex_property("int")
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            vweight.fa = 1
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        elif vweight.value_type() != "int32_t":
            vweight = vweight.copy(value_type="int32_t")
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        self.eweight = g.own_property(eweight)
        self.vweight = g.own_property(vweight)

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        self.is_weighted = False
        if ((g.num_edges() > 0 and self.eweight.fa.max() > 1) or
            kwargs.get("force_weighted", False)):
            self.is_weighted = True
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        # configure the main graph and block model parameters
        self.g = g
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        self.E = int(self.eweight.fa.sum())
        self.N = int(self.vweight.fa.sum())
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        self.deg_corr = deg_corr

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        # ensure we have at most as many blocks as nodes
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        if B is not None and b is None:
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            B = min(B, self.g.num_vertices())

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        if b is None:
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            # create a random partition into B blocks.
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            if B is None:
                B = get_max_B(self.N, self.E, directed=g.is_directed())
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            B = min(B, self.g.num_vertices())
            ba = random.randint(0, B, self.g.num_vertices())
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            ba[:B] = arange(B)        # avoid empty blocks
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            if B < self.g.num_vertices():
                random.shuffle(ba)
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            b = g.new_vertex_property("int")
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            b.fa = ba
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            self.b = b
        else:
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            # if a partition is available, we will incorporate it.
            if isinstance(b, numpy.ndarray):
                self.b = g.new_vertex_property("int")
                self.b.fa = b
            else:
                self.b = b = g.own_property(b.copy(value_type="int"))
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            if B is None:
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                B = int(self.b.fa.max()) + 1

        # if B > self.N:
        #     raise ValueError("B > N!")
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        if self.b.fa.max() >= B:
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            raise ValueError("Maximum value of b is larger or equal to B! (%d vs %d)" % (self.b.fa.max(), B))
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        # Construct block-graph
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        self.bg = get_block_graph(g, B, self.b, self.vweight, self.eweight)
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        self.bg.set_fast_edge_removal()

        self.mrs = self.bg.ep["count"]
        self.wr = self.bg.vp["count"]
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        del self.bg.ep["count"]
        del self.bg.vp["count"]

        self.mrp = self.bg.degree_property_map("out", weight=self.mrs)

        if g.is_directed():
            self.mrm = self.bg.degree_property_map("in", weight=self.mrs)
        else:
            self.mrm = self.mrp
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        self.vertices = libcommunity.get_vector(B)
        self.vertices.a = arange(B)
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        self.B = B
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        if clabel is not None:
            if isinstance(clabel, PropertyMap):
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                self.clabel = self.g.own_property(clabel.copy())
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            else:
                self.clabel = self.g.new_vertex_property("int")
                self.clabel.a = clabel
        else:
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            self.clabel = self.g.new_vertex_property("int")

        self.emat = None
        if max_BE is None:
            max_BE = 1000
        self.max_BE = max_BE

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        self.overlap = False

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        # used by mcmc_sweep()
        self.egroups = None
        self.nsampler = None
        self.sweep_vertices = None
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        self.overlap_stats = libcommunity.overlap_stats()
        self.partition_stats = libcommunity.partition_stats()
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        self.edges_dl = False
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        # computation cache
        libcommunity.init_safelog(int(5 * max(self.E, self.N)))
        libcommunity.init_xlogx(int(5 * max(self.E, self.N)))
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        libcommunity.init_lgamma(int(3 * max(self.E, self.N)))
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    def __del__(self):
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        try:
            BlockState._state_ref_count -= 1
            if BlockState._state_ref_count == 0:
                libcommunity.clear_safelog()
                libcommunity.clear_xlogx()
                libcommunity.clear_lgamma()
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        except (ValueError, AttributeError, TypeError):
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            pass
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    def __repr__(self):
        return "<BlockState object with %d blocks,%s for graph %s, at 0x%x>" % \
            (self.B, " degree corrected," if self.deg_corr else "", str(self.g),
             id(self))


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    def __init_partition_stats(self, empty=True, edges_dl=False):
        self.edges_dl = edges_dl
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        if not empty:
            self.partition_stats = libcommunity.init_partition_stats(self.g._Graph__graph,
                                                                     _prop("v", self.g, self.b),
                                                                     _prop("e", self.g, self.eweight),
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                                                                     self.N, self.B,
                                                                     edges_dl)
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        else:
            self.partition_stats = libcommunity.partition_stats()



    def copy(self, b=None, B=None, deg_corr=None, clabel=None, overlap=False):
        r"""Copies the block state. The parameters override the state properties, and
         have the same meaning as in the constructor. If ``overlap=True`` an
         instance of :class:`~graph_tool.community.OverlapBlockState` is
         returned."""

        if not overlap:
            state = BlockState(self.g,
                               eweight=self.eweight,
                               vweight=self.vweight,
                               b=self.b.copy() if b is None else b,
                               B=(self.B if b is None else None) if B is None else B,
                               clabel=self.clabel if clabel is None else clabel,
                               deg_corr=self.deg_corr if deg_corr is None else deg_corr,
                               max_BE=self.max_BE)
        else:
            state = OverlapBlockState(self.g,
                                      b=b if b is not None else self.b,
                                      B=(self.B if b is None else None) if B is None else B,
                                      clabel=self.clabel if clabel is None else clabel,
                                      deg_corr=self.deg_corr if deg_corr is None else deg_corr,
                                      max_BE=self.max_BE)

        if not state.__check_clabel():
            b = state.b.a + state.clabel.a * state.B
            continuous_map(b)
            state = state.copy(b=b)

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            if _bm_test():
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                assert state.__check_clabel()

        return state


    def __getstate__(self):
        state = dict(g=self.g,
                     eweight=self.eweight,
                     vweight=self.vweight,
                     b=self.b,
                     B=self.B,
                     clabel=self.clabel,
                     deg_corr=self.deg_corr,
                     max_BE=self.max_BE)
        return state

    def __setstate__(self, state):
        self.__init__(**state)
        return state

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    def get_block_state(self, b=None, vweight=False, deg_corr=False,
                        overlap=False, **kwargs):
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        r"""Returns a :class:`~graph_tool.community.BlockState`` corresponding to the
        block graph. The parameters have the same meaning as the in the constructor."""


        state = BlockState(self.bg, eweight=self.mrs,
                           vweight=self.wr if vweight else None,
                           b=self.bg.vertex_index.copy("int") if b is None else b,
                           clabel=self.get_bclabel(),
                           deg_corr=deg_corr,
                           max_BE=self.max_BE)
        if overlap:
            state = state.copy(overlap=True)
        n_map = self.b.copy()
        return state, n_map

    def get_bclabel(self):
        r"""Returns a :class:`~graph_tool.PropertyMap`` corresponding to constraint
        labels for the block graph."""

        bclabel = self.bg.new_vertex_property("int")
        reverse_map(self.b, bclabel)
        pmap(bclabel, self.clabel)
        return bclabel

    def __check_clabel(self):
        b = self.b.a + self.clabel.a * self.B
        continuous_map(b)
        b2 = self.b.copy()
        continuous_map(b2.a)
        return (b == b2.a).all()

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    def __get_emat(self):
        if self.emat is None:
            self.__regen_emat()
        return self.emat
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    def __regen_emat(self):
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        if self.B <= self.max_BE:
            self.emat = libcommunity.create_emat(self.bg._Graph__graph)
        else:
            self.emat = libcommunity.create_ehash(self.bg._Graph__graph)
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    def __build_egroups(self, empty=False):
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        self.esrcpos = self.g.new_edge_property("int")
        self.etgtpos = self.g.new_edge_property("int")
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        self.egroups = libcommunity.build_egroups(self.g._Graph__graph,
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                                                  self.bg._Graph__graph,
                                                  _prop("v", self.g, self.b),
                                                  _prop("e", self.g, self.eweight),
                                                  _prop("e", self.g, self.esrcpos),
                                                  _prop("e", self.g, self.etgtpos),
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                                                  self.is_weighted, empty)
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    def __build_nsampler(self, empty=False):
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        self.nsampler = libcommunity.init_neighbour_sampler(self.g._Graph__graph,
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                                                            _prop("e", self.g, self.eweight),
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                                                            True, empty)
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    def __cleanup_bg(self):
        emask = self.bg.new_edge_property("bool")
        emask.a = self.mrs.a[:len(emask.a)] > 0
        self.bg.set_edge_filter(emask)
        self.bg.purge_edges()
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        self.emat = None
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    def get_blocks(self):
        r"""Returns the property map which contains the block labels for each vertex."""
        return self.b

    def get_bg(self):
        r"""Returns the block graph."""
        return self.bg

    def get_ers(self):
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        r"""Returns the edge property map of the block graph which contains the :math:`e_{rs}` matrix entries.
        For undirected graphs, the diagonal values (self-loops) contain :math:`e_{rr}/2`."""
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        return self.mrs

    def get_er(self):
        r"""Returns the vertex property map of the block graph which contains the number
        :math:`e_r` of half-edges incident on block :math:`r`. If the graph is
        directed, a pair of property maps is returned, with the number of
        out-edges :math:`e^+_r` and in-edges :math:`e^-_r`, respectively."""
        if self.bg.is_directed():
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            return self.mrp, self.mrm
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        else:
            return self.mrp

    def get_nr(self):
        r"""Returns the vertex property map of the block graph which contains the block sizes :math:`n_r`."""
        return self.wr

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    def entropy(self, complete=True, dl=False, partition_dl=True,
                degree_dl=True, edges_dl=True, dense=False, multigraph=True,
                norm=False, dl_ent=False, **kwargs):
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        r"""Calculate the entropy associated with the current block partition.
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        Parameters
        ----------
        complete : ``bool`` (optional, default: ``False``)
            If ``True``, the complete entropy will be returned, including constant
            terms not relevant to the block partition.
        dl : ``bool`` (optional, default: ``False``)
            If ``True``, the full description length will be returned.
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        partition_dl : ``bool`` (optional, default: ``True``)
            If ``True``, and ``dl == True`` the partition description length
            will be considered.
        edges_dl : ``bool`` (optional, default: ``True``)
            If ``True``, and ``dl == True`` the edge matrix description length
            will be considered.
        degree_dl : ``bool`` (optional, default: ``True``)
            If ``True``, and ``dl == True`` the degree sequence description
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            length will be considered.
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        dense : ``bool`` (optional, default: ``False``)
            If ``True``, the "dense" variant of the entropy will be computed.
        multigraph : ``bool`` (optional, default: ``False``)
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            If ``True``, the multigraph entropy will be used.
        norm : ``bool`` (optional, default: ``True``)
            If ``True``, the entropy will be "normalized" by dividing by the
            number of edges.
        dl_ent : ``bool`` (optional, default: ``False``)
            If ``True``, the description length of the degree sequence will be
            approximated by its entropy.
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        Notes
        -----
        For the traditional blockmodel (``deg_corr == False``), the entropy is
        given by

        .. math::

          \mathcal{S}_t &\cong E - \frac{1}{2} \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{n_rn_s}\right), \\
          \mathcal{S}^d_t &\cong E - \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{n_rn_s}\right),

        for undirected and directed graphs, respectively, where :math:`e_{rs}`
        is the number of edges from block :math:`r` to :math:`s` (or the number
        of half-edges for the undirected case when :math:`r=s`), and :math:`n_r`
        is the number of vertices in block :math:`r` .

        For the degree-corrected variant with "hard" degree constraints the
        equivalent expressions are

        .. math::

            \mathcal{S}_c &\cong -E -\sum_kN_k\ln k! - \frac{1}{2} \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{e_re_s}\right), \\
            \mathcal{S}^d_c &\cong -E -\sum_{k^+}N_{k^+}\ln k^+!  -\sum_{k^-}N_{k^-}\ln k^-! - \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{e^+_re^-_s}\right),

        where :math:`e_r = \sum_se_{rs}` is the number of half-edges incident on
        block :math:`r`, and :math:`e^+_r = \sum_se_{rs}` and :math:`e^-_r =
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        \sum_se_{sr}` are the numbers of out- and in-edges adjacent to block
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        :math:`r`, respectively.

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        If ``dense == False`` and ``multigraph == True``, the entropy used will
        be of the "Poisson" model, with the additional term:

        .. math::

            {\mathcal{S}_{cm}^{(d)}} = \mathcal{S}_c^{(d)} + \sum_{i>j} \ln A_{ij}! + \sum_i \ln A_{ii}!!


        If ``dl == True``, the description length :math:`\mathcal{L}_t` of the
        model will be returned as well, as described in
        :func:`model_entropy`. Note that for the degree-corrected version the
        description length is

        .. math::

            \mathcal{L}_c = \mathcal{L}_t + \sum_r\min\left(\mathcal{L}^{(1)}_r, \mathcal{L}^{(2)}_r\right),

        with

        .. math::

              \mathcal{L}^{(1)}_r &= \ln{\left(\!\!{n_r \choose e_r}\!\!\right)}, \\
              \mathcal{L}^{(2)}_r &= \ln\Xi_r + \ln n_r! - \sum_k \ln n^r_k!,

        and :math:`\ln\Xi_r \simeq 2\sqrt{\zeta(2)e_r}`, where :math:`\zeta(x)`
        is the `Riemann zeta function
        <https://en.wikipedia.org/wiki/Riemann_zeta_function>`_, and
        :math:`n^r_k` is the number of nodes in block :math:`r` with degree
        :math:`k`. For directed graphs we have instead :math:`k \to (k^-, k^+)`,
        and :math:`\ln\Xi_r \to \ln\Xi^+_r + \ln\Xi^-_r` with :math:`\ln\Xi_r^+
        \simeq 2\sqrt{\zeta(2)e^+_r}` and :math:`\ln\Xi_r^- \simeq
        2\sqrt{\zeta(2)e^-_r}`.

        If ``dl_ent=True`` is passed, this will be approximated instead by
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        .. math::

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            \mathcal{L}_c \simeq \mathcal{L}_t - \sum_rn_r\sum_kp^r_k\ln p^r_k,
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        where :math:`p^r_k = n^r_k / n_r`.
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        If the "dense" entropies are requested (``dense=True``), they will be
        computed as
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        .. math::

            \mathcal{S}_t  &= \sum_{r>s} \ln{\textstyle {n_rn_s \choose e_{rs}}} + \sum_r \ln{\textstyle {{n_r\choose 2}\choose e_{rr}/2}}\\
            \mathcal{S}^d_t  &= \sum_{rs} \ln{\textstyle {n_rn_s \choose e_{rs}}},

        for simple graphs, and

        .. math::

            \mathcal{S}_m  &= \sum_{r>s} \ln{\textstyle \left(\!\!{n_rn_s \choose e_{rs}}\!\!\right)} + \sum_r \ln{\textstyle \left(\!\!{\left(\!{n_r\choose 2}\!\right)\choose e_{rr}/2}\!\!\right)}\\
            \mathcal{S}^d_m  &= \sum_{rs} \ln{\textstyle \left(\!\!{n_rn_s \choose e_{rs}}\!\!\right)},

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        for multigraphs (i.e. ``multigraph == True``). A dense entropy for the
        degree-corrected model is not available, and if requested will return a
        :exc:`NotImplementedError`.
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        If ``complete == False`` constants in the above equations which do not
        depend on the partition of the nodes will be omitted.
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        Note that in all cases if ``norm==True`` the value returned corresponds
        to the entropy `per edge`, i.e. :math:`(\mathcal{S}_{t/c}\; [\,+\,\mathcal{L}_{t/c}])/ E`.
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        """

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        xi_fast = kwargs.get("xi_fast", False)
        dl_deg_alt = kwargs.get("dl_deg_alt", True)

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        E = self.E
        N = self.N

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        if dense:
            if self.deg_corr:
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                raise NotImplementedError('A degree-corrected "dense" entropy is not yet implemented')
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            S = libcommunity.entropy_dense(self.bg._Graph__graph,
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                                            _prop("e", self.bg, self.mrs),
                                            _prop("v", self.bg, self.wr),
                                            multigraph)
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        else:
            S = libcommunity.entropy(self.bg._Graph__graph,
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                                      _prop("e", self.bg, self.mrs),
                                      _prop("v", self.bg, self.mrp),
                                      _prop("v", self.bg, self.mrm),
                                      _prop("v", self.bg, self.wr),
                                      self.deg_corr)
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            if _bm_test():
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                assert not isnan(S) and not isinf(S), "invalid entropy %g (%s) " % (S, str(dict(complete=complete,
                                                                                                random=random, dl=dl,
                                                                                                partition_dl=partition_dl,
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                                                                                                edges_dl=edges_dl,
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                                                                                                dense=dense, multigraph=multigraph,
                                                                                                norm=norm)))
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            if self.deg_corr:
                S -= E
            else:
                S += E

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            if complete:
                if self.deg_corr:
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                    S += libcommunity.deg_entropy_term(self.g._Graph__graph,
                                                       libcore.any(),
                                                       self.overlap_stats,
                                                       self.N)
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                if multigraph:
                    S += libcommunity.entropy_parallel(self.g._Graph__graph,
                                                       _prop("e", self.g, self.eweight))

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                if _bm_test():
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                    assert not isnan(S) and not isinf(S), "invalid entropy %g (%s) " % (S, str(dict(complete=complete,
                                                                                                    random=random, dl=dl,
                                                                                                    partition_dl=partition_dl,
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                                                                                                    edges_dl=edges_dl,
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                                                                                                    dense=dense, multigraph=multigraph,
                                                                                                    norm=norm)))
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        if dl:
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            if partition_dl:
                if self.partition_stats.is_enabled():
                    S += self.partition_stats.get_partition_dl()
                else:
                    self.__init_partition_stats(empty=False)
                    S += self.partition_stats.get_partition_dl()
                    self.__init_partition_stats(empty=True)

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                if _bm_test():
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                    assert not isnan(S) and not isinf(S), "invalid entropy %g (%s) " % (S, str(dict(complete=complete,
                                                                                                    random=random, dl=dl,
                                                                                                    partition_dl=partition_dl,
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                                                                                                    edges_dl=edges_dl,
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                                                                                                    dense=dense, multigraph=multigraph,
                                                                                                    norm=norm)))
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            if edges_dl:
                actual_B = (self.wr.a > 0).sum()
                S += model_entropy(actual_B, N, E, directed=self.g.is_directed(), nr=False)
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            if self.deg_corr and degree_dl:
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                if self.partition_stats.is_enabled():
                    S_seq = self.partition_stats.get_deg_dl(dl_ent, dl_deg_alt, xi_fast)
                else:
                    self.__init_partition_stats(empty=False)
                    S_seq = self.partition_stats.get_deg_dl(dl_ent, dl_deg_alt, xi_fast)
                    self.__init_partition_stats(empty=True)
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                S += S_seq
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                if _bm_test():
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                    assert not isnan(S_seq) and not isinf(S_seq), "invalid entropy %g (%s) " % (S_seq, str(dict(complete=complete,
                                                                                                                random=random, dl=dl,
                                                                                                                partition_dl=partition_dl,
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                                                                                                                edges_dl=edges_dl,
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                                                                                                                dense=dense, multigraph=multigraph,
                                                                                                                norm=norm)))

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        if _bm_test():
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            assert not isnan(S) and not isinf(S), "invalid entropy %g (%s) " % (S, str(dict(complete=complete,
                                                                                            random=random, dl=dl,
                                                                                            partition_dl=partition_dl,
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                                                                                            edges_dl=edges_dl,
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                                                                                            dense=dense, multigraph=multigraph,
                                                                                            norm=norm)))

        if norm:
            return S / E
        else:
            return S
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    def get_matrix(self):
        r"""Returns the block matrix (as a sparse :class:`~scipy.sparse.csr_matrix`),
        which contains the number of edges between each block pair.
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        .. warning::

           This corresponds to the adjacency matrix of the block graph, which by
           convention includes twice the amount of edges in the diagonal entries
           if the graph is undirected.

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        Examples
        --------

        .. testsetup:: get_matrix

           gt.seed_rng(42)
           np.random.seed(42)
           from pylab import *

        .. doctest:: get_matrix

           >>> g = gt.collection.data["polbooks"]
           >>> state = gt.BlockState(g, B=5, deg_corr=True)
           >>> for i in range(1000):
           ...     ds, nmoves = gt.mcmc_sweep(state)
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           >>> m = state.get_matrix()
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           >>> figure()
           <...>
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           >>> matshow(m.todense())
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           <...>
           >>> savefig("bloc_mat.pdf")

        .. testcleanup:: get_matrix

           savefig("bloc_mat.png")

        .. figure:: bloc_mat.*
           :align: center

           A  5x5 block matrix.

       """
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        return adjacency(self.bg, weight=self.mrs)
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def model_entropy(B, N, E, directed=False, nr=None):
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    r"""Computes the amount of information necessary for the parameters of the traditional blockmodel ensemble, for ``B`` blocks, ``N`` vertices, ``E`` edges, and either a directed or undirected graph.

    A traditional blockmodel is defined as a set of :math:`N` vertices which can
    belong to one of :math:`B` blocks, and the matrix :math:`e_{rs}` describes
    the number of edges from block :math:`r` to :math:`s` (or twice that number
    if :math:`r=s` and the graph is undirected).

    For an undirected graph, the number of distinct :math:`e_{rs}` matrices is given by,

    .. math::

       \Omega_m = \left(\!\!{\left(\!{B \choose 2}\!\right) \choose E}\!\!\right)

    and for a directed graph,

    .. math::
       \Omega_m = \left(\!\!{B^2 \choose E}\!\!\right)


    where :math:`\left(\!{n \choose k}\!\right) = {n+k-1\choose k}` is the
    number of :math:`k` combinations with repetitions from a set of size :math:`n`.

    The total information necessary to describe the model is then,

    .. math::

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       \mathcal{L}_t = \ln\Omega_m + \ln\left(\!\!{B \choose N}\!\!\right) + \ln N! - \sum_r \ln n_r!,

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    where the remaining term is the information necessary to describe the
    block partition, where :math:`n_r` is the number of nodes in block :math:`r`.
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    If ``nr`` is ``None``, it is assumed :math:`n_r=N/B`.

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    References
    ----------

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    .. [peixoto-parsimonious-2013] Tiago P. Peixoto, "Parsimonious module inference in large networks",
       Phys. Rev. Lett. 110, 148701 (2013), :doi:`10.1103/PhysRevLett.110.148701`, :arxiv:`1212.4794`.
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    .. [peixoto-hierarchical-2014] Tiago P. Peixoto, "Hierarchical block structures and high-resolution
       model selection in large networks ", Phys. Rev. X 4, 011047 (2014), :doi:`10.1103/PhysRevX.4.011047`,
       :arxiv:`1310.4377`.
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    """

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    if directed:
        x = (B * B);
    else:
        x = (B * (B + 1)) / 2;
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    if nr is False:
        L = lbinom(x + E - 1, E)
    else:
        L = lbinom(x + E - 1, E) + partition_entropy(B, N, nr)
    return L
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def lbinom(n, k):
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    return scipy.special.gammaln(float(n + 1)) - scipy.special.gammaln(float(n - k + 1)) - scipy.special.gammaln(float(k + 1))
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def partition_entropy(B, N, nr=None):
    if nr is None:
        S = N * log(B) + log1p(-(1 - 1./B) ** N)
    else:
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        S = lbinom(B + N - 1, N) + scipy.special.gammaln(N + 1) - scipy.special.gammaln(nr + 1).sum()
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    return S
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def get_max_B(N, E, directed=False):
    r"""Return the maximum detectable number of blocks, obtained by minimizing:

    .. math::

        \mathcal{L}_t(B, N, E) - E\ln B

    where :math:`\mathcal{L}_t(B, N, E)` is the information necessary to
    describe a traditional blockmodel with `B` blocks, `N` nodes and `E`
    edges (see :func:`model_entropy`).

    Examples
    --------

    >>> gt.get_max_B(N=1e6, E=5e6)
    1572

    References
    ----------
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    .. [peixoto-parsimonious-2013] Tiago P. Peixoto, "Parsimonious module inference in large networks",
       Phys. Rev. Lett. 110, 148701 (2013), :doi:`10.1103/PhysRevLett.110.148701`, :arxiv:`1212.4794`.
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    """

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    def Sdl(B, S, N, E, directed=False):
        return S + model_entropy(B, N, E, directed) / E

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    B = fminbound(lambda B: Sdl(B, -log(B), N, E, directed), 1, E,
                  xtol=1e-6, maxfun=1500, disp=0)
    if isnan(B):
        B = 1
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    return min(N, max(int(ceil(B)), 2))
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def get_akc(B, I, N=float("inf"), directed=False):
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    r"""Return the minimum value of the average degree of the network, so that some block structure with :math:`B` blocks can be detected, according to the minimum description length criterion.
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    This is obtained by solving

    .. math::

       \Sigma_b = \mathcal{L}_t(B, N, E) - E\mathcal{I}_{t/c} = 0,

    where :math:`\mathcal{L}_{t}` is the necessary information to describe the
    blockmodel parameters (see :func:`model_entropy`), and
    :math:`\mathcal{I}_{t/c}` characterizes the planted block structure, and is
    given by

    .. math::

        \mathcal{I}_t &= \sum_{rs}m_{rs}\ln\left(\frac{m_{rs}}{w_rw_s}\right),\\
        \mathcal{I}_c &= \sum_{rs}m_{rs}\ln\left(\frac{m_{rs}}{m_rm_s}\right),

    where :math:`m_{rs} = e_{rs}/2E` (or :math:`m_{rs} = e_{rs}/E` for directed
    graphs) and :math:`w_r=n_r/N`. We note that :math:`\mathcal{I}_{t/c}\in[0,
    \ln B]`. In the case where :math:`E \gg B^2`, this simplifies to

    .. math::

       \left<k\right>_c &= \frac{2\ln B}{\mathcal{I}_{t/c}},\\
       \left<k^{-/+}\right>_c &= \frac{\ln B}{\mathcal{I}_{t/c}},

    for undirected and directed graphs, respectively. This limit is assumed if
    ``N == inf``.

    Examples
    --------

    >>> gt.get_akc(10, log(10) / 100, N=100)
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    2.414413200430159
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    References
    ----------
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    .. [peixoto-parsimonious-2013] Tiago P. Peixoto, "Parsimonious module inference in large networks",
       Phys. Rev. Lett. 110, 148701 (2013), :doi:`10.1103/PhysRevLett.110.148701`, :arxiv:`1212.4794`.
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    """
    if N != float("inf"):
        if directed:
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            get_dl = lambda ak: model_entropy(B, N, N * ak, directed) / N * ak - N * ak * I
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        else:
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            get_dl = lambda ak: model_entropy(B, N, N * ak / 2., directed) * 2 / (N * ak)  - N * ak * I / 2.
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        ak = fsolve(lambda ak: get_dl(ak), 10)
        ak = float(ak)
    else:
        ak = 2 * log(B) / S
        if directed:
            ak /= 2
    return ak

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def mcmc_sweep(state, beta=1., c=1., niter=1, dl=False, dense=False,
               multigraph=False, node_coherent=False, confine_layers=False,
               sequential=True, parallel=False, vertices=None, verbose=False,
               **kwargs):
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    r"""Performs a Markov chain Monte Carlo sweep on the network, to sample the block partition according to a probability :math:`\propto e^{-\beta \mathcal{S}_{t/c}}`, where :math:`\mathcal{S}_{t/c}` is the blockmodel entropy.
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    Parameters
    ----------
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    state : :class:`~graph_tool.community.BlockState`, :class:`~graph_tool.community.OverlapBlockState` or :class:`~graph_tool.community.CovariateBlockState`
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        The block state.
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    beta : ``float`` (optional, default: `1.0`)
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        The inverse temperature parameter :math:`\beta`.
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    c : ``float`` (optional, default: ``1.0``)
        This parameter specifies how often fully random moves are attempted,
        instead of more likely moves based on the inferred block partition.
        For ``c == 0``, no fully random moves are attempted, and for ``c == inf``
        they are always attempted.
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    niter : ``int`` (optional, default: ``1``)
        Number of sweeps to perform.
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    dl : ``bool`` (optional, default: ``False``)
        If ``True``, the change in the whole description length will be
        considered after each vertex move, not only the entropy.
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    dense : ``bool`` (optional, default: ``False``)
        If ``True``, the "dense" variant of the entropy will be computed.
    multigraph : ``bool`` (optional, default: ``False``)
        If ``True``, the multigraph entropy will be used. Only has an effect
        if ``dense == True``.
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    node_coherent : ``bool`` (optional, default: ``False``)
        If ``True``, and if the ``state`` is an instance of
        :class:`~graph_tool.community.OverlapBlockState`, then all half-edges
        incident on the same node are moved simultaneously.
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    confine_layers : ``bool`` (optional, default: ``False``)
        If ``True``, and if the ``state`` is an instance of
        :class:`~graph_tool.community.CovariateBlockState`, with an
        *overlapping* partition, the half edges will only be moved in such a way
         that inside each layer the group membership remains non-overlapping.
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    sequential : ``bool`` (optional, default: ``True``)
        If ``True``, the move attempts on the vertices are done in sequential
        random order. Otherwise a total of `N` moves attempts are made, where
        `N` is the number of vertices, where each vertex can be selected with
        equal probability.
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    parallel : ``bool`` (optional, default: ``False``)
        If ``True``, the updates are performed in parallel (multiple
        threads).

        .. warning::

            If this is used, the Markov Chain is not guaranteed to be sampled with
            the correct probabilities. This is better used in conjunction with
            ``beta=float('inf')``, where this is not an issue.

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    vertices : ``list of ints`` (optional, default: ``None``)
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        A list of vertices which will be attempted to be moved. If ``None``, all
        vertices will be attempted.
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    verbose : ``bool`` (optional, default: ``False``)
        If ``True``, verbose information is displayed.

    Returns
    -------

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    dS : ``float``
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       The entropy difference (in nats) after the sweeps.
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    nmoves : ``int``
       The number of accepted block membership moves.


    Notes
    -----

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    This algorithm performs a Markov chain Monte Carlo sweep on the network,
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    where the block memberships are randomly moved, and either accepted or
    rejected, so that after sufficiently many sweeps the partitions are sampled
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    with probability proportional to :math:`e^{-\beta\mathcal{S}_{t/c}}`, where
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    :math:`\mathcal{S}_{t/c}` is the blockmodel entropy, given by

    .. math::

      \mathcal{S}_t &\cong - \frac{1}{2} \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{n_rn_s}\right), \\
      \mathcal{S}^d_t &\cong - \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{n_rn_s}\right),

    for undirected and directed traditional blockmodels (``deg_corr == False``),
    respectively, where :math:`e_{rs}` is the number of edges from block
    :math:`r` to :math:`s` (or the number of half-edges for the undirected case
    when :math:`r=s`), and :math:`n_r` is the number of vertices in block
    :math:`r`, and constant terms which are independent of the block partition
    were dropped (see :meth:`BlockState.entropy` for the complete entropy). For
    the degree-corrected variant with "hard" degree constraints the equivalent
    expressions are

    .. math::

       \mathcal{S}_c &\cong  - \frac{1}{2} \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{e_re_s}\right), \\
       \mathcal{S}^d_c &\cong - \sum_{rs}e_{rs}\ln\left(\frac{e_{rs}}{e^+_re^-_s}\right),

    where :math:`e_r = \sum_se_{rs}` is the number of half-edges incident on
    block :math:`r`, and :math:`e^+_r = \sum_se_{rs}` and :math:`e^-_r =
    \sum_se_{sr}` are the number of out- and in-edges adjacent to block
    :math:`r`, respectively.

    The Monte Carlo algorithm employed attempts to improve the mixing time of
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    the Markov chain by proposing membership moves :math:`r\to s` with
    probability :math:`p(r\to s|t) \propto e_{ts} + c`, where :math:`t` is the
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    block label of a random neighbour of the vertex being moved. See
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    [peixoto-efficient-2014]_ for more details.
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    This algorithm has a complexity of :math:`O(E)`, where :math:`E` is the
    number of edges in the network.

    Examples
    --------
    .. testsetup:: mcmc

       gt.seed_rng(42)
       np.random.seed(42)

    .. doctest:: mcmc

       >>> g = gt.collection.data["polbooks"]
       >>> state = gt.BlockState(g, B=3, deg_corr=True)
       >>> pv = None
       >>> for i in range(1000):        # remove part of the transient
       ...     ds, nmoves = gt.mcmc_sweep(state)
       >>> for i in range(1000):
       ...     ds, nmoves = gt.mcmc_sweep(state)
       ...     pv = gt.collect_vertex_marginals(state, pv)
       >>> gt.graph_draw(g, pos=g.vp["pos"], vertex_shape="pie", vertex_pie_fractions=pv, output="polbooks_blocks_soft.pdf")
       <...>

    .. testcleanup:: mcmc

       gt.graph_draw(g, pos=g.vp["pos"], vertex_shape="pie", vertex_pie_fractions=pv, output="polbooks_blocks_soft.png")

    .. figure:: polbooks_blocks_soft.*
       :align: center

       "Soft" block partition of a political books network with :math:`B=3`.

     References
    ----------

    .. [holland-stochastic-1983] Paul W. Holland, Kathryn Blackmond Laskey,
       Samuel Leinhardt, "Stochastic blockmodels: First steps",
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       Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.,
       :doi:`10.1016/0378-8733(83)90021-7`
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    .. [faust-blockmodels-1992] Katherine Faust, and Stanley
       Wasserman. "Blockmodels: Interpretation and Evaluation." Social Networks
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       14, no. 1-2 (1992): 5-61. :doi:`10.1016/0378-8733(92)90013-W`
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    .. [karrer-stochastic-2011] Brian Karrer, and M. E. J. Newman. "Stochastic
       Blockmodels and Community Structure in Networks." Physical Review E 83,
       no. 1 (2011): 016107. :doi:`10.1103/PhysRevE.83.016107`.
    .. [peixoto-entropy-2012] Tiago P. Peixoto "Entropy of Stochastic Blockmodel
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       Ensembles." Physical Review E 85, no. 5 (2012): 056122.
       :doi:`10.1103/PhysRevE.85.056122`, :arxiv:`1112.6028`.
    .. [peixoto-parsimonious-2013] Tiago P. Peixoto, "Parsimonious module
       inference in large networks", Phys. Rev. Lett. 110, 148701 (2013),
       :doi:`10.1103/PhysRevLett.110.148701`, :arxiv:`1212.4794`.
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    .. [peixoto-efficient-2014] Tiago P. Peixoto, "Efficient Monte Carlo and greedy
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       heuristic for the inference of stochastic block models", Phys. Rev. E 89,
       012804 (2014), :doi:`10.1103/PhysRevE.89.012804`, :arxiv:`1310.4378`.
    .. [peixoto-model-2015] Tiago P. Peixoto, "Model selection and hypothesis
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       testing for large-scale network models with overlapping groups",
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       Phys. Rev. X 5, 011033 (2015), :doi:`10.1103/PhysRevX.5.011033`,
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       :arxiv:`1409.3059`.
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    """

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    nmerges = kwargs.get("nmerges", 0)
    merge_map = kwargs.get("merge_map", None)
    coherent_merge = kwargs.get("coherent_merge", False)
    edges_dl = kwargs.get("edges_dl", False)

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    if state.B == 1:
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        return 0., 0

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    if vertices is not None:
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        vlist = libcommunity.get_vector(len(vertices))
        vlist.a = vertices
        vertices = vlist
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        state.sweep_vertices = vertices
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    if state.sweep_vertices is None:
        vertices = libcommunity.get_vector(state.g.num_vertices())
        vertices.a = state.g.vertex_index.copy("int").fa
        state.sweep_vertices = vertices

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    random_move = c == float("inf")

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    if nmerges == 0 or merge_map is None:
        merge_map = state.g.vertex_index.copy("int")

    if nmerges > 0:
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        beta = float("inf")

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    nsampler = []
    ncavity_sampler = []
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    main_state = state
    if isinstance(state, CovariateBlockState):
        states = state.states
        covariate = True
    else:
        states = [state]
        covariate = False
1021

1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
    for l, state in enumerate(states):

        if l == 0 and (random_move or nmerges > 0):
            state._BlockState__build_egroups(empty=True)
        elif state.egroups is None:
            state._BlockState__build_egroups(empty=False)

        if nmerges == 0:
            if state.nsampler is None:
                state._BlockState__build_nsampler(empty=state.overlap)
            nsampler.append(state.nsampler)
            ncavity_sampler.append(state.nsampler)
1034
        else:
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
            if kwargs.get("unweighted_merge", False):
                emask = state.mrs
            else:
                emask = state.mrs.copy()
                emask.a = emask.a > 0

            nsampler.append(libcommunity.init_neighbour_sampler(state.bg._Graph__graph,
                                                                _prop("e", state.bg, emask),
                                                                True, False))
            ncavity_sampler.append(libcommunity.init_neighbour_sampler(state.bg._Graph__graph,
                                                                       _prop("e", state.bg, emask),
                                                                       False, False))

        dl_enable = dl
        if dl and covariate and (state.slave or state.master):
            dl_enable = state.master
        if state.partition_stats.is_enabled() != dl_enable or edges_dl != state.edges_dl:
            if state.overlap:
                state._OverlapBlockState__init_partition_stats(empty=not dl_enable, edges_dl=edges_dl)
            else:
                state._BlockState__init_partition_stats(empty=not dl_enable, edges_dl=edges_dl)
1056

1057
1058
1059
1060
1061
    if _bm_test():
        assert main_state._BlockState__check_clabel(), "clabel already invalid!"
        S = main_state.entropy(dense=dense, multigraph=multigraph,
                               complete=False, dl=dl, edges_dl=edges_dl,
                               dl_deg_alt=False, xi_fast=True)
1062
        assert not (isinf(S) or isnan(S)), "invalid entropy before sweep: %g" % S
1063

1064
    nmoves = 1
1065
    try:
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
        if not covariate:
            state = states[0]
            if not state.overlap:
                dS, nmoves = libcommunity.move_sweep(state.g._Graph__graph,
                                                     state.bg._Graph__graph,
                                                     state._BlockState__get_emat(),
                                                     nsampler[0], ncavity_sampler[0],
                                                     _prop("e", state.bg, state.mrs),
                                                     _prop("v", state.bg, state.mrp),
                                                     _prop("v", state.bg, state.mrm),
                                                     _prop("v", state.bg, state.wr),
                                                     _prop("v", state.g, state.b),
                                                     _prop("v", state.bg, bclabel),
                                                     state.sweep_vertices,
                                                     state.deg_corr, dense, multigraph,
                                                     _prop("e", state.g, state.eweight),
                                                     _prop("v", state.g, state.vweight),
                                                     state.egroups,
                                                     _prop("e", state.g, state.esrcpos),
                                                     _prop("e", state.g, state.etgtpos),
                                                     float(beta), sequential,
                                                     parallel, random_move,
                                                     c, state.is_weighted,
                                                     nmerges,
                                                     _prop("v", state.g, merge_map),
                                                     niter,
                                                     state.partition_stats,
                                                     verbose, _get_rng())
            else:
                dS, nmoves = libcommunity.move_sweep_overlap(state.g._Graph__graph,
                                                             state.bg._Graph__graph,
                                                             state._BlockState__get_emat(),
                                                             nsampler[0],
                                                             ncavity_sampler[0],
                                                             _prop("e", state.bg, state.mrs),
                                                             _prop("v", state.bg, state.mrp),
                                                             _prop("v", state.bg, state.mrm),
                                                             _prop("v", state.bg, state.wr),
                                                             _prop("v", state.g, state.b),
                                                             _prop("v", state.bg, bclabel),
                                                             state.sweep_vertices,
                                                             state.deg_corr, dense, multigraph,
                                                             multigraph,
                                                             _prop("e", state.g, state.eweight),
                                                             _prop("v", state.g, state.vweight),
                                                             state.egroups,
                                                             _prop("e", state.g, state.esrcpos),
                                                             _prop("e", state.g, state.etgtpos),
                                                             float(beta),
                                                             sequential, parallel,
                                                             random_move, float(c),
                                                             ((nmerges == 0 and node_coherent) or
                                                              (nmerges > 0 and coherent_merge)),
                                                             state.is_weighted,
                                                             nmerges,
                                                             _prop("v", state.g, merge_map),
                                                             niter,
                                                             state.overlap_stats,
                                                             state.partition_stats,
                                                             verbose, _get_rng())
1126
        else:
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
            if _bm_test():
                for l, state in enumerate(states):
                    assert state.mrs.fa.sum() == state.eweight.fa.sum(), (l, state.mrs.fa.sum(), state.eweight.fa.sum())
                    #assert state.mrs.a.sum() == state.eweight.a.sum(), (l, state.mrs.a.sum(), state.eweight.a.sum())

            if confine_layers:
                node_coherent = True

            dS, nmoves = libcommunity.cov_move_sweep(main_state.g._Graph__graph,
                                                     _prop("e", main_state.g, main_state.ec),
                                                     _prop("v", main_state.g, main_state.vc),
                                                     _prop("v", main_state.g, main_state.vmap),
                                                     [state.g._Graph__graph for state in states],
                                                     [state.bg._Graph__graph for state in states],
                                                     [state._BlockState__get_emat() for state in states],
                                                     nsampler, ncavity_sampler,
                                                     [_prop("e", state.bg, state.mrs) for state in states],
                                                     [_prop("v", state.bg, state.mrp) for state in states],
                                                     [_prop("v", state.bg, state.mrm) for state in states],
                                                     [_prop("v", state.bg, state.wr) for state in states],
                                                     _prop("v", main_state.g, main_state.b),
                                                     [_prop("v", state.g, state.b) for state in states],
                                                     main_state.bmap,
                                                     [_prop("v", state.g, state.g.vp["brmap"]) for state in states],
                                                     [state.free_blocks for state in states],
                                                     [state.master for state in states],
                                                     [state.slave for state in states],
                                                     _prop("v", None, bclabel),
                                                     main_state.sweep_vertices,
                                                     main_state.deg_corr, dense, multigraph,
                                                     [_prop("e", state.g, state.eweight) for state in states],
                                                     [_prop("v", state.g, state.vweight) for state in states],
                                                     [state.egroups for state in states],
                                                     [_prop("e", state.g, state.esrcpos) for state in states],
                                                     [_prop("e", state.g, state.etgtpos) for state in states],
                                                     float(beta), sequential,
                                                     parallel, random_move,
                                                     (node_coherent, confine_layers),
                                                     c, main_state.is_weighted,
                                                     nmerges,
                                                     _prop("v", main_state.g, merge_map),
                                                     niter, main_state.B,
                                                     [state.partition_stats for state in states] if not main_state.overlap else [],
                                                     [state.partition_stats for state in states] if main_state.overlap else [],
                                                     [state.overlap_stats for state in states],
                                                     verbose, _get_rng())
1173
    finally:
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
        for state in states:
            if random_move:
                state.egroups = None
            if nmerges > 0:
                state.nsampler = None
                state.egroups = None
        if covariate and nmoves > 0:
            main_state._CovariateBlockState__bg = None

    if _bm_test():
        assert main_state._BlockState__check_clabel(), "clabel invalidated!"
1185
        assert not (isinf(dS) or isnan(dS)), "invalid after sweep: %g" % dS
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
        if not covariate or nmerges == 0:
            S2 = main_state.entropy(dense=dense, multigraph=multigraph,
                                    complete=False, dl=dl, edges_dl=edges_dl,
                                    dl_deg_alt=False, xi_fast=True)
            c_dS = S2 - S
            if not abs(dS - c_dS) < 1e-6 * state.E:
                S3 = main_state.copy().entropy(dense=dense, multigraph=multigraph, complete=False,
                                               dl=dl, edges_dl=False, dl_deg_alt=False, xi_fast=True)
                print(dS, c_dS, nmoves, state.overlap, dense, multigraph,
                      main_state.deg_corr, main_state.is_weighted, node_coherent, beta, S2, S3)
            assert abs(dS - c_dS) < 1e-6 * state.E, "invalid delta S (%g, %g)" % (dS, c_dS)
1197

1198
    return dS, nmoves
1199

1200

1201
1202
1203
1204
1205
1206
1207
1208
def pmap(prop, value_map):
    """Maps all the values of `prop` to the values given by `value_map`, which
    is indexed by the values of `prop`."""
    if isinstance(prop, PropertyMap):
        prop = prop.a
    if isinstance(value_map, PropertyMap):
        value_map = value_map.a
    if prop.max() >= len(value_map):
1209
1210
1211
1212
1213
1214
1215
1216
        raise ValueError("value map is not large enough! %s, %s" % (prop.max(),
                                                                    len(value_map)))
    if prop.dtype != value_map.dtype:
        value_map = array(value_map, dtype=prop.dtype)
    if prop.dtype == "int64":
        libcommunity.vector_map64(prop, value_map)
    else:
        libcommunity.vector_map(prop, value_map)
1217
1218
1219
1220
1221
1222
1223
1224
1225

def reverse_map(prop, value_map):
    """Modify `value_map` such that the positions indexed by the values in `prop`
    correspond to their index in `prop`."""
    if isinstance(prop, PropertyMap):
        prop = prop.a
    if isinstance(value_map, PropertyMap):
        value_map = value_map.a
    if prop.max() >= len(value_map):
1226
        raise ValueError("value map is not large enough! (%d, %d)" % (prop.max(), len(value_map)))
1227
1228
1229
1230
1231
1232
    if prop.dtype != value_map.dtype:
        prop = array(prop, dtype=value_map.dtype)
    if value_map.dtype == "int64":
        libcommunity.vector_rmap64(prop, value_map)
    else:
        libcommunity.vector_rmap(prop, value_map)
1233
1234
1235
1236
1237
1238
1239

def continuous_map(prop):
    """Remap the values of ``prop`` in the continuous range :math:`[0, N-1]`."""
    if isinstance(prop, PropertyMap):
        prop = prop.a
    if prop.max() < len(prop):
        rmap = -ones(len(prop), dtype=prop.dtype)
1240
1241
1242
1243
        if prop.dtype == "int64":
            libcommunity.vector_map64(prop, rmap)
        else:
            libcommunity.vector_map(prop, rmap)
1244
    else:
1245
1246
1247
1248
        if prop.dtype == "int64":
            libcommunity.vector_continuous_map64(prop)
        else:
            libcommunity.vector_continuous_map(prop)
1249
1250

def greedy_shrink(state, B, **kwargs):
1251
1252
    if B > state.B:
        raise ValueError("Cannot shrink to a larger size!")
1253

1254
1255
1256
    kwargs = kwargs.copy()
    if kwargs.get("nmerge_sweeps", None) is None:
        kwargs["nmerge_sweeps"] = max((2 * state.g.num_edges()) // state.g.num_vertices(), 1)
1257
1258
    if "beta" in kwargs:
        del kwargs["beta"]
1259
1260

    verbose = kwargs.get("verbose", False)
1261

1262
1263
    orig_state = state
    state = state.copy(B=state.B)
1264

1265
1266
1267
1268
    # merge according to indirect neighbourhood; we put all group-nodes in their
    # own groups, and merge/move them until the desired size is reached
    curr_B = (state.wr.a > 0).sum()
    assert curr_B >= B, "shrinking to a larger size ?! (%d, %d)" % (curr_B, B)
1269

1270
1271
1272
    random = kwargs.get("random_move", False)
    old_state = state
    if not state.overlap:
1273
1274
        state, n_map = state.get_block_state(vweight=True,
                                             deg_corr=state.deg_corr)
1275
1276
    merge_map = state.g.vertex_index.copy("int")

1277
1278
1279
    if _bm_test():
        assert curr_B == (state.wr.a > 0).sum(), (curr_B, (state.wr.a > 0).sum())

1280
1281
1282
1283
1284
    unweighted = False
    kwargs["c"] = 0 if not random else float("inf")
    kwargs["dl"] = False
    while curr_B > B:
        dS, nmoves = mcmc_sweep(state, beta=float("inf"),
1285
                                niter=kwargs["nmerge_sweeps"],
1286
1287
1288
1289
1290
1291
                                nmerges=curr_B - B,
                                merge_map=merge_map,
                                unweighted_merge=unweighted,
                                **kwargs)

        curr_B = (state.wr.a > 0).sum()
1292

1293
1294
1295
        if _bm_test():
            assert curr_B == len(set(state.b.a)), (curr_B, len(set(state.b.a)))

1296
        if verbose:
1297
1298
1299
1300
            print("merging, B=%d" % curr_B, "left:", curr_B - B,
                  "(%g, %d%s%s)" % (dS, nmoves, ", random" if random else "",
                                    ", unweighted" if unweighted else ""))

1301
        if nmoves == 0:
1302
1303
1304
1305
1306
1307
            if not unweighted:
                unweighted = True
            else:
                kwargs["c"] = float("inf")
                random = True

1308
1309
    if _bm_test():
        assert curr_B == (state.wr.a > 0).sum(), (curr_B, (state.wr.a > 0).sum())
1310

1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
    if not state.overlap:
        unilevel_minimize(state, **kwargs)  # block level moves
        pmap(merge_map, state.b)
        pmap(n_map, merge_map)
        continuous_map(n_map)
        state = orig_state.copy(b=n_map, B=B)
    else:
        pmap(merge_map, state.b)
        continuous_map(merge_map)
        state = orig_state.copy(b=merge_map, B=B)
1321
1322


1323
    if _bm_test():
1324
        assert state._BlockState__check_clabel(), "clabel already invalidated!"
1325
        assert curr_B == (state.wr.a > 0).sum(), (curr_B, (state.wr.a > 0).sum(), len(state.wr.a), state.B)
1326
        curr_B = (state.wr.a > 0).sum()
1327
1328
        assert state.B == curr_B, (state.B, curr_B)
        a